%%% -*-BibTeX-*-
%%% ====================================================================
%%%  BibTeX-file{
%%%     author-1        = "Norbert Juffa",
%%%     author-2        = "Nelson H. F. Beebe",
%%%     version         = "3.796",
%%%     date            = "26 February 2026",
%%%     time            = "09:17:35 MDT",
%%%     filename        = "fparith.bib",
%%%     address-1       = "2445 Mission College Blvd.,
%%%                        Santa Clara, CA 95054,
%%%                        USA",
%%%     address-2       = "University of Utah
%%%                        Department of Mathematics, 110 LCB
%%%                        155 S 1400 E RM 233
%%%                        Salt Lake City, UT 84112-0090
%%%                        USA",
%%%     telephone-1     = "+1 408 727 1885",
%%%     telephone-2     = "+1 801 581 5254",
%%%     FAX-1           = "+1 408 727 1265",
%%%     URL-2           = "https://www.math.utah.edu/~beebe",
%%%     checksum        = "48315 227209 1040805 10555485",
%%%     email-1         = "norbert at iit.com (Internet)",
%%%     email-2         = "beebe at math.utah.edu, beebe at acm.org,
%%%                        beebe at computer.org (Internet)",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "bibliography; BibTeX; constant-time
%%%                        arithmetic; fixed-point arithmetic;
%%%                        floating-point arithmetic; floating-point
%%%                        exceptions; floating-point summation;
%%%                        floating-point verification; IEEE 754
%%%                        arithmetic; inexact; Infinity; integer
%%%                        arithmetic; logarithmic number system (LNS)
%%%                        arithmetic; NaN (Not a Number); overflow;
%%%                        posit arithmetic; residue number system;
%%%                        rounding algorithms; Sets-Of-Real-Numbers
%%%                        (SORN) arithmetic; subnormal; underflow; unum
%%%                        arithmetic; zero divide",
%%%     license         = "public domain",
%%%     supported       = "yes",
%%%     docstring       = "[From Norbert Juffa:] This is a bibliography
%%%                        of material on floating-point arithmetic
%%%                        that I came up with while doing research on
%%%                        a floating-point package of my own.  I
%%%                        don't claim it to be anywhere near
%%%                        complete. The material listed is only what
%%%                        I myself possess.
%%%
%%%                        My main interest was in software based,
%%%                        binary floating-point arithmetic on a
%%%                        microprocessor, so you won't find much
%%%                        material about the hardware used in
%%%                        floating-point arithmetic (e.g., adders,
%%%                        carry propagation schemes, higher radix
%%%                        representation for multiplication and
%%%                        division, etc.) in this list. There is also
%%%                        not too much on non-binary floating-point
%%%                        arithmetic.
%%%
%%%                        For most fields covered in this
%%%                        bibliography, the important or historically
%%%                        relevant articles should be included. There
%%%                        is also some material on integer arithmetic
%%%                        in this list as some of the methods used
%%%                        with integer arithmetic contain interesting
%%%                        ideas that may be useful in the realization
%%%                        of a floating-point arithmetic package.
%%%
%%%                        Also, depending on the type of
%%%                        microprocessor used, one may need to
%%%                        implement integer multiplication and
%%%                        division for use in the floating-point
%%%                        package, so articles about this topic are
%%%                        included as well.
%%%
%%%                        As I am German, there is a bit of material
%%%                        in German in this bibliography.  However,
%%%                        English translations are provided for all
%%%                        non-English titles.
%%%
%%%                        Thanks to the people who have helped me with
%%%                        previous versions of this document by sending
%%%                        me papers or additional references: Steven
%%%                        Sommars (sesv at research.bell-labs.com), Jim
%%%                        Kiernan (jmk at teak.cray.com), Warren
%%%                        Ferguson (ferguson at seas.smu.edu), Nhuan
%%%                        Doduc (ndoduc at framentec.fr), K. C. Ng
%%%                        (kwok.ng at eng.sun.com).
%%%
%%%                        [From Nelson H. F. Beebe:] I took Norbert
%%%                        Juffa's unmarked-up bibliography data,
%%%                        converted it to BibTeX form, and then more
%%%                        than doubled the size of the bibliography
%%%                        by supplying additional entries on
%%%                        floating-point arithmetic extracted from
%%%                        my own extensive bibliography collections,
%%%                        and from several online journal databases,
%%%                        including the Compendex, OCLC, IEEE INSPEC,
%%%                        MathSciNet, and UnCover databases.  In August
%%%                        2010, access to an electronic copy of the
%%%                        bibliography of Sterbenz's 1974 book allowed
%%%                        further checks to make sure that all of his
%%%                        references to early work are included here.
%%%
%%%                        The computation of sums of floating-point
%%%                        numbers is a fundamental step in most
%%%                        numerical computations.  The special phrase
%%%                        ``accurate floating-point summation'' appears
%%%                        in the keywords values of publications that
%%%                        address this important problem.
%%%
%%%                        The Web site
%%%
%%%                            http://www.acsel-lab.com/arithmetic/
%%%
%%%                        archives papers from the IEEE conferences
%%%                        on computer arithmetic (ARITH-1, ARITH-2,
%%%                        ...).  Keyword values for those papers
%%%                        contain ARITH-n to more easily identify them.
%%%
%%%                        In \cite[p. 94]{Buchholz:1962:PCS}, S. G.
%%%                        Campbell remarks:
%%%
%%%                            ``To avoid difficulties of limited range
%%%                            and scaling in fixed-point arithmetic,
%%%                            G. R. Stibitz in the early 1940's
%%%                            proposed an automatic scaling procedure,
%%%                            called {\emph floating-point arithmetic},
%%%                            which was incorporated in the Bell
%%%                            Telephone Laboratories' Model V Relay
%%%                            Computer. A similar procedure was
%%%                            developed, apparently independently, for
%%%                            the Harvard Mark II computer.  Automatic
%%%                            scaling was a controversial subject for
%%%                            quite a few years. Many opposed it on the
%%%                            basis that the programmer could not be
%%%                            relieved of the responsibility of knowing
%%%                            the size of his numbers and that
%%%                            programmed scaling would give him better
%%%                            control over significance. Nevertheless,
%%%                            as early as 1950, users began to
%%%                            incorporate automatic scaling on
%%%                            fixed-point computers by means of
%%%                            subroutines, first on the
%%%                            plugboard-controlled CPC (Card Programmed
%%%                            Calculator) and later on stored-program
%%%                            machines. Then, after it had thus proved
%%%                            its usefulness, floating-point arithmetic
%%%                            was provided as a built-in feature,
%%%                            starting with the IBM 704 and NORC
%%%                            computers, and this gave an enormous
%%%                            increase in speed over the
%%%                            subroutines. Today floating-point
%%%                            operation is available, at least as an
%%%                            option, on all computers intended to be
%%%                            used full- or part-time on substantial
%%%                            scientific computing applications. In
%%%                            view of the almost universal use of
%%%                            floating-point arithmetic, it is
%%%                            remarkable that there is very little
%%%                            literature on the subject.''
%%%
%%%                        We now know that Leonardo Torres y Quevedo
%%%                        first suggested floating-point arithmetic on
%%%                        paper in 1914 in Spain
%%%                        \cite{TorresyQuevedo:1982:EAD}.  Konrad Zuse
%%%                        reinvented it independently in Germany in the
%%%                        early 1936, and had it operational in the Z3,
%%%                        an electromechanical computer, in 1941
%%%                        \cite{Zuse:1970:CML,Ceruzzi:1981:ECK,
%%%                        Randell:1982:ODC,Schwarz:1981:EYC,
%%%                        Zuse:1982:MAE,Zuse:1982:OCD,Zuse:1984:CML,
%%%                        Zuse:1993:CML,Smiley:2010:MWI}.  Zuse's work
%%%                        remained unknown in the USA until about 1948.
%%%                        F. L. Bauer's foreword to Zuse's
%%%                        autobiography \cite{Zuse:1993:CML} suggests a
%%%                        bust of Zuse engraved
%%%
%%%                            ``Creator of the first fully automated,
%%%                            program-controlled and freely
%%%                            programmable computer using binary
%%%                            floating-point calculation. It was
%%%                            operational in 1941.''
%%%
%%%                        The experience with floating-point arithmetic
%%%                        by George Stibitz on the Bell Labs Model V
%%%                        General Purpose Relay Calculator (1945, but
%%%                        floating-point arithmetic proposed in 1940
%%%                        Stibitz memo) \cite{Alt:1948:BTLa}, by
%%%                        Howard Aiken on the Harvard Mark II (1947),
%%%                        and by Gerald Alway and Jim Wilkinson on the
%%%                        Pilot ACE in Britain (1946--1948)
%%%                        \cite{Wilkinson:1975:PAA}, encouraged the
%%%                        provision of floating-point arithmetic in the
%%%                        American and British commercialization of
%%%                        scientific computers in the 1950s.  However,
%%%                        Zuse's use of Infinity and Indefinite
%%%                        predated by more than 15 years the Infinity
%%%                        of the IBM 7030 Stretch (1956--1958, with
%%%                        first customer delivery, to Los Alamos
%%%                        Laboratory, in April 1961), and the Infinity
%%%                        and Indefinite of the CDC 6400/6600/7600
%%%                        (1960--1963, with first customer delivery, to
%%%                        Lawrence Livermore Laboratory, in September
%%%                        1964)
%%%                        \cite{Thornton:1970:DCC,Thornton:1980:CP}.  I
%%%                        [NHFB] have so far been unable to find any
%%%                        definitive published statement about whether
%%%                        Zuse's ideas were known to, and inspired, the
%%%                        CDC and IBM architects, or whether they
%%%                        rediscovered them independently.
%%%
%%%                        It is our hope that this bibliography will
%%%                        help to remedy the deficiency noted in the
%%%                        last sentence of Campbell's remark, even
%%%                        though the first edition of this bibliography
%%%                        in 1994 appeared 32 years after the wonderful
%%%                        book about IBM's Project Stretch, and it took
%%%                        48 years for that book to be included here.
%%%
%%%                        At version 3.796, the year coverage looked
%%%                        like this:
%%%
%%%                             1703 (   1)    1811 (   0)    1919 (   0)
%%%                             1708 (   0)    1816 (   0)    1924 (   2)
%%%                             1709 (   0)    1817 (   0)    1925 (   1)
%%%                             1710 (   0)    1818 (   0)    1926 (   2)
%%%                             1711 (   0)    1819 (   0)    1927 (   1)
%%%                             1712 (   1)    1820 (   0)    1928 (   0)
%%%                             1714 (   0)    1822 (   0)    1930 (   2)
%%%                             1716 (   0)    1824 (   0)    1932 (   3)
%%%                             1717 (   0)    1825 (   0)    1933 (   1)
%%%                             1718 (   0)    1826 (   0)    1934 (   1)
%%%                             1719 (   0)    1827 (   0)    1935 (   1)
%%%                             1720 (   0)    1828 (   0)    1936 (   4)
%%%                             1721 (   0)    1829 (   0)    1937 (   3)
%%%                             1722 (   0)    1830 (   0)    1938 (   4)
%%%                             1723 (   0)    1831 (   0)    1939 (   2)
%%%                             1724 (   0)    1832 (   0)    1940 (   3)
%%%                             1725 (   0)    1833 (   0)    1941 (   1)
%%%                             1726 (   1)    1834 (   0)    1942 (   3)
%%%                             1727 (   0)    1835 (   0)    1943 (   4)
%%%                             1728 (   0)    1836 (   0)    1944 (   1)
%%%                             1729 (   0)    1837 (   1)    1945 (   3)
%%%                             1730 (   0)    1838 (   0)    1946 (   8)
%%%                             1731 (   0)    1839 (   0)    1947 (  10)
%%%                             1732 (   0)    1840 (   0)    1948 (   7)
%%%                             1733 (   0)    1841 (   0)    1949 (   4)
%%%                             1734 (   0)    1842 (   0)    1950 (   5)
%%%                             1735 (   0)    1843 (   0)    1951 (  10)
%%%                             1736 (   0)    1844 (   0)    1952 (   7)
%%%                             1737 (   0)    1845 (   0)    1953 (   5)
%%%                             1738 (   0)    1846 (   0)    1954 (   7)
%%%                             1739 (   0)    1847 (   0)    1955 (   9)
%%%                             1740 (   0)    1848 (   0)    1956 (  11)
%%%                             1741 (   0)    1849 (   0)    1957 (  17)
%%%                             1742 (   0)    1850 (   0)    1958 (  18)
%%%                             1743 (   0)    1851 (   0)    1959 (  26)
%%%                             1744 (   0)    1852 (   0)    1960 (  23)
%%%                             1745 (   0)    1853 (   0)    1961 (  31)
%%%                             1746 (   0)    1854 (   0)    1962 (  32)
%%%                             1747 (   0)    1855 (   0)    1963 (  25)
%%%                             1748 (   0)    1856 (   0)    1964 (  31)
%%%                             1749 (   0)    1857 (   0)    1965 (  59)
%%%                             1750 (   0)    1858 (   0)    1966 (  40)
%%%                             1751 (   0)    1859 (   0)    1967 (  51)
%%%                             1752 (   0)    1860 (   0)    1968 (  36)
%%%                             1753 (   0)    1861 (   0)    1969 (  57)
%%%                             1754 (   0)    1862 (   1)    1970 (  59)
%%%                             1755 (   0)    1863 (   0)    1971 (  66)
%%%                             1756 (   0)    1864 (   0)    1972 (  64)
%%%                             1757 (   0)    1865 (   0)    1973 (  84)
%%%                             1758 (   0)    1866 (   0)    1974 (  52)
%%%                             1759 (   0)    1867 (   0)    1975 ( 104)
%%%                             1760 (   0)    1868 (   0)    1976 (  58)
%%%                             1761 (   0)    1869 (   0)    1977 ( 101)
%%%                             1762 (   0)    1870 (   0)    1978 ( 109)
%%%                             1763 (   0)    1871 (   0)    1979 (  83)
%%%                             1764 (   0)    1872 (   0)    1980 ( 116)
%%%                             1765 (   0)    1873 (   0)    1981 ( 126)
%%%                             1766 (   0)    1874 (   0)    1982 (  90)
%%%                             1767 (   0)    1875 (   1)    1983 ( 158)
%%%                             1768 (   0)    1876 (   0)    1984 ( 108)
%%%                             1769 (   0)    1877 (   0)    1985 ( 152)
%%%                             1770 (   0)    1878 (   0)    1986 (  99)
%%%                             1771 (   0)    1879 (   1)    1987 ( 149)
%%%                             1772 (   0)    1880 (   0)    1988 ( 165)
%%%                             1773 (   0)    1881 (   1)    1989 ( 192)
%%%                             1774 (   0)    1882 (   0)    1990 ( 160)
%%%                             1775 (   0)    1883 (   0)    1991 ( 237)
%%%                             1776 (   0)    1884 (   0)    1992 ( 193)
%%%                             1777 (   0)    1885 (   0)    1993 ( 204)
%%%                             1778 (   0)    1886 (   0)    1994 ( 181)
%%%                             1779 (   0)    1887 (   0)    1995 ( 173)
%%%                             1780 (   0)    1888 (   1)    1996 ( 189)
%%%                             1781 (   0)    1889 (   0)    1997 ( 144)
%%%                             1782 (   0)    1890 (   0)    1998 ( 137)
%%%                             1783 (   0)    1891 (   0)    1999 ( 201)
%%%                             1784 (   0)    1892 (   1)    2000 ( 161)
%%%                             1785 (   0)    1893 (   2)    2001 ( 213)
%%%                             1786 (   0)    1894 (   0)    2002 ( 171)
%%%                             1787 (   0)    1895 (   0)    2003 ( 155)
%%%                             1788 (   0)    1896 (   0)    2004 ( 188)
%%%                             1789 (   0)    1897 (   1)    2005 ( 184)
%%%                             1790 (   0)    1898 (   1)    2006 ( 136)
%%%                             1791 (   0)    1899 (   0)    2007 ( 157)
%%%                             1792 (   0)    1900 (   0)    2008 (  91)
%%%                             1793 (   0)    1901 (   0)    2009 ( 128)
%%%                             1794 (   0)    1902 (   0)    2010 ( 107)
%%%                             1795 (   0)    1903 (   0)    2011 ( 149)
%%%                             1796 (   0)    1904 (   0)    2012 (  95)
%%%                             1797 (   0)    1905 (   0)    2013 (  96)
%%%                             1798 (   0)    1906 (   0)    2014 (  63)
%%%                             1799 (   0)    1907 (   0)    2015 ( 118)
%%%                             1800 (   0)    1908 (   0)    2016 ( 111)
%%%                             1801 (   0)    1909 (   1)    2017 ( 145)
%%%                             1802 (   0)    1910 (   1)    2018 ( 123)
%%%                             1803 (   0)    1911 (   0)    2019 ( 185)
%%%                             1804 (   0)    1912 (   0)    2020 ( 138)
%%%                             1805 (   0)    1913 (   0)    2021 ( 144)
%%%                             1806 (   0)    1914 (   0)    2022 ( 145)
%%%                             1807 (   0)    1915 (   1)    2023 ( 159)
%%%                             1808 (   0)    1916 (   0)    2024 ( 132)
%%%                             1809 (   0)    1917 (   0)    2025 ( 121)
%%%                             1810 (   0)    1918 (   0)    2026 (  13)
%%%                             19xx (   2)
%%%                             20xx (   3)
%%%
%%%                             Article:       3911
%%%                             Book:           379
%%%                             InBook:           6
%%%                             InCollection:    78
%%%                             InProceedings: 2349
%%%                             Manual:          72
%%%                             MastersThesis:  153
%%%                             Misc:           292
%%%                             Periodical:       3
%%%                             PhdThesis:       94
%%%                             Proceedings:    402
%%%                             TechReport:     424
%%%                             Unpublished:     11
%%%
%%%                             Total entries: 8174
%%%
%%%                        This bibliography is sorted by year, and
%%%                        within each year, by author and title key,
%%%                        with ``bibsort -byyear''.  Cross-referenced
%%%                        proceedings entries appear at the end,
%%%                        because of a restriction in the current
%%%                        BibTeX.
%%%
%%%                        The checksum field above contains a CRC-16
%%%                        checksum as the first value, followed by the
%%%                        equivalent of the standard UNIX wc (word
%%%                        count) utility output of lines, words, and
%%%                        characters.  This is produced by Robert
%%%                        Solovay's checksum utility.",
%%%  }
%%% ====================================================================

%%% A delimited macro \toenglish ... \endtoenglish is NECESSARY here.
%%% The more conventional undelimited form \toenglish{...} has braces
%%% that prevent BibTeX's downcasing operation, and the alternate form
%%% {\toenglish{...}} is considered a `special character' by BibTeX,
%%% and all of {...} gets downcased.  We avoid the name \english to
%%% prevent conflicts with language options in packages like Babel.
%%%
%%% To suppress output of English translations of non-English titles,
%%% use
%%%     "\def \toenglish #1\endtoenglish{\unskip}"
%%% instead.

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                Cor-dic
                COR-DIC
                Gleit-komma
                Gleit-komma-zahl-en
                Gleit-komma-pro-zess-or
                Gleit-komma-for-mat
                Mikro-rech-en-tech-nik
                Mikro-rech-ner-sys-tem-en
                Mikro-rech-ner
                Mi-yo-shi
                Quad-rat-wurz-eln
                Semi-nu-mer-i-cal
                Swartz-lan-der
               }"
}

%%% ====================================================================
%%% Acknowledgement abbreviations:

@String{ack-jg =   "Joe Grcar,
                  email: \path=jfgrcar@lbl.gov="}

@String{ack-jh =    "John Harrison,
                  email: \path=johnh@ichips.intel.com="}

@String{ack-jr =    "Jon Rokne,
                     Department of Computer Science,
                     The University of Calgary,
                     2500 University Drive N.W.,
                     Calgary, Alberta T2N 1N4,
                     Canada"}

@String{ack-kr =    "Karin Remington,
                  National Institute of Standards and Technology,
                  Building 820, Room 365,
                  Gaithersburg, MD 20899, USA,
                  Tel: +1 301 975-5119,
                  FAX: +1 301 990-4127,
                  e-mail: \path|karin@cam.nist.gov|"}

@String{ack-mfc = "Michael F. Cowlishaw,
                   IBM UK (MP5),
                   PO Box 31,
                   Birmingham Road,
                   Warwick, CV34 5JL,
                   UK,
                   e-mail: \path|mfc@uk.ibm.com|,
                   URL: \path|http://www2.hursley.ibm.com/decimal|"}

@String{ack-nhfb = "Nelson H. F. Beebe,
                    University of Utah,
                    Department of Mathematics, 110 LCB,
                    155 S 1400 E RM 233,
                    Salt Lake City, UT 84112-0090, USA,
                    Tel: +1 801 581 5254,
                    e-mail: \path|beebe@math.utah.edu|,
                            \path|beebe@acm.org|,
                            \path|beebe@computer.org| (Internet),
                    URL: \path|https://www.math.utah.edu/~beebe/|"}

@String{ack-nj =    "Norbert Juffa,
                  2445 Mission College Blvd.
                  Santa Clara, CA 95054
                  USA
                  email: \path=norbert@iit.com="}

@String{ack-pb =      "Preston Briggs,
                     Tera Computer Company,
                     2815 Eastlake East,
                     Seattle, WA 98102,
                     USA,
                     Tel: +1 206 325-0800,
                     e-mail: \path|preston@tera.com|"}

@String{ack-rfb = "Ronald F. Boisvert,
                  Applied and Computational Mathematics Division,
                  National Institute of Standards and Technology,
                  Gaithersburg, MD 20899, USA,
                  Tel: +1 301 975 3812,
                  e-mail: \path=boisvert@cam.nist.gov="}

@String{ack-sfo = "Stuart F. Oberman,
                   e-mail: \path=stuart.oberman@amd.com="}

%%% ====================================================================
%%% Institute abbreviations:

@String{inst-ANL                = "Argonne National Laboratory"}
@String{inst-ANL:adr            = "9700 South Cass Avenue, Argonne, IL
                                  60439-4801, USA"}

@String{inst-ATT-BELL           = "AT\&T Bell Laboratories"}
@String{inst-ATT-BELL:adr       = "Murray Hill, NJ, USA"}

@String{inst-BERKELEY           = "University of California"}
@String{inst-BERKELEY:adr       = "Berkeley, CA, USA"}

@String{inst-BERKELEY-CPAM      = "Center for Pure and Applied Mathematics,
                                  University of California"}
@String{inst-BERKELEY-CPAM:adr  = "Berkeley, CA, USA"}

@String{inst-BERKELEY-CS        = "Department of Computer Science, University
                                  of California"}
@String{inst-BERKELEY-CS:adr    = "Berkeley, CA, USA"}

@String{inst-BERKELEY-EECS      = "Department of Electrical Engineering and
                                  Computer Science, University of California,
                                  Berkeley"}
@String{inst-BERKELEY-EECS:adr  = "Berkeley, CA, USA"}

@String{inst-BERKELEY-MATH-EECS = "Department of Mathematics and Department of
                                  Electrical Engineering and Computer Science,
                                  University of California, Berkeley"}
@String{inst-BERKELEY-MATH-EECS:adr = "Berkeley, CA, USA"}

@String{inst-CS-PURDUE          = "Department of Computer Science, Purdue
                                  University"}
@String{inst-CS-PURDUE:adr      = "West Lafayette, IN 47907-2107, USA"}

@String{inst-CSC                = "Center for Scientific Computing,
                                  Department of Mathematics, University of
                                  Utah"}
@String{inst-CSC:adr            = "Salt Lake City, UT 84112, USA"}

@String{inst-ETH                = "ETH Z{\"u}rich"}
@String{inst-ETH:adr            = "Z{\"u}rich, Switzerland"}

@String{inst-HP                 = "Hewlett--Packard Corporation"}
@String{inst-HP:adr             = "Palo Alto, CA, USA"}

@String{inst-INST-ADV-STUDY     = "Institute for Advanced Study"}
@String{inst-INST-ADV-STUDY:adr = "Princeton, NJ, USA"}

@String{inst-INTEL              = "Intel Corporation"}
@String{inst-INTEL:adr          = "Santa Clara, CA, USA"}

@String{inst-LASL               = "Los Alamos Scientific Laboratory"}
@String{inst-LASL:adr           = "Los Alamos, NM, USA"}

@String{inst-LORIA-INRIA-LORRAINE = "LORIA/INRIA Lorraine"}
@String{inst-LORIA-INRIA-LORRAINE:adr = "B{\^a}timent A, Technop{\^o}le de
                                  Nancy-Brabois, 615 rue du jardin
                                  botanique, F-54602
                                  Villers-l{\`e}s-Nancy Cedex, France"}

@String{inst-NLRC               = "NASA Langley Research Center"}
@String{inst-NLRC:adr           = "Hampton, VA, USA"}

@String{inst-NPL                = "National Physical Laboratory"}
@String{inst-NPL:adr            = "Teddington, Middlesex TW11 0LW, UK"}

@String{inst-MATHWORKS          = "The MathWorks, Inc."}
@String{inst-MATHWORKS:adr      = "3 Apple Hill Drive, Natick, MA 01760-2098,
                                  USA"}

@String{inst-MRC-WISCONSIN      = "Mathematics Research Center, University of
                                  Wisconsin, Madison"}
@String{inst-MRC-WISCONSIN:adr  = "Madison, WI, USA"}

@String{inst-PRINCETON          = "Princeton University"}
@String{inst-PRINCETON:adr      = "Princeton, NJ, USA"}

@String{inst-STAN-CS            = "Stanford University, Department of
                                  Computer Science"}
@String{inst-STAN-CS:adr        = "Stanford, CA, USA"}

@String{inst-UT-CS              = "Department of Computer Science,
                                  University of Tennessee, Knoxville"}
@String{inst-UT-CS:adr          = "Knoxville, TN 37996, USA"}

%%% ====================================================================
%%% Journal abbreviations:

@String{j-ACTA-INFO             = "Acta Informatica"}

@String{j-ACTA-NUMERICA         = "Acta Numerica"}

@String{j-ACM-COMM-COMP-ALGEBRA = "ACM Communications in Computer Algebra"}

@String{j-ACM-J-EXP-ALGORITHMICS = "ACM Journal of Experimental Algorithmics"}

@String{j-ADA-LETT              = "Ada Letters"}

@String{j-ADV-COMPUT-MATH       = "Advances in Computational Mathematics"}

@String{j-ADV-SOFT-SCI-TECH     = "Advances in software science and
                                  technology"}

@String{j-ADV-THEORY-SIMUL      = "Advanced Theory and Simulations"}

@String{j-ALGORITHMICA          = "Algorithmica"}

@String{j-ALGORITHMS-BASEL      = "Algorithms ({Basel})"}

@String{j-ALTA-FREQ             = "Alta frequenza"}

@String{j-AM-J-MATH             = "American Journal of Mathematics"}

@String{j-AM-SCI                = "American Scientist"}

@String{j-AMER-J-PHYSICS        = "American Journal of Physics"}

@String{j-AMER-MATH-MONTHLY     = "American Mathematical Monthly"}

@String{j-AMER-STAT             = "The American Statistician"}

@String{j-ANN-HIST-COMPUT       = "Annals of the History of Computing"}

@String{j-ANN-MATH-ARTIF-INTELL = "Annals of Mathematics and Artificial
                                  Intelligence"}

@String{j-ANN-MATH-STAT         = "Annals of Mathematical Statistics"}

@String{j-ANN-NUM-MATH          = "Annals of Numerical Mathematics"}

@String{j-APL-QUOTE-QUAD        = "ACM SIGAPL APL Quote Quad"}

@String{j-APPL-ALGEBRA-ENG-COMMUN-COMPUT = "Applicable algebra in engineering,
                                  communication and computing"}

@String{j-APPL-MATH-COMP        = "Applied Mathematics and Computation"}

@String{j-APPL-MATH-LETT        = "Applied Mathematics Letters"}

@String{j-APPL-NUM-MATH         = "Applied Numerical Mathematics"}

@String{j-APPL-OPTICS           = "Applied Optics"}

@String{j-APPL-STAT             = "Applied Statistics"}

@String{j-ARCH-HIST-EXACT-SCI   = "Archive for History of Exact Sciences"}

@String{j-ASTA-ADV-STAT-ANAL    = "AStA. Advances in Statistical Analysis"}

@String{j-ASTRON-J              = "Astronomical Journal"}

@String{j-AUSTRALIAN-COMP-J     = "Australian Computer Journal"}

@String{j-AUTO-CTL-COMP-SCI     = "Automatic Control and Computer Sciences"}

@String{j-AUTOMATION-REMOTE-CTL = "Automation and Remote Control"}

@String{j-BELL-LABS-RECORD      = "Bell Laboratories Record"}

@String{j-BELL-SYST-TECH-J      = "The Bell System Technical Journal"}

@String{j-BER-WISSENSCHAFTGESCH = "{Berichte zur Wissenschaftsgeschichte}"}

@String{j-BIOL-CYBERN           = "Biological Cybernetics"}

@String{j-BIOMETRICS            = "Biometrics"}

@String{j-BIT                   = "BIT (Nordisk tidskrift for
                                  informationsbehandling)"}

@String{j-BIT-NUM-MATH          = "BIT Numerical Mathematics"}

@String{j-BRITISH-J-HIST-MATH   = "British Journal for the History of
                                  Mathematics"}

@String{j-BRITISH-J-HIST-SCI    = "British Journal for the History of Science"}

@String{j-BULL-AMS              = "Bulletin of the American Mathematical
                                  Society"}

@String{j-BULL-CALCUTTA-MATH-SOC = "Bulletin of the Calcutta Mathematical Society"}

@String{j-BYTE                  = "Byte Magazine"}

@String{j-C-R-ACAD-BULGARE-SCI  = "Comptes rendus de l'Acad{\'e}mie bulgare
                                  des sciences"}

@String{j-C-R-ACAD-SCI-PARIS-SER-I-MATH = "Comptes Rendus des S{\'e}ances de
                                  l'Acad{\'e}mie des Sciences. S{\'e}rie I.
                                  Math{\'e}matique"}

@String{j-CACM                  = "Communications of the Association for
                                  Computing Machinery"}

@String{j-CAD                   = "Computer Aided Design"}

@String{j-CCCUJ                 = "C/C++ Users Journal"}

@String{j-CCPE                  = "Concurrency and Computation: Prac\-tice and
                                   Experience"}

@String{j-CGF                   = "Com{\-}pu{\-}ter Graphics Forum"}

@String{j-COED                  = "CoED"}

@String{j-COLLEGE-MATH-J        = "College Mathematics Journal"}

@String{j-COMBIN-PROBAB-COMPUT  = "Combinatorics, Probability and Computing"}

@String{j-COMMUN-STAT-SIMUL-COMPUT = "Communications in Statistics: Simulation
                                  and Computation"}

@String{j-COMMUN-STAT-THEORY-METH = "Communications in Statistics: Theory and
                                  Methods"}

@String{j-COMP-ARCH-NEWS        = "ACM SIGARCH Computer Architecture News"}

@String{j-COMP-DESIGN           = "Computer Design"}

@String{j-COMP-EDU-J            = "Computers in education journal"}

@String{j-COMP-GEOM             = "Computational Geometry. Theory and
                                  Applications"}

@String{j-COMP-GEOSCI           = "Computers and Geosciences"}

@String{j-COMP-J                = "The Computer Journal"}

@String{j-COMP-LANG-MAG         = "Computer Language Magazine"}

@String{j-COMP-LANGS            = "Computer Languages"}

@String{j-COMP-NET-AMSTERDAM    = "Computer Networks (Amsterdam, Netherlands:
                                  1999)"}

@String{j-COMP-PHYS-COMM        = "Computer Physics Communications"}

@String{j-COMP-SURV             = "ACM Computing Surveys"}

@String{j-COMPUT-AIDED-ENG      = "Computer-aided engineering: CAE"}

@String{j-COMPUT-EDGE           = "ComputingEdge"}

@String{j-COMPUT-ELECTR-ENG     = "Computers and Electrical Engineering"}

@String{j-COMPUT-MATH-APPL      = "Computers and Mathematics with Applications"}

@String{j-COMPUT-PHYS           = "Computers in Physics"}

@String{j-COMPUT-SCI-ENG        = "Computing in Science and Engineering"}

@String{j-COMPUT-SECUR          = "Computers \& Security"}

@String{j-COMPUTE               = "Compute"}

@String{j-COMPUTER              = "Computer"}

@String{j-COMPUTING             = "Computing: Archiv fur informatik und
                                  numerik"}

@String{j-COMPUTING-SUPPLEMENTUM = "Computing. Supplementum"}

@String{j-CONG-NUM              = "Congressus Numerantium"}

@String{j-CONTEMP-PHYS          = "Contemporary physics"}

@String{j-CPE                   = "Concurrency: Prac\-tice and Experience"}

@String{j-CRYPTOLOGIA           = "Cryptologia"}

@String{j-CT                    = "c't"}

@String{j-CUJ                   = "C Users Journal"}

@String{j-CYBER                 = "Cybernetics"}

@String{j-DDJ                   = "Dr. Dobb's Journal of Software Tools"}

@String{j-DEC-TECH-J            = "Digital Technical Journal"}

@String{j-DEMOGRAPHY            = "Demography"}

@String{j-DESIGNS-CODES-CRYPTOGR = "Designs, Codes, and Cryptography"}

@String{j-DIGIT-SIGNAL-PROCESS  = "Digital Signal Processing"}

@String{j-DISCRETE-COMPUT-GEOM  = "Discrete and Computational Geometry"}

@String{j-DOKL-AKAD-NAUK        = "Doklady Akademii nauk SSSR"}

@String{j-DTRAP                 = "Digital Threats: Research and Practice
                                  (DTRAP)"}

@String{j-EDN                   = "EDN"}

@String{j-EDUC-STUD-MATH        = "Educational Studies in Mathematics"}

@String{j-ELECT-COMM-JAPAN-3-FUND-ELECT-SCI = "Electronics and communications in
                                  Japan. Part 3, Fundamental electronic
                                  science"}

@String{j-ELECT-LETTERS         = "Electronics Letters"}

@String{j-ELECT-NOTES-THEOR-COMP-SCI = "Electronic Notes in Theoretical
                                  Computer Science"}

@String{j-ELECTR-ENG            = "Electrical Engineering (American Institute of
                                  Electrical Engineers)"}

@String{j-ELECTRON-COMMUN-JPN   = "Electronics and communications in Japan"}

@String{j-ELECTRON-ENG          = "Electronic Engineering"}

@String{j-ELECTRON-TRANS-NUMER-ANAL = "Electronic Transactions on Numerical
                                  Analysis"}

@String{j-ELECTRONIC-DESIGN     = "Electronic Design"}

@String{j-ELECTRONIC-ENG-TIMES  = "Electronic engineering times"}

@String{j-ELECTRONICS           = "Electronics"}

@String{j-ELECTRONIK            = "Elektronik"}

@String{j-ELEK-RECHENANLAGEN    = "Elektronische Rechenanlagen"}

@String{j-ELEKTRONIKER          = "Elektroniker (Switzerland)"}

@String{j-EMBED-SYS-PROG        = "Embedded Systems Programming"}

@String{j-ENTROPY               = "Entropy"}

@String{j-EURASIP-J-ADV-SIGNAL-PROCESS = "EURASIP Journal on Advances in Signal
                                Processing"}

@String{j-EURASIP-J-EMBED-SYS   = "EURASIP Journal on Embedded Systems"}

@String{j-FIB-QUART             = "Fibonacci Quarterly"}

@String{j-FORM-METHODS-SYST-DES = "Formal Methods in System Design"}

@String{j-FORTH-DIMENSIONS      = "Forth Dimensions"}

@String{j-FORTRAN-FORUM         = "ACM Fortran Forum"}

@String{j-FOUND-SCI             = "Foundations of Science"}

@String{j-FUT-GEN-COMP-SYS      = "Future Generation Computer Systems"}

@String{j-FUZZY-SETS-SYSTEMS    = "Fuzzy Sets and Systems"}

@String{j-GAMM-MIT              = "Mitteilungen der Gesellschaft f{\\\"u}r
                                  Angewandte Mathematik und Mechanik"}

@String{j-GEOSCI-MODEL-DEV      = "Geoscientific Model Development"}

@String{j-HIST-MATH             = "Historia Mathematica"}

@String{j-HIST-SCI-2            = "Historia Scientiarum. Second Series.
                                  International Journal of the History
                                  of Science Society of Japan"}

@String{j-HIGH-PERFORM-SYST     = "High performance systems"}

@String{j-HEWLETT-PACKARD-J     = "Hewlett--Packard Journal"}

@String{j-HONEYWELL-COMP-J      = "Honeywell Computer Journal"}

@String{j-IBM-JRD               = "IBM Journal of Research and Development"}

@String{j-IBM-SYS-J             = "IBM Systems Journal"}

@String{j-IBM-TDB               = "IBM Technical Disclosure Bulletin"}

@String{j-IEE-PROC-COMPUT-DIGIT-TECH = "IEE Proceedings. Computers and Digital
                                  Techniques"}

@String{j-IEE-PROC-E            = "IEE proceedings, E: Computers and digital
                                  techniques"}

@String{j-IEEE-ACCESS           = "IEEE Access"}

@String{j-IEEE-ANN-HIST-COMPUT  = "IEEE Annals of the History of Computing"}

@String{j-IEEE-APM              = "IEEE Antennas and Propagation Magazine"}

@String{j-IEEE-CGA              = "IEEE Computer Graphics and Applications"}

@String{j-IEEE-COMMUN-LET       = "IEEE Communications Letters"}

@String{j-IEEE-COMPUT-ARCHIT-LETT = "IEEE Computer Architecture Letters"}

@String{j-IEEE-COMPUT-SCI-ENG   = "IEEE Computational Science \& Engineering"}

@String{j-IEEE-DES-TEST-COMPUT  = "IEEE Design \& Test of Computers"}

@String{j-IEEE-INT-CONF-ALG-ARCH-PAR-PROC = "IEEE International Conference on
                                  Algorithms and Architectures for Parallel
                                  Processing"}

@String{j-IEEE-INTERNET-COMPUT  = "IEEE Internet Computing"}

@String{j-IEEE-J-EMERG-SEL-TOP-CIRCUITS-SYST = "IEEE Journal on Emerging and
                                  Selected Topics in Circuits and Systems"}

@String{j-IEEE-J-SOLID-STATE-CIRCUITS = "IEEE Journal of Solid-State Circuits"}

@String{j-IEEE-MICRO            = "IEEE Micro"}

@String{j-IEEE-POT              = "IEEE Potentials"}

@String{j-IEEE-J-SEL-AREAS-COMMUN = "IEEE Journal on Selected Areas in
                                  Communications"}

@String{j-IEEE-SIGNAL-PROCESS-LETT = "IEEE Signal Processing Letters"}

@String{j-IEEE-SIGNAL-PROCESS-MAG = "IEEE Signal Processing Magazine"}

@String{j-IEEE-SOFTWARE         = "IEEE Software"}

@String{j-IEEE-SPECTRUM         = "IEEE Spectrum"}

@String{j-IEEE-TIT              = "IEEE Transactions on Information Theory"}

@String{j-IEEE-TRANS-ACOUST-SPEECH = "IEEE Transactions on Acoustics, Speech,
                                  and Signal Processing"}

@String{j-IEEE-TRANS-AEROSP-ELECTRON-SYST = "IEEE Transactions on Aerospace
                                  and Electronic Systems"}

@String{j-IEEE-TRANS-APPL-SUPERCOND = "IEEE Transactions on Applied
                                  Superconductivity"}

@String{j-IEEE-TRANS-AUDIO-ELECTROACOUST = "IEEE Transactions on Audio and
                                  Electroacoustics"}

@String{j-IEEE-TRANS-AUTOMAT-CONTR = "IEEE Transactions on Automatic Control"}

@String{j-IEEE-TRANS-BIOMED-ENG = "IEEE Transactions on Biomedical
                                  Engineering"}

@String{j-IEEE-TRANS-BROADCAST  = "IEEE Transactions on Broadcasting"}

@String{j-IEEE-TRANS-CAD-ICS    = "IEEE Transactions on Computer-Aided Design
                                  of Integrated Circuits and Systems"}

@String{j-IEEE-TRANS-CIRCUITS-SYST = "IEEE Transactions on Circuits and
                                  Systems"}

@String{j-IEEE-TRANS-CIRCUITS-SYST-1 = "IEEE Transactions on Circuits and
                                  Systems I: Regular Papers"}

@String{j-IEEE-TRANS-CIRCUITS-SYST-I-FUNDAM-THEORY-APPL = "IEEE Transactions on
                                Circuits and Systems I: Fundamental
                                Theory and Applications"}

@String{j-IEEE-TRANS-CIRCUITS-SYST-2 = "IEEE transactions on circuits and
                                  systems. 2, Analog and digital signal
                                  processing"}

@String{j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS = "IEEE Transactions on
                                  Circuits and Systems II: Express Briefs"}

@String{j-IEEE-TRANS-CIRCUITS-SYST-VIDEO-TECH = "IEEE Transactions on Circuits
                                  and Systems for Video Technology"}

@String{j-IEEE-TRANS-COMM       = "IEEE Transactions on Communications"}

@String{j-IEEE-TRANS-COMPUT     = "IEEE Transactions on Computers"}

@String{j-IEEE-TRANS-CONSUMER-ELECTRONICS = "IEEE Transactions on Consumer
                                  Electronics"}

@String{j-IEEE-TRANS-CONTROL-SYST-TECHNOL = "IEEE Transactions on Control
                                  Systems Technology"}

@String{j-IEEE-TRANS-ELEC-COMPUT = "IEEE Transactions on Electronic Computers"}

@String{j-IEEE-TRANS-EMERG-TOP-COMPUT = "IEEE Transactions on Emerging Topics in
                                  Computing"}

@String{j-IEEE-TRANS-IND-ELECTRON = "IEEE Transactions on Industrial
                                  Electronics"}

@String{j-IEEE-TRANS-INF-THEORY = "IEEE Transactions on Information Theory"}

@String{j-IEEE-TRANS-INSTRUM-MEAS = "IEEE Transactions on Instrumentation and
                                  Measurement"}

@String{j-IEEE-TRANS-NEURAL-NETW = "IEEE Transactions on Neural Networks"}

@String{j-IEEE-TRANS-NUCL-SCI   = "IEEE Transactions on Nuclear Science"}

@String{j-IEEE-TRANS-PAR-DIST-SYS = "IEEE Transactions on Parallel and
                                    Distributed Systems"}

@String{j-IEEE-TRANS-PATT-ANAL-MACH-INTEL = "IEEE Transactions on Pattern
                                  Analysis and Machine Intelligence"}

@String{j-IEEE-TRANS-PROF-COMMUN = "IEEE Transactions on Professional
                                  Communication"}

@String{j-IEEE-TRANS-SIG-PROC   = "IEEE Transactions on Signal Processing"}

@String{j-IEEE-TRANS-SOFTW-ENG  = "IEEE Transactions on Software Engineering"}

@String{j-IEEE-TRANS-VEH-TECHNOL = "IEEE Transactions on Vehicular Technology"}

@String{j-IEEE-TRANS-VIS-COMPUT-GRAPH = "IEEE Transactions on Visualization and
                                  Computer Graphics"}

@String{j-IEEE-TRANS-VLSI-SYST  = "IEEE Transactions on Very Large Scale
                                  Integration (VLSI) Systems"}

@String{j-IEEE-TRANS-WIREL-COMMUN = "IEEE Transactions on Wireless Communications"}

@String{j-IFIP-TRANS-A          = "IFIP Transactions. A. Computer Science and
                                  Technology"}

@String{j-IJQC                  = "International Journal of Quantum Chemistry"}

@String{j-IJSA                  = "The International Journal of Supercomputer
                                  Applications"}

@String{j-IJHPCA                = "The International Journal of High Performance
                                  Computing Applications"}

@String{j-IMA-J-NUMER-ANAL      = "IMA Journal of Numerical Analysis"}

@String{j-INC-STAT              = "The Incorporated Statistician"}

@String{j-INF-CONTROL           = "Information and Control"}

@String{j-INF-PROCESS-MACH      = "Information processing machines"}

@String{j-INFO-PROC             = "Journal of Information Processing (of
                                  Japan??)"}

@String{j-INFO-PROC-LETT        = "Information Processing Letters"}

@String{j-INFORM-THEOR-APPL     = "RAIRO. Informatique th{\'e}orique et
                                  applications := Theoretical
                                  informatics and applications"}

@String{j-INFORMATIK-SPEKTRUM   = "Informatik Spektrum"}

@String{j-INFORMS-J-COMPUT      = "INFORMS Journal on Computing"}

@String{j-INT-J-COMPUT-GEOM-APPL = "International Journal of
                                   Computational Geometry and Applications
                                   (IJCGA)"}

@String{j-INT-J-COMP-APPL       = "International Journal of Computer
                                  Applications"}

@String{j-INT-J-COMP-RESEARCH   = "International Journal of Computer Research"}

@String{j-INT-J-CONTROL         = "International Journal of Control"}

@String{j-INT-J-ELECTRON        = "International Journal of Electronics
                                  Theoretical \& Experimental"}

@String{j-INT-J-FOUND-COMP-SCI  = "International Journal of Foundations of
                                  Computer Science"}

@String{j-INT-J-INFO-SEC        = "International Journal of Information
                                  Security"}

@String{j-INT-J-NUM-METH-FLUIDS = "Int. J. Num. Meth. Fluids"}

@String{j-INT-J-HIGH-SPEED-COMPUTING = "International Journal of High Speed
                                  Computing"}

@String{j-INT-J-MINI-MICROCOMPUTERS = "International Journal of Mini and
                                  Microcomputers"}

@String{j-INT-J-PAR-EMER-DIST-SYS = "International Journal of Parallel, Emergent
                                  and Distributed Systems: IJPEDS"}

@String{j-INT-J-PARALLEL-PROG   = "International Journal of Parallel
                                   Programming"}

@String{j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER = "International Journal on
                                  Software Tools for Technology Transfer:
                                  STTT"}

@String{j-INT-J-SYST-SCI        = "International Journal of Systems Science"}

@String{j-INTEGRATION-VLSI-J    = "Integration, the VLSI journal"}

@String{j-INTEL-TECH-J          = "Intel Technology Journal"}

@String{j-INTERVAL-COMP         = "Interval Computations = Interval'nye
                                  vychisleniia"}

@String{j-IRE-PROC              = "IRE Proceedings"}

@String{j-IRE-TRANS-ELEC-COMPUT = "IRE Transactions on Electronic Computers"}

@String{j-ISIS                  = "Isis"}

@String{j-J-ACM                 = "Journal of the Association for Computing
                                  Machinery"}

@String{j-J-ACOUST-SOC-AM       = "Journal of the Acoustical Society of
                                  America"}

@String{j-J-ADV-MODEL-EARTH-SYST = "Journal of Advances in Modeling Earth
                                  Systems"}

@String{j-J-ALG                 = "Journal of Algorithms"}

@String{j-J-AM-STAT-ASSOC       = "Journal of the American Statistical
                                  Association"}

@String{j-J-APPL-MATH           = "Journal of Applied Mathematics"}

@String{j-J-APPL-PROBAB         = "Journal of Applied Probability"}

@String{j-J-APPL-STAT           = "Journal of Applied Statistics"}

@String{j-J-APPROX-THEORY       = "Journal of Approximation Theory"}

@String{j-J-AUSTRALIAN-MATH-SOC = "Journal of the Australian Mathematical
                                  Society"}

@String{j-J-AUTOM-REASON        = "Journal of Automated Reasoning"}

@String{j-J-CHINESE-INST-ENG    = "Journal of the Chinese Institute of Engineers
                                  = Chung-kuo kung ch'eng hsueh kan"}

@String{j-J-COMB-THEORY-A       = "Journal of Combinatorial Theory (Series A)"}

@String{j-J-COMP-SYS-SCI        = "Journal of Computer and System Sciences"}

@String{j-J-COMPUT-APPL-MATH    = "Journal of Computational and Applied
                                  Mathematics"}

@String{j-J-COMPUT-PHYS         = "Journal of Computational Physics"}

@String{j-J-COMPUT-SCI          = "Journal of Computational Science"}

@String{j-J-CRYPTO-ENG          = "Journal of Cryptographic Engineering"}

@String{j-J-CRYPTOLOGY          = "Journal of Cryptology: the journal of the
                                  International Association for Cryptologic
                                  Research"}

@String{j-J-ECON-LIT            = "Journal of Economic Literature"}

@String{j-J-FORTH-APPL-RES      = "Journal of FORTH Application and Research"}

@String{j-J-FRANKLIN-INST       = "Journal of the Franklin Institute"}

@String{j-J-HIST-ASTRON         = "Journal for the History of Astronomy"}

@String{j-J-INF-PROCESS         = "Journal of Information Processing"}

@String{j-J-INFO-PROC-CYBERNETICS-EIK = "Journal of Information Processing and
                                  Cybernetics: EIK"}

@String{j-J-INST-ACTUARIES      = "Journal of the Institute of Actuaries"}

@String{j-J-INST-MATH-APPL      = "Journal of the Institute of Mathematics and
                                  its Applications"}

@String{j-J-KOREA-INFO-SCI-SOCIETY = "Journal of the Korea Information Science
                                  Society = Chongbo Kwahakhoe nonmunji"}

@String{j-J-LOGIC-ALG-PROG      = "Journal of Logic and Algebraic Programming"}

@String{j-J-MATH-CHEM           = "Journal of Mathematical Chemistry"}

@String{j-J-MATH-CRYPTOL        = "Journal of Mathematical Cryptology"}

@String{j-J-NETW-COMPUT-APPL    = "Journal of Network and Computer
                                  Applications"}

@String{j-J-PAR-DIST-COMP       = "Journal of Parallel and Distributed
                                  Computing"}

@String{j-J-PAS-ADA             = "Journal of Pascal and Ada"}

@String{j-J-R-STAT-SOC         = "Journal of the Royal Statistical Society"}

@String{j-J-R-STAT-SOC-SER-D-STATISTICIAN = "Journal of the Royal Statistical
                                  Society. Series D (The Statistician)"}

@String{j-J-RES-NATL-BUR-STAND  = "Journal of Research of the National Bureau
                                  of Standards"}

@String{j-J-SCI-COMPUT          = "Journal of Scientific Computing"}

@String{j-J-SIAM                = "Journal of the Society for Industrial and
                                  Applied Mathematics"}

@String{j-J-STAT-COMPUT-SIMUL   = "Journal of Statistical Computation and
                                   Simulation"}

@String{j-J-STAT-SOFT           = "Journal of Statistical Software"}

@String{j-J-SUPERCOMPUTING      = "The Journal of Supercomputing"}

@String{j-J-SYMBOLIC-COMP       = "Journal of Symbolic Computation"}

@String{j-J-SYST-ARCH           = "Journal of Systems Architecture"}

@String{j-J-SYST-SOFTW          = "The Journal of Systems and Software"}

@String{j-J-UCS                 = "J.UCS: Journal of Universal Computer
                                  Science"}

@String{j-J-VLSI-SIGNAL-PROC    = "Journal of VLSI Signal Processing"}

@String{j-J-VLSI-SIGNAL-PROC-SSIVT = "Journal of VLSI Signal Processing Systems
                                  for Signal, Image and Video Technology"}

@String{j-JAPAN-J-INDUST-APPL-MATH = "Japan Journal of Industrial and Applied
                                  Mathematics"}

@String{j-JAVAWORLD             = "JavaWorld: IDG's magazine for the Java
                                  community"}

@String{j-JCLT                  = "The Journal of {C} Language Translation"}

@String{j-JETC                  = "ACM Journal on Emerging Technologies in
                                  Computing Systems (JETC)"}

@String{j-KYBERNETIKA           = "Kybernetika"}

@String{j-LECT-NOTES-COMP-SCI   = "Lecture Notes in Computer Science"}

@String{j-LECT-NOTES-MATH       = "Lecture Notes in Mathematics"}

@String{j-LINEAR-ALGEBRA-APPL   = "Linear Algebra and its Applications"}

@String{j-LIGHTWAVE-TECHNOL     = "Journal of Lightwave Technology"}

@String{j-LMS-J-COMPUT-MATH     = "LMS Journal of Computation and Mathematics"}

@String{j-LOGIN                 = ";login:"}

@String{j-LOND-MATH-SOC-NEWSL   = "LMS Newsletter"}

@String{j-LOPLAS                = "ACM Letters on Programming Languages and
                                  Systems"}

@String{j-MAPLE-TECH-NEWS       = "Maple Technical Newsletter"}

@String{j-MATH-COMPUT           = "Mathematics of Computation"}

@String{j-MATH-COMPUT-APPL      = "Mathematical and Computational Applications"}

@String{j-MATH-COMPUT-SCI       = "Mathematics in Computer Science"}

@String{j-MATH-COMPUT-SIMUL     = "Mathematics and Computers in Simulation"}

@String{j-MATH-GAZ              = "The Mathematical Gazette"}

@String{j-MATH-MAG              = "Mathematics Magazine"}

@String{j-MATH-NACHR            = "Math. Nachr."}

@String{j-MATH-SCI-ENG          = "Mathematics in Science and Engineering"}

@String{j-MATH-SEMESTERBER      = "Mathematische Semesterberichte"}

@String{j-MATH-STOS             = "Math. Stos."}

@String{j-MATH-TABLES-OTHER-AIDS-COMPUT = "Mathematical Tables and Other Aids
                                  to Computation"}

@String{j-MATH-TEACH            = "The Mathematics Teacher"}

@String{j-MATHEMATICA-EDUC      = "Mathematica in Education"}

@String{j-MATHEMATICA-J         = "Mathematica Journal"}

@String{j-MC                    = "mc"}

@String{j-MECH-ENG-BULL         = "Mechanical Engineering Bulletin (India)"}

@String{j-MEM-FAC-SCI-KYUSHU-UNIV-A = "Memoirs of the Faculty of Science,
                                  Kyushu Imperial University. Series A,
                                  Mathematics = Kyushu Teikoku Daigaku
                                  Rigakubu kiyo"}

@String{j-MICROELECT-J          = "Microelectronics Journal"}

@String{j-MICROPROC-MICROPROG   = "Microprocessing and Microprogramming"}

@String{j-MICROPROC-MICROSYS    = "Microprocessors and Microsystems"}

@String{j-MINI-MICRO-SYSTEMS    = "Mini-Micro Systems"}

@String{j-MONTHLY-NOT-ROY-ASTRON-SOC = "Monthly Notices of the Royal
                                  Astronomical Society"}

@String{j-NA-DIGEST             = "NA Digest"}

@String{j-NACH-ELEK             = "Nachrichtentechnik Elektronik"}

@String{j-NAMS                  = "Notices of the American Mathematical
                                  Society"}

@String{j-NATURE                = "Nature"}

@String{j-NEC-RES-DEV           = "Nippon Electric Company research and
                                  development"}

@String{j-NEC-TECH-J            = "NEC Technical Journal = NEC giho"}

@String{j-NEUROCOMPUTING        = "Neurocomputing"}

@String{j-NEW-GEN-COMP          = "New Generation Computing"}

@String{j-NEW-SCIENTIST         = "New Scientist"}

@String{j-NONLINEAR-THEORY-APPL = "Nonlinear Theory and Its Applications,
                                  {IEICE}"}

@String{j-NORDISK-TIDSKR-INFORM-BEHAND = "Nordisk tidskrift for
                                  informationsbehandling"}

@String{j-NUM-LIN-ALG-APPL      = "Numerical Linear Algebra with Applications"}

@String{j-NUM-MATH              = "Numerische Mathematik"}

@String{j-NUMER-ALGORITHMS      = "Numerical Algorithms"}

@String{j-NY-TIMES              = "New York Times"}

@String{j-OPEN-SYSTEMS-TODAY    = "Open Systems Today"}

@String{j-OPER-SYS-REV = "Operating Systems Review"}

@String{j-PAC-J-MATH            = "Pacific Journal of Mathematics"}

@String{j-PACMPL                = "Proceedings of the ACM on Programming
                                  Languages (PACMPL)"}

@String{j-PARALLEL-ALGORITHMS-APPL = "Parallel Algorithms and Applications"}

@String{j-PARALLEL-COMPUTING    = "Parallel Computing"}

@String{j-PARALLEL-PROCESS-LETT = "Parallel Processing Letters"}

@String{j-PC-MAGAZINE           = "PC Magazine"}

@String{j-PC-WEEK               = "PC Week"}

@String{j-PHILOS-TRANS-R-SOC-LOND = "Philosophical transactions of the Royal
                                  Society of London"}

@String{j-PHILOS-TRANS-R-SOC-LOND-SER-A = "Philosophical Transactions of the
                                  Royal Society A: Mathematical,
                                  Physical, and Engineering Sciences"}

@String{j-PHYS-TEACHER          = "The Physics Teacher"}

@String{j-PHYS-WORLD            = "Physics World"}

@String{j-PHYSICA-A             = "Physica A"}

@String{j-PHYSICA-D             = "Physica D"}

@String{j-POLIT-ANAL            = "Political Analysis"}

@String{j-PROC-AM-MATH-SOC      = "Proceedings of the American Mathematical
                                  Society"}

@String{j-PROC-AMER-PHIL-SOC    = "Proceedings of the American Philosophical
                                  Society"}

@String{j-PROC-CAMBRIDGE-PHIL-SOC = "Proceedings of the Cambridge
                                  Philosophical Society. Mathematical and
                                  physical sciences"}

@String{j-PROC-IEE              = "Proceedings of the Institution of Electrical
                                  Engineers"}

@String{j-PROC-IEEE             = "Proceedings of the IEEE"}

@String{j-PROC-SPIE             = "Proceedings of the SPIE --- The
                                  International Society for Optical
                                  Engineering"}

@String{j-PROC-VLDB-ENDOWMENT   = "Proceedings of the VLDB Endowment"}

@String{j-PROG-COMP-SOFT        = "Programming and Computer Software;
                                  translation of Programmirovaniye (Moscow,
                                  USSR) Plenum"}

@String{j-PROGRAM-J             = "Programmer's Journal"}

@String{j-PROGRAMMIROVANIE      = "Programmirovanie"}

@String{j-QUART-J-MECH-APPLIED-MATH = "Quarterly Journal of Mechanics and
                                  Applied Mathematics"}

@String{j-QUART-J-ROY-METEOROL-SOC = "Quarterly journal of the Royal
                                  Meteorological Society"}

@String{j-QUEUE                 = "ACM Queue: Tomorrow's Computing Today"}

@String{j-RADIO-ELECTRON-ENG    = "The Radio and Electronic Engineer"}

@String{j-RCA-REV               = "RCA Review"}

@String{j-RELIABLE-COMPUTING    = "Reliable Computing = Nadezhnye
                                  vychisleniia"}

@String{j-REV-GEN-SCI-PURES-APPL = "Revue G{\'e}n{\'e}rale des Sciences Pures
                                  et Appliqu{\'e}es"}

@String{j-REV-HIST-SCI          = "Revue d'Histoire des Sciences"}

@String{j-SCI-AMER              = "Scientific American"}

@String{j-SCI-COMPUT-PROGRAM    = "Science of Computer Programming"}

@String{j-SCI-MONTHLY           = "The Scientific Monthly"}

@String{j-SCI-PROC-ROY-DUBLIN-SOC = "Scientific proceedings of the Royal Dublin
                                  Society"}

@String{j-SCI-PROG              = "Scientific Programming"}

@String{j-SCI-REP               = "Scientific Reports"}

@String{j-SCPE                  = "Scalable Computing: Practice and Experience"}

@String{j-SCRIPTA-MATH          = "Scripta Mathematica"}

@String{j-SEJ                   = "Software Engineering Journal"}

@String{j-SIAM-J-COMPUT         = "SIAM Journal on Computing"}

@String{j-SIAM-J-APPL-MATH      = "SIAM Journal on Applied Mathematics"}

@String{j-SIAM-J-MAT-ANA-APPL   = "SIAM Journal on Matrix Analysis and
                                  Applications"}

@String{j-SIAM-J-NUMER-ANAL     = "SIAM Journal on Numerical Analysis"}

@String{j-SIAM-J-OPT            = "SIAM Journal on Optimization"}

@String{j-SIAM-J-SCI-COMP       = "SIAM Journal on Scientific Computing"}

@String{j-SIAM-J-SCI-STAT-COMP  = "SIAM Journal on Scientific and Statistical
                                  Computing"}

@String{j-SIAM-NEWS             = "SIAM News"}

@String{j-SIAM-REVIEW           = "SIAM Review"}

@String{j-SIGACT                = "SIGACT News (ACM Special Interest Group on
                                  Automata and Computability Theory)"}

@String{j-SIGADA-LETTERS        = "ACM SIGADA Ada Letters"}

@String{j-SIGCSE                = "SIGCSE Bulletin (ACM Special Interest Group
                                  on Computer Science Education)"}

@String{j-SIGMICRO              = "ACM SIG Micro Newsletter"}

@String{j-SIGMOD                = "SIGMOD Record (ACM Special Interest Group on
                                  Management of Data)"}

@String{j-SIGNUM                = "ACM SIGNUM Newsletter"}

@String{j-SIGPLAN               = "ACM SIGPLAN Notices"}

@String{j-SIGSAM                = "SIGSAM Bulletin (ACM Special Interest Group
                                  on Symbolic and Algebraic Manipulation)"}

@String{j-SIMULATION            = "Simulation"}

@String{j-SMITHSONIAN           = "Smithsonian"}

@String{j-SOC-STUD-SCI          = "Social Studies of Science"}

@String{j-SOFTW-CONCEPTS-TOOLS  = "Software --- Concepts and Tools"}

@String{j-SOFTWAREX             = "SoftwareX"}

@String{j-SPE                   = "Soft{\-}ware\emdash Prac{\-}tice and
                                  Experience"}

@String{j-SPIE                  = "SPIE Proceedings"}

@String{j-STAT-PROB-LETT        = "Statistics \& Probability Letters"}

@String{j-STOCH-ANAL-APPL       = "Stochastic Analysis and Applications"}

@String{j-STUD-CERCET-MAT       = "Studii {\c{s}}i cercet{\u{a}}ri Matematice"}

@String{j-SUPERCOMPUTER         = "Supercomputer"}

@String{j-SUPERFRI              = "Supercomputing Frontiers and Innovations"}

@String{j-SYS-ANA-MODEL-SIM     = "Systems analysis, modelling, simulation"}

@String{j-SYS-COMP-JAPAN        = "Systems and computers in Japan"}

@String{j-TACO                  = "ACM Transactions on Architecture and
                                  Code Optimization"}

@String{j-TALG                  = "ACM Transactions on Algorithms"}

@String{j-TECHNIQUE-SCI-INFORMATIQUES = "Technique et Science Informatiques"}

@String{j-TECHNOMETRICS         = "Technometrics"}

@String{j-TECS                  = "ACM Transactions on Embedded Computing
                                  Systems"}

@String{j-TELECOMM-RADIO-ENG    = "Telecommunications and Radio Engineering"}

@String{j-THEOR-COMP-SCI        = "Theoretical Computer Science"}

@String{j-THEORY-PROBAB-APPL    = "Theory of probability and its applications"}

@String{j-TOCL                  = "ACM Transactions on Computational Logic"}

@String{j-TOCS                  = "ACM Transactions on Computer Systems"}

@String{j-TODAES                = "ACM Transactions on Design Automation of
                                  Electronic Systems."}

@String{j-TOG                   = "ACM Transactions on Graphics"}

@String{j-TOMACS                = "ACM Transactions on Modeling and Computer
                                  Simulation"}

@String{j-TOMS                  = "ACM Transactions on Mathematical Software"}

@String{j-TOPC                  = "ACM Transactions on Parallel Computing
                                  (TOPC)"}

@String{j-TOPLAS                = "ACM Transactions on Programming Languages
                                  and Systems"}

@String{j-TOSEM                 = "ACM Transactions on Software Engineering and
                                   Methodology"}

@String{j-TRANS-AMER-INST-ELEC-ENG = "Transactions of the American Institute of
                                  Electrical Engineers"}

@String{j-TRANS-INFO-PROCESSING-SOC-JAPAN = "Transactions of the Information
                                  Processing Society of Japan"}

@String{j-TRANS-IRE             = "Transactions of the IRE"}

@String{j-TRANS-IRE-PROF-GROUP-ELEC-COMPUT = "Transactions of the I.R.E.
                                  Professional Group on Electronic Computers"}

@String{j-TRANS-SOC-COMP-SIM    = "Transactions of the Society for Computer
                                  Simulation"}

@String{j-TRETS                 = "ACM Transactions on Reconfigurable Technology
                                  and Systems"}

@String{j-TUGboat               = "TUGboat (Journal of the {\TeX} Users Group)"}

@String{j-WALL-ST-J             = "Wall Street Journal"}

@String{j-ZASTOS-MAT            = "Zastosowania Matematyki"}

@String{j-Z-ANGE-MATH-MECH      = "Zeitschrift f{\"u}r Angewandte Mathematik
                                  und Mechanik"}

@String{j-Z-ANGE-MATH-PHYS      = "{Zeitschrift f{\"u}r Angewandte Mathematik
                                  und Physik = Journal of Applied
                                  Mathematics and Physics}"}

%%% ====================================================================
%%% Publishers and their addresses:

@String{pub-A-K-PETERS          = "A. K. Peters, Ltd."}
@String{pub-A-K-PETERS:adr      = "Natick, MA, USA"}

@String{pub-ACADEMIC            = "Academic Press"}
@String{pub-ACADEMIC:adr        = "New York, NY, USA"}

@String{pub-ACM                 = "ACM Press"}
@String{pub-ACM:adr             = "New York, NY 10036, USA"}

@String{pub-AFIPS               = "AFIPS Press"}
@String{pub-AFIPS:adr           = "Montvale, NJ, USA"}

@String{pub-AIP                 = "American Institute of Physics"}
@String{pub-AIP:adr             = "Woodbury, NY, USA"}

@String{pub-AKADEMIE-VERLAG     = "Akademie-Verlag"}
@String{pub-AKADEMIE-VERLAG:adr = "Berlin, Germany"}

@String{pub-AMS                 = "American Mathematical Society"}
@String{pub-AMS:adr             = "Providence, RI, USA"}

@String{pub-ANSI                = "American National Standards Institute"}
@String{pub-ANSI:adr            = "1430 Broadway, New York, NY 10018, USA"}

@String{pub-ATT-BELL            = "AT\&T Bell Laboratories"}
@String{pub-ATT-BELL:adr        = "Murray Hill, NJ, USA"}

@String{pub-AW                  = "Ad{\-d}i{\-s}on-Wes{\-l}ey"}
@String{pub-AW:adr              = "Reading, MA, USA"}

@String{pub-BALTZER             = "J. C. Baltzer AG, Scientific
                                  Publishing Company"}
@String{pub-BALTZER:adr         = "Basel, Switzerland"}

@String{pub-BENCUM              = "Benjamin/Cummings Pub. Co."}
@String{pub-BENCUM:adr          = "Redwood City, CA, USA"}

@String{pub-BIB-INST            = "Bibliographisches Institut"}
@String{pub-BIB-INST:adr        = "Mannheim, Germany"}

@String{pub-BIRKHAUSER-BOSTON   = "Birkh{\"a}user Boston Inc."}
@String{pub-BIRKHAUSER-BOSTON:adr = "Cambridge, MA, USA"}

@String{pub-BIRKHAUSER          = "Birkh{\"a}user"}
@String{pub-BIRKHAUSER:adr      = "Cambridge, MA, USA; Berlin, Germany; Basel,
                                  Switzerland"}

@String{pub-BRADY               = "Robert J. Brady Co."}
@String{pub-BRADY:adr           = "Bowie, MD 20715, USA"}

@String{pub-CAMBRIDGE           = "Cambridge University Press"}
@String{pub-CAMBRIDGE:adr       = "Cambridge, UK"}

@String{pub-CHAPMAN-HALL        = "Chapman and Hall, Ltd."}
@String{pub-CHAPMAN-HALL:adr    = "London, UK"}

@String{pub-CLARENDON           = "Clarendon Press"}
@String{pub-CLARENDON:adr       = "Oxford, UK"}

@String{pub-CRC                 = "CRC Press"}
@String{pub-CRC:adr             = "2000 N.W. Corporate Blvd., Boca Raton,
                                  FL 33431-9868, USA"}

@String{pub-CSLI                = "CSLI Publications"}
@String{pub-CSLI:adr            = "Stanford, CA, USA"}

@String{pub-DOUBLEDAY           = "Doubleday"}
@String{pub-DOUBLEDAY:adr       = "New York, NY, USA"}

@String{pub-DOVER               = "Dover"}
@String{pub-DOVER:adr           = "New York, NY, USA"}

@String{pub-DOWDEN              = "Dowden, Hutchinson and Ross"}
@String{pub-DOWDEN:adr          = "Stroudsburg, PA, USA"}

@String{pub-DP                  = "Digital Press"}
@String{pub-DP:adr              = "12 Crosby Drive, Bedford, MA 01730, USA"}

@String{pub-ELLIS-HORWOOD       = "Ellis Horwood"}
@String{pub-ELLIS-HORWOOD:adr   = "New York, NY, USA"}

@String{pub-ELSEVIER            = "Elsevier"}
@String{pub-ELSEVIER:adr        = "Amsterdam, The Netherlands"}

@String{pub-ELSEVIER-MORGAN-KAUFMANN = "Elsevier\slash Morgan Kaufmann"}
@String{pub-ELSEVIER-MORGAN-KAUFMANN:adr = "San Francisco, CA, USA"}

@String{pub-ENH                 = "Elsevier North-Holland, Inc."}
@String{pub-ENH:adr             = "New York, NY, USA"}

@String{pub-FSF                 = "{Free Software Foundation, Inc.}"}
@String{pub-FSF:adr             = "51 Franklin Street, Fifth Floor, Boston,
                                  MA 02110-1301, USA, Tel: (617) 876-3296"}

@String{pub-GRUYTER             = "Walter de Gruyter"}
@String{pub-GRUYTER:adr         = "Berlin, Germany"}

@String{pub-HANSER              = "Carl Hanser"}
@String{pub-HANSER:adr          = "M{\"u}nchen, Germany"}

@String{pub-HARVARD             = "Harvard University Press"}
@String{pub-HARVARD:adr         = "Cambridge, MA, USA"}

@String{pub-HAYDEN-BOOK         = "Hayden Book Co."}
@String{pub-HAYDEN-BOOK:adr     = "Rochelle Park, NJ, USA"}

@String{pub-HMSO                = "HMSO"}
@String{pub-HMSO:adr            = "London, UK"}

@String{pub-HRW                 = "Holt, Reinhart, and Winston"}
@String{pub-HRW:adr             = "New York, NY, USA"}

@String{pub-IBM                 = "IBM Corporation"}
@String{pub-IBM:adr             = "San Jose, CA, USA"}

@String{pub-IBM-WATSON          = "IBM Thomas J. Watson Research Center"}
@String{pub-IBM-WATSON:adr      = "Yorktown Heights, NY, USA"}

@String{pub-IEC                 = "International Electrotechnical Commission"}
@String{pub-IEC:adr             = "3, rue de Varemb{\'e}, PO Box 131, CH-1211
                                  Geneva 20, Switzerland. Telephone: +41 22
                                  919 02 11. Telefax: +41 22 919 03 00.
                                  E-mail: {\tt info@\penalty0iec.\penalty0ch}. URL: {\tt
                                  http:\penalty0//\penalty0www.\penalty0iec.\penalty0ch}"}

@String{pub-IEE                 = "IEE (Institution of Electrical Engineers)"}
@String{pub-IEE:adr             = "London, UK"}

@String{pub-IEEE                = "IEEE Computer Society Press"}
@String{pub-IEEE:adr            = "1109 Spring Street, Suite 300, Silver
                                   Spring, MD 20910, USA"}

@String{pub-IEEE-STD            = "IEEE"}
@String{pub-IEEE-STD:adr        = "New York, NY, USA"}

@String{pub-IMACS               = "IMACS"}
@String{pub-IMACS:adr           = "Department of Computer Science, Rutgers
                                  University, New Brunswick, NJ"}

@String{pub-INTEL               = "Intel Corporation"}
@String{pub-INTEL:adr           = "Santa Clara, CA, USA"}

@String{pub-ISO                 = "International Organization for
                                  Standardization"}
@String{pub-ISO:adr             = "Geneva, Switzerland"}

@String{pub-IWT                 = "IWT"}
@String{pub-IWT:adr             = "Vaterstetten, Germany"}

@String{pub-JOSEPH-HENRY        = "Joseph Henry Press"}
@String{pub-JOSEPH-HENRY:adr    = "Washington, DC, USA"}

@String{pub-JW                  = "John Wiley"}
@String{pub-JW:adr              = "New York, NY, USA"}

@String{pub-KLUWER              = "Kluwer Academic Publishers Group"}
@String{pub-KLUWER:adr          = "Norwell, MA, USA, and Dordrecht,
                                  The Netherlands"}

@String{pub-MAC                 = "Macmillan Publishing Company"}
@String{pub-MAC:adr             = "New York, NY, USA"}

@String{pub-MATH-ASSOC-AMER     = "Mathematical Association of America"}
@String{pub-MATH-ASSOC-AMER:adr = "Washington, DC, USA"}

@String{pub-MCGRAW-HILL         = "Mc{\-}Graw-Hill"}
@String{pub-MCGRAW-HILL:adr     = "New York, NY, USA"}

@String{pub-MILLER-FREEMAN      = "Miller Freeman Publications"}
@String{pub-MILLER-FREEMAN:adr  = "San Francisco, CA, USA"}

@String{pub-MIT                 = "The MIT Press"}
@String{pub-MIT:adr             = "Cambridge, MA"}

@String{pub-MORGAN-KAUFMANN = "Morgan Kaufmann Publishers"}
@String{pub-MORGAN-KAUFMANN:adr = "Los Altos, CA 94022, USA"}

@String{pub-MORGAN-KAUFMANN-ELSEVIER = "Morgan Kaufmann\slash Elsevier"}
@String{pub-MORGAN-KAUFMANN-ELSEVIER:adr = "Waltham, MA, USA"}

@String{pub-MOTOROLA            = "Motorola Corporation"}
@String{pub-MOTOROLA:adr        = "Phoenix, AZ, USA"}

@String{pub-MT                  = "M\&T Books"}
@String{pub-MT:adr              = "M\&T Publishing, Inc., 501 Galveston Drive,
                                   Redwood City, CA 94063, USA"}

@String{pub-NASA                = "National Aeronautics and Space
                                  Administration"}
@String{pub-NASA:adr            = "Washington, DC, USA"}

@String{pub-NBS                 = "U.S. National Bureau of Standards"}
@String{pub-NBS:adr             = "Gaithersburg, MD, USA"}

@String{pub-NORTH-HOLLAND       = "North-Hol{\-}land"}
@String{pub-NORTH-HOLLAND:adr   = "Amsterdam, The Netherlands"}

@String{pub-OLDENBOURG          = "R. Oldenbourg Verlag"}
@String{pub-OLDENBOURG:adr      = "Munich, Germany and Vienna, Austria"}

@String{pub-ORA                 = "O'Reilly \& {Associates, Inc.}"}
@String{pub-ORA:adr             = "981 Chestnut Street, Newton, MA 02164, USA"}

@String{pub-ORACLE              = "Oracle Press (division of Osborne
                                  McGraw-Hill)"}
@String{pub-ORACLE:adr          = "Berkeley, CA, USA"}

@String{pub-OXFORD              = "Oxford University Press"}
@String{pub-OXFORD:adr          = "Walton Street, Oxford OX2 6DP, UK"}

@String{pub-PENGUIN             = "Penguin"}
@String{pub-PENGUIN:adr         = "London, UK"}

@String{pub-PERGAMON            = "Pergamon Press"}
@String{pub-PERGAMON:adr        = "New York, NY, USA"}

@String{pub-PH                  = "Pren{\-}tice-Hall"}
@String{pub-PH:adr              = "Upper Saddle River, NJ 07458, USA"}

@String{pub-PHPTR               = "Pren{\-}tice-Hall PTR"}
@String{pub-PHPTR:adr           = "Upper Saddle River, NJ 07458, USA"}

@String{pub-PITMAN              = "Pitman Publishing Ltd."}
@String{pub-PITMAN:adr          = "London, UK"}

@String{pub-PLENUM              = "Plenum Press"}
@String{pub-PLENUM:adr          = "New York, NY, USA"}

@String{pub-PROJECT-GUTENBERG   = "Project Gutenberg"}
@String{pub-PROJECT-GUTENBERG:adr = "P.O. Box 2782, Champaign, IL 61825-2782, USA"}

@String{pub-PRINCETON           = "Princeton University Press"}
@String{pub-PRINCETON:adr       = "Princeton, NJ, USA"}

@String{pub-R-E-KRIEGER         = "Robert E. Krieger Publishing Company"}
@String{pub-R-E-KRIEGER:adr     = "Huntington, NY, USA"}

@String{pub-RESTON              = "Reston Publishing Co. Inc."}
@String{pub-RESTON:adr          = "Reston, VA, USA"}

@String{pub-SF                  = "Scott, Foresman and Company"}
@String{pub-SF:adr              = "Glenview, IL, USA"}

@String{pub-SIAM                = "Society for Industrial and Applied
                                  Mathematics"}
@String{pub-SIAM:adr            = "Philadelphia, PA, USA"}

@String{pub-SIEMENS             = "Siemens Aktiengesellschaft"}
@String{pub-SIEMENS:adr         = "Berlin and Munich, Germany"}

@String{pub-SPIE                = "Society of Photo-optical
                                  Instrumentation Engineers (SPIE)"}
@String{pub-SPIE:adr            = "Bellingham, WA, USA"}

@String{pub-SPRINGER-WIEN       = "Spring{\-}er"}
@String{pub-SPRINGER-WIEN:adr   = "Wien / New York"}

@String{pub-SRNI                = "Software Research Northwest, Inc."}
@String{pub-SRNI:adr            = "17710 100th Avenue SW, Vashon Island, WA
                                  98070, USA"}

@String{pub-SUN                 = "Sun Microsystems"}
@String{pub-SUN:adr             = "2550 Garcia Avenue, Mountain View,
                                  CA 94043, USA"}

@String{pub-SV                  = "Spring{\-}er-Ver{\-}lag"}
@String{pub-SV:adr              = "Berlin, Germany~/ Heidelberg,
                                  Germany~/ London, UK~/ etc."}

@String{pub-SV-CHAM             = "Spring{\-}er-Ver{\-}lag"}
@String{pub-SV-CHAM:adr         = "Cham, Switzerland"}

@String{pub-SYNGRESS            = "Syngress Publishing, Inc."}
@String{pub-SYNGRESS:adr        = "Rockland, MA, USA"}

@String{pub-TEUBNER             = "B. G. Teubner"}
@String{pub-TEUBNER:adr         = "Stuttgart, Germany"}

@String{pub-TEWI                = "te-wi"}
@String{pub-TEWI:adr            = "M{\"u}nchen, Germany"}

@String{pub-TOMASH              = "Tomash Publishers"}
@String{pub-TOMASH:adr          = "Los Angeles, CA, USA"}

@String{pub-USENIX              = "USENIX"}
@String{pub-USENIX-EL-CERRITO:adr = "P.O. Box 7, El Cerrito 94530, CA,
                                  USA"}
@String{pub-USENIX:adr          = "San Francisco, CA, USA"}

@String{pub-USGPO               = "United States Government Printing Office"}
@String{pub-USGPO:adr           = "Washington, DC, USA"}

@String{pub-VEB-VERLAG-TECHNIK  = "VEB Verlag Technik"}
@String{pub-VEB-VERLAG-TECHNIK:adr  = "Berlin, Germany"}

@String{pub-VIKING              = "Viking"}
@String{pub-VIKING:adr          = "New York, NY, USA"}

@String{pub-WCB                 = "William C. Brown Company Publishers"}
@String{pub-WCB:adr             = "Dubuque, IA, USA"}

@String{pub-WEITEK              = "Weitek Corporation"}
@String{pub-WEITEK:adr          = "1060 E. Arques Ave., Sunnyvale, CA
                                  94086-BRM-9759, USA"}

@String{pub-WESTERN-PERIODICALS = "Western Periodicals Co.,"}
@String{pub-WESTERN-PERIODICALS:adr = "North Hollywood, CA"}

@String{pub-WILEY               = "Wiley"}
@String{pub-WILEY:adr           = "New York, NY, USA"}

@String{pub-WILEY-INTERSCIENCE  = "Wiley-In{\-}ter{\-}sci{\-}ence"}
@String{pub-WILEY-INTERSCIENCE:adr = "New York, NY, USA"}

@String{pub-WORLD-SCI           = "World Scientific Publishing
                                  Co. Pte. Ltd."}
@String{pub-WORLD-SCI:adr       = "P. O. Box 128, Farrer Road,
                                  Singapore 9128"}

%%% ====================================================================
%%% Series abbreviations:

@String{ser-APPL-MATH-SER-NBS   = "Applied Mathematics Series / National Bureau
                                  of Standards"}

@String{ser-LECT-NOTES-MATH     = "Lecture Notes in Mathematics"}

@String{ser-LNCS                = "Lecture Notes in Computer Science"}

@String{ser-LNCSE               = "Lecture Notes in Computational
                                   Science and Engineering"}

@String{ser-PROJECT-GUTENBERG   = "Project Gutenberg"}

@String{ser-SIGPLAN             = "ACM SIGPLAN Notices"}

%%% ====================================================================
%%% Bibliography entries, sorted by year, and within each year, by
%%% citation label, with ``bibsort -byyear''.
%%%
%%% NB: Some journals do not indicate a month for each issue, and a few
%%% have volumes, but no issue numbers, or issues without volumes.  Such
%%% cases are identified by xxmonth, xxnumber, and xxvolume entries with a
%%% value of "(none)", so that searches can still be used to identify
%%% other entries where such information is still missing.
%%%
%%% ISBNs were introduced in 1972, so books published before that do not
%%% have ISBN entries, unless the publisher supplied one in a post-1971
%%% printing.  A few books, and many conference proceedings, published
%%% since 1972, lack ISBNs; these are identified with xxISBN values of
%%% (none), again to facilitate searching for missing values.
%%%
%%% TO DO: Add entries for more of these US patents on floating-point
%%% arithmetic:
%%%
%%%     http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO2&Sect2=HITOFF&u=%2Fnetahtml%2FPTO%2Fsearch-adv.htm&r=0&p=1&f=S&l=50&Query=ttl%2F%28floating+and+point+and+arithmetic%29%0D%0A%0D%0A&d=PALL
%%%     Searched on 17 October 2019 for "ttl/(floating and point and arithmetic)"
%%%
%%% 1   10,416,962      Decimal and binary floating point arithmetic calculations
%%% 2   10,318,241      Fixed-point and floating-point arithmetic operator circuits in specialized processing blocks
%%% 3   10,289,413      Hybrid analog-digital floating point number representation and arithmetic
%%% 4   10,216,480      Shift and divide operations using floating-point arithmetic
%%% 5   10,216,479      Apparatus and method for performing arithmetic operations to accumulate floating-point numbers
%%% 6   10,175,944      Mixed-precision floating-point arithmetic circuitry in specialized processing blocks
%%% 7   10,073,676      Reduced floating-point precision arithmetic circuitry
%%% 8   10,042,606      Fixed-point and floating-point arithmetic operator circuits in specialized processing blocks
%%% 9   9,904,514       Fused floating-point arithmetic circuitry
%%% 10  9,665,346       Performing arithmetic operations using both large and small floating point values
%%%
%%% 11  9,600,234       Floating-point arithmetic device, semiconductor device and information processing system
%%% 12  8,984,041       Performing arithmetic operations using both large and small floating point values
%%% 13  8,909,690       Performing arithmetic operations using both large and small floating point values
%%% 14  8,793,533       Method and device for performing failsafe hardware-independent floating-point arithmetic
%%% 15  8,694,567       Method and apparatus for arithmetic operation on a value represented in a floating-point format
%%% 16  8,615,542       Multi-function floating point arithmetic pipeline
%%% 17  8,166,092       Arithmetic device for performing division or square root operation of floating point number and arithmetic method therefor
%%% 18  8,117,426       System and apparatus for group floating-point arithmetic operations
%%% 19  7,949,696       Floating-point number arithmetic circuit for handling immediate values
%%% 20  7,730,287       Method and software for group floating-point arithmetic operations
%%%
%%% 21  7,530,061       Programmatic access to the widest mode floating-point arithmetic supported by a processor
%%% 22  7,392,274       Multi-function floating point arithmetic pipeline
%%% 23  7,188,133       Floating point number storage method and floating point arithmetic device
%%% 24  7,069,288       Floating point system with improved support of interval arithmetic
%%% 25  6,965,908       Multi-function floating point arithmetic pipeline
%%% 26  6,785,701       Apparatus and method of performing addition and rounding operation in parallel for floating-point arithmetic logical unit
%%% 27  6,748,587       Programmatic access to the widest mode floating-point arithmetic supported by a processor
%%% 28  6,571,264       Floating-point arithmetic device
%%% 29  6,388,672       Graphic translate engine, floating point arithmetic unit and floating point multiply-add calculation unit
%%% 30  6,314,442       Floating-point arithmetic unit which specifies a least significant bit to be incremented
%%%
%%% 31  6,205,461       Floating point arithmetic logic unit leading zero count using fast approximate rounding
%%% 32  6,199,089       Floating point arithmetic logic unit rounding using at least one least significant bit
%%% 33  6,185,593       Method and apparatus for parallel normalization and rounding technique for floating point arithmetic operations
%%% 34  6,175,847       Shifting for parallel normalization and rounding technique for floating point arithmetic operations
%%% 35  6,173,299       Method and apparatus for selecting an intermediate result for parallel normalization and rounding technique for floating point arithmetic operations
%%% 36  6,151,615       Method and apparatus for formatting an intermediate result for parallel normalization and rounding technique for floating point arithmetic operations
%%% 37  6,094,668       Floating point arithmetic unit including an efficient close data path
%%% 38  6,088,715       Close path selection unit for performing effective subtraction within a floating point arithmetic unit
%%% 39  6,085,212       Efficient method for performing close path subtraction in a floating point arithmetic unit
%%% 40  6,085,211       Logic circuit and floating-point arithmetic unit
%%%
%%% 41  6,085,208       Leading one prediction unit for normalizing close path subtraction results within a floating point arithmetic unit
%%% 42  6,078,939       Apparatus useful in floating point arithmetic
%%% 43  5,931,896       Floating point addition and subtraction arithmetic circuit performing preprocessing of addition or subtraction operation rapidly
%%% 44  5,931,895       Floating-point arithmetic processing apparatus
%%% 45  5,901,076       Ripple carry shifter in a floating point arithmetic unit of a microprocessor
%%% 46  5,831,884       Apparatus for performing arithmetic operation of floating point numbers capable of improving speed of operation by performing canceling prediction operation in parallel
%%% 47  5,771,183       Apparatus and method for computation of sticky bit in a multi-stage shifter used for floating point arithmetic
%%% 48  5,748,516       Floating point processing unit with forced arithmetic results
%%% 49  5,726,926       Shifter for shifting floating point number utilizing arithmetic operation of redundant binary number, and adder containing the same
%%% 50  5,677,861       Arithmetic apparatus for floating-point numbers
%%%
%%% 51  5,633,818       Method and apparatus for performing floating point arithmetic operation and rounding the result thereof
%%% 52  5,631,859       Floating point arithmetic unit having logic for quad precision arithmetic
%%% 53  5,568,412       Rounding-off method and apparatus of floating point arithmetic apparatus for addition/subtraction
%%% 54  5,550,768       Rounding normalizer for floating point arithmetic operations
%%% 55  5,515,308       Floating point arithmetic unit using modified Newton-Raphson technique for division and square root
%%% 56  5,434,809       Method and apparatus for performing floating point arithmetic operation and rounding the result thereof
%%% 57  5,432,727       Apparatus for computing a sticky bit for a floating point arithmetic unit
%%% 58  5,375,196       Rapid line drawing in computer graphics employing floating-point arithmetic
%%% 59  5,359,548       Floating-point arithmetic system having multiple-input addition and subtraction means
%%% 60  5,341,321       Floating point arithmetic unit using modified Newton-Raphson technique for division and square root
%%%
%%% 61  5,313,415       Method and apparatus for performing floatinga point arithmetic operation and rounding the result thereof
%%% 62  5,303,175       Floating point arithmetic unit
%%% 63  5,301,137       Circuit for fixed point or floating point arithmetic operations
%%% 64  5,241,493       Floating point arithmetic unit with size efficient pipelined multiply-add architecture
%%% 65  5,222,037       Floating-point processor for performing an arithmetic operation on fixed-point part data with high speed rounding of a result
%%% 66  5,212,662       Floating point arithmetic two cycle data flow
%%% 67  5,212,661       Apparatus for performing floating point arithmetic operation and rounding the result thereof
%%% 68  5,200,916       Mantissa processing circuit of floating point arithmetic apparatus for addition and subtraction
%%% 69  5,128,889       Floating-point arithmetic apparatus with compensation for mantissa truncation
%%% 70  5,121,351       Floating point arithmetic system
%%%
%%% 71  5,075,882       Normalizing circuit of floating-point arithmetic circuit for two input data
%%% 72  4,999,803       Floating point arithmetic system and method
%%% 73  4,999,802       Floating point arithmetic two cycle data flow
%%% 74  4,991,130       Normalization control system for floating point arithmetic operation
%%% 75  4,961,162       Multiprocessing system for performing floating point arithmetic operations
%%% 76  4,908,788       Shift control signal generation circuit for floating-point arithmetic operation
%%% 77  4,896,286       Floating-point arithmetic apparatus
%%% 78  4,872,132       Method and means for block floating point arithmetic
%%% 79  4,839,846       Apparatus for performing floating point arithmetic operations and rounding the result thereof
%%% 80  4,811,272       Apparatus and method for an extended arithmetic logic unit for expediting selected floating point operations
%%%
%%% 81  4,796,218       Arithmetic circuit capable of executing floating point operation and fixed point operation
%%% 82  4,796,217       Rounding unit for use in arithmetic processing of floating point data
%%% 83  4,780,842       Cellular processor apparatus capable of performing floating point arithmetic operations
%%% 84  4,758,972       Precision rounding in a floating point arithmetic unit
%%% 85  4,683,547       Special accumulate instruction for multiple floating point arithmetic units which use a putaway bus to enhance performance
%%% 86  4,649,508       Floating-point arithmetic operation system
%%% 87  4,620,292       Arithmetic logic unit for floating point data and/or fixed point data
%%% 88  4,562,553       Floating point arithmetic system and method with rounding anticipation
%%% 89  4,217,657       Floating point arithmetic control
%%% 90  4,161,784       Microprogrammable floating point arithmetic unit capable of performing arithmetic operations on long and short operands
%%%
%%% 91  4,130,879       Apparatus for performing floating point arithmetic operations using submultiple storage
%%% 92  3,829,673       FLOATING POINT ARITHMETIC UNIT ADAPTED FOR CONVERTING A COMPUTER TO FLOATING POINT ARITHMETIC
%%% 93  3,701,976       FLOATING POINT ARITHMETIC UNIT FOR A PARALLEL PROCESSING COMPUTER
%%% 94  3,193,669       708/505
%%% 95  3,037,701       708/495
%%% 96  2,965,297       708/503 708/504 708/671

@Article{Leibniz:1703:EAB,
  author =       "G.-W. Leibniz",
  title =        "Explication de {l'Arithm{\'e}tique} Binaire.
                 ({French}) [{Explanation} of binary arithmetic]",
  journal =      "M{\'e}moires de math{\'e}matique et de physique de l
                 Acad{\'e}mie royale des sciences",
  volume =       "??",
  number =       "??",
  pages =        "85--89",
  month =        "????",
  year =         "1703",
  bibdate =      "Fri Mar 17 08:48:17 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Leibniz is often credited with the invention of the
                 binary number system, but there is other work from his
                 era, and detailed analysis of Leibniz's use of binary
                 numbers. See
                 \cite{Greve:1966:HLR,Glaser:1969:HMN,Glaser:1971:HBO,Lautz:1979:JLD,Glaser:1981:HBO,Esmay:2017:HNS,Strickland:2022:LBI,Zlatopolski:2023:PAV}",
  URL =          "https://hal.archives-ouvertes.fr/ads-00104781/document",
  acknowledgement = ack-nhfb,
  language =     "French",
}

@Book{Pelicano:1712:APQ,
  author =       "Wenceslao Josepho Pelicano",
  title =        "Arithmeticus Perfectus Qui tria numerare nescit,
                 \ldots{}. ({Latin}) [{A} Perfect Arithmetic for who
                 does not know how to count to three]",
  publisher =    "????",
  address =      "Prague, Czechoslovakia",
  pages =        "????",
  year =         "1712",
  bibdate =      "Fri Mar 17 08:56:14 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://play.google.com/books/reader?id=cNxdAAAAcAAJ",
  acknowledgement = ack-nhfb,
  longtitle =    "Arithmeticus Perfectus Qui tria numerare nescit, sen
                 Arithmetica dualis in qua Numerando non proceditur,
                 nisi ad duo, \& tamen omnes questiones Arithmetic{\ae}
                 negoti{\^o} facile enodar possunt ad perilsturem equite
                 Mathematic{\ae}. ({Latin}) [{A} Perfect Arithmetic for
                 who does not know how to count to three, is a dual
                 arithmetic in which he does not proceed to numbering
                 except to two, and yet all the questions of arithmetic
                 business can easily be entangled to the peril of the
                 mathematician]",
}

@Article{Colson:1726:SAN,
  author =       "John {Colson, F.R.S.}",
  title =        "A Short Account of Negativo-Affirmative Arithmetick",
  journal =      j-PHILOS-TRANS-R-SOC-LOND,
  volume =       "34",
  number =       "392--398",
  pages =        "161--173",
  month =        "????",
  year =         "1726",
  CODEN =        "PTRSAV",
  DOI =          "https://doi.org/10.1098/rstl.1726.0032",
  ISSN =         "0370-2316 (print), 2053-9207 (electronic)",
  bibdate =      "Tue Jul 28 14:21:05 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith22.gforge.inria.fr/slides/s2-ercegovac.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Philosophical transactions of the Royal Society of
                 London",
  journal-URL =  "http://rsta.royalsocietypublishing.org/",
  remark =       "Early work on signed-digit arithmetic, reported by
                 Milo{\v{s}} Ercegovac in a talk at the ARITH'22
                 conference, Lyon, France, June 2015.",
}

@Unpublished{Babbage:1837:MPC,
  author =       "Charles Babbage",
  title =        "On the mathematical powers of the calculating engine",
  month =        dec,
  year =         "1837",
  bibdate =      "Wed Oct 13 11:09:59 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Manuscript held by Museum of the History of Science,
                 Oxford, UK. Reprinted in \cite[\S
                 2.1]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
}

@Book{Nystrom:1862:PNS,
  author =       "John W. (John William) Nystrom",
  title =        "Project of a new system of arithmetic, weight, measure
                 and coins, proposed to be called the tonal system, with
                 sixteen to the base",
  publisher =    "J. B. Lippincott and Co.",
  address =      "Philadelphia, PA, USA",
  pages =        "106",
  year =         "1862",
  LCCN =         "QC96 .N95",
  bibdate =      "Sat Oct 29 10:28:27 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://unifoundry.com/tonal/;
                 https://catalog.hathitrust.org/Record/011602816;
                 https://lccn.loc.gov/04025433",
  acknowledgement = ack-nhfb,
  author-dates = "Johan Vilhelm Nystr{\"o}m (1824--1885)",
  remark =       "Thanks to Paul Hardy of Unifoundry in San Diego, CA,
                 USA, for information about Nystrom's promotion of
                 hexadecimal arithmetic, and for creating a Web site
                 about Nystrom's tonal system, as well as developing
                 Unicode-compatible fonts to represent the additional
                 digits needed by the system.",
  subject =      "Weights and measures; Numeration; base-16 arithmetic;
                 hexadecimal arithmetic",
}

@Article{Anonymous:1875:AOM,
  author =       "Anonymous",
  title =        "The Arithmetical Operations of Multiplication and
                 Division",
  journal =      j-SCI-AMER,
  volume =       "32",
  number =       "3",
  pages =        "41--42",
  day =          "16",
  month =        jan,
  year =         "1875",
  CODEN =        "SCAMAC",
  DOI =          "https://doi.org/10.1038/scientificamerican01161875-41",
  ISSN =         "0036-8733 (print), 1946-7087 (electronic)",
  ISSN-L =       "0036-8733",
  bibdate =      "Fri May 17 10:29:24 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sciam1870.bib",
  URL =          "http://www.nature.com/scientificamerican/journal/v32/n3/pdf/scientificamerican01161875-41.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientific American",
  journal-URL =  "http://www.nature.com/scientificamerican",
}

@Article{Anonymous:1879:TRA,
  author =       "Anonymous",
  title =        "Three Rules for Abbreviating Multiplication",
  journal =      j-SCI-AMER,
  volume =       "41",
  number =       "12",
  pages =        "184--184",
  day =          "20",
  month =        sep,
  year =         "1879",
  CODEN =        "SCAMAC",
  DOI =          "https://doi.org/10.1038/scientificamerican09201879-184",
  ISSN =         "0036-8733 (print), 1946-7087 (electronic)",
  ISSN-L =       "0036-8733",
  bibdate =      "Fri May 17 10:36:54 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sciam1870.bib",
  URL =          "http://www.nature.com/scientificamerican/journal/v41/n12/pdf/scientificamerican09201879-184.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientific American",
  journal-URL =  "http://www.nature.com/scientificamerican",
}

@Article{Newcomb:1881:NFU,
  author =       "Simon Newcomb",
  title =        "Note on the frequency of use of the different digits
                 in natural numbers",
  journal =      j-AM-J-MATH,
  volume =       "4",
  number =       "1/4",
  pages =        "39--40",
  year =         "1881",
  CODEN =        "AJMAAN",
  ISSN =         "0002-9327 (print), 1080-6377 (electronic)",
  ISSN-L =       "0002-9327",
  bibdate =      "Thu Feb 15 16:35:24 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://links.jstor.org/sici?sici=0002-9327%281881%294%3A1%2F4%3C39%3ANOTFOU%3E2.0.CO%3B2-K",
  abstract =     "That the ten digits do not occur with equal frequency
                 must be evident to any one making much use of
                 logarithmic tables, and noticing how much faster the
                 first pages wear out than the last ones. The first
                 significant figure is oftener 1 than any other digit,
                 and the frequency diminishes up to 9.",
  acknowledgement = ack-nhfb,
  fjournal =     "American Journal of Mathematics",
  journal-URL =  "https://www.jstor.org/journal/amerjmath",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  remark =       "From p. 40: ``The law of probability of the occurrence
                 of numbers is such that all mantissas of their
                 logarithms are equally probable.''",
}

@Article{Holman:1888:DPM,
  author =       "Silas W. Holman",
  title =        "Discussion of the precision of measurement",
  journal =      "Technol. Q.",
  volume =       "1",
  number =       "??",
  pages =        "194--207",
  month =        "????",
  year =         "1888",
  bibdate =      "Mon May 21 17:12:03 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite[ref. 14]{Carter:2013:ESF}.",
}

@Book{Holman:1892:DPM,
  author =       "Silas W. Holman",
  title =        "Discussion of the Precision of Measurements: With
                 Examples Taken Mainly From Physics And Electrical
                 Engineering",
  publisher =    "Ferris Brothers Printers",
  address =      "New York, NY, USA",
  pages =        "????",
  year =         "1892",
  bibdate =      "Mon May 21 17:14:39 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite[ref. 15]{Carter:2013:ESF}.",
}

@Article{Anonymous:1893:IDb,
  author =       "Anonymous",
  title =        "The Instantaneous Divider",
  journal =      j-SCI-AMER,
  volume =       "68",
  number =       "21",
  pages =        "325--325",
  day =          "27",
  month =        may,
  year =         "1893",
  CODEN =        "SCAMAC",
  DOI =          "https://doi.org/10.1038/scientificamerican05271893-325a",
  ISSN =         "0036-8733 (print), 1946-7087 (electronic)",
  ISSN-L =       "0036-8733",
  bibdate =      "Wed May 22 19:04:00 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sciam1890.bib",
  URL =          "http://www.nature.com/scientificamerican/journal/v68/n21/pdf/scientificamerican05271893-325a.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientific American",
  journal-URL =  "http://www.nature.com/scientificamerican",
}

@Article{Felt:1893:MA,
  author =       "Dorr E. Felt",
  title =        "Mechanical Arithmetic",
  journal =      j-SCI-AMER,
  volume =       "69",
  number =       "20",
  pages =        "309--310",
  day =          "11",
  month =        nov,
  year =         "1893",
  CODEN =        "SCAMAC",
  DOI =          "https://doi.org/10.1038/scientificamerican11111893-309b",
  ISSN =         "0036-8733 (print), 1946-7087 (electronic)",
  ISSN-L =       "0036-8733",
  bibdate =      "Wed May 22 19:04:25 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sciam1890.bib",
  URL =          "http://www.nature.com/scientificamerican/journal/v69/n20/pdf/scientificamerican11111893-309b.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientific American",
  journal-URL =  "http://www.nature.com/scientificamerican",
}

@Article{Aley:1897:DES,
  author =       "Robert J. Aley",
  title =        "A Device for Extracting the Square Root of Certain
                 Surd Quantities",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "4",
  number =       "8/9",
  pages =        "204--208",
  month =        aug # "\slash " # sep,
  year =         "1897",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:37:08 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Article{Anonymous:1898:OFA,
  author =       "Anonymous",
  title =        "Our Fingers as an Aid in Multiplication",
  journal =      j-SCI-AMER,
  volume =       "79",
  number =       "17",
  pages =        "265--266",
  day =          "22",
  month =        oct,
  year =         "1898",
  CODEN =        "SCAMAC",
  DOI =          "https://doi.org/10.1038/scientificamerican10221898-265",
  ISSN =         "0036-8733 (print), 1946-7087 (electronic)",
  ISSN-L =       "0036-8733",
  bibdate =      "Wed May 22 19:08:57 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sciam1890.bib",
  URL =          "http://www.nature.com/scientificamerican/journal/v79/n17/pdf/scientificamerican10221898-265.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientific American",
  journal-URL =  "http://www.nature.com/scientificamerican",
}

@Article{Ludgate:1909:PAM,
  author =       "P. E. Ludgate",
  title =        "On a proposed analytical machine",
  journal =      j-SCI-PROC-ROY-DUBLIN-SOC,
  volume =       "12",
  number =       "9",
  pages =        "77--91",
  year =         "1909",
  CODEN =        "SPRDAP",
  ISSN =         "0371-2303",
  bibdate =      "Wed Oct 13 11:14:08 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 2.4]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientific proceedings of the Royal Dublin Society",
}

@Article{Babbage:1910:BBA,
  author =       "H. P. Babbage",
  title =        "{Babbage}: {Babbage}'s analytical engine",
  journal =      j-MONTHLY-NOT-ROY-ASTRON-SOC,
  volume =       "70",
  number =       "??",
  pages =        "517--526, 645",
  year =         "1910",
  CODEN =        "MNRAA4",
  ISSN =         "0035-8711 (print), 1365-2966 (electronic)",
  ISSN-L =       "0035-8711",
  bibdate =      "Wed Oct 13 11:12:08 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 2.3]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Monthly Notices of the Royal Astronomical Society",
  journal-URL =  "https://academic.oup.com/mnras",
}

@Article{TorresyQuevedo:1915:EAS,
  author =       "L. {Torres y Quevedo}",
  title =        "Essais sur l'automatique. Sa definition. {{\'E}}tendue
                 th{\'e}orique de ses applications ({French}) [{Essays}
                 on automation. {Its} definition. {Theoretical} extent
                 of its applications]",
  journal =      j-REV-GEN-SCI-PURES-APPL,
  volume =       "??",
  number =       "??",
  pages =        "601--611",
  day =          "15",
  month =        nov,
  year =         "1915",
  ISSN =         "0370-7431",
  bibdate =      "Wed Oct 13 11:15:08 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 2.5]{Randell:1982:ODC}.
                 Translated by Mr. R. Basu.",
  acknowledgement = ack-nhfb,
  fjournal =     "Revue G{\'e}n{\'e}rale des Sciences Pures et
                 Appliqu{\'e}es",
  language =     "French",
}

@Article{Barrow:1924:QDD,
  author =       "D. F. Barrow",
  title =        "Questions and Discussions: Discussions: On Taking
                 Square Roots of Integers",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "31",
  number =       "10",
  pages =        "482--484",
  month =        dec,
  year =         "1924",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:37:29 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Article{Smith:1924:FPA,
  author =       "David Eugene Smith",
  title =        "The First Printed Arithmetic ({Treviso}, 1478)",
  journal =      j-ISIS,
  volume =       "6",
  number =       "3",
  pages =        "311--331",
  month =        "????",
  year =         "1924",
  CODEN =        "ISISA4",
  ISSN =         "0021-1753 (print), 1545-6994 (electronic)",
  ISSN-L =       "0021-1753",
  bibdate =      "Tue Jul 30 21:57:26 MDT 2013",
  bibsource =    "http://www.jstor.org/action/showPublication?journalCode=isis;
                 http://www.jstor.org/stable/i211087;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/isis1920.bib",
  URL =          "http://www.jstor.org/stable/224315",
  acknowledgement = ack-nhfb,
  fjournal =     "Isis",
  journal-URL =  "http://www.jstor.org/journal/isis",
}

@Book{Karpinski:1925:HA,
  author =       "Louis Charles Karpinski",
  title =        "The History of Arithmetic",
  publisher =    "Rand McNally \& Company",
  address =      "New York, NY, USA",
  pages =        "xi + 200",
  year =         "1925",
  bibdate =      "Fri Nov 28 18:09:05 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}

@Article{Cajori:1926:BRB,
  author =       "Florian Cajori",
  title =        "Book Review: {{\booktitle{The History of Arithmetic}}
                 by Louis Charles Karpinski}",
  journal =      j-ISIS,
  volume =       "8",
  number =       "1",
  pages =        "231--232",
  month =        feb,
  year =         "1926",
  CODEN =        "ISISA4",
  ISSN =         "0021-1753 (print), 1545-6994 (electronic)",
  ISSN-L =       "0021-1753",
  bibdate =      "Tue Jul 30 21:57:36 MDT 2013",
  bibsource =    "http://www.jstor.org/action/showPublication?journalCode=isis;
                 http://www.jstor.org/stable/i211094;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/isis1920.bib",
  URL =          "http://www.jstor.org/stable/223706",
  acknowledgement = ack-nhfb,
  fjournal =     "Isis",
  journal-URL =  "http://www.jstor.org/journal/isis",
}

@Article{Smith:1926:FGC,
  author =       "David Eugene Smith",
  title =        "The First Great Commercial Arithmetic",
  journal =      j-ISIS,
  volume =       "8",
  number =       "1",
  pages =        "41--49",
  month =        feb,
  year =         "1926",
  CODEN =        "ISISA4",
  ISSN =         "0021-1753 (print), 1545-6994 (electronic)",
  ISSN-L =       "0021-1753",
  bibdate =      "Tue Jul 30 21:57:36 MDT 2013",
  bibsource =    "http://www.jstor.org/action/showPublication?journalCode=isis;
                 http://www.jstor.org/stable/i211094;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/isis1920.bib",
  URL =          "http://www.jstor.org/stable/223673",
  acknowledgement = ack-nhfb,
  fjournal =     "Isis",
  journal-URL =  "http://www.jstor.org/journal/isis",
}

@Article{Cajori:1927:EAP,
  author =       "Florian Cajori",
  title =        "The Earliest Arithmetic Published in {America}",
  journal =      j-ISIS,
  volume =       "9",
  number =       "3",
  pages =        "391--401",
  month =        dec,
  year =         "1927",
  CODEN =        "ISISA4",
  ISSN =         "0021-1753 (print), 1545-6994 (electronic)",
  ISSN-L =       "0021-1753",
  bibdate =      "Tue Jul 30 21:57:45 MDT 2013",
  bibsource =    "http://www.jstor.org/action/showPublication?journalCode=isis;
                 http://www.jstor.org/stable/i214411;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/isis1920.bib",
  URL =          "http://www.jstor.org/stable/330806",
  acknowledgement = ack-nhfb,
  fjournal =     "Isis",
  journal-URL =  "http://www.jstor.org/journal/isis",
}

@Article{J:1930:RPRb,
  author =       "R. A. J.",
  title =        "Recent Publications: Reviews: {{\em Standard Table of
                 Square Roots}}, by {L. M. Milne-Thomson}",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "37",
  number =       "6",
  pages =        "314--314",
  month =        jun # "\slash " # jul,
  year =         "1930",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:35:55 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Article{Laughlin:1930:LND,
  author =       "Harry H. Laughlin",
  title =        "Large-Number Division by Calculating Machine",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "37",
  number =       "6",
  pages =        "287--293",
  month =        jun # "\slash " # jul,
  year =         "1930",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:35:55 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Article{Garver:1932:QDNb,
  author =       "Raymond Garver",
  title =        "Questions, Discussions, and Notes: a Square Root
                 Method and Continued Fractions",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "39",
  number =       "9",
  pages =        "533--535",
  month =        nov,
  year =         "1932",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:36:47 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Article{Polachek:1932:MMU,
  author =       "H. Polachek",
  title =        "A method of multiplication used by {Saadia Gaon} in
                 the 10th century",
  journal =      j-SCRIPTA-MATH,
  volume =       "1",
  number =       "??",
  pages =        "245--246",
  month =        "????",
  year =         "1932",
  ISSN =         "0036-9713",
  bibdate =      "Thu Oct 26 11:15:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Scripta Math.",
  fjournal =     "Scripta Mathematica: A Quarterly Journal Devoted to
                 the Philosophy, History, and Expository Treatment of
                 Mathematics",
  jfm =          "59.0019.03",
  ZBmath =       "2542288",
}

@Article{Simons:1932:IGA,
  author =       "T. E. Simons",
  title =        "{Isaac Greenwood}'s arithmetic",
  journal =      j-SCRIPTA-MATH,
  volume =       "1",
  number =       "??",
  pages =        "262--264",
  month =        "????",
  year =         "1932",
  ISSN =         "0036-9713",
  bibdate =      "Thu Oct 26 11:15:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Scripta Math.",
  fjournal =     "Scripta Mathematica: A Quarterly Journal Devoted to
                 the Philosophy, History, and Expository Treatment of
                 Mathematics",
  jfm =          "59.0026.02",
  ZBmath =       "2542316",
}

@Book{Couffignal:1933:MCL,
  author =       "L. Couffignal",
  title =        "Les machines {\`a} calculer, leurs principes, leur
                 {\'e}volution. ({French}) [{Calculating} machines,
                 their principles, their evolution]",
  publisher =    "Gauthier-Villars",
  address =      "Paris, France",
  year =         "1933",
  bibdate =      "Wed Oct 13 11:19:11 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Extracts reprinted in \cite[\S 3.2]{Randell:1982:ODC}.
                 Translated by Mr. R. Basu.",
  acknowledgement = ack-nhfb,
  language =     "French",
}

@Article{Kalbfell:1934:QDN,
  author =       "D. C. Kalbfell",
  title =        "Questions, Discussions and Notes: On a Method for
                 Calculating Square Roots",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "41",
  number =       "8",
  pages =        "504--506",
  month =        oct,
  year =         "1934",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:37:31 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Article{Simons:1935:EEC,
  author =       "L. G. Simons",
  title =        "An early eighteenth century {American} readyreckoner",
  journal =      j-SCRIPTA-MATH,
  volume =       "3",
  number =       "??",
  pages =        "94--96",
  month =        "????",
  year =         "1935",
  ISSN =         "0036-9713",
  bibdate =      "Thu Oct 26 11:15:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Scripta Math.",
  fjournal =     "Scripta Mathematica: A Quarterly Journal Devoted to
                 the Philosophy, History, and Expository Treatment of
                 Mathematics",
  jfm =          "61.0020.03",
  ZBmath =       "2531128",
}

@Article{Calvert:1936:DDS,
  author =       "H. R. Calvert",
  title =        "Decimal Division of Scales before the Metric System",
  journal =      j-ISIS,
  volume =       "25",
  number =       "2",
  pages =        "433--436",
  month =        sep,
  year =         "1936",
  CODEN =        "ISISA4",
  ISSN =         "0021-1753 (print), 1545-6994 (electronic)",
  ISSN-L =       "0021-1753",
  bibdate =      "Tue Jul 30 21:21:25 MDT 2013",
  bibsource =    "http://www.jstor.org/action/showPublication?journalCode=isis;
                 http://www.jstor.org/stable/i211115;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/isis1930.bib",
  URL =          "http://www.jstor.org/stable/225380",
  acknowledgement = ack-nhfb,
  fjournal =     "Isis",
  journal-URL =  "http://www.jstor.org/journal/isis",
}

@Book{LeVita:1936:ALI,
  author =       "Maurice H. {Le Vita}",
  title =        "An Arithmetic of Life Insurance",
  publisher =    "Life Office Management Association",
  address =      "New York",
  pages =        "xii + 132",
  year =         "1936",
  LCCN =         "HG8781 .L43",
  bibdate =      "Sat Aug 12 14:42:20 MDT 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://hdl.handle.net/2027/mdp.39015017290688;
                 https://babel.hathitrust.org/cgi/pt?id=mdp.39015017290688",
  abstract =     "We have determined this item to be in the public
                 domain according to US copyright law through
                 information in the bibliographic record and/or US
                 copyright renewal records. The digital version is
                 available for all educational uses worldwide. Please
                 contact HathiTrust staff at hathitrust-help <at>
                 umich.edu with any questions about this item. Life
                 insurance--Mathematics. (LCCN)36034103.
                 (OCoLC)ocm03161649. HG8781 .L43. HG 8781 .L66.
                 Http://hdl.handle.net/2027/mdp.39015017290688.",
  acknowledgement = ack-nhfb,
  remark =       "While not about computer arithmetic, this book is
                 about practical applications of arithmetic in the life
                 insurance industry. It considers compound interest
                 calculations, present values of financial instruments,
                 mortality tables, insurance premiums, bond returns, and
                 so on. In Table 1, which shows the growth of an
                 investment at 3 percent over 10 years, the author
                 [amusingly] comments ``Mathematicians have already
                 worked out the multiplications and have incorporated
                 them into a table. With the use of this table, the
                 result can be obtained by a single multiplication.''.
                 Although the MARC record indicates the book is in the
                 public domain, the URL only permits download of a
                 single page at a time, although it is possible to page
                 through the book.",
  tableofcontents = "Preface / vii \\
                 Index to Tables / xi \\
                 Notes on the Solution of Problems / xii \\
                 \\
                 I. Interest and Discount / 1 \\
                 Interest \\
                 Discount \\
                 Examples \\
                 Observations \\
                 Problems \\
                 \\
                 II. The Mortality Table and Easy Problems in Rate
                 Calculation at Age 90 / 6 \\
                 Natural or Net One-Year Term Premium \\
                 Net One-Year Pure Endowment \\
                 Net Single Premium Whole Life \\
                 Fundamental Principle \\
                 Observations \\
                 Problems \\
                 \\
                 III. Single Premium Contracts --- Age 35 / 14 \\
                 Mortality Table \\
                 (Net) Single Premium 10-Year Term \\
                 (Net) Single Premium 10-Year Pure Endowment \\
                 (Net) Single Premium 10-Year Endowment \\
                 (Net) Single Premium Whole Life \\
                 (Net) Single Premium 10-Year Temporary Annuity \\
                 (Net) Single Premium Life Annuity \\
                 \\
                 IV. Development of Net Annual Premiums / 22 \\
                 Extension of Use of Discount \\
                 (Net) Annual Premium, Whole Life Policy \\
                 (Net) Annual Premium, 10-Payment Life \\
                 (Net) Annual Premium, 10-Year Term \\
                 (Net) Annual Premium, 10-Year Endowment \\
                 The ``Practical' and `More Exact' Premium \\
                 Alternative Method of Obtaining Net Annual Premiums \\
                 Problems \\
                 \\
                 V. More About Premiums / 30 \\
                 The Yearly Renewable Term Policy \\
                 Loading the Premium \\
                 Partial or Instalment Premiums \\
                 Problems \\
                 \\
                 VI. Net Level Premium Reserves / 34 \\
                 10-Year Term Policy \\
                 10-Year Endowment Policy \\
                 Whole Life Policy \\
                 10-Payment Life Policy \\
                 Yearly Renewable Term \\
                 Problems \\
                 \\
                 VII. Reserve Fund, Mortality Fund and Cost of Insurance
                 / 44 \\
                 Reserve Credit \\
                 Payment of Death Claims \\
                 The Reserve Fund and Mortality Fund \\
                 Cost of Insurance \\
                 Problems \\
                 \\
                 VIII. Full Preliminary Term Valuation \\
                 Gross Level Annual Premiums \\
                 Preliminary Term \\
                 Terminal Reserves Policy P \\
                 Full Preliminary Term Valuation \\
                 Modified Preliminary Term \\
                 Problems \\
                 \\
                 IX. Initial, Mean, and Calendar Year Reserves \\
                 \\
                 Initial Reserve \\
                 Mean Reserve \\
                 Calendar Year Reserve \\
                 Initial and Mean Reserves, F.P.T. Basis \\
                 Problems \\
                 \\
                 X. Non-Foreiture Options; Cash VALUE; Paid-Up and
                 Extended Insurance; Loan Value / 61 \\
                 The Cash Value \\
                 What Happens When Policy is Surrendered \\
                 Non-Forfeiture Options (Option 1, Option 2, and Option
                 3) \\
                 Cash Values under F.P.T. Basis of Valuation \\
                 Loan Values \\
                 Problems \\
                 \\
                 XI. Profits to a Life Insurance Company / 67 \\
                 Actual and Expected Mortality \\
                 Actual and Expected Expenses \\
                 Actual and Expected Interest \\
                 Gain and Loss for the Year \\
                 Arithmetical Statement of Financial Status \\
                 Problems \\
                 \\
                 XII. Distribution of Surplus --- Dividend Options / 73
                 \\
                 Allocating Surplus to Policyholders \\
                 Share of Gain from Mortality, Loading and Interest \\
                 Dividend Formula \\
                 Variations in Dividend Formula \\
                 Dividend Options (Options 1 to 6) \\
                 Withdrawing the Dividend or Surrendering the Dividend
                 Credit \\
                 Problems \\
                 \\
                 XIII. Further Problems in Interest and Discount / 79
                 \\
                 Fundamental Principle \\
                 Annuity Certain (Present Value of) \\
                 Annuity Certain (Amount of) \\
                 Interest Compounded Oftener than Once a Year \\
                 Value of a Bond \\
                 Problems \\
                 \\
                 XIV. Deferred Annuity --- Certain and Continuous
                 Annuity --- Optional Modes of Settlement / 91 \\
                 Deferred Life Annuity \\
                 ``Combination'' Annuity Contract \\
                 Optional Modes of Settlement \\
                 Problems \\
                 \\
                 XV. Mortality Rates and Mortality Tables / 94 \\
                 Rate of Mortality \\
                 Building the Table \\
                 Changing Number at Initial Age \\
                 Selection and Select Tables \\
                 Indicating the Age (for Mortality Analysis) \\
                 Select Table \\
                 Ultimate Tables and Select and Ultimate Tables \\
                 Problems \\
                 \\
                 XVI. More About Reserves / 103 \\
                 Fundamental Principle Amended \\
                 Corollary to Amended Principle \\
                 Prospective and Retrospective Method of Obtaining the
                 Reserve \\
                 Reserves on Single Premium Policies \\
                 Reserves on Substandard Policies \\
                 Percentage Mortality Rating Table \\
                 Problems. \\
                 \\
                 XVII. Modified Preliminary Term Valuation / 109 \\
                 M.P.T. Basis of Valuation \\
                 Method A: M.P.T. Whole Life Basis \\
                 Method B: M.P.T. 20-Payment Life Basis \\
                 Method C: M.P.T. Original Plan Basis \\
                 Illinois Standard System of Valuation \\
                 Ohio Standard System of Valuation \\
                 New Jersey Standard System of Valuation \\
                 Problems \\
                 \\
                 Appendices: \\
                 I. Miscellaneous Examples / 118 \\
                 II. Chart 3B --- Single Premium Life Insurance (Age 35)
                 / 121 \\
                 III. Chart 5B -- Single Premium Life Annuity (Age 35) /
                 122 \\
                 IV. Answers to Problems and Miscellaneous Examples 123
                 \\
                 Index / 127",
  usmarc540 =    "[US Library of Congress record]: We have determined
                 this item to be in the public domain according to US
                 copyright law through information in the bibliographic
                 record and/or US copyright renewal records. The digital
                 version is available for all educational uses
                 worldwide.",
}

@Article{Phillips:1936:BC,
  author =       "E. W. Phillips",
  title =        "Binary calculation",
  journal =      j-J-INST-ACTUARIES,
  volume =       "67",
  number =       "??",
  pages =        "187--221",
  year =         "1936",
  ISSN =         "0020-2681",
  bibdate =      "Wed Oct 13 11:33:16 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 7.1]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Institute of Actuaries",
}

@Misc{Zuse:1936:VSD,
  author =       "K. Zuse",
  title =        "{Verfahren zur selbstt{\"a}tigen Durchfuhrung von
                 Rechnungen mit Hilfe von Rechenmaschinen}. ({German})
                 [{Procedure} for automatic execution of calculations by
                 calculating machines]",
  howpublished = "German patent application Z23624.",
  day =          "11",
  month =        apr,
  year =         "1936",
  bibdate =      "Wed Oct 13 11:22:03 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 4.1]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Escott:1937:QDN,
  author =       "E. B. Escott",
  title =        "Questions, Discussions, and Notes: Rapid Method for
                 Extracting a Square Root",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "44",
  number =       "10",
  pages =        "644--646",
  month =        dec,
  year =         "1937",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:38:44 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Book{Millikan:1937:MMP,
  author =       "Robert A. Millikan and Duane E. Roller and Earnest C.
                 Watson",
  title =        "Mechanics, Molecular Physics, Heat, and Sound",
  publisher =    pub-MIT,
  address =      pub-MIT:adr,
  pages =        "????",
  year =         "1937",
  bibdate =      "Mon May 21 17:16:04 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See Appendix: Significant Figures and Notations by
                 Powers of Ten.",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite[ref. 22]{Carter:2013:ESF}.",
}

@MastersThesis{Shannon:1937:SAR,
  author =       "Claude Elwood Shannon",
  title =        "A Symbolic Analysis of Relay and Switching Circuits",
  type =         "{Master of Science}",
  school =       "Department of Electrical Engineering, MIT",
  address =      "Cambridge, MA, USA",
  pages =        "72",
  day =          "10",
  month =        aug,
  year =         "1937",
  bibdate =      "Thu Nov 18 10:35:20 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Not submitted until 1940",
  URL =          "http://dspace.mit.edu/bitstream/handle/1721.1/11173/34541425.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "April 30, 1916--February 24, 2001",
  remark =       "Smiley \cite[p. 91]{Smiley:2010:MWI} claims: ``He
                 [Shannon] also had the insight, like Atanasoff, that
                 the binary arithmetic that relay switches represented
                 would simplify information systems. His master's
                 thesis, written when he as twenty-one and published
                 when he was twenty-two, is considered to be one of the
                 most important, if not the most important, master's
                 thesis of the twentieth century.''\par

                 Pages 59--61 of the thesis are a section called
                 ``Electric Adder to the Base Two'', and pages 62--68,
                 ``A Factor Table Machine'', describe a machine that
                 will print a table of factors and primes of all the
                 integers from 1 to 100,000,000. Shannon notes on page
                 68: ``As to the practicality of such a device, it might
                 be said that J. P. Kulik spent 20 years in constructing
                 a table of primes up to 100,000,000 and when finished
                 it was found to contain so many errors that it was not
                 worth publishing. The machine described here could
                 probably be made to handle 5 numbers per second so that
                 the table would require only about 2 months to
                 construct.''",
}

@Article{Benford:1938:LAN,
  author =       "Frank Benford",
  title =        "The Law of Anomalous Numbers",
  journal =      j-PROC-AMER-PHIL-SOC,
  volume =       "78",
  number =       "4",
  pages =        "551--572",
  month =        mar,
  year =         "1938",
  CODEN =        "PAPCAA",
  ISSN =         "0003-049X (print), 2326-9243 (electronic)",
  ISSN-L =       "0003-049X",
  bibdate =      "Thu Feb 15 16:28:28 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://links.jstor.org/sici?sici=0003-049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2-G",
  abstract =     "It has been observed that the first pages of a table
                 of common logarithms show more wear than do the last
                 pages, indicating that more used numbers begin with the
                 digit 1 than with the digit 9. A compilation of some
                 20,000 first digits taken from widely divergent sources
                 shows that there is a logarithmic distribution of first
                 digits when the numbers are composed of four or more
                 digits. An analysis of the numbers from different
                 sources shows that the numbers taken from unrelated
                 subjects, such as a group of newspaper items, show a
                 much better agreement with a logarithmic distribution
                 than do numbers from mathematical tabulations or other
                 formal data. There is here the peculiar fact that
                 numbers that individually are without relationship are,
                 when considered in large groups, in good agreement with
                 a distribution law---hence the name ``Anomalous
                 Numbers.''\par

                 A further analysis of the data shows a strong tendency
                 for bodies of numerical data to fall into geometric
                 series. If the series is made up of numbers containing
                 three or more digits the first digits form a
                 logarithmic series. If the numbers contain only single
                 digits the geometric relation still holds but the
                 simple logarithmic relation no longer applies.\par

                 An equation is given showing the frequencies of first
                 digits in the different orders of numbers 1 to 10, 10
                 to 100, etc.\par

                 The equation also gives the frequency of digits in the
                 second, third + place of a multi-digit number, and it
                 is shown that the same law applies to
                 reciprocals.\par

                 There are many instances showing that the geometric
                 series, or the logarithmic law, has long been
                 recognized as a common phenomenon in factual literature
                 and in the ordinary affairs of life. The wire gauge and
                 drill gauge of the mechanic, the magnitude scale of the
                 astronomer and the sensory response curves of the
                 psychologist are all particular examples of a
                 relationship that seems to extend to all human affairs.
                 The Law of Anomalous Numbers is thus a general
                 probability law of widespread application.",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the {American Philosophical Society}
                 held at {Philadelphia} for promoting useful knowledge",
  journal-URL =  "http://www.jstor.org/journal/procamerphilsoci",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  remark =       "From \cite{Logan:1978:FDP}: ``Benford's paper was
                 published in 1938 in a journal of rather limited
                 circulation and not usually read by mathematicians. It
                 so happened that it was immediately followed in the
                 same issue by a physics paper which became of some
                 importance for secret nuclear work during World War II
                 [H. A. Bethe, M. E. Rose, and L. P. Smith, `The
                 Multiple Scattering of Electrons', Proc. Amer. Phil.
                 Soc. 78(4), 573--585 (1938)]. That is why Benford's
                 paper caught the attention of physicists in the early
                 1940's and was much discussed. This led to the notes in
                 Nature by Goudsmit and Furry [3] and Furry and Hurwitz
                 [4] containing an effort to explain Benford's law. We
                 considered it at that time merely a welcome diversion
                 and did not expect that over thirty papers would be
                 devoted to this subject in subsequent years.'' The 2006
                 bibliography \cite{Hurlimann:2006:BLB} cites 325
                 publications about Benford's Law.",
}

@PhdThesis{Couffignal:1938:AMA,
  author =       "L. Couffignal",
  title =        "Sur l'analyse m{\'e}canique. Application aux machines
                 {\`a} calculer et aux calculs de la m{\'e}canique
                 c{\'e}leste. ({French}) [{On} mechanical analysis.
                 Application to calculating machines and to calculation
                 in celestial mechanics]",
  publisher =    "Gauthier-Villars",
  school =       "Facult{\'e} des Sciences de Paris",
  address =      "Paris, France",
  year =         "1938",
  bibdate =      "Wed Oct 13 11:17:22 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Extracts reprinted in \cite[\S 2.7]{Randell:1982:ODC}.
                 Translated by Mr. R. Basu.",
  acknowledgement = ack-nhfb,
  language =     "French",
}

@Book{Hardy:1938:ITN,
  author =       "G. H. (Godfrey Harold) Hardy and E. M. (Edward
                 Maitland) Wright",
  title =        "An Introduction to the Theory of Numbers",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "xvi + 403",
  year =         "1938",
  LCCN =         "QA241 .H28",
  bibdate =      "Fri Nov 30 06:49:15 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Shannon:1938:SAR,
  author =       "Claude E. Shannon",
  title =        "A Symbolic Analysis of Relay and Switching Circuits",
  journal =      j-TRANS-AMER-INST-ELEC-ENG,
  volume =       "57",
  number =       "??",
  pages =        "713--723",
  month =        dec,
  year =         "1938",
  CODEN =        "TAEEA5",
  ISSN =         "0096-3860",
  bibdate =      "Sat Nov 20 08:54:12 2010",
  bibsource =    "http://www2.research.att.com/~njas/doc/shannonbio.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Transactions of the American Institute of Electrical
                 Engineers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714",
  remark =       "This is Shannon's first published paper (his Master's
                 thesis). In 1940, it received the Alfred Noble Prize of
                 the combined engineering societies of the United
                 States, an award given each year to a person not over
                 thirty for a paper published in one of the journals of
                 the participating societies. H. H. Goldstine
                 \cite{Goldstine:1972:CPN} called this work ``one of the
                 most important master's theses ever written \ldots{} a
                 landmark in that it helped to change digital circuit
                 design from an art to a science.''",
}

@Article{Jager:1939:AAD,
  author =       "Robert Jager and Boyd C. Patterson",
  title =        "The Artificial Arithmetick in Decimals of {Robert
                 Jager} ({London}, 1651)",
  journal =      j-ISIS,
  volume =       "31",
  number =       "1",
  pages =        "25--31",
  month =        nov,
  year =         "1939",
  CODEN =        "ISISA4",
  ISSN =         "0021-1753 (print), 1545-6994 (electronic)",
  ISSN-L =       "0021-1753",
  bibdate =      "Tue Jul 30 21:26:49 MDT 2013",
  bibsource =    "http://www.jstor.org/action/showPublication?journalCode=isis;
                 http://www.jstor.org/stable/i302217;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/isis1930.bib",
  URL =          "http://www.jstor.org/stable/226014",
  acknowledgement = ack-nhfb,
  fjournal =     "Isis",
  journal-URL =  "http://www.jstor.org/journal/isis",
}

@Article{K:1939:BRBd,
  author =       "M. G. K.",
  title =        "Book Review: {{\booktitle{Duodecimal Arithmetic}}, by
                 George S. Terry}",
  journal =      j-J-R-STAT-SOC,
  volume =       "102",
  number =       "2",
  pages =        "299--300",
  month =        "????",
  year =         "1939",
  DOI =          "https://doi.org/10.2307/2980013",
  ISSN =         "0952-8385",
  bibdate =      "Sat Jan 24 11:18:08 MST 2015",
  bibsource =    "http://www.jstor.org/stable/i349540;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jrss-a-1930.bib",
  URL =          "http://www.jstor.org/stable/2980013",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Royal Statistical Society",
  journal-URL =  "http://www.jstor.org/journals/09528385.html",
}

@TechReport{Atanasoff:1940:CMS,
  author =       "J. V. Atanasoff",
  title =        "Computing machine for the solution of large systems of
                 linear algebraic equations",
  type =         "Unpublished memorandum",
  institution =  "Iowa State College",
  address =      "Ames, IA, USA",
  month =        aug,
  year =         "1940",
  bibdate =      "Wed Oct 13 11:36:11 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 7.2]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
}

@Misc{Bush:1940:AM,
  author =       "V. Bush",
  title =        "Arithmetical Machine",
  howpublished = "Vannevar Bush Papers, Container 18, Folder: Caldwell,
                 Samuel, 1939--1940",
  year =         "1940",
  bibdate =      "Wed Oct 13 11:37:32 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 7.3]{Randell:1982:ODC}.
                 Copyright interest in the unpublished writings of
                 Vannevar Bush has been dedicated to the public.",
  acknowledgement = ack-nhfb,
}

@TechReport{Stibitz:1940:C,
  author =       "G. R. Stibitz",
  title =        "Computer",
  type =         "Unpublished memorandum",
  institution =  "Bell Telephone Laboratories",
  address =      "New York, NY, USA",
  year =         "1940",
  bibdate =      "Wed Oct 13 11:30:38 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 6.1]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
}

@MastersThesis{Berry:1941:DED,
  author =       "Clifford Edward Berry",
  title =        "Design of electrical data recording and reading
                 mechanism",
  type =         "{M.S.} thesis",
  school =       "Iowa State College",
  address =      "Ames, IA, USA",
  pages =        "32",
  year =         "1941",
  bibdate =      "Thu Nov 18 11:18:18 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1918--1963",
  historical-note = "From
                 http://www.lib.iastate.edu/arch/rgrp/5-2-1-1.html:

                 ``John Vincent Atanasoff received his M.S. (1926) in
                 Mathematics from Iowa State College (University) and
                 received his Ph.D. (1930) in Theoretical Physics from
                 the University of Wisconsin-Madison. He returned to
                 Iowa State in 1930 as Assistant Professor in
                 mathematics and physics and was promoted to Associate
                 Professor (1936). Atanasoff began developing concepts
                 for an electronic computing machine in 1937. It was
                 shortly thereafter that he, along with graduate student
                 Clifford Berry, started work on the world's first
                 electronic digital computer. The computer would later
                 be named the Atanasoff-Berry Computer (ABC).

                 Work on the machine stopped at the start of World War
                 II in 1941 and the ABC was never patented. Atanasoff
                 and Berry were both called to support the war effort
                 and left Iowa State. By the end of the decade, the ABC
                 was removed from the basement of Physics Hall and
                 dismantled.

                 Atanasoff and the ABC were part of a major court case
                 between Honeywell, Inc. and Sperry Rand Corporation
                 which occurred 1967-1973. The case involved the ENIAC
                 patent which covered basic ownership rights to the
                 design of electronic digital computers. During the
                 trial, the judge concluded that the invention of the
                 ENIAC was derived from the work of John Vincent
                 Atanasoff at Iowa State University.

                 A replica of the Atanasoff-Berry Computer was completed
                 and unveiled to the public in 1996. The ABC replica was
                 constructed by a team of Iowa State scientists at the
                 Ames Laboratory and was exhibited at museums throughout
                 the country over the next several years.''",
  remark =       "This thesis may be one of the earliest surviving
                 records of the ABC computer built by John Atanasoff and
                 Clifford Berry in the late 1930s. The one-of-a-kind ABC
                 was destroyed in 1948, and most of its parts were lost.
                 Also cited in ``Charles W. Bradley Collection on the
                 ENIAC Trial, 1930--1966'', (found in
                 http://discover.lib.umn.edu/): CWB as an attorney for
                 the group retained by Honeywell in the Honeywell v.
                 Sperry Rand ENIAC trial. The ABC had a 50-bit word.",
}

@Article{Lancaster:1942:MME,
  author =       "Otis E. Lancaster",
  title =        "Machine Method for the Extraction of Cube Root",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "37",
  number =       "217",
  pages =        "112--115",
  month =        mar,
  year =         "1942",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Wed Jan 25 08:05:24 MST 2012",
  bibsource =    "http://www.jstor.org/journals/01621459.html;
                 http://www.jstor.org/stable/i314096;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc1940.bib",
  URL =          "http://www.jstor.org/stable/2279437",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@TechReport{Mauchly:1942:UHS,
  author =       "J. W. Mauchly",
  title =        "The use of high speed vacuum tube devices for
                 calculating",
  type =         "Privately circulated memorandum",
  institution =  "Moore School of Electrical Engineering, University of
                 Pennsylvania",
  address =      "Philadelphia, PA, USA",
  month =        aug,
  year =         "1942",
  bibdate =      "Wed Oct 13 11:52:54 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 7.6]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
}

@TechReport{Rajchman:1942:REP,
  author =       "J. A. Rajchman and G. A. Morton and A. W. Vance",
  title =        "Report on Electronic Predictors for Anti-Aircraft Fire
                 Control",
  institution =  "Research Laboratories, R.C.A. Manufacturing Company,
                 Inc.",
  address =      "Camden, NJ, USA",
  month =        apr,
  year =         "1942",
  bibdate =      "Sat Feb 8 10:28:55 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 7.4]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
}

@Article{Crawford:1943:DNS,
  author =       "W. S. H. Crawford",
  title =        "Discussions and Notes: Square Roots from a Table of
                 Cosines",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "50",
  number =       "3",
  pages =        "190--191",
  month =        mar,
  year =         "1943",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:36:57 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Article{Hotelling:1943:FPM,
  author =       "Harold Hotelling",
  title =        "Further Points on Matrix Calculation and Simultaneous
                 Equations",
  journal =      j-ANN-MATH-STAT,
  volume =       "14",
  number =       "4",
  pages =        "440--441",
  month =        dec,
  year =         "1943",
  CODEN =        "AASTAD",
  DOI =          "https://doi.org/10.1214/aoms/1177731364",
  ISSN =         "0003-4851 (print), 2168-8990 (electronic)",
  ISSN-L =       "0003-4851",
  MRclass =      "65.0X",
  MRnumber =     "0010061 (5,245g)",
  MRreviewer =   "W. Feller",
  bibdate =      "Sat May 31 09:10:30 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/annmathstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Hotelling:1943:SNM}",
  URL =          "http://projecteuclid.org/euclid.aoms/1177731364",
  acknowledgement = ack-nhfb,
  author-dates = "29 September 1895--26 December 1973",
  fjournal =     "Annals of Mathematical Statistics",
  journal-URL =  "http://projecteuclid.org/all/euclid.aoms/",
}

@Article{Hotelling:1943:SNM,
  author =       "Harold Hotelling",
  title =        "Some New Methods in Matrix Calculation",
  journal =      j-ANN-MATH-STAT,
  volume =       "14",
  number =       "1",
  pages =        "1--34",
  month =        mar,
  year =         "1943",
  CODEN =        "AASTAD",
  DOI =          "https://doi.org/10.1214/aoms/1177731489",
  ISSN =         "0003-4851 (print), 2168-8990 (electronic)",
  ISSN-L =       "0003-4851",
  MRclass =      "65.0X",
  MRnumber =     "0007851 (4,202g)",
  MRreviewer =   "W. Feller",
  bibdate =      "Sat May 31 09:10:29 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/annmathstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See comments \cite{Hotelling:1943:FPM} and note note
                 \cite{Waugh:1945:NCH}.",
  URL =          "http://projecteuclid.org/euclid.aoms/1177731489",
  acknowledgement = ack-nhfb,
  author-dates = "29 September 1895--26 December 1973",
  fjournal =     "Annals of Mathematical Statistics",
  journal-URL =  "http://projecteuclid.org/all/euclid.aoms/",
  remark =       "Higham \cite{Higham:2020:NLM} refers to this paper as
                 the source of an early pessimistic bound of $ O(2^(2
                 n)) $ ulps for the error in solution of $ n \times n $
                 linear equations. That would mean that with 16D
                 floating-point values (roughly the precision of the
                 IEEE 754 binary64 format), no significant digits would
                 remain in the answer for $ n > 26 $.",
}

@TechReport{Rademacher:1943:MTI,
  author =       "Hans Rademacher",
  title =        "Mathematical Topics of Interest in {PX}, Part Two:
                 Summary of Articles Dealing with Rounding off Errors",
  type =         "{PX} Report",
  number =       "14",
  institution =  "Moore School of Electrical Engineering, Office of the
                 Director Records, University of Pennsylvania",
  address =      "Philadelphia, PA, USA",
  day =          "30",
  month =        nov,
  year =         "1943",
  bibdate =      "Fri Jun 15 17:39:28 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited on page 34 of Haigh, Priestley, and Rope,
                 \booktitle{ENIAC in Action} (2016) (ISBN 0-262-03398-4)
                 as an annotated bibliography of rounding errors.",
}

@Article{Goudsmit:1944:SFN,
  author =       "S. A. Goudsmit and W. H. Furry",
  title =        "Significant Figures of Numbers in Statistical Tables",
  journal =      j-NATURE,
  volume =       "154",
  number =       "3921",
  pages =        "800--801",
  day =          "23",
  month =        dec,
  year =         "1944",
  CODEN =        "NATUAS",
  DOI =          "https://doi.org/10.1038/154800a0",
  ISSN =         "0028-0836 (print), 1476-4687 (electronic)",
  ISSN-L =       "0028-0836",
  bibdate =      "Sun Sep 18 11:57:19 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.nature.com/nature/journal/v154/n3921/pdf/154800a0.pdf",
  abstract =     "A rough qualitative explanation of this fact can
                 easily be given. If we consider tables in which the
                 entries become rarer the larger they are, we can draw
                 the obvious conclusion that in any interval, say,
                 between 10 and 99, or 10,000 and 99,999, there are more
                 entries on the small side than on the large side.",
  acknowledgement = ack-nhfb,
  fjournal =     "Nature",
  journal-URL =  "http://www.nature.com/nature/archive/",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Furry:1945:DND,
  author =       "W. H. Furry and Henry Hurwitz",
  title =        "Distribution of Numbers and Distribution of
                 Significant Figures",
  journal =      j-NATURE,
  volume =       "155",
  number =       "3924",
  pages =        "52--53",
  day =          "13",
  month =        jan,
  year =         "1945",
  CODEN =        "NATUAS",
  DOI =          "https://doi.org/10.1038/155052a0",
  ISSN =         "0028-0836 (print), 1476-4687 (electronic)",
  ISSN-L =       "0028-0836",
  bibdate =      "Sun Sep 18 11:51:37 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.nature.com/nature/journal/v155/n3924/pdf/155052a0.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Nature",
  journal-URL =  "http://www.nature.com/nature/archive/",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@TechReport{vonNeumann:1945:FDR,
  author =       "John von Neumann",
  title =        "First Draft of a Report on the {EDVAC}",
  institution =  "University of Pennsylvania",
  day =          "30",
  month =        jun,
  year =         "1945",
  bibdate =      "Mon Jun 06 19:17:03 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Ai/alife.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  remark =       "This is the report that got von Neumann's name
                 associated with the serial, stored-program, general
                 purpose, digital architecture upon which 99.99\% of all
                 computers today are based.",
  xxnote =       "Report prepared for U.S. Army Ordinance Department
                 under Contract W-670-ORD-4926. Reprinted in
                 \cite[pp.~177--246]{Stern:1981:EUA},
                 \cite[pp.~399--413]{Randell:1982:ODC},
                 \cite{vonNeumann:1993:FDR}, and
                 \cite{Laplante:1996:GPC}.",
}

@Article{Waugh:1945:NCH,
  author =       "F. V. Waugh",
  title =        "A Note Concerning {Hotelling}'s Method of Inverting a
                 Partitioned Matrix",
  journal =      j-ANN-MATH-STAT,
  volume =       "16",
  number =       "2",
  pages =        "216--217",
  month =        jun,
  year =         "1945",
  CODEN =        "AASTAD",
  DOI =          "https://doi.org/10.1214/aoms/1177731124",
  ISSN =         "0003-4851 (print), 2168-8990 (electronic)",
  ISSN-L =       "0003-4851",
  MRclass =      "65.0X",
  MRnumber =     "0012916 (7,84d)",
  MRreviewer =   "W. Feller",
  bibdate =      "Sat May 31 09:10:32 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/annmathstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Hotelling:1943:SNM}.",
  URL =          "http://projecteuclid.org/euclid.aoms/1177731124",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Mathematical Statistics",
  journal-URL =  "http://projecteuclid.org/all/euclid.aoms/",
}

@Article{Aiken:1946:ASC,
  author =       "H. H. Aiken and G. M. Hopper",
  title =        "The {Automatic Sequence Controlled Calculator}",
  journal =      j-ELECTR-ENG,
  volume =       "65",
  number =       "??",
  pages =        "384--391, 449--454, 522--528",
  year =         "1946",
  CODEN =        "ELENAC",
  ISSN =         "0095-9197",
  bibdate =      "Wed Oct 13 11:26:29 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 5.2]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Electrical Engineering (American Institute of
                 Electrical Engineers)",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6413714",
}

@TechReport{Burks:1946:PDL,
  author =       "Arthur W. Burks and Herman H. Goldstine and John von
                 Neumann",
  title =        "Preliminary discussion of the logical design of an
                 electronic computing instrument",
  institution =  inst-INST-ADV-STUDY,
  address =      inst-INST-ADV-STUDY:adr,
  pages =        "42",
  day =          "28",
  month =        jun,
  year =         "1946",
  MRnumber =     "MR22442",
  bibdate =      "Wed Oct 13 08:17:48 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.bib;
                 https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib;
                 https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Theory/arith.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Report to the U.S. Army Ordnance Department under
                 contract W-36-034-OKD-7481. Reprinted in \cite[Paper
                 2]{Taub:1963:JNCa}, \cite{Bell:1971:CSR}, \cite[pp.
                 221--259]{Swartzlander:1976:CDD} and \cite[pp.
                 97--146]{Aspray:1987:PJN}",
  URL =          "https://deepblue.lib.umich.edu/handle/2027.42/3972;
                 https://grch.com.ar/docs/p1/Apuntes/eng/Logical%20Design%20of%20an%20Electronic%20Computing%20Instrument.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "John von Neumann (28 December 1903--8 February 1957)",
  remark =       "Discusses floating-point versus fixed-point
                 computation, and concludes that floating-point is
                 probably not justifiable. They wrote:\par

                 ``There appear to be two major purposes in a `floating'
                 decimal point system both of which arise from the fact
                 that the number of digits in a word is a constant fixed
                 by design considerations for each particular machine.
                 The first of these purposes is to retain in a sum or
                 product as many significant digits as possible and the
                 second of these is to free the human operator from the
                 burden of estimating and inserting into a problem
                 `scale factors' --- multiplicative constants which
                 serve to keep numbers within the limits of the
                 machine.\par

                 There is, of course, no denying the fact that human
                 time is consumed in arranging for the introduction of
                 suitable scale factors. We only argue that the time so
                 consumed is a very small percentage of the total time
                 we will spend in preparing an interesting problem for
                 our machine. The first advantage of the floating point
                 is, we feel, somewhat illusory. In order to have such a
                 floating point, one must waste memory capacity which
                 could otherwise be used for carrying more digits per
                 word. It would therefore seem to us not at all clear
                 whether the modest advantages of a floating binary
                 point offset the loss of memory capacity and the
                 increased complexity of the arithmetic and control
                 circuits.''",
}

@Article{Cesareo:1946:RI,
  author =       "O. Cesareo",
  title =        "The Relay Interpolator",
  journal =      j-BELL-LABS-RECORD,
  volume =       "23",
  number =       "??",
  pages =        "457--460",
  year =         "1946",
  CODEN =        "BLRCAB",
  ISSN =         "0005-8564",
  bibdate =      "Wed Oct 13 11:31:47 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 6.2]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Bell Laboratories Record",
}

@Article{Comrie:1946:BDC,
  author =       "L. J. Comrie",
  title =        "{Babbage}'s Dream Come True",
  journal =      j-NATURE,
  volume =       "158",
  number =       "4017",
  pages =        "567--568",
  day =          "26",
  month =        oct,
  year =         "1946",
  CODEN =        "NATUAS",
  DOI =          "https://doi.org/10.1038/158567a0",
  ISSN =         "0028-0836 (print), 1476-4687 (electronic)",
  ISSN-L =       "0028-0836",
  bibdate =      "Wed Aug 9 07:30:09 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The black mark earned by the government of the day
                 more than a hundred years ago for its failure to see
                 Charles Babbage's difference engine brought to a
                 successful conclusion has still to be wiped out. It is
                 not too much to say that it cost Britain the leading
                 place in the art of mechanical computing. Babbage then
                 conceived and worked on his `analytical engine',
                 designed to store numbers and operate on them according
                 to a sequence of processes conveyed to the machine by
                 cards similar to those used in the Jacquard loom. This,
                 however, was never completed.",
  acknowledgement = ack-nhfb,
  fjournal =     "Nature",
  journal-URL =  "http://www.nature.com/nature/archive/",
  remark =       "The title in the Nature archive index is completely
                 wrong: it says ``A Manual of Operation for the
                 Automatic Sequence Controlled Calculator''. After the
                 critical introduction [see the abstract], the article
                 goes on to describe IBM's gift to Harvard of the
                 Automatic Sequence Controlled Calculator. It reports
                 about the ASCC: ``The machine contains seventy-two
                 storage counters, capable of holding twenty-three
                 digits and a sign. \ldots{} When working to the full
                 23-figure capacity of the machine, multiplication takes
                 about six seconds, and division twice as long;
                 additions and subtractions are done at the rate of
                 three a second, whatever their length.'' It then
                 describes the computation of logarithms via the Taylor
                 series expansion of $ \log (1 + x) $, and reports that
                 it can do exponential, trigonometric, and hyperbolic
                 functions as well.",
}

@TechReport{Dreyer:1946:REM,
  author =       "H.-J. Dreyer and A. Walther",
  title =        "{Der Rechenautomat Ipm. Entwicklung Mathematischer
                 Instrumente in Deutschland 1939 bis 1945}. ({German})
                 [{The} {Ipm} Calculator. {The} development of
                 mathematical instruments in {Germany} 1939--1945]",
  type =         "{Bericht}",
  number =       "A3",
  institution =  "Institut f{\"u}r Praktische Mathematik, Technische
                 Hochschule",
  address =      "Darmstadt, West Germany",
  day =          "19",
  month =        aug,
  year =         "1946",
  bibdate =      "Wed Oct 13 11:20:15 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 3.3]{Randell:1982:ODC}.
                 Translated by Mr. and Mrs. P. Jones",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Goldstine:1946:ENI,
  author =       "H. H. Goldstine and Adele Goldstine",
  title =        "The {Electronic Numerical Integrator and Computer
                 (ENIAC)}",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "2",
  number =       "15",
  pages =        "97--110",
  month =        jul,
  year =         "1946",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837",
  bibdate =      "Tue Oct 13 08:44:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  note =         "Reprinted in \cite[\S 7.7]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Tables Other Aids Comput.",
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Book{HUCL:1946:MOA,
  author =       "{Harvard University.Computation Laboratory}",
  title =        "A Manual of Operation for the {Automatic Sequence
                 Controlled Calculator}",
  publisher =    pub-HARVARD,
  address =      pub-HARVARD:adr,
  pages =        "561",
  year =         "1946",
  LCCN =         "QA3 .H3 v.1",
  bibdate =      "Mon Nov 4 07:46:57 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Its Annals v. 1",
  acknowledgement = ack-nhfb,
  keywords =     "electronic digital computers; mathematics ---
                 bibliography",
}

@TechReport{Turing:1946:PEC,
  author =       "A. M. Turing",
  title =        "Proposed Electronic Calculator",
  type =         "Report",
  number =       "E882",
  institution =  inst-NPL,
  address =      inst-NPL:adr,
  pages =        "48",
  year =         "1946",
  bibdate =      "Fri Nov 25 16:22:27 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.emula3.com/docs/Turing_Report_on_ACE.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Alan Mathison Turing (23 June 1912--7 June 1954)",
  xxnote =       "Reprinted in \cite{Turing:1972:MTO}.",
}

@TechReport{Goldstine:1947:PCPa,
  author =       "Herman H. Goldstine and John von Neumann",
  title =        "Planning and coding of problems for an electronic
                 computing instrument. {Part 1}, Vol. 1",
  type =         "Technical report",
  institution =  inst-INST-ADV-STUDY,
  address =      inst-INST-ADV-STUDY:adr,
  pages =        "??",
  month =        "????",
  year =         "1947",
  bibdate =      "Fri Nov 16 16:35:14 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Goldstine:1947:PCPb,
  author =       "Herman H. Goldstine and John von Neumann",
  title =        "Planning and coding of problems for an electronic
                 computing instrument. {Part 2}, Vol. 1",
  type =         "Technical report",
  number =       "1",
  institution =  inst-INST-ADV-STUDY,
  address =      inst-INST-ADV-STUDY:adr,
  pages =        "69",
  day =          "1",
  month =        apr,
  year =         "1947",
  MRnumber =     "MR22443",
  bibdate =      "Wed Jun 01 17:41:33 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Report prepared for U.S. Army Ordnance Department
                 under contract W-36-034-OKD-7481. Reprinted in
                 \cite[80--151]{Taub:1963:JNCa}. Knuth \cite[p.
                 278]{Knuth:1998:SA} cites pp. 142--151 of this report
                 as the first published treatment of double-precision
                 arithmetic on digital computers.",
  acknowledgement = ack-nhfb,
}

@TechReport{Goldstine:1947:PCPc,
  author =       "Herman H. Goldstine and John von Neumann",
  title =        "Planning and coding of problems for an electronic
                 computing instrument. {Part 1}, Vol. 2",
  type =         "Technical report",
  institution =  inst-INST-ADV-STUDY,
  address =      inst-INST-ADV-STUDY:adr,
  pages =        "??",
  month =        "????",
  year =         "1947",
  bibdate =      "Fri Nov 16 16:35:14 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Goldstine:1947:PCPd,
  author =       "Herman H. Goldstine and John von Neumann",
  title =        "Planning and coding of problems for an electronic
                 computing instrument. {Part 2}, Vol. 2",
  type =         "Technical report",
  institution =  inst-INST-ADV-STUDY,
  address =      inst-INST-ADV-STUDY:adr,
  pages =        "??",
  month =        "????",
  year =         "1947",
  bibdate =      "Fri Nov 16 16:35:14 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Goldstine:1947:PCPe,
  author =       "Herman H. Goldstine and John von Neumann",
  title =        "Planning and coding of problems for an electronic
                 computing instrument. {Part 1}, Vol. 3",
  type =         "Technical report",
  institution =  inst-INST-ADV-STUDY,
  address =      inst-INST-ADV-STUDY:adr,
  pages =        "??",
  month =        "????",
  year =         "1947",
  bibdate =      "Fri Nov 16 16:35:14 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Goldstine:1947:PCPf,
  author =       "Herman H. Goldstine and John von Neumann",
  title =        "Planning and coding of problems for an electronic
                 computing instrument. {Part 2}, Vol. 3",
  type =         "Technical report",
  institution =  inst-INST-ADV-STUDY,
  address =      inst-INST-ADV-STUDY:adr,
  pages =        "??",
  month =        "????",
  year =         "1947",
  bibdate =      "Fri Nov 16 16:35:14 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Juley:1947:BC,
  author =       "J. Juley",
  title =        "The Ballistic Computer",
  journal =      j-BELL-LABS-RECORD,
  volume =       "24",
  number =       "??",
  pages =        "5--9",
  year =         "1947",
  CODEN =        "BLRCAB",
  ISSN =         "0005-8564",
  bibdate =      "Wed Oct 13 11:32:38 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 6.3]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Bell Laboratories Record",
}

@InProceedings{Mauchly:1947:PPE,
  author =       "J. W. Mauchly",
  booktitle =    "{Proceedings of a Symposium on Large Scale Digital
                 Calculating Machinery, 7--10 January 1947}",
  title =        "Preparation of problems for {EDVAC}-type machines",
  publisher =    "Harvard University Press",
  address =      "Cambridge, MA, USA",
  year =         "1947",
  bibdate =      "Wed Oct 13 11:55:58 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in {\em Annals of the Computation Laboratory
                 of Harvard University}, {\bf 16}, 203--207 (1948).
                 Reprinted in \cite[\S 8.2]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
}

@Article{Richeson:1947:FAP,
  author =       "A. W. Richeson",
  title =        "The First Arithmetic Printed in {English}",
  journal =      j-ISIS,
  volume =       "37",
  number =       "1--2",
  pages =        "47--56",
  month =        may,
  year =         "1947",
  CODEN =        "ISISA4",
  ISSN =         "0021-1753 (print), 1545-6994 (electronic)",
  ISSN-L =       "0021-1753",
  bibdate =      "Tue Jul 30 21:27:09 MDT 2013",
  bibsource =    "http://www.jstor.org/action/showPublication?journalCode=isis;
                 http://www.jstor.org/stable/i302230;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/isis1940.bib",
  URL =          "http://www.jstor.org/stable/226161",
  acknowledgement = ack-nhfb,
  fjournal =     "Isis",
  journal-URL =  "http://www.jstor.org/journal/isis",
  remark =       "From the second paragraph: ``The earliest printed work
                 in English to discuss arithmetic, \booktitle{The
                 Myrrour of the World}, came from the press of William
                 Caxton in 1481. This work, however, contained only one
                 page devoted entirely to arithmetic. It is not until
                 1537 that we find another book printed in English
                 devoted entirely to arithmetic and dealing with the
                 Hindu--Arabic system of numbers. This is an anonymous
                 publication, from a press located at St. Albans, with
                 the title \booktitle{An Introduction for to Lerne to
                 Recken with the Pen, or with the Counters},'' This book
                 went through eight editions between 1537 and 1629. The
                 article quotes book sections on integer division.",
}

@Article{vonNeumann:1947:NIM,
  author =       "John von Neumann and Herman H. Goldstine",
  title =        "Numerical Inverting of Matrices of High Order",
  journal =      j-BULL-AMS,
  volume =       "53",
  number =       "11",
  pages =        "1021--1099",
  month =        nov,
  year =         "1947",
  CODEN =        "BAMOAD",
  ISSN =         "0002-9904 (print), 1936-881X (electronic)",
  ISSN-L =       "0002-9904",
  MRclass =      "65.0X",
  MRnumber =     "MR0024235 (9,471b)",
  MRreviewer =   "E. Bodewig",
  bibdate =      "Thu Nov 8 14:49:36 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/auto.diff.bib;
                 https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/computer.arithmetic.1.bib;
                 https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/Matrix.bib;
                 https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/sparse.linear.systems.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Goldstine:1951:NIM} for Part II. Reprinted
                 in \cite[vol. 5, pp. 479--557]{Taub:1961:JNCa}.",
  URL =          "http://projecteuclid.org/euclid.bams/1183511222",
  ZMnumber =     "0031.31402",
  acknowledgement = ack-nhfb # " and " # ack-jg,
  author-dates = "John von Neumann (28 December 1903--8 February 1957)",
  fjournal =     "Bulletin of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/bull/all_issues.html",
  kwds =         "nla, linear system, rounding error",
  referred =     "[Markov1999a].",
  remark =       "This may be the first journal publication about the
                 use of double-precision arithmetic on computers, used
                 for the accumulation of inner products and matrix
                 products. On pp. 1035--1038, the authors show that when
                 the sum of $m$ products of two $s$-digit numbers is
                 accumulated in precision $ 2 s $, with rounding to $s$
                 digits only after the final sum is complete, then the
                 rounding error is essentially one unit in the last
                 place, instead of $m$ times that value. Cited in
                 \cite{Sterbenz:1974:FPC}.",
}

@Article{Alt:1948:BTLa,
  author =       "Franz L. Alt",
  title =        "A {Bell Telephone Laboratories}' Computing
                 Machine---{I}",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "3",
  number =       "21",
  pages =        "1--13",
  month =        jan,
  year =         "1948",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837",
  bibdate =      "Tue Oct 13 08:44:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  note =         "Reprinted in \cite[\S 6.4]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Tables Other Aids Comput.",
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Eckert:1948:EC,
  author =       "W. J. Eckert",
  title =        "Electrons and computation",
  journal =      j-SCI-MONTHLY,
  volume =       "67",
  number =       "5",
  pages =        "315--323",
  month =        nov,
  year =         "1948",
  CODEN =        "SCMOAA",
  ISSN =         "0096-3771 (print), 2327-7513 (electronic)",
  bibdate =      "Wed Oct 13 11:27:40 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 5.3]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "The Scientific Monthly",
  journal-URL =  "http://www.jstor.org/journal/sciemont",
}

@InProceedings{Rademacher:1948:AEP,
  author =       "Hans A. Rademacher",
  title =        "On the Accumulation of Errors in Processes of
                 Integration on High-Speed Calculating Machines",
  crossref =     "Anonymous:1948:PSL",
  pages =        "176--187",
  year =         "1948",
  bibdate =      "Mon Jun 18 11:03:56 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "From page 186, remark by John W. Mauchly: ``I just
                 wanted to remark that this paper is probably one of the
                 first to appear as a result of the interaction between
                 computing machines and mathematics. I think many of us
                 have been looking forward with certainty to the day
                 when the advent of computing machines would influence
                 the course of mathematics, and there are still many
                 directions in which we can look forward to further such
                 impacts. This reaction is not, of course, one way.
                 Mathematics should also influence the computing
                 machine.''",
}

@TechReport{Tukey:1948:NSR,
  author =       "John W. Tukey",
  title =        "A note on the square-root iteration",
  type =         "SRG Memorandum report",
  number =       "10",
  institution =  inst-PRINCETON,
  address =      inst-PRINCETON:adr,
  pages =        "18",
  year =         "1948",
  bibdate =      "Tue May 15 08:00:09 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Turing:1948:REM,
  author =       "A. M. Turing",
  title =        "Rounding-Off Errors in Matrix Processes",
  journal =      j-QUART-J-MECH-APPLIED-MATH,
  volume =       "1",
  pages =        "287--308",
  month =        sep,
  year =         "1948",
  CODEN =        "QJMMAV",
  ISSN =         "0033-5614 (print), 1464-3855 (electronic)",
  ISSN-L =       "0033-5614",
  MRclass =      "65.0X",
  MRnumber =     "MR0028100 (10,405c)",
  MRreviewer =   "E. Bodewig",
  bibdate =      "Sat Nov 19 12:09:58 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/a/turing-alan-mathison.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite{Britton:1992:CWT} with summary and
                 notes (including corrections)",
  URL =          "http://turing.ecs.soton.ac.uk/browse.php/B/18",
  ZMnumber =     "0033.28501",
  acknowledgement = ack-nhfb,
  fjournal =     "Quarterly Journal of Mechanics and Applied
                 Mathematics",
  journal-URL =  "http://qjmam.oxfordjournals.org/content/by/year",
  mynote =       "The notes are not very good. They mainly correct
                 errors and fill in the gaps of derivations. Much better
                 would have been higher level comments from a numerical
                 analyst, e.g. on where Turing's ideas/predictions were
                 wrong.",
}

@Article{Williams:1948:EDC,
  author =       "F. C. Williams and T. Kilburn",
  title =        "Electronic digital computers",
  journal =      j-NATURE,
  volume =       "162",
  number =       "4117",
  pages =        "487--487",
  day =          "25",
  month =        sep,
  year =         "1948",
  CODEN =        "NATUAS",
  DOI =          "https://doi.org/10.1038/162487a0",
  ISSN =         "0028-0836 (print), 1476-4687 (electronic)",
  ISSN-L =       "0028-0836",
  bibdate =      "Wed Oct 13 12:00:02 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 8.4]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Nature",
  journal-URL =  "http://www.nature.com/nature/archive/",
  remark =       "Letter submitted 3 August 1948. Describes a small
                 prototype digital computer with 32 31-bit words for
                 instructions, data, and working storage.",
}

@Article{Davis:1949:MM,
  author =       "Harry M. Davis",
  title =        "Mathematical Machines",
  journal =      j-SCI-AMER,
  volume =       "180",
  number =       "4",
  pages =        "28--39",
  month =        apr,
  year =         "1949",
  CODEN =        "SCAMAC",
  DOI =          "https://doi.org/10.1038/scientificamerican0449-28",
  ISSN =         "0036-8733 (print), 1946-7087 (electronic)",
  ISSN-L =       "0036-8733",
  bibdate =      "Sat May 18 16:12:10 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sciam1940.bib",
  URL =          "http://www.jstor.org/stable/24967160;
                 http://www.nature.com/scientificamerican/journal/v180/n4/pdf/scientificamerican0449-28.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientific American",
  journal-URL =  "http://www.nature.com/scientificamerican",
  remark =       "Description of counting devices before 1950, including
                 an introduction to the binary number system.",
}

@Article{Hartree:1949:NSR,
  author =       "Douglas R. (Douglas Rayner) Hartree",
  title =        "Note On Systematic Roundoff Errors in Numerical
                 Integration",
  journal =      "Journal of Research of the National Bureau of
                 Standards",
  volume =       "42",
  number =       "??",
  pages =        "62--??",
  month =        "????",
  year =         "1949",
  bibdate =      "Wed Feb 14 19:07:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Huskey:1949:PCP,
  author =       "H. D. Huskey",
  title =        "On the Precision of a Certain Procedure of Numerical
                 Integration",
  journal =      j-J-RES-NATL-BUR-STAND,
  volume =       "42",
  number =       "1",
  pages =        "57--62",
  month =        jan,
  year =         "1949",
  CODEN =        "JRNBAG",
  DOI =          "https://doi.org/10.6028/jres.042.005",
  ISSN =         "0091-0635 (print), 2376-5305 (electronic)",
  ISSN-L =       "0091-0635",
  bibdate =      "Fri Aug 20 09:32:34 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "With an appendix by Douglas R. Hartree.",
  abstract =     "An example of numerical integration is given that
                 shows very systematic effects in the less significant
                 digits. This lack of randomness gives rounding-off
                 errors that exceed the predicted standard deviation by
                 a factor of three. The example considered in this paper
                 shows that systematic rounding-off errors can occur in
                 numerical in integration, irrespective of the number of
                 digits kept in the contributions to the integral. In
                 the appendix this phenomenon is examined, and criteria
                 are set up to detect the cases in which it may arise to
                 a serious extent.",
  acknowledgement = ack-nhfb,
  journal-URL =  "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@TechReport{Tukey:1949:TRA,
  author =       "John W. Tukey and M. F. Freeman",
  title =        "Transformation related to the angular and the
                 square-root",
  type =         "SRG Memorandum report",
  number =       "24",
  institution =  inst-PRINCETON,
  address =      inst-PRINCETON:adr,
  pages =        "??",
  year =         "1949",
  bibdate =      "Tue May 15 08:00:09 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{Forsythe:1950:NRE,
  author =       "George E. Forsythe",
  title =        "Note on rounding-off errors",
  publisher =    pub-NBS,
  address =      pub-NBS:adr,
  pages =        "3",
  year =         "1950",
  MRclass =      "65.0X",
  MRnumber =     "MR0037068 (12,208g)",
  MRreviewer =   "J. Todd",
  bibdate =      "Tue Nov 22 09:52:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  author-dates = "George Elmer Forsythe (8 January 1917--9 April 1972)",
}

@Article{Harrison:1950:BDC,
  author =       "J. O. {Harrison, Jr.}",
  title =        "Binary--Decimal Conversion on a Desk Calculator (in
                 Automatic Computing Machinery; Discussions)",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "4",
  number =       "32",
  pages =        "231--234",
  month =        oct,
  year =         "1950",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2002500",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Tables Other Aids Comput.",
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Book{Stifler:1950:HSC,
  editor =       "W. W. {Stifler, Jr.}",
  title =        "High-speed computing devices",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "xiii + 451",
  year =         "1950",
  LCCN =         "QA75 .E5",
  bibdate =      "Fri Aug 20 10:18:44 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  remark =       "Supervised by Charles Brown Tompkins and C. H.
                 Wakelin, Engineering Research Associates. The contents
                 of this volume were first assembled in the form of a
                 report to the Office of Naval Research, prepared under
                 a provision of contract N6-ONR-240, Task 1. Cited in
                 \cite{Sterbenz:1974:FPC}.",
  subject =      "computers",
}

@InProceedings{Wilkes:1950:E,
  author =       "M. V. Wilkes and W. Renwick",
  booktitle =    "{Report of a Conference on High Speed Automatic
                 Calculating Machines, 22--25 June 1949}",
  title =        "The {EDSAC}",
  publisher =    "University Mathematical Laboratory",
  address =      "Cambridge, UK",
  pages =        "9--11",
  month =        jan,
  year =         "1950",
  bibdate =      "Wed Oct 13 12:00:41 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 8.5]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Worsley:1950:ED,
  author =       "B. H. Worsley",
  booktitle =    "Report of a Conference on High Speed Automatic
                 Calculating Machines, {22--25 June 1949}",
  title =        "The {EDSAC} demonstration",
  publisher =    "University Mathematical Laboratory",
  address =      "Cambridge, UK",
  pages =        "12--16",
  month =        jan,
  year =         "1950",
  bibdate =      "Wed Oct 13 11:39:09 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 8.6]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
}

@Misc{Anonymous:1951:R,
  author =       "Anonymous",
  title =        "{RECIPROOT}",
  howpublished = "Manchester University Electronic Computer Web
                 document.",
  day =          "9",
  month =        jul,
  year =         "1951",
  bibdate =      "Sat Aug 19 09:57:33 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "To calculate square roots and reciprocal square
                 roots.",
  URL =          "https://0x5f37642f.com/documents/ManchesterRecipRoot.pdf",
  acknowledgement = ack-nhfb,
  remark =       "Code used on Ferranti Mark I.",
}

@Article{Booth:1951:SBM,
  author =       "Andrew D. Booth",
  title =        "A signed binary multiplication technique",
  journal =      j-QUART-J-MECH-APPLIED-MATH,
  volume =       "4",
  number =       "2",
  pages =        "236--240",
  month =        "????",
  year =         "1951",
  CODEN =        "QJMMAV",
  DOI =          "https://doi.org/10.1093/qjmam/4.2.236",
  ISSN =         "0033-5614 (print), 1464-3855 (electronic)",
  ISSN-L =       "0033-5614",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://academic.oup.com/qjmam/article-abstract/4/2/236/1874893",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  fjournal =     "Quarterly Journal of Mechanics and Applied
                 Mathematics",
  journal-URL =  "http://qjmam.oxfordjournals.org/content/by/year",
}

@InCollection{Brown:1951:HRR,
  author =       "G. W. Brown",
  title =        "History of {RAND}'s random digits",
  crossref =     "Householder:1951:MCM",
  pages =        "31--32",
  year =         "1951",
  bibdate =      "Sun Sep 18 12:02:43 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.rand.org/pubs/papers/2008/P113.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Gill:1951:PSS,
  author =       "S. Gill",
  title =        "A process for the step-by-step integration of
                 differential equations in an automatic digital
                 computing machine",
  journal =      j-PROC-CAMBRIDGE-PHIL-SOC,
  volume =       "47",
  pages =        "96--108",
  year =         "1951",
  CODEN =        "PCPSA4",
  ISSN =         "0008-1981",
  bibdate =      "Tue Aug 28 05:54:12 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the Cambridge Philosophical Society.
                 Mathematical and physical sciences",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=PSP",
  keywords =     "accurate floating-point summation; floating-point
                 arithmetic; rounding errors",
  remark =       "Higham \cite{Higham:1993:AFP} comments ``In 1951 Gill
                 [8] noticed that the rounding error in the sum of two
                 numbers could be estimated by subtracting one of the
                 numbers from the sum, and he made use of this estimate
                 in a Runge--Kutta code in a program library for the
                 EDSAC computer.''",
}

@Article{Goldstine:1951:NIM,
  author =       "Herman H. Goldstine and John von Neumann",
  title =        "Numerical Inverting of Matrices of High Order. {II}",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "2",
  pages =        "188--202",
  year =         "1951",
  CODEN =        "PAMYAR",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "65.0X",
  MRnumber =     "MR0041539 (12,861b)",
  MRreviewer =   "F. J. Murray",
  bibdate =      "Thu Nov 8 14:49:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{vonNeumann:1947:NIM} for Part I. Reprinted
                 in \cite[Paper 15, pp. 558--572]{Taub:1963:JNCa}.",
  URL =          "http://www.jstor.org/view/00029939/di970628/97p0185x/0",
  ZMnumber =     "043.12301",
  acknowledgement = ack-nhfb,
  author-dates = "John von Neumann (28 December 1903--8 February 1957)",
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
}

@Article{MacMillan:1951:FDC,
  author =       "Donald B. MacMillan and Richard H. Stark",
  title =        "{``Floating} Decimal'' Calculation on the {IBM} Card
                 Programmed Electronic Calculator (in Automatic
                 Computing Machinery; Discussions)",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "5",
  number =       "34",
  pages =        "86--92",
  month =        apr,
  year =         "1951",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Tables Other Aids Comput.",
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@InProceedings{Rademacher:1951:AEP,
  author =       "Hans Rademacher",
  booktitle =    "Proceedings of a Symposium on Large-scale Digital
                 Calculating Machinery",
  title =        "On the accumulation of errors in processes of
                 integration on high-speed calculating machines",
  publisher =    pub-HARVARD,
  address =      pub-HARVARD:adr,
  pages =        "176--185",
  year =         "1951",
  bibdate =      "Mon Jun 18 06:50:41 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Shirley:1951:BNB,
  author =       "John W. Shirley",
  title =        "Binary Numeration before {Leibniz}",
  journal =      j-AMER-J-PHYSICS,
  volume =       "19",
  number =       "8",
  pages =        "452--454",
  month =        nov,
  year =         "1951",
  CODEN =        "AJPIAS",
  DOI =          "https://doi.org/10.1119/1.1933042",
  ISSN =         "0002-9505 (print), 1943-2909 (electronic)",
  ISSN-L =       "0002-9505",
  bibdate =      "Sat Feb 8 10:29:20 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://scitation.aip.org/content/aapt/journal/ajp/19/8/10.1119/1.1933042",
  abstract =     "Though it is frequently stated that binary numeration
                 was first formally proposed by Leibniz as an
                 illustration of his dualistic philosophy, the
                 mathematical papers of Thomas Hariot (1560--1621) show
                 clearly that Hariot not only experimented with number
                 systems, but also understood clearly the theory and
                 practice of binary numeration nearly a century before
                 Leibniz's time.",
  acknowledgement = ack-nhfb,
  fjournal =     "American Journal of Physics",
  journal-URL =  "http://scitation.aip.org/content/aapt/journal/ajp",
  remark =       "Submitted 14 November 1950.",
}

@Book{Wilkes:1951:PPE,
  author =       "Maurice V. Wilkes and David J. Wheeler and Stanley
                 Gill",
  title =        "The Preparation of Programs for an Electronic Digital
                 Computer",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "167",
  year =         "1951",
  LCCN =         "QA76.5 .W55 1951",
  bibdate =      "Mon Feb 10 09:42:47 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also second edition \cite{Wilkes:1957:PPE}, and
                 reprint \cite{Wilkes:1982:PPE}.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Part I \\
                 Chapter 1. The Design of Programs for Electronic
                 Computing Machines / 1 \\
                 1-1 Introduction / 1 \\
                 1-2 Types of automatic computing machines / 2 \\
                 1-3 Description of the EDSAC / 3 \\
                 1-4 The EDSAC order code / 5 \\
                 1-5 Notes on the order code / 6 \\
                 1-6 The use of conditional orders / 7 \\
                 1-7 Modification of orders by the program / 8 \\
                 1-8 Multiaddress codes / 11 \\
                 1-9 Binary--decimal conversion / 12 \\
                 1-10 Checking facilities / 14 \\
                 Chapter 2. Input of Orders / 15 \\
                 2-1 Initial orders / 15 \\
                 2-2 Pseudo-orders / 17 \\
                 2-3 Examples / 17 \\
                 2-4 Control combinations / 17 \\
                 2-5 Starting the program / 18 \\
                 2-6 Use of code letters / 19 \\
                 2-7 Constants / 20 \\
                 2-8 Notation / 20 \\
                 Chapter 3. Subroutines and Parameters / 22 \\
                 3-1 Open subroutines / 22 \\
                 3-2 closed subroutines / 22 \\
                 3-3 preset parameters / 23 \\
                 3-4 program parameters / 23 \\
                 Chapter 4. Library Subroutines and their Use in
                 Constructing Programs / 25 \\
                 4-1 Library catalog / 25 \\
                 4-2 Input and output subroutines / 25 \\
                 4-3 Division subroutines / 27 \\
                 4-4 Trigonometrical and other functions / 27 \\
                 4-5 Quadrature / 27 \\
                 4-6 Assembly subroutines / 27 \\
                 4-7 Integration of differential equations / 32 \\
                 4-8 Processes, Interpretive subroutines / 34 \\
                 Chapter 5. Pitfalls / 38 \\
                 5-1 Proofreading of programs, points to be checked / 38
                 \\
                 5-2 Location of mistakes in a program / 39 \\
                 5-3 Counting operations / 41 \\
                 Chapter 6. Use of the EDSAC \& Its Associated Equipment
                 / 42 \\
                 6-1 Tape Punching \& editing facilities / 42 \\
                 6-2 Storage of library subroutines / 43 \\
                 6-3 EDSAC organization / 43 \\
                 6-4 EDSAC controls / 43 \\
                 Chapter 7. Examples / 45 \\
                 7-1 Example 1. Calculation of $\exp(-\sin x)$ / 45 \\
                 7-2 Example 2. Calculation of $\pi$ by evaluation of
                 definite integral / 48 \\
                 7-3 Alternative method for Example 2 / 52 \\
                 7-4 Example 2, with extra print orders for checking /
                 53 \\
                 7-5 Application of checking subroutine C11 to Example 2
                 / 54 \\
                 7-6 Example of integration of an ordinary differential
                 equation / 46 \\
                 7-7 Evaluation of a definite integral / 61 \\
                 7-8 Program to facilitate the solution of algebraic
                 equation / 66 \\
                 Part II. Specifications of Library Subroutines / 72 \\
                 A. Subroutines to carry out floating point arithmetic /
                 73 \\
                 B. Subroutines to carry out arithmetical operations on
                 complex numbers / 78 \\
                 C. Checking subroutines / 79 \\
                 D. Division subroutines / 82 \\
                 E. Exponential subroutines / 83 \\
                 F. General routines relating to functions / 84 \\
                 G. Subroutines for integration of ordinary differential
                 equations / 86 \\
                 J. Subroutines for calculating special functions
                 [Legendre polynomials] / 88 \\
                 K. Subroutines for the summation of power series / 88
                 \\
                 L. Subroutines for evaluating logarithms / 91 \\
                 M. Miscellaneous subroutines / 91 \\
                 P. Print subroutines / 92 \\
                 Q. Quadrature subroutines / 95 \\
                 R. Input subroutines / 96 \\
                 S. Subroutines for evaluation of fractional powers / 98
                 \\
                 T. Subroutines for calculating trigonometrical
                 functions / 99 \\
                 U. Subroutines for counting operations / 101 \\
                 V1. Multiplication of vector by symmetric matrix / 102
                 \\
                 V2. Addition and subtraction of $n$ dimensional vectors
                 / 103 \\
                 Part III. Programs of Selected Library Subroutines /
                 104 \\
                 Appendix A. Keyboard perforator code, etc. / 158 \\
                 Appendix B. The initial orders / 159 \\
                 Appendix C. Control combinations / 161 \\
                 Appendix D. Interpretive subroutines: example of
                 packing of orders / 162 \\
                 Appendix E. Methods of counting in a simple cycle / 164
                 \\
                 Index",
}

@InProceedings{Andrews:1952:RBL,
  author =       "E. G. Andrews",
  editor =       "J. C. McPherson",
  booktitle =    "Proceedings of the {AIEE-IRE '51}: Papers and
                 discussions presented at the December 10--12, 1951,
                 joint {AIEE-IRE} computer conference, Philadelphia,
                 {PA}: Review of electronic digital computers",
  title =        "A review of the {Bell Laboratories}' digital computer
                 developments",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  bookpages =    "vi + 114",
  pages =        "101--105",
  year =         "1952",
  DOI =          "https://doi.org/10.1145/1434770.1434787",
  LCCN =         "????",
  bibdate =      "Fri Dec 03 09:17:58 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Bell Laboratories Model 1--5 relay computers; complex
                 fixed-point decimal arithmetic; complex floating-point
                 decimal arithmetic",
  remark-1 =     "From page 101: ``The Bell Telephone Laboratories have
                 designed and built seven digital computers.''",
  remark-2 =     "From page 101: ``George R. Stibitz \ldots{} designed
                 and \ldots{} called it a ``complex number computer.''",
  remark-3 =     "From page 101: ``This computer operated with binary
                 coded decimal notation, with the decimal digits 0 to 9
                 being represented by the binary numbers 0011 to 1100.
                 The input and output information consisted of eight
                 place numbers, but the calculator carried operations
                 out to ten places, the two extra places being used to
                 improve accuracy when accumulating the results of
                 several problems.''",
  remark-4 =     "From page 104: ``Besides these advantages in operation
                 ease, another has been developed but it has not yet
                 been incorporated into a computer as far as is known.
                 This is the self-correcting code for numerical data.
                 Dr. R. W. Hamming devised this principle of coding. A
                 computer with this feature would show an unattended
                 operation performance superior to anything we know
                 today.'' [Refers to ``Error Detecting and Error
                 Correcting Codes'', The Bell System Technical Journal
                 {\bf 29}(2) 147--160, April 1960,
                 doi:10.1002/j.1538-7305.1950.tb00463.x].",
}

@Article{Davis:1952:ARS,
  author =       "K. Davis and R. Biddulph and S. Balashek",
  title =        "Automatic Recognition of Spoken Digits",
  journal =      j-J-ACOUST-SOC-AM,
  volume =       "24",
  number =       "6",
  pages =        "637--642",
  month =        nov,
  year =         "1952",
  CODEN =        "JASMAN",
  ISSN =         "0001-4966",
  ISSN-L =       "0001-4966",
  bibdate =      "Fri Nov 28 16:38:51 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "Journal of the Acoustical Society of America",
  journal-URL =  "http://scitation.aip.org/content/asa/journal/jasa",
}

@Article{Hammersley:1952:CSS,
  author =       "J. M. Hammersley",
  title =        "The computation of sums of squares and products on a
                 desk calculator",
  journal =      j-BIOMETRICS,
  volume =       "8",
  number =       "??",
  pages =        "156--168",
  year =         "1952",
  CODEN =        "BIOMB6",
  DOI =          "https://doi.org/10.2307/3001930",
  ISSN =         "0006-341X (print), 1541-0420 (electronic)",
  ISSN-L =       "0006-341X",
  MRclass =      "65.0X",
  MRnumber =     "48908",
  MRreviewer =   "E. Lukacs",
  bibdate =      "Thu Jun 25 17:01:03 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/biometrics1950.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Biometrics",
  fjournal =     "Biometrics",
  journal-URL =  "http://www.jstor.org/journal/biometrics",
}

@Article{Irani:1952:SMT,
  author =       "Rida A. K. Irani",
  title =        "A sexagesimal multiplication table in the {Arabic}
                 alphabetical system",
  journal =      j-SCRIPTA-MATH,
  volume =       "18",
  number =       "??",
  pages =        "92--93",
  month =        "????",
  year =         "1952",
  ISSN =         "0036-9713",
  ISSN-L =       "0036-9713",
  MRclass =      "01.0X",
  MRnumber =     "49109",
  bibdate =      "Thu Oct 26 11:15:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
  ZMnumber =     "0046.00102",
  acknowledgement = ack-nhfb,
  ajournal =     "Scripta Math.",
  fjournal =     "Scripta Mathematica: A Quarterly Journal Devoted to
                 the Philosophy, History, and Expository Treatment of
                 Mathematics",
  ZBmath =       "3070983",
}

@Article{Michaelson:1952:BA,
  author =       "R. L. Michaelson",
  title =        "Binary Arithmetic",
  journal =      j-INC-STAT,
  volume =       "3",
  number =       "1",
  pages =        "35--40",
  month =        feb,
  year =         "1952",
  CODEN =        "????",
  DOI =          "https://doi.org/10.2307/2986591",
  ISSN =         "1466-9404",
  ISSN-L =       "1466-9404",
  bibdate =      "Thu Jan 22 18:10:18 MST 2015",
  bibsource =    "http://www.jstor.org/stable/i349863;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jrss-d-1950.bib",
  URL =          "http://www.jstor.org/stable/2986591",
  acknowledgement = ack-nhfb,
  fjournal =     "The Incorporated Statistician",
  journal-URL =  "http://www.jstor.org/journals/14669404.html",
}

@Article{Morrill:1952:SEM,
  author =       "C. D. Morrill and R. V. Baum",
  title =        "A Stabilized Electronic Multiplier",
  journal =      j-TRANS-IRE-PROF-GROUP-ELEC-COMPUT,
  volume =       "EC-1",
  number =       "??",
  pages =        "52--59",
  month =        dec,
  year =         "1952",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Fri Jul 15 15:20:53 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Transactions of the I.R.E. Professional Group on
                 Electronic Computers",
}

@InProceedings{Sheldon:1952:ICP,
  author =       "J. W. Sheldon and L. Tatum",
  booktitle =    "Review of Electronic Digital Computers. {Joint
                 AIEE--IRE Computer Conference. 10--12 December 1951}",
  title =        "The {IBM} card-programmed electronic calculator",
  publisher =    "American Institute of Electrical Engineers",
  address =      "New York, NY, USA",
  pages =        "30--36",
  year =         "1952",
  bibdate =      "Wed Oct 13 11:28:45 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 5.4]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
}

@Article{Brooker:1953:FOE,
  author =       "R. A. Brooker and D. J. Wheeler",
  title =        "Floating Operations on the {EDSAC} (in Automatic
                 Computing Machinery; Discussions)",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "7",
  number =       "41",
  pages =        "37--47",
  month =        jan,
  year =         "1953",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1953-0052901-3",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
                 JSTOR database",
  abstract =     "The difficulties which arise when programming
                 calculations for large automatic calculating machines
                 which have a fixed decimal point are discussed. This
                 leads to a consideration of the possibility of using
                 floating decimal arithmetic for certain kinds of
                 calculations. A method by which floating decimal
                 arithmetic can be carried out with any fixed
                 decimal-point machine is outlined and the scheme
                 adopted for use with the EDSAC is described in
                 detail.",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Tables Other Aids Comput.",
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "floating-point decimal arithmetic",
  remark-01 =    "From page 38: ``The problem [of programmer-controlled
                 numeric scaling] does not arise with machines designed
                 to operate directly with numbers expressed in the
                 floating radix form. Numbers in this form are
                 represented by $a \cdot r^p$. The first machine of this
                 kind was the Bell Telephone Laboratories Relay Computer
                 Model V(1). This is a decimal machine (that is, $r =
                 10$) in which $1 > |a| > 0.1$, $19 > p > -19$ and $a$
                 is expressed to an accuracy of seven significant
                 figures. Since this was completed all important relay
                 machines have been equipped with similar facilities. No
                 electronic machine of this kind has yet been built but
                 we would remark that in our opinion an electronic
                 machine provided with a floating point arithmetical
                 unit would be a powerful computing instrument even if
                 it had a relatively slow store, a magnetic drum, for
                 example.''",
  remark-02 =    "From page 39: ``Two long and two short storage
                 locations are set aside to form a kind of `arithmetical
                 unit.' One long location holds the numerical part of a
                 number and one short location holds the exponent.
                 Together they form the {\em floating decimal
                 accumulator}. In a similar fashion the other long
                 location and the other short location form the {\em
                 floating decimal register}.''",
  remark-03 =    "From page 40: ``the floating decimal accumulator is
                 then `cleared' by replacing the number held in it by
                 zero, that is, by the special number $010^{-63}$.''",
  remark-04 =    "From page 40: `The use of two separate storage
                 locations for the floating decimal accumulator allows
                 the range and accuracy of numbers held therein to be
                 greater than those held in a single storage location
                 elsewhere. This enables products to be accumulated
                 without loss of accuracy due to intermediate
                 rounding-off errors.''",
  remark-05 =    "From the conclusion on page 46: ``From a direct
                 comparison it would seem that the floating 'orders,'
                 other than those used for reading and writing, are
                 about 60 times as slow as the machine orders and hence
                 that a programme using the interpretive subroutine
                 would be slower by the same factor. This is not
                 altogether true because in such a programme fewer
                 orders' are needed than would otherwise be necessary as
                 there are no scale factors to deal with and the
                 techniques for counting and for the modification of
                 orders' have been streamlined. Moreover, the time taken
                 by the C auxiliaries is about the same as that taken by
                 the corresponding subroutine in fixed decimal-point
                 working. These factors vary from problem to problem but
                 our experience has shown that the reduction in speed
                 varies from about 20 to 1 to about 4 to 1. The
                 reduction of the time taken to code a problem has to be
                 experienced to be believed!''",
}

@Book{IBM:1953:POT,
  author =       "{IBM Corporation}",
  title =        "Principles of Operation: Type 701 and Associated
                 Equipment",
  publisher =    pub-IBM,
  address =      pub-IBM:adr,
  pages =        "103",
  year =         "1953",
  bibdate =      "Wed Sep 14 23:17:49 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Samelson:1953:ORR,
  author =       "Klaus Samelson and Friedrich L. Bauer",
  title =        "{Optimale Rechengenauigkeit bei Rechenanlagen mit
                 gleitendem Komma}. ({German}) [{Optimal} calculation
                 accuracy for calculators with a floating point]",
  journal =      j-Z-ANGE-MATH-PHYS,
  volume =       "4",
  number =       "4",
  pages =        "312--316",
  month =        jul,
  year =         "1953",
  CODEN =        "ZAMPDB",
  DOI =          "https://doi.org/10.1007/bf02074638",
  ISSN =         "0044-2275 (print), 1420-9039 (electronic)",
  ISSN-L =       "0044-2275",
  bibdate =      "Sun Aug 16 18:04:35 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Digital automatic computing machines with floating
                 binary point are investigated with respect to their
                 accuracy. It is concluded that special devices can be
                 designed without difficulty, which guarantee the
                 highest accuracy obtainable with a fixed number of
                 digits. For binary computers, a modification of the
                 usual conversion routine is necessary, which is
                 discussed in detail.",
  acknowledgement = ack-nhfb,
  fjournal =     "{Zeitschrift f{\"u}r Angewandte Mathematik und Physik
                 = Journal of Applied Mathematics and Physics}",
  journal-URL =  "http://link.springer.com/journal/33",
  keywords =     "number base conversion",
  language =     "German",
}

@InCollection{Stiefel:1953:MCA,
  author =       "E. Stiefel",
  booktitle =    "Les machines {\`a} calculer et la pens{\'e}e humaine",
  title =        "La machine {\`a} calculer arithm{\'e}tique ``{Z4}'' de
                 l'{Ecole} {Polytechnique} {F}{\'e}d{\'e}rale {\`a}
                 {Zurich} ({Suisse}) et son application {\`a} la
                 r{\'e}solution d'une {\'e}quation aux d{\'e}riv{\'e}es
                 partielles de type elliptique. ({French}) [{The}
                 arithmetic calculator ``{Z4}'' of the {Swiss Federal
                 Polytechnical University in Zurich (Switzerland)} and
                 its application to the solution of an elliptical type
                 partial derivative equation]",
  publisher =    "Centre National de la Recherche Scientifique",
  address =      "Paris, France",
  pages =        "33--40",
  year =         "1953",
  MRclass =      "65.0X",
  MRnumber =     "0066093",
  bibdate =      "Wed Sep 2 16:23:13 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Colloques internationaux du Centre National de la
                 Recherche Scientifique, no 37",
  acknowledgement = ack-nhfb,
  author-dates = "Eduard Stiefel (21 April 1909--25 November 1978)",
  language =     "French",
}

@Article{vanWijngaarden:1953:EAC,
  author =       "Adriaan van Wijngaarden",
  title =        "Erreurs d'arrondiment dans les calculs systematiques.
                 ({French}) [{Rounding} errors in systematic
                 calculations]",
  journal =      "Centre National de Recherche Scientifique, Colloques
                 Internationaux",
  volume =       "37",
  number =       "??",
  pages =        "285--??",
  month =        "????",
  year =         "1953",
  bibdate =      "Sat Nov 01 06:40:10 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
}

@Article{Backus:1954:ISS,
  author =       "J. W. Backus",
  title =        "The {IBM 701 Speedcoding} System",
  journal =      j-J-ACM,
  volume =       "1",
  number =       "1",
  pages =        "4--6",
  month =        jan,
  year =         "1954",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Fri Nov 04 00:18:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://community.computerhistory.org/scc/projects/FORTRAN/paper/p4-backus.pdf",
  abstract =     "The IBM 701 Speedcoding System is a set of
                 instructions which causes the 701 to behave like a
                 three-address floating point calculator. Let us call
                 this the Speedcoding calculator. In addition to
                 operating in floating point, this Speedcoding
                 calculator has extremely convenient means for getting
                 information into the machine and for printing results;
                 it has an extensive set of operations to make the job
                 of programming as easy as possible. Speedcoding also
                 provides automatic address modification, flexible
                 tracing, convenient use of auxiliary storage, and
                 built-in checking.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}

@Manual{Burroughs:1954:DH,
  author =       "{Burroughs Corporation.ElectroData}",
  title =        "Datatron handbooks",
  organization = "The Division",
  address =      "Pasadena, CA, USA",
  year =         "1954",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "12 volumes in 1.",
  acknowledgement = ack-nhfb,
  keywords =     "Datatron (Computer)",
  remark =       "Datatron programming and coding manual --- Datatron
                 operation manual --- Central computer handbook ---
                 Paper tape system handbook --- Card converter Model 500
                 handbook --- Magnetic tape system handbook ---
                 Cardatron system handbook --- Model 560 DATAFILE
                 handbook --- Control console and consolette handbook
                 --- Floating point control unit handbook --- External
                 switching unit handbook --- Tape preparation unit
                 handbook.",
}

@Article{Freeman:1954:TSA,
  author =       "H. Freeman and E. Parsons",
  title =        "Time-Sharing Analog Multiplier ({TSAM})",
  journal =      j-TRANS-IRE-PROF-GROUP-ELEC-COMPUT,
  volume =       "EC-3",
  number =       "1",
  pages =        "11--17",
  month =        mar,
  year =         "1954",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Fri Jul 15 15:20:53 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Transactions of the I.R.E. Professional Group on
                 Electronic Computers",
  remark =       "Cited in US Patent 3,043,516 (10 July 1962): Time
                 Summing Device for Division, Multiplication, Root
                 Taking and Interpolation, by Harold W. Abbott and
                 Vernon P. Mathis.",
}

@Article{Gorn:1954:AAC,
  author =       "Saul Gorn",
  title =        "The Automatic Analysis and Control of Computing
                 Errors",
  journal =      j-J-SIAM,
  volume =       "2",
  number =       "2",
  pages =        "69--81",
  month =        jun,
  year =         "1954",
  CODEN =        "JSIMAV",
  ISSN =         "0368-4245 (print), 1095-712X (electronic)",
  bibdate =      "Thu Oct 15 18:16:06 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Society for Industrial and Applied
                 Mathematics",
  journal-URL =  "http://epubs.siam.org/loi/smjmap.1",
}

@Article{Kovach:1954:AMU,
  author =       "L. D. Kovach and W. Comley",
  title =        "An Analog Multiplier Using Thyrite",
  journal =      j-TRANS-IRE-PROF-GROUP-ELEC-COMPUT,
  volume =       "EC-3",
  number =       "2",
  pages =        "42--45",
  month =        jun,
  year =         "1954",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sun Jul 17 09:57:13 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Transactions of the I.R.E. Professional Group on
                 Electronic Computers",
}

@Article{Mayer:1954:ODF,
  author =       "M. A. Mayer and B. M. Gordon and R. N. Nicola",
  title =        "An operational digital feedback divider",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-3",
  number =       "1",
  pages =        "17--20",
  month =        mar,
  year =         "1954",
  CODEN =        "IRELAO",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Sun Jul 17 09:52:58 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Moshman:1954:GPR,
  author =       "Jack Moshman",
  title =        "The Generation of Pseudo-Random Numbers on a Decimal
                 Calculator",
  journal =      j-J-ACM,
  volume =       "1",
  number =       "2",
  pages =        "88--91",
  month =        apr,
  year =         "1954",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Fri Nov 04 00:18:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  keywords =     "decimal floating-point arithmetic",
}

@Article{Clenshaw:1955:NSC,
  author =       "C. W. Clenshaw",
  title =        "A note on the summation of {Chebyshev} series",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "9",
  number =       "51",
  pages =        "118--120",
  year =         "1955",
  CODEN =        "MTTCAS",
  DOI =          "https://doi.org/10.1090/S0025-5718-1955-0071856-0",
  ISSN =         "0891-6837 (print), 2326-4853 (electronic)",
  ISSN-L =       "0891-6837",
  MRclass =      "65.0X",
  MRnumber =     "0071856",
  bibdate =      "Thu Feb 08 16:17:25 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Tables Other Aids Comput.",
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Hidden inside \cite{Brenner:1955:TNS}, but important
                 in its own right for commentary on the recursive
                 algorithm for summation of Chebyshev series, and a
                 brief analysis of its accuracy.",
}

@Article{Crockett:1955:GMM,
  author =       "J. B. Crockett and H. Chernoff",
  title =        "Gradient Methods of Maximization",
  journal =      j-PAC-J-MATH,
  volume =       "5",
  number =       "??",
  pages =        "33--50",
  year =         "1955",
  CODEN =        "PJMAAI",
  ISSN =         "0030-8730 (print), 1945-5844 (electronic)",
  ISSN-L =       "0030-8730",
  bibdate =      "Fri Aug 20 08:54:24 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Pacific Journal of Mathematics",
  journal-URL =  "http://msp.org/pjm",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Book{Eckert:1955:FFS,
  author =       "W. J. (Wallace John) Eckert and Rebecca Bradley
                 Jones",
  title =        "Faster, faster; a simple description of a giant
                 electronic calculator and the problems it solves",
  publisher =    pub-IBM,
  address =      pub-IBM:adr,
  pages =        "160",
  year =         "1955",
  LCCN =         "QA76 .E25",
  bibdate =      "Fri Aug 20 08:57:56 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1902--1971",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
  subject =      "Computers",
  xxaddress =    pub-MCGRAW-HILL:adr,
  xxpublisher =  pub-MCGRAW-HILL,
}

@Book{Hastings:1955:ADC,
  author =       "Cecil B. {Hastings, Jr.} and Jeanne T. Hayward and
                 James P. {Wong, Jr.}",
  title =        "Approximations for Digital Computers",
  publisher =    pub-PRINCETON,
  address =      pub-PRINCETON:adr,
  pages =        "viii + 201",
  year =         "1955",
  LCCN =         "QA76 .H33",
  bibdate =      "Mon Sep 30 14:51:50 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Lenaerts:1955:ASR,
  author =       "E. H. Lenaerts",
  title =        "Automatic Square Rooting",
  journal =      j-ELECTRON-ENG,
  volume =       "27",
  number =       "??",
  pages =        "287--289",
  month =        jul,
  year =         "1955",
  CODEN =        "ELEGAP",
  ISSN =         "0013-4902",
  bibdate =      "Thu Sep 1 10:15:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronic Engineering",
}

@Article{Parsons:1955:SDC,
  author =       "Frances L. Parsons",
  title =        "A Simple Desk-Calculator Method for Checking Binary
                 Results of Digital Computer Arithmetic Operations",
  journal =      j-J-ACM,
  volume =       "2",
  number =       "3",
  pages =        "205--207",
  month =        jul,
  year =         "1955",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Wed Nov 09 01:00:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}

@Book{Richards:1955:AOD,
  author =       "Richard Kohler Richards",
  title =        "Arithmetic Operations in Digital Computers",
  publisher =    "D. Van Nostrand",
  address =      "New York, NY, USA",
  pages =        "iv + 397",
  year =         "1955",
  LCCN =         "QA75 .R5 1955",
  bibdate =      "Fri Nov 28 18:46:37 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Robertson:1955:TCM,
  author =       "J. E. Robertson",
  title =        "Two's Complement Multiplication in Binary Parallel
                 Digital Computers",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-4",
  number =       "3",
  pages =        "118--119",
  month =        sep,
  year =         "1955",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/IRETELC.1955.5407911",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jun 30 15:10:39 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5407911",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Book{Stiefel:1955:RID,
  author =       "Eduard Stiefel",
  title =        "{Rechenautomaten im Dienste der Technik. Erfahrungen
                 mit dem Zuse-Rechenautomaten Z4}. ({German})
                 [{Calculating} machines in the service of technology.
                 {Experience} with the {Zuse}-calculator {Z4}]",
  volume =       "45",
  publisher =    "Westdeutscher Verlag",
  address =      "Cologne and Opladen, West Germany",
  pages =        "29--45; Diskussion 47--65",
  year =         "1955",
  MRclass =      "68.0X",
  MRnumber =     "0073311",
  MRreviewer =   "H. H. Goldstine",
  bibdate =      "Wed Sep 2 16:23:13 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Arbeitsgemeinschaft f{\"{u}}r Forschung des Landes
                 Nordrhein-Westfalen. Heft",
  acknowledgement = ack-nhfb,
  author-dates = "Eduard Stiefel (21 April 1909--25 November 1978)",
  language =     "German",
}

@Article{Estrin:1956:NHS,
  author =       "G. Estrin and B. Gilchrist and J. H. Pomerene",
  title =        "A Note on High-Speed Digital Multiplication",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-5",
  number =       "3",
  pages =        "140--140",
  month =        sep,
  year =         "1956",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1956.5219936",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jun 30 15:46:27 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219936",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@TechReport{Fox:1956:NLS,
  author =       "Phyllis Fox",
  title =        "The {NYU} Library of Subroutines",
  type =         "Report",
  number =       "NYO-6483",
  institution =  "AEC Computing Facility, Institute of Mathematical
                 Sciences, New York University",
  address =      "New York, NY, USA",
  pages =        "11",
  day =          "1",
  month =        jan,
  year =         "1956",
  bibdate =      "Wed Dec 17 10:07:24 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://dn790009.ca.archive.org/0/items/nyulibraryofsubr00foxp/nyulibraryofsubr00foxp.pdf",
  abstract =     "A set of subroutines has been developed at the AEC
                 Computing Facility at New York University for
                 evaluating simple functions and for performing certain
                 standard procedures. Detailed descriptions of the
                 routines are available, and a library tape containing
                 the routines is kept at the Univac. The routines are
                 written to be compatible with the NYU Compiler System
                 (NYO-6478). The number of routines is constantly being
                 increased and the routines themselves may be modified
                 from time Lo Time on the basis of experience in
                 applying them to various problems. The list presented
                 here includes those routines currently in use, together
                 with a brief description of each. A revised index of
                 current routines will be issued at intervals, but
                 before using any of the routines the programmer should
                 check the library subroutine book near the computer for
                 the latest corrections and modifications.",
  acknowledgement = ack-nhfb,
  pdfpages =     "26",
  remark =       "This library was developed before the first high-level
                 language, Fortran, and the report contains only a few
                 lines of description for each component, without any
                 mention of computational algorithms. Its contents
                 nevertheless identify the computational needs of early
                 digital computer users. Its author went on to
                 co-develop the Bell Labs PORT Library
                 \cite{Fox:1977:PPM,Fox:1978:AFP,Fox:1978:PMS,Fox:1979:RFP}.",
  tableofcontents = "Introduction / 3 \\
                 Index / 4 \\
                 Arithmetic Routines / 4 \\
                 Block Output Routines / 5 \\
                 Debugging Routines / 5 \\
                 Differential Equation Routines / 7 \\
                 Edit Routines / 7 \\
                 Exponentials and Roots / 8 \\
                 Fill Routines / 9 \\
                 Ignore Squeeze Routines / 9 \\
                 Integration Routines / 9 \\
                 Logarithm Routines / 10 \\
                 Polynomial Routines / 11 \\
                 Sorting Routines / 11 \\
                 Trigonometric Routines / 11",
}

@Book{Hildebrand:1956:INA,
  author =       "Francis Begnaud Hildebrand",
  title =        "Introduction to Numerical Analysis",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "511",
  year =         "1956",
  LCCN =         "QA300 .H5",
  bibdate =      "Fri Aug 20 09:19:58 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "International series in pure and applied mathematics",
  acknowledgement = ack-nhfb,
  remark =       "See also second edition
                 \cite{Hildebrand:1974:INA,Hildebrand:1987:INA}.",
  subject =      "Numerical analysis",
  tableofcontents = "1. Introduction (significant figures, random
                 errors, error bounds, etc.) \\
                 2. Interpolation with divided differences \\
                 3. Lagrangian methods \\
                 4. Finite-difference interpolation \\
                 5. Operations with finite differences \\
                 6. Numerical solution of ordinary differential
                 equations \\
                 7. Least-squares polynomial approximation \\
                 8. Gaussian quadrature and related topics \\
                 9. Approximations of various types \\
                 10. Numerical solution of equations \\
                 Appendix: Justification of the Crout reduction",
}

@TechReport{Lazarus:1956:MI,
  author =       "R. B. Lazarus and N. Metropolis and W. Orvedahl and J.
                 H. Richardson and W. {Spack, Jr.} and R. L. Bivins and
                 J. V. Caulfield and I. Kral and A. F. Malmberg and G.
                 T. McKinley and R. E. Williamson",
  title =        "{MANIAC II}",
  type =         "Report",
  number =       "LA-2083",
  institution =  inst-LASL,
  address =      inst-LASL:adr,
  pages =        "54",
  day =          "1",
  month =        oct,
  year =         "1956",
  bibdate =      "Tue Mar 20 11:14:15 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://sgp.fas.org/othergov/doe/lanl/lib-www/la-pubs/00320765.pdf",
  acknowledgement = ack-nhfb,
  remark-1 =     "OSTI ID: 4382471",
  remark-2 =     "From page 9: ``The Maniac II \ldots{} has 12,288
                 48-bit words. It is asynchronous and has no clock. Its
                 speed is that appropriate to (1) a memory cycle of 8
                 microseconds, (2) a basic add time of 6 microseconds,
                 and (3) a shift time of about 1.3 microseconds per
                 stage. The average multiply time is about 160
                 microseconds.''",
  remark-3 =     "From page 14, the 48-bit floating-point word consists
                 of a 1-bit sign, a 3-bit exponent-of-65536, a 1-bit
                 sign of the exponent, and a 43-bit fraction in [0,1).
                 The range of nonzero numbers is (0x1p-155, 0x1p112), or
                 roughly (2e-47, 5e33). The report notes: ``Although
                 such a large base implies of possibility of as many as
                 15 lead[ing] zeros, the large word size of 48 bits
                 guarantees adequate significance.''",
}

@Article{Lilamand:1956:TDM,
  author =       "M. Lejet Lilamand",
  title =        "A Time-Division Multiplier",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-5",
  number =       "1",
  pages =        "26--34",
  month =        mar,
  year =         "1956",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1956.5219789",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jun 30 15:46:18 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219789",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Perkins:1956:EPC,
  author =       "Robert Perkins",
  title =        "{EASIAC}, a Pseudo-Computer",
  journal =      j-J-ACM,
  volume =       "3",
  number =       "2",
  pages =        "65--72",
  month =        apr,
  year =         "1956",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Fri Nov 04 23:46:26 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "One of the primary functions of the MIDAC installation
                 at the University of Michigan is the instruction of
                 beginners in the various aspects of digital machine use
                 including programming and coding. \ldots{} In
                 conducting these courses it was soon found to be
                 extremely difficult, in five or six instruction
                 periods, to bring a complete newcomer up to the point
                 where he can code and check out on MIDAC anything more
                 than a rather trivial routine. As might be expected the
                 difficulty centers around problems of scaling,
                 instruction modification and binary representation.
                 \ldots{} To alleviate these problems it was decided
                 that a new computer was needed: one designed to make
                 programming easier. At the cost of some of MIDAC's
                 speed and capacity plus two or three man-months of
                 programming time EASIAC, the EASy Instruction Automatic
                 Computer, was realized as a translation-interpretation
                 program in MIDAC.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  keywords =     "decimal floating-point arithmetic",
  remark =       "Early example of a decimal floating-point machine.",
}

@Article{Robertson:1956:NCD,
  author =       "J. E. Robertson",
  title =        "A new class of digital division methods",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-5",
  number =       "??",
  pages =        "65--73",
  month =        jun,
  year =         "1956",
  CODEN =        "IRELAO",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Fri Nov 09 19:14:45 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Stegun:1956:PC,
  author =       "Irene A. Stegun and Milton Abramowitz",
  title =        "Pitfalls in computation",
  journal =      "Journal of the Society for Industrial and Applied
                 Mathematics",
  volume =       "4",
  pages =        "207--219",
  year =         "1956",
  bibdate =      "Tue Aug 28 06:16:28 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Sydnor:1956:AMS,
  author =       "R. L. Sydnor and T. R. O'Meara and J. Strathman",
  title =        "Analog Multipliers and Squarers Using a Multigrid
                 Modulator",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-5",
  number =       "2",
  pages =        "82--85",
  month =        jun,
  year =         "1956",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1956.5219804",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jun 30 15:46:21 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219804",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Weinberger:1956:OMA,
  author =       "A. Weinberger and J. L. Smith",
  title =        "A One-Microsecond Adder Using One-Megacycle
                 Circuitry",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-5",
  number =       "??",
  pages =        "65--73",
  month =        jun,
  year =         "1956",
  CODEN =        "IRELAO",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Fri Nov 09 19:38:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Wolontis:1956:CFD,
  author =       "V. M. Wolontis",
  title =        "A Complete Floating-Decimal Interpretive System for
                 the {IBM 650 Magnetic Drum Calculator}",
  journal =      "IBM Technical Newsletter",
  volume =       "??",
  number =       "11",
  pages =        "xxi + 63",
  month =        mar,
  year =         "1956",
  bibdate =      "Mon Sep 04 13:55:28 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://babel.hathitrust.org/cgi/pt?id=coo.31924003945759&seq=7",
  acknowledgement = ack-nhfb,
}

@Book{Alt:1957:EDC,
  editor =       "Franz L. Alt",
  title =        "Electronic Digital Computers: Their Use in Science and
                 Engineering",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "x + 335",
  year =         "1957",
  bibdate =      "Sun Jun 17 18:53:23 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Section 2.3 discusses number representation and
                 decimal versus binary arithmetic.",
  xxnote =       "Check page count: incomplete view in Google books.
                 Price bibliography says 1958.",
}

@Article{Ercoli:1957:EDO,
  author =       "Paolo Ercoli and Roberto Vacca",
  title =        "Errors Due to Overflow in Arithmetic Operations
                 Particularly as Regards {FINAC} Electronic Computer",
  journal =      j-J-ACM,
  volume =       "4",
  number =       "4",
  pages =        "450--455",
  month =        oct,
  year =         "1957",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Thu Dec 08 09:28:48 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See letter \cite{Ercoli:1960:LEE}.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  keywords =     "floating-point arithmetic; overflow",
}

@Article{Gini:1957:SFD,
  author =       "Corrado Gini",
  title =        "Sulla frequenza delle cifre iniziali dei numeri
                 osservati. ({Italian}) [{On} the frequency of initial
                 digits of observed numbers]",
  journal =      "Bull. Inst. Internat. Stat.",
  volume =       "35",
  number =       "??",
  pages =        "57--76",
  year =         "1957",
  bibdate =      "Sun Sep 18 11:54:25 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "29th session, 2nd delivery, Rio de Janerio.",
  URL =          "",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  language =     "Italian",
}

@Article{Herzel:1957:SDD,
  author =       "Amato Herzel",
  title =        "Sulla distribuzione della cifre iniziali dei numeri
                 statistici. ({Italian}) [{On} the frequency of initial
                 digits of statistical numbers]",
  journal =      "Atti dell XV e XVII Riunione, Societa Italiana di
                 Statistica",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  year =         "1957",
  bibdate =      "Sun Sep 18 12:00:07 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  language =     "Italian",
}

@Article{Howe:1957:TRA,
  author =       "R. M. Howe and E. G. Gilbert",
  title =        "Trigonometric Resolution in Analog Computers by Means
                 of Multiplier Elements",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-6",
  number =       "2",
  pages =        "86--92",
  month =        jun,
  year =         "1957",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1957.5221576",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jun 30 16:07:27 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221576",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Kalbfell:1957:EAM,
  author =       "David C. Kalbfell",
  title =        "An Electronic Analog Multiplier",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-6",
  number =       "2",
  pages =        "100--103",
  month =        jun,
  year =         "1957",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1957.5221579",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jun 30 16:07:27 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221579",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Kogbetliantz:1957:CEN,
  author =       "E. G. Kogbetliantz",
  title =        "Computation of $ e^n $ for $ - \infty < n < + \infty $
                 Using an Electronic Computer",
  journal =      j-IBM-JRD,
  volume =       "1",
  number =       "2",
  pages =        "110--115",
  month =        apr,
  year =         "1957",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Tue Sep 06 18:04:49 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}

@Article{Lehman:1957:HSD,
  author =       "M. Lehman",
  title =        "High-Speed Digital Multiplication",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-6",
  number =       "3",
  pages =        "204--205",
  month =        sep,
  year =         "1957",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1957.5222025",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jun 30 16:07:34 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222025",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Luke:1957:CLZ,
  author =       "Y. L. Luke",
  title =        "On the Computation of $ \log {Z} $ and $ \arctan {Z}
                 $",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "11",
  number =       "??",
  pages =        "16--18",
  month =        "????",
  year =         "1957",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837",
  bibdate =      "Thu Sep 1 10:16:09 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  ajournal =     "Math. Tables Other Aids Comput.",
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@TechReport{Metze:1957:SPO,
  author =       "G. Metze",
  title =        "A Study of Parallel One's Complement Arithmetic Units
                 with Separate Carry or Borrow Storage",
  type =         "Report",
  number =       "81",
  institution =  "Digital Computer Laboratory, University of Illinois",
  address =      "Urbana, IL, USA",
  pages =        "77",
  year =         "1957",
  bibdate =      "Thu Nov 18 09:07:07 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Flores' book \cite[p. 485]{Flores:1963:LCA} cites this
                 report, and says that its conclusion is that the
                 disadvantages of one's complement arithmetic outweigh
                 the advantages.",
}

@Article{Murphy:1957:PIA,
  author =       "R. W. Murphy",
  title =        "A Positive-Integer Arithmetic for Data Processing",
  journal =      j-IBM-JRD,
  volume =       "1",
  number =       "2",
  pages =        "158--170",
  month =        apr,
  year =         "1957",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.12.0158",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  MRclass =      "68.0X",
  MRnumber =     "18,939d",
  bibdate =      "Tue Sep 11 15:35:33 MDT 2012",
  bibsource =    "http://www.research.ibm.com/journal/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
  URL =          "http://www.research.ibm.com/journal/rd/012/ibmrd0102G.pdf;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392735",
  abstract =     "It is hypothesized that positive numbers suffice for
                 the expression of quantities in accounting. New
                 arithmetic operations are devised that yield
                 non-negative results in computation, and the
                 applicability of these operations to data processing is
                 studied. These operations permit a wide variety of
                 functions to be computed with fewer and less complex
                 steps and imply the feasibility of constructing less
                 complex data-processing machines.",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  reviewer =     "C. C. Gotlieb",
}

@Article{Pawlak:1957:UEN,
  author =       "Z. Pawlak",
  title =        "Use of expansions with a negative basis in the
                 arithmometer of a digital computer",
  journal =      "Bull. Acad. Pol. Sci., Ser. Sci. Tech.",
  volume =       "5",
  number =       "??",
  pages =        "232--236",
  month =        "????",
  year =         "1957",
  bibdate =      "Thu Nov 06 05:56:32 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "negative base",
}

@TechReport{Taylor:1957:CCA,
  author =       "W. Bruce Taylor",
  title =        "{COIN} (Compile-Interpreter): an automatic
                 programming, fixed and floating-point library of
                 subroutines for the {ERA} 1103 computer",
  institution =  "Operations Research Office, Johns Hopkins University",
  address =      "Bethesda, MD, USA",
  pages =        "43",
  year =         "1957",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Staff paper / Johns Hopkins University, Operations
                 Research Office; ORO-SP-32 Staff paper (Johns Hopkins
                 University. Operations Research Office); ORO-SP-32.",
  acknowledgement = ack-nhfb,
  keywords =     "Military art and science --- Data processing.;
                 Military research --- Data processing.",
  remark =       "Cover title. ``Operating under contract with the
                 Department of the Army.'' ``Project COMPLAB.''
                 ``October 1957.'' ORO-SP-32",
}

@Article{Wadel:1957:NBN,
  author =       "L. B. Wadel",
  title =        "Negative base number systems",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-6",
  number =       "??",
  pages =        "123--??",
  month =        jun,
  year =         "1957",
  CODEN =        "IRELAO",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Nov 06 05:53:55 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
  keywords =     "negative base",
}

@Article{Walker:1957:EMA,
  author =       "R. M. Walker and D. E. Rosenheim and P. A. Lewis and
                 A. G. Anderson",
  title =        "An Experimental 50-Megacycle Arithmetic Unit",
  journal =      j-IBM-JRD,
  volume =       "1",
  number =       "3",
  pages =        "257--278",
  month =        jul,
  year =         "1957",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.13.0257",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Tue Sep 11 15:35:35 MDT 2012",
  bibsource =    "http://www.research.ibm.com/journal/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
  URL =          "http://www.research.ibm.com/journal/rd/013/ibmrd0103H.pdf;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392687",
  abstract =     "An experimental 50-megacycle arithmetic unit has been
                 built which performs a repetitive multiplication
                 program and checks the results for errors. The unit
                 uses pulse circuitry which has been developed to
                 perform digital operations at a 50-megacycle
                 pulse-repetition rate. This paper describes the
                 arithmetic system and the circuits which perform the
                 required functions. These circuits include a full
                 binary adder, a phase-locked frequency divider which
                 provides a 3.125-megacycle secondary timing source, a
                 reshaping and retiming circuit using germanium diodes
                 and capacitive storage, a high-speed shift register, a
                 high-speed indicator register, and a binary word
                 generator.\par

                 Various novel features of a digital system operating at
                 these high speeds are described. These include the use
                 of coaxial delay lines for the distribution of signals
                 and as storage elements, and the use of secondary
                 emission tubes in amplifier and multivibrator
                 circuits.\par

                 In a 50-megacycle system the interdependence of the
                 space and time dimensions is marked, and although this
                 introduces problems which are not ordinarily
                 encountered in computing systems, it may be used
                 advantageously to provide features such as the
                 variable-phase clock system used in the arithmetic
                 unit.\par

                 The performance and reliability of the arithmetic unit
                 are discussed as well as the reliability of the
                 components and circuits which make up the system.
                 Although the techniques and circuitry discussed here
                 have been applied only to a relatively simple
                 arithmetic unit, it is felt that they could be useful
                 in a variety of high-speed computing and measurements
                 applications.",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}

@Article{Weibel:1957:EAM,
  author =       "Erich S. Weibel",
  title =        "An Electronic Analog Multiplier Using Carriers",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-6",
  number =       "1",
  pages =        "30--34",
  month =        mar,
  year =         "1957",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1957.5221558",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jun 30 16:07:23 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5221558",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Book{Wilkes:1957:PPE,
  author =       "Maurice V. Wilkes and David J. Wheeler and Stanley
                 Gill",
  title =        "The Preparation of Programs for an Electronic Digital
                 Computer",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Second",
  pages =        "xiv + 238",
  year =         "1957",
  LCCN =         "QA76.5 .W52 1957",
  bibdate =      "Mon Feb 10 09:42:47 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also first edition \cite{Wilkes:1951:PPE}.",
  URL =          "https://b-ok.org/book/3668116/b363ff",
  acknowledgement = ack-nhfb,
  remark-1 =     "According to \cite{Anderson:2019:SAM}, this book
                 discusses the computation of integer population counts
                 on the Electronic Delay Storage Automatic Calculator
                 (EDSAC) computer using a recursive divide-and-conquer
                 algorithm. See also somewhat negative 1958 review by
                 Fernando J. Corbat{\'o}
                 \url{https://doi.org/10.1063/1.3062687}. Floating-point
                 arithmetic is discussed on pages 60, 90--91, and
                 135--137.",
  remark-2 =     "From page 5: ``Each storage location in the EDSAC
                 holds 17 binary digits. In words representing numbers,
                 the binary point is regarded as being to the right of
                 the extreme left-hand digit; this digit (the most
                 significant digit) is used as a sign indicator and is
                 referred to as the sign digit. \ldots{} the capacity of
                 the accumulator is 70 digits; there is, therefore,
                 plenty of room to hold the full 33-digit product of two
                 17-digit numbers. \ldots{} A negative number $-x$
                 (where $O < x \leq 1$) is represented by a $1$ in the
                 sign-digit position, followed by the digits of $(1 -
                 x)$; for example, $1.1100\ldots{}$ represents $-(1 -
                 3/4) = -1/4$. \ldots{} Another way of explaining the
                 representation of negative numbers is to regard the
                 sign digit as an ordinary numerical digit, and to say
                 that $-x$ is stored as the number $(2 - x)$. Note in
                 particular that $1.0000\ldots{}$ represents $-1$.''
                 [Page 59 calls this a {\em True complements}
                 representation, distinguished from one's complement.]",
  remark-3 =     "From page 35: ``The EDSAC has a facility which enables
                 an even-numbered storage location and the following
                 odd-numbered storage to be used as a single storage
                 location holding 35 binary digits.'' [This suggests the
                 word size in 18, not 17 as page 5 suggests. The
                 Wikipedia article on the EDSAC reports: ``The EDSAC's
                 main memory consisted of 1024 locations, though only
                 512 locations were initially installed. Each contained
                 18 bits, but the topmost bit was always unavailable due
                 to timing problems, so only 17 bits were used.'']",
  remark-4 =     "From page 36: ``The multiplier register of the
                 arithmetical unit is of sufficient capacity to hold a
                 long number, and the accumulator is of sufficient
                 capacity to hold the complete (69) binary digit
                 [including the sign bit] product of two long
                 numbers.''",
  remark-5 =     "From page 36: ``In some calculations, long numbers may
                 not provide sufficient precision. In such cases, the
                 programmer may make use of what is known as
                 double-length or double-precision working, in which two
                 long storage locations are used to hold the digits of a
                 single number.'' [this would be a quad-word number
                 holding 69 bits, including the sign bit.].",
  remark-6 =     "From page 60: ``\ldots{} two double-length numbers,
                 each stored in two locations, can be added and the
                 result put in two locations in the store, by means of
                 six orders''.",
  remark-7 =     "From page 90: ``Each number is expressed in the form
                 $a \cdot 10^p$, where $-10 \leq a \leq 10$ and $63 \leq
                 p < 63$ and is represented in the store by $a \cdot
                 2^{-11} + p \cdot 2^{-6}$.''",
  remark-8 =     "From page 91: ``Numbers are expressed in the form $a
                 \cdot 10^p$, where $a$ and $p$ are packed into a single
                 storage location. The number of digits defining $p$ may
                 be varied from 4 to 15 by means of a preset parameter,
                 so that a suitable value for the permissible range of
                 variation of numbers may be selected for a given
                 calculation.''",
  remark-9 =     "From page 91: ``Although the use of floating-point
                 operation can simplify the programmer's task by
                 relieving him of undue preoccupation with scaling, it
                 must not be thought that it solves all his
                 difficulties. In particular, the loss of significant
                 digits resulting from the subtraction of a number from
                 a nearly equal number can have serious consequences
                 unless proper precautions are taken.''",
  tableofcontents = "CHAPTER 1. THE ELEMENTS OF PROGRAM DESIGN / 1 \\
                 1-1 Introduction / 1 \\
                 1-2 Types of automatic computing machine / 1 \\
                 1-3 The EDSAC / 3 \\
                 1-4 Store / 5 \\
                 1-5 Arithmetical unit / 5 \\
                 1-6 Form of numbers in the machine / 5 \\
                 1-7 Form of orders in the machine / 6 \\
                 1-8 Storage of orders / 6 \\
                 1-9 Written form of orders / 7 \\
                 1-10 Some simple examples / 7 \\
                 Exercises A / 9 \\
                 1-11 Jump orders / 9 \\
                 Exercises B / 11 \\
                 1-12 Repeated groups of orders / 11 \\
                 1-13 The use of the B-register / 15 \\
                 Exercises C / 18 \\
                 1-14 Equivalence between orders and numbers;
                 pseudo-orders / 18 \\
                 1-15 Use of the arithmetical unit for constructing or
                 modifying orders / 20 \\
                 1-16 The mix order / 23 \\
                 Exercises D / 24 \\
                 CHAPTER 2. SUBROUTINES / 25 \\
                 2-1 Introduction / 25 \\
                 2-2 Relative numbering of addresses / 25 \\
                 2-3 Internal and external forms of orders / 26 \\
                 2-4 Reading of orders from the input tape / 28 \\
                 2-5 Open and closed subroutines / 29 \\
                 2-6 Entering and leaving a closed subroutine / 29 \\
                 2-7 Closed B subroutines / 30 \\
                 2-8 Closed A subroutines / 31 \\
                 2-9 Use of library subroutines / 32 \\
                 Exercises E / 33 \\
                 2-10 Long numbers / 35 \\
                 2-11 Some further orders in the order code / 36 \\
                 2-12 Scale factors / 38 \\
                 2-13 Control combinations / 39 \\
                 Exercises F / 40 \\
                 2-14 Relative addresses in control combinations / 41
                 \\
                 2-15 Extension of the use of relative addresses / 41
                 \\
                 2-16 Setting of the constants to be added by terminal
                 code letters / 43 \\
                 2-17 Complete table of terminal code letters / 44 \\
                 2-18 Parameters / 45 \\
                 2-19 Preset parameters / 46 \\
                 2-20 Program parameters / 46 \\
                 2-21 Standard procedure for setting preset parameters /
                 46 \\
                 2-22 Interpretive subroutines / 47 \\
                 Exercises G / 49 \\
                 CHAPTER 3. PROGRAMMING FOR OTHER MACHINES / 51 \\
                 3-1 Introduction / 51 \\
                 3-2 Single-address codes / 52 \\
                 3-3 Multi-address codes / 53 \\
                 3-4 Multiplication and division / 56 \\
                 3-5 Source-destination codes / 57 \\
                 3-6 Representation of negative numbers / 59 \\
                 3-7 Miscellaneous facilities / 60 \\
                 3-8 Minimum-access coding / 61 \\
                 3-9 The evaluation of an order code / 63 \\
                 3-10 Use of an auxiliary store / 64 \\
                 CHAPTER 4. INPUT AND OUTPUT / 66 \\
                 4-1 Introduction / 66 \\
                 4-2 Input of numbers / 66 \\
                 4-3 Output of numbers / 67 \\
                 4-4 Input of orders / 69 \\
                 4-5 Recognition of the code letter S / 72 \\
                 4-6 Economy of input and output time / 72 \\
                 4-7 Some features of input systems used with other
                 machines / 73 \\
                 4-8 Punched tape / 73 \\
                 4-9 Punched cards / 75 \\
                 CHAPTER 5. THE LIBRARY OF SUBROUTINES / 80 \\
                 5-1 Introduction / 80 \\
                 5-2 Library catalog / 80 \\
                 5-3 Input subroutines / 81 \\
                 5-4 Output subroutines / 81 \\
                 5-5 Division subroutines / 82 \\
                 5-6 Trigonometric and other functions / 82 \\
                 5-7 The economization of a power series by the use of
                 Chebyshev polynomials / 83 \\
                 5-8 Quadrature / 86 \\
                 5-9 Integration of ordinary differential equations / 87
                 \\
                 5-10 Library subroutines Gl2 and G13: Runge--Kutta
                 processes / 88 \\
                 5-11 The independent variable / 88 \\
                 5-12 Definition of the Runge--Kutta--Gill process / 89
                 \\
                 5-13 Taylor-series method / 90 \\
                 5-14 Interpretive subroutines / 90 \\
                 5-15 Floating-point subroutines / 90 \\
                 CHAPTER 6. DIAGNOSIS OF ERRORS IN PROGRAM / 92 \\
                 6-1 Introduction / 92 \\
                 6-2 Proofreading of programs / 93 \\
                 6-3 Punching / 93 \\
                 6-4 Locating mistakes in a program- / 94 \\
                 6-5 Subroutines for checking programs / 96 \\
                 6-6 The development of a program / 97 \\
                 CHAPTER 7. EXAMPLES OF COMPLETE PROGRAMS FOR THE EDSAC
                 / 99 \\
                 EXAMPLE 1 Calculation of $e^{-\sin x}$ / 99 \\
                 EXAMPLE 2 The evaluation of a definite integral / 102
                 \\
                 EXAMPLE 3 Integration of an ordinary differential
                 equation / 108 \\
                 EXAMPLE 4 Evaluation of a Fourier transform / 113 \\
                 EXAMPLE 5 Evaluation of a definite integral / 118 \\
                 CHAPTER 8. AUTOMATIC PROGRAMMING / 126 \\
                 8-1 Introduction / 126 \\
                 8-2 Conversion versus interpretation / 127 \\
                 8-3 Assembly of a program / 127 \\
                 8-4 Floating addresses / 129 \\
                 8-5 Formula recognition / 136 \\
                 Part Two: SPECIFICATIONS OF EDSAC LIBRARY SUBROUTINES /
                 139 \\
                 CATEGORY A. Subroutines to carry out floating-point
                 arithmetic / 140 \\
                 CATEGORY B. Subroutines to perform arithmetical
                 operations on complex numbers / 142 \\
                 CATEGORY C. Error-diagnosis subroutines / 144 \\
                 CATEGORY D. Division subroutines / 146 \\
                 CATEGORY E. Exponential subroutines / 148 \\
                 CATEGORY F. General subroutines relating to functions /
                 148 \\
                 CATEGORY G. Subroutines for the integration of
                 differential equations / 150 \\
                 CATEGORY L. Subroutines for evaluating logarithms / 153
                 \\
                 CATEGORY M. Miscellaneous subroutines / 154 \\
                 CATEGORY N. Operations on double-length numbers / 156
                 \\
                 CATEGORY P. Print subroutines / 158 \\
                 CATEGORY Q. Quadrature subroutines / 162 \\
                 CATEGORY R. Input subroutines / 164 \\
                 CATEGORY s. Subroutines for evaluating fractional
                 powers / 168 \\
                 CATEGORY T. Subroutines for calculating trigonometric
                 functions / 169 \\
                 CATEGORY Z. Post-mortem routines / 170 \\
                 PART THREE: PROGRAMS OF SELECTED EDSAC LIBRARY
                 SUBROUTINES / 173 \\
                 APPENDIX 1. Input and output codes of the EDSAC / 212
                 \\
                 APPENDIX 2. Order code and controls of the EDSAC / 214
                 \\
                 APPENDIX 3. The initial input routine of the EDSAC /
                 218 \\
                 APPENDIX 4. Control combinations / 221 \\
                 APPENDIX 5. Specimen solutions to programming exercises
                 / 223 \\
                 BIBLIOGRAPHY / 233 \\
                 INDEX / 237",
}

@TechReport{Anonymous:1958:ARM,
  author =       "Anonymous",
  title =        "Analysis and research memorandum 294",
  type =         "{AR} Memo",
  number =       "294 (AD 207929)",
  institution =  "Massachusetts Institute of Technology, Naval
                 Supersonic Laboratory",
  address =      "Cambridge, MA, USA",
  pages =        "7",
  day =          "23",
  month =        oct,
  year =         "1958",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Error functions.; Floating-point arithmetic.",
}

@Article{Bemer:1958:MMS,
  author =       "Robert W. Bemer",
  title =        "A Machine Method for Square-Root Computation",
  journal =      j-CACM,
  volume =       "1",
  number =       "1",
  pages =        "6--7",
  month =        jan,
  year =         "1958",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 15 18:35:46 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Article{Bemer:1958:SMC,
  author =       "R. W. Bemer",
  title =        "A Subroutine Method for Calculating Logarithms",
  journal =      j-CACM,
  volume =       "1",
  number =       "5",
  pages =        "5--7",
  month =        may,
  year =         "1958",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 1 10:16:09 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Article{Couleur:1958:BBD,
  author =       "J. F. Couleur",
  title =        "{BIDEC} --- a Binary-to-Decimal or Decimal-to-Binary
                 Converter",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-7",
  pages =        "313--316",
  year =         "1958",
  CODEN =        "IRELAO",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Fri Nov 28 16:28:12 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
  keywords =     "decimal floating-point arithmetic",
}

@Article{Delury:1958:CAN,
  author =       "Daniel B. Delury",
  title =        "Computation with Approximate Numbers",
  journal =      j-MATH-TEACH,
  volume =       "51",
  pages =        "521--530",
  month =        nov,
  year =         "1958",
  ISSN =         "0025-5769 (print), 2330-0582 (electronic)",
  bibdate =      "Fri Nov 28 11:47:47 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Mathematics Teacher",
}

@Article{Ershov:1958:PAO,
  author =       "Andrei P. Ershov",
  title =        "On Programming of Arithmetic Operations",
  journal =      j-CACM,
  volume =       "1",
  number =       "8",
  pages =        "3--6",
  month =        aug,
  year =         "1958",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Wed Jul 14 15:48:21 MDT 2004",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Ershov58;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "Ershov58",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Ershov58",
}

@Article{Gill:1958:BFH,
  author =       "S. Gill",
  title =        "A Binary Form of {Horner}'s Method",
  journal =      j-COMP-J,
  volume =       "1",
  number =       "2",
  pages =        "84--86",
  month =        jul,
  year =         "1958",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/1.2.84",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:47:23 MST 2012",
  bibsource =    "http://comjnl.oxfordjournals.org/content/1/2.toc;
                 https://www.math.utah.edu/pub/tex/bib/compj1950.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_02/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/1/2/84.full.pdf+html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_02/010084.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_02/tiff/84.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_02/tiff/85.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_02/tiff/86.tif",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Gower:1958:NIM,
  author =       "J. C. Gower",
  title =        "A Note on an Iterative Method for Root Extraction",
  journal =      j-COMP-J,
  volume =       "1",
  pages =        "142--143",
  year =         "1958",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Thu Sep 15 18:36:55 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  xxmonth =      "(none)",
  xxnumber =     "(none)",
}

@Article{Hammer:1958:PST,
  author =       "Franz Hammer",
  title =        "{Nicht Pascal sondern der T{\"u}binger Professor
                 Wilhelm Schickard erfand die Rechenmaschine!}.
                 ({German}) [{Not Pascal}, but the {T{\"u}bingen}
                 professor {William Schickard}, invented the
                 calculator!]",
  journal =      "{B{\"u}romarkt}",
  volume =       "20",
  number =       "??",
  pages =        "1023--1025",
  month =        "????",
  year =         "1958",
  ISSN =         "0007-3148",
  ISSN-L =       "0007-3148",
  bibdate =      "Sat Jul 27 11:05:26 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/scicontext.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Kogbetliantz:1958:CANa,
  author =       "E. G. Kogbetliantz",
  title =        "Computation of Arctan {$N$} for $ - \infty < {N} < +
                 \infty $ Using an Electronic Computer",
  journal =      j-IBM-JRD,
  volume =       "2",
  number =       "1",
  pages =        "43--53",
  month =        jan,
  year =         "1958",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Thu Sep 1 10:16:10 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}

@Article{Kogbetliantz:1958:CANb,
  author =       "E. G. Kogbetliantz",
  title =        "Computation of Arcsin {$N$} for $ 0 < {N} < 1 $ Using
                 an Electronic Computer",
  journal =      j-IBM-JRD,
  volume =       "2",
  number =       "3",
  pages =        "218--222",
  month =        jul,
  year =         "1958",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Thu Sep 1 10:16:10 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}

@Article{Metropolis:1958:SDC,
  author =       "N. Metropolis and R. L. Ashenhurst",
  title =        "Significant Digit Computer Arithmetic",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-7",
  number =       "4",
  pages =        "265--267",
  month =        dec,
  year =         "1958",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1958.5222657",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Wed Feb 14 19:23:38 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222657",
  abstract =     "The usual floating point arithmetic makes error
                 analysis difficult. This paper describes an alternative
                 system which offers a means of analyzing floating point
                 calculations more effectively and which also possesses
                 certain advantages from an equipment standpoint.",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
  keywords =     "MANIAC III",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Robertson:1958:NCDa,
  author =       "J. E. Robertson",
  title =        "A new class of digital division methods",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-7",
  number =       "3",
  pages =        "88--92",
  month =        sep,
  year =         "1958",
  CODEN =        "IRELAO",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Robertson:1958:NCDb,
  author =       "James E. Robertson",
  title =        "A New Class of Digital Division Methods",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-7",
  number =       "3",
  pages =        "218--222",
  month =        sep,
  year =         "1958",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1958.5222579",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jul 14 15:56:43 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222579",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Schmid:1958:TFQ,
  author =       "Hermann Schmid",
  title =        "A Transistorized Four-Quadrant Time-Division
                 Multiplier with an Accuracy of 0.1 Per Cent",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-7",
  number =       "1",
  pages =        "41--47",
  month =        mar,
  year =         "1958",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1958.5222094",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jul 14 15:56:43 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222094",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Sisson:1958:IDR,
  author =       "Roger L. Sisson",
  title =        "An Improved Decimal Redundancy Check",
  journal =      j-CACM,
  volume =       "1",
  number =       "5",
  pages =        "10--12",
  month =        may,
  year =         "1958",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 07:22:12 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Sisson58;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "As more emphasis is placed on improving the accuracy
                 of data fed into automatic computing systems, more
                 emphasis will be placed on redundancy checking of
                 predictable fields within the input. Two systems (at
                 least) of checking a field of decimal digits have been
                 proposed. In both of these it is assumed that the field
                 to be checked is all numeric and that the redundancy
                 must be of only one digit.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "decimal floating-point arithmetic",
  oldlabel =     "Sisson58",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sisson58",
}

@Article{Tocher:1958:TMD,
  author =       "K. D. Tocher",
  title =        "Techniques of Multiplication and Division for
                 Automatic Binary Computers",
  journal =      j-QUART-J-MECH-APPLIED-MATH,
  volume =       "11",
  number =       "3",
  pages =        "364--384",
  month =        "????",
  year =         "1958",
  CODEN =        "QJMMAV",
  ISSN =         "0033-5614 (print), 1464-3855 (electronic)",
  ISSN-L =       "0033-5614",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  fjournal =     "Quarterly Journal of Mechanics and Applied
                 Mathematics",
  journal-URL =  "http://qjmam.oxfordjournals.org/content/by/year",
}

@Article{Wadey:1958:TSR,
  author =       "W. G. Wadey",
  title =        "Two Square-Root Approximations",
  journal =      j-CACM,
  volume =       "1",
  number =       "11",
  pages =        "13--14",
  month =        nov,
  year =         "1958",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Wed Jul 14 15:48:22 MDT 2004",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm1.html#Wadey58;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "Wadey58",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Wadey58",
}

@Article{Ashenhurst:1959:UFP,
  author =       "Robert L. Ashenhurst and Nicholas Metropolis",
  title =        "Unnormalized Floating Point Arithmetic",
  journal =      j-J-ACM,
  volume =       "6",
  number =       "3",
  pages =        "415--428",
  month =        jul,
  year =         "1959",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/320986.320996",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  MRclass =      "68.00",
  MRnumber =     "MR0105833 (21 \#4568)",
  MRreviewer =   "H. H. Goldstine",
  bibdate =      "Fri Dec 08 13:06:24 1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jacm.bib",
  ZMnumber =     "0121.12102",
  abstract =     "Algorithms for floating point computer arithmetic are
                 described, in which fractional parts are not subject to
                 the usual normalization convention. These algorithms
                 give results in a form which furnishes some indication
                 of their degree of precision. An analysis of one-stage
                 error propagation is developed for each operation; a
                 suggested statistical model for long-run error
                 propagation is also set forth.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Association for Computing Machinery",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}

@Article{Buchholz:1959:FFC,
  author =       "Wilfried Buchholz",
  title =        "Fingers or Fists? (The Choice of Decimal or Binary
                 Representation)",
  journal =      j-CACM,
  volume =       "2",
  number =       "12",
  pages =        "3--11",
  month =        "????",
  year =         "1959",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:28:45 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Buchholz59;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "decimal floating-point arithmetic",
  oldlabel =     "Buchholz59",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Buchholz59",
  xxnote =       "Check author first name: article has W. Buchholz; I
                 think it should be Werner, not Wilfried.",
}

@Article{Carr:1959:EAF,
  author =       "John W. {Carr III}",
  title =        "Error Analysis in Floating Point Arithmetic",
  journal =      j-CACM,
  volume =       "2",
  number =       "5",
  pages =        "10--15",
  month =        may,
  year =         "1959",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Wed Jul 14 15:48:23 MDT 2004",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Carr59a;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "Carr59a",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Carr59a",
}

@InCollection{Carr:1959:PC,
  author =       "John W. {Carr III}",
  editor =       "Eugene M. Grabbe and Simon Ramo and Dean E.
                 Wooldridge",
  booktitle =    "Handbook of Automation, Computation, and Control",
  title =        "Programming and Coding",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  bookpages =    "????",
  year =         "1959",
  LCCN =         "TJ213 .G72",
  bibdate =      "Fri Aug 20 08:41:16 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Chapter 2.",
  acknowledgement = ack-nhfb,
  remark =       "1958--1961: Volume 1. Control fundamentals. Volume 2.
                 Computers and data processing. Volume 3. Systems and
                 components. Cited in \cite{Sterbenz:1974:FPC}.",
  subject =      "automation; mathematics; computers; operations
                 research",
}

@Article{Daggett:1959:DBC,
  author =       "D. H. Daggett",
  title =        "Decimal--Binary Conversions in {CORDIC}",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-8",
  number =       "5",
  pages =        "335--339",
  month =        sep,
  year =         "1959",
  CODEN =        "IRELAO",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Sep 08 08:14:00 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
  keywords =     "decimal floating-point arithmetic",
}

@Article{Ercoli:1959:BAD,
  author =       "Paolo Ercoli and Roberto Vacca",
  title =        "Binary Arithmetic for Discretely Variable Word Length
                 in a Serial Computer",
  journal =      j-CACM,
  volume =       "2",
  number =       "4",
  pages =        "13--15",
  month =        apr,
  year =         "1959",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Wed Jul 14 15:48:22 MDT 2004",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#ErcoliV59;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "ErcoliV59",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/ErcoliV59",
}

@Article{Forsythe:1959:RNR,
  author =       "George E. Forsythe",
  title =        "Reprint of a Note on Rounding-Off Errors",
  journal =      j-SIAM-REVIEW,
  volume =       "1",
  number =       "1",
  pages =        "66--67",
  month =        jan,
  year =         "1959",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1001011",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "65.00",
  MRnumber =     "MR0099119 (20 \#5563)",
  bibdate =      "Thu Mar 27 09:04:24 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/1/1;
                 https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  ZMnumber =     "0168.14002",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  keywords =     "numerical analysis; random rounding-off procedure",
  onlinedate =   "January 1959",
  received =     "7 February 1958",
  remark =       "From a footnote on the cover page: ``This note was
                 written in June 1950 at the National Bureau of
                 Standards, Los Angeles, and a few copies were
                 distributed in multilithed form by that organization as
                 an appendix to a reproduction of a well-known article
                 by Rademacher [1]. The note was abstracted in Math.
                 Reviews, Vol. 12 (1951), p. 208. Because he receives
                 frequent requests for copies of the note, which are
                 unavailable, the author has asked the editors to
                 reprint it in essentially its original form.''",
}

@Article{Garner:1959:RMS,
  author =       "Harvey L. Garner",
  title =        "A Ring Model for the Study of Multiplication for
                 Complement Codes",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-8",
  number =       "1",
  pages =        "25--30",
  month =        mar,
  year =         "1959",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1959.5222757",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jul 14 15:56:44 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222757",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Garner:1959:RNS,
  author =       "Harvey L. Garner",
  title =        "The Residue Number System",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-8",
  number =       "2",
  pages =        "140--147",
  month =        jun,
  year =         "1959",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1959.5219515",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jul 14 15:56:44 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219515",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@InProceedings{Gray:1959:NFP,
  author =       "H. L. Gray and C. Harrison",
  booktitle =    "Proceedings of the Eastern Joint Computer Conference,
                 Boston, {MA}, December 1--3, 1959",
  title =        "Normalized floating-point arithmetic with an index of
                 significance",
  volume =       "16",
  publisher =    pub-AFIPS,
  address =      pub-AFIPS:adr,
  pages =        "244--248",
  year =         "1959",
  LCCN =         "TK7885.A1 J6",
  bibdate =      "Tue Oct 09 09:43:31 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Henrici:1959:TES,
  author =       "Peter Henrici",
  editor =       "????",
  booktitle =    "Proceedings of the International Conference on
                 Information Processing, {UNESCO}",
  title =        "Theoretical and Experimental Studies on the
                 Accumulation of Error in the Numerical Solution of
                 Initial Value Problems for Systems of Ordinary
                 Differential Equations",
  publisher =    "????",
  address =      "????",
  pages =        "36--43",
  year =         "1959",
  LCCN =         "????",
  bibdate =      "Fri Aug 20 09:11:32 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Kogbetliantz:1959:CSC,
  author =       "E. G. Kogbetliantz",
  title =        "Computation of $ \sin {N} $, $ \cos {N} $, and {$M$
                 th} Root of {$N$} Using an Electronic Computer",
  journal =      j-IBM-JRD,
  volume =       "3",
  number =       "2",
  pages =        "147--152",
  month =        apr,
  year =         "1959",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Thu Sep 1 10:15:56 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}

@Article{Lucal:1959:AOD,
  author =       "Harold M. Lucal",
  title =        "Arithmetic Operations for Digital Computers Using a
                 Modified Reflected Binary Code",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-8",
  number =       "4",
  pages =        "449--458",
  month =        dec,
  year =         "1959",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1959.5222057",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jul 14 15:56:45 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5222057",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Muller:1959:CMG,
  author =       "Mervin E. Muller",
  title =        "A Comparison of Methods for Generating Normal Deviates
                 on Digital Computers",
  journal =      j-J-ACM,
  volume =       "6",
  number =       "3",
  pages =        "376--383",
  month =        jul,
  year =         "1959",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Tue Nov 1 09:33:26 1994",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/Pre.1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  descriptors =  "RVG",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Pawlak:1959:EDC,
  author =       "Z. Pawlak",
  title =        "An electronic digital computer based on the `$ - 2 $'
                 system",
  journal =      "Bull. Acad. Pol. Sci., Ser. Sci. Tech.",
  volume =       "7",
  number =       "??",
  pages =        "713--722",
  month =        "????",
  year =         "1959",
  bibdate =      "Thu Nov 06 05:58:31 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "negative base",
}

@Article{Pfeiffer:1959:FQM,
  author =       "Paul E. Pfeiffer",
  title =        "A Four-Quadrant Multiplier Using Triangular Waves,
                 Diodes, Resistors, and Operational Amplifiers",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-8",
  number =       "2",
  pages =        "222--227",
  month =        jun,
  year =         "1959",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1959.5219526",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jul 14 15:56:45 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219526",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Rothstein:1959:RBN,
  author =       "Jerome Rothstein",
  title =        "Residues of Binary Numbers Modulo Three",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-8",
  number =       "2",
  pages =        "229--229",
  month =        jun,
  year =         "1959",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1959.5219529",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jul 14 15:56:45 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219529",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Sarafyan:1959:NMC,
  author =       "Diran Sarafyan",
  title =        "A New Method of Computation of Square Roots Without
                 Using Division",
  journal =      j-CACM,
  volume =       "2",
  number =       "11",
  pages =        "23--24",
  month =        nov,
  year =         "1959",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Wed Jul 14 15:48:24 MDT 2004",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sarafyan59;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See comments \cite{Traub:1960:CNM}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "Sarafyan59",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sarafyan59",
}

@Article{Sheridan:1959:ATC,
  author =       "Peter B. Sheridan",
  title =        "The Arithmetic Translator Compiler of the {IBM FORTRAN
                 Automatic Coding System}",
  journal =      j-CACM,
  volume =       "2",
  number =       "2",
  pages =        "9--21",
  month =        feb,
  year =         "1959",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Wed Jul 14 15:48:22 MDT 2004",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Sheridan59;
                 http://ei.cs.vt.edu/~cs4304/bibliography.html;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "Sheridan59",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Sheridan59",
}

@Article{Strachey:1959:TSR,
  author =       "C. Strachey",
  title =        "On taking the square root of a complex number",
  journal =      j-COMP-J,
  volume =       "2",
  number =       "2",
  pages =        "89--89",
  month =        jul,
  year =         "1959",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/2.2.89",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:55:11 MDT 2000",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/020089.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_02/Issue_02/tiff/89.tif",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  remark =       "This 1/4-page note comments that if $ \sqrt {x + i y}
                 = u + i v $, then $ u = \sqrt {[\sqrt {x^2 + y^2} + x]
                 / 2} $ and $ v = \sqrt {[\sqrt {x^2 + y^2} - x] / 2} $,
                 where both inner and outer square roots should be
                 evaluated to twice working precision.",
}

@Article{Taranto:1959:BCF,
  author =       "Donald Taranto",
  title =        "Binary Conversion, with Fixed Decimal Precision, of a
                 Decimal Fraction",
  journal =      j-CACM,
  volume =       "2",
  number =       "7",
  pages =        "27--27",
  month =        jul,
  year =         "1959",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 07:25:37 MST 2001",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm2.html#Taranto59;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "decimal floating-point arithmetic",
  oldlabel =     "Taranto59",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Taranto59",
}

@Article{Volder:1959:CTC,
  author =       "Jack E. Volder",
  title =        "The {CORDIC} Trigonometric Computing Technique",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-8",
  number =       "5",
  pages =        "330--334",
  month =        sep,
  year =         "1959",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1959.5222693",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Sep 1 10:15:31 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Wensley:1959:CNA,
  author =       "J. H. Wensley",
  title =        "A Class of Non-Analytical Iterative Processes",
  journal =      j-COMP-J,
  volume =       "1",
  number =       "4",
  pages =        "163--167",
  month =        jan,
  year =         "1959",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/1.4.163",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:47:23 MST 2012",
  bibsource =    "Compiler/semantics.bib;
                 http://comjnl.oxfordjournals.org/content/1/4.toc;
                 https://www.math.utah.edu/pub/tex/bib/compj1950.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/1/4/163.full.pdf+html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/010163.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/163.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/164.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/165.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/166.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_04/tiff/167.tif",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  remark =       "The author describes digit-at-a-time algorithms for
                 divide, square root, fourth root, inverse cosine,
                 inverse tangent, inverse Jacobi elliptic function, and
                 logarithm.",
}

@Article{Wilkinson:1959:EZIa,
  author =       "J. H. Wilkinson",
  title =        "The evaluation of the zeros of ill-conditioned
                 polynomials. {I}",
  journal =      j-NUM-MATH,
  volume =       "1",
  pages =        "150--166",
  month =        dec,
  year =         "1959",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01386381",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65.00",
  MRnumber =     "MR0109435 (22 \#321)",
  MRreviewer =   "H. Rutishauser",
  bibdate =      "Mon Oct 18 01:28:20 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Wilkinson:1959:EZIb,
  author =       "J. H. Wilkinson",
  title =        "The evaluation of the zeros of ill-conditioned
                 polynomials. {II}",
  journal =      j-NUM-MATH,
  volume =       "1",
  pages =        "167--180",
  month =        dec,
  year =         "1959",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01386382",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65.00",
  MRnumber =     "MR0109435 (22 \#321)",
  MRreviewer =   "H. Rutishauser",
  bibdate =      "Mon Oct 18 01:28:20 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@MastersThesis{Young:1959:SSM,
  author =       "John Mackay Young",
  title =        "A study of some methods of numerical integration using
                 floating point arithmetic",
  type =         "Thesis ({M.S. in Mathematics})",
  school =       "Texas A.\&M. College",
  address =      "College Station, TX, USA",
  pages =        "50",
  year =         "1959",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Bockstaele:1960:NFA,
  author =       "P. Bockstaele",
  title =        "Notes on the First Arithmetics Printed in {Dutch} and
                 {English}",
  journal =      j-ISIS,
  volume =       "51",
  number =       "3",
  pages =        "315--321",
  month =        sep,
  year =         "1960",
  CODEN =        "ISISA4",
  ISSN =         "0021-1753 (print), 1545-6994 (electronic)",
  ISSN-L =       "0021-1753",
  bibdate =      "Tue Jul 30 21:28:03 MDT 2013",
  bibsource =    "http://www.jstor.org/action/showPublication?journalCode=isis;
                 http://www.jstor.org/stable/i302265;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/isis1960.bib",
  URL =          "http://www.jstor.org/stable/226510",
  acknowledgement = ack-nhfb,
  fjournal =     "Isis",
  journal-URL =  "http://www.jstor.org/journal/isis",
}

@Article{Brown:1960:EDC,
  author =       "David T. Brown",
  title =        "Error Detecting and Correcting Binary Codes for
                 Arithmetic Operations",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-9",
  number =       "3",
  pages =        "333--337",
  month =        sep,
  year =         "1960",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1960.5219855",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jul 14 15:34:12 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219855",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Cohen:1960:EAF,
  author =       "Eckford Cohen",
  title =        "The elementary arithmetical functions",
  journal =      j-SCRIPTA-MATH,
  volume =       "25",
  number =       "??",
  pages =        "221--228",
  month =        "????",
  year =         "1960",
  ISSN =         "0036-9713",
  ISSN-L =       "0036-9713",
  MRclass =      "10.00",
  MRnumber =     "118694",
  MRreviewer =   "H. Bergstr{\"{o}}m",
  bibdate =      "Thu Oct 26 11:15:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
  ZMnumber =     "0116.27101",
  acknowledgement = ack-nhfb,
  ajournal =     "Scripta Math.",
  fjournal =     "Scripta Mathematica: A Quarterly Journal Devoted to
                 the Philosophy, History, and Expository Treatment of
                 Mathematics",
  xxpages =      "221--227",
  ZBmath =       "3189455",
}

@Article{Croy:1960:IAD,
  author =       "John E. Croy",
  title =        "Improved Arrangement of a Decimal Multiplier",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-9",
  number =       "2",
  pages =        "263--263",
  month =        jun,
  year =         "1960",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1960.5219830",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jul 14 15:34:11 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219830",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Ercoli:1960:LEE,
  author =       "Paolo Ercoli",
  title =        "Letter to the {Editor}: {Errors} Due to Overflow in
                 Arithmetic Operations",
  journal =      j-CACM,
  volume =       "3",
  number =       "12",
  pages =        "A9--A9",
  month =        dec,
  year =         "1960",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:29 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Ercoli:1957:EDO}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Article{Gurzi:1960:HSM,
  author =       "Fred Gurzi",
  title =        "A High-Speed Multiplication Process for Digital
                 Computers",
  journal =      j-CACM,
  volume =       "3",
  number =       "4",
  pages =        "241--245",
  month =        apr,
  year =         "1960",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:26 MST 2005",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Gurzi60;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "Gurzi60",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Gurzi60",
}

@TechReport{Jensen:1960:CIF,
  author =       "B. A. Jensen",
  title =        "Coding instructions for floating point trigonometric,
                 inverse trigonometric hyperbolic and exponential
                 functions",
  type =         "Group report",
  number =       "30G-0009",
  institution =  "Massachusetts Institute of Technology, Lincoln
                 Laboratory",
  address =      "Lexington, MA, USA",
  pages =        "7",
  year =         "1960",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Trigonometrical functions --- Computer programs.",
  remark =       "Cover title. ``Millstone Hill Radar Station.'' ``1
                 November 1960.'' Air Force Contract",
}

@Article{Kanner:1960:NUA,
  author =       "Herbert Kanner",
  title =        "A Note on the Use of the Abacus in Number Conversion",
  journal =      j-CACM,
  volume =       "3",
  number =       "3",
  pages =        "167--167",
  month =        mar,
  year =         "1960",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/367149.367166",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:26 MST 2005",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Kanner60;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Conversion of integers in both directions between the
                 base ten and any desired base can be accomplished with
                 remarkable simplicity by use of the abacus. In fact,
                 the conversion procedures are far more cumbersome on
                 the electric desk calculator, for reasons which will be
                 apparent.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "number base conversion",
  oldlabel =     "Kanner60",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Kanner60",
}

@Article{Knuth:1960:INS,
  author =       "Donald E. Knuth",
  title =        "An Imaginary Number System",
  journal =      j-CACM,
  volume =       "3",
  number =       "4",
  pages =        "245--247",
  month =        apr,
  year =         "1960",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.99",
  MRnumber =     "23\#B554",
  MRreviewer =   "C. B. Haselgrove",
  bibdate =      "Fri Nov 25 18:19:26 MST 2005",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Knuth60;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database",
  note =         "Errata, {\sl Commun\-i\-ca\-tions of the ACM\/ \bf 4}
                 (August 1961), 355 \cite{Knuth:1961:EIN}. See
                 \cite{Nadler:1961:DSR} for extension to division and
                 square root.",
  abstract =     "For centuries the decimal number system reigned
                 supreme, except, perhaps, among the Mayan Indians,
                 until the advent of digital computers brought the
                 binary and octal systems into the limelight. This paper
                 introduces another number system which may prove useful
                 for manipulating complex numbers on machines.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "Knuth60",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Knuth60",
  ZMreviewer =   "C. B. Haselgrove",
}

@Article{Lowan:1960:PREa,
  author =       "Arnold N. Lowan",
  title =        "On the Propagation of Round-Off Errors in the
                 Numerical Integration of the Heat Equation",
  journal =      j-MATH-COMPUT,
  volume =       "14",
  number =       "70",
  pages =        "139--146",
  month =        apr,
  year =         "1960",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Lowan:1960:PREb,
  author =       "Arnold N. Lowan",
  title =        "On the Propagation of Round-Off Errors in the
                 Numerical Treatment of the Wave Equation",
  journal =      j-MATH-COMPUT,
  volume =       "14",
  number =       "71",
  pages =        "223--228",
  month =        jul,
  year =         "1960",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Pawlak:1960:ODC,
  author =       "Z. Pawlak",
  title =        "The organization of a digital computer based on the `$
                 - 2 $' system",
  journal =      "Bull. Acad. Pol. Sci., Ser. Tech. Sci.",
  volume =       "8",
  number =       "??",
  pages =        "253--258",
  month =        "????",
  year =         "1960",
  bibdate =      "Thu Nov 06 06:00:08 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "negative base",
}

@Article{Perlin:1960:HPC,
  author =       "I. E. Perlin and J. R. Garrett",
  title =        "High Precision Calculation of $ \operatorname {Arcsin}
                 x $, $ \operatorname {Arccos} x $, and $ \operatorname
                 {Arctan} x $ (in {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "14",
  number =       "71",
  pages =        "270--274",
  month =        jul,
  year =         "1960",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Perry:1960:CBF,
  author =       "C. Perry",
  title =        "Conversion between floating point representations",
  journal =      j-CACM,
  volume =       "3",
  year =         "1960",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "352.68.00",
  MRnumber =     "22\#8714",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Article{Pope:1960:MPA,
  author =       "D. A. Pope and M. L. Stein",
  title =        "Multiple Precision Arithmetic",
  journal =      j-CACM,
  volume =       "3",
  number =       "12",
  pages =        "652--654",
  month =        dec,
  year =         "1960",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@InCollection{Reitwiesner:1960:BA,
  author =       "G. W. Reitwiesner",
  title =        "Binary arithmetic",
  crossref =     "Alt:1960:AC",
  pages =        "231--308",
  year =         "1960",
  bibdate =      "Sat May 18 14:36:56 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Sarafyan:1960:DCS,
  author =       "Diran Sarafyan",
  title =        "Divisionless computation of square roots through
                 continued squaring",
  journal =      j-CACM,
  volume =       "3",
  number =       "5",
  pages =        "319--321",
  month =        may,
  year =         "1960",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.00",
  MRnumber =     "22\#8639",
  bibdate =      "Fri Nov 25 18:19:26 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\sqrt(x)$; elementary functions",
  ZMreviewer =   "M. Lotkin",
}

@Article{Silver:1960:LER,
  author =       "Roland Silver",
  title =        "Letter to the {Editor}: Rounding in Floating-Point
                 Arithmetic",
  journal =      j-CACM,
  volume =       "3",
  number =       "12",
  pages =        "A9--A9",
  month =        dec,
  year =         "1960",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:29 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "floating-point arithmetic; rounding errors",
}

@Article{Sklansky:1960:CSA,
  author =       "J. Sklansky",
  title =        "Conditional Sum Addition Logic",
  journal =      j-TRANS-IRE,
  volume =       "EC-9",
  number =       "2",
  pages =        "226--230",
  month =        jun,
  year =         "1960",
  bibdate =      "Fri Nov 09 19:17:08 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Transactions of the IRE",
}

@Article{Traub:1960:CNM,
  author =       "J. F. Traub",
  title =        "Comments on a recent paper [{``A New Method of
                 Computation of Square Roots Without Using
                 Division''}]",
  journal =      j-CACM,
  volume =       "3",
  number =       "2",
  pages =        "86--86",
  month =        feb,
  year =         "1960",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:25 MST 2005",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Traub60;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Sarafyan:1959:NMC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "Traub60",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Traub60",
}

@Article{Wadey:1960:FA,
  author =       "W. G. Wadey",
  title =        "Floating-Point Arithmetics",
  journal =      j-J-ACM,
  volume =       "7",
  number =       "2",
  pages =        "129--139",
  month =        apr,
  year =         "1960",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  MRclass =      "65.00 (68.00)",
  MRnumber =     "22\#6090",
  bibdate =      "Fri Dec 08 14:44:46 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Three types of floating-point arithmetics with error
                 control are discussed and compared with conventional
                 floating-point arithmetic. General multiplication and
                 division shift criteria are derived (for any base) for
                 Metropolis-style arithmetics. The limitations and most
                 suitable range of application for each arithmetic are
                 discussed.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
  reviewer =     "C. B. Haselgrove",
  xxmonth =      "none",
  xxnumber =     "none",
}

@Article{Wilkinson:1960:EAF,
  author =       "J. H. Wilkinson",
  title =        "Error Analysis of Floating-Point Computation",
  journal =      j-NUM-MATH,
  volume =       "2",
  pages =        "319--340",
  month =        dec,
  year =         "1960",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65.00",
  MRnumber =     "MR0116477 (22 \#7264)",
  MRreviewer =   "C. B. Haselgrove",
  bibdate =      "Fri May 14 17:18:08 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Amble:1961:AFP,
  author =       "O. Amble and Jan V. Garwick",
  title =        "On the Accuracy of Floating Point Computers {[BIT {\bf
                 1}(2), 1961, pp. 87--88]}",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "1",
  number =       "3",
  pages =        "220--222",
  month =        sep,
  year =         "1961",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01933434",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:07 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Garwick:1961:AFP,Garwick:1961:RAF}.",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=3&spage=220",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point accuracy; floating-point arithmetic",
  xxpages =      "220--221??",
}

@TechReport{Anonymous:1961:MCM,
  author =       "Anonymous",
  title =        "Modern Computing Methods",
  type =         "Notes on Applied Science",
  number =       "16",
  institution =  "National Physical Laboratory",
  address =      "Her Majesty's Stationery Office, London",
  year =         "1961",
  bibdate =      "Fri Aug 20 10:05:25 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Avizienis:1961:SDN,
  author =       "Algirdas Avi{\v{z}}ienis",
  title =        "Signed-Digit Number Representations for Fast Parallel
                 Arithmetic",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-10",
  number =       "3",
  pages =        "389--400",
  month =        sep,
  year =         "1961",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1961.5219227",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jul 14 14:45:04 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219227",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Cheney:1961:DCB,
  author =       "Philip Warren Cheney",
  title =        "A Digital Correlator Based on the Residue Number
                 System",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-10",
  number =       "1",
  pages =        "63--70",
  month =        mar,
  year =         "1961",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1961.5219154",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jul 14 14:45:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219154",
  abstract =     "A system design for a digital correlator based on the
                 application of the residue number system for
                 computation is presented. Areas of investigation
                 include sampling, analog-to-residue conversion, logical
                 design of the arithmetic units, residue-to-analog
                 conversion, and modes of operation of the proposed
                 digital correlator. The advantages of speed of
                 computation and simplicity of logic due to the use of a
                 residue number system are shown to result in a
                 significantly faster and simpler system than if a
                 conventional number system were used. The resulting
                 digital correlator is designed for megacycle sampling
                 and computation with a 0.1 per cent system precision.",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Cheney:1961:TNA,
  author =       "E. W. Cheney and H. L. Loeb",
  title =        "Two new algorithms for rational approximation",
  journal =      j-NUM-MATH,
  volume =       "3",
  number =       "1",
  pages =        "72--75",
  month =        dec,
  year =         "1961",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01386002",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sun Oct 17 19:01:15 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Clarkson:1961:DMI,
  author =       "W. K. Clarkson",
  title =        "A Divisionless Method of Integer Conversion",
  journal =      j-CACM,
  volume =       "4",
  number =       "7",
  pages =        "315--316",
  month =        jul,
  year =         "1961",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 08:14:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Article{Cox:1961:NMP,
  author =       "Albert G. Cox and H. A. Luther",
  title =        "A Note on Multiple Precision Arithmetic",
  journal =      j-CACM,
  volume =       "4",
  number =       "8",
  pages =        "353--353",
  month =        aug,
  year =         "1961",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/366678.366693",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Sat Dec 03 14:07:44 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Since computers have means to detect overflow on
                 addition or subtraction, this can be used in a multiple
                 precision addition-subtraction subroutine to obviate a
                 sign analysis. Consider all integers in the computer to
                 be expressed ``radix t'', that is, in the form $ a =
                 a_0 + a_1 t + \cdots + a_n t^n $ where $ a_i $ are of
                 like sign and have magnitudes less than $t$. $t$ is a
                 positive integer determined by the word length of the
                 computer. Consider the expression $ c = a \pm b = (a_0
                 \pm b_0) + (a_1 \pm b_1)t + \cdots + (a_n \pm b_n)t^n$.
                 Here $ a_i \pm b_i$ may exceed the storage capacity of
                 one word or may have a sign different from $c$.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Article{Croy:1961:RTM,
  author =       "John E. Croy",
  title =        "Rapid Technique of Manual or Machine Binary-to-Decimal
                 Integer Conversion Using Decimal Radix Arithmetic",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-10",
  number =       "4",
  pages =        "777--777",
  month =        dec,
  year =         "1961",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1961.5219286",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jul 14 14:45:05 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219286",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Freiman:1961:SAC,
  author =       "C. V. Freiman",
  title =        "Statistical analysis of certain binary division
                 algorithms",
  journal =      j-IRE-PROC,
  volume =       "49",
  number =       "1",
  pages =        "91--103",
  month =        jan,
  year =         "1961",
  DOI =          "https://doi.org/10.1109/JRPROC.1961.287780",
  bibdate =      "Mon Sep 16 16:12:21 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4066250",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  fjournal =     "IRE Proceedings",
  received =     "8 August 1960",
}

@TechReport{Garner:1961:RNS,
  author =       "H. L. Garner and R. F. Arnold and B. C. Benson and C.
                 G. Brockus and R. J. Gonzalez and D. P. Rozenberg",
  title =        "Residue number systems for computers",
  type =         "{ASD} Technical Report",
  number =       "61-483",
  institution =  "Electronic Technology Laboratory, The University of
                 Michigan",
  address =      "Ann Arbor, MI, USA",
  month =        oct,
  year =         "1961",
  bibdate =      "Thu Nov 18 09:27:06 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://deepblue.lib.umich.edu/bitstream/2027.42/5023/4/bac2784.0001.001.txt",
  abstract =     "The purpose of the research performed under this
                 contract was to investigate the feasibility of residue
                 number systems in their applications to digital
                 computers. The problems of such an application are the
                 ones of magnitude determination, sign determination,
                 overflow, scaling, and division. These problems are not
                 independent, but are found to be quite interrelated. A
                 theoretical treatment of residue number systems is
                 given which lays the foundation for a unified study of
                 the complete problem. Treatments of an organizational
                 nature are given which deal with multiplication,
                 division, and scaling. The matter of correlating the
                 theoretical and organizational studies to physical
                 realizations involving networks is treated also. The
                 question of whether the residue number system can be
                 successfully applied to general purpose computers is
                 still an open one. Their application to special purpose
                 machines is considered both feasible and practical.",
  acknowledgement = ack-nhfb,
  remark =       "This report represents the results of research
                 performed by the group at The University of Michigan
                 under the direction of Professor H. L. Garner.
                 Concurrently, research on the same subject was being
                 conducted at Harvard University under the direction of
                 Professor Howard Aiken, and at the Lockheed Missile
                 System Division under the direction of Dr. Richard
                 Tanaka. There was a considerable exchange of
                 information among the above groups during the course of
                 the research effort. The efforts attained exhibit
                 little overlap, rather they are complementary. A
                 portion of this report was extracted from the doctoral
                 dissertation of D. P. Rozenberg. His work was supported
                 by this contract, and led to the Ph.D..",
}

@Article{Garwick:1961:AFP,
  author =       "Jan V. Garwick",
  title =        "The Accuracy of Floating Point Computers",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "1",
  number =       "2",
  pages =        "87--88",
  month =        jun,
  year =         "1961",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01939221",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:07 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also comment and reply
                 \cite{Amble:1961:AFP,Garwick:1961:RAF}.",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=2&spage=87",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point accuracy; floating-point arithmetic",
}

@Article{Garwick:1961:RAF,
  author =       "J. V. Garwick",
  title =        "Reply to {``On the Accuracy of Floating Point
                 Computers'' [BIT {\bf 1}(3), 1961, pp. 220--221]}",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "1",
  number =       "3",
  pages =        "222--222",
  year =         "1961",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Mon Nov 16 14:36:22 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Garwick:1961:AFP,Amble:1961:AFP}.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point accuracy; floating-point arithmetic",
}

@InProceedings{Henderson:1961:RCE,
  author =       "D. S. Henderson",
  booktitle =    "{Proceedings of the 1961 16th ACM national meeting}",
  title =        "Residue class error checking codes",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "132.101--132.104",
  year =         "1961",
  DOI =          "https://doi.org/10.1145/800029.808563",
  bibdate =      "Thu Aug 07 19:04:58 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Error checking codes based on residues have the
                 advantage over parity-based codes of monitoring
                 arithmetic as well as transmission operations. Codes
                 may be devised to detect burst-type errors, to correct
                 single errors in a binary arithmetic operation, to
                 correct burst errors and finally to correct any
                 single-digit error in a decimal operation.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal arithmetic",
}

@Article{Kettel:1961:AAM,
  author =       "E. Kettel and W. Schneider",
  title =        "An Accurate Analog Multiplier and Divider",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-10",
  number =       "2",
  pages =        "269--272",
  month =        jun,
  year =         "1961",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1961.5219198",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jul 14 14:45:03 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219198",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Knuth:1961:EIN,
  author =       "Donald E. Knuth",
  title =        "Errata: {``An imaginary number system''}",
  journal =      j-CACM,
  volume =       "4",
  number =       "8",
  pages =        "355--355",
  month =        aug,
  year =         "1961",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Tue Jan 09 07:10:22 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Knuth:1960:INS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Article{Kovatch:1961:HEA,
  author =       "G. Kovatch and W. E. Meserve",
  title =        "The {Hall-Effect} Analog Multiplier",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-10",
  number =       "3",
  pages =        "512--515",
  month =        sep,
  year =         "1961",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1961.5219240",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jul 14 14:45:04 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219240",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Lehman:1961:STH,
  author =       "M. Lehman and N. Burla",
  title =        "Skip Techniques for High-Speed Carry-Propagation in
                 Binary Arithmetic Units",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-10",
  number =       "4",
  pages =        "691--698",
  month =        dec,
  year =         "1961",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1961.5219274",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jul 14 14:45:04 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219274",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{MacSorley:1961:HSA,
  author =       "O. L. MacSorley",
  title =        "High-speed arithmetic in binary computers",
  journal =      j-IRE-PROC,
  volume =       "49",
  number =       "1",
  pages =        "67--91",
  month =        jan,
  year =         "1961",
  DOI =          "https://doi.org/10.1109/JRPROC.1961.287779",
  bibdate =      "Sat May 18 14:34:55 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite{Swartzlander:1976:CDD}.",
  URL =          "https://ieeexplore.ieee.org/document/4066249",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Proceedings",
}

@Book{Morrison:1961:CBP,
  editor =       "Philip Morrison and Emily Morrison",
  title =        "{Charles Babbage} on the principles and development of
                 the calculator: and other seminal writings",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xxxviii + 400",
  year =         "1961",
  ISBN =         "0-486-24691-4 (paperback)",
  ISBN-13 =      "978-0-486-24691-8 (paperback)",
  LCCN =         "QA75 .C52 1961",
  bibdate =      "Sat Jan 12 22:30:15 MST 2013",
  bibsource =    "clio-db.cc.columbia.edu:7090/Voyager;
                 https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
                 https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$7.95",
  acknowledgement = ack-nhfb,
  subject =      "Calculators; Babbage, Charles",
  subject-dates = "Charles Babbage (26 December 1791--18 October 1871)",
  tableofcontents = "Chapters from Passages from the life of a
                 philosopher \\
                 Selections from Babbage's calculating engines \\
                 Appendix of miscellaneous papers",
}

@Article{Nadler:1961:DSR,
  author =       "Morton Nadler",
  title =        "Division and square root in the quater-imaginary
                 number system",
  journal =      j-CACM,
  volume =       "4",
  number =       "4",
  pages =        "192--193",
  month =        apr,
  year =         "1961",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.99",
  MRnumber =     "23\#B555",
  bibdate =      "Fri Nov 25 18:19:32 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Knuth:1960:INS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\sqrt(x)$; elementary functions",
  ZMreviewer =   "C. B. Haselgrove",
}

@Article{Pinkham:1961:DFS,
  author =       "Roger S. Pinkham",
  title =        "On the Distribution of First Significant Digits",
  journal =      j-ANN-MATH-STAT,
  volume =       "32",
  number =       "4",
  pages =        "1223--1230",
  month =        dec,
  year =         "1961",
  CODEN =        "AASTAD",
  ISSN =         "0003-4851 (print), 2168-8990 (electronic)",
  ISSN-L =       "0003-4851",
  bibdate =      "Thu Feb 15 15:07:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://links.jstor.org/sici?sici=0003-4851%28196112%2932%3A4%3C1223%3AOTDOFS%3E2.0.CO%3B2-T",
  abstract =     "It has been noticed by astute observers that well used
                 tables of logarithms are invariably dirtier at the
                 front than at the back. Upon reflection one is led to
                 inquire whether there are more physical constants with
                 low order first significant digits than high. Actual
                 counts by Benford [2] show that not only is this the
                 case but that it seems to be an empirical truth that
                 whenever one has a large body of physical data,
                 Farmer's Almanac, Census Reports, Chemical Rubber
                 Handbook, etc., the proportion of these data with first
                 significant digit $n$ or less is approximately $
                 \log_{10}(n + 1) $. Any reader formerly unaware of this
                 ``peculiarity'' will find an actual sampling experiment
                 wondrously tantalizing. Thus, for example,
                 approximately $ 0.7 $ of the physical constants in the
                 Chemical Rubber Handbook begin with $4$ or less ($
                 \log_{10}(4 + 1) = 0.699 $). This is to be contrasted
                 with the widespread intuitive evaluation $ 4 / 9 $
                 ths.",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Mathematical Statistics",
  journal-URL =  "http://projecteuclid.org/all/euclid.aoms/",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  remark =       "From p. 1223: ``\ldots{} the proportion of these data
                 with first significant digit $n$ or less is
                 approximately $ \log_{10}(n + 1) $.''\par

                 \ldots{} ``The only distribution for first significant
                 digits which is invariant under scale change of the
                 underlying distribution is $ \log_{10}(n + 1) $.
                 Contrary to suspicion this is a non-trivial
                 mathematical result, for the variable $n$ is
                 discrete.''.\par

                 From p. 1230: ``The foregoing results bear on questions
                 of round-off in computing machines. Since $ d(u v) = u
                 d v + v d u $, the error resulting from multiplying two
                 rounded numbers will be governed primarily by the first
                 significant digits of the two numbers being multiplied.
                 Now the distribution of first significant digits,
                 favoring as it does low order digits, tends to produce
                 less error than would be the case if first significant
                 digits were uniform as has sometimes been
                 assumed.''\par

                 Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Rabinowitz:1961:MPD,
  author =       "Philip Rabinowitz",
  title =        "Multiple-Precision Division",
  journal =      j-CACM,
  volume =       "4",
  number =       "2",
  pages =        "98--98",
  month =        feb,
  year =         "1961",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/366105.366171",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 00:29:25 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Article{Saltman:1961:RCT,
  author =       "Roy G. Saltman",
  title =        "Reducing Computing Time for Synchronous Binary
                 Division",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-10",
  number =       "2",
  pages =        "169--174",
  month =        jun,
  year =         "1961",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1961.5219186",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jul 14 14:45:03 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219186",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Spielberg:1961:ECF,
  author =       "Kurt Spielberg",
  title =        "Efficient Continued Fraction Approximations To
                 Elementary Functions",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "76",
  pages =        "409--417",
  month =        oct,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Spielberg:1961:RPS,
  author =       "K. Spielberg",
  title =        "Representation of Power Series in Terms of
                 Polynomials, Rational Approximations and Continued
                 Fractions",
  journal =      j-J-ACM,
  volume =       "8",
  number =       "4",
  pages =        "613--627",
  month =        oct,
  year =         "1961",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Sat Dec 09 14:01:44 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}

@Article{Thacher:1961:ISR,
  author =       "Henry C. {Thacher, Jr.}",
  title =        "Iterated Square Root Expansions for the Inverse Cosine
                 and Inverse Hyperbolic Cosine",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "76",
  pages =        "399--403",
  month =        oct,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@TechReport{Weik:1961:TSD,
  author =       "Martin H. Weik",
  title =        "A Third Survey of Domestic Electronic Digital
                 Computing Systems",
  type =         "Report",
  number =       "1115",
  institution =  "Ballistic Research Laboratories",
  address =      "Aberdeen Proving Ground, MD, USA",
  pages =        "1131",
  month =        mar,
  year =         "1961",
  bibdate =      "Fri Nov 28 19:37:51 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Based on the results of a third survey, the
                 engineering and programming characteristics of two
                 hundred twenty-two different electronic digital
                 computing systems are given. The data are presented
                 from the point of view of application, numerical and
                 arithmetic characteristics, input, output and storage
                 systems, construction and checking features, power,
                 space, weight, and site preparation and personnel
                 requirements, production records, cost and rental
                 rates, sale and lease policy, reliability, operating
                 experience, and time availability, engineering
                 modifications and improvements and other related
                 topics. An analysis of the survey data, fifteen
                 comparative tables, a discussion of trends, a revised
                 bibliography, and a complete glossary of computer
                 engineering and programming terminology are included.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}

@Article{Wilson:1961:ARB,
  author =       "J. B. Wilson and R. S. Ledley",
  title =        "An Algorithm for Rapid Binary Division",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-10",
  number =       "4",
  pages =        "662--670",
  month =        dec,
  year =         "1961",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1961.5219271",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jul 14 14:45:04 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219271",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@InProceedings{Ashenhurst:1962:MIA,
  author =       "R. L. Ashenhurst",
  title =        "The {Maniac III} Arithmetic System",
  crossref =     "AFIPS:1962:APS",
  pages =        "192--202",
  year =         "1962",
  bibdate =      "Wed Feb 14 17:14:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{Buchholz:1962:PCS,
  editor =       "Werner Buchholz",
  title =        "Planning a Computer System: {Project Stretch}",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "xvii + 322",
  year =         "1962",
  LCCN =         "1876",
  bibdate =      "Fri Nov 19 10:02:31 MST 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib;
                 library.ox.ac.uk:210/ADVANCE",
  note =         "This important book is the primary description of the
                 influential IBM 7030 Stretch computer, written by its
                 architects. See also a detailed critical review
                 \cite{Strachey:1962:BRP}.",
  URL =          "http://ed-thelen.org/comp-hist/IBM-7030-Planning-McJones.pdf",
  acknowledgement = ack-nhfb,
  remark =       "The text of the book is in the public domain, with the
                 permission of the author in 2003.

                 See \cite{MacKenzie:1991:IAL} for a remark about the
                 noisy mode for floating-point arithmetic in the IBM
                 7030 Stretch. That mode is first mentioned on page 25
                 of this book, and described in detail on page 102,
                 which states:

                 ``By definition of ordinary normalized FLP operations,
                 numbers are frequently extended on the right by
                 attaching zeros. During addition the n-digit operand
                 that is not preshifted is extended with n zeros, so as
                 to provide the extra positions to which the preshifted
                 operand can be added. Any operand or result that is
                 shifted left to be normalized requires a corresponding
                 number of zeros to be shifted in at the right. Both
                 sets of zeros tend to produce numbers smaller in
                 absolute value than they would have been if more digits
                 had been carried. In the noisy mode these numbers are
                 simply extended with 1's instead of zeros (1's in a
                 binary machine, 9's in a decimal machine). So all
                 numbers tend to be too large in absolute value. The
                 true value, if there had been no significance loss,
                 should lie between these two extremes. Hence, two runs,
                 one made without and one made with the noisy mode,
                 should show differences in result that indicate which
                 digits may have been affected by significance loss.

                 The principal weakness of the noisy-mode procedure is
                 that it requires two runs for the same problem. A much
                 less important weakness is that the loss of
                 significance cannot be guaranteed to show up --- it
                 merely has a very high probability of showing up ---
                 whereas built-in significance checks can be made
                 slightly pessimistic, so that actual significance loss
                 will not be greater than indicated. On the other hand,
                 little extra hardware and no extra storage are required
                 for the noisy-mode approach. Furthermore, significance
                 loss is relatively rare, so that running a problem
                 twice when Significance loss is suspected does not pose
                 a serious problem. What is serious is the possibility
                 of unsuspected significance loss.

                 In discussions of significance two points are often
                 overlooked. The first of these is trivial: the best way
                 of ensuring significant results is to use an adequate
                 number of fraction digits. The second is almost equally
                 mundane: for a given procedure, normalized FLP
                 arithmetic will ordinarily produce the greatest
                 precision possible for the number of fraction digits
                 used. Normalized FLP arithmetic has been criticized
                 with respect to significance loss, because such loss is
                 not indicated by the creation of leading zeros, as it
                 is with fixed-point arithmetic. In other words, the
                 contention is not that normalized FLP arithmetic is
                 more prone to significance loss than equivalent
                 fixed-point arithmetic, which would be untrue, but that
                 an equivalent indication of such loss is not provided.
                 Loss of significance, however, is also a serious
                 problem in fixed-point arithmetic; multiplication and
                 division do not handle it at all correctly by means of
                 leading zeros. (In particular, fixed-point
                 multiplication may lead to serious or even total
                 significance loss, which would not have occurred with
                 normalized FLP arithmetic: and although leading zeros
                 in addition and subtraction of fixed-point operands do
                 give correct significance indications, the use of other
                 operations and of built-in scaling loops frequently
                 destroys entirely the leading-zeros method of counting
                 significance.)''",
  subject =      "Computer architecture",
  tableofcontents = "Foreword v \\
                 Preface vii \\
                 1. Project Stretch 1 \\
                 [by W. Buchholz] \\
                 2. Architectural Philosophy 5 \\
                 [by F. P. Brooks, Jr.] \\
                 2.1. The Two Objectives of Project Stretch 5 \\
                 2.2. Resources 6 \\
                 2.3. Guiding Principles 7 \\
                 2.4. Contemporary Trends in Computer Architecture 10
                 \\
                 2.5. Hindsight 15 \\
                 3. System Summary of IBM 7030 17 \\
                 [by W. Buchholz] \\
                 3.1. System Organization 17 \\
                 3.2. Memory Units 17 \\
                 3.3. Index Memory 19 \\
                 3.4. Special Registers 19 \\
                 3.5. Input and Output Facilities 19 \\
                 3.6. High-speed Disk Units 20 \\
                 3.7. Central Processing Unit 20 \\
                 3.8. Instruction Controls 21 \\
                 3.9. Index-arithmetic Unit 21 \\
                 3.10. Instruction Look-ahead 21 \\
                 3.11. Arithmetic Unit 22 \\
                 3.12. Instruction Set 24 \\
                 3.13. Data Arithmetic 24 \\
                 3.14. Radix-conversion Operations 27 \\
                 3.15. Connective Operations 27 \\
                 3.16. Index-arithmetic Operations 27 \\
                 3.17. Branching Operations 28 \\
                 3.18. Transmission Operations 28 \\
                 3.19. Input-Output Operations 29 \\
                 3.20. New Features 29 \\
                 3.21. Performance 32 \\
                 4. Natural Data Units 33 \\
                 [by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz]
                 \\
                 4.1. Lengths and Structures of Natural Data Units 33
                 \\
                 4.2. Procedures for Specifying Natural Data Units 36
                 \\
                 4.3. Data Hierarchies 39 \\
                 4.4. Classes of Operations 40 \\
                 5. Choosing a Number Base 42 \\
                 [by W. Buchholz] \\
                 5.1. Introduction 42 \\
                 5.2. Information Content 45 \\
                 5.3. Arithmetic Speed 49 \\
                 5.4. Numerical Data 50 \\
                 5.5. Nonnumerical Data 51 \\
                 5.6. Addresses 52 \\
                 5.7. Transformation 53 \\
                 5.8. Partitioning of Memory 54 \\
                 5.9. Program Interpretation 56 \\
                 5.10. Other Number Bases 58 \\
                 5.11. Conclusion 58 \\
                 6. Character Set 60 \\
                 [by R. W. Bemer and W. Buchholz] \\
                 6.1. Introduction 60 \\
                 6.2. Size of Set 62 \\
                 6.3. Subsets 62 \\
                 6.4. Expansion of Set 63 \\
                 6.5. Code 63 \\
                 6.6. Parity Bit 66 \\
                 6.7. Sequence 66 \\
                 6.8. Blank 67 \\
                 6.9. Decimal Digits 68 \\
                 6.10. Typewriter Keyboard 68 \\
                 6.11. Adjacency 69 \\
                 6.12. Uniqueness 69 \\
                 6.13. Signs 70 \\
                 6.14. Tape-recording Convention 71 \\
                 6.15. Card-punching Convention 71 \\
                 6.16. List of 7030 Character Set 72 \\
                 7. Variable-field-length Operation 75 \\
                 [by G. P. Blaauw, F. P. Brooks, Jr., and W. Buchholz]
                 \\
                 7.1. Introduction 75 \\
                 7.2. Addressing of Variable-field-length Data 76 \\
                 7.3. Field Length 77 \\
                 7.4. Byte Size 78 \\
                 7.5. Universal Accumulator 79 \\
                 7.6. Accumulator Operand 79 \\
                 7.7. Binary and Decimal Arithmetic 80 \\
                 7.8. Integer Arithmetic 81 \\
                 7.9. Numerical Signs 82 \\
                 7.10. Indicators 84 \\
                 7.11. Arithmetical Operations 85 \\
                 7.12. Radix-conversion Operation 87 \\
                 7.13. Logical Connectives of Two Variables 87 \\
                 7.14. Connective Operations 89 \\
                 8. Floating-point Operation 92 \\
                 [by S. G. Campbell] \\
                 General Discussion \\
                 8.1. Problems of Fixed-point Arithmetic 92 \\
                 8.2. Floating-point Arithmetic 94 \\
                 8.3. Normalization 97 \\
                 8.4. Floating-point Singularities 98 \\
                 8.5. Range and Precision 99 \\
                 8.6. Round-off Error 100 \\
                 8.7. Significance Checks 101 \\
                 8.8. Forms of Floating-point Arithmetic 103 \\
                 8.9. Structure of Floating-point Data 104 \\
                 Floating-point Features of the 7030 \\
                 8.10. Floating-point Instruction Format 106 \\
                 8.11. Floating-point Data Formats 106 \\
                 8.12. Singular Floating-point Numbers 108 \\
                 8.13. Indicators 112 \\
                 8.14. Universal Accumulator 113 \\
                 8.15. Fraction Arithmetic 114 \\
                 8.16. Floating-point-arithmetic Operations 114 \\
                 8.17. Fixed-point Arithmetic Using Unnormalized \\
                 Floating-point Operations 118 \\
                 8.18. Special Functions and Forms of Arithmetic 119 \\
                 8.19. Multiple-precision Arithmetic 119 \\
                 8.20. General Remarks 121 \\
                 9. Instruction Formats 122 \\
                 [by W. Buchholz] \\
                 9.1. Introduction 122 \\
                 9.2. Earlier Instruction Languages 122 \\
                 9.3. Evolution of the Single-address Instruction 124
                 \\
                 9.4. Implied Addresses 125 \\
                 9.5. Basic 7030 Instruction Formats 126 \\
                 9.6. Instruction Efficiency 127 \\
                 9.7. The Simplicity of Complexity 131 \\
                 9.8. Relationship to Automatic Programming Languages
                 132 \\
                 10. Instruction Sequencing 133 \\
                 [by F. P. Brooks, Jr.] \\
                 10.1. Modes of Instruction Sequencing 133 \\
                 10.2. Instruction Counter 134 \\
                 10.3. Unconditional Branching 135 \\
                 10.4. Conditional Branching 136 \\
                 10.5. Program-interrupt System 136 \\
                 10.6. Components of the Program-interrupt System 137
                 \\
                 10.7. Examples of Program-interrupt Techniques 140 \\
                 10.8. Execute Instructions 146 \\
                 10.9. Execute Operations in the 7030 148 \\
                 11. Indexing 150 \\
                 [by G. P. Blaauw] \\
                 11.1. Introduction 150 \\
                 11.2. Indexing Functions 151 \\
                 11.3. Instruction Format for Indexing 155 \\
                 11.4. Incrementing 157 \\
                 11.5. Counting 159 \\
                 11.6. Advancing by One 161 \\
                 11.7. Progressive Indexing 161 \\
                 11.8. Data Transmission 162 \\
                 11.9. Data Ordering 163 \\
                 11.10. Refilling 165 \\
                 11.11. Indirect Addressing and Indirect Indexing 167
                 \\
                 11.12. Indexing Applications 169 \\
                 11.13. Record-handling Applications 172 \\
                 11.14. File Maintenance 175 \\
                 11.15. Subroutine Control 177 \\
                 11.16. Conclusion 178 \\
                 12. Input-Output Control 179 \\
                 [by W. Buchholz] \\
                 12.1. A Generalized Approach to Connecting \\
                 Input-Output and External Storage 179 \\
                 12.2. Input-Output Instructions 180 \\
                 12.3. Defining the Memory Area 181 \\
                 12.4. Writing and Reading 182 \\
                 12.5. Controlling and Locating 183 \\
                 12.6. An Alternative Approach 184 \\
                 12.7. Program Interruptions 184 \\
                 12.8. Buffering 180 \\
                 12.9. Interface 188 \\
                 12.10. Operator Control of Input-Output Units 190 \\
                 13. Multiprogramming 192 \\
                 [by E. F. Codd, E. S. Lowry, E. McDonough, and C. A.
                 Scalzi] \\
                 13.1. Introduction 192 \\
                 13.2. Multiprogramming Requirements 193 \\
                 13.3. 7030 Features that Assist Multiprogramming 195
                 \\
                 13.4. Programmed Logic 197 \\
                 13.5. Concluding Remarks 200 \\
                 13.6. References 201 \\
                 14. The Central Processing Unit 202 \\
                 [by E. Bloch] \\
                 14.1. Concurrent System Operation 202 \\
                 14.2. Concurrency within the Central Processing Unit
                 204 \\
                 14.3. Data Flow 204 \\
                 14.4. Arithmetic Unit 208 \\
                 14.5. Checking 216 \\
                 14.6. Component Count 216 \\
                 14.7. Performance 217 \\
                 14.8. Circuits 218 \\
                 14.9. Packaging 223 \\
                 15. The Look-ahead Unit 228 \\
                 [by R. S. Balance, J. Cocke, and H. G. Kolsky] \\
                 15.1. General Description 228 \\
                 15.2. Timing-simulation Program 230 \\
                 15.3. Description of the Look-ahead Unit 238 \\
                 15.4. Forwarding 240 \\
                 15.5. Counter Sequences 241 \\
                 15.6. Recovery after Interrupt 246 \\
                 15.7. A Look-back at the Look-ahead 247 \\
                 16. The Exchange 248 \\
                 [by W. Buchholz] \\
                 16.1. General Description 248 \\
                 16.2. Starting a WRITE or READ Operation 250 \\
                 16.3. Data Transfer during Writing 250 \\
                 16.4. Data Transfer during Reading 251 \\
                 16.5. Terminating a WRITE or READ Operation 252 \\
                 16.6. Multiple Operations 252 \\
                 16.7. CONTROL and LOCATE Operations 252 \\
                 16.8. Interrogating the Control Word 253 \\
                 16.9. Forced Termination 253 \\
                 17. A Nonarithmetical System Extension 254 \\
                 [by S. G. Campbell, P. S. Herwitz, and J. H. Pomerene]
                 \\
                 17.1. Nonarithmetical Processing 254 \\
                 17.2. The Set-up Mode 258 \\
                 17.3. Byte-sequence Formation 259 \\
                 17.4. Pattern Selection 260 \\
                 17.5. Transformation Facilities 261 \\
                 17.6. Statistical Aids 263 \\
                 17.7. The BYTE-BY-BYTE Instruction 263 \\
                 17.8. Monitoring for Special Conditions 264 \\
                 17.9. Instruction Set 265 \\
                 17.10. Collating Operations 266 \\
                 17.11. Table Look-up Operations 267 \\
                 17.12. Example 267 \\
                 Appendix A. Summary Data 273 \\
                 A.1. List of the Larger IBM Stored-program Computers
                 273 \\
                 A.2. Instruction Formats 275 \\
                 A.3. List of Registers and Special Addresses 276 \\
                 A.4. Summary of Operations and Modifiers 277 \\
                 A.5. Summary of Indicators 287 \\
                 Appendix B. Programming Examples 292 \\
                 Notation 292 \\
                 B.1. Polynomial Evaluation 295 \\
                 B.2. Cube-root Extraction 296 \\
                 B.3. Matrix Multiplication 298 \\
                 B.4. Conversion of Decimal Numbers to a \\
                 Floating-point Normalized Vector 299 \\
                 B.5. Editing a Typed Message 301 \\
                 B.6. Transposition of a Large Bit Matrix 303 \\
                 Index 305",
}

@InCollection{Campbell:1962:FPO,
  author =       "S. G. Campbell",
  editor =       "Werner Buchholz",
  booktitle =    "Planning a Computer System: {Project Stretch}",
  title =        "Floating-Point Operation",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  bookpages =    "322",
  pages =        "92--121",
  year =         "1962",
  LCCN =         "QA76.8.I2 I5",
  bibdate =      "Wed Feb 14 17:24:27 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "IBM 7030 (Computer); IBM Stretch",
}

@Article{Cantor:1962:LEF,
  author =       "D. Cantor and G. Estrin and R. Turn",
  title =        "Logarithmic and Exponential Function Evaluation in a
                 Variable Structure Digital Computer",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-11",
  number =       "2",
  pages =        "155--164",
  month =        apr,
  year =         "1962",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1962.5219348",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jul 14 09:11:49 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219348",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@TechReport{Descloux:1962:REF,
  author =       "J. Descloux",
  title =        "Remarks on errors in first order iterative processes
                 with floating-point computers",
  institution =  "University of Illinois Graduate College, Digital
                 Computer Laboratory",
  address =      "Urbana, IL, USA",
  pages =        "7",
  year =         "1962",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Report / University of Illinois, Digital Computer
                 Laboratory; no. 113 Report (University of Illinois
                 (Urbana-Champaign campus). Digital Computer
                 Laboratory); no. 113.",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers.; Numerical
                 calculations.",
  remark =       "Supported by: National Science Foundation under grant
                 G16489. ``March 22, 1962.''",
}

@Article{Fischler:1962:TRA,
  author =       "M. A. Fischler and E. A. Poe",
  title =        "Threshold Realization of Arithmetic Circuits",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-11",
  number =       "2",
  pages =        "287--288",
  month =        apr,
  year =         "1962",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1962.5219366",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jul 14 09:11:50 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219366",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Fraser:1962:CRA,
  author =       "W. Fraser and J. F. Hart",
  title =        "On the computation of rational approximations to
                 continuous functions",
  journal =      j-CACM,
  volume =       "5",
  number =       "7",
  pages =        "401--403",
  month =        jul,
  year =         "1962",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/368273.368578",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:39 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\abs(x)$; $\cos(x)$; $\Gamma(1+x)$; $\sin(x)$;
                 elementary functions; Remes algorithm; special
                 functions",
}

@Article{Grau:1962:FNR,
  author =       "A. A. Grau",
  title =        "On a floating-point number representation for use with
                 algorithmic languages",
  journal =      j-CACM,
  volume =       "5",
  number =       "3",
  pages =        "160--161",
  month =        mar,
  year =         "1962",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "68.00",
  MRnumber =     "26\#4506",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Algorithmic languages, such as ALGOL, make provision
                 for two types of numbers, real and integer, which are
                 usually implemented on the computer by means of
                 floating-point and fixed-point numbers respectively.
                 The concepts real and integer, however, are taken from
                 mathematics, where the set of integers forms a proper
                 subset of the set of real numbers. In implementation a
                 real problem is posed by the fact that the set of
                 fixed-point numbers is not a proper subset of the set
                 of floating-point numbers; this problem becomes very
                 apparent in attempts to implement ALGOL 60.
                 Furthermore, the {\em one\/} mathematical operation of
                 addition is implemented in the machine by one of {\em
                 two\/} machine operations, fixed-point addition or
                 floating-point addition.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  reviewer =     "R. L. Ashenhurst",
}

@Article{Guffin:1962:CSL,
  author =       "Ronald M. Guffin",
  title =        "A Computer for Solving Linear Simultaneous Equations
                 Using the Residue Number System",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-11",
  number =       "2",
  pages =        "164--173",
  month =        apr,
  year =         "1962",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1962.5219349",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jul 14 09:11:49 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219349",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Book{Hamming:1962:NMS,
  author =       "R. W. (Richard Wesley) Hamming",
  title =        "Numerical methods for scientists and engineers",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "411",
  year =         "1962",
  LCCN =         "QA297 .H28",
  bibdate =      "Fri Aug 20 09:12:08 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "International series in pure and applied mathematics",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
  subject =      "Numerical analysis; Electronic digital computers",
}

@Article{Jones:1962:FPF,
  author =       "F. B. Jones and A. W. Wymore",
  title =        "Floating Point Feature on the {IBM Type 1620}",
  journal =      j-IBM-TDB,
  volume =       "05-62",
  pages =        "43--46",
  month =        may,
  year =         "1962",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Fri Nov 28 11:26:02 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Technical Disclosure Bulletin",
  keywords =     "decimal floating-point arithmetic",
  remark =       "The IBM 1620 normalized variable-precision arithmetic
                 provides up to 100 decimal digits with an exponent
                 range of $ \pm 99 $.",
}

@Article{Karatsuba:1962:MMN,
  author =       "A. Karatsuba and Y. Ofman",
  title =        "Multiplication of multidigit numbers on automata",
  journal =      j-DOKL-AKAD-NAUK,
  volume =       "145",
  number =       "??",
  pages =        "293--294",
  month =        "????",
  year =         "1962",
  CODEN =        "DANKAS",
  ISSN =         "0002-3264",
  bibdate =      "Tue Jul 05 10:35:11 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Doklady Akademii nauk SSSR",
  journal-URL =  "http://istina.msu.ru/journals/366838/",
}

@Article{Keir:1962:DOD,
  author =       "Y. A. Keir and P. W. Cheney and M. Tannenbaum",
  title =        "Division and overflow detection in residue number
                 systems",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-11",
  number =       "4",
  pages =        "501--507",
  month =        aug,
  year =         "1962",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1962.5219389",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  MRclass =      "68.00",
  MRnumber =     "MR0150990 (27 \#976)",
  MRreviewer =   "N. H. Choksy",
  bibdate =      "Thu Jul 14 09:11:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219389",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Kesner:1962:FPA,
  author =       "O. Kesner",
  title =        "Floating-point arithmetic in {COBOL}",
  journal =      j-CACM,
  volume =       "5",
  number =       "5",
  pages =        "269--271",
  month =        may,
  year =         "1962",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/367710.367739",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:38 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Article{Knuth:1962:EPC,
  author =       "Donald E. Knuth",
  title =        "Evaluation of polynomials by computer",
  journal =      j-CACM,
  volume =       "5",
  number =       "12",
  pages =        "595--599",
  month =        dec,
  year =         "1962",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355580.369074",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "68.00 (12.00)",
  MRnumber =     "27 \#970",
  bibdate =      "Thu Dec 08 11:11:03 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database",
  note =         "See letter \cite{Knuth:1963:LEE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "The author that Motzkin (1962) showed that Horner's
                 rule for polynomial evaluation may not be optimal, and
                 develops the idea further for arbitrary polynomials,
                 but also observes that the coefficients of the revised
                 polynomials may be difficult to find. He also asks
                 about, but does not answer, the question of error
                 analysis of the various methods.",
}

@Article{Lake:1962:LEH,
  author =       "G. T. Lake",
  title =        "Letter to the Editor: Hardware Conversion of Decimal
                 and Binary Numbers",
  journal =      j-CACM,
  volume =       "5",
  number =       "9",
  pages =        "468--469",
  month =        sep,
  year =         "1962",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 28 18:16:30 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "decimal floating-point arithmetic",
}

@Article{Lynch:1962:WBD,
  author =       "W. C. Lynch",
  title =        "On a Wired-In Binary-to-Decimal Conversion Scheme",
  journal =      j-CACM,
  volume =       "5",
  number =       "3",
  pages =        "159--159",
  month =        mar,
  year =         "1962",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 28 18:21:41 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "decimal floating-point arithmetic",
}

@Article{MacSorley:1962:RBA,
  author =       "O. L. MacSorley",
  title =        "Review: \booktitle{An Algorithm for Rapid Binary
                 Division}, by {J. B. Wilson and R. S. Ledley}",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-11",
  number =       "3",
  pages =        "420--420",
  month =        jun,
  year =         "1962",
  CODEN =        "IRELAO",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Sat Jul 16 20:52:08 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{McGee:1962:BM,
  author =       "W. C. McGee",
  title =        "A Binary Multiplication",
  journal =      j-SIAM-REVIEW,
  volume =       "4",
  number =       "3",
  pages =        "256--256",
  month =        "????",
  year =         "1962",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1004066",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu Mar 27 09:04:54 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/4/3;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "July 1962",
}

@Article{Meggitt:1962:PDP,
  author =       "J. E. Meggitt",
  title =        "Pseudo Division and Pseudo Multiplication Processes",
  journal =      j-IBM-JRD,
  volume =       "6",
  number =       "2",
  pages =        "210--226",
  month =        apr,
  year =         "1962",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.62.0210",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Thu Sep 1 10:15:31 1994",
  bibsource =    "http://www.research.ibm.com/journal/;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392356",
  ZMnumber =     "201.48709",
  acknowledgement = ack-nhfb,
  ajournal =     "IBM J. Res. Develop.",
  book-URL =     "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "binary arithmetic; decimal arithmetic; divide;
                 exponential; inverse square root; inverse tangent;
                 logarithm; multiply; square root; tangent",
  remark =       "This paper shows how common digit-at-a-time hardware
                 circuitry can be used to compute several different
                 functions, with the only difference among the functions
                 being initial conditions and stored tables of
                 particular constants, with an error than does not
                 exceed 3 units in the lowest-order decimal digit of the
                 result (assuming base-10 arithmetic). The steps are
                 similar to those in CORDIC algorithms. If M is the time
                 for one multiplication, then other functions are found
                 in these times: cosine (7M), division (3M?),
                 exponential (3M), inverse tangent (3M), logarithm (3M),
                 sine (7M), square root (3M?), and tangent (4M). For
                 $n$-digit numbers, the calculation requires two
                 registers, one of length $ n + 2 $ digits, and the
                 other of length $ 2 n + 2 $ digits.",
}

@Article{Metze:1962:CBD,
  author =       "Gernot Metze",
  title =        "A Class of Binary Divisions Yielding Minimally
                 Represented Quotients",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-11",
  number =       "6",
  pages =        "761--764",
  month =        dec,
  year =         "1962",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1962.5219460",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jul 14 09:11:53 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219460",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Mitchell:1962:CMD,
  author =       "John N. Mitchell",
  title =        "Computer Multiplication and Division Using Binary
                 Logarithms",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-11",
  number =       "4",
  pages =        "512--517",
  month =        aug,
  year =         "1962",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1962.5219391",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jul 14 09:11:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219391",
  abstract =     "A method of computer multiplication and division is
                 proposed which uses binary logarithms. The logarithm of
                 a binary number may be determined approximately from
                 the number itself by simple shifting and counting. A
                 simple add or subtract and shift operation is all that
                 is required to multiply or divide. Since the logarithms
                 used are approximate there can be errors in the result.
                 An error analysis is given and a means of reducing the
                 error for the multiply operation is show",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Rozier:1962:DBC,
  author =       "Charles P. Rozier",
  title =        "Decimal-to-Binary Conversion Using Octal Radix
                 Arithmetic",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-11",
  number =       "5",
  pages =        "708--709",
  month =        oct,
  year =         "1962",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1962.5219436",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Thu Jul 14 09:11:52 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219436",
  acknowledgement = ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}

@Article{Shanks:1962:CD,
  author =       "Daniel Shanks and John W. {Wrench, Jr.}",
  title =        "Calculation of $ \pi $ to 100,000 Decimals",
  journal =      j-MATH-COMPUT,
  volume =       "16",
  number =       "77",
  pages =        "76--99",
  month =        jan,
  year =         "1962",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Misc{Sierra:1962:FDP,
  author =       "Huberto M. Sierra",
  title =        "Floating Decimal Point Arithmetic Control Means for
                 Calculator",
  howpublished = "US Patent 3,037,701",
  day =          "5",
  month =        jun,
  year =         "1962",
  bibdate =      "Sat Mar 24 05:59:45 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://patents.google.com/patent/US3037701A",
  abstract =     "The invention relates to digital computers and more
                 particularly to digital computers for making
                 calculations with numbers having a wide range of values
                 with a limited number of digit storing positions.",
  acknowledgement = ack-nhfb,
  remark =       "US Patent filed 21 November 1956, granted to IBM on 5
                 June 1962, expired 5 June 1979 (17 years after grant).
                 This may be the earliest US patent on floating-point
                 arithmetic.",
}

@Article{Smith:1962:ACDa,
  author =       "Robert L. Smith",
  title =        "{Algorithm 116}: {Complex} Division",
  journal =      j-CACM,
  volume =       "5",
  number =       "8",
  pages =        "435--435",
  month =        aug,
  year =         "1962",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/368637.368661",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:40 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Article{Spielberg:1962:PCF,
  author =       "Kurt Spielberg",
  title =        "Polynomial and Continued-Fraction Approximations for
                 Logarithmic Functions",
  journal =      j-MATH-COMPUT,
  volume =       "16",
  number =       "78",
  pages =        "205--217",
  month =        apr,
  year =         "1962",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Strachey:1962:BRP,
  author =       "Christopher Strachey",
  title =        "Book Reviews: {{\booktitle{Planning a Computer System:
                 Project Stretch}}. Edited by Werner Buchholz. 322
                 pp.(London: McGraw-Hill)}",
  journal =      j-COMP-J,
  volume =       "5",
  number =       "2",
  pages =        "152--153",
  month =        aug,
  year =         "1962",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/5.2.152",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Wed Sep 25 09:59:25 2024",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  note =         "See \cite{Buchholz:1962:PCS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "IBM 7030 (Stretch); IBM 7950 (Harvest)",
}

@Article{Wynn:1962:AAP,
  author =       "P. Wynn",
  title =        "An Arsenal of {ALGOL} Procedures for Complex
                 Arithmetic",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "2",
  number =       "4",
  pages =        "232--255",
  month =        dec,
  year =         "1962",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01940171",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:07 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=2&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=2&issue=4&spage=232",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "ALGOL; complex arithmetic; confluence hypergeometric
                 function; continued fractions; incomplete beta
                 function; incomplete gamma function; Stieltjes
                 $S$-fractions; Weber parabolic cylinder function",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@InCollection{Zuse:1962:ERE,
  author =       "K. Zuse",
  editor =       "W. Hoffman",
  booktitle =    "{Digitale Informationswandler}",
  title =        "{Entwicklungslinien einer Rechenger{\"a}te-Entwicklung
                 von der Mechanik zur Elektronik}. ({German}) [Lines of
                 development of computing equipment development from
                 mechanics to electronics]",
  publisher =    "Vieweg \& Sohn, GmbH",
  address =      "Braunschweig, West Germany",
  pages =        "508--532",
  year =         "1962",
  bibdate =      "Wed Oct 13 11:23:04 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 4.3]{Randell:1982:ODC}.
                 Translated by Mr. and Mrs. P. Jones.",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Bemer:1963:NRT,
  author =       "R. W. Bemer",
  title =        "A Note on Range Transformations for Square Root and
                 Logarithm",
  journal =      j-CACM,
  volume =       "6",
  number =       "6",
  pages =        "306--307",
  month =        jun,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:47 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\log(x)$; $\sqrt(x)$; elementary functions",
}

@Article{Clenshaw:1963:ASF,
  author =       "C. W. Clenshaw and G. F. Miller and M. Woodger",
  title =        "Algorithms for Special Functions {I}",
  journal =      j-NUM-MATH,
  volume =       "4",
  pages =        "403--419",
  year =         "1963",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Fri Sep 16 10:21:31 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  xxmonth =      "(none)",
  xxnumber =     "(none)",
}

@Article{Daly:1963:HSA,
  author =       "W. G. Daly and J. F. Kruy",
  title =        "A High-Speed Arithmetic Unit Using Tunnel Diodes",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-12",
  number =       "5",
  pages =        "503--511",
  month =        oct,
  year =         "1963",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1963.263644",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 08:10:42 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037964",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Article{Descloux:1963:NRE,
  author =       "J. Descloux",
  title =        "Note on the Round-Off Errors in Iterative Processes",
  journal =      j-MATH-COMPUT,
  volume =       "17",
  number =       "81",
  pages =        "18--27",
  month =        jan,
  year =         "1963",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Dietmeyer:1963:CPN,
  author =       "Donald L. Dietmeyer",
  title =        "Conversion from Positive to Negative and Imaginary
                 Radix",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-12",
  number =       "1",
  pages =        "20--22",
  month =        feb,
  year =         "1963",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1963.263391",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 08:10:36 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037765",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
  keywords =     "imaginary base; negative base",
}

@Article{Eisman:1963:PER,
  author =       "S. H. Eisman",
  title =        "Polynomial Evaluation Revisited",
  journal =      j-CACM,
  volume =       "6",
  number =       "7",
  pages =        "384--385",
  month =        jul,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 1 10:15:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Article{Eve:1963:SAI,
  author =       "J. Eve",
  title =        "Starting Approximations for the Iterative Calculation
                 of Square Roots",
  journal =      j-COMP-J,
  volume =       "6",
  number =       "3",
  pages =        "274--276",
  month =        nov,
  year =         "1963",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/6.3.274",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:47:30 MST 2012",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://comjnl.oxfordjournals.org/content/6/3.toc;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_03/;
                 https://www.math.utah.edu/pub/tex/bib/compj1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Several starting approximations are given which, in
                 conjunction with a well-known iterative process, lead
                 to square root approximations, with a relative error in
                 the range $ (2^{-55}, 2^{-45}) $, at the expense of
                 three divisions. More accurate approximations are given
                 which require in addition a single multiplication.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Book{Flores:1963:LCA,
  author =       "I. Flores",
  title =        "The Logic of Computer Arithmetic",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xii + 493",
  year =         "1963",
  LCCN =         "QA76.5 .F46",
  bibdate =      "Thu Sep 1 10:12:51 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Geier:1963:ACD,
  author =       "A. Geier and I. Sturz",
  title =        "The approximate calculation of a definite integral
                 with automatic choice of integration steps (intervals).
                 The program for the computer {$ {\rm MECIPTI} $} in a
                 floating point regime. ({Romanian})",
  journal =      "An. Univ. Timi{\c{s}}oara Ser. {\c{S}}ti. Mat.-Fiz.",
  volume =       "1",
  pages =        "133--139",
  year =         "1963",
  MRclass =      "68.00",
  MRnumber =     "30\#3588",
  bibdate =      "Fri Dec 08 13:52:47 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  reviewer =     "R. N. Goss",
}

@Article{Goldstein:1963:SAD,
  author =       "Max Goldstein",
  title =        "Significance arithmetic on a digital computer",
  journal =      j-CACM,
  volume =       "6",
  number =       "3",
  pages =        "111--117",
  month =        mar,
  year =         "1963",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/366274.366339",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:45 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The 7090 at NYU has been modified to include a
                 ``Significance Mode'' of operation which is intended to
                 facilitate the identification of significant bits in
                 the results of floating-point arithmetic operations.
                 The manner in which floating-point arithmetic is
                 handled in this mode is discussed. Several numerical
                 experiments using this mode are described and
                 comparisons are made with the ordinary ``normalized
                 mode.'' Examples include power series evaluation,
                 linear equations solution, determinant evaluation and
                 matrix inversion.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Article{Knuth:1963:LEE,
  author =       "Donald E. Knuth",
  title =        "Letter to the {Editor}: {Evaluation} of polynomials by
                 computer",
  journal =      j-CACM,
  volume =       "6",
  number =       "2",
  pages =        "51--51",
  month =        feb,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Tue Dec 26 16:31:38 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Knuth:1962:EPC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@Article{Krishnamurthy:1963:CMD,
  author =       "E. V. Krishnamurthy",
  title =        "On Computer Multiplication and Division Using Binary
                 Logarithms",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-12",
  number =       "3",
  pages =        "319--320",
  month =        jun,
  year =         "1963",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1963.263572",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 08:10:39 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037874",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Article{Lehman:1963:MAB,
  author =       "M. Lehman",
  title =        "The Minimization of Assimilations in Binary
                 Carry-Storage Arithmetic Units",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-12",
  number =       "4",
  pages =        "409--410",
  month =        aug,
  year =         "1963",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1963.263479",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 08:10:40 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037921",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Article{Lehmer:1963:RDO,
  author =       "D. H. Lehmer",
  title =        "{R63--17} Division and Overflow Detection in Residue
                 Number Systems",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-12",
  number =       "1",
  pages =        "36--37",
  month =        feb,
  year =         "1963",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1963.263493",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 08:10:36 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4037754;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4037786",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
  keywords =     "residue arithmetic; residue number system",
}

@Article{Lindamood:1963:MCO,
  author =       "George E. Lindamood and George Shapiro",
  title =        "Magnitude Comparison and Overflow Detection in Modular
                 Arithmetic Computers",
  journal =      j-SIAM-REVIEW,
  volume =       "5",
  number =       "4",
  pages =        "342--350",
  month =        "????",
  year =         "1963",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1005095",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu Mar 27 09:05:07 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/5/4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "October 1963",
}

@Article{Metropolis:1963:BOU,
  author =       "N. Metropolis and R. L. Ashenhurst",
  title =        "Basic Operations in an Unnormalized Arithmetic
                 System",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-12",
  number =       "6",
  pages =        "896--904",
  month =        dec,
  year =         "1963",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1963.263593",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 08:10:44 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038037",
  ZMnumber =     "0124.07910",
  abstract =     "A particular set of unnormalized arithmetic operations
                 termed ``basic'' are described, in the context of the
                 University of Chicago Maniac III Computer. Each basic
                 operation involves three operand words and generates
                 two result words, all in unnormalized floating point
                 format. The use of these operations in the
                 implementation of multi-precision arithmetic is
                 explained; in particular, it is demonstrated that
                 multiprecision division can be effected in a
                 nontentative manner with their aid.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753",
  keywords =     "MANIAC III",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Book{Mood:1963:ITS,
  author =       "Alexander McFarlane Mood and Franklin A. Graybill",
  title =        "Introduction to the theory of statistics",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  edition =      "Second",
  pages =        "443",
  year =         "1963",
  LCCN =         "HA29 .M75 1963",
  bibdate =      "Fri Aug 20 10:02:03 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "McGraw-Hill series in probability and statistics",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
  subject =      "Mathematical statistics",
}

@Article{Stern:1963:CSR,
  author =       "T. E. Stern and R. M. Lerner",
  title =        "A circuit for the square root of the sum of the
                 squares",
  journal =      j-PROC-IEEE,
  volume =       "51",
  number =       "4",
  pages =        "593--596",
  month =        apr,
  year =         "1963",
  CODEN =        "IEEPAD",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
  summary =      "A piecewise-linear network can produce an output
                 proportional to the square root of the sum of the
                 squares of a set of input voltages, using resistors and
                 diodes alone. The required relationship between
                 voltages can be represented by a multi- \ldots{}",
}

@Article{Stroud:1963:MPF,
  author =       "A. H. Stroud and D. Secrest",
  title =        "A multiple-precision floating-point interpretive
                 program for the {Control Data} 1604",
  journal =      j-COMP-J,
  volume =       "6",
  number =       "1",
  pages =        "62--66",
  month =        apr,
  year =         "1963",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:55:45 MDT 2000",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/060062.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/62.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/63.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/64.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/65.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_01/tiff/66.tif",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Svoboda:1963:AD,
  author =       "A. Svoboda",
  title =        "An algorithm for division",
  journal =      j-INF-PROCESS-MACH,
  volume =       "9",
  number =       "??",
  pages =        "25--33",
  month =        "????",
  year =         "1963",
  CODEN =        "IPRMDD",
  ISSN =         "0373-885X",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  fjournal =     "Information processing machines",
}

@InProceedings{Wilkinson:1963:PSA,
  author =       "J. H. Wilkinson",
  title =        "Plane rotations in floating-point arithmetic",
  crossref =     "Metropolis:1963:PFS",
  pages =        "185--198",
  year =         "1963",
  MRclass =      "65.35",
  MRnumber =     "28\#1744",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  reviewer =     "A. S. Householder",
}

@Article{Aiken:1964:PAC,
  author =       "H. H. Aiken and A. G. Oettinger and T. C. Bartee",
  title =        "Proposed automatic calculating machine",
  journal =      j-IEEE-SPECTRUM,
  volume =       "1",
  number =       "8",
  pages =        "62--69",
  month =        aug,
  year =         "1964",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.1964.6500770",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Tue Jan 14 11:14:17 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "Previously unpublished memorandum written by Aiken and
                 dated by an unknown recipient as 4 November 1937.
                 Reprinted in \cite[\S 5.1]{Randell:1982:ODC}.",
  abstract =     "Here presented is the memorandum that 20 years ago
                 initiated a series of events whose revolutionary
                 implications are only beginning to manifest themselves
                 a description of the first large-scale general-purpose
                 automatic digital computer. Twenty years ago, on August
                 7, 1944, Mark I, the first large-scale general-purpose
                 automatic digital computer ever to be put in operation
                 was dedicated at Harvard University by James B. Conant,
                 then president of Harvard, and the late Thomas J.
                 Watson, founder of IBM.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  remark =       "Pages 66--69 discuss computation of the elementary
                 functions with minimal intermediate storage: recipes
                 are given for integral and fractional power, log,
                 exponential, trigonometric, inverse trigonometric,
                 hyperbolic, and inverse hyperbolic. Mention is also
                 made of the probability integral, elliptic functions,
                 and Bessel functions, but the text says they will be
                 discussed later (meaning, in a future publication). The
                 methods involve recurrences and series summations, and
                 thus, can be regarded as precision independent.",
}

@Manual{Anonymous:1964:PPF,
  author =       "Anonymous",
  title =        "{PINT}: {Purdue} floating point interpretive system:
                 for the {RPC 4000 General Precision} electronic
                 computer",
  organization = "General Precision, Inc.",
  address =      "West Lafayette, IN, USA",
  pages =        "45",
  year =         "1964",
  bibdate =      "Mon May 06 10:24:31 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers --- Programming.; Purdue
                 University School of Electrical Engineering; RPC 4000
                 (Computer)",
  remark =       "Program no. H1-02.0",
}

@Article{Ashenhurst:1964:FEU,
  author =       "R. L. Ashenhurst",
  title =        "Function Evaluation in Unnormalized Arithmetic",
  journal =      j-J-ACM,
  volume =       "11",
  number =       "2",
  pages =        "168--187",
  month =        apr,
  year =         "1964",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Thu Nov 03 22:33:52 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}

@Article{Baer:1964:MPA,
  author =       "Robert M. Baer and Martin G. Redlich",
  title =        "Multiple-precision arithmetic and the exact
                 calculation of the $ 3 - j $, $ 6 - j $ and $ 9 - j $
                 symbols",
  journal =      j-CACM,
  volume =       "7",
  number =       "11",
  pages =        "657--659",
  month =        nov,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.25",
  MRnumber =     "31\#865",
  bibdate =      "Mon Oct 24 09:33:02 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Described in this paper is a system of general-purpose
                 multiple-precision fixed-point routines and their use
                 in subroutines which calculate exactly the
                 quantum-mechanical 3-j, 6-j and 9-j symbols of large
                 arguments.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@MastersThesis{Bookhart:1964:SFP,
  author =       "Thomas Woodward Bookhart",
  title =        "A study of floating point arithmetic",
  type =         "Thesis ({M.S. in Math.})",
  school =       "Georgia Institute of Technology",
  address =      "Atlanta, GA, USA",
  pages =        "51",
  year =         "1964",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers.; Number theory.;
                 Numerical calculations --- Computer programs.",
}

@Article{Brooker:1964:PPS,
  author =       "R. A. Brooker",
  title =        "A programming package for some general modes of
                 arithmetic",
  journal =      j-CACM,
  volume =       "7",
  number =       "2",
  pages =        "119--127",
  month =        feb,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Oct 24 09:33:00 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "An interpretive programming package is described for
                 computation with operands which may be real, complex,
                 single or double precision, or real multiple precision.
                 It also performs operations on matrices formed from
                 these elements. A simple language structure is used to
                 describe the computation.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Manual{Burroughs:1964:BBI,
  author =       "{Burroughs Corporation}",
  title =        "{Burroughs B5500} Information Processing Systems
                 Reference Manual",
  organization = "Burroughs Corporation",
  address =      "Detroit, MI, USA",
  year =         "1964",
  bibdate =      "Wed Nov 22 21:15:11 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
  remark =       "The B5500 uses a decimal integer or fixed-point
                 coefficient of 21 or 22 digits, with an exponent range
                 of $ \pm 63 $.",
}

@Article{Cody:1964:DPS,
  author =       "W. J. {Cody, Jr.}",
  title =        "Double-Precision Square Root for the {CDC-3600}",
  journal =      j-CACM,
  volume =       "7",
  number =       "12",
  pages =        "715--718",
  month =        dec,
  year =         "1964",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355588.365122",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 1 10:15:43 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In January of 1960, the late Hans J. Maehly completed
                 a summary of approximations to the elementary functions
                 for the CDC-1604 computer. The approximations and
                 techniques suggested by Maehly are equally applicable
                 to the second large computer in the CDC line, the 3600.
                 Unlike the 1604, however, the 3600 has built-in
                 double-precision floating-point arithmetic. The present
                 work, largely inspired by the successes of Maehly and
                 his associates, concerns the extension of one of
                 Maehly's ideas to a double-precision subroutine for the
                 3600.",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$sqrt(x)$; CDC 3600; elementary functions",
}

@Article{Cowgill:1964:LEB,
  author =       "D. Cowgill",
  title =        "Logic Equations for a Built-In Square Root Method",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-13",
  number =       "2",
  pages =        "156--157",
  month =        apr,
  year =         "1964",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1964.263791",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:56:59 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038119",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Article{Eve:1964:EP,
  author =       "J. Eve",
  title =        "The Evaluation of Polynomials",
  journal =      j-NUM-MATH,
  volume =       "6",
  pages =        "17--21",
  year =         "1964",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Fri Sep 16 10:21:47 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  xxmonth =      "(none)",
  xxnumber =     "(none)",
}

@MastersThesis{Goldschmidt:1964:ADC,
  author =       "Robert E. Goldschmidt",
  title =        "Applications of Division by Convergence",
  type =         "Thesis ({M.S.})",
  school =       "Department of Electrical Engineering, Massachusetts
                 Institute of Technology",
  address =      "Cambridge, MA, USA",
  pages =        "44",
  month =        jun,
  year =         "1964",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://dspace.mit.edu/handle/1721.1/11113",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  advisor =      "Alfred K. Susskind",
  remark =       "This thesis introduced the quadratically convergent
                 Goldschmidt algorithm for iterative division, as an
                 alternative to Newton--Raphson iteration: see
                 \cite{Flynn:1966:VHS, Anderson:1967:ISMb,
                 Flynn:1970:DFI, Ito:1995:EIAb, Oberman:1996:FIR,
                 Ercegovac:1999:IGD, Ercegovac:2000:IGD,
                 Gallagher:2000:FTN, Even:2003:PEA, Markstein:2004:SDS,
                 Even:2005:PEA, Piso:2006:OMD, Schulte:2007:FPD,
                 Kong:2008:RMI, Piso:2008:FOS, Piso:2008:NRA,
                 Ruiz:2008:EIR, Kong:2010:RMR, Kong:2011:GDM,
                 Piso:2011:VLG, Panhaleux:2012:CFP} for improvements and
                 error analysis. For computing $ Q = N / D $,
                 Newton--Raphson starts with $ Y \approx 1 / D $, and
                 iterates $ Y \leftarrow (2 - Y D) Y $, or equivalently,
                 $ Y \leftarrow Y - (Y (Y D - 1)) $. With the same
                 starting point, Goldschmidt instead iterates $ N
                 \leftarrow N Y $, $ D \leftarrow D Y $, $ Y = 2 - D $,
                 which converges to $ Y = 1 $. When parallel multipliers
                 are available, the two multiplies can be done at the
                 same time, whereas Newton--Raphson requires two
                 sequential multiplies. In addition, the update $ 2 D $
                 can be computed in hardware by a fast bitwise two's
                 complement operation, instead of a slower
                 floating-point subtraction. The Goldschmidt algorithm
                 has been used in CPUs of the IBM S/360 model 91 and the
                 AMD K7. Unfortunately, unlike Newton--Raphson, each
                 iteration of the Goldschmidt algorithm increases
                 rounding error. Numerical tests of the Goldschmidt
                 algorithm show worst-case errors in ulps roughly equal
                 to the number of iterations. Without an FMA, the
                 Newton--Raphson worst case errors are about 1.7 ulps,
                 and with an FMA, about 1.0 ulps. In hardware in both
                 cases, a few bits of extra intermediate precision can
                 lead to correctly rounded results. Without extra
                 precision, additional fixups are needed for correct
                 rounding.",
}

@Article{Gram:1964:RZF,
  author =       "Christian Gram",
  title =        "On the Representation of Zero in Floating-Point
                 Arithmetic",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "4",
  number =       "3",
  pages =        "156--161",
  month =        sep,
  year =         "1964",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01956026",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "68.00",
  MRnumber =     "29\#5412",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=4&issue=3&spage=156",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point arithmetic; rounding errors",
}

@Article{Gregory:1964:FAN,
  author =       "Robert T. Gregory and James L. Raney",
  title =        "Floating-point arithmetic with $ 84 $-bit numbers",
  journal =      j-CACM,
  volume =       "7",
  pages =        "10--13",
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "68.00",
  MRnumber =     "30\#2706",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Book{Henrici:1964:ENA,
  author =       "Peter Henrici",
  title =        "Elements of numerical analysis",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xv + 328",
  year =         "1964",
  LCCN =         "QA297 .H4",
  bibdate =      "Fri Aug 20 09:17:19 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  remark =       "Based on the author's lecture notes for a course
                 entitled {\em Numerical Mathematical Analysis\/} at the
                 University of California, Los Angeles. Cited in
                 \cite{Sterbenz:1974:FPC}.",
  subject =      "Numerical analysis",
}

@Article{Jacobsohn:1964:SFM,
  author =       "D. Jacobsohn",
  title =        "A Suggestion for a Fast Multiplier",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-13",
  number =       "6",
  pages =        "754--754",
  month =        dec,
  year =         "1964",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1964.263942",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:57:06 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038318",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Book{Khinchin:1964:CF,
  author =       "Aleksandr Iakovlevich Khinchin",
  title =        "Continued fractions",
  publisher =    "P. Noordhoff",
  address =      "Groningen, The Netherlands",
  pages =        "101",
  year =         "1964",
  LCCN =         "QA295 .K513 1964a",
  bibdate =      "Fri Nov 30 06:55:53 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Translated by Peter Wynn",
  URL =          "http://www.loc.gov/catdir/description/dover032/97008056.html;
                 http://www.loc.gov/catdir/toc/dover031/97008056.html",
  acknowledgement = ack-nhfb,
  author-dates = "1894--1959",
}

@Article{Klokacev:1964:RNF,
  author =       "I. V. Kloka{\v{c}}ev",
  title =        "A refinement of the normalized floating point number
                 notation on digital computers. ({Russian})",
  journal =      "{\v{Z}}. Vy{\v{c}}isl. Mat. i Mat. Fiz.",
  volume =       "4",
  pages =        "192--194",
  year =         "1964",
  MRclass =      "68.00",
  MRnumber =     "28\#4694",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@Article{Kundu:1964:TMD,
  author =       "P. Kundu and S. Banerji",
  title =        "Transistorized Multiplier and Divider and Its
                 Applications",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-13",
  number =       "3",
  pages =        "288--295",
  month =        jun,
  year =         "1964",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1964.263919",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:57:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038157",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Article{Lamson:1964:DAD,
  author =       "Roger C. Lamson",
  title =        "A Division Algorithm for a Digital Differential
                 Analyzer",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-13",
  number =       "1",
  pages =        "54--55",
  month =        feb,
  year =         "1964",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1964.263838",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:56:57 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038079",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Article{Lynn:1964:REM,
  author =       "M. Stuart Lynn",
  title =        "On the Round-Off Error in the Method of Successive
                 Over-Relaxation",
  journal =      j-MATH-COMPUT,
  volume =       "18",
  number =       "85",
  pages =        "36--49",
  month =        jan,
  year =         "1964",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Book{Maley:1964:MDC,
  author =       "Gerald A. Maley and Edward J. Skiko",
  title =        "Modern digital computers",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xiv + 216",
  year =         "1964",
  LCCN =         "QA76.5 .M192",
  bibdate =      "Thu Nov 18 10:04:00 MST 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Prentice-Hall electrical engineering series",
  acknowledgement = ack-nhfb,
  keywords =     "binary arithmetic",
  subject =      "Electronic digital computers",
}

@Book{McCracken:1964:NMF,
  author =       "Daniel D. McCracken and William S. Dorn",
  title =        "Numerical methods and {FORTRAN} programming, with
                 applications in engineering and science",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xii + 457",
  year =         "1964",
  bibdate =      "Sat Jan 27 13:40:57 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Numerical analysis --- Data processing.; {Fortran}
                 (Computer program language)",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Merrill:1964:IDC,
  author =       "Roy D. Merrill",
  title =        "Improving Digital Computer Performance Using Residue
                 Number Theory",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-13",
  number =       "2",
  pages =        "93--101",
  month =        apr,
  year =         "1964",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1964.263776;
                 https://doi.org/10.1109/PGEC.1964.263777",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:56:58 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4038099;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038105",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Residue arithmetic has the interesting characteristic
                 that in multiplication, addition and subtraction any
                 digit in the result is dependent only on its two
                 corresponding operand digits. Consequently, for these
                 operations, residue arithmetic is \ldots{}",
}

@Article{Miller:1964:ESD,
  author =       "R. H. Miller",
  title =        "An example in ``significant-digit'' arithmetic",
  journal =      j-CACM,
  volume =       "7",
  number =       "1",
  pages =        "21--21",
  month =        jan,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Oct 24 09:33:00 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Different methods of handling the summing process for
                 the geometric series are shown to give results
                 indicating widely differing significances when carried
                 out in a machine incorporating ``significant-digit''
                 arithmetic.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@MastersThesis{Moss:1964:RDC,
  author =       "George Joseph {Moss, Jr.}",
  title =        "Recording digital counter with floating point output
                 format",
  type =         "Thesis ({M.S.})",
  school =       "University of Maryland",
  address =      "College Park, MD, USA",
  pages =        "155",
  year =         "1964",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{Rice:1964:AFV,
  author =       "John R. Rice",
  title =        "The Approximation of Functions",
  volume =       "1",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "various",
  year =         "1964",
  LCCN =         "QA221 .R5 V.1-2",
  bibdate =      "Fri Dec 08 13:02:52 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Santos:1964:BVB,
  author =       "J. Santos and H. Arango",
  title =        "Base $3$ vs Base $2$ Synchronous Arithmetic Units",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-13",
  number =       "5",
  pages =        "608--609",
  month =        oct,
  year =         "1964",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1964.263734",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:57:04 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038256",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Article{Stein:1964:DCM,
  author =       "M. L. Stein",
  title =        "Divide-and-Correct Methods for Multiple Precision
                 Division",
  journal =      j-CACM,
  volume =       "7",
  number =       "8",
  pages =        "472--474",
  month =        aug,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@MastersThesis{Sweo:1964:SFP,
  author =       "David Ernest Sweo",
  title =        "A study of floating point arithmetic with the residue
                 number system",
  type =         "Thesis ({M.S.})",
  school =       "UCLA - Engineering",
  address =      "Los Angeles, CA, USA",
  pages =        "89",
  year =         "1964",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Congruences and residues.; Electronic digital
                 computers --- Programming.",
}

@Article{Wallace:1964:SFM,
  author =       "C. S. Wallace",
  title =        "A Suggestion for a Fast Multiplier",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-13",
  number =       "1",
  pages =        "14--17",
  month =        feb,
  year =         "1964",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1964.263830",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:56:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038071",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Article{Wolfe:1964:RTE,
  author =       "Jack M. Wolfe",
  title =        "Reducing Truncation Errors by Programming",
  journal =      j-CACM,
  volume =       "7",
  number =       "6",
  pages =        "355--356",
  month =        jun,
  year =         "1964",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/512274.512287",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:54 MST 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In accumulating a sum such as in a numerical
                 integration with a large number of intervals, the sum
                 itself becomes much larger than the individual addends.
                 This may produce a less accurate sum as the number of
                 intervals is increased. Separate variables can be
                 established as accumulators to hold partial sums within
                 various distinct intervals. Thus, the extensive
                 successive truncations are eliminated.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "floating-point arithmetic; truncation errors",
  remark =       "This algorithm is a precursor of Kahan's compensated
                 summation algorithm \cite{Kahan:1965:PFR}; see \cite[p.
                 384]{Lange:2020:NDF} for a discussion.",
}

@Article{Ashenhurst:1965:EEC,
  author =       "R. L. Ashenhurst and N. Metropolis",
  title =        "Error Estimation in Computer Calculation",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "72",
  number =       "2 (Part 2)",
  pages =        "47--58",
  year =         "1965",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "65.80",
  MRnumber =     "MR0192671 (33 \#896)",
  MRreviewer =   "James H. Wilkinson",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in Department of Economics, Graduate School
                 of Business, University of Chicago, Center for
                 Mathematical Studies in Business and Economics, number
                 45.",
  ZMnumber =     "0216.49602",
  acknowledgement = ack-jr,
  fjournal =     "The American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
  keywords =     "error estimation; floating-point arithmetic",
}

@InProceedings{Ashenhurst:1965:EIU,
  author =       "R. L. Ashenhurst",
  editor =       "L. B. Rall",
  booktitle =    "Error in digital computation",
  title =        "Experimental investigation of unnormalized
                 arithmetic",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "3--37",
  year =         "1965",
  bibdate =      "Thu Nov 8 14:49:59 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARI FLP",
}

@InProceedings{Ashenhurst:1965:TAE,
  author =       "R. L. Ashenhurst",
  editor =       "L. B. Rall",
  booktitle =    "Error in digital computation",
  title =        "Techniques for automatic error monitoring and
                 control",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "43--59",
  year =         "1965",
  bibdate =      "Tue Oct 9 09:42:56 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARI FLP",
}

@Article{Atrubin:1965:ODR,
  author =       "A. J. Atrubin",
  title =        "A One-Dimensional Real-Time Iterative Multiplier",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "3",
  pages =        "394--399",
  month =        jun,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.264145",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:33 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038457",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Article{Blum:1965:EAP,
  author =       "B. I. Blum",
  title =        "An Extended Arithmetic Package",
  journal =      j-CACM,
  volume =       "8",
  number =       "5",
  pages =        "318--320",
  month =        may,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 8 08:20:53 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Article{Combet:1965:CBT,
  author =       "M. Combet and H. {Van Zonneveld} and L. Verbeek",
  title =        "Computation of the Base Two Logarithm of Binary
                 Numbers",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "6",
  pages =        "863--867",
  month =        dec,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.264080",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:41 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038605",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Article{Dadda:1965:SSP,
  author =       "Luigi Dadda",
  title =        "Some Schemes for Parallel Multipliers",
  journal =      j-ALTA-FREQ,
  volume =       "34",
  number =       "??",
  pages =        "349--356",
  month =        mar,
  year =         "1965",
  CODEN =        "ALFRAJ",
  ISSN =         "0002-6557",
  ISSN-L =       "0002-6557",
  bibdate =      "Fri Nov 09 10:47:42 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[pages
                 118--225]{Swartzlander:1990:CAa}.",
  URL =          "http://en.wikipedia.org/wiki/Dadda_multiplier;
                 http://en.wikipedia.org/wiki/luigi_dadda",
  acknowledgement = ack-nhfb,
  author-dates = "29 April 1923--26 October 2012",
  fjournal =     "Alta frequenza",
  remark =       "According to an ARITH'21 conference attendee, this is
                 a recommended article for understanding the Wallace and
                 Dadda multipliers.",
}

@Article{Deiters:1965:ODD,
  author =       "Robert M. Deiters",
  title =        "Optimum Design of a Diode Squarer by Applying the
                 Criterion of Square Root of the Integral of Per Cent
                 Error Squared",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "3",
  pages =        "456--463",
  month =        jun,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.264153",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:34 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038465",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Article{Dodd:1965:RSB,
  author =       "George G. Dodd",
  title =        "Remarks on Simulation of {Boolean} Functions",
  journal =      j-CACM,
  volume =       "8",
  number =       "8",
  pages =        "517--517",
  month =        aug,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:01 MST 2005",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Recently M. Morris Mano presented a method for
                 performing Boolean OR, AND and NOT operations by means
                 of arithmetic and conditional transfer operations in a
                 decimal computer lacking builtin logical
                 instructions.",
  acknowledgement = ack-nhfb,
  checked =      "19940407",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Boolean operations; decimal arithmetic",
  sjb =          "Commenting on \cite{Mano:1965:PSB}.",
}

@Article{Earle:1965:LCS,
  author =       "J. G. Earle",
  title =        "Latched Carry-Save Adder",
  journal =      j-IBM-TDB,
  volume =       "7",
  number =       "??",
  pages =        "909--910",
  month =        mar,
  year =         "1965",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Fri Nov 09 10:49:36 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Technical Disclosure Bulletin",
}

@Article{Fraser:1965:SMC,
  author =       "W. Fraser",
  title =        "A Survey of Methods for Computing Minimax and
                 Near-Minimax Polynomial Approximations for Functions of
                 a Single Independent Variable",
  journal =      j-J-ACM,
  volume =       "12",
  number =       "3",
  pages =        "295--314",
  month =        jul,
  year =         "1965",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/321281.321282",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Thu Nov 03 08:47:50 1994",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jacm.bib",
  abstract =     "Methods are described for the derivation of minimax
                 and near-minimax polynomial approximations. For minimax
                 approximations techniques are considered for both
                 analytically defined functions and functions defined by
                 a table of values. For near-minimax approximations
                 methods of determining the coefficients of the
                 Fourier--Chebyshev expansion are first described. These
                 consist of the rearrangement of the coefficients of a
                 power polynomial, and also direct determination of the
                 coefficients from the integral which defines them, or
                 the differential equation which defines the function.
                 Finally there is given a convenient modification of an
                 interpolation scheme which finds coefficients of a
                 near-minimax approximation without requiring numerical
                 integration or the numerical solution of a system of
                 equations.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "https://dl.acm.org/loi/jacm",
}

@InCollection{Garner:1965:NSA,
  author =       "H. L. Garner",
  title =        "Number systems and arithmetic",
  crossref =     "Alt:1965:AC",
  volume =       "6",
  pages =        "131--194",
  year =         "1965",
  bibdate =      "Sat May 18 14:18:19 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Garner:1965:RID,
  author =       "H. L. Garner",
  title =        "{R65-22} Improving Digital Computer Performance Using
                 Residue Number Theory",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "2",
  pages =        "277--277",
  month =        apr,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.263975",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:23 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4038385;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038430",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
  keywords =     "residue arithmetic; residue number system",
}

@Article{Hammel:1965:RLC,
  author =       "D. Hammel",
  title =        "{R65-54} The Logic of Computer Arithmetic",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "4",
  pages =        "670--670",
  month =        aug,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.264031",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:40 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038535",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Article{Hammer:1965:BRBa,
  author =       "Preston C. Hammer",
  title =        "Book Review: {{\booktitle{Experimental Arithmetic,
                 High Speed Computing and Mathematics}} by N. C.
                 Metropolis; A. H. Taub; John Todd; C. B. Tompkins}",
  journal =      j-TECHNOMETRICS,
  volume =       "7",
  number =       "1",
  pages =        "82--82",
  month =        feb,
  year =         "1965",
  CODEN =        "TCMTA2",
  DOI =          "https://doi.org/10.2307/1266139",
  ISSN =         "0040-1706 (print), 1537-2723 (electronic)",
  ISSN-L =       "0040-1706",
  bibdate =      "Sat Jun 21 13:17:45 MDT 2014",
  bibsource =    "http://www.jstor.org/journals/00401706.html;
                 http://www.jstor.org/stable/i254241;
                 https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/technometrics1960.bib",
  URL =          "http://www.jstor.org/stable/1266139",
  acknowledgement = ack-nhfb,
  fjournal =     "Technometrics",
  journal-URL =  "http://www.jstor.org/journals/00401706.html",
}

@Article{Hammer:1965:BRBb,
  author =       "Preston C. Hammer",
  title =        "Book Review: {{\booktitle{Experimental Arithmetic,
                 High Speed Computing and Mathematics}} by N. C.
                 Metropolis, A. H. Taub, John Todd, and C. B.
                 Tompkins}",
  journal =      j-TECHNOMETRICS,
  volume =       "7",
  number =       "1",
  pages =        "82--82",
  month =        feb,
  year =         "1965",
  CODEN =        "TCMTA2",
  ISSN =         "0040-1706 (print), 1537-2723 (electronic)",
  ISSN-L =       "0040-1706",
  bibdate =      "Tue Mar 20 13:44:52 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/technometrics1960.bib",
  URL =          "http://links.jstor.org/sici?sici=0040-1706%28196502%297%3A1%3C82%3AEAHSCA%3E2.0.CO%3B2-9",
  acknowledgement = ack-nhfb,
  fjournal =     "Technometrics",
  journal-URL =  "http://www.jstor.org/journals/00401706.html",
}

@Article{Hamming:1965:NLB,
  author =       "R. W. Hamming and W. L. Mammel",
  title =        "A Note on the Location of the Binary Point in a
                 Computing Machine",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "2",
  pages =        "260--261",
  month =        apr,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.264258",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038414",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
  remark =       "The authors consider the low-level multiplication
                 circuit efficiency of placing the binary point before
                 or after the first bit. If the leading bit is equally
                 likely to be a 0 or a 1, then their analysis shows that
                 it is better to place the point before the leading bit.
                 However, they report that a more likely distribution is
                 logarithmic (as predicted by Benford's Law, although
                 the Newcomb / Benford work is neither mentioned nor
                 cited), in which case there is no advantage for either
                 choice of placement of the binary point. The conclude
                 that it would be humane to place it after the leading
                 digit, by analogy with how people learn decimal
                 arithmetic.",
}

@Article{Ikebe:1965:NTP,
  author =       "Yasuhiko Ikebe",
  title =        "Note on Triple-Precision Floating-Point Arithmetic
                 with 132-Bit Numbers",
  journal =      j-CACM,
  volume =       "8",
  number =       "3",
  pages =        "175--177",
  month =        mar,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "68.00",
  MRnumber =     "30\#2707",
  bibdate =      "Fri Dec 08 14:32:51 1995",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In a recent paper, Gregory and Raney described a
                 technique for double-precision floating-point
                 arithmetic. A similar technique can be developed for
                 triple-precision floating-point arithmetic and its is
                 the purpose of this note to describe this technique.
                 Only the multiplication and the division algorithms are
                 described, since the addition-subtraction algorithm can
                 be obtained by a trivial modification of the algorithm
                 in Gregory's and Raney's paper.",
  acknowledgement = ack-nhfb,
  checked =      "19940404",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Article{James:1965:GSR,
  author =       "Wendy James and P. Jarratt",
  title =        "The Generation of Square Roots on a Computer with
                 Rapid Multiplication Compared with Division (in
                 {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "91",
  pages =        "497--500",
  month =        jul,
  year =         "1965",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@InCollection{Kahan:1965:FPO,
  author =       "W. Kahan",
  booktitle =    "Programmer's Reference Manual",
  title =        "The Floating-Point Over\slash Underflow Trap Routine
                 {{\tt FPTRP}}",
  publisher =    "Institute of Computer Science, University of Toronto",
  address =      "Toronto, Ontario, Canada",
  year =         "1965",
  LCCN =         "????",
  bibdate =      "Wed Feb 14 19:11:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Section 4.1.",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Kahan:1965:PFR,
  author =       "W. Kahan",
  title =        "Pracniques: {Further} Remarks on Reducing Truncation
                 Errors",
  journal =      j-CACM,
  volume =       "8",
  number =       "1",
  pages =        "40--40",
  month =        jan,
  year =         "1965",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363707.363723",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 00:18:17 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "floating-point arithmetic; truncation errors",
  remark =       "Gives summation error estimate formula `s = fl(a + b);
                 error = (a - s) + b', also discovered independently by
                 \cite{Moller:1965:QDP}. Extends Gill's earlier
                 fixed-point result \cite{Gill:1951:PSS}. See
                 improvement \cite{Ozawa:1993:SAE}.",
}

@Article{Kanner:1965:NBC,
  author =       "Herbert Kanner",
  title =        "Number Base Conversion in Significant Digit
                 Arithmetic",
  journal =      j-J-ACM,
  volume =       "12",
  number =       "2",
  pages =        "242--246",
  month =        apr,
  year =         "1965",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Thu Nov 03 08:47:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{King:1965:LED,
  author =       "R. King",
  title =        "Letter to the {Editor}: On the Double-Precision Square
                 Root Routine",
  journal =      j-CACM,
  volume =       "8",
  number =       "4",
  pages =        "202",
  month =        apr,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 1 10:15:43 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\sqrt(x)$; elementary functions; floating-point
                 arithmetic",
}

@Article{Krishnamurthy:1965:DCM,
  author =       "E. V. Krishnamurthy",
  title =        "On a Divide-and-Correct Method for Variable Precision
                 Division",
  journal =      j-CACM,
  volume =       "8",
  number =       "3",
  pages =        "179--181",
  month =        mar,
  year =         "1965",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363791.363829",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "68.00",
  MRnumber =     "30\#2709",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Described in this paper is a divide-and-correct method
                 for variable precision division in digital computers.
                 Unlike the earlier methods of Stein and Pope, the
                 present method uses a suitably rounded form of the
                 normalized divisor for getting an estimate of the
                 quotient characters. This result is a correction of at
                 most plus or minus one to the estimate, to obtain the
                 exact quotient character. It is believed that this
                 method will be widely applicable for division
                 operations in variable word-length character-oriented
                 machines.",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "correct rounding; floating-point arithmetic",
}

@TechReport{Lederer:1965:FPP,
  author =       "E. Lederer",
  title =        "Floating-point-Pegasus, {FLPPEG}",
  type =         "{ISD-Bericht}",
  number =       "12",
  institution =  "ISD, Inst. f{\"u}r Statik u. Dynamik d. Luft- u.
                 Raumfahrtkonstruktionen, Universit{\"a}t Stuttgart",
  address =      "Stuttgart, Germany",
  pages =        "5",
  year =         "1965",
  bibdate =      "Thu May 09 09:05:51 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lehman:1965:SAT,
  author =       "M. Lehman",
  title =        "Serial Arithmetic Techniques",
  crossref =     "AFIPS:1965:FJC",
  pages =        "715--725",
  year =         "1965",
  bibdate =      "Tue Jan 08 23:08:35 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@MastersThesis{Liddiard:1965:DPF,
  author =       "Lawrence Anthony Liddiard",
  title =        "Double precision floating point arithmetic",
  type =         "Thesis ({M.S.})",
  school =       "University of Minnesota",
  address =      "????",
  pages =        "various",
  year =         "1965",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Calculators.; Numerical calculations.",
}

@Book{Lyusternik:1965:HCE,
  author =       "L. A. Lyusternik and O. A. Chervonenkis and A. R.
                 Yanpolski",
  title =        "Handbook for Computing Elementary Functions",
  publisher =    pub-PERGAMON,
  address =      pub-PERGAMON:adr,
  pages =        "xiii + 251",
  year =         "1965",
  LCCN =         "QA221.L513",
  bibdate =      "Thu Sep 1 10:13:16 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Translated from the Russian by G. J. Tee. Translation
                 edited by K. L. Stewart.",
  acknowledgement = ack-nj,
}

@Article{Mano:1965:PSB,
  author =       "M. Morris Mano",
  title =        "Pracniques: {Simulation} of {Boolean} functions in a
                 decimal computer",
  journal =      j-CACM,
  volume =       "8",
  number =       "1",
  pages =        "39--40",
  month =        jan,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:58 MST 2005",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See remarks \cite{Dodd:1965:RSB}.",
  acknowledgement = ack-nhfb,
  checked =      "19940304",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  sjb =          "Describes how to perform Boolean operations by means
                 of arithmetic and conditional transfer operations on a
                 decimal computer lacking any built in logical
                 instructions. See also \cite{Dodd:cacm:65}.",
}

@Article{Martin:1965:SHS,
  author =       "A. R. Martin and A. B. Rosenstein",
  title =        "A Shiftrix for High-Speed Multiplication",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "4",
  pages =        "639--643",
  month =        aug,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.264010",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:39 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038521",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@InProceedings{Metropolis:1965:AIE,
  author =       "N. Metropolis",
  title =        "Analysis of Inherent Errors in Matrix Decomposition
                 Using Unnormalized Arithmetic",
  crossref =     "Kalenich:1965:IPP",
  volume =       "2",
  pages =        "441--442",
  year =         "1965",
  bibdate =      "Wed Feb 14 19:21:38 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0161.35502",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Metropolis:1965:AUA,
  author =       "N. Metropolis",
  title =        "Algorithms in unnormalized arithmetic. {I}.
                 {Recurrence} relations",
  journal =      j-NUM-MATH,
  volume =       "7",
  number =       "2",
  pages =        "104--112",
  month =        apr,
  year =         "1965",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "68.00",
  MRnumber =     "MR0178589 (31 \#2846)",
  MRreviewer =   "G. Dahlquist",
  bibdate =      "Wed Nov 14 19:04:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See erratum \cite{Metropolis:1965:BAU}.",
  ZMnumber =     "0128.36301",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Metropolis:1965:BAU,
  author =       "N. Metropolis",
  title =        "Berichtigung: {Algorithms} in unnormalized arithmetic.
                 {I}. {Recurrence} relations",
  journal =      j-NUM-MATH,
  volume =       "7",
  number =       "4",
  pages =        "354",
  month =        aug,
  year =         "1965",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "Contributed Item",
  MRnumber =     "MR1553943",
  bibdate =      "Wed Nov 14 19:04:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Metropolis:1965:RCU,
  author =       "N. Metropolis and R. L. Ashenhurst",
  title =        "Radix Conversion in an Unnormalized Arithmetic
                 System",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "91",
  pages =        "435--441",
  month =        jul,
  year =         "1965",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  URL =          "http://links.jstor.org/sici?sici=0025-5718%28196507%2919%3A91%3C435%3ARCIAUA%3E2.0.CO%3B2-D",
  ZMnumber =     "0146.14607",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Metze:1965:MSR,
  author =       "Gernot Metze",
  title =        "Minimal Square Rooting",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "2",
  pages =        "181--185",
  month =        apr,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.263963",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038397",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Article{Miller:1965:ASF,
  author =       "G. F. Miller",
  title =        "Algorithms for Special Functions {II}",
  journal =      j-NUM-MATH,
  volume =       "7",
  pages =        "194--196",
  year =         "1965",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Fri Sep 16 10:22:10 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  xxmonth =      "(none)",
  xxnumber =     "(none)",
}

@Article{Moller:1965:NQD,
  author =       "Ole M{\o}ller",
  title =        "Note on Quasi Double-Precision",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "5",
  number =       "4",
  pages =        "251--255",
  month =        dec,
  year =         "1965",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01937505",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Sat Nov 14 09:14:57 1998",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=5&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Moller:1965:QDP}.",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=5&issue=4&spage=251",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "accurate floating-point summation; floating-point
                 arithmetic; rounding errors",
}

@Article{Moller:1965:QDP,
  author =       "Ole M{\o}ller",
  title =        "Quasi Double-Precision in Floating Point Addition",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "5",
  number =       "1",
  pages =        "37--50",
  month =        mar,
  year =         "1965",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01975722",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65.80",
  MRnumber =     "MR0181130 (31 \#5359)",
  bibdate =      "Wed Jan 4 18:52:08 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=5&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also \cite{Moller:1965:NQD}.",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=5&issue=1&spage=37",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "accurate floating-point summation; floating-point
                 arithmetic; rounding errors",
  remark =       "Gives summation error estimate formula `s = fl(a + b);
                 error = (a - s) + b', also discovered independently by
                 \cite{Kahan:1965:PFR}. Extends Gill's earlier
                 fixed-point result \cite{Gill:1951:PSS}.",
}

@InCollection{Moore:1965:AACa,
  author =       "Ramon E. Moore",
  title =        "The automatic analysis and control of error in digital
                 computing based on the use of interval numbers",
  crossref =     "Rall:1965:EDCa",
  chapter =      "2",
  bookpages =    "????",
  pages =        "61--130",
  year =         "1965",
  MRclass =      "65.61 (65.80)",
  MRnumber =     "MR0176614 (31 \#886)",
  MRreviewer =   "T. E. Hull",
  bibdate =      "Thu Jun 20 10:51:40 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://interval.louisiana.edu/Moores_early_papers/Moore_in_Rall_V1.pdf",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@InCollection{Moore:1965:AACb,
  author =       "Ramon E. Moore",
  title =        "Automatic local coordinate transformations to reduce
                 the growth of error bounds in interval computation of
                 solutions of ordinary differential equations",
  crossref =     "Rall:1965:EDCb",
  chapter =      "2",
  pages =        "103--140",
  year =         "1965",
  MRclass =      "65.80 (65.60)",
  MRnumber =     "MR0185839 (32 \#3299)",
  MRreviewer =   "T. E. Hull",
  bibdate =      "Thu Jun 20 10:51:40 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://interval.louisiana.edu/Moores_early_papers/Moore_in_Rall_V2.pdf",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Moore:1965:CMC,
  author =       "Gordon E. Moore",
  title =        "Cramming More Components onto Integrated Circuits",
  journal =      "Electronics",
  volume =       "38",
  number =       "8",
  pages =        "114--117",
  year =         "1965",
  bibdate =      "Tue Nov 18 15:31:38 2008",
  bibsource =    "https://www.intel.com/content/www/us/en/history/virtual-vault/articles/moores-law.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/intel-ia-64.bib",
  URL =          "http://www.intel.com/technology/mooreslaw/index.htm;
                 https://hasler.ece.gatech.edu/Published_papers/Technology_overview/gordon_moore_1965_article.pdf;
                 https://www.cs.utexas.edu/~fussell/courses/cs352h/papers/moore.pdf",
  acknowledgement = ack-nhfb,
  remark =       "This paper is the origin of {\em Moore's Law\/}:
                 semiconductor performance roughly doubles every two
                 years or so.  Reprinted in \cite{Moore:1998:CMC}.",
}

@Article{Morrison:1965:MCC,
  author =       "D. R. Morrison",
  title =        "A Method for Computing Certain Inverse Functions",
  journal =      j-MATH-TABLES-OTHER-AIDS-COMPUT,
  volume =       "10",
  number =       "??",
  pages =        "202--208",
  month =        "????",
  year =         "1965",
  CODEN =        "MTTCAS",
  ISSN =         "0891-6837",
  bibdate =      "Thu Sep 1 10:16:10 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  ajournal =     "Math. Tables Other Aids Comput.",
  fjournal =     "Mathematical Tables and Other Aids to Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Nathan:1965:CM,
  author =       "Amos Nathan",
  title =        "The Cascade Multiplier",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "2",
  pages =        "243--247",
  month =        apr,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.264250",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038406",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Article{Penney:1965:BSC,
  author =       "Walter Penney",
  title =        "A {``Binary''} System for Complex Numbers",
  journal =      j-J-ACM,
  volume =       "12",
  number =       "2",
  pages =        "247--248",
  month =        apr,
  year =         "1965",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Thu Nov 03 08:47:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}

@Book{Ralston:1965:FCN,
  author =       "Anthony Ralston",
  title =        "A first course in numerical analysis",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "xix + 578",
  year =         "1965",
  LCCN =         "QA297 .R3",
  bibdate =      "Fri Aug 20 10:13:32 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "International series in pure and applied mathematics",
  acknowledgement = ack-nhfb,
  remark =       "See also second edition
                 \cite{Ralston:1978:FCN,Ralston:2001:FCN}. Cited in
                 \cite{Sterbenz:1974:FPC}.",
  subject =      "Numerical analysis",
}

@Article{Riordan:1965:UAT,
  author =       "R. H. S. Riordan and R. R. A. Morton",
  title =        "The Use of Analog Techniques in Binary Arithmetic
                 Units",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "1",
  pages =        "29--35",
  month =        feb,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.264051",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038346",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Article{Ross:1965:RTE,
  author =       "D. R. Ross",
  title =        "Reducing Truncation Errors Using Cascading
                 Accumulators",
  journal =      j-CACM,
  volume =       "8",
  number =       "1",
  pages =        "32--33",
  month =        jan,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Sun Sep 18 22:55:00 1994",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/bevan.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "When accumulating a large number of quantities as in
                 numerical integration, the sum itself may become much
                 larger than the individual addends. This results in
                 truncation error. Much of this error can be eliminated
                 using cascading accumulators as noted in a recent
                 article by Wolfe. A simpler and slightly more flexible
                 algorithm is presented which deals also with the case
                 of negative addends.",
  acknowledgement = ack-nhfb,
  checked =      "19940304",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "accurate floating-point summation",
  sjb =          "Refers to \cite{Wolfe:cacm:196,Wilhelm:1977:GMPb}.",
}

@Article{Schreiber:1965:BRB,
  author =       "Alvin L. Schreiber",
  title =        "Book Review: {{\booktitle{A Binary Multiplication}}
                 (W. C. McGee)}",
  journal =      j-SIAM-REVIEW,
  volume =       "7",
  number =       "1",
  pages =        "134--136",
  month =        "????",
  year =         "1965",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1007016",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu Mar 27 09:05:20 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/7/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "January 1965",
}

@Article{Smith:1965:ASO,
  author =       "Francis J. Smith",
  title =        "An Algorithm for Summing Orthogonal Polynomial Series
                 and their Derivatives with Applications to
                 Curve-Fitting and Interpolation",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "89",
  pages =        "33--36",
  month =        apr,
  year =         "1965",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Specker:1965:CAL,
  author =       "W. H. Specker",
  title =        "A Class of Algorithms for $ \ln x $, $ \exp x $, $
                 \sin x $, $ \cos x $, $ \tan^{-1} x $, and $ \cot^{-1}
                 x $",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "1",
  pages =        "85--86",
  month =        feb,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.264066",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:21 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038361",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Article{Swarztrauber:1965:LED,
  author =       "P. N. Swarztrauber",
  title =        "Letter to the {Editor}: On the Double-Precision Square
                 Root Routine",
  journal =      j-CACM,
  volume =       "8",
  number =       "4",
  pages =        "202",
  month =        apr,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Wed Aug 31 14:02:19 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\sqrt(x)$; elementary functions; floating-point
                 arithmetic",
}

@Article{Sweeney:1965:AFP,
  author =       "D. W. Sweeney",
  title =        "An analysis of floating-point addition",
  journal =      j-IBM-SYS-J,
  volume =       "4",
  number =       "1",
  pages =        "31--42",
  year =         "1965",
  CODEN =        "IBMSA7",
  DOI =          "https://doi.org/10.1147/sj.41.0031",
  ISSN =         "0018-8670",
  bibdate =      "Thu Sep 15 18:42:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ibmsysj.bib",
  note =         "Reprinted in
                 \cite[pp.~317--328]{Swartzlander:1990:CAa}.",
  URL =          "http://www.research.ibm.com/journal/sj/041/ibmsjIVRID.pdf",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  fjournal =     "IBM Systems Journal",
  remark =       "Page 34, containing a critical table, was originally
                 missing from the PDF file, and this was finally
                 corrected by IBM in November 2008.",
  xxmonth =      "(none)",
}

@Article{Winograd:1965:TRP,
  author =       "Shmuel Winograd",
  title =        "On the Time Required to Perform Addition",
  journal =      j-J-ACM,
  volume =       "12",
  number =       "2",
  pages =        "277--285",
  month =        apr,
  year =         "1965",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Wed Nov 14 19:04:40 2007",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/Multi.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}

@Article{Arango:1966:FCP,
  author =       "H. Arango and J. Santos",
  title =        "A Fast Carry-Propagation Circuit for Base $3$ Signed
                 Non redundant Arithmetic",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-15",
  number =       "2",
  pages =        "254--255",
  month =        apr,
  year =         "1966",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1966.264311",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 05:46:31 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038725",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Article{Brooker:1966:MFA,
  author =       "R. A. Brooker and J. S. Rohl and S. R. Clark",
  title =        "The main features of {Atlas Autocode}",
  journal =      j-COMP-J,
  volume =       "8",
  number =       "4",
  pages =        "303--310",
  month =        jan,
  year =         "1966",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:56:10 MDT 2000",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See comment \cite{Clark:1966:CMP}.",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/080303.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/303.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/304.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/305.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/306.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/307.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/308.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/309.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_04/tiff/310.tif",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@MastersThesis{Chang:1966:DHR,
  author =       "Henry Kwan-cheung Chang",
  title =        "Design of a high rate floating point digital
                 accumulator",
  type =         "Thesis ({M.S. in Engineering})",
  school =       "University of California, Davis",
  address =      "Davis, CA, USA",
  pages =        "60",
  year =         "1966",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Dissertations, Academic --- California ---
                 Engineering.",
}

@Article{Chartres:1966:ACP,
  author =       "Bruce A. Chartres",
  title =        "Automatic Controlled Precision Calculations",
  journal =      j-J-ACM,
  volume =       "13",
  number =       "3",
  pages =        "386--403",
  month =        jul,
  year =         "1966",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Fri Nov 28 16:23:06 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Recent developments in computer design and error
                 analysis have made feasible the use of variable
                 precision arithmetic and the preparation of programs
                 that automatically determine their own precision
                 requirements. Such programs enable the user to specify
                 the accuracy he wants, and yield answers guaranteed to
                 lie within the bounds prescribed. A class of such
                 programs, called ``contracting error programs'', is
                 defined in which the precision is determined by
                 prescribing error bounds on the data. A variant of
                 interval arithmetic is defined which enables a limited
                 class of algorithms to be programmed as contracting
                 error programs. A contracting error program for the
                 solution of simultaneous linear equations is described,
                 demonstrating the application of the idea to a wider
                 class of problems.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}

@Article{Clark:1966:CMP,
  author =       "S. R. Clark and W. F. Lunnon",
  title =        "Correspondence: Multiple precision arithmetic (real
                 and complex)",
  journal =      j-COMP-J,
  volume =       "9",
  number =       "2",
  pages =        "174--174",
  month =        aug,
  year =         "1966",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:56:14 MDT 2000",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_02/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Brooker:1966:MFA}.",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_02/tiff/174.tif",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Clark:1966:MPA,
  author =       "S. R. Clark and W. F. Lunnon",
  title =        "Multiple precision arithmetic in {Atlas Autocode}",
  journal =      j-COMP-J,
  volume =       "9",
  number =       "2",
  pages =        "174--174",
  month =        aug,
  year =         "1966",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/9.2.174",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:47:36 MST 2012",
  bibsource =    "http://comjnl.oxfordjournals.org/content/9/2.toc;
                 https://www.math.utah.edu/pub/tex/bib/compj1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/9/2/174.full.pdf+html",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Fike:1966:SAS,
  author =       "C. T. Fike",
  title =        "Starting Approximations for Square Root Calculation on
                 {IBM System\slash 360}",
  journal =      j-CACM,
  volume =       "9",
  number =       "4",
  pages =        "297--299",
  month =        apr,
  year =         "1966",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/365278.365556",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 1 10:15:43 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See letter \cite{Fike:1967:LER}.",
  abstract =     "Several starting approximations for square root
                 calculation by Newton's method are presented in a form
                 to facilitate their use in IBM System/360 square root
                 routines. These approximations include several for the
                 range [1/16, 1], which is the interval of primary
                 interest on IBM System/360.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\sqrt(x)$; elementary functions; IBM S/360",
}

@Article{Filippi:1966:BEE,
  author =       "S. Filippi",
  title =        "{Die Berechnung einiger elementarer transzendenter
                 Funktionen mit Hilfe des Richardson-Algorithmus}
                 \toenglish {The Computation of Some Elementary
                 Transcendental Functions by Means of the Richardson
                 Algorithm} \endtoenglish",
  journal =      j-COMPUTING,
  volume =       "1",
  number =       "??",
  pages =        "127--132",
  month =        "????",
  year =         "1966",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Article{Flehinger:1966:PRI,
  author =       "B. J. Flehinger",
  title =        "On the Probability that a Random Integer Has Initial
                 Digit `{A}'",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "73",
  number =       "??",
  pages =        "1056--1061",
  year =         "1966",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Wed Feb 14 18:53:58 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
  remark =       "Probably November or December issue; missing from
                 amermathmonthly1960.bib.",
}

@Article{Flynn:1966:VHS,
  author =       "M. J. Flynn",
  title =        "Very high-speed computing systems",
  journal =      j-PROC-IEEE,
  volume =       "54",
  number =       "12",
  pages =        "1901--1909",
  year =         "1966",
  CODEN =        "IEEPAD",
  DOI =          "https://doi.org/10.1109/proc.1966.5273",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Wed Dec 13 08:39:04 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
  keywords =     "floating-point arithmetic; Goldschmidt division",
}

@Article{Garner:1966:ECA,
  author =       "Harvey L. Garner",
  title =        "Error Codes for Arithmetic Operations",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-15",
  number =       "5",
  pages =        "763--770",
  month =        oct,
  year =         "1966",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1966.264566",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 05:46:38 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038884",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Article{Grau:1966:BRB,
  author =       "A. A. Grau",
  title =        "Book Review: {{\booktitle{Rounding Errors in Algebraic
                 Processes}} (J. H. Wilkinson)}",
  journal =      j-SIAM-REVIEW,
  volume =       "8",
  number =       "3",
  pages =        "397--398",
  month =        "????",
  year =         "1966",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1008087",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu Mar 27 09:05:37 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/8/3;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "July 1966",
}

@Article{Gregory:1966:DAU,
  author =       "Robert T. Gregory",
  title =        "On the Design of the Arithmetic Unit of a
                 Fixed-Word-Length Computer from the Standpoint of
                 Computational Accuracy",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-15",
  number =       "2",
  pages =        "255--257",
  month =        apr,
  year =         "1966",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1966.264312",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 05:46:31 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038726",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Book{Greve:1966:HLR,
  author =       "J. Greve and H. Gumin and E. Hochsteller",
  title =        "{Herrn von Leibniz' Rechnung mit Null und Ein}.
                 ({German}) [{Mister von Leibniz'} calculation with zero
                 and one]",
  publisher =    "{Siemens AG}",
  address =      "Berlin and M{\"u}nchen, West Germany",
  pages =        "59",
  year =         "1966",
  bibdate =      "Fri Mar 17 08:31:51 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Gottfried Wilhelm Freiherr von Leibnitz",
  language =     "German",
}

@InProceedings{Harding:1966:ISF,
  author =       "L. J. {Harding, Jr.}",
  editor =       "????",
  booktitle =    "{SHARE} {XXVII}, Toronto, Canada, August 1966",
  title =        "Idiosyncracies of {System\slash 360} Floating-Point",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "1966",
  LCCN =         "????",
  bibdate =      "Wed Feb 14 19:04:14 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Misc{Harding:1966:MSF,
  author =       "L. J. {Harding, Jr.}",
  title =        "Modifications of {System\slash 360} Floating-Point",
  number =       "SSD 157, C4470",
  howpublished = "SHARE Secretarial Distribution",
  pages =        "11--27",
  month =        "????",
  year =         "1966",
  bibdate =      "Wed Feb 14 19:05:45 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Henrici:1966:TPM,
  author =       "Peter Henrici",
  title =        "Test of probabilistic models for the propagation of
                 roundoff errors",
  journal =      j-CACM,
  volume =       "9",
  number =       "6",
  pages =        "409--410",
  month =        jun,
  year =         "1966",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:07 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "floating-point arithmetic; rounding errors",
}

@Article{Hull:1966:TPM,
  author =       "T. E. Hull and J. R. Swenson",
  title =        "Tests of Probabilistic Models for Propagation of
                 Roundoff Errors",
  journal =      j-CACM,
  volume =       "9",
  number =       "2",
  pages =        "108--113",
  month =        feb,
  year =         "1966",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.80",
  MRnumber =     "32\#3297",
  bibdate =      "Fri Nov 25 18:20:04 MST 2005",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Theory/gvl.bib;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In any prolonged computation it is generally assumed
                 that the accumulated effect of roundoff errors is in
                 some sense statistical. The purpose of this paper is to
                 give precise descriptions of certain probabilistic
                 models for roundoff error, and then to describe a
                 series of experiments for testing the validity of these
                 models. It is concluded that the models are in general
                 very good. Discrepancies are both rare and mild. The
                 test techniques can also be used to experiment with
                 various types of special arithmetic.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "decimal floating-point arithmetic; rounding errors",
}

@Manual{IBM:1966:ISM,
  key =          "IBM",
  title =        "{IBM System\slash 360 Model 91}: Functional
                 Characteristics",
  publisher =    pub-IBM,
  address =      pub-IBM:adr,
  year =         "1966",
  bibdate =      "Fri Aug 20 09:34:43 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "File No. S360-01, Form A22-6907-2.",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Book{Isaacson:1966:ANM,
  author =       "Eugene Isaacson and Herbert Bishop Keller",
  title =        "Analysis of numerical methods",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xv + 541",
  year =         "1966",
  LCCN =         "QA297 .I8",
  bibdate =      "Fri Aug 20 09:37:14 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}. Reprinted in
                 \cite{Isaacson:1994:ANM}.",
  subject =      "Numerical analysis",
}

@Misc{Kahan:1966:ISS,
  author =       "W. Kahan",
  title =        "{7094 II} System Support for Numerical Analysis",
  howpublished = "SHARE Secretary Distribution 159, C4537",
  pages =        "1--54",
  month =        aug,
  year =         "1966",
  bibdate =      "Wed Nov 07 08:39:33 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.arithmazium.org/classroom/lib/Kahan_7094_II_System_Support.pdf",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@InCollection{Kogbetliantz:1966:GEF,
  author =       "E. G. Kogbetliantz",
  title =        "Generation of Elementary Functions",
  crossref =     "Ralston:1966:MMD",
  pages =        "7--35",
  year =         "1966",
  bibdate =      "Sat Dec 09 14:09:27 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Kuki:1966:EGS,
  author =       "H. Kuki and E. Hanson and J. J. Ortega and J. C.
                 Butcher and P. G. Anderson",
  title =        "Evaluation Guidelines {SHARE Numerical Analysis
                 Project (N.A.P.)}",
  journal =      "{SHARE Secretary Distribution}",
  volume =       "SSD 150, part II",
  number =       "C4304",
  pages =        "1--42",
  year =         "1966",
  bibdate =      "Fri Aug 20 09:45:16 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Lam:1966:COG,
  author =       "Lay-yong Lam",
  title =        "On the {Chinese} origin of the {Galley} method of
                 arithmetical division",
  journal =      j-BRITISH-J-HIST-SCI,
  volume =       "3",
  number =       "part 1, 9",
  pages =        "66--69",
  year =         "1966",
  CODEN =        "BJHSAT",
  DOI =          "https://doi.org/10.1017/S0007087400000200",
  ISSN =         "0007-0874 (print), 1474-001X (electronic)",
  ISSN-L =       "0007-0874",
  MRclass =      "01.10",
  MRnumber =     "0204243 (34 \#4087)",
  MRreviewer =   "I. N. Veselovski{\u\i}",
  bibdate =      "Wed Sep 22 18:01:23 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database",
  ZMnumber =     "0143.24202",
  acknowledgement = ack-nhfb,
  fjournal =     "British Journal for the History of Science",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=BJH",
  keywords =     "history",
}

@Article{Mancino:1966:MPF,
  author =       "O. G. Mancino",
  title =        "Multiple precision floating-point conversion from
                 decimal-to-binary and vice versa",
  journal =      j-CACM,
  volume =       "9",
  number =       "5",
  pages =        "347--348",
  month =        may,
  year =         "1966",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355592.365635",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:06 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Decimal-to-binary and binary-to-decimal floating-point
                 conversion is often performed by using a table of the
                 powers $ 10^i $ ($i$ a positive integer) for converting
                 from base $ 10$ to base $2$, and by using a table of
                 the coefficients of a polynomial approximation of $
                 10^x (0 \leq x < 1)$ for converting from base $2$ to
                 base $ 10$. These tables occupy a large storage region
                 in the case of a nonsingle precision conversion. This
                 paper shows that a single small table suffices for a
                 floating-point conversion from decimal to binary, and
                 vice versa, in any useful precision.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "floating-point arithmetic; Multiple precision
                 arithmetic; number base conversion",
}

@Unpublished{Mazor:1966:FSI,
  author =       "Stan Mazor",
  title =        "{Fairchild Symbol II} Decimal Floating Point Unit",
  year =         "1966",
  bibdate =      "Wed Nov 22 21:18:53 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Cited in \cite[p. 106]{Cowlishaw:2003:DFP}.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@TechReport{McCarthy:1966:CCA,
  author =       "John McCarthy and James Painter",
  title =        "Correctness of a Compiler for Arithmetic Expressions",
  type =         "Technical Report",
  number =       "STAN-CS-66-38 (AIM-40, AD662880)",
  institution =  inst-STAN-CS,
  address =      inst-STAN-CS:adr,
  pages =        "13",
  month =        apr,
  year =         "1966",
  bibdate =      "Fri Nov 21 14:21:14 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/stanford-cstr.bib",
  URL =          "",
  acknowledgement = ack-nhfb,
  author-dates = "John McCarthy (4 September 1927--24 October 2011)",
}

@Book{Moore:1966:IA,
  author =       "Ramon E. Moore",
  title =        "Interval analysis",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xi + 145",
  year =         "1966",
  LCCN =         "QA297 .M63",
  bibdate =      "Sat Feb 14 08:15:54 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Nickel:1966:NFA,
  author =       "K. Nickel",
  title =        "{{\"U}ber die Notwendigkeit einer Fehlerschranken-
                 Arithmetik f{\"u}r Rechenautomaten}",
  journal =      j-NUM-MATH,
  volume =       "9",
  pages =        "69--79",
  year =         "1966",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-jr,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Book{Parker:1966:SNS,
  author =       "Francis D. Parker",
  title =        "The structure of number systems",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xi + 137",
  year =         "1966",
  LCCN =         "QA241 .P3; QA241 .P239",
  bibdate =      "Fri Nov 9 19:10:47 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  series =       "Teachers' mathematics reference series",
  acknowledgement = ack-nhfb,
  subject =      "Number theory",
}

@Book{Richards:1966:EDS,
  author =       "R. K. (Richard Kohler) Richards",
  title =        "Electronic Digital Systems",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "ix + 637",
  year =         "1966",
  LCCN =         "TK7888.3 .R52",
  bibdate =      "Mon Oct 24 05:33:53 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1921--",
  remark =       "According to \cite[pp. 168--170]{Smiley:2010:MWI},
                 this was the first book to draw attention to the
                 pre-World War II work by John Atanasoff (1903--1995)
                 and Clifford Berry (1918--1963) at Iowa State College
                 of Agricultural and Mechanic Arts (renamed on 4 July
                 1959 to Iowa State University of Science and
                 Technology), and to name their computer the ABC.
                 Richards is quoted with ``The ancestry of all
                 electronic digital systems appears to be traceable to a
                 computer which will be called the Atanasoff--Berry
                 Computer.'' The book provided important evidence in the
                 priority dispute and courtroom battles over who
                 invented the computer (Atanasoff and Berry versus
                 Mauchly and Eckert). Berry died in unresolved
                 circumstances: suicide or murder?",
  subject =      "Electronic digital computers",
  tableofcontents = "1: History and Introduction / 1 \\
                 2: Theory of Digital Systems / 50 \\
                 3: The Stored-Program Concept / 109 \\
                 4: Automatic Programming / 293 \\
                 5: Digital Data Transmission / 362 \\
                 6: Combined Analog and Digital Techniques / 451 \\
                 7: Telephone and Message Switching Systems / 481 \\
                 8: The Relationship between Thinking and Digital
                 Systems / 519 \\
                 9: Miscellaneous Digital Systems / 541 \\
                 10: Digital System Reliability / 571 \\
                 11: The Automatic Design of Digital Systems / 610 \\
                 Index / 631",
}

@Article{Saidan:1966:EEA,
  author =       "A. S. Saidan",
  title =        "The Earliest Extant {Arabic} Arithmetic:
                 {{\booktitle{Kitab al-Fusul fi al Hisab al-Hindi}}} of
                 {Abu al-Hasan, Ahmad ibn Ibrahim al-Uqlidisi}",
  journal =      j-ISIS,
  volume =       "57",
  number =       "4",
  pages =        "475--490",
  month =        "Winter",
  year =         "1966",
  CODEN =        "ISISA4",
  ISSN =         "0021-1753 (print), 1545-6994 (electronic)",
  ISSN-L =       "0021-1753",
  bibdate =      "Tue Jul 30 21:22:16 MDT 2013",
  bibsource =    "http://www.jstor.org/action/showPublication?journalCode=isis;
                 http://www.jstor.org/stable/i211145;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/isis1960.bib",
  URL =          "http://www.jstor.org/stable/228518",
  acknowledgement = ack-nhfb,
  fjournal =     "Isis",
  journal-URL =  "http://www.jstor.org/journal/isis",
}

@Article{Smith:1966:CP,
  author =       "John Smith",
  title =        "The Challenge of {Pi}",
  journal =      j-IEEE-SPECTRUM,
  volume =       "3",
  number =       "10",
  pages =        "5--5",
  month =        oct,
  year =         "1966",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.1966.5217340",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Wed Jan 15 08:45:04 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "Computer errors; Digital arithmetic; Educational
                 institutions; Hardware; Physics computing; Power
                 engineering computing; Programming profession;
                 Registers; Testing; Upper bound",
  remark =       "Report of a computation of $ \pi $ to 17,935 places
                 using base-1,000,000 arithmetic. A footnote reports
                 ``The AIL result to 17,940 places was identical with
                 the reference to 17,935 places. Reference: D. Shanks
                 and J. W. Wrench, Jr., `Calculation of Pi to 100,000
                 Decimals', Mathematics of Computation, January 1962,
                 Vol. 16, No. 77, pp. 67--99.''",
}

@Article{Spielberg:1966:CEU,
  author =       "K. Spielberg",
  title =        "Computation of $ e^x $ with the use of large tables",
  journal =      j-IBM-SYS-J,
  volume =       "5",
  number =       "2",
  pages =        "102--114",
  year =         "1966",
  CODEN =        "IBMSA7",
  ISSN =         "0018-8670",
  bibdate =      "Thu Sep 15 18:43:03 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Systems Journal",
  xxmonth =      "(none)",
}

@Article{Tienari:1966:SPM,
  author =       "M. Tienari and V. Suokonautio",
  title =        "A Set of Procedures Making Real Arithmetic of
                 Unlimited Accuracy Possible Within {Algol 60}",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "6",
  number =       "4",
  pages =        "332--338",
  month =        jul,
  year =         "1966",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01966093",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Mon Sep 12 08:07:38 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=6&issue=4&spage=332",
  acknowledgement = ack-nj,
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{vanWijngaarden:1966:NAI,
  author =       "Adriaan van Wijngaarden",
  title =        "Numerical Analysis as an Independent Science",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "6",
  number =       "1",
  pages =        "66--81",
  month =        mar,
  year =         "1966",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01939551",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:09 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=6&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=6&issue=1&spage=66",
  abstract =     "The paper describes how a number of well-known
                 mathematical concepts ought to be modified in order to
                 make sense within the scope of numerical analysis. It
                 is also shown how obvious difficulties can be overcome
                 in a logical way. All algorithms suggested are given as
                 ALGOL procedures.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Watson:1966:SCC,
  author =       "R. W. Watson and C. W. Hastings",
  title =        "Self-Checked Computation using Residue Arithmetic",
  journal =      j-PROC-IEEE,
  volume =       "54",
  number =       "12",
  pages =        "1920--1931",
  month =        dec,
  year =         "1966",
  CODEN =        "IEEPAD",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Fri Nov 09 19:37:52 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
}

@Article{Whitney:1966:PCR,
  author =       "D. E. Whitney",
  title =        "Propagation and control of roundoff error in the
                 matrix exponential method",
  journal =      j-PROC-IEEE,
  volume =       "54",
  number =       "10",
  pages =        "1483--1484",
  month =        oct,
  year =         "1966",
  CODEN =        "IEEPAD",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
}

@TechReport{Wiegel:1966:MBA,
  author =       "R. E. Wiegel",
  title =        "Methods of Binary Addition",
  type =         "Technical report",
  number =       "195",
  institution =  "Department of Computer Science, University of
                 Illinois",
  address =      "Urbana, IL, USA",
  month =        feb,
  year =         "1966",
  bibdate =      "Fri Nov 09 19:40:18 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Adams:1967:SCP,
  author =       "Duane A. Adams",
  title =        "A stopping criterion for polynomial root finding",
  journal =      j-CACM,
  volume =       "10",
  number =       "10",
  pages =        "655--658",
  month =        oct,
  year =         "1967",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.50",
  MRnumber =     "39\#2314",
  bibdate =      "Fri Nov 25 18:20:15 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "When searching for the root of a polynomial, it is
                 generally difficult to know just when to accept a
                 number as an adequate approximation to the root. In
                 this paper an algorithm is presented which allows one
                 to terminate the iteration process on the basis of
                 calculated bounds for the roundoff error which occurs
                 in evaluating the polynomial. This stopping criterion
                 has been tested on numerous examples and has been found
                 to serve as a satisfactory means for accepting a
                 complex number as a zero of a real polynomial.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "floating-point arithmetic; rounding errors",
}

@Article{Anderson:1967:ISMb,
  author =       "S. F. Anderson and J. G. Earle and R. E. Goldschmidt
                 and D. M. Powers",
  title =        "The {IBM System\slash 360 Model 91}: Floating-point
                 execution unit",
  journal =      j-IBM-JRD,
  volume =       "11",
  number =       "1",
  pages =        "34--53",
  month =        jan,
  year =         "1967",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.111.0034",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Tue Sep 11 15:36:09 MDT 2012",
  bibsource =    "http://www.research.ibm.com/journal/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392016",
  abstract =     "The principal requirement for the Model 91
                 floating-point execution unit was that it be designed
                 to support the instruction-issuing rate of the
                 processor. The chosen solution was to develop separate,
                 instruction-oriented algorithms for the add, multiply,
                 and divide functions. Linked together by the
                 floating-point instruction unit, the multiple execution
                 units provide concurrent instruction execution at the
                 burst rate of one instruction per cycle.",
  acknowledgement = ack-nhfb # "\slash " # ack-nj,
  book-URL =     "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}

@TechReport{Clark:1967:PSF,
  author =       "N. A. Clark and W. J. Cody and K. E. Hillstrom and E.
                 A. Thieleker",
  title =        "Performance Statistics of the {FORTRAN IV (H)} Library
                 for the {IBM System\slash 360}",
  type =         "Technical Report",
  number =       "ANL-7231",
  institution =  inst-ANL,
  address =      inst-ANL:adr,
  year =         "1967",
  bibdate =      "Fri Aug 20 08:47:24 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in SHARE Secretary Distribution, SDD 169,
                 C4473, pp. 12 46.",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Cody:1967:CFI,
  author =       "W. J. Cody",
  title =        "Critique of the {FORTRAN IV (H)} Library for the {IBM
                 System\slash 360}",
  journal =      "{SHARE Secretary Distribution}",
  volume =       "SSD 169",
  number =       "C4473",
  pages =        "4--11",
  year =         "1967",
  bibdate =      "Fri Aug 20 08:52:04 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@InProceedings{Cody:1967:IMD,
  author =       "W. J. Cody",
  title =        "The influence of machine design on numerical
                 algorithms",
  crossref =     "AFIPS:1967:ACP",
  pages =        "305--309",
  year =         "1967",
  bibdate =      "Sat Sep 24 00:18:32 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Cody:1967:LEA,
  author =       "William J. {Cody, Jr.}",
  title =        "Letter to the {Editor}: Another Aspect of Economical
                 Polynomials",
  journal =      j-CACM,
  volume =       "10",
  number =       "9",
  pages =        "531--531",
  month =        sep,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363566.363577",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Nov 17 10:20:03 1994",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Fike:1967:MEP}.",
  abstract =     "In his paper ``Methods of Evaluating Polynomial
                 Approximations in Function Evaluation Routines'' [Comm.
                 ACM 10, (March 1967)], C. T. Fike fails to discuss one
                 very important aspect of the ``economical'' methods for
                 polynomials. Since these evaluation methods involve a
                 decreased number of arithmetic operations over the
                 usual Horner's method (or at least replace a
                 multiplication by an addition) the implication is that
                 they are faster to execute. Dr. Fike points out that
                 these methods can be poorly conditioned for particular
                 polynomials, thus requiring extended precision or
                 fixed-point arithmetic to maintain accuracy and costing
                 more in time than Horner's method. But even if we
                 assume the methods are well conditioned, the need to
                 store away and retrieve intermediate results in some
                 machines with only one floating-point arithmetic
                 register can wipe out the time savings effected by a
                 reduction in the number of arithmetic operations. On
                 many of today's high-performance computers the time
                 required to store away and retrieve a result is about
                 the same as the time required for a floating-point
                 addition. It is no longer sufficient to estimate the
                 efficiency of a method by a count of arithmetic
                 operations alone.",
  acknowledgement = ack-wjc # " and " # ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "floating-point arithmetic",
}

@Article{Crisansan-Zverca:1967:PED,
  author =       "Mariana Cri{\c{s}}an-Zverca",
  title =        "Pseudo-operations of an electronic digital machine
                 with floating point. ({Romanian})",
  journal =      j-STUD-CERCET-MAT,
  volume =       "19",
  pages =        "1413--1424",
  year =         "1967",
  ISSN =         "0039-4068, 0567-6401",
  MRclass =      "68.00",
  MRnumber =     "40\#3753",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Studii {\c{s}}i cercet{\u{a}}ri Matematice",
}

@Article{Curry:1967:ART,
  author =       "E. Curry",
  title =        "The analysis of round-off and truncation errors in a
                 hybrid control system",
  journal =      j-IEEE-TRANS-AUTOMAT-CONTR,
  volume =       "12",
  number =       "5",
  pages =        "601--604",
  month =        oct,
  year =         "1967",
  CODEN =        "IETAA9",
  ISSN =         "0018-9286 (print), 1558-2523 (electronic)",
  ISSN-L =       "0018-9286",
  bibdate =      "Sat Jul 16 11:25:03 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Automatic Control",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
  summary =      "The round-off and truncation errors of a
                 digital-analog (hybrid) servo system are studied in
                 terms of the least upper bound and second moment, or
                 variance. The study was applied to the azimuth function
                 of a guided missile launcher system and a \ldots{}",
}

@Article{DeRegt:1967:NRA,
  author =       "M. P. DeRegt",
  title =        "Negative radix arithmetic",
  journal =      j-COMP-DESIGN,
  volume =       "6",
  number =       "??",
  pages =        "52--63",
  month =        may,
  year =         "1967",
  CODEN =        "CMPDAM",
  ISSN =         "0010-4566",
  bibdate =      "Thu Nov 06 06:07:24 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Design",
  keywords =     "negative base",
}

@Article{Ferrari:1967:DMU,
  author =       "Domenico Ferrari",
  title =        "A Division Method Using a Parallel Multiplier",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-16",
  number =       "2",
  pages =        "224--226",
  month =        apr,
  year =         "1967",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264580",
  ISSN =         "0367-7508",
  bibdate =      "Wed Jul 13 21:15:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  note =         "See correction \cite{Ferrari:1969:CDM}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039036",
  abstract =     "The use of a parallel multiplier for performing
                 high-speed binary division requires that an algorithm
                 be devised that obtains the quotient by means of
                 multiplications and additions. Furthermore, its
                 hardware implementation must be as simple and as fast
                 as possible. A suitable algorithm, which applies to a
                 first approximation to the reciprocal of the divisor,
                 has already been proposed [1]. A similar algorithm is
                 presented in this paper. The comparison between the two
                 methods for equal numbers of multiplications shows that
                 the latter is more accurate. Conversely, a given
                 accuracy can often be obtained with a higher speed. The
                 generation of a piecewise-linear initial approximation
                 is also discussed.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Article{Fike:1967:LER,
  author =       "C. T. Fike",
  title =        "Letter to the {Editor}: {A} rational approximation
                 optimal by {Moursund}'s criterion",
  journal =      j-CACM,
  volume =       "10",
  number =       "11",
  pages =        "683--684",
  month =        nov,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363790.363795",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:16 MST 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Moursund:1967:OSV,Fike:1966:SAS}",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "elementary function; square root",
  remark =       "Gives a starting value for $ \sqrt {x} $ ($x$ on $ [1
                 / 16, 1]$) of $ R*(x) = 1.68212586 - 1.28977371 / (x +
                 0.84106293)$, with an error of $ 2^{-12.496}$.",
}

@Article{Fike:1967:MEP,
  author =       "C. T. Fike",
  title =        "Methods of Evaluating Polynomial Approximations in
                 Function Evaluation Routines",
  journal =      j-CACM,
  volume =       "10",
  number =       "3",
  pages =        "175--178",
  month =        mar,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363162.363200",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:12 MST 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See remark on efficiency \cite{Cody:1967:LEA}.",
  abstract =     "The method of nested multiplication is commonly used
                 in function evaluation routines to evaluate
                 approximation polynomials. New polynomial evaluation
                 methods have been developed in recent years which
                 require fewer multiplications than nested
                 multiplication and may therefore be preferable for use
                 in function evaluation routines. Although some of these
                 methods do not appear to be practically useful because
                 of rounding-error difficulties, several methods of
                 evaluating low-degree polynomials have been found to be
                 satisfactory. Three such methods are described and
                 illustrated.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Article{Fike:1967:RAO,
  author =       "C. T. Fike",
  title =        "A Rational Approximation Optimal by {Moursund}'s
                 Criterion (letter to the editor)",
  journal =      j-CACM,
  volume =       "10",
  number =       "11",
  pages =        "683--684",
  month =        nov,
  year =         "1967",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 1 10:15:43 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Article{Filho:1967:AGF,
  author =       "A. M. S. Filho and G. Schwachheim",
  title =        "Algorithm 309: Gamma Function with Arbitrary
                 Precision",
  journal =      j-CACM,
  volume =       "10",
  number =       "8",
  pages =        "511--512",
  month =        aug,
  year =         "1967",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 1 10:16:10 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Book{Forsythe:1967:CSL,
  author =       "George E. Forsythe and Cleve B. Moler",
  title =        "Computer Solution of Linear Algebraic Systems",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xi + 148",
  year =         "1967",
  LCCN =         "QA297 .F57 1967",
  MRclass =      "65.35",
  MRnumber =     "MR0219223 (36 \#2306)",
  MRreviewer =   "N. Gastinel",
  bibdate =      "Tue May 25 08:52:32 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/gvl.bib",
  ZMnumber =     "0154.40401",
  acknowledgement = ack-nhfb,
  keywords =     "numerical analysis; software",
  remark =       "Translated to Russian (1969), Japanese (1969), and
                 German (1971). Cited in \cite{Sterbenz:1974:FPC}.",
  subject =      "numerical analysis; data processing; matrices",
  tableofcontents = "Reader's background and purpose of book \\
                 Vector and matrix norms \\
                 Diagonal form of a matrix under orthogonal equivalence
                 \\
                 Proof of diagonal-form theorem \\
                 Types of computational problems in linear algebra \\
                 Types of matrices encountered impractical problems \\
                 Sources of computational problems of linear algebra \\
                 Condition of a linear system \\
                 Gaussian elimination and LU decomposition \\
                 Need for interchanging rows \\
                 Scaling equations and unknowns \\
                 The Crout and Doolittle variants \\
                 Iterative improvement \\
                 Computing the determinant \\
                 Nearly singular matrices \\
                 Algol 60 program \\
                 Fortran, extended Algol, and PL/1 programs \\
                 Matrix inversion \\
                 An example: Hilbert matrices \\
                 Floating-point round-off analysis \\
                 Rounding error in Gaussian elimination \\
                 Convergence of iterative improvement \\
                 Positive definite matrices; band matrices \\
                 Iterative methods for solving linear systems \\
                 Nonlinear systems of equations",
}

@Article{Freeman:1967:CMS,
  author =       "Herbert Freeman",
  title =        "Calculation of Mean Shift for a Binary Multiplier
                 Using $2$, $3$, or $4$ Bits at a Time",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-16",
  number =       "6",
  pages =        "864--866",
  month =        dec,
  year =         "1967",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264752",
  ISSN =         "0367-7508",
  bibdate =      "Wed Jul 13 21:15:06 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039205",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Article{Freiman:1967:CDU,
  author =       "C. V. Freiman and others",
  title =        "Composite Division Unit",
  journal =      j-IBM-TDB,
  volume =       "9",
  number =       "8",
  pages =        "994--995",
  month =        jan,
  year =         "1967",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Tue Jan 08 22:40:53 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Technical Disclosure Bulletin",
}

@Article{Friedland:1967:AAV,
  author =       "Paul Friedland",
  title =        "{Algorithm 312}: {Absolute} Value and Square Root of a
                 Complex Number",
  journal =      j-CACM,
  volume =       "10",
  number =       "10",
  pages =        "665--665",
  month =        oct,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363717.363780",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:15 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\abs(z)$; $\sqrt(z)$; elementary functions",
}

@Article{Goldberg:1967:BED,
  author =       "I. Bennett Goldberg",
  title =        "$ 27 $ Bits Are Not Enough For $8$-Digit Accuracy",
  journal =      j-CACM,
  volume =       "10",
  number =       "2",
  pages =        "105--106",
  month =        feb,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363067.363112",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:11 MST 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "From the inequality $ 10^8 < 2^{27} $, we are likely
                 to conclude that we can represent 8-digit decimal
                 floating-point numbers accurately by 27-bit [binary]
                 floating-point numbers. However, we need 28 significant
                 bits to represent some 8-digit numbers accurately. In
                 general, we can show that if $ 10^p < 2^{q - 1} $, then
                 $q$ significant bits are always enough for $p$-digit
                 decimal accuracy. Finally, we can define a compact
                 27-bit floating-point representation that will give 28
                 significant bits, for numbers of practical
                 importance.",
  acknowledgement = ack-nj # " and " # ack-mfc # " and " # ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "decimal floating-point arithmetic",
  received =     "August 1966 (revised October 1966)",
}

@Book{Gschwind:1967:DDC,
  author =       "H. W. Gschwind",
  title =        "Design of Digital Computers: An Introduction",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 530",
  year =         "1967",
  LCCN =         "TK7888.3 .G72",
  bibdate =      "Fri Nov 09 18:56:39 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Misc{Hertz:1967:CHF,
  author =       "Theodore M. Hertz",
  title =        "Computer Having Floating Point Multiplication",
  howpublished = "US Patent 3,304,417.",
  day =          "14",
  month =        feb,
  year =         "1967",
  bibdate =      "Sat Mar 24 06:05:12 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Filed 1 October 1962.",
  URL =          "https://patentimages.storage.googleapis.com/47/86/c8/897ec6540ff584/US3304417.pdf;
                 https://patents.google.com/patent/US3304417",
  abstract =     "Prior art digital computers utilized fixed point
                 arithmetic processes in executing computer operations.
                 In performing fixed point arithmetic processes a
                 computer assumes the binary point (analogous to a
                 decimal point) to be between the sign of a number and
                 the most significant digit of the number. Thus the
                 number is considered to have an absolute value of less
                 than one. As explained in patent application filed
                 September 24, 1962, Serial No. 225,676, now abandoned,
                 for a ``Computer Having Floating Point Addition and
                 Floating Point Subtraction'' invented by me, in order
                 to execute fixed point addition and subtraction
                 operations, numbers to be operated upon by a computer
                 must first be appropriately scaled prior to computation
                 in order to obtain the scaling of the numbers is
                 accomplished prior to entering them into the computer
                 or by shifting them through programming afterwards.
                 Fixed point multiplication needs to have numbers scale
                 prior to performing computations with them. In
                 multiplication, shifting of the result through
                 programming is desirable in order to prevent loss of
                 significant portions which should be retained for use
                 in later computations. Particularly is it true where
                 after a multiplication operation has been performed,
                 the product must be added or subtracted from or with
                 other numbers, in which case scaling would first have
                 to be done before the additional computation could be
                 made.",
  acknowledgement = ack-nhfb,
}

@Article{Howell:1967:MPA,
  author =       "K. M. Howell",
  title =        "Multiple precision arithmetic techniques",
  journal =      j-COMP-J,
  volume =       "9",
  number =       "4",
  pages =        "383--387",
  month =        feb,
  year =         "1967",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:56:19 MDT 2000",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/090383.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/383.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/384.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/385.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/386.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_09/Issue_04/tiff/387.tif",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Jarden:1967:EAL,
  author =       "Dov Jarden",
  title =        "Existence of Arbitrarily Long Sequences of Consecutive
                 Members in Arithmetic Progressions Divisible by
                 Arbitrarily Many Different Primes",
  journal =      j-FIB-QUART,
  volume =       "5",
  number =       "3",
  pages =        "280--??",
  month =        oct,
  year =         "1967",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:04:54 MDT 2011",
  bibsource =    "http://www.fq.math.ca/5-3.html;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.fq.math.ca/Scanned/5-3/jarden1.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Krishnamurthy:1967:NRD,
  author =       "E. V. Krishnamurthy and S. K. Nandi",
  title =        "On the Normalization Requirement of Divisor in
                 Divide-and-Correct Methods",
  journal =      j-CACM,
  volume =       "10",
  number =       "12",
  pages =        "809--813",
  month =        dec,
  year =         "1967",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Article{Kuki:1967:CAE,
  author =       "H. Kuki",
  title =        "Comments on the {ANL} Evaluation of the {OS\slash 360
                 FORTRAN} Math Function Library",
  journal =      "{SHARE Secretary Distribution}",
  volume =       "SSD 169",
  number =       "C4773",
  pages =        "47--53",
  year =         "1967",
  bibdate =      "Fri Aug 20 09:42:04 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Lewis:1967:CFP,
  author =       "H. R. {Lewis, Jr.} and E. J. {Stovall, Jr.}",
  title =        "Comments on a Floating-Point Version of {Nordsieck}'s
                 Scheme for the Numerical Integration of Differential
                 Equations",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "98",
  pages =        "157--161",
  month =        apr,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Long:1967:LAS,
  author =       "C. T. Long and J. H. Jordan",
  title =        "A Limited Arithmetic on Simple Continued Fractions",
  journal =      j-FIB-QUART,
  volume =       "5",
  number =       "2",
  pages =        "113--128",
  month =        apr,
  year =         "1967",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:04:52 MDT 2011",
  bibsource =    "http://www.fq.math.ca/5-2.html;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.fq.math.ca/Scanned/5-2/long.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Mandelbaum:1967:CLS,
  author =       "David Mandelbaum",
  title =        "A Comparison of Linear Sequential Circuits and
                 Arithmetic Sequences",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-16",
  number =       "2",
  pages =        "151--157",
  month =        apr,
  year =         "1967",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264810",
  ISSN =         "0367-7508",
  bibdate =      "Wed Jul 13 21:15:01 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039022",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@Article{Massell:1967:RAP,
  author =       "E. Massell",
  title =        "{R67-41} An Analog Photoresistive Multiplier",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-16",
  number =       "3",
  pages =        "380--380",
  month =        jun,
  year =         "1967",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264730",
  ISSN =         "0367-7508",
  bibdate =      "Wed Jul 13 21:15:03 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  note =         "See comment \cite{Azgapetian:1968:CAP}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039094",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}

@InProceedings{Matula:1967:BCM,
  author =       "David W. Matula",
  booktitle =    "{Proceedings of the AFIPS 1967 Spring Joint Computer
                 Conference}",
  title =        "Base Conversion Mappings",
  volume =       "30",
  publisher =    pub-AFIPS,
  address =      pub-AFIPS:adr,
  pages =        "311--318",
  year =         "1967",
  bibdate =      "Wed Feb 14 19:18:24 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Book{McCalla:1967:INM,
  author =       "Thomas Richard McCalla",
  title =        "Introduction to Numerical Methods and {Fortran}
                 Programming",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xiii + 359",
  month =        jan,
  year =         "1967",
  ISBN =         "0-471-58125-9",
  ISBN-13 =      "978-0-471-58125-3",
  LCCN =         "QA297 .M25",
  bibdate =      "Sat Sep 27 17:58:26 MDT 1997",
  bibsource =    "http://www.amazon.com/exec/obidos/ISBN=0471581259/wholesaleproductA/;
                 http://www.cbooks.com/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "US\$27.95",
  URL =          "http://www.cbooks.com/sqlnut/SP/search/gtsumt?source=&isbn=0471581259",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers --- Programming.; FORTRAN
                 (Computer program language); Numerical analysis.",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{McKeeman:1967:RER,
  author =       "W. M. McKeeman",
  title =        "Representation Error for Real Numbers in Binary
                 Computer Arithmetic",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-16",
  number =       "5",
  pages =        "682--683",
  month =        oct,
  year =         "1967",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264781",
  ISSN =         "0367-7508",
  bibdate =      "Wed Jul 13 21:15:05 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039164",
  abstract =     "Real numbers can be represented in a binary computer
                 by the form $ i \cdot B^e $ where $i$ is the integer
                 part, $B$ the base, and $e$ the exponent. The accuracy
                 of the representation will depend upon the number of
                 bits allocated to the integer part and exponent part as
                 well as what base is chosen. If $ L(i) $ and $ L(e) $
                 are the number of bits allocated to the magnitudes of
                 the integer and exponent parts and we define $ I =
                 2^{L(i)} $ and $ E = 2^{L(e)} $, the exponent range is
                 given by $ B^{\pm E} $, the maximum relative
                 representation error is given by $ B / 2 I $, and the
                 average relative representation error is given by $ (B
                 - 1) / (4 I \ln B) $. The formulas provide quantitative
                 comparison for the effectiveness of alternative formats
                 for real number representations.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
  remark =       "McKeeman discusses the maximum and average relative
                 errors in binary (with and without a hidden bit),
                 octal, and hexadecimal bases for floating-point
                 arithmetic with a 48-bit computer word. Errors are
                 smallest with binary and a hidden bit.",
}

@Article{Menzel:1967:AUA,
  author =       "M. Menzel and N. Metropolis",
  title =        "Algorithms in unnormalized arithmetic. {II}.
                 {Unrestricted} polynomial evaluation",
  journal =      j-NUM-MATH,
  volume =       "10",
  number =       "5",
  pages =        "451--462",
  month =        nov,
  year =         "1967",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF02162878",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65.80",
  MRnumber =     "MR0255093 (40 \#8300)",
  bibdate =      "Wed Nov 14 19:04:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0225.65059",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Book{Minsky:1967:CFI,
  author =       "Marvin Lee Minsky",
  title =        "Computation: Finite and Infinite Machines",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xvii + 317",
  year =         "1967",
  LCCN =         "QA267 .M55",
  bibdate =      "Thu Oct 17 06:05:56 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1927--2016",
  tableofcontents = "Physical machines and their abstract counterparts
                 \\
                 Part 1: Finite-state machines \\
                 Neural networks. Automata made up of parts \\
                 The memories of events in finite-state machines \\
                 Part 2: Infinite machines \\
                 Computability, effective procedures, and algorithms.
                 Infinite machines \\
                 Turing machines \\
                 Universal Turing machines \\
                 Limitations of effective computability: some problems
                 not solvable by instruction-obeying machines \\
                 The computable real numbers \\
                 The relations between Turing machines and recursive
                 functions \\
                 Models similar to digital computers \\
                 Part 3: Symbol-manipulation systems and computability
                 \\
                 The symbol-manipulation systems of post \\
                 Post's normal-form theorem \\
                 Very simple bases for computability \\
                 Solutions to selected problems",
}

@Article{Moler:1967:IRF,
  author =       "C. B. Moler",
  title =        "Iterative Refinement in Floating Point",
  journal =      j-J-ACM,
  volume =       "14",
  number =       "2",
  pages =        "316--321",
  month =        apr,
  year =         "1967",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Tue Nov 1 09:43:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  keywords =     "ir, nla, lud, iterative refinement",
}

@Article{Mosteller:1967:DSR,
  author =       "Frederick Mosteller and Cleo Youtz and Douglas Zahn",
  title =        "The Distribution of Sums of Rounded Percentages",
  journal =      j-DEMOGRAPHY,
  volume =       "4",
  number =       "2",
  pages =        "850--858",
  month =        jun,
  year =         "1967",
  CODEN =        "????",
  ISSN =         "0070-3370 (print), 1533-7790 (electronic)",
  ISSN-L =       "0070-3370",
  bibdate =      "Thu Nov 24 08:03:16 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Diaconis:1979:RP} for further work.",
  URL =          "http://muse.jhu.edu/journals/dem/;
                 http://www.biomedsearch.com/nih/Distribution-Sums-Rounded-Percentages/21318695.html;
                 http://www.jstor.org/stable/2060324",
  abstract =     "When percentages are computed for counts in several
                 categories or for several positive measurements0 each
                 taken as a fraction of their sum, the rounded
                 percentages often fail to add to 100 percent. We
                 investigate how frequently this failure occurs and what
                 the distributions of sums of rounded percentages are
                 for (1) an empirical set of data, (2) the multinomial
                 distribution in small samples, (3) spacings between
                 points dropped on an interval --- the broken-stick
                 model; and (4) for simulation for several categories.
                 The several methods produce similar distributions.We
                 find that the probability that the sum of rounded
                 percentages adds to exactly 100 percent is certain for
                 two categories, about three-fourths for three
                 categories, about two-thirds for four categories, and
                 about [Formula: see text] for larger numbers of
                 categories, c, on the average when categories are not
                 improbable.",
  acknowledgement = ack-nhfb,
  fjournal =     "Demography",
  pubmedid =     "21318695",
}

@Article{Moursund:1967:OSV,
  author =       "David G. Moursund",
  title =        "Optimal starting values for {Newton--Raphson}
                 calculation of $ \sqrt {x} $",
  journal =      j-CACM,
  volume =       "10",
  number =       "7",
  pages =        "430--432",
  month =        jul,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363427.363454",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.25",
  MRnumber =     "39\#2297",
  bibdate =      "Thu Sep 1 10:15:43 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See letter \cite{Fike:1967:LER}.",
  abstract =     "The problem of obtaining starting values for the
                 Newton-Raphson calculation of $ \sqrt {x} $ on a
                 digital computer is considered. It is shown that the
                 conventionally used best uniform approximations to $
                 \sqrt {x} $ do not provide optimal starting values. The
                 problem of obtaining optimal starting values is stated,
                 and several basic results are proved. A table of
                 optimal polynomial starting values is given.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\sqrt(x)$; elementary functions",
  remark =       "Title of article has incorrect $ \sqrt (x^{1 / 2}) $:
                 the article discusses computation of {\tt sqrt(x)}.",
}

@Article{Nandi:1967:STD,
  author =       "Salil K. Nandi and E. V. Krishnamurthy",
  title =        "A simple technique for digital division",
  journal =      j-CACM,
  volume =       "10",
  number =       "5",
  pages =        "299--301",
  month =        may,
  year =         "1967",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:13 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@InProceedings{Noble:1967:REI,
  author =       "Ben Noble",
  title =        "Rounding Error, Ill-Conditioning, and Instability",
  crossref =     "Anonymous:1967:PAN",
  pages =        "209--228",
  year =         "1967",
  bibdate =      "Fri Oct 31 09:42:07 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://apps.dtic.mil/sti/tr/pdf/AD0825963.pdf",
  acknowledgement = ack-nhfb,
  remark =       "rounding error; polynomial root finding; ordinary
                 differential equations; least-squares solution of
                 linear equations",
}

@Article{Sandberg:1967:FPR,
  author =       "I. W. Sandberg",
  title =        "Floating-Point-Roundoff Accumulation in Digital-Filter
                 Realizations",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "46",
  number =       "8",
  pages =        "1775--1791",
  month =        oct,
  year =         "1967",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  bibdate =      "Tue Nov 9 11:15:55 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1967/BSTJ.1967.4608.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol46/bstj46-8-1775.pdf",
  abstract =     "In this paper, several results are presented
                 concerning the effects of roundoff in the
                 floating-point realization of a general discrete filter
                 governed ideally by a stable difference equation of the
                 form\par

                  $$ w_n = \sum_{k = 0}^M b_k x_{n - k} - \sum {k = 1}^N
                 a_k w_{n - k}, \qquad n \geq N \qquad (1) $$ \par

                 in which $ \{ w_n \} $ and $ \{ x_n \} $ are output and
                 input sequences, respectively.\par

                 In particular, for a large class of filters it is
                 proved that there is a function $ f(K) $ with $ f(K)
                 \to 0 $ as $ K \to \infty $ and a constant $c$, both
                 dependent on the $ b_k $, the $ a_k $, the order in
                 which the products on the right side of (1) are summed
                 in the machine, and $t$, the number of bits allotted to
                 the mantissa, such that\par

                  $$ \langle e \rangle_K \leq c \langle y \rangle_K +
                 f(K) $$ \par

                 for all $ K \geq N $, in which, with the computed
                 output sequence of the realized filter,\par

                  $$ \langle y \rangle_K = \left (\frac {1}{K + 1}
                 \sum_{n = 0}^K |y_n|^2 \right)^{1 / 2} $$ \par

                 and\par

                  $$ \langle e \rangle_K = \left (\frac {1}{K + 1}
                 \sum_{n = 0}^K |w_n - y_n|^2 \right)^{1 / 2} $$
                 \par

                 Bounds on $ f(K) $ and $c$ are given that are not
                 difficult to evaluate, and which, in many realistic
                 cases, are informative. For example, for the
                 second-order bandpass filter:\par

                  $$ w_n = x_n - a_1 w_{n - 1} - a_2 w_{n - 2}, \qquad n
                 \geq 2 \qquad (2) $$ \par

                 with $ a_1 $ and $ a_2 $ chosen so that its poles arc
                 at approximately $ \pm 45^\circ $ and at distance
                 approximately (but not less than) $ 0.001 $ from the
                 unit circle, we find that $c$, an upper bound on the
                 ``asymptotic output error-to-signal ratio'', is not
                 greater than $ 0.58 \times 10^{-4} $, assuming that $ t
                 = 27 $, that the terms on the right side of (2) are
                 summed in the machine in the order indicated (from
                 right to left), and that the $ x_n $ in (2) are machine
                 numbers. If the $ x_n $ are not machine numbers, and
                 hence must be quantized before processing, then $ c
                 \leq 0.76 \times 10^{-4} $.\par

                 In addition to error bounds, an inequality is derived
                 which, if satisfied, rules out certain types of
                 generally undesirable behavior such as self-sustained
                 output limit cycles due to roundoff effects. This
                 inequality is satisfied for the example described
                 above.",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}

@Article{Sasaki:1967:ASR,
  author =       "Akio Sasaki",
  title =        "Addition and Subtraction in the Residue Number
                 System",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-16",
  number =       "2",
  pages =        "157--164",
  month =        apr,
  year =         "1967",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264811",
  ISSN =         "0367-7508",
  bibdate =      "Wed Jul 13 21:15:01 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4037753;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4039015;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4039023",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Improved residue expression and new arithmetic
                 algorithms for addition and subtraction are proposed.
                 In the proposed system positive and negative integers
                 of any magnitude can be handled regardless of the
                 particular choice of the set of relatively \ldots{}",
}

@TechReport{Schoenfeld:1967:FPE,
  author =       "L. Schoenfeld",
  title =        "Floating point error estimates",
  chapter =      "9",
  type =         "Technical Summary Report",
  number =       "721",
  institution =  inst-MRC-WISCONSIN,
  address =      inst-MRC-WISCONSIN:adr,
  month =        aug,
  year =         "1967",
  bibdate =      "Sat Nov 01 07:29:49 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@MastersThesis{Smith:1967:ZFA,
  author =       "Brian Thomas Smith",
  title =        "A Zero-Finding Algorithm Using {Laguerre}'s Method",
  type =         "{Master's} thesis",
  school =       "Department of Computer Science, University of
                 Toronto",
  address =      "Toronto, ON, Canada",
  year =         "1967",
  bibdate =      "Fri Oct 31 07:05:47 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://en.wikipedia.org/wiki/Laguerre%27s_method",
  acknowledgement = ack-nhfb,
  advisor =      "William M. Kahan",
  remark-1 =     "Cited in \cite[p. 163]{Palmer:1984:P} as the source of
                 a faster converging algorithm than Newton's for root
                 finding, $f(x) = 0$: Laguerre's method (1878) takes
                 this form for a polynomial of degree $n$: $x_{i + 1} =
                 x_i - f(x_i) / (f'(x_i) \pm \sqrt{(n - 1)^2 (f'(x_i))^2
                 n (n - 1) f(x_i) f'(x_i)})$. Palmer says earlier in his
                 book on the Intel 8087 that CORDIC iterations, which
                 are linear in the number of significant bits, are
                 sometimes stopped early, and switched to faster
                 converging iterative methods. Wikipedia has a somewhat
                 different definition of the iteration. Laguerre's and
                 Halley's methods are cubically convergent, but the
                 first needs only f(x) and f'(x), and a square root,
                 while the second needs f(x), f'(x), and f''(x), but no
                 square root.",
  remark-2 =     "The author later completed a doctoral degree at the
                 UofToronto \cite{Smith:1969:EBB}. According to
                 \cite{Smith:1967:ZZF}, this work was done under the
                 direction of William Kahan when the latter was at
                 Toronto, before his move to Berkeley, CA. That may be
                 how Kahan's student, John Palmer, learned of Laguerre's
                 method. Kahan and Smith both presented papers at the
                 1967 Army Numerical Analysis Conference in Madison, WI
                 \cite{Smith:1967:ZZF,Kahan:1967:ISS}. Smith later was
                 part of the team that developed EISPACK (1976) and
                 co-authored a book on Fortran 95
                 \cite{Adams:1997:FHC}.",
}

@InProceedings{Smith:1967:ZZF,
  author =       "Brian Thomas Smith",
  title =        "{ZERPOL}, a Zero Finding Algorithm for Polynomials
                 using {Laguerre}'s Method",
  crossref =     "Anonymous:1967:PAN",
  pages =        "153--174",
  year =         "1967",
  bibdate =      "Fri Oct 31 07:22:55 2025",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://apps.dtic.mil/sti/tr/pdf/AD0825963.pdf",
  abstract =     "ZERPOL is a subroutine which computes the N zeros of
                 the polynomial P(z) when given just its real
                 coefficients A(I):\par

                 $ P(z) = A(1)z^N + A(2) z^{N - 1} + \cdots {} + A(N)z +
                 A(N + 1). $ \par

                 The zeros are stored in the complex array Z with the
                 complex zeros appearing in complex conjugate pairs.
                 Except for polynomials of degrees one and two, ZERPOL
                 iterates towards a zero using Laguerre's method, which
                 is cubically convergent for isolated zeros and linearly
                 convergent for multiple zeros. The maximum length of
                 the step between successive iterates is restricted so
                 that the iterate $ x_{j + 2} $ lies inside a certain
                 region about the iterate $ x_j $ proved to contain a
                 zero of the polynomial. An iterate is accepted as a
                 zero when the polynomial value at that iterate is
                 smaller than a computed bound for the rounding error in
                 the polynomial value at that iterate. The original
                 polynomial is deflated after each real zero or pair of
                 complex zeros is found, and subsequent zeros are found
                 using the deflated polynomial.",
  acknowledgement = ack-nhfb,
  remark =       "The footnote on the first page says: ``\,`The program
                 Zerpol discussed in this article was developed under
                 the direction of Professor William M. Kahan, University
                 of Toronto, Toronto, Canada. This material was
                 presented at the Conference by Professor Kahan who
                 described the rationale for the program Zerpol
                 described here by Mr. Smith.' The next article in these
                 Proceedings was submitted by Dr. Kahan and is intended
                 to support the material in this article.''",
}

@Book{Szabo:1967:RAA,
  author =       "Nicholas S. Szab{\'o} and Richard I. Tanaka",
  title =        "Residue arithmetic and its applications to computer
                 technology",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "xvi + 236",
  year =         "1967",
  LCCN =         "QA247.35 .S95",
  bibdate =      "Fri Jun 24 16:02:00 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "McGraw-Hill series in information processing and
                 computers",
  acknowledgement = ack-nhfb,
  remark =       "Based on the authors' Report on residue (modular)
                 arithmetic survey.",
  subject =      "Modular arithmetic; Algorithms; Computer programming",
}

@Article{Tomasulo:1967:EAE,
  author =       "R. M. Tomasulo",
  title =        "An Efficient Algorithm for Exploiting Multiple
                 Arithmetic Units",
  journal =      j-IBM-JRD,
  volume =       "11",
  number =       "1",
  pages =        "25--33",
  month =        jan,
  year =         "1967",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Fri Aug 26 10:27:10 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}

@Book{Wilkinson:1967:BZW,
  author =       "J. H. Wilkinson",
  title =        "Bledy Zaokragle{\'n} w Procesach Algebraicznych.
                 ({Polish}) [{Rounding} errors in algebraic Processes]",
  publisher =    "PWW",
  address =      "Warszawa, Poland",
  pages =        "????",
  year =         "1967",
  bibdate =      "Thu Aug 25 09:28:02 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Polish translation of \cite{Wilkinson:1963:REA}",
  acknowledgement = ack-nhfb,
  language =     "Polish",
}

@Article{Winograd:1967:TRP,
  author =       "Shmuel Winograd",
  title =        "On the Time Required to Perform Multiplication",
  journal =      j-J-ACM,
  volume =       "14",
  number =       "4",
  pages =        "793--802",
  month =        oct,
  year =         "1967",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/321420.321438",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Sat Feb 8 10:29:30 2020",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/Multi.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}

@Article{Yarbrough:1967:PCC,
  author =       "Lynn Yarbrough",
  title =        "Precision calculations of $e$ and $ \pi $ constants",
  journal =      j-CACM,
  volume =       "10",
  number =       "9",
  pages =        "537--537",
  month =        sep,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363566.363578",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:15 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "floating-point arithmetic; number base conversion",
  remark =       "Gives decimal, octal, and hexadecimal values of $e$
                 and $ \pi $ to 100 digits, and notes ``The difficulty
                 arises because assemblers and compilers are hardly ever
                 designed to convert decimal constants to a precision of
                 more than a dozen or so digits. Thus, if calculations
                 to greater precision are to be done, constants usually
                 must be input in octal or other binary-derived
                 representation.''. Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Atkins:1968:HRD,
  author =       "D. E. Atkins",
  title =        "Higher-radix division using estimates of the divisor
                 and partial remainders",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-17",
  number =       "10",
  pages =        "925--934",
  month =        oct,
  year =         "1968",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1968.226439",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1960.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@TechReport{Azen:1968:DMS,
  author =       "S. Azen and S. Derr",
  title =        "On the Distribution of the Most Significant
                 Hexadecimal Digit",
  type =         "Technical Report",
  number =       "RM 5496 PR",
  institution =  "Rand Report",
  address =      "Santa Monica, CA, USA",
  year =         "1968",
  bibdate =      "Wed Feb 14 17:22:53 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Azgapetian:1968:CAP,
  author =       "V. Azgapetian",
  title =        "Comment on {``An Analog Photoresistive Multiplier''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-17",
  number =       "2",
  pages =        "188--188",
  month =        feb,
  year =         "1968",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1968.229083",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 17:40:47 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1960.bib",
  note =         "See \cite{Massell:1967:RAP}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687312",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Brennan:1968:FTA,
  author =       "J. F. Brennan",
  title =        "The Fastest Time of Addition and Multiplication",
  journal =      "IBM Research Reports",
  volume =       "4",
  number =       "1",
  pages =        "??--??",
  month =        "????",
  year =         "1968",
  bibdate =      "Fri Nov 09 10:43:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Dean:1968:GRB,
  author =       "K. J. Dean",
  title =        "Generator for the reciprocals of binary numbers",
  journal =      j-PROC-IEE,
  volume =       "115",
  number =       "6",
  pages =        "787",
  month =        jun,
  year =         "1968",
  CODEN =        "PIEEAH",
  DOI =          "https://doi.org/10.1049/piee.1968.0142",
  ISSN =         "0020-3270 (print), 2053-7891 (electronic)",
  ISSN-L =       "0020-3270",
  bibdate =      "Thu Apr 10 13:07:02 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the Institution of Electrical
                 Engineers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5247218",
}

@Article{Dietmeyer:1968:GPI,
  author =       "D. L. Dietmeyer and J. R. Duley",
  title =        "Generating prime implicants via ternary encoding and
                 decimal arithmetic",
  journal =      j-CACM,
  volume =       "11",
  number =       "7",
  pages =        "520--523",
  month =        jul,
  year =         "1968",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363397.363565",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Aug 07 17:25:16 2008",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Decimal arithmetic, ternary encoding of cubes, and
                 topological considerations are used in an algorithm to
                 obtain the extremals and prime implicants of Boolean
                 functions. The algorithm, which has been programmed in
                 the FORTRAN language, generally requires less memory
                 than other minimization procedures, and treats DON'T
                 CARE terms in an efficient manner.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "cubical complexes; extremal; minimization; prime
                 implicants; switching function; ternary encoding",
}

@Article{Elliott:1968:EAA,
  author =       "David Elliott",
  title =        "Error analysis of an algorithm for summing certain
                 finite series",
  journal =      j-J-AUSTRALIAN-MATH-SOC,
  volume =       "8",
  number =       "2",
  pages =        "213--221",
  month =        may,
  year =         "1968",
  CODEN =        "JAUMAX",
  DOI =          "https://doi.org/10.1017/s1446788700005267",
  ISSN =         "0004-9735 (print), 2059-9234 (electronic)",
  ISSN-L =       "0004-9735",
  MRclass =      "65.25",
  MRnumber =     "0230452",
  MRreviewer =   "U. C. Guha",
  bibdate =      "Fri Feb 9 15:20:35 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Australian Mathematical Society",
  remark =       "Analysis of Clenshaw algorithm for Chebyshev summation
                 \cite{Clenshaw:1955:NSC}, and report of region of
                 instability of that procedure",
}

@Book{Fike:1968:CEM,
  author =       "C. T. Fike",
  title =        "Computer Evaluation of Mathematical Functions",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xii + 227",
  year =         "1968",
  LCCN =         "QA297 .F5",
  bibdate =      "Thu Sep 1 10:12:51 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Fraser:1968:AUA,
  author =       "M. Fraser and N. Metropolis",
  title =        "Algorithms in unnormalized arithmetic. {III}. {Matrix}
                 inversion",
  journal =      j-NUM-MATH,
  volume =       "12",
  number =       "5",
  pages =        "416--428",
  month =        dec,
  year =         "1968",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65.80",
  MRnumber =     "MR0255094 (40 \#8301)",
  bibdate =      "Wed Nov 14 19:04:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0184.37503",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Harman:1968:ADI,
  author =       "M. G. Harman",
  title =        "An Attempt to Design an Improved Multiplication
                 System",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-17",
  number =       "11",
  pages =        "1090--1090",
  month =        nov,
  year =         "1968",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1968.226864",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 17:40:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1960.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687268",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Book{Hart:1968:CAa,
  author =       "John F. Hart and E. W. Cheney and Charles L. Lawson
                 and Hans J. Maehly and Charles K. Mesztenyi and John R.
                 Rice and Henry G. {Thatcher, Jr.} and Christoph
                 Witzgall",
  title =        "Computer Approximations",
  publisher =    pub-R-E-KRIEGER,
  address =      pub-R-E-KRIEGER:adr,
  pages =        "x + 343",
  year =         "1968",
  ISBN =         "0-88275-642-7",
  ISBN-13 =      "978-0-88275-642-4",
  LCCN =         "QA 297 C64 1978",
  bibdate =      "Tue Dec 14 22:55:11 1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "Reprinted 1978 with corrections.",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "1: The Design of a Function Subroutine / 1 \\
                 2: General Methods of Computing Functions / 10 \\
                 3: Least Maximum Approximations / 42 \\
                 4: The Choice and Application of Approximations / 58
                 \\
                 5: Description and Use of the Tables / 82 \\
                 6: Function Notes / 89 \\
                 7: Tables of Coefficients / 155 \\
                 Appendix A: Conversion Algorithms / 307 \\
                 Appendix B: Bibliography of Approximations / 313 \\
                 Appendix C: Decimal and Octal Constants / 333 \\
                 References / 336 \\
                 Index / 341",
  tableofcontents = "1: The Design of a Function Subroutine / 1 \\
                 1.1 Introduction / 1 \\
                 1.2 General Considerations in Writing a Function
                 Subroutine / 2 \\
                 1.3 Relation of the Function Subroutine to the Computer
                 System / 3 \\
                 1.4 The Three Main Types of Function Subroutine / 4 \\
                 1.5 Special Programming Techniques / 7 \\
                 1.6 Subroutine Errors / 7 \\
                 1.7 Final Steps / 9 \\
                 2: General Methods of Computing Functions / 10 \\
                 2.1 Introduction / 10 \\
                 2.2 Application of Infinite Expansions / 11 \\
                 2.3 Recurrence and Difference Relations / 23 \\
                 2.4 Iterative Techniques / 27 \\
                 2.5 Integral Representations / 28 \\
                 2.6 Differential Equations / 29 \\
                 2.7 Tabular Data / 32 \\
                 2.8 Convergence Acceleration / 33 \\
                 3: Least Maximum Approximations / 42 \\
                 3.1 Introduction / 42 \\
                 3.2 Properties of Least Maximum Approximations / 43 \\
                 3.3 Nearly Least Maximum Approximations / 46 \\
                 3.4 Rational Approximation / 51 \\
                 3.5 Segmented Approximation / 54 \\
                 3.6 Computation of the Tables / 55 \\
                 4: The Choice and Application of Approximations / 58
                 \\
                 4.1 Introduction / 5 8 \\
                 4.2 Domain Considerations / 58 \\
                 4.3 Machine Considerations / 62 \\
                 4.4 Conditioning of Approximations / 65 \\
                 4.5 Polynomial Forms / 67 \\
                 4.6 Rational Forms / 73 \\
                 4.7 Transformation Algorithms / 78 \\
                 5: Description and Use of the Tables / 82 \\
                 5.1 Introduction / 22 \\
                 5.2 Function Notes / 82 \\
                 5.3 Accuracy of the Coefficients / 83 \\
                 5.4 How to Use the Tables / 86 \\
                 5.5 Preparation of the Tables / 88 \\
                 6: Function Notes / 89 \\
                 6.1 Square Root, Cube Root / 89 \\
                 6.2 Exponential and Hyperbolic Functions / 96 \\
                 6.3 The Logarithm Function / 105 \\
                 6.4 Trigonometric Functions / 112 \\
                 6.5 The Inverse Trigonometric Functions / 120 \\
                 6.6 The Gamma Function and Its Logarithm / 130 \\
                 6.7 The Error Function / 136 \\
                 6.8 Bessel Functions / 141 \\
                 6.9 Complete Elliptic Integrals / 150 \\
                 7: Tables of Coefficients / 155 \\
                 Appendix A: Conversion Algorithms / 307 \\
                 Appendix B: Bibliography of Approximations / 313 \\
                 Appendix C: Decimal and Octal Constants / 333 \\
                 References / 336 \\
                 Index / 341",
}

@Book{Hart:1968:CAb,
  author =       "John F. Hart and E. W. Cheney and Charles L. Lawson
                 and Hans J. Maehly and Charles K. Mesztenyi and John R.
                 Rice and Henry G. {Thatcher, Jr.} and Christoph
                 Witzgall",
  title =        "Computer Approximations",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "x + 343",
  year =         "1968",
  ISBN =         "0-471-35630-1",
  ISBN-13 =      "978-0-471-35630-1",
  LCCN =         "QA297 .C64",
  bibdate =      "Sat Jan 14 14:53:06 2006",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "The SIAM series in applied mathematics",
  acknowledgement = ack-nhfb,
}

@Book{IBM:1968:ISP,
  author =       "{IBM Corporation}",
  title =        "{IBM System}\slash 360 Principles of Operation",
  publisher =    pub-IBM,
  address =      pub-IBM:adr,
  edition =      "Eighth",
  pages =        "175",
  year =         "1968",
  LCCN =         "QA76.8.I12 I59 1968",
  bibdate =      "Wed Sep 14 23:12:39 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1968:ISS,
  author =       "W. Kahan",
  title =        "{7094-II} system support for numerical analysis",
  howpublished = "SHARE Secretarial Distribution SSD-159.",
  year =         "1968",
  bibdate =      "Mon Sep 16 16:14:28 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kaneko:1968:PSA,
  author =       "T. Kaneko and B. Liu",
  title =        "Round-off error of floating-point digital filters",
  crossref =     "Anonymous:1968:PSA",
  pages =        "219--227",
  year =         "1968",
  MRclass =      "65.80",
  MRnumber =     "41\#7878",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Matula:1968:BCT,
  author =       "David W. Matula",
  title =        "The Base Conversion Theorem",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "19",
  number =       "3",
  pages =        "716--723",
  month =        jun,
  year =         "1968",
  CODEN =        "PAMYAR",
  DOI =          "https://doi.org/10.1090/s0002-9939-1968-0234908-9",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  bibdate =      "Fri Apr 21 07:26:39 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A demonstration that, in converting numbers from base
                 $ \beta $ to base $ \nu $, where $ \beta^i \neq \nu^j $
                 for any positive integers $ i, j $, a one-to-one
                 mapping exists only if $ \nu^{m - 1} \geq \beta^n - 1
                 $. Here $m$ is the number of digits in base $ \nu $ and
                 $n$ that in base $ \beta $.\par

                 The implications of this result are discussed in the
                 author's earlier paper [Proc. Amer. Fed. Information
                 Processing Soc. 30 (1967), 311--318].",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
  received =     "9 February 1967",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Matula:1968:C,
  author =       "David W. Matula",
  title =        "In-and-out conversions",
  journal =      j-CACM,
  volume =       "11",
  number =       "1",
  pages =        "47--50",
  month =        jan,
  year =         "1968",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/362851.362887",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.80",
  MRnumber =     "39\#2360",
  bibdate =      "Fri Nov 25 18:20:17 MST 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also \cite{Goldberg:1967:BED,Matula:1968:BCT}",
  abstract =     "By an in-and-out conversion we mean that a
                 floating-point number in one base is converted into a
                 floating-point number in another base and then
                 converted back to a floating-point number in the
                 original base. For all combinations of rounding and
                 truncation conversions the question is considered of
                 how many significant digits are needed in the
                 intermediate base to allow such in-and-out conversions
                 to return the original number (when possible), or at
                 least significant digit.",
  acknowledgement = ack-nhfb # "\slash " # ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "floating-point numbers; number base conversion;
                 rounding error; significance; truncation error",
  received =     "April 1967 (revised August 1967)",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Metropolis:1968:ANA,
  author =       "N. Metropolis",
  title =        "Algorithms in un-normalized arithmetic: Polynomial
                 evaluation and matrix decomposition",
  journal =      "Colloques internationaux, Centre National de la
                 Recherche Scientifique, Paris",
  volume =       "165",
  pages =        "293--303",
  year =         "1968",
  bibdate =      "Wed Nov 14 19:04:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0207.15804",
  acknowledgement = ack-nhfb,
  classmath =    "*65H05 (Single nonlinear equations (numerical
                 methods)) 65F05 (Direct methods for linear systems)",
}

@Article{Nathan:1968:IVS,
  author =       "A. Nathan and J. Molcho",
  title =        "Improved Voltage Selector and Cascade Multiplier
                 Circuits",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-17",
  number =       "4",
  pages =        "380--382",
  month =        apr,
  year =         "1968",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1968.229386",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 17:40:48 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1960.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687350",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Nickel:1968:EBC,
  author =       "K. Nickel",
  booktitle =    "Proceedings of the {IFIP} Congress",
  title =        "Error Bounds and Computer Arithmetic",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "54--60",
  year =         "1968",
  LCCN =         "????",
  bibdate =      "Fri Aug 20 10:09:47 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Nievergelt:1968:CCP,
  author =       "J. Nievergelt",
  title =        "Computers and computing --- Past present Future",
  journal =      j-IEEE-SPECTRUM,
  volume =       "5",
  number =       "1",
  pages =        "57--61",
  month =        jan,
  year =         "1968",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.1968.5215633",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Wed Jan 15 09:30:58 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum1960.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "Computer science; Concurrent computing; Digital
                 arithmetic; Hardware; History; Instruments;
                 Maintenance; Manufacturing; Programming; Relays",
}

@Article{Padegs:1968:SAS,
  author =       "A. Padegs",
  title =        "Structural aspects of the {SYSTEM\slash 360 Model 85},
                 Part {III}: Extensions to floating-point architecture",
  journal =      j-IBM-SYS-J,
  volume =       "7",
  number =       "1",
  pages =        "22--29",
  year =         "1968",
  CODEN =        "IBMSA7",
  ISSN =         "0018-8670",
  bibdate =      "Tue Mar 19 17:38:46 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Systems Journal",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Phillips:1968:EME,
  author =       "G. M. Phillips",
  title =        "Estimate of the maximum error in best polynomial
                 approximations",
  journal =      j-COMP-J,
  volume =       "11",
  pages =        "110--111",
  year =         "1968",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Thu Sep 15 18:39:47 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  xxmonth =      "(none)",
  xxnumber =     "(none)",
}

@Article{Rao:1968:ECL,
  author =       "T. R. N. Rao",
  title =        "Error-Checking Logic for Arithmetic-Type Operations of
                 a Processor",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-17",
  number =       "9",
  pages =        "845--849",
  month =        sep,
  year =         "1968",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1968.229144",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 17:40:50 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1960.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687471",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@TechReport{Ross:1968:UMF,
  author =       "Richard D. Ross",
  title =        "{University of Mississippi} floating point subroutines
                 ({UMFS})",
  institution =  "Computer Center, University of Mississippi",
  address =      "University",
  pages =        "31",
  year =         "1968",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic data processing.",
  remark =       "Cover title.",
}

@Article{Sasaki:1968:BIA,
  author =       "A. Sasaki",
  title =        "The Basis for Implementation of Additive Operations in
                 the Residue Number System",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-17",
  number =       "11",
  pages =        "1066--1073",
  month =        nov,
  year =         "1968",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264810;
                 https://doi.org/10.1109/TC.1968.226466",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 17:40:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1960.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35582;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687264",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A new residue number system algebra has been
                 previously proposed by the author. The algebra has
                 solved an essential theoretical barrier in the residue
                 number system and has enabled one to pursue additive
                 operations in the residue \ldots{}",
}

@Article{Schmookler:1968:HSB,
  author =       "M. S. Schmookler",
  title =        "High Speed Binary to Decimal Conversion",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-17",
  pages =        "506--508",
  year =         "1968",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1968.226913",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 28 19:09:15 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1960.bib",
  abstract =     "This note describes several methods of performing
                 fast, efficient, binary-to-decimal conversion. With a
                 modest amount of circuitry, an order of magnitude speed
                 improvement can is obtained. This achievement offers a
                 unique advantage to general-purpose computers requiring
                 special hardware to translate between binary and
                 decimal numbering systems.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "decimal floating-point arithmetic",
}

@Book{Scott:1968:OET,
  author =       "Th{\'e}odore G. Scott",
  title =        "Ordinateurs {\'e}lectroniques, techniques de
                 programmation: Computer programming techniques",
  publisher =    "Tournai, Ed. Gamma",
  address =      "Paris, France",
  pages =        "662",
  year =         "1968",
  bibdate =      "Thu May 09 09:52:34 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Cinq volumes. Version fran{\c{c}}aise de Juliette
                 Charbonneau-Kohiyama.",
  acknowledgement = ack-nhfb,
  contents =     "1. Pr{\'e}sentation du Tutac. Etude du registre - base
                 et de ses fonctions. Le registre base. - 2. Les sous
                 programmes. L'entr{\'e}e. La sorite. - 3. La bande
                 magn{\'e}tique. La d{\'e}tection des erreurs. - 4. Les
                 calculs en virgule flottante. L'{\'e}dition des
                 programmes. - 5. La programmation symbolique. Le
                 language Cobol. Fortran et Algol",
}

@Manual{Smith:1968:CC,
  author =       "Smith, Robert E. (Robert Elijah)",
  title =        "Competence course",
  organization = "Control Data Corp.",
  address =      "Minneapolis, MN, USA",
  pages =        "vi + 296",
  year =         "1968",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers --- Programming.;
                 Floating-point arithmetic.; FORTRAN (Computer program
                 language)",
  remark =       "``Computer programming using FORTRAN and card inputs
                 without key punching!'' Cover title: Competence course,
                 FORTRAN computer programming. At head of title: School
                 computer-use plan.",
}

@Book{Stuart:1968:FP,
  author =       "Fredric Stuart",
  title =        "{Fortran} programming",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xix + 353",
  year =         "1968",
  ISBN =         "0-471-83477-7",
  ISBN-13 =      "978-0-471-83477-9",
  LCCN =         "QA76.5 .S8",
  bibdate =      "Sat Jan 27 13:40:57 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers --- Programming.;
                 {Fortran} (Computer program language)",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}, but given year
                 1969.",
}

@Article{Tung:1968:DAS,
  author =       "Chin Tung",
  title =        "A Division Algorithm for Signed-Digit Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-17",
  number =       "9",
  pages =        "887--889",
  month =        sep,
  year =         "1968",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1968.229150",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 17:40:50 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1960.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1687477",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Urabe:1968:RED,
  author =       "Minoru Urabe",
  title =        "Roundoff Error Distribution in Fixed-Point
                 Multiplication and a Remark about the Rounding Rule",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "5",
  number =       "2",
  pages =        "202--210",
  month =        jun,
  year =         "1968",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@TechReport{Veltkamp:1968:APV,
  author =       "G. W. Veltkamp",
  title =        "{ALGOL} procedures voor het berekenen van een inwendig
                 product in dubbele precisie. ({Dutch}) [{ALGOL}
                 procedures for calculating an inner product in double
                 precision]",
  type =         "Technical report",
  number =       "22",
  institution =  "RC-Informatie, Technische Hogeschool Eindhoven",
  address =      "Eindhoven, The Netherlands",
  year =         "1968",
  bibdate =      "Tue Dec 26 14:53:03 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "Dutch",
}

@Article{Vitenko:1968:OAA,
  author =       "{\=I}. V. V{\=\i}ten'{k}o",
  title =        "Optimal algorithms for addition and multiplication on
                 machines with floating point. ({Russian})",
  journal =      "{\v{Z}}. Vy{\v{c}}isl. Mat. i Mat. Fiz",
  volume =       "8",
  pages =        "1076--1084",
  year =         "1968",
  MRnumber =     "40\#2250",
  bibdate =      "Sat Dec 16 16:45:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
  reviewer =     "J. Kuntzmann",
}

@TechReport{Yohe:1968:CPA,
  author =       "J. Michael Yohe",
  title =        "Computer Programming for Accuracy",
  type =         "{MRC} Technical Summary Report",
  number =       "866",
  institution =  inst-MRC-WISCONSIN,
  address =      inst-MRC-WISCONSIN:adr,
  month =        apr,
  year =         "1968",
  bibdate =      "Sun Dec 30 21:42:55 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://apps.dtic.mil/sti/citations/AD0674459",
  abstract =     "In most computations, it is tacitly assumed that the
                 results produced by the program are 'accurate enough'.
                 This assumption is not always valid. In this report, we
                 discuss several possible sources of error in digital
                 computation, and we list several steps which can be
                 taken to guard against some types of error and
                 determine an upper bound for the effects of other
                 types. We illustrate these techniques with our
                 experience in writing a program to locate zeros of the
                 Riemann zeta function.",
  acknowledgement = ack-nhfb,
}

@Article{Anonymous:1969:VPD,
  author =       "Anonymous",
  title =        "Video Probability Distributions",
  journal =      j-IEEE-SPECTRUM,
  volume =       "6",
  number =       "4",
  pages =        "5--5",
  month =        apr,
  year =         "1969",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.1969.5214042",
  ISSN =         "1939-9340",
  ISSN-L =       "0018-9235",
  bibdate =      "Wed Jan 15 11:58:06 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum1960.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "Arithmetic; Circuit noise; Detectors; Distribution
                 functions; Gaussian noise; Probability distribution;
                 Signal to noise ratio; Tail; Testing; Voltage",
}

@InProceedings{Babuska:1969:NSM,
  author =       "Ivo Babu{\v{s}}ka",
  title =        "Numerical stability in mathematical analysis",
  crossref =     "Morrell:1969:IPP",
  pages =        "11--23",
  year =         "1969",
  bibdate =      "Tue Nov 22 05:36:22 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}

@Article{Banerji:1969:SDR,
  author =       "D. K. Banerji and J. A. Brzozowski",
  title =        "Sign Detection in Residue Number Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-18",
  number =       "4",
  pages =        "313--320",
  month =        apr,
  year =         "1969",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264810;
                 https://doi.org/10.1109/T-C.1969.222658",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 16:55:18 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1960.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35034;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671251",
  abstract =     "This paper is concerned with the sign detection
                 problem in residue number systems. The proposed
                 solution is applicable only to nonredundant systems. It
                 is shown that under rather general conditions an
                 explicit, closed formula for the sign function can be
                 obtained. In a special case, when one of the moduli is
                 $2$, the sign function becomes an EXCLUSIVE-OR
                 function. A sign detection algorithm is proposed and
                 methods of implementing the algorithm are presented.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
}

@Manual{BrinchHansen:1969:RCR,
  author =       "Per {Brinch Hansen}",
  title =        "{RC-4000 Computer} Reference Manual",
  number =       "RCSL No: 55-D1",
  organization = "A/S Regnecentralen",
  address =      "Copenhagen, Denmark",
  pages =        "85",
  month =        jun,
  year =         "1969",
  bibdate =      "Sat Mar 09 14:14:25 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://bitsavers.org/pdf/regnecentralen/RC_4000_Reference_Manual_Jun69.pdf;
                 https://www.math.utah.edu/~beebe/RC-4000",
  acknowledgement = ack-nhfb,
  remark =       "The RC-4000 has a 24-bit word, and supplies 12-bit and
                 24-bit integer arithmetic, and 48-bit floating-point
                 arithmetic. The latter has a signed 36-bit normalized
                 two's-complement binary fraction stored at the left of
                 a double word, followed by a 12-bit two's-complement
                 signed exponent. The representable range is therefore
                 [-0x1p-2049, +0x1p2047), or about [-1.547e-617,
                 1.615e+161]. The sign, and zero value, can be
                 determined by examining only the first word. Its
                 floating-point arithmetic can exactly represent 35-bit
                 integer arithmetic.",
  tableofcontents = "1. RC 4000 Specifications / 9 \\
                 2. Design Considerations / 11 \\
                 2.1. Word Length / 11 \\
                 2.2. Register Structure / 11 \\
                 2.3. Address Modification / 11 \\
                 2.4. Monitor Control / 12 \\
                 2.5. Input/Output Control / 13 \\
                 3. Data and Instruction Formats / 15 \\
                 3.1. Data Formats / 15 \\
                 3.2. Storage Addressing / 15 \\
                 3.3. Working Registers / 16 \\
                 3.4. Instruction Format / 17 \\
                 3.5. Address Modify Instruction / 18 \\
                 4. Integer Arithmetic / 19 \\
                 4.1. Number Representation / 19 \\
                 4.2. Byte Arithmetic / 19 \\
                 4.3. Multiplication and Division / 20 \\
                 4.4. Overflow and Carry Indication / 21 \\
                 5. Floating-Point Arithmetic / 22 \\
                 5.1. Number Representation / 22 \\
                 5.2. Arithmetic Operations / 23 \\
                 5.3. Normalization and Rounding / 23 \\
                 5.4. Precision Modes / 24 \\
                 5.5. Underflow, Overflow, and Non-Normalized Operands /
                 25 \\
                 5.6. Number Conversion / 26 \\
                 5.7. Exact Arithmetic with Floating-Point Instructions
                 / 26 \\
                 6. Protection System / 28 \\
                 6.1. Storage Protection / 28 \\
                 6.2. Privileged Instructions / 29 \\
                 6.3. Summary of Protection System / 29 \\
                 6.4. An Example of Protected Areas / 30 \\
                 7. Interruption System / 32 \\
                 7.1. Interruption Logic / 32 \\
                 7.2. Interruption Conditions / 33 \\
                 8. Low-Speed Data Channel / 35 \\
                 8.1. Main Characteristics / 35 \\
                 8.2. Input/Output Instruction / 35 \\
                 8.3. Channel Operation / 36 \\
                 8.4. Disconnected and Busy Indication / 37 \\
                 8.5. Device Commands / 37 \\
                 8.6. Read / 37 \\
                 8.7. Sense / 37 \\
                 8.8. Write / 38 \\
                 8.9. Control / 39 \\
                 8.10. Summary of Low-Speed Channel / 39 \\
                 9. High-Speed Data Channel / 41 \\
                 10. Standard Peripheral Devices / 43 \\
                 10.1. Console Devices / 43 \\
                 10.2. Interval Timer / 43 \\
                 11. Operator Control Panel / 44 \\
                 11.1. Indicators and Control Keys / 44 \\
                 11.2. Machine Errors / 44 \\
                 11.3. Reset Control / 44 \\
                 11.4. Start Control / 45 \\
                 11.5. Autoload Control / 45 \\
                 11.6. Local/Remote Indication / 46 \\
                 12. Technical Control Panel / 47 \\
                 12.1. Operating Modes / 47 \\
                 12.2. Instruction Step Keys / 47 \\
                 12.3. Register Setting and Display / 47 \\
                 12.4. Microinstruction Selection and Display / 48 \\
                 12.5. Parity Control / 48 \\
                 13. Instruction Set / 49 \\
                 14. Definition of Instructions / 51 \\
                 14.1. Algol Notation / 51 \\
                 14.2. Register Structure / 51 \\
                 14.3. Elementary Operations / 54 \\
                 14.4. Control Panel Functions / 55 \\
                 14.5. Instruction Fetch Cycle / 55 \\
                 14.6. Protection Procedures / 56 \\
                 14.7. Arithmetic Procedures / 57 \\
                 14.8. Instruction Execution / 58 \\
                 Appendix / 79 \\
                 A.1. Reserved Storage Locations / 79 \\
                 A.2. Numeric Instruction Codes / 80 \\
                 A.3. Instruction Execution Times / 81 \\
                 Index / 83",
}

@Article{Brown:1969:CB,
  author =       "W. S. Brown and P. L. Richman",
  title =        "The Choice of Base",
  journal =      j-CACM,
  volume =       "12",
  number =       "10",
  pages =        "560--561",
  month =        oct,
  year =         "1969",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "68.00",
  MRnumber =     "43\#5755",
  bibdate =      "Mon Mar 24 21:38:51 MST 1997",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A digital computer is considered, whose memory words
                 are composed of $N$ $r$-state devices plus two sign
                 bits (two state devices). The choice of base $ \beta $
                 for the internal representation floating-point numbers
                 on such a computer is discussed. It is shown that in a
                 certain sense $ \beta = r $ is best.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Bell Telephone Labs. Inc., Murray Hill, NJ, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "accuracy; base choice; digital arithmetic;
                 floating-point; number representations",
}

@InProceedings{Clark:1969:SCE,
  author =       "N. W. Clark and W. J. Cody",
  title =        "Self-contained exponentiation",
  crossref =     "AFIPS:1969:ACPb",
  volume =       "35",
  pages =        "701--706",
  year =         "1969",
  bibdate =      "Thu Sep 1 10:16:10 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@InProceedings{Cody:1969:PTF,
  author =       "W. J. Cody",
  title =        "Performance testing of function subroutines",
  crossref =     "AFIPS:1969:ACPa",
  volume =       "34",
  pages =        "759--763",
  year =         "1969",
  bibdate =      "Thu Sep 1 10:15:07 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Duke:1969:DFP,
  author =       "K. A. Duke",
  title =        "Decimal Floating Point Processor",
  journal =      j-IBM-TDB,
  volume =       "11-69",
  pages =        "862--862",
  month =        nov,
  year =         "1969",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Fri Nov 28 11:29:48 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Technical Disclosure Bulletin",
  keywords =     "decimal floating-point arithmetic",
  remark =       "Decimal arithmetic with unnormalized binary integers
                 of unspecified length for coefficient and exponent.",
}

@MastersThesis{Duncan:1969:FFA,
  author =       "Daniel D. A. Duncan",
  title =        "{FLOP}: a floating-point arithmetic package",
  type =         "Thesis ({M.S.})",
  school =       "University of Southwestern Louisiana",
  address =      "Lafayette, LA, USA",
  pages =        "108",
  year =         "1969",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithms.; Arithmetic --- Foundations.; FLOP
                 (Computer program language).; Transformations
                 (Mathematics).",
}

@Article{Dunworth:1969:ECB,
  author =       "A. Dunworth and J. I. Roche",
  title =        "The Error Characteristics of the Binary Rate
                 Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-18",
  number =       "8",
  pages =        "741--745",
  month =        aug,
  year =         "1969",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1969.222757",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 16:55:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1960.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671350",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@TechReport{Ehrman:1969:SFP,
  author =       "J. R. Ehrman",
  title =        "A Study of Floating-Point Conversions in Some
                 {OS\slash 360} Components",
  number =       "SDD 196, C5207",
  institution =  "SHARE Secretary Distribution",
  address =      "????",
  pages =        "1--6",
  year =         "1969",
  bibdate =      "Wed Feb 14 18:50:19 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Fenstad:1969:NSM,
  author =       "Jens Erik Fenstad",
  title =        "Non-standard models for arithmetic and analysis",
  journal =      j-LECT-NOTES-MATH,
  volume =       "118",
  pages =        "30--47",
  year =         "1969",
  CODEN =        "LNMAA2",
  DOI =          "https://doi.org/10.1007/BFb0060250",
  ISBN =         "3-540-04907-X (print), 3-540-36246-0 (e-book)",
  ISBN-13 =      "978-3-540-04907-4 (print), 978-3-540-36246-3
                 (e-book)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  ISSN-L =       "0075-8434",
  bibdate =      "Thu May 8 17:39:14 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lnm1960.bib",
  URL =          "http://link.springer.com/chapter/10.1007/BFb0060250/",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/BFb0060247",
  book-URL =     "http://www.springerlink.com/content/978-3-540-36246-3",
  fjournal =     "Lecture Notes in Mathematics",
  journal-URL =  "http://link.springer.com/bookseries/304",
}

@Article{Fenwick:1969:BMO,
  author =       "P. M. Fenwick",
  title =        "Binary Multiplication with Overlapped Addition
                 Cycles",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-18",
  number =       "1",
  pages =        "71--74",
  month =        jan,
  year =         "1969",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1969.222527",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 16:55:17 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1960.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671120",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Ferrari:1969:CDM,
  author =       "D. Ferrari",
  title =        "Correction to {``A Division Method Using a Parallel
                 Multiplier''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-18",
  number =       "10",
  pages =        "960--960",
  month =        oct,
  year =         "1969",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1969.222555",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 16:55:21 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1960.bib",
  note =         "See \cite{Ferrari:1967:DMU}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671148",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Field:1969:OFP,
  author =       "J. A. Field",
  title =        "Optimizing floating-point arithmetic via post addition
                 shift probabilities",
  crossref =     "AFIPS:1969:ACPa",
  pages =        "597--??",
  year =         "1969",
  bibdate =      "Tue Oct 09 07:54:02 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Flores:1969:BRB,
  author =       "Ivan Flores",
  title =        "Book Review: {{\booktitle{Residue Arithmetic and Its
                 Application to Computer Technology}} (Nicholas S. Szabo
                 and Richard I. Tanaka)}",
  journal =      j-SIAM-REVIEW,
  volume =       "11",
  number =       "1",
  pages =        "103--104",
  month =        "????",
  year =         "1969",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1011027",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu Mar 27 09:06:04 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/11/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "January 1969",
}

@Book{Froberg:1969:INA,
  author =       "Carl Erik Fr{\"o}berg",
  title =        "Introduction to numerical analysis",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Second",
  pages =        "xii + 433",
  year =         "1969",
  LCCN =         "QA297 .F6813 1969",
  bibdate =      "Fri Aug 20 09:03:07 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  remark =       "Translation of Swedish original {\em L{\"a}robok i
                 numerisk analys}. Cited in \cite{Sterbenz:1974:FPC}.",
  subject =      "Numerical analysis",
}

@PhdThesis{Glaser:1969:HMN,
  author =       "Anton Glaser",
  title =        "History of Modern Numeration Systems",
  type =         "{Educat.D.} thesis",
  school =       "Temple University",
  address =      "Philadelphia, PA, USA",
  pages =        "261",
  year =         "1969",
  bibdate =      "Fri Mar 17 08:18:07 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See subsequent books
                 \cite{Glaser:1971:HBO,Glaser:1981:HBO}.",
  URL =          "https://www.proquest.com/pqdtglobal/docview/302503306/A48758ED17C34A1APQ/1",
  acknowledgement = ack-nhfb,
  remark =       "ProQuest dissertation number 7016666.",
}

@Article{Hammersley:1969:NAP,
  author =       "P. Hammersley",
  title =        "Note on {Algorithm 34}: Procedures for the Basic
                 Arithmetical Operations in Multi-Length Working",
  journal =      j-COMP-J,
  volume =       "12",
  number =       "1",
  pages =        "102--103",
  month =        feb,
  year =         "1969",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:51:33 MDT 2000",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_01/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_01/tiff/102.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_01/tiff/103.tif",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Holzwarth:1969:VBB,
  author =       "A. Holzwarth",
  title =        "{Ein Verfahren zur Bestimmung bester
                 Tscheb\-y\-scheff- Ap\-prox\-i\-ma\-tion\-en der
                 Quadratwurzelfunktion} \toenglish {A Method for
                 Determination of Best Chebyshev Approximations to the
                 Square Root Function} \endtoenglish",
  journal =      j-COMPUTING,
  volume =       "4",
  number =       "2",
  pages =        "168--177",
  year =         "1969",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  affiliation =  "T{\"u}bingen, West Germany",
  classification = "C4130",
  description =  "Chebyshev approximation; numerical analysis",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  language =     "German",
}

@Article{Howell:1969:ASLa,
  author =       "Jo Ann Howell and Robert T. Gregory",
  title =        "An algorithm for solving linear algebraic equations
                 using residue arithmetic. {I}",
  journal =      j-BIT,
  volume =       "9",
  pages =        "200--224",
  year =         "1969",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65.35",
  MRnumber =     "MR0261775 (41 \#6388a)",
  bibdate =      "Thu Nov 8 14:50:15 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Howell:1969:ASLb,
  author =       "Jo Ann Howell and Robert T. Gregory",
  title =        "An algorithm for solving linear algebraic equations
                 using residue arithmetic. {II}",
  journal =      j-BIT,
  volume =       "9",
  pages =        "324--337",
  year =         "1969",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65.35",
  MRnumber =     "MR0261776 (41 \#6388b)",
  MRreviewer =   "J. Legras",
  bibdate =      "Thu Nov 8 14:50:18 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@MastersThesis{Huey:1969:DFP,
  author =       "Ben Milton Huey",
  title =        "Design of a floating point processor for the {PDP-9}
                 computer",
  type =         "Thesis ({M.S. - Electrical Engineering})",
  school =       "University of Arizona",
  address =      "Tucson, AZ, USA",
  pages =        "175",
  year =         "1969",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer storage devices.; Hybrid computers.",
}

@Article{Huttenhoff:1969:AUC,
  author =       "J. H. Huttenhoff and R. R. Shively",
  title =        "Arithmetic Unit of a Computing Element in a Global,
                 Highly Parallel Computer",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-18",
  number =       "8",
  pages =        "695--698",
  month =        aug,
  year =         "1969",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1969.222751",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 16:55:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1960.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671344",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{King:1969:LEN,
  author =       "Richard F. King and David L. Phillips",
  title =        "The Logarithmic Error and {Newton}'s Method for the
                 Square Root",
  journal =      j-CACM,
  volume =       "12",
  number =       "2",
  pages =        "87--88",
  month =        feb,
  year =         "1969",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/362848.362861",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.50",
  MRnumber =     "44\#2333",
  bibdate =      "Fri Nov 25 18:20:24 MST 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The problem of obtaining optimal starting values for
                 the calculation of the square root using Newton's
                 method is considered. It has been pointed out elsewhere
                 that if relative error is used as the measure of
                 goodness of fit, optimal results are not obtained when
                 the initial approximation is a best fit. It is shown
                 here that if, instead, the so-called logarithmic error
                 is used, then a best initial fit is optimal for both
                 types of error. Moreover, use of the logarithmic error
                 appears to simplify the problem of determining the
                 optimal initial approximation.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C4120 (Functional analysis)",
  corpsource =   "Argonne Nat. Lab., Argonne, IL, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\sqrt(x)$; elementary functions; function evaluation;
                 iterative methods",
}

@Article{Kirsch:1969:ACA,
  author =       "Arnold Kirsch",
  title =        "An analysis of commercial arithmetic",
  journal =      j-EDUC-STUD-MATH,
  volume =       "1",
  number =       "3",
  pages =        "300--311",
  month =        jan,
  year =         "1969",
  CODEN =        "EDSMAN",
  DOI =          "https://doi.org/10.1007/BF00558315",
  ISSN =         "0013-1954 (print), 1573-0816 (electronic)",
  ISSN-L =       "0013-1954",
  bibdate =      "Sat Jan 14 17:12:11 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/educstudmath.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer.com/accesspage/article/10.1007/BF00558315",
  acknowledgement = ack-nhfb,
  fjournal =     "Educational Studies in Mathematics",
  journal-URL =  "http://link.springer.com/journal/10649",
}

@MastersThesis{Knight:1969:FPS,
  author =       "Douglas Wayne Knight",
  title =        "A floating point software package in {BCD} format for
                 small, fixed word length, digital computers",
  type =         "Thesis ({M.S.})",
  school =       "Arizona State University, Electrical Engineering",
  address =      "Tempe, AZ, USA",
  pages =        "151",
  year =         "1969",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{Knuth:1969:SA,
  author =       "Donald E. Knuth",
  title =        "Seminumerical Algorithms",
  volume =       "2",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "xi + 624",
  year =         "1969",
  ISBN =         "0-201-03802-1",
  ISBN-13 =      "978-0-201-03802-6",
  LCCN =         "QA76.5 .K57",
  MRclass =      "68.00 (65.00)",
  MRnumber =     "44 \#3531",
  MRreviewer =   "M. Muller",
  bibdate =      "Wed Dec 15 15:47:38 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/cryptography.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\$19.75",
  series =       "The Art of Computer Programming",
  acknowledgement = ack-nhfb,
  remark =       "Benford's Law is discussed on pp. 219--229. Cited in
                 \cite{Sterbenz:1974:FPC}.",
  tableofcontents = "3: Random Numbers \\
                 3.1. Introduction / 1 \\
                 3.2. Generating Uniform Random Numbers / 9 \\
                 3.2.1. The Linear Congruential Method / 9 \\
                 3.2.1.1. Choice of modulus / 11 \\
                 3.2.1.2. Choice of multiplier / 15 \\
                 3.2.1.3. Potency / 21 \\
                 3.2.2. Other Methods / 25 \\
                 3.3. Statistical Tests / 34 \\
                 3.3.1. General Test Procedures for Studying Random Data
                 / 35 \\
                 3.3.2. Empirical Tests / 54 \\
                 *3.3.3. Theoretical Tests / 69 \\
                 3.3.4. The Spectral Test / 82 \\
                 3.4. Other Types of Random Quantities / 100 \\
                 3.4.1. Numerical Distributions / 101 \\
                 3.4.2. Random Sampling and Shuffling / 121 \\
                 *3.5. What is a Random Sequence? / 127 \\
                 3.6. Summary / 155 \\
                 4: Arithmetic \\
                 4.1. Positional Number Systems / 162 \\
                 4.2. Floating-Point Arithmetic / 180 \\
                 4.2.1. Single-Precision Calculations / 180 \\
                 4.2.2. Accuracy of Floating-Point Arithmetic / 195 \\
                 *4.2.3. Double-Precision Calculations / 210 \\
                 4.2.4. Statistical Distribution / 218 \\
                 4.3. Multiple-Precision Arithmetic / 229 \\
                 4.3.1. The Classical Algorithms / 229 \\
                 *4.3.2. Modular Arithmetic / 248 \\
                 *4.3.3. How Fast Can We Multiply? / 258 \\
                 4.4. Radix Conversion / 280 \\
                 4.5. Rational Arithmetic / 290 \\
                 4.5.1. Fractions / 290 \\
                 4.5.2. The Greatest Common Divisor / 293 \\
                 *4.5.3. Analysis of Euclid's Algorithm / 316 \\
                 4.5.4. Factoring into Primes / 339 \\
                 4.6. Polynomial Arithmetic / 360 \\
                 4.6.1. Division of Polynomials / 363 \\
                 *4.6.2. Factorization of Polynomials / 381 \\
                 4.6.3. Evaluation of Powers / 398 \\
                 4.6.4. Evaluation of Polynomials / 422 \\
                 *4.7. Manipulation of Power Series / 444 \\
                 Answers to Exercises / 452 \\
                 Appendix A: MIX / 565 \\
                 1. Description of MIX / 565 \\
                 2. The MIX Assembly Language / 584 \\
                 Appendix B: Tables of Numerical Quantities / 596 \\
                 1. Fundamental Constants (decimal) / 596 \\
                 2. Fundamental Constants (octal) / 597 \\
                 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci
                 Numbers / 598 \\
                 Appendix C: Index to Notations / 600 \\
                 Index and Glossary / 605",
  xxyear =       "{\noopsort{1968c}}1969",
}

@Book{Knuth:ACP69-2,
  author =       "Donald E. Knuth",
  title =        "Seminumerical Algorithms",
  volume =       "2",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "xi + 624",
  year =         "1969",
  ISBN =         "0-201-03802-1",
  ISBN-13 =      "978-0-201-03802-6",
  LCCN =         "QA76.5 .K57",
  MRclass =      "68.00 (65.00)",
  MRnumber =     "44 \#3531",
  MRreviewer =   "M. Muller",
  bibdate =      "Wed Dec 15 15:47:38 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/cryptography.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\$19.75",
  series =       "The Art of Computer Programming",
  acknowledgement = ack-nhfb,
  remark =       "Benford's Law is discussed on pp. 219--229.",
  tableofcontents = "3: Random Numbers \\
                 3.1. Introduction / 1 \\
                 3.2. Generating Uniform Random Numbers / 9 \\
                 3.2.1. The Linear Congruential Method / 9 \\
                 3.2.1.1. Choice of modulus / 11 \\
                 3.2.1.2. Choice of multiplier / 15 \\
                 3.2.1.3. Potency / 21 \\
                 3.2.2. Other Methods / 25 \\
                 3.3. Statistical Tests / 34 \\
                 3.3.1. General Test Procedures for Studying Random Data
                 / 35 \\
                 3.3.2. Empirical Tests / 54 \\
                 *3.3.3. Theoretical Tests / 69 \\
                 3.3.4. The Spectral Test / 82 \\
                 3.4. Other Types of Random Quantities / 100 \\
                 3.4.1. Numerical Distributions / 101 \\
                 3.4.2. Random Sampling and Shuffling / 121 \\
                 *3.5. What is a Random Sequence? / 127 \\
                 3.6. Summary / 155 \\
                 4: Arithmetic \\
                 4.1. Positional Number Systems / 162 \\
                 4.2. Floating-Point Arithmetic / 180 \\
                 4.2.1. Single-Precision Calculations / 180 \\
                 4.2.2. Accuracy of Floating-Point Arithmetic / 195 \\
                 *4.2.3. Double-Precision Calculations / 210 \\
                 4.2.4. Statistical Distribution / 218 \\
                 4.3. Multiple-Precision Arithmetic / 229 \\
                 4.3.1. The Classical Algorithms / 229 \\
                 *4.3.2. Modular Arithmetic / 248 \\
                 *4.3.3. How Fast Can We Multiply? / 258 \\
                 4.4. Radix Conversion / 280 \\
                 4.5. Rational Arithmetic / 290 \\
                 4.5.1. Fractions / 290 \\
                 4.5.2. The Greatest Common Divisor / 293 \\
                 *4.5.3. Analysis of Euclid's Algorithm / 316 \\
                 4.5.4. Factoring into Primes / 339 \\
                 4.6. Polynomial Arithmetic / 360 \\
                 4.6.1. Division of Polynomials / 363 \\
                 *4.6.2. Factorization of Polynomials / 381 \\
                 4.6.3. Evaluation of Powers / 398 \\
                 4.6.4. Evaluation of Polynomials / 422 \\
                 *4.7. Manipulation of Power Series / 444 \\
                 Answers to Exercises / 452 \\
                 Appendix A: MIX / 565 \\
                 1. Description of MIX / 565 \\
                 2. The MIX Assembly Language / 584 \\
                 Appendix B: Tables of Numerical Quantities / 596 \\
                 1. Fundamental Constants (decimal) / 596 \\
                 2. Fundamental Constants (octal) / 597 \\
                 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci
                 Numbers / 598 \\
                 Appendix C: Index to Notations / 600 \\
                 Index and Glossary / 605",
  xxyear =       "{\noopsort{1968c}}1969",
}

@TechReport{Kulisch:1969:AAR,
  author =       "Ulrich W. Kulisch",
  title =        "An axiomatic approach to rounded computations",
  type =         "Technical Summary Report",
  number =       "1020",
  institution =  inst-MRC-WISCONSIN,
  address =      inst-MRC-WISCONSIN:adr,
  month =        nov,
  year =         "1969",
  bibdate =      "Sat Nov 01 07:26:28 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Published in \cite{Kulisch:1971:AAR}.",
}

@Article{Linhardt:1969:DDT,
  author =       "R. J. Linhardt and H. S. Miller",
  title =        "Digit-by-Digit Transcendental-Function Computation",
  journal =      j-RCA-REV,
  volume =       "30",
  number =       "2",
  pages =        "209--247",
  month =        jun,
  year =         "1969",
  CODEN =        "RCARCI",
  ISSN =         "0033-6831",
  bibdate =      "Fri Sep 16 10:31:06 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.worldradiohistory.com/ARCHIVE-RCA/RCA-Review/RCA-Review-1969-06.pdf",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  ajournal =     "RCA Rev.",
  fjournal =     "RCA Review",
  journal-URL =  "https://www.worldradiohistory.com/ARCHIVE-RCA/RCA_Review_Issue_Key.htm",
}

@Article{Liu:1969:EAD,
  author =       "B. Liu and T. Kaneko",
  title =        "Error analysis of digital filters realized with
                 floating-point arithmetic",
  journal =      j-PROC-IEEE,
  volume =       "57",
  number =       "10",
  pages =        "1735--1747",
  month =        oct,
  year =         "1969",
  CODEN =        "IEEPAD",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See correction \cite{Liu:1970:CEA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
  summary =      "This paper calculates the error at the output of a
                 digital filter using floating-point arithmetic
                 operations due to roundoff accumulation and input
                 quantization. Expressions are derived for the mean
                 square error for each of the three canonical forms
                 \ldots{}",
}

@InProceedings{Matula:1969:TAM,
  author =       "David W. Matula",
  title =        "Towards an Abstract Mathematical Theory of
                 Floating-Point Arithmetic",
  crossref =     "AFIPS:1969:ACPa",
  pages =        "765--772",
  year =         "1969",
  bibdate =      "Fri Oct 19 23:01:32 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Posnov:1969:FPR,
  author =       "N. N. Posnov and M. K. Buza and V. K. Kravcov",
  title =        "The floating point in a residue class number system.
                 ({Russian})",
  journal =      "Vestnik Beloruss. Gos. Univ. Ser. I",
  volume =       "3",
  pages =        "21--27",
  year =         "1969",
  MRclass =      "10A10",
  MRnumber =     "45 3303e",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
  reviewer =     "J. B. Roberts",
}

@Book{Rice:1969:AFV,
  author =       "John R. Rice",
  title =        "The Approximation of Functions",
  volume =       "2",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "various",
  year =         "1969",
  LCCN =         "QA221 .R5 V.1-2",
  bibdate =      "Fri Dec 08 13:02:54 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@TechReport{Rigby:1969:DFP,
  author =       "G. W. Rigby",
  title =        "To draw a floating point number on the graph
                 plotter({PRP 2})",
  type =         "Group Research report",
  institution =  "British Steel Corporation",
  address =      "London, UK",
  year =         "1969",
  bibdate =      "Thu May 09 08:32:48 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Rosen:1969:ECH,
  author =       "Saul Rosen",
  title =        "Electronic Computers: a Historical Survey",
  journal =      j-COMP-SURV,
  volume =       "1",
  number =       "1",
  pages =        "7--36",
  month =        mar,
  year =         "1969",
  CODEN =        "CMSVAN",
  DOI =          "https://doi.org/10.1145/356540.356543",
  ISSN =         "0010-4892",
  ISSN-L =       "0360-0300",
  bibdate =      "Mon Sep 19 18:18:44 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The first large scale electronic computers were built
                 in connection with university projects sponsored by
                 government military and research organizations. Many
                 established companies, as well as new companies,
                 entered the computer field during the first generation,
                 1947-1959, in which the vacuum tube was almost
                 universally used as the active component in the
                 implementation of computer logic. The second generation
                 was characterized by the transistorized computers that
                 began to appear in 1959. Some of the computers built
                 then and since are considered super computers; they
                 attempt to go to the limit of current technology in
                 terms of size, speed, and logical complexity. From 1965
                 onward, most new computers belong to a third
                 generation, which features integrated circuit
                 technology and multiprocessor multiprogramming
                 systems.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J204",
  keywords =     "computer history; electronic computers; magnetic drum
                 computers; super computers; time-sharing;
                 transistorized computers; university computer projects;
                 vacuum tube computers",
}

@Article{S:1969:BRQ,
  author =       "D. S.",
  title =        "Book Review: {{\em Square Roots of Integers $2$ to $
                 15 $ in Various Bases $2$ to $ 10 $: $ 88062 $ Binary
                 Digits or Equivalent} by W. A. Beyer, N. Metropolis,
                 and J. R. Neergaard}",
  journal =      j-MATH-COMPUT,
  volume =       "23",
  number =       "107",
  pages =        "679--679",
  month =        jul,
  year =         "1969",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Mar 20 13:34:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://links.jstor.org/sici?sici=0025-5718%28196907%2923%3A107%3C679%3ASROI2T%3E2.0.CO%3B2-C",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Shea:1969:NDN,
  author =       "Dale D. Shea",
  title =        "On the Number of Divisions Needed in Finding the
                 Greatest Common Divisor",
  journal =      j-FIB-QUART,
  volume =       "7",
  number =       "4",
  pages =        "337--340",
  month =        nov,
  year =         "1969",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:05:19 MDT 2011",
  bibsource =    "http://www.fq.math.ca/7-4.html;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.fq.math.ca/Scanned/7-4/shea.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@PhdThesis{Smith:1969:EBB,
  author =       "Brian Thomas Smith",
  title =        "Error Bounds, Based Upon {Gerschgorin}'s Theorem, for
                 the Zeros of a Polynomial",
  type =         "{Ph.D.}",
  school =       "Department of Computer Science, University of
                 Toronto",
  address =      "Toronto, ON, Canada",
  day =          "13",
  month =        jun,
  year =         "1969",
  bibdate =      "Fri Oct 31 07:28:17 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.proquest.com/pqdtglobal/docview/302455669",
  acknowledgement = ack-nhfb,
  remark =       "See also \cite{Smith:1967:ZFA}.",
}

@Article{Sterbenz:1969:OSA,
  author =       "P. H. Sterbenz and C. T. Fike",
  title =        "Optimal Starting Approximations for {Newton}'s
                 Method",
  journal =      j-MATH-COMPUT,
  volume =       "23",
  number =       "106",
  pages =        "313--318",
  month =        apr,
  year =         "1969",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  abstract =     "Various writers have dealt with the subject of optimal
                 starting approximations for square-root calculation by
                 Newton's method. Three optimality criteria that have
                 been used can be shown to lead to closely related
                 approximations. This fact makes it surprisingly easy to
                 choose a starting approximation of some prescribed form
                 so that the maximum relative error after any number of
                 Newton iterations is as small as possible.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Svoboda:1969:DAS,
  author =       "A. Svoboda",
  title =        "Decimal Adder with Signed Digit Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-18",
  number =       "3",
  pages =        "212--215",
  month =        mar,
  year =         "1969",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1969.222633",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jun 24 20:44:42 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1960.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "decimal floating-point arithmetic",
}

@Article{Troelstra:1969:EA,
  author =       "A. S. Troelstra",
  title =        "Elementary arithmetic",
  journal =      j-LECT-NOTES-MATH,
  volume =       "95",
  pages =        "12--13",
  year =         "1969",
  CODEN =        "LNMAA2",
  DOI =          "https://doi.org/10.1007/BFb0080646",
  ISBN =         "3-540-04614-3 (print), 3-540-36130-8 (e-book)",
  ISBN-13 =      "978-3-540-04614-1 (print), 978-3-540-36130-5
                 (e-book)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  ISSN-L =       "0075-8434",
  bibdate =      "Thu May 8 17:39:14 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lnm1960.bib",
  URL =          "http://link.springer.com/chapter/10.1007/BFb0080646",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/BFb0080643",
  book-URL =     "http://www.springerlink.com/content/978-3-540-36130-5",
  fjournal =     "Lecture Notes in Mathematics",
  journal-URL =  "http://link.springer.com/bookseries/304",
}

@Article{Turner:1969:CSI,
  author =       "L. Richard Turner",
  title =        "Comment on Some {IBM} Software",
  journal =      "{SHARE Secretary Distribution}",
  volume =       "SSD 199",
  number =       "C5279",
  pages =        "40--43",
  year =         "1969",
  bibdate =      "Fri Aug 20 10:23:55 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Turner:1969:DSC,
  author =       "L. Richard Turner",
  title =        "Difficulty in {\tt sin\slash cos} Routine",
  journal =      j-SIGNUM,
  volume =       "4",
  number =       "3",
  pages =        "13--13",
  month =        oct,
  year =         "1969",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Thu Feb 15 15:23:23 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@TechReport{Turner:1969:IOC,
  author =       "L. R. Turner",
  title =        "Input-Output Conversion in {System\slash 360}",
  number =       "SSD 194, C5173",
  institution =  "SHARE Secretary Distribution",
  address =      "????",
  pages =        "1--8",
  year =         "1969",
  bibdate =      "Thu Feb 15 15:21:42 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Usow:1969:SSC,
  author =       "Karl H. Usow",
  title =        "{SIGNUM} subroutine certification committee",
  journal =      j-SIGNUM,
  volume =       "4",
  number =       "3",
  pages =        "15--18",
  month =        oct,
  year =         "1969",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Mon Mar 5 17:26:29 MST 2007",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@TechReport{Veltkamp:1969:APV,
  author =       "G. W. Veltkamp",
  title =        "{ALGOL} procedures voor het rekenen in dubbele lengte.
                 ({Dutch}) [{ALGOL} procedures for double-length
                 arithmetic]",
  type =         "Technical report",
  number =       "21",
  institution =  "RC-Informatie, Technische Hogeschool Eindhoven",
  address =      "Eindhoven, The Netherlands",
  year =         "1969",
  bibdate =      "Tue Dec 26 14:53:03 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "Dutch",
}

@Article{Weinstein:1969:CCR,
  author =       "C. Weinstein and A. V. Oppenheim",
  title =        "Correction to {``A comparison of roundoff noise in
                 floating point and fixed point digital filter
                 realizations''}",
  journal =      j-PROC-IEEE,
  volume =       "57",
  number =       "8",
  pages =        "1466--1466",
  month =        aug,
  year =         "1969",
  CODEN =        "IEEPAD",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Weinstein:1969:CRN}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
}

@Article{Weinstein:1969:CRN,
  author =       "C. Weinstein and A. V. Oppenheim",
  title =        "A comparison of roundoff noise in floating point and
                 fixed point digital filter realizations",
  journal =      j-PROC-IEEE,
  volume =       "57",
  number =       "6",
  pages =        "1181--1183",
  month =        jun,
  year =         "1969",
  CODEN =        "IEEPAD",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See correction \cite{Weinstein:1969:CCR}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
  summary =      "A statistical model for roundoff noise in floating
                 point digital filters, proposed by Kaneko and Liu, is
                 tested experimentally for first- and second-order
                 digital filters. Good agreement between theory and
                 experiment is obtained. The model is used to \ldots{}",
}

@Article{Weinstein:1969:RNF,
  author =       "C. Weinstein",
  title =        "Roundoff noise in floating point fast {Fourier}
                 transform computation",
  journal =      j-IEEE-TRANS-AUDIO-ELECTROACOUST,
  volume =       "17",
  number =       "3",
  pages =        "209--215",
  month =        sep,
  year =         "1969",
  CODEN =        "ITADAS",
  ISSN =         "0018-9278 (print), 1558-2582 (electronic)",
  ISSN-L =       "0018-9278",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Audio and Electroacoustics",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8337",
  summary =      "A statistical model for roundoff errors is used to
                 predict output noise-to-signal ratio when a fast
                 Fourier transform is computed using floating point
                 arithmetic. The result, derived for the case of white
                 input signal, is that the ratio of mean-square
                 \ldots{}",
}

@Article{Whipple:1969:CHR,
  author =       "W. L. Whipple",
  title =        "Comments on {``Higher-Radix Division Using Estimates
                 of the Divisor and Partial Remainders''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-18",
  number =       "2",
  pages =        "183--183",
  month =        feb,
  year =         "1969",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1969.222623",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 16:55:18 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1960.bib",
  note =         "See \cite{Atkins:1968:HRD}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671216",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Young:1969:SCN,
  author =       "David M. Young and Alvis E. McDonald",
  title =        "On the surveillance and control of number range and
                 accuracy in numerical computation (with discussion)",
  crossref =     "Morrell:1970:IPP",
  pages =        "145--152",
  year =         "1969",
  MRclass =      "65.80",
  MRnumber =     "40\#8303",
  bibdate =      "Thu Jan 18 13:48:21 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}, but given year
                 1968.",
}

@Article{Atkins:1970:DAU,
  author =       "D. E. Atkins",
  title =        "Design of the Arithmetic Units of {ILLIAC III}: Use of
                 Redundancy and Higher Radix Methods",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "8",
  pages =        "720--723",
  month =        aug,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.223022",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Oct 09 19:03:30 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Atkins.pdf",
  abstract =     "In keeping with the experimental nature of the
                 Illinois Pattern Recognition Computer (ILLIAC III), the
                 arithmetic units are intended to be a practical testing
                 ground for recent theoretical work in computer
                 arithmetic. This paper describes the use of redundant
                 number systems and the design of a structure with which
                 multiplication and division are executed radix 256. The
                 heart of the unit is the stored-sign subtracter, a
                 recently discovered member of the family of borrow-save
                 subtracters and carry-save adders. A cascade of these
                 subtracters, controlled by a multiplier recoder,
                 provides multiplication. The same structure, controlled
                 by a ``model division'' (a quotient recoder), performs
                 division.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "arithmetic unit; computer arithmetic; division; higher
                 radix arithmetic; ILLIAC III; multiplication; redundant
                 number systems; signed-digit subtracter; stored-sign
                 subtracter; stored-sign subtracter. Arithmetic unit",
  remark =       "Despite statements elsewhere that the ILLIAC III used
                 base 256, that is incorrect. The original manuals for
                 the machine clearly show an IBM System/360-style
                 base-16 encoding. This paper reveals the source of the
                 confusion: the multiplier uses a Wallace recoding
                 scheme, first defined for radix 4, but extended for the
                 ILLIAC III to radix 256. Thus, multiplication is done 8
                 bits at a time. Division is done 4 bits at a time.",
}

@Article{Avizienis:1970:UAB,
  author =       "Algirdas Avi{\v{z}}ienis and Chin Tung",
  title =        "A Universal Arithmetic Building Element ({ABE}) and
                 Design Methods for Arithmetic Processors",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "8",
  pages =        "733--745",
  month =        aug,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.223023",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Nov 15 07:59:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Avizienis.pdf",
  abstract =     "The advent of large-scale integration of logic
                 circuits requires the definition of digital computer
                 structure in terms of large functional arrays of logic
                 of very few types. This paper describes a
                 single-package arithmetic processor called the
                 arithmetic building element (ABE). The ABE accepts
                 operands in either conventional or signed-digit radix-r
                 representation and produces signed-digit results, which
                 the ABE can reconvert to conventional form. Radix 16 is
                 chosen for illustrations. Arrays of ABE's may be
                 arranged to implement unit-time parallel addition,
                 all-combinational multiplication, and more complex
                 functions which are presently computed by subroutines.
                 To facilitate such arithmetic design, a graph model is
                 developed which permits a translation of the given
                 arithmetical algorithm into an interconnection diagram
                 of ABE's. The design procedure is illustrated by an
                 array for polynomial evaluation. Speed, cost, and
                 roundoff error of the array are considered. A computer
                 program has been written for the automatic translation
                 of the algorithm graph to an interconnection graph, and
                 for the evaluation of the cost and speed for a given
                 polynomial degree and a given precision requirement.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-1",
}

@Article{Behringer:1970:BFI,
  author =       "F. A. Behringer",
  title =        "{Eine bedingte Form der Integral-Ungleichun von
                 Gronwal, leichte Verallgemeinerung eins
                 Stabilit{\"a}tsatzes von Perron und {\"u}berlauffreie
                 Skalierung von Analogrechenschaltungen}. ({German})
                 [{A} conditional version of the integral inequality of
                 {Gronwall}, a slight generalization of a stability
                 theorem of {Perron}, and overflow-free scaling of
                 analogue computer set-ups]",
  journal =      j-COMPUTING,
  volume =       "5",
  number =       "4",
  pages =        "333--348",
  year =         "1970",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Jan 2 17:40:51 MST 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 INSPEC Axiom database (1968--date)",
  acknowledgement = ack-ec # " and " # ack-nhfb,
  affiliation =  "Tech. Hochschule, M{\"u}nchen, West Germany",
  classification = "C5460",
  description =  "analogue computer methods; differential equations",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  language =     "German",
}

@Article{Beyer:1970:GST,
  author =       "W. A. Beyer and N. Metropolis and J. R. Neergaard",
  title =        "The Generalized Serial Test Applied to Expansions of
                 Some Irrational Square Roots in Various Bases",
  journal =      j-MATH-COMPUT,
  volume =       "24",
  number =       "111",
  pages =        "745--747",
  month =        jul,
  year =         "1970",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65.15",
  MRnumber =     "MR0273773 (42 \#8649)",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  URL =          "http://links.jstor.org/sici?sici=0025-5718%28197007%2924%3A111%3C745%3ATGSTAT%3E2.0.CO%3B2-2",
  ZMnumber =     "0227.10044",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Beyer:1970:SSD,
  author =       "W. A. Beyer and N. Metropolis and J. R. Neergaard",
  title =        "Statistical Study of Digits of Some Square Roots of
                 Integers in Various Bases",
  journal =      j-MATH-COMPUT,
  volume =       "24",
  number =       "110",
  pages =        "455--473",
  month =        apr,
  year =         "1970",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "62.70",
  MRnumber =     "MR0272129 (42 \#7010)",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  URL =          "http://links.jstor.org/sici?sici=0025-5718%28197004%2924%3A110%3C455%3ASSODOS%3E2.0.CO%3B2-I",
  ZMnumber =     "0208.19505",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Brent:1970:ABN,
  author =       "R. Brent",
  title =        "On the Addition of Binary Numbers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "8",
  pages =        "758--759",
  month =        aug,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.223027",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Nov 15 07:59:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Brent.pdf",
  abstract =     "An upper bound is derived for the time required to add
                 numbers modulo $ 2^n $, using circuit elements with a
                 limited fan-in and unit delay, and assuming that all
                 numbers have the usual binary encoding. The upper bound
                 is within a factor $ (1 + \epsilon) $ of Winograd's
                 lower bound (which holds for all encodings), where $
                 \epsilon \rightarrow 0 $ as $ n \rightarrow \infty $,
                 and only $ O(n \log n) $ circuit elements are
                 required.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "addition; ARITH-1; binary numbers; computational
                 complexity; group multiplication; logic circuits;
                 logical design",
}

@TechReport{deLugish:1970:CAA,
  author =       "B. G. de Lugish",
  title =        "A Class of Algorithms for Automatic Evaluation of
                 Certain Elementary Function in a Binary Computer",
  type =         "Report",
  number =       "399",
  institution =  "Department of Computer Science, University of
                 Illinois",
  pages =        "??",
  month =        jun,
  year =         "1970",
  bibdate =      "Fri Sep 02 22:49:20 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  remark =       "Also Ph.D. dissertation same year.",
}

@Article{Flynn:1970:DFI,
  author =       "M. J. Flynn",
  title =        "On Division by Functional Iteration",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "8",
  pages =        "702--706",
  month =        aug,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.223019",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Nov 15 07:59:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "Reprinted in \cite{Swartzlander:1990:CAa}.",
  URL =          "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Flynn.pdf",
  abstract =     "In order to avoid the time delays associated with
                 linearly convergent division based on subtraction,
                 other iterative schemes can be used. These are based on
                 (1) series expansion of the reciprocal, (2)
                 multiplicative sequence, or (3) additive sequence
                 convergent to the quotient. These latter techniques are
                 based on finding the root of an arbitrary function at
                 either the quotient or reciprocal value. A
                 Newton--Raphson iteration or root finding iteration can
                 be used.

                 The most useful techniques are quadratically convergent
                 (i.e., $ \mathrm {error}_{i + 1} = O((\mathrm
                 {error}_i)^2) $). These techniques generally require
                 two arithmetic operations (add or multiply) to double
                 the precision of the quotient.",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-1",
}

@Article{Forsythe:1970:PCW,
  author =       "George E. Forsythe",
  title =        "Pitfalls in Computation, or Why a Math Book Isn't
                 Enough",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "77",
  number =       "9",
  pages =        "931--956",
  month =        nov,
  year =         "1970",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "Contributed Item",
  MRnumber =     "MR1536090",
  bibdate =      "Tue Nov 22 09:08:17 MST 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  ZMnumber =     "0207.15401",
  acknowledgement = ack-nhfb,
  classmath =    "*65G50 Roundoff error 65Y20 Complexity and performance
                 of numerical algorithms",
  fjournal =     "The American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@TechReport{Gardiner:1970:SDA,
  author =       "V. Gardiner and N. Metropolis",
  title =        "Significant Digit Arithmetic on a {CDC 6600}",
  type =         "Technical Report",
  number =       "LA--4470",
  institution =  inst-LASL,
  address =      inst-LASL:adr,
  pages =        "4",
  day =          "1",
  month =        jan,
  year =         "1970",
  bibdate =      "Tue Mar 20 11:46:17 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=4093265&query_id=0",
  acknowledgement = ack-nhfb,
}

@Article{Good:1970:CIA,
  author =       "Donald I. Good and Ralph L. London",
  title =        "Computer Interval Arithmetic: Definition and Proof of
                 Correct Implementation",
  journal =      j-J-ACM,
  volume =       "17",
  number =       "4",
  pages =        "603--612",
  month =        oct,
  year =         "1970",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Sun Nov 6 11:55:54 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}

@Article{Habibi:1970:FM,
  author =       "A. Habibi and P. A. Wintz",
  title =        "Fast Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "2",
  pages =        "153--157",
  month =        feb,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.222881",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 08:01:30 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671474",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Hall:1970:GPQ,
  author =       "E. L. Hall and D. D. Lynch and S. J. Dwyer",
  title =        "Generation of Products and Quotients Using Approximate
                 Binary Logarithms for Digital Filtering Applications",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "2",
  pages =        "97--105",
  month =        feb,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.222874",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 08:01:30 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671467",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Hamming:1970:DN,
  author =       "R. W. Hamming",
  title =        "On the Distribution of Numbers",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "49",
  number =       "8",
  pages =        "1609--1625",
  month =        oct,
  year =         "1970",
  CODEN =        "BSTJAN",
  DOI =          "https://doi.org/10.1002/j.1538-7305.1970.tb04281.x",
  ISSN =         "0005-8580 (print), 2376-7154 (electronic)",
  ISSN-L =       "0005-8580",
  bibdate =      "Tue Nov 9 11:15:55 MST 2010",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://bstj.bell-labs.com/oldfiles/year.1970/BSTJ.1970.4908.html;
                 http://www.alcatel-lucent.com/bstj/vol49-1970/bstj-vol49-issue08.html;
                 https://www.math.utah.edu/pub/bibnet/authors/h/hamming-richard-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/bstj1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol49/bstj49-8-1609.pdf;
                 http://www.alcatel-lucent.com/bstj/vol49-1970/articles/bstj49-8-1609.pdf",
  abstract =     "This paper examines the distribution of the mantissas
                 of floating-point numbers and shows how the arithmetic
                 operations of a computer transform various
                 distributions toward the limiting distribution $$ r(x)
                 = 1 / (x \ln b) \qquad (1 / b \leq x \leq 1) $$ (where
                 $b$ is the base of the number system). The paper also
                 gives a number of applications to hardware, software,
                 and general computing which show that this distribution
                 is not merely an amusing curiosity. A brief examination
                 of the distribution of exponents is included.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}

@Article{Hansen:1970:APN,
  author =       "Rodney T. Hansen",
  title =        "Arithmetic of Pentagonal Numbers",
  journal =      j-FIB-QUART,
  volume =       "8",
  number =       "1",
  pages =        "83--86",
  month =        feb,
  year =         "1970",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:05:23 MDT 2011",
  bibsource =    "http://www.fq.math.ca/8-1.html;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.fq.math.ca/Scanned/8-1/hansen.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Harris:1970:NND,
  author =       "V. C. Harris",
  title =        "Note on the Number of Divisions Required in Finding
                 the Greatest Common Divisor",
  journal =      j-FIB-QUART,
  volume =       "8",
  number =       "1",
  pages =        "104--??",
  month =        feb,
  year =         "1970",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:05:23 MDT 2011",
  bibsource =    "http://www.fq.math.ca/8-1.html;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.fq.math.ca/Scanned/8-1/harris2.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@MastersThesis{Harvey:1970:SSP,
  author =       "Michael P. Harvey",
  title =        "A system study and problem solution in polynomial
                 evaluation",
  type =         "Thesis ({M.S.})",
  school =       "California State College",
  address =      "Long Beach, CA, USA",
  pages =        "vi + 119",
  year =         "1970",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers.; Numerical
                 calculations.; Polynomials.",
  remark =       "Title on spine: Automated floating point polynomial
                 evaluation.",
}

@TechReport{Hillstrom:1970:PSF,
  author =       "K. E. Hillstrom",
  title =        "Performance Statistics for the {FORTRAN IV (H)} and
                 {PL/I} (Version 5) Libraries in the {IBM OS\slash 360
                 Release 18}",
  type =         "Report",
  number =       "ANL-7666",
  institution =  inst-ANL,
  address =      inst-ANL:adr,
  year =         "1970",
  bibdate =      "Fri Aug 20 09:29:37 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Hornbuckle:1970:LMA,
  author =       "G. D. Hornbuckle and E. I. Ancona",
  title =        "The {LX-1} Microprocessor and Its Application to
                 Real-Time Signal Processing",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "8",
  pages =        "710--720",
  month =        aug,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.223021",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Nov 15 07:59:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Hornbuckle.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-1",
}

@Article{Howell:1970:SLE,
  author =       "Jo Ann Howell and Robert T. Gregory",
  title =        "Solving linear equations using residue arithmetic ---
                 {Algorithm II}",
  journal =      j-BIT,
  volume =       "10",
  pages =        "23--37",
  year =         "1970",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65.35",
  MRnumber =     "MR0261777 (41 \#6389)",
  MRreviewer =   "J. Legras",
  bibdate =      "Thu Nov 8 14:50:19 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Kailas:1970:AMC,
  author =       "M. V. Kailas",
  title =        "Another method of converting from hexadecimal to
                 decimal",
  journal =      j-CACM,
  volume =       "13",
  number =       "3",
  pages =        "193--193",
  month =        mar,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Tue Mar 25 13:26:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "There is a simple paper-and-pencil method of
                 converting a hexadecimal number N to decimal.",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "digital arithmetic",
}

@Article{Knuth:1970:VNF,
  author =       "Donald E. Knuth",
  title =        "{Von Neumann}'s First Computer Program",
  journal =      j-COMP-SURV,
  volume =       "2",
  number =       "4",
  pages =        "247--260",
  month =        dec,
  year =         "1970",
  CODEN =        "CMSVAN",
  DOI =          "https://doi.org/10.1145/356580.356581",
  ISSN =         "0010-4892",
  ISSN-L =       "0360-0300",
  bibdate =      "Sat Mar 23 15:03:00 2002",
  bibsource =    "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/compsurv.bib;
                 ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/HBP/ACMCS.bib;
                 https://www.math.utah.edu/pub/tex/bib/compsurv.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite{Aspray:1987:PJN}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J204",
}

@Article{Krishnamurthy:1970:OIS,
  author =       "E. V. Krishnamurthy",
  title =        "On Optimal Iterative Schemes For High-Speed Division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "3",
  pages =        "227--231",
  month =        mar,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.222901",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jan 08 23:09:36 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Krishnamurthy:1970:RTT,
  author =       "E. V. Krishnamurthy",
  title =        "On Range-Transformation Techniques for Division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "2",
  pages =        "157--160",
  month =        feb,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.222882",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 08:01:30 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671475",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Ling:1970:HSC,
  author =       "H. Ling",
  title =        "High-Speed Computer Multiplication Using a
                 Multiple-Bit Decoding Algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "8",
  pages =        "706--709",
  month =        aug,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.223020",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Nov 15 07:59:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Ling.pdf",
  abstract =     "This paper presents a method of performing the binary
                 multiplication beyond the scheme of multiple ADD and
                 SHIFT. The binary multiplication algorithm will be
                 discussed first, followed by block decoding method,
                 logic implementation, hardware consideration, and two
                 examples which are at the end of the discussion.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-1",
}

@Article{Linz:1970:AFP,
  author =       "Peter Linz",
  title =        "Accurate Floating-Point Summation",
  journal =      j-CACM,
  volume =       "13",
  number =       "6",
  pages =        "361--362",
  month =        jun,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.25",
  MRnumber =     "44\#3468",
  MRreviewer =   "R. P. Brent",
  bibdate =      "Tue Mar 25 13:26:09 MST 1997",
  bibsource =    "Compendex database;
                 ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1970.bib;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper describes an alternate method for summing a
                 set of floating-point numbers. Comparison of the error
                 bound for this method with that of the standard
                 summation method shows that it is considerably less
                 sensitive to propagation of round-off error.",
  acknowledgement = ack-nhfb # "\slash " # ack-nj,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "New York University, NY, USA",
  descriptors =  "Simulation; statistics; numeric calculation",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  journalabr =   "Commun ACM",
  keywords =     "accurate floating-point summation; computers, data
                 processing; digital arithmetic; floating point
                 arithmetic; floating-point addition; mathematics;
                 numerical methods; round-off error; round-off errors;
                 round-off propagation; summation",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Liu:1970:CEA,
  author =       "B. Liu and T. Kaneko",
  title =        "Correction to {``Error analysis of digital filters
                 realized with floating-point arithmetic''}",
  journal =      j-PROC-IEEE,
  volume =       "58",
  number =       "3",
  pages =        "376--376",
  month =        mar,
  year =         "1970",
  CODEN =        "IEEPAD",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Liu:1969:EAD}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
}

@Article{Long:1970:LAS,
  author =       "C. T. Long and J. H. Jordan",
  title =        "A Limited Arithmetic on Simple Continued Fractions ---
                 {II}",
  journal =      j-FIB-QUART,
  volume =       "8",
  number =       "2",
  pages =        "135--157",
  month =        mar,
  year =         "1970",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:05:25 MDT 2011",
  bibsource =    "http://www.fq.math.ca/8-2.html;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.fq.math.ca/Scanned/8-2/long.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@TechReport{Malcolm:1970:AFP,
  author =       "Michael A. Malcolm",
  title =        "An algorithm for floating-point accumulation of sums
                 with small relative error",
  type =         "Technical Report",
  number =       "STAN-CS-70-163 (AD708691)",
  institution =  inst-STAN-CS,
  address =      inst-STAN-CS:adr,
  pages =        "21",
  month =        jun,
  year =         "1970",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/stanford-cstr.bib",
  URL =          "http://i.stanford.edu/TR/CS-TR-70-163.html",
  abstract =     "A practical algorithm for floating-point accumulation
                 is presented. Through the use of multiple accumulators,
                 errors due to cancellation are avoided. An example in
                 Fortran is included. An error analysis providing a
                 sharp bound on the relative error is also given.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation; Algorithms.;
                 FORTRAN (Computer program language); Numerical
                 calculations --- Computer programs.",
  pdfpages =     "26",
  remark =       "Reproduced by National Technical Information Service.
                 AD 708 691.",
  xxnumber =     "CS-TR-70-163",
}

@MastersThesis{Marasa:1970:AAE,
  author =       "John D. Marasa",
  title =        "Accumulated arithmetic error in floating-point and
                 alternative logarithmic number systems",
  type =         "Thesis ({M.S.})",
  school =       "Washington University, Sever Institute of Technology,
                 Department of Applied Mathematics and Computer
                 Science",
  address =      "St. Louis, MO, USA",
  pages =        "vii + 88",
  year =         "1970",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Programming (Mathematics)",
}

@Article{Matula:1970:ECA,
  author =       "David W. Matula",
  title =        "The emergence of computational arithmetic as a
                 component of the computer science curriculum",
  journal =      j-SIGCSE,
  volume =       "2",
  number =       "3",
  pages =        "41--44",
  month =        nov,
  year =         "1970",
  CODEN =        "SIGSD3",
  DOI =          "https://doi.org/10.1145/873641.873650",
  ISSN =         "0097-8418 (print), 2331-3927 (electronic)",
  ISSN-L =       "0097-8418",
  bibdate =      "Sun Nov 18 08:53:42 MST 2012",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigcse1970.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGCSE Bulletin (ACM Special Interest Group on
                 Computer Science Education)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J688",
}

@Article{Matula:1970:FFP,
  author =       "D. W. Matula",
  title =        "A Formalization of Floating-Point Numeric Base
                 Conversion",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "8",
  pages =        "681--692",
  month =        aug,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.223017",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 08:01:35 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Matula.pdf;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671610",
  abstract =     "The process of converting arbitrary real numbers into
                 a floating-point format is formalized as a mapping of
                 the reals into a specified subset of real numbers. The
                 structure of this subset, the set of $n$ significant
                 digit base $b$ floating-point numbers, is analyzed and
                 properties of conversion mappings are determined. For a
                 restricted conversion mapping of the $n$ significant
                 digit base $b$ numbers to the $m$ significant-digit
                 base $d$ numbers, the one-to-one, onto, and
                 order-preserving properties of the mapping are
                 summarized. Multiple conversions consisting of a
                 composition of individual conversion mappings are
                 investigated and some results of the invariant points
                 of such compound conversions are presented. The
                 hardware and software implications of these results
                 with regard to establishing goals and standards for
                 floating-point formats and conversion procedures are
                 considered.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-1",
}

@Article{Mifsud:1970:MDA,
  author =       "C. J. Mifsud",
  title =        "A multiple-precision division algorithm",
  journal =      j-CACM,
  volume =       "13",
  number =       "11",
  pages =        "666--668",
  month =        nov,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Tue Mar 25 13:26:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See addendum \cite{Mifsud:1973:AMP}.",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Mitre Corp., McLean, VA, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "digital arithmetic",
}

@Article{Nickel:1970:KBS,
  author =       "K. Nickel",
  title =        "{Das Kahan--Babu{\v{s}}kasche Summierungsverfahren in
                 Triplex-ALGOL 60}. ({German}) [{The
                 Kahan--Babu{\v{s}}ka} summation method in
                 {Triplex-ALGOL 60}]",
  journal =      j-Z-ANGE-MATH-MECH,
  volume =       "50",
  pages =        "369--373",
  year =         "1970",
  CODEN =        "ZAMMAX",
  ISSN =         "0044-2267 (print), 1521-4001 (electronic)",
  ISSN-L =       "0044-2267",
  bibdate =      "Tue Aug 28 06:12:04 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "{Zeitschrift f{\"u}r Angewandte Mathematik und
                 Mechanik}",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
  keywords =     "accurate floating-point summation",
  language =     "German",
}

@Article{Ninomiya:1970:BRS,
  author =       "Ichizo Ninomiya",
  title =        "Best Rational Starting Approximations and Improved
                 {Newton} Iteration for the Square Root",
  journal =      j-MATH-COMPUT,
  volume =       "24",
  number =       "110",
  pages =        "391--404",
  month =        apr,
  year =         "1970",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  ajournal =     "Math. Comput.",
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Nagoya University, Chikua ku, Japan",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "computing procedure; function approximation; iterative
                 methods; Newton iteration; rational approximation;
                 square root",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Oppenheim:1970:RDF,
  author =       "A. Oppenheim",
  title =        "Realization of digital filters using
                 block-floating-point arithmetic",
  journal =      j-IEEE-TRANS-AUDIO-ELECTROACOUST,
  volume =       "18",
  number =       "2",
  pages =        "130--136",
  month =        jun,
  year =         "1970",
  CODEN =        "ITADAS",
  ISSN =         "0018-9278 (print), 1558-2582 (electronic)",
  ISSN-L =       "0018-9278",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Audio and Electroacoustics",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8337",
  summary =      "Recently, statistical models for the effects of
                 roundoff noise in fixed-point and floating-point
                 realizations of digital filters have been proposed and
                 verified, and a comparison between these realizations
                 presented. In this paper a structure for \ldots{}",
}

@Article{Phillips:1970:GLE,
  author =       "David L. Phillips",
  title =        "Generalized Logarithmic Error and {Newton}'s Method
                 for the $m$ th Root",
  journal =      j-MATH-COMPUT,
  volume =       "24",
  number =       "110",
  pages =        "383--389",
  month =        apr,
  year =         "1970",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Rao:1970:BEC,
  author =       "T. R. N. Rao",
  title =        "Biresidue Error-Correcting Codes for Computer
                 Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "5",
  pages =        "398--402",
  month =        may,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.222937",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 08:01:32 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671530",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Rao:1970:BLR,
  author =       "T. R. N. Rao and A. K. Trehan",
  title =        "Binary Logic for Residue Arithmetic Using Magnitude
                 Index",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "8",
  pages =        "752--757",
  month =        aug,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.223026",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Nov 15 07:59:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Rao.pdf",
  abstract =     "We consider a residue number system using n pairwise
                 relatively prime moduli $ m_1, \ldots {}, m_n $ to
                 represent any integer $X$ in the range $ M / 2 \leq X >
                 M / 2 $, when $ M = \prod m_i $. The moduli $ m_i $ are
                 chosen to be of the $ 2 - 1 $ type, in order that the
                 residue arithmetic can be implemented by means of
                 binary registers and binary logic. Further, for each
                 residue number $X$, a magnitude index $ P_x $ is
                 maintained for all arithmetic operations. We
                 investigate the properties of such a system and derive
                 the addition, subtraction, multiplication, sign
                 determination, and overflow detection algorithms. The
                 proposed organization is found to improve the operation
                 times for sign detection and overflow detection
                 operations, while rendering multiplication to be a
                 difficult operation.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-1; base extension; index generation logic;
                 magnitude index; modular adders; naturalized form;
                 overflow detection; residue multiplication; residue
                 number system; scale by 2; sign determination",
}

@Article{Robertson:1970:CBM,
  author =       "J. E. Robertson",
  title =        "The Correspondence Between Methods of Digital Division
                 and Multiplier Recoding Procedures",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "8",
  pages =        "692--701",
  month =        aug,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.223018",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Nov 15 07:59:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Robertson.pdf",
  abstract =     "This paper relates previous analyses of the binary SRT
                 division to the theory of multiplier recoding. Since
                 each binary quotient digit has three possible values,
                 the quotient resulting from the SRT division is in
                 recoded form; in this paper it is shown that the
                 recoding is a function of the divisor, and the method
                 for determining the characteristic Boolean function of
                 the recoding is presented. The relationship between the
                 division and the recoding is established by scaling the
                 division in such a way that the scaled ``visor''
                 becomes a constant. Higher radix results are also
                 discussed.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-1",
}

@TechReport{Rothmaier:1970:BQN,
  author =       "B. Rothmaier",
  title =        "{Die Berechnung der Quadratwurzel nebst Schranken auf
                 Dualmaschinen} \toenglish {The Computation of the
                 Square Root together with [Interval] Bounds on Binary
                 Machines} \endtoenglish",
  type =         "{Interner Bericht}",
  number =       "Nr. 70/17",
  institution =  "Institut f{\"u}r Informatik, Universit{\"a}t
                 Karlsruhe",
  pages =        "??",
  year =         "1970",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@TechReport{Rothmaier:1970:DSB,
  author =       "B. Rothmaier",
  title =        "{Dokumentation der Standardfunktionen des
                 Betriebssystems Hydra X8} \toenglish {Documentation} of
                 the Elementary Functions of the Operating System {Hydra
                 X8} \endtoenglish",
  type =         "{Interner Bericht}",
  number =       "Nr. 70/8",
  institution =  "Institut f{\"u}r Informatik, Universit{\"a}t
                 Karlsruhe",
  pages =        "??",
  year =         "1970",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Shively:1970:PFI,
  author =       "Richard R. Shively",
  title =        "Preface: {First IEEE Conference on Computer
                 Arithmetic, Minneapolis, Minnesota, June 16, 1969}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "8",
  pages =        "679--680",
  month =        aug,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.223016",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Nov 15 07:59:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_contents.pdf;
                 http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Shively.pdf;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671609",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-1",
}

@Article{Sikdar:1970:DMM,
  author =       "K. Sikdar",
  title =        "Determination of Multipliers Mapping an Arbitrary
                 Integer into a Range of Certain Type",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "12",
  pages =        "1221--1222",
  month =        dec,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.222863",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 08:01:39 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671456",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Svoboda:1970:ADC,
  author =       "A. Svoboda",
  title =        "Adder With Distributed Control",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "8",
  pages =        "749--751",
  month =        aug,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.223025",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Nov 15 07:59:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Svoboda.pdf",
  abstract =     "An adder is described for addition of a large number
                 of binary numbers $ x_j, j = 1, 2, \ldots {}, m $,
                 where $ x_j = \sum_i x_{j, i} 2^i, x_{j, i} = 0, 1, i =
                 0, 1, \ldots {}, n - 1 $. The adder's algorithm has two
                 parts: (1) the bits $ x_{j, i} $ are added
                 independently for each binary order $ i : s_i = \sum_j
                 x_{j, i} \leq m $ and the result expressed in the
                 binary form $ s_i = \sum_k a_{i, k} 2^k, a_{i, k} = 0,
                 1, k = 0, 1, \ldots {}, p - 1 $ (where $ 2^{p - 1} \leq
                 m < 2^p $) ; (2) the sum $ y = \sum_j x_j $ is formed
                 by adding terms $ s_{i, k} {2^{i + k}} $ as
                 contributions of the bit $ s_{i, k} $ to the total $y$.
                 A hardware implementation of this algorithm is
                 suggested where the sum $ s_i $ is obtained by a
                 sequential circuit which reorders the values $ x_{j,
                 i}' $ so that their sum $ s_i $, remains unchanged and
                 so that after the reordering the new values $ x_{j, i}'
                 $ obey the conditions $ x_{j + 1, i} \leq x_{j, i} $
                 for every $ j = 1, 2, \ldots {}, m - 1 $. The
                 implementation with integrated circuits should be quite
                 rewarding because the control of the circuit is done
                 with independent control elements distributed all over
                 the chip.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "adder; adder for large number of numbers; ARITH-1;
                 distributed control; reordering",
}

@Article{Taub:1970:ECS,
  author =       "D. M. Taub and C. E. Owen and B. P. Day",
  title =        "Experimental Computer for Schools",
  journal =      "Proceedings of the IEE",
  volume =       "117",
  number =       "2",
  pages =        "303--312",
  month =        feb,
  year =         "1970",
  bibdate =      "Fri Nov 28 19:30:38 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The computer is a small desk-top machine designed for
                 teaching schoolchildren how computers work. It works in
                 decimal notation and has a powerful instruction set
                 which includes 3-address floating-point instructions
                 implemented as `extracode' subroutines. Addressing can
                 be absolute, relative or indirect. For input it uses a
                 capacitive touch keyboard, and for output and display a
                 perfectly normal TV receiver is used. Another
                 input/output device is an ordinary domestic tape
                 recorder, used mainly for long term storage of
                 programs. To make the operation of the machine easy to
                 follow, it can be made to stop at certain stages in the
                 processing of an instruction and automaticaly display
                 the contents of all registers and storage locations
                 relevant at that time. The paper gives a description of
                 the machine and a discussion of the factors that hav
                 influenced its design.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
  remark =       "IBM Schools computer with scaled integer format, six
                 decimal digits and exponent range of $ [ - 6, 0] $.",
}

@Book{Thornton:1970:DCC,
  author =       "James E. Thornton",
  title =        "Design of a Computer: the {Control Data 6600}",
  publisher =    pub-SF,
  address =      pub-SF:adr,
  pages =        "v + 181",
  year =         "1970",
  ISBN =         "0-07-057302-6, 0-07-057303-4",
  ISBN-13 =      "978-0-07-057302-4, 978-0-07-057303-1",
  LCCN =         "TK7889.C6 T5 1970",
  bibdate =      "Wed Sep 14 22:45:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://archive.computerhistory.org/resources/text/CDC/cdc.6600.thornton.design_of_a_computer_the_control_data_6600.1970.102630394.pdf",
  acknowledgement = ack-nhfb,
  remark =       "See Table V: Nonstandard Floating Point Arithmetic on
                 page 79 for the rules governing Indefinite, Infinity,
                 and Negative Zero operands.",
  tableofcontents = "I: Introduction / 1 \\
                 A. Justification for Large Computers / 1 \\
                 B. Building Blocks / 4 \\
                 C. The Approach / 5 \\
                 II: Organization of the 6600 / 9 \\
                 A. General / 9 \\
                 B. Peripheral Subsystem / 10 \\
                 C. Central Processor-CPU / 12 \\
                 D. Central Storage / 15 \\
                 E. Extended Core Storage / 17 \\
                 III: Basic Circuit Properties / 19 \\
                 A. The Silicon Transistor / 19 \\
                 B. DCTL Logic Circuits / 21 \\
                 C. Logic Symbols / 24 \\
                 D. Transmission Lines / 28 \\
                 E. Packaging / 32 \\
                 IV: Central Storage System / 37 \\
                 A. Storage Module / 37 \\
                 B. Theory of Interleaved Storage / 44 \\
                 C. Stunt Box / 47 \\
                 D. Storage Bus System / 51 \\
                 E. Extended Core Storage / 53 \\
                 F. ECS Coupler and Controller / 55 \\
                 V: Central Processor Functional Units / 57 \\
                 A. Boolean Unit / 59 \\
                 B. Fixed Add Unit / 63 \\
                 C. Data Trunks / 69 \\
                 D. Shift Unit / 71 \\
                 E. Add Unit / 77 \\
                 F. Multiply Unit / 88 \\
                 G. Divide Unit / 101 \\
                 H. Increment Unit / 105 \\
                 I. Branch Unit / 111 \\
                 J. ECS Coupler-Controller / 114 \\
                 VI: Central Processor Control / 117 \\
                 A. Exchange Jump / 117 \\
                 B. Instruction Fetch / 120 \\
                 C. Instruction Issue / 123 \\
                 D. Scoreboard / 125 \\
                 Register Entry/Exit Control / 134 \\
                 F. Summary / 137 \\
                 VII: Peripheral Subsystem / 141 A. Peripheral
                 Processors / 141 \\
                 B. Dead Start / 154 \\
                 C. Disk Storage / 157 \\
                 VIII: Systems Operation / 163 \\
                 A. Files / 163 \\
                 B. Tables / 165 \\
                 C. Circular Buffer for 1/0 / 166 \\
                 D. Job Processing / 167 \\
                 E. System Monitor MTR / 168 \\
                 F. Control Points / 169 \\
                 G. Summary / 171 \\
                 Appendix / 173 \\
                 Index / 177",
}

@Article{Tienari:1970:SMR,
  author =       "Martti Tienari",
  title =        "A Statistical Model of Roundoff Error for Varying
                 Length Floating-Point Arithmetic",
  journal =      j-BIT,
  volume =       "10",
  number =       "3",
  pages =        "355--365",
  month =        sep,
  year =         "1970",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01934204",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "68.00 (65.00)",
  MRnumber =     "42\#7108",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=10&issue=3&spage=355",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point arithmetic; rounding errors",
  reviewer =     "R. W. Hamming",
}

@Article{Tung:1970:SDD,
  author =       "Chin Tung",
  title =        "Signed-Digit Division Using Combinational Arithmetic
                 Nets",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "8",
  pages =        "746--748",
  month =        aug,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.223024",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Nov 15 07:59:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith1/papers/ARITH1_Tung.pdf",
  abstract =     "To meet the challenge created by the advent of large-
                 scale integration, a unique microelectronic arithmetic
                 building element and combinational arithmetic nets,
                 composed of the building elements, have been studied
                 and proposed for arithmetic processor design. A fast
                 division algorithm, particularly suitable for floating-
                 point arithmetic, has also been developed for
                 signed-digit arithmetic. This algorithm is
                 characterized by the need of preprocessing the divisor
                 and then exact generation of quotient digits. This
                 paper describes the implementation of this division
                 algorithm with the arithmetic building element and
                 combinational arithmetic nets. The intention here is to
                 explore the feasibility of applying large-scale
                 integration technology to arithmetic processors.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-1; arithmetic building element; combinational
                 arithmetic net; division; large-scale integration;
                 microelectronic block; signed-digit number system",
}

@Article{Usow:1970:CB,
  author =       "K. H. Usow",
  title =        "Certification Bibliography",
  journal =      j-SIGNUM,
  volume =       "5",
  number =       "2",
  pages =        "14--15",
  month =        mar,
  year =         "1970",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Fri Aug 20 10:26:49 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Waksman:1970:WAI,
  author =       "A. Waksman",
  title =        "On {Winograd}'s Algorithm for Inner Products",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "4",
  pages =        "360--361",
  month =        apr,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.222926",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Oct 09 18:54:12 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  abstract =     "This correspondence demonstrates an improvement on
                 Winograd's algorithm for inner products as applied to
                 the multiplication of two matrices.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "fast matrix multiplication; product of matrices;
                 sufficient number of arithmetical operations",
}

@Article{Wilson:1970:OSA,
  author =       "M. Wayne Wilson",
  title =        "Optimal Starting Approximations for Generating Square
                 Root for Slow or No Divide",
  journal =      j-CACM,
  volume =       "13",
  number =       "9",
  pages =        "559--560",
  month =        sep,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.50",
  MRnumber =     "44\#2338",
  MRreviewer =   "J. E. {Dennis, Jr.}",
  bibdate =      "Thu Sep 1 10:15:43 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "On computing machines with slow or no division, it is
                 preferable to use an iterative scheme for the square
                 root different from the classical Heron scheme. The
                 problem of optimal initial approximants is considered,
                 and some optimal polynomial initial approximations are
                 tabulated.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "IBM, Houston, TX, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  journalabr =   "Commun ACM",
  keywords =     "CACMA; digital arithmetic; ele; iterative methods;
                 mathematics; numerical methods; optimisation",
}

@TechReport{Yohe:1970:ACB,
  author =       "J. Michael Yohe",
  title =        "Accurate Conversion Between Number Bases",
  type =         "{MRC} Technical Summary Report",
  number =       "1109",
  institution =  inst-MRC-WISCONSIN,
  address =      inst-MRC-WISCONSIN:adr,
  month =        oct,
  year =         "1970",
  bibdate =      "Sun Dec 30 21:39:41 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://apps.dtic.mil/sti/html/tr/AD0725091/",
  abstract =     "The author presents and proves algorithms for taking a
                 number expressed in base gamma and finding, for a
                 predetermined floating point representation in base
                 beta, its least upper bound, greatest lower bound, and
                 closest approximation.",
  acknowledgement = ack-nhfb,
}

@TechReport{Yohe:1970:BPF,
  author =       "J. Michael Yohe",
  title =        "Best possible floating point arithmetic",
  type =         "{MRC} Technical Summary Report",
  number =       "1054",
  institution =  inst-MRC-WISCONSIN,
  address =      inst-MRC-WISCONSIN:adr,
  pages =        "ii + 27",
  month =        mar,
  year =         "1970",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://apps.dtic.mil/sti/html/tr/AD0713699",
  abstract =     "The report presents an algorithm for floating point
                 arithmetic, using single-length arithmetic registers,
                 which yields the most accurate approximation which can
                 be expressed in the given floating point format, the
                 greatest lower bound, or the least upper bound for the
                 result of the operation, whichever is specified by the
                 programmer. This makes the algorithm particularly
                 useful for implementation of interval arithmetic.",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.",
  remark =       "March 1970. Sponsored by Army Research Office, Durham,
                 N.C.",
}

@TechReport{Yohe:1970:RBC,
  author =       "J. Michael Yohe",
  title =        "Rigorous bounds on computed approximations to square
                 roots and cube roots",
  type =         "{MRC} Technical Summary Report",
  number =       "1088",
  institution =  inst-MRC-WISCONSIN,
  address =      inst-MRC-WISCONSIN:adr,
  year =         "1970",
  bibdate =      "Sat Nov 01 07:35:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "From \cite[page 586, column 2]{Yohe:1973:RFP}: ``In
                 [this 1970 report], it is proved that on a binary
                 computer with optimal directed rounding, the square
                 root of a machine representable number can be
                 calculated exactly if it is machine representable, and
                 bracketed by two consecutive machine numbers if it is
                 not machine representable; this is accomplished without
                 using interval arithmetic. Similar, although not as
                 tight, bounds are obtained for the cube root.",
}

@Article{Yong:1970:GBA,
  author =       "Lam Lay Yong",
  title =        "The Geometrical Basis of the {Ancient Chinese}
                 Square-Root Method",
  journal =      j-ISIS,
  volume =       "61",
  number =       "1",
  pages =        "92--102",
  month =        "Spring",
  year =         "1970",
  CODEN =        "ISISA4",
  ISSN =         "0021-1753 (print), 1545-6994 (electronic)",
  ISSN-L =       "0021-1753",
  bibdate =      "Tue Jul 30 21:28:39 MDT 2013",
  bibsource =    "http://www.jstor.org/action/showPublication?journalCode=isis;
                 http://www.jstor.org/stable/i302287;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/isis1970.bib",
  URL =          "http://www.jstor.org/stable/229151",
  acknowledgement = ack-nhfb,
  fjournal =     "Isis",
  journal-URL =  "http://www.jstor.org/journal/isis",
}

@Article{Zohar:1970:NRC,
  author =       "S. Zohar",
  title =        "Negative Radix Conversion",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-19",
  number =       "3",
  pages =        "222--226",
  month =        mar,
  year =         "1970",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1970.222900",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 08:01:31 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See comments \cite{Pawlak:1971:ACN,Wadel:1971:CNR}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671493",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "negative base",
}

@Book{Zuse:1970:CML,
  author =       "Konrad Zuse",
  title =        "{Der Computer, mein Lebenswerk}",
  publisher =    "Verlag moderne Industrie",
  address =      "M{\"u}nchen, Germany",
  pages =        "221",
  year =         "1970",
  LCCN =         "QA76.2.Z8 A3",
  bibdate =      "Mon Nov 4 07:46:57 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "computer engineers --- Germany --- biography;
                 computers --- Germany --- history; Zuse, Konrad",
}

@Article{Abdelmalek:1971:REA,
  author =       "Nabih N. Abdelmalek",
  title =        "Round-off Error Analysis for {Gram--Schmidt} Method
                 and Solution of Linear Least Squares Problems",
  journal =      j-BIT,
  volume =       "11",
  number =       "4",
  pages =        "345--367",
  month =        dec,
  year =         "1971",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01939404",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:12 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=11&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=11&issue=4&spage=345",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point arithmetic; rounding errors",
}

@Article{Alway:1971:GFA,
  author =       "G. G. Alway",
  title =        "A general factorising algorithm",
  journal =      j-COMP-J,
  volume =       "14",
  number =       "2",
  pages =        "166--168",
  month =        may,
  year =         "1971",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:51:53 MDT 2000",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/140166.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/tiff/166.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/tiff/167.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_02/tiff/168.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Nat. Phys. Lab., Teddington, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "computer algorithm; digital arithmetic; general
                 factorising algorithm; primality of large numbers",
  treatment =    "T Theoretical or Mathematical",
}

@TechReport{Banerji:1971:RAC,
  author =       "D. K. Banerji",
  title =        "Residue arithmetic in computer design",
  institution =  "University of Waterloo",
  address =      "Waterloo, ON, Canada",
  year =         "1971",
  bibdate =      "Thu Nov 18 09:13:45 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://books.google.com/books?id=YNVcPgAACAAJ",
  acknowledgement = ack-nhfb,
}

@Article{Bataille:1971:GCW,
  author =       "M. Bataille",
  title =        "The {Gamma 60}: The computer that was ahead of its
                 time",
  journal =      j-HONEYWELL-COMP-J,
  volume =       "5",
  number =       "3",
  pages =        "99--105",
  month =        "????",
  year =         "1971",
  CODEN =        "HNCJA3",
  ISSN =         "0046-7847",
  bibdate =      "Thu Nov 25 09:37:15 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Honeywell Computer Journal",
  keywords =     "decimal floating-point arithmetic",
  remark =       "The Gamma 60 decimal floating-point system provides 11
                 to 19 decimal digits with an exponent range of $ \pm 40
                 $.",
}

@Article{Berg:1971:SAO,
  author =       "R. O. Berg and L. L. Kinney",
  title =        "Serial Adders with Overflow Correction",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "6",
  pages =        "668--671",
  month =        jun,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223321",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:16 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671914",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Bright:1971:SST,
  author =       "H. S. Bright and B. A. Colhoun and F. B. Mallory",
  title =        "A software system for tracing numerical significance
                 during computer program execution",
  crossref =     "Macon:1971:SJC",
  pages =        "387--391",
  year =         "1971",
  DOI =          "https://doi.org/10.1145/1478786.1478841",
  bibdate =      "Tue Jan 06 11:24:21 2026",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This report will describe and discuss a
                 presently-operational software system for tracing and
                 displaying numerical accuracy in digital computer
                 calculation. A FORTRAN program processed by the system
                 is executed in an artificial arithmetic, in which every
                 arithmetic step produces, in addition to the numerical
                 result, an estimate of the number of significant digits
                 in that result. Programs have been processed
                 successfully with significance mode segments totalling
                 as many as 1400 FORTRAN statements.",
  acknowledgement = ack-nhfb,
}

@Article{Caprani:1971:ILR,
  author =       "Ole Caprani",
  title =        "Implementation of a Low Round-Off Summation Method",
  journal =      j-BIT,
  volume =       "11",
  number =       "3",
  pages =        "271--275",
  month =        sep,
  year =         "1971",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01931808",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Sat Nov 14 09:14:57 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=11&issue=3&spage=271",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "accurate floating-point summation; floating-point
                 arithmetic; rounding errors",
}

@Misc{Chen:1971:BAU,
  author =       "Tien Chi Chen",
  title =        "Binary arithmetic unit implementing a multiplicative
                 iteration for the exponential, logarithm, quotient and
                 square root functions",
  howpublished = "United States Patent 3,631,230",
  day =          "28",
  month =        dec,
  year =         "1971",
  bibdate =      "Tue Jan 08 21:54:11 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.freepatentsonline.com/3631230.html",
  abstract =     "Apparatus and a method is described for efficiently
                 achieving arithmetic evaluations for functions such as
                 exponential, logarithm, quotient, and square root with
                 a minimum use of multiplications or divisions.
                 Basically, use is made of the fact that $ x(1 \pm
                 2^{-m}) $ can be evaluated by a shift followed by an
                 add. A pair of numbers $ (x_k, y_k) $ can represent a
                 function $ x : f(x) = g(x_k, y_k) $, such that $ g(l,
                 y_n) = y_n $ for logarithm, quotient and square root.
                 Then, multiplication by shifting is applied to $ x_k $
                 with suitable adjustments on $ y_k $, until $ x_k $ is
                 close to unity, at which time $ y_k $ represents the
                 desired answer. The exponential is computed by
                 essentially reversing the logarithm procedure. A
                 termination algorithm further improves accuracy. The
                 apparatus involves two registers for $ x_k $ and $ y_k
                 $, a local memory, an adder and a shift register.",
  acknowledgement = ack-nhfb,
}

@Article{Chen:1971:BMS,
  author =       "Tien Chi Chen",
  title =        "A Binary Multiplication Scheme Based on Squaring",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "6",
  pages =        "678--680",
  month =        jun,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223325",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:16 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671918",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Misc{Chen:1971:DNC,
  author =       "Tien Chi Chen",
  title =        "Decimal Number Compression",
  howpublished = "Internal IBM memo to Dr. Irving T. Ho.",
  pages =        "4",
  day =          "29",
  month =        mar,
  year =         "1971",
  bibdate =      "Fri Nov 28 16:24:59 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The fact that four bits can represent 16 different
                 states, but a decimal digit exploits only 10 of then
                 (0--9) has been a valid criticism against decimal
                 arithmetic.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@Article{Chen:1971:EAA,
  author =       "Tien Chi Chen",
  title =        "Efficient Arithmetic Apparatus and Method",
  journal =      j-IBM-TDB,
  volume =       "14",
  number =       "1",
  pages =        "328--330",
  month =        jun,
  year =         "1971",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Tue Jan 08 22:33:33 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Technical Disclosure Bulletin",
}

@InCollection{Clark:1971:SCP,
  author =       "N. W. Clark and W. J. Cody and H. Kuki",
  title =        "Self-Contained Power Routines",
  crossref =     "Rice:1971:MS",
  pages =        "399--415",
  year =         "1971",
  bibdate =      "Thu Sep 15 18:56:49 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Cody:1971:DHC,
  author =       "W. J. Cody",
  title =        "Desirable Hardware Characteristics for Scientific
                 Computation",
  journal =      j-SIGNUM,
  volume =       "6",
  number =       "1",
  pages =        "16--31",
  month =        jan,
  year =         "1971",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/1052614.1052616",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:49:57 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  xxtitle =      "Hardware characteristics (pages missing from print)",
}

@InCollection{Cody:1971:SEF,
  author =       "W. J. Cody",
  title =        "Software for the Elementary Functions",
  crossref =     "Rice:1971:MS",
  pages =        "171--186",
  year =         "1971",
  bibdate =      "Thu Sep 15 18:56:47 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Dekker:1971:FPT,
  author =       "Theodorus J. Dekker",
  title =        "A Floating-Point Technique for Extending the Available
                 Precision",
  journal =      j-NUM-MATH,
  volume =       "18",
  number =       "3",
  pages =        "224--242",
  month =        jun,
  year =         "1971",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01397083",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "68A55",
  MRnumber =     "MR0299007 (45 \#8056)",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath.bib;
                 Parallel/par.lin.alg.bib",
  URL =          "http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN362160546_0018",
  abstract =     "A technique is described for expressing multilength
                 floating-point arithmetic in terms of singlelength
                 floating point arithmetic, i.e. the arithmetic for an
                 available (say: single or double precision)
                 floating-point number system. The basic algorithms are
                 exact addition and multiplication of two singlelength
                 floating-point numbers, delivering the result as a
                 doublelength floating-point number. A straight-forward
                 application of the technique yields a set of algorithms
                 for doublelength arithmetic which are given as ALGOL 60
                 procedures.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classification = "C5230 (Digital arithmetic methods)",
  corpsource =   "Math. Centre, Amsterdam, Netherlands",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "accurate floating-point summation; ALGOL 60
                 procedures; available precision; digital arithmetic;
                 double precision; multilength; single; single length
                 floating point arithmetic; subroutines",
  remark =       "Report MR 118/70, Computation Department, Mathematical
                 Centre, Amsterdam. Part of this research was done while
                 the author was visiting Bell Telephone Laboratories,
                 Murray Hill, New Jersey.",
  treatment =    "T Theoretical or Mathematical",
}

@Article{DeLong:1971:UPA,
  author =       "Howard DeLong",
  title =        "Unsolved Problems in Arithmetic",
  journal =      j-SCI-AMER,
  volume =       "224",
  number =       "3",
  pages =        "50--60",
  month =        mar,
  year =         "1971",
  CODEN =        "SCAMAC",
  DOI =          "https://doi.org/10.1038/scientificamerican0371-50",
  ISSN =         "0036-8733 (print), 1946-7087 (electronic)",
  ISSN-L =       "0036-8733",
  bibdate =      "Wed May 22 12:00:01 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sciam1970.bib",
  URL =          "http://www.nature.com/scientificamerican/journal/v224/n3/pdf/scientificamerican0371-50.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientific American",
  journal-URL =  "http://www.nature.com/scientificamerican",
}

@Article{Dutka:1971:SRD,
  author =       "Jacques Dutka",
  title =        "The Square Root of $2$ to $ 1, 000, 000 $ Decimals",
  journal =      j-MATH-COMPUT,
  volume =       "25",
  number =       "116",
  pages =        "927--930",
  month =        oct,
  year =         "1971",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Gentleman:1971:OMC,
  author =       "W. Morven Gentleman",
  title =        "Optimal multiplication chains for computing a power of
                 a symbolic polynomial",
  journal =      j-SIGSAM,
  volume =       "??",
  number =       "18",
  pages =        "23--30",
  month =        apr,
  year =         "1971",
  CODEN =        "SIGSBZ",
  DOI =          "https://doi.org/10.1145/1093425.1093426",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Tue Jun 17 19:14:25 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper shows that in a certain model of symbolic
                 manipulation of algebraic formulae, the simple method
                 of computing a power of a symbolic polynomial by
                 repeated multiplication by the original polynomial is,
                 in essence, the optimal method.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGSAM Bulletin",
  issue =        "18",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}

@TechReport{Ghest:1971:TCD,
  author =       "R. C. Ghest",
  title =        "A Two's Complement Digital Multiplier, the {Am25S05}",
  type =         "Technical report",
  institution =  "Advanced Micro Devices",
  address =      "Sunnyvale, CA, USA",
  pages =        "????",
  year =         "1971",
  bibdate =      "Fri Nov 09 18:50:36 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Ginsberg:1971:NID,
  author =       "Myron Ginsberg",
  booktitle =    "Proceedings of the First Annual Rocky Mountain
                 Symposium on Microprocessors",
  title =        "Numerical influences on the design of floating-point
                 arithmetic for microcomputers",
  publisher =    "????",
  address =      "????",
  pages =        "24--72",
  year =         "1971",
  bibdate =      "Fri Nov 09 18:52:22 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{Glaser:1971:HBO,
  author =       "Anton Glaser",
  title =        "History of Binary and Other Nondecimal Numeration",
  publisher =    "Anton Glaser",
  address =      "Southampton, PA, USA",
  pages =        "ix + 196",
  year =         "1971",
  ISBN =         "0-9600324-1-X",
  ISBN-13 =      "978-0-9600324-1-9",
  LCCN =         "QA141.2 .G55",
  bibdate =      "Fri Mar 17 08:12:27 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "See also revised edition \cite{Glaser:1981:HBO}.",
  acknowledgement = ack-nhfb,
  author-dates = "1924--",
  remark =       "Based on the author's thesis, Temple University, with
                 title: History of modern numeration systems.",
  subject =      "Numeration; History",
  tableofcontents = "Before Leibniz \\
                 Leibniz (1646--1716) \\
                 The rest of the 1700s \\
                 The nineteenth century \\
                 The twentieth century up to the computer age \\
                 Applications to computers \\
                 Contemporary literature",
}

@Article{Golub:1971:CAC,
  author =       "G. H. Golub and L. B. Smith",
  title =        "{Chebyshev} Approximation of Continuous Functions by a
                 {Chebyshev} System of Functions",
  journal =      j-CACM,
  volume =       "14",
  number =       "11",
  pages =        "737--746",
  month =        nov,
  year =         "1971",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Aug 15 09:54:14 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "ACM Algorithm 414.",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@TechReport{Haavie:1971:SMA,
  author =       "T. H{\aa}vie",
  title =        "Some Methods for Automatic Integration and their
                 Implementation on the {CERN CDC 65\slash 6600}
                 Computers",
  type =         "Report",
  number =       "CERN 71-26",
  institution =  "CERN",
  address =      "Geneva, Switzerland",
  day =          "1",
  month =        dec,
  year =         "1971",
  bibdate =      "Thu Jan 04 13:15:46 2024",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://cds.cern.ch/record/190218/files/CERN-71-26.pdf",
  abstract =     "Two schemes for automatic integration using modified
                 Romberg and Clenshaw--Curtis quadratures are discussed.
                 The experience gained testing FORTRAN routines, using
                 both rounded and unrounded arithmetic, on a set of 20
                 test examples are reported.",
  acknowledgement = ack-nhfb,
  keywords =     "automatic integration; CDC arithmetic; Clenshaw\slash
                 Curtis; Romberg; rounding corrections",
  onlinedate =   "iv + 43",
  remark =       "The report gives results, and recommendations, for
                 default (unrounded) and rounded arithmetic computation
                 in the peculiar arithmetic of the CDC 6000\slash 7000
                 family computers, for single precision (48-bit
                 significand, about 14 decimal digits) and double
                 precision (96-bit significand, almost 29 decimal
                 digits). Unlike Wirth's compiler work
                 \cite{Wirth:1972:PCG}, it does not get down to
                 instruction set details, or discuss the problems of
                 integer arithmetic.",
}

@Article{Honey:1971:CCD,
  author =       "D. W. Honey",
  title =        "Correspondence: Calculation of a double-length square
                 root from a double length number using single precision
                 techniques",
  journal =      j-COMP-J,
  volume =       "14",
  number =       "4",
  pages =        "443--443",
  month =        nov,
  year =         "1971",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:51:58 MDT 2000",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/140443.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_14/Issue_04/tiff/443.tif",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Kagan:1971:FPS,
  author =       "Claude A. R. Kagan",
  title =        "Floating point sub-language of a string language",
  journal =      j-SIGPLAN,
  volume =       "6",
  number =       "10",
  pages =        "20--22",
  month =        nov,
  year =         "1971",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/1317448.1317449",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sat Dec 2 08:35:10 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigplan1970.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=1317449",
  abstract =     "The facilities for floating point computation within
                 the framework of a string language currently operating
                 on the PDP-10 at the Western Electric Company
                 Engineering Research Center are considered to be a
                 sublanguage. This sublanguage is accessed through use
                 of the * (asterisk) as a function marker in lieu of the
                 colon, and such use causes execution of all of the
                 available arithmetic functions as well as a family of
                 additional functions whose names are the same as those
                 used in Fortran. The list of functions that will
                 execute in this sublanguage is displayed through
                 execution of ** (LF), expression.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}

@InProceedings{Kahan:1971:SEA,
  author =       "W. M. Kahan",
  title =        "A Survey of Error Analysis",
  crossref =     "Freiman:1971:PIC",
  pages =        "1214--1239",
  year =         "1971",
  MRclass =      "65G05",
  MRnumber =     "MR0458845 (56 \#17045)",
  bibdate =      "Tue Aug 28 05:24:53 2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Information Processing 71",
  URL =          "http://dblp.uni-trier.de/db/conf/ifip/ifip71-2.html#Kahan71",
  acknowledgement = ack-jr # " and " # ack-nhfb,
  keywords =     "accurate floating-point summation",
  remark =       "This paper contains the modified compensating
                 summation algorithm wherein `e = (temp - s) + y' is
                 replaced by `f = 0; if (sign(temp) == sign(y)) {f =
                 (0.46*s - s) + s} e = ((temp - f) - (s - f)) + y',
                 cited in e.g.,
                 \cite{Dalhquist:1974:NM,Higham:1993:AFP}.",
}

@Article{Kan:1971:EAD,
  author =       "E. Kan and J. Aggarwal",
  title =        "Error analysis of digital filter employing
                 floating-point arithmetic",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "18",
  number =       "6",
  pages =        "678--686",
  month =        nov,
  year =         "1971",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See correction \cite{Kan:1973:CEA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "The error accumulation in a digital filter employing
                 floating-point arithmetic is studied. Sources of errors
                 are considered to originate from (1) roundoff in the
                 arithmetic operations, (2) quantization of both the
                 input and the initial states, and (3) \ldots{}",
}

@Article{Kingsbury:1971:DFU,
  author =       "N. G. Kingsbury and P. J. W. Rayner",
  title =        "Digital filtering using logarithmic arithmetic",
  journal =      j-ELECT-LETTERS,
  volume =       "7",
  number =       "2",
  pages =        "56--58",
  day =          "28",
  month =        jan,
  year =         "1971",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:19710039",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Mon May 30 07:32:20 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}

@Article{Krishnamurthy:1971:CTW,
  author =       "E. V. Krishnamurthy",
  title =        "Complementary Two-Way Algorithms for Negative Radix
                 Conversions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "5",
  pages =        "543--550",
  month =        may,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223288",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:14 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671881",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "negative base",
}

@Article{Krishnamurthy:1971:EIR,
  author =       "E. V. Krishnamurthy",
  title =        "Economical Iterative and Range-Transformation Schemes
                 for Division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "4",
  pages =        "470--472",
  month =        apr,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223270",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:14 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671863",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Kuki:1971:FEP,
  author =       "H. Kuki and J. Ascoly",
  title =        "{FORTRAN} extended-precision library",
  journal =      j-IBM-SYS-J,
  volume =       "10",
  number =       "1",
  pages =        "39--61",
  year =         "1971",
  CODEN =        "IBMSA7",
  ISSN =         "0018-8670",
  bibdate =      "Thu Sep 15 18:51:32 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Systems Journal",
  xxmonth =      "(none)",
}

@InCollection{Kuki:1971:MFS,
  author =       "H. Kuki",
  title =        "Mathematical Function Subprograms for Basic System
                 Libraries\emdash Objectives, Constraints, and
                 Trade-Off",
  crossref =     "Rice:1971:MS",
  pages =        "187--199",
  year =         "1971",
  bibdate =      "Fri Sep 16 16:27:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}

@Article{Kulisch:1971:AAR,
  author =       "Ulrich W. Kulisch",
  title =        "An axiomatic approach to rounded computations",
  journal =      j-NUM-MATH,
  volume =       "18",
  number =       "1",
  pages =        "1--17",
  month =        feb,
  year =         "1971",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01398455",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sun Oct 17 16:12:48 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also \cite{Kulisch:1969:AAR}.",
  abstract =     "The present paper is intended to give an axiomatic
                 approach to rounded computations. A rounding is defined
                 as a monotone mapping of an ordered set into a subset,
                 which in general is called a lower respectively an
                 upper screen. The first chapter deals with roundings in
                 ordered sets. In the second chapter further properties
                 of roundings in linearly ordered sets are studied. The
                 third chapter deals with the two most important
                 applications, the approximation of the real arithmetic
                 on a finite screen and the approximation of the real
                 interval arithmetic on an upper screen. Beyond these
                 examples various further applications are possible.",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Kupka:1971:SRA,
  author =       "I. Kupka",
  title =        "Simulation of real arithmetic and real functions in
                 finite sets",
  journal =      j-NUM-MATH,
  volume =       "17",
  number =       "2",
  pages =        "143--152",
  year =         "1971",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C1220 (Simulation, modelling and identification);
                 C4110 (Error analysis in numerical methods)",
  corpsource =   "Univ. Hamburg, West Germany",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "error estimation; errors; estimation theory; finite
                 set; floating point arithmetic; real functions;
                 simulation",
  language =     "German",
  treatment =    "T Theoretical or Mathematical",
}

@TechReport{Lindsay:1971:RAF,
  author =       "D. S. Lindsay",
  title =        "A rounded arithmetic {FORTRAN} compiler for {CDC 6000}
                 machines",
  type =         "Report",
  number =       "????",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "????",
  month =        dec,
  year =         "1971",
  bibdate =      "Thu Jan 04 13:08:56 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "rounding corrections",
  remark =       "No copy of this report seems to be available online;
                 it is cited in \cite[p. 34]{Wirth:1972:PCG}. See the
                 remarks in that entry about the challenges of the CDC
                 arithmetic system.",
}

@Article{Majithia:1971:CAN,
  author =       "J. C. Majithia and R. Kitai",
  title =        "A Cellular Array for the Nonrestoring Extraction of
                 Square Roots",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "12",
  pages =        "1617--1618",
  month =        dec,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223191",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671784",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Majithia:1971:IAM,
  author =       "J. C. Majithia and R. Kitai",
  title =        "An Iterative Array for Multiplication of Signed Binary
                 Numbers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "2",
  pages =        "214--216",
  month =        feb,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223216",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:12 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671809",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Malcolm:1971:AFP,
  author =       "Michael A. Malcolm",
  title =        "On Accurate Floating-Point Summation",
  journal =      j-CACM,
  volume =       "14",
  number =       "11",
  pages =        "731--736",
  month =        nov,
  year =         "1971",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/362854.362889",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65G05 (68-XX)",
  MRnumber =     "47 4434",
  MRreviewer =   "P. Brock",
  bibdate =      "Mon Jan 22 07:01:06 MST 2001",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm14.html#Malcolm71;
                 https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Stanford University, CA, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "accurate floating-point summation; digital arithmetic;
                 error analysis",
  oldlabel =     "Malcolm71",
  treatment =    "P Practical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Malcolm71",
}

@TechReport{Malcolm:1971:ARP,
  author =       "Michael A. Malcolm",
  title =        "Algorithm to reveal properties of floating-point
                 arithmetic",
  institution =  "Stanford University",
  address =      "Stanford, Ca.",
  pages =        "8",
  year =         "1971",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "AD-727 104",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithms.; Floating-point arithmetic.",
  remark =       "``STAN-CS-71-211.''",
}

@Article{Morris:1971:TFP,
  author =       "R. Morris",
  title =        "Tapered Floating Point: a New Floating-Point
                 Representation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "12",
  pages =        "1578--1579",
  month =        dec,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223174",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671767",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Mullet:1971:NME,
  author =       "Gary M. Mullet and Tracy W. Murray",
  title =        "A New Method for Examining Rounding Error in
                 Least-Squares Regression Computer Programs",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "66",
  number =       "335",
  pages =        "496--498",
  month =        sep,
  year =         "1971",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Wed Jan 25 08:05:44 MST 2012",
  bibsource =    "http://www.jstor.org/journals/01621459.html;
                 http://www.jstor.org/stable/i314211;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib",
  URL =          "http://www.jstor.org/stable/2283514",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@Article{Nicoud:1971:IAR,
  author =       "Jean-Daniel Nicoud",
  title =        "Iterative Arrays for Radix Conversion",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "12",
  pages =        "1479--1489",
  month =        dec,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223160",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Oct 10 13:44:30 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  abstract =     "The general study of the conversion of a number from
                 the radix p to the radix q number system leads to four
                 different algorithms for integers, and to four similar
                 ones for fractions. Most transform algorithms can be
                 implemented by iterative arrays of cells characterized
                 by simple equations. Such arrays are very attractive
                 with present-time large-scale integration technology.
                 Two kinds of cells, that is, two iterative arrays, are
                 sufficient for the near instantaneous conversion of
                 fixed-point numbers from radix p to radix q, or vice
                 versa. For the important special case of binary-decimal
                 conversion, the structure of the cells is studied, and
                 different realizations using the BCD code are
                 described. One of them is specially suited for an LSI
                 realization in MOS technology. The advantages of other
                 codes are discussed. In particular, the use of the
                 biquinary code allows the realization of the fastest
                 cells, with only one gate delay for each line of
                 cells.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "base conversion; binary-decimal conversion; cellular
                 arrays; code conversion; iterative arrays; large-scale
                 integration; MOS technology; number systems; radix
                 conversion algorithms",
}

@Article{Paker:1971:BFP,
  author =       "Y. Paker",
  title =        "A Binary Floating-Point Resistor",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "1",
  pages =        "7--11",
  month =        jan,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223074",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:11 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671667",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@TechReport{Paus:1971:FPA,
  author =       "Dag Paus",
  title =        "Floating point arithmetikk til {Nord-2B}",
  type =         "Hovedoppgave i fysikk",
  institution =  "Universitetet i Oslo",
  address =      "Oslo, Norway",
  pages =        "156",
  year =         "1971",
  bibdate =      "Thu May 09 08:11:14 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "Norwegian",
}

@Article{Pawlak:1971:ACN,
  author =       "Z. Pawlak",
  title =        "Another Comment on {``Negative Radix Conversion''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "5",
  pages =        "587--587",
  month =        may,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223301",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:15 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See \cite{Wadel:1971:CNR,Zohar:1970:NRC}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671894",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "negative base",
}

@Article{Pezaris:1971:BBA,
  author =       "S. D. Pezaris",
  title =        "A 40ns 17-bit by 17-bit array multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "4",
  pages =        "442--447 (??)",
  month =        apr,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223261",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 19:12:55 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Pezaris:1971:NBB,
  author =       "S. D. Pezaris",
  title =        "A 40-ns 17-Bit by 17-Bit Array Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "4",
  pages =        "442--447",
  month =        apr,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223261",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:14 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671854",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Rhyne:1971:SPN,
  author =       "V. T. Rhyne",
  title =        "A Simple Postcorrection for Nonrestoring Division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "2",
  pages =        "213--214",
  month =        feb,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223215",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:12 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671808",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@PhdThesis{Rothmaier:1971:BEF,
  author =       "B. Rothmaier",
  title =        "{Die Berechnung der elementaren Funktionen mit
                 beliebiger Genauigkeit} \toenglish {The Computation of
                 Elementary Functions with Arbitrary Accuracy}
                 \endtoenglish",
  type =         "Dissertation",
  school =       "Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "??",
  year =         "1971",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Sarkar:1971:EPP,
  author =       "B. P. Sarkar and E. V. Krishnamurthy",
  title =        "Economic Pseudodivision Processes for Obtaining Square
                 Root, Logarithm, and Arctan",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "12",
  pages =        "1589--1593",
  month =        dec,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223178",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:22 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671771",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Schmookler:1971:HSD,
  author =       "Martin S. Schmookler and Arnold Weinberger",
  title =        "High speed decimal addition",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "8",
  pages =        "862--867",
  month =        aug,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223362",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 28 19:10:32 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  abstract =     "Parallel decimal arithmetic capability is becoming
                 increasingly attractive with new applications of
                 computers in a multiprogramming environment. The direct
                 production of decimal sums offers a significant
                 improvement in addition over methods requiring decimal
                 correction. These techniques are illustrated in the
                 eight-digit adder which appears in the System/360 Model
                 195.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "decimal floating-point arithmetic",
}

@Article{Schonhage:1971:SMG,
  author =       "A. Sch{\"o}nhage and V. Strassen",
  title =        "{Schnelle Multiplikation gro{\ss}er Zahlen}.
                 ({German}) [{Fast} multiplication of large numbers]",
  journal =      j-COMPUTING,
  volume =       "7",
  number =       "3--4",
  pages =        "281--292",
  year =         "1971",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Thu Jan 04 08:42:36 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 INSPEC Axiom database (1968--date)",
  note =         "Check pages??",
  acknowledgement = ack-ec # " and " # ack-nhfb,
  affiliation =  "University, Konstanz, West Germany",
  classification = "C5230",
  description =  "digital arithmetic",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "algorithm; binary numbers; logical nets; multitape
                 Turing machines; product",
  language =     "German",
}

@Article{Shepherd:1971:RSL,
  author =       "B. J. Shepherd",
  title =        "Right Shift for Low-Cost Multiply and Divide",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "12",
  pages =        "1586--1589",
  month =        dec,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223177",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671770",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Book{Stein:1971:IMA,
  author =       "Marvin L. Stein and William D. Munro",
  title =        "Introduction to machine arithmetic",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "viii + 295",
  year =         "1971",
  LCCN =         "QA76.5 .S752",
  bibdate =      "Fri Nov 9 19:20:08 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  subject =      "Electronic digital computers; Arithmetic",
}

@Article{Stein:1971:SMA,
  author =       "M. L. Stein and W. D. Munro",
  title =        "Scaling Machine Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "6",
  pages =        "675--678",
  month =        jun,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223324",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:16 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671917",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Wadel:1971:CNR,
  author =       "L. B. Wadel",
  title =        "Comment on {``Negative Radix Conversion''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-20",
  number =       "5",
  pages =        "587--587",
  month =        may,
  year =         "1971",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1971.223300",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 06:38:15 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See \cite{Pawlak:1971:ACN,Zohar:1970:NRC}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1671893",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "negative base",
}

@Article{Walker:1971:BS,
  author =       "R. J. Walker",
  title =        "Binary Summation",
  journal =      j-CACM,
  volume =       "14",
  number =       "6",
  pages =        "417--417",
  month =        jun,
  year =         "1971",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 07:27:52 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm14.html#Walker71;
                 https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Cornell University, Ithaca, NY, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "binary summation; digital arithmetic; floating point;
                 roundoff errors; space; storage",
  oldlabel =     "Walker71",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Walker71",
}

@InProceedings{Walther:1971:UAE,
  author =       "J. S. Walther",
  title =        "A unified algorithm for elementary functions",
  crossref =     "Macon:1971:SJC",
  pages =        "379--385",
  year =         "1971",
  DOI =          "https://doi.org/10.1145/1478786.1478840",
  bibdate =      "Thu Sep 1 10:15:31 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite{Walther:1972:UAE,Hwang:1979:CAP}.",
  abstract =     "This paper describes a single unified algorithm for
                 the calculation of elementary functions including
                 multiplication, division, sin, cos, tan, arctan, sinh,
                 cosh, tanh, arctanh, ln, exp and square-root. The basis
                 for the algorithm is coordinate rotation in a linear,
                 circular, or hyperbolic coordinate system depending on
                 which function is to be calculated. The only operations
                 required are shifting, adding, subtracting and the
                 recall of prestored constants. The limited domain of
                 convergence of the algorithm is calculated, leading to
                 a discussion of the modifications required to extend
                 the domain for floating-point calculations",
  acknowledgement = ack-nj,
}

@Article{Wlodarski:1971:FLN,
  author =       "J. Wlodarski",
  title =        "{Fibonacci} and {Lucas} Numbers Tend to Obey
                 {Benford's Law}",
  journal =      j-FIB-QUART,
  volume =       "9",
  number =       "1",
  pages =        "87--88",
  month =        feb,
  year =         "1971",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:05:33 MDT 2011",
  bibsource =    "http://www.fq.math.ca/9-1.html;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.fq.math.ca/Scanned/9-1/wlodarski2.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
  journal-URL =  "http://www.fq.math.ca/",
}

@InProceedings{Yohe:1971:R,
  author =       "J. Michael Yohe",
  booktitle =    "Proceedings of the 1971 Army Numerical Analysis and
                 Computers Conference",
  title =        "Rounding",
  publisher =    "US Army Research Office",
  address =      "Durham, NC, USA",
  pages =        "213--223",
  year =         "1971",
  LCCN =         "????",
  bibdate =      "Sun Dec 30 21:37:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "ARO-D Report 71-4",
  acknowledgement = ack-nhfb,
}

@MastersThesis{Abdelmagid:1972:DFP,
  author =       "Mohamed Nabil Fouad Abdelmagid",
  title =        "Design of a floating point arithmetic unit",
  type =         "Thesis ({M.S.})",
  school =       "Illinois Institute of Technology",
  address =      "Chicago, IL.",
  pages =        "v + 60",
  year =         "1972",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Ahmad:1972:ISH,
  author =       "M. Ahmad",
  title =        "Iterative schemes for high speed division",
  journal =      j-COMP-J,
  volume =       "15",
  number =       "4",
  pages =        "333--336",
  month =        nov,
  year =         "1972",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:52:07 MDT 2000",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/150333.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/tiff/333.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/tiff/334.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/tiff/335.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_04/tiff/336.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Univ. Manchester, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "digital arithmetic; digital computers; high speed
                 division; iterative methods; iterative schemes;
                 multiplicative",
  treatment =    "A Application; T Theoretical or Mathematical",
}

@Article{Bandyopadhyay:1972:IAM,
  author =       "S. Bandyopadhyay and S. Basu and A. K. Choudhury",
  title =        "An Iterative Array for Multiplication of Signed Binary
                 Numbers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "8",
  pages =        "921--922",
  month =        aug,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1972.5009055",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 18:58:46 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009055",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Banerji:1972:TAR,
  author =       "D. K. Banerji and J. A. Brzozowski",
  title =        "On Translation Algorithms in Residue Number Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "12",
  pages =        "1281--1285",
  month =        dec,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264810;
                 https://doi.org/10.1109/T-C.1972.223499",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 18:58:48 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35066;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672092",
  abstract =     "This paper considers translation problems in residue
                 number systems. The conversion from a fixed-base
                 representation to a residue representation can be done
                 using residue adders only; we show that relatively
                 simple combinational logic can be used to replace one
                 level of residue addition. In the reverse translation
                 problem, we examine the conditions under which base
                 extension can be used to compute the fixed-base digits
                 from a residue code number, and we study the efficiency
                 of the algorithm.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "base extension; input translation; modular arithmetic;
                 output translation; residue arithmetic; residue number
                 systems",
}

@Article{Brakefield:1972:OFP,
  author =       "James C. Brakefield",
  title =        "An optimal floating point format",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "1",
  number =       "4",
  pages =        "16--17",
  month =        oct,
  year =         "1972",
  CODEN =        "CANED2",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Fri May 12 09:41:08 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
}

@Article{Chen:1972:ACE,
  author =       "Tien Chi Chen",
  title =        "Automatic Computation of Exponentials, Logarithms,
                 Ratios and Square Roots",
  journal =      j-IBM-JRD,
  volume =       "16",
  number =       "4",
  pages =        "380--388",
  month =        jul,
  year =         "1972",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  MRclass =      "65D20",
  MRnumber =     "49 \#1738",
  bibdate =      "Tue Mar 25 14:26:59 MST 1997",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.research.ibm.com/journal/rd/164/chen.pdf",
  abstract =     "It is shown how a relatively simple device can
                 evaluate exponentials, logarithms, ratios and square
                 roots for fraction arguments, employing only shifts,
                 adds, high-speed table lookups, and bit counting. The
                 scheme is based on the cotransformation of a number
                 pair $ (x, y) $ such that the $ F(x, y) = f(x_0) $ is
                 invariant; when $x$ is driven towards a known value $
                 x_w $, $y$ is driven towards the result. For an $N$-bit
                 fraction about $ N / 4 $ iterations are required, each
                 involving two or three adds; then a termination
                 algorithm, based on an add and an abbreviated multiply,
                 completes the process, for a total cost of about one
                 conventional multiply time. Convergence, errors and
                 simulation using APL are discussed.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "IBM, San Jose, CA, USA",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "adds; APL; bit counting; convergence;
                 cotransformation; digital arithmetic; errors;
                 exponentials; high speed table; iteration; logarithms;
                 lookups; ratios; shifts; simulation; square roots;
                 termination algorithm",
  reviewer =     "F. Gotze",
  treatment =    "P Practical",
}

@Article{Chiang:1972:NAB,
  author =       "A. C. L. Chiang and I. S. Reed",
  title =        "Notes on the Arithmetic {BN} Modulo {A} Codes",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "8",
  pages =        "891--894",
  month =        aug,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1972.5009046",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 18:58:46 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009046",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Chien:1972:ECH,
  author =       "R. T. Chien and Se June Hong",
  title =        "Error Correction in High-Speed Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "5",
  pages =        "433--438",
  month =        may,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1972.223538",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 18:58:43 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672131",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Chinal:1972:SCP,
  author =       "J. P. Chinal",
  title =        "Some Comments on Postcorrections for Nonrestoring
                 Division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "12",
  pages =        "1385--1394",
  month =        dec,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1972.223511",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 18:58:49 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672104",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{DeMori:1972:PSS,
  author =       "R. {De Mori} and A. Serra",
  title =        "A Parallel Structure for Signed-Number Multiplication
                 and Addition",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "12",
  pages =        "1453--1454",
  month =        dec,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1972.223525",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 18:58:49 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672118",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Fenwick:1972:BRD,
  author =       "Peter M. Fenwick",
  title =        "A Binary Representation for Decimal Numbers",
  journal =      j-AUSTRALIAN-COMP-J,
  volume =       "4",
  number =       "4",
  pages =        "146--149",
  month =        nov,
  year =         "1972",
  CODEN =        "ACMJB2",
  ISSN =         "0004-8917",
  bibdate =      "Fri Nov 28 11:31:38 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Australian Computer Journal",
  keywords =     "decimal floating-point arithmetic",
}

@Article{Fettweis:1972:CBM,
  author =       "A. Fettweis",
  title =        "On the connection between multiplier word length
                 limitation and roundoff noise in digital filters",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "19",
  number =       "5",
  pages =        "486--491",
  month =        sep,
  year =         "1972",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "It is shown that for digital filters there exists a
                 direct and an indirect connection between the
                 generation of roundoff noise by a multiplier and the
                 effect that the coefficient word length limitation of
                 this multiplier has upon the response \ldots{}",
}

@Article{Franklin:1972:ZDA,
  author =       "J. W. Franklin",
  title =        "Zoned Decimal Arithmetic",
  journal =      j-IBM-TDB,
  volume =       "15",
  number =       "7",
  pages =        "2123--2124",
  month =        dec,
  year =         "1972",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
  keywords =     "decimal floating-point arithmetic",
}

@Book{Goldstine:1972:CPN,
  author =       "Herman H. Goldstine",
  title =        "The Computer: {From Pascal} to {von Neumann}",
  publisher =    pub-PRINCETON,
  address =      pub-PRINCETON:adr,
  pages =        "xii + 378",
  year =         "1972",
  ISBN =         "0-691-02367-0; 0-691-08104-2",
  ISBN-13 =      "978-0-691-02367-0; 978-0-691-08104-5",
  bibdate =      "Mon Jun 06 19:17:03 2005",
  bibsource =    "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib;
                 ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/Matrix.bib;
                 ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/sparse.linear.systems.bib;
                 ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/TUBScsd/1972.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Second printing, 1973. Paperback edition 1980. Fifth
                 printing, 1993 with new preface. Reprint 2000 by Books
                 on Demand, Ann Arbor, MI, USA.",
  acknowledgement = ack-nhfb,
  descriptor =   "Computer, ENIAC, Entwicklung, Geschichte, Pascal, Von
                 Neumann",
  kwds =         "book, history, computer",
}

@TechReport{Gosper:1972:HCF,
  author =       "R. W. Gosper",
  title =        "{HAKMEM} 101: Continued Fractions",
  type =         "Memo",
  number =       "AIM 239",
  institution =  "MIT AI Laboratory",
  address =      "Cambridge, MA, USA",
  pages =        "37--44",
  year =         "1972",
  bibdate =      "Fri Nov 30 06:37:23 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.inwap.com/pdp10/hbaker/hakmem/cf.html#item101a",
  acknowledgement = ack-nhfb,
  remark =       "From the document: ``The familiar transcendental
                 functions of rational arguments also have simple
                 continued fractions, but these are generally not
                 regular and cannot be reconstructed from numerical
                 values by a simple algorithm, since nonregular
                 representations aren't unique. The point is, however,
                 that numbers like e, pi, sqrt(2), sin 0.5, sqrt(7),
                 arctan sqrt(7), etc. can be expressed to unlimited
                 precision by simple programs which produce the terms on
                 demand.'' Also: ``Rational number arithmetic often
                 loses because numerators and denominators grow so large
                 as to require icky multiprecision. Algorithms for
                 arithmetic on continued fractions seem generally
                 unknown. The next items describe how to arithmetically
                 combine continued fractions to produce new ones, one
                 term at a time.'' and ``Continued fractions let us
                 perform numerical calculations a little at a time
                 without ever introducing any error, such as roundoff or
                 truncation. As if this weren't enough, the calculations
                 provide automatic error analysis, and obviate most
                 forms of successive approximation.''",
}

@Article{Gregory:1972:CFP,
  author =       "James Gregory",
  title =        "A Comparison of Floating Point Summation Methods",
  journal =      j-CACM,
  volume =       "15",
  number =       "9",
  pages =        "838--838",
  month =        sep,
  year =         "1972",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:46:23 MST 2001",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Gregory72;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Argonne Nat. Lab., IL, USA",
  descriptors =  "Simulation; statistics; numeric calculation",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "accurate floating-point summation; comparison; digital
                 arithmetic; error; error propagation; floating point
                 summation methods; truncation",
  oldlabel =     "Gregory72",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Gregory72",
}

@Article{Gregory:1972:URA,
  author =       "Robert Todd Gregory",
  title =        "The use of residue arithmetic with automatic digital
                 computers",
  journal =      "Delta (Waukesha)",
  volume =       "3",
  number =       "2",
  pages =        "1--27",
  year =         "1972\slash 1973",
  MRclass =      "68A10",
  MRnumber =     "MR0321348 (47 \#9881)",
  MRreviewer =   "A. D. Booth",
  bibdate =      "Thu Nov 8 14:50:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Hallin:1972:PAF,
  author =       "T. G. Hallin and M. J. Flynn",
  title =        "Pipelining of Arithmetic Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "8",
  pages =        "880--886",
  month =        aug,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1972.5009044",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 18:57:52 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Heising:1972:MM,
  author =       "W. Heising and M. O. Rabin and Shmuel Winograd",
  title =        "Multiplication Method",
  journal =      j-IBM-TDB,
  volume =       "15",
  number =       "4",
  pages =        "1147--1148",
  month =        sep,
  year =         "1972",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:15:07 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
}

@Manual{IBM:1972:ISR,
  author =       "{International Business Machines Corporation}",
  title =        "{IBM System\slash 360} reference data: direct
                 evaluation of floating point numbers in hexadecimal:
                 debugging aid",
  organization = "IBM Corporation",
  address =      "White Plains, NY, USA",
  pages =        "18",
  year =         "1972",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "IBM 360 (Computer)",
  remark =       "``GX20-1787-0.''",
}

@Article{Kamal:1972:HSM,
  author =       "A. A. Kamal and M. A. N. Ghannam",
  title =        "High-Speed Multiplication Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "9",
  pages =        "1017--1021",
  month =        sep,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1972.5009082",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 18:58:46 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009082",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Ling:1971:HSD,
  author =       "H. Ling",
  title =        "High speed division for binary computers",
  crossref =     "Macon:1971:SJC",
  pages =        "373--378",
  year =         "1971",
  DOI =          "https://doi.org/10.1145/1478786.1478839",
  acknowledgement = ack-nhfb,
  bibdate =      "Tue Jan 06 11:21:23 2026",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Beyond the steps of SHIFT and SUBTRACT, division used
                 in early machines generally relied upon Newton's
                 method. In order to increase the speed of division the
                 following two approaches, namely the S-R-T recoding
                 method and the iterative multiplication scheme, have
                 resulted. The S-R-T-method offering an average shifting
                 distance of 2.6 bits is very close to the scheme used
                 in Stretch, the iterative multiplication scheme
                 providing a quadratic convergence rate with preselected
                 starting block has been used in IBM 360/91. However,
                 the shifting distance of the S-R-T method varies with
                 the format of the denominator; the required number of
                 multiplication and the starting table of the quadratic
                 convergence scheme need further improvement. This paper
                 is concerned about the second approach, i.e., the
                 iterative multiplication scheme. Recently the author
                 has developed a method in which one of the iterative
                 multiplication is replaced by a fixed point
                 subtraction. In this paper a better method is
                 developed, this new method not only eliminates one of
                 the iterative multiplication but also reduces the size
                 of the starting table. The detailed derivation of the
                 algorithm will be presented first, followed by a
                 detailed description of the implementation procedure
                 along with two examples. The comparison of the proposed
                 division scheme with the others are also enclosed.",
}

@Article{Liu:1972:REF,
  author =       "B. Liu and M. {Van Valkenburg}",
  title =        "On roundoff error of fixed-point digital filters using
                 sign-magnitude truncation",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "19",
  pages =        "536--537",
  month =        sep,
  year =         "1972",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "This correspondence gives the statistical mean squared
                 error at the output of a digital filter due to roundoff
                 accumulation when fixed-point arithmetic with
                 sign-magnitude truncation is \ldots{}",
}

@Article{Loevenbruck:1972:CNR,
  author =       "A. P. Loevenbruck",
  title =        "Conversion of Number Representations",
  journal =      j-IBM-TDB,
  volume =       "15",
  number =       "7",
  pages =        "2148--2151",
  month =        dec,
  year =         "1972",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:16:10 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
}

@Article{Majithia:1972:CAE,
  author =       "J. C. Majithia",
  title =        "Cellular Array for Extraction of Squares and Square
                 Roots of Binary Numbers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "9",
  pages =        "1023--1024",
  month =        sep,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1972.5009084",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 18:58:46 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009084",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Malcolm:1972:ARP,
  author =       "Michael A. Malcolm",
  title =        "Algorithms to Reveal Properties of Floating-Point
                 Arithmetic",
  journal =      j-CACM,
  volume =       "15",
  number =       "11",
  pages =        "949--951",
  month =        nov,
  year =         "1972",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355606.361870",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 1 10:14:16 1994",
  bibsource =    "Compendex database;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Malcolm72;
                 https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also \cite{Gentleman:1974:MAR}.",
  abstract =     "Two algorithms are presented in the form of Fortran
                 subroutines. Each subroutine computes the radix and
                 number of digits of the floating-point numbers and
                 whether rounding or chopping is done by the machine on
                 which it is run. The methods are shown to work on any
                 ``reasonable'' floating-point computer.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  classification = "723",
  corpsource =   "Stanford University, CA, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  journalabr =   "Commun ACM",
  keywords =     "chopping; computer programming; computer programming
                 languages --- Fortran; digital arithmetic; digits;
                 floating point arithmetic; Fortran subroutines;
                 mathematical techniques --- Digital Arithmetic; number
                 of; properties; radix; rounding",
  oldlabel =     "Malcolm72",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Malcolm72",
}

@Article{Mandelbaum:1972:ECR,
  author =       "David Mandelbaum",
  title =        "Error correction in residue arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  pages =        "538--545",
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1972.5009006",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "94A10 (94A20)",
  MRnumber =     "MR0345709 (49 \#10440)",
  MRreviewer =   "P. Deussen",
  bibdate =      "Thu Nov 8 14:50:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@TechReport{Manos:1972:CCA,
  author =       "Paul Manos and L. Richard Turner",
  title =        "Constrained {Chebyshev} approximations to some
                 elementary functions suitable for evaluation with
                 floating-point arithmetic",
  type =         "{NASA} Technical Note",
  number =       "TN D-6698",
  institution =  "NASA",
  address =      "Washington, DC, USA",
  pages =        "iii + 68",
  month =        mar,
  year =         "1972",
  bibdate =      "Mon May 22 11:27:24 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19720010958_1972010958.pdf",
  acknowledgement = ack-nhfb,
}

@MastersThesis{Maple:1972:FPA,
  author =       "Christopher Marion Maple",
  title =        "A floating point analog to digital and digital to
                 analog converter",
  type =         "Thesis ({B.S.})",
  school =       "Massachusetts Institute of Technology. Dept. of
                 Electrical Engineering",
  address =      "Cambridge, MA, USA",
  pages =        "18",
  year =         "1972",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Marino:1972:NAA,
  author =       "D. Marino",
  title =        "New Algorithms for the Approximate Evaluation in
                 Hardware of Binary Logarithms and Elementary
                 Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "21",
  number =       "12",
  pages =        "1416--1421",
  month =        dec,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1972.223516",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 08 08:05:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Matula:1972:NTF,
  author =       "David W. Matula",
  title =        "Number Theoretic Foundations of Finite Precision
                 Arithmetic",
  crossref =     "Zaremba:1972:ANT",
  pages =        "479--489",
  year =         "1972",
  bibdate =      "Fri Oct 19 22:58:55 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "base conversion; finite-precision rational arithmetic;
                 number theory; overflow; radix conversion; tape
                 updating problem",
}

@TechReport{Metropolis:1972:ABCa,
  author =       "N. Metropolis",
  title =        "Analyzed Binary Computing",
  type =         "Technical Report",
  number =       "LA-DC--72-783; CONF-720916--2",
  institution =  inst-LASL,
  address =      inst-LASL:adr,
  pages =        "4",
  day =          "12",
  month =        sep,
  year =         "1972",
  bibdate =      "Tue Mar 20 11:25:24 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=4647144&query_id=0",
  acknowledgement = ack-nhfb,
}

@InProceedings{Metropolis:1972:ABCb,
  author =       "N. Metropolis",
  title =        "Analyzed Binary Computing",
  crossref =     "IEEE:1972:IAD",
  pages =        "81--84",
  year =         "1972",
  bibdate =      "Wed Mar 21 09:24:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A single format for the representation of numbers in a
                 computer is proposed to accommodate both exact and
                 inexact quantities. A consistent set of rules is
                 described for addition (subtraction), multiplication
                 and division of such quantities, both within their
                 separate types, as well as in combination. Error
                 correlation aside, the propagation of inherent errors
                 is monitored in operations with at least one imprecise
                 value. A definitive algorithm must, of course take into
                 account any correlations of inherent errors; these
                 correlations must be recognized and incorporated into
                 the algorithm by the numerical analyst, not by the
                 logical designer of the computer.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Metropolis:1972:ABCc,
  author =       "Nicholas C. Metropolis",
  title =        "Analyzed binary computing",
  crossref =     "IEEE:1972:ITS",
  pages =        "1--14",
  year =         "1972",
  DOI =          "https://doi.org/10.1109/ARITH.1972.6153912",
  bibdate =      "Tue Mar 5 08:31:37 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6153912",
  acknowledgement = ack-nhfb,
  journal-URL =  "https://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6148543",
}

@MastersThesis{Miller:1972:DFD,
  author =       "Peter Edwin Miller",
  title =        "The design of a floating-point, double-precision
                 arithmetic unit for the {Digital Equipment
                 Corporation}'s {PDP-9} computer",
  type =         "Thesis ({M.S.})",
  school =       "Ohio State University",
  address =      "Columbus, OH, USA",
  pages =        "83",
  year =         "1972",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Arithmetic --- Computer programs; PDP-9 (Computer)",
}

@InProceedings{Neely:1972:CSN,
  author =       "Peter M. Neely",
  title =        "On conventions for systems of numerical
                 representation",
  crossref =     "ACM:1972:PAA",
  pages =        "644--561",
  year =         "1972",
  bibdate =      "Fri Nov 28 11:28:06 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Present conventions for numeric representation are
                 considered inadequate to serve the needs of applied
                 computing. Thus an augmented digital number system is
                 proposed for use in programming languages and in
                 digital computers. Special symbols are proposed for
                 numbers too large, too small or too close to zero to be
                 represented in the normal digital number system, or
                 which are undefined. Properties of mappings among and
                 between digital number systems are used to justify the
                 augments chosen. Finally a suggestion is made for a new
                 floating point word format that will serve all the
                 above needs and will greatly extend the exponent range
                 of floating point numbers.",
  acknowledgement = ack-nhfb,
}

@Article{Oberman:1972:FRM,
  author =       "R. M. M. Oberman",
  title =        "A Flexible Rate Multiplier Circuit with Uniform Pulse
                 Distribution Outputs",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "8",
  pages =        "896--899",
  month =        aug,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1972.5009048",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 18:58:46 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009048",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Paris:1972:MA,
  author =       "J. B. Paris",
  title =        "On models of arithmetic",
  journal =      j-LECT-NOTES-MATH,
  volume =       "255",
  pages =        "251--280",
  year =         "1972",
  CODEN =        "LNMAA2",
  DOI =          "https://doi.org/10.1007/BFb0059548",
  ISBN =         "3-540-05744-7 (print), 3-540-37162-1 (e-book)",
  ISBN-13 =      "978-3-540-05744-4 (print), 978-3-540-37162-5
                 (e-book)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  ISSN-L =       "0075-8434",
  MRclass =      "02H05 (02H13)",
  MRnumber =     "0392552 (52 \#13369)",
  MRreviewer =   "W. Marek",
  bibdate =      "Fri May 9 19:07:09 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lnm1970.bib",
  URL =          "http://link.springer.com/chapter/10.1007/BFb0059548/",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/BFb0059533",
  book-URL =     "http://www.springerlink.com/content/978-3-540-37162-5",
  fjournal =     "Lecture Notes in Mathematics",
  journal-URL =  "http://link.springer.com/bookseries/304",
}

@Article{Pettus:1972:IDC,
  author =       "C. Pettus",
  title =        "Indeterminate $ 0 \div 0 $ check in {APL}",
  journal =      j-SIGPLAN,
  volume =       "7",
  number =       "4",
  pages =        "40--41",
  month =        apr,
  year =         "1972",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Thu May 25 06:58:23 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "One unique feature of the APL system is the definition
                 $ (0 \div 0) = 1 $. Although there is obvious merit in
                 this decision, in real analysis $ (0 \div 0) $ is
                 indeterminate. If one wishes to be alerted to the fact
                 that a denominator is zero and does not want the result
                 $1$ if the numerator is also zero, one can replace the
                 expression $ X \div Y $ with $ X \times \div Y $. Then
                 if $X$ and $Y$ are both zero, a Domain Error will be
                 reported instead of yielding.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "floating-point arithmetic; zero divide",
}

@Article{Phillips:1972:ICF,
  author =       "C. Phillips",
  title =        "Instabilities caused by floating-point arithmetic
                 quantization",
  journal =      j-IEEE-TRANS-AUTOMAT-CONTR,
  volume =       "17",
  number =       "2",
  pages =        "242--243",
  month =        apr,
  year =         "1972",
  CODEN =        "IETAA9",
  ISSN =         "0018-9286 (print), 1558-2523 (electronic)",
  ISSN-L =       "0018-9286",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Automatic Control",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
  summary =      "It is shown that an otherwise stable digital control
                 system may become unstable due to signal quantization
                 if the controller operates on floating-point
                 arithmetic. Sufficient conditions for instability are
                 developed \ldots{}",
}

@Article{Pichat:1972:CSA,
  author =       "M. Pichat",
  title =        "Correction d'une Somme en Arithm{\'e}tique {\`a}
                 Virgule Flottante. ({French}) {[Correction of a Sum in
                 Floating-Point Arithmetic]}",
  journal =      j-NUM-MATH,
  volume =       "19",
  number =       "5",
  pages =        "400--406",
  year =         "1972",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sat Sep 17 18:30:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "From Douglas Priest:
                 (\path=Douglas.Priest@eng.sun.com=) writing in Usenet
                 newsgroup sci.math.num-analysis on 13 Sep 1994 16:04:56
                 GMT: ``\ldots{} An iterative algorithm for computing a
                 protracted sum to working precision by repeatedly
                 applying the sum-and-roundoff method.''",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods)",
  corpsource =   "Conservatoire Nat. Arts M{\'e}tiers, Paris, France",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "accurate floating-point summation; correct rounding;
                 correction; digital arithmetic; floating point
                 arithmetic; rounding off law; sum; truncature with
                 guard digit",
  language =     "French",
  treatment =    "T Theoretical or Mathematical",
  xxmonth =      "(none)",
  xxnumber =     "(none)",
}

@Article{Ramamoorthy:1972:SPI,
  author =       "C. V. Ramamoorthy and James R. Goodman and K. H. Kim",
  title =        "Some Properties of Iterative Square-Rooting Methods
                 Using High-Speed Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "8",
  pages =        "837--847",
  month =        aug,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1972.5009039",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 18:58:45 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009039",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@TechReport{Randell:1972:ATO,
  author =       "Brian Randell",
  title =        "On {Alan Turing} and the origins of digital
                 computers",
  type =         "Technical report",
  number =       "33",
  institution =  "University of Newcastle upon Tyne, Computing
                 Laboratory",
  address =      "Newcastle upon Tyne, UK",
  pages =        "36",
  year =         "1972",
  LCCN =         "TK7888.3 .R35",
  bibdate =      "Wed Oct 13 09:24:25 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "University of Newcastle upon Tyne. Computing
                 Laboratory. Technical report series",
  acknowledgement = ack-nhfb,
  subject =      "Von Neumann, John; Turing, Alan Mathison; Electronic
                 digital computers; History",
  subject-dates = "1903--1957 (John von Neumann); 1912--1954 (Alan
                 Turing)",
}

@TechReport{Randell:1972:ODC,
  author =       "Brian Randell",
  title =        "The origins of digital computers: a bibliography",
  type =         "Technical report",
  number =       "38",
  institution =  "Computing Laboratory, University of Newcastle upon
                 Tyne",
  address =      "Newcastle upon Tyne, UK",
  pages =        "iii + 59",
  year =         "1972",
  LCCN =         "TK7888.3 .R35",
  bibdate =      "Wed Oct 13 09:24:25 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "University of Newcastle upon Tyne, Computing
                 laboratory. Technical report series",
  acknowledgement = ack-nhfb,
  subject =      "Electronic digital computers; History; Bibliography",
}

@Article{Richman:1972:AEA,
  author =       "Paul L. Richman",
  title =        "Automatic Error Analysis for Determining Precision",
  journal =      j-CACM,
  volume =       "15",
  number =       "9",
  pages =        "813--817",
  month =        sep,
  year =         "1972",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65G05",
  MRnumber =     "47 2808",
  bibdate =      "Mon Jan 22 07:15:56 MST 2001",
  bibsource =    "Compendex database;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm15.html#Richman72;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The problem considered is that of evaluating a
                 rational expression to within any desired tolerance on
                 a computer which performs variable-precision
                 floating-point arithmetic operations. An automatic
                 error analysis technique is given for determining,
                 directly from the results of a trial low-precision
                 interval arithmetic calculation, just how much
                 precision and data accuracy are required to achieve a
                 desired final accuracy. The technique given generalize
                 easily to the evaluation of many nonrational
                 expressions.",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290B (Error analysis in numerical methods); C4110
                 (Error analysis in numerical methods); C5230 (Digital
                 arithmetic methods)",
  classification = "921",
  corpsource =   "Bell Telephone Labs. Inc., Denver, CO, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  journalabr =   "Commun ACM",
  keywords =     "automatic error analysis; control; digital arithmetic;
                 error analysis; floating point arithmetic; interval
                 arithmetic; mathematical techniques; precision;
                 precision control",
  oldlabel =     "Richman72",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Richman72",
}

@PhdThesis{Ripley:1972:PFP,
  author =       "Jerald Lester Ripley",
  title =        "On proofs of floating-point program correctness and a
                 measure of their relative efficiency",
  type =         "Thesis ({Ph.D.})",
  school =       "University of Oklahoma",
  address =      "????",
  pages =        "vi + 105",
  year =         "1972",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Numerical calculations.",
}

@Article{Rohl:1972:NCA,
  author =       "J. S. Rohl and J. A. Linn",
  title =        "A Note on Compiling Arithmetic Expressions",
  journal =      j-COMP-J,
  volume =       "15",
  number =       "1",
  pages =        "13--14",
  month =        feb,
  year =         "1972",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/15.1.13",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:47:49 MST 2012",
  bibsource =    "http://comjnl.oxfordjournals.org/content/15/1.toc;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_01/;
                 https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/15/1/13.full.pdf+html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_01/150013.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_01/tiff/13.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_01/tiff/14.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods); C6130 (Data
                 handling techniques); C6150C (Compilers, interpreters
                 and other processors)",
  corpsource =   "Univ. Manchester, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "arithmetic expressions; compilers; compiling; data
                 handling; digital arithmetic; minimisation;
                 minimization; program; single accumulator; storing;
                 temporary",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Samet:1972:CDL,
  author =       "P. A. Samet and D. W. Honey",
  title =        "Calculation of a Double-Length Square Root from
                 Double-Length Number using Single Precision
                 Techniques",
  journal =      j-COMP-J,
  volume =       "15",
  number =       "2",
  pages =        "116--116",
  month =        may,
  year =         "1972",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/15.2.116",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:47:49 MST 2012",
  bibsource =    "http://comjnl.oxfordjournals.org/content/15/2.toc;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_02/;
                 https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/15/2/116.full.pdf+html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_15/Issue_02/tiff/116.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Univ. Coll., London, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "digital arithmetic; double length; precision
                 techniques; single; square root",
  treatment =    "T Theoretical or Mathematical",
}

@TechReport{Schulenberg:1972:RSS,
  author =       "Craig Schulenberg and James E. Kernan",
  title =        "Results of space shuttle computer floating-point
                 precision study",
  type =         "Report",
  number =       "E-2637",
  institution =  "M.I.T. Charles Stark Draper Laboratory",
  address =      "Cambridge",
  pages =        "various",
  year =         "1972",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic data processing --- Space trajectories.;
                 Reusable space vehicles.",
  remark =       "At head of title: Apollo guidance, navigation and
                 control.",
}

@Article{Schurmann:1972:MEA,
  author =       "A. Schurmann",
  title =        "On the minimum error in addition processes of positive
                 floating-point numbers",
  journal =      j-ZASTOS-MAT,
  volume =       "13",
  pages =        "351--366",
  year =         "1972--1973",
  CODEN =        "ZAMTAK",
  MRclass =      "65G05",
  MRnumber =     "48 3242",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Zastosowania Matematyki",
  reviewer =     "A. D. Booth",
}

@Article{Shaham:1972:NDA,
  author =       "Z. Shaham and Z. Riesel",
  title =        "A Note on Division Algorithms Based on
                 Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "5",
  pages =        "513--514",
  month =        may,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1972.223557",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 18:58:43 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672150",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Stallings:1972:CPM,
  author =       "W. T. Stallings and T. L. Boullion",
  title =        "Computation of Pseudoinverse Matrices Using Residue
                 Arithmetic",
  journal =      j-SIAM-REVIEW,
  volume =       "14",
  number =       "1",
  pages =        "152--163",
  month =        "????",
  year =         "1972",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1014005",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu Mar 27 09:06:35 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/14/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "January 1972",
}

@Article{Stefanelli:1972:SHS,
  author =       "R. Stefanelli",
  title =        "A Suggestion for a High-Speed Parallel Binary
                 Divider",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-21",
  number =       "1",
  pages =        "42--55",
  month =        jan,
  year =         "1972",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1972.223430",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jan 08 22:42:31 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  abstract =     "family of four procedures to compute the inverse $ 1 /
                 X $ of a given binary number $X$ normalized between 0.5
                 and 1 is described. The quotient is obtained in
                 redundant binary form, i.e., in a base 2 code in which
                 digits can assume any positive or negative integer
                 value. All methods here described can be implemented by
                 combinatorial networks; the dividers realized in this
                 way are very fast because all carry propagations take
                 place at the same time.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InCollection{Tung:1972:A,
  author =       "C. Tung",
  title =        "Arithmetic",
  crossref =     "Cardenas:1972:CS",
  pages =        "??--??",
  year =         "1972",
  bibdate =      "Sat May 18 14:39:14 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Urabae:1972:CEA,
  author =       "Minoru Urabae",
  title =        "Component-wise error analysis of iterative methods
                 practiced on a floating-point system",
  type =         "{MRC} Technical Summary Report",
  number =       "1268",
  institution =  inst-MRC-WISCONSIN,
  address =      inst-MRC-WISCONSIN:adr,
  pages =        "57",
  year =         "1972",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Error analysis (Mathematics); Floating-point
                 arithmetic.; Iterative methods (Mathematics)",
  remark =       "``Received August 11, 1972.'' Sponsored by Army
                 Research Office, Durham, N.C.",
}

@Article{Varian:1972:LEB,
  author =       "Hal R. Varian",
  title =        "Letter to the {Editor}: {Benford's Law}",
  journal =      j-AMER-STAT,
  volume =       "26",
  number =       "3",
  pages =        "65--66",
  month =        jun,
  year =         "1972",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Fri Mar 30 11:34:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://links.jstor.org/sici?sici=0003-1305%28197206%2926%3A3%3C62%3ALTTE%3E2.0.CO%3B2-Q",
  abstract =     "Around 1938 the physicist Frank Benford observed a
                 rather strange fact: tables of logarithms in libraries
                 tend to be dirtier at the beginning than at the end.
                 This indicated to Benford that people had more occasion
                 to calculate with numbers beginning with 1 or 2 than
                 with 8 or 9.\par

                 Benford also found that the frequency of the digit p
                 being the first digit of a decimal number was very
                 closely approximated by $ \log (p + 1) - \log p $
                 [i.e., $ \log (1 + 1 / p) $ ]. This has become known as
                 Benford's law.",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@InCollection{Walther:1972:UAE,
  author =       "J. S. Walther",
  title =        "A Unified Algorithm for Elementary Functions",
  crossref =     "Petrocelli:1972:BCP",
  pages =        "69--81",
  year =         "1972",
  bibdate =      "Wed Oct 29 06:02:29 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprint of \cite{Walther:1971:UAE}.",
  acknowledgement = ack-nhfb,
}

@TechReport{Wirth:1972:PCG,
  author =       "Niklaus Wirth",
  title =        "On ``{Pascal}'', Code Generation, and the {CDC 6000}
                 Computer",
  type =         "Report",
  number =       "STAN-CS-72-257",
  institution =  inst-STAN-CS,
  address =      inst-STAN-CS:adr,
  pages =        "i + 38",
  month =        feb,
  year =         "1972",
  bibdate =      "Thu Jan 04 12:57:12 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "``PASCAL'' is a general purpose programming language
                 with characteristics similar to ALGOL 60, but with an
                 enriched set of program- and data structuring
                 facilities. It has been implemented on the CDC 6000
                 computer. This paper discusses selected topics of code
                 generation, in particular the selection of instruction
                 sequences to represent simple operations on arithmetic,
                 Boolean, and powerset operands. Methods to implement
                 recursive procedures are briefly described, and it is
                 hinted that the more sophisticated solutions are not
                 necessarily also the best. The CDC 6000 architecture
                 appears as a frequent source of pitfalls and nuisances,
                 and its main trouble spots are scrutinized and
                 discussed.",
  acknowledgement = ack-nhfb,
  author-dates = "15 February 1934--1 January 2024",
  remark =       "This report contains an interesting discussion of the
                 problems for compiler writers with a hardware
                 arithmetic design that subsumes integer arithmetic
                 inside one's complement floating-point arithmetic, and
                 is unable to detect integer overflow. The CDC 6000 and
                 7000, and Burroughs 5000 and 6000 families, share some
                 of these difficulties.",
}

@Book{Young:1972:SNM,
  author =       "David M. Young and Robert Todd Gregory",
  title =        "A Survey of Numerical Mathematics",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "x + 492 (A1--A18 and B1--B14 and I1--I19)",
  year =         "1972",
  ISBN =         "0-201-08773-1, 0-486-65691-8 (Dover paperback)",
  ISBN-13 =      "978-0-201-08773-4, 978-0-486-65691-5 (Dover
                 paperback)",
  LCCN =         "QA297 .Y63 1972",
  MRclass =      "65-02",
  MRnumber =     "53 11954a",
  bibdate =      "Wed Jan 17 10:57:04 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  reviewer =     "D. Greenspan",
  tableofcontents = "1: Numerical Analysis as a Subject Area \\
                 1.1 Introduction \\
                 1.2 Some pitfalls in computation \\
                 1.3 Mathematical and computer aspects of an algorithm
                 \\
                 1.4 Numerical instability of algorithms and
                 ill-conditioned problems \\
                 1.5 Typical problems of interest to the numerical
                 analyst \\
                 1.6 Iterative methods \\
                 2: Elementary Operations with Automatic Digital
                 Computers \\
                 2.1 Introduction \\
                 2.2 Binary arithmetic \\
                 2.3 Conversion from base $D$ to base $B$ representation
                 \\
                 2.4 Representation of integers on a binary computer \\
                 2.5 Floating-point representations \\
                 2.6 Computer-representable numbers \\
                 2.7 Floating-point arithmetic operations \\
                 2.8 Fortran analysis of a floating-point number \\
                 2.9 Calculation of elementary functions \\
                 3: Surveillance of Number Ranges \\
                 3.1 Introduction \\
                 3.2 Allowable number ranges \\
                 3.3 Basic real arithmetic operations \\
                 3.4 The quadratic equation \\
                 3.5 Complex arithmetic operations \\
                 4: Solution of Equations \\
                 4.1 Introduction \\
                 4.2 Attainable accuracy \\
                 4.3 Graphical methods \\
                 4.4 The method of bisection \\
                 4.5 The method of false position \\
                 4.6 The secant method \\
                 4.7 General properties of iterative methods \\
                 4.8 Generation of iterative methods \\
                 4.9 The Newton method \\
                 4.10 Muller's method \\
                 4.11 Orders of convergence of iterative methods \\
                 4.12 Acceleration of the convergence \\
                 4.13 Systems of nonlinear equations \\
                 5: Roots of Polynomial Equations \\
                 5.1 Introduction \\
                 5.2 General properties of polynomials \\
                 5.3 The Newton method and related methods \\
                 5.4 Muller's method and Cauchy's method \\
                 5.5 Location of the roots \\
                 5.6 Root acceptance and refinement \\
                 5.7 Matrix related methods: the modified Bernoulli
                 method \\
                 5.8 Matrix related methods: the IP method \\
                 5.9 Polyalgorithms \\
                 5.10 Other methods \\
                 6: Interpolation and Approximation \\
                 6.1 Introduction \\
                 6.2 Linear interpolation \\
                 6.3 Convergence and accuracy of linear interpolation
                 \\
                 6.4 Lagrangian interpolation \\
                 6.5 Convergence and accuracy of Lagrangian
                 interpolation \\
                 6.6 Interpolation with equal intervals \\
                 6.7 Hermite interpolation \\
                 6.8 Limitations on polynomial interpolation: smooth
                 interpolation \\
                 6.9 Inverse interpolation \\
                 6.10 Approximation by polynomials \\
                 6.11 Least squares approximation by polynomials \\
                 6.12 Rational approximation \\
                 6.13 Trigonometric interpolation and approximation \\
                 6.14 Interpolation in two variables \\
                 7: Numerical Differentiation and Quadrature \\
                 7.1 Introduction \\
                 7.2 The method of undetermined weights \\
                 7.3 Numerical differentiation \\
                 7.4 Numerical quadrature --- equal intervals \\
                 7.5 The Euler--MacLaurin formula \\
                 7.6 Romberg integration \\
                 7.7 Error determination \\
                 7.8 Numerical quadrature --- unequal intervals \\
                 8: Ordinary Differential Equations \\
                 8.1 Introduction \\
                 8.2 Existence and uniqueness \\
                 8.3 Analytic methods \\
                 8.4 Integral equation formulation --- the Picard method
                 of successive approximations \\
                 8.5 The Euler method \\
                 8.6 Methods based on numerical quadrature \\
                 8.7 Error estimation for predictor-corrector methods
                 \\
                 8.8 A numerical example \\
                 8.9 Runge--Kutta methods \\
                 8.10 Methods based on numerical differentiation \\
                 8.11 Higher-order equations and systems of first-order
                 equations \\
                 8.12 The use of high-speed computers \\
                 Appendix A \\
                 Appendix B \\
                 Appendix C \\
                 Bibliography \\
                 Index",
}

@Article{Aird:1973:SUM,
  author =       "T. Aird and D. Dodson and E. Houstis and J. Rice",
  title =        "Statistics on the Use of Mathematical Subroutines from
                 a Computer Center Library",
  journal =      j-SIGNUM,
  volume =       "8",
  number =       "4",
  pages =        "8--9",
  month =        oct,
  year =         "1973",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Thu Sep 1 10:14:44 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}

@MastersThesis{Anjoorian:1973:EME,
  author =       "Harry Anjoorian",
  title =        "An example of microprogrammed extended-precision
                 floating-point arithmetic",
  type =         "Thesis ({M.A.})",
  school =       "California State University, Chico",
  address =      "Chico, CA, USA",
  pages =        "ix + 94",
  year =         "1973",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic and logic units.; Electronic
                 digital computers --- Design and construction.",
}

@Article{Atkins:1973:PCA,
  author =       "David E. {Atkins, III} and Harvey L. Garner",
  title =        "Preface: Computer Arithmetic: An Introduction and
                 Overview [{Second IEEE Symposium on Computer
                 Arithmetic, May 15--16, 1972, University of
                 Maryland}]",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "549--551",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009104",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 19:18:24 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Atkins.pdf;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009104",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2",
}

@Article{Avizienis:1973:AAE,
  author =       "Algirdas Avi{\v{z}}ienis",
  title =        "Arithmetic Algorithms for Error-Coded Operands",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "567--572",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009108",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 19:18:24 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Avizienis.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2",
}

@Book{Barna:1973:ICD,
  author =       "Arpad Barna and Dan I. Porat",
  title =        "Integrated Circuits in Digital Electronics",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xi + 483",
  year =         "1973",
  ISBN =         "0-471-05050-4",
  ISBN-13 =      "978-0-471-05050-6",
  LCCN =         "TK7868.D5 B43",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}

@Article{Barsi:1973:ECP,
  author =       "F. Barsi and P. Maestrini",
  title =        "Error Correcting Properties of Redundant Residue
                 Number Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "3",
  pages =        "307--315",
  month =        mar,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264810;
                 https://doi.org/10.1109/T-C.1973.223711",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:18 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35074;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672304",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The error correcting properties of the redundant
                 residue number systems (RNS) are investigated through a
                 more natural a approach than was previously known. The
                 necessary and sufficient condition for the correction
                 of a given error affecting a single \ldots{}",
}

@Article{Baugh:1973:TCP,
  author =       "C. R. Baugh and B. A. Wooley",
  title =        "A Two's Complement Parallel Array Multiplication
                 Algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "12",
  pages =        "1045--1047",
  month =        dec,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1973.223648",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:37 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See comments
                 \cite{Blankenship:1974:CTC,Kroft:1974:CTC}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672241",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Besslich:1973:MDS,
  author =       "P. W. Besslich and S. Raman",
  title =        "Multiplication, Division and Square Root Extraction
                 Methods for Electronic Desk Calculators",
  journal =      "Journal of the Institution of Telecommunication
                 Engineers (India)",
  volume =       "19",
  number =       "4",
  month =        apr,
  year =         "1973",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Brent:1973:PAV,
  author =       "Richard P. Brent",
  title =        "On the Precision Attainable with Various
                 Floating-Point Number Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "601--607",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009113",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:14:15 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Brent.pdf",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2",
}

@Article{Brent:1973:PEA,
  author =       "R. Brent and D. Kuck and K. Maruyama",
  title =        "The Parallel Evaluation of Arithmetic Expressions
                 Without Division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "5",
  pages =        "532--534",
  month =        may,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1973.223757",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:23 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672350",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Cappa:1973:AIA,
  author =       "M. Cappa and V. C. Hamacher",
  title =        "An Augmented Iterative Array for High-Speed Binary
                 Division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "2",
  pages =        "172--175",
  month =        feb,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1973.223680",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:15 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See comments \cite{Gardiner:1974:CAI}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672273",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Cody:1973:SDN,
  author =       "William J. {Cody, Jr.}",
  title =        "Static and Dynamic Numerical Characteristics of
                 Floating-Point Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "598--601",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009112",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:14:15 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Cody.pdf",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2",
}

@Article{Dorr:1973:REC,
  author =       "Fred W. Dorr and Cleve B. Moler",
  title =        "Roundoff error on the {CDC 6600\slash 7600}
                 computers",
  journal =      j-SIGNUM,
  volume =       "8",
  number =       "2",
  pages =        "24--26",
  month =        apr,
  year =         "1973",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:49:59 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Univ. California, Los Alamos, NM, USA",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "arithmetic; CDC 6600/7600 computers; computer; digital
                 arithmetic; program; roundoff error",
  treatment =    "P Practical; X Experimental",
}

@Article{Du:1973:CSS,
  author =       "Min-Wen Du and C. Dennis Weiss",
  title =        "Circuit Structure and Switching Function
                 Verification",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "618--625",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009116",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 19:18:24 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Du.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2",
}

@Article{Ercegovac:1973:REC,
  author =       "Milo{\v{s}} D. Ercegovac",
  title =        "Radix-16 Evaluation of Certain Elementary Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "561--566",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009107",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:15:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Ercegovac.pdf;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009107",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2",
}

@TechReport{Erkio:1973:EAV,
  author =       "Hannu Erkio",
  title =        "An extension of {ALGOL} with variable precision
                 floating-point arithmetic",
  type =         "Series {A}. Report",
  number =       "1973/2",
  institution =  "University of Helsinki, Department of Computer
                 Science",
  address =      "Helsinki",
  pages =        "ii + 20",
  year =         "1973",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ALGOL (Computer program language); Floating-point
                 arithmetic",
}

@Article{Fettweis:1973:RNA,
  author =       "A. Fettweis",
  title =        "Roundoff noise and attenuation sensitivity in digital
                 filters with fixed-point arithmetic",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "20",
  number =       "2",
  pages =        "174--175",
  month =        mar,
  year =         "1973",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "A general expression is established which relates the
                 output roundoff noise generated by a fixed-point
                 multiplier in a digital filter to the sensitivity of
                 the filter attenuation with respect to the
                 corresponding multiplier coefficient. It confirms
                 \ldots{}",
}

@Article{Gelenbe:1973:UAE,
  author =       "Erol Gelenbe",
  title =        "A Unified Approach to the Evaluation of a Class of
                 Replacement Algorithms",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "611--618",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009115",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 19:18:24 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Gelenbe.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2",
}

@Article{Green:1973:NTF,
  author =       "D. H. Green and R. G. Kelsch",
  title =        "Nonlinear Ternary Feedback Shift Registers",
  journal =      j-COMP-J,
  volume =       "16",
  number =       "4",
  pages =        "360--367",
  month =        nov,
  year =         "1973",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Sep 29 08:52:16 MDT 2000",
  bibsource =    "Compendex database;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/160360.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/360.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/361.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/362.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/363.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/364.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/365.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/366.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_16/Issue_04/tiff/367.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "B1260 (Pulse circuits); B1265 (Digital electronics);
                 C5120 (Logic and switching circuits); C5230 (Digital
                 arithmetic methods)",
  classification = "722",
  corpsource =   "Univ. Manchester Inst. Sci. Technol., UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "arithmetic; coding theory; communications; computers,
                 digital; digital arithmetic; digital computers;
                 feedback shift registers; functions; nonlinear;
                 polynomial domain representation; shift registers;
                 ternary",
  treatment =    "T Theoretical or Mathematical",
}

@Book{Hamming:1973:NMS,
  author =       "R. W. (Richard Wesley) Hamming",
  title =        "Numerical methods for scientists and engineers",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  edition =      "Second",
  pages =        "ix + 721",
  year =         "1973",
  ISBN =         "0-07-025887-2",
  ISBN-13 =      "978-0-07-025887-7",
  LCCN =         "QA297 .H28 1973",
  bibdate =      "Fri Aug 20 09:12:08 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "International series in pure and applied mathematics",
  acknowledgement = ack-nhfb,
  subject =      "Numerical analysis; Data processing",
}

@Article{Hwang:1973:RRS,
  author =       "W. G. Hwang and John Todd",
  title =        "A recurrence relation for the square root",
  journal =      j-J-APPROX-THEORY,
  volume =       "9",
  pages =        "299--306",
  year =         "1973",
  CODEN =        "JAXTAZ",
  DOI =          "https://doi.org/10.1016/0021-9045(73)90075-0",
  ISSN =         "0021-9045,1096-0430",
  ISSN-L =       "0021-9045",
  MRclass =      "65H05",
  MRnumber =     "373270",
  MRreviewer =   "L. Fox",
  bibdate =      "Sat Oct 21 14:25:01 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0271.65032",
  acknowledgement = ack-nhfb,
  author-dates = "John Todd (16 May 1911--21 June 2007)",
  fjournal =     "Journal of Approximation Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219045",
  received =     "19 April 1971",
  ZBmath =       "3426800",
}

@Article{Jacobsohn:1973:CDA,
  author =       "David H. Jacobsohn",
  title =        "A Combinatoric Division Algorithm for Fixed-Integer
                 Divisors",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "608--610",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009114",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 19:18:24 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Jacobsohn.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2",
}

@TechReport{Kahan:1973:IAL,
  author =       "W. Kahan",
  title =        "Implementation of algorithms (lecture notes by {W. S.
                 Haugeland} and {D. Hough})",
  type =         "Technical report",
  number =       "20",
  institution =  "Department of Computer Science",
  address =      "Berkeley, CA, USA",
  year =         "1973",
  bibdate =      "Tue Aug 28 05:28:07 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
  remark =       "This paper contains the modified compensating
                 summation algorithm wherein `e = (temp - s) + y' is
                 replaced by `f = 0; if (sign(temp) == sign(y)) {f =
                 (0.46*s - s) + s} e = ((temp - f) - (s - f)) + y',
                 cited in e.g.,
                 \cite{Dalhquist:1974:NM,Higham:1993:AFP}. Kahan remarks
                 ``The mysterious constant 0.46, which could perhaps be
                 any number between 0.25 and 0.50, and the fact that the
                 proof requires a consideration of known machines
                 designs, indicate that this algorithm is not an advance
                 in computer science.''",
}

@Article{Kan:1973:CEA,
  author =       "E. Kan and J. Aggarwal",
  title =        "Correction to {``Error Analysis of Digital Filters
                 Employing Floating-Point Arithmetic''}",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "20",
  number =       "5",
  pages =        "617--618",
  month =        sep,
  year =         "1973",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Kan:1971:EAD}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
}

@Article{Kanani:1973:NCS,
  author =       "Dhirubhai V. Kanani and Kenneth H. O'Keefe",
  title =        "A Note on Conditional-Sum Addition for Base $ - 2 $
                 Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "626--626",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009117",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:26 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Kanani.pdf;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009117",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2; negative base",
}

@Article{Kaneko:1973:LCO,
  author =       "T. Kaneko",
  title =        "Limit-cycle oscillations in floating-point digital
                 filters",
  journal =      j-IEEE-TRANS-AUDIO-ELECTROACOUST,
  volume =       "21",
  number =       "2",
  pages =        "100--106",
  month =        apr,
  year =         "1973",
  CODEN =        "ITADAS",
  ISSN =         "0018-9278 (print), 1558-2582 (electronic)",
  ISSN-L =       "0018-9278",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Audio and Electroacoustics",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8337",
  summary =      "In a digital filter realized with fixed-point
                 arithmetic, there is a peculiar phenomenon known as
                 limit-cycle oscillation, which is due to roundoff
                 errors. For floating-point arithmetic, it has been
                 conjectured that its amplitude is negligibly small,
                 \ldots{}",
}

@Article{Kaneko:1973:LRE,
  author =       "Toyohisa Kaneko and Bede Liu",
  title =        "On Local Roundoff Errors in Floating-Point
                 Arithmetic",
  journal =      j-J-ACM,
  volume =       "20",
  number =       "3",
  pages =        "391--398",
  month =        jul,
  year =         "1973",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/321765.321771",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  MRclass =      "65G05",
  MRnumber =     "49 8318",
  bibdate =      "Tue Oct 09 10:18:49 2007",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jacm.bib",
  abstract =     "A bound on the relative error in floating-point
                 addition using a single-precision accumulator with
                 guard digits is derived. It is shown that even with a
                 single guard digit, the accuracy can be almost as good
                 as that using a double-precision accumulator. A
                 statistical model for the roundoff error in
                 double-precision multiplication and addition is also
                 derived. The model is confirmed by experimental
                 measurements.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  reviewer =     "V. V. Ivanov",
}

@TechReport{Kent:1973:PDS,
  author =       "Jan G. Kent",
  title =        "Procedures for the description and simulation of
                 floating point instructions",
  type =         "Report",
  number =       "426",
  institution =  "Norwegian Computing Center",
  address =      "Oslo, Norway",
  month =        sep,
  year =         "1973",
  bibdate =      "Sat Jan 09 06:27:20 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Kent:1973:TDA,
  author =       "Jan G. Kent",
  title =        "Theoretical definition, analysis and comparison of
                 floating point instructions",
  type =         "Report",
  number =       "425",
  institution =  "Norwegian Computing Center",
  address =      "Oslo, Norway",
  month =        sep,
  year =         "1973",
  bibdate =      "Sat Jan 09 06:27:20 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Kielbasinski:1973:SAC,
  author =       "Andrzej Kie{\l}basi{\'n}ski",
  title =        "Summation algorithm with corrections and some of its
                 applications",
  journal =      j-MATH-STOS,
  volume =       "1",
  pages =        "22--41",
  year =         "1973",
  bibdate =      "Tue Aug 28 06:06:57 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "In Polish.",
  acknowledgement = ack-nhfb,
  fjournal =     "Math. Stos.",
  keywords =     "accurate floating-point summation",
  remark =       "The author's name is correct [verified by a Polish
                 colleague who knows the author]: some references have
                 it incorrectly as Kie{\l}baszi{\'n}ski.",
}

@Article{Kinoshita:1973:GDS,
  author =       "E. Kinoshita and H. Kosako and Y. Kojima",
  title =        "General Division in the Symmetric Residue Number
                 System",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "2",
  pages =        "134--142",
  month =        feb,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264810;
                 https://doi.org/10.1109/T-C.1973.223674",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35073;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672267",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "In the residue number system, the arithmetic
                 operations of addition, subtraction, and multiplication
                 are executed in the same period of time without the
                 need for interpositional carry. There is a hope for
                 high-speed operation if residue arithmetic \ldots{}",
}

@Article{Kreifelts:1973:OBF,
  author =       "T. Kreifelts",
  title =        "{Optimale Basiswahl f{\"u}r eine
                 Gleitkomma-Arithmetik} \toenglish {Optimal Choice of
                 Basis for a Floating-Point Arithmetic} \endtoenglish",
  journal =      j-COMPUTING,
  volume =       "11",
  number =       "??",
  pages =        "353--363",
  month =        "????",
  year =         "1973",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Fri Sep 16 16:30:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Article{Kreifelts:1973:OBG,
  author =       "Thomas Kreifelts",
  title =        "{Optimale Basiswahl f{\"u}r eine
                 Gleitkomma-Arithmetik}. ({German}) [{Optimal} Choice of
                 Basis for a Floating-Point Arithmetic]",
  journal =      j-COMPUTING,
  volume =       "11",
  number =       "4",
  pages =        "353--363",
  month =        dec,
  year =         "1973",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Jan 2 17:40:51 MST 2001",
  bibsource =    "Compendex database;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 INSPEC Axiom database (1968--date)",
  note =         "See correction \cite{Kreifelts:1975:OBF}.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliation =  "Inst. Numerische Datenverarbeitung, Bonn, West
                 Germany",
  classification = "723; 921; C5230",
  description =  "digital arithmetic",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Comput (Vienna/NY)",
  keywords =     "base; computer programming; correct rounding; floating
                 point arithmetic; mathematical techniques; optimal
                 choice; rounding errors",
  language =     "German",
}

@Article{Kuki:1973:SSA,
  author =       "H. Kuki and W. J. Cody",
  title =        "A Statistical Study of the Accuracy of Floating Point
                 Number Systems",
  journal =      j-CACM,
  volume =       "16",
  number =       "4",
  pages =        "223--230",
  month =        apr,
  year =         "1973",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "68A20 (65G05)",
  MRnumber =     "51 2344",
  MRreviewer =   "I. Kaufmann",
  bibdate =      "Wed Aug 31 13:47:33 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper presents the statistical results of tests
                 of the accuracy of certain arithmetic systems in
                 evaluating sums, products and inner products, and
                 analytic error estimates for some of the computations.
                 The arithmetic systems studied are 6-digit hexadecimal
                 and 22-digit binary floating point number
                 representations combined with the usual chop and round
                 modes of arithmetic with various numbers of guard
                 digits, and with a modified round mode with guard
                 digits. In a certain sense, arithmetic systems
                 differing only in their use of binary or hexadecimal
                 number representations are shown to be approximately
                 statistically equivalent in accuracy. Further, the
                 usual round mode with guard digits is shown to be
                 statistically superior in accuracy to the usual chop
                 mode in all cases save one. The modified round mode is
                 found to be superior to the chop mode in all cases.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C5230 (Digital arithmetic methods)",
  classification = "723",
  corpsource =   "Univ. Chicago, IL, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  journalabr =   "Commun ACM",
  keywords =     "accuracy; arithmetic; computer programming; digital
                 arithmetic; error analysis; floating point arithmetic;
                 floating point number systems; guard digits; number
                 representation; rounding; statistical study",
  oldlabel =     "KukiC73",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/KukiC73",
}

@Article{Larson:1973:HSM,
  author =       "R. H. Larson",
  title =        "High Speed Multiply Using Four Input Carry Save
                 Adder",
  journal =      j-IBM-TDB,
  volume =       "??",
  number =       "??",
  pages =        "2053--2054",
  month =        dec,
  year =         "1973",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Fri Jun 24 20:46:32 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Technical Disclosure Bulletin",
}

@Article{Larson:1973:MSM,
  author =       "R. H. Larson",
  title =        "Medium Speed Multiply",
  journal =      j-IBM-TDB,
  volume =       "??",
  number =       "??",
  pages =        "2055--2055",
  month =        dec,
  year =         "1973",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Fri Jun 24 20:42:28 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Technical Disclosure Bulletin",
}

@PhdThesis{Lee:1973:SFP,
  author =       "Keng Ho Lee",
  title =        "Survey of floating-point software arithmetics and
                 basic library mathematical functions",
  type =         "Thesis ({Ph.D.})",
  school =       "Glasgow University",
  address =      "Glasgow, Scotland",
  year =         "1973",
  bibdate =      "Thu May 09 08:34:15 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Majithia:1973:NBL,
  author =       "J. C. Majithia and D. Levan",
  title =        "A note on base-2 logarithm computations",
  journal =      j-PROC-IEEE,
  volume =       "61",
  number =       "10",
  pages =        "1519--1520",
  month =        oct,
  year =         "1973",
  CODEN =        "IEEPAD",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Sat Jul 16 18:05:03 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
  summary =      "The well-known methods of iteration used suitably can
                 yield a more accurate and rapidly convergent
                 computation for the values of many functions. One
                 typical example is the base-2 logarithm-antilogarithm
                 computation. Some recently proposed techniques
                 \ldots{}",
}

@TechReport{Malcolm:1973:MIA,
  author =       "Michael A. Malcolm",
  title =        "A Machine Independent {ALGOL} Procedure for Accurate
                 Floating-Point Summation",
  type =         "Technical Report",
  number =       "STAN-CS-73-374 (AD-764 275)",
  institution =  inst-STAN-CS,
  address =      inst-STAN-CS:adr,
  pages =        "iii + 6",
  month =        jun,
  year =         "1973",
  bibdate =      "Fri Nov 21 14:21:14 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/stanford-cstr.bib",
  URL =          "https://apps.dtic.mil/sti/tr/pdf/AD0764275.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
  pdfpages =     "9",
  remark =       "This is an extract from the author's thesis.",
}

@PhdThesis{Malcolm:1973:PAF,
  author =       "Michael A. Malcolm",
  title =        "Part {I}: On accurate floating-point summation; Part
                 {II}: Computation of nonlinear spline functions",
  type =         "Thesis ({Ph.D.})",
  school =       "Department of Computer Science, Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "ix + 129",
  year =         "1973",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation; Interpolation;
                 spline theory",
}

@Article{Marasa:1973:SSC,
  author =       "John D. Marasa and David W. Matula",
  title =        "A simulated study of correlated error propagation in
                 various finite-precision arithmetics",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "587--597",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009111",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon May 20 05:07:23 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Marasa.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2",
}

@Article{Metropolis:1973:ABC,
  author =       "Nicholas C. Metropolis",
  title =        "Analyzed Binary Computing",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "573--576",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009109",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Mar 21 09:24:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  abstract =     "A single format for the representation of numbers in a
                 computer is proposed to accommodate both exact and
                 inexact quantities. A consistent set of rules is
                 described for addition (subtraction), multiplication,
                 and division of such quantities, both within their
                 separate types, as well as in combination. Error
                 correlation aside, the propagation of inherent errors
                 is monitored in operations with at least one imprecise
                 value. A definitive algorithm must, of course take into
                 account any correlations of inherent errors; these
                 correlations must be recognized and incorporated into
                 the algorithm by the numerical analyst, not by the
                 logical designer of the computer.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2; control of propagated errors; floating-point
                 representation; representation error; significant digit
                 arithmetic",
}

@Article{Metropolis:1973:SAC,
  author =       "N. Metropolis and Gian-Carlo Rota and S. Tanny",
  title =        "Significance arithmetic: the carrying algorithm",
  journal =      j-J-COMB-THEORY-A,
  volume =       "14",
  pages =        "386--421",
  month =        may,
  year =         "1973",
  CODEN =        "JCBTA7",
  ISSN =         "0097-3165 (print), 1096-0899 (electronic)",
  ISSN-L =       "0097-3165",
  MRclass =      "10A30 (02E10)",
  MRnumber =     "MR0321857 (48 \#222)",
  MRreviewer =   "R. L. Goodstein",
  bibdate =      "Thu Nov 8 14:50:22 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0259.00001",
  abstract =     "It has been remarked that, in mathematics, a
                 notational deficiency is often a symptom of conceptual
                 obscurity. The starting point of this work is one such
                 deficiency. In ordinary binary arithmetic, a number
                 ending in a string of ones, such as $ 0.0110111 \ldots
                 {} $ is equal to the number obtained by replacing the
                 digit zero next to the string of ones by the digit one,
                 and the string of succeeding ones by zeros; in the
                 example, $ 0.0111000 $",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Combinatorial Theory. Series A",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00973165",
}

@Article{Mifsud:1973:AMP,
  author =       "Charles J. Mifsud and Michael J. Bohlen",
  title =        "Addendum to a Multiple-Precision Division Algorithm",
  journal =      j-CACM,
  volume =       "16",
  number =       "10",
  pages =        "628--??",
  year =         "1973",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 07:04:18 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#MifsudB73;
                 https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Mifsud:1970:MDA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "MifsudB73",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/MifsudB73",
}

@Article{Newbery:1973:EAF,
  author =       "A. C. R. Newbery",
  title =        "Error Analysis for {Fourier} Series Evaluation",
  journal =      j-MATH-COMPUT,
  volume =       "27",
  number =       "123",
  pages =        "639--644",
  month =        jul,
  year =         "1973",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "B0290B (Error analysis in numerical methods); C4110
                 (Error analysis in numerical methods)",
  corpsource =   "Univ. Kentucky, Lexington, KY, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "error analysis; evaluation; floating point; Fourier
                 series evaluation; numerical methods; polynomials;
                 recursive method; series (mathematics); trigonometric
                 polynomials",
  treatment =    "T Theoretical or Mathematical",
}

@Article{OKeefe:1973:RBE,
  author =       "Kenneth H. O'Keefe and John L. Wright",
  title =        "Remarks on Base Extension for Modular Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "9",
  pages =        "833--835",
  month =        sep,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009173",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:31 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009173",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@MastersThesis{Parker:1973:DHF,
  author =       "Tony Edwin Parker",
  title =        "Design of a hardware floating point processor for the
                 {PDP-8s}",
  type =         "Thesis ({B.S.})",
  school =       "Massachusetts Institute of Technology. Dept. of
                 Electrical Engineering",
  address =      "Cambridge, MA, USA",
  pages =        "19",
  year =         "1973",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Paterson:1973:NNM,
  author =       "Michael S. Paterson and Larry J. Stockmeyer",
  title =        "On the Number of Nonscalar Multiplications Necessary
                 to Evaluate Polynomials",
  journal =      j-SIAM-J-COMPUT,
  volume =       "2",
  number =       "1",
  pages =        "60--66",
  month =        mar,
  year =         "1973",
  CODEN =        "SMJCAT",
  ISSN =         "0097-5397 (print), 1095-7111 (electronic)",
  ISSN-L =       "0097-5397",
  bibdate =      "Mon Nov 29 10:57:40 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/2/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Theory/Matrix.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Computing",
  journal-URL =  "http://epubs.siam.org/sicomp",
  kwds =         "na, polynomial, complexity",
  xxnote =       "Cited in \cite{govl:89}.",
}

@Article{Pittnauer:1973:AA,
  author =       "E. Pittnauer",
  title =        "{Eine Aussage {\"u}ber Alternanten} \toenglish {??}
                 \endtoenglish",
  journal =      j-NUM-MATH,
  volume =       "23",
  number =       "??",
  pages =        "427--432",
  month =        "????",
  year =         "1973",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Pittnauer:1973:NPK,
  author =       "E. Pittnauer",
  title =        "{Numerische Polynomapproximation mit Knotenpolynomen}
                 \toenglish {Numerical Polynomial Approximations with
                 Knot Polynomials} \endtoenglish",
  journal =      j-NUM-MATH,
  volume =       "21",
  number =       "3",
  pages =        "256--263",
  year =         "1973",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  xxmonth =      "(none)",
}

@Book{Randell:1973:ODC,
  editor =       "Brian Randell",
  title =        "The origins of digital computers: selected papers",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xvi + 464",
  year =         "1973",
  ISBN =         "0-387-06169-X, 3-540-06169-X",
  ISBN-13 =      "978-0-387-06169-6, 978-3-540-06169-4",
  LCCN =         "TK7888.3 .R36",
  bibdate =      "Wed Oct 13 09:24:25 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "See also later editions
                 \cite{Randell:1975:ODC,Randell:1982:ODC}.",
}

@Article{Richman:1973:VPE,
  author =       "Paul L. Richman",
  title =        "Variable-Precision Exponentiation",
  journal =      j-CACM,
  volume =       "16",
  number =       "1",
  pages =        "38--40",
  month =        jan,
  year =         "1973",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65D20",
  MRnumber =     "51 4631",
  MRreviewer =   "V. V. Ivanov",
  bibdate =      "Mon Jan 22 07:15:57 MST 2001",
  bibsource =    "Compendex database;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm16.html#Richman73;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A previous paper presented an efficient algorithm,
                 called the Recomputation Algorithm, for evaluating a
                 rational expression to within any desired tolerance on
                 a computer which performs variable-precision arithmetic
                 operations. The Recomputation Algorithm can be applied
                 to expressions involving any variable-precision
                 operations having $ O(10^( - p) + \sum_i|E_i|) $ error
                 bounds, where $p$ denotes the operation's precision and
                 $ E_i $ denotes the error in the operation's $i$-th
                 argument. \par

                 This paper presents an efficient variable-precision
                 exponential operation with an error bound of the above
                 order. Other operations such as log, sin, and cos,
                 which have simple series expansions, can be handled
                 similarly.",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  classification = "723; 921",
  corpsource =   "Bell Telephone Labs. Inc., Denver, CO, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  journalabr =   "Commun ACM",
  keywords =     "computer programming; digital arithmetic; error
                 analysis; exponential function; exponentiation;
                 interval arithmetic; mathematical programming; variable
                 precision; variable-precision",
  oldlabel =     "Richman73",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Richman73",
}

@Article{Robertson:1973:SIC,
  author =       "James E. Robertson and Kishor S. Trivedi",
  title =        "The status of investigations into computer hardware
                 design based on the use of continued fractions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "555--560",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009106",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Nov 8 14:50:24 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Robertson.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2; continued fractions",
}

@Article{Roy:1973:ARC,
  author =       "P. K. Sinha Roy and C. L. Sheng",
  title =        "Author's Reply to Comments on {``Decomposition Method
                 of Determining Maximum Compatibles''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "627--627",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009119",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 19:18:24 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See \cite{Sureshchander:1973:CDM}.",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Sureshchander.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2",
}

@MastersThesis{Rubinfield:1973:FM,
  author =       "Louis P. Rubinfield",
  title =        "A floating-point macromodule",
  type =         "Thesis ({M.S.})",
  school =       "Washington University, Department of Electrical
                 Engineering",
  address =      "St. Louis, MO, USA",
  pages =        "vii + 111",
  year =         "1973",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers --- Design and
                 construction.",
}

@Article{Sankar:1973:AAN,
  author =       "P. V. Sankar and S. Chakrabarti and E. V.
                 Krishnamurthy",
  title =        "Arithmetic Algorithms in a Negative Base",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "2",
  pages =        "120--125",
  month =        feb,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1973.223671",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:14 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672264",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "negative base",
}

@Article{Sankar:1973:DDA,
  author =       "P. V. Sankar and S. Chakrabarti and E. V.
                 Krishnamurthy",
  title =        "Deterministic Division Algorithm in a Negative Base",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "2",
  pages =        "125--128",
  month =        feb,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1973.223672",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:14 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672265",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "negative base",
}

@Article{Schatte:1973:VMG,
  author =       "Peter Schatte",
  title =        "{Zur Verteilung der Mantisse in der
                 Gleitkommadarstellung einer Zufallsgr{\"o}{\ss}e}.
                 ({German}) [Distribution of the mantissa in the
                 floating-point representation of a random variable]",
  journal =      j-Z-ANGE-MATH-MECH,
  volume =       "53",
  number =       "??",
  pages =        "553--565",
  month =        "????",
  year =         "1973",
  CODEN =        "ZAMMAX",
  ISSN =         "0044-2267 (print), 1521-4001 (electronic)",
  ISSN-L =       "0044-2267",
  bibdate =      "Mon Nov 14 16:35:28 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "{Zeitschrift f{\"u}r Angewandte Mathematik und
                 Mechanik}",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
  language =     "German",
}

@Article{Schmid:1973:BLIa,
  author =       "H. Schmid",
  title =        "{BCD} logic {I}: {BCD} -- logic of many uses",
  journal =      j-ELECTRONIC-DESIGN,
  volume =       "21",
  number =       "13",
  pages =        "90--95",
  month =        jun,
  year =         "1973",
  CODEN =        "ELODAW",
  ISSN =         "0013-4872 (print), 1944-9550 (electronic)",
  ISSN-L =       "0013-4872",
  bibdate =      "Thu Sep 08 08:17:30 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronic Design",
}

@Article{Schmid:1973:BLIb,
  author =       "H. Schmid",
  title =        "{BCD} logic {II}: {BCD} multiplication",
  journal =      j-ELECTRONIC-DESIGN,
  volume =       "21",
  number =       "14",
  pages =        "62--69",
  month =        jul,
  year =         "1973",
  CODEN =        "ELODAW",
  ISSN =         "0013-4872 (print), 1944-9550 (electronic)",
  ISSN-L =       "0013-4872",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronic Design",
}

@Article{Schmid:1973:BLIc,
  author =       "H. Schmid",
  title =        "{BCD} logic {III}: {BCD} division",
  journal =      j-ELECTRONIC-DESIGN,
  volume =       "21",
  number =       "15",
  pages =        "86--92",
  month =        jul,
  year =         "1973",
  CODEN =        "ELODAW",
  ISSN =         "0013-4872 (print), 1944-9550 (electronic)",
  ISSN-L =       "0013-4872",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronic Design",
}

@Article{Schmid:1973:BLId,
  author =       "H. Schmid",
  title =        "{BCD} logic {IV}: {BCD} decimal-point location",
  journal =      j-ELECTRONIC-DESIGN,
  volume =       "21",
  number =       "16",
  pages =        "80--84",
  month =        aug,
  year =         "1973",
  CODEN =        "ELODAW",
  ISSN =         "0013-4872 (print), 1944-9550 (electronic)",
  ISSN-L =       "0013-4872",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronic Design",
  keywords =     "decimal floating-point arithmetic",
}

@Article{Schmid:1973:BLVa,
  author =       "H. Schmid",
  title =        "{BCD} logic {V}: {BCD} square root",
  journal =      j-ELECTRONIC-DESIGN,
  volume =       "21",
  number =       "17",
  pages =        "62--69",
  month =        aug,
  year =         "1973",
  CODEN =        "ELODAW",
  ISSN =         "0013-4872 (print), 1944-9550 (electronic)",
  ISSN-L =       "0013-4872",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronic Design",
}

@Article{Schmid:1973:BLVb,
  author =       "H. Schmid",
  title =        "{BCD} logic {VI}: {BCD} logarithms and exponentials",
  journal =      j-ELECTRONIC-DESIGN,
  volume =       "21",
  number =       "18",
  pages =        "118--123",
  month =        sep,
  year =         "1973",
  CODEN =        "ELODAW",
  ISSN =         "0013-4872 (print), 1944-9550 (electronic)",
  ISSN-L =       "0013-4872",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronic Design",
}

@Article{Schmid:1973:BLVc,
  author =       "H. Schmid",
  title =        "{BCD} logic {VII}: {BCD} trig and hyperbolic
                 functions",
  journal =      j-ELECTRONIC-DESIGN,
  volume =       "21",
  number =       "19",
  pages =        "68--73",
  month =        sep,
  year =         "1973",
  CODEN =        "ELODAW",
  ISSN =         "0013-4872 (print), 1944-9550 (electronic)",
  ISSN-L =       "0013-4872",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronic Design",
}

@Article{Sentance:1973:FAB,
  author =       "W. A. Sentance",
  title =        "A Further Analysis of {Benford's Law}",
  journal =      j-FIB-QUART,
  volume =       "11",
  number =       "5",
  pages =        "490--494",
  month =        dec,
  year =         "1973",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 17:58:46 MDT 2011",
  bibsource =    "http://www.fq.math.ca/11-5.html;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.fq.math.ca/Scanned/11-5/sentance.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Shea:1973:NDN,
  author =       "Dale D. Shea",
  title =        "On the Number of Divisions Needed in Finding the
                 Greatest Common Divisor",
  journal =      j-FIB-QUART,
  volume =       "11",
  number =       "5",
  pages =        "508--510",
  month =        dec,
  year =         "1973",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 17:58:46 MDT 2011",
  bibsource =    "http://www.fq.math.ca/11-5.html;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.fq.math.ca/Scanned/11-5/shea.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Singh:1973:MOA,
  author =       "S. Singh and R. Waxman",
  title =        "Multiple Operand Addition and Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "2",
  pages =        "113--120",
  month =        feb,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1973.223670",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:14 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672263",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Sites:1973:FPS,
  author =       "Richard L. Sites",
  title =        "Floating point significance interrupt proposal",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "2",
  number =       "1",
  pages =        "10--12",
  month =        jan,
  year =         "1973",
  CODEN =        "CANED2",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Fri May 12 09:40:28 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The purpose of this proposal is to aid numerical
                 analysts in observing the significance of results in
                 floating-point calculations. This proposal is not a
                 cure-all, but it does attempt to a first, high-payoff
                 step in understanding and analyzing floating-point
                 algorithms. This proposal is specifically for IBM
                 360/370 architecture, but the ideas are applicable to
                 all machines.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
  remark =       "The author observes that register clearing by
                 subtraction is common, and is one of the reasons that
                 ``all IBM language processors execute with significance
                 masked off.'' He proposes suppressing the significance
                 interrupt in subtractions when both operands are
                 equal.",
}

@Article{Sjoding:1973:NVR,
  author =       "T. Sjoding",
  title =        "Noise variance for rounded two's complement product
                 quantization",
  journal =      j-IEEE-TRANS-AUDIO-ELECTROACOUST,
  volume =       "21",
  number =       "4",
  pages =        "378--380",
  month =        aug,
  year =         "1973",
  CODEN =        "ITADAS",
  ISSN =         "0018-9278 (print), 1558-2582 (electronic)",
  ISSN-L =       "0018-9278",
  bibdate =      "Sat Jul 16 11:25:03 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Audio and Electroacoustics",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8337",
  summary =      "The Halyo-McAlpine discrete model for product
                 quantization is reconstructed using an error variable
                 set having an even number of members. It is shown in
                 this case that the noise variance associated with a
                 continuous model becomes an upper rather \ldots{}",
}

@Article{Spira:1973:CTA,
  author =       "Philip M. Spira",
  title =        "Computation Times of Arithmetic and {Boolean}
                 functions in $ (d, r) $ circuits",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "552--555",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009105",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 19:18:24 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Spira.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2",
}

@Book{Stone:1973:DMS,
  author =       "Harold S. Stone",
  title =        "Discrete mathematical structures and their
                 applications",
  publisher =    "Science Research Associates",
  address =      "Chicago, IL, USA",
  pages =        "401",
  year =         "1973",
  LCCN =         "QA162 .S877d; QA162 .S77",
  bibdate =      "Fri Nov 9 19:24:02 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  series =       "The SRA computer science series",
  acknowledgement = ack-nhfb,
  subject =      "Algebra, Abstract; Group theory; Machine theory",
  tableofcontents = "Foundations of discrete mathematics \\
                 Groups \\
                 The P{\'o}lya theory of enumeration \\
                 Applications of group theory to computer design \\
                 Group codes \\
                 Semigroups \\
                 Finite-state machines \\
                 Rings and fields \\
                 Linear -finite-state machines \\
                 Boolean algebra with applications to computer design",
}

@Article{Sureshchander:1973:CDM,
  author =       "Sureshchander",
  title =        "Comments on {``Decomposition Method of Determining
                 Maximum Compatibles''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "627--627",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009118",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 19:18:24 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See \cite{Roy:1973:ARC}.",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Sureshchander.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2",
  xxnote =       "Author has only a single name",
}

@Article{Swartzlander:1973:QSM,
  author =       "E. E. {Swartzlander, Jr.}",
  title =        "The Quasi-Serial Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "4",
  pages =        "317--321",
  month =        apr,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1973.223717",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672310",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@PhdThesis{Tanny:1973:SSA,
  author =       "Stephen Michael Tanny",
  title =        "Studies in Significance Arithmetic",
  type =         "{Ph.D.} thesis",
  school =       "Massachusetts Institute of Technology",
  address =      "Cambridge, MA, USA",
  pages =        "195",
  year =         "1973",
  bibdate =      "Tue Oct 22 06:18:19 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://search.proquest.com/pqdtglobal/docview/302720894",
  acknowledgement = ack-nhfb,
  remark =       "Full text is not available in ProQuest.",
}

@Article{Urabe:1973:CEA,
  author =       "Minoru Urabe",
  title =        "Component-wise error analysis of iterative methods
                 practiced on a floating-point system",
  journal =      j-MEM-FAC-SCI-KYUSHU-UNIV-A,
  volume =       "27",
  pages =        "23--64",
  year =         "1973",
  CODEN =        "MFKAAF",
  ISSN =         "0373-6385 (print), 1883-2172 (electronic)",
  ISSN-L =       "0373-6385",
  MRclass =      "65H10",
  MRnumber =     "48 1457",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Memoirs of the Faculty of Science, Kyushu Imperial
                 University. Series A, Mathematics = Kyushu Teikoku
                 Daigaku Rigakubu kiyo",
  reviewer =     "D. C. Handscomb",
}

@Misc{Walther:1973:EFP,
  author =       "J. S. Walther",
  title =        "Elementary Floating Point {CORDIC} Function Processor
                 and Shifter",
  howpublished = "US Patent 3,766,370.",
  day =          "16",
  month =        oct,
  year =         "1973",
  bibdate =      "Wed Oct 29 05:59:20 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Filed 14 May 1971.",
  URL =          "https://patentimages.storage.googleapis.com/30/7f/a0/1201036cf71cea/US3766370.pdf",
  acknowledgement = ack-nhfb,
  pagecount =    "271",
  remark =       "See the quotation in remark-3 in entry
                 Walther:2000:SUC about the significance of this patent
                 for the computing industry.",
}

@PhdThesis{Wiatrowski:1973:DFP,
  author =       "Claude A. Wiatrowski",
  title =        "Design of a floating-point processor for digital
                 simulation",
  type =         "Thesis ({Ph.D.} - Electrical Engineering)",
  school =       "University of Arizona",
  address =      "Tucson, AZ, USA",
  pages =        "107",
  year =         "1973",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic and logic units.; Computer storage
                 devices.",
}

@Article{Yau:1973:ECR,
  author =       "S. S.-S. Yau and Yu-Cheng Liu",
  title =        "Error Correction in Redundant Residue Number Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "1",
  pages =        "5--11",
  month =        jan,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264810;
                 https://doi.org/10.1109/T-C.1973.223594",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:11 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35069;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672187",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Two error-correcting algorithms for redundant residue
                 number systems are presented, one for single
                 residue-error correction and the other for burst
                 residue-error correction. Neither algorithm requires
                 table lookup, and hence their implementation \ldots{}",
}

@TechReport{Yohe:1973:FFPa,
  author =       "J. Michael Yohe",
  title =        "Foundations of floating point computer arithmetic",
  type =         "{MRC} Technical Summary Report",
  number =       "1302",
  institution =  inst-MRC-WISCONSIN,
  address =      inst-MRC-WISCONSIN:adr,
  pages =        "25",
  month =        jan,
  year =         "1973",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A formal structure, within which computer arithmetic
                 operations may be defined, is described. Several
                 floating point arithmetic schemes are defined within
                 this context. The structure described in the paper
                 includes, as a sub-structure, the significance spaces
                 of Matula.",
  acknowledgement = ack-nhfb,
  keywords =     "Computers.; Floating-point arithmetic.",
  remark =       "January 1973. Sponsored by Army Research Office,
                 Durham, NC, USA.",
}

@Article{Yohe:1973:IBS,
  author =       "J. Michael Yohe",
  title =        "Interval Bounds for Square Roots and Cube Roots",
  journal =      j-COMPUTING,
  volume =       "11",
  number =       "1",
  pages =        "51--57",
  month =        mar,
  year =         "1973",
  CODEN =        "CMPTA2",
  DOI =          "http://link.springer.com/journal/607",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Jan 2 17:40:51 MST 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 INSPEC Axiom database (1968--date)",
  acknowledgement = ack-jr # " and " # ack-nhfb,
  affiliation =  "Univ. Wisconsin, Madison, WI, USA",
  classification = "C5230",
  description =  "digital arithmetic; error analysis",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "binary computers; cube roots; error analysis; interval
                 bounds; machine representable number; optimal upward
                 directed rounding; smallest machine representable
                 interval; square roots",
}

@Article{Yohe:1973:RFP,
  author =       "J. Michael Yohe",
  title =        "Roundings in Floating-Point Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "6",
  pages =        "577--586",
  month =        jun,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009110",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:25 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith2/papers/ARITH2_Yohe.pdf;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009110",
  abstract =     "In this paper we discuss directed roundings and
                 indicate how hardware might be designed to produce
                 proper upward directed, downward directed, and certain
                 commonly used symmetric roundings. Algorithms for the
                 four binary arithmetic operations and for rounding are
                 presented, together with proofs of their correctness;
                 appropriate formulas for a priori error analysis of
                 these algorithms are presented. Some of the basic
                 applications of directed roundings are surveyed.",
  acknowledgement = ack-jr # "\slash " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-2; correct rounding; floating-point arithmetic",
  remark-1 =     "This is an early paper that formalizes the handling of
                 rounding, and calls for four rounding modes: to
                 +Infinity, to -Infinity, to zero, and to nearest
                 (except that in case of a tie, to the larger
                 magnitude). It builds on previous work
                 \cite{Kulisch:1969:AAR,Kulisch:1971:AAR}.",
  remark-2 =     "From page 586, column 1: ``The rounding [to nearest]
                 has applications in almost every computation using
                 floating-point arithmetic. It is this rounding that we
                 expect to get, and (usually erroneously) assume we do
                 get, from a piece of equipment costing several million
                 dollars.''",
}

@Book{Zacher:1973:HDG,
  author =       "H. J. Zacher",
  title =        "{Die Hauptschriften zur Dyadik von G. W. Leibniz: Ein
                 Beitr. zur Geschichte des bin{\"a}ren Zahlen-systems}.
                 ({German}) [{The} main writings on the dyadic by {G. W.
                 Leibniz}: a contribution to the history of the binary
                 number system]",
  publisher =    "V. Klostermann",
  address =      "Frankfurt am Main, West Germany",
  pages =        "viii + 384",
  year =         "1973",
  LCCN =         "QA141.4.Z3; QA141.4.Z3 1973",
  bibdate =      "Fri Mar 17 09:19:21 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Ver{\"o}ffentlichungen des Leibniz-Archivs",
  acknowledgement = ack-nhfb,
  language =     "German",
  remark =       "Selected original texts and correspondence in French,
                 German or Latin.",
  subject =      "Leibniz, Gottfried Wilhelm; Freiherr von; Yi jing;
                 Freiherr von,; Binary system (Mathematics); History;
                 Sources; Syst{\'e}me binaire (Math{\'e}matiques);
                 Histoire; Binary system (Mathematics)",
}

@Article{Zohar:1973:DCR,
  author =       "Shalhav Zohar",
  title =        "{A/D} Conversion for Radix ($ - 2$)",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-22",
  number =       "7",
  pages =        "698--701",
  month =        jul,
  year =         "1973",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1973.5009137",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 16:45:28 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009137",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "negative base",
}

@Article{Agrawal:1974:NCL,
  author =       "D. P. Agrawal",
  title =        "Negabinary carry-look-ahead adder and fast
                 multiplier",
  journal =      j-ELECT-LETTERS,
  volume =       "10",
  number =       "??",
  pages =        "312--313",
  month =        jul,
  year =         "1974",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Thu Nov 06 06:16:38 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "negative base",
}

@Article{Banerji:1974:NIM,
  author =       "D. K. Banerji",
  title =        "A Novel Implementation Method for Addition and
                 Subtraction in Residue Number Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-23",
  number =       "1",
  pages =        "106--109",
  month =        jan,
  year =         "1974",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264810;
                 https://doi.org/10.1109/T-C.1974.223790",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 11:27:29 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35077;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672383",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "This correspondence describes an implementation scheme
                 for the operations of addition and subtraction in the
                 residue number systems. The method is based on the
                 property that the set of residues modulo m form a
                 finite group under addition and \ldots{}",
}

@Article{Banerji:1974:URA,
  author =       "D. K. Banerji",
  title =        "On the Use of Residue Arithmetic for Computation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-23",
  number =       "12",
  pages =        "1315--1317",
  month =        dec,
  year =         "1974",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1974.223855",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 11:27:38 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672448",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Barsi:1974:EDC,
  author =       "F. Barsi and P. Maestrini",
  title =        "Error Detection and Correction by Product Codes in
                 Residue Number Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-23",
  number =       "9",
  pages =        "915--924",
  month =        sep,
  year =         "1974",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264810;
                 https://doi.org/10.1109/T-C.1974.224055",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 11:27:35 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35088;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672648",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The arithmetic error detecting and correcting
                 capabilities of product (AN) codes in residue number
                 systems (RNS) are described. The redundancy necessary
                 and sufficient to allow single residue digit error
                 detection or correction is determined, under \ldots{}",
}

@Article{Bauer:1974:CGR,
  author =       "F. L. Bauer",
  title =        "Computational Graphs and Rounding Error",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "11",
  number =       "1",
  pages =        "87--96",
  month =        mar,
  year =         "1974",
  CODEN =        "SJNAAM",
  DOI =          "https://doi.org/10.1137/0711010",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65G05",
  MRnumber =     "356482",
  MRreviewer =   "L. B. Rall",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/bauer-friedrich-ludwig.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
                 JSTOR database; Theory/auto.diff.bib",
  note =         "In memoriam George Forsythe.",
  URL =          "https://www.jstor.org/stable/2156433",
  ZMID =         "03527739",
  ZMnumber =     "0337.65028",
  acknowledgement = ack-nhfb,
  author-dates = "Friedrich (``Fritz'') Ludwig Bauer (10 June 1924--26
                 March 2015)",
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
  referred =     "[Char91a]; [Irim91a].",
}

@Article{Blankenship:1974:CTC,
  author =       "P. E. Blankenship",
  title =        "Comments on {``A Two's Complement Parallel Array
                 Multiplication Algorithm''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-23",
  number =       "12",
  pages =        "1327--1327",
  month =        dec,
  year =         "1974",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1974.223862",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 11:27:38 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See \cite{Baugh:1973:TCP,Kroft:1974:CTC}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672455",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Boyes:1974:BNS,
  author =       "J. D. Boyes",
  title =        "Binary Noise Sources Incorporating Modulo-{$N$}
                 Dividers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-23",
  number =       "5",
  pages =        "550--552",
  month =        may,
  year =         "1974",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1974.223980",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 11:27:33 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672573",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Brent:1974:FEP,
  author =       "Barry Brent",
  title =        "Functional Equations with Prime Roots from Arithmetic
                 Expressions for {$ G_\alpha $}",
  journal =      j-FIB-QUART,
  volume =       "12",
  number =       "2",
  pages =        "199--207",
  month =        apr,
  year =         "1974",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 17:58:50 MDT 2011",
  bibsource =    "http://www.fq.math.ca/12-2.html;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.fq.math.ca/Scanned/12-2/brent1.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Brown:1974:BDE,
  author =       "D. A. H. Brown",
  title =        "Biquinary Decimal Error Detection Codes with One, Two
                 and Three Check Digits",
  journal =      j-COMP-J,
  volume =       "17",
  number =       "3",
  pages =        "201--204",
  month =        aug,
  year =         "1974",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "Compendex database;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/tiff/201.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/tiff/202.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/tiff/203.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_03/tiff/204.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  classification = "722; 723",
  corpsource =   "Royal Radar Establ., Malvern, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "biquinary decimal error detection codes; check digits;
                 computer systems, digital; computers --- Debugging;
                 decimal floating-point arithmetic; digital arithmetic;
                 error detection codes; polynomial coding",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Brown:1974:SEC,
  author =       "D. A. H. Brown",
  title =        "Some Error Correcting Codes for Certain Transposition
                 and Transcription Errors in Decimal Integers",
  journal =      j-COMP-J,
  volume =       "17",
  number =       "1",
  pages =        "9--12",
  month =        feb,
  year =         "1974",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Nov 28 16:12:29 2003",
  bibsource =    "Compendex database;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/tiff/10.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/tiff/11.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/tiff/12.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_17/Issue_01/tiff/9.tif",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods); C6130 (Data
                 handling techniques)",
  classification = "731",
  corpsource =   "Royal Radar Establ., Malvern, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "algorithm; block; codes, symbolic; cyclic; decimal
                 floating-point arithmetic; decimal integers; digital
                 arithmetic; error correcting codes; error correction
                 codes; modulus 11; transcription; transposition",
  treatment =    "P Practical",
}

@Article{Carta:1974:HLR,
  author =       "David G. Carta",
  title =        "Help!!: {The} Lost Reference: ({A} Modified {Newton}
                 Method for Square Roots)",
  journal =      j-SIGNUM,
  volume =       "9",
  number =       "4",
  pages =        "9--9",
  month =        oct,
  year =         "1974",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/1206085.1206086",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Jun 17 18:47:00 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Around 1970 I saw a journal article describing a
                 modified Newton iteration for square roots. It involved
                 changing the usual factor of 0.5 in $ x_{n + 1} = 0.5
                 (x_n + a / x_n) $ to $ c_n $ where $ c_n \rightarrow
                 0.5 $, thereby increasing the asymptotic rate of
                 convergence from $ e_{n + 1} = 0.5 e_n^2 $ to $ e_{n +
                 1} = 0.25 e_n^2 $.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}

@Article{Catlin:1974:MR,
  author =       "Paul A. Catlin",
  title =        "On the Multiplication of Recurrences",
  journal =      j-FIB-QUART,
  volume =       "12",
  number =       "4",
  pages =        "365--367",
  month =        dec,
  year =         "1974",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 17:58:54 MDT 2011",
  bibsource =    "http://www.fq.math.ca/12-4.html;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.fq.math.ca/Scanned/12-4/catlin2.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Chakrabarti:1974:DCA,
  author =       "S. Chakrabarti",
  title =        "Divide-and-Correct Algorithm for Division in a
                 Negative Base",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-23",
  number =       "9",
  pages =        "981--983",
  month =        sep,
  year =         "1974",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1974.224066",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 11:27:35 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672659",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Chan:1974:REM,
  author =       "O. Chan and E. Jury",
  title =        "Roundoff error in multidimensional generalized
                 discrete transforms",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "21",
  number =       "1",
  pages =        "100--108",
  month =        jan,
  year =         "1974",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "The analysis of rounding error in the one-dimensional
                 fast Fourier transform (FFT) is extended to a class of
                 generalized orthogonal transforms [1] with a common
                 fast algorithm similar to the FFT algorithm. This class
                 includes the BInary FOurier \ldots{}",
}

@Book{Dahlquist:1974:NM,
  author =       "Germund Dahlquist and {\AA}ke Bj{\"o}rck and Ned
                 Anderson",
  title =        "Numerical Methods",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xviii + 573",
  year =         "1974",
  ISBN =         "0-13-627315-7",
  ISBN-13 =      "978-0-13-627315-8",
  LCCN =         "QA297 .D131 1969",
  bibdate =      "Tue Dec 14 22:44:59 1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  note =         "Translated by Ned Anderson.",
  series =       "Prentice-Hall Series in Automatic Computation",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "1: Some General Principles of Numerical
                 Calculation / 1 \\
                 2: How to Obtain and Estimate Accuracy in Numerical
                 Calculations / 21 \\
                 3: Numerical Uses of Series / 60 \\
                 4: Approximation of Functions / 81 \\
                 5: Numerical Linear Algebra / 137 \\
                 6: Nonlinear Equations / 218 \\
                 7: Finite Differences with Applications to Numerical
                 Integration, Differentiation, and Interpolation / 255
                 \\
                 8: Differential Equations / 330 \\
                 9: Fourier Methods / 405 \\
                 10: Optimization / 422 \\
                 11: The Monte Carlo Method and Simulation / 448 \\
                 12: Solutions to Problems / 465 \\
                 13: Bibliography and Published Algorithms / 536 \\
                 Index by Subject to Algorithms, 1960--1970 / 548 \\
                 Appendix Tables / 563 \\
                 Index / 565",
  tableofcontents = "Preface / xvii \\
                 Conventions / xix \\
                 1: Some General Principles of Numerical Calculation / 1
                 \\
                 1.1. Introduction / 1 \\
                 1.2. Some Common Ideas and Concepts in Numerical
                 Methods / 2 \\
                 1.3. Numerical Problems and Algorithms / 13 \\
                 1.3.1. Definitions / 13 \\
                 1.3.2. Recursive Formulas; Homer's Rule / 14 \\
                 1.3.3. An Example of Numerical Instability / 16 \\
                 2: How to Obtain and Estimate Accuracy in Numerical
                 Calculations / 21 \\
                 2.1. Basic Concepts in Error Estimation / 21 \\
                 2.1.1. Introduction / 21 \\
                 2.1.2. Sources of Error / 22 \\
                 2.1.3. Absolute and Relative Errors / 23 \\
                 2.1.4. Rounding and Chopping / 24 \\
                 2.2 Propagation of Errors / 26 \\
                 2.2.1. Simple Examples of Error Analysis / 26 \\
                 2.2.2. The General Formula for Error Propagation;
                 Maximum Error and Standard Error / 29 \\
                 2.2.3. On the Practical Application of Error Estimation
                 / 34 \\
                 2.2.4. The Use of Experimental Perturbations / 36 \\
                 2.2.5. Automatic Control of Accuracy / 37 \\
                 2.3. Number Systems; Floating and Fixed Representation
                 / 42 \\
                 2.3.1. The Position System / 42 \\
                 2.3.2. Floating and Fixed Representation / 43 \\
                 2.3.3. Floating Decimal Point / 44 \\
                 2.3.4. Fixed Decimal Point / 46 \\
                 2.3.5. Round-off Errors in Computation with Floating
                 Arithmetic Operations / 46 \\
                 2.4. Backward Error Analysis; Condition Numbers / 51
                 \\
                 2.4.1. Backward Error Analysis / 51 \\
                 2.4.2. Condition Numbers for Problems and Algorithms /
                 53 \\
                 2.4.3. Geometrical Illustration of Error Analysis / 56
                 \\
                 3: Numerical Uses of Series / 60 \\
                 3.1. Elementary Uses of Series / 60 \\
                 3.1.1. Simple Examples / 60 \\
                 3.1.2. Estimating the Remainder / 62 \\
                 3.1.3. Power Series / 65 \\
                 3.2. Acceleration of Convergence / 71 \\
                 3.2.1. Slowly Converging Alternating Series / 71 \\
                 3.2.2. Slowly Converging Series with Positive Terms /
                 73 \\
                 3.2.3. Other Simple Ways to Accelerate Convergence / 74
                 \\
                 3.2.4. Ill-Conditioned Series / 75 \\
                 3.2.5. Numerical Use of Divergent Series / 77 \\
                 4: Approximation of Functions / 81 \\
                 4.1. Basic Concepts in Approximation / 81 \\
                 4.1.1. Introduction / 81 \\
                 4.1.2. The Idea of a Function Space / 84 \\
                 4.1.3. Norms and Seminorms / 85 \\
                 4.1.4. Approximation of Functions as a Geometric
                 Problem in Function Space / 87 \\
                 4.2. The Approximation of Functions by the Method of
                 Least Squares / 88 \\
                 4.2.t. Statement of the Problems / 88 \\
                 4.2.2. Orthogonal Systems / 89 \\
                 4.2.3. Solution of the Approximation Problem / 92 \\
                 4.3. Polynomials / 97 \\
                 4.3.1. Basic Terminology; the Weierstrass Approximation
                 Theorem / 97 \\
                 4.3.2. Triangle Families of Polynomials / 98 \\
                 4.3.3. A Triangle Family and Its Application to
                 Interpolation / 99 \\
                 4.3.4. Equidistant Interpolation and the Runge
                 Phenomenon / 101 \\
                 4.4. Orthogonal Polynomials and Applications / 104 \\
                 4.4.1. Tchebycheff Polynomials / 104 \\
                 4.4.2. Tchebycheff Interpolation and Smoothing / 106
                 \\
                 4.4.3. General Theory of Orthogonal Polynomials / 108
                 \\
                 4.4.4. Legendre Polynomials and Gram Polynomials / 113
                 \\
                 4.5. Complementary Observations on Polynomial
                 Approximation / 117 \\
                 4.5.1. Summary of the Use of Polynomials / 117 \\
                 4.5.2. Some Inequalities for $E_n(f)$ with Applications
                 to the Computation of Linear Functionals / 120 \\
                 4.5.3. Approximation in the Maximum Norm / 124 \\
                 4.5.4. Economization of Power Series; Standard
                 Functions / 125 \\
                 4.5.5. Some Statistical Aspects of the Method of Least
                 Squares / 126 \\
                 4.6. Spline Functions / 131 \\
                 5: Numerical Linear Algebra / 137 \\
                 5,1. Introduction / 137 \\
                 5.2. Basic Concepts of Linear Algebra / 138 \\
                 5.2.1. Fundamental Definitions / 138 \\
                 5.2.2. Partitioned Matrices / 140 \\
                 5.2.3. Linear Vector Spaces / 141 \\
                 5.2.4. Eigenvalues and Similarity Transformations / 142
                 \\
                 5.2.5. Singular-Value Decomposition and Pseudo-Inverse
                 / 143 \\
                 5.3. Direct Methods for Solving Systems of Linear
                 Equations / 146 \\
                 5.3.1. Triangular Systems / 146 \\
                 5.3.2. Gaussian Elimination / 147 \\
                 5.3.3. Pivoting Strategies / 150 \\
                 5.3.4. $L U$-Decomposition / 152 \\
                 5.3.5. Compact Schemes for Gaussian Elimination / 157
                 \\
                 5.3.6. Inverse Matrices / 159 \\
                 5.4. Special Matrices / 162 \\
                 5.4.1. Symmetric Positive-Definite Matrices / 162 \\
                 5.4.2. Band Matrices / 165 \\
                 5.4.3. Large-Scale Linear Systems / 168 \\
                 5.4.4. Other Sparse Matrices / 169 \\
                 5.5. Error Analysis for Linear Systems / 174 \\
                 5.5.1. An Ill-Conditioned Example / 174 \\
                 5.5.2. Vector and Matrix Norms / 175 \\
                 5.5.3. Perturbation Analysis / 176 \\
                 5.5.4. Rounding Errors in Gaussian Elimination / 177
                 \\
                 5.5.5. Scaling of Linear Systems / 181 \\
                 5.5.6. Iterative Improvement of a Solution / 183 \\
                 5.6. Iterative Methods / 188 \\
                 5.7. Overdetermined Linear Systems / 196 \\
                 5.7.1. The Normal Equations / 197 \\
                 5.7.2. Orthogonalization Methods / 201 \\
                 5.7.3. Improvement of Least-Squares Solutions / 204 \\
                 5.7.4. Least-Squares Problems with Linear Constraints /
                 205 \\
                 5.8. Computation of Eigenvalues and Eigenvectors / 208
                 \\
                 5.8.1. The Power Method / 209 \\
                 5.8.2. Methods Based on Similarity Transformations /
                 211 \\
                 5.8.3. Eigenvalues by Equation Solving / 215 \\
                 5.8.4. The $Q R$-Algorithm / 216 \\
                 6: Nonlinear Equations / 218 \\
                 6.1. Introduction / 218 \\
                 6.2. Initial Approximations; Starting Methods / 219 \\
                 6.2.1. Introduction / 219 \\
                 6.2.2. The Bisection Method / 220 \\
                 6.3. Newton--Raphson's Method / 222 \\
                 6.4. The Secant Method / 227 \\
                 6.4.1. Description of the Method / 227 \\
                 6.4.2. Error Analysis for the Secant Method / 228 \\
                 6.4.3. Regula Falsi / 230 \\
                 6.4.4. Other Related Methods / 230 \\
                 6.5. General Theory of Iteration Methods / 233 \\
                 6.6. Error Estimation and Attainable Accuracy in
                 Iteration Methods / 238 \\
                 6.6.1. Error Estimation / 238 \\
                 6.6.2. Attainable Accuracy; Termination Criteria / 240
                 \\
                 6.7. Multiple Roots / 242 \\
                 6.8. Algebraic Equations / 243 \\
                 6.8.1. Introduction / 243 \\
                 6.8.2. Deflation / 245 \\
                 6.8.3. Ill-Conditioned Algebraic Equations / 246 \\
                 6.9. Systems of Nonlinear Equations / 248 \\
                 6.9.1. Iteration / 249 \\
                 6.9.2. Newton--Raphson's Method and Some Modifications
                 / 249 \\
                 6.9.3. Other Methods / 251 \\
                 7: Finite Differences with Applications to Numerical
                 Integration, Differentiation, and Interpolation / 255
                 \\
                 7.1. Difference Operators and Their Simplest Properties
                 / 255 \\
                 7.2. Simple Methods for Deriving Approximation Formulas
                 and Error Estimates / 263 \\
                 7.2.1. Statement of the Problems and Some Typical
                 Examples / 263 \\
                 7.2.2, Repeated Richardson Extrapolation / 269 \\
                 7.3. Interpolation / 275 \\
                 7.3.1. Introduction / 275 \\
                 7.3.2. When is Linear Interpolation Sufficient? / 276
                 \\
                 7.3.3. Newton's General Interpolation Formula / 277 \\
                 7.3.4. Formulas for Equidistant Interpolation / 279 \\
                 7.3.5. Complementary Remarks on Interpolation / 282 \\
                 7.3.6. Lagrange's Interpolation Formula / 284 \\
                 7.3.7. Hermite Interpolation / 285 \\
                 7.3.8. Inverse Interpolation / 286 \\
                 7.4. Numerical Integration / 290 \\
                 7.4.1. The Rectangle Rule, Trapezoidal Rule, and
                 Romberg's Method / 291 \\
                 7.4.2. The Truncation Error of the Trapezoidal Rule /
                 293 \\
                 7.4.3. Some Difficulties and Possibilities in Numerical
                 Integration / 294 \\
                 7.4.4. The Euler--Maclaurin Summation Formula / 297 \\
                 7.4.5. Uses of the Euler--Maclaurin Formula / 300 \\
                 7.4.6. Other Methods for Numerical Integration / 302
                 \\
                 7.5. Numerical Differentiation / 307 \\
                 7.6. The Calculus of Operators / 311 \\
                 7.6.1. Operator Algebra / 311 \\
                 7.6.2. Operator Series with Applications / 312 \\
                 7.7. Functions of Several Variables / 318 \\
                 7.7.1. Working with One Variable at a Time / 319 \\
                 7.7.2. Rectangular Grids / 319 \\
                 7.7.3. Irregular Triangular Grids / 322 \\
                 8: Differential Equations / 330 \\
                 8.1. Theoretical Background / 330 \\
                 8.1.1. Initial-Value Problems for Ordinary Differential
                 Equations / 330 \\
                 8.1.2. Error Propagation / 333 \\
                 8.1.3. Other Differential Equation Problems / 337 \\
                 8.2. Euler's Method, with Repeated Richardson
                 Extrapolation / 338 \\
                 8.3. Other Methods for Initial-Value Problems in
                 Ordinary Differential Equations / 342 \\
                 8.3.1. The Modified Midpoint Method / 342 \\
                 8.3.2. The Power-Series Method / 345 \\
                 8.3.3. Runge--Kutta Methods / 346 \\
                 8.3.4. Implicit Methods / 347 \\
                 8.3.5. Stiff Problems / 349 \\
                 8.3.6. Control of Step Size / 350 \\
                 8.3.7. A Finite-Difference Method for a Second-Order
                 Equation / 352 \\
                 8.4. Orientation on Boundary and Eigenvalue Problems
                 for Ordinary Differential Equations / 359 \\
                 8.4.1. Introduction / 359 \\
                 8.4.2. The Shooting Method / 359 \\
                 8.4.3. The Band Matrix Method / 361 \\
                 8.4.4. Numerical Example of an Eigenvalue Problem / 363
                 \\
                 8.5. Difference Equations / 367 \\
                 8.5.1. Homogeneous Linear Difference Equations with
                 Constant Coefficients / 368 \\
                 8.5.2. General Linear Difference Equations / 370 \\
                 8.5.3. Analysis of a Numerical Method with the Help of
                 a Test Problem / 372 \\
                 8.5.4. Linear Multistep Methods / 375 \\
                 8.6. Partial Differential Equations / 383 \\
                 8.6.1. Introduction / 383 \\
                 8.6.2. An Example of an Initial-Value Problem / 384 \\
                 8.6.3. An Example of a Boundary-Value Problem / 389 \\
                 8.6.4. Methods of Undetermined Coefficients and
                 Variational Methods / 392 \\
                 8.6.5. Finite-Element Methods / 395 \\
                 8.6.6. Integral Equations / 397 \\
                 9: Fourier Methods / 405 \\
                 9.1. Introduction / 405 \\
                 9.2. Basic Formulas and Theorems in Fourier Analysis /
                 406 \\
                 9.2.1. Functions of One Variable / 406 \\
                 9.2.2. Functions of Several Variables / 411 \\
                 9.3. Fast Fourier Analysis / 413 \\
                 9.3.1. An Important Special Case / 413 \\
                 9.3.2. Fast Fourier Analysis, General Case / 414 \\
                 9.4. Periodic Continuation of a Nonperiodic Function /
                 417 \\
                 9.5. The Fourier Integral Theorem / 419 \\
                 10: Optimization / 422 \\
                 10.1. Statement of the Problem, Definitions, and Normal
                 Form / 422 \\
                 10.2. The Simplex Method / 426 \\
                 10.3. Duality / 435 \\
                 10.4. The Transportation Problem and Some Other
                 Optimization Problems / 436 \\
                 10.5. Nonlinear Optimization Problems / 438 \\
                 10.5.1. Basic Concepts and Introductory Examples / 438
                 \\
                 10.5.2. Line Search / 440 \\
                 10.5.3. Algorithms for Unconstrained Optimization / 441
                 \\
                 10.5.4. Overdetermined Nonlinear Systems / 443 \\
                 10.5.5. Constrained Optimization / 444 \\
                 11: The Monte Carlo Method and Simulation / 448 \\
                 11.1. Introduction / 448 \\
                 11.2. Random Digits and Random Numbers / 449 \\
                 11.3. Applications; Reduction of Variance / 455 \\
                 11.4. Pseudorandom Numbers / 463 \\
                 12: Solutions to Problems / 465 \\
                 13: Bibliography and Published Algorithms / 536 \\
                 13.1. Introduction / 536 \\
                 13.2. General Literature in Numerical Analysis / 536
                 \\
                 13.3. Tables, Collections of Formulas, and Problems /
                 539 \\
                 13.4. Error Analysis and Approximation of Functions /
                 540 \\
                 13.5. Linear Algebra and Nonlinear Systems of Equations
                 / 541 \\
                 13.6. Interpolation, Numerical Integration, and
                 Numerical Treatment of Differential Equations / 543 \\
                 13.7. Optimization; Simulation / 545 \\
                 13.8. Reviews, Abstracts and Other Periodicals / 547
                 \\
                 13.9. Survey of Published Algorithms / 548 \\
                 Index by Subject to Algorithms, 1960--1970 / 548 \\
                 Appendix Tables / 563 \\
                 Index / 565",
}

@Article{Davis:1974:USN,
  author =       "R. L. Davis",
  title =        "Uniform Shift Networks",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "3",
  pages =        "317--322",
  month =        mar,
  year =         "1974",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224214",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 10:48:43 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Fateman:1974:PMP,
  author =       "Richard J. Fateman",
  title =        "Polynomial Multiplication, Powers, and asymptotic
                 Analysis: {Some} Comments",
  journal =      j-SIAM-J-COMPUT,
  volume =       "3",
  number =       "3",
  pages =        "196--213",
  month =        "????",
  year =         "1974",
  CODEN =        "SMJCAT",
  ISSN =         "0097-5397 (print), 1095-7111 (electronic)",
  ISSN-L =       "0097-5397",
  bibdate =      "Mon Nov 29 10:57:57 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/3/3;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Theory/auto.diff.bib; Theory/Comp.Alg.1.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Computing",
  journal-URL =  "http://epubs.siam.org/sicomp",
  referred =     "[Bren78a].",
}

@Article{Fettweis:1974:PFP,
  author =       "A. Fettweis",
  title =        "On properties of floating-point roundoff noise",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "22",
  number =       "2",
  pages =        "149--151",
  month =        apr,
  year =         "1974",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  summary =      "The probability density and related properties of the
                 relative error due to rounding after floating-point
                 arithmetic operations can be computed from the
                 distributions of the mantissa and its absolute error.
                 Various results obtained, in particular, \ldots{}",
}

@Article{Fischer:1974:FLI,
  author =       "Michael J. Fischer and Larry J. Stockmeyer",
  title =        "Fast on-line integer multiplication",
  journal =      j-J-COMP-SYS-SCI,
  volume =       "9",
  number =       "3",
  pages =        "317--331",
  month =        dec,
  year =         "1974",
  CODEN =        "JCSSBM",
  DOI =          "https://doi.org/10.1016/S0022-0000(74)80047-4",
  ISSN =         "0022-0000 (print), 1090-2724 (electronic)",
  ISSN-L =       "0022-0000",
  bibdate =      "Tue Jan 29 15:25:28 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcompsyssci.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022000074800474",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computer and System Sciences",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00220000",
}

@MastersThesis{Fischer:1974:FPP,
  author =       "David Michael Fischer",
  title =        "Floating point processor for teleoperator studies",
  type =         "Thesis ({M.S.})",
  school =       "Massachusetts Institute of Technology. Dept. of
                 Mechanical Engineering",
  address =      "Cambridge, MA, USA",
  pages =        "35 + 14",
  year =         "1974",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Gardiner:1974:CAI,
  author =       "A. B. Gardiner",
  title =        "Comments on {``An Augmented Iterative Array for High
                 Speed Division''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-23",
  number =       "3",
  pages =        "326--327",
  month =        mar,
  year =         "1974",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1974.223931",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 11:27:31 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See \cite{Cappa:1973:AIA}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672524",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Gentleman:1974:MAR,
  author =       "W. Morven Gentleman and Scott B. Marovich",
  title =        "More on Algorithms that Reveal Properties of Floating
                 Point Arithmetic Units",
  journal =      j-CACM,
  volume =       "17",
  number =       "5",
  pages =        "276--277",
  month =        may,
  year =         "1974",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/360980.361003",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:43:47 MST 2001",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#GentlemanM74;
                 https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Malcolm:1972:ARP}.",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Univ. Waterloo, Ont., Canada",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "algorithms; base of the arithmetic; digital
                 arithmetic; floating point arithmetic units; high
                 level; languages; trailing digits",
  oldlabel =     "GentlemanM74",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/GentlemanM74",
}

@Book{Hildebrand:1974:INA,
  author =       "Francis Begnaud Hildebrand",
  title =        "Introduction to numerical analysis",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  edition =      "Second",
  pages =        "xiii + 669",
  year =         "1974",
  ISBN =         "0-07-028761-9",
  ISBN-13 =      "978-0-07-028761-7",
  LCCN =         "QA297 .H54 1974",
  bibdate =      "Fri Aug 20 09:19:58 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "International series in pure and applied mathematics",
  acknowledgement = ack-nhfb,
  remark =       "Reprinted in \cite{Hildebrand:1987:INA}.",
  subject =      "Numerical analysis",
}

@Article{Hill:1974:RFF,
  author =       "Bruce M. Hill",
  title =        "The rank-frequency form of {Zipf}'s law",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "69",
  number =       "348",
  pages =        "1017--1026",
  month =        dec,
  year =         "1974",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  MRclass =      "62E15",
  MRnumber =     "0426242 (54 \#14188)",
  MRreviewer =   "S. M. Samuels",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  ZMnumber =     "Zbl 0301.60011",
  acknowledgement = ack-nhfb,
  classification = "B0240 (Probability and statistics); C1140
                 (Probability and statistics)",
  corpsource =   "Department of Statistics, University of Michigan, Ann
                 Arbor, MI, USA",
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
  keywords =     "Bose--Einstein allocation; distribution; random
                 processes; rank frequency form; statistics; Zipf's
                 law",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Hitotumatu:1974:CAT,
  author =       "Sin Hitotumatu",
  title =        "Complex arithmetic through {CORDIC}",
  journal =      "K{\=o}dai Math. Semin Rep.",
  volume =       "26",
  pages =        "176--186",
  year =         "1974/75",
  ISSN =         "0023-2599",
  MRclass =      "65E05",
  MRnumber =     "413450",
  MRreviewer =   "P. Brock",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://projecteuclid.org/euclid.kmj/1138846999",
  acknowledgement = ack-nhfb,
  fjournal =     "K{\=o}odai Mathematical Seminar Reports",
}

@Article{Hitotumatu:1974:NMC,
  author =       "Sin Hitotumatu",
  title =        "A new method for the computation of square root,
                 exponential, and logarithmic functions through
                 hyperbolic {CORDIC}",
  journal =      "Revue d'Analyse Num{\'e}rique et de la Th{\'e}orie de
                 l'Approximation",
  volume =       "3",
  number =       "2",
  pages =        "173--180",
  month =        "????",
  year =         "1974",
  bibdate =      "Sat Oct 18 15:36:08 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Hull:1974:LFM,
  author =       "T. E. Hull and J. J. Hofbauer",
  title =        "Language facilities for multiple precision floating
                 point computation, with examples, and the description
                 of a preprocessor",
  type =         "Technical report",
  number =       "63",
  institution =  "University of Toronto, Department of Computer
                 Science",
  address =      "Toronto, ON, Canada",
  pages =        "vi + 84",
  year =         "1974",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic; Electronic digital
                 computers --- Programming",
}

@Article{Kinoshita:1974:FPA,
  author =       "Eisuke Kinoshita and Hideo Kosako and Yoshiaki
                 Kojima",
  title =        "Floating-Point Arithmetic Algorithms in the Symmetric
                 Residue Number System",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-23",
  number =       "1",
  pages =        "9--20",
  month =        jan,
  year =         "1974",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264810;
                 https://doi.org/10.1109/T-C.1974.223772",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "68A10",
  MRnumber =     "50 9042",
  bibdate =      "Tue Jul 12 11:27:29 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35077;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672365",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  reviewer =     "M. S. Cheema",
  summary =      "The residue number system is an integer number system
                 and is inconvenient to represent numbers with
                 fractional parts. In the symmetric residue system, a
                 new representation of floating-point numbers and
                 arithmetic algorithms for its addition, \ldots{}",
}

@Article{Kroft:1974:CTC,
  author =       "D. Kroft",
  title =        "Comments on {``A Two's Complement Parallel Array
                 Multiplication Algorithm''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-23",
  number =       "12",
  pages =        "1327--1328",
  month =        dec,
  year =         "1974",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1974.223863",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 11:27:38 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See \cite{Baugh:1973:TCP,Blankenship:1974:CTC}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672456",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Kulisch:1974:PCC,
  author =       "U. Kulisch",
  title =        "Formalization and implementation of floating-point
                 arithmetics",
  crossref =     "Panagiotopoulos:1974:PCC",
  pages =        "328--369",
  year =         "1974",
  MRclass =      "65G05",
  MRnumber =     "57 14392",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  reviewer =     "R. H. Bartels",
}

@Article{Ling:1974:CSA,
  author =       "Robert F. Ling",
  title =        "Comparison of several algorithms for computing sample
                 means and variances",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "69",
  number =       "348",
  pages =        "859--866",
  month =        dec,
  year =         "1974",
  CODEN =        "JSTNAL",
  DOI =          "https://doi.org/10.1080/01621459.1974.10480219",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Wed Jan 25 08:05:46 MST 2012",
  bibsource =    "Distributed/QLD.bib; Distributed/QLD/1974.bib;
                 http://www.jstor.org/journals/01621459.html;
                 http://www.jstor.org/stable/i314230;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib;
                 Theory/Matrix.bib",
  URL =          "http://www.jstor.org/stable/2286154;
                 https://www.tandfonline.com/doi/abs/10.1080/01621459.1974.10480219;
                 https://www.tandfonline.com/doi/pdf/10.1080/01621459.1974.10480219",
  acknowledgement = ack-nhfb,
  country =      "USA",
  date =         "13/05/93",
  descriptors =  "Simulation; statistics; numeric calculation",
  enum =         "7605",
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
  keywords =     "mean; standard deviation; stat; updating; variance",
  location =     "SEL: Wi",
  remark =       "This is an early paper on the numerical difficulties
                 associated with two important statistical algorithms.
                 See also entry \cite{McCullough:2019:WTS} in
                 fparith.bib that shows that even after 45 years, some
                 statistics code in database software remains poor.",
  revision =     "16/01/94",
  xxtitle =      "Comparison of Several Algorithms for Computing Means
                 and Variances",
}

@Article{Linnainmaa:1974:ASK,
  author =       "Seppo Linnainmaa",
  title =        "Analysis of Some Known Methods of Improving the
                 Accuracy of Floating-Point Sums",
  journal =      j-BIT,
  volume =       "14",
  number =       "2",
  pages =        "167--202",
  month =        jun,
  year =         "1974",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01932946",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65G05",
  MRnumber =     "MR0483373 (58 \#3381)",
  bibdate =      "Fri Dec 08 13:05:19 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=14&issue=2&spage=167",
  acknowledgement = ack-nj,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "accurate floating-point summation; floating-point
                 arithmetic; rounding errors",
  reviewer =     "H. Ratschek",
}

@InCollection{Metropolis:1974:SAA,
  author =       "N. Metropolis and Gian-Carlo Rota",
  booktitle =    "Studies in numerical analysis (papers in honour of
                 {Cornelius Lanczos} on the occasion of his 80th
                 birthday)",
  title =        "Significance arithmetic---on the algebra of binary
                 strings",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "241--251",
  year =         "1974",
  MRclass =      "02F43 (68A15)",
  MRnumber =     "MR0354335 (50 \#6815)",
  MRreviewer =   "Stephen Tanny",
  bibdate =      "Wed Nov 14 19:04:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0311.65031",
  acknowledgement = ack-nhfb,
}

@InProceedings{Miller:1974:CCN,
  author =       "Webb Miller",
  title =        "Computational complexity and numerical stability",
  crossref =     "ACM:1974:CRS",
  pages =        "317--322",
  year =         "1974",
  bibdate =      "Wed Nov 24 12:46:29 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Manual{Moon:1974:MRM,
  author =       "David A. Moon",
  title =        "{MacLISP} Reference Manual",
  organization = "MIT Project MAC",
  address =      "Cambridge, MA, USA",
  month =        apr,
  year =         "1974",
  bibdate =      "Wed Jan 29 16:47:55 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
  remark =       "From \cite{Steele:2004:RHP}: ``In early 1971, he
                 [White] began to analyze the machine-language algorithm
                 used in the implementation of MacLisp (described in
                 this report) to convert PDP-10 floating-point numbers
                 into decimal notation.''",
}

@Article{Neumaier:1974:REV,
  author =       "A. Neumaier",
  title =        "{Rundungsfehleranalyse Einiger Verfahren Zur Summation
                 Endlicher Summen}. ({German}) [{Rounding} error
                 analysis of a method for summation of finite sums]",
  journal =      j-Z-ANGE-MATH-MECH,
  volume =       "54",
  pages =        "39--51",
  year =         "1974",
  CODEN =        "ZAMMAX",
  ISSN =         "0044-2267 (print), 1521-4001 (electronic)",
  ISSN-L =       "0044-2267",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-jr,
  fjournal =     "{Zeitschrift f{\"u}r Angewandte Mathematik und
                 Mechanik}",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
  keywords =     "accurate floating-point summation",
  language =     "German",
}

@Article{Newbery:1974:EAP,
  author =       "A. C. R. Newbery",
  title =        "Error Analysis for Polynomial Evaluation",
  journal =      j-MATH-COMPUT,
  volume =       "28",
  number =       "127",
  pages =        "789--793",
  month =        jul,
  year =         "1974",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "B0290B (Error analysis in numerical methods); B0290D
                 (Functional analysis); C4110 (Error analysis in
                 numerical methods); C4120 (Functional analysis)",
  corpsource =   "Univ. Kentucky, Lexington, KY, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "analysis; Chebyshev; computable error bound; error
                 analysis; floating point error; function evaluation;
                 Horner's scheme; polynomial evaluation; polynomials",
  treatment =    "T Theoretical or Mathematical",
}

@MastersThesis{Prezas:1974:FPA,
  author =       "Pericles Panos Prezas",
  title =        "Floating point arithmetic unit",
  type =         "Thesis ({M.S.})",
  publisher =    "The author",
  school =       "Illinois Institute of Technology",
  address =      "Chicago, IL.",
  pages =        "ix + 77",
  year =         "1974",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Rauscher:1974:MUX,
  author =       "Tomlinson G. Rauscher",
  title =        "Microprogramming the {AN\slash UYK-17(XB-1)(V)} signal
                 processing element signal processing arithmetic unit",
  journal =      j-SIGMICRO,
  volume =       "5",
  number =       "2",
  pages =        "29--63",
  month =        apr,
  year =         "1974",
  CODEN =        "SIGMDJ",
  DOI =          "https://doi.org/10.1145/1217157.1217160",
  ISSN =         "0163-5751, 1050-916X",
  ISSN-L =       "0163-5751",
  bibdate =      "Fri Apr 16 10:27:17 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigmicro.bib",
  URL =          "https://dl.acm.org/doi/10.1145/1217157.1217160",
  abstract =     "The AN/UYK-17(XB-1)(V) Signal Processing Element (SPE)
                 is a high performance computer system being developed
                 at the Naval Research Laboratory for radar, sonar, and
                 communication applications. To perform signal
                 processing tasks efficiently, the SPE comprises
                 multiple functional units that execute different
                 processes in parallel. Due to the inherent parallelism
                 in signal processing tasks, horizontal microprograms
                 are used to control the functional units [references 5
                 and 6]. This report overviews the SPE, describes the
                 Signal Processing Arithmetic Unit (SPAU) in detail,
                 discusses ANIMIL --- the microprogramming language for
                 representing SPAU microprograms, and illustrates the
                 use of the ANIMIL translator with a simple
                 microprogram. Companion documents describe the SPAU
                 simulator program (reference 3) and the formal syntax
                 and semantics of the ANIMIL language (reference 4).",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMICRO Newsletter",
  journal-URL =  "https://dl.acm.org/loi/sigmicro",
}

@Article{Renner:1974:RRN,
  author =       "K. Renner and S. Gupta",
  title =        "Reduction of roundoff noise in wave digital filters",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "21",
  number =       "2",
  pages =        "305--310",
  month =        mar,
  year =         "1974",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "Roundoff noise generated by arithmetic operations in a
                 digital-filter computational sequence is undesirable in
                 that it serves to distort the true signal at the
                 output. Furthermore, coefficient wordlength is directly
                 related to the generated noise. \ldots{}",
}

@Book{Scaife:1974:SNA,
  editor =       "B. K. P. Scaife",
  title =        "Studies in numerical analysis",
  publisher =    "The Royal Irish Academy",
  address =      "Dublin, Ireland",
  pages =        "xxii + 333",
  year =         "1974",
  MRclass =      "65-06",
  MRnumber =     "MR0347039 (49 \#11759)",
  bibdate =      "Thu Nov 8 19:02:54 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Papers in honour of Cornelius Lanczos on the occasion
                 of his 80th birthday",
  acknowledgement = ack-nhfb,
}

@Book{Schmid:1974:DC,
  author =       "Hermann Schmid",
  title =        "Decimal Computation",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xi + 266",
  year =         "1974",
  ISBN =         "0-471-76180-X",
  ISBN-13 =      "978-0-471-76180-8",
  LCCN =         "QA75 .S34",
  bibdate =      "Thu Sep 1 10:14:05 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted \cite{Schmid:1983:DC}.",
  acknowledgement = ack-nj,
  keywords =     "decimal floating-point arithmetic",
}

@Article{Sites:1974:SBD,
  author =       "R. L. Sites",
  title =        "Serial Binary Division by Ten",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "23",
  number =       "12",
  pages =        "1299--1301",
  month =        dec,
  year =         "1974",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1974.223849",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Aug 07 18:02:35 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  abstract =     "A technique is presented for dividing a positive
                 binary integer by ten, in which the bits of the input
                 are presented serially, low-order bit first. A complete
                 division by ten is performed in two word times
                 (comparable to the time needed for two serial
                 additions). The technique can be useful in serial
                 conversions from binary to decimal, or in scaling
                 binary numbers by powers of 10.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "decimal arithmetic",
}

@Book{Sterbenz:1974:FPC,
  author =       "Pat H. Sterbenz",
  title =        "Floating Point Computation",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xiv + 316",
  year =         "1974",
  ISBN =         "0-13-322495-3",
  ISBN-13 =      "978-0-13-322495-5",
  LCCN =         "QA76.8.I12 S771 1974",
  MRclass =      "68A05 (65G05)",
  MRnumber =     "50 1556",
  bibdate =      "Sat May 29 08:01:36 1999",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  series =       "Prentice-Hall Series in Automatic Computation.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  keywords =     "Compiling (Electronic computers); Computation by
                 computer systems --- Floating point representation;
                 Floating-point arithmetic; IBM 360 (Computer) ---
                 Programming",
  remark =       "From p. 116: ``There is general agreement that the
                 mantissas of floating-point numbers are not uniformly
                 distributed. [See Hamming (1962)
                 [\cite{Hamming:1962:NMS}], Pinkham (1961)
                 [Pinkham:1961:DFS], or Knuth (1969) [Knuth:1969:SNM].]
                 Instead, it is customary to assume that they are
                 distributed logarithmically, that is, that the
                 probability density function is

                  $$ (3.12.9) f(m) = \frac {1}{m \ln r}, \qquad r^{-1}
                 \leq m \leq 1. $$

                 This assumption is based on the following observations:
                 First, this distribution reproduces itself under
                 multiplication, but a uniform distribution does not.
                 [See Hamming (1962) [\cite{Hamming:1962:NMS}] and
                 Exercise 20.] A second justification is based on the
                 fact that many of the numbers that arise in computation
                 represent measurable quantities such as lengths,
                 forces, etc., and it is reasonable to believe that the
                 distribution of the mantissas of such quantities is
                 independent of the units in which they are measured.
                 Pinkham (1961) shows that this leads to the conclusion
                 that the distribution of mantissas must be
                 logarithmic.''",
  reviewer =     "F. J. Murray",
  tableofcontents = "Preface / ix \\
                 1. Floating-Point Number Systems / 1 \\
                 1.1 Fixed-Point Calculation / 1 \\
                 1.2 Floating-Decimal Representation of Numbers / 4 \\
                 1.3 Floating-Decimal Arithmetic / 6 \\
                 1.4 Floating-Point Number Systems / 9 \\
                 1.5 FP(r, p, c) and FP(r, p, R) / 12 \\
                 1.6 Laws of Algebra / 14 \\
                 1.7 Inequalities in FP(r,p, c) / 21 \\
                 1.8 FP(r, p, clq) / 22 \\
                 1.9 The Solution of a * x = b in FP(r,p, c) / 29 \\
                 1.10 Division / 33 \\
                 Exercises / 35 \\
                 2. Floating-Point Overflow and Underflow / 39 \\
                 2.1 Bounds for Exponents / 39 \\
                 2.2 $\Omega$-Zero Fixup / 41 \\
                 2.3 Interrupt / 44 \\
                 2.4 Messages and Tests / 46 \\
                 2.5 ON OVERFLOW and ON UNDERFLOW in PL/I / 49 \\
                 2.6 Example / 50 \\
                 2.7 Counting Mode / 57 \\
                 2.8 Gradual Underflow / 59 \\
                 2.9 Imprecise Interrupt / 61 \\
                 2.10 Changing the Treatment of Spill / 62 \\
                 2.11 Virtual Overflow and Underflow / 64 \\
                 2.12 Division by Zero and Indeterminant Forms / 66 \\
                 Exercises / 67 \\
                 3. Error Analysis / 71 \\
                 3.1 Significant Digits / 71 \\
                 3.2 Relative Error / 73 \\
                 3.3 Relative Error in FP(r,p, clq) / 75 \\
                 3.4 Approximate Laws of Algebra / 80 \\
                 3.5 Propagation of Rounding Error / 87 \\
                 3.6 X**N / 92 \\
                 3.7 Condition / 98 \\
                 3.8 Error Analysis of a Program / 103 \\
                 3.9 Backward Error Analysis / 105 \\
                 3.10 Examples / 107 \\
                 3.11 Changing the Problem / 109 \\
                 3.12 Statistical Error Analysis / 113 \\
                 Exercises / 117 \\
                 4. Example / 123 \\
                 4.1 Quadrature / 123 \\
                 4.2 Power Series / 130 \\
                 4.3 Exact Sums and Differences in FP(r, p, clq) / 137
                 \\
                 4.4 Dismantling Floating-Point Numbers / 143 \\
                 Exercises / 146 \\
                 5. Double-Precision Calculation / 154 \\
                 5.1 Programs Using Double-Precision Arithmetic / 155
                 \\
                 5.2 Implicit Typing of Names / 162 \\
                 5.3 Routines to Perform Double-Precision Arithmetic /
                 163 \\
                 5.4 Double-Precision Multiplication / 165 \\
                 5.5 Double-Precision Addition and Subtraction / 168 \\
                 5.6 Double-Precision Division / 171 \\
                 5.7 Writing Double-Precision Programs Without Language
                 Support / 178 \\
                 5.8 Uses of Double-Precision / 180 \\
                 5.9 Higher-Precision Arithmetic / 185 \\
                 Exercises / 186 \\
                 6. Rounding / 189 \\
                 6.1 General Considerations / 189 \\
                 6.2 Uses of Rounding / 191 \\
                 6.3 Implementation of Rounding / 192 \\
                 6.4 Bias Removal / 194 \\
                 6.5 Other ``Rounding'' Procedures / 197 \\
                 Exercises / 198 \\
                 7. Automatic Analysis of Error / 201 \\
                 7.1 Introduction / 201 \\
                 7.2 Significance Arithmetic / 202 \\
                 7.3 Noisy Mode / 205 \\
                 7.4 Interval Arithmetic / 207 \\
                 7.5 Rerunning the Program in Higher-Precision / 213 \\
                 Exercises / 222 \\
                 8. Radix Conversion / 224 \\
                 8.1 Equivalent Number of Digits / 224 \\
                 8.2 Properties of Conversion Transformations / 228 \\
                 8.3 Conversion Techniques / 232 \\
                 Exercises / 238 \\
                 9/ Carefully Written Programs / 240 \\
                 9.1 Introduction / 240 \\
                 9.2 Average Problem / 240 \\
                 9.3 Quadratic Equation / 246 \\
                 Exercises / 252 \\
                 10. Checking and Testing / 255 \\
                 10.1 Range Checking / 255 \\
                 10.2 Mathematical Checks / 256 \\
                 10.3 Testing / 259 \\
                 Exercises / 261 \\
                 11. Language Features for Floating-Point Computation /
                 263 \\
                 11.1 Introduction / 263 \\
                 11.2 Predictability, Controllability, Observability /
                 264 \\
                 11.3 Ease of Programming / 265 \\
                 11.4 Machine Independence / 267 \\
                 Exercises / 269 \\
                 12. Floating-Point Hardware / 271 \\
                 12.1 Choice of Radix / 271 \\
                 12.2 The Representation of Floating-Point Numbers / 273
                 \\
                 12.3 FP(r, p, c) and FP(r, p, R) / 277 \\
                 12.4 Unnormalized Numbers and Unnormalized Arithmetic /
                 278 \\
                 Exercises / 282 \\
                 13. Complex Numbers / 285 \\
                 13.1 Programs Using Complex Numbers / 285 \\
                 13.2 Relative Error / 286 \\
                 13.3 Complex Arithmetic / 287 \\
                 Exercises / 297 \\
                 Bibliography / 301 \\
                 Glossary of Symbols / 309 \\
                 Index / 311",
}

@Article{Suter:1974:MAA,
  author =       "B. W. Suter",
  title =        "The Modular Arithmetic of Arbitrarily Long Sequences
                 of Digits",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-23",
  number =       "12",
  pages =        "1301--1303",
  month =        dec,
  year =         "1974",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1974.223850",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 11:27:38 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672443",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Syslo:1974:RAP,
  author =       "M. M. Syslo",
  title =        "Remarks on addition processes of positive
                 floating-point numbers",
  journal =      j-ZASTOS-MAT,
  volume =       "14",
  pages =        "415--417",
  year =         "1974",
  CODEN =        "ZAMTAK",
  MRclass =      "65G05",
  MRnumber =     "50 8953",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Zastosowania Matematyki",
  reviewer =     "Sven-{\AA}ke Gustafson",
}

@PhdThesis{Thompson:1974:IUF,
  author =       "Jackie Lloyd Thompson",
  title =        "An implementation of user-oriented floating point
                 arithmetic",
  type =         "Dissertation ({Ph.D.} in {Computing Science})",
  school =       "Texas A\&M University",
  address =      "College Station, TX, USA",
  pages =        "150",
  year =         "1974",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Tsao:1974:DSD,
  author =       "Nai Kuan Tsao",
  title =        "On the Distributions of Significant Digits and
                 Roundoff Errors",
  journal =      j-CACM,
  volume =       "17",
  number =       "5",
  pages =        "269--271",
  month =        may,
  year =         "1974",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65G05",
  MRnumber =     "49 6595",
  MRreviewer =   "N. N. Abdelmalek",
  bibdate =      "Mon Jan 22 07:26:38 MST 2001",
  bibsource =    "Compendex database;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Tsao74;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Generalized logarithmic law is derived for the
                 distribution of the first $t$ significant digits of a
                 random digital integer. This result is then used to
                 determine the distribution of the roundoff errors in
                 floating-point operations, which is a mixture of
                 uniform and reciprocal distributions.",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  classification = "921",
  corpsource =   "Aerospace Res. Labs., Wright-Patterson AFB, OH, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  journalabr =   "Commun ACM",
  keywords =     "Benford's Law; digital arithmetic; digital integer;
                 distributions; error analysis; floating point
                 operations; Law of Anomalous Numbers; logarithmic law;
                 mathematical techniques; mean value; random;
                 reciprocal; roundoff errors; significant digits;
                 uniform distribution; variance; Zipf's Law",
  oldlabel =     "Tsao74",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Tsao74",
}

@Article{Tsao:1974:SPE,
  author =       "Nai-Kuan Tsao",
  title =        "Some a Posteriori Error Bounds in Floating-Point
                 Computations",
  journal =      j-J-ACM,
  volume =       "21",
  number =       "1",
  pages =        "6--17",
  month =        jan,
  year =         "1974",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  MRclass =      "65G05",
  MRnumber =     "49 8319",
  bibdate =      "Fri Dec 08 13:06:33 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  reviewer =     "N. N. Abdelmalek",
}

@Article{Walker:1974:FGU,
  author =       "A. J. Walker",
  title =        "Fast generation of uniformly distributed pseudorandom
                 numbers with floating-point representation",
  journal =      j-ELECT-LETTERS,
  volume =       "10",
  number =       "25--26",
  pages =        "533--534",
  day =          "12",
  month =        dec,
  year =         "1974",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:19740423",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Fri Dec 30 16:39:46 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4245313",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}

@Article{Agrawal:1975:AAN,
  author =       "D. P. Agrawal",
  title =        "Arithmetic Algorithms in a Negative Base",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "10",
  pages =        "998--1000",
  month =        oct,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224109",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:57 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672702",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Agrawal:1975:OAL,
  author =       "Dharma P. Agrawal",
  title =        "Optimum Array-Like Structures for High-Speed
                 Arithmetic",
  crossref =     "IEEE:1975:SCA",
  pages =        "208--219",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Agrawal.pdf",
  abstract =     "Array-like structures for high-speed multiplication,
                 division, square and square-root operations have been
                 described in this paper. In these designs the division
                 and square-rooting time have been made to approach to
                 that of multiplication operation. These structures are
                 optimum from speed and versatility point of view. Most
                 of the cellular arrays described in the literature are
                 adequately slow. The time delay is particularly
                 significant in the division and square-rooting
                 operations due to the ripple effect of the carries.
                 Though the carry-save technique has been widely
                 utilized for multiplication operation, it has been only
                 recently employed by Cappa et al. in the design of a
                 nonrestoring divider array. This requires sign-bit
                 detection that makes the array non-uniform. Such an
                 array has been named as an array-like structure. The
                 carry-save method has been extended here for restoring
                 division operation. Due to sign-detection and overflow
                 correction requirements, the restoring method is
                 slightly complex. But the main advantage of such
                 restoring array is in its simple extension for
                 multiplication operation. The array for the two
                 operations, when pipelined, will have more computing
                 power than all other multiplier-divider arrays.
                 Suggestions have also been included for further speed
                 improvement.\par

                 The technique applied for division operation is as well
                 applicable for the square-rooting and an array-like
                 structure for square-square-rooting operations has also
                 been given. For performing any one of the four
                 operations, the only manipulation to be done is to
                 combine the two arrays; one for multiplication-division
                 and another for square-square-rooting. Possible.
                 methods of combining the two arrays have been indicated
                 and their relative advantages and disadvantages have
                 been mentioned. Finally, a generalized pipeline
                 array-like structure with complete internal details and
                 for 4-bit operation, has been shown. Due consideration
                 has also been given to the possibility of
                 large-scale-integration of different arrays presented
                 in this paper.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@InProceedings{Atkins:1975:HRN,
  author =       "Daniel E. Atkins",
  title =        "Higher Radix, Non-restoring Division: History and
                 recent Developments",
  crossref =     "IEEE:1975:SCA",
  pages =        "158--167",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:43:08 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Atkins.pdf",
  abstract =     "This paper reviews work related to the theory and
                 application of higher-radix. non-restoring division as
                 originally defined by Robertson in 1958.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@Article{Atkins:1975:IRR,
  author =       "D. E. Atkins",
  title =        "Introduction to the Role of Redundancy in Computer
                 Arithmetic",
  journal =      j-COMPUTER,
  volume =       "8",
  number =       "6",
  pages =        "74--77",
  month =        jun,
  year =         "1975",
  CODEN =        "CPTRB4",
  DOI =          "https://doi.org/10.1109/C-M.1975.219001",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Sat May 7 16:08:43 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computer1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}

@InProceedings{Avizienis:1975:RNR,
  author =       "Algirdas Avi{\v{z}}ienis",
  title =        "Redundancy in Number Representations as an Aspect of
                 Computational Complexity of Arithmetic Functions",
  crossref =     "IEEE:1975:SCA",
  pages =        "87--89",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Avizienis.pdf",
  abstract =     "Recent research has led to the derivation of bounds
                 for the time required to perform arithmetic operations
                 by means of logical elements with a limited number of
                 inputs [1--4]. The model of a $ (d, r) $ logical
                 circuit $C$ employed in these studies consists of a set
                 of $ (d, r) $ logical elements and a rule of
                 interconnection with designated sets of input and
                 output lines. The $ (d, r) $ logical element has $r$
                 input lines and one output line; these lines can assume
                 one of $d$ distinct states. The $ (d, r) $ logical
                 element has a unit time delay; that is, the state of
                 the output line at the time $ t + 1 $ is a function of
                 the states of the input lines at time $t$.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@Article{Baker:1975:MER,
  author =       "P. W. Baker",
  title =        "More Efficient Radix-2 Algorithms for Some Elementary
                 Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "11",
  pages =        "1049--1054",
  month =        nov,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224132",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:15:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Banerji:1975:CLS,
  author =       "D. K. Banerji",
  title =        "On Combinational Logic for Sign Detection in Residue
                 Number Systems",
  crossref =     "IEEE:1975:SCA",
  pages =        "113--116",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Banerji.pdf",
  abstract =     "This paper is concerned with the algebraic sign
                 detection of a number in a residue number system. The
                 proposed solution is applicable only to nonredundant
                 systems. The method utilizes a systematic decomposition
                 of the sign function $S$ that is based on some special
                 properties of $S$. Starting with the canonical
                 sum-of-products expression for $S$, we transform the
                 expression to a form whose realization is simpler than
                 the canonical form realization and, if possible, also
                 simpler than the minimal sum-of-products realization.
                 In some cases, the proposed method yields savings as
                 high as 85\% compared to the minimal sum-of-products
                 realization for $S$.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@Article{Basu:1975:SPN,
  author =       "D. Basu and T. Jayashree",
  title =        "On a Simple Postcorrection for Nonrestoring Division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "10",
  pages =        "1019--1020",
  month =        oct,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224116",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:57 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672709",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Benedek:1975:DLB,
  author =       "M. Benedek",
  title =        "Developing Large Binary to {BCD} Conversion
                 Structures",
  crossref =     "IEEE:1975:SCA",
  pages =        "188--196",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Benedek.pdf",
  abstract =     "Static binary to BCD conversion has been described in
                 many papers during the last decade, but none of the
                 methods presented were practical for the conversion of
                 large number of binary bits.\par

                 In this paper it is intended to further develop static
                 conversions by the expansion of the original BIDEC
                 method (Ref. 1). There are quite a few static
                 conversion schemes published which use other methods of
                 conversion. The static method, developed from the
                 BIDEC, lends itself best for the expansion to larger
                 structures as in its original ``correct and shift''
                 form there were no basic limitations on the size of the
                 binary words to be converted. with the appearance of
                 large bipolar ROMs and the even larger but somewhat
                 slower MOS ROMs there is a renewed interest in large
                 structures for fast binary to BCD conversions.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@InProceedings{Bivins:1975:SAA,
  author =       "R. L. Bivins and N. Metropolis",
  title =        "Significance Arithmetic: Application to a Partial
                 Differential Equation",
  crossref =     "IEEE:1975:SCA",
  pages =        "64--66",
  year =         "1975",
  DOI =          "https://doi.org/10.1109/ARITH.1975.6156973",
  bibdate =      "Mon Mar 19 18:17:32 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Also available as Los Alamos Technical Report
                 LA-UR-75-1763 CONF-751103-1.",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Bivins.pdf",
  abstract =     "The methods of significance arithmetic are applied to
                 the numerical solution of a nonlinear partial
                 differential equation. The authors approach permits the
                 use of initial values having imprecision considerably
                 greater than that of rounding error; moreover, the
                 intermediate and final quantities are monitored so that
                 at any stage the precision of such quantities is
                 available. An algorithm is found that represents
                 faithfully the solution to a difference equation
                 approximation to Burger's equation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3; significance arithmetic",
}

@InProceedings{Bohlender:1975:FPC,
  author =       "G. Bohlender",
  title =        "Floating-Point Computation of Functions with Maximum
                 Accuracy",
  crossref =     "IEEE:1975:SCA",
  pages =        "14--23",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Bohlender.pdf",
  abstract =     "Algorithms are given which compute multiple sums and
                 products and arbitrary roots of floating-point numbers
                 with maximum accuracy. The summation algorithm can be
                 applied to compute scalar products, matrix products,
                 etc. For all these functions, simple error formulas and
                 the smallest floating-point intervals containing the
                 exact result can be obtained.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@TechReport{Brent:1975:FMP,
  author =       "R. P. Brent",
  title =        "A {Fortran} Multiple-Precision Arithmetic Package",
  type =         "Technical report",
  institution =  "Department of Computer Science, Australian National
                 University",
  address =      "Canberra, Australia",
  year =         "1975",
  bibdate =      "Fri Jan 06 07:38:05 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; multiple-precision
                 arithmetic",
}

@TechReport{Brent:1975:MZM,
  author =       "R. P. (Richard P.) Brent",
  title =        "Multiple-precision zero-finding methods and the
                 complexity of elementary function evaluation",
  institution =  "Department of Computer Science, Carnegie-Mellon
                 University",
  address =      "Pittsburgh, PA, USA",
  pages =        "26",
  year =         "1975",
  bibdate =      "Sat Jan 11 10:14:06 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Iterative methods (Mathematics)",
  searchkey =    "ti:elementary n1 function",
}

@Article{Brubaker:1975:MUL,
  author =       "T. A. Brubaker and J. C. Becker",
  title =        "Multiplication Using Logarithms Implemented with
                 Read-Only Memory",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "8",
  pages =        "761--765",
  month =        aug,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224307",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672900",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Caprani:1975:REF,
  author =       "Ole Caprani",
  title =        "Round-off Errors in Floating-Point Summation",
  journal =      j-BIT,
  volume =       "15",
  number =       "1",
  pages =        "5--9",
  month =        mar,
  year =         "1975",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01932993",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65G05",
  MRnumber =     "58 19088",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "accurate floating-point summation; floating-point
                 arithmetic; rounding errors",
  xxtitle =      "Roundoff errors in floating-point summation",
}

@Article{Chen:1975:SER,
  author =       "Tien Chi Chen and Irving T. Ho",
  title =        "Storage-Efficient Representation of Decimal Data",
  journal =      j-CACM,
  volume =       "18",
  number =       "1",
  pages =        "49--52",
  month =        jan,
  year =         "1975",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "94A15 (68A20)",
  MRnumber =     "50 16105",
  MRreviewer =   "R. N. Goss",
  bibdate =      "Mon Jan 22 06:30:44 MST 2001",
  bibsource =    "Compendex database;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#ChenH75;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Collection of articles honoring {Alston S.
                 Householder}. See comment \cite{Smith:1975:CPC}.",
  abstract =     "Usually $n$ decimal digits are represented by $ 4 n $
                 bits in computers. Actually, two BCD digits can be
                 compressed optimally and reversibly into $7$ bits, and
                 three digits into $ 10 $ bits, by a very simple
                 algorithm based on the fixed-length combination of two
                 variable field-length encodings. In over half of the
                 cases the compressed code results from the conventional
                 BCD code by simple removal of redundant $0$ bits. A
                 long decimal message can be subdivided into three-digit
                 blocks, and separately compressed; the result differs
                 from the asymptotic minimum length by only $ 0.34 $
                 percent. The hardware requirement is small, and the
                 mappings can be done manually.",
  acknowledgement = ack-nhfb,
  classcodes =   "C6130 (Data handling techniques)",
  classification = "722; 921",
  corpsource =   "IBM San Jose Res. Lab., CA, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  journalabr =   "Commun ACM",
  keywords =     "asymptotic minimum; binary coded decimal; codes;
                 compressed code; data compression; data storage units;
                 decimal data; decimal floating-point arithmetic; fixed
                 length combination; hardware; length; length encodings;
                 mathematical techniques --- Digital Arithmetic;
                 representation; storage efficient; variable field",
  oldlabel =     "ChenH75",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/ChenH75",
}

@InProceedings{Chinal:1975:LMA,
  author =       "Jean P. Chinal",
  title =        "The Logic of Modulo $ 2^k + 1 $ Adders",
  crossref =     "IEEE:1975:SCA",
  pages =        "126--136",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Chinal_2.pdf",
  abstract =     "The design of modulo $ 2^k + 1 $ adders for arbitrary
                 $k$ is considered, with the objective of achieving a
                 logic structure as regular as possible so as to allow a
                 convenient implementation in large-scale integration
                 technology (LSI). It is shown how the design problem
                 can be reduced. to the recursive generation of a
                 subtract signal and to the merging, in various degrees,
                 of the corresponding logic with the logic of an
                 ordinary adder or, alternately, of a so-called {\em
                 signed-carry adder\/} which is defined and designed
                 itself in general, with both recursive and explicit
                 carry schemes. Modulo $ 2^k + 1 $ adder designs are
                 given, one with conventional adder, another based on
                 signed-carry adder and a third, derived from the
                 signed-carry scheme, where subtract signal generation
                 and carry logic are merged. This last scheme can be set
                 up with two backward recursion chains and five or six
                 forward ones. Two more basic variants are finally
                 indicated for this integrated scheme, aiming at
                 reducing as much as possible the residual logic
                 structure irregularity presented by the most
                 significant position in the word.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@InProceedings{Chinal:1975:MA,
  author =       "Jean P. Chinal",
  title =        "Mirror Arithmetic",
  crossref =     "IEEE:1975:SCA",
  pages =        "98--107",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Chinal_1.pdf",
  abstract =     "Mirror coding for signed numbers is defined by means
                 of a set of primitive powers of two $ \{ + 2^n, - 2^{n
                 - 1}, \ldots {}, - 2^0 \} $ where signs of the usual
                 set used in 2's complement representation are reversed.
                 Use of the mirror representation is shown as an
                 alternate design approach and is illustrated by a
                 special purpose adder design in mirror code, by an
                 alternate proof of a basic property of signed-digit
                 arithmetic and as another interpretation of cells used
                 in some array multipliers for signed numbers. Lastly,
                 the concept is used to define a variable mode redundant
                 coding, allowing simple sign-flipping without
                 overflow.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@InProceedings{Cobb:1975:IPS,
  author =       "Gary W. Cobb",
  title =        "The Impact of Parallelism on Software",
  crossref =     "IEEE:1975:SCA",
  pages =        "220--222",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Cobb.pdf",
  abstract =     "There seems to be a tug-of-war raging between computer
                 procurement technical evaluation committees, computer
                 designers and scholars of computer science and
                 numerical analysis over the issue of parallelism in
                 computations. Caught in the middle seems to be the user
                 community and the compiler writers. For the scope of
                 this paper, the term ``user community'' will be assumed
                 to be Fortran programmers who are involved in solving
                 problems that require large computer resources, e.g.,
                 plasma research, weather prediction, ray tracing,
                 seismic analysis, econometric modeling, weapons
                 research, reactor calculation, etc.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@InProceedings{DeMori:1975:MMM,
  author =       "Renato {De Mori} and Michele Elia and Angelo Serra",
  title =        "Minimization Methods for Macrocellular Arithmetic
                 Networks",
  crossref =     "IEEE:1975:SCA",
  pages =        "232--240",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_DeMori.pdf",
  abstract =     "This paper presents a new method to study arithmetic
                 combinatorial circuits. Using polynomial associated to
                 the input-output sequences and to the system, it is
                 possible to solve the problem of minimization of the
                 number of the component blocks. Particularly, the
                 important case of the multiple outputs elementary units
                 can be treated.\par

                 Applications of the introduced procedures to multiplier
                 and to fast networks for performing convolution are
                 presented.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@Article{Deverell:1975:PIA,
  author =       "J. Deverell",
  title =        "Pipeline Iterative Arithmetic Arrays",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "3",
  pages =        "317--322",
  month =        mar,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224214",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 18:46:50 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Elias:1975:UCS,
  author =       "P. Elias",
  title =        "Universal codeword sets and representations of the
                 integers",
  journal =      j-IEEE-TRANS-INF-THEORY,
  volume =       "21",
  number =       "2",
  pages =        "194--203",
  month =        mar,
  year =         "1975",
  CODEN =        "IETTAW",
  DOI =          "https://doi.org/10.1109/tit.1975.1055349",
  ISSN =         "0018-9448 (print), 1557-9654 (electronic)",
  ISSN-L =       "0018-9448",
  bibdate =      "Fri Dec 15 15:10:16 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Information Theory",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
}

@PhdThesis{Ercegovac:1975:GMEa,
  author =       "Milo{\v{s}} Dragutin Ercegovac",
  title =        "A General Method for Evaluation of Functions and
                 Computations in a Digital Computer",
  type =         "{Ph.D.} Thesis",
  school =       "Department of Computer Science, University of Illinois
                 at Urbana-Champaign",
  address =      "Urbana-Champaign, IL, USA",
  pages =        "viii + 109",
  month =        jul,
  year =         "1975",
  bibdate =      "Mon Feb 10 07:18:12 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://search.proquest.com/pqdtglobal/docview/302756306",
  acknowledgement = ack-nhfb,
  advisor =      "James E. Robertson",
}

@InProceedings{Ercegovac:1975:GMEb,
  author =       "Milo{\v{s}} D. Ercegovac",
  title =        "A General Method for Evaluation of Functions in a
                 Digital Computer",
  crossref =     "IEEE:1975:SCA",
  pages =        "147--157",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Ercegovac.pdf",
  abstract =     "This paper presents a recently discovered general
                 computational method, amenable for efficient
                 implementation in digital computing systems. The method
                 provides a unique, simple and fast algorithm for
                 solving many computational problems, such as the
                 evaluation of polynomials, rational functions and
                 arithmetic expressions, or solving a class of systems
                 of linear equations, or performing the basic
                 arithmetics. In particular, the method is well suited
                 for fast evaluation of commonly used mathematical
                 functions.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@MastersThesis{Fawcett:1975:MCR,
  author =       "B. K. Fawcett",
  title =        "Maximal Clocking Rates for Pipelined Digital Systems",
  type =         "{M.S.} thesis",
  school =       "Department of Electrical Engineering, University of
                 Illinois at Urbana-Champaign",
  address =      "Urbana-Champaign, IL, USA",
  year =         "1975",
  bibdate =      "Fri Nov 09 10:50:56 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Foster:1975:CNM,
  author =       "Caxton Foster and Edward Riseman and Fred Stockton and
                 Conrad Wogrin",
  title =        "{CHARGOGGAGGOGGMANCHAUGAGOGGCHAUBUNAGUNGAMAUG}: a
                 Novel Multiply-by-Three Circuit",
  crossref =     "IEEE:1975:SCA",
  pages =        "185--187",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Foster.pdf",
  abstract =     "Recently, while considering the connection of a 48 bit
                 word computer to a 16 bit computer, we felt the need
                 for a fast and inexpensive device that would multiply a
                 binary address by a factor of three. Since $ 3 N = N +
                 2 N $, there is an obvious solution of providing a
                 normal adder circuit and presenting one set of inputs
                 with $N$ and the other with $N$-shifted left one place.
                 But, there is a great deal of redundancy here since
                 knowing one input we have complete knowledge of the
                 other.\par

                 Seeking to take advantage of this redundancy, we have
                 spent some twenty man hours and have saved one gate per
                 stage over a conventional full adder. Since the
                 ultimate circuit is to be a ``one-of'' this is scarcely
                 economic, but it has been fun. Before going further,
                 the interested reader may enjoy puzzling over the
                 problem for himself. We make no pretense of minimality,
                 but we have a circuit with 6 gates per stage and a
                 propagation delay of one gate per stage.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
  remark =       "Footnote to title: The title of this paper refers to
                 the Indian name of a lake in Massachusetts which
                 reputedly means ``You fish on your side, I fish on my
                 side, nobody fish in the middle.'",
}

@InProceedings{Gabrielian:1975:FSN,
  author =       "Armen Gabrielian",
  title =        "Formal Systems of Numerals",
  crossref =     "IEEE:1975:SCA",
  pages =        "76--81",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Gabrielian.pdf",
  abstract =     "A new system of numerals is introduced for
                 representing numbers in base $ 2^N $, for $ N \leq 8 $.
                 The new notation greatly simplifies arithmetical
                 operations on numbers. For example, for $ N = 3 (4) $
                 one obtains a notation for octal (hexadecimal) numbers
                 in which one can perform addition and multiplication
                 much more easily than in the standard notation. For $ N
                 = 8 $ one obtains a practical way of representing
                 numbers to the base 256. A simplification of the
                 decimal notation is also presented.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@Article{George:1975:ARR,
  author =       "James E. George",
  title =        "Algorithms to Reveal the Representation of Characters,
                 Integers, and Floating-Point Numbers",
  journal =      j-TOMS,
  volume =       "1",
  number =       "3",
  pages =        "210--216",
  month =        sep,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355644.355647",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Aug 26 23:44:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gibson:1975:SCT,
  author =       "J. A. Gibson and R. W. Gibbard",
  title =        "Synthesis and Comparison of Two's Complement Parallel
                 Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "10",
  pages =        "1020--1027",
  month =        oct,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224117",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:57 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672710",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@TechReport{Ginsberg:1975:DUFa,
  author =       "Myron Ginsberg and Dennis J. Frailey",
  title =        "The design and use of a floating-point (software)
                 simulator for testing the arithmetic behavior of
                 mathematical software",
  type =         "Technical report",
  number =       "CP 74028",
  institution =  "Department of Computer Science, Institute of
                 Technology, Southern Methodist University",
  address =      "Dallas",
  pages =        "26",
  year =         "1975",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Revised October 1975.",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic and logic units --- Testing.;
                 Computer programs --- Testing.; Floating-point
                 arithmetic.",
}

@InProceedings{Ginsberg:1975:DUFb,
  author =       "Myron Ginsberg and Dennis J. Frailey",
  title =        "The Design and Use of a Floating-Point (Software)
                 Simulator for Testing the Arithmetic Behavior of
                 Mathematical Software",
  crossref =     "IEEE:1975:SCA",
  pages =        "56--63",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Ginsberg.pdf",
  abstract =     "An important aspect of any evaluative procedure for
                 developing high quality mathematical software is
                 testing the effects of arithmetic behavior on
                 algorithmic implementations. This paper describes a
                 proposed design approach and various applications of a
                 high-level language floating-point simulator which has
                 two inputs: the program to be tested and a description
                 of the floating-point arithmetic under which the
                 routine is to be executed. A brief discussion of the
                 motivation for this approach is given along with a
                 review of existing efforts to study the influences of
                 computer arithmetic on the accuracy and reliability of
                 mathematical. software. An overview of the simulator's
                 structure is presented as well as suggestions for
                 experiments to assist in determining the effects of
                 floating-point behavior across several different
                 computer architectures. Present and future uses of the
                 simulator are also indicated.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@Article{Goodman:1975:REP,
  author =       "R. Goodman and A. Feldstein",
  title =        "Round-Off Error in Products",
  journal =      j-COMPUTING,
  volume =       "15",
  number =       "3",
  pages =        "263--273",
  month =        sep,
  year =         "1975",
  CODEN =        "CMPTA2",
  DOI =          "https://doi.org/10.1007/BF02242373",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Jan 2 17:40:52 MST 2001",
  bibsource =    "Compendex database;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 INSPEC Axiom database (1968--date)",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliation =  "Department of Math., University of Miami, Coral
                 Gables, FL, USA",
  classification = "921; C5230",
  description =  "digital arithmetic",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Comput (Vienna/NY)",
  keywords =     "digit by digit deviation; floating point numbers;
                 fraction; logarithmic distribution; mathematical
                 techniques; mean; multiplication; products; roundoff
                 errors; variance",
}

@InProceedings{Goyal:1975:DAE,
  author =       "Lakshmi N. Goyal",
  title =        "Design of an Arithmetic Element for Serial Processing
                 in an Iterative Structure",
  crossref =     "IEEE:1975:SCA",
  pages =        "223--231",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Goyal.pdf",
  abstract =     "This paper describes the arithmetic and logic design
                 of the digit processing logic of an arithmetic element.
                 The arithmetic element is used in an iterative
                 structure and arithmetic processing takes place
                 serially on a digit by digit basis with the most
                 significant digit first. Starting from the arithmetic
                 specification of the digit processing logic, the
                 arithmetic design (namely, the choice of number system,
                 number representation and the digit algorithm) is
                 developed. Algebraic and logic designs of the logic
                 necessary to execute the digit algorithm and its
                 implication for LSI implementation are discussed.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@Article{Grant:1975:TAS,
  author =       "J. A. Grant and G. D. Hitchins",
  title =        "Two Algorithms for the Solution of Polynomial
                 Equations to Limiting Machine Precision",
  journal =      j-COMP-J,
  volume =       "18",
  number =       "3",
  pages =        "258--264",
  month =        aug,
  year =         "1975",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/18.3.258",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:47:56 MST 2012",
  bibsource =    "Compendex database;
                 http://comjnl.oxfordjournals.org/content/18/3.toc;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/;
                 https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/18/3/258.full.pdf+html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/258.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/259.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/260.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/261.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/262.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/263.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/264.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  classification = "723; 921",
  corpsource =   "Department of Math., University of Bradford, Bradford,
                 UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "algorithms; complex coefficients; computer programming
                 --- Subroutines; limiting machine; mathematical
                 techniques; polynomial equations; polynomials;
                 precision; real coefficients",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Gregory:1975:BCR,
  author =       "Robert Todd Gregory and David W. Matula",
  title =        "Base Conversion in Residue Number Systems",
  crossref =     "IEEE:1975:SCA",
  pages =        "117--125",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Gregory.pdf",
  abstract =     "We are concerned in this paper with the representation
                 of an integer in a (multiple-modulus) residue number
                 system and, in particular, with an algorithm for
                 changing the base vector of the residue number system.
                 Szabo and Tanaka [1, p.47] describe such an algorithm
                 when each modulus of the second base vector is
                 relatively prime to each modulus of the first base
                 vector. However, we show that a much simpler algorithm
                 exists if we allow the moduli of the second base vector
                 to have factors in common with the moduli of the first
                 base vector (even though the moduli of the second base
                 vector are pairwise relatively prime among
                 themselves).",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@Article{Hitotumatu:1975:CAT,
  author =       "Sin Hitotumatu",
  title =        "Complex arithmetic through {CORDIC}",
  journal =      "K{\=o}dai Math. Semin. Rep.",
  volume =       "26",
  pages =        "176--186",
  year =         "1975",
  DOI =          "https://doi.org/10.2996/kmj/1138846999",
  ISSN =         "0023-2599",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0303.65012",
  acknowledgement = ack-nhfb,
  fjournal =     "Kodai Mathematical Seminar Reports",
  keywords =     "65D20,65G50,68W99",
  ZBmath =       "3474829",
}

@Article{Hunter:1975:QMP,
  author =       "G. Hunter",
  title =        "A quantitative measure of precision",
  journal =      j-COMP-J,
  volume =       "18",
  number =       "3",
  pages =        "231--233",
  month =        aug,
  year =         "1975",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "Compendex database;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/231.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/232.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_03/tiff/233.tif",
  abstract =     "The precision $ z_b $ of a real number is defined
                 quantitatively in terms of the fractional error in the
                 number, and the base of the arithmetic in which it is
                 represented. The definition is an extension of the
                 traditional rough measure of precision as the number of
                 signification digits in the number. In binary
                 arithmetic the integral part of $ z_b $ is the number
                 of binary digits required to store the number.
                 Conversion of the precision from one base to another
                 (such as binary/decimal) is discussed, and applied to
                 consideration of the intrinsic precision of
                 input/output routines and floating point arithmetic.",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  classification = "723; 921",
  corpsource =   "York University, Department of Chem., Downsview, Ont.,
                 Canada",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "binary arithmetic; digital arithmetic; digits;
                 floating; fractional error; input/output routines;
                 mathematical techniques; point arithmetic; precision;
                 real number; significant",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Kehl:1975:MMA,
  author =       "T. H. Kehl and Kenneth Burkhardt",
  title =        "A Minicomputer Microprogrammable, Arithmetic
                 Processor",
  crossref =     "IEEE:1975:SCA",
  pages =        "174--178",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kehl.pdf",
  abstract =     "Except for a few notable examples, all computers have
                 been designed as ``adder-central'' architectures.
                 ``Adder-central,'' as used here, refers to an
                 organization which places the Arithmetic Logic Unit
                 (ALU) at that junction of the system through which all
                 data must flow --- thus creating a bottleneck. In the
                 early days, when adders were expensive, cost
                 considerations precluded more than one ALU. Nowadays
                 powerful ALU's are available at very low cost and a
                 designer, even of minicomputers, can consider placing
                 more than one ALU in a system.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@InProceedings{Keir:1975:CNR,
  author =       "Roy A. Keir",
  title =        "Compatible number representations",
  crossref =     "IEEE:1975:SCA",
  pages =        "82--87",
  year =         "1975",
  bibdate =      "Fri Nov 28 11:38:18 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Keir_2.pdf",
  abstract =     "A compatible number system for mixed fixed-point and
                 floating-point arithmetic is described in terms of
                 number formats and opcode sequences (for hardwired or
                 microcoded control). This inexpensive system can be as
                 fast as fixed-point arithmetic on integers, is faster
                 than normalized arithmetic in floating point, gets
                 answers identical to those of normalized arithmetic,
                 and automatically satisfies the Algol-60 mixed-mode
                 rules. The central concept is the avoidance of
                 meaningless ``normalization'' following arithmetic
                 operations. Adoption of this system could lead to
                 simpler compilers.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3; decimal floating-point arithmetic",
}

@InProceedings{Keir:1975:PCR,
  author =       "Roy A. Keir",
  title =        "Programmer-controlled roundoff and the selection of a
                 stable roundoff rule",
  crossref =     "IEEE:1975:SCA",
  pages =        "73--76",
  year =         "1975",
  bibdate =      "Fri Nov 28 18:11:30 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Keir_1.pdf",
  abstract =     "The author suggests that every computer with
                 floating-point addition and subtraction should have PSW
                 controllable roundoff facilities. Yohe's catalog should
                 be included. There should also be a stable roundoff
                 mode using the round-to-off [{\em -odd\/}] or
                 round-to-even rule based on whether the radix is
                 divisible by four or only by two.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  keywords =     "ARITH-3",
}

@Article{Keir:1975:SSR,
  author =       "R. A. Keir",
  title =        "Should the stable rounding rule be radix-dependent?",
  journal =      j-INFO-PROC-LETT,
  volume =       "3",
  number =       "6",
  pages =        "188--189",
  day =          "??",
  month =        jul,
  year =         "1975",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Tue Nov 17 10:49:43 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods)",
  corpsource =   "Department of Computer Sci., University of Utah, Salt
                 Lake City, UT, USA",
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  keywords =     "digital arithmetic; drift; floating point addition;
                 radices; round to even rule; round to odd rule; stable
                 rounding rule",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Kent:1975:CSU,
  author =       "Jan G. Kent",
  title =        "Comparison Sets: a Useful Partitioning of the Space of
                 Floating-Point Operand Pairs",
  crossref =     "IEEE:1975:SCA",
  pages =        "36--39",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kent.pdf",
  abstract =     "In this paper the definition of comparison sets and a
                 discussion of their usefulness are presented based on
                 the research work reported in (14). In addition some
                 new results concerning the distribution of floating
                 point (FLP) operand pairs over comparison sets are
                 given.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@InProceedings{Klatte:1975:CPI,
  author =       "R. Klatte and Ch. Ullrich",
  title =        "Consequences of a Properly Implemented Computer
                 Arithmetic for Periodicities of Iterative Methods",
  crossref =     "IEEE:1975:SCA",
  pages =        "24--32",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Klatte.pdf",
  abstract =     "In ordered sets it is possible to show under certain
                 assumptions two basic theorems concerning the cycle
                 length of sequences of iterates generated by monotone
                 operators. These results are applied to different
                 iterative methods, where the conclusions are valid for
                 the sequences of iterates produced by the numerical
                 computations only, if the used computer arithmetic is
                 properly implemented.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3; cycle, weakly cyclic vector function;
                 floating-point arithmetic; Rounding invariant
                 structures",
}

@InProceedings{Kornerup:1975:UND,
  author =       "Peter Kornerup",
  title =        "A Unified Numeric Data Type in {Pascal}",
  crossref =     "IEEE:1975:SCA",
  pages =        "40--47",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kornerup.pdf",
  abstract =     "It is proposed to substitute the standard data type
                 {\em real\/} of a high level language, with a unified
                 data representation which can include a variety of
                 interpretations as well as formats, in order to allow
                 experiments with an environment containing a spectrum
                 of non-standard arithmetics, as well as
                 standard.\par

                 The implementation of a system is described where
                 syntactic extensions to a language are made to support
                 a microprogrammed virtual arithmetic unit which can
                 treat variants such as integers, normalized, and
                 unnormalized floating point numbers and intervals,
                 within a unified representation.\par

                 More specifically Pascal is chosen as the base
                 language, because it allows the user to define new data
                 types, and the extension then mainly consists in
                 substituting the simple (unstructured) data type {\em
                 real\/} with a skeletal structured type (which will be
                 called {\em numeric\/}).\par

                 The system is intended to be implemented on a
                 microprogrammable processor (called MATHILDA) with a 64
                 bit wide datapath. The language Pascal has already been
                 partially implemented based on a stack machine
                 specifically designed for that language, and realized
                 by interpretation in microcode. The present compiler
                 was constructed with the aid of a parser-generator
                 system, which will allow the language extensions to be
                 made with a moderate effort.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@Article{Kreifelts:1975:OBF,
  author =       "T. Kreifelts",
  title =        "{Optimale Basiswahl f{\"u}r eine Gleitkomma-Arithmetik
                 (Berichtigung)} \toenglish {Optimal Basis Choice for a
                 Floating-Point Arithmetic (Correction)} \endtoenglish",
  journal =      j-COMPUTING,
  volume =       "14",
  number =       "??",
  pages =        "313--314",
  month =        "????",
  year =         "1975",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Fri Sep 16 16:30:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@InProceedings{Krishnamurthy:1975:MPU,
  author =       "E. V. Krishnamurthy",
  title =        "Matrix Processors Using $p$-{ADIC} Arithmetic for
                 Exact Linear Computations",
  crossref =     "IEEE:1975:SCA",
  pages =        "92--97",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Krishnamurthy.pdf",
  abstract =     "A unique code (called Hensel's code) is derived for a
                 rational number, by truncating its infinite $p$-adic
                 expansion. The four basic arithmetic algorithms for
                 these codes are described and their application to
                 rational matrix computations is demonstrated by solving
                 a system of linear equations exactly, using the
                 Gaussian elimination procedure.\par

                 A comparative study of the computational complexity
                 involved in this arithmetic and the multiple prime
                 module arithmetic is made with reference to matrix
                 computations. On this basis, a multiple $p$-adic scheme
                 is suggested for the design of a highly parallel matrix
                 processor.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@Article{Ku:1975:FPC,
  author =       "W. Ku and Siu-Ming Ng",
  title =        "Floating-point coefficient sensitivity and roundoff
                 noise of recursive digital filters realized in ladder
                 structures",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "22",
  number =       "12",
  pages =        "927--936",
  month =        dec,
  year =         "1975",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "Coefficient sensitivity and roundoff error with
                 floating-point rounding have been investigated for
                 several digital ladder filter structures. It is found
                 that in all the cases studied, the ladder structures
                 first proposed by Fettweis show a much lower \ldots{}",
}

@InProceedings{Kuck:1975:RRN,
  author =       "D. J. Kuck and D. S. Parker and A. H. Sameh",
  title =        "{ROM}-Rounding: a New Rounding Scheme",
  crossref =     "IEEE:1975:SCA",
  pages =        "67--72",
  year =         "1975",
  bibdate =      "Thu Sep 01 12:13:06 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kuck.pdf",
  abstract =     "ROM-rounding is introduced and is shown to compare
                 favorably with existing floating-point rounding methods
                 on design considerations and on performance over a
                 series of error tests. The error-retarding value of
                 guard digits, of rounding the aligned operand, and of
                 rounding in general are discussed.",
  acknowledgement = ack-nj,
  keywords =     "ARITH-3",
}

@Article{Kulisch:1975:FIF,
  author =       "U. Kulisch",
  title =        "Formalization and implementation of floating-point
                 arithmetics",
  journal =      j-COMPUTING,
  volume =       "14",
  number =       "4",
  pages =        "323--348",
  year =         "1975",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65G05 (68A10)",
  MRnumber =     "53 14897",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  reviewer =     "A. D. Booth",
}

@InProceedings{Kulisch:1975:MFC,
  author =       "U. Kulisch",
  title =        "Mathematical Foundation of Computer Arithmetic",
  crossref =     "IEEE:1975:SCA",
  pages =        "1--13",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Kulisch.pdf",
  abstract =     "During the last years a number of papers concerning a
                 mathematical foundation of computer arithmetic have
                 been written. Some of these papers are still
                 unpublished. The papers consider the spaces which occur
                 in numerical computations on computers in dependence of
                 a properly defined computer arithmetic. The following
                 treatment gives a summary of the main ideas of these
                 papers. Many of the proofs had to be sketched or
                 completely omitted. In such cases the full information
                 can be found in the references.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@InProceedings{Lacroix:1975:PEM,
  author =       "Arild Lacroix",
  title =        "Limit cycles in floating point digital filters",
  crossref =     "Swamy:1975:PEM",
  pages =        "475--479",
  year =         "1975",
  MRclass =      "94A05",
  MRnumber =     "55 12278",
  bibdate =      "Fri Dec 08 12:19:10 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  reviewer =     "Krzysztof Sapiecha",
}

@Article{Landauro:1975:ODC,
  author =       "A. Landauro and J. Lienard",
  title =        "On Overflow Detection and Correction in Digital
                 Filters",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "12",
  pages =        "1226--1228",
  month =        dec,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224168",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:59 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672761",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Lang:1975:DPA,
  author =       "Allan L. Lang and Bruce D. Shriver",
  title =        "The Design of a Polymorphic Arithmetic Unit",
  crossref =     "IEEE:1975:SCA",
  pages =        "48--55",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Lang.pdf",
  abstract =     "This paper presents results which stem from a research
                 effort concerned with the specification and design of
                 arithmetic units which can execute nonstandard integer
                 and floating-point arithmetic. An arithmetic unit is
                 proposed whose characteristics are based on user
                 specifications and subsequently is termed a Polymorphic
                 Arithmetic Unit (PAU). The user binds the identity of
                 the PAU by specifying the contents of various
                 descriptors and semantic interpretation tables which
                 the PAU accesses during its execution. This capability
                 removes several of the restrictions found in
                 commercially available arithmetic units and potentially
                 assists in making mathematically software portable.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@Article{Laurie:1975:PIR,
  author =       "D. P. Laurie",
  title =        "Propagation of Initial Rounding Error in
                 {Romberg}-Like Quadrature",
  journal =      j-BIT,
  volume =       "15",
  number =       "3",
  pages =        "277--282",
  month =        sep,
  year =         "1975",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01933660",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:14 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=15&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=15&issue=3&spage=277",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point arithmetic; rounding errors",
}

@Article{Lemeire:1975:CEI,
  author =       "Frans Lemeire",
  title =        "Computation of Equivalent Inherent Rounding Errors in
                 the Solution of a Set of Linear Equations",
  journal =      j-BIT,
  volume =       "15",
  number =       "1",
  pages =        "65--71",
  month =        mar,
  year =         "1975",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01932997",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:14 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=15&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=15&issue=1&spage=65",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point arithmetic; rounding errors",
}

@Article{Linnainmaa:1975:TAS,
  author =       "Seppo Linnainmaa",
  title =        "Towards Accurate Statistical Estimation of Rounding
                 Errors in Floating-Point Computations",
  journal =      j-BIT,
  volume =       "15",
  number =       "2",
  pages =        "165--173",
  month =        jun,
  year =         "1975",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01932690",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65G05",
  MRnumber =     "58 19090",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=15&issue=2&spage=165",
  abstract =     "A new method of estimating a posteriori the
                 statistical characteristics of the rounding errors of
                 an arbitrary algorithm is presented. This method is
                 based on a discrete model of the distribution of
                 rounding errors which makes more accurate estimates
                 possible. The analysis is given for both rounding and
                 truncating arithmetic. Finally, some experimental
                 results are reported.",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point arithmetic; rounding errors",
}

@InProceedings{Lipovski:1975:RND,
  author =       "G. J. Lipovski",
  title =        "On Residue Number {A/D} and {D/A} Converters",
  crossref =     "IEEE:1975:SCA",
  pages =        "197--199",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Lipovski.pdf",
  abstract =     "A very simple analog to digital converter and digital
                 to analog converter is described for residue number
                 digital processing. These simple devices make it
                 feasible to replace analog components with
                 comparatively inexpensive digital processors that use
                 residue, or modulus, arithmetic capable of operating at
                 very high speeds. Using off-the-shelf integrated
                 circuits, addition, subtraction or multiplication of
                 about 15 bits of accuracy can easily be done in as
                 little as fifty nanoseconds. Any function using these
                 operations (polynomial expansions, linear filters, Fast
                 Fourier Transforms) can be economically implemented in
                 a pipeline or other structure to get very fast systems.
                 Moreover, a stage in the pipeline can correct for
                 nonlinearities in the A/D or D/A converters. The simple
                 devices described herein make residue arithmetic
                 digital processors extremely attractive for use in fast
                 analog systems.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3; residue number system",
}

@Article{Liu:1975:REF,
  author =       "B. Liu and T. Kaneko",
  title =        "Roundoff error in fast {Fourier} transforms",
  journal =      j-PROC-IEEE,
  volume =       "63",
  number =       "6",
  pages =        "991--992",
  month =        jun,
  year =         "1975",
  CODEN =        "IEEPAD",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
  summary =      "The finite word length used in the computer causes
                 round-off error in the calculation of Fourier
                 coefficients. When the fast Fourier transform method is
                 used, the statistical mean-square error has been
                 previously determined [3] for the case of the
                 \ldots{}",
}

@Article{Lorez:1975:BGB,
  author =       "H. Lorez and F. J. Urbanek and H. Will and R. Weiss
                 and W. Baron and others",
  title =        "{Buchbesprechungen} ({German}) {Book Reviews}",
  journal =      j-COMPUTING,
  volume =       "14",
  number =       "3",
  pages =        "315--322",
  month =        sep,
  year =         "1975",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Fri Sep 16 16:30:39 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Kreifelts:1973:OBG}.",
  acknowledgement = ack-nj,
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  language =     "German",
}

@Book{Luke:1975:MFT,
  author =       "Yudell L. Luke",
  title =        "Mathematical Functions and Their Approximations",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xvii + 568",
  year =         "1975",
  ISBN =         "0-12-459950-8, 1-4832-6245-6 (e-book)",
  ISBN-13 =      "978-0-12-459950-5, 978-1-4832-6245-1 (e-book)",
  LCCN =         "QA55 .L96 1975",
  bibdate =      "Fri Jun 30 05:58:16 MDT 2023",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  URL =          "https://shop.elsevier.com/books/mathematical-functions-and-their-approximations/luke/978-0-12-459950-5",
  acknowledgement = ack-nhfb,
  libnote =      "Not in my library.",
  remark =       "An updated version of part of Handbook of mathematical
                 functions with formulas, graphs, and mathematical
                 tables, edited by M. Abramowitz and I. A. Stegun.
                 Includes indexes.",
  subject =      "Mathematics; Tables; Fonctions (Math{\'e}ematiques);
                 Math{\'e}ematiques; Calculus; Mathematical Analysis;
                 Mathematics; Approximation; Funktion; Mathematik;
                 Spezielle Funktion",
  tableofcontents = "Preface / xv \\
                 \\
                 I. The Gamma Function and Related Functions \\
                 \\
                 1.1 Definitions and Elementary Properties / 1 \\
                 1.2 Power Series and Other Series Expansions / 1 \\
                 1.3 Asymptotic Expansions / 7 \\
                 1.4 Rational Approximations for y (z) / 13 \\
                 1.5 Inequalities / 17 \\
                 1.6 Bibliographic and Numerical Data / 20 \\
                 1.6.1 General References / 20 \\
                 1.6.2 Description of and References to Tables / 21 \\
                 1.6.3 Description of and References to Other
                 Approximations and Expansions / 22 \\
                 \\
                 II. The Binomial Function \\
                 \\
                 2.1 Power Series / 24 \\
                 2.2 Expansions in Series of Jacobi and Chebyshev
                 Polynomials / 24 \\
                 2.3 Expansions in Series of Bessel Functions / 26 \\
                 2.4 Pad{\'e} Approximations / 27 \\
                 24.1 $(1 + 1 / z)^{-c}$ / 27 \\
                 2.4.2 The Square Root / 28 \\
                 2.4.3 Pad{\'e} Coefficients / 30 \\
                 2.4.4 The Function $e^{-w}$ / 31 \\
                 2.5 Inequalities / 34 \\
                 \\
                 III. Elementary Functions \\
                 \\
                 3.1 Logarithmic Functions / 36 \\
                 3.1.1 Power Series / 36 \\
                 3.1.2 Expansion in Series of Chebyshev Polynomials / 38
                 \\
                 3.1.3 Pad{\'e} Approximations / 39 \\
                 3.1.4 Inequalities / 41 \\
                 3.2 Exponential Function / 42 \\
                 3.2.1 Series Expansions / 42 \\
                 3.2.2 Expansions in Series of Jacobi and Chebyshev
                 Polynomials and Bessel Functions / 42 \\
                 3.2.3 Pad{\'e} Approximations / 46 \\
                 3.2.4 Inequalities / 51 \\
                 3.3 Circular and Hyperbolic Functions / 52 \\
                 3.3.1 Power Series / 52 \\
                 3.3.2 Expansions in Series of Jacobi and Chebyshev
                 Polynomials and Bessel Functions / 52 \\
                 3.3.3 Rational and Pad{\'e} Approximations / 57 \\
                 3.3.4 Inequalities / 60 \\
                 3.4 Inverse Circular and Hyperbolic Functions / 61 \\
                 3.4.1 Power Series / 61 \\
                 3.4.2 Expansions in Series of Chebyshev Polynomials /
                 63 \\
                 3.4.3 Pad{\'e} Approximations / 68 \\
                 3.4.4 Inequalities / 72 \\
                 3.5 Bibliographic and Numerical Data / 74 \\
                 3.5.1 Description of and References to Tables / 74 \\
                 3.5.2 Description of and References to Other
                 Approximations and Expansions / 74 \\
                 \\
                 IV. Incomplete Gamma Functions \\
                 \\
                 4.1 Definitions and Series Expansions / 77 \\
                 4.2 Differential Equations and Difference Equations /
                 78 \\
                 4.3 Pad{\'e} Approximations / 79 \\
                 4.3.1 $_1F_1(1; \nu + 1; -z)$ / 79 \\
                 4.3.2 $z^{1 - \nu} e^z \Gamma(\nu, z)$ / 82 \\
                 4.3.3 The Error $T_n(\nu, z)$ for $|{\rm arg} z/k| \leq
                 \pi$ / 84 \\
                 4.3.4 The Negative Real Axis and the Zeros of $F_n(\nu,
                 z)$ / 89 \\
                 4.4 Inequalities / 95 \\
                 4.4.1 $H(\nu, z)$ / 95 \\
                 4.4.2 $\Gamma(\nu, z)$ / 96 \\
                 4.5 Notes on the Computation of the Incomplete Gamma
                 Function / 97 \\
                 4.6 Exponential Integrals / 103 \\
                 4.6.1 Relation to Incomplete Gamma Function and Other
                 Properties / 103 \\
                 4.6.2 Expansions in Series of Chebyshev Polynomials /
                 104 \\
                 4.6.3 Rational and Pad Approximations / 106 \\
                 4.7 Cosine and Sine Integrals / 115 \\
                 4.7.1 Relation to Exponential Integral and Other
                 Properties / 115 \\
                 4.7.2 Expansions in Series of Chebyshev Polynomials /
                 116 \\
                 4.8 Error Functions / 119 \\
                 4.8.1 Relation to Incomplete Gamma Function and Other
                 Properties / 119 \\
                 4.8.2 Expansions in Series of Chebyshev Polynomials and
                 Bessel Functions / 122 \\
                 4.8.3 Pad{\'e} Approximations / 124 \\
                 4.8.4 Trapezoidal Rule Approximations / 134 \\
                 4.8.5 Inequalities / 137 \\
                 4.9 Fresnel Integrals / 139 \\
                 4.9.1 Relation to Error Functions and Other Properties
                 / 139 \\
                 4.9.2 Expansions in Series of Chebyshev Polynomials /
                 140 \\
                 4.10 Bibliographic and Numerical Data / 143 \\
                 4.10.1 References / 143 \\
                 4.10.2 Description of and References to Tables / 143
                 \\
                 4.10.3 Description of and References to Other
                 Approximations and Expansions / 149 \\
                 \\
                 V. The Generalized Hypergeometric Function $_pF_g$ and
                 the $G$-Function \\
                 \\
                 5.1 Introduction / 154 \\
                 5.2 The $_pF_q$ / 155 \\
                 5.2.1 Power Series / 155 \\
                 5.2.2 Derivatives and Contiguous Relations / 159 \\
                 5.2.3 Integral Representations and Integrals Involving
                 the $_pF_q$ / 160 \\
                 5.2.4 Evaluation for Special Values of the Variable and
                 Parameters / 163 \\
                 5.3 The $G$-Function / 170 \\
                 5.3.1 Definition and Relation to the $_pF_q$ / 170 \\
                 5.3.2 Elementary Properties / 176 \\
                 5.3.3 Analytic Continuation of $G_{p, p}^{m, n}(z)$ /
                 178 \\
                 5.4 The Confluence Principle / 179 \\
                 5.5 Multiplication Theorems / 184 \\
                 5.6 Integrals Involving $G$-Functions / 186 \\
                 5.7 Differential Equations / 190 \\
                 5.7.1 The $_pF_q$ / 190 \\
                 5.7.2 The $G$-Function / 192 \\
                 5.8 Series of $G$-Functions / 194 \\
                 5.8.1 Introduction / 194 \\
                 5.8.2 Notation / 194 \\
                 5.8.3 Expansion Theorems / 197 \\
                 5.9 Asymptotic Expansions / 199 \\
                 5.9.1 $G_{p, q}^{q, n}(z)$, $n = 0, 1$ / 199 \\
                 5.9.2 $G_{p, q}^{m, n}(z)$ / 201 \\
                 5.9.3 $_pF_q(z)$ / 206 \\
                 5.10 Expansions in Series of Generalized Jacobi,
                 Generalized Laguerre and Chebyshev Polynomials / 213
                 \\
                 5.10.1 Expansions for $G$-Functions / 213 \\
                 5.10.2 Expansions for $_pF_q$ / 220 \\
                 5.11 Expansions in Series of Bessel Functions / 223 \\
                 5.12 Polynomial and Rational Approximations / 224 \\
                 5.13 Recurrence Formulas for Polynomials and Functions
                 Occurring in Approximations to Generalized
                 Hypergeometric Functions / 234 \\
                 5.13.1 Introduction / 234 \\
                 5.13.2 Recursion Formulas for Extended Jacobi and
                 Laguerre Functions / 235 \\
                 5.13.3 Recursion Formulas for the Numerator and
                 Denominator Polynomials in the Rational Approximations
                 for the Generalized Hypergeometric Function / 244 \\
                 5.13.4 Recursion Formula for Coefficients in the
                 Expansion of the $G$-Function in Series of Extended
                 Jacobi Polynomials / 247 \\
                 5.14 Inequalities / 252 \\
                 \\
                 VI. The Gaussian Hypergeometric Function $_2F_1$ \\
                 \\
                 6.1 Introduction / 257 \\
                 6.2 Elementary Properties / 257 \\
                 6.2.1 Derivatives / 257 \\
                 6.2.2 Contiguous Relations / 258 \\
                 6.2.3 Integral Representations / 259 \\
                 6.3 Differential Equations / 260 \\
                 6.4 Kummer Solutions and Transformation Formulae / 262
                 \\
                 6.5 Analytic Continuation / 263 \\
                 6.6 The Complete Solution and Wronskians / 265 \\
                 6.7 Quadratic Transformations / 270 \\
                 6.8 The $_2F_1$ for Special Values of the Argument /
                 271 \\
                 6.9 Expansion in Series of Chebyshev Polynomials / 274
                 \\
                 6.10 Pad{\'e} Approximations for $_2F_1(1, \sigma;\rho
                 + 1;-1/z)$ / 274 \\
                 6.11 Inequalities / 278 \\
                 6.12 Bibliographic and Numerical Data / 279 \\
                 6.12.1 References / 279 \\
                 6.12.2 Description of and References to Tables / 279
                 \\
                 \\
                 VII. The Confluent Hypergeometric Function \\
                 \\
                 7.1 Introduction / 284 \\
                 7.2 Integral Representations / 284 \\
                 7.3 Elementary Relations / 285 \\
                 7.3.1 Derivatives / 285 \\
                 7.3.2 Contiguous Relations / 285 \\
                 7.3.3 Products of Confluent Functions / 286 \\
                 7.4 Differential Equations / 287 \\
                 7.5 The Complete Solution and Wronskians / 288 \\
                 7.6 Asymptotic Expansions / 291 \\
                 7.7 Expansions in Series of Chebyshev Polynomials / 293
                 \\
                 7.8 Expansions in Series of Besse! Functions / 294 \\
                 7.9 Inequalities / 295 \\
                 7.10 Other Notations and Related Functions / 295 \\
                 7.11 Bibliographic and Numerical Data / 296 \\
                 7.11.1 References / 296 \\
                 7.11.2 Description of and References to Tables and
                 Other Approximations / 296 \\
                 \\
                 VIII. Identification of the $_pF_q$, and $G$-Functions
                 with the Special Functions \\
                 \\
                 8.1 Introduction / 298 \\
                 8.2 Named Special Functions Expressed as $_pF_q$'s /
                 298 \\
                 8.2.1 Elementary Functions / 298 \\
                 8.2.2 The Incomplete Gamma Function and Related
                 Functions / 298 \\
                 8.2.3 The Gaussian Hypergeometric Function / 298 \\
                 8.2.4 Legendre Functions / 299 \\
                 8.2.5 Orthogonal Polynomials / 299 \\
                 8.2.6 Complete Elliptic Integrals / 299 \\
                 8.2.7 Confluent Hypergeometric Functions, Whittaker
                 Functions and Bessel Functions / 300 \\
                 8.3 Named Functions Expressed in Terms of the
                 $G$-Function / 300 \\
                 8.4 The $G$-Function Expressed as a Named Function /
                 306 \\
                 \\
                 IX. Bessel Functions and Their Integrals \\
                 \\
                 9.1 Introduction / 311 \\
                 9.2 Definitions, Connecting Relations and Power Series
                 / 311 \\
                 9.3 Difference--Differential Formulas / 313 \\
                 9.4 Products of Bessel Functions / 314 \\
                 9.5 Asymptotic Expansions for Large Variable / 315 \\
                 9.6 Integrals of Bessel Functions / 315 \\
                 9.7 Expansions in Series of Chebyshev Polynomials / 316
                 \\
                 9.8 Expansions in Series of Bessel Functions / 360 \\
                 9.9 Rational Approximations / 361 \\
                 9.9.1 Introduction / 361 \\
                 9.9.2 $I_\nu(z)$, $z$ Small / 361 \\
                 9.9.3 $K_\nu(z)$, $z$ Large / 366 \\
                 9.10 Computation of Bessel Functions by Use of
                 Recurrence Formulas / 380 \\
                 9.10.1 Introduction / 380 \\
                 9.10.2 Backward Recurrence Schemata for Generating
                 $I_\nu(z)$ / 380 \\
                 9.10.3 Closed Form Expressions / 382 \\
                 9.10.4 Expressions for $J_\nu(z)$ / 389 \\
                 9.10.5 Numerical Examples / 392 \\
                 9.11 Evaluation of Bessel Functions by Application of
                 Trapezoidal Type Integration Formulas / 395 \\
                 9.12 Inequalities / 399 \\
                 9.13 Bibliographic and Numerical Data / 403 \\
                 9.13.1 References / 403 \\
                 9.13.2 Description of and References to Tables / 404
                 \\
                 9.13.3 Description of and References to Other
                 Approximations and Expansions / 410 \\
                 \\
                 X. Lommel Functions, Struve Functions, and Associated
                 Bessel Functions \\
                 \\
                 10.1 Definitions, Connecting Relations and Power Series
                 / 413 \\
                 10.2 Asymptotic Expansions / 415 \\
                 10.3 Expansions in Series of Chebyshev Polynomials and
                 Bessel Functions / 415 \\
                 10.4 Rational Approximations for $H_\nu(z) - Y_\nu(z)$
                 and the Errors in These Approximations / 422 \\
                 10.5 Bibliographic and Numerical Data / 426 \\
                 10.5.1 References / 426 \\
                 10.5.2 Description of and References to Tables / 426
                 \\
                 \\
                 XI. Orthogonal Polynomials \\
                 \\
                 11.1 Introduction / 428 \\
                 11.2 Orthogonal Properties / 428 \\
                 11.3 Jacobi Polynomials / 436 \\
                 11.3.1 Expansion Formulae / 436 \\
                 11.3.2 Difference--Differential Formulae / 439 \\
                 11.3.3 Integrals / 439 \\
                 11.3.4 Expansion of $x^\rho$ in Series of Jacobi
                 Polynomials / 440 \\
                 11.3.5 Convergence Theorems for the Expansion of
                 Arbitrary Functions in Series of Jacobi Polynomials /
                 442 \\
                 11.3.6 Evaluation and Estimation of the Coefficients in
                 the Expansion of a Given Function $f(x)$ in Series of
                 Jacobi Polynomials / 443 \\
                 11.4 The Chebyshev Polynomials $T_n(x)$ and $U_n(x)$ /
                 453 \\
                 11.5 The Chebyshev Polynomials $T_n^*(x)$ and
                 $U_n^*(x)$ / 459 \\
                 11.6 Coefficients for Expansion of Integrals of
                 Functions in Series of Chebyshev Polynomials of the
                 First Kind / 464 \\
                 11.6.1 Introduction / 464 \\
                 11.6.2 Series of Shifted Chebyshev Polynomials / 464
                 \\
                 11.6.3 Series of Chebyshev Polynomials of Even Order /
                 468 \\
                 11.6.4 Series of Chebyshev Polynomials of Odd Order /
                 468 \\
                 11.7 Orthogonality Properties of Chebyshev Polynomials
                 with Respect to Summation / 469 \\
                 11.8 A Nesting Procedure for the Computation of
                 Expansions in Series of Functions Where the Functions
                 Satisfy a Linear Finite Difference Equation / 475 \\
                 \\
                 XII. Computation by Use of Recurrence Formulas \\
                 \\
                 12.1 Introduction / 483 \\
                 12.2 Homogeneous Difference Equations / 483 \\
                 12.3 Inhomogeneous Difference Equations / 487 \\
                 \\
                 XIII. Some Aspects of Rational and Polynomial
                 Approximations \\
                 \\
                 13.1 Introduction / 490 \\
                 13.2 Approximations in Series of Chebyshev Polynomials
                 of the First Kind / 490 \\
                 13.3 The Pad{\'e} Table / 493 \\
                 13.4 Approximation of Functions Defined by a
                 Differential Equation --- The $\tau$-Method / 495 \\
                 13.5 Approximations of Functions Defined by a Series /
                 499 \\
                 13.6 Solution of Differential Equations in Series of
                 Chebyshev Polynomials of the First Kind / 500 \\
                 \\
                 XIV. Miscellaneous Topics \\
                 \\
                 14.1 Introduction / 505 \\
                 14.2 Bernoulli Polynomials and Numbers / 505 \\
                 14.3 $D$ and $\delta$ Operators / 507 \\
                 14.4 Computation and Check of the Tables / 509 \\
                 14.5 Mathematical Constants / 512 \\
                 14.6 Late Bibliography / 516 \\
                 \\
                 Bibliography / 517 \\
                 \\
                 Notation Index / 545 \\
                 \\
                 Subject Index / 551",
}

@Article{Martinson:1975:DMF,
  author =       "L. Martinson and R. Smith",
  title =        "Digital matched filtering with pipelined floating
                 point fast {Fourier} transforms ({FFT}'s)",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "23",
  number =       "2",
  pages =        "222--234",
  month =        apr,
  year =         "1975",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  summary =      "A special floating point arithmetic technique for fast
                 Fourier transform (FFT) processors has been developed.
                 The implementation of a high-speed pipeline FFT matched
                 filter using the method employs significantly fewer
                 components than a fixed-point \ldots{}",
}

@InProceedings{Matula:1975:FSF,
  author =       "D. W. Matula",
  title =        "Fixed-Slash and Floating-Slash Arithmetic",
  crossref =     "IEEE:1975:SCA",
  pages =        "90--91",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:45:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Matula.pdf",
  abstract =     "A finite precision rational number system provides for
                 representation of a collection of rational numbers
                 subject to limitations on numerator and denominator
                 magnitude. In fixed-point and floating-point radix
                 number systems, only rationals of the form $ i /
                 \beta^j $, where $ \beta $ is the base, can be
                 realized. In contrast, a finite precision rational
                 number system will allow representation of practically
                 all simple fractions encountered in applications.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@Article{McDonald:1975:TCQ,
  author =       "T. G. McDonald and R. K. Guha",
  title =        "The Two's Complement Quasi-Serial Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "12",
  pages =        "1233--1235",
  month =        dec,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224170",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:59 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672763",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Meo:1975:ANT,
  author =       "A. R. Meo",
  title =        "Arithmetic Networks and Their Minimization Using a New
                 Line of Elementary Units",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "3",
  pages =        "258--280",
  month =        mar,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224207",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672800",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Miller:1975:SRA,
  author =       "Webb Miller",
  title =        "Software for Roundoff Analysis",
  journal =      j-TOMS,
  volume =       "1",
  number =       "2",
  pages =        "108--128",
  month =        jun,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355637.355639",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65G05",
  MRnumber =     "53 \#9622",
  bibdate =      "Fri Aug 26 23:44:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "James H. Wilkinson",
}

@Article{Nance:1975:IFR,
  author =       "Richard E. Nance and Claude {Overstreet, Jr.}",
  title =        "Implementation of {Fortran} Random Number Generators
                 on Computers with One's Complement Arithmetic",
  journal =      j-J-STAT-COMPUT-SIMUL,
  volume =       "4",
  number =       "3",
  pages =        "235--243",
  month =        "????",
  year =         "1975",
  CODEN =        "JSCSAJ",
  DOI =          "https://doi.org/10.1080/00949657508810126",
  ISSN =         "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
  ISSN-L =       "0094-9655",
  bibdate =      "Thu Jan 05 10:58:18 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/00949657508810126",
  abstract =     "Random number generators can be programmed in FORTRAN
                 using several methods on 1's complement machines. We
                 have presented several methods for the SRU 1107--1108
                 and CDC 6000 and CYBER series, the two most popular
                 that utilize 1's complement arithmetic. We believe the
                 logical mask method to be the most efficient technique
                 based on execution time on both machines. This method
                 requires only a little more than one-half the time of
                 the signed residue method on the SRU 1107--1108 and a
                 little more than two thirds the time of the unsigned
                 residue method on the CDC 6000--CYBER. A fast composite
                 generator in FORTRAN uses the logical mask method
                 combined with the FLD function to implement the table
                 approach of MacLaren and Marsaglia (1965). This
                 generator proves to be more than twice as fast as a
                 previous one for the SRU 1108, Marsaglia and Bray
                 (1968)",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Computation and Simulation",
  journal-URL =  "http://www.tandfonline.com/loi/gscs20",
  onlinedate =   "20 Mar 2007",
}

@Article{Nelson:1975:PPF,
  author =       "James M. Nelson and Charles E. Cohn",
  title =        "Parallel Processing in {FORTRAN} with Floating-Point
                 Hardware",
  journal =      j-SPE,
  volume =       "5",
  number =       "1",
  pages =        "65--68",
  month =        jan # "\slash " # mar,
  year =         "1975",
  CODEN =        "SPEXBL",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Sat May 31 13:36:16 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/spe.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Software---Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
}

@Article{Newbery:1975:PES,
  author =       "A. C. R. Newbery",
  title =        "Polynomial Evaluation Schemes",
  journal =      j-MATH-COMPUT,
  volume =       "29",
  number =       "132",
  pages =        "1046--1050",
  month =        oct,
  year =         "1975",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "B0290D (Functional analysis); C4120 (Functional
                 analysis)",
  corpsource =   "Department of Computer Sci., University of Kentucky,
                 Lexington, KY, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "floating; function evaluation; point arithmetic;
                 polynomial evaluation algorithm; polynomials; round off
                 error",
  treatment =    "T Theoretical or Mathematical",
}

@Manual{NSC:1975:IFP,
  author =       "{National Semiconductor Corporation}",
  title =        "{IMP-16F\slash 400} floating point firmware technical
                 description",
  type =         "Publication - National Semiconductor Corporation no.
                 4200072A",
  organization = "National Semiconductor Corporation",
  address =      "Santa Clara, CA, USA",
  pages =        "16",
  year =         "1975",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Microprocessors --- Handbooks, manuals, etc.;
                 Microprogramming --- Handbooks, manuals, etc.",
  remark =       "At head of title: Integrated microprocessor-16.",
}

@Article{OKeefe:1975:NFB,
  author =       "K. H. O'Keefe",
  title =        "A Note on Fast Base Extension for Residue Number
                 Systems with Three Moduli",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "11",
  pages =        "1132--1133",
  month =        nov,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264810;
                 https://doi.org/10.1109/T-C.1975.224147",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:58 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35091;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672740",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "An algorithm is given for the base-extension (BE)
                 computation in residue number systems that requires the
                 standard four steps (for systems with three moduli) but
                 which saves hardware. Furthermore, for the particular
                 moduli m-1, m, and m+1 it is \ldots{}",
}

@InCollection{Phillips:1975:BC,
  author =       "E. William Phillips",
  title =        "Binary Calculation",
  crossref =     "Randell:1975:ODC",
  pages =        "293--304",
  year =         "1975",
  bibdate =      "Wed Oct 13 09:51:37 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "The 1936 epigraph credited to this author in
                 \cite[Chapter 7]{Coonen:1984:CPS} says: ``The ultimate
                 aim is to persuade all of the civilized world to
                 abandon the decimal numeration and to use octonal in
                 its place; to discontinue counting in tens and to count
                 in eights instead. However, it seems unlikely that the
                 whole civilized world will be persuaded to complete
                 this change during the next twelve months, having
                 previously declined similar invitations.''",
}

@InProceedings{Rao:1975:TIS,
  author =       "T. R. N. Rao and D. W. Matula",
  title =        "The {Third IEEE Symposium on Computer Arithmetic}:
                 Foreword",
  crossref =     "IEEE:1975:SCA",
  pages =        "v--v",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_contents.pdf;
                 http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_foreword.pdf;
                 http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_preface.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@Article{Reiser:1975:EDF,
  author =       "John F. Reiser and Donald E. Knuth",
  title =        "Evading the Drift in Floating-Point Addition",
  journal =      j-INFO-PROC-LETT,
  volume =       "3",
  number =       "3",
  pages =        "84--87",
  month =        jan,
  year =         "1975",
  CODEN =        "IFPLAT",
  DOI =          "https://doi.org/10.1016/0020-0190(75)90022-8",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Sun Dec 04 12:21:37 1994",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/infoproc1970.bib",
  note =         "See erratum \cite{Reiser:1975:EED}.",
  acknowledgement = ack-nhfb # "\slash " # ack-nj,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  remark =       "From p. 87: ``Actually Tannery's and Scarborough's
                 contradictory arguments [round-up and round-to-even]
                 are both incorrect; for example, the logarithmic law of
                 distribution of leading digits [3] [Benford's Law]
                 implies that the least significant digit of a
                 floating-point number will be odd slightly less often
                 than it will be even, assuming that $b$ is even and $ p
                 > 1$. The real justification for stable rounding is
                 that it eliminates drift.''",
}

@Article{Reiser:1975:EED,
  author =       "John F. Reiser and Donald E. Knuth",
  title =        "Erratum: {``Evading the Drift in Floating-Point
                 Addition''}",
  journal =      j-INFO-PROC-LETT,
  volume =       "3",
  number =       "5",
  pages =        "164--164",
  month =        may,
  year =         "1975",
  CODEN =        "IFPLAT",
  DOI =          "https://doi.org/10.1016/0020-0190(75)90031-9",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Sun Dec 04 12:21:42 1994",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/infoproc1970.bib",
  note =         "See \cite{Reiser:1975:EDF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}

@Article{Rokne:1975:ACI,
  author =       "J. Rokne and P. Lancaster",
  title =        "Algorithm 86. Complex Interval Arithmetic",
  journal =      j-COMP-J,
  volume =       "18",
  number =       "1",
  pages =        "83--85",
  month =        feb,
  year =         "1975",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods); C7310 (Mathematics
                 computing)",
  corpsource =   "Univ. Calgary, Alta., Canada",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "algorithm; complex interval arithmetic; digital
                 arithmetic; floating point; real numbers; subroutines",
  treatment =    "A Application; T Theoretical or Mathematical",
}

@Article{Rubinfield:1975:PMB,
  author =       "L. P. Rubinfield",
  title =        "A Proof of the Modified {Booth}'s Algorithm for
                 Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "10",
  pages =        "1014--1015",
  month =        oct,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224114",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:57 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672707",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Senzig:1975:CA,
  author =       "Don Senzig",
  title =        "Calculator Algorithms",
  journal =      "IEEE Compcon Reader Digest",
  pages =        "139--141",
  year =         "1975",
  bibdate =      "Fri Nov 28 19:19:40 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog number 75CH0920-9C.",
  abstract =     "This paper discusses algorithms for generating the
                 trigonometric, exponential, and hyperbolic functions
                 and their inverses. No invention is claimed here. The
                 algorithm for logarithm was used by Briggs in compiling
                 his table of logarithms in the 1600's. Other earlier
                 references are [cited]. The development presented here
                 is, perhaps, more direct than those given in the above
                 references but leads to the same result.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}

@Article{Shimizu:1975:REF,
  author =       "Tatsujiro Shimizu and Tsunemichi Oohashi",
  title =        "Rounding errors in floating point addition",
  journal =      "TRU Math.",
  volume =       "11",
  pages =        "41--50",
  year =         "1975",
  MRclass =      "65G05",
  MRnumber =     "55 4646",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  reviewer =     "R. P. Brent",
}

@InProceedings{Shriver:1975:BCA,
  author =       "B. D. Shriver and E. K. Reuter",
  title =        "A Bibliography on Computer Arithmetic",
  crossref =     "IEEE:1975:SCA",
  pages =        "241--249",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Biography.pdf",
  abstract =     "This bibliography on computer arithmetic uses, by and
                 large, the format and abbreviations employed by
                 Computing Reviews. It is presented in alphabetical
                 order only and not by individual topics. The topics
                 included, however, span the abstract and implementation
                 problems associated with finite precision computer
                 arithmetic.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@InProceedings{Shriver:1975:UUN,
  author =       "Bruce D. Shriver and Peter Kornerup",
  title =        "The {UNRAU} --- a {Unified Numeric Representation
                 Arithmetic Unit}",
  crossref =     "IEEE:1975:SCA",
  pages =        "179--184",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:46:23 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Shriver.pdf",
  abstract =     "A companion paper entitled, ``A Unified Numeric Data
                 Type in Pascal'', proposes the substitution of the
                 standard data type {\em real\/} of the language Pascal
                 with a unified data representation termed {\em
                 numeric}. The {\em numeric\/} data type can represent a
                 variety of arithmetic operands such as integers,
                 normalized floating point numbers, and centered-radius
                 intervals.\par

                 This paper describes an arithmetic unit which is
                 capable of executing the standard arithmetic operations
                 (addition, subtraction, multiplication, and division)
                 on pairs of operands specified to be of the {\em
                 numeric\/} data type. This arithmetic unit, called the
                 UNRAU --- Unified Numeric Representation Arithmetic
                 Unit, supports operations on operands externally
                 represented as 5-tuples $ (t, a, e, f, r) $. The UNRAU
                 provides for automatic conversion among the various
                 data types and can also be used to perform an explicit
                 conversion on a single operand.\par

                 It is intended to implement the UNRAU on a dynamically
                 microprogrammable microprocessor to determine what host
                 facilities are required to efficiently realize such an
                 arithmetic unit and to experiment with the high level
                 language support of such a unit.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@Article{Smith:1975:CPC,
  author =       "Alan Jay Smith",
  title =        "Comments on a paper by {T. C. Chen} and {I. T. Ho}",
  journal =      j-CACM,
  volume =       "18",
  number =       "8",
  pages =        "463--463",
  month =        aug,
  year =         "1975",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 07:22:40 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#Smith75a;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Chen:1975:SER}.",
  acknowledgement = ack-nhfb,
  classcodes =   "C6130 (Data handling techniques)",
  corpsource =   "University of California, Berkeley, CA, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "advantages; alternatives; binary coded decimal; codes;
                 coding; compression of numbers; data handling; decimal
                 data; decimal floating-point arithmetic; decoding;
                 deletions; Huffman codes; insertions; permutations;
                 storage efficient representation; variable length
                 codes",
  oldlabel =     "Smith75a",
  treatment =    "G General Review; T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Smith75a",
}

@Book{Smith:1975:SAP,
  author =       "Jon M. Smith",
  title =        "Scientific Analysis on the Pocket Calculator",
  publisher =    pub-Wiley,
  address =      pub-Wiley:adr,
  pages =        "xii + 380",
  year =         "1975",
  ISBN =         "0-471-79997-1",
  ISBN-13 =      "978-0-471-79997-9",
  LCCN =         "QA75 .S555",
  bibdate =      "Wed Jun 12 16:56:02 2024",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "Part I: Introduction to Pocket Calculator Analysis
                 \\
                 1: The Pocket Calculator / 3 \\
                 2: Difference Tables, Data Analysis, and Function
                 Evaluation / 53 \\
                 Part II: Numerical Evaluation of Functions on the
                 Pocket Calculator \\
                 3: Elementary Analysis with the Pocket Calculator / 81
                 \\
                 4: Numerical Evaluation of Advanced Functions / 114 \\
                 Part III: Advanced Analysis on the Pocket Calculator
                 \\
                 5: Fourier Analysis / 139 \\
                 6: Numerical Integration / 154 \\
                 7: Linear Systems Simulation / 180 \\
                 8: Chebyshev and Rational Polynomial Approximations for
                 Analytic Substitution / 198 \\
                 9: Determining the Roots of a Function / 224 \\
                 10: Statistics and Probability / 242 \\
                 Part IV: The Programmable Pocket Calculator \\
                 11: The Programmable Pocket Calculator / 283 \\
                 12: Optimization / 300 \\
                 Appendix 1: Some Tricks of the Pocket Calculator Trade
                 / 323 \\
                 Appendix 2: Matrix Analysis on the Pocket Calculator /
                 333 \\
                 Appendix 3: Complex Numbers and Functions / 336 \\
                 Appendix 4: Key Stroke Sequences for Complex Variable
                 Analysis and Hyperbolic Inverse Functions / 340 \\
                 Index",
}

@Article{Smith:1975:SCO,
  author =       "Cyril Stanley Smith",
  title =        "A {Seventeenth-Century} Octonary Arithmetic",
  journal =      j-ISIS,
  volume =       "66",
  number =       "3",
  pages =        "390--394",
  month =        sep,
  year =         "1975",
  CODEN =        "ISISA4",
  ISSN =         "0021-1753 (print), 1545-6994 (electronic)",
  ISSN-L =       "0021-1753",
  bibdate =      "Tue Jul 30 21:29:19 MDT 2013",
  bibsource =    "http://www.jstor.org/action/showPublication?journalCode=isis;
                 http://www.jstor.org/stable/i302314;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/isis1970.bib",
  URL =          "http://www.jstor.org/stable/228846",
  acknowledgement = ack-nhfb,
  fjournal =     "Isis",
  journal-URL =  "http://www.jstor.org/journal/isis",
}

@Article{Soule:1975:AAB,
  author =       "Stephen Soule",
  title =        "Addition in an Arbitrary Base Without Radix
                 Conversion",
  journal =      j-CACM,
  volume =       "18",
  number =       "6",
  pages =        "344--346",
  month =        jun,
  year =         "1975",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 07:23:30 MST 2001",
  bibsource =    "Compendex database;
                 ftp://ftp.ira.uka.de/pub/bibliography/Theory/Seiferas/1975.bib;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm18.html#Soule75;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper presents a generalization of an old
                 programming technique; using it, one may add and
                 subtract numbers represented in any radix, including a
                 mixed radix, and stored one digit per byte in bytes of
                 sufficient size. Radix conversion is unnecessary, no
                 looping is required, and numbers may even be stored in
                 a display (I/O) format. Applications to Cobol, MIX, and
                 hexadecimal sums are discussed.",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods); C6130 (Data
                 handling techniques)",
  classification = "723; 921",
  corpsource =   "University of Calgary, Calgary, Alta., Canada",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  journalabr =   "Commun ACM",
  keywords =     "add; addition; arbitrary base; arbitrary radix
                 arithmetic; Cobol display arithmetic; computer systems
                 programming; data handling; decimal arithmetic; decimal
                 floating-point arithmetic; digital arithmetic;
                 mathematical techniques --- Digital Arithmetic; MIX
                 arithmetic; mixed radix arithmetic; numbers;
                 programming; radix conversion; subtract; subtraction;
                 without radix conversion",
  oldlabel =     "Soule75",
  treatment =    "A Application; T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Soule75",
}

@InProceedings{Stephenson:1975:CSP,
  author =       "Charles Stephenson",
  title =        "Case Study of the Pipelined Arithmetic Unit for the
                 {TI Advanced Scientific Computer}",
  crossref =     "IEEE:1975:SCA",
  pages =        "168--173",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Stephenson.pdf",
  abstract =     "Many scientific applications today require computers
                 which are very fast and capable of processing large
                 amounts of data. Some advances in scientific processing
                 have been slowed due to the lack of supercomputer
                 capabilities which are required primarily in the area
                 of Central Processor speed and the availability of
                 large amounts of high speed memory. Particularly in the
                 fields of modeling and simulation, additional speed and
                 memory capacity are desired to allow increased
                 resolution of the experiment. Technological
                 developments: In such things as integrated circuits,
                 multilayer printed circuit boards, memory speeds, and
                 others have contributed to the ability of computer
                 manufacturers to serve this market. In addition to
                 these developments, however, large advances had to be
                 realized from the standpoint of the basic computer
                 architecture. The concept of pipelining has provided an
                 answer to the large data execution rate required.
                 Pipelined capabilities in the form of arithmetic units
                 and special purpose functional units are included in
                 machines such as the CDC 7600, IBM 360/195, CDC
                 STAR-100, etc. The Texas Instruments Advanced
                 Scientific Computer (ASC) uses the pipeline concept
                 throughout the Central Processor and carries the
                 concept throughout the Central Processor and carries
                 the concept further to include vector instructions in
                 response to the high execution rates required. 3",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@InProceedings{Sterbenz:1975:UA,
  author =       "Pat H. Sterbenz",
  title =        "Understandable Arithmetic",
  crossref =     "IEEE:1975:SCA",
  pages =        "33--35",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Sterbenz.pdf",
  abstract =     "Since the floating-point operations form the basic
                 steps in our programs, the programmer has to understand
                 the results that will be produced by these operations.
                 This paper discusses operations which have been or
                 might be implemented in the hardware. The emphasis is
                 on making the results easy for the user to
                 understand.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@Book{Stone:1975:ICA,
  editor =       "Harold S. Stone and Tien Chi Chen and Michael J. Flynn
                 and Samuel H. Fuller and others",
  title =        "Introduction to computer architecture",
  publisher =    "Science Research Associates",
  address =      "Chicago, IL, USA",
  pages =        "x + 565",
  year =         "1975",
  ISBN =         "0-574-18405-8",
  ISBN-13 =      "978-0-574-18405-4",
  LCCN =         "QA76.5 .I7; QA76.9.A73 I57; QA76.5 .I63; QA76.9.A73
                 I57 1975",
  bibdate =      "Fri Nov 9 19:22:07 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  series =       "SRA computer science series",
  acknowledgement = ack-nhfb,
  subject =      "Electronic digital computers",
}

@InProceedings{Svoboda:1975:SCA,
  author =       "Antonin Svoboda",
  title =        "Self-Checking Adder for Large Scale Integration",
  crossref =     "IEEE:1975:SCA",
  pages =        "108--112",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Svoboda.pdf",
  abstract =     "The testing of LSI chips is expensive and
                 unsatisfactory. On the other hand there are cases (as
                 in space ship computers) where a damaged chip must be
                 localized and replaced. The use of self-checking chips
                 seems to be one of several possible solutions of this
                 problem. The theory of the structure of self-checking
                 logical circuit is covered by literature at least at
                 the fundamental form (see References). However, even
                 when the design principles are supposed to be known,
                 their application to the actual creation of a
                 self-checking circuit of an average complexity is and
                 will remain an art. The reason is quite simple and
                 fundamental optimization of design criteria
                 (engineering qualifications, performance and physical
                 properties of components of the circuits are entities
                 possessing different physical dimensions --- it is
                 impossible to qualify, for instance, two circuits A, B
                 designed for the same task by comparing their speeds
                 and costs if A is faster than B but B is cheaper than
                 A) will never be objective and independent of the
                 talent or whim of the circuit designer.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@Article{Swartzlander:1975:SLN,
  author =       "E. E. {Swartzlander, Jr.} and A. G. Alexopoulos",
  title =        "The Sign\slash Logarithm Number System",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "12",
  pages =        "1238--1242",
  month =        dec,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224172",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:59 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See \cite{Hongyuan:1986:CSL}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672765",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Toma:1975:CLA,
  author =       "C. I. Toma",
  title =        "Cellular Logic Array for High-Speed Signed Binary
                 Number Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "9",
  pages =        "932--935",
  month =        sep,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224340",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:57 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672933",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Trivedi:1975:LAD,
  author =       "Kishor S. Trivedi and Milo{\v{s}} D. Ercegovac",
  title =        "On-Line Algorithms for Division and Multiplication",
  crossref =     "IEEE:1975:SCA",
  pages =        "161--177",
  year =         "1975",
  bibdate =      "Fri Dec 08 10:45:59 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Trivedi_2.pdf",
  abstract =     "In this paper we are considering problems of division
                 and multiplication in a computational environment in
                 which all but basic arithmetic operations satisfy
                 ``on-line'' property: to generate $ j^{\mbox {th}} $
                 digits of the result it is necessary and sufficient to
                 have argument(s) available up to the $ (j +
                 \delta)^{\mbox {th}} $ digit, where the index
                 difference $ \delta $ is a small positive
                 constant.

                 Such an environment, due to its potential to perform a
                 sequence of operations in an overlapped fashion, could
                 conveniently speed up an arithmetic multiprocessor
                 structure it could be useful in certain real-time
                 applications, with inherent on-line properties. The
                 on-line property implies a left-to-right digit-by-digit
                 type of algorithm and consequently, a redundant
                 representation, at least of the results. For addition
                 and subtraction such algorithms satisfying on-line
                 property can be easily specified. Multiplication
                 requires a somewhat more elaborate approach and there
                 are several possible ways of defining an on-line
                 algorithm. However, the existence of an on-line
                 division algorithm is not obvious and its analysis
                 appears interesting.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@InProceedings{Trivedi:1975:UCF,
  author =       "Kishor S. Trivedi",
  title =        "On the Use of Continued Fractions for Digital Computer
                 Arithmetic",
  crossref =     "IEEE:1975:SCA",
  pages =        "137--146",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Trivedi_1.pdf",
  abstract =     "Recently, there has been some interest in the use of
                 continued fractions for digital hardware calculations.
                 We require that the coefficients of the continued
                 fractions be integral powers of two. As a result well
                 known continued fraction expansions of functions cannot
                 be used. Methods of expansion of a large number of
                 functions are presented.\par

                 We show that the problem of selection of coefficients
                 of the continued fractions does not have practical
                 solution in most of the cases we have considered. We
                 conjecture that the solution of a polynomial equation
                 is the only problem that can be solved in our
                 formulation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@MastersThesis{Tzaferos:1975:EBD,
  author =       "Konstantina Tzaferos",
  title =        "Error bounds due to index of significance
                 specifications in floating-point operations with
                 encoded mantissa lengths",
  type =         "Thesis ({M.S.})",
  school =       "California State University, Chico",
  address =      "Chico, CA, USA",
  pages =        "vi + 43",
  year =         "1975",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers --- Programming.;
                 Floating-point arithmetic.",
}

@Manual{Wadsworth:1975:MLP,
  author =       "Nat Wadsworth",
  title =        "Machine Language Programming for the 8008 (and Similar
                 Microcomputers)",
  organization = "Scelbi Computer Consulting. Inc.",
  address =      "1322 Rear --- Boston Post Road, Milford, CT 0646,
                 USA",
  pages =        "172 (chapter numbering)",
  year =         "1975",
  bibdate =      "Fri Dec 01 15:53:00 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.scelbi.com/files/docs/books/Machine%20Language%20Programming%20For%20The%208008.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; multiple-precision
                 arithmetic",
  remark =       "Chapter 5 discusses implementation of floating-point
                 arithmetic in software on the Intel 8008, with
                 assembly-code routines for each operation.",
}

@Article{Wakerly:1975:DUM,
  author =       "J. F. Wakerly",
  title =        "Detection of Unidirectional Multiple Errors Using
                 Low-Cost Arithmetic Codes",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "2",
  pages =        "210--212",
  month =        feb,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224187",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:37 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672780",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Weinberger:1975:HSZ,
  author =       "Arnold Weinberger",
  title =        "High-Speed Zero-Sum Detection",
  crossref =     "IEEE:1975:SCA",
  pages =        "200--207",
  year =         "1975",
  bibdate =      "Wed Nov 14 17:44:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith3/papers/ARITH3_Weinberger.pdf",
  abstract =     "A common requirement accompanying high-speed parallel
                 addition is the early detection that the sum is equal
                 to zero. Normally, this condition is detected from the
                 sum, generally at least two logic gate levels after the
                 sum.\par

                 This paper derives expressions for detecting a zero-sum
                 condition concurrently with or even earlier than the
                 determination of the sum digits proper. As a result, a
                 branch operation based on detecting a zero-sum can be
                 executed earlier.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3",
}

@Article{Wilkinson:1975:PAA,
  author =       "J. H. Wilkinson",
  title =        "The {Pilot ACE at the NPL}",
  journal =      j-RADIO-ELECTRON-ENG,
  volume =       "45",
  number =       "7",
  pages =        "336--340",
  month =        jul,
  year =         "1975",
  CODEN =        "RDEEA4",
  ISSN =         "0033-7722",
  bibdate =      "Mon Nov 1 18:34:26 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Radio and Electronic Engineer",
}

@TechReport{Wozniakowski:1975:NSI,
  author =       "H. Wozniakowski",
  title =        "Numerical stability of iterations for solution of
                 nonlinear equations and large linear systems",
  institution =  "Department of Computer Science, Carnegie-Mellon
                 University",
  address =      "Pittsburgh, PA, USA",
  pages =        "16",
  year =         "1975",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Differential equations, Nonlinear.; Floating-point
                 arithmetic.; Iterative methods (Mathematics); Linear
                 systems.",
}

@Article{Yamashita:1975:EEF,
  author =       "Shin-ichiro Yamashita",
  title =        "On the error estimation in floating-point arithmetic",
  journal =      "Information Processing in Japan",
  volume =       "15",
  pages =        "64--69",
  year =         "1975",
  MRclass =      "65G05",
  MRnumber =     "54 4081",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  reviewer =     "Artenio De Matteis",
}

@Article{Yuen:1975:FPR,
  author =       "C. K. Yuen",
  title =        "On the Floating Point Representation of Complex
                 Numbers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "8",
  pages =        "846--848",
  month =        aug,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224321",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See comments \cite{Bauer:1977:CFP}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672914",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Yuen:1975:NBA,
  author =       "C. K. Yuen",
  title =        "A Note on Base $ - 2 $ Arithmetic Logic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-24",
  number =       "3",
  pages =        "325--329",
  month =        mar,
  year =         "1975",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/T-C.1975.224216",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 07:57:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See comments \cite{Agrawal:1977:CNB}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1672809",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "negative base",
  received =     "25 January 1974; revised 3 June 1978",
  remark-1 =     "From page 328: ``[In base $-2$,] the product of two
                 $n$-bit numbers may have $2 n + 1$ bits.''",
  remark-2 =     "From page 329: ``In general circumstances, however, it
                 is at present difficult to see base $-2$ as a strong
                 competitor against positive base arithmetic. We have
                 seen that arithmetic operations are usually more
                 complex, and fast adders are difficult to design. The
                 range of base $-2$ numbers is not symmetrical: either
                 there are twice as many positive numbers as negative
                 ones, or vice versa.''",
  remark-3 =     "The appendix on page 329 shows a simple algorithm for
                 converting between numbers with base $b$ and base
                 $-b$.",
}

@InProceedings{Andrews:1976:ESR,
  author =       "M. Andrews and S. F. McCormick and G. D. Taylor",
  editor =       "John Gosden",
  booktitle =    "{ACM '76: Proceedings of the 1976 annual conference,
                 Houston Texas USA October 20--22, 1976}",
  title =        "Evaluation of the square root function on
                 microprocessors",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  bookpages =    "576",
  year =         "1976",
  DOI =          "https://doi.org/10.1145/800191.805571",
  ISBN =         "1-4503-7489-1",
  ISBN-13 =      "978-1-4503-7489-7",
  LCCN =         "????",
  bibdate =      "Mon Nov 10 10:11:48 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "ACM 76",
  acknowledgement = ack-nhfb,
  collection =   "ACM 76",
}

@Article{Asai:1976:RRC,
  author =       "H. Asai",
  title =        "A recursive radix conversion formula and its
                 application to multiplication and division",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "2",
  number =       "3--4",
  pages =        "255--265",
  month =        "????",
  year =         "1976",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 18:51:13 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122176900183",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Assmus:1976:NFS,
  author =       "E. F. {Assmus, Jr.} and H. F. {Mattson, Jr.} and
                 Howard E. Sachar",
  title =        "A New Form of the Square Root Bound",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "30",
  number =       "2",
  pages =        "352--354",
  month =        mar,
  year =         "1976",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  bibdate =      "Thu Oct 15 18:16:06 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classification = "B0250 (Combinatorial mathematics); C1160
                 (Combinatorial mathematics)",
  corpsource =   "Department of Math., Lehigh University, Bethlehem, PA,
                 USA",
  fjournal =     "SIAM Journal on Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/siap",
  keywords =     "combinatorial mathematics; linear codes; square root
                 bound; sufficient combinatorial conditions",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Baker:1976:SFB,
  author =       "P. W. Baker",
  title =        "Suggestion for a fast binary sine\slash cosine
                 generator",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-25",
  number =       "??",
  pages =        "1134--1137",
  month =        nov,
  year =         "1976",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1976.1674566",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon May 20 05:24:26 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Brent:1976:FMP,
  author =       "Richard P. Brent",
  title =        "Fast Multiple-Precision Evaluation of Elementary
                 Functions",
  journal =      j-J-ACM,
  volume =       "23",
  number =       "2",
  pages =        "242--251",
  month =        apr,
  year =         "1976",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/321941.321944",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  MRclass =      "68A20 (68A10)",
  MRnumber =     "52 \#16111",
  MRreviewer =   "Amnon Barak",
  bibdate =      "Wed Jan 15 18:12:53 MST 1997",
  bibsource =    "Compendex database;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Let $ f(x) $ be one of the usual elementary functions
                 ($ \exp $, $ \log $, $ \artan $, $ \sin $, $ \cosh $,
                 etc.), and let $ M(n) $ be the number of
                 single-precision operations required to multiply
                 $n$-bit integers. It is shown that $ f(x) $ can be
                 evaluated, with relative error $ O(2 - n) $, in $
                 O(M(n)l o g (n)) $ operations as $ n \rightarrow \infty
                 $, for any floating-point number $x$ (with an $n$-bit
                 fraction) in a suitable finite interval. From the
                 Sch{\"o}nhage--Strassen bound on $ M(n) $, it follows
                 that an $n$-bit approximation to $ f(x) $ may be
                 evaluated in $ O(n \log_(n) \log \log (n)) $
                 operations. Special cases include the evaluation of
                 constants such as $ \pi $ $e$, and $ e^\pi $. The
                 algorithms depend on the theory of elliptic integrals,
                 using the arithmetic-geometric mean iteration and
                 ascending Landen transformations.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  classification = "723",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  journalabr =   "J Assoc Comput Mach",
  keywords =     "computational complexity; computer arithmetic;
                 computer programming",
}

@InProceedings{Brent:1976:MPZ,
  author =       "Richard P. Brent",
  title =        "Multiple-precision zero-finding methods and the
                 complexity of elementary function evaluation",
  crossref =     "Traub:1976:ACC",
  pages =        "151--176",
  year =         "1976",
  MRclass =      "68A20",
  MRnumber =     "54 \#11843",
  MRreviewer =   "Claus-Peter Schnorr",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@MastersThesis{Carter:1976:ANT,
  author =       "Allison Birchard Carter",
  title =        "Applications of number theory to the avoidance of
                 round-off in digital computer systems",
  type =         "Thesis ({M.S.})",
  school =       "University of Florida",
  address =      "Gainesville, FL, USA",
  pages =        "v + 74",
  year =         "1976",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers.; Floating-point
                 arithmetic.; Number theory.",
}

@Article{Cohen:1976:EFD,
  author =       "Daniel I. A. Cohen",
  title =        "An explanation of the first digit phenomenon",
  journal =      j-J-COMB-THEORY-A,
  volume =       "20",
  number =       "3",
  pages =        "367--370",
  month =        may,
  year =         "1976",
  CODEN =        "JCBTA7",
  ISSN =         "0097-3165 (print), 1096-0899 (electronic)",
  ISSN-L =       "0097-3165",
  bibdate =      "Thu Feb 15 16:29:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Combinatorial Theory. Series A",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00973165",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Davies:1976:IPS,
  author =       "M. Davies and B. Dawson",
  title =        "The incrementation parameter in square root
                 iteration",
  journal =      j-J-INST-MATH-APPL,
  volume =       "17",
  number =       "2",
  pages =        "219--223",
  year =         "1976",
  CODEN =        "JMTAA8",
  ISSN =         "0020-2932",
  MRclass =      "65H05",
  MRnumber =     "55 \#9514",
  MRreviewer =   "Luciano Biasini",
  bibdate =      "Fri Apr 5 07:38:01 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0319.65039",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Institute of Mathematics and its
                 Applications",
  journal-URL =  "http://imamat.oxfordjournals.org/content/by/year",
}

@Book{DEC:1976:DHM,
  author =       "{Digital Equipment Corporation}",
  title =        "{DECsystem}-10\slash 20 Hardware Manual",
  publisher =    pub-DP,
  address =      pub-DP:adr,
  edition =      "Fourth",
  pages =        "various",
  month =        mar,
  year =         "1976",
  bibdate =      "Fri Dec 08 13:03:19 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Also published as Stanford Artificial Intelligence
                 Laboratory Operating Note 75, November 1976.",
  acknowledgement = ack-nhfb,
}

@Misc{DeSandre:1976:FPF,
  author =       "Giovanni {De Sandre} and Angelo Subrizi and Franco
                 Bretti",
  title =        "Fixed point to floating point conversion in an
                 electronic computer",
  howpublished = "US Patent US3961170.",
  day =          "1",
  month =        jun,
  year =         "1976",
  bibdate =      "Sat Mar 24 06:14:58 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Patent filed 17 April 1974.",
  URL =          "https://patents.google.com/patent/US3961170A;
                 https://tinyurl.com/ybz9rrqy",
  abstract =     "In a digital electronic computer which comprises a
                 memory including a first and a second register, the
                 first register is receptive of a number to be converted
                 from fixed to floating point notation and the second
                 register is receptive of a significant zero digit with
                 an associated decimal point. Shifting means including a
                 register is operable to shift the contents of either
                 register and aligning means is operable to cause
                 shifting of the second register until the decimal point
                 stored therein is aligned with the decimal point in the
                 first register. Indicating means indicates whether the
                 number stored in the first register is greater or less
                 than one and the shifting means next begins shifting
                 the contents of one or the other of the registers when
                 the number is indicated greater or less than one
                 respectively. A control means includes a detecting
                 means for stopping the shifting means when the decimal
                 point of the second register becomes aligned with the
                 location of the next higher order with respect to the
                 highest significant digit of the first register. The
                 control means also includes counting means which is
                 incremented or decremented by one for each shifting
                 operation in dependence on the direction of shifting.
                 The resultant numbers in the first and second registers
                 represent the mantissa and exponent respectively, of
                 the desired floating point number.",
  acknowledgement = ack-nhfb,
}

@Article{Detlefsen:1976:CRN,
  author =       "Michael Detlefsen and Douglas K. Erlandson and J.
                 Clark Heston and Charles M. Young",
  title =        "Computation with {Roman} numerals",
  journal =      j-ARCH-HIST-EXACT-SCI,
  volume =       "15",
  number =       "2",
  pages =        "141--148",
  month =        jun,
  year =         "1976",
  CODEN =        "AHESAN",
  DOI =          "https://doi.org/10.1007/BF00348497",
  ISSN =         "0003-9519 (print), 1432-0657 (electronic)",
  ISSN-L =       "0003-9519",
  MRclass =      "00A05 (01A20)",
  MRnumber =     "0453407 (56 \#11671)",
  MRreviewer =   "Richard L. Francis",
  bibdate =      "Fri Feb 4 21:50:12 MST 2011",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=15&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/archhistexactsci.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=15&issue=2&spage=141",
  acknowledgement = ack-nhfb,
  fjournal =     "Archive for History of Exact Sciences",
  journal-URL =  "http://link.springer.com/journal/407",
  MRtitle =      "Computation with {Roman} numerals",
}

@MastersThesis{Dickinson:1976:PAA,
  author =       "Fred Kenneth Dickinson",
  title =        "Pseudo-round: an alternative approach for
                 floating-point representation",
  type =         "Thesis ({M.S.})",
  school =       "Southwest Texas State University",
  address =      "San Marcos, TX, USA",
  pages =        "vi + 53",
  year =         "1976",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Numerical calculations ---
                 Computer programs.",
}

@Article{Fateman:1976:MAP,
  author =       "R. J. Fateman",
  title =        "{Macsyma} Arbitrary Precision Floating Point
                 Arithmetic Package --- Philosophy and an Overview of
                 its Implementation",
  journal =      j-SIAM-REVIEW,
  volume =       "18",
  number =       "4",
  pages =        "802--802",
  month =        "????",
  year =         "1976",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri Jun 21 11:25:02 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
}

@Article{Feldstein:1976:CED,
  author =       "Alan Feldstein and Richard Goodman",
  title =        "Convergence Estimates for the Distribution of Trailing
                 Digits",
  journal =      j-J-ACM,
  volume =       "23",
  number =       "2",
  pages =        "287--297",
  month =        apr,
  year =         "1976",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/321941.321948",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Wed Jan 15 18:12:53 MST 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "An analysis is made of the distribution of trailing
                 digits (tail end digits) of positive real
                 floating-point numbers represented in arbitrary base $
                 \beta $ and randomly chosen from a logarithmic
                 distribution. The analysis shows that the $n$ th digit
                 for $ n \geq 2 $ is actually approximately uniformly
                 distributed. The approximation depends upon both $n$
                 and the base beta. It becomes better as $n$ increases,
                 and it is exact in the limit as $ n \rightarrow \infty
                 $. A table of this distribution is presented for
                 various $ \beta $ and $n$, along with a table of the
                 maximum digit by digit deviation $ \Delta $ of the
                 logarithmic distribution from the uniform distribution.
                 Various asymptotic results for $ \Delta $ are
                 included.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  classification = "723",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  journalabr =   "J Assoc Comput Mach",
  keywords =     "Benford's Law; computer arithmetic; computer
                 programming; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Garner:1976:SSR,
  author =       "H. L. Garner",
  title =        "A Survey of Some Recent Contributions to Computer
                 Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-25",
  number =       "12",
  pages =        "1277--1282",
  month =        dec,
  year =         "1976",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1976.1674595",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:14:15 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Goldstein:1976:FCF,
  author =       "M. J. Goldstein",
  title =        "Further Comparison of Floating Point Summation
                 Methods",
  journal =      j-SIAM-REVIEW,
  volume =       "18",
  number =       "4",
  pages =        "805--805",
  month =        "????",
  year =         "1976",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri Jun 21 11:25:02 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  keywords =     "accurate floating-point summation",
}

@Article{Goodman:1976:EGD,
  author =       "R. Goodman and A. Feldstein",
  title =        "Effect of Guard Digits and Normalization Options on
                 Floating Point Multiplication",
  journal =      j-SIAM-REVIEW,
  volume =       "18",
  number =       "4",
  pages =        "806--806",
  month =        "????",
  year =         "1976",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri Jun 21 11:25:02 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
}

@Article{Goodman:1976:REF,
  author =       "Richard Goodman",
  title =        "On round-off error in fixed-point multiplication",
  journal =      j-BIT,
  volume =       "16",
  number =       "1",
  pages =        "41--51",
  month =        mar,
  year =         "1976",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01940776",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:14 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=16&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=16&issue=1&spage=41",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "fixed-point arithmetic; floating-point arithmetic;
                 rounding errors",
}

@Article{Goyal:1976:NAR,
  author =       "L. N. Goyal",
  title =        "A Note on {Atrubin}'s Real-Time Iterative Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-25",
  number =       "5",
  pages =        "546--548",
  month =        may,
  year =         "1976",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1976.1674646",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 06:24:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674646",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Hannington:1976:FPM,
  author =       "G. Hannington and D. G. Whitehead",
  title =        "A Floating-Point Multiplexed {DDA} System",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-25",
  number =       "11",
  pages =        "1074--1077",
  month =        nov,
  year =         "1976",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1976.1674557",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 06:24:54 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See comments \cite{McCrea:1978:CFP}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674557",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Higbie:1976:VFP,
  author =       "L. C. Higbie",
  title =        "Vector Floating-Point Data Format",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-25",
  number =       "1",
  pages =        "25--32",
  month =        jan,
  year =         "1976",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1976.5009201",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 06:24:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009201",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Book{IBM:1976:ISP,
  author =       "{IBM Corporation}",
  title =        "{IBM System}\slash 370: Principles of Operation:
                 Systems",
  publisher =    pub-IBM,
  address =      pub-IBM:adr,
  pages =        "326",
  year =         "1976",
  LCCN =         "QA76.8.I122 I57 1976",
  bibdate =      "Fri Sep 16 16:30:13 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Jayashree:1976:BMU,
  author =       "T. Jayashree and D. Basu",
  title =        "On Binary Multiplication Using the Quarter Square
                 Algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-25",
  number =       "9",
  pages =        "957--960",
  month =        sep,
  year =         "1976",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1976.1674723",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 06:24:54 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674723",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Kulisch:1976:FIF,
  author =       "U. Kulisch and G. Bohlender",
  title =        "Formalization and implementation of floating-point
                 matrix operations",
  journal =      j-COMPUTING,
  volume =       "16",
  number =       "3",
  pages =        "239--261",
  year =         "1976",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65G05 (68A10)",
  MRnumber =     "53 7010",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  reviewer =     "F. Szidarovszky",
}

@Book{Kulisch:1976:GNR,
  author =       "Ulrich W. Kulisch",
  title =        "{Grundlagen des numerischen Rechnens: mathematische
                 Begr{\"u}ndung der Rechnerarithmetik} \toenglish
                 {Fundamental Principles of Numerical Computation:
                 Mathematical Foundations of Computer Arithmetic}
                 \endtoenglish",
  volume =       "19",
  publisher =    pub-BIB-INST,
  address =      pub-BIB-INST:adr,
  pages =        "467",
  year =         "1976",
  ISBN =         "3-411-01517-9",
  ISBN-13 =      "978-3-411-01517-7",
  LCCN =         "QA162 .K85",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Reihe Informatik",
  acknowledgement = ack-nhfb,
  keywords =     "Algebra, Abstract.; Floating-point arithmetic.;
                 Mathematics --- Data processing.",
}

@Article{Lacroix:1976:LCF,
  author =       "Arild Lacroix",
  title =        "Limit cycles in floating point digital filters",
  journal =      "AE{\"U}---Arch. Elektron. {\"U}bertragungstech.",
  volume =       "30",
  number =       "7/8",
  pages =        "277--284",
  year =         "1976",
  MRclass =      "94A05",
  MRnumber =     "56 15123",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Linnainmaa:1976:TEA,
  author =       "Seppo Linnainmaa",
  title =        "{Taylor} expansion of the accumulated rounding error",
  journal =      j-BIT,
  volume =       "16",
  number =       "2",
  pages =        "146--160",
  month =        jun,
  year =         "1976",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01931367",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:14 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=16&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=16&issue=2&spage=146",
  abstract =     "The article describes analytic and algorithmic methods
                 for determining the coefficients of the Taylor
                 expansion of an accumulated rounding error with respect
                 to the local rounding errors, and hence determining the
                 influence of the local errors on the accumulated error.
                 Second and higher order coefficients are also
                 discussed, and some possible methods of reducing the
                 extensive storage requirements are analyzed.",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point arithmetic; rounding errors",
}

@MastersThesis{Lipschutz:1976:OPS,
  author =       "David Lipschutz",
  title =        "Optimization of a practical system for high fidelity
                 digital audio",
  type =         "Thesis ({M.S.})",
  school =       "Massachusetts Institute of Technology. Dept. of
                 Electrical Engineering and Computer Science",
  address =      "Cambridge, MA, USA",
  pages =        "53",
  year =         "1976",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Supervised by Francis F. Lee.",
  acknowledgement = ack-nhfb,
  keywords =     "Computer sound processing.; Digital electronics.;
                 Floating-point arithmetic.; High-fidelity sound
                 systems.; Noise --- Psychological aspects.",
}

@Article{Majithia:1976:SCC,
  author =       "J. C. Majithia",
  title =        "Some Comments Concerning Design of Pipeline Arithmetic
                 Arrays",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-25",
  number =       "11",
  pages =        "1132--1134",
  month =        nov,
  year =         "1976",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1976.1674565",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 19:06:10 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@TechReport{Maples:1976:FPI,
  author =       "Michael D. Maples",
  title =        "Floating-point package for {INTEL} 8008 and 8080
                 microprocessors",
  institution =  "Lawrence Livermore Laboratory, University of
                 California/Livermore; National Technical Information
                 Service [distributor]",
  address =      "Livermore, CA, USA",
  pages =        "8 + A-33",
  year =         "1976",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Intel 8080
                 (Microprocessor); Microprocessors.",
  remark =       "Prepared for U.S. Energy Research and Development
                 Administration, under Contract No. W-7405-Eng-43.
                 Microfiche reproduction: Springfield, Va.: National
                 Technical Information Service, 1976. --- 1 microfiche;
                 10 x 15 cm.",
}

@PhdThesis{Martinez:1976:SSS,
  author =       "Ralph Martinez",
  title =        "A semi-portable simulation system using both fixed and
                 floating point derivative blocks",
  type =         "Thesis ({Ph.D.} - Electrical Engineering)",
  school =       "University of Arizona",
  address =      "Tucson, AZ, USA",
  pages =        "xii + 169",
  year =         "1976",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Digital computer simulation.; Dynamics --- Data
                 processing.",
}

@TechReport{Metropolis:1976:MSA,
  author =       "N. Metropolis",
  title =        "Methods of significance arithmetic",
  type =         "Technical report",
  number =       "LA-UR-76-661;CONF-760428-1",
  institution =  inst-LASL,
  address =      inst-LASL:adr,
  day =          "1",
  month =        jan,
  year =         "1976",
  bibdate =      "Tue Mar 20 11:16:47 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Presented at the Conference on the state of the art in
                 numerical analysis, 12 April 1976, University of York,
                 England, UK",
  URL =          "http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=7189580&query_id=0",
  abstract =     "A preliminary report is given of two applications of
                 the methods of significance arithmetic. These are a
                 simple nonlinear partial differential equation and
                 matrix inversion.",
  acknowledgement = ack-nhfb,
  remark =       "OSTI ID: 7189580",
}

@Article{Miller:1976:AGF,
  author =       "Webb Miller and David L. Spooner",
  title =        "Automatic Generation of Floating-Point Test Data",
  journal =      j-IEEE-TRANS-SOFTW-ENG,
  volume =       "SE-2",
  number =       "3",
  pages =        "223--226",
  month =        sep,
  year =         "1976",
  CODEN =        "IESEDJ",
  DOI =          "https://doi.org/10.1109/TSE.1976.233818",
  ISSN =         "0098-5589 (print), 1939-3520 (electronic)",
  ISSN-L =       "0098-5589",
  MRclass =      "68A05",
  MRnumber =     "55 1787",
  bibdate =      "Thu Feb 1 08:07:37 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranssoftweng1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1702369",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Software Engineering",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=32",
  keywords =     "floating-point testing",
  remark =       "Special section on testing",
  reviewer =     "George Marsaglia",
}

@Article{Mohn:1976:IPA,
  author =       "K. Mohn and R. V. Roman",
  title =        "An interactive polynomial approximation algorithm",
  journal =      j-COMP-J,
  volume =       "19",
  number =       "1",
  pages =        "74--78",
  month =        feb,
  year =         "1976",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Thu Sep 15 18:39:43 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Ni:1976:EAT,
  author =       "Ming Duenn Ni and J. K. Aggarwal",
  title =        "Error analysis of two-dimensional recursive digital
                 filters employing floating-point arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-25",
  number =       "7",
  pages =        "755--759",
  year =         "1976",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1976.1674684",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "65D99 (93E10)",
  MRnumber =     "55 6802",
  bibdate =      "Sat Dec 16 16:45:24 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  reviewer =     "Sven-{\AA}ke Gustafson",
}

@TechReport{Paoni:1976:PFI,
  author =       "C. Paoni and M. Maples",
  title =        "A {PLM} floating-point interface program",
  institution =  "Lawrence Livermore Laboratory; National Technical
                 Information Service",
  address =      "Livermore, CA, USA",
  pages =        "iii + 39",
  year =         "1976",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@MastersThesis{Parker:1976:STR,
  author =       "Douglass Stott Parker",
  title =        "The statistical theory of relative errors in
                 floating-point computation",
  type =         "Thesis ({M.S.})",
  school =       "Department of Computer Science, University of Illinois
                 at Urbana-Champaign",
  address =      "Urbana, IL, USA",
  pages =        "62",
  year =         "1976",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Report no. UIUCDCS-R-76-787",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Roundoff errors.",
}

@Article{Patel:1976:ASB,
  author =       "M. R. Patel and K. H. Bennett",
  title =        "Analysis of Speed of a Binary Multiplier Using a
                 Variable Number of Shifts Per Cycle",
  journal =      j-COMP-J,
  volume =       "19",
  number =       "3",
  pages =        "254--257",
  month =        aug,
  year =         "1976",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/19.3.254",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:47:58 MST 2012",
  bibsource =    "Compendex database;
                 http://comjnl.oxfordjournals.org/content/19/3.toc;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_19/Issue_03/;
                 https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/19/3/254.full.pdf+html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_19/Issue_03/tiff/254.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_19/Issue_03/tiff/255.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_19/Issue_03/tiff/256.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_19/Issue_03/tiff/257.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C5210 (Logic design methods); C5230 (Digital
                 arithmetic methods)",
  classification = "723",
  corpsource =   "Department of Computer Sci., University of Keele,
                 Keele, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "binary multiplication; binary multiplier; computers,
                 digital; digital arithmetic; logic design;
                 multiplication; multiplying circuits; shift per cycle;
                 speed",
}

@Article{Paul:1976:SEF,
  author =       "George Paul and M. Wayne Wilson",
  title =        "Should the Elementary Function Library Be Incorporated
                 Into Computer Instruction Sets?",
  journal =      j-TOMS,
  volume =       "2",
  number =       "2",
  pages =        "132--142",
  month =        jun,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355681.355684",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 00:30:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@PhdThesis{Pichat:1976:CEE,
  author =       "Mich{\`e}le Pichat",
  title =        "Contributions {\`a} l'{\`e}tude des erreurs d'arrondi
                 en arithm{\`e}tique {\`a} virgule flottante. ({French})
                 [Contributions to the error analysis of rounding errors
                 in floating-point arithmetic]",
  type =         "Th{\`e}se",
  school =       "Universit{\'e} de Grenoble 1",
  address =      "Grenoble, France",
  year =         "1976",
  bibdate =      "Thu May 27 07:44:27 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://tel.archives-ouvertes.fr/tel-00287209/",
  acknowledgement = ack-nhfb,
  language =     "French",
}

@TechReport{Randell:1976:ODC,
  author =       "Brian Randell",
  title =        "The origins of digital computers: supplementary
                 bibliography to {``Origins of digital computers:
                 selected papers''}",
  type =         "Technical report",
  number =       "91",
  institution =  "Computing Laboratory, University of Newcastle upon
                 Tyne",
  address =      "Newcastle upon Tyne, UK",
  pages =        "3 + 37",
  year =         "1976",
  LCCN =         "Z5642.2 .R36 1979",
  bibdate =      "Wed Oct 13 09:24:25 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  subject =      "electronic digital computers; history; calculators",
}

@Article{Rankin:1976:FPR,
  author =       "Roy Rankin and Steve Wozniak",
  title =        "Floating Point Routines for the 6502",
  journal =      j-DDJ,
  volume =       "1",
  number =       "??",
  pages =        "17--19",
  month =        aug,
  year =         "1976",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Sat Jan 15 06:04:06 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.6502.org/source/floats/wozfp1.txt",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
  keywords =     "HP 2100; MOS Technology",
}

@Article{Riesel:1976:FPU,
  author =       "Zvi H. Riesel",
  title =        "The floating point unit of the {Golem B} computer",
  journal =      j-RADIO-ELECTRON-ENG,
  volume =       "46",
  number =       "7",
  pages =        "355--359",
  month =        jul,
  year =         "1976",
  CODEN =        "RDEEA4",
  DOI =          "https://doi.org/10.1049/ree.1976.0057",
  ISSN =         "0033-7722",
  bibdate =      "Fri Dec 03 15:11:57 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Golem B computer is a fast machine using
                 emitter-coupled logic and multi-layer circuits. The
                 autonomous floating point arithmetic unit obtains its
                 instructions and operands from buffers loaded ahead of
                 need. Its main part, for 56-bit fractions, uses two
                 4-operand adder complexes with stored carries. In
                 multiplication instructions, 4 bits of the multiplier
                 are used to form a new partial product in each pass
                 through an adder complex. Division instructions use a
                 base-4 non-restoring algorithm. Addition favours the
                 case of equal or nearly equal exponents, but 112 sum
                 bits are accumulated for all exponent differences. An
                 effort has been made to provide instructions and number
                 formats that will aid the writing of compilers and
                 operating systems.",
  acknowledgement = ack-nhfb,
  fjournal =     "The Radio and Electronic Engineer",
  keywords =     "adder complex; autonomous floating point arithmetic
                 unit; buffers; division instructions; emitter coupled
                 logic; exponent differences; Golem B computer; multi
                 layer circuits; multiplication instructions; partial
                 product",
}

@Article{Ris:1976:UDF,
  author =       "Frederic N. Ris",
  title =        "A Unified Decimal Floating-Point Architecture For the
                 Support of High-Level Languages",
  journal =      j-SIGNUM,
  volume =       "11",
  number =       "3",
  pages =        "18--23",
  month =        oct,
  year =         "1976",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:03 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper summarizes a proposal for a decimal
                 floating-point arithmetic interface for the support of
                 high-level languages, consisting both of the arithmetic
                 operations observed by application programs and
                 facilities to produce subroutine libraries accessible
                 from these programs. What is not included here are the
                 detailed motivations, examinations of alternatives, and
                 implementation considerations which will appear in the
                 full work.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C5230 (Digital arithmetic methods); C6120 (File
                 organisation)C6140D (High level languages)",
  corpsource =   "IBM Thomas J. Watson Res. Center, Yorktown Heights,
                 NY, USA",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "arithmetic operations; decimal floating point
                 arithmetic; digital arithmetic; high level languages;
                 one level store",
  remark =       "Normalized decimal floating-point arithmetic with a
                 fractional coefficient, three directed rounding modes,
                 and a trap mechanism. Three precisions are provided,
                 with up to 31 decimal digits, and an exponent range of
                 $ \pm 9999 $. Cowlishaw \cite{Cowlishaw:2003:DFP} says
                 that this is the first implementation of the Chen-Ho
                 \cite{Chen:1975:SER} compressed format, allowing
                 storage of 31 digits and 4 exponent digits in a 128-bit
                 value. More modern encodings get 34 digits in the same
                 number of bits, at somewhat reduced exponent range ($ [
                 - 6143, 6144] $).",
  treatment =    "P Practical; T Theoretical or Mathematical",
}

@TechReport{Rosser:1976:CRE,
  author =       "J. Barkley Rosser and J. Michael Yohe",
  title =        "Cancellation and Rounding Errors",
  type =         "Technical Summary Report",
  number =       "1588",
  institution =  inst-MRC-WISCONSIN,
  address =      inst-MRC-WISCONSIN:adr,
  month =        apr,
  year =         "1976",
  bibdate =      "Sun Dec 30 21:30:27 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The fact that a calculating machine can usually hold
                 only an approximation to the number that one is
                 concerned with leads to cancellation errors and
                 rounding errors. These concepts are defined precisely
                 and examples are given. Suggestions are given for
                 reducing (when possible) the size of errors arising
                 from these two effects.",
  acknowledgement = ack-nhfb,
}

@Article{Rowland:1976:BRB,
  author =       "John H. Rowland",
  title =        "Book Review: {{\booktitle{Floating-Point Computation}}
                 (Pat H. Sterbenz)}",
  journal =      j-SIAM-REVIEW,
  volume =       "18",
  number =       "1",
  pages =        "138--139",
  month =        "????",
  year =         "1976",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1018026",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Sat Mar 29 09:52:30 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/18/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "January 1976",
}

@Article{Rudeanu:1976:SRF,
  author =       "S. Rudeanu",
  title =        "Square Roots and Functional Decompositions of
                 {Boolean} Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-25",
  number =       "5",
  pages =        "528--532",
  month =        may,
  year =         "1976",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1976.1674641",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 06:24:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674641",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@PhdThesis{Sanderson:1976:PCT,
  author =       "James George Sanderson",
  title =        "A proof of convergence for the tridiagonal {QL}
                 algorithm in floating-point arithmetic",
  type =         "Thesis ({Ph.D.})",
  school =       "University of New Mexico",
  address =      "Albuquerque, NM, USA",
  pages =        "vi + 69",
  year =         "1976",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithms.; Arithmetic --- Foundations.",
}

@Article{Shi:1976:SLC,
  author =       "S.-Y. Shi",
  title =        "Shortcut to Logarithms Combines Table Lookup and
                 Computation",
  journal =      j-COMP-DESIGN,
  volume =       "15",
  number =       "5",
  pages =        "184--186",
  month =        may,
  year =         "1976",
  CODEN =        "CMPDAM",
  ISSN =         "0010-4566",
  bibdate =      "Thu Sep 08 08:07:38 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computer Design",
}

@PhdThesis{Slekys:1976:DCN,
  author =       "Arunas George Slekys",
  title =        "Design of complex number digital arithmetic units
                 based on a modified bi-imaginary number system",
  type =         "{Ph.D. thesis}",
  school =       "University of California, Los Angeles",
  address =      "Los Angeles, CA, USA",
  pages =        "223",
  year =         "1976",
  bibdate =      "Sat Aug 22 09:03:47 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "ProQuest order number AAI7707685.",
}

@Book{Spaniol:1976:AR,
  author =       "Otto Spaniol",
  title =        "{Arithmetik in Rechenanlagen: Logik und Entwurf}
                 \toenglish {Computer Arithmetic: Logic and Design}
                 \endtoenglish",
  publisher =    pub-TEUBNER,
  address =      pub-TEUBNER:adr,
  pages =        "208",
  year =         "1976",
  ISBN =         "3-519-02332-6",
  ISBN-13 =      "978-3-519-02332-6",
  LCCN =         "QA76.6 .S66",
  bibdate =      "Fri Sep 16 16:30:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "For an English translation, see
                 \cite{Spaniol:1981:CAL}.",
  price =        "DM24.80",
  acknowledgement = ack-nj,
}

@TechReport{Warren:1976:MDT,
  author =       "H. S. {Warren, Jr.} and A. S. Fox and P. W.
                 Markstein",
  title =        "Modulus Division on a Two's Complement Machine",
  type =         "Research Report",
  number =       "RC7712",
  institution =  "IBM",
  address =      "Yorktown Heights, NY, USA",
  month =        jun,
  year =         "1976",
  bibdate =      "Fri Nov 09 19:32:44 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  xxnote =       "Check: Waser/Flynn book dates this as 1979.",
}

@Article{Wyatt:1976:PEP,
  author =       "W. T. {Wyatt Jr.} and D. W. Lozier and D. J. Orser",
  title =        "A Portable Extended Precision Arithmetic Package and
                 Library With {Fortran} Precompiler",
  journal =      j-TOMS,
  volume =       "2",
  number =       "3",
  pages =        "209--231",
  month =        sep,
  year =         "1976",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 12 08:07:55 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1976-2-3/p209-lozier/",
  acknowledgement = ack-nj,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Yau:1976:DMA,
  author =       "S. S. Yau and J. Chung",
  title =        "On the Design of Modulo Arithmetic Units Based on
                 Cyclic Groups",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-25",
  number =       "11",
  pages =        "1057--1067",
  month =        nov,
  year =         "1976",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1976.1674555",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 06:24:54 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674555",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Zohar:1976:RTR,
  author =       "S. Zohar",
  title =        "Rounding and Truncation in Radix (-2) Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-25",
  number =       "5",
  pages =        "464--469",
  month =        may,
  year =         "1976",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1976.1674634",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 12 06:24:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674634",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Agrawal:1977:CNB,
  author =       "D. P. Agrawal",
  title =        "Comments on {``A Note on Base-$2$ Arithmetic
                 Logic''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "5",
  pages =        "511--511",
  month =        may,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674869",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 21:56:54 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See \cite{Yuen:1975:NBA}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674869",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Aird:1977:IFC,
  author =       "T. J. Aird",
  title =        "The {IMSL Fortran} converter: an approach to solving
                 portability problems",
  crossref =     "Cowell:1977:PNS",
  pages =        "368--388",
  year =         "1977",
  DOI =          "https://doi.org/10.1007/3-540-08446-0_49",
  bibdate =      "Thu Dec 11 15:15:52 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{Albrecht:1977:GC,
  author =       "Rudolf Albrecht and Ulrich Kulisch",
  title =        "{Grundlagen der Computer-Arithmetik}",
  publisher =    "Springer-Verlag",
  address =      "Wien, Austria",
  pages =        "viii + 150",
  year =         "1977",
  ISBN =         "0-387-81410-8",
  ISBN-13 =      "978-0-387-81410-0",
  LCCN =         "????",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Computing: Supplementum; 1 Computing
                 (Springer-Verlag). Supplementum; 1.",
  acknowledgement = ack-nhfb,
  keywords =     "Algebra, Abstract.; Floating-point arithmetic.;
                 Mathematics --- Data processing.",
  remark =       "``Diese Artikel stellen eine Auswahl von Vortragen
                 dar, die auf einer vom 4. bis 8. August 1975 im
                 `Mathematischen Forschungsinstitut Oberwolfach'
                 stattgefundenen Tagung gehalten wurden.''",
}

@Book{Albrecht:1977:GCA,
  editor =       "R. Albrecht and U. Kulisch",
  title =        "{Grundlagen der Computer-Arithmetik} \toenglish
                 {Foundations of Computer Arithmetic} \endtoenglish",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 150",
  year =         "1977",
  ISBN =         "0-387-81410-8",
  ISBN-13 =      "978-0-387-81410-0",
  LCCN =         "QA162 .G78",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Diese Artikel stellen eine Auswahl von Vortragen dar,
                 die auf einer vom 4. bis 8. August 1975 im
                 `Mathematischen Forschungsinstitut Oberwolfach'
                 stattgefundenen Tagung gehalten wurden.",
  acknowledgement = ack-nhfb,
}

@Article{Alexander:1977:SRR,
  author =       "V. L. Alexander",
  title =        "Square Root Routine",
  journal =      j-IBM-TDB,
  volume =       "20",
  number =       "3",
  pages =        "1222",
  month =        aug,
  year =         "1977",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:15:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
}

@Article{Anonymous:1977:CAF,
  author =       "Anonymous",
  title =        "Computer Arithmetic: Foreword and Survey",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "7",
  pages =        "609--609",
  month =        jul,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674892",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 21:56:55 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674892",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Manual{AppleComputer:1977:ARM,
  author =       "{Apple Computer, Inc}",
  title =        "{APPLESOFT} reference manual: extended precision
                 floating point {BASIC} language",
  organization = "Apple Computer, Inc.",
  address =      "Cupertino, CA, USA",
  pages =        "75",
  year =         "1977",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Apple computer --- Programming.; BASIC (Computer
                 program language) --- Programming.; Microcomputers ---
                 Programming.",
}

@Article{Barak:1977:MAT,
  author =       "A. B. Barak",
  title =        "Multiplicative Algorithms for Ternary Arithmetic Using
                 Binary Logic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "8",
  pages =        "823--826",
  month =        aug,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674922",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 21:56:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674922",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Bauer:1977:CFP,
  author =       "Henry R. Bauer",
  title =        "Comments on {``On the Floating Point Representation of
                 Complex Numbers''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "2",
  pages =        "191--191",
  month =        feb,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.5009301",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 21:56:52 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See \cite{Yuen:1975:FPR}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009301",
  abstract =     "A recent paper [Burroughs B7700 Information Processing
                 Systems Reference Manual, p. 2-9, 1973, Burroughs
                 Corporation] discussed an integrated notation for
                 complex numbers. A second choice of the radix point
                 position will increase the number of values near the
                 origin. An argument is also made for unnormalized
                 notation of both parts of a complex number.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Bentley:1977:EPW,
  author =       "J. Bentley and B. Ford",
  title =        "On the enhancement of portability within the {NAG}
                 project --- a statistical survey",
  crossref =     "Cowell:1977:PNS",
  pages =        "505--528",
  year =         "1977",
  DOI =          "https://doi.org/10.1007/3-540-08446-0_57",
  bibdate =      "Thu Dec 11 15:15:52 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Bivins:1977:SAA,
  author =       "Robert L. Bivins and Nicholas C. Metropolis",
  title =        "Significance Arithmetic: Application to a Partial
                 Differential Equation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "7",
  pages =        "639--642",
  month =        jul,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674896",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "http://dblp.uni-trier.de/db/journals/tc/tc26.html#BivinsM77;
                 https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/iel5/12/35159/01674896.pdf?tp=&isnumber=35159&arnumber=1674896&punumber=12",
  ZMnumber =     "0405.65056",
  abstract =     "The methods of significance arithmetic are applied to
                 the numerical solution of a nonlinear
                 partial-differential equation. Our approach permits the
                 use of initial values having imprecision considerably
                 greater than that of rounding error; moreover, the
                 intermediate and final quantities are monitored so that
                 at any stage the precision of such quantities is
                 available. An algorithm is found that represents
                 faithfully the solution to a difference-equation
                 approximation to Burgers' equation.",
  acknowledgement = ack-jr,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Bohlender:1977:FPC,
  author =       "Gerd Bohlender",
  title =        "Floating-Point Computation of Functions with Maximum
                 Accuracy",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "7",
  pages =        "621--632",
  month =        jul,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674894",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "65D15 (68A99)",
  MRnumber =     "56 9908",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "accurate floating-point summation",
  reviewer =     "Bernard H. Rosman",
}

@InProceedings{Boyle:1977:MST,
  author =       "James M. Boyle",
  title =        "Mathematical software transportability systems ---
                 have the variations a theme?",
  crossref =     "Cowell:1977:PNS",
  pages =        "305--360",
  year =         "1977",
  DOI =          "https://doi.org/10.1007/3-540-08446-0_47",
  bibdate =      "Thu Dec 11 15:15:52 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@MastersThesis{Brinkmann:1977:FPT,
  author =       "Hubert Eldie Brinkmann",
  title =        "A floating-point processor for the {Texas Instruments}
                 model {980A} computer",
  type =         "Electrical Engineering Thesis ({M.S.})",
  publisher =    "Brinkmann",
  school =       "Texas A\&M University",
  address =      "College Station, TX, USA",
  pages =        "x + 68",
  year =         "1977",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Microprocessors.; Microprogramming.; Miniature
                 computers --- Programming.",
}

@InProceedings{Brown:1977:FPM,
  author =       "W. S. Brown and A. D. Hall",
  title =        "{Fortran} portability via models and tools",
  crossref =     "Cowell:1977:PNS",
  pages =        "158--164",
  year =         "1977",
  DOI =          "https://doi.org/10.1007/3-540-08446-0_41",
  bibdate =      "Thu Dec 11 15:15:52 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Brown:1977:MSI,
  author =       "W. S. Brown",
  title =        "A realistic model of floating-point computation",
  crossref =     "Rice:1977:MSI",
  number =       "39",
  pages =        "343--360",
  year =         "1977",
  DOI =          "https://doi.org/10.1016/B978-0-12-587260-7.50017-0",
  MRclass =      "68A05",
  MRnumber =     "58 3605",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  URL =          "https://www.sciencedirect.com/science/article/abs/pii/B9780125872607500170",
  acknowledgement = ack-nhfb,
  reviewer =     "Costica Cazacu",
}

@InProceedings{Cody:1977:MPN,
  author =       "William J. {Cody, Jr.}",
  title =        "Machine parameters for numerical analysis",
  crossref =     "Cowell:1977:PNS",
  pages =        "49--67",
  year =         "1977",
  DOI =          "https://doi.org/10.1007/3-540-08446-0_35",
  bibdate =      "Thu Dec 11 15:15:52 2025",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Collins:1977:APS,
  author =       "George E. Collins and David R. Musser",
  title =        "Analysis of the {Pope--Stein} Division Algorithm",
  journal =      j-INFO-PROC-LETT,
  volume =       "6",
  number =       "5",
  pages =        "151--155",
  day =          "??",
  month =        oct,
  year =         "1977",
  CODEN =        "IFPLAT",
  DOI =          "https://doi.org/10.1016/0020-0190(77)90012-6",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Tue Nov 17 10:49:43 MST 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/infoproc1970.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classification = "C4240 (Programming and algorithm theory)",
  corpsource =   "Computer Sci. Dept., University of Wisconsin, Madison,
                 WI, USA",
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190/",
  keywords =     "algorithm; algorithm theory; digital arithmetic;
                 integer division; multiple precision integer division;
                 trial quotient digits",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Colquhoun:1977:FAS,
  author =       "D. G. Colquhoun",
  title =        "A Fast Approximation to the Sine Function",
  journal =      j-SPE,
  volume =       "7",
  number =       "2",
  pages =        "227--229",
  month =        mar # "--" # apr,
  year =         "1977",
  CODEN =        "SPEXBL",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Fri Dec 08 13:06:08 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Software---Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
}

@InProceedings{Dahlstrand:1977:SPT,
  author =       "Ingemar Dahlstrand",
  title =        "A study of portability in technical and scientific
                 computing",
  crossref =     "Cowell:1977:PNS",
  pages =        "529--539",
  year =         "1977",
  DOI =          "https://doi.org/10.1007/3-540-08446-0_58",
  bibdate =      "Thu Dec 11 15:15:52 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{DEC:1977:VAH,
  author =       "{Digital Equipment Corporation}",
  title =        "{VAX-11}\slash 780 Architecture Handbook",
  publisher =    pub-DP,
  address =      pub-DP:adr,
  pages =        "328",
  year =         "1977",
  LCCN =         "QA76.8 .V12D5 B 2 829 348",
  bibdate =      "Thu Sep 15 18:50:55 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  xxISBN =       "(none)",
}

@InProceedings{Dekker:1977:MRR,
  author =       "T. J. Dekker",
  title =        "Machine Requirements for Reliable Portable Software",
  crossref =     "Cowell:1977:PNS",
  pages =        "22--36",
  year =         "1977",
  DOI =          "https://doi.org/10.1007/3-540-08446-0_33",
  bibdate =      "Wed Nov 07 08:38:01 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Delves:1977:ALN,
  author =       "L. M. Delves",
  title =        "{Algol 68} as a language for numerical software",
  crossref =     "Cowell:1977:PNS",
  pages =        "95--126",
  year =         "1977",
  DOI =          "https://doi.org/10.1007/3-540-08446-0_38",
  bibdate =      "Thu Dec 11 15:15:52 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Derenzo:1977:AHC,
  author =       "Stephen E. Derenzo",
  title =        "Approximations for Hand Calculators Using Small
                 Integer Coefficients",
  journal =      j-MATH-COMPUT,
  volume =       "31",
  number =       "137",
  pages =        "214--222",
  month =        jan,
  year =         "1977",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  ajournal =     "Math. Comput.",
  classcodes =   "B0290D (Functional analysis); B0290F (Interpolation
                 and function approximation); C4120 (Functional
                 analysis); C4130 (Interpolation and function
                 approximation); C7310 (Mathematics computing)",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "approximations; function approximation; function
                 evaluation; hand calculators; programmable calculators;
                 small integer coefficients",
  treatment =    "A Application; T Theoretical or Mathematical",
}

@InProceedings{Dritz:1977:MPR,
  author =       "Kenneth W. Dritz",
  title =        "Multiple program realizations using the {TAMPR}
                 system",
  crossref =     "Cowell:1977:PNS",
  pages =        "405--423",
  year =         "1977",
  DOI =          "https://doi.org/10.1007/3-540-08446-0_51",
  bibdate =      "Thu Dec 11 15:15:52 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{DuCroz:1977:APW,
  author =       "J. J. {Du Croz} and S. J. Hague and J. L.
                 Siemieniuch",
  title =        "Aids to portability within the {NAG} project",
  crossref =     "Cowell:1977:PNS",
  pages =        "389--404",
  year =         "1977",
  DOI =          "https://doi.org/10.1007/3-540-08446-0_50",
  bibdate =      "Thu Dec 11 15:15:52 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Egbert:1977:PCAa,
  author =       "W. E. Egbert",
  title =        "Personal Calculator Algorithms {I}: Square Roots",
  journal =      j-HEWLETT-PACKARD-J,
  volume =       "28",
  number =       "9",
  pages =        "22--24",
  month =        may,
  year =         "1977",
  CODEN =        "HPJOAX",
  ISSN =         "0018-1153",
  bibdate =      "Thu Sep 1 10:15:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C5420 (Mainframes and minicomputers); C7310
                 (Mathematics computing)",
  fjournal =     "Hewlett-Packard Journal: technical information from
                 the laboratories of Hewlett-Packard Company",
  keywords =     "electronic calculators; HP personal calculator; square
                 root algorithm",
  treatment =    "A Application; T Theoretical or Mathematical",
}

@Article{Egbert:1977:PCAb,
  author =       "W. E. Egbert",
  title =        "Personal Calculator Algorithms {II}: Trigonometric
                 Functions",
  journal =      j-HEWLETT-PACKARD-J,
  volume =       "28",
  number =       "10",
  pages =        "17--20",
  month =        jun,
  year =         "1977",
  CODEN =        "HPJOAX",
  ISSN =         "0018-1153",
  bibdate =      "Thu Sep 1 10:15:56 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Hewlett-Packard Journal: technical information from
                 the laboratories of Hewlett-Packard Company",
}

@Article{Egbert:1977:PCAc,
  author =       "W. E. Egbert",
  title =        "Personal Calculator Algorithms {III}: Inverse
                 Trigonometric Functions",
  journal =      j-HEWLETT-PACKARD-J,
  volume =       "29",
  number =       "3",
  pages =        "22--23",
  month =        nov,
  year =         "1977",
  CODEN =        "HPJOAX",
  ISSN =         "0018-1153",
  bibdate =      "Thu Sep 1 10:16:10 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Hewlett-Packard Journal: technical information from
                 the laboratories of Hewlett-Packard Company",
}

@Article{Ercegovac:1977:GHO,
  author =       "Milo{\v{s}} D. Ercegovac",
  title =        "A General Hardware-Oriented Method for Evaluation of
                 Functions and Computations in a Digital Computer",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "7",
  pages =        "667--680",
  month =        jul,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674900",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 21:56:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674900",
  abstract =     "A parallel computational method, amenable for
                 efficient hardware-level implementation, is described.
                 It provides a simple and fast algorithm for the
                 evaluation of polynomials, certain rational functions
                 and arithmetic expressions, solving a class of systems
                 of linear equations, or performing the basic arithmetic
                 operations in a fixed-point number representation
                 system. The time required to perform the computation is
                 of the order of $m$ carry-free addition operations, $m$
                 being the number of digits in the solution. In
                 particular, the method is suitable for fast evaluation
                 of mathematical functions in hardware.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Arithmetic expressions; digital computer arithmetic;
                 E-method; evaluation of real-valued functions;
                 fixed-point representation; hardware-level
                 implementation; integral powers; linear systems;
                 on-line algorithms; parallel computation; polynomials;
                 rational functions; redundant number systems",
}

@Article{Evans:1977:AAT,
  author =       "Gillian R. Evans",
  title =        "From abacus to algorism: Theory and practice in
                 medieval arithmetic",
  journal =      j-BRITISH-J-HIST-SCI,
  volume =       "10",
  number =       "2",
  pages =        "114--131",
  month =        jul,
  year =         "1977",
  CODEN =        "BJHSAT",
  DOI =          "https://doi.org/10.1017/S0007087400015375",
  ISSN =         "0007-0874 (print), 1474-001X (electronic)",
  ISSN-L =       "0007-0874",
  MRclass =      "01A35 (Mathematics in the medieval)",
  MRnumber =     "522510 (80e:01006)",
  MRreviewer =   "M. Folkerts",
  bibdate =      "Thu Sep 23 07:34:43 MDT 2010",
  bibsource =    "http://journals.cambridge.org/action/displayJournal?jid=BJH;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database",
  URL =          "http://www.jstor.org/stable/4025865",
  ZMnumber =     "0358.01003",
  abstract =     "This paper deals primarily with the change in
                 practical procedures of calculation which took place
                 during the course of the twelfth century in Western
                 Europe. At the beginning of the period, the abacus was
                 in relatively common use; towards the end, it was being
                 superseded by the method of calculation which was known
                 as the algorism. Certain differences of theory are
                 apparent. Among the textbooks which were most
                 influential in bringing about the change was
                 Sacrobosco's Algorithmus Vulgaris. Authors of both
                 abacus and algorism treatises give an account of
                 number-symbols and discuss elementary number theory
                 briefly, but the algorism treatise show how much more
                 confident the authors were in using Arabic numerals.
                 The algorisms employ a symbol for zero; although it has
                 antecedents in some abacus treatises, its usefulness
                 was clearly not fully perceived by the authors, because
                 the columns of the abacus made it unnecessary to use a
                 counter to indicate that the number under consideration
                 was, for example, 306, not 36. The algorisms deal with
                 a far wider range of operations; while the abacus
                 treatises confine themselves to multiplication and
                 division of whole numbers and fractions, the algorisms
                 have addition, subtraction, doubling, halving,
                 multiplication, division, the extraction of roots and
                 progression, as well as numeration. Changes in
                 technical terminology are discussed. There are two
                 appendices, one dealing with the compilation of
                 arithmetical texts in Bodleian Library Oxford,
                 MS.~Laud.~Misc.~644, and the other on the arithmetical
                 sense of the term equipollentia, which was a technical
                 term of dialectic.",
  acknowledgement = ack-nhfb,
  fjournal =     "British Journal for the History of Science",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=BJH",
  ZMreviewer =   "Gillian R. Evans",
}

@Article{Feldman:1977:EEA,
  author =       "Michael B. Feldman",
  title =        "Embedding extended arithmetic in {SNOBOL4}",
  journal =      j-SIGPLAN,
  volume =       "12",
  number =       "1",
  pages =        "67--72",
  month =        jan,
  year =         "1977",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:13:59 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods); C6140D (High
                 level languages)",
  corpsource =   "George Washington University, Washington, DC, USA",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "complex numbers; data structure; data structures;
                 digital arithmetic; embedded; extended arithmetic;
                 procedure oriented languages; rotational numbers;
                 SNOBOL4",
  treatment =    "P Practical",
}

@InProceedings{Ford:1977:PCP,
  author =       "Brian Ford",
  title =        "Preparing conventions for parameters for transportable
                 numerical software",
  crossref =     "Cowell:1977:PNS",
  pages =        "68--91",
  year =         "1977",
  DOI =          "https://doi.org/10.1007/3-540-08446-0_36",
  bibdate =      "Thu Dec 11 15:15:52 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{Forsythe:1977:CMM,
  author =       "George E. (George Elmer) Forsythe and Michael A.
                 Malcolm and Cleve B. Moler",
  title =        "Computer Methods for Mathematical Computations",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xi + 259",
  year =         "1977",
  ISBN =         "0-13-165332-6",
  ISBN-13 =      "978-0-13-165332-0",
  LCCN =         "QA297 .F5681",
  MRclass =      "65-01",
  MRnumber =     "MR0458783 (56 \#16983)",
  MRreviewer =   "Sven-{\AA}ke Gustafson",
  bibdate =      "Tue May 25 09:01:08 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
                 squares, which is available by anonymous ftp from
                 \path=math.liu.se= in \path=pub/references=",
  price =        "US\$16.95",
  series =       "Prentice-Hall series in automatic computation",
  ZMnumber =     "0361.65002",
  acknowledgement = ack-nhfb,
  classmath =    "*65-01 Textbooks (numerical analysis) 68-01 Textbooks
                 (computer science)",
  keywords =     "Fortran (computer program language); numerical
                 analysis -- data processing",
  remark =       "Subroutines and exercises for the computer solution of
                 problems involving matrices, integrals, differential
                 equations, spline functions, zeros and extrema of
                 functions, least squares, and Monte Carlo techniques.",
  subject =      "Numerical analysis; Data processing; Computer
                 programs; Problems, exercises, etc; FORTRAN (Computer
                 program language)",
  tableofcontents = "Introduction \\
                 Floating-point computation \\
                 Linear systems of equations \\
                 Interpolation \\
                 Numerical integration \\
                 Initial value problems in ordinary differential
                 equations \\
                 Solution of nonlinear equations \\
                 Optimization \\
                 Least squares and the singular value decomposition \\
                 Random number generation and Monte Carlo methods",
}

@InProceedings{Fox:1977:PPM,
  author =       "Phyllis A. Fox",
  title =        "{Port} --- A portable mathematical subroutine
                 library",
  crossref =     "Cowell:1977:PNS",
  pages =        "165--177",
  year =         "1977",
  DOI =          "https://doi.org/10.1007/3-540-08446-0_42",
  bibdate =      "Thu Dec 11 15:15:52 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Frenckner:1977:MFP,
  author =       "K. Frenckner and M. Persson and S. Romberger and Y.
                 Sundblad",
  title =        "Microprogrammed floating-point arithmetic for the
                 {Varian-73} computer",
  type =         "Technical report",
  number =       "TRITA-NA-7702",
  institution =  "Kungl. Tekniska H{\"o}gskolan",
  address =      "Stockholm, Sweden",
  pages =        "37",
  month =        jun,
  year =         "1977",
  bibdate =      "Fri May 25 05:52:09 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://weblib.cern.ch/format/showfull?uid=1451323_18194&base=CERCER&sysnb=0028467",
  acknowledgement = ack-nhfb,
}

@InProceedings{Fullerton:1977:PSF,
  author =       "L. Wayne Fullerton",
  title =        "Portable special function routines",
  crossref =     "Cowell:1977:PNS",
  pages =        "452--483",
  year =         "1977",
  DOI =          "https://doi.org/10.1007/3-540-08446-0_54",
  bibdate =      "Thu Dec 11 15:15:52 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Ginsberg:1977:NID,
  author =       "Myron Ginsberg",
  title =        "Numerical influences on the design of floating-point
                 arithmetic for microcomputers",
  type =         "Technical report",
  number =       "CS 7708",
  institution =  "Department of Computer Science, Southern Methodist
                 University",
  address =      "Dallas, TX, USA",
  pages =        "72",
  year =         "1977",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic --- Data processing.",
}

@TechReport{Goldsmith:1977:ICF,
  author =       "Theodore C. Goldsmith",
  title =        "An integrated circuit floating point accumulator",
  type =         "{NASA} technical note",
  number =       "NASA TN D-8509 NASA",
  institution =  "National Aeronautics and Space Administration; for
                 sale by the National Technical Information Service",
  address =      "Washington, DC, USA",
  pages =        "26",
  year =         "1977",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  govtdocnumber = "NAS 1.14:D-8509",
  remark =       "Issued June 1977.",
}

@Article{Goodman:1977:EGD,
  author =       "R. Goodman and A. Feldstein",
  title =        "Effect of Guard Digits and Normalization Options on
                 Floating Point Multiplication",
  journal =      j-COMPUTING,
  volume =       "18",
  number =       "2",
  pages =        "93--106",
  month =        "????",
  year =         "1977",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65G05",
  MRnumber =     "55 11596",
  bibdate =      "Fri Dec 08 12:02:42 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  reviewer =     "N. N. Abdelmalek",
}

@Article{Goodwin:1977:CUO,
  author =       "D. T. Goodwin",
  title =        "Conditions for Underflow and Overflow of an Arithmetic
                 Stack",
  journal =      j-COMP-J,
  volume =       "20",
  number =       "1",
  pages =        "56--62",
  month =        feb,
  year =         "1977",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/20.1.56",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:47:59 MST 2012",
  bibsource =    "Compendex database;
                 http://comjnl.oxfordjournals.org/content/20/1.toc;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/;
                 https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/20/1/56.full.pdf+html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/56.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/57.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/58.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/59.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/60.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/61.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_20/Issue_01/tiff/62.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C4210 (Formal logic)",
  classification = "721; 723",
  corpsource =   "Department of Computer Sci., University of Keele,
                 Keele, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "arbitrary string; arithmetic stack; automata theory
                 --- Context Free Languages; behaviour; computer
                 metatheory; computer operating systems --- Program
                 Compilers; context free language; context-free
                 languages; loading; overflow; underflow",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Gregory:1977:BCR,
  author =       "Robert Todd Gregory and David W. Matula",
  title =        "Base conversion in residue number systems",
  journal =      j-BIT,
  volume =       "17",
  number =       "3",
  pages =        "286--302",
  month =        sep,
  year =         "1977",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01932149",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "10A30 (68A10)",
  MRnumber =     "MR0476627 (57 \#16186)",
  MRreviewer =   "L. Carlitz",
  bibdate =      "Wed Jan 4 18:52:15 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=17&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=17&issue=3&spage=286",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "Interval arithmetic; residue arithmetic",
}

@Article{Hashizume:1977:FPA,
  author =       "B. Hashizume",
  title =        "Floating Point Arithmetic",
  journal =      j-BYTE,
  volume =       "2",
  number =       "11",
  pages =        "76--78, 180--188",
  month =        nov,
  year =         "1977",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Thu Sep 1 10:14:44 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "BYTE Magazine",
}

@Article{Hastings:1977:FPH,
  author =       "Jordan Towner Hastings",
  title =        "Floating point half-word packing for {Control Data
                 Corporation 6000/7000 series} hardware",
  journal =      j-SPE,
  volume =       "7",
  number =       "1",
  pages =        "146--147",
  month =        jan,
  year =         "1977",
  CODEN =        "SPEXBL",
  DOI =          "https://doi.org/10.1002/spe.4380070111",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Wed Sep 10 12:36:39 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/spe.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Software --- Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  onlinedate =   "27 Oct 2006",
}

@InProceedings{Hemker:1977:CTA,
  author =       "Pieter W. Hemker",
  title =        "Criteria for transportable {Algol} libraries",
  crossref =     "Cowell:1977:PNS",
  pages =        "145--157",
  year =         "1977",
  DOI =          "https://doi.org/10.1007/3-540-08446-0_40",
  bibdate =      "Thu Dec 11 15:15:52 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@PhdThesis{Hough:1977:EAI,
  author =       "David Granville Hough",
  title =        "Explaining and ameliorating the ill-condition of zeros
                 of polynomials",
  type =         "{Ph.D.} Thesis",
  school =       "Electronics Research Lab., University of California,
                 Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "303",
  month =        feb,
  year =         "1977",
  bibdate =      "Thu Jan 12 09:05:57 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://wwwlib.umi.com/dissertations/fullcit/7731401",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hull:1977:SFP,
  author =       "T. E. Hull",
  title =        "Semantics of floating point arithmetic and elementary
                 functions",
  crossref =     "Cowell:1977:PNS",
  pages =        "37--48",
  year =         "1977",
  DOI =          "https://doi.org/10.1007/3-540-08446-0_34",
  bibdate =      "Thu Dec 11 15:15:52 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Jenkins:1977:URN,
  author =       "W. Jenkins and B. Leon",
  title =        "The use of residue number systems in the design of
                 finite impulse response digital filters",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "24",
  number =       "4",
  pages =        "191--201",
  month =        apr,
  year =         "1977",
  CODEN =        "ICSYBT",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264810",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23467",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A technique is presented for implementing a finite
                 impulse response (FIR) digital filter in a residue
                 number system (RNS). For many years residue number
                 coding has been recognized as a system which provides a
                 capability for the implementation of \ldots{}",
}

@InProceedings{Jullien:1977:HRD,
  author =       "G. Jullien and W. Miller and J. Soltis and A.
                 Baraniecka and B. Tseng",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing, {ICASSP '77}",
  title =        "Hardware realization of digital signal processing
                 elements using the residue number system",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "506--510",
  year =         "1977",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1049/el:19770117",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "In the past, hardware realization of digital signal
                 processing elements have been based upon binary
                 arithmetic concepts. Because of the dependence between
                 digits in binary arithmetic operations, the hardware
                 required to construct arithmetic elements \ldots{}",
}

@TechReport{Kahan:1977:CYC,
  author =       "W. M. Kahan and B. N. Parlett",
  title =        "Can You Count on Your Calculator?",
  type =         "Memorandum",
  number =       "UCB/ERL M77/21",
  institution =  "Electronics Research Laboratory, College of
                 Engineering, University of California, Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "ii + 28",
  day =          "6",
  month =        apr,
  year =         "1977",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "German Transl. Published In: Jahrbuch {\"U}berblicke
                 Mathematik 1978, Ed. by B. Fuchssteiner and others,
                 Bibliographisches Institut, Mannheim-Wien-Z{\"u}rich,
                 199--216, 1978",
  URL =          "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
  acknowledgement = ack-jr,
}

@Misc{Kahan:1977:ISS,
  author =       "William Kahan",
  title =        "Implementation of software systems and modules, part
                 1, {First West Coast Computer Faire}",
  howpublished = "Audio tapes archived at the Computer History Museum,
                 Mountain View, CA, USA.",
  month =        apr,
  year =         "1977",
  bibdate =      "Sat Aug 23 07:07:47 2025",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Kahan's talk begins at 26m50s on side A, and continues
                 to side B.",
  URL =          "https://www.computerhistory.org/collections/catalog/102706817",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kemp:1977:WEF,
  author =       "P. Kemp",
  title =        "Writing the elementary function procedures for the
                 {ALGOL68C} compiler",
  crossref =     "Cowell:1977:PNS",
  pages =        "127--144",
  year =         "1977",
  DOI =          "https://doi.org/10.1007/3-540-08446-0_39",
  bibdate =      "Thu Dec 11 15:15:52 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Kent:1977:HSF,
  author =       "Jan G. Kent",
  title =        "Highlights of a Study of Floating-Point Instructions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "7",
  pages =        "660--666",
  month =        jul,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674899",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:14:15 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  abstract =     "The research work that this paper is based on resulted
                 in the development of tools for the theoretical
                 definition, analysis and comparison of floating-point
                 instructions as mathematical mappings. These tools can
                 be used to study the properties of most floating-point
                 instructions and their operands.",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Kent:1977:HST,
  author =       "S. A. Kent",
  title =        "A High-Speed Threshold Gate Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "12",
  pages =        "1279--1283",
  month =        dec,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674790",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 21:56:59 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674790",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Kornerup:1977:UNR,
  author =       "P. Kornerup and B. D. Shriver",
  title =        "A Unified Numeric Representation Arithmetic Unit and
                 Its Language Support",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "7",
  pages =        "651--659",
  month =        jul,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674898",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 21:56:55 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674898",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Krishnamurthy:1977:MPU,
  author =       "E. V. Krishnamurthy",
  title =        "Matrix Processors Using $p$-adic Arithmetic for Exact
                 Linear Computations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "7",
  pages =        "633--639",
  month =        jul,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674895",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 21:56:55 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674895",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Krogh:1977:FFP,
  author =       "Fred T. Krogh",
  title =        "Features for {Fortran} portability",
  crossref =     "Cowell:1977:PNS",
  pages =        "361--367",
  year =         "1977",
  DOI =          "https://doi.org/10.1007/3-540-08446-0_48",
  bibdate =      "Thu Dec 11 15:15:52 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Kuck:1977:ARM,
  author =       "David J. Kuck and Douglass S. {Parker Jr.} and Ahmed
                 H. Sameh",
  title =        "Analysis of Rounding Methods in Floating-Point
                 Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "7",
  pages =        "643--650",
  month =        jul,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674897",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "65G05",
  MRnumber =     "57 7979",
  bibdate =      "Fri Dec 08 12:00:49 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  reviewer =     "V. V. Ivanov",
}

@Article{Kulisch:1977:MFC,
  author =       "Ulrich Kulisch",
  title =        "Mathematical foundations of computer arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "7",
  pages =        "610--620",
  month =        jul,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674893",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat May 18 14:33:16 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Lawson:1977:TNA,
  author =       "C. L. Lawson and J. K. Reid",
  title =        "Two numerical analysts' views on the {Draft Proposed
                 ANS Fortran}",
  crossref =     "Cowell:1977:PNS",
  pages =        "257--268",
  year =         "1977",
  DOI =          "https://doi.org/10.1007/3-540-08446-0_44",
  bibdate =      "Thu Dec 11 15:15:52 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Lee:1977:FNS,
  author =       "S. C. Lee and A. D. Edgar",
  title =        "The {Focus} Number System",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "11",
  pages =        "1167--1170",
  month =        nov,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674770",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 21:56:57 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See comments
                 \cite{Lee:1979:AFN,Swartzlander:1979:CFN}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674770",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Ligomenides:1977:SSF,
  author =       "P. A. Ligomenides",
  title =        "The Skip-and-Set Fast-Division Algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "10",
  pages =        "1030--1032",
  month =        oct,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674740",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 13 10:17:27 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674740",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Book{Luke:1977:ACM,
  author =       "Yudell L. Luke",
  title =        "Algorithms for the Computation of Mathematical
                 Functions",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xiii + 284",
  year =         "1977",
  ISBN =         "0-12-459940-0",
  ISBN-13 =      "978-0-12-459940-6",
  LCCN =         "QA351 .L7961",
  bibdate =      "Wed Dec 15 10:38:19 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "Preface / xi \\
                 1: Basic Formulas / 1 \\
                 1.1 Introduction / 1 \\
                 1.2 The Generalized Hypergeometric Function and the
                 $G$-Function / 1 \\
                 1.3 Expansion of $_pF_q(z)$ and $G^{q - r, 1}_{p + 1,
                 q}(z)$, $r = 0$ or $r = 1$, in Series of Chebyshev
                 Polynomials of the First Kind / 4 \\
                 1.4 Efficient Evaluation of Series of Chebyshev
                 Polynomials / 17 \\
                 1.5 Rational Approximations for Generalized
                 Hypergeometric Functions / 20 \\
                 1.6 The Pad{\'e} Table / 27 \\
                 1.7 Computations of and Checks on Coefficients and
                 Tables / 29 \\
                 1.8 Tables of the Functions $e^{-\zeta}$, and
                 $e^{-\xi}$ / 35 \\
                 2: Identification of Functions / 41 \\
                 2.1 Introduction / 41 \\
                 2.2 The Generalized Hypergeometric Function $_pF_q(z)$
                 / 41 \\
                 2.3 The G-Function / 47 \\
                 2.4 Miscellaneous Functions / 48 \\
                 3: General Remarks on the Algorithms and Programs / 49
                 \\
                 3.1 Introduction / 49 \\
                 3.2 Precision and Complex Arithmetic / 49 \\
                 4: Chebyshev Coefficients for $_2F_1(a.b;c;z)$ / 52 \\
                 5: Coefficients for the Expansion of the Confluent
                 Hypergeometric Function $_1F_1(a;c;z)$ in Ascending
                 Series of Chebyshev Polynomials / 70 \\
                 6: Chebyshev Coefficients for $_0F_1(c;z)$ / 77 \\
                 7: Coefficients for the Expansion of $_1F_2(a;b,c;z)$
                 in Ascending Series of Chebyshev Polynomials / 82 \\
                 8: Coefficients for the Expansion of the Confluent
                 Hypergeometric Functions $U(a;c;z)$ and $_1F_1(a;c;-z)$
                 in Descending Series of Chebyshev Polynomials / 88 \\
                 9: Coefficients for the Expansion of the Functions
                 $G^{m,1}_{1,3}(z^2/4|^1_{a,b,c})$, $m = 3$ or $m = 2$,
                 in Descending Series of Chebyshev Polynomials / 101 \\
                 10: Differential and Integral Properties of Expansions
                 in Series of Chebyshev Polynomials of the First Kind /
                 116 \\
                 11: Expansion of Exponential Type Integrals in Series
                 of Chebyshev Polynomials of the First Kind / 126 \\
                 11.1 Introduction / 126 \\
                 11.2 The Representation for $g(x)$ / 127 \\
                 11.3 The Representation for $G(x)$ / 129 \\
                 11.4 Exponential Type Integrals Involving Logarithms /
                 133 \\
                 11.5 Numerical Examples / 135 \\
                 11.6 Errata / 139 \\
                 12: Conversion of a Power Series into a Series of
                 Chebyshev Polynomials of the First Kind / 154 \\
                 13: Rational Approximations for $_2F_1(a,b;c;-z)$ / 159
                 \\
                 14: Pad{\'e} Approximations for $_2F_1(1,b;c;-z)$ / 174
                 \\
                 15: Rational Approximations for $_1F_1(a;c;-z)$ / 182
                 \\
                 16: Pad{\'e} Approximations for $_1F_1(1;c;-z)$ / 192
                 \\
                 17: Rational Approximations for Bessel Functions of the
                 First Kind / 203 \\
                 18: Pad{\'e} Approximations for $I_{\nu +
                 1}(z)/I_\nu(z)$ / 220 \\
                 19: Evaluation of Bessel Functions of the First Kind by
                 Use of the Backward Recurrence Formula \\
                 19.1 Introduction / 230 \\
                 19.2 Backward Recurrence Schemata for $I_\nu(z)$ and
                 $J_\nu(z)$ / 230 \\
                 19.3 Numerical Examples / 240 \\
                 19.4 Mathematical Description of Programs / 243 \\
                 19.4.1 Evaluation of Functions Related to $I_{m +
                 \nu}(z)$ and $J_{m + \nu}(z)$ / 243 \\
                 19.4.2 Evaluation of Functions Related to $e^{-l}I_{m +
                 \nu}(z)$ / 245 \\
                 20: Rational Approximations for $z^aU(a;1 + a - b;z)$ /
                 252 \\
                 21: Pad{\'e} Approximations for $z U(1;2-b;z)$ / 265
                 \\
                 Appendices \\
                 Bibliography / 280 \\
                 Notation Index / 281 \\
                 Subject Index / 283",
  wrongisbn =    "0-12-459940-6",
}

@TechReport{Maag:1977:SRE,
  author =       "Werner Maag and Rudolf Wehrli",
  title =        "Survey on rounding effects in floating-point
                 arithmetic",
  type =         "Report",
  institution =  "CM Sch{\"a}nis AG",
  address =      "Sch{\"a}nis, Switzerland",
  pages =        "73",
  year =         "1977",
  bibdate =      "Thu May 09 09:10:32 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{Merzbach:1977:GSF,
  author =       "Uta C. Merzbach",
  title =        "{Georg Scheutz} and the first printing calculator",
  volume =       "36",
  publisher =    "Smithsonian Institution Press",
  address =      "Washington, DC, USA",
  pages =        "iii + 74",
  year =         "1977",
  LCCN =         "QA75 .M46",
  bibdate =      "Mon Jan 21 21:21:54 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
                 https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Smithsonian studies in history and technology",
  acknowledgement = ack-nhfb,
  subject =      "Calculators; History; Scheutz, George",
  subject-dates = "1785--1873",
}

@InCollection{Metropolis:1977:MSA,
  author =       "N. Metropolis",
  title =        "Methods of significance arithmetic",
  crossref =     "Jacobs:1977:SAN",
  pages =        "179--192",
  year =         "1977",
  MRclass =      "65G05 (68A99)",
  MRnumber =     "MR0451673 (56 \#9955)",
  MRreviewer =   "N. N. Abdelmalek",
  bibdate =      "Thu Nov 8 14:50:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Metropolis:1977:SAP,
  author =       "N. Metropolis and Stephen M. Tanny",
  title =        "Significance arithmetic: the probability of carrying",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "3",
  number =       "1",
  pages =        "77--81",
  year =         "1977",
  CODEN =        "CMAPDK",
  ISSN =         "0886-9561",
  ISSN-L =       "0898-1221",
  MRclass =      "65G05 (10A30 65C10)",
  MRnumber =     "MR0458846 (56 \#17046)",
  MRreviewer =   "Artenio De Matteis",
  bibdate =      "Thu Nov 8 14:50:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0371.60015",
  abstract =     "This article develops a number of probabilistic
                 results related to a combinatorial representation of
                 the real number system. This representation employs an
                 algorithmic definition of the arithmetic operations
                 analogous to that used by a computer. A carry function
                 for each place is defined and the distribution of these
                 functions is characterized in terms of classical
                 combinatorial polynomials",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers \& Mathematics with Applications. An
                 International Journal. Part B",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Mitra:1977:CDI,
  author =       "Debasis Mitra",
  title =        "Criteria for Determining if a High-Order Digital
                 Filter Using Saturation Arithmetic is Free of Overflow
                 Oscillations",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "56",
  number =       "9",
  pages =        "1679--1699",
  month =        nov,
  year =         "1977",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  bibdate =      "Tue Nov 9 11:15:56 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1977/BSTJ.1977.5609.html;
                 http://www.alcatel-lucent.com/bstj/vol56-1977/bstj-vol56-issue09.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol56/bstj56-9-1679.pdf;
                 http://www.alcatel-lucent.com/bstj/vol56-1977/articles/bstj56-9-1679.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}

@Article{Ninke:1977:SRB,
  author =       "W. H. Ninke and G. R. Ritchie",
  title =        "Shift Register Binary Rate Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "3",
  pages =        "276--278",
  month =        mar,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674819",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 21:56:53 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674819",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Oliver:1977:EAM,
  author =       "J. Oliver",
  title =        "An Error Analysis of the Modified {Clenshaw} Method
                 for Evaluating {Chebyshev} and {Fourier} Series",
  journal =      j-J-INST-MATH-APPL,
  volume =       "20",
  number =       "3",
  pages =        "379--391",
  year =         "1977",
  CODEN =        "JMTAA8",
  ISSN =         "0020-2932",
  ISSN-L =       "0020-2932",
  MRclass =      "65G05 (41A50)",
  MRnumber =     "57 #4508",
  MRreviewer =   "David L. Elliott",
  bibdate =      "Fri Apr 5 07:38:01 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jinstmathappl.bib",
  ZMnumber =     "0397.65013",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Institute of Mathematics and its
                 Applications",
  journal-URL =  "http://imamat.oxfordjournals.org/content/by/year",
  xxtitle =      "An error analysis of the modified {Clenshaw} methods
                 for evaluating {Chebyshev} and {Fourier} series",
}

@Article{Oliver:1977:SRE,
  author =       "J. Oliver",
  title =        "On the sensitivity to rounding errors of {Chebyshev}
                 series approximations",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "3",
  number =       "2",
  pages =        "89--98",
  month =        jun,
  year =         "1977",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:16 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0771050X77900031",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Palmer:1977:ISF,
  author =       "John Palmer",
  title =        "The {Intel} Standard for Floating Point Arithmetic",
  crossref =     "IEEE:1977:ICS",
  pages =        "107--112",
  year =         "1977",
  bibdate =      "Fri Nov 09 19:09:10 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Microprocessors will inevitably enter the realm of
                 serious floating-point computation. At the present
                 there are some software packages and bit-slice boards
                 that perform floating-point computation, but LSI
                 technology will soon be capable of numeric calculation
                 with respectable speeds. If we are to avoid the chaotic
                 situation that exists in this area among mainframes and
                 minicomputers, it is imperative that a standard be
                 adopted. A standard, just because it is standard, will
                 confer some benefits; but to have any hope of
                 permanence the standard should be carefully developed,
                 paying particular attention to those with experience in
                 the field. We have studied the present situation and
                 consulted with known experts and have adopted an
                 internal standard for floating-point formats and
                 arithmetic that we believe could be adopted for
                 microprocessors in general.",
  acknowledgement = ack-nhfb,
  remark-1 =     "From page 108: ``A software Floating-Point Arithmetic
                 Library (FPAL) for the 8080 and a Math Board (SBC-310)
                 made of series 3000 bit slices have already been
                 produced using this standard.''",
  remark-2 =     "From page 109: ``\ldots{} it was decided to provide
                 two exponent ranges. In the short [32-bit] word the
                 range is small to provide as much precision as possible
                 while in the long [64-bit] word the exponent range is
                 very large. (This choice also has the interesting
                 advantage that the long product of two short numbers
                 cannot overflow or underflow.) Another balancing
                 criterion is that the mantissa of the long word should
                 be more than twice as long as the short mantissa to
                 provide for almost error-free accumulation of inner
                 products.''",
  remark-3 =     "From page 111: ``One of the consequences of
                 implementing a sticky bit is that it is easy to provide
                 directed rounding. In directed rounding one rounds
                 toward the right or left on a standard number line as
                 directed. With a directed rounding capability, Interval
                 Arithmetic may be efficiently implemented with the
                 minimum possible growth in interval size. Interval
                 Arithmetic, if implemented efficiently, could be a
                 significant computational aid.''",
}

@Article{Papantoni-Kazakos:1977:CRE,
  author =       "P. Papantoni-Kazakos",
  title =        "Consideration of round off errors in the design of
                 mean square estimators",
  journal =      j-IEEE-TRANS-AUTOMAT-CONTR,
  volume =       "22",
  number =       "2",
  pages =        "276--279",
  month =        apr,
  year =         "1977",
  CODEN =        "IETAA9",
  ISSN =         "0018-9286 (print), 1558-2523 (electronic)",
  ISSN-L =       "0018-9286",
  bibdate =      "Sat Jul 16 11:25:03 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Automatic Control",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
  summary =      "In this correspondence, a search for the optimal
                 polynomial mean-square (ms) estimator is undertaken;
                 when the input is a vector with fixed dimensionality
                 and at the calculation of the estimator characteristics
                 the round off errors are considered. \ldots{}",
}

@Article{Randell:1977:CGC,
  author =       "B. Randell",
  title =        "{Colossus}: Godfather of the Computer",
  journal =      j-NEW-SCIENTIST,
  volume =       "73",
  number =       "1038",
  pages =        "346--348",
  day =          "10",
  month =        feb,
  year =         "1977",
  CODEN =        "NWSCAL",
  ISSN =         "0262-4079, 0028-6664",
  ISSN-L =       "0262-4079",
  bibdate =      "Wed Oct 13 11:51:16 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[\S 7.5]{Randell:1982:ODC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "New Scientist",
  journal-URL =  "http://www.sciencedirect.com/science/journal/02624079",
}

@Article{Reimer:1977:AFO,
  author =       "M. Reimer",
  title =        "{Auswertungsalgorithmen fast-optimaler numerischer
                 Stabilit{\"a}t f{\"u}r Polynome} \toenglish {Algorithms
                 of Near-optimal Numerical Stability for the Evaluation
                 of Polynomials} \endtoenglish",
  journal =      j-COMPUTING,
  volume =       "17",
  number =       "4",
  pages =        "289--296",
  month =        "????",
  year =         "1977",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@InProceedings{Reinsch:1977:SSE,
  author =       "Christian H. Reinsch",
  title =        "Some Side Effects of Striving for Portability",
  crossref =     "Cowell:1977:PNS",
  pages =        "3--19",
  year =         "1977",
  DOI =          "https://doi.org/10.1007/3-540-08446-0_31",
  bibdate =      "Thu Dec 11 15:15:52 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Christian H. Reinsch (?? ?? 1934--8 October 2022)",
}

@Article{Ris:1977:UDF,
  author =       "Frederic N. Ris",
  title =        "A unified decimal floating-point architecture for the
                 support of high-level languages",
  journal =      j-SIGPLAN,
  volume =       "12",
  number =       "9",
  pages =        "60--70",
  month =        sep,
  year =         "1977",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:14:09 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods); C6140D (High
                 level languages)",
  corpsource =   "IBM Thomas J. Watson Res. Center, Yorktown Heights,
                 NY, USA",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "architecture; decimal floating-point arithmetic;
                 digital arithmetic; high level languages; procedure
                 oriented languages; unified",
  treatment =    "P Practical",
}

@Article{Rjabko:1977:AHM,
  author =       "B. Ja. Rjabko",
  title =        "An analogue of {Haffmen}'s method for the optimal
                 summation of floating point numbers. ({Russian})",
  journal =      "Diskret. Analiz",
  volume =       "30",
  pages =        "38--45, 77",
  year =         "1977",
  MRclass =      "68C05 (68E99)",
  MRnumber =     "80c:68023",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
  reviewer =     "Vladimir Sleinikov",
  xxjournal =    "Metody Diskret. Anal. v Reshenii Kombinatornykh
                 Zadach",
}

@Article{Sanyal:1977:AND,
  author =       "S. Sanyal",
  title =        "An algorithm for nonrestoring division",
  journal =      j-COMP-DESIGN,
  volume =       "16",
  number =       "5",
  pages =        "124--127",
  month =        may,
  year =         "1977",
  CODEN =        "CMPDAM",
  ISSN =         "0010-4566",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computer Design",
}

@InProceedings{Schonfelder:1977:PTS,
  author =       "J. L. Schonfelder",
  title =        "The production and testing of special function
                 software in the {NAG} library",
  crossref =     "Cowell:1977:PNS",
  pages =        "425--451",
  year =         "1977",
  DOI =          "https://doi.org/10.1007/3-540-08446-0_53",
  bibdate =      "Thu Dec 11 15:15:52 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@MastersThesis{Simmons:1977:SRA,
  author =       "David Michael Simmons",
  title =        "Signal-to-noise ration analysis of block floating
                 point {FFTS}",
  type =         "Electrical Engineering Thesis ({M.S.})",
  school =       "University of Missouri--Rolla",
  address =      "Rolla, MO, USA",
  pages =        "114",
  year =         "1977",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Smith:1977:FPA,
  author =       "Brian T. Smith",
  title =        "{Fortran} poisoning and antidotes",
  crossref =     "Cowell:1977:PNS",
  pages =        "178--256",
  year =         "1977",
  DOI =          "https://doi.org/10.1007/3-540-08446-0_43",
  bibdate =      "Thu Dec 11 15:15:52 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Soderstrand:1977:HSL,
  author =       "M. A. Soderstrand",
  title =        "A high-speed low-cost recursive digital filter using
                 residue number arithmetic",
  journal =      j-PROC-IEEE,
  volume =       "65",
  number =       "7",
  pages =        "1065--1067",
  month =        jul,
  year =         "1977",
  CODEN =        "IEEPAD",
  DOI =          "https://doi.org/10.1109/PGEC.1967.264810",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=31255",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Use of table look-up multiplication by fractional
                 coefficients allows implementation of high-speed,
                 low-cost recursive digital filters using residue number
                 arithmetic. An 8-bit equivalent filter based on the
                 lossless discrete integrator (LDI) \ldots{}",
}

@Article{Soderstrand:1977:MRN,
  author =       "M. A. Soderstrand and E. L. Fields",
  title =        "Multipliers for residue-number-arithmetic digital
                 filters",
  journal =      j-ELECT-LETTERS,
  volume =       "13",
  number =       "6",
  pages =        "164--166",
  day =          "17",
  month =        mar,
  year =         "1977",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:19770117",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4249252",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A recently proposed residue-number-arithmetic digital
                 filter offers major cost and speed advantages over
                 binary-arithmetic digital filters, but suffers one
                 major drawback. The filter coefficients must be
                 constant, since the lack of a fast method of \ldots{}",
}

@Article{Steer:1977:DHS,
  author =       "D. G. Steer and S. R. Penstone",
  title =        "Digital Hardware for Sine-Cosine Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "12",
  pages =        "1283--1286",
  month =        dec,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674791",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:15:56 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Stenzel:1977:CHS,
  author =       "W. J. Stenzel",
  title =        "A Compact High-Spped Multiplication Scheme",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "10",
  pages =        "948--957",
  month =        oct,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674730",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 19:20:56 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Stoutemyer:1977:AEA,
  author =       "David R. Stoutemyer",
  title =        "Automatic Error Analysis Using Computer Algebraic
                 Manipulation",
  journal =      j-TOMS,
  volume =       "3",
  number =       "1",
  pages =        "26--43",
  month =        mar,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355719.355721",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 02 22:30:11 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper shows how the inherent error and the
                 fixed-point or floating-point roundoff of chopoff error
                 of an expression can be determined automatically using
                 a computer algebra language such as {REDUCE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Thong:1977:ARE,
  author =       "Tran Thong and Bede Liu",
  title =        "Accumulation of roundoff errors in floating point
                 {FFT}",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "24",
  number =       "3",
  pages =        "132--143",
  month =        mar,
  year =         "1977",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  MRclass =      "65G05",
  MRnumber =     "55 1722",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  reviewer =     "Sven-{\AA}ke Gustafson",
  summary =      "A statistical model for roundoff error is used to
                 predict the output noise to signal ratio of the two
                 common FFT algorithms, the decimation in time and the
                 decimation in frequency algorithms. A unified approach
                 is used to obtain the error in both algorithms
                 \ldots{}",
}

@Article{Tran-Thong:1977:FPF,
  author =       "Tr{\^a}{\`n}-Th{\^o}{\'n}g and Bede Liu",
  title =        "Floating Point Fast {Fourier} Transform Computation
                 Using Double Precision Floating Point Accumulators",
  journal =      j-TOMS,
  volume =       "3",
  number =       "1",
  pages =        "54--59",
  month =        mar,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355719.355723",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65T05",
  MRnumber =     "55 \#11658",
  bibdate =      "Sat Aug 27 22:12:55 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Most commonly available fast Fourier transform (FFT)
                 subroutines use single precision chopping arithmetic,
                 and the resulting normalized roundoff error, in
                 computing an $N$-point transform with $ N = \prod_{i =
                 1}^M a_i $ is $ O(M^2) $. This paper proposes a
                 modification of these subroutines for use on computers
                 with a hardwired double precision arithmetic unit. The
                 resulting normalized roundoff error is $ O(M) $ and is
                 independent of the $ a_i $. The modification leads to a
                 negligible increase in storage. For most computers, the
                 increase in the execution time is small. For certain
                 computers, such as IBM System/360 models 91 and 195,
                 the modification can result in a decrease in the
                 execution time.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "computer arithmetic; double-length summation; fast
                 Fourier transform; roundoff error",
}

@Article{Trivedi:1977:LAD,
  author =       "Kishor S. Trivedi and Milo{\v{s}} D. Ercegovac",
  title =        "On-line algorithms for division and multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "7",
  pages =        "681--687",
  month =        jul,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674901",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 30 07:29:16 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Trivedi:1977:UCF,
  author =       "K. S. Trivedi",
  title =        "On the Use of Continued Fractions for Digital Computer
                 Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "7",
  pages =        "700--704",
  month =        jul,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674903",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 21:56:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See corrections \cite{Trivedi:1978:CUC}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674903",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Ushijima:1977:SEP,
  author =       "Kazuo Ushijima",
  title =        "Step to an Efficient Program for Floating-point
                 Summation",
  journal =      j-SPE,
  volume =       "7",
  number =       "6",
  pages =        "759--769",
  month =        nov # "\slash " # dec,
  year =         "1977",
  CODEN =        "SPEXBL",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Sat May 31 13:36:16 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Software---Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
}

@InProceedings{Victor:1977:ISI,
  author =       "N. Victor and M. Sund",
  title =        "The importance of standardized interfaces for portable
                 statistical software",
  crossref =     "Cowell:1977:PNS",
  pages =        "484--503",
  year =         "1977",
  DOI =          "https://doi.org/10.1007/3-540-08446-0_55",
  bibdate =      "Thu Dec 11 15:15:52 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Waite:1977:ILC,
  author =       "W. M. Waite",
  title =        "Intermediate languages: Current status",
  crossref =     "Cowell:1977:PNS",
  pages =        "269--303",
  year =         "1977",
  DOI =          "https://doi.org/10.1007/3-540-08446-0_45",
  bibdate =      "Thu Dec 11 15:15:52 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Williams:1977:SIA,
  author =       "R. P. Williams",
  title =        "Serial Integer Arithmetic with Magnetic Bubbles",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "3",
  pages =        "260--264",
  month =        mar,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674814",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 21:56:52 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1674814",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Wozniakowski:1977:NSC,
  author =       "H. Wo{\'z}niakowski",
  title =        "Numerical Stability of the {Chebyshev} Method for the
                 Solution of Large Linear Systems",
  journal =      j-NUM-MATH,
  volume =       "28",
  number =       "2",
  pages =        "191--209",
  year =         "1977",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C4110 (Error analysis in numerical methods); C4140
                 (Linear algebra)",
  corpsource =   "Department of Computer Sci., Carnegie-Mellon
                 University, Pittsburgh, PA, USA",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "Chebyshev approximation; Chebyshev method; computed
                 residuals; error analysis; floating point arithmetic;
                 iterative methods; large linear systems; linear
                 systems; numerical stability; rounding error analysis",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Yuen:1977:NRD,
  author =       "C. K. Yuen",
  title =        "A New Representation for Decimal Numbers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-26",
  number =       "12",
  pages =        "1286--1288",
  month =        dec,
  year =         "1977",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1977.1674792",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Aug 07 18:00:38 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  abstract =     "A new representation for decimal numbers is proposed.
                 It uses a mixture of positive and negative radixes to
                 ensure that the maximum value of a four bit decimal
                 digit is 9. This eliminates the more complex carry
                 generation process required in BCD addition.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "decimal arithmetic",
}

@InProceedings{Abu-El-Haija:1978:AER,
  author =       "A. Abu-El-Haija and A. Peterson",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing: {ICASSP '78}",
  title =        "An approach to eliminate roundoff errors in digital
                 filters",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "75--78",
  year =         "1978",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Roundoff noise and limit cycle oscillations due to
                 postmultiplication rounding can seriously limit the
                 application of recursive digital filters in practice,
                 particularly for poles near the unit circle or near z =
                 +1. Rounding is usually performed by \ldots{}",
}

@InProceedings{Agrawal:1978:AIR,
  author =       "Dharma P. Agrawal",
  title =        "On Arithmetic Inter-relationships and Hardware
                 Interchangeability of Negabinary and Binary Systems",
  crossref =     "IEEE:1978:PSC",
  pages =        "88--96",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Agrawal.pdf",
  abstract =     "Recent use of the negabinary system in the application
                 oriented digital hardware, has encouraged the search
                 for suitable arithmetic algorithms in $ - 2 $ base.
                 These algorithms have been directly utilized in
                 designing logic circuits and several logic
                 implementations have been reported in the literature.
                 The main objective of this paper is to show the close
                 relationship between $ + 2 $ base addition and $ - 2 $
                 base negative addition. Two possible ways of utilizing
                 binary adders for performing negabinary addition and
                 their underlying theories are presented. Two similar
                 techniques of using negabinary adders for binary
                 addition are also considered in detail. An interesting
                 aspect of this investigation about negabinary base is
                 that negative addition (rather than just addition)
                 seems to be the primitive operation from logic
                 complexity and interchangeability of $ + 2 $ and $ - 2
                 $ adders point of view.\par

                 The technique of adding two numbers in one system by
                 the adders of the other system is extended here for
                 multiple operand addition. This requires inclusion of
                 an additional correction factor. Further, the additive
                 algorithms of this work lead to four simple conversion
                 processes of number from one system to another. This
                 paper seems to be a realistic step towards the use of
                 similar hardware for $ + 2 $ and $ - 2 $ bases and
                 hence this allows an instantaneous flexibility on the
                 selection of number system. It is believed that this
                 paper will attract more attention on the use of $ - 2 $
                 base system for the design of special purpose digital
                 machines and process controllers.",
  acknowledgement = ack-nhfb,
  keywords =     "Addition; ARITH-4; base conversion; binary numbers;
                 even positioned bits; multiple addition; negabinary
                 system; negative addition; negative radix; odd
                 positioned bits.",
}

@InProceedings{Agrawal:1978:MAL,
  author =       "Dharma P. Agrawal and T. R. N. Rao",
  title =        "On Modular $ (2^n + 1) $ Arithmetic Logic",
  crossref =     "IEEE:1978:PSC",
  pages =        "104--108",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Agrawal_Rao.pdf",
  abstract =     "A novel format for representing modulo $ (2^n + 1) $
                 numbers, is shown to be helpful in achieving modular
                 addition and complementation. Logic for fast addition
                 using carry-look-ahead and modular complementation is
                 also presented.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}

@Article{Andrews:1978:EFM,
  author =       "M. Andrews and S. F. McCormick and G. D. Taylor",
  title =        "Evaluation of Functions on Microcomputers: Square
                 Root",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "4",
  number =       "4",
  pages =        "359--367",
  year =         "1978",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Thu Sep 15 18:40:29 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  xxmonth =      "(none)",
}

@Article{Andrews:1978:IAN,
  author =       "M. Andrews",
  title =        "Influence of architecture on numerical algorithms",
  journal =      j-MICROPROC-MICROSYS,
  volume =       "2",
  number =       "3",
  pages =        "130--137",
  month =        jun,
  year =         "1978",
  CODEN =        "MIMID5",
  ISSN =         "0141-9331 (print), 1872-9436 (electronic)",
  ISSN-L =       "0141-9331",
  bibdate =      "Thu Sep 1 10:14:44 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Microprocessors and Microsystems",
}

@Article{Andrews:1978:PCA,
  author =       "Michael Andrews and Daniel E. Eggerding",
  title =        "A Pipelined Computer Architecture for Unified
                 Elementary Function Evaluation",
  journal =      j-COMPUT-ELECTR-ENG,
  volume =       "5",
  number =       "2",
  pages =        "189--202",
  month =        jun,
  year =         "1978",
  CODEN =        "CPEEBQ",
  DOI =          "https://doi.org/10.1016/0045-7906(78)90030-7",
  ISSN =         "0045-7906 (print), 1879-0755 (electronic)",
  ISSN-L =       "0045-7906",
  bibdate =      "Sat Oct 18 14:58:07 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.sciencedirect.com/science/article/abs/pii/0045790678900307",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Electrical Engineering",
  keywords =     "arccos; arccosh; arccot; arcsin; arcsinh; CORDIC;
                 cosine; Digital Arithmetic; exp(x); Iterative
                 Algorithms; ln(x); Pipeline; sine; sqrt(x); Unified
                 Elementary Functions; x**y; x/y",
}

@Article{Andrews:1978:UEF,
  author =       "M. Andrews and T. Mraz",
  title =        "Unified elementary function generator",
  journal =      j-MICROPROC-MICROSYS,
  volume =       "2",
  number =       "5",
  pages =        "270--273",
  month =        oct,
  year =         "1978",
  CODEN =        "MIMID5",
  ISSN =         "0141-9331 (print), 1872-9436 (electronic)",
  ISSN-L =       "0141-9331",
  bibdate =      "Thu Sep 1 10:15:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Microprocessors and Microsystems",
}

@Manual{Apple:1978:AIR,
  key =          "Apple",
  title =        "{Applesoft II} reference manual: extended
                 floating-point {BASIC}",
  organization = "Apple Computer, Inc.",
  address =      "Cupertino, CA, USA",
  pages =        "63",
  year =         "1978",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Apple II (Computer) --- Programming; BASIC (Computer
                 program language)",
}

@InProceedings{Atkins:1978:CTA,
  author =       "D. E. Atkins and S. C. Ong",
  title =        "A Comparison of Two Approaches to Multi-Operand Binary
                 Addition",
  crossref =     "IEEE:1978:PSC",
  pages =        "125--139",
  year =         "1978",
  bibdate =      "Wed Nov 14 17:47:38 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Atkins.pdf",
  abstract =     "This paper presents the results of one phase of a
                 study concerning methods for addition of $ P > 2 $
                 numbers, each encoded as a vector of digits (digit
                 vector) of length $N$. Such multi-operand addition has
                 been studied most often in the context of reducing a
                 set of partial products to a single result in the
                 implementation of multiplication. More generalized
                 multi-operand addition, most notably in the form of
                 inner product calculations is, however, central to
                 numerous scientific applications of digital computers.
                 Although multioperand addition is trivially
                 accomplished by accumulation (iteration in time) in any
                 general purpose machine, demands for very high-speed
                 computation, typified by 2- and 3-D signal processing
                 prompt implementation of dedicated, hardware-intensive
                 structures for multi-operand addition. This study, for
                 example, is motivated in part by requirements for rapid
                 simultaneous addition of up to 100, 16-bit operands in
                 the design of a dedicated processor for real-time
                 reconstruction of 3-D images of the beating heart and
                 breathing lungs.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}

@TechReport{Banerji:1978:HSD,
  author =       "Dilip K. Banerji and To-Yat Cheung and V. Ganesan",
  title =        "A high speed division method in residue arithmetic",
  institution =  "Department of Computer Science, University of Ottawa",
  address =      "Ottawa, ON, Canada K1N 6N5",
  pages =        "7",
  year =         "1978",
  bibdate =      "Thu Nov 18 09:44:27 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://books.google.com/books?id=q8fBIwAACAAJ",
  acknowledgement = ack-nhfb,
  remark =       "Credited to CH1630-3/81/0000/0158 IEEE 1981; where did
                 this appear?",
}

@Article{Baraniecka:1978:DTR,
  author =       "A. Baraniecka and G. Jullien",
  title =        "On decoding techniques for residue number system
                 realizations of digital signal processing hardware",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "25",
  number =       "11",
  pages =        "935--936",
  month =        nov,
  year =         "1978",
  CODEN =        "ICSYBT",
  DOI =          "https://doi.org/10.1049/el:19770117",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23475",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
  summary =      "In a recent issue of this journal, a hardware
                 implementation of the Chinese Remainder Theorem was
                 proposed for the translation of residue coded outputs
                 into natural integer for an FIR filter realization. The
                 method requires a modulo M adder- \ldots{}",
}

@Book{Bareiss:1978:PEA,
  author =       "Erwin H. Bareiss and Jesse L. Barlow",
  title =        "Probabilistic error analysis of computer arithmetics",
  publisher =    "Department of Electrical Engineering and Computer
                 Science, Northwestern University",
  address =      "Evanston, IL, USA",
  pages =        "97",
  year =         "1978",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 12:09:29 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Barsi:1978:ACR,
  author =       "F. Barsi and P. Maestrini",
  title =        "Arithmetic Codes in Residue Number Systems with
                 Magnitude Index",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-27",
  number =       "12",
  pages =        "1185--1188",
  month =        dec,
  year =         "1978",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1978.1675023",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 08:13:33 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35165;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675023",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The idea of adding a magnitude index to the residue
                 representation of numbers is reconsidered. The range of
                 a given residue number system is supposed to be divided
                 into intervals of equal width, and the magnitude index
                 of a number X is defined as an \ldots{}",
}

@Manual{BellHowellCo:1978:BHF,
  author =       "{Bell and Howell Co} and {Apple Computer, Inc}",
  title =        "[{Bell and Howell} floating point {Basic} programming
                 reference manual]",
  organization = "Bell and Howell, Audio-Visual Products Division",
  address =      "Chicago, IL, USA",
  pages =        "xiii + 168",
  year =         "1978",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Apple II (Computer) --- Programming.; BASIC (Computer
                 program language)",
  remark =       "Cover title. ``Reprinted with permission of Apple
                 Computer, Inc.'' Companion volume: Floating point Basic
                 tutorial manual. Quick reference guide on folded,
                 inserted leaf.",
}

@Article{Blue:1978:PFP,
  author =       "James L. Blue",
  title =        "A Portable {Fortran} Program to Find the {Euclidean}
                 Norm of a Vector",
  journal =      j-TOMS,
  volume =       "4",
  number =       "1",
  pages =        "15--23",
  month =        mar,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355769.355771",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "68A10",
  MRnumber =     "57 \#18205",
  bibdate =      "Sat Aug 27 23:14:36 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "BLAS; floating-point arithmetic; floating-point
                 overflow; floating-point underflow; nla; norm;
                 software",
  reviewer =     "A. D. Booth",
}

@TechReport{Boehmer:1978:TAF,
  author =       "K. Boehmer and J. Michael Yohe",
  title =        "{Triplex} Arithmetic for {Fortran}",
  type =         "MRC Technical Summary",
  number =       "1901",
  institution =  inst-MRC-WISCONSIN,
  address =      inst-MRC-WISCONSIN:adr,
  pages =        "38",
  month =        dec,
  year =         "1978",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/intarith.bib",
  abstract =     "Triplex arithmetic is a variant of interval arithmetic
                 in which a 'main' value is computed in addition to the
                 endpoints of the containing interval. The 'main' value
                 is, in general, the value that would have been computed
                 had properly-rounded real arithmetic been used to
                 compute the results of the calculation; it may in some
                 sense, be regarded as the 'most probable' value of the
                 result of the calculation. The endpoints of the
                 interval define the worst-case range of the possible
                 values of the computation. This report describes a
                 FORTRAN implementation of triplex arithmetic in both
                 single and multiple precision. The package described in
                 this report is designed to be used with the AUGMENT
                 precompiler: this makes triplex arithmetic particularly
                 easy to use.",
  acknowledgement = ack-jr,
  keywords =     "Approximation theory.; Equations, Abelian.; Spline
                 theory.",
}

@PhdThesis{Bohlender:1978:GBM,
  author =       "G. Bohlender",
  title =        "{Genaue Berechnung mehrfacher Summen, Produkte und
                 Wurzeln von Gleitkommazahlen und allgemeine Arithmetik
                 in h{\"o}heren Programmiersprachen} \toenglish
                 {Accurate Computation of Multiple Sums, Products and
                 Roots of Floating-Point Numbers and General Arithmetic
                 in High-Level Programming Languages} \endtoenglish",
  type =         "Dissertation",
  school =       "Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "??",
  year =         "1978",
  bibdate =      "Fri Sep 16 16:30:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  keywords =     "accurate floating-point summation",
}

@Article{Boney:1978:MRW,
  author =       "J. Boney",
  title =        "Math in the Real World",
  journal =      j-BYTE,
  volume =       "3",
  number =       "9",
  pages =        "114--119",
  month =        sep,
  year =         "1978",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Thu Sep 1 10:14:44 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "BYTE Magazine",
}

@Article{Brady:1978:MBL,
  author =       "W. G. Brady",
  title =        "More on {Benford}'s Law",
  journal =      j-FIB-QUART,
  volume =       "16",
  number =       "1",
  pages =        "51--52",
  month =        feb,
  year =         "1978",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 17:59:24 MDT 2011",
  bibsource =    "http://www.fq.math.ca/16-1.html;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.fq.math.ca/Scanned/16-1/brady.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
  journal-URL =  "http://www.fq.math.ca/",
}

@TechReport{Brent:1978:AIB,
  author =       "R. P. Brent and J. A. Hooper and J. Michael Yohe",
  title =        "An {Augment} Interface for {Brent}'s {Multiple
                 Precision Arithmetic Package}",
  type =         "MRC Technical Summary",
  number =       "1868",
  institution =  inst-MRC-WISCONSIN,
  address =      inst-MRC-WISCONSIN:adr,
  year =         "1978",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Published In: ACM Trans. Math. Software 6, 146--149,
                 1980",
  acknowledgement = ack-jr,
}

@Article{Brent:1978:AMF,
  author =       "Richard P. Brent",
  title =        "Algorithm 524: {MP}, {A Fortran} Multiple-Precision
                 Arithmetic Package [{A1}]",
  journal =      j-TOMS,
  volume =       "4",
  number =       "1",
  pages =        "71--81",
  month =        mar,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355769.355776",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 22:49:15 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also \cite{Brent:1979:RMF,Brent:1980:AIB}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Brent:1978:FMP,
  author =       "Richard P. Brent",
  title =        "{A Fortran} Multiple-Precision Arithmetic Package",
  journal =      j-TOMS,
  volume =       "4",
  number =       "1",
  pages =        "57--70",
  month =        mar,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355769.355775",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Case:1978:AIS,
  author =       "Richard P. Case and Andris Padegs",
  title =        "Architecture of the {IBM System}\slash 370",
  journal =      j-CACM,
  volume =       "21",
  number =       "1",
  pages =        "73--96",
  month =        jan,
  year =         "1978",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Sat Jan 29 18:00:28 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@TechReport{Cherry:1978:BAP,
  author =       "Lorinda L. Cherry and Robert Morris",
  title =        "{BC} --- An Arbitrary Precision Desk Calculator
                 Language",
  type =         "Technical Memorandum",
  number =       "1053",
  institution =  inst-ATT-BELL,
  address =      inst-ATT-BELL:adr,
  pages =        "2 + 14",
  day =          "12",
  month =        nov,
  year =         "1978",
  bibdate =      "Tue Jun 06 08:07:45 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  abstract =     "BC is a language and a compiler for doing arbitrary
                 precision arithmetic on the PDP-11 under the UNIX
                 time-sharing system. The output of the compiler is
                 interpreted and executed by a collection of routines
                 which can input, output. and do arithmetic on
                 indefinitely large integers and on scaled fixed-point
                 numbers.\par

                 These routines are themselves based on a dynamic
                 storage allocator. Overflow does not occur until all
                 available core storage is exhausted.\par

                 The language has a complete control structure as well
                 as immediate-mode operation. Functions can be defined
                 and saved for later execution.\par

                 Two five hundred-digit numbers can be multiplied to
                 give a thousand digit result in about ten
                 seconds.\par

                 A small collection of library functions is also
                 available, including sin. cos, arctan, log,
                 exponential, and Bessel functions of integer
                 order.\par

                 Some of the uses of this compiler are\par

                 * to do computation with large integers.\par

                 * to do computation accurate to many decimal
                 places,\par

                 * conversion of numbers from one base to another
                 base.",
  abstract-2 =   "BC is a language and a compiler for doing arbitrary
                 precision arithmetic on the PDP-11 und UNIX
                 Time-Sharing System.",
  acknowledgement = ack-nhfb,
  author-dates = "Lorinda L. Cherry (18 November 1944--February 2022);
                 Robert Morris (25 July 1932--26 June 2011)",
  remark =       "Available in PDF file of \cite[pp.
                 383--398]{Dolotta:1977:DPU}.",
}

@InProceedings{Chow:1978:LDR,
  author =       "Catherine Y. Chow and James E. Robertson",
  title =        "Logical Design of a Redundant Binary Adder",
  crossref =     "IEEE:1978:PSC",
  pages =        "109--115",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Chow.pdf",
  abstract =     "This paper investigates the logical design of a
                 redundant binary adder with two input digits and one
                 output digit, all in the digit set $ \{ \bar {1}, 0, 1
                 \} $. Redundant binary arithmetic structures in which
                 all digit sets are $ \{ \bar {1}, 0, 1 \} $ were first
                 discussed by Avizienis in 1961. Borovec studied the
                 logical design of a class of such binary adders and
                 subtracters in 1968. At that time, a variation of the
                 adder\slash subtracter was overlooked. This paper
                 studies the logical design of this variation. The sum
                 digit is still a function only of the digits in three
                 adjacent digital positions of the operands. ``Coupled
                 don't cares'' are encountered, but have not introduced
                 too much difficulty. The nine distinct formats (under
                 permutation and negation) of representing three values
                 with two bits given by Robertson are used. The simplest
                 adder\slash subtracter designs from this variation are
                 less complex than the simplest designs previously
                 known.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}

@InProceedings{Cohen:1978:MAI,
  author =       "Danny Cohen",
  title =        "Mathematical Approach to Iterative Computation
                 Networks",
  crossref =     "IEEE:1978:PSC",
  pages =        "226--237",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Cohen.pdf",
  abstract =     "This paper deals with design principles for iterative
                 computation networks. Such computation networks are
                 used for performing repetitive computations which
                 typically are not data dependent. Most of the signal
                 processing algorithms. like FFT and filtering, belong
                 to this class.\par

                 The main idea in this paper is the development of
                 mathematical notation for expressing such designs. This
                 notation captures the important features and properties
                 of these computation networks, and can be used both for
                 analyzing and for designing computational networks.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}

@TechReport{Coonen:1978:SPS,
  author =       "Jerome T. Coonen",
  title =        "Specification for a proposed standard for floating
                 point arithmetic",
  type =         "Memorandum",
  number =       "ERL M78/72",
  institution =  "University of California, Berkeley",
  address =      "Berkeley, CA, USA",
  year =         "1978",
  bibdate =      "Wed Nov 24 09:10:35 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Corsini:1978:USM,
  author =       "P. Corsini and G. Frosini",
  title =        "Uniform Shift Multiplication Algorithms Without
                 Overflow",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-27",
  number =       "3",
  pages =        "256--258",
  month =        mar,
  year =         "1978",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1978.1675081",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 08:13:27 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675081",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@TechReport{Crary:1978:APT,
  author =       "F. D. Crary and J. Michael Yohe",
  title =        "The {Augment} Precompiler as a Tool for the
                 Development of Special Purpose Arithmetic Packages",
  type =         "MRC Technical Summary",
  number =       "1892",
  institution =  inst-MRC-WISCONSIN,
  address =      inst-MRC-WISCONSIN:adr,
  year =         "1978",
  bibdate =      "Fri Jan 12 11:37:56 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-jr,
}

@InProceedings{Dadda:1978:MAB,
  author =       "Luigi Dadda",
  title =        "Multiple Addition of Binary Serial Numbers",
  crossref =     "IEEE:1978:PSC",
  pages =        "140--148",
  year =         "1978",
  bibdate =      "Wed Nov 14 17:48:30 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Dadda.pdf",
  abstract =     "It is shown how circuits for the addition of several
                 serial binary numbers can be obtained as a combination
                 of parallel counters and memory cells.\par

                 The various schemes belong to one of three different
                 classes, characterized by the way in which carries,
                 produced by parallel counters, are treated.\par

                 A comparison is made between the various schemes, in
                 terms of speed and complexity.",
  acknowledgement = ack-nhfb,
  author-dates = "29 April 1923--26 October 2012",
  keywords =     "ARITH-4",
}

@Article{Debnath:1978:EMO,
  author =       "R. C. Debnath and D. A. Pucknell",
  title =        "Erratum: On multiplicative overflow detection in
                 residue number system",
  journal =      j-ELECT-LETTERS,
  volume =       "14",
  number =       "12",
  pages =        "385",
  day =          "8",
  month =        jun,
  year =         "1978",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:19780260",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Debnath:1978:MOD}",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4241130",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "residue arithmetic; residue number system",
}

@Article{Debnath:1978:MOD,
  author =       "R. C. Debnath and D. A. Pucknell",
  title =        "On multiplicative overflow detection in residue number
                 system",
  journal =      j-ELECT-LETTERS,
  volume =       "14",
  number =       "5",
  pages =        "129--130",
  month =        "????",
  year =         "1978",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:19780088",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See erratum \cite{Debnath:1978:EMO}.",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4240881",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A general method for the detection of multiplicative
                 overflow has been developed. The method has been found
                 suitable in 16--15-mod residue system from the
                 consideration of cost and speed. A circuit for
                 16--15-mod-multiplicative overflow detection \ldots{}",
}

@Misc{DEC-ES:1978:VIS,
  author =       "{Digital Equipment Corporation.Educational Services}",
  title =        "{VAX-11} instruction set",
  publisher =    "Digital Equipment Corporation",
  address =      "Maynard, MA, USA",
  year =         "1978",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "13 videocassettes (ca. 585 min.)",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic; VAX-11 (Computer)
                 --- Programming.",
  remark =       "Accompanied by 11 volumes of print materials, 1981.
                 [1] Instruction formats and addressing modes, lesson 1
                 --- [2] Instruction formats and addressing modes,
                 lessons 2 and 3 --- [3] Integer, logical, and branch
                 instructions, lessons 1 and 2 --- [4] Integer, logical,
                 and branch instructions, lessons 3 and 4 --- [5]
                 Character string instructions, lessons 1 and 2 --- [6]
                 Character string instructions, lessons 3 and 4 --- [7]
                 Decimal string instructions, lessons 1 and 2 --- [8]
                 Decimal string instructions, lessons 3, 4, and 5 ---
                 [9] Special instructions --- [10] Procedures and
                 subroutine instructions --- [11] Stack and address
                 instructions --- [12] Variable bit field instructions
                 --- [13] Floating point instructions. Provides an
                 introduction to the VAX-11 computer system.",
}

@Article{Diamond:1978:SRI,
  author =       "Harold G. Diamond",
  title =        "Stability of Rounded Off Inverses Under Iteration",
  journal =      j-MATH-COMPUT,
  volume =       "32",
  number =       "141",
  pages =        "227--232",
  month =        jan,
  year =         "1978",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 JSTOR database; Parallel/par.lin.alg.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Department of Math., University of Illinois, Urbana,
                 IL, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "function approximation; iterative methods; positive
                 integer; rounded off inverse stability",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Egbert:1978:PCA,
  author =       "W. E. Egbert",
  title =        "Personal Calculator Algorithms {IV}: Logarithmic
                 Functions",
  journal =      j-HEWLETT-PACKARD-J,
  volume =       "29",
  number =       "8",
  pages =        "29--32",
  month =        apr,
  year =         "1978",
  CODEN =        "HPJOAX",
  ISSN =         "0018-1153",
  bibdate =      "Thu Sep 1 10:16:09 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Hewlett-Packard Journal: technical information from
                 the laboratories of Hewlett-Packard Company",
}

@InProceedings{Ercegovac:1978:AME,
  author =       "M. D. Ercegovac and M. M. Takata",
  title =        "An Arithmetic Module for Efficient Evaluation of
                 Functions",
  crossref =     "IEEE:1978:PSC",
  pages =        "190--199",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Ercegovac_Takata.pdf",
  abstract =     "The organization and design of an arithmetic module
                 (Basic Byte-Slice Module --- BBM) is presented. A
                 network of BBWs implements an efficient digit-by-digit
                 method for fast evaluation of polynomial and rational
                 functions. Verification of the BBW design, its
                 feasibility in present LSI technologies and its
                 performance are discussed. The proposed BBW is
                 characterized by a small number of input\slash output
                 terminals, a uniform internal structure, and simple
                 control and inter-module communication requirements.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}

@InProceedings{Ercegovac:1978:FIS,
  author =       "Milo{\v{s}} D. Ercegovac and Algirdas Avizienis",
  title =        "The {Fourth IEEE Symposium on Computer Arithmetic}:
                 Foreword",
  crossref =     "IEEE:1978:PSC",
  pages =        "v--v",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_contents.pdf;
                 http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_foreword.pdf;
                 http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_preface.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}

@InProceedings{Ercegovac:1978:LSR,
  author =       "Milo{\v{s}} D. Ercegovac",
  title =        "An On-Line Square Rooting Algorithm",
  crossref =     "IEEE:1978:PSC",
  pages =        "183--189",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Ercegovac.pdf",
  abstract =     "An on-line algorithm for computing square roots in a
                 radix 2, normalized floating-point number system with
                 the redundant digit set $ \{ - 1, 0, 1 \} $ is
                 described. The algorithm has on-line delay of one and
                 it is amenable for modular implementation. A systematic
                 approach, used in deriving this algorithm, is presented
                 in detail.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}

@TechReport{Espelid:1978:FPS,
  author =       "Terje O. Espelid",
  title =        "On floating-point summation",
  type =         "Report",
  number =       "67",
  institution =  "Department of Applied Mathematics, University of
                 Bergen",
  address =      "Bergen, Norway",
  pages =        "24",
  year =         "1978",
  bibdate =      "Thu May 09 08:03:27 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}

@Periodical{FloatingPointSystems:1978:P,
  author =       "{Floating Point Systems, Inc}",
  title =        "To the point",
  publisher =    "Floating Point Systems",
  address =      "Portland, OR, USA",
  year =         "1978",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  alttitle =     "To the point (Portland, Or.)",
  keywords =     "Floating Point Systems, Inc. --- Periodicals.",
  remark =       "``Employee newsletter.'' Title from caption.",
}

@Article{Fox:1978:AFP,
  author =       "P. A. Fox and A. D. Hall and N. L. Schryer",
  title =        "{Algorithm 528}: Framework for a Portable Library
                 [{Z}]",
  journal =      j-TOMS,
  volume =       "4",
  number =       "2",
  pages =        "177--188",
  month =        jun,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355780.355789",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:30:46 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See remarks \cite{Fox:1979:RFP,Gay:1999:SAF}.",
  acknowledgement = ack-nhfb,
  annote =       "The three program packages presented here provide a
                 framework for a portable FORTRAN subroutine library.
                 They were developed for the BELL Laboratories library
                 PORT(1). The packages are: machine-dependent constants,
                 automatic error handling, and dynamic storage
                 allocation using a stack.",
  country =      "USA",
  date =         "19/03/80",
  descriptors =  "Reliability; program construction; mathematical
                 method; FORTRAN; portability; error handling; memory
                 management; library",
  enum =         "988",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  language =     "English",
  location =     "RWTH-AC-DFV: TELL",
  references =   "1",
  revision =     "20/03/92",
}

@Article{Fox:1978:PMS,
  author =       "P. A. Fox and A. D. Hall and N. L. Schryer",
  title =        "The {PORT} Mathematical Subroutine Library",
  journal =      j-TOMS,
  volume =       "4",
  number =       "2",
  pages =        "104--126",
  month =        jun,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355780.355783",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The development at Bell Laboratories of PORT, a
                 library of portable Fortran programs for numerical
                 computation, is discussed. Portability is achieved by
                 careful language specification, together with the key
                 technique of specifying computer classes by means of
                 predefined machine constants. The library is built
                 around an automatic error-handling facility and a
                 dynamic storage allocation scheme, both of which are
                 implemented portably. These, together with the modular
                 structure of the library, lead to simplified calling
                 sequences and ease of use.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "dynamic storage allocation; error handling; libraries;
                 numerical analysis; portability",
}

@Manual{FPS:1978:AAP,
  key =          "FPS",
  title =        "{AP-120B} Array Processor handbook",
  organization = "Floating Point Systems, Inc.",
  address =      "Portland, OR, USA",
  pages =        "????",
  year =         "1978",
  bibdate =      "Fri Nov 09 10:52:30 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Fraley:1978:ZIR,
  author =       "B. Fraley",
  title =        "Zeros and Infinities Revisited and Gradual Underflow",
  type =         "Technical report",
  institution =  "HP Laboratories",
  address =      "3500 Deer Creek Road, Palo Alto, CA 94304, USA",
  pages =        "????",
  day =          "28",
  month =        dec,
  year =         "1978",
  bibdate =      "Fri Nov 09 10:53:38 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Frankowski:1978:RME,
  author =       "Krzysztof S. Frankowski",
  title =        "A Realistic Model for Error Estimates in the
                 Evaluation of Elementary Functions",
  crossref =     "IEEE:1978:PSC",
  pages =        "70--74",
  year =         "1978",
  bibdate =      "Thu Sep 01 11:22:03 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Frankowski.pdf",
  abstract =     "Floating point error analysis, as described by J. H.
                 Wilkinson (1963) has two known drawbacks: it is too
                 pessimistic and too cumbersome for everyday use. This
                 paper describes a realistic model for error analysis,
                 gives examples of simple formulae frequently used in
                 the calculation of elementary functions, and analyses
                 the error generated in single precision computations
                 with these formulae, using the proposed model for error
                 analysis. The paper also presents error bounds for
                 various polynomial evaluations, as predicted by the
                 model. Model verification is done using double
                 precision arithmetic.",
  acknowledgement = ack-nj,
  keywords =     "ARITH-4",
}

@InProceedings{Gajski:1978:DAE,
  author =       "Daniel D. Gajski and L. P. Rubinfield",
  title =        "Design of Arithmetic Elements for {Burroughs
                 Scientific Processor}",
  crossref =     "IEEE:1978:PSC",
  pages =        "245--256",
  year =         "1978",
  bibdate =      "Fri Nov 09 10:54:59 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Gajski.pdf",
  abstract =     "The design criteria and implementation of the
                 Arithmetic Element (AE) of the Burroughs Scientific
                 Processor, a vector machine intended for scientific
                 computation requiring speed of up to 50 million
                 floating-point operations per second, is discussed. An
                 array of 16 AEs operate in lockstep mode, executing the
                 same instruction on 16 sets of data. The 16 AEs are one
                 stage in a pipeline which consists of 17 memory
                 modules, an input alignment network, and an output
                 alignment net-work. The AE itself is not pipelined. It
                 can perform over one hundred different operations
                 including a floating-point addition\slash subtraction
                 and multiplication, division, square root, among the
                 others. Eight registers are provided for the storage of
                 intermediate values and results. Modulo 3 residue
                 arithmetic is used for checking hardware failures.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}

@InProceedings{Garcia:1978:AES,
  author =       "Oscar N. Garcia and Harvey Glass and Stanley C.
                 Haines",
  title =        "An Approximate and Empirical Study of the Distribution
                 of Adder Inputs and Maximum Carry Length Propagation",
  crossref =     "IEEE:1978:PSC",
  pages =        "97--103",
  year =         "1978",
  bibdate =      "Wed Nov 14 17:49:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Garcia.pdf",
  abstract =     "This paper investigates, using sampled data, the
                 commonly used hypothesis that integer operands reaching
                 the adder of a computer are uniformly distributed.
                 Questions raised on the validity of that hypothesis are
                 reinforced and their impact on the calculation of the
                 average of the worst case length of carry propagation
                 is considered. An approximate formula is developed for
                 the worst case carry chain length when the arithmetic
                 operands are restricted in magnitude.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4; average worst case carry chain; binary
                 addition; carry propagation",
}

@Article{Garner:1978:TCA,
  author =       "H. L. Garner",
  title =        "Theory of Computer Addition and Overflows",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-27",
  number =       "4",
  pages =        "297--301",
  month =        apr,
  year =         "1978",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1978.1675101",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 08:13:28 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675101",
  abstract =     "Computer addition is a groupoid. If an additive
                 identity exists it is unique. If(and only if) addition
                 is defined with the compute through the overflow (CTO)
                 property, then a finite ring of integers is the
                 homomorphic image of the computer number system and
                 addition. Stated another way, the necessary and
                 sufficient condition for CTO is a congruence relation
                 on the integers. Also, if the number system has CTO
                 capabilities for addition, it also has extended CTO
                 properties for addition. A technique is presented for
                 determining the correct sum in the extended compute
                 through overflow (ECTO) mode of computation.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "additive identity; compute through overflow (CTO);
                 computer arithmetic; models of computer arithmetic;
                 number systems; overflow behavior",
}

@InCollection{Gautschi:1978:QNC,
  author =       "Walter Gautschi",
  booktitle =    "Recent advances in numerical analysis ({Proc. Sympos.,
                 Math. Res. Center, University of Wisconsin, Madison,
                 Wis., 1978})",
  title =        "Questions of numerical conditions related to
                 polynomials",
  volume =       "41",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "45--72",
  year =         "1978",
  MRclass =      "65D99",
  MRnumber =     "519056",
  MRreviewer =   "Gerhard Merz",
  bibdate =      "Fri Feb 9 15:26:45 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Publ. Math. Res. Center University of Wisconsin",
  acknowledgement = ack-nhfb,
}

@Article{Good:1978:CMA,
  author =       "I. J. Good",
  title =        "{C 24}. {A} method for avoiding overflows and
                 underflows",
  journal =      j-J-STAT-COMPUT-SIMUL,
  volume =       "8",
  number =       "2",
  pages =        "162--163",
  year =         "1978",
  CODEN =        "JSCSAJ",
  DOI =          "https://doi.org/10.1080/00949657808810261",
  ISSN =         "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
  ISSN-L =       "0094-9655",
  bibdate =      "Tue Apr 22 09:10:43 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Computation and Simulation",
  journal-URL =  "http://www.tandfonline.com/loi/gscs20",
}

@Article{Goodman:1978:ITD,
  author =       "R. Goodman and J. Bustoz and A. Feldstein",
  title =        "Improved Trailing Digits Estimates Applied to Optimal
                 Computer Arithmetic",
  journal =      j-SIAM-REVIEW,
  volume =       "20",
  number =       "3",
  pages =        "625--625",
  month =        "????",
  year =         "1978",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri Jun 21 11:25:02 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
}

@Book{Hamacher:1978:CO,
  author =       "V. Carl Hamacher and Zvonko G. Vranesic and Safwat G.
                 Zaky",
  title =        "Computer Organization",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "xiv + 465",
  year =         "1978",
  ISBN =         "0-07-025681-0",
  ISBN-13 =      "978-0-07-025681-1",
  LCCN =         "QA76.9.A73 H35",
  bibdate =      "Sat May 18 14:24:11 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "McGraw-Hill series in computer organization and
                 architecture",
  acknowledgement = ack-nhfb,
  tableofcontents = "Preface \\
                 Basic Structure of Computer Hardware and Software / 1
                 \\
                 Addressing Methods and Machine Program Sequencing / 21
                 \\
                 The Processing Unit / 111 \\
                 Input-Output Organization / 152 \\
                 The Memory / 207 \\
                 Arithmetic / 257 \\
                 Pipelining / 302 \\
                 Examples of CISC, RISC, and Stack Processors / 339 \\
                 Computer Peripherals / 370 \\
                 Large Computer Systems / 398 \\
                 Appendix A: Logic Circuits / 441 \\
                 Appendix B: PowerPC Instruction Set / 509 \\
                 Appendix C: Character Set for Motorola 68000
                 Microprocessor / 523 \\
                 Appendix D: Character Codes and Number Conversion / 541
                 \\
                 Index / 547",
}

@InProceedings{Horspool:1978:EAU,
  author =       "R. Nigel Horspool and Eric C. R. Hehner",
  title =        "Exact Arithmetic Using a Variable-Length $p$-adic
                 Representation",
  crossref =     "IEEE:1978:PSC",
  pages =        "10--14",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Horspool.pdf",
  abstract =     "The $p$-adic number system is introduced and developed
                 into a form suitable for performing exact arithmetic in
                 computers. The proposed representation has several
                 desirable attributes: the four standard arithmetic
                 operations have a simple consistent form, the
                 programmer has the ability to choose the precise degree
                 of accuracy in his calculations and the variable-length
                 nature of the representation achieves compact
                 encodings",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}

@InProceedings{Hull:1978:DFP,
  author =       "T. E. Hull",
  title =        "Desirable Floating-Point Arithmetic and Elementary
                 Functions for Numerical Computation",
  crossref =     "IEEE:1978:PSC",
  pages =        "63--69",
  year =         "1978",
  DOI =          "https://doi.org/10.1109/arith.1978.6155780",
  bibdate =      "Thu Sep 01 12:14:34 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Hull.pdf",
  abstract =     "The purpose of this paper is to summarize proposed
                 specifications for floating-point arithmetic and
                 elementary functions. The topics considered are: the
                 base of the number system, precision control, number
                 representation, arithmetic operations, other basic
                 operations, elementary functions, and exception
                 handling. The possibility of doing without fixed-point
                 arithmetic is also discussed.\par

                 The specifications are intended to be entirely at the
                 level of a programming language such as Fortran. The
                 emphasis is on convenience and simplicity from the
                 user's point of view. The specifications are not
                 complete in every detail, but it is intended that they
                 be complete ``in spirit'' --- some further details,
                 especially syntactic details, would have to be
                 provided, but the proposals are otherwise relatively
                 complete.",
  acknowledgement = ack-nj,
  keywords =     "ARITH-4; decimal floating-point arithmetic",
  remark =       "Refined and implemented later by
                 \cite{Cohen:1983:CCP}. The paper begins with the
                 quote

                 ``\ldots{} the expression $ 25 + 1 / 3 $ yields the
                 value $ 5.333333 $ in PL/I, and $ .333334 $ in PL/C
                 \ldots{}'', Conway and Gries, An Introduction to
                 Programming, 1975, p. 24.",
}

@InProceedings{Hwang:1978:IRR,
  author =       "Kai Hwang and T. P. Chang",
  title =        "An Interleaved Rational\slash Radix Arithmetic System
                 for High-Precision Computations",
  crossref =     "IEEE:1978:PSC",
  pages =        "15--24",
  year =         "1978",
  bibdate =      "Wed Nov 14 17:49:59 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Hwang.pdf",
  abstract =     "A new interleaved rational\slash radix number system
                 is proposed for upgrading the precision of normalized
                 Floating-Point (FLP) arithmetic operations without
                 increasing the basic word length. A complete set of
                 rational rounding and arithmetic algorithms are
                 developed. The Average Relative Representation Error
                 (ARRE) of the proposed flexible FLP system is computed
                 through a series of simulation studies on CDC 6500. Our
                 results show a 10\% improvement of representation
                 accuracy when compared with the ARRE of conventional
                 FLP system. The architecture of a rational FLP
                 arithmetic processor is also presented. Tradeoffs
                 between operating speed and computing accuracy are
                 discussed.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4; Farey rational numbers",
}

@Manual{Intel:1978:FAL,
  author =       "{Intel Corporation}",
  title =        "8080\slash 8085 floating-point arithmetic library:
                 user's manual",
  organization = "Intel Corporation",
  address =      "Santa Clara, CA, USA",
  pages =        "various",
  year =         "1978",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Intel 8080 (Microprocessor) --- Programming.; Intel
                 8085 (Microprocessor) --- Programming.",
  remark =       "``Manual order number: 9800452B.''",
}

@InProceedings{Jullien:1978:ARN,
  author =       "G. A. Jullien and W. C. Miller",
  title =        "Application of the Residue Number System to Computer
                 Processing of Digital Signals",
  crossref =     "IEEE:1978:PSC",
  pages =        "220--225",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Jullien.pdf",
  abstract =     "The residue number system offers parallel processing,
                 digital hardware implementations for the binary
                 operations of addition, subtraction and multiplication.
                 This paper discusses the use of the residue number
                 system in implementing digital signal processing
                 functions, in which these binary operations abound. The
                 paper covers implementations using arrays of read only
                 memories, and briefly discusses the use of parallel
                 microprocessor structures. ROM array implementations of
                 scaling operations are also presented.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4; residue number system",
}

@Article{Jullien:1978:RNS,
  author =       "G. A. Jullien",
  title =        "Residue Number Scaling and Other Operations Using
                 {ROM} Arrays",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-27",
  number =       "4",
  pages =        "325--336",
  month =        apr,
  year =         "1978",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1978.1675105",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 08:13:28 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35168;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675105",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Over the last two decades there has been considerable
                 interest in the implementation of digital computer
                 elements using hardware based on the residue number
                 system. This paper considers implementing such systems
                 with arrays of look-up tables placed \ldots{}",
}

@Article{Kahan:1978:KSI,
  author =       "W. Kahan and B. N. Parlett",
  title =        "{K{\"o}nnen Sie sich auf Ihren Rechner verlassen?}
                 ({German}) [Can you count on your calculator?]",
  journal =      "{Jahrbuch {\"U}berblicke Mathematik}",
  volume =       "??",
  pages =        "199--216",
  year =         "1978",
  bibdate =      "Fri Nov 11 06:36:51 MST 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0397.65081",
  acknowledgement = ack-nhfb,
  classmath =    "*65Y99 Computer aspects of numerical algorithms 65D20
                 Computation of special functions 00A99 Miscellaneous
                 topics in general mathematics",
  keywords =     "Automated Algorithms; Error of Computation; Pocket
                 Calculator",
  language =     "German",
}

@InProceedings{Koren:1978:UAC,
  author =       "Israel Koren and Yoram Maliniak",
  title =        "A Unified Approach to a Class of Number Systems",
  crossref =     "IEEE:1978:PSC",
  pages =        "25--28",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Koren.pdf",
  abstract =     "A unified approach to a broad class of number systems
                 is proposed in this paper. This class contains all
                 positive and negative radix systems and other
                 well-known number systems. The proposed approach
                 enables us to develop a single set of algorithms for
                 arithmetic operations and conversion methods between
                 number systems.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}

@InProceedings{Kornerup:1978:FAF,
  author =       "Peter Kornerup and David W. Matula",
  title =        "A Feasibility Analysis of Fixed-Slash and
                 Floating-Slash Arithmetic",
  crossref =     "IEEE:1978:PSC",
  pages =        "{39--47}",
  year =         "1978",
  bibdate =      "Wed Nov 14 17:50:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Kornerup.pdf",
  abstract =     "An investigation of the feasibility of a finite
                 precision approximate rational arithmetic based on
                 fixed-slash representation of rational numbers is
                 presented. Worst-case and average-case complexity
                 analyses of the involved rounding algorithm (an
                 extended shift-subtract gcd algorithm) are presented.
                 The results are applied to a proposed hardware
                 realization of a fixed-slash arithmetic unit.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}

@InProceedings{Krishnamurthy:1978:MPP,
  author =       "E. V. Krishnamurthy and H. Venkateswaran",
  title =        "Multivariable Polynomial Processing --- Applications
                 to Interpolation",
  crossref =     "IEEE:1978:PSC",
  pages =        "81--87",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Krishnamurthy.pdf",
  abstract =     "A data-structure suitable for multivariable polynomial
                 processing in introduced. Using this data structure,
                 arithmetic algorithms are described for addition,
                 subtraction and multiplication of multivariable
                 polynomials; also algorithms are described for forming
                 the inner product and tensor product of vectors, Those
                 components are multivariable polynomials. Application
                 of these algorithms for multivariable cardinal spline
                 approximation is described in detail.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}

@Book{Kuck:1978:SCC,
  author =       "David J. Kuck",
  title =        "The structure of computers and computations",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xxii + 611",
  year =         "1978",
  ISBN =         "0-471-02716-2 (vol. 1), 0-471-08138-8",
  ISBN-13 =      "978-0-471-02716-4 (vol. 1), 978-0-471-08138-8",
  LCCN =         "QA76.9.A73 K83",
  bibdate =      "Mon May 20 05:05:46 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See Chapter 3 for floating-point arithmetic
                 discussion.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Liddiard:1978:RSF,
  author =       "L. A. Liddiard",
  title =        "Required Scientific Floating Point Arithmetic",
  crossref =     "IEEE:1978:PSC",
  pages =        "56--62",
  year =         "1978",
  bibdate =      "Thu Sep 01 11:06:57 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Liddiard.pdf",
  abstract =     "Previous papers in computer arithmetic have shown that
                 correct rounded floating point with good arithmetic
                 properties can be attained using guard digits and
                 careful algorithms on the floating point fractions.
                 This paper combines that body of knowledge with
                 proposed exponent forms that are closed with respect to
                 inversion and detection and recovery of exponent under-
                 and overflow. In addition radix 2 is shown to be the
                 only base radix meeting minimal variation of precision,
                 a condition necessary for the safe use of floating
                 point. An effort is made to establish objective
                 criteria in answer to the question ``What is the best
                 division of the computer word into exponent and
                 fraction parts?''. Combining the previous results
                 allows a required scientific floating point arithmetic
                 to be portrayed and compared with available arithmetic
                 on current computers.",
  acknowledgement = ack-nj,
  keywords =     "ARITH-4; arithmetic properties; correct rounding;
                 exponent over; Floating point exponents; floating-point
                 arithmetic; optimal base radix",
}

@InProceedings{Lillevik:1978:CDA,
  author =       "Sigurd L. Lillevik and P. David Fisher",
  title =        "Computational Design Alternatives with
                 Microprocessor-Based Systems",
  crossref =     "IEEE:1978:PSC",
  pages =        "267--272",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Lillevik.pdf",
  abstract =     "This paper examines and characterizes four elemental
                 hardware computational design alternatives (CDA's) and
                 presents a structured approach to computational section
                 design which incorporates a rigorous, theoretic
                 foundation. The DIRECT CDA incorporates a single
                 microprocessor ($ \mu $P) and memory. The AU CDA
                 contains a $ \mu $P, memory, and arithmetic unit. $ \mu
                 $P, memory, and calculator chip comprise the CALC CDA.
                 Finally, several $ \mu $P's and memories in a
                 Master\slash Slave arrangement implement the multiple-$
                 \mu $P m$ \mu $P CDA. A common set of attributes ---
                 precision, speed and cost --- facilitates comparison.
                 Using these attributes, Multiattribute Utility Theory
                 assesses a numeric quantity, the utility, to represent
                 each CDA's relative usefulness. Thus, design involves
                 selecting the CDA with the greatest utility.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}

@InProceedings{Lim:1978:HSM,
  author =       "Raymond S. Lim",
  title =        "High-Speed Multiplication and Multiple Summand
                 Addition",
  crossref =     "IEEE:1978:PSC",
  pages =        "149--153",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Lim.pdf",
  abstract =     "The problem of high-speed multiplication is considered
                 from the viewpoint of summand generation and summand
                 summation. The goal is to obtain at least a
                 2's-complement, 32-bit floating-point (sign plus 24-bit
                 fraction) multiplication in 10 to 20 ns using ECL LSI
                 packages. Summand generation is implemented by $ m
                 \times m $-bit multipliers. The optimum values for $m$
                 are 9, 13, 17, or 21. Summand summation is implemented
                 by a row of $ (p, 2) $ column-summing counters. The $
                 (0, 2) $, $ (5, 2) $, and $ (7, 2) $ counters are
                 optimum choices. These counters compress $p$ inputs
                 into two outputs plus nonpropagating carry bits, where
                 these bits are added to the next higher-order stage
                 with at most two full adder delays.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}

@Article{Liu:1978:ECC,
  author =       "Chao-Kai Liu and Tse Lin Wang",
  title =        "Error-Correcting Codes in Binary-Coded-Decimal
                 Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-27",
  number =       "11",
  pages =        "977--984",
  month =        nov,
  year =         "1978",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1978.1674987",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Aug 07 17:26:15 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  abstract =     "Error-correcting coding schemes devised for binary
                 arithmetic are not in general applicable to BCD
                 arithmetic. In this paper, we investigate the new
                 problem of using such coding schemes in BCD systems. We
                 first discuss the general characteristics of arithmetic
                 errors and define the arithmetic weight and distance in
                 BCD systems. We show that the distance is a metric
                 function. Number theory is used to construct a class of
                 single-error-correcting codes for BCD arithmetic. It is
                 shown that the generator of these codes possesses a
                 very simple form and the structure of these codes can
                 be analytically determined.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "BCD arithmetic; decimal arithmetic",
}

@Article{Logan:1978:FDP,
  author =       "Jonothan L. Logan and Samuel A. Goudsmit",
  title =        "The First Digit Phenomenon",
  journal =      j-PROC-AMER-PHIL-SOC,
  volume =       "122",
  number =       "4",
  pages =        "193--197",
  day =          "18",
  month =        aug,
  year =         "1978",
  CODEN =        "PAPCAA",
  ISSN =         "0003-049X (print), 2326-9243 (electronic)",
  ISSN-L =       "0003-049X",
  bibdate =      "Fri Mar 30 11:20:35 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "This paper contains derivations of both Stigler's Law
                 and Benford's Law, and receives strong criticism in
                 \cite{Raimi:1985:FDP}. This paper contains an important
                 historical note that is recorded in entry
                 \cite{Benford:1938:LAN}.",
  URL =          "http://links.jstor.org/sici?sici=0003-049X(19780818)122%3A4%3C193%3ATFDP%3E2.0.CO%3B2-C;
                 http://www.jstor.org/stable/986530",
  abstract =     "Forty years ago an article appeared in these
                 Proceedings, which has since then attracted much
                 attention of mathematicians and some physicists. It was
                 written by Frank Benford, a physicist from the General
                 Electric Company at Schenectady. He had examined a
                 large number of numerical tables, the kind that are
                 printed in almanacs, and in scientific and technical
                 handbooks. He noticed a most unusual and unexpected
                 property of many of these tables. Consider, for
                 example, the numbers representing the populations of
                 states or all the countries in the world, or their
                 areas, their budgets, their numbers of hospital beds,
                 etc. One would expect that on the average just as many
                 of these entries would begin with the digit $1$ as with
                 $2$ or $3$ or $4$, and so on. But Benford noticed that
                 small values of the first digits occur far more
                 often.",
  acknowledgement = ack-nhfb,
  author-dates = "Samuel A. Goudsmit (July 11, 1902--December 4, 1978)",
  fjournal =     "Proceedings of the {American Philosophical Society}
                 held at {Philadelphia} for promoting useful knowledge",
  journal-URL =  "http://www.jstor.org/journal/procamerphilsoci",
  remark =       "In 1925, Samuel Goudsmit and George Uhlenbeck proposed
                 the concept of electron spin, a critical step forward
                 in the quantum mechanics of many-electron systems.
                 Surprisingly, that work did not get them the Nobel
                 Prize, but it did spur Wolfgang Pauli to present his
                 Exclusion Principle in 1925, for which he received the
                 1945 Nobel Prize in Physics. After World War II,
                 Goudsmit was the scientific head of the Alsos mission
                 to capture German nuclear scientists. In the 1950s, he
                 founded the journal Physical Review Letters. During the
                 1960s and 1970s, he was Editor-in-Chief of the main
                 American physics journal, the Physical Review.",
}

@InProceedings{Matula:1978:BDS,
  author =       "David W. Matula",
  title =        "Basic Digit Sets for Radix Representation of the
                 Integers",
  crossref =     "IEEE:1978:PSC",
  pages =        "1--9",
  year =         "1978",
  bibdate =      "Wed Nov 14 17:51:32 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Matula.pdf",
  abstract =     "Let $Z$ denote the set of integers. A digit set $ D
                 \in Z $ is basic for base $ \beta \in Z $ if the set of
                 polynomials $ \{ d_m \beta^m + d_{m - 1} \beta^{m - 1}
                 + \ldots {} + d_1 \beta + d_0 | d_i \in D \} $ contains
                 a unique representation for every $ n \in Z $. We give
                 necessary and sufficient conditions for D to be basic
                 for $ \beta $. We exhibit efficient procedures for
                 verifying that $D$ is basic for $S$, and for computing
                 the representation of any $ n \in Z $ when a
                 representation exists. There exist $D$, $S$ with $D$
                 basic for $S$ where $ \max \{ |d| \vert d \in D \} > |
                 \beta | $, and more generally, an infinite class of
                 basic digit sets is shown to exist for every base $S$
                 with $ \beta \geq 3 $. The natural extension to
                 infinite precision radix representation using basic
                 digit sets is considered and a summary of results is
                 presented.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4; base; digit representation; finite and
                 infinite precision; non-standard number",
}

@InProceedings{Matula:1978:FAF,
  author =       "David W. Matula and Peter Kornerup",
  title =        "A Feasibility Analysis of Fixed-Slash and
                 Floating-Slash Number Systems",
  crossref =     "IEEE:1978:PSC",
  pages =        "{29--38}",
  year =         "1978",
  bibdate =      "Wed Nov 14 17:52:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Matula_Kornerup.pdf",
  abstract =     "Design and analysis of finite precision rational
                 number systems based on fixed-slash and floating-slash
                 representation is pursued. Natural formats for binary
                 fixed-slash and binary floating-slash number
                 representation in computer words are described.
                 Compatibility with standard integer representation is
                 obtained. Redundancy in the representation is shown to
                 be minimal. Arithmetic register requirements are
                 considered. Worst case and average case rounding errors
                 are determined, and the concept of adaptive variable
                 precision in the rounding is developed.",
  acknowledgement = ack-nhfb,
  keywords =     "adaptive variable precision; adjacent fractions;
                 ARITH-4; binary numeric word format; Farey fractions;
                 finite precision; fixed-slash numbers; floating-slash
                 numbers; integer compatibility; mediant roundings;
                 range of number system; rational arithmetic;
                 redundancy; worst case and average case rounding
                 error",
}

@Article{McCrea:1978:CFP,
  author =       "P. G. McCrea and P. C. Maxwell and P. W. Baker",
  title =        "Comments on {``A Floating-Point Multiplexed DDA
                 System''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-27",
  number =       "12",
  pages =        "1226--1226",
  month =        dec,
  year =         "1978",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1978.1675033",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 08:13:33 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See \cite{Hannington:1976:FPM}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675033",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Mitra:1978:ITD,
  author =       "S. K. Mitra and G. K. Sorknes",
  title =        "On the Implementation of a Two-Dimensional {FIR}
                 Filter Using a Single Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-27",
  number =       "8",
  pages =        "762--764",
  month =        aug,
  year =         "1978",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1978.1675186",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 08:13:30 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675186",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@TechReport{Morris:1978:DID,
  author =       "Robert Morris and Lorinda Cherry",
  title =        "{DC} --- An Interactive Desk Calculator",
  type =         "Technical Memorandum",
  number =       "1056",
  institution =  inst-ATT-BELL,
  address =      inst-ATT-BELL:adr,
  pages =        "8",
  day =          "15",
  month =        nov,
  year =         "1978",
  bibdate =      "Tue Jun 06 08:07:45 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  abstract =     "DC is an arbitrary precision arithmetic package
                 implemented on the UNIX time-sharing system in the form
                 of an interactive desk calculator. It works like a
                 stacking calculator using reverse Polish notation.
                 Ordinarily DC operates on decimal integers, but one may
                 specify an input base, output base, and a number of
                 fractional digits to be maintained.",
  abstract-2 =   "DC is an interactive desk calculator program
                 implemented on the UNIX Time-Sharing System \ldots{}
                 arbitrary-precision integer arithmetic.",
  acknowledgement = ack-nhfb,
  author-dates = "Lorinda L. Cherry (18 November 1944--February 2022);
                 Robert Morris (25 July 1932--26 June 2011)",
  remark =       "Available in PDF file of \cite[pp.
                 399--406]{Dolotta:1977:DPU}.",
}

@Article{Murphy:1978:SRP,
  author =       "T. R. Murphy and P. L. Rickard",
  title =        "Square-Root Procedure for Floating-Point Numbers",
  journal =      j-IBM-TDB,
  volume =       "21",
  number =       "2",
  pages =        "785",
  month =        jul,
  year =         "1978",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:15:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
}

@Article{Nussabaumer:1978:FMN,
  author =       "H. J. Nussabaumer",
  title =        "Fast Multipliers for Number Theoretic Transforms",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-27",
  number =       "8",
  pages =        "764--765",
  month =        aug,
  year =         "1978",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1978.1675187",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 08:13:30 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675187",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{OLeary:1978:DHS,
  author =       "G. P. O'Leary",
  title =        "The design of a high-speed arithmetic processor",
  crossref =     "COMPSAC:1978:CPC",
  pages =        "175--176",
  year =         "1978",
  bibdate =      "Wed Sep 07 22:19:45 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Olver:1978:NAE,
  author =       "F. W. J. Olver",
  title =        "New Approach to Error Arithmetic",
  journal =      j-SIAM-REVIEW,
  volume =       "20",
  number =       "3",
  pages =        "632--632",
  month =        "????",
  year =         "1978",
  CODEN =        "SIREAD",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri Jun 21 11:25:02 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
}

@Article{Patel:1978:ASB,
  author =       "M. R. Patel and K. H. Bennett",
  title =        "Analysis of Speed of a Binary Divider Using a Variable
                 Number of Shifts Per Cycle",
  journal =      j-COMP-J,
  volume =       "21",
  number =       "3",
  pages =        "246--252",
  month =        aug,
  year =         "1978",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/21.3.246",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:48:03 MST 2012",
  bibsource =    "Compendex database;
                 http://comjnl.oxfordjournals.org/content/21/3.toc;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/;
                 https://www.math.utah.edu/pub/tex/bib/compj1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/21/3/246.full.pdf+html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/246.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/247.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/248.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/249.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/250.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/251.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/252.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  classification = "721",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "analysis; computers, digital; cycle; digital
                 arithmetic; discrete time; discrete time systems;
                 finite state system model; ICL 2980; optimisation;
                 optimum hardware configuration; Patel and Bennett
                 (1976); speed of a binary divider; variable number of
                 shifts per",
  treatment =    "T Theoretical or Mathematical",
}

@TechReport{Payne:1978:DPF,
  author =       "M. Payne and W. Strecker",
  title =        "Draft Proposal for Floating Point Standard",
  type =         "Technical report",
  institution =  "Digital Equipment Corporation",
  address =      "Maynard, MA, USA",
  day =          "11",
  month =        dec,
  year =         "1978",
  bibdate =      "Fri Nov 09 19:11:42 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Preston:1978:NAT,
  author =       "F. S. Preston",
  title =        "A New Algorithm for the Tangent",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-27",
  number =       "2",
  pages =        "167",
  month =        feb,
  year =         "1978",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1978.1675052",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:16:10 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Book{Ralston:1978:FCN,
  author =       "Anthony Ralston and Philip Rabinowitz",
  title =        "A first course in numerical analysis",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  edition =      "Second",
  pages =        "xix + 556",
  year =         "1978",
  ISBN =         "0-07-051158-6",
  ISBN-13 =      "978-0-07-051158-3",
  LCCN =         "QA297 .R3 1978",
  bibdate =      "Fri Aug 20 10:13:32 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "US\$19.50",
  series =       "International series in pure and applied mathematics",
  acknowledgement = ack-nhfb,
  remark =       "See also first edition \cite{Ralston:1965:FCN}.
                 Reprinted in \cite{Ralston:2001:FCN}.",
  subject =      "Numerical analysis",
}

@Article{Rashed:1978:LRI,
  author =       "Roshd{\=\i} R{\=a}shed",
  title =        "{L}'Extraction de la Racine $ n^{\rm \scriptstyle
                 i{\grave e}me} $ et {l'Invention} des Fractions
                 D{\'e}cimales ({XI}$^e$--{XII}$^e$ Si{\`e}cles).
                 ({French}) [{The} extraction of the n$^{{\rm th}}$ root
                 and the invention of decimal fractions (11$^{{\rm
                 th}}$--12$^{{\rm th}}$ centuries)]",
  journal =      j-ARCH-HIST-EXACT-SCI,
  volume =       "18",
  number =       "3",
  pages =        "191--243",
  month =        sep,
  year =         "1978",
  CODEN =        "AHESAN",
  ISSN =         "0003-9519 (print), 1432-0657 (electronic)",
  ISSN-L =       "0003-9519",
  MRclass =      "01A35",
  MRnumber =     "0484970 (58 \#4829)",
  MRreviewer =   "H. L. L. Busard",
  bibdate =      "Fri Feb 4 21:50:14 MST 2011",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=18&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=18&issue=3&spage=191",
  acknowledgement = ack-nhfb,
  fjournal =     "Archive for History of Exact Sciences",
  journal-URL =  "http://link.springer.com/journal/407",
  language =     "French",
  MRtitle =      "{L}'extraction de la racine {$n$}i{\`e}me et
                 l'invention des fractions d{\'e}cimales ({XIe--XIIe}
                 si{\`e}cles)",
  MRyear =       "1977/78",
}

@InProceedings{Reuter:1978:SEU,
  author =       "Eric K. Reuter and John P. Jeter and J. Wayne Anderson
                 and Bruce D. Shriver",
  title =        "Some Experiments Using Interval Arithmetic",
  crossref =     "IEEE:1978:PSC",
  pages =        "75--80",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Reuter.pdf",
  abstract =     "This paper reviews past experiences and discusses
                 future work in the area of interval arithmetic at the
                 University of Southwestern Louisiana (USL). Two
                 versions of interval arithmetic were developed and
                 implemented at USL. An interval data type declaration
                 and the necessary mathematical functions for this data
                 type were added to Fortran via the preprocessor Augment
                 (4,5). In the first version the endpoints of the
                 intervals were represented as single precision floating
                 point numbers. In the other version, the endpoints were
                 represented to 56 decimal digits. Production
                 engineering programs were run as benchmarks (8). The
                 accumulation of computational and algorithmic error
                 could be observed as a widening of the intervals. The
                 benchmarks were also run in normal single and double
                 precision arithmetic. In some instances, the result
                 obtained from a single or double precision calculation
                 was not bounded by the corresponding interval result
                 indicating some problem with the algorithm. The
                 widening of an interval does not necessarily indicate a
                 data sensitivity nor error in an algorithm. However,
                 these large intervals can be used as indicator of no
                 problems. As could be expected, the 56-decimal digit
                 precision interval gave better results in terms of
                 smaller intervals due to the increased amount of
                 precision. The obvious problem with this version is
                 that the amount of overhead required for its execution
                 is high.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}

@Manual{Richardson:1978:ATB,
  author =       "Caryl Richardson and Jef Raskin",
  title =        "The {Apple} tutorial: based on the {Apple} {II} Basic
                 programming manual",
  organization = "Bell and Howell, Audio-Visual Products Division",
  address =      "Chicago, IL, USA",
  pages =        "vii + 157",
  year =         "1978",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Apple II (Computer) --- Programming.; BASIC (Computer
                 program language)",
  remark =       "Cover title: Floating point Basic tutorial manual.
                 ``Reprinted with the permission of Apple Computer
                 Inc.'' Companion volume: Bell and Howell floating point
                 Basic programming reference manual.",
}

@Article{Ruckdeschel:1978:FA,
  author =       "F. Ruckdeschel",
  title =        "Functional Approximations",
  journal =      j-BYTE,
  volume =       "3",
  number =       "11",
  pages =        "34--46",
  month =        nov,
  year =         "1978",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Thu Sep 1 10:15:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "BYTE Magazine",
}

@Article{Russell:1978:CCS,
  author =       "Richard M. Russell",
  title =        "The {Cray-1} Computer System",
  journal =      j-CACM,
  volume =       "21",
  number =       "1",
  pages =        "63--72",
  month =        jan,
  year =         "1978",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Dec 08 13:08:43 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "grecommended91, existing classic architecture, maeder
                 biblio: parallel hardware and devices, implementation,
                 ginsberg biblio: bhibbard enm, j\-lb",
  remark =       "The original paper describing the Cray-1. This paper
                 is reproduced in Kuhn and Padua's (1981, IEEE) survey
                 ``Tutorial on Parallel Processing.'' Also reproduced in
                 ``Computer Structures: Principles and Examples'' by
                 Daniel P. Siewiorek, C. Gordon Bell, and Allen Newell,
                 McGraw-Hill, 1982, pp. 743-752. Reproduced in Dharma P.
                 Agrawal's (ed.) ``Advanced Computer Architecture,''
                 IEEE, 1986, pp. 15--24. Literature search yields:
                 00712248 E. I. Monthly No: EI7804023850 E. I. Yearly
                 No: EI78014612 Title: Cray-1 Computer System. Author:
                 Russell, Richard M. Corporate Source: Cray Res Inc,
                 Minneapolis, Minn Source: Communications of the ACM v
                 21 n 1 Jan 1978 p 63--72 Publication Year: 1978 CODEN:
                 CACMA2 ISSN: 0001-0782 Language: ENGLISH Journal
                 Announcement: 7804 Abstract: The CRAY-1 is described,
                 the evolution of its architecture is discussed, and an
                 account is given of some of the problems that were
                 overcome during its manufacture. The CRAY-1 is the only
                 computer to have been built to date that satisfies
                 ERDA's Class VI requirement (a computer capable of
                 processing from 20 to 60 million floating point
                 operations per second). The CRAY-1's Fortran compiler
                 (CFT) is designed to give the scientific user immediate
                 access to the benefits of the CRAY-1's vector
                 processing architecture. An optimizing compiler, CFT,
                 ``vectorizes'' innermost DO loops. Compatible with the
                 ANSI 1966 Fortran Standard and with many commonly
                 supported Fortran extensions, CFT does not require any
                 source program modifications or the use of additional
                 nonstandard Fortran statements to achieve
                 vectorization. 6 refs. Descriptors: *COMPUTER
                 ARCHITECTURE; COMPUTER SYSTEMS, DIGITAL Classification
                 Codes: 722 (Computer Hardware); 723 (Computer Software)
                 72 (COMPUTERS \& DATA PROCESSING)",
}

@Book{Schmid:1978:EDS,
  author =       "Hermann Schmid",
  title =        "{Elektronische Dezimalrechner, Schaltungen und
                 Verfahren} \toenglish {Electronic Decimal Computers,
                 Wiring and Methods} \endtoenglish",
  publisher =    pub-OLDENBOURG,
  address =      pub-OLDENBOURG:adr,
  pages =        "275",
  year =         "1978",
  ISBN =         "3-486-20211-1",
  ISBN-13 =      "978-3-486-20211-3",
  LCCN =         "????",
  bibdate =      "Fri Sep 16 16:30:39 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  keywords =     "decimal floating-point arithmetic",
}

@InProceedings{Schreiber:1978:TMF,
  author =       "F. A. Schreiber and R. Stefanelli",
  title =        "Two Methods for Fast Binary-{BCD} Conversion",
  crossref =     "IEEE:1978:PSC",
  pages =        "200--207",
  year =         "1978",
  bibdate =      "Sat Nov 12 21:58:26 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Schreiber.pdf",
  abstract =     "Two methods for performing binary--BCD conversion of
                 positive integers are discussed. The principle which
                 underlies both methods in the repeated division by five
                 and then by two, obtained the first by means of
                 subtractions performed from left to right, the second
                 by shifting bits before next subtraction.\par

                 It is shown that these methods work in a time which is
                 linear with the length in bit of the number to be
                 converted.\par

                 A ROM solution is proposed and its complexity is
                 compared with that of other methods.",
  acknowledgement = ack-nj,
  keywords =     "ARITH-4",
}

@Book{Seck:1978:WSA,
  editor =       "Friedrich Seck",
  title =        "{Wilhelm Schickard, 1592--1635: Astronom, Geograph,
                 Orientalist, Erfinder der Rechenmaschine}. ({German})
                 [{Wilhelm Schickard}, 1592--1635: Astronomer,
                 Geographer, Orientalist, Inventor of the calculator]",
  volume =       "25",
  publisher =    "Mohr",
  address =      "T{\"u}bingen, West Germany",
  pages =        "422",
  year =         "1978",
  ISBN =         "3-16-939772-9",
  ISBN-13 =      "978-3-16-939772-3",
  LCCN =         "QB36.S312 W54",
  bibdate =      "Sat Jul 27 11:00:08 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/scicontext.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Contubernium",
  acknowledgement = ack-nhfb,
  language =     "German",
  remark =       "Includes texts in Latin.",
  subject =      "Schickard, Wilhelm; Astronomers; Germany; Biography;
                 Middle East specialists",
  subject-dates = "1592--1635",
}

@Article{Shen:1978:CSA,
  author =       "D. T. Shen and A. Weinberger",
  title =        "4-2 carry-save adder implementation using send
                 circuits",
  journal =      j-IBM-TDB,
  volume =       "20",
  number =       "9",
  pages =        "??--??",
  month =        feb,
  year =         "1978",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Mon Dec 24 10:18:16 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Technical Disclosure Bulletin",
}

@InProceedings{Slekys:1978:MBI,
  author =       "Arunas G. Slekys and Algirdas Avi{\v{z}}ienis",
  title =        "A Modified Bi-Imaginary Number Systems",
  crossref =     "IEEE:1978:PSC",
  pages =        "48--55",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Slekys.pdf",
  abstract =     "In this paper the properties of $p$-imaginary number
                 systems are reviewed and a modified bi-imaginary number
                 system is introduced as a special case with $ p = 2 $.
                 Major properties, including conversion of integer and
                 floating point operands represented in a radix $ + p $
                 system, range, sign and zero tests, and shifting are
                 discussed. The ability to represent the operands as
                 vectors of radix-2 digits suggests advantages in
                 implementing machine-usable arithmetic algorithms.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}

@Article{Sripad:1978:QEF,
  author =       "A. Sripad and D. Snyder",
  title =        "Quantization errors in floating-point arithmetic",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "26",
  number =       "5",
  pages =        "456--463",
  month =        oct,
  year =         "1978",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  summary =      "In this paper, the quantization of the mantissa in a
                 normalized floating-point number is investigated. A
                 necessary and sufficient condition is given for the
                 mantissa to have a reciprocal probability density. A
                 model to represent a floating-point quantity \ldots{}",
}

@Unpublished{Stone:1978:DMF,
  author =       "Harold Stone and William Kahan and Jerome Coonen",
  title =        "Draft of Material on a Floating-Point Standard",
  pages =        "58",
  day =          "24",
  month =        apr,
  year =         "1978",
  bibdate =      "Sat Aug 23 06:51:19 2025",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "First draft of what came to be known as the KCS
                 proposal to the IEEE 754 subcommittee, with details
                 connected to the early 8087 design.",
  URL =          "https://ieeemilestones.ethw.org/w/images/9/96/Wk_hs_jc_draft_of_material_on_a_floating_point_standard_apr78.pdf",
  abstract =     "This paper is a recommendation for a standard
                 floating-point system that can be implemented on a
                 variety of computers. The proposed standard is defined
                 to include a standard storage representation and a
                 functional description of how the floating-point unit
                 carries out computations, what numbers are produced,
                 and which exception conditions are flagged by the
                 unit.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Svoboda:1978:ACF,
  author =       "Antonin Svoboda",
  title =        "Arithmetic Circuit Fault Detection by Modular
                 Encoding",
  crossref =     "IEEE:1978:PSC",
  pages =        "208--219",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Svoboda.pdf",
  abstract =     "Design principles of self checking digital circuits
                 are in the focus of the general interest and many
                 papers exist treating that subject. The use of special
                 data encoding techniques, suitable algorithms of
                 arithmetic, special hardware elements have been
                 proposed long ago. The purpose of this paper is to show
                 that the design can produce rather simple self checking
                 circuit when the design principles are chosen which
                 collaborate harmoniously:\par

                 (1) decimal numerical system is used\par

                 (2) decimal digit $ d \in \{ 0, 1, \ldots {}, 9 \} $ is
                 represented in the Diamond Code by the 5-bit binary
                 number $ f = 3 d + 2 $ \par

                 (3) decimal digit' addition algorithm introduced here
                 is simple and effective so that 10 decimal digits can
                 be added in parallel\par

                 (4) implementation of the addition algorithm by
                 conventional Full Adders results in a single fault
                 detecting circuit.\par

                 The design of a decimal adder for 10 decimal numbers,
                 each with 10 digits. is described here as an
                 illustration. It shows the way how to design other
                 decimal arithmetic circuits which are single fault
                 detecting, for instance a multiplier (derived from the
                 adder for 10 decimal numbers).",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4; decimal arithmetic",
}

@InProceedings{Swartzlander:1978:MAS,
  author =       "E. E. {Swartzlander, Jr.}",
  title =        "Merged Arithmetic for Signal Processing",
  crossref =     "IEEE:1978:PSC",
  pages =        "239--244",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Swartzlander.pdf",
  abstract =     "The concept of merged arithmetic is introduced and
                 applied to signal processing. The basic idea involves
                 synthesizing a composite arithmetic function (e.g., a
                 complex multiply) directly instead of decomposing it
                 into multiply and add operations as is conventional
                 practice. This approach results in a simpler design
                 which is also faster.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}

@InProceedings{Tan:1978:TIH,
  author =       "Kwang G. Tan",
  title =        "The theory and implementation of high-radix division",
  crossref =     "IEEE:1978:PSC",
  pages =        "154--163",
  year =         "1978",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Tan.pdf",
  abstract =     "This report derives the theory of high-radix division
                 in terms of the properties of the overlapped regions of
                 the P-D plot. The minimum precision requirements in
                 quotient selection are discussed. The methods of
                 implementations in hardware and in read-only memory are
                 explored.",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  keywords =     "ARITH-4",
}

@Article{Trivedi:1978:CUC,
  author =       "K. S. Trivedi",
  title =        "Corrections to {``On the Use of Continued Fractions
                 for Digital Computer Arithmetic''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-27",
  number =       "3",
  pages =        "288--288",
  month =        mar,
  year =         "1978",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1978.1675093",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 08:13:27 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See \cite{Trivedi:1977:UCF}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675093",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Trivedi:1978:HRL,
  author =       "Kishor S. Trivedi and Joseph G. Rusnak",
  title =        "Higher Radix On-Line Division",
  crossref =     "IEEE:1978:PSC",
  pages =        "164--174",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Trivedi.pdf",
  abstract =     "We present a formal proof of correctness of the
                 on-line division algorithm specified in an earlier
                 paper [1]. We also derive two radix 4 on-line division
                 algorithms, with non-redundant and redundant operands
                 respectively.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}

@InProceedings{Tseng:1978:EAF,
  author =       "B. Tseng and W. Miller and G. Jullien and J. Soltis
                 and A. Baraniecka",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing, {ICASSP '78}",
  title =        "An error analysis of a {FFT} implementation using the
                 residue number system",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "800--803",
  year =         "1978",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1049/el:19780088",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper considers an implementation of the FFT
                 based upon the residue number system. This system
                 offers the advantages of using integer based arithmetic
                 operations and a simple hardware realization involving
                 table look-up arrays. The proposed \ldots{}",
}

@Article{Wang:1978:EPF,
  author =       "J. Y. Wang",
  title =        "The Evaluation of Periodic Functions with Large Input
                 Arguments",
  journal =      j-SIGNUM,
  volume =       "13",
  number =       "4",
  pages =        "7--9",
  month =        dec,
  year =         "1978",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Thu Sep 1 10:15:56 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}

@Article{Waser:1978:HMM,
  author =       "Shlomo Waser",
  title =        "High-speed monolithic multipliers for real-time
                 digital signal processing",
  journal =      j-COMPUTER,
  volume =       "11",
  number =       "10",
  pages =        "19--29",
  month =        oct,
  year =         "1978",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Thu Dec 12 07:20:54 MST 1996",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "An analysis is made of arithmetic requirements for
                 signal processing and monolithic multipliers are
                 characterized. It is shown that real-time digital
                 signal processing requires very fast multiplication,
                 which is now becoming possible using mathematical
                 techniques to take advantage of single-chip
                 multipliers.",
  acknowledgement = ack-nhfb,
  classification = "713; 721; 723",
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
  journalabr =   "Computer",
  keywords =     "signal processing",
}

@Article{Waser:1978:SAH,
  author =       "S. Waser",
  title =        "State of the Art in High-Spped Arithmetic {ICs}",
  journal =      j-COMP-DESIGN,
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        jul,
  year =         "1978",
  CODEN =        "CMPDAM",
  ISSN =         "0010-4566",
  bibdate =      "Fri Nov 09 19:34:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Design",
}

@InProceedings{Waser:1978:SAI,
  author =       "Shlomo Waser",
  title =        "Survey of Arithmetic Integrated Circuits",
  crossref =     "IEEE:1978:PSC",
  pages =        "257--266",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Waser.pdf",
  abstract =     "The purpose of this report is to provide the
                 state-of-the-art of high performance arithmetic
                 integrated circuits (ICs). The survey concentrates on
                 arithmetic ICs that are designed to improve execution
                 speed over software techniques, therefore, no
                 calculator chips are surveyed.\par

                 In order to understand the difficulties encountered in
                 fabricating high speed arithmetic ICs, we start the
                 article with a discussion on semiconductor technology.
                 Next, we survey the various arithmetic elements that
                 are available in monolithic form: ALUs, Data Slices,
                 Multipliers, Floating Point Processors, and ROMs.
                 Finally, we conclude with a comment on digital signal
                 processing and a discussion of the future trends in
                 arithmetic ICs.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4",
}

@InProceedings{Weinberger:1978:PAU,
  author =       "Arnold Weinberger",
  title =        "Parallel Adders Using Standard {PLAs}",
  crossref =     "IEEE:1978:PSC",
  pages =        "116--124",
  year =         "1978",
  bibdate =      "Thu Nov 15 10:49:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Weinberger.pdf",
  abstract =     "PLA adders are described that add in one cycle and
                 require a reasonable number of product terms for an 8,
                 16, or even a 32-bit adder. A procedure is also
                 described for minimizing the number of product terms
                 for any size adder.",
  acknowledgement = ack-nhfb,
  keywords =     "adder; ARITH-4; carry-look-ahead; input decoders;
                 output exclusive-ors; product term minimization;
                 Programmable Logic Array (PLA)",
}

@Article{Wittmayer:1978:APP,
  author =       "W. R. Wittmayer",
  title =        "Array Processor Provides High Throughput Rate",
  journal =      j-COMP-DESIGN,
  volume =       "??",
  number =       "??",
  pages =        "93--100",
  month =        mar,
  year =         "1978",
  CODEN =        "CMPDAM",
  ISSN =         "0010-4566",
  bibdate =      "Fri Nov 09 19:45:09 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Design",
}

@Article{Wozniakowski:1978:REA,
  author =       "H. Wo{\'z}niakowski",
  title =        "Round-off error analysis of iterations for large
                 linear systems",
  journal =      j-NUM-MATH,
  volume =       "30",
  number =       "3",
  pages =        "301--314",
  year =         "1978",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290B (Error analysis in numerical methods); C4110
                 (Error analysis in numerical methods)",
  corpsource =   "Department of Computer Sci., Carnegie-Mellon
                 University, Pittsburgh, PA, USA",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "equations; error analysis; floating point arithmetic;
                 Gauss Seidel iteration; iteration round off error
                 analysis; iterative methods; residual vector; sparse
                 linear systems",
  treatment =    "A Application; T Theoretical or Mathematical",
}

@InProceedings{Wrathall:1978:CGI,
  author =       "Celia Wrathall and Tien Chi Chen",
  title =        "Convergence Guarantee and Improvements for a fast
                 Hardware Exponential and Logarithm Evaluation Scheme",
  crossref =     "IEEE:1978:PSC",
  pages =        "175--182",
  year =         "1978",
  bibdate =      "Thu Sep 01 11:46:12 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith4/papers/ARITH4_Wrathall.pdf",
  abstract =     "In one iteration, Chen's algorithm for evaluating
                 exponentials and logarithms advances by 2 bits on the
                 average, yet may not advance at all. Analysis reveals
                 that the no-advance situation actually paves the way
                 for sizable advance in the next iteration, and the
                 guaranteed advance, after a one iteration overhead, is
                 one bit per iteration.\par

                 Two new schemes raise the guaranteed advance to 1.5
                 bits per iteration, after a two-iteration overhead,
                 while maintaining the original requirement of one
                 stored constant per operand bit.\par

                 Adopting as a figure of merit the following
                 quantity\par

                  $$ Q = \textrm {advance per iteration} \over \textrm
                 {memory words per operand hit} $$ \par

                 for the steady-state iterations, the new schemes
                 appears to be better than other methods heretofore
                 proposed.",
  acknowledgement = ack-nj,
  keywords =     "ARITH-4",
}

@Article{Abu-El-Haija:1979:AER,
  author =       "A. Abu-El-Haija and A. Peterson",
  title =        "An approach to eliminate roundoff errors in digital
                 filters",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "27",
  number =       "2",
  pages =        "195--198",
  month =        apr,
  year =         "1979",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  summary =      "``Second-order quantizers'' are introduced which can
                 be used for implementing recursive digital filters with
                 practically no roundoff errors or limit-cycle
                 oscillations. Based on the idea of changing the
                 transfer function used to compute roundoff \ldots{}",
}

@Article{Aggarwal:1979:REM,
  author =       "Vijay B. Aggarwal and James W. Burgmeier",
  title =        "A round-off error model with applications to
                 arithmetic expressions",
  journal =      j-SIAM-J-COMPUT,
  volume =       "8",
  number =       "1",
  pages =        "60--72",
  month =        "????",
  year =         "1979",
  CODEN =        "SMJCAT",
  ISSN =         "0097-5397 (print), 1095-7111 (electronic)",
  ISSN-L =       "0097-5397",
  MRclass =      "68C01 (65G05)",
  MRnumber =     "81b:68031",
  bibdate =      "Mon Nov 29 10:58:59 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/8/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Computing",
  journal-URL =  "http://epubs.siam.org/sicomp",
}

@Article{Agrawal:1979:HSA,
  author =       "D. P. Agrawal",
  title =        "High-Speed Arithmetic Arrays",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-28",
  number =       "3",
  pages =        "215--224",
  month =        mar,
  year =         "1979",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1979.1675322",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 06:49:36 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675322",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Alt:1979:SRD,
  author =       "H. Alt",
  title =        "Square Rooting Is as Difficult as Multiplication",
  journal =      j-COMPUTING,
  volume =       "21",
  number =       "3",
  pages =        "221--232",
  year =         "1979",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "68C25",
  MRnumber =     "82m:68081",
  bibdate =      "Tue Jan 2 17:40:54 MST 2001",
  bibsource =    "Compendex database;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 INSPEC Axiom database (1968--date); MathSciNet
                 database",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliation =  "Math. \& Information, University of Saarlandes,
                 Saarbrucken, West Germany",
  classification = "723; C5230",
  description =  "digital arithmetic",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Computing (Vienna/New York)",
  keywords =     "algorithm; computer programming; square rooting",
}

@Article{Atkins:1979:FSC,
  author =       "D. E. Atkins",
  title =        "{Fourth Symposium on Computer Arithmetic}: crunching
                 with quality and {LSI}",
  journal =      j-COMPUTER,
  volume =       "12",
  number =       "4",
  pages =        "94--97",
  month =        apr,
  year =         "1979",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Thu Dec 12 07:20:54 MST 1996",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Computer arithmetic problems --- faster computation
                 rates and more efficient representations of real
                 numbers --- are considered in the paper. Floating-point
                 arithmetic standardization, novel implementation of
                 basic arithmetic operators, evaluation of elementary
                 functions --- these are the main considerations of the
                 conference review.",
  acknowledgement = ack-nhfb,
  classification = "722; 723",
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
  journalabr =   "Computer",
  keywords =     "computer arithmetic; computer systems, digital; data
                 processing --- data description; mathematical
                 techniques --- digital arithmetic",
}

@MastersThesis{Barlow:1979:PEA,
  author =       "Jesse Louis Barlow",
  title =        "Probabilistic error analysis of computer arithmetics",
  type =         "{M.S. (Computer Science)}",
  school =       "Northwestern University",
  address =      "Evanston, IL, USA",
  pages =        "????",
  year =         "1979",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers --- Programming.;
                 Floating-point arithmetic.; Numbers, Real.; Numerical
                 calculations --- Computer programs.",
}

@MastersThesis{Biddulph:1979:MFC,
  author =       "Thomas P. Biddulph",
  title =        "A modified {FORTRAN\slash 77} compiler that will
                 implement the proposed {IEEE\slash KCS} floating point
                 standard via calls to emulation routines",
  type =         "{Master of Science, Plan II}",
  school =       "Department of Electrical Engineering and Computer
                 Sciences",
  address =      "Berkeley, CA, USA",
  pages =        "????",
  year =         "1979",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Brent:1979:RLP,
  author =       "R. P. Brent and H. T. Kung",
  title =        "A regular layout for parallel adders",
  institution =  "Computer Science Department, Carnegie-Mellon
                 University",
  address =      "Pittsburgh, PA, USA",
  pages =        "20",
  year =         "1979",
  bibdate =      "Thu Nov 18 09:31:44 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://books.google.com/books?id=mutgGwAACAAJ",
  abstract =     "With VLSI architecture the chip area is a better
                 measure of cost than the conventional gate count. We
                 show that addition of n-bit binary numbers can be
                 performed on a chip in time proportional to $ \log n $
                 and with area proportional to $ n \log n $.",
  acknowledgement = ack-nhfb,
}

@Article{Brent:1979:RMF,
  author =       "R. P. Brent",
  title =        "Remark on ``{Algorithm} 524: {MP}, {A Fortran}
                 Multiple-Precision Arithmetic Package [{A1}]''",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "518--519",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355868",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 22:49:18 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Brent:1978:AMF,Brent:1980:AIB}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@InProceedings{Brown:1979:EPB,
  author =       "W. S. Brown and S. I. Feldman",
  title =        "Environment parameters and basic functions for
                 floating-point computation",
  crossref =     "ACM:1979:PSC",
  pages =        "42--45",
  year =         "1979",
  bibdate =      "Fri Nov 28 17:31:00 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Bustoz:1979:ITD,
  author =       "Joaqu{\'i}n Bustoz and Alan Feldstein and Richard
                 Goodman and Seppo Linnainmaa",
  title =        "Improved Trailing Digits Estimates Applied to Optimal
                 Computer Arithmetic",
  journal =      j-J-ACM,
  volume =       "26",
  number =       "4",
  pages =        "716--730",
  month =        oct,
  year =         "1979",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Wed Oct 26 23:35:40 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "New results are given on the distribution of trailing
                 digits for logarithmically distributed numbers and on
                 error in floating-point multiplication. Some of the
                 results have application to computer design. In
                 particular, there are certain values of the base
                 (indeed, $ \beta = 2, 4, 6 $, and sometimes, $8$, but
                 {\em not} $ 16 $) which, when carefully balanced with
                 other design parameters, minimize the mean
                 multiplicative error. For these special minimizing
                 situations, it suffices to have only one guard $ \beta
                 $ it provided that postnormalization occurs after
                 symmetric rounding.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  keywords =     "computer arithmetic; floating-point multiplication;
                 floating-point numbers; floating-point precision and
                 significance; fraction error; guard digits;
                 logarithmically distributed numbers; mean and standard
                 deviation of error; nonleading digits; normalization
                 options; roundoff error; trailing digits; uniformly
                 distributed numbers",
}

@Article{Chen:1979:PMB,
  author =       "I-Ngo Chen and R. Willoner",
  title =        "An {$ O(n) $} Parallel Multiplier with Bit-Sequential
                 Input and Output",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-28",
  number =       "10",
  pages =        "721--727",
  month =        oct,
  year =         "1979",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1979.1675239",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 06:49:41 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675239",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Cody:1979:IPI,
  author =       "W. J. Cody",
  title =        "Impact of The Proposed {IEEE} Floating Point Standard
                 on Numerical Software",
  journal =      j-SIGNUM,
  volume =       "14",
  number =       "3S (Special issue)",
  pages =        "29--30",
  month =        oct,
  year =         "1979",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:07 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C4100 (Numerical analysis); C5230 (Digital arithmetic
                 methods); C7310 (Mathematics computing)",
  corpsource =   "Appl. Math. Div., Argonne Nat. Lab., Argonne, IL,
                 USA",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "digital arithmetic; floating point; IEEE; numerical
                 analysis; numerical software; standard; standards",
  treatment =    "P Practical",
  xxnumber =     "si-2",
}

@Article{Coonen:1979:PSB,
  author =       "Jerome Coonen and William Kahan and John Palmer and
                 Tom Pittman and David Stevenson",
  title =        "A Proposed Standard for Binary Floating Point
                 Arithmetic: Draft 5.11",
  journal =      j-SIGNUM,
  volume =       "14",
  number =       "3S (Special issue)",
  pages =        "4--12",
  month =        oct,
  year =         "1979",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/1057520.1057521",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:07 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/signum.bib",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C5230 (Digital arithmetic methods)",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "arithmetic; binary; digital arithmetic; floating
                 point; IEEE Computer Society; Microprocessor; standard;
                 standards; Standards Subcommittee",
  treatment =    "P Practical",
  xxnumber =     "si-2",
}

@TechReport{Coonen:1979:SPS,
  author =       "Jerome T. Coonen",
  title =        "Specifications for a Proposed Standard for
                 Floating-Point Arithmetic",
  type =         "Memorandum",
  number =       "{UCB\slash ERL M78\slash 72}",
  institution =  "University of California, Berkeley",
  address =      "Berkeley, CA, USA",
  day =          "25",
  month =        jan,
  year =         "1979",
  bibdate =      "Mon Dec 24 08:33:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cybenko:1979:REP,
  author =       "G. Cybenko",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing: {ICASSP '79}",
  title =        "Round-off error propagation in {Durbin}'s,
                 {Levinson}'s, and {Trench}'s algorithms",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "498--501",
  year =         "1979",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The subject matter of this paper concerns the
                 round-off error propagation in order $n^2$ algorithms
                 for solving problems involving Toeplitz matrices. Since
                 linear predictive techniques owe much of their appeal
                 to the computational efficiency \ldots{}",
}

@Article{Diaconis:1979:RP,
  author =       "Persi Diaconis and David Freedman",
  title =        "On Rounding Percentages",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "74",
  number =       "366",
  pages =        "359--364",
  month =        jun,
  year =         "1979",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Wed Nov 23 11:24:59 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/bethe-hans.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  note =         "The authors extend prior work on correctness of sums
                 of rounded percentages \cite{Mosteller:1967:DSR}, and
                 criticize biased rounding practices in
                 \cite{Benford:1938:LAN}.",
  URL =          "http://www.jstor.org/stable/2284288",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
  keywords =     "Benford's Law; correct rounding; floating-point
                 arithmetic",
  remark =       "When percentage-column entries are rounded, their sum
                 may differ from 100\%. The authors use a prior proof
                 \cite{Mosteller:1967:DSR} that for $ n \gg 2 $ rounded
                 values, the probability of a correct sum is $ \sqrt {6
                 / (\pi n)} \approx 1.382 / \sqrt {n} $. They show that
                 rounding may produce large changes in computed
                 chi-squared values, and they conclude their article
                 with this recommendation: ``it is important to
                 calculate with many-digit accuracy when computing $
                 \chi^2 $ for large sample sizes.''",
}

@Article{Edgar:1979:FMN,
  author =       "Albert D. Edgar and Samuel C. Lee",
  title =        "{FOCUS} Microcomputer Number System",
  journal =      j-CACM,
  volume =       "22",
  number =       "3",
  pages =        "166--177",
  month =        mar,
  year =         "1979",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:37:26 MST 2001",
  bibsource =    "Compendex database;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm22.html#EdgarL79;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "FOCUS is a number system and supporting computational
                 algorithms especially useful for microcomputer control
                 and other signal processing applications. FOCUS has the
                 wide-ranging character of floating-point numbers with a
                 uniformity of state distributions that give FOCUS
                 better than a twofold accuracy advantage over an equal
                 word length floating-point system. FOCUS computations
                 are typically five times faster than single precision
                 fixed-point or integer arithmetic for a mixture of
                 operations, comparable in speed with hardware
                 arithmetic for many applications. Algorithms for 8-bit
                 and 16-bit implementations of FOCUS are included.",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods); C5250
                 (Microcomputer techniques)",
  classification = "723",
  corpsource =   "University of Oklahoma, Norman, OK, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  journalabr =   "Commun ACM",
  keywords =     "algorithms; arithmetic; computational; computers,
                 microprocessor; digital arithmetic; floating point
                 numbers; FOCUS; microcomputer; microcomputer control;
                 microcomputers; number system; signal processing",
  oldlabel =     "EdgarL79",
  treatment =    "P Practical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/EdgarL79",
}

@InProceedings{Eggers:1979:HFP,
  author =       "Thomas W. Eggers and Judson S. Leonard and Mary H.
                 Payne",
  title =        "Handling of floating point exceptions",
  crossref =     "ACM:1979:PSC",
  pages =        "100--108",
  year =         "1979",
  bibdate =      "Fri Nov 28 17:31:00 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Feldman:1979:IPS,
  author =       "Stuart I. Feldman",
  title =        "The Impact of the Proposed Standard for Floating Point
                 Arithmetic on Languages and Systems",
  journal =      j-SIGNUM,
  volume =       "14",
  number =       "3S (Special issue)",
  pages =        "31--32",
  month =        oct,
  year =         "1979",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:07 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C5230 (Digital arithmetic methods); C6140D (High level
                 languages)",
  corpsource =   "Bell Labs., Murray Hill, NJ, USA",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "arithmetic; digital arithmetic; floating point;
                 languages; programming languages; proposed; standard;
                 standards; systems",
  xxnumber =     "si-2",
}

@MastersThesis{Fogler:1979:BFP,
  author =       "Robert Joseph Fogler",
  title =        "On a block floating point implementation of an
                 intrusion-detection algorithm",
  type =         "Thesis ({M.S.})",
  school =       "Kansas State University",
  address =      "Manhattan, KS, USA",
  pages =        "71",
  year =         "1979",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic alarm systems.; Signal processing.",
}

@Article{Fox:1979:RFP,
  author =       "Phyllis Fox",
  title =        "Remark on ``{Algorithm} 528: Framework for a Portable
                 Library [{Z}]''",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "524--524",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355871",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:06 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Fox:1978:AFP}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fraley:1979:PED,
  author =       "Bob Fraley and Steve Walther",
  title =        "Proposal to Eliminate Denormalized Numbers",
  journal =      j-SIGNUM,
  volume =       "14",
  number =       "3S (Special issue)",
  pages =        "22--23",
  month =        oct,
  year =         "1979",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:07 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Hewlett--Packard Labs., Palo Alto, CA, USA",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "denormalized numbers; digital arithmetic; expense;
                 floating point",
  treatment =    "P Practical",
  xxnumber =     "si-2",
}

@Article{Gargantini:1979:NSS,
  author =       "Irene Gargantini",
  title =        "The Numerical Stability of Simultaneous Iterations Via
                 Square-Rooting",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "5",
  number =       "1",
  pages =        "25--31",
  month =        "????",
  year =         "1979",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(81)90136-X",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 18:51:16 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/089812218190136X",
  acknowledgement = ack-jr # " and " # ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@TechReport{Ginsberg:1979:MFE,
  author =       "Myron Ginsberg",
  title =        "Monitoring floating-point error propagation in
                 scientific computation",
  type =         "Technical report",
  number =       "CSE 7910",
  institution =  "Department of Computer Science and Engineering,
                 Southern Methodist University",
  address =      "Dallas, TX, USA",
  pages =        "32",
  year =         "1979",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.",
}

@Article{Gregory:1979:EFC,
  author =       "Robert Todd Gregory",
  title =        "Error-free computation with finite number systems",
  journal =      j-SIGNUM,
  volume =       "14",
  number =       "3",
  pages =        "9--16",
  month =        sep,
  year =         "1979",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:07 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "University of Tennessee, Knoxville, TN, USA",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "automatic digital computer; computer-representable
                 numbers; error free computation; finite; finite number
                 systems; floating point numbers; machine; numerical
                 methods; real numbers",
  treatment =    "T Theoretical or Mathematical",
}

@PhdThesis{Gruener:1979:ARD,
  author =       "K. Gr{\"u}ner",
  title =        "{Allgemeine Rechnerarithmetik und deren
                 Implementierung mit optimaler Genauigkeit} \toenglish
                 {General Computer Arithmetic and its Implementation
                 with Optimal Accuracy} \endtoenglish",
  type =         "Dissertation",
  school =       "Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "??",
  year =         "1979",
  bibdate =      "Fri Sep 16 16:30:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Book{Hardy:1979:ITN,
  author =       "G. H. (Godfrey Harold) Hardy and E. M. (Edward
                 Maitland) Wright",
  title =        "An Introduction to the Theory of Numbers",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  edition =      "Fifth",
  pages =        "xvi + 426",
  year =         "1979",
  ISBN =         "0-19-853170-2, 0-19-853171-0 (paperback)",
  ISBN-13 =      "978-0-19-853170-8, 978-0-19-853171-5 (paperback)",
  LCCN =         "A241 .H28 1979",
  bibdate =      "Fri Nov 30 06:49:15 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Reprinted in 1988 and 1998 with corrections.",
}

@InProceedings{Hastings:1979:SMM,
  author =       "C. Hastings",
  title =        "Shift Matrices: The Missing Teeth in the Number
                 Cruncher",
  crossref =     "Anonymous:1979:WCR",
  pages =        "??--??",
  year =         "1979",
  bibdate =      "Fri Nov 09 18:59:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Paper number 18/3.",
  acknowledgement = ack-nhfb,
}

@Article{Heath:1979:RDF,
  author =       "J. Heath and H. {Nagle, Jr.} and S. Shiva",
  title =        "Realization of digital filters using input-scaled
                 floating-point arithmetic",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "27",
  number =       "5",
  pages =        "469--477",
  month =        oct,
  year =         "1979",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See note \cite{Heath:1986:NRD}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  summary =      "Fixed-point and floating-point realizations of digital
                 filters are abundant in the literature of digital
                 signal processing. A block-floating-point realization
                 which has some advantages of both fixed-point and
                 floating-point has been reported and \ldots{}",
}

@Article{Hehner:1979:NRR,
  author =       "E. C. R. Hehner and R. N. S. Horspool",
  title =        "A new representation of the rational numbers for fast
                 easy arithmetic",
  journal =      j-SIAM-J-COMPUT,
  volume =       "8",
  number =       "2",
  pages =        "124--134",
  month =        "????",
  year =         "1979",
  CODEN =        "SMJCAT",
  ISSN =         "0097-5397 (print), 1095-7111 (electronic)",
  ISSN-L =       "0097-5397",
  MRclass =      "68C05 (10A30 68A05)",
  MRnumber =     "80h:68027",
  MRreviewer =   "P. J. Weinberger",
  bibdate =      "Mon Nov 29 10:59:01 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/8/2;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See corrigendum \cite{Hehner:1980:CNR}.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Computing",
  journal-URL =  "http://epubs.siam.org/sicomp",
}

@InProceedings{Hull:1979:DFP,
  author =       "T. E. Hull",
  title =        "Desirable floating-point arithmetic and elementary
                 functions for numerical computation",
  crossref =     "ACM:1979:PSC",
  pages =        "96--99",
  year =         "1979",
  bibdate =      "Mon Jan 08 11:06:31 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The purpose of this talk is to summarize proposed
                 specifications for floating-polar arithmetic and
                 elementary functions. The topics considered are: the
                 base of the number system, precision control, number
                 representation, arithmetic operations, ocher basic
                 operations, elementary functions, and exception
                 handling. The possibility of doing without fixed-point
                 arithmetic is also mentioned. The specifications are
                 intended to be entirely at the level of a programming
                 language such as Fortran. The emphasis is on
                 convenience and simplicity from the user's point of
                 view. Conforming to such specifications would have
                 obvious beneficial implications for the portability of
                 numerical software, and for proving programs correct,
                 as well as attempting to provide facilities which are
                 most suitable for the user. The specifications are not
                 complete in every detail, but it is intended that they
                 be complete ``in spirit'' --- some further details,
                 especially syntactic details, would have to be
                 provided, but the proposals are otherwise relatively
                 complete.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@Book{Hwang:1979:CAP,
  author =       "Kai Hwang",
  title =        "Computer Arithmetic: Principles, Architecture, and
                 Design",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xiii + 423",
  year =         "1979",
  ISBN =         "0-471-03496-7",
  ISBN-13 =      "978-0-471-03496-4",
  LCCN =         "TK7888.3 .H9",
  bibdate =      "Sat May 18 14:15:19 2002",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Hwang:1979:GMT,
  author =       "Kai Hwang",
  title =        "Global and Modular Two's Complement Cellular Array
                 Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-28",
  number =       "4",
  pages =        "300--306",
  month =        apr,
  year =         "1979",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1979.1675350",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 06:49:37 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675350",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{IEEE:1979:PIF,
  author =       "Anonymous",
  title =        "The Proposed {IEEE} floating-point standard",
  journal =      j-SIGNUM,
  pages =        "32",
  month =        oct,
  year =         "1979",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "Floating-point arithmetic --- Standards.",
}

@Manual{IntelCorporation:1979:FAL,
  author =       "Intel Corporation",
  title =        "8080\slash 8085 floating-point arithmetic library
                 user's manual",
  organization = "The Corporation",
  address =      "Santa Clara, CA, USA",
  pages =        "v + 20",
  year =         "1979",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Assembly language (Computer program language).; Intel
                 8080 (Microprocessor) --- Programming.; INTEL 8085
                 (Computer) --- Programming.; PL/M-80 (Computer program
                 language).",
  remark =       "``Manual Order Number: 9800452-03''.",
}

@Article{Jenkins:1979:RAR,
  author =       "W. Jenkins",
  title =        "Recent advances in residue number techniques for
                 recursive digital filtering",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "27",
  number =       "1",
  pages =        "19--30",
  month =        feb,
  year =         "1979",
  CODEN =        "IETABA",
  DOI =          "https://doi.org/10.1049/el:19780088",
  ISSN =         "0096-3518",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26137",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A new algorithm for scaling in residue number systems
                 (RNS's) is presented for applying residue number theory
                 to recursive digital filtering. The algorithm provides
                 an efficient method for scaling the output of each
                 recursive filter section for use \ldots{}",
}

@Article{Johnson:1979:RAF,
  author =       "Donald B. Johnson and Webb Miller and Brian Minnihan
                 and Celia Wrathall",
  title =        "Reducibility Among Floating-Point Graphs",
  journal =      j-J-ACM,
  volume =       "26",
  number =       "4",
  pages =        "739--760",
  month =        oct,
  year =         "1979",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  MRclass =      "65G05",
  MRnumber =     "80i:65045",
  bibdate =      "Fri Dec 08 11:55:10 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The graph-theoretic models of this paper can be used
                 to compare the rounding-error behavior of numerical
                 programs. The models follow the approach, popularized
                 by Wilkinson, of assuming independent rounding errors
                 in each arithmetic operation. Models constructed on
                 this assumption are more tractable than would be the
                 case under more realistic assumptions. There are
                 identified two easily tested conditions on programs
                 which guarantee that error analyses are relatively
                 insensitive to the particular graph model employed. The
                 development has the additional benefit of sometimes
                 providing an elementary proof that one program is
                 comparable in stability to another. Examples of such
                 results are given.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}

@Article{Kahan:1979:PCK,
  author =       "William M. Kahan",
  title =        "Personal Calculator Has Key to Solve Any Equation $
                 f(x) = 0 $",
  journal =      j-HEWLETT-PACKARD-J,
  volume =       "30",
  number =       "12",
  pages =        "20--26",
  month =        dec,
  year =         "1979",
  CODEN =        "HPJOAX",
  ISSN =         "0018-1153",
  MRclass =      "65-01 (65G05 65H05)",
  MRnumber =     "MR574853 (81k:65002)",
  MRreviewer =   "R. P. Brent",
  bibdate =      "Tue Mar 25 14:12:15 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/hpj.bib",
  note =         "Lecture notes for Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/SOLVEkey.pdf",
  acknowledgement = ack-nhfb,
  classcodes =   "C5420 (Mainframes and minicomputers); C7310
                 (Mathematics computing)",
  corpsource =   "Univ. of California, Berkeley, CA, USA",
  fjournal =     "Hewlett--Packard Journal",
  keywords =     "electronic calculators; equation solving; finding;
                 handheld calculator; HP 34C; linear algebra; personal
                 calculator; root; SOLVE",
  reviewer =     "R. P. Brent",
  treatment =    "P Practical",
}

@Article{Kahan:1979:PFP,
  author =       "W. Kahan and J. Palmer",
  title =        "On a Proposed Floating-Point Standard",
  journal =      j-SIGNUM,
  volume =       "14",
  number =       "3S (Special issue)",
  pages =        "13--21",
  month =        oct,
  year =         "1979",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/1057520.1057522",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Wed Mar 19 23:00:11 MST 1997",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/signum.bib",
  abstract =     "A standard for binary floating-point arithmetic is
                 being proposed and there is a very real possibility
                 that it will be adopted by many manufacturers and
                 implemented on a wide range of computers. This
                 development matters to all of us concerned with
                 numerical software. One of the principal motivations
                 for the standard is to distribute more evenly the
                 burden of portability between hardware and software. At
                 present, any program intended to be portable must be
                 designed for a mythical computer that enjoys no
                 capability not supported by every computer on which the
                 program will be run. That mythical computer is so much
                 grubbier than almost any real computer that a portable
                 program will frequently be denigrated as ``suboptimal''
                 and then supplanted by another program supposedly
                 ``optimal'' for the real computer in question but often
                 inferior in critical respects like reliability. A
                 standard --- almost any reasonable standard --- will
                 surely improve the situation. A standard environment
                 for numerical programs will promote fair comparisons
                 and sharing of numerical codes, thereby lowering costs
                 and prices. Furthermore, we have chosen repeatedly to
                 enrich that environment in order that applications
                 programs be simpler and more reliable. Thus will the
                 onus of portability be shared among hardware
                 manufacturers and software producers.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "University of California, Berkeley, CA, USA",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "arithmetic; digital arithmetic; floating point;
                 proposal; standard; standards",
  treatment =    "P Practical",
  xxnumber =     "si-2",
}

@PhdThesis{Kent:1979:TPS,
  author =       "Jan Kent",
  title =        "The theoretical and practical study of floating point
                 instructions: Consisting of Theoretical definition,
                 analysis and comparison of floating point instruction,
                 and procedures for the description and simulation of
                 floating point instructions",
  type =         "{Dr. Avhandling}",
  school =       "Universitetet i Oslo",
  address =      "Oslo, Norway",
  year =         "1979",
  bibdate =      "Thu May 09 08:05:31 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  xxnote =       "Bibsys library catalog gave both 1977 and 1979 as
                 year??",
}

@TechReport{Kolze:1979:BFP,
  author =       "Thomas Joseph Kolze",
  title =        "Block floating point {FFT} statistical noise analysis
                 program",
  type =         "Technical report",
  number =       "CSR-79-2",
  institution =  "Department of Electrical Engineering, University of
                 Missouri--Rolla",
  address =      "Rolla, MO, USA",
  pages =        "vii + 180",
  year =         "1979",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Communications and signal processing research.",
  acknowledgement = ack-nhfb,
  keywords =     "Radio noise --- Computer programs.; Signals and
                 signaling --- Computer programs.",
}

@MastersThesis{Kolze:1979:SNA,
  author =       "Thomas Joseph Kolze",
  title =        "Statistical noise analysis of a block floating point
                 {FFT} and an example application",
  type =         "Electrical Engineering Thesis ({M.S.})",
  school =       "University of Missouri--Rolla",
  address =      "Rolla, MO, USA",
  pages =        "viii + 88",
  year =         "1979",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Kornerup:1979:NRA,
  author =       "Peter Kornerup",
  title =        "A note on rational arithmetic",
  journal =      j-SIGMICRO,
  volume =       "10",
  number =       "2",
  pages =        "28--28",
  month =        jun,
  year =         "1979",
  CODEN =        "SIGMDJ",
  DOI =          "https://doi.org/10.1145/1218003.1218004",
  ISSN =         "0163-5751, 1050-916X",
  ISSN-L =       "0163-5751",
  bibdate =      "Fri Apr 16 10:27:24 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigmicro.bib",
  note =         "See \cite{Thacker:1979:MPR,Thacker:1979:R}.",
  URL =          "https://dl.acm.org/doi/10.1145/1218003.1218004",
  abstract =     "A recent paper in SIGMICRO [1] contained a comparison
                 of the accuracy of floating point vs. rational
                 representations, which is very unfair to the latter.
                 The format chosen for rational numbers utilizes 16 bits
                 for numerators and 16 bits for denominators. This
                 implies that the spacing between consecutive numbers in
                 the system is in most cases of the order $ 2 {-32} $.
                 Only around simple rational numbers (e.g. 1/1, 2/3) is
                 the spacing of the order $ 2 {-16}. $ However the
                 rounding algorithm presented in [1] will almost
                 certainly introduce a rounding error of the order $ 2
                 {-16} $, i.e. introduce an error which in most cases is
                 of the order $ 2^{16} $ larger than necessary.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMICRO Newsletter",
  journal-URL =  "https://dl.acm.org/loi/sigmicro",
}

@Article{Kusterer:1979:SEP,
  author =       "Roland Kusterer and Manfred Reimer",
  title =        "Stable Evaluation of Polynomials in Time $ \log n $",
  journal =      j-MATH-COMPUT,
  volume =       "33",
  number =       "147",
  pages =        "1019--1031",
  month =        jul,
  year =         "1979",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-1979-0528054-X;
                 https://doi.org/10.2307/2006075",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65G05 (68C25)",
  MRnumber =     "80d:65050 (528054)",
  MRreviewer =   "C. W. Clenshaw",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/t/todd-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Math. Inst., University of Dortmund, Dortmund, West
                 Germany",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "algorithm; approximation theory; number of
                 multiplications to evaluate a polynomial; polynomials",
  reviewer-dates = "Charles William Clenshaw (15 March 1926--23
                 September 2004)",
  treatment =    "A Application; T Theoretical or Mathematical",
}

@Article{Lautz:1979:JLD,
  author =       "G{\"u}nter Lautz",
  title =        "{300 Jahre leibnizsches dualzahlensystem}. ({German})
                 [300 years of the {Leibniz} binary number system]",
  journal =      j-BIOL-CYBERN,
  volume =       "35",
  number =       "3",
  pages =        "175--181",
  month =        dec,
  year =         "1979",
  CODEN =        "BICYAF",
  DOI =          "https://doi.org/10.1007/bf00337062",
  ISSN =         "0340-1200 (print), 1432-0770 (electronic)",
  ISSN-L =       "0340-1200",
  bibdate =      "Fri Mar 17 08:46:29 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "300 years ago G. W. Leibniz has invented his binary
                 number system, now widely used in computer sciences.
                 The paper recapitulates some informations about the
                 contents of the first private notes from 1679, partly
                 reproduced in facsimiles, and the scientific background
                 of that time. The circumstances and the genesis of the
                 first treatise on this matter, published in 1703/5 by
                 Leibniz at the Academy of Sciences, Paris, are
                 discussed in detail.",
  acknowledgement = ack-nhfb,
  fjournal =     "Biological cybernetics",
  journal-URL =  "http://link.springer.com/journal/422",
  language =     "German",
}

@Article{Lee:1979:AFN,
  author =       "S. C. Lee and A. D. Edgar",
  title =        "Addendum to {``The Focus Number System''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-28",
  number =       "9",
  pages =        "693--693",
  month =        sep,
  year =         "1979",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1979.1675442",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 06:49:40 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See \cite{Lee:1977:FNS,Swartzlander:1979:CFN}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675442",
  abstract =     "In 1971 Kingsbury and Rayner, publishing under the
                 title ``Digital Filtering Using Logarithmic
                 Arithmetic'' disclosed a sign-plus-logarithm number
                 system, and a means of performing addition through
                 single dimensional lookup using the formula $ c = b +
                 F(a b) $. The system was demonstrated on a computer. In
                 1975 Swartzlander and Alexopoulos disclosed Kingsbury's
                 logarithmic arithmetic as ``The Sign\slash Logarithm
                 Number System''. In 1977, without knowledge of prior
                 art, we reinvented the wheel a third time, dubbing it
                 ``Focus,'' after the focus of resolution around the
                 zero origin [3]. We wish now to acknowledge Kingsbury
                 and Rayner as the pioneer authors, and also
                 Swartzlander and Alexopoulos as prior to our
                 publication.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{McDonnell:1979:FR,
  author =       "Eugene McDonnell",
  title =        "Fuzzy residue",
  journal =      j-APL-QUOTE-QUAD,
  volume =       "9",
  number =       "4",
  pages =        "42--46",
  year =         "1979",
  CODEN =        "APLQD9",
  DOI =          "https://doi.org/10.1145/390009.804437",
  ISSN =         "0163-6006 (print), 1558-3392 (electronic)",
  ISSN-L =       "0163-6006",
  bibdate =      "Thu Aug 07 19:13:11 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Certain pairs of arguments to the residue function, as
                 implemented on many APL systems, give results which
                 make it seem as if the ordinary decimal relationships
                 we remember from grade school no longer hold. As far as
                 we can tell, it looks as if a given modulus should
                 divide the right argument, but the implementation tells
                 us it doesn't. A definition for a fuzzed residue
                 function is proposed which resolves the difficulties
                 users have complained of. However, certain points of
                 continuing difficulty remain, where the limitations of
                 machine arithmetic continue to defeat the attempt to
                 model the real number system. The representation
                 function is defined in terms of the residue function,
                 and so is affected by the change in residue. The nature
                 of this effect is also discussed in this paper.",
  acknowledgement = ack-nhfb,
  fjournal =     "APL Quote Quad",
}

@Book{Oberman:1979:DCB,
  author =       "R. M. M. (Roelof Maarten Marie) Oberman",
  title =        "Digital circuits for binary arithmetic",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xii + 340",
  year =         "1979",
  ISBN =         "0-470-26373-3",
  ISBN-13 =      "978-0-470-26373-0",
  LCCN =         "TK7868.L6 O23 1979",
  bibdate =      "Wed Nov 14 17:33:15 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  remark =       "A Halsted Press book.",
  subject =      "logic circuits; digital integrated circuits; switching
                 theory",
}

@Article{Oliver:1979:REP,
  author =       "J. Oliver",
  title =        "Rounding error propagation in polynomial evaluation
                 schemes",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "5",
  number =       "2",
  pages =        "85--97",
  month =        jun,
  year =         "1979",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:18 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1970.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0771050X79900020",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Palmer:1979:MMM,
  author =       "John F. Palmer",
  title =        "Making Mainframe Mathematics Accessible to
                 Microcomputers",
  journal =      j-ELECTRONICS,
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "8",
  month =        may,
  year =         "1979",
  bibdate =      "Fri Oct 31 06:05:49 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics",
  journal-URL =  "https://www.mdpi.com/journal/electronics",
  remark =       "The ISSN for this journal is for the MDPI journal of
                 the same name as an older journal; the MDPI archives
                 begin with volume 1, number 1, September 2012.",
  xxISSN =       "2079-9292",
}

@Article{Payne:1979:DPB,
  author =       "Mary Payne and William Strecker",
  title =        "Draft Proposal for a Binary Normalized Floating Point
                 Standard",
  journal =      j-SIGNUM,
  volume =       "14",
  number =       "3S (Special issue)",
  pages =        "24--28",
  month =        oct,
  year =         "1979",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:07 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Digital Equipment Corp., Maynard, MA, USA",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "binary; digital arithmetic; floating point;
                 normalized; proposal; standard; standards",
  treatment =    "P Practical",
  xxnumber =     "si-2",
}

@InProceedings{Payne:1979:FPS,
  author =       "Mary Payne",
  editor =       "{IEEE}",
  booktitle =    "{COMPCON Proceedings (Fall 1979)}",
  title =        "Floating Point Standardization",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "166--169",
  year =         "1979",
  DOI =          "https://doi.org/10.1109/CMPCON.1979.729102",
  bibdate =      "Mon Aug 25 06:10:38 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
}

@TechReport{Randell:1979:ABO,
  author =       "Brian Randell",
  title =        "An annotated bibliography on the origins of digital
                 computers",
  type =         "Technical report",
  number =       "140",
  institution =  "Computing Laboratory, University of Newcastle upon
                 Tyne",
  address =      "Newcastle upon Tyne, UK",
  pages =        "146",
  year =         "1979",
  LCCN =         "Z5642.2 .R36 1979",
  bibdate =      "Wed Oct 13 09:24:25 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  subject =      "Electronic digital computers; History; Bibliography;
                 Calculators",
}

@InCollection{Rauch:1979:EAA,
  author =       "E. Rauch",
  title =        "{Einige Aspekte der Auswahl und Realisierung
                 numerischer Verfahren in anwendungsorientierten
                 Systemen} \toenglish {Several Aspects of the Choice and
                 Realisation of Numerical Procedures in
                 Application-Oriented Systems} \endtoenglish",
  crossref =     "Meinardus:1979:ATP",
  pages =        "??--??",
  year =         "1979",
  bibdate =      "Fri Sep 16 16:30:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Redinbo:1979:FFA,
  author =       "G. R. Redinbo",
  title =        "Finite Field Arithmetic on an Array Processor",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-28",
  number =       "7",
  pages =        "461--471",
  month =        jul,
  year =         "1979",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1979.1675390",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 06:49:39 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675390",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Reid:1979:FMF,
  author =       "John Reid",
  title =        "Functions for Manipulating Floating-Point Numbers",
  journal =      j-SIGNUM,
  volume =       "14",
  number =       "4",
  pages =        "11--13",
  month =        dec,
  year =         "1979",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:08 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Computer Sci. and Systems Div., AERE, Harwell, UK",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "complex numbers; digital arithmetic; floating;
                 FORTRAN; point arithmetic; portability; precision",
  treatment =    "P Practical",
}

@InCollection{Reinsch:1979:BRN,
  author =       "Christian Reinsch",
  booktitle =    "{Jahrbuch {\"U}berblicke Mathematik}, 1979",
  title =        "{Die Behandlung von Rundungsfehlern in der numerischen
                 Analysis}. ({German}) [{Treatment} of rounding errors
                 in numerical analysis]",
  publisher =    "Bibliographisches Institut",
  address =      "Mannheim, Germany",
  pages =        "43--62",
  year =         "1979",
  ISBN =         "3-411-01559-4",
  ISBN-13 =      "978-3-411-01559-7",
  MRclass =      "65G50 65G30 65-02 65F15 65F05",
  MRnumber =     "554358",
  MRreviewer =   "Joachim Hirche",
  bibdate =      "Sat Aug 2 15:39:45 2025",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/r/reinsch-christian-h.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0406.65021",
  acknowledgement = ack-nhfb,
  ajournal =     "Jahrb. {\"U}berblicke Math.",
  author-dates = "Christian H. Reinsch (?? ?? 1934--8 October 2022)",
  language =     "German",
  ZBmath =       "3631856",
}

@Article{Reinsch:1979:PPC,
  author =       "Christian H. Reinsch",
  title =        "Principles and Preferences for Computer Arithmetic",
  journal =      j-SIGNUM,
  volume =       "14",
  number =       "1",
  pages =        "12--27",
  month =        mar,
  year =         "1979",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/1053417.1053418",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:06 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/bibnet/authors/g/gear-c-w.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/r/reinsch-christian-h.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/signum.bib",
  abstract =     "This working paper arose out of discussions on
                 desirable hardware features for numerical calculation
                 in the IFIP Working Group 2.5 on Numerical Software. It
                 reflects the views of all members of the group,
                 although no formal vote of approval has been taken; it
                 is not an official IFIP document. Many people
                 contributed ideas to this paper, especially T. J.
                 Dekker, C. W. Gear, T. E. Hull, J. R. Rice, and J. L.
                 Schonfeldor.",
  acknowledgement = ack-nhfb,
  author-dates = "Christian H. Reinsch (?? ?? 1934--8 October 2022)",
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Leibniz-Rechenzentrum, Munich, West Germany",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "computer arithmetic; digital arithmetic",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Rink:1979:CEF,
  author =       "R. Rink and H. Chong",
  title =        "Covariance equation for a floating-point regulator
                 system",
  journal =      j-IEEE-TRANS-AUTOMAT-CONTR,
  volume =       "24",
  number =       "6",
  pages =        "980--982",
  month =        dec,
  year =         "1979",
  CODEN =        "IETAA9",
  ISSN =         "0018-9286 (print), 1558-2523 (electronic)",
  ISSN-L =       "0018-9286",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Automatic Control",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
  summary =      "Derived are linear equations that can be solved for
                 the steady-state covariance matrix of the plant and
                 observer states of a closed-loop regulator system which
                 employs finite wordlength A/D conversion and
                 floating-point computation in the observer/ \ldots{}",
}

@Article{Rink:1979:PSR,
  author =       "R. Rink and Hoi Chong",
  title =        "Performance of state regulator systems with
                 floating-point computation",
  journal =      j-IEEE-TRANS-AUTOMAT-CONTR,
  volume =       "24",
  number =       "3",
  pages =        "411--421",
  month =        jun,
  year =         "1979",
  CODEN =        "IETAA9",
  ISSN =         "0018-9286 (print), 1558-2523 (electronic)",
  ISSN-L =       "0018-9286",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See correction \cite{Rink:1980:CPS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Automatic Control",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
  summary =      "The performance of a digital state regulator system
                 having an A/D converter of finite wordlength and a
                 floating-point estimator/ controller computer of finite
                 mantissa-length is analyzed. An upper bound on the
                 mean-square state error, as a function \ldots{}",
}

@Article{Robertson:1979:VPA,
  author =       "D. A. Robertson",
  title =        "Variable precision arithmetic on {CDC 6000\slash 7000}
                 machines",
  journal =      j-SPE,
  volume =       "9",
  number =       "3",
  pages =        "247--248",
  month =        mar,
  year =         "1979",
  CODEN =        "SPEXBL",
  DOI =          "https://doi.org/10.1002/spe.4380090310",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Wed Sep 10 12:36:39 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/spe.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Software --- Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  onlinedate =   "27 Oct 2006",
}

@MastersThesis{Scharf:1979:HRW,
  author =       "Stuart Lee Scharf",
  title =        "A hardware realization of the {Winograd Fourier}
                 Transform Algorithm",
  type =         "Thesis ({M.S.})",
  school =       "Massachusetts Institute of Technology. Dept. of
                 Electrical and Engineering and Computer Science",
  address =      "Cambridge, MA, USA",
  pages =        "109",
  year =         "1979",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Supervised by James H. McClellan.",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithms.; Computer engineering.; Floating-point
                 arithmetic.; Fourier transformations --- Computer
                 programs.",
}

@InProceedings{Shapiro:1979:ELM,
  author =       "G. Shapiro",
  title =        "Exploit {LSI} Memory Components Today, Instead of
                 Waiting for Arithmetic Devices",
  crossref =     "Anonymous:1979:WCR",
  pages =        "??--??",
  year =         "1979",
  bibdate =      "Fri Nov 09 19:15:35 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Paper 18/5.",
  acknowledgement = ack-nhfb,
}

@Book{Shauman:1979:OMA,
  author =       "Aleksandr Mikhailovich Shauman",
  title =        "Osnovy mashinnoi arifmetiki \toenglish {Principles of
                 Machine Arithmetic} \endtoenglish",
  publisher =    "Izd-vo LGU (Leningrad State University Publishers)",
  address =      "Leningrad, USSR",
  pages =        "311",
  year =         "1979",
  LCCN =         "QA76.6 .S516",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic and logic units.; Electronic
                 digital computers --- Programming.; Floating-point
                 arithmetic.",
  remark =       "At head of title: Leningradskii Gosudarstvennyi
                 universitet imeni A. A. Zhdanova. Bibliography: p.
                 306-[309]",
}

@Article{Sheue:1979:TCM,
  author =       "A. E. Sheue",
  title =        "Two's-Complement Multiplication",
  journal =      j-SIGMICRO,
  volume =       "10",
  number =       "1",
  pages =        "21--23",
  month =        mar,
  year =         "1979",
  CODEN =        "SIGMDJ",
  ISSN =         "0163-5751, 1050-916X",
  ISSN-L =       "0163-5751",
  bibdate =      "Thu Sep 1 10:15:07 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIG Micro Newsletter",
}

@Article{Swartzlander:1979:CFN,
  author =       "E. E. {Swartzlander, Jr.}",
  title =        "Comment on {``The Focus Number System''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-28",
  number =       "9",
  pages =        "693--693",
  month =        sep,
  year =         "1979",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1979.1675441",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 06:49:40 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  note =         "See \cite{Lee:1977:FNS,Lee:1979:AFN}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675441",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Thacker:1979:MPR,
  author =       "William I. Thacker and G. W. Gorsline",
  title =        "Micro programming rational arithmetic operations",
  journal =      j-SIGMICRO,
  volume =       "10",
  number =       "1",
  pages =        "10--13",
  month =        mar,
  year =         "1979",
  CODEN =        "SIGMDJ",
  DOI =          "https://doi.org/10.1145/1217236.1217238",
  ISSN =         "0163-5751, 1050-916X",
  ISSN-L =       "0163-5751",
  bibdate =      "Fri Apr 16 10:27:24 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigmicro.bib",
  note =         "See critical comments \cite{Kornerup:1979:NRA} and
                 response \cite{Thacker:1979:R}.",
  URL =          "https://dl.acm.org/doi/10.1145/1217236.1217238",
  abstract =     "For many years, real number arithmetic, whether
                 accomplished in hardware, software, or firmware, has
                 utilized a floating point scheme. This paper summarizes
                 the results of a study assessing rational
                 representation as a possible replacement for floating
                 point representation. The Hewlett-Packard 2100A
                 microprogrammable computer was used as the test
                 vehicle. Both accuracy and speed comparisons were used
                 to judge the usefulness of the substitution.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMICRO Newsletter",
  journal-URL =  "https://dl.acm.org/loi/sigmicro",
}

@Article{Thacker:1979:R,
  author =       "W. I. Thacker and G. W. Gorsline",
  title =        "Response",
  journal =      j-SIGMICRO,
  volume =       "10",
  number =       "2",
  pages =        "29--29",
  month =        jun,
  year =         "1979",
  CODEN =        "SIGMDJ",
  DOI =          "https://doi.org/10.1145/1218003.1218005",
  ISSN =         "0163-5751, 1050-916X",
  ISSN-L =       "0163-5751",
  bibdate =      "Fri Apr 16 10:27:24 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigmicro.bib",
  note =         "See \cite{Thacker:1979:MPR,Kornerup:1979:NRA}.",
  URL =          "https://dl.acm.org/doi/10.1145/1218003.1218005",
  abstract =     "Within the context of our study; that is, the direct
                 substitution of a pure rational scheme for a floating
                 point scheme of arithmetic and storage within an extant
                 FORTRAN system with no changes to the compiler (and
                 thus to the storage space available for a single
                 numerical quantity), we continue to claim that our
                 results are valid. We again wish to note that our
                 investigation was limited to the pure rational scheme
                 using the same storage space available to a floating
                 point scheme.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMICRO Newsletter",
  journal-URL =  "https://dl.acm.org/loi/sigmicro",
}

@Article{Tseng:1979:IFS,
  author =       "Ben-Dau Tseng and G. A. Jullien and W. C. Miller",
  title =        "Implementation of {FFT} Structures Using the Residue
                 Number System",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-28",
  number =       "11",
  pages =        "831--845",
  month =        nov,
  year =         "1979",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1979.1675263",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 06:49:41 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35176;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675263",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper considers the implementation of a fast
                 Fourier transform (FFT) structure using arrays of
                 read-only memories. The arithmetic operations are based
                 entirely on the residue number system. The most
                 important aspect of the structure relates to \ldots{}",
}

@Article{Ukkonen:1979:AER,
  author =       "Esko Ukkonen",
  title =        "An analysis of the effect of rounding errors on the
                 flow of control in numerical processes",
  journal =      j-BIT,
  volume =       "19",
  number =       "1",
  pages =        "116--133",
  month =        mar,
  year =         "1979",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01931229",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65G05",
  MRnumber =     "81a:65048",
  bibdate =      "Wed Jan 4 18:52:16 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=19&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=19&issue=1&spage=116",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point arithmetic; rounding errors",
}

@InProceedings{vanHulzen:1979:NMS,
  author =       "J. A. {van Hulzen}",
  title =        "A note on methods for solving systems of polynomial
                 equations with floating point coefficients",
  crossref =     "Ng:1979:SAC",
  pages =        "346--357",
  year =         "1979",
  MRclass =      "65H10",
  MRnumber =     "81h:65049",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  reviewer =     "Frederick N. Fritsch",
}

@Article{Wichmann:1979:ID,
  author =       "B. A. Wichmann",
  title =        "Integer division",
  journal =      j-SPE,
  volume =       "9",
  number =       "6",
  pages =        "507--508",
  month =        jun,
  year =         "1979",
  CODEN =        "SPEXBL",
  DOI =          "https://doi.org/10.1002/spe.4380090610",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Wed Sep 10 12:36:39 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/spe.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Software --- Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  onlinedate =   "27 Oct 2006",
}

@Article{Wichmann:1979:PCG,
  author =       "B. A. Wichmann and J. {Du Croz}",
  title =        "A program to calculate the {GAMM} measure",
  journal =      j-COMP-J,
  volume =       "22",
  number =       "4",
  pages =        "317--322",
  month =        nov,
  year =         "1979",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C4240 (Programming and algorithm theory); C7430
                 (Computer engineering)",
  classification = "723",
  corpsource =   "Computing Services Unit, Nat. Phys. Lab., Teddington,
                 UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "analysis; complete computer programs; computer
                 performance; computer programs; computer selection and;
                 confidence check; error; evaluation; floating point
                 calculation; FORTRAN program; GAMM measure; performance
                 evaluation",
  treatment =    "P Practical",
}

@MastersThesis{Wilbanks:1979:MFI,
  author =       "Thomas D. Wilbanks",
  title =        "Microcoding floating-point instructions for a
                 bit-slice processor",
  type =         "Thesis ({M.S.})",
  school =       "University of South Carolina",
  address =      "Columbia, SC, USA",
  pages =        "vi + 131",
  year =         "1979",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Bit slice microprocessors.; Microprocessors ---
                 Programming.",
}

@InProceedings{Winnigstad:1979:ULC,
  author =       "C. N. Winnigstad",
  title =        "Using {LSI} to Crunch Numbers at High Speed: An
                 Overview",
  crossref =     "Anonymous:1979:WCR",
  pages =        "??--??",
  year =         "1979",
  bibdate =      "Fri Nov 09 19:43:13 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Yohe:1979:INA,
  author =       "J. Michael Yohe",
  title =        "Implementing Nonstandard Arithmetics",
  journal =      j-SIAM-REVIEW,
  volume =       "21",
  number =       "1",
  pages =        "34--56",
  month =        "????",
  year =         "1979",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1021003",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri Jun 21 11:25:02 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb # " and " # ack-jr,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
}

@Article{Agrawal:1980:NBA,
  author =       "D. P. Agrawal",
  title =        "On Negabinary-Binary Arithmetic Relationships and
                 Their Hardware Reciprocity",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-29",
  number =       "11",
  pages =        "1032--1035",
  month =        nov,
  year =         "1980",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1980.1675502",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 19:15:30 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675502",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Albrecht:1980:RAO,
  author =       "R. Albrecht",
  title =        "Roundings and Approximations in Ordered Sets",
  crossref =     "Alefeld:1980:FNC",
  pages =        "17--31",
  year =         "1980",
  bibdate =      "Tue Oct 23 08:17:48 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "interval arithmetic; rounding error",
}

@Article{Ambikairajah:1980:TPM,
  author =       "E. Ambikairajah and M. J. Carey",
  title =        "Technique for Performing Multiplication on a 16-bit
                 Microprocessor Using an Extension of {Booth}'s
                 Algorithm",
  journal =      j-ELECT-LETTERS,
  volume =       "16",
  number =       "2",
  pages =        "53--54",
  month =        jan,
  year =         "1980",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Thu Sep 1 10:15:07 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}

@Article{Anonymous:1980:BRCg,
  author =       "Anonymous",
  title =        "Book Review: {{\booktitle{Computer arithmetic: IEEE C:
                 Proceedings of the 4th Symposium on Computer
                 Arithmetic, Santa Monica, 25--27 October 1978}}. IEEE
                 Service Center, 78CH1412-6, 1979. 274 pages,
                 {US\$22.00}}",
  journal =      j-MATH-COMPUT-SIMUL,
  volume =       "22",
  number =       "2",
  pages =        "155--156",
  month =        jul,
  year =         "1980",
  CODEN =        "MCSIDR",
  DOI =          "https://doi.org/10.1016/0378-4754(80)90034-8",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  bibdate =      "Mon Aug 18 16:03:25 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomputsimul1980.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/0378475480900348",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput. Simul.",
  fjournal =     "Mathematics and Computers in Simulation",
  journal-URL =  "https://www.sciencedirect.com/science/journal/03784754",
}

@Article{Baraniecka:1980:RNS,
  author =       "A. Baraniecka and G. Jullien",
  title =        "Residue number system implementations of number
                 theoretic transforms in complex residue rings",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "28",
  number =       "3",
  pages =        "285--291",
  month =        jun,
  year =         "1980",
  CODEN =        "IETABA",
  DOI =          "https://doi.org/10.1109/TC.1979.1675263",
  ISSN =         "0096-3518",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26146",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper discusses the implementation of number
                 theoretic transforms defined in complex residue rings.
                 A selection of transform parameters for lookup table
                 and microprocessor realizations are discussed. When the
                 length of the convolution is \ldots{}",
}

@Article{Bareiss:1980:RED,
  author =       "E. H. Bareiss and J. L. Barlow",
  title =        "Roundoff error distribution in fixed point
                 multiplication",
  journal =      j-BIT,
  volume =       "20",
  number =       "2",
  pages =        "247--250",
  month =        jun,
  year =         "1980",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01933198",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65G05",
  MRnumber =     "81j:65066",
  MRreviewer =   "Seppo Linnainmaa",
  bibdate =      "Wed Jan 4 18:52:16 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=20&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=20&issue=2&spage=247",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point arithmetic; rounding errors",
}

@Article{Barsi:1980:ECC,
  author =       "Ferruccio Barsi and Piero Maestrini",
  title =        "Error codes constructed in residue number systems with
                 non-pairwise-prime moduli",
  journal =      j-INF-CONTROL,
  volume =       "46",
  number =       "1",
  pages =        "16--25",
  month =        jul,
  year =         "1980",
  CODEN =        "IFCNA4",
  DOI =          "https://doi.org/10.1016/S0019-9958(80)90471-4",
  ISSN =         "0019-9958 (print), 1878-2981 (electronic)",
  ISSN-L =       "0019-9958",
  bibdate =      "Thu Nov 18 09:54:38 2010",
  bibsource =    "http://www.sciencedirect.com/science/journal/00199958;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Codes constructed in a Residue Number System (RNS) of
                 moduli $ m_1, m_2, \ldots {}, m_n $ are non-binary,
                 arithmetic codes whose codewords are vectors where the
                 $i$ th component is $ m_i $-valued $ (1 \leq i \leq n)
                 $. A new class of codes in RNS is described, where
                 redundancy is introduced by removing the constraint
                 that the moduli of the RNS be pairwise prime. The
                 error-detecting and correcting capabilities of such
                 codes are discussed and a simple approach to error
                 detection, localization and correction is presented.
                 Although the codes under consideration are quite
                 inefficient in some respects, it is shown that codes is
                 examined in more detail. Codes in this subclass,
                 besides correcting all single errors, also correct
                 almost all of double errors and localize some errors of
                 higher multiplicity, with less redundancy than required
                 to construct optimal 2-correcting codes in RNS.",
  acknowledgement = ack-nhfb,
  fjournal =     "Information and Control",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00199958",
}

@Article{Brent:1980:AIB,
  author =       "Richard P. Brent and Judith A. Hooper and J. Michael
                 Yohe",
  title =        "An {AUGMENT} Interface for {Brent}'s Multiple
                 Precision Arithmetic Package",
  journal =      j-TOMS,
  volume =       "6",
  number =       "2",
  pages =        "146--149",
  month =        jun,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355887.355889",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 22:49:19 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Brent:1978:AMF,Brent:1979:RMF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "arithmetic, multiple precision, extended precision,
                 floating point, portable software, software package,
                 precompiler interface, AUGMENT interface",
}

@InProceedings{Brent:1980:UAE,
  author =       "R. P. Brent",
  title =        "Unrestricted Algorithms for Elementary and Special
                 Functions",
  crossref =     "Lavington:1980:IPP",
  pages =        "613--619",
  year =         "1980",
  bibdate =      "Thu Sep 01 11:55:31 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Brown:1980:EPB,
  author =       "W. S. Brown and S. I. Feldman",
  title =        "Environment Parameters and Basic Functions for
                 Floating-Point Computation",
  journal =      j-TOMS,
  volume =       "6",
  number =       "4",
  pages =        "510--523",
  month =        dec,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355921.355924",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Sep 1 10:15:05 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "environment parameters, floating-point arithmetic,
                 software portability",
}

@TechReport{Brown:1980:SRM,
  author =       "W. S. Brown",
  title =        "A Simple But Realistic Model of Floating-Point
                 Computation",
  type =         "Computer Science Technical Report",
  number =       "83",
  institution =  "Bell Laboratories",
  address =      "Murray Hill, NJ, 07974, USA",
  month =        may,
  year =         "1980",
  bibdate =      "Wed Oct 13 06:30:12 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Revised November 1980.",
  acknowledgement = ack-nhfb,
  remark =       "See \cite[pp. 1.9--1.10]{Coonen:1984:CPS} for negative
                 comments about the model in this report.",
}

@Article{Burmeister:1980:OIE,
  author =       "W. Burmeister",
  title =        "Optimal interval enclosing of certain sets of
                 matrices, with application to monotone enclosing of
                 square roots",
  journal =      j-COMPUTING,
  volume =       "25",
  number =       "3",
  pages =        "283--295",
  year =         "1980",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65F30 (15A57)",
  MRnumber =     "82e:65044",
  bibdate =      "Tue Jan 2 17:40:54 MST 2001",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 INSPEC Axiom database (1968--date); MathSciNet
                 database",
  acknowledgement = ack-nhfb,
  affiliation =  "Sektion Math., Tech. University of Dresden, Dresden,
                 East Germany",
  classification = "C4140",
  description =  "matrix algebra",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "cone; elementwise inclusion; interval enclosing;
                 matrix interval; optimal bounds; partial ordering",
}

@Article{Bursky:1980:CIF,
  author =       "Dave Bursky",
  title =        "Coprocessor implements floating-point math",
  journal =      j-ELECTRONIC-DESIGN,
  volume =       "28",
  pages =        "35--37",
  day =          "10",
  month =        may,
  year =         "1980",
  CODEN =        "ELODAW",
  ISSN =         "0013-4872 (print), 1944-9550 (electronic)",
  ISSN-L =       "0013-4872",
  bibdate =      "Sat Aug 23 06:46:22 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Summary of Intel 8087 features in an early trade press
                 note.",
  URL =          "https://ieeemilestones.ethw.org/w/images/b/b6/Electronic_Design_8087_May80.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronic Design",
}

@Article{Chang:1980:CAE,
  author =       "T. Chang",
  title =        "Comments on {``An} approach to eliminate roundoff
                 errors in digital filters''",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "28",
  number =       "2",
  pages =        "244--244",
  month =        apr,
  year =         "1980",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
}

@InProceedings{Cheng:1980:ASC,
  author =       "S. Cheng and K. Rallapalli",
  title =        "Am9512: Single Chip Floating-Point Processor",
  crossref =     "Electro:1980:ECR",
  pages =        "14/4/1--6",
  year =         "1980",
  bibdate =      "Wed Sep 7 22:31:27 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  remark =       "The Am 9512 floating-point processor is claimed on at
                 least one Web page to be compatible with the Intel
                 8232, and that page claims the 8232 has IEEE
                 floating-point, while the earlier 8231 and 8231A were
                 some other format (see \cite{Intel:19xx:IAP} for a
                 brief description of the 8231A 32-bit floating-point
                 encoding).",
}

@PhdThesis{Chow:1980:VPP,
  author =       "Catherine Yuk-Fun Chow",
  title =        "A variable precision processor module",
  type =         "Thesis ({Ph.D.})",
  school =       "Department of Computer Science, University of Illinois
                 at Urbana-Champaign",
  address =      "Urbana, IL, USA",
  pages =        "vi + 183",
  month =        jul,
  year =         "1980",
  LCCN =         "QA76 .I4 no. 1032",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "UIUCDCS-R 80-1032",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  keywords =     "Floating-point arithmetic.; Parallel processing
                 (Electronic computers)",
}

@Article{Cluley:1980:DCB,
  author =       "J. C. Cluley",
  title =        "Digital Circuits for Binary Arithmetic",
  journal =      j-COMP-J,
  volume =       "23",
  number =       "3",
  pages =        "269--269",
  month =        aug,
  year =         "1980",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/23.3.269",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:48:08 MST 2012",
  bibsource =    "http://comjnl.oxfordjournals.org/content/23/3.toc;
                 https://www.math.utah.edu/pub/tex/bib/compj1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/23/3/269.full.pdf+html",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Book{Cody:1980:SME,
  author =       "William J. {Cody, Jr.} and William Waite",
  title =        "Software Manual for the Elementary Functions",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "x + 269",
  year =         "1980",
  ISBN =         "0-13-822064-6",
  ISBN-13 =      "978-0-13-822064-8",
  LCCN =         "QA331 .C635 1980",
  bibdate =      "Tue Dec 14 23:28:38 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "Preface / ix \\
                 1. Introduction / 1 \\
                 2. Preliminaries / 3 \\
                 3. Performance Testing / 11 \\
                 4. SQRT / 17 \\
                 5. ALOG/ALOG10 / 35 \\
                 6. EXP / 60 \\
                 7. POWER (**) / 84 \\
                 8. SIN/COS / 125 \\
                 9. TAN/COT / 150 \\
                 10. ASIN/ACOS / 174 \\
                 11. ATAN/ATAN2 / 194 \\
                 12. SINH/COSH / 217",
  tableofcontents = "Preface / ix \\
                 1. Introduction / 1 \\
                 2. Preliminaries / 3 \\
                 3. Performance Testing / 11 \\
                 4. SQRT / 17 \\
                 a. General Discussion / 17 \\
                 b. Flow Chart for SQRT(X) / 18 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 19 \\
                 d. Implementation Notes, Binary Floating-Point Machines
                 / 23 \\
                 e. Implementation Notes, Non-Binary Floating-Point
                 Machines / 25 \\
                 f. Testing / 28 \\
                 5. ALOG/ALOG10 / 35 \\
                 a. General Discussion / 35 \\
                 b. Flow Chart for ALOG(X)/ALOG10(X) / 37 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 38 \\
                 d. Implementation Notes, Non-Decimal Floating-Point
                 Machines / 42 \\
                 e. Implementation Notes, Decimal Floating-Point
                 Machines / 46 \\
                 f. Testing / 49 \\
                 6. EXP / 60 \\
                 a. General Discussion / 60 \\
                 b. Flow Chart for EXP(X) / 62 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 63 \\
                 d. Implementation Notes, Non-Decimal Floating-Point
                 Machines / 67 \\
                 e. Implementation Notes, Decimal Floating-Point
                 Machines / 71 \\
                 f. Testing / 75 \\
                 7. POWER (**) / 84 \\
                 a. General Discussion / 84 \\
                 b. Flow Chart for POWER(X,Y) / 88 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 90 \\
                 d. Implementation Notes, Non-Decimal Floating-Point
                 Machines / 97 \\
                 e. Implementation Notes, Decimal Floating-Point
                 Machines / 106 \\
                 f. Testing / 113 \\
                 8. SIN/COS / 125 \\
                 a. General Discussion / 125 \\
                 b. Flow Chart for SIN(X)/COS(X) / 127 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 129 \\
                 d. Implementation Notes, All Floating-Point Machines /
                 134 \\
                 e. Testing / 139 \\
                 9. TAN/COT / 150 \\
                 a. General Discussion / 150 \\
                 b. Flow Chart for TAN(X)/COTAN(X) / 152 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 154 \\
                 d. Implementation Notes, All Floating-Point Machines /
                 159 \\
                 e. Testing / 164 \\
                 10. ASIN/ACOS / 174 \\
                 a. General Discuss i on / 174 \\
                 b. Flow Chart for AS IN(X)/ACOS(X) / 176 \\
                 c. Implementation Not es, Non-Decimal Fixed-Point
                 Machines / 177 \\
                 d. Implementation Notes, All Floating-Point Machines /
                 181 \\
                 e. Testing / 185 \\
                 11. ATAN/ATAN2 / 194 \\
                 a. General Discussion / 194 \\
                 b. Flow Chart for ATAN(X)/ATAN2(V,U) / 196 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 198 \\
                 d. Implementation Notes, All Floating-Point Machines /
                 203 \\
                 e. Testing / 207 \\
                 12. SINH/COSH / 217 \\
                 a. General Discussion / 217 \\
                 b. Flow Chart for SINH(X)/COSH(X) / 220 \\
                 c. Implementation Notes, Non-Decimal Fixed-Point
                 Machines / 221 \\
                 d. Implementation Notes, All Floating-Point Machines /
                 225 \\
                 e. Testing / 229",
}

@Article{Coonen:1980:IGP,
  author =       "Jerome T. Coonen",
  title =        "An Implementation Guide to a Proposed Standard for
                 Floating-Point Arithmetic",
  journal =      j-COMPUTER,
  volume =       "13",
  number =       "1",
  pages =        "68--79",
  month =        jan,
  year =         "1980",
  CODEN =        "CPTRB4",
  DOI =          "https://doi.org/10.1109/MC.1980.1653344",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Sun May 02 09:17:48 1999",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/computer1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See errata in \cite{Coonen:1981:EIG}. See
                 \cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
  acknowledgement = ack-nj,
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}

@Article{Dao:1980:CNA,
  author =       "T. T. Dao and M. Davio and C. Gossart",
  title =        "Complex Number Arithmetic with Odd-Valued Logic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-29",
  number =       "7",
  pages =        "604--611",
  month =        jul,
  year =         "1980",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1980.1675631",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 19:15:27 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675631",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{DeVaal:1980:SZI,
  author =       "C. {De Vaal} and R. Nouta",
  title =        "On the suppression of zero-input parasitic
                 oscillations in floating point wave digital filters",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "27",
  number =       "2",
  pages =        "144--145",
  month =        feb,
  year =         "1980",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "Fettweis [1] has given a condition which guarantees,
                 if satisfied, the absence of zero-input parasitic
                 oscillations in wave digital filters. In this paper a
                 method is given which can be used to implement this
                 condition in the case of floating point \ldots{}",
}

@Article{Etzel:1980:RRN,
  author =       "M. Etzel and W. Jenkins",
  title =        "Redundant residue number systems for error detection
                 and correction in digital filters",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "28",
  number =       "5",
  pages =        "538--545",
  month =        oct,
  year =         "1980",
  CODEN =        "IETABA",
  DOI =          "https://doi.org/10.1109/TC.1979.1675263",
  ISSN =         "0096-3518",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26148",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  keywords =     "residue arithmetic; residue number system",
  summary =      "In spite of rapid advances during the last few years
                 in the design and realization of digital filters, very
                 little attention has been given to the problems of
                 error detection and correction in digital filters. This
                 paper describes how redundant \ldots{}",
}

@InProceedings{Farrell:1980:PFP,
  author =       "L. Farrell",
  title =        "8232: a Peripheral for Floating-Point Arithmetic",
  crossref =     "IEEE:1980:PMA",
  pages =        "13--18",
  year =         "1980",
  bibdate =      "Wed Sep 07 22:25:18 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Unpublished{Fraley:1980:PSB,
  author =       "R. A. Fraley and J. S. Walther",
  title =        "A Proposed Standard for Binary Floating-Point
                 Arithmetic, Alternative 3, Draft 1",
  day =          "4",
  month =        jan,
  year =         "1980",
  bibdate =      "Thu Nov 25 10:19:54 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Cited in \cite{Payne:1980:VFPb}.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Fraley:1980:STO,
  author =       "R. A. Fraley and J. S. Walther",
  title =        "Safe Treatment of Overflow and Underflow Conditions",
  crossref =     "Electro:1980:ECR",
  pages =        "18/2/1--5",
  year =         "1980",
  bibdate =      "Wed Sep 07 21:38:30 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Gajski:1980:PC,
  author =       "D. D. Gajski",
  title =        "Parallel Compressors",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-29",
  number =       "5",
  pages =        "393--398",
  month =        may,
  year =         "1980",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1980.1675589",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 10:56:18 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Gargantini:1980:PSR,
  author =       "Irene Gargantini",
  title =        "Parallel Square-Root Iterations for Multiple Roots",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "6",
  number =       "3",
  pages =        "279--288",
  month =        "????",
  year =         "1980",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 18:51:19 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122180900358",
  acknowledgement = ack-jr # " and " # ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221/",
}

@Article{Ginsberg:1980:MFE,
  author =       "Myron Ginsberg",
  title =        "Monitoring floating-point error propagation in
                 scientific computation",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "6",
  number =       "1",
  pages =        "23--43",
  year =         "1980",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  MRclass =      "65G10 (65-04)",
  MRnumber =     "82a:65031",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  xxnote =       "Special Issue",
}

@Article{Ginsberg:1980:MFP,
  author =       "Myron Ginsberg",
  title =        "Monitoring Floating-Point Error Propagation in
                 Scientific Computation",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "6",
  number =       "1",
  pages =        "23--43",
  month =        "????",
  year =         "1980",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(80)90057-7",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  MRclass =      "65G10 (65-04)",
  MRnumber =     "82a:65031",
  bibdate =      "Wed Mar 1 18:51:18 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122180900577",
  acknowledgement = ack-jr # " and " # ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221/",
  keywords =     "AUGMENT preprocessor; error propagation; interval
                 analysis; rounding error; Yohe interval analysis
                 package",
  xxnote =       "Special Issue",
}

@Article{Goodwin:1980:PNU,
  author =       "D. T. Goodwin",
  title =        "Partial Non-Underflow and Non-Overflow of an
                 Arithmetic Stack",
  journal =      j-COMP-J,
  volume =       "23",
  number =       "2",
  pages =        "153--160",
  month =        may,
  year =         "1980",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/23.2.153",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  MRclass =      "68B20",
  MRnumber =     "81i:68039",
  bibdate =      "Tue Dec 4 14:48:08 MST 2012",
  bibsource =    "Compendex database;
                 http://comjnl.oxfordjournals.org/content/23/2.toc;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/;
                 https://www.math.utah.edu/pub/tex/bib/compj1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/23/2/153.full.pdf+html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/153.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/154.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/155.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/156.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/157.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/158.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/159.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_23/Issue_02/tiff/160.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C6150J (Operating systems)",
  classification = "723",
  corpsource =   "Department of Computer Sci., University of Keele,
                 Newcastle-under-Lyme, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "arithmetic stack; computer programming; high level
                 language compile time; overflow; stack; storage
                 allocation; underflow",
  reviewer =     "K. S. Fu",
  treatment =    "P Practical",
}

@Book{Gosling:1980:DAU,
  author =       "John B. Gosling",
  title =        "Design of Arithmetic Units for Digital Computers",
  publisher =    pub-MAC,
  address =      pub-MAC:adr,
  pages =        "x + 139",
  year =         "1980",
  ISBN =         "0-387-91171-5, 0-333-26397-9, 0-333-26398-7",
  ISBN-13 =      "978-0-387-91171-7, 978-0-333-26397-6,
                 978-0-333-26398-3",
  LCCN =         "QA76.6.G668, TK7888.3 .G64 1980",
  bibdate =      "Wed Sep 07 20:43:22 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  tableofcontents = "Front Matter / iii--x \\
                 Preliminary Notes / 1--5 \\
                 Addition / 6--21 \\
                 Multiplication / 22--38 \\
                 Negative Numbers and Their Effect on Arithmetic /
                 39--54 \\
                 Division / 55--73 \\
                 Floating Point Operation / 74--104 \\
                 Other Functions of the Arithmetic Unit / 105--114 \\
                 Practical Design Problems / 115--119 \\
                 Mathematical Functions and Array Processing / 120--129
                 \\
                 Back Matter / 130--139",
}

@Article{Grappel:1980:IZP,
  author =       "R. Grappel and J. Hemenway",
  title =        "Increase {Z8000} power with floating-point routines",
  journal =      j-EDN,
  volume =       "25",
  number =       "8",
  pages =        "179--185",
  month =        apr,
  year =         "1980",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 1 10:15:06 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}

@Book{Gregory:1980:ECW,
  author =       "Robert Todd Gregory",
  title =        "Error-Free Computation: Why it is Needed and Methods
                 for Doing it",
  publisher =    pub-R-E-KRIEGER,
  address =      pub-R-E-KRIEGER:adr,
  pages =        "vi + 152",
  year =         "1980",
  ISBN =         "0-89874-240-4",
  ISBN-13 =      "978-0-89874-240-4",
  LCCN =         "QA297.5 .G73",
  MRclass =      "65G05",
  MRnumber =     "MR586772 (83f:65061)",
  bibdate =      "Sat Sep 03 10:09:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Approximation theory --- Data processing;
                 Floating-point arithmetic",
  tableofcontents = "1: Mathematics vs. Numerical Mathematics \\
                 2: Ill-Conditioned Problems vs. Numerically Unstable
                 Algorithms \\
                 3: A Scaling Problem \\
                 4: ?? \\
                 5: ?? \\
                 Index",
}

@Article{Gruner:1980:IUC,
  author =       "K. Gr{\"u}ner",
  title =        "Implementation of Universal Computer Arithmetic with
                 Optimal Accuracy",
  journal =      j-COMPUTING,
  volume =       "24",
  number =       "2--3",
  pages =        "181--193",
  year =         "1980",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65G99 (68A05)",
  MRnumber =     "83c:65118",
  bibdate =      "Tue Jan 2 17:40:54 MST 2001",
  bibsource =    "Compendex database;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 INSPEC Axiom database (1968--date); MathSciNet
                 database",
  acknowledgement = ack-nhfb,
  affiliation =  "University of Karlsruhe, Karlsruhe, West Germany",
  classification = "C4240",
  description =  "computational complexity",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Computing (Vienna/New York)",
  keywords =     "computer arithmetic; computer programming; fast
                 algorithms; intervals; mapping properties; matrices;
                 numerical computations; universal computer arithmetic;
                 vectors; word length",
}

@TechReport{Hamacher:1980:DCV,
  author =       "V. Carl Hamacher",
  title =        "Design of a {CPU} for variable precision, decimal
                 arithmetic",
  type =         "Technical Report",
  number =       "ABC",
  institution =  "Department of Electrical Engineering, University of
                 Toronto",
  address =      "Toronto, ON, Canada",
  month =        "????",
  year =         "1980",
  bibdate =      "Sun Dec 30 15:37:50 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal arithmetic",
}

@Article{Havender:1980:DBF,
  author =       "J. W. Havender",
  title =        "Decimal-to-binary floating point number conversion
                 mechanism",
  journal =      j-IBM-TDB,
  volume =       "23",
  number =       "2",
  pages =        "706--708",
  month =        jul,
  year =         "1980",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:16:10 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Floating point numbers may be converted from decimal
                 to binary using a high speed natural logarithm and
                 exponential function calculation mechanism and a fixed
                 point divide/multiply unit.\par

                 The problem solved is to convert numbers expressed in a
                 radix 10 floating point form to numbers expressed in a
                 radix 2 floating point form.",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
  keywords =     "decimal floating-point arithmetic",
}

@Article{Havender:1980:DBN,
  author =       "J. W. Havender",
  title =        "Decimal-to-binary Number Conversion",
  journal =      j-IBM-TDB,
  volume =       "23",
  number =       "3",
  pages =        "1126--1127",
  month =        aug,
  year =         "1980",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:16:10 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
  keywords =     "decimal floating-point arithmetic",
}

@Article{Haviland:1980:CAPa,
  author =       "G. L. Haviland and A. A. Tuszynski",
  title =        "A {CORDIC} Arithmetic Processor Chip",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-29",
  number =       "2",
  pages =        "68--79",
  month =        feb,
  year =         "1980",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1980.1675529",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675529",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Haviland:1980:CAPb,
  author =       "G. L. Haviland and A. A. Tuszynski",
  title =        "A {CORDIC} Arithmetic Processor Chip",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "15",
  number =       "1",
  pages =        "4--15",
  year =         "1980",
  CODEN =        "IJSCBC",
  DOI =          "https://doi.org/10.1109/JSSC.1980.1051332",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "Application software; Arithmetic; CMOS technology;
                 Cost function; Equations; Hardware; Instruments;
                 Mathematics; Navigation; Read only memory",
}

@Article{Head:1980:MM,
  author =       "A. K. Head",
  title =        "Multiplication modulo $n$",
  journal =      j-BIT,
  volume =       "20",
  number =       "1",
  pages =        "115--116",
  month =        mar,
  year =         "1980",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01933594",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "68-04 (65G10)",
  MRnumber =     "81g:68001",
  MRreviewer =   "K. Kilberth",
  bibdate =      "Wed Jan 4 18:52:16 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=20&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=20&issue=1&spage=115",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Hehner:1980:CNR,
  author =       "E. C. R. Hehner and R. N. S. Horspool",
  title =        "Corrigendum: {``A new representation of the rational
                 numbers for fast easy arithmetic'' [SIAM J. Comput.
                 {\bf 8} (1979), no. 2, 124--134, MR 80h:68027]}",
  journal =      j-SIAM-J-COMPUT,
  volume =       "9",
  number =       "1",
  pages =        "217--217",
  month =        "????",
  year =         "1980",
  CODEN =        "SMJCAT",
  ISSN =         "0097-5397 (print), 1095-7111 (electronic)",
  ISSN-L =       "0097-5397",
  MRclass =      "68C05 (10A30)",
  MRnumber =     "81f:68044",
  bibdate =      "Mon Nov 29 10:59:12 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/9/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Hehner:1979:NRR}.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Computing",
  journal-URL =  "http://epubs.siam.org/sicomp",
}

@Article{Henrich:1980:FPA,
  author =       "C. J. Henrich",
  title =        "Floating-point arithmetic: can it be trusted?",
  journal =      j-MINI-MICRO-SYSTEMS,
  volume =       "13",
  number =       "11",
  pages =        "143--151",
  month =        nov,
  year =         "1980",
  CODEN =        "XWJXEH",
  ISSN =         "1000-1220",
  bibdate =      "Wed Sep 14 19:14:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Mini-Micro Systems",
}

@InProceedings{Henrici:1980:MPR,
  author =       "Peter Henrici",
  booktitle =    "Interval mathematics, 1980 ({Freiburg}, 1980)",
  title =        "A model for the propagation of rounding error in
                 floating arithmetic",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "49--73",
  year =         "1980",
  DOI =          "https://doi.org/10.1016/B978-0-12-518850-0.50009-3",
  ISBN =         "0-12-518850-1",
  ISBN-13 =      "978-0-12-518850-0",
  MRclass =      "65G05",
  MRnumber =     "651358",
  bibdate =      "Mon Jan 28 07:08:10 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/B9780125188500500093",
  abstract =     "The subject of propagation of rounding error, while of
                 undisputed importance in numerical analysis, is
                 notorious for the difficulties that it presents when it
                 is to be taught in the classroom in such a manner that
                 the student is neither insulted by lack of mathematical
                 content nor bored by lack of transparence and clarity.
                 On examination of some classical approaches, it appears
                 that the effect of tedium is often achieved by the
                 attempt of being absolutely rigorous. Absolute rigor in
                 error analysis is a triviality. Perhaps, what is
                 required in error analysis is not so much rigor but
                 rather an understanding why some algorithms work and
                 others do not. This chapter presents a model for the
                 propagation of rounding error in floating arithmetic
                 that aims at such an understanding. To bring to light
                 the essential consequences of floating arithmetic, the
                 model makes certain idealizing or simplifying
                 assumptions that are not always satisfied on real-life
                 computers. The model nevertheless furnishes realistic
                 descriptions of the numerical performance of a large
                 class of algorithms that can be described in terms of
                 operations on real numbers.",
  acknowledgement = ack-nhfb,
  author-dates = "Peter Karl Henrici (13 September 1923--13 March
                 1987)",
}

@PhdThesis{Holm:1980:FAP,
  author =       "John Erick Holm",
  title =        "Floating-point arithmetic and program correctness
                 proofs",
  type =         "Thesis ({Ph.D.})",
  school =       "Cornell University",
  address =      "Ithaca, NY, USA",
  pages =        "vii + 133",
  month =        aug,
  year =         "1980",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.",
}

@Article{Horna:1980:FAC,
  author =       "O. A. Horna",
  title =        "Fast algorithms for the computation of binary
                 logarithms",
  journal =      "COMSAT Technical Review",
  volume =       "10",
  number =       "1",
  pages =        "91--101",
  month =        "Spring",
  year =         "1980",
  bibdate =      "Thu Sep 1 10:16:09 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@InProceedings{Hough:1980:APS,
  author =       "D. Hough",
  title =        "Applications of a Proposed Standard for Floating-Point
                 Arithmetic",
  crossref =     "Electro:1980:ECR",
  pages =        "18/3/1--6",
  year =         "1980",
  bibdate =      "Wed Sep 07 21:39:26 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@TechReport{Hull:1980:PPI,
  author =       "Thomas E. Hull and Christian H. Reinsch and John R.
                 Rice",
  title =        "Principles, Preferences and Ideals for Computer
                 Arithmetic",
  type =         "Technical report",
  number =       "TR-339",
  institution =  inst-CS-PURDUE,
  address =      inst-CS-PURDUE:adr,
  pages =        "13",
  day =          "1",
  month =        jun,
  year =         "1980",
  bibdate =      "Sun Dec 30 13:46:29 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.purdue.edu/research/technical_reports/1980/TR%2080-339.pdf",
  abstract =     "This paper presents principles and preferences for the
                 implementation of computer arithmetic and ideals for
                 the arithmetic facilities in future programming
                 languages. The implementation principles and
                 preferences are for the current approaches to the
                 design of arithmetic units. The ideals are for the long
                 term development of programming languages, with the
                 hope that arithmetic units will be built to support the
                 requirements of programming languages.",
  acknowledgement = ack-nhfb,
  author-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022)",
  keywords =     "decimal floating-point arithmetic",
}

@Manual{Intel:1980:FUM,
  author =       "{Intel Corporation}",
  title =        "The 8086 Family User's Manual: Numerics Supplement",
  organization = pub-INTEL,
  address =      pub-INTEL:adr,
  pages =        "xii + S-88 + A-5 + B-16 (132 total)",
  month =        jul,
  year =         "1980",
  bibdate =      "Sat Aug 23 06:09:50 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeemilestones.ethw.org/w/images/2/2f/Intel_8086_family_users_numeric_supp.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Jenkins:1980:CRN,
  author =       "W. K. Jenkins",
  title =        "Complex residue number arithmetic for high-speed
                 signal processing",
  journal =      j-ELECT-LETTERS,
  volume =       "16",
  number =       "17",
  pages =        "660--661",
  day =          "14",
  month =        aug,
  year =         "1980",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:19800468",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  MRclass =      "94A05",
  MRnumber =     "MR583226 (81h:94003)",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4244229",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Complex residue number arithmetic is developed for
                 high-speed processing of complex waveforms. An
                 important feature of complex residue arithmetic is that
                 complex multiplication can be implemented by a real
                 index calculus, thereby providing a highly \ldots{}",
}

@Article{Johannes:1980:DSE,
  author =       "J. D. Johannes and C. Dennis Pegden and F. E. Petry",
  title =        "Decimal Shifting for an Exact Floating Point
                 Representation",
  journal =      j-COMPUT-ELECTR-ENG,
  volume =       "7",
  number =       "3",
  pages =        "149--155",
  month =        sep,
  year =         "1980",
  CODEN =        "CPEEBQ",
  ISSN =         "0045-7906 (print), 1879-0755 (electronic)",
  ISSN-L =       "0045-7906",
  bibdate =      "Fri Nov 28 11:42:59 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Electrical Engineering",
  keywords =     "decimal floating-point arithmetic",
}

@Article{Johnson:1980:DQS,
  author =       "E. L. Johnson",
  title =        "A Digital Quarter Square Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-29",
  number =       "3",
  pages =        "258--261",
  month =        mar,
  year =         "1980",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1980.1675558",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 19:15:24 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675558",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Jullien:1980:IMM,
  author =       "G. A. Jullien",
  title =        "Implementation of Multiplication, Modulo a Prime
                 Number, with Applications to Number Theoretic
                 Transforms",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-29",
  number =       "10",
  pages =        "899--905",
  month =        oct,
  year =         "1980",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1980.1675473",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 19:15:29 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675473",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Kahan:1980:HCE,
  author =       "William M. Kahan",
  title =        "Handheld Calculator Evaluates Integrals",
  journal =      j-HEWLETT-PACKARD-J,
  volume =       "31",
  number =       "8",
  pages =        "23--32",
  month =        aug,
  year =         "1980",
  CODEN =        "HPJOAX",
  ISSN =         "0018-1153",
  MRclass =      "65-04 (65D30)",
  MRnumber =     "MR590837 (82d:65001)",
  MRreviewer =   "S. Dubuc",
  bibdate =      "Tue Mar 25 14:12:15 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/hpj.bib",
  note =         "Lecture notes for Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/INTGTkey.pdf",
  acknowledgement = ack-nhfb,
  classcodes =   "C4160 (Numerical integration and differentiation);
                 C5230 (Digital arithmetic methods)",
  corpsource =   "Hewlett--Packard Co., Palo Alto, CA, USA",
  fjournal =     "Hewlett--Packard Journal",
  keywords =     "34C; digital arithmetic; handheld calculator; HP;
                 integrals; integration; numerical integration;
                 numerical methods",
  reviewer =     "S. Dubuc",
  treatment =    "G General Review; P Practical",
}

@Unpublished{Kahan:1980:SPI,
  author =       "W. Kahan",
  title =        "Software $ \sqrt x $ for the Proposed {IEEE}
                 Floating-Point Standard",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  day =          "25",
  month =        aug,
  year =         "1980",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kleinsteiber:1980:IHM,
  author =       "James R. Kleinsteiber",
  title =        "{IBM} 4341 hardware\slash microcode trade-off
                 decisions",
  crossref =     "Johnson:1980:MPA",
  pages =        "190--192",
  year =         "1980",
  bibdate =      "Thu Aug 07 18:22:42 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The design of IBM's 4341 Processor, as with other
                 processors, involved many cost/performance tradeoffs.
                 The designer is continually under pressure to increase
                 processor speed without increasing cost or to decrease
                 processor cost without decreasing performance. This
                 paper will examine some of the engineering decisions
                 that were made in the attempt to make the 4341 a
                 high-performing yet low cost processor. These decisions
                 include searching for, or developing, algorithms that
                 make the best use of hardware properties, such as data
                 path width, arithmetic/logical operations and special
                 functions. Functions were sought such that a small
                 amount of added hardware would go a long way towards
                 improving system performance. Hardware designers,
                 microcoders and performance analysis people worked
                 together to implement instructions, functions and
                 algorithms with the proper mixture of hardware
                 functions and microcode in order to build a viable
                 processor. Some specific functions will be covered to
                 examine a few of the decisions. The TEST UNDER MASK
                 performance problem will be discussed with its
                 resulting implementation decision. The method of using
                 EXCLUSIVE OR to clear storage and the resulting
                 algorithm design will be shown. Other topics to be
                 discussed include multiple hardware functions and the
                 resulting effect on floating point, fixed point and
                 decimal multiply; the divide function and its effect on
                 floating point and fixed point divide; and the effect
                 of an 8-byte data path for decimal arithmetic.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal arithmetic",
}

@InProceedings{Kulisch:1980:AOI,
  author =       "U. W. Kulisch and W. L. Miranker",
  title =        "Arithmetic Operations in Interval Spaces",
  crossref =     "Alefeld:1980:FNC",
  pages =        "51--67",
  year =         "1980",
  bibdate =      "Tue Oct 23 08:17:48 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "interval arithmetic",
}

@Article{Ladner:1980:PPC,
  author =       "Richard E. Ladner and Michael J. Fischer",
  title =        "Parallel Prefix Computation",
  journal =      j-J-ACM,
  volume =       "27",
  number =       "4",
  pages =        "831--838",
  month =        oct,
  year =         "1980",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/322217.322232",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Wed Oct 26 22:55:08 1994",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/Par.Arch.Indep.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jacm.bib",
  abstract =     "The prefix problem is to compute all the products $
                 x_1 * x_2 * \cdots * x_k $ for $ 1 \leq k \leq n $,
                 where $*$ is an associative operation. A recursive
                 construction is used to obtain a product circuit for
                 solving the prefix problem which has depth exactly $
                 \lceil \log n \rceil $ and size bounded by $ 4 n $ An
                 application yields fast, small Boolean circuits to
                 simulate finite-state transducers. By simulating a
                 sequential adder, a Boolean circuit which has depth $ 2
                 \lceil \log_2 n \rceil + 2 $ and size bounded by $ 14 n
                 $ is obtained for $n$-bit binary addition. The size can
                 be decreased significantly by permitting the depth to
                 increase by an additive constant.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the Association for Computing Machinery",
  journal-URL =  "https://dl.acm.org/loi/jacm",
}

@Article{Lemaire:1980:INR,
  author =       "C. A. Lemaire and J. C. Svercek",
  title =        "Improved Non-restoring Division",
  journal =      j-IBM-TDB,
  volume =       "23",
  number =       "3",
  pages =        "1149--1151",
  month =        aug,
  year =         "1980",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
}

@Book{Levy:1980:CPA,
  author =       "Henry M. Levy and Richard H. {Eckhouse, Jr.}",
  title =        "Computer Programming and Architecture --- the
                 {VAX-11}",
  publisher =    pub-DP,
  address =      pub-DP:adr,
  pages =        "xxi + 407",
  year =         "1980",
  ISBN =         "0-932376-07-X",
  ISBN-13 =      "978-0-932376-07-7",
  LCCN =         "QA76.8 .V37 L48 1980",
  bibdate =      "Wed Dec 15 10:38:14 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "Part 1: The user architecture \\
                 Architecture and implementation \\
                 Computer structures and elementary AX-11 programming
                 \\
                 Instruction and addressing fundamentals \\
                 More advanced programming techniques \\
                 Data types and data structures \\
                 Comparative architectures \\
                 Part 2: The system architecture \\
                 Physical input and output \\
                 The support of an operating system \\
                 The structure of a VAX-11 operating system \\
                 The operating system interface \\
                 The efficient implementation of an architecture",
}

@MastersThesis{Macke:1980:DMF,
  author =       "Edward T. Macke",
  title =        "Design of a modular floating point arithmetic unit",
  type =         "Thesis ({M.S.})",
  school =       "Washington University, Department of Electrical
                 Engineering",
  address =      "St. Louis, MO, USA",
  pages =        "ix + 174",
  year =         "1980",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Microprocessors --- Design
                 and construction.",
}

@InProceedings{Matula:1980:FFP,
  author =       "D. W. Matula",
  title =        "Foundations of Finite Precision Rational Arithmetic",
  crossref =     "Alefeld:1980:FNC",
  pages =        "85--111",
  year =         "1980",
  bibdate =      "Tue Oct 23 08:17:48 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "interval arithmetic; rational arithmetic",
}

@InProceedings{McMinn:1980:IND,
  author =       "C. McMinn",
  title =        "The {Intel 8087}: a Numeric Data Processor",
  crossref =     "Electro:1980:ECR",
  pages =        "14/5/1--8",
  year =         "1980",
  bibdate =      "Mon Sep 12 08:30:36 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Book{Mead:1980:IVS,
  author =       "Carver Mead and Lynn Conway",
  title =        "Introduction to {VLSI} Systems",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "xvi + 396",
  year =         "1980",
  ISBN =         "0-201-04358-0",
  ISBN-13 =      "978-0-201-04358-7",
  LCCN =         "TK7874 .M371",
  bibdate =      "Mon Sep 16 16:25:00 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "MOS devices and circuits \\
                 Integrated system fabrication \\
                 Data and control flow in systematic structures \\
                 Implementing integrated system designs: from circuit
                 topology to patterning geometry to wafer fabrication
                 \\
                 Overview of an LSI computer system, and the design of
                 the OM2 data path chip \\
                 Architecture and design of system controllers, and the
                 design of the OM2 controller chip \\
                 System timing \\
                 Highly concurrent systems \\
                 Physics of computational systems",
}

@Article{Meinardus:1980:OPN,
  author =       "G{\"u}nter Meinardus and G. D. Taylor",
  title =        "Optimal Partitioning of {Newton}'s Method for
                 Calculating Roots",
  journal =      j-MATH-COMPUT,
  volume =       "35",
  number =       "152",
  pages =        "1221--1230",
  month =        oct,
  year =         "1980",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65H05 (41A30)",
  MRnumber =     "81j:65069",
  MRreviewer =   "Derek W. Arthur",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "C4130 (Interpolation and function approximation)",
  corpsource =   "Fachbereich Math., University of Siegen, Siegen, West
                 Germany",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "cube root; domain interval; function approximation;
                 iterative methods; method; Newton; optimal
                 partitioning; reciprocal square root; square root;
                 subinterval",
  treatment =    "A Application; T Theoretical or Mathematical",
}

@Article{Metropolis:1980:SIN,
  author =       "N. Metropolis",
  title =        "Summation of imprecise numbers",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "6",
  number =       "3",
  pages =        "297--299",
  year =         "1980",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(80)90037-1",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  MRclass =      "65U05",
  MRnumber =     "MR604094 (82d:65092)",
  bibdate =      "Sat Feb 8 10:29:40 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0458.65029",
  abstract =     "An algorithm is presented for computer summation of
                 imprecise numbers that may have quite disparate
                 magnitudes and variances. Each number is represented by
                 its expected value and variance. Exact numbers form a
                 subset and are treated in a consistent manner.
                 Cancellation effects are minimized.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers \& Mathematics with Applications. An
                 International Journal",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Moore:1980:MIA,
  author =       "R. E. Moore",
  title =        "Microprogrammed interval arithmetic",
  journal =      j-SIGNUM,
  volume =       "15",
  number =       "2",
  pages =        "30--30",
  month =        jun,
  year =         "1980",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:08 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}

@InProceedings{Nave:1980:NDP,
  author =       "Rafi Nave and John F. Palmer",
  title =        "A numeric data processor",
  crossref =     "IEEE:1980:IIS",
  pages =        "108--109",
  year =         "1980",
  DOI =          "https://doi.org/10.1109/ISSCC.1980.1156144e",
  bibdate =      "Wed Sep 07 22:22:14 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/document/1156144",
  acknowledgement = ack-nj,
  keywords =     "CORDIC algorithms; Intel 8086; Intel 8087; Intel
                 8088",
  remark =       "From the first page: ``This functionality is
                 implemented in HMOS on a single chip larger than 280
                 mils square containing the equivalent of over 65,000
                 devices. The internal evaluation stack requires more
                 than 700 bits of RAM and the microcode (including
                 constants) utilizes over 30,000 bits of ROM. This
                 amount of microcode was made possible by a four-state
                 ROM in HMOS. \ldots{} Performance was also enhanced by
                 a fast shifter (0 to 63 places in one clock), special
                 hardware for counting leading zeros and a hardware
                 module to implement the various rounding modes
                 specified in the proposed standard. \ldots{} The
                 transcendental functions are all computed with an error
                 of less than 3 units in the last place of Temporary
                 Real (80b[its]).''",
}

@Article{North:1980:BRS,
  author =       "J. D. North",
  title =        "Book Review: a {Sixteenth Century} Polymath,
                 {{\booktitle{Wilhelm Schickard, 1592--1635: Astronom,
                 Geograph, Orientalist, Erfinder der Rechenmaschine}}}",
  journal =      j-J-HIST-ASTRON,
  volume =       "11",
  number =       "2",
  pages =        "138--140",
  month =        jun,
  year =         "1980",
  CODEN =        "JHSAA2",
  DOI =          "https://doi.org/10.1177/002182868001100210",
  ISSN =         "0021-8286 (print), 1753-8556 (electronic)",
  ISSN-L =       "0021-8286",
  bibdate =      "Mon Sep 29 17:17:57 MDT 2014",
  bibsource =    "http://jha.sagepub.com/content/11/2.toc;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jhistastron.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal for the History of Astronomy",
  journal-URL =  "https://journals.sagepub.com/home/JHA",
}

@InProceedings{Oberaigner:1980:AMG,
  author =       "W. Oberaigner",
  title =        "Algorithms for Multiplication with Given Precision",
  crossref =     "Alefeld:1980:FNC",
  pages =        "121--129",
  year =         "1980",
  bibdate =      "Tue Oct 23 08:17:48 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "interval arithmetic",
}

@InProceedings{Palmer:1980:IND,
  author =       "J. Palmer",
  title =        "The {Intel} 8087 Numeric Data Processor",
  crossref =     "Anonymous:1980:CPA",
  pages =        "174--181",
  year =         "1980",
  bibdate =      "Mon Sep 12 08:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "CORDIC algorithms",
}

@InProceedings{Palmer:1980:LIN,
  author =       "J. Palmer",
  title =        "An {LSI} Implementation of a New System for
                 Floating-Point Arithmetic",
  crossref =     "Electro:1980:ECR",
  pages =        "18/4/1--8",
  year =         "1980",
  bibdate =      "Wed Sep 7 22:31:27 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Palmer:1980:MMM,
  author =       "J. Palmer and R. Rave and C. Wymore and R. Koehler and
                 C. McMinn",
  title =        "Making Mainframe Mathematics Accessible to
                 Minicomputers",
  journal =      "Mini Computers, Electronics",
  volume =       "23",
  number =       "??",
  pages =        "??--??",
  day =          "8",
  month =        may,
  year =         "1980",
  bibdate =      "Sat Oct 18 14:54:24 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Misc{Palmer:1980:UND,
  author =       "John F. Palmer and Bruce W. Ravenel and Rafi Nave",
  title =        "{US4338675}: Numeric data processor",
  howpublished = "U.S. Patent",
  day =          "13",
  month =        feb,
  year =         "1980",
  bibdate =      "Sat Nov 09 10:23:07 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Published July 6, 1982. This patent was reissued on
                 July 2, 1991 as patent USRE33629.",
  abstract =     "A floating point, integrated, arithmetic circuit is
                 organized around a file format having a floating point
                 numeric domain exceeding that of any single or double
                 precision floating point numbers, long or short integer
                 words or BCD data upon which it must operate. As a
                 result the circuit has a greater reliability, range and
                 precision than ever previously achieved without
                 entailing additional circuit complexity. Reliability is
                 further enhanced by a systematic three bit rounding
                 field, and by including means for detecting every error
                 or exception condition with an optional expected
                 response provided thereto by hardware. As a result of
                 such organization, an unexpected increase of capacity
                 is achieved wherein transcendental functions can be
                 computed totally in hardware, and whereby mixed mode
                 arithmetic can be implemented without difficulty. The
                 numeric processor also includes a programmable shifter
                 capable of arbitrary numbers of bit and byte shifts in
                 a single clock cycle, as well as an arithmetic unit
                 capable of implementing multiplication, division,
                 modulo reduction and square roots directly in
                 hardware.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Payne:1980:VFPa,
  author =       "M. Payne and D. Bhandarkar",
  title =        "{VAX} Floating Point: a Solid Foundation for Numerical
                 Computation",
  crossref =     "Electro:1980:ECR",
  pages =        "18/1/1--12",
  year =         "1980",
  bibdate =      "Wed Sep 07 21:37:14 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://dl.acm.org/doi/pdf/10.1145/641845.641849",
  abstract =     "[From the first paragraph of the introduction] This
                 paper describes the environment provided by the
                 recently announced enhanced VAX floating point
                 architecture and compares it with the features
                 described in various proposals for an IEEE Floating
                 Point Standard. The IEEE Standards Committee created a
                 Working Group on Floating Point Arithmetic late in
                 1977. Four formal proposals for a floating point
                 standard have been submitted to the Working Group. Of
                 these, three have received extensive discussion. The
                 fourth describes a floating point system in which range
                 and precision are dynamically traded off against each
                 other in order to avoid overflow and underflow; it was
                 submitted after agreement had already been reached on
                 the basic specifications for a floating point
                 representation, and never received serious
                 consideration. The other three proposals are in
                 substantial agreement on the representation and
                 arithmetic for ordinary floating point numbers. There
                 has, however, been sharp disagreement on the handling
                 of exceptions and on how extra precision should be made
                 available for ``critical'' calculations.",
  acknowledgement = ack-nj,
}

@Article{Payne:1980:VFPb,
  author =       "Mary Payne and Dileep Bhandarkar",
  title =        "{VAX} floating point: a solid foundation for numerical
                 computation",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "8",
  number =       "4",
  pages =        "22--33",
  month =        jun,
  year =         "1980",
  CODEN =        "CANED2",
  DOI =          "https://doi.org/10.1145/641845.641849",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Sat Jun 24 12:02:21 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
}

@Article{Pedersen:1980:HBM,
  author =       "P. W. Pedersen",
  title =        "Hvordan beregner man kvadratroden? \toenglish {How do
                 you calculate the square root?} \endtoenglish",
  journal =      "Elektronik (Denmark)",
  volume =       "??",
  number =       "4",
  pages =        "18--21",
  month =        apr,
  year =         "1980",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Purtilo:1980:IAP,
  author =       "Jim Purtilo",
  title =        "On implementing arbitrary precision arithmetic in
                 {NIL}: an exercise in data abstraction",
  journal =      j-SIGSAM,
  volume =       "14",
  number =       "1",
  pages =        "14--18",
  month =        feb,
  year =         "1980",
  CODEN =        "SIGSBZ",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Wed Oct 5 08:31:56 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGSAM Bulletin",
  issue =        "??",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}

@Article{Rallapalli:1980:CMF,
  author =       "K. Rallapalli and J. Kroeger",
  title =        "Chips make fast math a snap for microprocessors",
  journal =      j-ELECTRONICS,
  volume =       "53",
  number =       "10",
  pages =        "153--157",
  month =        apr,
  year =         "1980",
  ISSN =         "0883-4989",
  bibdate =      "Wed Sep 07 22:27:11 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronics",
  journal-URL =  "https://www.mdpi.com/journal/electronics",
}

@Article{Reid:1980:CDP,
  author =       "John Reid",
  title =        "Complex double precision in association with {Fortran
                 77}",
  journal =      j-SIGNUM,
  volume =       "15",
  number =       "1",
  pages =        "16--17",
  month =        mar,
  year =         "1980",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:08 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages)",
  corpsource =   "Computer Sci. and Systems Div., AERE Harwell, UK",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "compilers; complex double precision arithmetic;
                 digital arithmetic; FORTRAN; FORTRAN 77; portability",
  treatment =    "P Practical",
}

@Article{Reid:1980:FMF,
  author =       "J. K. Reid",
  title =        "Functions for manipulating floating-point numbers",
  journal =      j-SIGPLAN,
  volume =       "15",
  number =       "6",
  pages =        "68--76",
  month =        jun,
  year =         "1980",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sat Apr 25 11:46:37 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods)",
  corpsource =   "Computer Sci. and Systems Div., AERE, Harwell, Didcot,
                 UK",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "complete computer programs; digital arithmetic;
                 floating point numbers; function manipulation;
                 portability; software portability",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Rink:1980:CPS,
  author =       "R. Rink",
  title =        "Correction to {``Performance of state regulator
                 systems with floating-point computation''}",
  journal =      j-IEEE-TRANS-AUTOMAT-CONTR,
  volume =       "25",
  number =       "3",
  pages =        "612--612",
  month =        jun,
  year =         "1980",
  CODEN =        "IETAA9",
  ISSN =         "0018-9286 (print), 1558-2523 (electronic)",
  ISSN-L =       "0018-9286",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Rink:1979:PSR}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Automatic Control",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
}

@PhdThesis{Rump:1980:KFM,
  author =       "Siegfried M. Rump",
  title =        "{Kleine Fehlerschranken bei Matrixproblemen}.
                 ({German}) [Small error bounds for matrix problems]",
  type =         "{Ph.D.} Thesis",
  school =       "Institut f{\"u}r Angewandte Mathematik der
                 Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "vi + 131 + 49",
  year =         "1980",
  bibdate =      "Fri Jan 06 07:57:41 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ti3.tuhh.de/rump/Research/topics.php#PhD",
  acknowledgement = ack-nhfb,
  keywords =     "accurate dot products; accurate floating-point
                 summation; long accumulator",
  language =     "German",
}

@InProceedings{Scherer:1980:SNR,
  author =       "R. Scherer and K. Zeller",
  title =        "Shorthand Notation for Rounding Errors",
  crossref =     "Alefeld:1980:FNC",
  pages =        "165--168",
  year =         "1980",
  bibdate =      "Tue Oct 23 08:17:48 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "interval arithmetic; rounding error",
}

@Manual{SOITA:1980:AIE,
  key =          "SOITA",
  title =        "{Applesoft II}: extended floating-point {BASIC}: quick
                 reference guide",
  organization = "Southwestern Ohio Instructional Television
                 Association",
  address =      "Oxford, OH, USA",
  year =         "1980",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "1 pamphlet",
  series =       "SOITA \#2008",
  acknowledgement = ack-nhfb,
  keywords =     "Apple II (Computer) --- Programming; BASIC (Computer
                 program language)",
}

@Article{Speiser:1980:RCZ,
  author =       "A. P. Speiser",
  title =        "The Relay Calculator {Z4}",
  journal =      j-ANN-HIST-COMPUT,
  volume =       "2",
  number =       "3",
  pages =        "242--245",
  month =        jul # "\slash " # sep,
  year =         "1980",
  CODEN =        "AHCOE5",
  DOI =          "https://doi.org/10.1109/MAHC.1980.10026",
  ISSN =         "0164-1239",
  ISSN-L =       "0164-1239",
  bibdate =      "Fri Nov 1 15:29:17 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://dlib.computer.org/an/books/an1980/pdf/a3242.pdf;
                 http://www.computer.org/annals/an1980/a3242abs.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of the History of Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
}

@Article{Stevenson:1980:RPI,
  author =       "David Stevenson",
  title =        "A report on the proposed {IEEE Floating Point Standard
                 (IEEE task p754)}",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "8",
  number =       "5",
  pages =        "11--12",
  month =        aug,
  year =         "1980",
  CODEN =        "CANED2",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Wed Nov 24 10:59:34 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
}

@Book{Stone:1980:ICA,
  editor =       "Harold S. Stone and Tien Chi Chen and Michael J. Flynn
                 and Samuel H. Fuller and others",
  title =        "Introduction to Computer Architecture",
  publisher =    "Science Research Associates",
  address =      "Chicago, IL, USA",
  edition =      "Second",
  pages =        "673",
  year =         "1980",
  ISBN =         "0-574-21225-6",
  ISBN-13 =      "978-0-574-21225-2",
  LCCN =         "QA76.9.A73 I57 1980",
  bibdate =      "Fri Nov 9 19:22:07 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  price =        "US\$16.95 (est.)",
  series =       "The SRA computer science series",
  acknowledgement = ack-nhfb,
  subject =      "Computer architecture",
  tableofcontents = "Part I: Basic computer architecture \\
                 Introduction / Harold S. Stone \\
                 Data representation / Herschel H. Loomis, Jr. \\
                 Microprocessor architecture / Thomas M. Whitney \\
                 Introduction to microcomputers / K. B. Magleby \\
                 Memory and storage / Richard E. Matick \\
                 Input/output processing / William G. Lane \\
                 Part II: Advanced topics \\
                 Stack computers / William M. McKeeman \\
                 Parallel computers / Harold S. Stone \\
                 Overlap and pipeline processing / Tien Chi Chen \\
                 Interpretation, microprogramming, and the control of a
                 computer / Michael J. Flynn \\
                 Performance evaluation / Samuel H. Fuller \\
                 Operating systems and computer architecture / Richard
                 L. Sites",
}

@InProceedings{Stone:1980:TFP,
  author =       "H. S. Stone",
  title =        "Towards a Floating-Point Standard",
  crossref =     "Electro:1980:ECR",
  pages =        "18/0/1--5",
  year =         "1980",
  bibdate =      "Wed Sep 07 21:33:52 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@InProceedings{Stummel:1980:REA,
  author =       "F. Stummel",
  title =        "Rounding Error Analysis of Elementary Numerical
                 Algorithms",
  crossref =     "Alefeld:1980:FNC",
  pages =        "169--195",
  year =         "1980",
  bibdate =      "Tue Aug 28 06:19:13 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "interval arithmetic; rounding error",
}

@Article{Swartzlander:1980:AUH,
  author =       "E. E. {Swartzlander, Jr.} and B. K. Gilbert",
  title =        "Arithmetic for Ultra-High-Speed Tomography",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-29",
  number =       "5",
  pages =        "341--353",
  month =        may,
  year =         "1980",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1980.1675584",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 19:15:25 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675584",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Book{Swartzlander:1980:CA,
  editor =       "Earl E. {Swartzlander, Jr.}",
  title =        "Computer Arithmetic",
  publisher =    pub-DOWDEN,
  address =      pub-DOWDEN:adr,
  pages =        "xiii + 378",
  year =         "1980",
  ISBN =         "0-87933-350-2",
  ISBN-13 =      "978-0-87933-350-8",
  LCCN =         "QA76.6 .C633",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Benchmark papers in electrical engineering and
                 computer science; 21",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  keywords =     "Computer arithmetic; Electronic digital computers ---
                 Programming; Floating-point arithmetic",
  tableofcontents = "Arithmetic operations in a binary computer \\
                 High-speed arithmetic in binary computers \\
                 Fast carry logic for digital computers \\
                 A logic for high-speed addition \\
                 Conditional-sum addition logic \\
                 An evaluation of several two-summand binary \\
                 Adder with distributed control \\
                 Multiple addition by residue threshold, functions and
                 their representation by Array logic \\
                 Counting responders in an associative memory \\
                 Parallel counters \\
                 A signed binary multiplication technique \\
                 Multiplying made easy for digital assemblies \\
                 A binary multiplication scheme based on squaring \\
                 A suggestion for a fast multiplier \\
                 Some schemes for parallel multipliers \\
                 On parallel digital multipliers \\
                 A compact high-speed parallel multiplication scheme \\
                 A two' complement parallel array multiplication
                 algorithm \\
                 Comments on ``A two's complement parallel array
                 multiplication algorithm'' \\
                 The quasi-serial multiplier \\
                 The two's complement quasi-serial multiplier \\
                 Division \\
                 A new class of digital division methods \\
                 An algorithm for rapid binary \\
                 Higher-radix division using estimates of the divisor
                 and partial remainders \\
                 An algorithm for division \\
                 A division method using a parallel multiplier \\
                 On division by functional iteration \\
                 Logarithms \\
                 Computation of the base two logarithm of binary
                 logarithms and elementary \\
                 A note on base-2 logarithm computations \\
                 Digital filtering using \\
                 The sign / logarithm number system \\
                 Elementary functions \\
                 The CORDIC trigonometric computing technique \\
                 Digit-by-digit transcendental-function computation \\
                 A unified algorithm for elementary functions \\
                 Some properties of iterative square-rooting methods
                 using high-speed multiplication \\
                 Radix-16 evaluation of certain elementary functions \\
                 Floating-point arithmetic \\
                 On the distribution of numbers \\
                 An analysis of floating-point addition \\
                 The IBM System/360 Model 91: floating-point execution
                 unit \\
                 Design of large high-speed floating-point-arithmetic
                 units \\
                 Analysis of rounding methods in floating-point
                 arithmetic",
}

@Article{Swartzlander:1980:MA,
  author =       "E. E. {Swartzlander, Jr.}",
  title =        "Merged Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-29",
  number =       "10",
  pages =        "946--950",
  month =        oct,
  year =         "1980",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1980.1675482",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 19:31:28 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675482",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Thornton:1980:CP,
  author =       "James E. Thornton",
  title =        "The {CDC 6600} Project",
  journal =      j-ANN-HIST-COMPUT,
  volume =       "2",
  number =       "4",
  pages =        "338--348",
  month =        oct # "\slash " # dec,
  year =         "1980",
  CODEN =        "AHCOE5",
  DOI =          "https://doi.org/10.1109/MAHC.1980.10044",
  ISSN =         "0164-1239",
  bibdate =      "Fri Nov 1 15:29:17 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://dlib.computer.org/an/books/an1980/pdf/a4338.pdf;
                 http://www.computer.org/annals/an1980/a4338abs.htm",
  abstract =     "This article is an account of the development of the
                 Control Data 6600 computer first developed in 1964. Of
                 historical interest is the design team approach adopted
                 by Control Data in which a small staff of engineers was
                 isolated from the main operations of the company. Some
                 review is made of the design process as well as the
                 unique features of the machine. The article also
                 includes some comments in retrospect about the results
                 of certain of the initial design objectives.",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of the History of Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
}

@MastersThesis{Ting:1980:MCU,
  author =       "I-chyng Ting",
  title =        "A microprocessor-based controller using floating-point
                 arithmetic",
  type =         "Thesis ({M.S.})",
  school =       "Auburn University",
  address =      "Auburn, AL, USA",
  pages =        "ix + 167",
  year =         "1980",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Microprocessors.",
}

@MastersThesis{Tucker:1980:IAD,
  author =       "Richard Wesley Tucker",
  title =        "Implementation of arithmetic for the data flow machine
                 processing unit",
  type =         "Thesis ({B.S.})",
  school =       "Massachusetts Institute of Technology. Dept. of
                 Electrical and Engineering and Computer Science",
  address =      "Cambridge, MA, USA",
  pages =        "i + 58",
  year =         "1980",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Supervised by Jack B. Dennis.",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Microprocessors ---
                 Programming.; Val (Computer program language).",
}

@InProceedings{Ulrich:1980:IMS,
  author =       "Ch. Ulrich",
  title =        "Iterative Methods in the Spaces of Rounded
                 Computations",
  crossref =     "Alefeld:1980:FNC",
  pages =        "197--209",
  year =         "1980",
  bibdate =      "Tue Oct 23 08:17:48 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "interval arithmetic; rounding error",
}

@InProceedings{Undheim:1980:CFP,
  author =       "T. Undheim",
  title =        "Combinatorial Floating Point Processor as an Integral
                 Part of the Computer",
  crossref =     "Electro:1980:ECR",
  pages =        "14/1/1--6",
  year =         "1980",
  bibdate =      "Wed Sep 7 22:31:27 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Verma:1980:MPF,
  author =       "S. B. Verma and Maithili Sharan",
  title =        "Multiple Precision Floating-point Computation in
                 {FORTRAN}",
  journal =      j-SPE,
  volume =       "10",
  number =       "3",
  pages =        "163--173",
  month =        mar,
  year =         "1980",
  CODEN =        "SPEXBL",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Thu Sep 8 08:20:53 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Software---Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
}

@TechReport{Virkkunen:1980:UAF,
  author =       "V.-E. Juhani Virkkunen",
  title =        "A unified approach to floating-point rounding with
                 applications to multiple-precision summation",
  type =         "{Diss. Helsingfors}",
  institution =  "Department of Computer Science, University of
                 Helsinki",
  address =      "Helsinki, Finland",
  pages =        "66",
  year =         "1980",
  ISBN =         "951-45-1948-5",
  ISBN-13 =      "978-951-45-1948-2",
  bibdate =      "Thu May 09 08:25:02 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@PhdThesis{vonGudenberg:1980:EAR,
  author =       "J. Wolff {von Gudenberg}",
  title =        "{Einbettung allgemeiner Rechnerarithmetik in Pascal
                 mittels eines Operatorkonzepts und Implementierung der
                 Standardfunktionen mit optimaler Genauigkeit}
                 \toenglish {Embedding a General Computer Arithmetic in
                 Pascal by Means of an Operator Concept and the
                 Implementation of Elementary Functions with Optimal
                 Accuracy} \endtoenglish",
  type =         "Dissertation",
  school =       "Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "??",
  year =         "1980",
  bibdate =      "Fri Sep 16 16:30:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Waldecker:1980:NSR,
  author =       "D. E. Waldecker",
  title =        "Nonrestoring Square Root with Simplified Answer
                 Generation",
  journal =      j-IBM-TDB,
  volume =       "22",
  number =       "11",
  pages =        "4807--4808",
  month =        apr,
  year =         "1980",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:15:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
}

@Article{Waser:1980:EGP,
  author =       "S. Waser",
  title =        "{Entwicklung von Gleitkomma-Prozessoren} \toenglish
                 {Development of Floating-Point Processors}
                 \endtoenglish",
  journal =      j-ELECTRONIK,
  volume =       "29",
  number =       "9",
  pages =        "50--54",
  month =        apr,
  year =         "1980",
  CODEN =        "EKRKAR",
  ISSN =         "0013-5658",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektronik",
}

@MastersThesis{Watkins:1980:MFU,
  author =       "Timothy Ervin Watkins",
  title =        "A microprogrammed {FFT} utilizing floating point
                 hardware",
  type =         "Thesis ({M.S.})",
  school =       "UCLA",
  address =      "Los Angeles, CA, USA",
  pages =        "v + 56",
  year =         "1980",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Fourier transformations
                 --- Computer programs.; Microprogramming.",
}

@MastersThesis{Wong:1980:IOF,
  author =       "Clement Sau-Fai Wong",
  title =        "Input\slash output and floating-point arithmetic
                 package",
  type =         "Thesis ({M.S.})",
  school =       "University of Tennessee, Knoxville",
  address =      "Knoxville, TN, USA",
  pages =        "vi + 61",
  year =         "1980",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer input-output equipment.; Electronic digital
                 computers --- Programming.; Floating-point arithmetic.;
                 Microcomputers.",
}

@InProceedings{Yohe:1980:FPE,
  author =       "J. Michael Yohe",
  title =        "Floating point exception handling for interval
                 arithmetic",
  crossref =     "Nickel:1980:IMP",
  pages =        "547--554",
  year =         "1980",
  MRclass =      "65G10",
  MRnumber =     "83c:65115",
  bibdate =      "Fri Dec 08 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Yohe:1980:PSI,
  author =       "J. Michael Yohe",
  title =        "Portable Software for Interval Arithmetic",
  crossref =     "Alefeld:1980:FNC",
  pages =        "211--229",
  year =         "1980",
  bibdate =      "Tue Oct 23 08:17:48 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A portable multiple precision interval arithmetic
                 package for FORTRAN has been developed by substituting
                 the multiple precision arithmetic package of Richard P.
                 Brent for the underlying arithmetic in the author's
                 earlier single precision interval arithmetic package.
                 This package, like the earlier version, offers a
                 complete range of operations and functions for interval
                 calculations.\par

                 In this paper, we outline the design philosophy of the
                 earlier package and show how this design facilitated
                 the incorporation of the Brent package. We discuss
                 several desirable host system features and possible
                 adaptations of the interval package, and explain how
                 the design of the package would allow it to serve in
                 differing environments with only relatively minor
                 changes.\par

                 Since the package may be of direct use to many
                 individuals, we also discuss its installation on other
                 host systems and its use via the AUGMENT precompiler
                 for Fortran.",
  acknowledgement = ack-nhfb,
  keywords =     "interval arithmetic; multiple precision arithmetic",
}

@Article{Zeman:1980:HSM,
  author =       "J. Zeman and H. T. {Nagle, Jr.}",
  title =        "A High-Speed Microprogrammable Digital Signal
                 Processor Employing Distributed Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-29",
  number =       "2",
  pages =        "134--144",
  month =        feb,
  year =         "1980",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1980.1675537",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 19:15:24 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675537",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Agrawal:1981:NAM,
  author =       "D. P. Agrawal and R. C. Joshi",
  title =        "Negabinary Addition and Multiplication Using Binary
                 Circuits",
  crossref =     "IEEE:1981:PSC",
  pages =        "270--273",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Agrawal_Joshi.pdf",
  abstract =     "This paper deals with design techniques that allow
                 adoption of off-the-shelf binary arithmetic circuits to
                 perform multi-operand addition and multiplication of
                 negabinary numbers. The multiple operands could be
                 easily added with augmented binary adders connected in
                 the form of a tree. The same hardware could be used to
                 perform multiplication. But, from an LSI implementation
                 viewpoint, the use of cellular array structures is
                 explored and necessary challenges to design a combined
                 binary/negabinary multiplier unit, are also outlined.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@InProceedings{Ahmed:1981:VSA,
  author =       "H. M. Ahmed and M. Morf and D. T. L. Lee and P. H.
                 Ang",
  editor =       "????",
  booktitle =    "{Proceedings of 1981 ICASSP. Atlanta. GA, 1981}",
  title =        "A {VLSI} speech analysis chip set based on square-root
                 normalized ladder forms",
  publisher =    "????",
  address =      "????",
  pages =        "648--653",
  year =         "1981",
  DOI =          "",
  ISBN =         "",
  ISBN-13 =      "",
  LCCN =         "",
  bibdate =      "Wed Oct 29 10:23:36 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "",
  acknowledgement = ack-nhfb,
}

@Article{Andrews:1981:EFM,
  author =       "M. Andrews and D. Jaeger and S. F. McCormick and G. D.
                 Taylor",
  title =        "Evaluation of Functions on Microcomputers: $ \exp (x)
                 $",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "7",
  number =       "6",
  pages =        "503--508",
  year =         "1981",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(81)90034-1",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Thu Sep 15 18:40:45 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122181900341",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@MastersThesis{Arnold:1981:PFP,
  author =       "Jeffrey M. Arnold",
  title =        "{PSI}, a floating point processor for the {NU}
                 Computer",
  type =         "Thesis ({B.S.})",
  school =       "Massachusetts Institute of Technology. Dept. of
                 Electrical and Engineering and Computer Science",
  address =      "Cambridge, MA, USA",
  pages =        "42",
  year =         "1981",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Supervised by Stephen A. Ward.",
  acknowledgement = ack-nhfb,
  keywords =     "Computer architecture.; Floating-point arithmetic.;
                 Intel 8086 (Microprocessor); Microprocessors --- Design
                 and construction.",
}

@InProceedings{Arora:1981:CSR,
  author =       "R. K. Arora and Saroj Kaushik",
  title =        "Conversion Scheme in Residue Code",
  crossref =     "IEEE:1981:PSC",
  pages =        "152--156",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Arora_Kaushik.pdf",
  abstract =     "In this paper, an implementation scheme involving
                 decoders and residue adders has been suggested to
                 convert input data in fixed radix representation to
                 residue representation. A method dealing with the
                 reverse process is also demonstrated. A comparison has
                 been made with the methods known hitherto.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5; residue number system",
}

@InProceedings{Atkins:1981:FIS,
  author =       "D. E. Atkins and K. S. Trivedi",
  title =        "The {Fifth IEEE Symposium on Computer Arithmetic}:
                 Foreword",
  crossref =     "IEEE:1981:PSC",
  pages =        "iv--iv",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Trivedi_Atkins.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@InProceedings{Avizienis:1981:LCR,
  author =       "Algirdas Avi{\v{z}}ienis",
  title =        "Low-Cost Residue and Inverse Residue Error-Detecting
                 Codes for Signed-Digit Arithmetic",
  crossref =     "IEEE:1981:PSC",
  pages =        "165--168",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Avizienis.pdf",
  abstract =     "Low-cost residue and inverse residue codes for error
                 detection in signed-digit arithmetic are defined in
                 this paper. Checking algorithms are presented for both
                 digit-serial and parallel computation of the residues.
                 Residue digit operations are defined for two-operand
                 addition, multi-operand addition, multiplication,
                 conversion, and reconversion algorithms. All algorithms
                 employ the same Arithmetic Building Element ``ABE''
                 that has been previously developed for signed-digit
                 arithmetic.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@InProceedings{Banerji:1981:HSD,
  author =       "Dilip K. Banerji and To-Yat Cheung and V. Ganesan",
  title =        "A High-Speed Division Method in Residue Arithmetic",
  crossref =     "IEEE:1981:PSC",
  pages =        "158--164",
  year =         "1981",
  bibdate =      "Wed Nov 14 17:53:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Banerji_Cheung_Ganesan.pdf",
  abstract =     "This paper is concerned with the operation of division
                 in residue number systems. Residue codes are introduced
                 and the basic residue arithmetic operations are
                 defined. Previous results on residue division are
                 outlined. A well-known integer division algorithm is
                 used and adapted for residue division. A new method is
                 proposed for choosing an approximate divisor,
                 approximate dividends, and the partial quotients. The
                 proposed method yields correct quotients faster than
                 the existing methods and is general in its application
                 i.e., it is not restricted by the choice of moduli as
                 long as they are relatively prime.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@InProceedings{Barlow:1981:DAA,
  author =       "Jesse Barlow",
  title =        "On the Distribution af Accumulated Roundoff Error in
                 Floating Point Arithmetic",
  crossref =     "IEEE:1981:PSC",
  pages =        "100--105",
  year =         "1981",
  bibdate =      "Wed Nov 14 17:53:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Barlow.pdf",
  abstract =     "This paper discusses longstanding problems in the
                 probabilistic error analysis of numerical algorithms
                 when they are performed in floating point
                 arithmetic.\par

                 Local roundoff error in floating point addition is
                 characterized and its mean and variance are
                 approximated. We apply these results to finding
                 distributions for the roundoff error accumulated in
                 sums and long inner products.\par

                 We state theorems which resolve questions left open in
                 Bustoz et al. [5] and Hamming [11]. These theorems are
                 proven in [3].",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@PhdThesis{Barlow:1981:PEA,
  author =       "Jesse Louis Barlow",
  title =        "Probabilistic error analysis of floating point and
                 {CRD} arithmetics",
  type =         "{Ph.D.} (Electrical Engineering and Computer
                 Science)",
  school =       "Northwestern University",
  address =      "Evanston, IL, USA",
  pages =        "????",
  year =         "1981",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Bashe:1981:AIE,
  author =       "C. J. Bashe and W. Buchholz and G. V. Hawkins and J.
                 J. Ingram and N. Rochester",
  title =        "The Architecture of {IBM}'s Early Computers",
  journal =      j-IBM-JRD,
  volume =       "25",
  number =       "5",
  pages =        "363--375",
  month =        sep,
  year =         "1981",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Mon Jan 24 21:36:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}

@MastersThesis{Benjamin:1981:FPF,
  author =       "Bruce P. Benjamin",
  title =        "Fixed point to floating point converter",
  type =         "{Master of Science, Plan II}",
  school =       "University of California, Berkeley. Dept. of
                 Electrical Engineering and Computer Sciences",
  address =      "Berkeley, CA, USA",
  pages =        "60",
  year =         "1981",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bhuyan:1981:MAP,
  author =       "L. Bhuyan and D. P. Agrawal",
  title =        "Multiple Addition and Parallel Counter in Generalized
                 Binary and Negabinary Systems",
  crossref =     "IEEE:1981:PSC",
  pages =        "264--269",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Bhuyan_Agrawal.pdf",
  abstract =     "This paper explores the possibility of utilizing
                 counters for reducing the partial products generated
                 from multiplication of two numbers represented in a
                 generalized binary system. Algorithm for multi operand
                 addition of Koren's generalized number system are
                 worked out. A carry look-ahead adder is developed and
                 hardware aspects of possible counters for this class of
                 binary number system are discussed. Negabinary counters
                 are also introduced in line with those proposed for
                 binary multiplication by Stenzel et al.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@Article{Bice:1981:AAS,
  author =       "P. K. Bice",
  title =        "Algorithm adds square root to micro's arithmetic
                 capability",
  journal =      j-ELECTRONIC-DESIGN,
  volume =       "29",
  number =       "11",
  pages =        "146",
  month =        may,
  year =         "1981",
  CODEN =        "ELODAW",
  ISSN =         "0013-4872 (print), 1944-9550 (electronic)",
  ISSN-L =       "0013-4872",
  bibdate =      "Thu Sep 1 10:15:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronic Design",
}

@Article{Blikle:1981:CTI,
  author =       "Andrzej Blikle",
  title =        "The Clean Termination of Iterative Programs",
  journal =      j-ACTA-INFO,
  volume =       "16",
  number =       "2",
  pages =        "199--217",
  month =        oct,
  year =         "1981",
  CODEN =        "AINFA2",
  ISSN =         "0001-5903 (print), 1432-0525 (electronic)",
  ISSN-L =       "0001-5903",
  MRclass =      "68B10",
  MRnumber =     "83c:68015",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 ftp://ftp.ira.uka.de/pub/bibliography/Misc/HBP/ACTAI.bib;
                 ftp://ftp.ira.uka.de/pub/bibliography/Misc/leavens.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  catcode =      "D.2; D.2.4; F.3",
  content =      "Most correctness proofs assume that elementary
                 instructions represent total functions. In fact this is
                 not always the case: for instance, in dealing with real
                 numbers, Brown's model of floating point computation
                 [1], a model which has been accepted by the designers
                 of ADA, uses interval analysis. If the interval of x
                 overlaps the interval of y, the Boolean value of x r y
                 is not well defined.\par

                 In this paper the author studies the clean termination
                 (i.e., without abortion) of iterative programs, not
                 supposing that the test functions are total. The
                 relational approach to computing, which the author has
                 largely worked out (cf. Sanderson [2] for an account
                 from the starting point) is very well suited for that
                 design. A general theorem links the ``global
                 correctness'' of a program with a ``well-founded''
                 breakdown of the program relation. Next the author
                 gives new validation rules, in which a Z b depart from
                 the usual meaning. Last (but not least) one finds an
                 exhaustive study of the integer square root in a
                 realistic arithmetic.\par

                 Due to the great significance of the matter, we must
                 call attention to this paper. \par

                 M. F. Aribaud, Paris, France \par

                 REFERENCES \par

                 [1] BROWN, W. S. A simple but realistic model of
                 floating-point computation, ACM Trans. Math. Softw. 7
                 (1981), 445 480. \par

                 [2] SANDERSON, J. G. A relational theory of computing,
                 Lecture Notes in Computer \ldots{}",
  CRclass =      "D.2.4 Program Verification; D.2.4 Program
                 Verification; D.2.4 Correctness proofs; F.3.1
                 Specifying and Verifying and Reasoning about Programs",
  CRnumber =     "39409",
  descriptor =   "Software, SOFTWARE ENGINEERING, Program Verification;
                 Software, SOFTWARE ENGINEERING, Program Verification,
                 Correctness proofs; Theory of Computation, LOGICS AND
                 MEANINGS OF PROGRAMS, Specifying and Verifying and
                 Reasoning about Programs",
  fjournal =     "Acta Informatica",
  genterm =      "LANGUAGES; RELIABILITY; THEORY; VERIFICATION",
  journal-URL =  "http://www.springerlink.com/content/0001-5903",
  reviewer =     "M. F. Aribaud",
  subject =      "D. Software; D.2 SOFTWARE ENGINEERING; D. Software;
                 D.2 SOFTWARE ENGINEERING; F. Theory of Computation; F.3
                 LOGICS AND MEANINGS OF PROGRAMS",
}

@TechReport{Brent:1981:MUG,
  author =       "Richard P. Brent",
  title =        "{MP} User's Guide",
  number =       "TR-CS-81-08",
  institution =  "Department of Computer Science, Australian National
                 University",
  address =      "Canberra, ACT, Australia",
  edition =      "Fourth",
  pages =        "73",
  month =        jun,
  year =         "1981",
  bibdate =      "Fri Nov 28 15:59:05 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "MP is a multiple-precision floating-point arithmetic
                 package. It is almost completely machine-independent,
                 and should run on any machine with an ANSI Standard
                 Fortran (ANS X3.9-1966) compiler, sufficient memory,
                 and a wordlength (for integer arithmetic) of at least
                 16 bits. A precompiler (Augment) which facilitates the
                 use of the MP package is available.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}

@InProceedings{Bridge:1981:AAA,
  author =       "Carol L. Bridge and P. David Fisher and Robert G.
                 Reynolds",
  title =        "Asynchronous Arithmetic Algorithms for Data-Driven
                 Machines",
  crossref =     "IEEE:1981:PSC",
  pages =        "56--62",
  year =         "1981",
  bibdate =      "Wed Nov 14 17:53:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Bridge_Fisher_Reynolds.pdf",
  abstract =     "With data-driven machines a statement associated with
                 a given processing element fires the moment its input
                 operands become available. In order to take full
                 advantage of this computer structure and achieve
                 maximum throughput, the processing elements themselves
                 should also be asynchronous; i.e., instruction
                 execution times should be data dependent to minimize
                 overall delays. Five general procedures are described
                 that may be used to design self-timing processing
                 units: task completion prediction, task completion
                 detection, operand preprocessing, pre-estimation of
                 input operand values, and significance control.
                 Analysis and simulations suggest that the greatest
                 potential for speed improvement over synchronous
                 counterparts comes with self-timing algorithms for both
                 division and the evaluation of special functions.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@Article{Brown:1981:SRM,
  author =       "W. S. Brown",
  title =        "A Simple but Realistic Model of Floating-Point
                 Computation",
  journal =      j-TOMS,
  volume =       "7",
  number =       "4",
  pages =        "445--480",
  month =        dec,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355972.355975",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 23:03:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "computer arithmetic; environment parameters; error
                 analysis; Euclidean norm; floating-point arithmetic;
                 software portability",
}

@MastersThesis{Cariker:1981:RFM,
  author =       "Earnest Allan Cariker",
  title =        "A rapid-approximation floating-point mathematics
                 package for the {INTEL} 8080 microprocessor",
  type =         "Computing Science Thesis ({M.S.})",
  school =       "Texas A\&M University",
  address =      "College Station, TX, USA",
  pages =        "viii + 152",
  year =         "1981",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Mathematical analysis.; Microprocessors.; Programming
                 (Electronic computers); Programming languages
                 (Electronic computers)",
}

@MastersThesis{Cary:1981:BFP,
  author =       "David A. Cary",
  title =        "The {Berkeley} floating point project",
  type =         "{Master of Science, Plan II}",
  school =       "University of California, Berkeley. Dept. of
                 Electrical and Engineering and Computer Sciences",
  address =      "Berkeley, CA, USA",
  pages =        "107",
  year =         "1981",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Noted as posthumous in \cite{Aspinwall:1985:RVM}.",
}

@Article{Ceruzzi:1981:ECK,
  author =       "Paul E. Ceruzzi",
  title =        "The Early Computers of {Konrad Zuse}, 1935 to 1945",
  journal =      j-ANN-HIST-COMPUT,
  volume =       "3",
  number =       "3",
  pages =        "241--262",
  month =        jul # "\slash " # sep,
  year =         "1981",
  CODEN =        "AHCOE5",
  ISSN =         "0164-1239",
  bibdate =      "Fri Nov 1 15:29:18 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://dlib.computer.org/an/books/an1981/pdf/a3241.pdf;
                 http://www.computer.org/annals/an1981/a3241abs.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of the History of Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
}

@Manual{Cheng:1981:AAF,
  author =       "Steven Cheng",
  title =        "{Am9511A\slash Am9512} floating point processor
                 manual",
  organization = "Advanced Micro Devices",
  address =      "Sunnyvale, CA, USA",
  pages =        "55",
  year =         "1981",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic and logic units.; Floating-point
                 arithmetic.",
}

@InProceedings{Chow:1981:PDA,
  author =       "P. Chow and Z. G. Vranesic and J. L. Yen",
  title =        "A Pipelined Distributed Arithmetic {PFFT} Processor",
  crossref =     "IEEE:1981:PSC",
  pages =        "198--206",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Chow_Vranesic_Yen.pdf",
  abstract =     "Previous experience i,n implementing the Prime Factor
                 Fourier Transform showed that it was much more
                 difficult to do than the FFT because of its complicated
                 structure. In most FFT implementations the
                 ``butterfly'' structure is the basic arithmetic unit
                 implemented. It is much simpler than the equivalent
                 PFFT unit.\par

                 This paper describes a different architecture for
                 implementing PFFT machines using distributed arithmetic
                 and ROM's to perform the computations. It is found to
                 be much simpler and more modular than a design which
                 uses multipliers and adders. The implementation of a
                 PFFT processor with a throughput of 104 kHz for complex
                 data points is described.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5; Prime Factor Fourier Transform (PFFT)",
}

@Article{Chroust:1981:MAD,
  author =       "G. Chroust",
  title =        "Method of Adding Decimal Numbers by Means of Binary
                 Arithmetic",
  journal =      j-IBM-TDB,
  volume =       "23",
  number =       "10",
  pages =        "4525--4526",
  month =        mar,
  year =         "1981",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
  keywords =     "decimal floating-point arithmetic",
}

@InProceedings{Ciminiera:1981:AAF,
  author =       "L. Ciminiera and A. Serra",
  title =        "Arithmetic Array for Fast Inner Product Evaluation",
  crossref =     "IEEE:1981:PSC",
  pages =        "207--214",
  year =         "1981",
  bibdate =      "Wed Nov 14 17:53:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Ciminiera_Serra.pdf",
  abstract =     "The paper presents a new fast arithmetic array,
                 suitable for VLSI implementation, which computes the
                 inner product of two vectors. The operands and the
                 result are expressed using the 2's complement notation,
                 which is the most general and flexible one. Cells
                 performing the $ 2 \times 2 $ bit full multiplication
                 are used for obtaining a reduction of the operation
                 time.\par

                 A particular pipelining scheme, with different degrees
                 of latching, is used in order to implement parallel
                 computations with a moderate cost increase. Graphs
                 showing the characteristics and the advantage domain of
                 the proposed array are presented. An IC implementation
                 of the proposed array could have a speed from 5 to 10
                 times greater than the multiplier-accumulator circuits
                 currently available.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@InProceedings{Ciminiera:1981:FAM,
  author =       "L. Ciminiera and A. Serra and A. Valenzano",
  title =        "{Fast and Accurate Matrix Triangularization Using an
                 Iterative Structure}",
  crossref =     "IEEE:1981:PSC",
  pages =        "215--221",
  year =         "1981",
  bibdate =      "Wed Nov 14 17:53:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Ciminiera_Serra_Valenzano.pdf",
  abstract =     "The paper presents a new iterative array, which
                 performs the triangularization of a dense matrix, using
                 the Givens rotation algorithm. Two slightly different
                 arrays are presented: the first one performs the
                 factorization of a single matrix; the second one
                 performs the recursive triangularization. The
                 implementation of the cell in the array is based on the
                 on-line arithmetic, which allows us to obtain high
                 performances. Furthermore, the cell implementation
                 requires only three types of arithmetic units
                 (multiplication\slash addition, square root, division)
                 and shift registers for data buffering and for
                 generating the timing signals.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@Article{Cody:1981:APF,
  author =       "William J. {Cody, Jr.}",
  title =        "Analysis of Proposals for the Floating-Point
                 Standard",
  journal =      j-COMPUTER,
  volume =       "14",
  number =       "3",
  pages =        "63--68",
  month =        mar,
  year =         "1981",
  CODEN =        "CPTRB4",
  DOI =          "https://doi.org/10.1109/C-M.1981.220379",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Sat Sep 24 09:21:33 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/computer1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
  URL =          "https://ethw.org/w/images/f/fb/Analysis_of_Proposals_Cody.pdf",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}

@InProceedings{Cohen:1981:CAU,
  author =       "M. Cohen and V. C. Hamacher and T. E. Hull",
  title =        "{CADAC}: An Arithmetic Unit for Clean Decimal
                 Arithmetic and Controlled Precision",
  crossref =     "IEEE:1981:PSC",
  pages =        "106--112",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Cohen_Hamacher_Bull.pdf",
  abstract =     "This paper describes the design of an arithmetic unit
                 called CADAC (Clean Arithmetic with Decimal base And
                 Controlled Precision). A brief indication of
                 programming language specifications for carrying out
                 ``ideal'' floating-point arithmetic is given. These
                 specifications include detailed requirements for
                 precision control and exception handling at the level
                 of a programming language such as Fortran. CADAC is an
                 arithmetic unit which performs the four floating-point
                 operations add\slash subtract \slash multiply\slash
                 divide on decimal base numbers in accordance with the
                 language requirements. A three-level pipeline is used
                 to overlap 2-digit-at-a-time (``double digit'') serial
                 processing of the partial products\slash remainders.
                 Although the logic design is relatively complex, the
                 performance is efficient and the advantages gained by
                 implementing programmer-controlled precision directly
                 in the hardware are significant.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@Article{Coonen:1981:EIG,
  author =       "Jerome T. Coonen",
  title =        "Errata: {An Implementation Guide to a Proposed
                 Standard for Floating Point Arithmetic}",
  journal =      j-COMPUTER,
  volume =       "14",
  number =       "3",
  pages =        "62--62",
  month =        mar,
  year =         "1981",
  CODEN =        "CPTRB4",
  DOI =          "https://doi.org/10.1109/C-M.1981.220378",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Wed Sep 14 21:15:55 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computer1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See
                 \cite{Coonen:1980:IGP,IEEE:1985:AIS,IEEE:1985:ASI}.",
  acknowledgement = ack-nj,
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}

@Article{Coonen:1981:UDN,
  author =       "Jerome T. Coonen",
  title =        "Underflow and the Denormalized Numbers",
  journal =      j-COMPUTER,
  volume =       "14",
  number =       "3",
  pages =        "75--87",
  month =        mar,
  year =         "1981",
  CODEN =        "CPTRB4",
  DOI =          "https://doi.org/10.1109/C-M.1981.220382",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Fri Sep 2 23:38:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computer1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
  acknowledgement = ack-nj,
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}

@MastersThesis{Curley:1981:PPN,
  author =       "A. Curley",
  title =        "{PNCL}: a Prototype Numerical Computation Language",
  type =         "{M.Sc.} thesis",
  school =       "Department of Computer Science, University of
                 Toronto",
  address =      "Toronto, ON, Canada",
  year =         "1981",
  bibdate =      "Sun Dec 30 15:41:22 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Davis:1981:EFA,
  author =       "Diane F. Davis",
  title =        "Elementary Functions on an Array Processor",
  crossref =     "IEEE:1981:PSC",
  pages =        "170--178",
  year =         "1981",
  bibdate =      "Wed Nov 14 17:53:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Davis.pdf",
  abstract =     "The algorithms used for elementary functions on the
                 FPS-164 array processor are described. In each case,
                 the choice of the algorithm depends on the parallel
                 hardware, the capability of the instruction word, and
                 the precision desired. For some, the choice depends on
                 the version, either scalar or vector. Algorithms for
                 the divide, square root, cosine\slash sine,
                 exponential, and logarithm are discussed. Those for
                 arctangent, tangent, arc-cosine\slash sine, cosh, sinh,
                 and tanh are summarized.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5; Floating-Point Systems FPS-164",
}

@Manual{DECESD:1981:VIS,
  author =       "{Digital Equipment Corporation.Educational Services
                 Dept}",
  title =        "{VAX-11} instruction set",
  organization = "Digital Equipment Corporation",
  address =      "Maynard, MA, USA",
  edition =      "Revised",
  pages =        "various",
  year =         "1981",
  bibdate =      "Sun May 02 09:19:03 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "VAX-11 (Computer) --- Programming.",
  remark =       "In container. Student guide --- Programming examples
                 --- Character string instructions --- Instruction
                 formats and addressing modes --- Variable bit field
                 instructions --- Stack and address instructions ---
                 Integer, logical and branch instructions --- Floating
                 point instructions --- Decimal string instructions
                 --Procedure and subroutine instructions --- Special
                 instructions --- Module tests --- Evaluation sheets ---
                 Selected tables.",
}

@InProceedings{Demmel:1981:EUS,
  author =       "James Demmel",
  title =        "Effects of Underflow on Solving Linear Systems",
  crossref =     "IEEE:1981:PSC",
  pages =        "113--119",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Demmel.pdf",
  abstract =     "Software to solve systems of linear equations by
                 Gaussian elimination has in the past ignored the
                 effects of underflow. But when underflows are replaced
                 by zeroes, this software can give spurious though
                 plausible results much worse than would be blamed on
                 roundoff. When underflow is gradual, as in the proposed
                 IEEE standard for floating point arithmetic, the same
                 software gives provably more reliable results. To
                 achieve the same reliability without gradual underflow,
                 but with underflows set to zero, complicated tests must
                 be inserted into the software.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@InProceedings{Efe:1981:MOA,
  author =       "Kemal Efe",
  title =        "Multi-Operand Addition with Conditional Sum Logic",
  crossref =     "IEEE:1981:PSC",
  pages =        "251--255",
  year =         "1981",
  bibdate =      "Wed Nov 14 17:53:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Efe.pdf",
  abstract =     "Column-wise addition schemes involve counting the
                 number of 1's in a column and representing this number
                 in binary weighted form. In Conditional Sum Logic
                 (CSL), partial results are first generated for every
                 column, then one of these results is selected depending
                 on the incoming carry value. A compact scheme for
                 counting the number of 1's and generating partial
                 results for all possible distributions of incoming
                 carries is introduced. Application of such counters to
                 CSL yields a high speed in multi-operand addition.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@TechReport{Eide:1981:FPA,
  author =       "Vigleik Eide",
  title =        "Floating-point arithmetic on a micro-computer",
  type =         "Hovedoppgave i informatikk (cand. real)",
  institution =  "Universitetet i Oslo",
  address =      "Oslo, Norway",
  pages =        "71",
  year =         "1981",
  bibdate =      "Thu May 09 08:12:55 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@PhdThesis{Farmwald:1981:DHP,
  author =       "P. M. Farmwald",
  title =        "On the Design of High Performance Digital Arithmetic
                 Units",
  type =         "Thesis ({Ph.D.})",
  school =       "Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "????",
  month =        aug,
  year =         "1981",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}

@InProceedings{Farmwald:1981:HBE,
  author =       "P. Michael Farmwald",
  title =        "High bandwidth evaluation of certain elementary
                 functions",
  crossref =     "IEEE:1981:PSC",
  pages =        "139--142",
  year =         "1981",
  bibdate =      "Mon May 20 05:27:32 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Farmwald.pdf",
  abstract =     "Among the requirements currently being imposed on
                 high-performance digital computers to an increasing
                 extent are the high-bandwidth computations of
                 elementary functions, which are relatively
                 time-consuming procedures when conducted in software.
                 In this paper, we elaborate on a technique for
                 computing piecewise quadratic approximations to many
                 elementary functions. This method permits the effective
                 use of large RAMs or ROMs and parallel multipliers for
                 rapidly generating single-precision floating-point
                 function values (e.g., 30-45 bits of fraction, with
                 current RAM and ROM technology). The technique, based
                 on the use of Taylor series, may be readily pipelined.
                 Its use for calculating values for floating-point
                 reciprocal, square root, sine, cosine, arctangent,
                 logarithm, exponential and error functions is
                 discussed.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@Article{Fredette:1981:RES,
  author =       "G. Fredette",
  title =        "68000 routine extracts square roots",
  journal =      j-EDN,
  volume =       "26",
  number =       "16",
  pages =        "185--194",
  month =        aug,
  year =         "1981",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 1 10:15:56 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}

@Article{Ganesan:1981:GSC,
  author =       "K. Ganesan and A. Augustine",
  title =        "8086 generates sines and cosines",
  journal =      j-EDN,
  volume =       "26",
  number =       "6",
  pages =        "186--188",
  month =        mar,
  year =         "1981",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 1 10:15:56 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}

@Book{Glaser:1981:HBO,
  author =       "Anton Glaser",
  title =        "History of Binary and Other Nondecimal Numeration",
  publisher =    pub-TOMASH,
  address =      pub-TOMASH:adr,
  edition =      "Revised",
  pages =        "xiii + 218",
  year =         "1981",
  ISBN =         "0-938228-00-5",
  ISBN-13 =      "978-0-938228-00-4",
  LCCN =         "QA141.2 .G55 1981",
  bibdate =      "Fri Mar 17 08:12:27 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "See also original edition \cite{Glaser:1971:HBO}.",
  acknowledgement = ack-nhfb,
  author-dates = "1924--",
  remark =       "Based on the author's thesis (Ph.D.--Temple
                 University), presented under the title: History of
                 modern numeration systems.",
  subject =      "Numeration; History; 31.14 number theory; 15.00
                 history: general; Numeration; Dualsystem; Geschichte;
                 Talstelsels; History; Num{\'e}ration; Histoire;
                 Dualsystem; Geschichte.",
}

@Book{Gorin:1981:IDA,
  author =       "Ralph E. Gorin",
  title =        "Introduction to {DECSYSTEM-20} Assembly Language
                 Programming",
  publisher =    pub-DP,
  address =      pub-DP:adr,
  pages =        "xxx + 545",
  year =         "1981",
  ISBN =         "0-932376-12-6",
  ISBN-13 =      "978-0-932376-12-1",
  LCCN =         "QA76.8.D17 .G67",
  bibdate =      "Tue Dec 14 22:54:14 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$40.00",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gorji-Sinaki:1981:DDS,
  author =       "A. Gorji-Sinaki and M. D. Ercegovac",
  title =        "Design of a Digit-Slice On-Line Arithmetic Unit",
  crossref =     "IEEE:1981:PSC",
  pages =        "72--80",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_GorjiSinaki_Ercegovac.pdf",
  abstract =     "A gate level design of a digit-slice on-line
                 arithmetic unit is presented. This unit is designed as
                 a set of basic modules Processing Elements (PE), each
                 of which operates on a single digit of the operands and
                 the results. It is capable of executing four basic
                 operations of addition\slash subtraction,
                 multiplication and division in an on-line manner. The
                 results are generated during the digit-serial input of
                 the operands, beginning always with the most
                 significant digit. A general (with respect to radix)
                 analysis of the cost and speed of the proposed unit is
                 also given.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@InProceedings{Gosling:1981:CSH,
  author =       "J. B. Gosling and J. H. P. Zurawski and D. B. G.
                 Edwards",
  title =        "A Chip-Set for a High-Speed Low-cost Floating-Point
                 Unit",
  crossref =     "IEEE:1981:PSC",
  pages =        "50--55",
  year =         "1981",
  bibdate =      "Wed Nov 14 17:53:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Gosling_Zurawski_Edwards.pdf",
  abstract =     "Although the advent of microprocessors has put
                 considerable computing power in the hands of large
                 numbers of users, there is still an important group who
                 have yet to benefit fully from large scale
                 integration., As a step in the direction of rectifying
                 this situation, a highly flexible chip set is being
                 designed, with a view to reducing the cost of a
                 powerful floating point processor by a factor of about
                 4. Processing speed will be up to twice that of an
                 equivalent unit built from MSI devices, before
                 allowance is made for savings on wiring delays. It will
                 be possible to construct a unit satisfying all
                 published standards, proposed and existing (de facto),
                 as well as permitting a number of extensions not
                 specifically in these standards. At a cost between 100
                 and 150 ICs, and with a floating-point add time of
                 around 120ns, the proposed unit is cost-effective
                 compared to currently available coprocessors.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@Article{Grappel:1981:RDB,
  author =       "R. D. Grappel",
  title =        "68000 routine divides 32-bit numbers",
  journal =      j-EDN,
  volume =       "26",
  number =       "5",
  pages =        "161--162",
  month =        mar,
  year =         "1981",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}

@InProceedings{Gregory:1981:RAR,
  author =       "R. T. Gregory",
  title =        "Residue Arithmetic with Rational Operands",
  crossref =     "IEEE:1981:PSC",
  pages =        "144--145",
  year =         "1981",
  bibdate =      "Wed Nov 14 17:53:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Gregory.pdf",
  abstract =     "A method is described for doing residue arithmetic
                 when the operands are rational numbers. A rational
                 operand $ a / b $ is mapped onto the integer $ a
                 b^{-1}|_p $ and the arithmetic is performed in $
                 \mathrm {GF}(p) $. A method is given for taking an
                 integer result and finding its rational equivalent (the
                 one which corresponds to the correct rational
                 result).",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5; residue number system",
}

@Article{Griffiths:1981:BDC,
  author =       "L. K. Griffiths",
  title =        "Binary-to-Decimal Conversion",
  journal =      j-IBM-TDB,
  volume =       "24",
  number =       "1A",
  pages =        "237--238",
  month =        jun,
  year =         "1981",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Fri Nov 28 17:04:53 2003",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Binary to decimal conversion can be achieved by
                 multiplying $ 1 / 10 $ as $ 51 / 512 \times 256 / 255 $
                 and using the fact that $ 256 / 255 = 1 + 1 / 256 + 1 /
                 256^2 + \cdots $, i.e., $ 256 / 255 = 257 - 256 $
                 rounded up.\par

                 This method can be performed efficiently on short word
                 computers with only adding and shifting operations,
                 i.e., first multiplying by $ 51 / 512 $ and then
                 correcting by multiplying by $ 256 / 255 $.",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
  keywords =     "decimal floating-point arithmetic",
}

@Article{Grote:1981:CIS,
  author =       "H. Grote",
  title =        "Code improves on a square-root routine",
  journal =      j-EDN,
  volume =       "26",
  number =       "11",
  pages =        "198--200",
  month =        may,
  year =         "1981",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 1 10:15:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}

@MastersThesis{Hazlerig:1981:CES,
  author =       "Steven Jackson Hazlerig",
  title =        "Comparison and evaluation of several floating-point
                 schemes for the {Motorola} 68000 microprocessor",
  type =         "Thesis ({M.S.})",
  school =       "Massachusetts Institute of Technology. Dept. of
                 Electrical and Engineering and Computer Science",
  address =      "Cambridge, MA, USA",
  pages =        "103",
  year =         "1981",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Supervised by Richard E. Zippel.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  keywords =     "Floating-point arithmetic.; Microprocessors ---
                 Programming.; Microprogramming.",
}

@TechReport{Hendra:1981:FPS,
  author =       "R. G. Hendra",
  title =        "A floating point software package for use on {LSI-11}
                 computers at {SLAC}",
  type =         "Technical note",
  number =       "SLAC TN 81-3",
  institution =  "SLAC",
  address =      "Stanford, CA, USA",
  pages =        "8",
  month =        jun,
  year =         "1981",
  bibdate =      "Fri May 25 05:50:26 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://weblib.cern.ch/format/showfull?uid=1451323_18194&base=CERCER&sysnb=0046833",
  acknowledgement = ack-nhfb,
}

@Article{Hough:1981:API,
  author =       "David Hough",
  title =        "Applications of the Proposed {IEEE-754} Standard for
                 Floating Point Arithmetic",
  journal =      j-COMPUTER,
  volume =       "14",
  number =       "3",
  pages =        "70--74",
  month =        mar,
  year =         "1981",
  CODEN =        "CPTRB4",
  DOI =          "https://doi.org/10.1109/C-M.1981.220381",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Fri Sep 2 23:38:14 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computer1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}

@Article{Huang:1981:IFD,
  author =       "Chao Huang and D. Peterson and H. Rauch and J. Teague
                 and D. Fraser",
  title =        "Implementation of a fast digital processor using the
                 residue number system",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "28",
  number =       "1",
  pages =        "32--38",
  month =        jan,
  year =         "1981",
  CODEN =        "ICSYBT",
  DOI =          "https://doi.org/10.1049/el:19800468",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23509",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper contains a description of a special purpose
                 digital processor which has been implemented using
                 residue arithmetic. The processor does two-dimensional
                 pulse matching by convolving a two-dimensional
                 five-by-five filter with the Incoming data \ldots{}",
}

@MastersThesis{Hwang:1981:CFF,
  author =       "Shu-Hwa Hwang",
  title =        "Computation in a finite field using rational
                 operands",
  type =         "Thesis ({M.S.})",
  school =       "University of Tennessee, Knoxville",
  address =      "Knoxville, TN, USA",
  pages =        "v + 80",
  year =         "1981",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithms.; Floating-point arithmetic.; Modular
                 arithmetic.; Programming (Electronic computers)",
}

@InProceedings{Hwang:1981:PAV,
  author =       "Kai Hwang and Yen-Heng Cheng",
  title =        "Partitioned Algorithms and {VLSI} Structures for
                 Large-Scale Matrix Computations",
  crossref =     "IEEE:1981:PSC",
  pages =        "222--232",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Hwang_Cheng.pdf",
  abstract =     "VLSI modular arithmetic structures and new partitioned
                 matrix algorithms are developed in this paper to
                 perform hardware matrix computations in solving
                 large-scale linear system of equations. Gaussian
                 elimination and inversion of triangular matrices are
                 shown systematically partitionable. All the partitioned
                 algorithms being developed can achieve linear
                 computation time $ O(n) $, where $n$ is the order of
                 the linear system. The partitioned matrix computations
                 are feasible for modular VLSI implementation with
                 constrained I/O terminals. Performance analysis and
                 design tradeoffs of the partitioned VLSI arithmetic
                 structures are also provided.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@InProceedings{Irwin:1981:RAP,
  author =       "Mary Jane Irwin and Dwight R. Smith",
  title =        "A Rational Arithmetic Processor",
  crossref =     "IEEE:1981:PSC",
  pages =        "241--245",
  year =         "1981",
  bibdate =      "Wed Nov 14 17:53:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Irwin_Smith.pdf",
  abstract =     "An arithmetic processor based upon a rational
                 representation scheme is examined. The key feature of
                 this rational processor is its ability to efficiently
                 reduce a result ratio to its irreducible form (the
                 greatest common divisor of the numerator and
                 denominator is unity). The reduction algorithm
                 presented generates the reduced ratio in parallel with
                 the evaluation of the ratio's greatest common divisor.
                 Hardware designs for the reduction algorithm and the
                 basic arithmetic operations are given.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@Article{Jenkins:1981:CSP,
  author =       "W. K. Jenkins and M. H. Etzel",
  title =        "Correction to {``Special} properties of complement
                 codes for redundant residue number systems''",
  journal =      j-PROC-IEEE,
  volume =       "69",
  number =       "8",
  pages =        "1086--1086",
  month =        aug,
  year =         "1981",
  CODEN =        "IEEPAD",
  DOI =          "https://doi.org/10.1049/el:19800468",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Jenkins:1981:SPC}.",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=31304",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
  keywords =     "residue arithmetic; residue number system",
}

@Article{Jenkins:1981:SPC,
  author =       "W. K. Jenkins and M. H. Etzel",
  title =        "Special properties of complement codes for redundant
                 residue number systems",
  journal =      j-PROC-IEEE,
  volume =       "69",
  number =       "1",
  pages =        "132--133",
  month =        jan,
  year =         "1981",
  CODEN =        "IEEPAD",
  DOI =          "https://doi.org/10.1049/el:19800468",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See correction \cite{Jenkins:1981:CSP}.",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=31297",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Redundant residue number systems are of interest
                 because they have properties that are useful for error
                 control and failure recovery in digital processors.
                 This letter shows how complement coding interferes with
                 error detection in redundant residue \ldots{}",
}

@TechReport{Kahan:1981:WDW,
  author =       "W. Kahan",
  title =        "Why Do We Need a Floating-Point Arithmetic Standard?",
  type =         "Technical Report",
  institution =  inst-BERKELEY,
  address =      inst-BERKELEY:adr,
  pages =        "41",
  day =          "12",
  month =        feb,
  year =         "1981",
  bibdate =      "Fri Apr 7 12:22:17 GMT 1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Available in a retypeset version
                 \cite{Kahan:2001:WDW}.",
}

@Article{Karplus:1981:ASI,
  author =       "W. J. Karplus and D. Cohen",
  title =        "Architectural and Software Issues in the Design of
                 Peripheral Array Processors",
  journal =      j-COMPUTER,
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        sep,
  year =         "1981",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Fri Nov 09 19:01:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}

@InProceedings{Kaushik:1981:SDS,
  author =       "Saroj Kaushik and R. K. Arora",
  title =        "Sign Detection in the Symmetric Residue Number
                 System",
  crossref =     "IEEE:1981:PSC",
  pages =        "146--150",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Kaushik_Arora.pdf",
  abstract =     "This paper is concerned with the algebraic sign
                 detection of a number in the Symmetric Residue Number
                 System. A new approach has been suggested which
                 completely avoids the time consuming process of the
                 Symmetric Mixed Radix Conversion (SMRC). An algorithm
                 based on the above approach implementable in parallel
                 for sign detection is also presented. The hardware
                 representation of the above algorithm is shown. The
                 time and hardware complexity required for the process
                 have also been computed.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@Article{Kielbasinski:1981:IRL,
  author =       "Andrzej Kie{\l}basi{\'n}ski",
  title =        "Iterative refinement for linear systems in
                 variable-precision arithmetic",
  journal =      j-BIT,
  volume =       "21",
  number =       "1",
  pages =        "97--103",
  month =        mar,
  year =         "1981",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01934074",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65G05",
  MRnumber =     "83a:65042",
  bibdate =      "Wed Jan 4 18:52:17 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=21&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=21&issue=1&spage=97",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point arithmetic; variable-precision
                 arithmetic",
}

@Book{Knuth:1981:SA,
  author =       "Donald E. Knuth",
  title =        "Semi\-nu\-mer\-i\-cal Algorithms",
  volume =       "2",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Second",
  pages =        "xi + 624",
  year =         "1981",
  ISBN =         "0-201-03822-6",
  ISBN-13 =      "978-0-201-03822-4",
  LCCN =         "QA76.6 .K64",
  bibdate =      "Wed Dec 15 15:47:38 1993",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$19.75",
  series =       "The Art of Computer Programming",
  acknowledgement = ack-nj,
}

@InProceedings{Kobayashi:1981:FMO,
  author =       "Hideaki Kobayashi",
  title =        "A Fast Multi-Operand Multiplication Scheme",
  crossref =     "IEEE:1981:PSC",
  pages =        "246--250",
  year =         "1981",
  bibdate =      "Wed Nov 14 17:53:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Kobayashi.pdf",
  abstract =     "Recent developments in integrated circuit technology
                 have made efficient schemes for computer arithmetic
                 possible. This paper discusses a generation-summation
                 scheme for fast multi-operand multiplication. Synthesis
                 of three-operand multipliers utilizing a single type of
                 standard LSI device is also discussed.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@Misc{Koehler:1981:AMC,
  author =       "Robert J. Koehler and John A. Bayliss",
  title =        "Apparatus and Method for Cooperative and Concurrent
                 Coprocessing of Digital Information",
  howpublished = "US Patent 4,270,167.",
  day =          "26",
  month =        may,
  year =         "1981",
  bibdate =      "Sat Aug 23 06:38:58 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Filed 30 June 1978. This patent discusses the
                 mechanism enabling the 8087 coprocessor to operate
                 alongside the 8086 and 8088 CPUs.",
  URL =          "https://ieeemilestones.ethw.org/w/images/1/15/Patent_8087_coprocessor_mechanism.pdf",
  abstract =     "The data processing capacity of a practical
                 semiconductor computer system, having both local and
                 system uses, can be expanded both in degree of
                 complexity and magnitude by providing a method and
                 means for cooperatively and concurrently coprocessing
                 digital information among a plurality of processors
                 sharing the same local bus and collectively accessing
                 the system bus as a system unit. In other words, a
                 central processor has primary control and access to a
                 local bus and may have access to a system or common bus
                 shared among many other processors. Also sharing the
                 local bus with the central processor is a plurality of
                 specialized or dedicated processors which are
                 continuously apprised of or actively monitor the
                 internal operational status and operation then being
                 performed by the central processor. The active
                 monitoring of the activity of the other processors
                 sharing the local bus distinguishes these dedicated
                 processors from conventional direct memory accessing
                 processors. Certain ones of the instructions fetched
                 simultaneously by the central processor and the
                 specialized processor from the system memory are re
                 served for execution in one of the dedicated processors
                 which then shares the local bus with the central
                 processor by means of communicating through a plurality
                 of signals with respect to the status, mode,
                 arbitration, and control of the local bus.",
  acknowledgement = ack-nhfb,
}

@Book{Kogge:1981:APC,
  author =       "Peter M. Kogge",
  title =        "The Architecture of Pipelined Computers",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "xii + 334",
  year =         "1981",
  ISBN =         "0-07-035237-2",
  ISBN-13 =      "978-0-07-035237-7",
  LCCN =         "QA76.5 .K587",
  bibdate =      "Wed Dec 15 10:37:46 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "Introduction \\
                 Hardware design and stage cascading \\
                 Timing, control, and performance \\
                 Static pipelined systems: vector processors \\
                 The programming of pipelined vector processors \\
                 Pipelining in SISD machine designs \\
                 Future trends \\
                 Appendix: Collision vector characteristics",
}

@Article{Koren:1981:CPN,
  author =       "I. Koren and Y. Maliniak",
  title =        "On Classes of Positive, Negative, and Imaginary Radix
                 Number Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "30",
  number =       "5",
  pages =        "212--317",
  month =        may,
  year =         "1981",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1981.1675788",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Aug 22 09:00:57 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  abstract =     "A unified approach to a broad class of finite number
                 representation systems is proposed. This class contains
                 aDl positive and negative radix systems and other
                 well-known number systems. In addition, it can be
                 extended to include imaginary radix number systems. The
                 proposed approach enables us to develop a single set of
                 algorithms for arithmetic operations.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Kornerup:1981:IRA,
  author =       "Peter Kornerup and David W. Matula",
  title =        "An Integrated Rational Arithmetic Unit",
  crossref =     "IEEE:1981:PSC",
  pages =        "233--240",
  year =         "1981",
  bibdate =      "Wed Nov 14 17:53:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Kornerup_Matula.pdf",
  abstract =     "Based on the classical Euclidian Algorithm, we develop
                 the foundations of an arithmetic unit performing Add,
                 Subtract, Multiply and Divide on rational operands. The
                 unit uses one unified algorithm for all operations,
                 including rounding. A binary implementation, based on
                 techniques known from the SRT division, is described.
                 Finally, a hardware implementation using ripple-free,
                 carry-save addition is analyzed, and adapted to a
                 floating-slash representation of the rational
                 operands.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@Book{Kulisch:1981:CAT,
  author =       "Ulrich W. Kulisch and Willard L. Miranker",
  title =        "Computer Arithmetic in Theory and Practice",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xiii + 249",
  year =         "1981",
  ISBN =         "0-12-428650-X",
  ISBN-13 =      "978-0-12-428650-4",
  LCCN =         "QA162 .K84",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Computer science and applied mathematics",
  acknowledgement = ack-nhfb,
  keywords =     "Algebra, Abstract.; Computer arithmetic.;
                 Floating-point arithmetic.; Interval analysis
                 (Mathematics)",
  remark =       "See \cite[pp. 1.10--1.11]{Coonen:1984:CPS} for
                 negative comments about the floating-point model in
                 this book, and the impracticality of implementing it in
                 early-1980s technology. Coonen comments: ``their scheme
                 is {\em sufficient\/} to perform reliable computation,
                 aided by devious algorithms; there is no evidence that
                 their scheme is {\em necessary}. nor that the
                 deviousness of their algorithms is unavoidable.''",
}

@Article{Kunz:1981:QZ,
  author =       "W. Kunz",
  title =        "{Quadratwurzel mit dem $ \mu $P Z80} \toenglish
                 {Square Roots with the Z80 Microprocessor}
                 \endtoenglish",
  journal =      j-ELECTRONIK,
  volume =       "7",
  pages =        "109--110",
  year =         "1981",
  CODEN =        "EKRKAR",
  ISSN =         "0013-5658",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektronik",
}

@InProceedings{Ligomenides:1981:CRF,
  author =       "P. Ligomenides and R. Newcomb",
  title =        "Complement Representations in the {Fibonacci}
                 Computer",
  crossref =     "IEEE:1981:PSC",
  pages =        "6--9",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Ligomenides_Newcomb.pdf",
  abstract =     "Two complement representations and a sign-magnitude
                 one are introduced which allow for handling negative
                 numbers using only binary coefficients in Fibonacci
                 base expansions. These are developed for practical
                 implementation in Fibonacci computers.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@Article{Ling:1981:HSB,
  author =       "Huey Ling",
  title =        "High-speed binary adder",
  journal =      j-IBM-JRD,
  volume =       "25",
  number =       "2/3",
  pages =        "156--166",
  month =        may # "\slash " # jun,
  year =         "1981",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Tue Mar 25 14:26:59 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C5120 (Logic and switching circuits)",
  corpsource =   "IBM Thomas J. Watson Res. Center, Yorktown Heights,
                 NY, USA",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "adders; fewer logic levels; high; neighbouring bit;
                 new carry propagation; new scheme; pairs; reduced
                 component count; speed binary adder; uniform fanin
                 loading; uniform fanout loading",
  treatment =    "N New Development",
}

@Article{Linnainmaa:1981:CEU,
  author =       "Seppo Linnainmaa",
  title =        "Combatting the effects of underflow and overflow in
                 determining real roots of polynomials",
  journal =      j-SIGNUM,
  volume =       "16",
  number =       "2",
  pages =        "11--16",
  month =        jun,
  year =         "1981",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:09 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}

@Article{Linnainmaa:1981:SDP,
  author =       "Seppo Linnainmaa",
  title =        "Software for Doubled-Precision Floating-Point
                 Computations",
  journal =      j-TOMS,
  volume =       "7",
  number =       "3",
  pages =        "272--283",
  month =        sep,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355958.355960",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "68B99 (65G99 68C05)",
  MRnumber =     "82h:68041",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://doi.acm.org/10.1145/355958.355960",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "accurate floating-point summation; exact
                 multiplication; floating-point arithmetic; rounding
                 errors; software portability",
}

@Article{Louie:1981:APS,
  author =       "T. Louie",
  title =        "Array Processors: a Selected Bibliography",
  journal =      j-COMPUTER,
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        sep,
  year =         "1981",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Fri Nov 09 19:04:04 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}

@InProceedings{Markov:1981:IAA,
  author =       "Svetoslav Markov",
  title =        "On an Interval Arithmetic and Its Applications",
  crossref =     "IEEE:1981:PSC",
  pages =        "274--278",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Markov.pdf",
  abstract =     "It is our point of view that familiar interval
                 arithmetic defined by $ A*B = \{ a * b : a \in A, b \in
                 B \} $, $ * \in \{ +, -, \times, : \} $ is inefficient
                 in certain respects. For instance, it is not in a
                 position to produce exact representations of sets of
                 the form $ \{ f(x, y, \ldots {}, z) : x \in X. y \in Y,
                 \ldots {}, z \in Z \} $ even for simple functions $f$
                 of one variable. We make use of another interval
                 arithmetic which is very convenient for computer
                 computations and for construction of interval
                 algorithms. As an example we consider a method for the
                 construction of interval expressions for sets of the
                 form $ \{ f(x) : x \in [x_1, x_2] \} $, where $f$ is an
                 elementary function.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5; interval arithmetic",
}

@Article{Maron:1981:IAP,
  author =       "N. Maron and T. A. Brengle",
  key =          "Maron \& Brengle",
  title =        "Integrating an Array Processor into a Scientific
                 Computing System",
  journal =      j-COMPUTER,
  volume =       "14",
  number =       "9",
  pages =        "41--44",
  month =        sep,
  year =         "1981",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Wed Nov 14 19:04:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Parallel/Multi.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}

@Article{Matsui:1981:OUF,
  author =       "S. Matsui and M. Iri",
  title =        "An overflow\slash underflow-free floating-point
                 representation of numbers",
  journal =      j-J-INF-PROCESS,
  volume =       "4",
  number =       "3",
  pages =        "123--133",
  year =         "1981",
  CODEN =        "JIPRDE",
  ISSN =         "0387-6101",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.0",
  content =      "The authors propose a floating-point number
                 representation whereby the allocation of digits between
                 exponent and mantissa would vary with the size of the
                 number. In extreme cases in which the entire word is
                 not long enough to contain the exponent, they move to a
                 different ``level'' and work with exponents of
                 exponents. They have implemented the scheme in
                 software, and they claim that a hardware implementation
                 is possible without loss of efficiency. Their examples
                 include Graeffe's method, which seems to survive better
                 in their environment than in a conventional
                 floating-point environment, and Racah symbols, which
                 are functions of factorials.\par

                 The examples are not totally convincing.
                 Polynomial-factoring is not a computational bottleneck.
                 The Racah symbols would indeed cause trouble if
                 computed in a direct manner in conventional floating
                 point; however, the use of a log-gamma function would
                 largely eliminate the problem.\par

                 By using certain bit-configurations to denote
                 ``nonnumbers'' the authors make good their claim of
                 overflow-free arithmetic. The system clearly has the
                 merit of convenience. In the absence of a formal error
                 analysis it is not yet clear what price has to be paid
                 for the convenience. \par

                 A. C. R. Newbery, Lexington.",
  CRclass =      "G.1.0 General; G.1.0 Computer arithmetic",
  CRnumber =     "40691",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Computer arithmetic",
  fjournal =     "Journal of Information Processing",
  genterm =      "DESIGN; PERFORMANCE",
  reviewer =     "A. C. R. Newbery; Newbery, A. C. R",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Miller:1981:RGU,
  author =       "W. Miller",
  title =        "A Remark on Gradual Underflow",
  journal =      j-COMPUTING,
  volume =       "27",
  number =       "3",
  pages =        "217--225",
  year =         "1981",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Oct 12 16:33:42 MDT 1999",
  bibsource =    "Compendex database;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliation =  "Univ of Ariz, Tucson, USA",
  classification = "723",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Computing (Vienna/New York)",
  keywords =     "computer arithmetic; computer metatheory;
                 floating-point arithmetic; IEEE 754 arithmetic",
}

@Article{Mitra:1981:CRA,
  author =       "D. Mitra and V. Lawrence",
  title =        "Controlled rounding arithmetics, for second-order
                 direct-form digital filters, that eliminate all
                 self-sustained oscillations",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "28",
  number =       "9",
  pages =        "894--905",
  month =        sep,
  year =         "1981",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 11:25:03 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "Quantization often allows a recursive second-order
                 filter to oscillate even when the underlying linear
                 model is absolutely stable and there is no external
                 signal present to excite the filter. One of the
                 significant innovative ideas recently \ldots{}",
}

@Article{Munson:1981:FPR,
  author =       "David C. {Munson, Jr.} and Bede Liu",
  title =        "Floating point roundoff error in the prime factor
                 {FFT}",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "29",
  number =       "4",
  pages =        "877--882",
  month =        aug,
  year =         "1981",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  MRclass =      "65R10 (94A05)",
  MRnumber =     "82f:65132",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The prime factor fast Fourier transform (PF FFT),
                 developed by Kolba and Parks, makes use of recent
                 computational complexity results by Winograd to compute
                 the DFT with a fewer number of multiplications than
                 that required by the FFT. Patterson and McClellan have
                 derived an expression for the mean squared error (MSE)
                 in the PF FFT, assuming finite precision fixed point
                 arithmetic. In this paper, we derive an expression for
                 the MSE in the PF FFT, assuming floating point
                 arithmetic. This expression is quite complicated, so an
                 upper bound on the MSE is also derived which is easier
                 to compute. Simulation results are presented comparing
                 the error in the PF FFT with both the derived bound and
                 the error observed in a radix-2 FFT.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
}

@InProceedings{Nguyen:1981:SAD,
  author =       "Diem Dinh Nguyen",
  title =        "A Systematic Approach to the Design of Structures for
                 Addition and Subtraction --- Case of Radix $ r = m^k
                 $",
  crossref =     "IEEE:1981:PSC",
  pages =        "42--49",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Nguyen.pdf",
  abstract =     "The results of Robertson concerning a systematic
                 approach to the design of Adder\slash Subtracter
                 structures of radix $ r = 2^k $, $ k \geq I $ are
                 generalised to cover all structures of radix $ r = m^k
                 $, $ k \geq I $ and $ m \geq 2 $. The use of
                 quasibinary representations help reduce the number of
                 types of fundamental structures required. In addition
                 to the types encountered in the earlier case, only one
                 new type of fundamental structure called Radix-$m$
                 Carry Generator is needed. Examples in the particular
                 case of Decimal Adder\slash Subtracter structures are
                 used to illustrate the results.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@InProceedings{Ong:1981:TQC,
  author =       "S. Ong and D. E. Atkins",
  title =        "Towards Quantitative Comparison of Computer Number
                 Systems",
  crossref =     "IEEE:1981:PSC",
  pages =        "21--33",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Ong_Atkins.pdf",
  abstract =     "This paper describes an evolving Arithmetic Design
                 System (ADS) to support the quantitative evaluation of
                 alternate number systems with respect to a given
                 application and realization technology. In computer
                 arithmetic we are concerned with establishing a
                 correspondence between abstract quantities (numbers)
                 and some physical representation (symbols), and with
                 simulating the operations on these symbols. The ADS is
                 intended to help study the cost and performance of
                 alternate simulations. A finite number system is a
                 triple consisting of a symbol set (elements are called
                 ``digit-vectors''), an interpretation set, a mapping
                 between these two sets, and a set of operators
                 (digit-vector algorithms) defined on its symbol set. A
                 set of these digit vector algorithms are proposed for
                 conducting arithmetic design. A number system matrix
                 defines the digit vector algorithm for numerous number
                 systems and a method for computing time and space
                 complexity of compositions of these algorithms is
                 proposed. An example of how the system could be used to
                 compare addition, with and without overflow detection,
                 for three number systems is given.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@InProceedings{Owens:1981:CAD,
  author =       "Robert Michael Owens",
  title =        "Compound Algorithms for Digit On-Line Arithmetic",
  crossref =     "IEEE:1981:PSC",
  pages =        "64--71",
  year =         "1981",
  bibdate =      "Wed Nov 14 17:53:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Owens.pdf",
  abstract =     "This paper describes a systematic method which has
                 been. successfully used to create several digit online
                 algorithms. Basically, the method entails converting in
                 a systematic way a known continued sums\slash products
                 algorithm and combining the converted form of the
                 continued sums\slash product algorithm with a
                 generalized digitization algorithm. Not only does the
                 method seem to have wide applicability in the creation
                 of digit online algorithms for many elementary
                 functions but the algorithms which have resulted from
                 this method themselves have several desirable
                 properties.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@Article{Padegs:1981:SB,
  author =       "A. Padegs",
  title =        "{System\slash 360} and Beyond",
  journal =      j-IBM-JRD,
  volume =       "25",
  number =       "5",
  pages =        "377--390",
  month =        sep,
  year =         "1981",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Sat Jan 29 17:56:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}

@Article{Pan:1981:BCA,
  author =       "V. Pan",
  title =        "The bit-complexity of arithmetic algorithms",
  journal =      j-J-ALG,
  volume =       "2",
  number =       "2",
  pages =        "144--163",
  month =        jun,
  year =         "1981",
  CODEN =        "JOALDV",
  DOI =          "https://doi.org/10.1016/0196-6774(81)90016-X",
  ISSN =         "0196-6774 (print), 1090-2678 (electronic)",
  ISSN-L =       "0196-6774",
  bibdate =      "Tue Dec 11 09:13:49 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jalg.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/019667748190016X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Algorithms",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01966774",
}

@InProceedings{Papachristou:1981:APA,
  author =       "C. A. Papachristou",
  title =        "Algorithms for Parallel Addition and Parallel
                 Polynomial Evaluation",
  crossref =     "IEEE:1981:PSC",
  pages =        "256--263",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Papachristou.pdf",
  abstract =     "This paper presents two related algorithms for
                 implementing parallel $n$-bit binary addition and
                 evaluating $n$-th degree polynomials, respectively. The
                 approach taken makes use of an iterative construction,
                 the computation tree. The algorithms are particularly
                 effective for moderate values of $n$ and are in accord
                 with well-known asymptotic bounds. In the case of
                 $n$-bit addition, the implementations constitute
                 lookahead tree circuits of $r$-input standard logic
                 elements. Extensions to modular tree structures for
                 lookahead adders are also considered. In the case of
                 parallel polynomial evaluation, the operations of
                 ordinary addition and multiplication are assumed with
                 the capability to employ $r$ arguments
                 simultaneously.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@InProceedings{Peng:1981:AES,
  author =       "Hong Peng",
  title =        "Algorithms for extracting square roots and cube
                 roots",
  crossref =     "IEEE:1981:PSC",
  pages =        "121--126",
  year =         "1981",
  bibdate =      "Thu Sep 01 11:37:17 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Peng.pdf",
  abstract =     "This paper describes a kind of algorithms for fast
                 extracting square roots and cube roots, their
                 mathematical proofs, their revised algorithm formulae,
                 and hardware implementation of the square root
                 algorithm. These algorithms may be of no significance
                 for large scale computer with fast division. But I am
                 sure that it is effective and economical to apply these
                 algorithms to the circuit designs of some mini- and
                 microcomputers with general multiplication and
                 division, such as nonrestoring division.",
  acknowledgement = ack-nj,
  keywords =     "ARITH-5",
}

@Article{Peters:1981:EFB,
  author =       "James V. Peters",
  title =        "An Equivalent Form of {Benford's Law}",
  journal =      j-FIB-QUART,
  volume =       "19",
  number =       "1",
  pages =        "74--75",
  month =        feb,
  year =         "1981",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 17:59:53 MDT 2011",
  bibsource =    "http://www.fq.math.ca/19-1.html;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.fq.math.ca/Scanned/19-1/peters.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
  journal-URL =  "http://www.fq.math.ca/",
}

@InProceedings{Raghavendra:1981:SLA,
  author =       "C. S. Raghavendra and M. D. Ercegovac",
  title =        "A Simulator for On-Line Arithmetic",
  crossref =     "IEEE:1981:PSC",
  pages =        "92--98",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Raghavendra_Ercegovac.pdf",
  abstract =     "On-line arithmetic is a special class of serial
                 arithmetic where algorithms produce results with the
                 most significant digit first during the serial input of
                 the operands. Speedup of computations can be achieved
                 by overlapping or pipelining successive operations with
                 small delays. This paper describes the design and
                 implementation of a simulator for on-line arithmetic
                 algorithms. The simulator was designed primarily to
                 serve as\par

                 (1) an experimental tool for synthesis of on-line
                 algorithms;\par

                 (2) a performance evaluation tool of on-line
                 arithmetic;\par

                 (3) an on-line calculator in solving some problems
                 involving linear and non-linear recurrences.\par

                 The simulator evaluates arithmetic expressions given in
                 a highly functional form. Presently, the set of
                 operations supported include addition, subtraction,
                 multiplication, division, and square root. Several
                 examples are presented in this paper to illustrate the
                 usage of the simulator. The simulator package is
                 implemented in 'C' language on a VAX 11/780 system.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@InProceedings{Rao:1981:AFF,
  author =       "T. R. N. Rao",
  title =        "Arithmetic of Finite Fields",
  crossref =     "IEEE:1981:PSC",
  pages =        "2--5",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Rao.pdf",
  abstract =     "The arithmetic operations in finite fields and their
                 implementation are important to the construction of
                 error detecting and correcting codes. The addition,
                 multiplication and division in the field $ \mathrm
                 {GF}(2^m) $ are implemented as polynomial operations
                 using binary logic of flip-flops and EXOR's. For fields
                 of nonbinary characteristic, modular arithmetic (with
                 modulus $p$, a prime) becomes important. This paper
                 focuses on problems relating to the arithmetic of $
                 \mathrm {GF}(p) $, and some recent results and new
                 ideas on this topic are presented here.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@InProceedings{Rao:1981:CHC,
  author =       "T. M. Rao and R. T. Gregory",
  title =        "The Conversion of {Hensel} Codes to Rational Numbers",
  crossref =     "IEEE:1981:PSC",
  pages =        "10--14",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Rao_Gregory.pdf",
  abstract =     "In a finite-segment p-adic number system one of the
                 difficult problems is concerned with converting Hensel
                 codes back into rational numbers. An algorithm for this
                 conversion is proposed which is based on a
                 sophisticated table look-up procedure.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@InProceedings{Redinbo:1981:SRN,
  author =       "G. Redinbo and W. Hunnebeck",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing, {ICASSP '81}",
  title =        "On the simulation of residue number systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "339--342",
  year =         "1981",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1049/el:19800468",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "It is sometimes difficult to simulate on general
                 purpose computers the performance of digital systems
                 that use residue number systems. This paper
                 demonstrates a new technique that makes effective use
                 of a Fast Fourier Transform (FFT) to simulate the
                 \ldots{}",
}

@InProceedings{Robertson:1981:SAD,
  author =       "J. E. Robertson",
  title =        "A Systematic Approach to the Design of Structures for
                 Arithmetic",
  crossref =     "IEEE:1981:PSC",
  pages =        "35--41",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Robertson.pdf",
  abstract =     "A design tool for the decomposition of binary digital
                 structures for addition and subtraction has been
                 developed. A simplified theory reduces a complex
                 structure to a collection of basic structures of one
                 type, namely, a full adder. The simplified theory is
                 applicable to the design of parallel counters and array
                 multipliers. A general theory is used for decomposition
                 to three types of basic structures, whose complexity is
                 usually on the order of a half-adder. The general
                 theory is applicable to redundant array multipliers and
                 signed-digit adders.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@Article{Rodrigues:1981:HEM,
  author =       "M. R. D. Rodrigues and J. H. P. Zurawski and J. B.
                 Gosling",
  title =        "Hardware evaluation of mathematical functions",
  journal =      j-IEE-PROC-E,
  volume =       "128",
  number =       "4",
  pages =        "155--164",
  month =        jul,
  year =         "1981",
  CODEN =        "IPETD3",
  ISSN =         "0143-7062",
  bibdate =      "Thu Sep 1 10:15:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IEE proceedings, E: Computers and digital techniques",
}

@InProceedings{Rutenbar:1981:CSV,
  author =       "R. A. Rutenbar and Y. E. Park",
  title =        "Case Study of a {VLSI} Design Project: a Simple Inner
                 Product Machine",
  crossref =     "IEEE:1981:PSC",
  pages =        "184--189",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Rutenbar_Park.pdf",
  abstract =     "We present a case study of the application of recently
                 evolved structured VLSI design methodologies to the
                 design and implementation of a simple VLSI quasi-serial
                 inner product machine.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@Article{Schonfelder:1981:ECP,
  author =       "J. L. Schonfelder and M. Razaz",
  title =        "Error control with polynomial approximations",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "1",
  number =       "1",
  pages =        "105--114",
  year =         "1981",
  CODEN =        "IJNADH",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65D15",
  MRnumber =     "83d:65043, 607250",
  bibdate =      "Sat Dec 23 17:06:35 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
}

@TechReport{Schryer:1981:TCF,
  author =       "N. L. Schryer",
  title =        "A Test of a Computer's Floating-Point Arithmetic
                 Unit",
  number =       "Computer Science Technical Report 89",
  institution =  "AT\&T Bell Laboratories",
  pages =        "66",
  month =        feb,
  year =         "1981",
  bibdate =      "Fri Nov 30 11:20:24 2001",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://plan9.bell-labs.com/cm/cs/cstr/89.ps.gz;
                 http://www.bell-labs.com/topic/swdist/",
  acknowledgement = ack-nj,
  keywords =     "floating-point testing",
}

@Article{Schwarz:1981:EYC,
  author =       "H. R. Schwarz",
  title =        "The Early Years of Computing in {Switzerland}",
  journal =      j-ANN-HIST-COMPUT,
  volume =       "3",
  number =       "2",
  pages =        "121--132",
  month =        apr # "\slash " # jun,
  year =         "1981",
  CODEN =        "AHCOE5",
  DOI =          "https://doi.org/10.1109/MAHC.1981.10013",
  ISSN =         "0164-1239",
  ISSN-L =       "0164-1239",
  bibdate =      "Fri Nov 1 15:29:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/bibnet/authors/r/rutishauser-heinz.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
                 https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://dlib.computer.org/an/books/an1981/pdf/a2121.pdf;
                 http://www.computer.org/annals/an1981/a2121abs.htm",
  acknowledgement = ack-nhfb,
  content =      "Schwartz describes two early computers used at the
                 Swiss Federal Institute of Technology (whose German
                 acronym is ETH) during the 1950s. Despite the more
                 general title, he does not mention any non-ETH
                 computers in this article. According to Schwartz, the
                 first programmable computer in Switzerland was the Z4
                 developed by Konrad Zuse in Germany during World War II
                 and installed at the ETH in 1950. Except for the ERMETH
                 (also at the ETH), he does not mention any subsequent
                 Swiss installations during the period, leaving a weak
                 implication that there were none.\par

                 The Z4 was an electromechanical machine with a total
                 data memory of 64 32-bit words and no program memory.
                 Programs were executed while being read from punched
                 tape. Conditional test instructions permitted
                 instructions on the tape to be skipped; other control
                 instructions caused an alternate tape reader to begin
                 processing a program (a form of subroutine-call). The
                 arithmetic unit could perform true floating-point
                 operations. This arithmetic unit contained built-in
                 functions for computing squares, reciprocals, and
                 square roots. (Ten years later, mere integer division
                 was still optional at an extra cost on the IBM 1401.)
                 There were special representations for infinity and
                 ``undefined'' so that operations such as division by
                 zero could continue without interruption but with a
                 meaningful result.",
  CRclass =      "K.2.7 ERMETH; K.2 Hardware; K.2 Software",
  CRnumber =     "39473",
  descriptor =   "Computing Milieux, HISTORY OF COMPUTING; Computing
                 Milieux, HISTORY OF COMPUTING, ERMETH; Computing
                 Milieux, HISTORY OF COMPUTING, Hardware; Computing
                 Milieux, HISTORY OF COMPUTING, Software",
  fjournal =     "Annals of the History of Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
  reviewer =     "D. Ross",
  subject =      "K. Computing Milieux; K.2 HISTORY OF COMPUTING",
  subject-dates = "Ambros Speiser (13 November 1922--10 May 2003); Heinz
                 Rutishauser (30 January 1918--10 November 1970); Eduard
                 Stiefel (21 April 1909--25 November 1978)",
}

@Article{Smith:1981:ERA,
  author =       "J. M. Smith and F. W. J. Olver and D. W. Lozier",
  title =        "Extended-Range Arithmetic and Normalized {Legendre}
                 Polynomials",
  journal =      j-TOMS,
  volume =       "7",
  number =       "1",
  pages =        "93--105",
  month =        mar,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355934.355940",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20 (65G05)",
  MRnumber =     "83a:65017",
  bibdate =      "Mon Aug 29 22:02:12 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://doi.acm.org/10.1145/355934.355940",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "angular momentum; extended-range arithmetic; Legendre
                 polynomials; overflow; underflow",
}

@Book{Spaniol:1981:CAL,
  author =       "Otto Spaniol",
  title =        "Computer Arithmetic: Logic and Design",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "280",
  year =         "1981",
  ISBN =         "0-471-27926-9",
  ISBN-13 =      "978-0-471-27926-6",
  LCCN =         "QA76.6 .S6613, TK7888.3.S7",
  bibdate =      "Thu Sep 01 22:26:58 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "English translation of \cite{Spaniol:1976:AR}.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Notation \\
                 Adders \\
                 Multiplication \\
                 Division \\
                 Redundant notation \\
                 Calculation of special functions \\
                 Time complexity of arithmetic operations",
}

@Misc{Stark:1981:MBR,
  author =       "Moshe Stark",
  title =        "Multiple Bit Read-Only Memory Cell and Its Sense
                 Amplifier",
  howpublished = "US Patent 4,287,570.",
  day =          "1",
  month =        sep,
  year =         "1981",
  bibdate =      "Sat Aug 23 06:41:51 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Filed 1 June 1979. See discussion
                 \cite{Shirriff:2018:TBP}.",
  URL =          "https://ieeemilestones.ethw.org/w/images/e/e1/Patent_Moshe_Stark_Intel_two_bit_ROM.pdf",
  abstract =     "The bit density of stored information in a read-only
                 memory (ROM) can be substantially increased by
                 increasing the number of bits which can be stored in
                 each memory cell. This can be accomplished without
                 increasing the size or complexity of the memory cell by
                 having the read only memory capacity stored in each
                 memory cell as one of a multiple number of discrete
                 states achievable by the cell. In a semiconductor chip
                 element, such as a transistor, capable of assuming one
                 of a multiple of parametric values or states. For
                 example, conductor transistor can be varied to assume
                 one of four different states. The state assigned to a
                 selected memory cell is bracketed by the value of the
                 outputs of a plurality of comparator circuits coupled
                 thereto. The outputs of the comparator circuits are
                 then analyzed by a logic circuit to provide the
                 appropriate binary readout representative of the
                 parametric state of the selected cell.",
  acknowledgement = ack-nhfb,
}

@Article{Stevenson:1981:ITP,
  author =       "David Stevenson",
  title =        "{IEEE Task 754}: a Proposed Standard for Binary
                 Floating-Point Arithmetic: Draft 8.0",
  journal =      j-COMPUTER,
  volume =       "14",
  number =       "3",
  pages =        "51--62",
  month =        mar,
  year =         "1981",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Thu Sep 1 10:14:17 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  annote =       "Offered here for public comment, this proposed
                 standard facilitates transportation of numerically
                 oriented programs and encourages development of
                 high-quality numerical software.",
  country =      "USA",
  date =         "30/10/88",
  descriptors =  "Standardization; computer arithmetic; IEEE 754;
                 floating point; computation structure; numerical
                 software",
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}

@Article{Stevenson:1981:PSBa,
  author =       "David Stevenson",
  title =        "A Proposed Standard for Binary Floating-Point
                 Arithmetic",
  journal =      j-COMPUTER,
  volume =       "14",
  number =       "3",
  pages =        "51--62",
  month =        mar,
  year =         "1981",
  CODEN =        "CPTRB4",
  DOI =          "https://doi.org/10.1109/C-M.1981.220377",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Sun May 2 09:21:54 1999",
  bibsource =    "Distributed/QLD.bib; Distributed/QLD/1981.bib;
                 https://www.math.utah.edu/pub/tex/bib/computer1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  annote =       "Offered here for public comment, this proposed
                 standard facilitates transportation of numerically
                 oriented programs and encourages development of
                 high-quality numerical software.",
  country =      "USA",
  date =         "30/10/88",
  descriptors =  "Standardization; computer arithmetic; IEEE 754;
                 floating point; computation structure; numerical
                 software",
  enum =         "2967",
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
  location =     "PKI-OG: Li-Ord.Le; RWTH-AC-DFV: Bibl.",
  references =   "0",
  revision =     "21/04/91",
}

@Book{Stevenson:1981:PSBb,
  author =       "David Stevenson",
  title =        "A proposed standard for binary floating-point
                 arithmetic: draft 8.0 of {IEEE} Task {P754}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "36",
  year =         "1981",
  bibdate =      "Sun May 02 09:22:07 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{IEEE:1985:AIS,IEEE:1985:ASI}.",
  acknowledgement = ack-nhfb,
  keywords =     "Compiling (Electronic computers).; Floating-point
                 arithmetic.",
  remark =       "Reprinted from: Computer, v. 14, no. 3 (Mar. 1981):
                 51--87. Includes articles by W. J. Cody, David Hough,
                 and Jerome T. Coonen.",
}

@InProceedings{Stummel:1981:PAM,
  author =       "F. Stummel",
  title =        "Optimal error estimates for {Gaussian} elimination in
                 floating-point arithmetic",
  crossref =     "GAMM:1981:PAM",
  journal =      j-Z-ANGE-MATH-MECH,
  volume =       "62",
  number =       "5",
  pages =        "T355--T357",
  year =         "1981",
  CODEN =        "ZAMMAX",
  ISSN =         "0044-2267 (print), 1521-4001 (electronic)",
  ISSN-L =       "0044-2267",
  MRclass =      "65G05 (65F10)",
  MRnumber =     "84j:65039",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "{Zeitschrift f{\"u}r Angewandte Mathematik und
                 Mechanik}",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
}

@InProceedings{Tan:1981:ADC,
  author =       "C.-I. Tan and B. C. McInnis",
  booktitle =    "20th {IEEE} Conference on Decision and Control
                 including the Symposium on Adaptive Processes",
  title =        "Adaptive digital control implemented using residue
                 number systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "808--812",
  year =         "1981",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/CDC.1981.269326",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The application of residue number systems for the
                 implementation of adaptive digital controllers is
                 presented. Division operations are avoided through the
                 use of iteration to solve for the value of the control.
                 Decoding computations are simplified \ldots{}",
}

@InProceedings{Taylor:1981:CHD,
  author =       "George S. Taylor",
  title =        "Compatible hardware for division and square root",
  crossref =     "IEEE:1981:PSC",
  pages =        "127--134",
  year =         "1981",
  bibdate =      "Mon Sep 16 16:30:51 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Taylor.pdf",
  abstract =     "Hardware for radix four division and radix two square
                 root is shared in a processor designed to implement the
                 proposed IEEE floating-point standard. The division
                 hardware looks ahead to find the next quotient digit in
                 parallel with the next partial remainder. An 8-bit ALU
                 estimates the next remainder's leading bits. The
                 quotient digit look-up table is addressed with a
                 truncation of the estimate rather than a truncation of
                 the full partial remainder. The estimation ALU and the
                 look-up table are asymmetric for positive and negative
                 remainders. This asymmetry reduces the width of the ALU
                 and the number of minterms in the logic equations for
                 the look-up table. The square root algorithm obtains
                 the correctly rounded result in about two division
                 times using small extensions to the division
                 hardware.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5; correct rounding; floating-point arithmetic",
}

@Article{Taylor:1981:FPR,
  author =       "Fred J. Taylor and Chao H. Huang",
  title =        "A floating-point residue arithmetic unit",
  journal =      j-J-FRANKLIN-INST,
  volume =       "311",
  number =       "1",
  pages =        "33--53",
  month =        jan,
  year =         "1981",
  CODEN =        "JFINAB",
  ISSN =         "0016-0032 (print), 1879-2693 (electronic)",
  ISSN-L =       "0016-0032",
  MRclass =      "94A11 (68A05)",
  MRnumber =     "82a:94013",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  catcode =      "B.2; G.1.0",
  content =      "This paper describes the logical design of a floating
                 point arithmetic unit using a hybrid residue number
                 system. Mantissas of numbers are operated in a residue
                 system while the exponents are in binary. Some basic
                 operations, such as scaling and underflow/overflow
                 detection, are described, and circuit implementation
                 using ROMs indicated. ``For example, let m(z)` be a
                 2N-bit work in integer form and H_0 and H_1 represent
                 the two following hypotheses. If m(z`) e H_1, then
                 m(z`) W 1-2- 2^2N = 2^2N 1. If m(z)` e H_0, then m(z)`
                 < 1-2- 2^2N = 2^2N 1. The hypothesis testing is
                 accomplished by comparing each of the mixed-radix
                 digits of m(z)` to that of 2^2N 1 through L independent
                 binary comparators.'' Circuits for multiplication,
                 addition, and subtraction are derived. The procedures
                 seem reasonable and the proofs rigorous. Table look up
                 cycle times and memory requirements for different
                 implementation of the arithmetic units are estimated.
                 These are comparable with corresponding times and
                 memory needs for PDP/11. Use in algorithms such as FFT
                 is argued for.\par

                 The exposition is somewhat difficult. As with many
                 logical designs one is not sure whether the approach
                 given is optimum (for any sense of the word
                 ``optimum''). In the absence of a working system one
                 can not be sure",
  CRclass =      "B.2.1 Design Styles; G.1.0 General; G.1.0 Computer
                 arithmetic",
  CRnumber =     "39211",
  descriptor =   "Hardware, ARITHMETIC AND LOGIC STRUCTURES, Design
                 Styles; Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Computer arithmetic",
  fjournal =     "Journal of {The Franklin Institute}",
  genterm =      "DESIGN",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00160032",
  reviewer =     "B. Hazeltine; Hazeltine, B",
  subject =      "B. Hardware; B.2 ARITHMETIC AND LOGIC STRUCTURES; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@InProceedings{Taylor:1981:VHP,
  author =       "George S. Taylor and David A. Patterson",
  title =        "{VAX} Hardware for the Proposed {IEEE} Floating-Point
                 Standard",
  crossref =     "IEEE:1981:PSC",
  pages =        "190--196",
  year =         "1981",
  bibdate =      "Wed Nov 14 17:53:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Taylor_Patterson.pdf",
  abstract =     "The proposed IEEE floating-point standard has been
                 implemented in a substitute floating-point accelerator
                 for the VAX-11/760. We explain how features of the
                 proposed standard influenced the design of the new
                 processor. By comparing it with the original VAX
                 accelerator, we illustrate the differences between
                 hardware for the proposed standard and hardware for a
                 more traditional floating-point architecture.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@Article{Todericiu:1981:AOBb,
  author =       "Doru Todericiu",
  title =        "Analyses d'ouvrages: {{\booktitle{Whilhelm Schickard
                 (1592--1635), Astronom, Geograph, Orientalist, Erfinder
                 der Rechenmaschine}} par Friedrich Seck}",
  journal =      j-REV-HIST-SCI,
  volume =       "34",
  number =       "3--4",
  pages =        "374--374",
  month =        "juillet--octobre",
  year =         "1981",
  CODEN =        "RHSAAM",
  DOI =          "https://doi.org/10.2307/23632469",
  ISSN =         "0151-4105 (print), 1969-6582 (electronic)",
  ISSN-L =       "0048-7996",
  bibdate =      "Tue Jun 16 11:06:47 MDT 2015",
  bibsource =    "http://www.jstor.org/stable/i23631674;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/revhistsci.bib",
  URL =          "http://www.jstor.org/stable/23632469",
  acknowledgement = ack-nhfb,
  ajournal =     "Rev. hist. sci.",
  fjournal =     "Revue d'Histoire des Sciences",
  journal-URL =  "http://www.jstor.org/journals/00487996.html;
                 http://www.persee.fr/collection/rhs",
  language =     "French",
}

@Book{Tyner:1981:GDP,
  author =       "Paul Tyner",
  title =        "{iAPX} 432 General Data Processor Architecture
                 Reference Manual",
  publisher =    pub-INTEL,
  address =      pub-INTEL:adr,
  pages =        "various",
  year =         "1981",
  LCCN =         "TK7895.M5 T85 1981",
  bibdate =      "Fri Dec 08 13:03:20 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  xxISBN =       "(none)",
}

@Manual{vonGudenberg:1981:GAP,
  author =       "J. Wolff von Gudenberg",
  title =        "{Gesamte Arithmetik des Pascal-SC Rechners.
                 Benutzerhandbuch}. ({German}) [{Complete} Arithmetic of
                 the {Pascal-SC} Computer: User Handbook]",
  organization = "Institute for Applied Mathematics, University of
                 Karlsruhe",
  address =      "Karlsruhe, West Germany",
  pages =        "????",
  year =         "1981",
  bibdate =      "Wed Oct 13 22:27:27 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@InProceedings{Walker:1981:EMA,
  author =       "Gregory Walker",
  title =        "Extension of the {MC68000} Architecture to Include
                 Standard Floating-Point Arithmetic",
  crossref =     "IEEE:1981:PSC",
  pages =        "179--182",
  year =         "1981",
  bibdate =      "Wed Nov 14 17:53:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Walker.pdf",
  abstract =     "The synthetic aspect of designing a computer
                 architecture is particularly evident when the design is
                 highly constrained from two independent directions.
                 Floating-point extensions of the MC68000 architecture
                 incorporate the IEEE Proposed Floating-point Standard
                 into the existing MC68000 architecture.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@Article{Washington:1981:BLF,
  author =       "Lawrence C. Washington",
  title =        "{Benford's Law} for {Fibonacci} and {Lucas} Numbers",
  journal =      j-FIB-QUART,
  volume =       "19",
  number =       "2",
  pages =        "175--176",
  month =        apr,
  year =         "1981",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 17:59:55 MDT 2011",
  bibsource =    "http://www.fq.math.ca/19-2.html;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.fq.math.ca/Scanned/19-2/washington.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
  journal-URL =  "http://www.fq.math.ca/",
}

@TechReport{Watanuki:1981:FOAa,
  author =       "Osaaki Watanuki",
  title =        "Floating-point on-line arithmetic for highly
                 concurrent digit-serial computation: application to
                 mesh problems",
  institution =  "Computer Science Dept. Research Laboratory",
  address =      "Los Angeles, CA, USA",
  pages =        "xvi + 149",
  year =         "1981",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "UCLA-ENG; 8107 ReRport [sic] / UCLA Computer Science
                 Department; no. CSD 810529 Report (University of
                 California, Los Angeles. Computer Science Dept.); no.
                 CSD-810529",
  acknowledgement = ack-nhfb,
  keywords =     "Differential equations, Partial.; Floating-point
                 arithmetic.",
  remark =       "Consists of the author's thesis ({Ph.D.})--UCLA, 1981.
                 Bibliography: p. 146-149.",
}

@PhdThesis{Watanuki:1981:FOAb,
  author =       "Osaaki Watanuki",
  title =        "Floating-point on-line arithmetic for highly
                 concurrent digit-serial computation: application to
                 mesh problems",
  type =         "Thesis ({Ph.D.})",
  school =       "UCLA",
  address =      "Los Angeles, CA, USA",
  pages =        "xvi + 149",
  year =         "1981",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Differential equations, Partial.; Floating-point
                 arithmetic.",
}

@InProceedings{Watanuki:1981:FPLa,
  author =       "O. Watanuki and M. D. Ercegovac",
  title =        "Floating-point On-Line Arithmetic: Algorithms",
  crossref =     "IEEE:1981:PSC",
  pages =        "81--86",
  year =         "1981",
  bibdate =      "Wed Nov 14 17:53:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Watanuki_Ercegovac_a.pdf",
  abstract =     "For effective application of on-line arithmetic to
                 practical numerical problems, floating-point algorithms
                 for on-line addition\slash subtraction and
                 multiplication have been implemented by introducing the
                 notion of quasi-normalization. Those proposed are
                 normalized fixed-precision FLPOL (floating-point
                 on-line) algorithms.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@InProceedings{Watanuki:1981:FPLb,
  author =       "O. Watanuki and M. D. Ercegovac",
  title =        "Floating-point On-Line Arithmetic: Error Analysis",
  crossref =     "IEEE:1981:PSC",
  pages =        "87--91",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Watanuki_Ercegovac_b.pdf",
  abstract =     "The properties of redundant number system in mantissa
                 representation are studied and the range of the
                 redundant mantissa is derived. From the range of the
                 mantissa and the absolute error of on-line operations,
                 the MRRE (maximum relative representation error) is
                 defined and analyzed for redundant floating-point
                 numbers.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@Article{Wehringer:1981:FSA,
  author =       "A. Wehringer",
  title =        "{Flie{\ss}komma-Arithmetik} \toenglish {Floating-point
                 Arithmetic} \endtoenglish",
  journal =      "Elektronikschau",
  volume =       "5",
  pages =        "34--36",
  year =         "1981",
  bibdate =      "Fri Sep 16 16:30:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Wehringer:1981:SBM,
  author =       "A. Wehringer",
  title =        "{Schnelle 16-bit-Multiplikation und Division}
                 \toenglish {Fast 16-bit Multiplication and Division}
                 \endtoenglish",
  journal =      "Elektronikschau",
  volume =       "10",
  pages =        "36--37",
  year =         "1981",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Manual{Weinreb:1981:LMM,
  author =       "Daniel Weinreb and David Moon",
  title =        "{LISP} Machine Manual",
  organization = "MIT Artificial Intelligence Laboratory",
  address =      "Cambridge, MA, USA",
  edition =      "Third",
  month =        mar,
  year =         "1981",
  bibdate =      "Wed Jan 29 17:08:51 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "From \cite{Steele:2004:RHP}: ``The number of digits
                 printed is the `correct' number; no information present
                 in the flonum is lost, and no extra trailing digits are
                 printed that do not represent information in the
                 flonum. Feeding the [printed representation] of a
                 flonum back to the reader is always supposed to produce
                 an equal flonum.''",
}

@InProceedings{Willoner:1981:AME,
  author =       "Robert Willoner and I-Ngo Chen",
  title =        "An Algorithm for Modular Exponentiation",
  crossref =     "IEEE:1981:PSC",
  pages =        "135--138",
  year =         "1981",
  bibdate =      "Thu Nov 15 11:37:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith5/papers/ARITH5_Willoner_Chen.pdf",
  abstract =     "The best known algorithm for {\em modular
                 exponentiation}, $ M^e \bmod t $ for arbitrary $M$,
                 $e$, and $t$ is of $ O(n^3) $ where $n$ is the number
                 ot bits in the largest of $M$, $e$ and $t$. This paper
                 presents an $ O(n) $ algorithm for the problem where $
                 M^e \bmod t $ is required for many values of $M$ and
                 $e$ with constant $t$. Some preprocessing is done on
                 $t$, and the results are applied repeatedly to
                 different values of $M$ and $e$. The main algorithm
                 involves {\em on-line} arithmetic in a {\em redundant}
                 number system. An immediate application is in
                 encoding\slash decoding of messages in an RSA-based
                 {\em public-key cryptosystem}.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5",
}

@Article{Zurawski:1981:DHS,
  author =       "J. H. P. Zurawski and J. B. Gosling",
  title =        "Design of High-Speed Digital Divider Units",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-30",
  number =       "9",
  pages =        "691--699",
  month =        sep,
  year =         "1981",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1981.1675869",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 18:45:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675869",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InCollection{Aiken:1982:ASC,
  author =       "Howard H. Aiken and Grace M. Hopper",
  title =        "The Automatic Sequence Controlled Calculator (1946)",
  crossref =     "Randell:1982:ODC",
  pages =        "203--222",
  year =         "1982",
  bibdate =      "Sun Nov 03 08:36:11 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Andrews:1982:MMS,
  author =       "M. Andrews",
  title =        "Mathematical Microprocessor Software: a $ \sqrt {x} $
                 Comparison",
  journal =      j-IEEE-MICRO,
  volume =       "2",
  number =       "3",
  pages =        "63--79",
  month =        aug,
  year =         "1982",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.1982.290970",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Dec 14 06:08:58 MST 2000",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeemicro.bib;
                 Science Citation Index database (1980--2000)",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  ajournal =     "IEEE Micro",
  classcodes =   "C4130 (Interpolation and function approximation);
                 C6150G (Diagnostic, testing, debugging and evaluating
                 systems)",
  corpsource =   "Colorado State Univ., Fort Collins, CO, USA",
  fjournal =     "IEEE Micro",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=40",
  keywords =     "16-bit machines; 8-bit machine; accuracy; Chen method;
                 computer testing; Cordic method; direct method;
                 function approximation; hardware; Intel 8080; Newton
                 method; PDP-11/20; software requirements; speed;
                 square-roots",
  remark =       "This article compares instruction-level implementation
                 on the Intel 8080 and DEC PDP-11/20 of the square root
                 using five methods: direct, CORDIC, Chen's, and two
                 variations of Newton's iteration. The concluding
                 paragraph says: ``The conclusions are fairly obvious:
                 Even with the availability of hardware features most
                 suitable to any of the other methods, Newton's method
                 remains the technique of choice. Although the advent of
                 hardware multiple-bit-shift instructions will alter
                 this comparison somewhat, Newton's method, with optimal
                 initialization, will again prove to be the best when
                 hardware multiply\slash divide becomes generally
                 available.''",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Andrews:1982:SRX,
  author =       "M. Andrews",
  title =        "Square-Root-{X} Comparison --- New Results Discovered
                 --- Reply",
  journal =      j-IEEE-MICRO,
  volume =       "2",
  number =       "4",
  pages =        "5--6",
  month =        oct # "\slash " # dec,
  year =         "1982",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.1982.291010",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Dec 14 06:08:58 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Science Citation Index database (1980--2000)",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}

@Article{Anonymous:1982:ARBf,
  author =       "Anonymous",
  title =        "Article Review: {{\booktitle{Ada model arithmetic:
                 costs and benefits}}: Wallis, P. J. L. \booktitle{IEE
                 Proc.-E Comput. Dig. Tech.} Vol 129 No 2 (March 1982)
                 pp 75--80}",
  journal =      j-MICROPROC-MICROSYS,
  volume =       "6",
  number =       "9",
  pages =        "497--498",
  month =        nov,
  year =         "1982",
  CODEN =        "MIMID5",
  DOI =          "https://doi.org/10.1016/0141-9331(82)90515-4",
  ISSN =         "0141-9331 (print), 1872-9436 (electronic)",
  ISSN-L =       "0141-9331",
  bibdate =      "Mon Jan 14 21:50:13 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0141933182905154",
  acknowledgement = ack-nhfb,
  fjournal =     "Microprocessors and Microsystems",
}

@TechReport{Anonymous:1982:MKF,
  author =       "Anonymous",
  title =        "{Materialiensammlung zum 5. Kolloquium (mit Floating
                 Point Systems) Neue Rechnerarchitekturen:
                 Anwendungsgebiete und Realisierungen: Hannover, (18.Mai
                 1982)}",
  type =         "{Bericht}",
  number =       "30",
  institution =  "Regionales Rechenzentrum f{\"u}r Niedersachsen bei der
                 Universit{\"a}t Hannover",
  address =      "Hannover, Germany",
  pages =        "58",
  year =         "1982",
  bibdate =      "Thu May 09 09:13:36 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Anonymous:1982:NPAa,
  author =       "Anonymous",
  title =        "New product applications: Array processor performs 5
                 million floating-point operations per second, has
                 200-ns operation time",
  journal =      j-IEEE-SPECTRUM,
  volume =       "19",
  number =       "1",
  pages =        "104--118",
  month =        jan,
  year =         "1982",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.1982.6366777",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Sat Jan 18 16:51:45 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "Algorithms; Arrays; Microcomputers; Microprocessors;
                 Process control; Speech; Standards",
}

@MastersThesis{Arnold:1982:EPS,
  author =       "Mark Gordon Arnold",
  title =        "Extending the Precision of the Sign Logarithm Number
                 System",
  type =         "{M.S.} Thesis",
  school =       "University of Wyoming",
  address =      "Laramie, WY, USA",
  year =         "1982",
  bibdate =      "Fri Jun 24 16:06:13 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Bairstow:1982:FPP,
  author =       "R. Bairstow and J. Barlow and M. Jires and M. Waters",
  title =        "A floating point processor for {Intel 8080A}
                 microprocessor systems",
  type =         "Technical report",
  number =       "RL 82-020",
  institution =  "Rutherford Appleton Lab.",
  address =      "Harwell, Oxon, UK",
  pages =        "44",
  month =        mar,
  year =         "1982",
  bibdate =      "Fri May 25 05:47:40 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://weblib.cern.ch/format/showfull?uid=1451323_18194&base=CERCER&sysnb=0050018",
  acknowledgement = ack-nhfb,
}

@InProceedings{Baraniecki:1982:QEL,
  author =       "A. Baraniecki and G. Jullien",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing, {ICASSP '82}",
  title =        "Quantization error and limit cycles analysis in
                 residue number system coded recursive filters",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "52--55",
  year =         "1982",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1049/el:19820632",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The paper discusses the Residue Number System (RNS)
                 implementation of second order recursive digital filter
                 sections. The RNS offers the advantage of using integer
                 based arithmetic operations and a simple hardware
                 realization involving arrays of \ldots{}",
}

@Article{Barnes:1982:RNI,
  author =       "C. Barnes and T. Miyawaki",
  title =        "Roundoff Noise Invariants in Normal Digital Filters",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "29",
  number =       "4",
  pages =        "251--256",
  month =        apr,
  year =         "1982",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "The unit noise gains for optimal and parallel normal
                 realizations of digital filters can be expressed in
                 terms of a set of noise gain parameters that are simply
                 related to the pole locations and pole residues. These
                 noise gain parameters are shown \ldots{}",
}

@Article{Bernhard:1982:CCS,
  author =       "R. Bernhard",
  title =        "Computers: Computing at the speed limit: Computers
                 1000 times faster than today's supercomputers would
                 benefit vital scientific applications",
  journal =      j-IEEE-SPECTRUM,
  volume =       "19",
  number =       "7",
  pages =        "26--31",
  month =        jul,
  year =         "1982",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.1982.6366940",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Sat Jan 18 16:51:45 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/super.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "Computational modeling; Computer architecture;
                 computer industry; Computers; Educational institutions;
                 engineering applications; floating-point operations per
                 second; flops; Program processors; scientific
                 applications; Solid modeling; special purpose
                 computers; very large-scale integration; VLSI",
}

@Article{Bernhard:1982:GSP,
  author =       "R. Bernhard",
  title =        "Giants in small packages [array processors]",
  journal =      j-IEEE-SPECTRUM,
  volume =       "19",
  number =       "2",
  pages =        "39--44",
  month =        feb,
  year =         "1982",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.1982.6366796",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Sat Jan 18 16:51:45 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "architecture; array processor; Arrays; arrays of
                 numbers; computer; computer architecture; digital
                 arithmetic; digital computers; Hardware; matrices;
                 Microcomputers; Pipelines; Program processors;
                 repetitive arithmetic operations; Vectors; vectors",
}

@Article{Bohannan:1982:MAP,
  author =       "J. W. Bohannan and D. J. Bradley and D. A. Kummer and
                 J. A. Saenz",
  title =        "Multiplication Algorithm for Packed {BCD} Numbers",
  journal =      j-IBM-TDB,
  volume =       "25",
  number =       "4",
  pages =        "2225",
  month =        sep,
  year =         "1982",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
}

@Article{Bohlender:1982:ROA,
  author =       "G. Bohlender and K. Gr{\"u}ner and J. Wolff {von
                 Gudenberg}",
  title =        "{Realisierung einer optimalen Arithmetik} \toenglish
                 {Realization of Optimal Arithmetic} \endtoenglish",
  journal =      j-ELEK-RECHENANLAGEN,
  volume =       "24",
  number =       "2",
  pages =        "68--72",
  month =        apr,
  year =         "1982",
  CODEN =        "ELRAA4",
  ISSN =         "0013-5720",
  bibdate =      "Sat Feb 10 12:41:07 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektronische Rechenanlagen",
}

@Article{Brent:1982:RLP,
  author =       "R. P. Brent and H. T. Kung",
  title =        "A regular layout for parallel adders",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-31",
  number =       "??",
  pages =        "260--264",
  year =         "1982",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1982.1675982",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Sep 16 16:06:24 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Brooks:1982:OCL,
  author =       "R. A. Brooks and R. P. Gabriel and G. L. {Steele
                 Jr.}",
  title =        "An optimizing compiler for lexically scoped {LISP}",
  journal =      j-SIGPLAN,
  volume =       "17",
  number =       "6",
  pages =        "261--275",
  month =        jun,
  year =         "1982",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sat Apr 25 11:46:37 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C6140D (High level languages); C6150C (Compilers,
                 interpreters and other processors)",
  conflocation = "Boston, MA, USA; 23--25 June 1982",
  conftitle =    "Proceedings of the SIGPLAN '82 Symposium on Compiler
                 Construction",
  corpsource =   "MIT, Cambridge, MA, USA",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "BLISS-11; complex numbers; floating-point; FORTRAN;
                 lexically scoped LISP; LISP; list manipulation;
                 multiprocessing supercomputer; optimizing compiler;
                 PASCAL; PQCC compiler; program compilers; S-1 PASCAL;
                 stable-driven; symbolic processing; TNBIND technique;
                 vectors",
  sponsororg =   "ACM",
  treatment =    "P Practical",
}

@Article{Burr:1982:CCR,
  author =       "S. A. Burr",
  title =        "Computing cube roots when a fast square root is
                 available",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "8",
  number =       "3",
  pages =        "181--183",
  month =        "????",
  year =         "1982",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(82)90041-4",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 18:51:22 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122182900414",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221/",
}

@Article{Cassola:1982:FPA,
  author =       "R. L. Cassola",
  title =        "Floating Point Algorithm Design",
  journal =      j-COMP-DESIGN,
  volume =       "21",
  number =       "6",
  pages =        "107--114",
  month =        jun,
  year =         "1982",
  CODEN =        "CMPDAM",
  ISSN =         "0010-4566",
  bibdate =      "Wed Sep 7 22:31:27 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computer Design",
}

@Article{Cassola:1982:FPM,
  author =       "R. L. Cassola",
  title =        "A Floating Point Module for Military Computers",
  journal =      j-COMP-DESIGN,
  volume =       "21",
  number =       "2",
  pages =        "67--76",
  month =        feb,
  year =         "1982",
  CODEN =        "CMPDAM",
  ISSN =         "0010-4566",
  bibdate =      "Wed Sep 7 22:31:27 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computer Design",
}

@MastersThesis{Cavanagh:1982:DCA,
  author =       "Joseph J. F. Cavanagh",
  title =        "Digital computer arithmetic: design and
                 implementation",
  type =         "Thesis ({M.S.})",
  school =       "University of Santa Clara",
  address =      "Santa Clara, CA, USA",
  pages =        "vii + 503",
  year =         "1982",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic and logic units.; Floating-point
                 arithmetic.",
}

@InProceedings{Cody:1982:BCC,
  author =       "W. J. Cody",
  title =        "Basic concepts for computational software",
  crossref =     "Messina:1982:PMM",
  pages =        "1--23",
  year =         "1982",
  DOI =          "https://doi.org/10.1007/3-540-11603-6_1",
  bibdate =      "Fri Sep 23 23:12:32 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cody:1982:FPM,
  author =       "W. J. Cody",
  title =        "Floating-point parameters, models, and standards",
  crossref =     "Reid:1982:RBN",
  pages =        "51--69",
  year =         "1982",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.0; D.3.0",
  CRclass =      "G.1.0 General; G.1.0 Computer arithmetic; D.3.0
                 General; D.3.0 Standards",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Computer arithmetic; Software, PROGRAMMING LANGUAGES,
                 General, Standards",
  genterm =      "THEORY; STANDARDIZATION",
  guideno =      "10367",
  keywords =     "languages; standardization",
  review =       "ACM CR 8402-0092",
  reviewer =     "Hansen, E",
  subject =      "D.3.0 Software, PROGRAMMING LANGUAGES, General,
                 Standards \\ G.1.0 Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic; G. Mathematics
                 of Computing; G.1 NUMERICAL ANALYSIS; D. Software; D.3
                 PROGRAMMING LANGUAGES",
}

@TechReport{Cody:1982:GPI,
  author =       "W. J. Cody",
  title =        "A Generalization of the Proposed {IEEE} Standard for
                 Floating-Point Arithmetic",
  type =         "Technical Report",
  number =       "??",
  institution =  inst-ANL,
  address =      inst-ANL:adr,
  pages =        "20",
  year =         "1982",
  bibdate =      "Thu Nov 17 10:40:11 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Republished in \cite{Cody:1983:GPI}.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cody:1982:ITF,
  author =       "W. J. Cody",
  title =        "Implementation and Testing of Function Software",
  crossref =     "Messina:1982:PMM",
  pages =        "24--47",
  year =         "1982",
  DOI =          "https://doi.org/10.1007/3-540-11603-6_1",
  bibdate =      "Sat Sep 24 01:18:12 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "range reduction",
}

@Article{Corbett:1982:EAF,
  author =       "R. P. Corbett",
  title =        "Enhanced arithmetic for {Fortran}",
  journal =      j-SIGPLAN,
  volume =       "17",
  number =       "12",
  pages =        "41--48",
  month =        dec,
  year =         "1982",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sat Apr 25 11:46:37 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C6140D (High level languages)",
  corpsource =   "Department of Computer Sci., University of California,
                 Berkeley, CA, USA",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "accuracy; arithmetic; digital arithmetic; efficiency;
                 FORTRAN; Fortran; programmers; speed; widest need
                 evaluation",
  treatment =    "P Practical",
}

@InProceedings{Dao:1982:KCA,
  author =       "T. T. Dao",
  editor =       "{IEEE}",
  booktitle =    "Proceedings of the 12th International Symposium on
                 Multiple-Valued Logic, May 1982",
  title =        "{Knuth}'s Complex Arithmetic with Quaternary
                 Hardware",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "94--98",
  month =        may,
  year =         "1982",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Aug 22 09:14:13 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dekker:1982:PCM,
  author =       "T. J. Dekker",
  editor =       "Paul C. Messina and Almerico Murli",
  booktitle =    "Problems and Methodologies in Mathematical Software
                 Production",
  title =        "Program Correctness and Machine Arithmetic",
  volume =       "142",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "48--80",
  year =         "1982",
  bibdate =      "Sat May 1 15:24:45 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
}

@Book{DeSautels:1982:ALP,
  author =       "Edouard J. DeSautels",
  title =        "Assembly language programming for {PDP-11} and
                 {LSI-11} computers: an introduction to computer
                 organization",
  publisher =    "William C. Brown Co. Publ.",
  address =      "Dubuque, IA",
  pages =        "xviii + 574",
  year =         "1982",
  ISBN =         "0-697-08164-8",
  ISBN-13 =      "978-0-697-08164-3",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$21.95",
  acknowledgement = ack-nhfb,
  catcode =      "A; C.1.1; D.3; D.3.2; D.3.2",
  content =      "The author has provided material on the Assembler
                 language for the PDP-11 or LSI-11 computers in an
                 original and comprehensive manner. Users of this
                 Assembler or even of this computer should find this
                 text especially valuable as a student text or as a
                 permanent reference. Much of the material in the
                 PDP-11, MACRO-11 Reference Manual, Processor Handbook,
                 Peripheral Handbook, and Terminals and Communications
                 Handbook is organized in this book in a readable,
                 step-by-step manner. Required is access to a PDP-11 (or
                 LSI-11) and some knowledge of programming in a
                 high-level language.\par

                 Topics include the following: \par

                 * Very accessible and detailed material on introduction
                 to computers and programming. It is unlikely that a
                 reader would require much if any prior knowledge of
                 computers.\par

                 * An early introduction to machine language to explain
                 the functioning of a computer, and then a lead-in into
                 Assembler language.\par

                 * Development of the use of registers, Assembler
                 Directives, indexing, immediate operands, arithmetic
                 for signed and unsigned data, subroutines, stacks,
                 passing parameters, input/output, floating-point
                 arithmetic, and more.\par

                 * An interesting chapter, ``Selected Topics,'' covering
                 such subjects as tables, lists, queues, trees, threaded
                 code, and reentrant co",
  CRclass =      "C.1.1 Single Data Stream Architectures; C.1.1 PDP-11;
                 D.3.2 Language Classifications; D.3.2 Language
                 Classifications; D.3.2 Macro and assembly languages;
                 D.3.2 Language Classifications; D.3.2 PDP-11 assembly
                 language",
  CRnumber =     "40452",
  descriptor =   "General Literature, INTRODUCTORY AND SURVEY; Computer
                 Systems Organization, PROCESSOR ARCHITECTURES, Single
                 Data Stream Architectures, PDP-11; Software,
                 PROGRAMMING LANGUAGES, Language Classifications;
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Macro and assembly languages;
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, PDP-11 assembly language",
  genterm =      "LANGUAGES",
  pubname =      "William C. Brown Co. Publ., Dubuque, IA",
  reviewer =     "P. Abel; Abel, P",
  subject =      "A. General Literature; A.1 INTRODUCTORY AND SURVEY; C.
                 Computer Systems Organization; C.1 PROCESSOR
                 ARCHITECTURES; D. Software; D.3 PROGRAMMING LANGUAGES;
                 D. Software; D.3 PROGRAMMING LANGUAGES; D. Software;
                 D.3 PROGRAMMING LANGUAGES",
}

@InCollection{Dreyer:1982:ACI,
  author =       "H.-J. Dreyer and A. Walther",
  title =        "The Automatic Calculator {IPM} (1946)",
  crossref =     "Randell:1982:ODC",
  pages =        "155--161",
  year =         "1982",
  bibdate =      "Sun Nov 03 08:36:11 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Epstein:1982:UAF,
  author =       "C. Epstein and W. L. Miranker and T. J. Rivlin",
  title =        "Ultra-arithmetic {I}: function data types",
  journal =      j-MATH-COMPUT-SIMUL,
  volume =       "24",
  number =       "1",
  pages =        "1--18",
  month =        feb,
  year =         "1982",
  CODEN =        "MCSIDR",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1; G.1.2; G.1.2",
  CRclass =      "G.1.5 Roots of Nonlinear Equations; G.1.2
                 Approximation; G.1.2 Chebyshev approximation and
                 theory; G.1.2 Approximation; G.1.2 Elementary function
                 approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
                 Nonlinear Equations; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Chebyshev
                 approximation and theory; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Elementary function
                 approximation",
  fjournal =     "Mathematics and Computers in Simulation",
  genterm =      "algorithms",
  guideno =      "09324",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784754",
  jrldate =      "Feb. 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Epstein:1982:UAI,
  author =       "C. Epstein and W. L. Miranker and T. J. Rivlin",
  title =        "Ultra-arithmetic {II}: intervals of polynomials",
  journal =      j-MATH-COMPUT-SIMUL,
  volume =       "24",
  number =       "1",
  pages =        "19--29",
  month =        feb,
  year =         "1982",
  CODEN =        "MCSIDR",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.2; G.1.1; G.1.0",
  CRclass =      "G.1.2 Approximation; G.1.2 Elementary function
                 approximation; G.1.1 Interpolation; G.1.1 Spline and
                 piecewise polynomial interpolation; G.1.0 General;
                 G.1.0 Error analysis",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation;
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation, Spline and piecewise polynomial
                 interpolation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Error analysis",
  fjournal =     "Mathematics and Computers in Simulation",
  genterm =      "algorithms",
  guideno =      "09325",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784754",
  jrldate =      "Feb. 1982",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{Fateman:1982:HLL,
  author =       "Richard J. Fateman",
  title =        "High-Level Language Implications of the Proposed
                 {IEEE} Floating-Point Standard",
  journal =      j-TOPLAS,
  volume =       "4",
  number =       "2",
  pages =        "239--257",
  month =        apr,
  year =         "1982",
  CODEN =        "ATPSDT",
  DOI =          "https://doi.org/10.1145/357162.357168",
  ISSN =         "0164-0925 (print), 1558-4593 (electronic)",
  ISSN-L =       "0164-0925",
  bibdate =      "Thu Nov 8 14:50:28 2007",
  bibsource =    "Compiler/bevan.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "An IEEE Computer Society working group on
                 floating-point arithmetic has recommended a standard
                 for binary floating-point number formats, operations,
                 and semantics. This paper, which has evolved in part
                 during the deliberations of that committee, describes
                 the significance to languages and, in particular, to
                 FORTRAN and its variants, of various novel features of
                 the recommended standard.",
  acknowledgement = ack-pb,
  checked =      "19940302",
  fjournal =     "ACM Transactions on Programming Languages and
                 Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J783",
  keywords =     "computer arithmetic; control structures; data types
                 and structures; error handling and recovery;
                 floating-point arithmetic; FORTRAN; run-time
                 environments",
  source =       "Dept. Library",
}

@TechReport{Feldstein:1982:EPI,
  author =       "A. Feldstein and R. Goodman",
  title =        "The evaluation of probability integrals for the loss
                 of significance in floating point subtraction and
                 addition",
  type =         "Technical report",
  institution =  "Department of Mathematics, Arizona State University",
  address =      "Tempe, AZ, USA",
  year =         "1982",
  bibdate =      "Tue Oct 09 09:50:41 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Feldstein:1982:LSF,
  author =       "A. Feldstein and R. Goodman",
  title =        "Loss of Significance in Floating Point Subtraction and
                 Addition",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-31",
  number =       "4",
  pages =        "328--335",
  month =        apr,
  year =         "1982",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1982.1676002",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:15:07 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  abstract =     "We study the loss of significant $ \beta $ its (base $
                 \beta $ digits) in floating point addition or
                 subtraction. To do this, we calculate the conditional
                 probability of a post-arithmetic normalization shift of
                 $m$ $ \beta $ its, given an exponent difference of $k$
                 $ \beta $ its. The study is done for various bases $
                 \beta $, under two different assumptions---that the
                 operands are selected at random from the logarithmic
                 distribution or from the uniform distribution.",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Fulton:1982:BJB,
  author =       "T. A. Fulton and L. N. Dunkleberger",
  title =        "{B.S.T.J.} Briefs: a {Josephson} Parallel Multiplier",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "61",
  number =       "5",
  pages =        "931--933",
  month =        may # "--" # jun,
  year =         "1982",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  bibdate =      "Tue Nov 9 11:15:56 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1982/BSTJ.1982.6105.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol61/bstj61-5-931.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}

@Article{Gerrity:1982:CRR,
  author =       "G. W. Gerrity",
  title =        "Computer Representation of Real Numbers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-31",
  number =       "8",
  pages =        "709--714",
  month =        aug,
  year =         "1982",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1982.1676076",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:33:14 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676076",
  abstract =     "Hwang's model for the computer representation of real
                 numbers is extended to explicitly distinguish between
                 the representational system used to denote real numbers
                 and the internal encoding of the digits of the
                 representation in the computer memory. The encoding
                 function can then be chosen to preserve certain
                 properties of the real number system and to optimize
                 the computer arithmetic in a sense to be described
                 herein. Two examples of optimal computer arithmetics
                 are discussed.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Goodrich:1982:VEP,
  author =       "J. L. Goodrich",
  title =        "Very efficient 8080 program multiplies and divides",
  journal =      j-ELECTRONICS,
  volume =       "55",
  number =       "4",
  pages =        "144--145",
  month =        feb,
  year =         "1982",
  ISSN =         "0883-4989",
  bibdate =      "Thu Sep 1 10:15:07 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronics",
  journal-URL =  "https://www.mdpi.com/journal/electronics",
}

@InProceedings{Gordon:1982:BFS,
  author =       "E. Gordon and C. Hastings",
  booktitle =    "Conference Record, {SOUTHCON, 1982}",
  title =        "Big, Fast and Simple Algorithms, Architecture and
                 Components for High-end Minis",
  publisher =    "????",
  address =      "????",
  pages =        "????",
  year =         "1982",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Fri Nov 09 18:54:03 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Paper 21/3.",
  acknowledgement = ack-nhfb,
}

@Article{Hantler:1982:ESS,
  author =       "S. L. Hantler and A. H. Karp",
  title =        "Exponential by Sequential Squaring",
  journal =      j-IBM-TDB,
  volume =       "25",
  number =       "1",
  pages =        "171--173",
  month =        jun,
  year =         "1982",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:16:09 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
}

@InProceedings{Hull:1982:PCE,
  author =       "T. E. Hull",
  title =        "Precision Control, Exception Handling and a Choice of
                 Numerical Algorithms",
  crossref =     "Watson:1982:NAP",
  pages =        "169--178",
  year =         "1982",
  DOI =          "https://doi.org/10.1007/BFb0093156",
  bibdate =      "Sat Feb 8 10:29:52 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
  remark =       "Proposes precision control as later provided in
                 Numerical Turing.",
}

@InProceedings{Hull:1982:UCP,
  author =       "T. E. Hull",
  title =        "The uses of controlled precision",
  crossref =     "Reid:1982:RBN",
  pages =        "71--82",
  year =         "1982",
  bibdate =      "Fri Jan 04 12:57:37 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
  xxpages =      "71--84",
}

@Article{Hwang:1982:PMA,
  author =       "Kai Hwang and Yeng-Heng Cheng",
  title =        "Partitioned Matrix Algorithms for {VLSI} Arithmetic
                 Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-31",
  number =       "12",
  pages =        "1215--1224",
  month =        dec,
  year =         "1982",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1982.1675945",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:33:17 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675945",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Jenkins:1982:FRD,
  author =       "W. Jenkins",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing, {ICASSP '82}",
  title =        "Failure resistant digital filters based on residue
                 number system product codes",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "60--63",
  year =         "1982",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1049/el:19820632",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Residue number system product codes are proposed for
                 the design of self-checking digital filters. It is
                 shown that product codes require redundancy that is
                 similar to, but slightly less than that of systematic
                 codes for simultaneous overflow \ldots{}",
}

@Article{Jenkins:1982:RNS,
  author =       "W. K. Jenkins",
  title =        "Residue number system error checking using expanded
                 projection",
  journal =      j-ELECT-LETTERS,
  volume =       "18",
  number =       "21",
  pages =        "927--928",
  day =          "14",
  month =        oct,
  year =         "1982",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:19820632",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4246948",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A new concept called expanded projection is presented
                 that simplifies the process of error detection and
                 location in redundant residue number codes. Expanded
                 projection simplifies the circuit complexity of the
                 error checker, resulting in a structure \ldots{}",
}

@InProceedings{Kahan:1982:NOS,
  author =       "W. Kahan and Jerome T. Coonen",
  title =        "The Near Orthogonality of Syntax, Semantics, and
                 Diagnostics in Numerical Programming Environments",
  crossref =     "Reid:1982:RBN",
  pages =        "103--115",
  year =         "1982",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  catcode =      "D.3; G.1.0; F.3.2; D.2.5; D.2; D.3",
  content =      "Programmers of early computers had to content
                 themselves with what the machine designers offered and
                 be glad that the hardware worked at all. Later, with
                 the introduction of higher-level languages, the
                 computing environment was modified by the language
                 designers who attempted to resolve a three-cornered
                 tug-of-war among implementation efficiency, program
                 portability, and usefulness to the programmer. The
                 conflict between the first two resulted in languages
                 that reflected the least common denominator of
                 available hardware, since language designers were
                 disinclined to mention any capability not available on
                 all computers. A case in point is floating-point
                 arithmetic, where the subtleties of overflow,
                 underflow, and rounding are generally well beyond the
                 control of the programmer in a high-level language. The
                 new standard for binary floating-point arithmetic that
                 has been proposed by IEEE Computer Society's
                 Floating-Point Committee, Task P754 [1], makes an
                 attempt to escape from this situation. It represents
                 the Committee's view of the floating-point requirements
                 of the \ldots{}",
  CRclass =      "D.3.1 Formal Definitions and Theory; G.1.0 General;
                 G.1.0 Computer arithmetic; F.3.2 Semantics of
                 Programming Languages; F.3.2 Algebraic approaches to
                 semantics; D.2.5 Testing and Debugging; D.2.5
                 Diagnostics; D.2.6 Programming Environments; D.3.3
                 Language Constructs",
  CRnumber =     "8401-0021",
  descriptor =   "Software, PROGRAMMING LANGUAGES, Formal Definitions
                 and Theory; Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic; Theory of
                 Computation, LOGICS AND MEANINGS OF PROGRAMS, Semantics
                 of Programming Languages, Algebraic approaches to
                 semantics; Software, SOFTWARE ENGINEERING, Testing and
                 Debugging, Diagnostics; Software, SOFTWARE ENGINEERING,
                 Programming Environments; Software, PROGRAMMING
                 LANGUAGES, Language Constructs",
  genterm =      "LANGUAGES; STANDARDIZATION",
  keywords =     "floating-point arithmetic; rounding errors",
  remark =       "This article forms the body of \cite[Chapter
                 3]{Coonen:1984:CPS}.",
  reviewer =     "M. Marcotty; Marcotty, M",
  source =       "in the relationship between numerical computation and
                 programming languages. Proc. IFIP TC2 working
                 conference (Boulder, CO, Aug. 3--7, 1981) J. K. Reid
                 (Ed.) Elsevier North-Holland, Inc., New York, 1982",
  subject =      "D. Software; D.3 PROGRAMMING LANGUAGES; G. Mathematics
                 of Computing; G.1 NUMERICAL ANALYSIS; F. Theory of
                 Computation; F.3 LOGICS AND MEANINGS OF PROGRAMS; D.
                 Software; D.2 SOFTWARE ENGINEERING; D. Software; D.2
                 SOFTWARE ENGINEERING; D. Software; D.3 PROGRAMMING
                 LANGUAGES",
}

@Book{Katzan:1982:IAA,
  author =       "Harry Katzan",
  title =        "Invitation to {Ada} and {Ada} reference manual ({July
                 1980})",
  publisher =    "PBI",
  address =      "New York, NY, USA",
  pages =        "xi + 429",
  year =         "1982",
  ISBN =         "0-89433-132-9",
  ISBN-13 =      "978-0-89433-132-9",
  LCCN =         "QA76.73.A35 K37 1982",
  bibdate =      "Wed Oct 13 06:37:40 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  remark =       "See \cite[p. 1.10]{Coonen:1984:CPS} for negative
                 comments about the floating-point model for Ada in this
                 book.",
  subject =      "Ada (computer program language)",
}

@InProceedings{Kerkhoff:1982:LDM,
  author =       "H. G. Kerkhoff and H. A. J. Robroek",
  editor =       "{IEEE}",
  booktitle =    "Proceedings of the 12th International Symposium on
                 Multiple-Valued Logic, May 1982",
  title =        "The Logic Design of Multiple-valued Logic Functions
                 Using {CCD}'s",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "35--44",
  year =         "1982",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Aug 22 09:16:45 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Korn:1982:EDF,
  author =       "G. A. Korn",
  title =        "{EARLY DESIRE}: a floating-point equation language
                 simulation system for minicomputers and
                 microcomputers",
  journal =      j-SIMULATION,
  volume =       "38",
  number =       "5",
  pages =        "151--159",
  month =        may,
  year =         "1982",
  CODEN =        "SIMUA2",
  ISSN =         "0037-5497 (print), 1741-3133 (electronic)",
  ISSN-L =       "0037-5497",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  catcode =      "I.6; G; D.4.7",
  CRclass =      "I.6.2 Simulation Languages; D.4.7 Organization and
                 Design; D.4.7 Interactive systems",
  descriptor =   "Computing Methodologies, SIMULATION AND MODELING,
                 Simulation Languages; Mathematics of Computing,
                 MISCELLANEOUS; Software, OPERATING SYSTEMS,
                 Organization and Design, Interactive systems",
  fjournal =     "Simulation",
  genterm =      "DESIGN; LANGUAGES",
  guideno =      "08785",
  journal-URL =  "http://sim.sagepub.com/content/by/year",
  subject =      "I. Computing Methodologies; I.6 SIMULATION AND
                 MODELING; G. Mathematics of Computing; G.m
                 MISCELLANEOUS; D. Software; D.4 OPERATING SYSTEMS",
}

@Article{Leuprecht:1982:PAR,
  author =       "H. Leuprecht and W. Oberaigner",
  title =        "Parallel Algorithms for the Rounding-Exact Summation
                 of Floating-Point Numbers",
  journal =      j-COMPUTING,
  volume =       "28",
  number =       "2",
  pages =        "89--104",
  month =        "????",
  year =         "1982",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "68A05 (65G05)",
  MRnumber =     "83c:68009",
  bibdate =      "Fri Dec 08 11:53:42 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "accurate floating-point summation",
}

@Article{McCormick:1982:EFM,
  author =       "S. F. McCormick and G. D. Taylor and D. V. Pryor",
  title =        "Evaluation of Functions on Microcomputers: $ \ln (x)
                 $",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "8",
  number =       "5",
  pages =        "389--392",
  year =         "1982",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Thu Sep 15 18:41:01 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  xxmonth =      "(none)",
}

@Article{McPherson:1982:LSG,
  author =       "John C. McPherson and Frank E. Hamilton and Robert R.
                 {Seeber, Jr.}",
  title =        "A Large-Scale, general-Purpose Electronic Digital
                 calculator: The {SSEC}",
  journal =      j-ANN-HIST-COMPUT,
  volume =       "4",
  number =       "4",
  pages =        "313--326",
  month =        oct # "\slash " # dec,
  year =         "1982",
  CODEN =        "AHCOE5",
  ISSN =         "0164-1239",
  ISSN-L =       "0164-1239",
  bibdate =      "Fri Nov 1 15:29:19 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://dlib.computer.org/an/books/an1982/pdf/a4313.pdf;
                 http://www.computer.org/annals/an1982/a4313abs.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of the History of Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
}

@Article{Monroe:1982:FFP,
  author =       "Alfred J. Monroe",
  title =        "{Forth} Floating Point Package",
  journal =      j-DDJ,
  volume =       "7",
  number =       "9",
  pages =        "16--??",
  month =        sep,
  year =         "1982",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@Article{Oklobdzija:1982:LSR,
  author =       "V. G. Oklobdzija and M. D. Ercegovac",
  title =        "An On-Line Square Root Algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-31",
  number =       "1",
  pages =        "70--75",
  month =        jan,
  year =         "1982",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1982.1675887",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:33:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675887",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Misc{Palmer:1982:NDP,
  author =       "John Palmer and Bruce Ravenel and Rafi Nave",
  title =        "Numeric Data Processor",
  howpublished = "US Patent 4,338,675.",
  pages =        "22",
  day =          "6",
  month =        jul,
  year =         "1982",
  bibdate =      "Sat Aug 23 06:33:14 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Filed 13 February, 1980. This general patent covers
                 the breadth of 8087 features.",
  URL =          "https://ieeemilestones.ethw.org/w/images/6/6c/Patent_8087_coprocessor.pdf",
  abstract =     "A floating point, integrated, arithmetic circuit is
                 organized around a file format having a floating point
                 numeric domain exceeding that of any single or double
                 precision floating point numbers, long or short integer
                 words or BCD data upon which it must operate. As a
                 result the circuit has a greater reliability, range and
                 precision than ever previously achieved without
                 entailing additional circuit complexity. Reliability is
                 further enhanced by a systematic three bit rounding
                 field, and by including means for detecting every error
                 or exception condition with an optional expected
                 response provided thereto by hardware. As a result of
                 such organization, an unexpected increase of capacity
                 is achieved wherein transcendental functions can be
                 computed totally in hardware, and whereby mixed mode
                 arithmetic can be implemented without difficulty. The
                 numeric processor also includes a programmable shifter
                 capable of arbitrary numbers of bit and byte shifts in
                 a single clock cycle, as well as an arithmetic unit
                 capable of implementing multiplication, division,
                 modulo reduction and square roots directly in
                 hardware.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Palmer:1982:VRN,
  author =       "J. F. Palmer",
  title =        "{VLSI} and the Revolution in Numeric Computation",
  crossref =     "Ruschitzka:1982:IWC",
  pages =        "339--341",
  year =         "1982",
  bibdate =      "Wed Sep 7 22:31:27 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@InCollection{Phillips:1982:BC,
  author =       "E. William Phillips",
  title =        "Binary Calculation",
  crossref =     "Randell:1982:ODC",
  pages =        "303--314",
  year =         "1982",
  bibdate =      "Wed Oct 13 09:51:37 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "The 1936 epigraph credited to this author in
                 \cite[Chapter 7]{Coonen:1984:CPS} says: ``The ultimate
                 aim is to persuade all of the civilized world to
                 abandon the decimal numeration and to use octonal in
                 its place; to discontinue counting in tens and to count
                 in eights instead. However, it seems unlikely that the
                 whole civilized world will be persuaded to complete
                 this change during the next twelve months, having
                 previously declined similar invitations.''",
}

@InProceedings{Rall:1982:ACA,
  author =       "L. B. Rall",
  editor =       "Anonymous",
  booktitle =    "{Proceedings of the 1982 Army Numerical Analysis and
                 Computers Conference}",
  title =        "Accurate computer arithmetic for scientific
                 computation",
  volume =       "82--83",
  publisher =    "US Army Research Office",
  address =      "Research Triangle Park, NC, USA",
  bookpages =    "xiv + 606",
  pages =        "343--356",
  month =        aug,
  year =         "1982",
  bibdate =      "Wed Oct 13 21:52:01 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Two volumes.",
  URL =          "http://books.google.com/books?id=pFb-QQAACAAJ",
  abstract =     "The operations of accurate arithmetic can be
                 implemented easily on a microcomputer or a computer
                 with microprogrammable arithmetic operations. In
                 addition, for accurate final results, a compiler is
                 necessary which will select the appropriate operations.
                 A language of this type (PASCAL-SC) was developed.
                 Along with accurate real arithmetic, this compiler
                 provides accurate complex arithmetic, real and complex
                 interval arithmetic, and vector and matrix arithmetic
                 over these data types. Some features of PASCAL-SC
                 related to scientific and engineering computation are
                 described. In most cases, the operations of accurate
                 arithmetic are performed at the same speed as ordinary
                 (uncontrolled) floating-point arithmetic.",
  acknowledgement = ack-nhfb,
  keywords =     "analysis (mathematics); arithmetic; computation;
                 microcomputers; microprogramming; Pascal (programming
                 language)",
  meetingname =  "Army Numerical Analysis and Computers Conference (1982
                 : Vicksburg, Miss.)",
  remark =       "The theme of the 1982 Conference was Grid Techniques
                 for Partial Differential Equations.",
  subject =      "Numerical analysis; Computer programs; Congresses;
                 Numerical Mathematics. Computer Hardware. Computers.
                 Partial differential equations. Symposia. Numerical
                 analysis. Grids. Computations. Methodology.
                 Mathematical programming. Finite difference theory.
                 Finite element analysis. Boundaries. Hydrodynamics. Gas
                 dynamics. Interior ballistics. Autofrettage. Land
                 mines. Blast loads. Conduction(heat transfer) Magnet
                 coils. Water waves. Currents",
  xxtitle =      "Accurate arithmetic for scientific computation",
  xxvolume =     "82-3",
}

@InProceedings{Ramnarayan:1982:AER,
  author =       "R. Ramnarayan and F. Taylor",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing, {ICASSP '82}",
  title =        "Analysis of errors in residue number system ({RNS})
                 based {IIR} digital filters",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "56--59",
  year =         "1982",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1049/el:19820632",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The problem of analyzing errors in Residue Number
                 System (RNS) based IIR Digital filters is considered in
                 this paper. There are basically three types of errors
                 in RNS based digital filters, They are coefficient
                 quantization errors(1), scaling errors \ldots{}",
}

@Article{Rix:1982:UQA,
  author =       "P. Rix",
  title =        "{Universeller Quad\-rat\-wurz\-el-Al\-go\-rith\-mus}
                 \toenglish {Universal Square Root Algorithms}
                 \endtoenglish",
  journal =      j-ELECTRONIK,
  volume =       "23",
  pages =        "81--82",
  year =         "1982",
  CODEN =        "EKRKAR",
  ISSN =         "0013-5658",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektronik",
}

@Article{Rump:1982:CR,
  author =       "Siegfried M. Rump",
  title =        "{Computer und Rechengenauigkeit} \toenglish {Computer
                 and Computational Precision} \endtoenglish",
  journal =      j-ELEK-RECHENANLAGEN,
  volume =       "24",
  number =       "6",
  pages =        "268--277",
  month =        dec,
  year =         "1982",
  CODEN =        "ELRAA4",
  ISSN =         "0013-5720",
  bibdate =      "Sat Feb 10 12:41:06 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektronische Rechenanlagen",
}

@Article{Sacks-Davis:1982:ARN,
  author =       "R. Sacks-Davis",
  title =        "Applications of Redundant Number Representations to
                 Decimal Arithmetic",
  journal =      j-COMP-J,
  volume =       "25",
  number =       "4",
  pages =        "471--477",
  month =        nov,
  year =         "1982",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "Compendex database;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/471.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/472.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/473.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/474.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/475.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/476.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_04/tiff/477.tif",
  abstract =     "A decimal arithmetic unit is proposed for both integer
                 and floating-point computations. To achieve comparable
                 speed to a binary arithmetic unit, the decimal unit is
                 based on a redundant number representation. With this
                 representation no loss of compactness is made relative
                 to binary coded decimal (BCD) form. In this paper the
                 hardware required for the implementation of the basic
                 operations of addition, subtraction, multiplication and
                 division are described and the properties of
                 floating-point arithmetic based on a redundant number
                 representation are investigated.",
  acknowledgement = ack-nhfb,
  classcodes =   "C5260 (Digital signal processing)",
  classification = "721; 723",
  corpsource =   "Department of Computer Sci., Monash University,
                 Clayton, Vic., Australia",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "addition; binary; binary arithmetic unit; coded
                 decimal; computers, digital; decimal floating-point
                 arithmetic; digital arithmetic; division; floating
                 point arithmetic; floating-point; integer;
                 multiplication; redundant number representations;
                 subtraction",
  remark =       "The redundant number representation postpones the need
                 to carry during add, subtract, multiply, and divide,
                 delaying it until the final rounding step in a store
                 instruction. See
                 \cite{Fahmy:2003:CRF,Fahmy:2003:RDF}.",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Samsen:1982:AFP,
  author =       "G. R. Samsen",
  title =        "An Advanced Floating Point Processor to Enhance Speed
                 of Mathematical Processing",
  crossref =     "Southcon:1982:SCR",
  pages =        "16/1/1--3",
  year =         "1982",
  bibdate =      "Wed Sep 7 22:31:27 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Sasaki:1982:EGE,
  author =       "T. Sasaki and H. Murao",
  key =          "Symbolic_determinant; Symbolic_linear_systems;
                 Gaussian_elimination",
  title =        "Efficient {Gaussian} elimination method for symbolic
                 determinants and linear systems",
  journal =      j-TOMS,
  volume =       "8",
  number =       "3",
  pages =        "277--289",
  month =        sep,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356004.356007",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  catcode =      "F.2; G.1.3; I.1.2",
  content =      "The computation of the solution of a linear system
                 whose entries are indeterminates or polynomials is of
                 interest both for theoretic and practical reasons. The
                 similar problem of computing the determinant is
                 important because of the relationship of the
                 determinant and resultant to factorization, polynomial
                 greatest-common-divisor calculations, and computation
                 with algebraic functions. Engineering application areas
                 of this material include the analysis of electrical or
                 other networks.\par

                 These computation problems are quite distinct from
                 others which would appear to be superficially similar,
                 namely numerical linear algebra problems. The result of
                 computing a numerical determinant is a floating point
                 number with an associated error. The result of
                 computing an exact algebraic determinant is, typically,
                 a large expression whose terms may be rearranged into
                 various ``factored'' forms for savings in computation
                 time and space. This answer has no error
                 whatsoever.\par

                 Clever and efficient programs in each domain have been
                 shown to be disastrous in the other. Thus one of the
                 best algebraic techniques for determinant calculations
                 for ``sparse polynomial'' matrices is expansion by
                 minors [1]; whereas Gaussian elimination is far
                 superior \ldots{}",
  CRclass =      "F.2.1 Numerical Algorithms and Problems; G.1.3
                 Numerical Linear Algebra; G.1.3 Linear systems (direct
                 and iterative methods); I.1.2 Algorithms; I.1.2
                 Algebraic algorithms",
  CRnumber =     "40106",
  descriptor =   "Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems;
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra, Linear systems (direct and iterative
                 methods); Computing Methodologies, ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  genterm =      "ALGORITHMS; PERFORMANCE",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "R. J. Fateman; Fateman, R. J",
  subject =      "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
                 G.1 NUMERICAL ANALYSIS; I. Computing Methodologies; I.1
                 ALGEBRAIC MANIPULATION",
}

@Article{Sasaki:1982:PFM,
  author =       "T. Sasaki and Y. Kanada",
  title =        "Practically Fast Multiple Precision Evaluation of
                 {LOG} ($ {X} $)",
  journal =      j-INFO-PROC,
  volume =       "5",
  number =       "4",
  pages =        "247--250",
  month =        "????",
  year =         "1982",
  bibdate =      "Thu Sep 8 08:20:54 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Schatte:1982:FPF,
  author =       "P. Schatte",
  title =        "The Frequency of Postshifts in Floating-Point
                 Multiplication",
  journal =      "Elektronische Informationsverarbeitung und
                 Kybernetik",
  volume =       "18",
  number =       "9",
  pages =        "523--526",
  month =        "????",
  year =         "1982",
  bibdate =      "Thu Sep 1 10:15:07 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Sewell:1982:RLT,
  author =       "B. T. Sewell",
  title =        "A Rapid Lookup Table Method for Trigonometric
                 Functions",
  journal =      j-SPE,
  volume =       "12",
  number =       "10",
  pages =        "885--887",
  month =        oct,
  year =         "1982",
  CODEN =        "SPEXBL",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Thu Sep 1 10:15:56 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Software---Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  keywords =     "algorithms",
  subject =      "G Mathematics of Computing, MISCELLANEOUS \\ J.2
                 Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Chemistry",
}

@InCollection{Sheldon:1982:ICP,
  author =       "John W. Sheldon and Liston Tatum",
  title =        "The {IBM} Card-Programmed Electronic Calculator
                 (1951)",
  crossref =     "Randell:1982:ODC",
  pages =        "233--239",
  year =         "1982",
  bibdate =      "Sun Nov 03 08:36:11 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@MastersThesis{Sippel:1982:FRI,
  author =       "Timothy N. Sippel",
  title =        "Floating {RISCS}: implementation and analysis of
                 floating point on {RISC} {I}",
  type =         "Electrical Engineering and Computer Sciences Master of
                 Science Report",
  school =       "University of California, Department of Electrical
                 Engineering and Computer Sciences",
  address =      "Berkeley, CA, USA",
  pages =        "various",
  year =         "1982",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Sips:1982:CPM,
  author =       "H. J. Sips",
  title =        "Comments on {``An $ O(n) $ Parallel Multiplier with
                 Bit-Sequential Input and Output''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-31",
  number =       "4",
  pages =        "325--327",
  month =        apr,
  year =         "1982",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1982.1676000",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:33:11 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676000",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Strader:1982:CBS,
  author =       "N. R. Strader and V. T. Rhyne",
  title =        "A Canonical Bit-Sequential Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-31",
  number =       "8",
  pages =        "791--795",
  month =        aug,
  year =         "1982",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1982.1676085",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:33:14 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676085",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Tan:1982:ADC,
  author =       "Chung-I Tan and B. McInnis",
  title =        "Adaptive digital control implemented using residue
                 number systems",
  journal =      j-IEEE-TRANS-AUTOMAT-CONTR,
  volume =       "27",
  number =       "2",
  pages =        "499--502",
  month =        apr,
  year =         "1982",
  CODEN =        "IETAA9",
  DOI =          "https://doi.org/10.1109/CDC.1981.269326",
  ISSN =         "0018-9286 (print), 1558-2523 (electronic)",
  ISSN-L =       "0018-9286",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See comments \cite{Pei:1984:CAD}.",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=24189",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Automatic Control",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The application of residue number systems for the
                 implementation of adaptive digital controllers is
                 presented. Division operations are avoided through the
                 use of iteration to solve for the value of the control.
                 Decoding computations are simplified \ldots{}",
}

@Article{Taylor:1982:ARM,
  author =       "F. J. Taylor and C. H. Huang",
  title =        "An Autoscale Residue Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-31",
  number =       "4",
  pages =        "321--325",
  month =        apr,
  year =         "1982",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1982.1675999",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 09 19:30:01 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Taylor:1982:VRA,
  author =       "F. J. Taylor",
  title =        "A {VLSI} Residue Arithmetic Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-31",
  number =       "6",
  pages =        "540--546",
  month =        jun,
  year =         "1982",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1982.1676036",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:33:12 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676036",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Teachey:1982:SRX,
  author =       "R. D. Teachey",
  title =        "Square-Root-{X} Comparison --- New Results
                 Discovered",
  journal =      j-IEEE-MICRO,
  volume =       "2",
  number =       "4",
  pages =        "5--5",
  month =        oct # "\slash " # dec,
  year =         "1982",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.1982.290929",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Dec 14 06:08:58 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Science Citation Index database (1980--2000)",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}

@InCollection{TorresyQuevedo:1982:EAD,
  author =       "Leonardo {Torres y Quevedo}",
  title =        "Essays on Automatics --- Its Definitions ---
                 Theoretical Extent of its Applications (1914)",
  crossref =     "Randell:1982:ODC",
  pages =        "89--107",
  year =         "1982",
  bibdate =      "Sun Nov 03 08:36:11 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "This translation and reprint contains a description of
                 what is believed to be the first design, albeit purely
                 theoretical, and for an electromechanical device, of
                 floating-point arithmetic. See, however, the
                 independent work, and first practical implementation of
                 floating-point arithmetic of Zuse
                 \cite{Zuse:1982:MAE,Zuse:1982:OCD}.",
}

@Article{Turner:1982:DLS,
  author =       "Peter R. Turner",
  title =        "The distribution of leading significant digits",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "2",
  number =       "4",
  pages =        "407--412",
  year =         "1982",
  CODEN =        "IJNADH",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65G99 (60E05)",
  MRnumber =     "84f:65038",
  MRreviewer =   "Seppo Linnainmaa",
  bibdate =      "Sat Dec 23 17:06:35 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Velasevic:1982:RLC,
  author =       "Dusan M. Velasevi{\'c}",
  title =        "Right-to-Left Code Generation for Arithmetic
                 Expressions",
  journal =      j-COMP-J,
  volume =       "25",
  number =       "3",
  pages =        "316--326",
  month =        aug,
  year =         "1982",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/25.3.316",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:48:13 MST 2012",
  bibsource =    "Compendex database;
                 http://comjnl.oxfordjournals.org/content/25/3.toc;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/;
                 https://www.math.utah.edu/pub/tex/bib/compj1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/25/3/316.full.pdf+html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/316.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/317.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/318.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/319.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/320.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/321.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/322.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/323.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/324.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/325.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_25/Issue_03/tiff/326.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C6110 (Systems analysis and programming); C6120 (File
                 organisation)",
  classification = "723",
  corpsource =   "Faculty of Electrical Engng., University of Belgrade,
                 Belgrade, Yugoslavia",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "arithmetic; automatic programming; binary tree
                 structure; code generator; codes, symbolic; data
                 structures; expressions; FORTRAN; notation; postfix;
                 right-to-left code generation; translation grammar;
                 vector-generatrice",
  treatment =    "P Practical",
}

@Article{Ware:1982:BMF,
  author =       "F. A. Ware and W. H. McAllister and J. R. Carlson and
                 D. K. Sun and R. J. Vlach",
  title =        "64 Bit Monolithic Floating Point Processors",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "SC-17",
  number =       "5",
  pages =        "898--907",
  month =        oct,
  year =         "1982",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "Describes a set of three processor chips capable of
                 performing 32 and 64 bit floating point add/subtract,
                 multiply, and divide operations. The chips can perform
                 over one million scalar floating point operations per
                 second, and over four million vector \ldots{}",
}

@Book{Waser:1982:IAD,
  author =       "Shlomo Waser and Michael J. Flynn",
  title =        "Introduction to Arithmetic for Digital Systems
                 Designers",
  publisher =    pub-HRW,
  address =      pub-HRW:adr,
  pages =        "xvii + 308",
  year =         "1982",
  ISBN =         "0-03-060571-7",
  ISBN-13 =      "978-0-03-060571-0",
  LCCN =         "TK7895 A65 W37 1982",
  bibdate =      "Sat Sep 03 09:25:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Master copy output on Alphatype CRS high-resolution
                 phototypesetter. This book went to press while the IEEE
                 754 Floating-Point Standard was still in development;
                 consequently, some of the material on that system was
                 invalidated by the final Standard (1985)
                 \cite{IEEE:1985:AIS}.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  tableofcontents = "Preface\\
                 Acknowledgments\\
                 Abbreviations and Symbols\\
                 1. Numeric Data Representation\\
                 2. Residue Numbers and the Limits of Fast Arithmetic\\
                 3. Addition and Subtraction\\
                 4. Multiplication\\
                 5. Division\\
                 6. Pipelining of Arithmetic Operations\\
                 Appendix.\\
                 References.\\
                 Index.",
}

@Book{Wilkes:1982:PPE,
  author =       "M. V. (Maurice Vincent) Wilkes and David J. Wheeler
                 and Stanley Gill",
  title =        "The Preparation of Programs for an Electronic Digital
                 Computer: with Special Reference to the {EDSAC} and the
                 Use of a Library of Subroutines",
  volume =       "1",
  publisher =    pub-TOMASH,
  address =      pub-TOMASH:adr,
  pages =        "xxxi + 167",
  year =         "1982",
  ISBN =         "0-262-23118-2 (MIT Press 1984), 0-938228-03-X",
  ISBN-13 =      "978-0-262-23118-3 (MIT Press 1984),
                 978-0-938228-03-5",
  LCCN =         "QA76.6 .W545 1982",
  bibdate =      "Mon Feb 10 11:33:59 MST 2020",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "With a new introduction by Martin Campbell-Kelly.",
  series =       "Charles Babbage Institute reprint series for the
                 history of computing",
  acknowledgement = ack-nhfb,
}

@InCollection{Wilson:1982:PC,
  author =       "Kenneth G. Wilson",
  title =        "Experiences with a floating point systems array
                 processor",
  crossref =     "Rodrigue:1982:AC",
  pages =        "279--314",
  year =         "1982",
  MRclass =      "65W05",
  MRnumber =     "759 559",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@MastersThesis{Wu:1982:DFA,
  author =       "Market Wen-Han Wu",
  title =        "Design of a fast addressable hardware floating-point
                 arithmetic package for small computer",
  type =         "Thesis ({M.S.})",
  school =       "Tufts University. Department of Engineering",
  address =      "Boston, MA, USA",
  pages =        "iii + 102",
  year =         "1982",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Microcomputers ---
                 Programming.",
}

@InCollection{Zuse:1982:MAE,
  author =       "Konrad Zuse",
  title =        "Method for Automatic Execution of Calculations with
                 the aid of Computers (1936)",
  crossref =     "Randell:1982:ODC",
  pages =        "163--170",
  year =         "1982",
  bibdate =      "Sun Nov 03 08:36:11 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "This translation and reprint of a German patent
                 application of 11 April 1936 briefly describes the
                 floating-point system that was first successfully
                 implemented in a digital computer, the Zuse Z3, in
                 1941.",
}

@InProceedings{Agrawal:1983:DPV,
  author =       "Dharma P. Agrawal and Girish C. Pathak and Nikunja K.
                 Swain and Shuwan K. Agrawal",
  title =        "On Design and Performance of {VLSI} Based Parallel
                 Multiplier",
  crossref =     "IEEE:1983:PSC",
  pages =        "17--21",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Agrawal_Pathak_Swain_Agrawal.pdf",
  abstract =     "This paper introduces the VLSI design and layout of a
                 $ (\log^2 n) $ time $n$-bit binary parallel multiplier
                 for two unsigned operands. Proposed design consists of
                 partitioning the multiplier and multiplicand bits into
                 four groups of $ n / 4 $ bits each and then reducing
                 the matrix of sixteen product terms using three to two
                 parallel counters and Brent-Kung $ (\log n) $ time
                 parallel adder. Area-time performance of the present
                 scheme has been compared with the existing schemes for
                 parallel multipliers. Regular and recursive design of
                 the multiplier is shown to be suitable for VLSI
                 implementation and an improved table look up multiplier
                 has been used to form the basis of the recursive design
                 scheme.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}

@Article{Agrawal:1983:ICA,
  author =       "D. P. Agrawal and T. R. N. Rao",
  title =        "Introduction: Computer Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "4",
  pages =        "329--330",
  month =        apr,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676232",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:08 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676232",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Akamine:1983:SMQ,
  author =       "Masami Akamine and Tatsuo Higuchi",
  title =        "Synthesis of minimum quantization error digital
                 filters using floating-point arithmetic",
  journal =      j-ELECTRON-COMMUN-JPN,
  volume =       "66",
  number =       "10",
  pages =        "29--38",
  year =         "1983",
  CODEN =        "ECOJAL",
  ISSN =         "0424-8368",
  MRclass =      "94A12",
  MRnumber =     "85k:94010",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics and communications in Japan",
}

@InProceedings{Annaratone:1983:MME,
  author =       "M. Annaratone and R. Stefanelli",
  title =        "A Multiplier with Multiple Error Correction
                 Capability",
  crossref =     "IEEE:1983:PSC",
  pages =        "44--51",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Annaratone_Stefanelli.pdf",
  abstract =     "This paper presents a technique for increasing the
                 reliability of arithmetic units. An error model is then
                 presented: this model well represents the faulty
                 behavior of many arithmetic units. The Residue Number
                 System and its related properties are used in order to
                 obtain a simple architecture (called Reliability
                 Network, R-Net). The main characteristics of the
                 presented technique are a significant reduction in the
                 number of gates and a limited increase of global
                 execution times. The extensive use of combinational
                 logic makes it possible to implement the R-Net almost
                 completely by means of Programmable Logic Arrays
                 (PLA's). Finally, both the intrinsic regularity of the
                 R-Net and its simple internal interconnection scheme
                 make this approach suitable for a practical VLSI
                 implementation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}

@Article{Armer:1983:DCR,
  author =       "Paul Armer",
  title =        "11. The {Defense Calculator} at the {Rand
                 Corporation}",
  journal =      j-ANN-HIST-COMPUT,
  volume =       "5",
  number =       "2",
  pages =        "202--202",
  month =        apr # "\slash " # jun,
  year =         "1983",
  CODEN =        "AHCOE5",
  ISSN =         "0164-1239",
  ISSN-L =       "0164-1239",
  bibdate =      "Fri Nov 1 15:29:20 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://dlib.computer.org/an/books/an1983/pdf/a2202a.pdf;
                 http://www.computer.org/annals/an1983/a2202aabs.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of the History of Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
}

@Article{Asai:1983:CPI,
  author =       "H. Asai",
  title =        "A Consideration of a Practical Implementation For a
                 New Convergence Division",
  journal =      j-INFO-PROC-LETT,
  volume =       "17",
  number =       "5",
  pages =        "273--281",
  month =        dec,
  year =         "1983",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}

@Article{Asai:1983:SOM,
  author =       "Hitohisa Asai and C. K. Cheng",
  title =        "Speeding Up an Overrelaxation Method of Division in
                 Radix-$ 2^n $ Machine",
  journal =      j-CACM,
  volume =       "26",
  number =       "3",
  pages =        "216--220",
  year =         "1983",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:22:06 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm26.html#AsaiC83;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "arithmetic",
  oldlabel =     "AsaiC83",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/AsaiC83",
}

@MastersThesis{Aspinwall:1983:IIF,
  author =       "David Brian Masters Aspinwall",
  title =        "An implementation of the {IEEE} floating point
                 standard on a {VAX-11\slash 780}",
  type =         "Thesis ({M.S.})",
  school =       "San Francisco State University",
  address =      "San Francisco, CA, USA",
  pages =        "ix + 138",
  year =         "1983",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer architecture.; Floating-point arithmetic.;
                 Microprogramming.; VAX-11 (Computer) --- Programming.",
}

@Article{Aspinwall:1983:MVM,
  author =       "David B. Aspinwall and Yale N. Patt",
  title =        "Modifications to the {VAX-11\slash 780}
                 microarchitecture to support {IEEE} floating point
                 arithmetic",
  journal =      j-SIGMICRO,
  volume =       "14",
  number =       "4",
  pages =        "61--69",
  month =        dec,
  year =         "1983",
  CODEN =        "SIGMDJ",
  DOI =          "https://doi.org/10.1145/1096419.1096429",
  ISSN =         "0163-5751, 1050-916X",
  ISSN-L =       "0163-5751",
  bibdate =      "Fri Apr 16 10:27:31 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigmicro.bib",
  URL =          "https://dl.acm.org/doi/10.1145/1096419.1096429",
  abstract =     "The VAX-11/780 was designed specifically to implement
                 the VAX architecture. As such, it does not support the
                 IEEE standard for floating point arithmetic. A project
                 was undertaken to provide this support by modifying the
                 11/780 microarchitecture. Our objective was to produce
                 a microengine that would efficiently execute a modified
                 VAX instruction set, in particular, one that executes
                 VAX floating point instructions consistent with the
                 IEEE standard. We made minimal changes to the 11/780
                 hardware, relying primarily on changes to the
                 microcode. This paper describes the work of this
                 project.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMICRO Newsletter",
  journal-URL =  "https://dl.acm.org/loi/sigmicro",
}

@InProceedings{Avizienis:1983:AAE,
  author =       "Algirdas Avizienis and C. S. Raghavendra",
  title =        "Applications for Arithmetic Error Codes in Large,
                 High-Performance Computers",
  crossref =     "IEEE:1983:PSC",
  pages =        "169--173",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Avizienis_Raghavendra.pdf",
  abstract =     "Large, high-performance computers are too costly to
                 allow full replication for fault detection and error
                 correction in the communication and processing of
                 numerical information. For this reason more
                 cost-effective arithmetic error code applications offer
                 an attractive alternative.\par

                 Part I of this paper presents a generalization of
                 low-cost inverse residue codes into two-dimensional
                 encodings. Error detecting and error correcting
                 properties of two-dimensional inverse residue codes are
                 discussed.\par

                 Part II discusses a multi-phase application of inverse
                 residue codes in which the form of encoding is altered
                 and additional time is allocated after faults occur.
                 The goal is to defer repair and to continue operation
                 at a slower speed until scheduled maintenance can take
                 place.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}

@Article{Bandeira:1983:TCA,
  author =       "N. Bandeira and K. Vaccaro and J. A. Howard",
  title =        "A Two's Complement Array Multiplier Using True Values
                 of the Operands",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "8",
  pages =        "745--747",
  month =        aug,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676312",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:11 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676312",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Banerji:1983:RPF,
  author =       "D. K. Banerji and S. Kaushik",
  title =        "Representation and Processing of Fractions in a
                 Residue System",
  crossref =     "IEEE:1983:PSC",
  pages =        "29--36",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Banerji_Kaushik.pdf",
  abstract =     "This paper proposes a scheme for the representation
                 and processing of fractions in a residue system. The
                 scheme is based on a mixed radix representation of a
                 fraction in a residue system. The algorithms for basic
                 arithmetic operations of addition, subtraction, and
                 multiplication involving fractions are developed and
                 are shown to provide some improvement over an existing
                 method. Application of these algorithms to division of
                 two integers in the residue system has been shown.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; residue number systems",
}

@Article{Baxter:1983:CRS,
  author =       "I. Baxter",
  title =        "Code replication speeds multiplication",
  journal =      j-EDN,
  volume =       "28",
  number =       "4",
  pages =        "261--262",
  month =        feb,
  year =         "1983",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}

@InProceedings{Bayoumi:1983:MVI,
  author =       "M. A. Bayoumi and G. A. Jullien and W. C. Miller",
  title =        "Models for {VLSI} Implementation of Residue Number
                 System Arithmetic Modules",
  crossref =     "IEEE:1983:PSC",
  pages =        "174--183",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Bayoumi_Jullien_Miller.pdf",
  abstract =     "This paper discusses the implementation of RNS
                 arithmetic modules using VLSI technology. The modules
                 are based on the interconnection of readonly memory
                 look-up tables. The paper first outlines a memory model
                 for a single look-up table which allows the selection
                 of the most efficient layout for memories which do not
                 have power of $2$ dimensions. The paper then discusses
                 various examples of interconnected memory modules with
                 associated optimizing layout algorithms. Finally, an
                 example is given of the application of one of the
                 modules to a large prime modulus multiplier.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; residue number systems",
}

@InProceedings{Bhat:1983:HPF,
  author =       "J. Bhat",
  title =        "High Performance Floating Point Co-Processor for
                 Protected Multi-User Systems",
  crossref =     "Mini-Micro:1983:MMN",
  pages =        "7/2/1--5",
  year =         "1983",
  bibdate =      "Wed Sep 7 22:31:27 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Blakley:1983:MAI,
  author =       "G. R. Blakley and I. Borosh",
  title =        "Modular arithmetic of iterated powers",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "9",
  number =       "4",
  pages =        "567--581",
  month =        "????",
  year =         "1983",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 18:51:24 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122183901141",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221/",
}

@InProceedings{Boney:1983:FPPa,
  author =       "J. Boney and V. Shahan",
  title =        "Floating-point Power for the {M68000} Family",
  crossref =     "Mini-Micro:1983:MMN",
  pages =        "7/3/1--9",
  year =         "1983",
  bibdate =      "Wed Sep 7 22:31:27 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@InProceedings{Boney:1983:FPPb,
  author =       "J. Boney and V. Shahan",
  title =        "Floating-point Power for the {M68000} Family",
  crossref =     "Mini-Micro:1983:MMW",
  pages =        "16/5/1--10",
  year =         "1983",
  bibdate =      "Mon Sep 12 22:01:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@InProceedings{Boney:1983:FPPc,
  author =       "J. Boney and V. Shahan and P. Harvey",
  editor =       "????",
  booktitle =    "Proceedings of {Maecon, September 1983}",
  title =        "Floating-point Power for the {M68000} Family",
  publisher =    "????",
  address =      "????",
  pages =        "1--9",
  year =         "1983",
  bibdate =      "Thu Nov 13 10:21:25 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Brown:1983:NEA,
  author =       "W. S. Brown and C. S. Wetherell",
  title =        "A Numeric Error Algebra",
  crossref =     "IEEE:1983:PSC",
  pages =        "86--93",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Brown_Wetherell.pdf",
  abstract =     "Wetherell recently described an algebra of error
                 values that could be added to the ordinary arithmetic
                 of a programming language. Along with ordinary
                 arithmetic values, error values were included in the
                 set of computational quantities. The error values could
                 participate in all arithmetic operations and return
                 meaningful results. Unfortunately, the definitions of
                 the error values were not precise enough. Using Brown's
                 model of computer arithmetic, we supply precise
                 definitions for the error values, define the
                 fundamental arithmetic operations on the new values,
                 comment on their properties, and discuss briefly how
                 they might be used and implemented. We also compare our
                 model to the error handling features of the proposed
                 IEEE floating point standard",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}

@Article{Bushard:1983:MTS,
  author =       "L. B. Bushard",
  title =        "A Minimum Table Size Result for Higher Radix
                 Nonrestoring Division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "6",
  pages =        "521--526",
  month =        jun,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676273",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676273",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Caraiscos:1983:REA,
  author =       "C. Caraiscos and Bede Liu",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing: {ICASSP '83}",
  title =        "A round-off error analysis of the {LMS} adaptive
                 algorithm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "29--32",
  year =         "1983",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The steady state output error of the Least Mean Square
                 (LMS) Adaptive Algorithm due to the finite precision
                 arithmetic of a digital processor is analyzed. It is
                 found to consist of three terms: (1) the error due to
                 the input data quantization, (2) \ldots{}",
}

@Article{Chamrad:1983:FFP,
  author =       "V. Chamrad",
  title =        "A Fast Floating-Point Square-Rooting Routine for the
                 8080\slash 8085 Microprocessors",
  journal =      j-KYBERNETIKA,
  volume =       "19",
  number =       "4",
  pages =        "335--344",
  month =        "????",
  year =         "1983",
  CODEN =        "KYBNAI",
  ISSN =         "0023-5954",
  bibdate =      "Wed Sep 14 20:24:32 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Kybernetika",
}

@Article{Chan:1983:ACS,
  author =       "Tony F. Chan and Gene H. Golub and Randall J.
                 LeVeque",
  title =        "Algorithms for computing the sample variance: Analysis
                 and recommendations",
  journal =      j-AMER-STAT,
  volume =       "37",
  number =       "3",
  pages =        "242--247",
  month =        aug,
  year =         "1983",
  CODEN =        "ASTAAJ",
  DOI =          "https://doi.org/10.2307/2683386",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  MRclass =      "62-04",
  MRnumber =     "84k:62003",
  bibdate =      "Mon May 5 09:19:29 MDT 1997",
  bibsource =    "Distributed/QLD.bib; Distributed/QLD/1983.bib;
                 ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.jstor.org/stable/2683386",
  acknowledgement = ack-nhfb,
  author-dates = "Gene Howard Golub (February 29, 1932--November 16,
                 2007)",
  country =      "USA",
  date =         "13/05/93",
  descriptors =  "Simulation; statistics; numeric calculation",
  enum =         "7109",
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
  location =     "SEL: Wi",
  references =   "0",
  revision =     "16/01/94",
}

@Article{Chang:1983:HSN,
  author =       "Tung-Liang Chang and P. Fisher",
  title =        "High-speed normalization and rounding circuits for
                 pipelined floating-point processors",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "31",
  number =       "6",
  pages =        "1403--1408",
  month =        dec,
  year =         "1983",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  summary =      "A fast leading/trailing-zero detection circuit
                 (LZDC/TZDC) is described, and then applied to the
                 design of a pipelined floating-point (FLP) processor.
                 This circuit has a total delay of 5{\Delta} and a
                 hardware complexity of(m + 1)(3 log_{2}(p) + 4
                 \ldots{}).",
}

@Article{Chow:1983:PDA,
  author =       "P. Chow and Z. Vranesic and Jui Lin Yen",
  title =        "A Pipelined Distributed Arithmetic {PFFT} Processor",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "12",
  pages =        "1128--1136",
  month =        dec,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676173",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:13 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  note =         "See correction \cite{Anonymous:1984:CPD}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676173",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Ciminiera:1983:FIM,
  author =       "L. Ciminiera and A. Serra",
  title =        "Fast Iterative Multiplying Array",
  crossref =     "IEEE:1983:PSC",
  pages =        "60--66",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ciminiera_Serra.pdf",
  abstract =     "A high speed multiplying array is presented. It is
                 based on a new cell, which is able to generate and add
                 a rectangular block of elementary products. A careful
                 design of the cell allows us to obtain a small delay
                 for the signals which should be propagated through the
                 whole array. This feature leads to a remarkable
                 improvement in the array speed.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}

@Article{Cloutier:1983:PAR,
  author =       "Mark J. Cloutier and Matthew J. Friedman",
  title =        "Precision Averaging for Real-Time Analysis",
  journal =      j-CACM,
  volume =       "26",
  number =       "7",
  pages =        "525--529",
  year =         "1983",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:31:47 MST 2001",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm26.html#CloutierF83;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "CloutierF83",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/CloutierF83",
}

@InProceedings{Cody:1983:GPI,
  author =       "W. J. Cody",
  title =        "A generalization of the proposed {IEEE} standard for
                 floating-point arithmetic",
  crossref =     "Gentle:1983:CSS",
  pages =        "133--139",
  year =         "1983",
  bibdate =      "Thu Nov 17 10:41:05 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Republication of \cite{Cody:1982:GPI}.",
  acknowledgement = ack-nhfb,
  keywords =     "standardization",
  subject =      "G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Computer arithmetic \\ K.7 Computing Milieux,
                 THE COMPUTING PROFESSION, Miscellaneous \\ K.1
                 Computing Milieux, THE COMPUTER INDUSTRY, Standards",
}

@Article{Cohen:1983:CCP,
  author =       "Marty S. Cohen and T. E. Hull and V. Carl Hamacher",
  title =        "{CADAC}: a Controlled-Precision Decimal Arithmetic
                 Unit",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "4",
  pages =        "370--377",
  month =        apr,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676238",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:08 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676238",
  abstract =     "This paper describes the design of an arithmetic unit
                 called CADAC (clean arithmetic with decimal base and
                 controlled precision). Programming language
                 specifications for carrying out `ideal' floating-point
                 arithmetic are described first. These specifications
                 include detailed requirements for dynamic precision
                 control and exception handling, along with both complex
                 and interval arithmetic at the level of a programming
                 language such as Fortran or PL/I.\par

                 CADAC is an arithmetic unit which performs the four
                 floating-point operations add\slash subtract\slash
                 multiply\slash divide on decimal numbers in such a way
                 as to support all the language requirements
                 efficiently. A three-level pipeline is used to overlap
                 two-digit-at-a-time serial processing of the partial
                 products\slash remainders. Although the logic design is
                 relatively complex, the performance is efficient, and
                 the advantages gained by implementing
                 programmer-controlled precision directly in the
                 hardware are significant.",
  acknowledgement = ack-nhfb # "\slash " # ack-jr,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "decimal floating-point arithmetic",
  remark =       "From MFC: Normalized decimal floating-point. Need for
                 variable precision (intermediate > final, increasing
                 precision, etc.). Base representation is BCD (2-32
                 digits). Hardware prototype built",
}

@Article{Collis:1983:MSZ,
  author =       "B. Collis",
  title =        "Macros speed 8080, {Z80} multiplication",
  journal =      j-EDN,
  volume =       "28",
  number =       "24",
  pages =        "225",
  month =        nov,
  year =         "1983",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}

@Article{Corbett:1983:EAF,
  author =       "Robert Paul Corbett",
  title =        "Enhanced arithmetic for {Fortran}",
  journal =      j-SIGNUM,
  volume =       "18",
  number =       "1",
  pages =        "24--28",
  month =        jan,
  year =         "1983",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:11 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}

@Article{Coupe:1983:SPZ,
  author =       "B. Coupe",
  title =        "Superefficient programs for 8080 and {Z80} multiply",
  journal =      j-ELECTRONICS,
  volume =       "56",
  number =       "6",
  pages =        "142--143",
  month =        mar,
  year =         "1983",
  ISSN =         "0883-4989",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronics",
  journal-URL =  "https://www.mdpi.com/journal/electronics",
}

@InProceedings{Dadda:1983:SSF,
  author =       "Luigi Dadda",
  title =        "Some Schemes for Fast Serial Input Multipliers",
  crossref =     "IEEE:1983:PSC",
  pages =        "52--59",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Dadda.pdf",
  abstract =     "The design of fast multipliers for binary numbers
                 represented in serial form is considered according to a
                 general scheme composed by an array generator and a
                 summator. The bits of the product are generated with
                 the least delay with respect to the operators bits. The
                 array generator computes the elements of the multiplier
                 array. The summator computes the sum of the array
                 elements in order to generate the product bits. The
                 array elements can be generated according to two
                 different general schemes: the first computes all the
                 new array elements at each step (arranged on a diagonal
                 and on a row of the multiplier array), the second
                 computes the multiplier array elements column by
                 column. Several schemes of array generators are given
                 and compared, and for each of them a suitable summator
                 using parallel counters is illustrated.",
  acknowledgement = ack-nhfb,
  author-dates = "29 April 1923--26 October 2012",
  keywords =     "ARITH-6",
}

@InProceedings{Dao:1983:QCA,
  author =       "T. T. Dao",
  editor =       "{IEEE}",
  booktitle =    "Proceedings of the 13th International Symposium on
                 Multiple-valued Logic, May 1983",
  title =        "A Quaternary Cellular Array Complex Number
                 Multiplier",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "255--262",
  year =         "1983",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Aug 22 09:15:45 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Davis:1983:HSD,
  author =       "George R. Davis and Thomas M. King",
  title =        "A High-Speed Digital Divider",
  journal =      j-IEEE-TRANS-INSTRUM-MEAS,
  volume =       "IM-32",
  number =       "2",
  pages =        "309--312",
  month =        jun,
  year =         "1983",
  CODEN =        "IEIMAO",
  DOI =          "https://doi.org/10.1109/TIM.1983.4315069",
  ISSN =         "0018-9456 (print), 1557-9662 (electronic)",
  ISSN-L =       "0018-9456",
  bibdate =      "Tue Jan 08 22:43:51 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper describes an efficient method for
                 generating the quotient of two binary numbers at speeds
                 comparable to existing multiplier chips. A digital
                 divider is designed using the BEST LINE segmentation
                 approximation. The reciprocal curve is subdivided into
                 small sections, and a least squares straight line
                 approximation is used to recreate each section. An
                 analysis is presented to determine the segmentation
                 granularity and the binary word length of constants
                 needed to closely approximate the curve. A compromise
                 design based on statistical performance as well as the
                 complexity of the hardware requirements are
                 evaluated.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Instrument \& Measurement",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=19",
}

@Article{Demsky:1983:MMC,
  author =       "J. Demsky and M. Schlesinger and R. D. Kent",
  title =        "Micro\slash mini computer program for calculating the
                 square root of rationals at arbitrary precision",
  journal =      j-COMP-PHYS-COMM,
  volume =       "29",
  number =       "3",
  pages =        "237--244",
  month =        may,
  year =         "1983",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(83)90004-8",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 10:28:04 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465583900048",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Dietrich:1983:VQF,
  author =       "D. Dietrich",
  title =        "{Verfahren zur L{\"o}sung von Quadratwurzeln f{\"u}r
                 Mikrorechnerprozeduren} \toenglish {Methods for the
                 Solution of Square Roots for Microprocessor
                 Subroutines} \endtoenglish",
  journal =      j-ELEKTRONIKER,
  volume =       "8",
  pages =        "EL-1--EL-6",
  year =         "1983",
  CODEN =        "ELKRBL",
  ISSN =         "0531-9218",
  bibdate =      "Fri Dec 08 13:05:49 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektroniker (Switzerland)",
}

@InProceedings{Donthi:1983:BSM,
  author =       "Ravindra V. Donthi and Mohammed Saleem and Harpreet
                 Singh",
  title =        "On Bit Sequential Multipliers",
  crossref =     "IEEE:1983:PSC",
  pages =        "104--108",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Donthi_Saleem_Singh.pdf",
  abstract =     "Recently bit sequential multiplier algorithms have
                 been found more useful in the area of interconnection
                 of multiple processors within a VLSI structure [1],
                 [2]. The object of the present paper is to suggest
                 modified bit sequential algorithms to achieve more
                 speed and to attain its conformity with other
                 algorithms such as division, square-rooting, etc. with
                 a view to utilize them in future arithmetic arrays. In
                 the present paper the following has been taken up: (a)
                 Bit sequential multiplier using carry look-ahead
                 technique, (b) Bit sequential multiplier using most
                 significant bit first,and (c) Negabinary bit sequential
                 multiplier.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}

@Article{Dubrulle:1983:CNM,
  author =       "Augustin A. Dubrulle",
  title =        "Class of Numerical Methods for the Computation of
                 {Pythagorean} Sums",
  journal =      j-IBM-JRD,
  volume =       "27",
  number =       "6",
  pages =        "582--589",
  month =        nov,
  year =         "1983",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Tue Mar 25 14:26:59 MST 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Moler:1983:RSR} and generalization
                 \cite{Jamieson:1989:SNR}.",
  abstract =     "Moler and Morrison have described an iterative
                 algorithm for the computation of the Pythagorean sum
                 (a**2 plus b**2)** one-half of two real numbers a and
                 b. This algorithm is immune to unwarranted
                 floating-point overflows, has a cubic rate of
                 convergence, and is easily transportable. This paper,
                 which shows that the algorithm is essentially Halley's
                 method applied to the computation of square roots,
                 provides a generalization to any order of convergence.
                 Formulas of orders 2 through 9 are illustrated with
                 numerical examples. The generalization keeps the number
                 of floating-point divisions constant and should be
                 particularly useful for computation in high-precision
                 floating-point arithmetic.",
  acknowledgement = ack-nhfb,
  classcodes =   "C4190 (Other numerical methods); C5230 (Digital
                 arithmetic methods)",
  classification = "723; 921",
  corpsource =   "IBM Sci. Centre, Palo Alto, CA, USA",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  journalabr =   "IBM J Res Dev",
  keywords =     "computer programming; digital arithmetic;
                 floating-point divisions; Halley's method;
                 high-precision floating-point arithmetic; iterative
                 algorithm; iterative methods; mathematical techniques
                 --- Numerical Methods; Pythagorean sums; rate of
                 convergence; square roots",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Dyer:1983:ZRP,
  author =       "D. C. Dyer",
  title =        "{Z80} routine performs 16-bit multiply",
  journal =      j-EDN,
  volume =       "28",
  number =       "5",
  pages =        "144",
  month =        mar,
  year =         "1983",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}

@InProceedings{Ercegovac:1983:HRD,
  author =       "Milo{\v{s}} D. Ercegovac",
  title =        "A Higher-Radix Division with Simple Selection of
                 Quotient Digits",
  crossref =     "IEEE:1983:PSC",
  pages =        "94--98",
  month =        jun,
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ercegovac.pdf",
  abstract =     "A higher-radix division algorithm with simple
                 selection of quotient digits is described. The proposed
                 scheme is a combination of the multiplicative
                 normalization used in the continued-product algorithms
                 and the recursive division algorithm. The scheme
                 consists of two parts: in the first part, the divisor
                 and the dividend are transformed into the range which
                 allows the quotient digits to be selected by rounding
                 partial remainders to the most significant radix-$r$
                 digit in the second part. Since the selection requires
                 only the most significant part of the partial
                 remainder, limited carry-propagation adders can be used
                 to form the partial remainders. The divisor and
                 dividend transformations are performed in three steps
                 using multipliers of the form $ 1 + s_k r^{-k} $ as in
                 the continued product algorithm. The higher radix of
                 the form $ r = 2^k, k = 2, 4, 8, \ldots {} $ can be
                 used to reduce the number of steps while retaining the
                 simple quotient selection rules.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; division",
}

@InProceedings{Ferguson:1983:DTE,
  author =       "Joel Ferguson and John Paul Shen",
  title =        "The Design of Two Easily-Testable {VLSI} Array
                 Multipliers",
  crossref =     "IEEE:1983:PSC",
  pages =        "2--9",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ferguson_Shen.pdf",
  abstract =     "Array multipliers are well-suited for VLSI
                 implementation because of the regularity in their
                 iterative structure. However, most VLSI circuits are
                 very difficult to test. This paper shows that, with
                 appropriate cell design, array multipliers can be
                 designed to be very easily-testable. An array
                 multiplier is called C-testable if all its adder cells
                 can be exhaustively tested while requiring only a
                 constant number of test patterns. The testability of
                 two well-known array multiplier structures are [sic]
                 studied. The conventional design of the carry-save
                 array multiplier is shown to be not C-testable.
                 However, a modified design, using a modified adder
                 cell, is generated and shown to be C-testable and
                 requires only 16 test patterns. Similar results are
                 obtained for the Baugh--Wooley two's complement array
                 multiplier. A modified design of the Baugh--Wooley
                 array multiplier is shown to be C-testable and requires
                 55 test patterns. The implementation of a practical
                 C-testable $ 16 \times 16 $ array multiplier is also
                 presented.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}

@InProceedings{Fraenkel:1983:SN,
  author =       "A. S. Fraenkel",
  title =        "Systems of Numeration",
  crossref =     "IEEE:1983:PSC",
  pages =        "37--42",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Fraenkel.pdf",
  abstract =     "A numeration system is a set of integers (basis
                 elements) such that every integer can be represented
                 uniquely over the set using integer digits of bounded
                 size. Such systems are scattered in many fields in
                 mathematics and computer science. Many of the known
                 ones and new ones are unified and derived from a basic
                 result on recursively defined basis elements.
                 Applications are indicated.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; number systems",
}

@Article{Gaitanis:1983:NPC,
  author =       "N. Gaitanis and C. Halatsis",
  title =        "Near-Perfect Codes for Binary-Coded Radix-$r$
                 Arithmetic Units",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "5",
  pages =        "494--497",
  month =        may,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676261",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676261",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Galand:1983:FD,
  author =       "C. Galand",
  title =        "Fast Division",
  journal =      j-IBM-TDB,
  volume =       "26",
  number =       "3B",
  pages =        "1537--1539",
  month =        aug,
  year =         "1983",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
}

@Article{Gavrielov:1983:CSF,
  author =       "M. Gavrielov and A. Kaminker and Y.-T. Sidi",
  title =        "Coprocessors Speed Floating Point Calculations",
  journal =      j-COMP-DESIGN,
  volume =       "22",
  number =       "11",
  pages =        "197--204",
  month =        oct,
  year =         "1983",
  CODEN =        "CMPDAM",
  ISSN =         "0010-4566",
  bibdate =      "Sun Sep 11 11:55:54 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computer Design",
}

@Article{Gnanasekaran:1983:BSI,
  author =       "R. Gnanasekaran",
  title =        "On a Bit-Serial Input and Bit-Serial Output
                 Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "9",
  pages =        "878--880",
  month =        sep,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676341",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:12 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676341",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Gosling:1983:STF,
  author =       "J. B. Gosling",
  title =        "Some Tricks of the (Floating-Point) Trade",
  crossref =     "IEEE:1983:PSC",
  pages =        "218--220",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Gosling.pdf",
  abstract =     "In designing a floating-point arithmetic unit there
                 are a number of places where the characteristics of the
                 operations and the operands permit simplifications in
                 the logical design. These have not been well
                 documented, with the result that each new generation of
                 designers has made the same mistakes as their
                 predecessors. This paper describes some of these
                 simplifications as they affect the mantissa section of
                 a floating-point addition and subtraction unit. The
                 areas covered include normalisation and rounding.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}

@Article{Grappel:1983:FPP,
  author =       "R. D. Grappel",
  title =        "Floating-point-processing unit improves 16-bit-$ \mu
                 {P} $ performance",
  journal =      j-EDN,
  volume =       "28",
  number =       "19",
  pages =        "181--188",
  month =        sep,
  year =         "1983",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Wed Sep 7 22:31:27 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}

@InProceedings{Grnarov:1983:LMN,
  author =       "A. L. Grnarov and M. D. Ercegovac",
  title =        "On-line multiplicative normalization",
  crossref =     "IEEE:1983:PSC",
  pages =        "151--155",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:44:54 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Grnarov_Ercegovac.pdf",
  abstract =     "In this article we describe a derivation and an
                 algorithm for on-line multiplicative normalization of
                 fractions. The algorithm is a variation of the
                 continued product normalization algorithm and it is
                 used for on-line evaluation of elementary functions.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; elementary functions; on-line arithmetic",
}

@InProceedings{Guibas:1983:FBA,
  author =       "L. Guibas and J. E. Vuillemin",
  title =        "On Fast Binary Addition in {MOS} Technologies",
  crossref =     "IEEE:1983:PSC",
  pages =        "22--23",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Guibas_Vuillemin.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "addition; ARITH-6",
  remark =       "Paper did not arrive in time for the proceedings.",
}

@Article{Halatsis:1983:ECC,
  author =       "C. Halatsis and N. Gaitanis and M. Sigala",
  title =        "Error-Correcting Codes in Binary-Coded Radix-$r$
                 Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "3",
  pages =        "326--328",
  month =        mar,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676227",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:08 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676227",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Hamada:1983:UUR,
  author =       "H. Hamada",
  title =        "{URR}: Universal representation of real numbers",
  journal =      j-NEW-GEN-COMP,
  volume =       "1",
  number =       "2",
  pages =        "205--209",
  month =        jun,
  year =         "1983",
  CODEN =        "NGCOE5",
  DOI =          "https://doi.org/10.1007/BF03037427",
  ISSN =         "0288-3635 (print), 1882-7055 (electronic)",
  ISSN-L =       "0288-3635",
  bibdate =      "Thu Dec 14 16:45:14 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "New Generation Computing",
  journal-URL =  "https://dl.acm.org/loi/newg",
}

@Article{Heninger:1983:ZZF,
  author =       "A. Heninger",
  title =        "{Zilog}'s {Z8070} Floating Point Processor",
  crossref =     "Mini-Micro:1983:MMN",
  pages =        "16/2/1--7",
  year =         "1983",
  bibdate =      "Wed Sep 7 22:31:27 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@InCollection{HP:1983:CDR,
  author =       "{Hewlett Packard}",
  booktitle =    "Software Internal Design Specification for the
                 {HP-71}, Vol. 1",
  title =        "Chapter 13: Data Representations",
  publisher =    "Hewlett Packard Company",
  address =      "Palo Alto, CA, USA",
  pages =        "13.1--13.17",
  month =        dec,
  year =         "1983",
  bibdate =      "Fri Nov 28 17:17:29 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Part \#00071-90068. Manual available from {\em The
                 Museum of HP Calculators}.",
  URL =          "http://www.hpmuseum.org/",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}

@Article{Huang:1983:FPM,
  author =       "C. H. Huang",
  title =        "A Fully Parallel Mixed-Radix Conversion Algorithm for
                 Residue Number Applications",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "4",
  pages =        "398--402",
  month =        apr,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676242",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:08 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35226;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676242",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A new, fully parallel mixed-radix conversion (MRC)
                 algorithm which utilizes the maximum parallelism that
                 exists in the residues (RNS) to mixed-radix (MR) digits
                 conversion to achieve high throughput rate and very
                 short conversion time is presented. \ldots{}",
}

@Article{Huntsman:1983:MFP,
  author =       "Clayton Huntsman and Duane Cawthron",
  title =        "The {MC68881} Floating-Point Coprocessor",
  journal =      j-IEEE-MICRO,
  volume =       "3",
  number =       "6",
  pages =        "44--54",
  month =        nov # "\slash " # dec,
  year =         "1983",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.1983.291185",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Dec 14 06:08:58 MST 2000",
  bibsource =    "Compendex database;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeemicro.bib;
                 Science Citation Index database (1980--2000)",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  ajournal =     "IEEE Micro",
  classcodes =   "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5230 (Digital arithmetic
                 methods)",
  classification = "714; 723; 902",
  corpsource =   "Motorola Inc., Austin, TX, USA",
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html;
                 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=40",
  keywords =     "arithmetic; computer architecture; computers;
                 coprocessor; digital arithmetic; floating-point;
                 floating-point arithmetic; IEEE arithmetic; IEEE
                 standard; integrated circuits, VLSI --- Applications;
                 M68000 family; M68000 microprocessor; MC68881
                 floating-point processor; microprocessor chips;
                 real-number computations; satellite; standards",
  treatment =    "P Practical; T Theoretical or Mathematical",
}

@Article{Iffrig:1983:ULC,
  author =       "L. D. Iffrig",
  title =        "Use less code for fast 8080 multiply",
  journal =      j-EDN,
  volume =       "28",
  number =       "13",
  pages =        "293",
  month =        jun,
  year =         "1983",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}

@TechReport{Ingram:1983:ACW,
  author =       "Windell F. Ingram and Radhakrishnan, N. (Narayanswamy)
                 and Deborah F. Dent",
  title =        "Accuracy considerations when using some minicomputers
                 for scientific and engineering problems",
  institution =  "U.S. Army Engineer Waterways Experiment Station;
                 available from National Technical Information Service",
  address =      "Vicksburg, MS, USA",
  pages =        "76 + 6 + 3",
  year =         "1983",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Technical report; K-83-2 Technical report (U.S. Army
                 Engineer Waterways Experiment Station); K-83-2.",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Minicomputers.;
                 Programming (Electronic computers).",
  remark =       "Cover title. ``September 1983.'' ``Prepared for
                 Office, Chief of Engineers, U.S. Army.'' Funded by
                 Office, Chief of Engineers.",
}

@Book{Intel:1983:HRM,
  author =       "Intel",
  title =        "The {iAPX} 286 Hardware Reference Manual",
  publisher =    pub-INTEL,
  address =      pub-INTEL:adr,
  year =         "1983",
  LCCN =         "QA76.8.I264 I14 1983",
  bibdate =      "Wed Feb 9 09:02:53 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "The definitive statement of the 80286 and 80287
                 hardware at a strongly technical level. Not an
                 instruction set reference, but does contain instruction
                 timing tables. See also \cite{Intel:1985:PRM}.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Irwin:1983:NLD,
  author =       "Mary Jane Irwin and Robert Michael Owens",
  title =        "Numerical Limitation on the Design of Digit On-Line
                 Networks",
  crossref =     "IEEE:1983:PSC",
  pages =        "156--161",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:50:08 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Owens_Irwin.pdf",
  abstract =     "A fully digit online arithmetic unit generates at
                 least the $i$ most (least) significant digits of the
                 result after having been supplied no more than the $ (i
                 + k) $ most (least) significant digits of each operand,
                 where $k$ is a small constant. This digit serial
                 property can be used to reduce the aggregate fill and
                 flush times of a chained array of digit online
                 arithmetic units and to reduce their VLSI
                 interconnection complexity. However, because of this
                 digit serial property, unique and inherent limitations
                 may have to be imposed on any arithmetic unit which
                 performs digit online operations. For some
                 calculations, these limitations may be so severe as to
                 make digit online evaluation virtually impossible. We
                 show several important signal processing problems where
                 these limitations have either been avoided or their
                 effect greatly reduced.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; on-line arithmetic",
}

@Article{James:1983:RDB,
  author =       "F. V. James",
  title =        "An 8085 routine divides 32-bit unsigned numbers",
  journal =      j-ELECTRONICS,
  volume =       "56",
  number =       "22",
  pages =        "163--165",
  month =        nov,
  year =         "1983",
  ISSN =         "0883-4989",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronics",
  journal-URL =  "https://www.mdpi.com/journal/electronics",
}

@Article{Jankowski:1983:NFS,
  author =       "M. Jankowski and A. Smoktunowicz and H.
                 Wo{\'z}niakowski",
  title =        "A note on floating-point summation of very many
                 terms",
  journal =      "Elektron. Informationsverarb. Kybernet.",
  volume =       "19",
  number =       "9",
  pages =        "435--440",
  year =         "1983",
  MRclass =      "65V05",
  MRnumber =     "85c:65161",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  altjournal =   "Journal of Information Processing and Cybernetics ---
                 EIK",
  keywords =     "accurate floating-point summation",
}

@Article{Jenkins:1983:DEC,
  author =       "W. K. Jenkins",
  title =        "The Design of Error Checkers for Self-Checking Residue
                 Number Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "4",
  pages =        "388--396",
  month =        apr,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676240",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:08 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35226;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676240",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "During the last few years residue number (RNS)
                 arithmetic has gained increasing importance for
                 providing high speed fault tolerant performance in
                 dedicated digital signal processors. One factor that
                 has limited the use of redundant RNS theory in
                 \ldots{}",
}

@InProceedings{Johnsen:1983:IFP,
  author =       "K. Johnsen",
  title =        "An {IEEE} Floating Point Arithmetic Implementation",
  crossref =     "IEEE:1983:PSC",
  pages =        "130--135",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:50:08 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Johnsen.pdf",
  abstract =     "This article describes some of the methods and
                 algorithms used in an implementation of floating point
                 arithmetic following (almost) the IEEE standard defined
                 in (1). The description is more directly
                 algorithm-oriented than the `Implementation Guide' for
                 this standard (2), since the latter does not treat an
                 actual implementation. The article consists of two
                 parts. One concerns the problem of getting the
                 preliminary result from each of the arithmetic
                 operations, this result is the basis for a correct
                 rounding. The other part treats the multiword
                 arithmetic, i.e., the routines to perform an $ m \times
                 n $ bit operation, using the corresponding $n$ bit
                 operation supplied by the hardware. Only multiplication
                 and division are described, since the add\slash
                 subtract routines are trivial. For division also a
                 method for getting an $n$ bit inverse is included,
                 since the hardware in the case had no division
                 operation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; correct rounding; floating-point arithmetic;
                 IEEE 754",
}

@MastersThesis{Jung:1983:BRR,
  author =       "C. Jung",
  title =        "{Berechnung der reellen und reellintervallwertigen
                 Standard- funktionen mit maximaler Genauigkeit in einem
                 hexadezimalen Gleitkommaformat} \toenglish {Computation
                 of the Real and Real Interval Valued Standard Functions
                 with Maximal Accuracy in a Hexadecimal Floating-Point
                 Format} \endtoenglish",
  type =         "{Diplomarbeit}",
  school =       "Institut f{\"u}r Angewandte Mathematik,
                 Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "??",
  month =        sep,
  year =         "1983",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@TechReport{Kahan:1983:M,
  author =       "W. Kahan",
  title =        "Minimizing $ q {\rm *} m - n $",
  institution =  "Department of Mathematics and Department of Electrical
                 Engineering and Computer Science, University of
                 California, Berkeley",
  address =      "Berkeley, CA, USA",
  month =        mar,
  year =         "1983",
  bibdate =      "Fri May 03 12:26:29 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/testpi/nearpi.c",
  acknowledgement = ack-nhfb,
  remark =       "Nearpi, a C program to exhibit large floating-point
                 numbers $ Z = m * 2^L $ very close to integer multiples
                 of $ \pi / 2 $.",
}

@InProceedings{Kahan:1983:MWS,
  author =       "W. Kahan",
  title =        "Mathematics Written in Sand --- The {HP-15C}, {Intel
                 8087}, etc.",
  crossref =     "Anonymous:1983:PSC",
  bookpages =    "vi + 344",
  pages =        "12--26",
  year =         "1983",
  bibdate =      "Fri May 03 12:02:15 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MathSand.pdf",
  acknowledgement = ack-nhfb,
  remark =       "The original published version was a photoreduction of
                 dot-matrix printer output; the URL points to a cleaner
                 version.",
}

@TechReport{Kanada:1983:CDP,
  author =       "Y. Kanada and Y. Tamura and S. Yoshino and Y. Ushiro",
  title =        "Calculation of $ \pi $ to 10,013,395 Decimal Places
                 Based on the {Gauss--Legendre} Algorithm and {Gauss}
                 Arctangent Relation",
  type =         "Technical report",
  number =       "CCUT-TR-84-01",
  institution =  "Computer Centre, University of Tokyo",
  address =      "Bunkyo-ky, Yayoi 2-11-16, Tokyo 113, Japan",
  month =        dec,
  year =         "1983",
  bibdate =      "Mon Jul 18 17:50:42 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kaushik:1983:SDN,
  author =       "S. Kaushik",
  title =        "Sign Detection in Non-Redundant Residue Number System
                 with Reduced Information",
  crossref =     "IEEE:1983:PSC",
  pages =        "24--28",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:50:08 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Kaushik.pdf",
  abstract =     "A necessary and sufficient condition for sign
                 detection in Non-Redundant Residue Number System by
                 reducing the information of a residue digit has been
                 obtained. The function to reduce the information of a
                 residue digit $ x_p $ corresponding to a modulus $ m_p
                 $ has been assumed to be periodic with the period
                 length $ \hat {m}_p $, where $ \hat {m}_p = M / m_p $
                 and $ M = \prod_{i = 1}^n m_i $. A sequential method
                 for determining the sign of a number is shown to
                 demonstrate the applicability of the results thus
                 proved.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; residue number systems",
}

@MastersThesis{Kirk:1983:MFP,
  author =       "Patrick Donald Kirk",
  title =        "Microcomputer and floating point firmware design",
  type =         "Thesis ({M.S.})",
  school =       "California State University, Long Beach",
  address =      "Long Beach, CA, USA",
  pages =        "2 + xi + 237",
  year =         "1983",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Microcomputers ---
                 Programming.",
}

@InProceedings{Kobayashi:1983:AHS,
  author =       "Hideaki Kobayashi and Ronald D. Bonnell",
  title =        "Arithmetic for a High-Speed Adaptive Learning Network
                 Element",
  crossref =     "IEEE:1983:PSC",
  pages =        "164--168",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Kobayashi_Bonnel.pdf",
  abstract =     "This paper presents a novel arithmetic scheme for a
                 high-speed adaptive learning network (ALN) element. An
                 ALN is a self-organizing scheme for implementing the
                 Kolmogorov--Gabor (K-G) polynomial which maps an input
                 vector $X$ into an output scalar $Y$. In the first
                 layer of an ALN there are $ n(n - 1) / 2 $ elements. In
                 the next layer the number of elements needed depends
                 upon the number of outputs that are propagated from the
                 first layer. In this paper only the design of a single
                 element is considered. An array of memories (RAMs) and
                 a parallel adder are used to perform multinomial
                 arithmetic for the element. The memory array contains
                 subfunction values which are calculated by an external
                 host computer and downloaded to the memory array. All
                 the memories operate on the input variables
                 concurrently via a common address bus. The subfunction
                 values from the memory array are then summed by a
                 parallel adder to obtain the output of the element.
                 complete ALN implemented with the proposed ALN elements
                 has advantages in operation speed and less hardware.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}

@Article{Kornerup:1983:FPR,
  author =       "Peter Kornerup and David W. Matula",
  title =        "Finite precision rational arithmetic: An arithmetic
                 unit",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "4",
  pages =        "378--388",
  month =        apr,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676239",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:08 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676239",
  abstract =     "The foundations of an arithmetic unit performing the
                 add, subtract, multiply, and divide operations on
                 rational operands are developed. The unit uses the
                 classical Euclidean algorithm as one unified algorithm
                 for all the arithmetic operations, including rounding.
                 Binary implementations are discussed, based on
                 techniques known from SRT division, and utilizing
                 ripple-free borrow-save and carry-save addition.
                 Average time behavior is investigated.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Krishnamurthy:1983:FID,
  author =       "E. V. Krishnamurthy and V. K. Murthy",
  title =        "Fast Iterative Division of $p$-adic Numbers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "4",
  pages =        "396--398",
  month =        apr,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676241",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:08 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676241",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Lastman:1983:DFP,
  author =       "G. J. Lastman",
  title =        "Determination of Floating Point Characteristics for a
                 Personal Computer",
  crossref =     "IEEE:1983:IEE",
  pages =        "424--427",
  year =         "1983",
  bibdate =      "Thu Sep 01 12:11:33 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Linnainmaa:1983:ELE,
  author =       "Seppo Linnainmaa",
  title =        "Error linearization as an effective tool for
                 experimental analysis of the numerical stability of
                 algorithms",
  journal =      j-BIT,
  volume =       "23",
  number =       "3",
  pages =        "346--359",
  month =        sep,
  year =         "1983",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01934463",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65G05 (65J05)",
  MRnumber =     "85e:65020",
  bibdate =      "Wed Jan 4 18:52:18 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=23&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=23&issue=3&spage=346",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Lozier:1983:UFP,
  author =       "Daniel W. Lozier",
  title =        "The use of floating-point and interval arithmetic in
                 the computation of error bounds",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "4",
  pages =        "411--417",
  month =        apr,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676245",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "65G05",
  MRnumber =     "85f:65042",
  bibdate =      "Sun Jul 10 10:01:08 MDT 2011",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676245",
  abstract =     "Three forms of interval floating-point arithmetic are
                 defined in terms of absolute precision, relative
                 precision, and combined absolute and relative
                 precision. The absolute-precision form corresponds to
                 the centered form of conventional rounded-interval
                 arithmetic. The three forms are compared on the basis
                 of the number of floating-point operations needed to
                 generate error bounds for inner-product accumulation.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  catcode =      "G.1.0",
  CRclass =      "G.1.0 General; G.1.0 Error analysis",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis",
  fjournal =     "IEEE Transactions on Computers",
  genterm =      "ALGORITHMS; PERFORMANCE",
  guideno =      "06575",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  reviewer =     "N. N. Abdelmalek",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@InProceedings{Majerski:1983:SRA,
  author =       "Stanislaw Majerski",
  title =        "Square-Root Algorithms for High-Speed Digital
                 Circuits",
  crossref =     "IEEE:1983:PSC",
  pages =        "99--102",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Majerski.pdf",
  abstract =     "Two binary algorithms for the square rooting of a sum
                 of two numbers are presented. They are designed for
                 high-speed digital circuits and are based on the
                 classical nonrestoring method. The main difference lies
                 in the replacement of subtractions and additions by the
                 parallel reduction of three summands to two, their sum
                 being unchanged to eliminate a carry propagation. The
                 term ``parallel reduction'' is introduced here for the
                 carry-save addition of three summands, positive and
                 negative as well. The two result summands form a
                 successive partial remainder. Their most significant
                 three-bit groups are used to determine the ``digits''
                 $1$, $0$, $ + 1 $ of the square root in a redundant
                 notation. These digits are transformed into the
                 conventional-notation bits, which are used in the
                 further steps of the square-rooting process",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; square root",
}

@Article{Maric:1983:PBC,
  author =       "I. Maric and L. Cucancic",
  title =        "On the Possibilities of the {BCD} Code Application in
                 the Floating-Point Arithmetic Algorithms",
  journal =      j-INT-J-MINI-MICROCOMPUTERS,
  volume =       "5",
  number =       "2",
  pages =        "19--22",
  month =        "????",
  year =         "1983",
  CODEN =        "IJMMDE",
  ISSN =         "0702-0481",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "International Journal of Mini and Microcomputers",
}

@InProceedings{Markov:1983:NAF,
  author =       "Svetoslav Markov",
  title =        "On the Numerical Algorithms Formulated in Computer
                 Arithmetic",
  crossref =     "IEEE:1983:PSC",
  pages =        "82--85",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Markov.pdf",
  abstract =     "We discuss some mathematical tools and techniques
                 supporting the construction of rigorous bounds
                 producing, numerically convergent algorithms, which are
                 formulated in terms of computer arithmetic operations.
                 Two important computer-arithmetic effects are
                 considered and their application as stopping criteria
                 is illustrated.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}

@InProceedings{Martin:1983:FPS,
  author =       "G. R. Martin",
  title =        "Floating Point Support for the {NS16000} Family -- The
                 {NS16081}",
  crossref =     "Mini-Micro:1983:MMW",
  pages =        "16/3/1--3",
  year =         "1983",
  bibdate =      "Wed Sep 07 22:33:22 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@InProceedings{Matula:1983:OPF,
  author =       "David W. Matula and Peter Kornerup",
  title =        "An Order Preserving Finite Binary Encoding of the
                 Rationals",
  crossref =     "IEEE:1983:PSC",
  pages =        "201--209",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:50:08 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Matula_Kornerup.pdf",
  abstract =     "We describe a new binary encoding for numbers termed
                 lexicographic continued fraction (LCF) representation
                 that provides a one-to-one order preserving finite bit
                 string representation for every rational. Conversion
                 either way between binary integer numerator-denominator
                 pair representation and LCF representation is shown
                 feasible in time linear with bit string length, given
                 registers of length sufficient to hold the numerator
                 and denominator. LCF bit string length is about $ 2
                 \max \{ \log_2 P, \log_2 q \} $ for the irreducible
                 fraction $ p / q $. Realization of arithmetic $ ( +, -,
                 \times, \divide) $ on LCF bit string encoded operands
                 is shown feasible. Some relations between the theory of
                 best rational approximation and the values represented
                 by truncated LCF bit strings are noted to assess the
                 feasibility of a finite precision arithmetic based on
                 LCF representation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; lexicographic continued fraction (LCF);
                 rational arithmetic",
}

@Article{McCool:1983:NDC,
  author =       "Thomas E. McCool",
  title =        "4. {NSA}'s {Defense Calculator}, 1952--1953",
  journal =      j-ANN-HIST-COMPUT,
  volume =       "5",
  number =       "2",
  pages =        "186--187",
  month =        apr # "\slash " # jun,
  year =         "1983",
  CODEN =        "AHCOE5",
  ISSN =         "0164-1239",
  ISSN-L =       "0164-1239",
  bibdate =      "Fri Nov 1 15:29:20 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://dlib.computer.org/an/books/an1983/pdf/a2186.pdf;
                 http://www.computer.org/annals/an1983/a2186abs.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of the History of Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
}

@Article{McGuire:1983:PCB,
  author =       "D. W. McGuire",
  title =        "8048 program computes 16-by-8-bit quotient",
  journal =      j-ELECTRONICS,
  volume =       "56",
  number =       "10",
  pages =        "152--153",
  month =        may,
  year =         "1983",
  ISSN =         "0883-4989",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronics",
  journal-URL =  "https://www.mdpi.com/journal/electronics",
}

@TechReport{Midttun:1983:FMP,
  author =       "G. Midttun",
  title =        "A fast micro-programmable floating point processor",
  type =         "Technical report",
  number =       "CERN DD 83-16",
  institution =  "CERT",
  address =      "Geneva, Switzerland",
  pages =        "31",
  month =        sep,
  year =         "1983",
  bibdate =      "Fri May 25 05:43:42 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://weblib.cern.ch/format/showfull?uid=1451323_18194&base=CERCER&sysnb=0058382",
  acknowledgement = ack-nhfb,
  keywords =     "emulation; MICE; microcode; PDP11",
}

@Article{Mikov:1983:PAFa,
  author =       "A. I. Mikov",
  title =        "Probabilistic analysis of floating-point addition
                 ({Russian})",
  journal =      "Kibernetika (Kiev)",
  volume =       "3",
  pages =        "87--93",
  year =         "1983",
  MRclass =      "60K99 (65G05)",
  MRnumber =     "85h:60154",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "English translation in \cite{Mikov:1983:PAFb}.",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@Article{Mikov:1983:PAFb,
  author =       "A. I. Mikov",
  title =        "Probabilistic analysis of floating-point addition",
  journal =      j-CYBER,
  volume =       "19",
  number =       "3",
  pages =        "401--410",
  month =        may,
  year =         "1983",
  CODEN =        "CYBNAW",
  DOI =          "https://doi.org/10.1007/BF01072156",
  ISSN =         "0011-4235 (print), 2375-0189 (electronic)",
  MRclass =      "60K99 (65G05)",
  MRnumber =     "85h:60154",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Translated from \cite{Mikov:1983:PAFa}.",
  URL =          "http://link.springer.com/article/10.1007/BF01072156",
  acknowledgement = ack-nhfb,
  fjournal =     "Cybernetics",
  journal-URL =  "http://link.springer.com/journal/10559",
}

@Article{Miller:1983:RNS,
  author =       "D. D. Miller and J. N. Polky",
  title =        "A Residue Number System Implementation of the {LMS}
                 Algorithm Using Optical Waveguide Circuits",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "11",
  pages =        "1013--1028",
  month =        nov,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676152",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:12 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35222;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676152",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A detailed design of a real-time data processor based
                 on the residue number system is presented which uses
                 near-term optical waveguide devices and concepts. The
                 optical computational units consist of cascaded,
                 mask-programmable arrays of total \ldots{}",
}

@InProceedings{Miola:1983:UVA,
  author =       "A. Miola",
  title =        "A Unified View of Approximate Rational Arithmetic and
                 Rational Interpolation",
  crossref =     "IEEE:1983:PSC",
  pages =        "210--215",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Miola.pdf",
  abstract =     "In this paper we cover the problem of approximation of
                 numbers and of functions by presenting some well known
                 results in a unified view that could help in better
                 understanding the algebraic bases of the problem. In
                 fact, the Extended Euclid's algorithm happens to be the
                 unique and common tool solving the approximation
                 problems both for numbers and for functions.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; rational arithmetic; rational interpolation",
}

@Article{Moler:1983:RSR,
  author =       "Cleve B. Moler and Donald Morrison",
  title =        "Replacing Square Roots by {Pythagorean} Sums",
  journal =      j-IBM-JRD,
  volume =       "27",
  number =       "6",
  pages =        "577--581",
  month =        nov,
  year =         "1983",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Thu Sep 1 10:15:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Dubrulle:1983:CNM} and generalization
                 \cite{Jamieson:1989:SNR}.",
  URL =          "http://www.research.ibm.com/journal/rd/276/ibmrd2706P.pdf",
  abstract =     "An algorithm is presented for computing a 'Pythagorean
                 sum' a(+)b= square root a/sup 2/+b/sup 2/ directly from
                 a and b without computing their squares or taking a
                 square root. No destructive floating point overflows or
                 underflows are possible. The algorithm can be extended
                 to compute the Euclidean norm of a vector. The
                 resulting subroutine is short, portable, robust, and
                 accurate, but not as efficient as some other
                 possibilities. The algorithm is particularly attractive
                 for computers where space and reliability are more
                 important than speed",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classcodes =   "C4190 (Other numerical methods); C5230 (Digital
                 arithmetic methods)",
  corpsource =   "Department of Computer Sci., University of New Mexico,
                 Albuquerque, NM, USA",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "algorithms; digital arithmetic; Euclidean norm;
                 floating-point arithmetic; iterative methods;
                 performance; Pythagorean sums; subroutine; vector",
  review =       "ACM CR 8406-0463",
  subject =      "G.1 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Roots of Nonlinear Equations \\ F.2.1 Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials \\ F.2.2 Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Geometrical problems and computations",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Moran:1983:BRB,
  author =       "Bruce T. Moran",
  title =        "Book Review: {{\booktitle{Wissenschaftsgeschichte um
                 Wilhelm Schickard: Vortr{\"a}ge bei dem Symposion der
                 Universitat T{\"u}bingen im 500 Jahr ihres Bestehens am
                 24. und 25. Juni 1977}} by Friedrich Seck}",
  journal =      j-ISIS,
  volume =       "74",
  number =       "3",
  pages =        "448--449",
  month =        sep,
  year =         "1983",
  CODEN =        "ISISA4",
  ISSN =         "0021-1753 (print), 1545-6994 (electronic)",
  ISSN-L =       "0021-1753",
  bibdate =      "Tue Jul 30 21:22:47 MDT 2013",
  bibsource =    "http://www.jstor.org/action/showPublication?journalCode=isis;
                 http://www.jstor.org/stable/i211164;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/isis1980.bib",
  URL =          "http://www.jstor.org/stable/232640",
  acknowledgement = ack-nhfb,
  fjournal =     "Isis",
  journal-URL =  "http://www.jstor.org/journal/isis",
}

@InProceedings{Morrison:1983:EHL,
  author =       "R. Morrison and A. J. Cole and P. J. Bailey and M. A.
                 Wolfe and M. Shearer",
  title =        "Experience with a High Level Language that Supports
                 Interval Arithmetic",
  crossref =     "IEEE:1983:PSC",
  pages =        "74--78",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Morrison_Cole_Bailey_Wolfe_Shearer.pdf",
  abstract =     "An extension of the language S-algol called Triplex
                 which facilitates the use of interval arithmetic and
                 which is similar to triplex algol 60 is described.
                 Experience in the use of Triplex is reported. In
                 particular, a Triplex program corresponding to a
                 triplex algol 60 program of Nickel is given, together
                 with numerical results.",
  acknowledgement = ack-nhfb,
  keywords =     "Algol 60; ARITH-6; interval arithmetic; S-Algol;
                 Triplex (Algol)",
}

@Article{Murugesan:1983:ACF,
  author =       "S. Murugesan and V. K. Agrawal",
  title =        "Algorithm converts fractions to {BCD}",
  journal =      j-EDN,
  volume =       "28",
  number =       "19",
  pages =        "245--246",
  month =        sep,
  year =         "1983",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 1 10:16:10 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}

@Article{Nagpal:1983:PAT,
  author =       "H. K. Nagpal and G. A. Jullien and W. C. Miller",
  title =        "Processor Architectures for Two-Dimensional Convolvers
                 Using a Single Multiplexed Computational Element with
                 Finite Field Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "11",
  pages =        "989--1001",
  month =        nov,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676150",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:12 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676150",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Nave:1983:ITF,
  author =       "R. Nave",
  title =        "Implementation of Transcendental Functions on a
                 Numerics Processor",
  journal =      j-MICROPROC-MICROPROG,
  volume =       "11",
  number =       "3--4",
  pages =        "221--225",
  month =        mar # "--" # apr,
  year =         "1983",
  CODEN =        "MMICDT",
  DOI =          "https://doi.org/10.1016/0165-6074(83)90151-5",
  ISSN =         "0165-6074 (print), 1878-7061 (electronic)",
  ISSN-L =       "0165-6074",
  bibdate =      "Fri Dec 08 13:05:28 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeemilestones.ethw.org/w/images/8/8b/Nave_implenent_transcendental_algos_1983.pdf;
                 https://www.sciencedirect.com/science/article/pii/0165607483901515",
  acknowledgement = ack-nj,
  fjournal =     "Microprocessing and Microprogramming",
  journal-URL =  "https://www.sciencedirect.com/journal/microprocessing-and-microprogramming/issues",
}

@InProceedings{Ni:1983:VRM,
  author =       "Lionel M. Ni and Kai Hwang",
  title =        "Vector Reduction Methods for Arithmetic Pipelines",
  crossref =     "IEEE:1983:PSC",
  pages =        "144--150",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ni_Hwang.pdf",
  abstract =     "Vector reduction arithmetic accepts a vector as input
                 and produces a scalar output. This class of vector
                 operations forms the basis of many scientific
                 computations. In a pipelined processor, a feedback loop
                 is required to reduce vectors. Since the output of the
                 pipeline depends on previous outputs, improper control
                 of the feedback loop will destroy the benefit from
                 pipelining. A generalized computing model is proposed
                 to schedule the activities in a vector reduction
                 pipeline. Two new vector reduction methods, symmetric
                 and asymmetric, are proposed and analyzed for pipelined
                 processing. These two methods compare favorably with
                 the known recursive reduction method in achieving
                 higher pipeline utilization and in eliminating large
                 memory for intermediate results. An interleaving method
                 is proposed to reduce multiple vectors to multiple
                 scalars in a single arithmetic pipeline. The pipeline
                 can be fully utilized by interleaved multiple vector
                 processing.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}

@InProceedings{Ohlsson:1983:MML,
  author =       "Lennart Ohlsson and Bertil Svensson",
  title =        "Matrix Multiplication on {LUCAS}",
  crossref =     "IEEE:1983:PSC",
  pages =        "116--122",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ohlsson_Svensson.pdf",
  abstract =     "Multiplication of two $N$ by $N$ matrices involves $
                 N^3 $ multiplications of elements. The task allows a
                 large amount of parallelism to be utilized, indicating
                 that it can be efficiently executed on a parallel
                 computer. This paper describes how matrix
                 multiplication is performed on LUCAS, an SIMD type
                 parallel processor with bit-serial processing elements.
                 The interconnection network is of Perfect Shuffle\slash
                 Exchange type. The case of study is when the number of
                 processing elements is between $ N^2 $ and $ N^3 $. The
                 algorithm presented can be applied to any computer with
                 the same interconnection structure. Formulas showing
                 how the execution time depends on data length and
                 matrix size are presented together with measured values
                 from execution on LUCAS.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; LUCAS (Lund University Content Addressable
                 System)",
}

@InProceedings{Ong:1983:CAS,
  author =       "Shauchi Ong and D. E. Atkins",
  title =        "A Comparison of {ALU} Structures for {VLSI}
                 Technology",
  crossref =     "IEEE:1983:PSC",
  pages =        "10--16",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Ong_Atkins.pdf",
  abstract =     "Although many of the basic techniques of computer
                 arithmetic have been known since the earliest days of
                 electronic computing, there is a continuing need to
                 re-evaluate them in the context of developments in VLSI
                 circuit technology. Furthermore, recent work in
                 complexity of algorithms, particularly the solution of
                 recurrence relations, suggests new candidate structures
                 for generating the carry vector and raises the
                 questions as to their practicality in modern logic
                 design practice.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}

@Article{Owens:1983:TRI,
  author =       "R. M. Owens",
  title =        "Techniques to Reduce the Inherent Limitations of Fully
                 Digit On-Line Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "4",
  pages =        "406--411",
  month =        apr,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676244",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:08 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676244",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Ozawa:1983:AIK,
  author =       "K. Ozawa",
  title =        "Analysis and Improvement of {Kahan}'s Summation
                 Algorithm",
  journal =      j-INFO-PROC,
  volume =       "6",
  number =       "4",
  pages =        "226--230",
  year =         "1983",
  bibdate =      "Mon Sep 12 08:06:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  keywords =     "accurate floating-point summation",
}

@InProceedings{Palmer:1983:VSN,
  author =       "J. F. Palmer",
  title =        "{VLSI} starts a numeric revolution",
  crossref =     "IEEE:1983:PII",
  pages =        "186--189",
  year =         "1983",
  bibdate =      "Wed Sep 7 22:31:27 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Pan:1983:ALC,
  author =       "V. Ya Pan",
  title =        "The additive and logical complexities of linear and
                 bilinear arithmetic algorithms",
  journal =      j-J-ALG,
  volume =       "4",
  number =       "1",
  pages =        "1--34",
  month =        mar,
  year =         "1983",
  CODEN =        "JOALDV",
  DOI =          "https://doi.org/10.1016/0196-6774(83)90031-7",
  ISSN =         "0196-6774 (print), 1090-2678 (electronic)",
  ISSN-L =       "0196-6774",
  bibdate =      "Tue Dec 11 09:14:02 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jalg.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0196677483900317",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Algorithms",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01966774",
}

@Article{Patel:1983:CED,
  author =       "J. H. Patel and L. Y. Fung",
  title =        "Concurrent Error Detection in Multiply and Divide
                 Arrays",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "4",
  pages =        "417--422",
  month =        apr,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676246",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:08 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676246",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Payne:1983:DRT,
  author =       "M. H. Payne and R. N. Hanek",
  title =        "Degree Reduction for Trigonometric Functions",
  journal =      j-SIGNUM,
  volume =       "18",
  number =       "2",
  pages =        "18--19",
  month =        apr,
  year =         "1983",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/1057605.1057606",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Thu Sep 1 10:15:56 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This report is a companion to Reference 1 on radian
                 reduction. As in Reference 1 \cite{Payne:1983:RRT}, the
                 motivation arises from a desire to eliminate messages
                 like ``argument too large'' in trigonometric function
                 routines. The presence of very large arguments in the
                 VAX H format, on the Cray 1, and on an IEEE machine
                 with extended registers, make this a real problem. As
                 for the radian reduction algorithm, the degree
                 algorithm will reduce any argument, however large, so
                 long as it is representable; its speed is nearly
                 independent of the size of the argument to be reduced;
                 and full accuracy is maintained in the neighborhoods of
                 the zeros of the desired function. We believe that the
                 approach is new and represents a significant
                 improvement over procedures currently in use. A variant
                 of the procedure is used in Version 3 of the VAX Math
                 Library.",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "range reduction",
}

@Article{Payne:1983:RRT,
  author =       "M. H. Payne and R. N. Hanek",
  title =        "Radian Reduction for Trigonometric Functions",
  journal =      j-SIGNUM,
  volume =       "18",
  number =       "1",
  pages =        "19--24",
  month =        jan,
  year =         "1983",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/1057600.1057602",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Thu Sep 1 10:15:56 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "An accurate reduction poses little difficulty for
                 arguments of a few radians. However for, say, a CRAY 1,
                 H format on the VAX, or double extended in the proposed
                 IEEE standard, the maximum argument which might be
                 presented for reduction is of the order of $ 2^{16000}
                 $ radians. Accurate reduction of such an argument would
                 require storage of $ \pi $ (or its reciprocal) to over
                 16,000 bits. Direct reduction by division (or
                 multiplication) then requires generation of a somewhat
                 larger number of bits in the result in order to
                 guarantee the accuracy of the reduction. Of these bits
                 only the low few bits of the integer part of the
                 quotient (product) and enough bits to correctly round
                 the remainder are relevant; the rest will be
                 discarded.",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "correct rounding; floating-point arithmetic; range
                 reduction",
}

@Article{Preparata:1983:MCA,
  author =       "F. P. Preparata",
  title =        "A Mesh-Connected Area-Time Optimal {VLSI} Multiplier
                 of Large Integers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "2",
  pages =        "194--198",
  month =        feb,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676203",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:07 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676203",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Prosser:1983:NCS,
  author =       "C. J. Prosser",
  title =        "A note on computing the square root of an integer",
  journal =      j-COMP-J,
  volume =       "26",
  number =       "2",
  pages =        "187--188",
  month =        may,
  year =         "1983",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/;
                 https://www.math.utah.edu/pub/tex/bib/compj1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/tiff/187.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/tiff/188.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C4190 (Other numerical methods); C7310 (Mathematics
                 computing)",
  corpsource =   "Rutherford and Appleton Lab., Chilton, Didcot, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "binary; computer; fixed-point number; integer;
                 interactive methods; iterative methods; PASCAL; Pascal
                 implementation; square root; subroutines; successive
                 subtraction",
  treatment =    "P Practical",
}

@Article{Prosser:1983:SNN,
  author =       "C. J. Prosser",
  title =        "Short Notes: a Note on Computing the Square Root of an
                 Integer",
  journal =      j-COMP-J,
  volume =       "26",
  number =       "2",
  pages =        "187--188",
  month =        may,
  year =         "1983",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/26.2.187",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:48:14 MST 2012",
  bibsource =    "http://comjnl.oxfordjournals.org/content/26/2.toc;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/;
                 https://www.math.utah.edu/pub/tex/bib/compj1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/26/2/187.full.pdf+html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/tiff/187.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_26/Issue_02/tiff/188.tif",
  acknowledgement = ack-nhfb,
  classcodes =   "C4190 (Other numerical methods); C7310 (Mathematics
                 computing)",
  corpsource =   "Rutherford and Appleton Lab., Chilton, Didcot, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "binary; computer; fixed-point number; integer;
                 iterative methods; PASCAL; Pascal implementation;
                 square root; subroutines; successive subtraction",
  treatment =    "P Practical",
}

@Article{Quinn:1983:EPR,
  author =       "Kevin Quinn",
  title =        "Ever Had Problems Rounding Off Figures? {This} Stock
                 Exchange Has",
  journal =      j-WALL-ST-J,
  volume =       "??",
  number =       "??",
  pages =        "37--37",
  day =          "8",
  month =        nov,
  year =         "1983",
  CODEN =        "WSJOAF",
  ISSN =         "0099-9660",
  bibdate =      "Thu Oct 17 06:28:35 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Wall Street Journal",
}

@Article{Rall:1983:BRB,
  author =       "L. B. Rall",
  title =        "Book Review: {{\booktitle{Computer Arithmetic in
                 Theory and Practice}} (Ulrich W. Kulisch and Willard L.
                 Miranker)}",
  journal =      j-SIAM-REVIEW,
  volume =       "25",
  number =       "4",
  pages =        "585--588",
  month =        "????",
  year =         "1983",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1025138",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Sat Mar 29 09:53:41 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/25/4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "October 1983",
}

@Article{Rall:1983:CAT,
  author =       "L. B. Rall",
  title =        "Computer Arithmetic in Theory and Practice ---
                 {Kulisch, U. W., Miranker, W. L.}",
  journal =      j-SIAM-REVIEW,
  volume =       "25",
  number =       "4",
  pages =        "585--588",
  month =        "????",
  year =         "1983",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1025138",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri Jun 21 11:25:02 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
}

@Article{Ramachandran:1983:SRE,
  author =       "V. Ramachandran",
  title =        "Single Residue Error Correction in Residue Number
                 Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "5",
  pages =        "504--507",
  month =        may,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676264",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35227;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676264",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "We present a new method to correct single errors in an
                 n-residue number system through the use of r redundant
                 moduli. The method requires {\lceil}2n/r{\rceil} + 2
                 recombinations of n residues in the worst case. This is
                 of lower complexity than any \ldots{}",
}

@InProceedings{Rao:1983:ICS,
  author =       "T. R. N. Rao and P. Kornerup",
  title =        "{IEEE Computer Society Sixth Symposium on Computer
                 Arithmetic}",
  crossref =     "IEEE:1983:PSC",
  pages =        "1--1",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Rao_Kornerup.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}

@InProceedings{Robertson:1983:CDM,
  author =       "James E. Robertson",
  title =        "Conditions for the Distributivity of Multiplication
                 with Respect to Set Addition and Their Effect on the
                 Design of Array Multipliers",
  crossref =     "IEEE:1983:PSC",
  pages =        "67--71",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Robertson.pdf",
  abstract =     "Some conditions for distributivity of multiplication
                 with respect to set addition are determined. In
                 particular, distributivity holds if positive numbers
                 are used, but does not hold for negative numbers in
                 radix complement form. Use of simple recoding methods
                 to achieve distributivity is not helpful, since costs
                 of elementary multipliers and summing networks are
                 increased. Distributivity does hold for the digit sets
                 used for signed-digit arithmetic, and the requirement
                 for distributivity provides guidance for the design of
                 elementary multipliers.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}

@Article{Robison:1983:USF,
  author =       "A. D. Robison",
  title =        "Use Squares for Fast Multiplication",
  journal =      j-EDN,
  volume =       "28",
  number =       "21",
  pages =        "263, 267",
  month =        oct,
  year =         "1983",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 1 10:15:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}

@MastersThesis{Rosenblum:1983:IIS,
  author =       "David Samuel Rosenblum",
  title =        "An implementation of the {IEEE} standard for binary
                 floating-point arithmetic for the {Motorola} 6809
                 microprocessor",
  type =         "Thesis ({M.S.})",
  school =       "North Texas State University",
  address =      "Denton, TX, USA",
  pages =        "vi + 83",
  month =        aug,
  year =         "1983",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic.; Microprocessors ---
                 Programming.",
}

@InProceedings{Rump:1983:SAP,
  author =       "Siegfried M. Rump",
  title =        "Solving algebraic problems with high accuracy",
  crossref =     "Kulisch:1983:NAS",
  pages =        "51--120",
  year =         "1983",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1; G.1.3; G.1.0; G.1.0",
  content =      "Numerical methods for the following applications are
                 surveyed in this paper: solving systems of linear
                 algebraic equations; obtaining the inverse of a given
                 matrix; finding zeros of functions and polynomials;
                 computing eigenvalues and eigenvectors of a matrix;
                 treating linear, quadratic and convex programming
                 problems; and calculating the values of arithmetic
                 expressions. Both the case where the coefficient matrix
                 is square and the case where the coefficient matrix is
                 rectangular are handled in connection with the solution
                 of systems of linear algebraic equations. Moreover,
                 methods for the special, but important, cases where the
                 coefficient matrix of a system of linear algebraic
                 equations is band or sparse are given. (In the latter
                 case, it is assumed that the system is solved by
                 iterative processes.) The common feature of all these
                 methods is that by studying carefully the basic
                 properties of the computer arithmetic (sketched in the
                 beginning of the paper), one can avoid the round-off
                 errors and, thus, achieve a high degree of accuracy. If
                 the data are exactly representable on the computer
                 under consideration, \ldots{}",
  CRclass =      "G.1.3 Numerical Linear Algebra; G.1.3 Numerical Linear
                 Algebra; G.1.3 Sparse and very large systems; G.1.0
                 General; G.1.0 Computer arithmetic; G.1.0 General;
                 G.1.0 Error analysis",
  CRnumber =     "8503-0216",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Numerical Linear Algebra; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse
                 and very large systems; Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Computer arithmetic;
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis",
  genterm =      "ALGORITHMS; PERFORMANCE",
  reviewer =     "Z. Zlatev; Zlatev, Z",
  source =       "in A new approach to scientific computation. Proc. of
                 the symposium on a new approach to scientific
                 computation (Yorktown Heights, NY, August 3, 1982), U.
                 Kulisch and W. Miranker (Eds.), Academic Press, Inc.,
                 New York, NY, 1983",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@InProceedings{Sand:1983:DIP,
  author =       "J. R. Sand and J. O. Bumgarner",
  title =        "{Dysan IEEE P-754} Binary Floating Point
                 Architecture",
  crossref =     "Ranocchia:1983:RFA",
  pages =        "185--194",
  year =         "1983",
  bibdate =      "Sat Nov 12 21:59:00 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@InProceedings{Sandesara:1983:ZZF,
  author =       "S. Sandesara",
  title =        "{Zilog}'s {Z8070} Floating-Point Processor",
  crossref =     "Mini-Micro:1983:MMN",
  pages =        "7/4/1--3",
  year =         "1983",
  bibdate =      "Mon Sep 12 08:05:44 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Schelin:1983:CFA,
  author =       "Charles W. Schelin",
  title =        "Calculator function approximation",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "90",
  number =       "5",
  pages =        "317--325",
  month =        may,
  year =         "1983",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2975781",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "65D15 (65-03 65-04)",
  MRnumber =     "84h:65021",
  MRreviewer =   "J. Albrycht",
  bibdate =      "Wed Dec 3 17:17:33 MST 1997",
  bibsource =    "http://www.jstor.org/journals/00029890.htm;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.jstor.org/stable/2975781",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
  keywords =     "Computer Function Evaluation; CORDIC Scheme; tabular
                 function values",
}

@InProceedings{Scherson:1983:MOA,
  author =       "Isaac Scherson and Smil Ruhman",
  title =        "Multi-operand Associative Arithmetic",
  crossref =     "IEEE:1983:PSC",
  pages =        "123--129",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Scherson_Ruhman.pdf",
  abstract =     "Multi-operand associative techniques attain their full
                 power in algorithms where the data may be recast into
                 disjoint data sets, all acted upon concurrently, each
                 by a different operand common to the set. But the
                 multi-operand approach can also serve to enhance
                 arithmetic operations significantly. The speed-up of
                 associative multiplication by handling a number of
                 multiplier bits at a time is described and analyzed,
                 including an effective algorithm for a limited sum of
                 products. The most complex process treated is
                 convolution, which serves to illustrate the enhancement
                 of an extended sum of products. Any number of vectors
                 stored in memory can be convolved simultaneously by a
                 common filter vector. Execution time is 45 milliseconds
                 for 1024 element data and filter vectors, 2048 element
                 results, and 16-bit precision.",
  acknowledgement = ack-nhfb,
}

@Book{Schmid:1983:DC,
  author =       "Hermann Schmid",
  title =        "Decimal Computation",
  publisher =    pub-R-E-KRIEGER,
  address =      pub-R-E-KRIEGER:adr,
  pages =        "xi + 266",
  year =         "1983",
  ISBN =         "0-89874-318-4",
  ISBN-13 =      "978-0-89874-318-0",
  LCCN =         "QA75 .S34 1983",
  bibdate =      "Thu Sep 1 10:14:05 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprint of \cite{Schmid:1974:DC}.",
  acknowledgement = ack-nhfb,
  keywords =     "binary-coded decimal system; calculators--circuits;
                 decimal floating-point arithmetic",
}

@InProceedings{Seidensticker:1983:CFH,
  author =       "R. B. Seidensticker",
  title =        "Continued Fractions For High-Speed and High-Accuracy
                 Computer Arithmetic",
  crossref =     "IEEE:1983:PSC",
  pages =        "184--193",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:50:08 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Seidensticker.pdf",
  abstract =     "Continued fraction representation has many advantages
                 for fast and high-accuracy computation when compared
                 with positional notation. A continued fraction is a
                 number of the form\par

                  $$ p_1 + q_1 / (p_2 + q_2 / (p_3 + \cdots {}))
                 $$,\par

                 \noindent where $p$ and $q$ are integers. Some of the
                 benefits of continued fraction representation for
                 computer arithmetic are: faster multiply and divide
                 than with positional notation, fast evaluation of
                 trigonometric, logarithmic, and other unary functions,
                 easy extension to infinite-precision arithmetic,
                 infinite-precision representation of many
                 transcendental numbers, no roundoff or truncation
                 errors, and improved software transportability because
                 accuracy is not hardware dependent. A unified system
                 for continued fraction arithmetic is given along with
                 an outline of a hardware architecture for evaluating
                 these functions.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; continued fractions",
}

@MastersThesis{Shah:1983:FPP,
  author =       "Kamalesh Ramanlal Shah",
  title =        "Floating point processor for {STOIC} instrumentation",
  type =         "Thesis ({M.S. in Engineering})",
  school =       "University of Texas at Austin",
  address =      "Austin, TX, USA",
  pages =        "xi + 188",
  year =         "1983",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Medical electronics.; Medical instruments and
                 apparatus --- Design and construction.;
                 Microprocessors.",
}

@Article{Simington:1983:INP,
  author =       "R. B. Simington",
  title =        "The {Intel 8087} Numerics Processor Extension: this
                 chip lets you perform mathematical operations with
                 18-decimal digits of accuracy.",
  journal =      j-BYTE,
  volume =       "8",
  number =       "4",
  pages =        "154--175",
  month =        apr,
  year =         "1983",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Sat Aug 23 06:48:26 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Overview of the 8087 and its close ties to the host
                 8086 or 8088 CPU.",
  URL =          "https://ieeemilestones.ethw.org/w/images/8/85/Simington_The_Intel_8087_Numerics_Processor_Extension.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "BYTE Magazine",
}

@Article{Smith:1983:FPA,
  author =       "Burks Smith",
  title =        "Floating Point Arithmetic and Numeric Representation
                 in Computers [letter] in {DDC}",
  journal =      j-DDJ,
  volume =       "8",
  number =       "2",
  pages =        "55--??",
  month =        feb,
  year =         "1983",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@Article{Soderstrand:1983:IRN,
  author =       "M. Soderstrand and C. Vernia and Jui-Hua Chang",
  title =        "An improved residue number system digital-to-analog
                 converter",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "30",
  number =       "12",
  pages =        "903--907",
  month =        dec,
  year =         "1983",
  CODEN =        "ICSYBT",
  DOI =          "https://doi.org/10.1049/el:19820632",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23540",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A new technique for Residue Number System (RNS)
                 Digital-to-Binary or Digital-to-Analog conversion based
                 on the Chinese Remainder Theorem allows conversion with
                 only one level of ROM and one level of Adders. The
                 ROM's are small (e.g., 256 x 8) and \ldots{}",
}

@TechReport{Spafford:1983:RAP,
  author =       "Eugene Howard Spafford",
  title =        "A report on the accuracy of {PRIME} computers'
                 floating point software and hardware and the {SWT} math
                 library user's guide",
  type =         "{GIT-ICS}",
  number =       "83/09",
  institution =  "School of Information and Computer Science, Georgia
                 Institute of Technology",
  address =      "Atlanta, GA, USA",
  pages =        "v + 57",
  year =         "1983",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computers.",
}

@Article{Speiser:1983:SFP,
  author =       "Jeffrey Speiser",
  title =        "{Savage} Floating Point Benchmark in {PASCAL} in
                 {16BST}",
  journal =      j-DDJ,
  volume =       "8",
  number =       "11",
  pages =        "112--??",
  month =        nov,
  year =         "1983",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@TechReport{Springer:1983:FP,
  author =       "Charles Towne Springer",
  title =        "Floating point",
  institution =  "Mountain View Pr.",
  address =      "Mountain View, CA, USA",
  pages =        "22",
  year =         "1983",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "MVP-FORTH series; v. 3",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers --- Programming.;
                 Floating-point arithmetic.; FORTH (Computer program
                 language)",
  remark =       "Title on cover: FORTH floating point.
                 ``Pre-publication.''",
}

@Article{Swartzlander:1983:SLA,
  author =       "E. E. {Swartzlander, Jr.} and D. V. Satish Chandra and
                 H. T. {Nagle, Jr.} and S. A. Starks",
  title =        "Sign\slash Logarithm Arithmetic for {FFT}
                 Implementation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "6",
  pages =        "526--534",
  month =        jun,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676274",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  note =         "See comments \cite{Hongyuan:1986:CSL}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676274",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Takefuji:1983:FMS,
  author =       "Yoshiyasu Takefuji and Takakazu Kurokawa and Hideo
                 Aiso",
  title =        "Fast Matrix Solver in {$ \mathrm {GF}(2) $}",
  crossref =     "IEEE:1983:PSC",
  pages =        "138--143",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Takefuji_Kurokawa_Aiso.pdf",
  abstract =     "In this paper a parallel and pipelined fast matrix
                 equation solver in $ \mathrm {GF}(2) $ is proposed
                 where the elements are 0s or 1s. The solver employing
                 the iterative logic circuits which are suitable for
                 VLSI implementation can be realized by the conventional
                 Gauss--Jordan Elimination Method. $ O(n) $ gate stages
                 in the pipeline and $ O(n^2) $ total gates are required
                 for solving $ A X = b $ where $A$ is a matrix of $ n
                 \times n $, $X$ and $b$ are vectors respectively. The
                 organization of the solver is discussed in this
                 paper.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}

@TechReport{Tamura:1983:CDB,
  author =       "Y. Tamura and Y. Kanada",
  title =        "Calculation of $ \pi $ to 4,194,293 Decimals Based on
                 the {Gauss--Legendre} Algorithm",
  type =         "Technical report",
  number =       "CCUT-TR-83-01",
  institution =  "Computer Centre, University of Tokyo",
  address =      "Tokyo, Japan",
  month =        may,
  year =         "1983",
  bibdate =      "Mon Jul 18 17:46:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Taylor:1983:AE,
  author =       "George S. Taylor",
  title =        "Arithmetic on the {ELXSI 6400}",
  crossref =     "IEEE:1983:PSC",
  pages =        "110--115",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:50:05 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Taylor.pdf",
  abstract =     "The ELXSI System 6400 is a new 64-bit general-purpose
                 mainframe computer [1]. This paper describes its
                 arithmetic instruction set architecture and the
                 organization of the arithmetic processor. The ELXSI
                 instruction set supports a complete implementation of
                 the proposed IEEE floating point standard [2], plus
                 integer and decimal arithmetic. The System 6400
                 arithmetic processor uses ECL gate arrays to execute
                 these instructions at high speed using a single board
                 of hardware.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; ELXSI 6400",
}

@Article{Taylor:1983:OFR,
  author =       "F. J. Taylor",
  title =        "An Overflow-Free Residue Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "5",
  pages =        "501--504",
  month =        may,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676263",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676263",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@MastersThesis{Thomas:1983:HLM,
  author =       "James W. Thomas",
  title =        "High-level language management of the {IEEE}
                 floating-point environment: research project",
  type =         "Thesis ({M.S. in Electrical Engineering})",
  school =       "University of California, Berkeley. Dept. of
                 Electrical Engineering and Computer Sciences",
  address =      "Berkeley, CA, USA",
  pages =        "27",
  year =         "1983",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@MastersThesis{Tseng:1983:FIP,
  author =       "Yeong-Jeng Tseng",
  title =        "A floating-point inner product step processor for use
                 in a {VLSI} Systolic array",
  type =         "Thesis ({M.S.})",
  school =       "Michigan State University",
  address =      "East Lansing, MI 48824, USA",
  pages =        "ix + 63",
  year =         "1983",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic and logic units; Electronic
                 digital computers --- Circuits; Floating-point
                 arithmetic; Integrated circuits --- Very large scale
                 integration.",
}

@Article{Ulman:1983:SDI,
  author =       "Z. D. Ulman",
  title =        "Sign Detection and Implicit-Explicit Conversion of
                 Numbers in Residue Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "6",
  pages =        "590--594",
  month =        jun,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676282",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 10:01:10 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676282",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Vogt:1983:AFM,
  author =       "R. Vogt and R. Waser",
  title =        "{Arithmetikroutinen f{\"u}r die
                 Me{\ss}\-dat\-en\-ver\-ar\-beit\-ung} \toenglish
                 {Arithmetic Routines for Measurement Applications}
                 \endtoenglish",
  journal =      j-ELECTRONIK,
  volume =       "20",
  pages =        "85--92",
  year =         "1983",
  CODEN =        "EKRKAR",
  ISSN =         "0013-5658",
  bibdate =      "Fri Sep 16 16:30:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektronik",
}

@Article{Volz:1983:CAA,
  author =       "H. V{\"o}lz",
  title =        "{CORDIC und {\"a}hnliche Algorithmen der elementaren
                 Funktionen mit besonderer Eignung f{\"u}r
                 Mikrorechner}. ({German}) [{CORDIC} and Similar
                 Algorithms for Elementary Functions with Particular
                 Aptitude for Microcomputers]",
  journal =      j-NACH-ELEK,
  volume =       "33",
  number =       "12",
  pages =        "506--510",
  month =        "????",
  year =         "1983",
  CODEN =        "NTELAP",
  ISSN =         "0323-4657",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Nachrichtentechnik Elektronik",
  itle =         "{CORDIC und {\"a}hnliche Algorithmen der elementaren
                 Funktionen mit besonderer Eignung f{\"u}r
                 Mikrorechner}. ({German}) [{CORDIC} and Similar
                 Algorithms for Elementary Functions with Particular
                 Aptitude for Microcomputers]",
}

@Article{Vuillemin:1983:VFM,
  author =       "Jean E. Vuillemin",
  title =        "A very fast multiplication algorithm {VLSI}
                 implementation",
  journal =      j-INTEGRATION-VLSI-J,
  volume =       "1",
  number =       "1",
  pages =        "30--52",
  month =        apr,
  year =         "1983",
  CODEN =        "IVJODL",
  DOI =          "https://doi.org/10.1016/0167-9260(83)90005-6",
  ISSN =         "0167-9260 (print), 1872-7522 (electronic)",
  ISSN-L =       "0167-9260",
  bibdate =      "Thu Nov 13 08:11:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/0167926083900056",
  acknowledgement = ack-nhfb,
  fjournal =     "Integration, the VLSI Journal",
  journal-URL =  "https://www.sciencedirect.com/journal/integration/issues",
}

@InProceedings{Wallis:1983:AFP,
  author =       "Peter J. L. Wallis",
  title =        "{Ada} Floating-Point Arithmetic as a Basis for
                 Portable Numerical Software",
  crossref =     "IEEE:1983:PSC",
  pages =        "79--81",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Wallis.pdf",
  abstract =     "Ada supports two different schemes for floating-point
                 arithmetic portability -- one based on the use of the
                 underlying machine arithmetic and the other based on
                 the `model arithmetic' that the underlying machine
                 supports, Features of both schemes are explained in the
                 context of their suitability as bases for the
                 production of portable numerical software.",
  acknowledgement = ack-nhfb,
  keywords =     "Ada; ARITH-6",
}

@MastersThesis{Walsh:1983:FGE,
  author =       "Edmund John Walsh",
  title =        "Floating gatefield effect transistor operating point
                 changes: causes, characterization, and effect on
                 electric field measurement by the device",
  type =         "Thesis ({M.S.})",
  school =       "Boston University",
  address =      "Boston, MA, USA",
  pages =        "v + 121",
  year =         "1983",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Boston University. --- College of Engineering ---
                 Theses.",
}

@Article{Watanuki:1983:EAC,
  author =       "Osaaki Watanuki and Milo{\v{s}} D. Ercegovac",
  title =        "Error analysis of certain floating-point on-line
                 algorithms",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-32",
  number =       "4",
  pages =        "352--358",
  month =        apr,
  year =         "1983",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1983.1676236",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "65G05",
  MRnumber =     "85h:65099",
  bibdate =      "Sun Jul 10 10:01:08 MDT 2011",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676236",
  abstract =     "he properties of redundant number system in
                 significand (mantissa) representation are studied and
                 the range of redundant significand is derived. From the
                 range of the redundant significand and the absolute
                 error of on-line operations, the MRRE (maximum relative
                 representation error) is defined and analyzed for
                 floating-point on-line addition and multiplication.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  catcode =      "G.1.0; G.1.0",
  CRclass =      "G.1.0 General; G.1.0 Error analysis; G.1.0 General;
                 G.1.0 Parallel algorithms",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis; Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Parallel algorithms",
  fjournal =     "IEEE Transactions on Computers",
  guideno =      "06565",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  reviewer =     "Oliver, J",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@MastersThesis{Williams:1983:BFP,
  author =       "Bertrand Jeffery Williams",
  title =        "A bit-serial floating point multiply\slash add
                 architecture for signal processing applications",
  type =         "Electrical Engineering Thesis ({M.S.})",
  school =       "Texas A\&M University",
  address =      "College Station, TX, USA",
  pages =        "x + 97",
  year =         "1983",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer architecture.; Floating-point arithmetic.;
                 Signal processing.",
}

@Article{Wingert:1983:ITA,
  author =       "J. A. Wingert",
  title =        "Improved Table-assisted Addition and Multiplication
                 Methods",
  journal =      j-IBM-TDB,
  volume =       "25",
  number =       "9",
  pages =        "4742--4743",
  month =        feb,
  year =         "1983",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
}

@InProceedings{Yoshida:1983:FPR,
  author =       "Kaoru Yoshida",
  title =        "Floating-Point Recurring Rational Arithmetic System",
  crossref =     "IEEE:1983:PSC",
  pages =        "194--200",
  year =         "1983",
  bibdate =      "Tue Nov 13 15:58:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/ARITH6_Yoshida.pdf",
  abstract =     "Major computer arithmetic systems are based on the
                 concept of realizing only terminate rationals in
                 positional notation. This paper proposes a new
                 arithmetic scheme of indicating periodicity in the
                 radix representation of a mantissa to realize recurring
                 rationals as well as terminate rationals. A new
                 arithmetic system adopting the scheme, called the
                 ``FLP/R* arithmetic system'', is proposed. Properties
                 of the FLP/R* numbers and the procedure of the FLP/R*
                 arithmetic are described.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6; rational arithmetic",
}

@Article{Ypma:1983:ERE,
  author =       "T. J. Ypma",
  title =        "The effect of rounding errors on {Newtonlike}
                 methods",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "3",
  number =       "1",
  pages =        "109--118",
  year =         "1983",
  CODEN =        "IJNADH",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65G05 (65H05)",
  MRnumber =     "84h:65047",
  MRreviewer =   "Ren{\'e} Alt",
  bibdate =      "Sat Dec 23 17:06:35 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
}

@InProceedings{Abruzzo:1984:ACA,
  author =       "J. Abruzzo",
  title =        "Applicability of {CORDIC} Algorithm to Arithmetic
                 Processing",
  crossref =     "Kirk:1984:CRE",
  pages =        "79--86",
  year =         "1984",
  bibdate =      "Thu Sep 01 11:21:05 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@InProceedings{Abuzzo:1984:ACA,
  author =       "J. Abuzzo",
  editor =       "????",
  booktitle =    "{IEEE Eighteenth Asilomar Conf. on Circuits, Systems
                 and Computers, Pacific Grove, CA, USA, November 5--7,
                 1984}",
  title =        "Applicability of {CORDIC} algorithm to arithmetic
                 processing",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "??--??",
  year =         "1984",
  DOI =          "",
  ISBN =         "",
  ISBN-13 =      "",
  LCCN =         "",
  bibdate =      "Wed Oct 29 10:19:20 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "",
  acknowledgement = ack-nhfb,
}

@Article{Agrawal:1984:ACB,
  author =       "V. K. Agrawal and S. Murugesan",
  title =        "Algorithm converts {BCD} fractions to binary",
  journal =      j-EDN,
  volume =       "29",
  number =       "13",
  pages =        "278--280",
  month =        jun,
  year =         "1984",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 1 10:16:10 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}

@Article{Alia:1984:VAD,
  author =       "G. Alia and E. Martinelli",
  title =        "A {VLSI} algorithm for direct and reverse conversion
                 from weighted binary number system to residue number
                 system",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "31",
  number =       "12",
  pages =        "1033--1039",
  month =        dec,
  year =         "1984",
  CODEN =        "ICSYBT",
  DOI =          "https://doi.org/10.1109/TC.1984.1676355",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23552",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Residue Number Systems (RNS) are proved to be useful
                 in many applications, as for example in signal
                 processing. In this paper, a VLSI computing
                 architecture is proposed for converting an integer
                 number N from the weighted binary representation into
                 \ldots{}",
}

@InProceedings{Ancona:1984:PET,
  author =       "M. Ancona and G. Dodero and F. Ricci",
  title =        "A portable environment for teaching mathematical
                 software development",
  crossref =     "Ford:1984:TML",
  pages =        "135--145",
  year =         "1984",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See main entry CR, Rev. 8508--0689.",
  acknowledgement = ack-nhfb,
  content =      "ALGORITHMS; DESIGN; LANGUAGES; STANDARDIZATION",
  procloc =      "Proceedings paper",
  subject =      "G. Mathematics of Computing; G.4 MATHEMATICAL
                 SOFTWARE; K. Computing Milieux; K.6 MANAGEMENT OF
                 COMPUTING AND INFORMATION SYSTEMS; D. Software; D.2
                 SOFTWARE ENGINEERING; K. Computing Milieux; K.3
                 COMPUTERS AND EDUCATION",
  subjects =     "mathematics of computing, mathematical software,
                 portability; computing milieux, management of computing
                 and information systems, software management, software
                 development; software, software engineering,
                 distribution and maintenance, portability; computing
                 milieux, computers and education, computer and
                 information science education, computer science
                 education",
  wsub =         "A. C. R. Newbery",
}

@Article{Anonymous:1984:CPD,
  author =       "Anonymous",
  title =        "Correction to {``A Pipelined Distributed Arithmetic
                 PFFT Processor''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-33",
  number =       "3",
  pages =        "288--288",
  month =        mar,
  year =         "1984",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1984.1676429",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 09:22:50 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  note =         "See \cite{Chow:1983:PDA}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676429",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Bell:1984:RMR,
  author =       "M. {Bell, Jr.} and W. Jenkins",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing, {ICASSP '84}",
  title =        "A residue to mixed radix converter and error checker
                 for a five-moduli residue number system",
  volume =       "??",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "242--245",
  year =         "1984",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A design is presented for an experimental device which
                 converts data from residue representation to mixed
                 radix representation while simultaneously checking for
                 single digit errors. The experimental system has a high
                 speed pipelined architecture and \ldots{}",
}

@Article{Black:1984:NIS,
  author =       "Cheryl M. Black and Robert P. Burton and Thomas M.
                 Miller",
  title =        "The Need for an Industry Standard of Accuracy for
                 Elementary-Function Programs",
  journal =      j-TOMS,
  volume =       "10",
  number =       "4",
  pages =        "361--366",
  month =        dec,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2701.356101",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 20:32:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bollen:1984:NSD,
  author =       "J. A. M. Bollen",
  title =        "Numerical Stability of Descent Methods for Solving
                 Linear Equations",
  journal =      j-NUM-MATH,
  volume =       "43",
  number =       "3",
  pages =        "361--377",
  year =         "1984",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65G05 (65F10)",
  MRnumber =     "85f:65041",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290B (Error analysis in numerical methods); C4110
                 (Error analysis in numerical methods)",
  corpsource =   "Department of Appl. Maths., Twente University of
                 Technol., Enschede, Netherlands",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "descent methods; digital arithmetic; error analysis;
                 floating point arithmetic; Gauss-Southwell method;
                 gradient method; linear differential equations; linear
                 equations; linear systems; numerical stability;
                 roundoff error analysis; stability",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Boney:1984:GTD,
  author =       "J. Boney",
  title =        "Goals and tradeoffs in the design of the {MC68881}
                 floating point coprocessor",
  crossref =     "NCC:1984:ACP",
  pages =        "107--113",
  year =         "1984",
  bibdate =      "Wed Sep 7 22:31:45 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Borwein:1984:AGM,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "The Arithmetic-Geometric Mean and Fast Computation of
                 Elementary Functions",
  journal =      j-SIAM-REVIEW,
  volume =       "26",
  number =       "3",
  pages =        "351--366",
  month =        jul,
  year =         "1984",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1026073",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "65D20 (26A09)",
  MRnumber =     "86d:65029",
  MRreviewer =   "S. Conde",
  bibdate =      "Sat Mar 29 09:53:48 MDT 2014",
  bibsource =    "Compendex database;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 http://epubs.siam.org/toc/siread/26/3;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  abstract =     "We produce a self contained account of the
                 relationship between the Gaussian arithmetic-geometric
                 mean iteration and the fast computation of elementary
                 functions. A particularly pleasant algorithm for pi is
                 one of the by-products.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliationaddress = "Dalhousie Univ, Halifax, NS, Can",
  classification = "723; 921",
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  journalabr =   "SIAM Rev",
  keywords =     "AGM (Arithmetic-Geometric Mean); arithmetic-geometric
                 mean; calculation of pi; computational methods;
                 elliptic functions; Iterative Methods; mathematical
                 techniques; numerical mathematics",
  onlinedate =   "July 1984",
}

@InProceedings{Braddock:1984:ASP,
  author =       "M. Braddock and V. Shahan",
  title =        "Amplifying System Performance in Floating-point
                 Intensive Applications with the {MC68881}",
  crossref =     "Mini-Micro:1984:MMS",
  pages =        "6/2/1--7",
  year =         "1984",
  bibdate =      "Wed Sep 7 22:31:45 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Butterfield:1984:MT,
  author =       "J. Butterfield",
  title =        "Math and Tables",
  journal =      j-COMPUTE,
  volume =       "6",
  number =       "9",
  pages =        "134--135",
  month =        sep,
  year =         "1984",
  CODEN =        "COMPER",
  ISSN =         "0194-357X",
  bibdate =      "Thu Sep 1 10:15:30 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Compute",
}

@Article{Caraiscos:1984:REA,
  author =       "C. Caraiscos and Bede Liu",
  title =        "A roundoff error analysis of the {LMS} adaptive
                 algorithm",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "32",
  number =       "1",
  pages =        "34--41",
  month =        feb,
  year =         "1984",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  summary =      "The steady state output error of the least mean square
                 (LMS) adaptive algorithm due to the finite precision
                 arithmetic of a digital processor is analyzed. It is
                 found to consist of three terms: (1) the error due to
                 the input data quantization, (2) the \ldots{}",
}

@Book{Cavanagh:1984:DCA,
  author =       "Joseph J. F. Cavanagh",
  title =        "Digital Computer Arithmetic: Design and
                 Implementation",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xi + 468",
  year =         "1984",
  ISBN =         "0-07-010282-1",
  ISBN-13 =      "978-0-07-010282-8",
  LCCN =         "QA76.9.C62 C38 1984",
  bibdate =      "Sat May 18 14:16:35 2002",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$21.95",
  acknowledgement = ack-nj,
}

@MastersThesis{Cheng:1984:FPC,
  author =       "Doreen Y. Cheng",
  title =        "A floating point coprocessor for the {Butterfly}
                 multiprocessor system: research project",
  type =         "Thesis ({M.S. in Electrical Engineering})",
  school =       "University of California, Berkeley. Dept. of
                 Electrical Engineering and Computer Sciences",
  address =      "Berkeley, CA, USA",
  pages =        "51 + 38",
  month =        may,
  year =         "1984",
  bibdate =      "Wed Nov 25 08:35:11 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Clarke:1984:AAR,
  author =       "M. R. Clarke",
  title =        "An Analytical Approach to Rounding",
  journal =      j-J-APPL-STAT,
  volume =       "11",
  number =       "1",
  pages =        "12--20",
  year =         "1984",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/02664768400000003",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  bibdate =      "Tue Sep 6 11:15:48 MDT 2011",
  bibsource =    "http://www.tandf.co.uk/journals/routledge/02664763.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
  onlinedate =   "28 Jul 2006",
}

@Article{Clenshaw:1984:BFP,
  author =       "C. W. Clenshaw and F. W. J. Olver",
  title =        "Beyond Floating Point",
  journal =      j-J-ACM,
  volume =       "31",
  number =       "2",
  pages =        "319--328",
  month =        apr,
  year =         "1984",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/62.322429",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  MRclass =      "65G05",
  MRnumber =     "819 141",
  bibdate =      "Wed Jan 15 18:12:53 MST 1997",
  bibsource =    "Compendex database;
                 ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jacm.bib",
  abstract =     "A new number system is proposed for computer
                 arithmetic based on iterated exponential functions. The
                 main advantage is to eradicate overflow and underflow,
                 but there are several other advantages and these are
                 described and discussed.",
  acknowledgement = ack-nhfb,
  affiliationaddress = "Univ of Lancaster, Dep of Mathematics,
                 Lancaster, Engl",
  classification = "723",
  fjournal =     "Journal of the Association for Computing Machinery",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  journalabr =   "J Assoc Comput Mach",
  keywords =     "computer arithmetic; computer metatheory; error
                 analysis; mathematical techniques --- Digital
                 Arithmetic; overflow; rounding error; underflow",
}

@Article{Cody:1984:PRW,
  author =       "William J. {Cody, Jr.} and Jerome T. Coonen and David
                 M. Gay and K. Hanson and David Hough and W. Kahan and
                 R. Karpinski and John F. Palmer and F. N. Ris and D.
                 Stevenson",
  title =        "A Proposed Radix- and Word-length-independent Standard
                 for Floating-Point Arithmetic",
  journal =      j-IEEE-MICRO,
  volume =       "4",
  number =       "4",
  pages =        "86--100",
  month =        jul # "\slash " # aug,
  year =         "1984",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.1984.291224",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Nov 8 14:50:28 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}

@PhdThesis{Coonen:1984:CPS,
  author =       "Jerome Toby Coonen",
  title =        "Contributions to a Proposed Standard for Binary
                 Floating-Point Arithmetic",
  type =         "Thesis ({Ph.D.} in Mathematics)",
  school =       "Department of Mathematics, University of California at
                 Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "320",
  day =          "18",
  month =        dec,
  year =         "1984",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.proquest.com/pqdtglobal/docview/303300605",
  abstract =     "In the fall of 1977 the Institute of Electrical and
                 Electronics Engineers commissioned working group 754 to
                 draft a standard for binary floating-point arithmetic.
                 It was intended to prevent the proliferation of
                 disparate arithmetics in the new microprocessor
                 industry. At that time there were so many different
                 flavors of arithmetic available on mainframes and
                 minicomputers that the cost of reconciling their
                 differences in numerical software had become, and
                 remains, staggering. Now, more than five years later,
                 draft 10.0 of the proposed standard has been voted out
                 of the working group for IEEE approval.\par

                 This thesis consists of a set of ``footnotes'' to the
                 proposed standard. The first of them, an implementation
                 guide published in January 1980, served as a working
                 draft of the standard for over a year. The remaining
                 chapters unfolded as the proposed standard did. They
                 include an analysis of gradual underflow, the most
                 controversial feature of the standard; an exhaustive
                 discussion of radix conversion, which has been
                 specified in the proposed standard only up to a
                 worst-case error bound; and a revised version of the
                 arithmetic test suite which has been available in
                 machine-readable form from the working group.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  advisor =      "William M. Kahan",
  remark =       "Doctoral degree conferred December 18, 1984.",
}

@InCollection{Corliss:1984:AGT,
  author =       "George F. Corliss and Louis B. Rall",
  title =        "Automatic generation of {Taylor} series in
                 {Pascal-SC}: {Basic} operations and applications to
                 differential equations",
  crossref =     "Anonymous:1984:TFA",
  pages =        "177--209",
  year =         "1984",
  bibdate =      "Fri Dec 8 13:09:09 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Pascal-SC supports user-defined data types,
                 user-defined operators, and accurate floating point and
                 interval arithmetic for numerical computations. The
                 authors implement data types TAYLOR and ITAYLOR
                 (Interval Taylor) with operators $+$, $-$, $*$, $/$, $
                 ** $, and the functions SQR, SQRT, EXP, SIN, COS,
                 ARCTAN, and LN. An initial value problem $ y' = y^2 $,
                 $ y(0) = 1 $, is solved with TAYLOR and with ITAYLOR
                 types to show that the series generation exhibits a
                 mild instability which has no significant effect on the
                 values of the solution computed by analytic
                 continuation.",
  acknowledgement = ack-nj,
  comment =      "Also appeared as {\sl MRC Technical Summary Report No.
                 2497}, Mathematics Research Center, University of
                 Wisconsin-Madison, 1983.",
  keywords =     "automatic differentiation; stability.; Taylor series",
}

@Article{Cowlishaw:1984:DRL,
  author =       "M. F. Cowlishaw",
  title =        "The Design of the {REXX} Language",
  journal =      j-IBM-SYS-J,
  volume =       "23",
  number =       "4",
  pages =        "326--335",
  year =         "1984",
  CODEN =        "IBMSA7",
  ISSN =         "0018-8670",
  bibdate =      "Wed Jan 08 16:35:07 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "First published as IBM Hursley Technical Report
                 TR12.223, October 1983.",
  abstract =     "One way of classifying computer languages is by two
                 classes: languages needing skilled programmers, and
                 personal languages used by an expanding population of
                 general users. REstructured eXtended eXecutor (REXX) is
                 a flexible personal language designed with particular
                 attention to feedback from its users. It has proved to
                 be effective and easy to use, yet it is sufficiently
                 general and powerful to fulfill the needs of many
                 demanding professional applications. REXX is system and
                 hardware independent, so that it has been possible to
                 integrate it experimentally into several operating
                 systems. Here REXX is used for such purposes as command
                 and macro programming, prototyping, education, and
                 personal programming. This study introduces REXX and
                 describes the basic design principles that were
                 followed in developing it.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM UK Ltd, Scientific Cent, Winchester, Engl",
  affiliationaddress = "IBM UK Ltd, Scientific Cent, Winchester, Engl",
  classification = "723",
  fjournal =     "IBM Systems Journal",
  journalabr =   "IBM Syst J",
  keywords =     "command program interpreters; computer operating
                 systems; computer programming languages; decimal
                 floating-point arithmetic; language concepts; personal
                 language; REXX language",
  remark =       "REXX supports arbitrary precision arithmetic with up
                 to $ 10^9 $ digits, and an exponent range of $ \pm 10^9
                 $. This capability was added to REXX in 1981.",
}

@Article{Demmel:1984:URN,
  author =       "James Demmel",
  title =        "Underflow and the reliability of numerical software",
  journal =      j-SIAM-J-SCI-STAT-COMP,
  volume =       "5",
  number =       "4",
  pages =        "887--919",
  month =        dec,
  year =         "1984",
  CODEN =        "SIJCD4",
  ISSN =         "0196-5204",
  MRclass =      "65G05",
  MRnumber =     "85m:65035",
  MRreviewer =   "G. Alefeld",
  bibdate =      "Tue Apr 29 19:18:28 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods)",
  corpsource =   "Div. of Computer Science, California University,
                 Berkeley, CA, USA",
  fjournal =     "SIAM Journal on Scientific and Statistical Computing",
  journal-URL =  "http://epubs.siam.org/loi/sijcd4",
  keywords =     "codes; digital arithmetic; eigenvalue calculation;
                 Gaussian elimination; gradual underflow; numerical
                 software; polynomial evaluation; reliability; roundoff;
                 roundoff errors; store zero; uncertainty; underflow
                 mechanisms",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Demsky:1984:MMC,
  author =       "J. Demsky and M. Schlesinger and R. D. Kent",
  title =        "Micro\slash mini computer program for calculating the
                 square root of rationals at arbitrary precision",
  journal =      j-COMP-PHYS-COMM,
  volume =       "35",
  number =       "1--3",
  pages =        "C-877",
  month =        "????",
  year =         "1984",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(84)82981-1",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 25 10:56:58 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465584829811",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Dietrich:1984:FPR,
  author =       "D. Dietrich and R. Fischer",
  title =        "{Floating-Point-Routinen, entwickelt f{\"u}r
                 Mikrorechner} \toenglish {Floating-point Routines
                 Developed for Microcomputers} \endtoenglish",
  journal =      j-ELEKTRONIKER,
  volume =       "8",
  pages =        "49--54",
  year =         "1984",
  CODEN =        "ELKRBL",
  ISSN =         "0531-9218",
  bibdate =      "Fri Sep 16 16:30:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektroniker (Switzerland)",
}

@Article{Duncan:1984:FSF,
  author =       "Ray Duncan and Martin Tracy",
  title =        "The {FVG} Standard Floating-Point Extension",
  journal =      j-DDJ,
  volume =       "9",
  number =       "9",
  pages =        "110--??",
  month =        sep,
  year =         "1984",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
  xxnote =       "??Check author order??",
}

@Article{Dunford:1984:SFPa,
  author =       "Christopher J. Dunford",
  title =        "{Savage} floating-point benchmark in 8088\slash 8087
                 assembly language in {16BST}",
  journal =      j-DDJ,
  volume =       "9",
  number =       "7",
  pages =        "116--??",
  month =        jul,
  year =         "1984",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@Article{Dunford:1984:SFPb,
  author =       "Christopher J. Dunford",
  title =        "{Savage} floating-point benchmark in {Modula-2} in
                 {16BST}",
  journal =      j-DDJ,
  volume =       "9",
  number =       "8",
  pages =        "106--??",
  month =        aug,
  year =         "1984",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@Article{Ercegovac:1984:LAO,
  author =       "Milo{\v{s}} D. Ercegovac",
  title =        "On-line arithmetic: An overview",
  journal =      j-SPIE,
  volume =       "495",
  pages =        "86--93",
  year =         "1984",
  bibdate =      "Fri Nov 30 06:32:39 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Real Time Signal Processing VII.",
  acknowledgement = ack-nhfb,
}

@Article{Ferguson:1984:SFP,
  author =       "Kenneth M. Ferguson",
  title =        "{Savage} floating-point benchmark deficiencies of in
                 {16BST}",
  journal =      j-DDJ,
  volume =       "9",
  number =       "8",
  pages =        "107--??",
  month =        aug,
  year =         "1984",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@Article{Fisher:1984:UAP,
  author =       "Gerry Fisher",
  title =        "Universal Arithmetic Packages",
  journal =      j-SIGADA-LETTERS,
  volume =       "3",
  number =       "6",
  pages =        "30--47",
  month =        may # "\slash " # jun,
  year =         "1984",
  CODEN =        "AALEE5",
  DOI =          "https://doi.org/10.1145/998388.998389",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Thu Sep 28 07:33:23 MDT 2000",
  bibsource =    "ftp://ftp.uu.net/library/bibliography;
                 http://www.adahome.com/Resources/Bibliography/articles.ref;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  note =         "See erratum \cite{Froggatt:2015:EAU}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "universal integer, universal real, rational
                 arithmetic",
}

@InCollection{Gautschi:1984:QNC,
  author =       "Walter Gautschi",
  title =        "Questions of numerical condition related to
                 polynomials",
  crossref =     "Golub:1984:SNA",
  volume =       "24",
  pages =        "140--177",
  year =         "1984",
  MRclass =      "65F35 (65H05)",
  MRnumber =     "925213",
  bibdate =      "Fri Feb 9 15:28:14 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@PhdThesis{Gleditsch:1984:FTR,
  author =       "Torstein Gleditsch",
  title =        "Forslag til rask prosessor for flerformat
                 floating-point aritmetikk. ({Norwegian}) [{Proposal}
                 for a fast processor for multiformat floating-point
                 arithmetic]",
  type =         "Hovedoppgave i informatikk (cand.scient)",
  school =       "Universitetet i Oslo",
  address =      "Oslo, Norway",
  year =         "1984",
  bibdate =      "Thu May 09 08:19:32 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "Norwegian",
}

@Article{Goldberg:1984:LVS,
  author =       "Morton Goldberg",
  title =        "{LISP} Version of the {Savage} Floating Point
                 Benchmark in {16BST}",
  journal =      j-DDJ,
  volume =       "9",
  number =       "6",
  pages =        "82--??",
  month =        jun,
  year =         "1984",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@Book{Gregory:1984:MAE,
  author =       "Robert Todd Gregory and E. V. Krishnamurthy",
  title =        "Methods and Applications of Error-Free Computation",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xii + 194",
  year =         "1984",
  ISBN =         "0-387-90967-2",
  ISBN-13 =      "978-0-387-90967-7",
  LCCN =         "QA297.5 .G735 1984",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Texts and monographs in computer science",
  acknowledgement = ack-nhfb,
  keywords =     "Approximation theory --- Data processing.;
                 Floating-point arithmetic.",
  shorttableofcontents = "Glossary of Notation / xi \\
                 I: Residue or Modular Arithmetic / 1 \\
                 II: Finite-Segment p-adic Arithmetic / 63 \\
                 III: Exact Computation of Generalized Inverses / 109
                 IV: Integer Solutions to Linear Equations / 134 \\
                 V: Iterative Matrix Inversion and the Iterative
                 Solution of Linear Equations / 162 \\
                 VI: The Exact Computation of the Characteristic
                 Bibliography / 186 \\
                 Index / 191",
  tableofcontents = "Glossary of Notation / xi \\
                 I: Residue or Modular Arithmetic / 1 \\
                 1. Introduction / 1 \\
                 2. Single-Modulus Residue Arithmetic / 3 \\
                 3. Multiple-Modulus Residue Arithmetic / 11 \\
                 4. Mapping Standard Residue Representations onto
                 Integers / 17 \\
                 5. Single-Modulus Residue Arithmetic with Rational
                 Numbers / 23 \\
                 6. The Forward Mapping and the Inverse Mapping / 31 \\
                 7. Multiple-Modulus Residue Arithmetic with Rational
                 Numbers / 49 \\
                 II: Finite-Segment p-adic Arithmetic / 63 \\
                 1. Introduction / 63 \\
                 2. The Field of p-adic Numbers / 63 \\
                 3. Arithmetic in QP / 73 \\
                 4. A Finite-Segment p-adic Number System / 79 \\
                 5. Arithmetic Operations on Hensel Codes / 90 \\
                 6. Removing a Leading Zero from a Hensel Code / 99 \\
                 7. Mapping a Hensel Code onto a Unique Order-N Farey
                 Fraction / 100 \\
                 III: Exact Computation of Generalized Inverses / 109
                 \\
                 1. Introduction / 109 \\
                 2. Properties of g-inverses / 110 \\
                 3. Applications of g-inverses / 116 \\
                 4. Exact Computation of A+ if A Is a Rational Matrix /
                 118 \\
                 5. Failures of Residue Arithmetic and Precautionary
                 Measures / 131 \\
                 IV: Integer Solutions to Linear Equations / 134 \\
                 1. Introduction / 134 \\
                 2. Theoretical Background / 135 \\
                 3. The Matrix Formulation of Chemical Equations / 138
                 \\
                 4. Solving the Homogeneous System / 140 \\
                 5. Solving a Non-Homogeneous System / 148 \\
                 6. Solving Interval Linear Programming Problems / 150
                 \\
                 7. The Solution of Systems of Mixed-Integer Linear
                 Equations / 155 \\
                 V: Iterative Matrix Inversion and the Iterative
                 Solution of Linear Equations / 162 \\
                 1. Introduction / 162 \\
                 2. The Newton--Schultz Method for the Matrix Inverse /
                 163 \\
                 3. Iterative Solution of a Linear System / 169 \\
                 4. Iterative Computation of g-inverses / 174 \\
                 VI: The Exact Computation of the Characteristic
                 Polynomial of a Matrix / 180 \\
                 1. Introduction / 180 \\
                 2. The Algorithm Applied to Lower Hessenberg Matrices /
                 181 \\
                 Bibliography / 186 \\
                 Index / 191",
}

@Article{Guest:1984:RNS,
  author =       "C. C. Guest and M. M. Mirsalehi and T. K. Gaylord",
  title =        "Residue Number System Truth-Table Look-Up Processing
                 --- Moduli Selection and Logical Minimization",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-33",
  number =       "10",
  pages =        "927--931",
  month =        oct,
  year =         "1984",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1984.1676355",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 09:22:55 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35232;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676355",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Truth table look-up processing using binary coded
                 residue numbers is investigated for full-precision
                 addition and multiplication for implementations using
                 either electronic or optical technologies. The
                 logically minimized numbers of input \ldots{}",
}

@Book{Hamacher:1984:CO,
  author =       "V. Carl Hamacher and Zvonko G. Vranesic and Safwat G.
                 Zaky",
  title =        "Computer organization",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  edition =      "Second",
  pages =        "xvi + 590",
  year =         "1984",
  ISBN =         "0-07-025683-7",
  ISBN-13 =      "978-0-07-025683-5",
  LCCN =         "QA76.9.A73 H351 1984",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$34.95",
  series =       "McGraw-Hill series in computer organization and
                 architecture",
  acknowledgement = ack-nhfb,
  catcode =      "C; B",
  content =      "The reviewer recommends this book to those who are
                 interested in learning the basics of computer
                 organization, particularly at the hardware and device
                 level. This book does not deal with the concepts
                 related to computer organization from an abstract,
                 mathematical level. It also does not attempt to
                 describe the computer organization using a high-level
                 language. Instead, the authors concentrate on
                 uniprocessing systems, with a large number of examples
                 drawn from VAX-11, IBM 370, and HP 3000. The book does
                 not cover multiprocessors.\par

                 The organization of the book is summarized here.
                 Chapter 1 introduces a number of terms. Chapters 2 and
                 3 concentrate in detail (a total of 101 pages) on the
                 addressing methods and instruction sets, with examples
                 taken primarily from the above mentioned machines.
                 Chapters 4 and 5 (a total of 50 pages) deal with the
                 control unit for the instruction fetch and execute,
                 with Chapter 5 being devoted to microprogrammed control
                 and bit slice designs. In Chapter 6 (a total of 64
                 pages) the authors cover Input/Output organization,
                 which includes a good deal about the
                 synchronous/asynchronous I/O operations, I/O
                 interfaces, etc. Chapter 7 presents the usual material
                 on the fixed- and floating-point arithmetic. \ldots{}",
  CRnumber =     "8509-0786",
  descriptor =   "Computer Systems Organization, GENERAL; Hardware,
                 GENERAL",
  genterm =      "DESIGN",
  reviewer =     "A. Deb",
  subject =      "C. Computer Systems Organization; C.0 GENERAL; B.
                 Hardware; B.0 GENERAL",
  tableofcontents = "Basic structure of computers \\
                 Addressing methods and machine program sequencing \\
                 Instruction sets \\
                 The processing Unit \\
                 Microprogrammed control \\
                 Input--output organization- \\
                 Arithmetic \\
                 The main memory \\
                 Computer peripherals and work stations \\
                 Software \\
                 Microprocessors \\
                 Computer communications",
}

@Article{Honma:1984:IAE,
  author =       "Hitoshi Honma and Masahiko Sagawa",
  title =        "Improving the accuracy and error analysis in
                 floating-point {FFT} computation",
  journal =      j-ELECTRON-COMMUN-JPN,
  volume =       "67",
  number =       "11",
  pages =        "9--18",
  year =         "1984",
  CODEN =        "ECOJAL",
  ISSN =         "0424-8368",
  MRclass =      "65T05 (65G05 94A11)",
  MRnumber =     "86g:65238",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics and communications in Japan",
}

@TechReport{IBM:1984:ISR,
  author =       "{IBM Corporation}",
  title =        "{IBM System\slash 370 RPQ}. High Accuracy Arithmetic",
  type =         "Technical report",
  number =       "SA22-7093-0",
  institution =  pub-IBM,
  address =      pub-IBM:adr,
  month =        jan,
  year =         "1984",
  bibdate =      "Wed Oct 04 09:39:49 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://bitsavers.trailing-edge.com/pdf/ibm/370/princOps/SA22-7093-0_High_Accuracy_Arithmetic_Jan84.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point dot product; accurate
                 floating-point summation; ACRITH",
  remark =       "According to IBM Web pages, ACRITH was withdrawn in
                 1991, and replaced by ACRITH XSC; however, I have yet
                 to be able to find online documentation for that
                 system.",
  tableofcontents = "HIGH-ACCURACY-ARITHMETIC FACILITY / 1 \\
                 Floating-Point Instructions With Rounding Options / 1
                 \\
                 Normalization / 2 \\
                 Rounding / 2 \\
                 Rounding Modes / 2 \\
                 Guard Digit, Rounding Digit, and Sticky Bit / 3 \\
                 Arithmetic Exceptions / 4 \\
                 Default Result for Exponent Underflow / 5 \\
                 Floating-Point Accumulator / 5 \\
                 Vectors / 5 \\
                 Accumulator Layout / 6 \\
                 Accumulator Status Area / 8 \\
                 Accumulator Overflow / 9 \\
                 Storage-Operand Consistency / 9 \\
                 Instructions / 10 \\
                 ADD ACCUMULATOR TO ACCUMULATOR / 11 \\
                 ADD TO ACCUMULATOR / 12 \\
                 ADD WITH ROUNDING / 12 \\
                 CLEAR ACCUMULATOR / 13 \\
                 DIVIDE WITH ROUNDING / 13 \\
                 LOAD WITH ROUNDING / 14 \\
                 MULTIPLY AND ACCUMULATE / 15 \\
                 MULTIPLY WITH ROUNDING / 17 \\
                 ROUND FROM ACCUMULATOR / 17 \\
                 SUBTRACT ACCUMULATOR FROM ACCUMULATOR / 18 \\
                 SUBTRACT FROM ACCUMULATOR / 18 \\
                 SUBTRACT WITH ROUNDING / 19 \\
                 INDEX / 21",
}

@Book{ISO:1984:IID,
  author =       "{International Organization for Standardization}",
  key =          "ISO",
  title =        "{ISO\slash IEC DIS 10858}: {Information} technology
                 --- {Radix-independent} floating-point arithmetic",
  publisher =    pub-ISO,
  address =      pub-ISO:adr,
  pages =        "????",
  year =         "1984",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Fri May 28 21:52:25 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.iso.ch/cate/d18890.html",
  acknowledgement = ack-nhfb,
}

@Article{Jones:1984:SRM,
  author =       "Christopher B. Jones",
  title =        "A Significance Rule for Multiple-Precision
                 Arithmetic",
  journal =      j-TOMS,
  volume =       "10",
  number =       "1",
  pages =        "97--107",
  month =        mar,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356068.356076",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65G05 (65G10)",
  MRnumber =     "86e:65063",
  bibdate =      "Sun Sep 04 20:02:26 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Multiple-precision arithmetic overcomes the round-off
                 error incurred in conventional floating-point
                 arithmetic, at the cost of increased processing
                 overhead. Significance arithmetic takes into account
                 the inexactness of the operands of a calculation, but
                 can lead to loss of significant digits after a long
                 series of operations. A new technique is described
                 which alleviates the overhead of multiple-precision
                 arithmetic by allowing nonsignificant digits to be
                 discarded, while limiting the significance loss per
                 operation to a controllable and acceptable rate. The
                 technique is based on storing an inexact number
                 interval, using a criterion of significance to
                 determine the precision with which the limits of
                 interval should be stored. A procedure referred to as a
                 significance rule uses this criterion to remove some of
                 the nonsignificant digits from the limits of an
                 interval prior to storage. A certain number of
                 nonsignificant digits are retained as guard digits.
                 Calculations are performed using exact interval
                 arithmetic and the significance-rule procedure is
                 invoked after each operation to remove superfluous
                 digits. Round-off in the procedure causes a slight
                 increase in the interval width on each operation. This
                 results in a cumulative loss of significance at a rate
                 related to the number of guard digits.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Karp:1984:ELS,
  author =       "A. H. Karp",
  title =        "Exponential and Logarithm by Sequential Squaring",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-33",
  number =       "5",
  pages =        "462--464",
  month =        may,
  year =         "1984",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1984.1676464",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:16:09 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Book{Katzan:1984:IA,
  author =       "Harry Katzan",
  title =        "Invitation to {Ada}",
  publisher =    "PBI",
  address =      "New York, NY, USA",
  pages =        "x + 173",
  year =         "1984",
  ISBN =         "0-89433-239-2 (paperback)",
  ISBN-13 =      "978-0-89433-239-5 (paperback)",
  LCCN =         "QA76.73.A35 K36 1984",
  bibdate =      "Wed Oct 13 06:37:40 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "US\$14.95",
  series =       "Petrocelli invitation to series",
  acknowledgement = ack-nhfb,
  remark =       "See \cite[p. 1.10]{Coonen:1984:CPS} for negative
                 comments about the floating-point model for Ada in the
                 predecessor of this book \cite{Katzan:1982:IAA}.",
  subject =      "Ada (Computer program language)",
}

@Article{Kawabata:1984:SFP,
  author =       "Hugh M. Kawabata",
  title =        "{Savage} Floating Point Benchmark in {Fortran} in
                 {16BST}",
  journal =      j-DDJ,
  volume =       "9",
  number =       "1",
  pages =        "83--??",
  month =        jan,
  year =         "1984",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@Book{Koopman:1984:FFP,
  author =       "Philip J. Koopman",
  title =        "{FORTH} floating point",
  publisher =    "Mountain View Pr.",
  address =      "Mountain View, CA, USA",
  edition =      "Second",
  pages =        "346",
  year =         "1984",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "MVP-FORTH series; v. 3",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers --- Programming.;
                 Floating-point arithmetic.; FORTH (Computer program
                 language)",
}

@Article{Korn:1984:ISD,
  author =       "G. A. Korn",
  title =        "Interactive simulation with a direct-executing,
                 floating-point equation language",
  journal =      j-SYS-ANA-MODEL-SIM,
  volume =       "1",
  number =       "1",
  pages =        "45--54",
  year =         "1984",
  CODEN =        "SAMSEC",
  ISSN =         "0232-9298",
  ISSN-L =       "0232-9298",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "The University of Arizona, Tucson",
  bibno =        "43792",
  catcode =      "I.6.2; I.6.3",
  CRclass =      "I.6.2 Simulation Languages; I.6.3 Applications",
  descriptor =   "Computing Methodologies, SIMULATION AND MODELING,
                 Simulation Languages; Computing Methodologies,
                 SIMULATION AND MODELING, Applications",
  fjournal =     "Systems analysis, modelling, simulation",
  genterm =      "THEORY; DESIGN; LANGUAGES",
  guideno =      "1988-14427",
  journalabbrev = "Syst. Anal. Model. Simul.",
  subject =      "I. Computing Methodologies; I.6 SIMULATION AND
                 MODELING; I. Computing Methodologies; I.6 SIMULATION
                 AND MODELING",
}

@Article{Kornerup:1984:CFP,
  author =       "Peter Kornerup and David W. Matula",
  title =        "Correction to `{`Finite Precision Rational Arithmetic:
                 An Arithmetic Unit''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-33",
  number =       "7",
  pages =        "682--682",
  month =        jul,
  year =         "1984",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1984.5009346",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 09:22:53 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009346",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Lin:1984:DSD,
  author =       "Ming-Liang Lin and Ernst Leiss and Bayliss McInnis",
  title =        "Division and sign detection algorithms for residue
                 number systems",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "10",
  number =       "4--5",
  pages =        "331--342",
  month =        "????",
  year =         "1984",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 19:00:50 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122184900610",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@InProceedings{Ling:1984:NAS,
  author =       "Fuyun Ling and J. Proakis",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing: {ICASSP '84}",
  title =        "Numerical accuracy and stability: Two problems of
                 adaptive estimation algorithms caused by round-off
                 error",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "571--574",
  year =         "1984",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper investigates the numerical accuracy and the
                 numerical stability of adaptive estimation algorithms.
                 A feedback system model is provided to investigate the
                 numerical stability of the algorithms. Simulation
                 results on the comparison of \ldots{}",
}

@Article{Longo:1984:CFU,
  author =       "S. A. Longo",
  title =        "Calculating Functions using {Ada}",
  journal =      j-J-PAS-ADA,
  volume =       "3",
  number =       "4",
  pages =        "34--36",
  month =        jul # "--" # aug,
  year =         "1984",
  ISSN =         "0735-1232",
  bibdate =      "Fri Dec 08 13:05:34 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Journal of Pascal and Ada",
}

@InProceedings{Look:1984:CSH,
  author =       "H. W. Look",
  title =        "Compatible software and hardware implementations
                 permitted by {IEEE} standards for binary floating-point
                 arithmetic",
  crossref =     "NCC:1984:ACP",
  pages =        "101--105",
  year =         "1984",
  bibdate =      "Wed Sep 7 22:31:45 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Lorenz:1984:MIL,
  author =       "E. Lorenz and R. Sandau",
  title =        "{M{\"o}glichkeiten der Implementierung
                 leistungsf{\"a}higer Multiplikationsprogramme in
                 Mikrorechnersystemen} \toenglish {Possibilities of the
                 Implementation of Efficient Multiplication Instructions
                 in Microcomputer Systems} \endtoenglish",
  journal =      j-NACH-ELEK,
  volume =       "34",
  number =       "8",
  pages =        "288--290",
  month =        "????",
  year =         "1984",
  CODEN =        "NTELAP",
  ISSN =         "0323-4657",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Nachrichtentechnik Elektronik",
}

@TechReport{Mackin:1984:FFG,
  author =       "Michael A. Mackin and James F. Soeder",
  title =        "Floating-point function generation routines for 16-bit
                 microcomputers",
  institution =  "National Aeronautics and Space Administration",
  address =      "Washington DC, USA",
  pages =        "????",
  year =         "1984",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "NASA technical memorandum; 83783",
  acknowledgement = ack-nhfb,
  govtdocnumber = "NAS 1.15:83783 830-D (MF)",
  keywords =     "Microcomputers --- Programming.",
  remark =       "Distributed to depository libraries in microfiche.
                 Microfiche. [Washington, D.C.?: National Aeronautics
                 and Space Administration], 1984. 1 microfiche.",
}

@Article{Mactaggart:1984:SCR,
  author =       "I. Ross Mactaggart and Mervyn A. Jack",
  title =        "A single chip radix-$2$ {FFT} butterfly architecture
                 using parallel data distributed arithmetic",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "SC-19",
  number =       "3",
  pages =        "368--373",
  month =        jun,
  year =         "1984",
  CODEN =        "IJSCBC",
  DOI =          "https://doi.org/10.1109/JSSC.1984.1052151",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Thu Jul 07 10:57:50 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
}

@Article{Mansfield:1984:CAC,
  author =       "Richard Mansfield",
  title =        "A Complete Axiomatization of Computer Arithmetic",
  journal =      j-MATH-COMPUT,
  volume =       "42",
  number =       "166",
  pages =        "623--635",
  month =        apr,
  year =         "1984",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65G99 (03B70 03C70 68Q40)",
  MRnumber =     "85k:65040",
  MRreviewer =   "R. P. Brent",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "C5230 (Digital arithmetic methods)",
  corpsource =   "Department of Math., Pennsylvania State University,
                 University Park, PA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "axiom system; complete axiomatization; computer
                 arithmetic; digital arithmetic; multiplication; rounded
                 addition; rounded arithmetic",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Miller:1984:ILA,
  author =       "D. Miller and J. Polky",
  title =        "An implementation of the {LMS} algorithm in the
                 residue number system",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "31",
  number =       "5",
  pages =        "452--461",
  month =        may,
  year =         "1984",
  CODEN =        "ICSYBT",
  DOI =          "https://doi.org/10.1109/TC.1984.1676355",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23556",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The Residue Arithmetic Adaptive Filter (RAAF)
                 processor performs the least mean square (LMS)
                 algorithm using 60 ns discrete PROM-latch combinations
                 for the residue operations. Parallel and pipeline
                 techniques are used throughout. Since the LMS
                 \ldots{}",
}

@Article{Moran:1984:SST,
  author =       "Thomas W. Moran",
  title =        "Some Spreadsheet Tests of the {Savage} Floating-Point
                 Benchmark in {16BST}",
  journal =      j-DDJ,
  volume =       "9",
  number =       "8",
  pages =        "106--??",
  month =        aug,
  year =         "1984",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@InCollection{Munzel:1984:RAE,
  author =       "Georg M{\"u}nzel",
  booktitle =    "Parallel computing 83 (Berlin, 1983)",
  title =        "Residue arithmetic for exact calculations on the
                 {DAP}",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "199--204",
  year =         "1984",
  MRclass =      "65W05",
  MRnumber =     "MR809397 (86k:65141)",
  bibdate =      "Thu Nov 8 14:50:29 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Murray:1984:SFA,
  author =       "J. T. Murray",
  title =        "Sin\slash Cos Functions via Approximations Plus Error
                 Compensation",
  journal =      j-IBM-TDB,
  volume =       "26",
  number =       "10A",
  pages =        "4967--4968",
  month =        mar,
  year =         "1984",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Sep 1 10:15:56 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Technical Disclosure Bulletin",
}

@PhdThesis{Naseem:1984:IPC,
  author =       "Asif Naseem",
  title =        "Implementation of Parallel Computational Algorithms on
                 a Modified {CORDIC} Arithmetic Logic Unit",
  type =         "{Ph.D.} thesis",
  school =       "Michigan State University",
  address =      "East Lansing, MI, USA",
  pages =        "137",
  year =         "1984",
  ISBN-13 =      "979-84-13-17501-9",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://login.ezproxy.lib.utah.edu/login?url=https://www.proquest.com/dissertations-theses/implementation-parallel-computational-algorithms/docview/303294026/se-2",
  acknowledgement = ack-nhfb,
  keywords =     "0544:Electrical engineering; Applied sciences;
                 Electrical engineering",
  ris-m1 =       "8503253",
}

@Misc{OliverWhiteheadQuintet:1984:FN,
  author =       "Oliver Whitehead Quintet",
  title =        "Free for now",
  publisher =    "Justin Time Records",
  address =      "????",
  year =         "1984",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "1 sound disc",
  acknowledgement = ack-nhfb,
  keywords =     "Jazz --- 1981-1990.",
  remark =       "Brief record. Free for now --- Six-string waltz ---
                 Old friend --- Invention; Excuses, excuses --- Getting
                 away --- Woman in blue --- Floating point --- Crazy
                 season --- Do it with your socks on. Performed by the
                 Oliver Whitehead Quintet. JUST 4; Justin Time Records",
}

@Misc{Palmer:1984:FBU,
  author =       "John Palmer and Bruce Ravenel and Rafi Nave",
  title =        "Fraction Bus for Use in a Numeric Data Processor",
  howpublished = "US Patent 4,484,259.",
  day =          "10",
  month =        nov,
  year =         "1984",
  bibdate =      "Sat Aug 23 06:36:20 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Filed 22 January, 1982. This patent discusses the
                 67-bit data path in the 8087, supporting both the use
                 of three extra bits --- Guard, Round, and Sticky --- in
                 computing 64-bit results and the use of full 67-bit
                 chopped arithmetic in the computation of the
                 transcendental functions.",
  URL =          "https://ieeemilestones.ethw.org/w/images/3/3d/Patent_8087_fraction_bus.pdf",
  abstract =     "A floating point, integrated, arithmetic circuit is
                 organized around a file format having a floating point
                 numeric domain exceeding that of any single or double
                 precision floating point numbers, long or short integer
                 words of BCD data upon which it must operate. As a
                 result the circuit has a greater reliability, range and
                 precision than ever previously achieved without
                 entailing additional circuit complexity. Reliability is
                 further enhanced by a systematic three bit rounding
                 field, and by including means for detecting every error
                 or exception condition with an optional expected
                 response provided thereto by hardware. As a result of
                 such organization, an unexpected increase of capacity
                 is achieved wherein transcendental functions can be
                 computed to tally in hardware, and whereby mixed mode
                 arithmetic can be implemented without difficulty. The
                 numeric processor also includes a programmable shifter
                 capable of arbitrary numbers of bit and byte shifts in
                 a single clock cycle, as well as an arithmetic unit
                 capable of implementing multiplication, division,
                 modulo reduction and square roots directly in
                 hardware.",
  acknowledgement = ack-nhfb,
}

@Book{Palmer:1984:P,
  author =       "John F. Palmer and Stephen P. Morse",
  title =        "The 8087 Primer",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "viii + 182",
  year =         "1984",
  ISBN =         "0-471-87569-4",
  ISBN-13 =      "978-0-471-87569-7",
  LCCN =         "QA76.8.I2923 P34 1984",
  bibdate =      "Wed Dec 15 10:40:38 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Excellent coverage of the 8087 numeric coprocessor by
                 the chief architects of the Intel 8087 (Palmer) and
                 8086 (Morse). Contains many candid statements about
                 design decisions in these processors. A must for
                 serious assembly language coding of the 8087 and 80287
                 chips. See also \cite{Intel:1985:PRM}.",
  URL =          "https://ieeemilestones.ethw.org/w/images/d/d2/Palmer_Morse_Elementary_Functions_Chapter.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Parker:1984:CCS,
  author =       "J. R. Parker",
  title =        "On Converting Character Strings to Integers",
  journal =      j-INFO-PROC-LETT,
  volume =       "19",
  number =       "1",
  pages =        "17--19",
  day =          "26",
  month =        jul,
  year =         "1984",
  CODEN =        "IFPLAT",
  DOI =          "https://doi.org/10.1016/0020-0190(84)90122-4",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Wed Nov 11 12:16:26 MST 1998",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/infoproc1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0020019084901224",
  acknowledgement = ack-nhfb,
  classification = "723; C4240 (Programming and algorithm theory)",
  corpsource =   "Department of Computer Sci., University of Calgary,
                 Calgary, Alta., Canada",
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  journalabr =   "Inf Process Lett",
  keywords =     "character strings; character to integer conversion;
                 computer programming; integer overflow; programming
                 theory",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Pei:1984:CAD,
  author =       "Soo-Chang Pei and Kuo-Chih Ho",
  title =        "Comments on {``Adaptive digital control implemented
                 using residue number systems''}",
  journal =      j-IEEE-TRANS-AUTOMAT-CONTR,
  volume =       "29",
  number =       "9",
  pages =        "863--863",
  month =        sep,
  year =         "1984",
  CODEN =        "IETAA9",
  DOI =          "https://doi.org/10.1109/TC.1984.1676355",
  ISSN =         "0018-9286 (print), 1558-2523 (electronic)",
  ISSN-L =       "0018-9286",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Tan:1982:ADC}.",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=24217",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Automatic Control",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The aim of this correspondence is to correct some
                 errors and modify Tan and McInnis residue number
                 decoding scheme into a simplified \ldots{}",
}

@Article{Pfenninger:1984:DES,
  author =       "E. Pfenninger",
  title =        "{Divisionsalgorithmus -- einfach und schnell}
                 \toenglish {Division Algorithms -- Simple and Fast}
                 \endtoenglish",
  journal =      j-ELEKTRONIKER,
  volume =       "15",
  pages =        "62--64",
  year =         "1984",
  CODEN =        "ELKRBL",
  ISSN =         "0531-9218",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektroniker (Switzerland)",
}

@Article{Pountain:1984:PM,
  author =       "D. Pountain",
  title =        "{PROLOG} on Microcomputers",
  journal =      j-BYTE,
  volume =       "9",
  number =       "13",
  pages =        "355--62",
  month =        dec,
  year =         "1984",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  LCCN =         "QA 76.5 B98",
  bibdate =      "Thu Nov 8 14:50:29 2007",
  bibsource =    "/usr/local/src/bib/bibliography/Ai/log.prog.85.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Discusses micro-PROLOG, a dialect of PROLOG originally
                 written for the z80 microprocessor, which was the first
                 microcomputer implementation of the language. The
                 micro-PROLOG language is an interpreted language. A
                 program consists of a database of facts and rules that
                 you can query to solve problems. Logical propositions
                 replace computer-oriented instructions. Micro-PROLOG
                 has floating point arithmetic.",
  acknowledgement = ack-nhfb,
  fjournal =     "BYTE Magazine",
  keywords =     "PROLOG",
}

@Article{Prince:1984:SFP,
  author =       "Thomas Prince",
  title =        "{Savage} Floating Point Benchmark in Logo in {16BST}",
  journal =      j-DDJ,
  volume =       "9",
  number =       "6",
  pages =        "82--??",
  month =        jun,
  year =         "1984",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@InProceedings{Rauchwerk:1984:MBF,
  author =       "M. D. Rauchwerk",
  title =        "A micro\-pro\-cess\-or-based fast floating point
                 library",
  crossref =     "IEEE:1984:CPI",
  pages =        "488--490",
  year =         "1984",
  bibdate =      "Thu Sep 01 12:03:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Regener:1984:MID,
  author =       "Eric Regener",
  title =        "Multiprecision Integer Division Examples Using
                 Arbitrary Radix",
  journal =      j-TOMS,
  volume =       "10",
  number =       "3",
  pages =        "325--328",
  month =        sep,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1271.2738",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65V05",
  MRnumber =     "86g:65241",
  bibdate =      "Sun Sep 04 20:18:56 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/hansen-per-brinch.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{BrinchHansen:1994:MLD}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@InCollection{Schryer:1984:DCF,
  author =       "N. L. Schryer",
  title =        "Determination of Correct Floating-Point Model
                 Parameters",
  crossref =     "Cowell:1984:SDM",
  pages =        "360--366",
  year =         "1984",
  bibdate =      "Thu Sep 08 17:23:39 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Shahan:1984:MIF,
  author =       "V. Shahan",
  title =        "The {MC68881}: The {IEEE} Floating Point Standard
                 Reduced to One {VLSI} Chip",
  crossref =     "IEEE:1984:ILD",
  pages =        "172--176",
  year =         "1984",
  bibdate =      "Wed Sep 7 22:31:44 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Shen:1984:DET,
  author =       "J. P. Shen and F. J. Ferguson",
  title =        "The Design of Easily Testable {VLSI} Array
                 Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-33",
  number =       "6",
  pages =        "554--560",
  month =        jun,
  year =         "1984",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1984.1676480",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 09:22:52 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676480",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Shively:1984:CTG,
  author =       "R. R. Shively and W. V. Robinson and D. E. Orton",
  title =        "Cascading Transmission Gates to Enhance Multiplier
                 Performance",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-33",
  number =       "7",
  pages =        "677--679",
  month =        jul,
  year =         "1984",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1984.5009343",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 09:22:53 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009343",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Sips:1984:BSA,
  author =       "Henk J. Sips",
  title =        "Bit-Sequential Arithmetic for Parallel Processors",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-33",
  number =       "1",
  pages =        "7--20",
  month =        jan,
  year =         "1984",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1984.5009311",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 09:22:49 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009311",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Smoktunowicz:1984:BCI,
  author =       "Alicja Smoktunowicz and Jolanta Sokolnicka",
  title =        "Binary cascades iterative refinement in
                 doubled-mantissa arithmetics",
  journal =      j-BIT,
  volume =       "24",
  number =       "1",
  pages =        "123--127",
  month =        mar,
  year =         "1984",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01934524",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65F05 (65G05)",
  MRnumber =     "85i:65039",
  MRreviewer =   "A. Bultheel",
  bibdate =      "Wed Jan 4 18:52:18 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=24&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=24&issue=1&spage=123",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@InProceedings{Soderstrand:1984:AQL,
  author =       "M. Soderstrand and G. Poe",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing, {ICASSP '84}",
  title =        "Application of quadratic-like complex residue number
                 system arithmetic to ultrasonics",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "484--487",
  year =         "1984",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The concept of a ``Quadratic-Like'' Complex Residue
                 Number System is introduced in which certain purely
                 imaginary numbers exist as reals within the system. It
                 is shown that the desirable properties of a Quadratic
                 Complex Residue Number System with \ldots{}",
}

@Article{Soderstrand:1984:PRR,
  author =       "M. Soderstrand and B. Sinha",
  title =        "A pipelined recursive residue number system digital
                 filter",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "31",
  number =       "4",
  pages =        "415--417",
  month =        apr,
  year =         "1984",
  CODEN =        "ICSYBT",
  DOI =          "https://doi.org/10.1109/TC.1983.1676240",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Nov 9 11:38:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23555",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The well-known advantages of pipelining as applied to
                 Finite Impulse Response (FIR) Residue Number System
                 (RNS) arithmetic digital filters is extended to the
                 important area of Infinite Impulse Response (IIR)
                 digital filters through a new technique \ldots{}",
}

@Book{Steele:1984:CLL,
  author =       "Guy L. Steele",
  title =        "{COMMON LISP}: the language",
  publisher =    pub-DP,
  address =      pub-DP:adr,
  pages =        "xii + 465",
  year =         "1984",
  ISBN =         "0-932376-41-X (paperback)",
  ISBN-13 =      "978-0-932376-41-1 (paperback)",
  LCCN =         "QA76.73.L23S73 1984",
  bibdate =      "Wed Jan 29 17:05:18 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "With contributions by Scott E. Fahlman and Richard P.
                 Gabriel and David A. Moon and Daniel L. Weinreb.",
  acknowledgement = ack-nhfb,
  keywords =     "COMMON LISP (Computer program language)",
  remark =       "From \cite{Steele:2004:RHP}: ``In general,
                 computations with floating-point numbers are only
                 approximate.''",
}

@InProceedings{Stetter:1984:SDC,
  author =       "Hans J. Stetter",
  title =        "Sequential defect correction for high-accuracy
                 floating-point algorithms",
  crossref =     "Griffiths:1984:NAP",
  pages =        "186--202",
  year =         "1984",
  DOI =          "https://doi.org/10.1007/BFb0099525",
  MRclass =      "65V05 (65B05 65G05)",
  MRnumber =     "86j:65188",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Stewart:1984:PWG,
  author =       "R. G. Stewart",
  title =        "{P854} Working Group Completes Radix-Independent
                 Floating-Point Draft",
  journal =      j-IEEE-MICRO,
  volume =       "4",
  number =       "1",
  pages =        "82--83",
  month =        jan # "\slash " # feb,
  year =         "1984",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.1984.291326",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Dec 14 06:08:58 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeemicro.bib;
                 Science Citation Index database (1980--2000)",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}

@Article{Takla:1984:MBF,
  author =       "N. Takla and M. Hecker",
  title =        "A Monolithic 64 Bit Floating-Point Coprocessor",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "SC-19",
  number =       "4",
  pages =        "538--539",
  month =        aug,
  year =         "1984",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "A double/single-precision floating-point processor
                 using a titanium disilicide 3.5-$\mu$m NMOS process
                 achieves double-precision add/subtract, multiply, and
                 divide in 2, 8, and 16 $\mu$s respectively. The chip
                 has about 35K devices and is about \ldots{}",
}

@Article{Taylor:1984:BFP,
  author =       "F. Taylor",
  title =        "Block floating-point distributed filters",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "31",
  number =       "3",
  pages =        "300--304",
  month =        mar,
  year =         "1984",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "Distributed filters have been shown to offer an
                 impressive complexity-throughput tradeoff. In this
                 correspondence, a precision improvement is made in
                 distributed filtering using block floating-point
                 arithmetic. Performance improvement is predicted
                 \ldots{}",
}

@Article{Taylor:1984:RAT,
  author =       "Fred J. Taylor",
  title =        "Residue Arithmetic: a Tutorial with Examples",
  journal =      j-COMPUTER,
  volume =       "17",
  number =       "5",
  pages =        "50--62",
  month =        may,
  year =         "1984",
  CODEN =        "CPTRB4",
  DOI =          "https://doi.org/10.1109/MC.1984.1659138",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Thu Nov 13 07:15:07 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computer1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
  keywords =     "Arithmetic; Cathode ray tubes; Digital arithmetic;
                 Digital systems; Gaussian processes; Parallel
                 processing; Real time systems; Tutorials",
}

@InProceedings{Teufel:1984:HAO,
  author =       "Thomas Teufel",
  title =        "A hardware architecture of an optimal
                 {BCD}-floating-point processor",
  crossref =     "Feilmeier:1984:PCP",
  pages =        "553--560",
  year =         "1984",
  MRclass =      "65G05",
  MRnumber =     "86j:65055",
  bibdate =      "Mon Apr 14 17:57:50 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@PhdThesis{Teufel:1984:OG,
  author =       "T. Teufel",
  title =        "{Ein optimaler Gleitkommaprozessor} \toenglish {An
                 Optimal Floating-Point Processor} \endtoenglish",
  type =         "Dissertation",
  school =       "Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "??",
  year =         "1984",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Tricker:1984:ERM,
  author =       "A. R. Tricker",
  title =        "Effects of Rounding on the Moments of a Probability
                 Distribution",
  journal =      j-J-R-STAT-SOC-SER-D-STATISTICIAN,
  volume =       "33",
  number =       "4",
  pages =        "381--390",
  month =        dec,
  year =         "1984",
  CODEN =        "????",
  DOI =          "https://doi.org/10.2307/2987741",
  ISSN =         "0039-0526 (print), 1467-9884 (electronic)",
  ISSN-L =       "0039-0526",
  bibdate =      "Thu Jan 22 18:10:22 MST 2015",
  bibsource =    "http://www.jstor.org/stable/i349978;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jrss-d-1980.bib",
  URL =          "http://www.jstor.org/stable/2987741",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Royal Statistical Society. Series D
                 (The Statistician)",
  journal-URL =  "http://www.jstor.org/journals/00390526.html",
}

@MastersThesis{Trivedi:1984:DVF,
  author =       "Mrugesh Popatlal Trivedi",
  title =        "Dianostics of {VLSI} floating-point processors",
  type =         "Thesis ({M.S.})",
  school =       "The University of Tennessee, Knoxville",
  address =      "Knoxville, TN, USA",
  pages =        "viii + 98",
  year =         "1984",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers --- Programming.;
                 Floating-point arithmetic.",
}

@MastersThesis{Truong:1984:FPP,
  author =       "Hung Si Truong",
  title =        "A floating point processor",
  type =         "Project ({M.S., Electrical and Electronic
                 Engineering})",
  school =       "California State University",
  address =      "Sacramento, CA, USA",
  pages =        "viii + 81",
  year =         "1984",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Charles Lytle, Chairperson",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.",
}

@Article{Uya:1984:CFP,
  author =       "M. Uya and K. Kaneko and J. Yasui",
  title =        "A {CMOS} floating point multiplier",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "19",
  number =       "5",
  pages =        "697--702",
  month =        oct,
  year =         "1984",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "A 32-bit CMOS floating-point multiplier is described.
                 The chip can perform 32-bit floating-point
                 multiplication (based on the proposed IEEE Standard
                 format) and 24-bit fixed-point multiplication (two's
                 complement format) in less than 78.7 and 71.1 ns
                 \ldots{}",
}

@Article{vonGudenberg:1984:BMG,
  author =       "J. Wolff von Gudenberg",
  title =        "{Berechnung maximal genauer Standardfunktionen mit
                 einfacher Mantissenl{\"a}nge} \toenglish {Computation
                 of Maximally Accurate Elementary Functions Using Simple
                 Mantissa Length} \endtoenglish",
  journal =      j-ELEK-RECHENANLAGEN,
  volume =       "26",
  number =       "5",
  pages =        "230--238",
  month =        oct,
  year =         "1984",
  CODEN =        "ELRAA4",
  ISSN =         "0013-5720",
  bibdate =      "Sat Feb 10 12:41:08 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektronische Rechenanlagen",
}

@InCollection{Ware:1984:CMC,
  author =       "F. Ware and W. McAllister",
  title =        "{C-MOS} chip set streamlines floating-point
                 processing",
  crossref =     "Evanczuk:1984:MSS",
  pages =        "374--377",
  year =         "1984",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.0; C.5; C.5",
  CRclass =      "G.1.0 General; G.1.0 Computer arithmetic; C.5.3
                 Microcomputers; C.5.4 VLSI Systems",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Computer arithmetic; Computer Systems Organization,
                 COMPUTER SYSTEM IMPLEMENTATION, Microcomputers;
                 Computer Systems Organization, COMPUTER SYSTEM
                 IMPLEMENTATION, VLSI Systems",
  genterm =      "DESIGN",
  guideno =      "00769",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 C. Computer Systems Organization; C.5 COMPUTER SYSTEM
                 IMPLEMENTATION; C. Computer Systems Organization; C.5
                 COMPUTER SYSTEM IMPLEMENTATION",
}

@MastersThesis{Wehmeyer:1984:EFF,
  author =       "Keith R. Wehmeyer",
  title =        "Effects of fixed and floating point mathematics on
                 digital filters",
  type =         "Thesis ({M.S.})",
  school =       "University of Cincinnati",
  address =      "Cincinnati, OH, USA",
  pages =        "vi + 92",
  year =         "1984",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "University of Cincinnati --- Theses. M.S. (Electrical
                 and Computer Engineering (1984))",
}

@Article{Wolrich:1984:HPF,
  author =       "G. Wolrich and E. McLellan and L. Harada and J.
                 Montanaro and R. A. J. Yodlowski",
  title =        "A High Performance Floating Point Coprocessor",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "SC-19",
  number =       "5",
  pages =        "690--696",
  month =        oct,
  year =         "1984",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "A 34000-transistor single-chip floating-point
                 coprocessor fabricated in 3-$\mu$m double metal NMOS
                 technology is described. The fraction data path,
                 including a shifter and 60-bit carry propagate ALU, is
                 cycled in 100 ns for all operations requiring
                 \ldots{}",
}

@InCollection{Woo:1984:AMC,
  author =       "B. Woo and L. Lin and R. E. Owen",
  title =        "{ALU}, multiplier chips zip through {IEEE}
                 floating-point operations",
  crossref =     "Evanczuk:1984:MSS",
  pages =        "354--359",
  year =         "1984",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  catcode =      "C.1.2; G.1.0",
  CRclass =      "C.1.2 Multiple Data Stream Architectures
                 (Multiprocessors); C.1.2 Pipeline processors; G.1.0
                 General; G.1.0 Computer arithmetic",
  descriptor =   "Computer Systems Organization, PROCESSOR
                 ARCHITECTURES, Multiple Data Stream Architectures
                 (Multiprocessors), Pipeline processors; Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Computer
                 arithmetic",
  genterm =      "DESIGN",
  guideno =      "00766",
  subject =      "C. Computer Systems Organization; C.1 PROCESSOR
                 ARCHITECTURES; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS",
}

@Book{Zuse:1984:CML,
  author =       "Konrad Zuse",
  title =        "{Der Computer, mein Lebenswerk}",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xv + 218",
  year =         "1984",
  ISBN =         "0-387-13814-5 (U.S.)",
  ISBN-13 =      "978-0-387-13814-5 (U.S.)",
  LCCN =         "TK7885.22.Z87 A33 1984",
  bibdate =      "Mon Nov 4 07:46:57 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Based on the author's autobiography with the same
                 title published in 1970.",
  acknowledgement = ack-nhfb,
  keywords =     "computer engineers --- Germany --- biography;
                 computers --- Germany --- history; Zuse, Konrad",
}

@Book{Ahmed:1985:AAU,
  author =       "H. M. Ahmed",
  title =        "Alternative arithmetic unit architectures for {VLSI}
                 digital signal processors",
  publisher =    "Prentice-Hall",
  address =      "Englewood Cliffs, NJ, USA",
  pages =        "",
  year =         "1985",
  DOI =          "",
  ISBN =         "",
  ISBN-13 =      "",
  LCCN =         "",
  bibdate =      "Wed Oct 29 10:25:39 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "",
  acknowledgement = ack-nhfb,
}

@Article{Aridgides:1985:EIQ,
  author =       "A. Aridgides and D. Morgan",
  title =        "Effects of input quantization in floating-point
                 digital pulse compression",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "33",
  number =       "2",
  pages =        "434--435",
  month =        apr,
  year =         "1985",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  summary =      "A computer simulation of an FFT-based digital LFM
                 pulse compressor using vector floating point arithmetic
                 is presented, showing the effects of retaining various
                 number of mantissa bits at the input quantizer. Plots
                 of the compressed pulse waveforms \ldots{}",
}

@TechReport{Armstrong:1985:PLHa,
  author =       "Robert Clyde Armstrong",
  title =        "Procedural layout of a high-speed floating-point
                 arithmetic unit",
  institution =  "Massachusetts Institute of Technology, Research
                 Laboratory of Electronics",
  address =      "Cambridge, MA, USA",
  pages =        "116",
  year =         "1985",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Technical report; no 508 Technical report
                 (Massachusetts Institute of Technology. Research
                 Laboratory of Electronics); no. 508.",
  acknowledgement = ack-nhfb,
  remark =       "Originally presented as author's thesis (Electrical
                 Engineer --- Massachusetts Institute of Technology)
                 1985. Bibliography: leaf 116. Supported in part by the
                 U.S. Air Force Office of Scientific Research contract",
}

@PhdThesis{Armstrong:1985:PLHb,
  author =       "Robert Clyde Armstrong",
  title =        "Procedural layout of a high-speed floating-point
                 arithmetic unit",
  type =         "Thesis ({Elect. E.})",
  school =       "Massachusetts Institute of Technology. Dept. of
                 Electrical Engineering and Computer Science",
  address =      "Cambridge, MA, USA",
  pages =        "116",
  year =         "1985",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Supervised by Jonathan Allen.",
  acknowledgement = ack-nhfb,
}

@Article{Aspinwall:1985:RVM,
  author =       "D. B. Aspinwall and Y. N. Patt",
  title =        "Retrofitting the {VAX-11\slash 780} Microarchitecture
                 for {IEEE} Floating Point Arithmetic --- Implementation
                 Issues, Measurements, and Analysis",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "8",
  pages =        "692--708",
  month =        aug,
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.1676615",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 08:33:17 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676615",
  abstract =     "The VAX-11/7801 was designed specifically to implement
                 the VAX architecture. As such, it does not support the
                 IEEE standard for floating point arithmetic. A project
                 was undertaken to provide this support by modifying the
                 11/780 microarchitecture. Our objective was to produce
                 a microengine that would efficiently execute the VAX
                 instruction set, modified to handle VAX floating point
                 instructions in accordance with the IEEE standard. Our
                 methodology was to make minimal changes to the 11/780
                 hardware, relying primarily on changes to the
                 microcode. This paper describes the modifications
                 required to implement the IEEE standard, examines the
                 various design alternatives available to us, presents
                 measurements of our implementation, and analyzes our
                 results. We also offer some comments on the matter of
                 retrofitting an existing architecture to a new
                 unintended use.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Auzinger:1985:AAR,
  author =       "W. Auzinger and H. J. Stetter",
  title =        "Accurate arithmetic results for decimal data on
                 non-decimal computers",
  journal =      "Computing (New York)",
  volume =       "35",
  number =       "2",
  pages =        "141--151",
  year =         "1985",
  CODEN =        "????",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.0",
  content =      "One potentially useful feature absent from the High
                 Accuracy Arithmetic Subroutine Library (ACRITH) is the
                 generation of tight and guaranteed bounds on the
                 computed solution of numerical problems in cases where
                 some of the original data values are not representable
                 exactly as machine numbers. At present, such data
                 values must be replaced by enclosing machine intervals;
                 for ill-conditioned problems, the final interval
                 defining the solution may be relatively wide.\par

                 The authors here discuss the implementation of some
                 earlier ideas of Stetter's [1], relating to the
                 coupling of a conversion procedure for decimal data to
                 the evaluation algorithm proper, with the objective of
                 generating much narrower inclusions. A clear indication
                 of how this might be done is presented by means of an
                 illustrative example. A detailed specification is given
                 for a linear equation solver which should compute last
                 bit accurate inclusions of the solution for decimal
                 data using a hexadecimal machine. Also included are
                 four varied numerical examples, for which the results
                 are most impressive, and which appear to justify the
                 authors' claim. \par

                 -J. Oliver, Essex, UK \par

                 REFERENCES \par

                 [1] STETTER, H. J. Sequential defect correction for
                 high-accuracy floating-point algorithms, in Numerical
                 analysis, Proc. of the conference (Dundee, 1983),
                 Springer-Verlag",
  CRclass =      "G.1.0 General; G.1.0 Computer arithmetic",
  CRnumber =     "8607-0617",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Computer arithmetic",
  genterm =      "THEORY; ALGORITHMS",
  guideno =      "04640",
  keywords =     "decimal floating-point arithmetic",
  reviewer =     "J. Oliver",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@InProceedings{Avizienis:1985:AAO,
  author =       "Algirdas Avi{\v{z}}ienis",
  title =        "Arithmetic Algorithms for Operands Encoded in
                 Two-Dimensional Low-Cost Arithmetic Error Code",
  crossref =     "Hwang:1985:PSC",
  pages =        "285--292",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Avizienis.pdf",
  abstract =     "A generalization of low-cost residue codes into
                 two-dimensional encodings was presented and error
                 detecting and error correcting properties of two
                 dimensional inverse residue codes were discussed
                 previously. This paper presents byte-serial checking,
                 additive inverse (complementation), and addition
                 algorithms for operands encoded in two-dimensional
                 residue and inverse residue codes.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@InProceedings{Bannur:1985:VIS,
  author =       "J. Bannur and A. Varma",
  title =        "The {VLSI} Implementation of a Square Root Algorithm",
  crossref =     "Hwang:1985:PSC",
  pages =        "159--165",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Bannur_Varma.pdf",
  abstract =     "VLSI implementation of a square root algorithm is
                 studied. Two possible implementations of the basic
                 nonrestoring algorithm are presented --- the second is
                 more area-efficient and modular than the first. The
                 implementations are simple and easy to control, but, at
                 the same time, are more area-time efficient than many
                 existing designs. A hardware algorithm suited to
                 microprogram implementation is also given. Extension of
                 the algorithms to achieve $ 1 / 2 $-bit precision is
                 discussed.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@Article{Barlow:1985:PEA,
  author =       "J. L. Barlow and E. H. Bareiss",
  title =        "Probabilistic error analysis of {Gaussian} elimination
                 in floating point and logarithmic arithmetic",
  journal =      j-COMPUTING,
  volume =       "34",
  number =       "4",
  pages =        "349--364",
  year =         "1985",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65G05",
  MRnumber =     "87c:65046",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  reviewer =     "N. N. Abdelmalek",
}

@Article{Barlow:1985:RED,
  author =       "J. L. Barlow and E. H. Bareiss",
  title =        "On Roundoff Error Distributions in Floating Point and
                 Logarithmic Arithmetic",
  journal =      j-COMPUTING,
  volume =       "34",
  number =       "4",
  pages =        "325--347",
  month =        dec,
  year =         "1985",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65G05",
  MRnumber =     "87c:65045",
  MRreviewer =   "N. N. Abdelmalek",
  bibdate =      "Tue Oct 12 16:33:42 MDT 1999",
  bibsource =    "Compendex database;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  affiliation =  "Pennsylvania State Univ, Computer Science Dep,
                 University Park, PA, USA",
  affiliationaddress = "USA",
  classification = "723",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Computing (Vienna/New York)",
  keywords =     "computer arithmetic; computer metatheory; floating
                 point arithmetic; logarithmic arithmetic; roundoff
                 error distributions",
}

@Article{Barnes:1985:SFP,
  author =       "C. Barnes and Boi Tran and Shu Leung",
  title =        "On the statistics of fixed-point roundoff error",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "33",
  number =       "3",
  pages =        "595--606",
  month =        jun,
  year =         "1985",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  summary =      "Roundoff error after fixed-point multiplication is
                 commonly modeled as uniformly distributed white noise
                 that is uncorrelated with the signal. This paper
                 presents a statistical analysis of fixed-point roundoff
                 error that identifies the conditions \ldots{}",
}

@Article{Bayoumi:1985:HVA,
  author =       "M. A. Bayoumi and G. A. Jullien and W. C. Miller",
  title =        "Hybrid {VLSI} architecture of {FIR} filters using
                 residue number systems",
  journal =      j-ELECT-LETTERS,
  volume =       "21",
  number =       "8",
  pages =        "358--359",
  day =          "11",
  month =        apr,
  year =         "1985",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:19850252",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4251043",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "residue arithmetic; residue number system",
  summary =      "An efficient VLSI architecture of FIR filters based on
                 large moduli set is described. The structure is hybrid,
                 combining both binary-based elements and look-up
                 tables. The binary-based section is arranged as a
                 two-dimensional systolic array using \ldots{}",
}

@Article{Bittner:1985:WPD,
  author =       "L. Bittner",
  title =        "{Weiteres {\"u}ber Pseudo-Divisionsverfahren zur
                 Berechnung der Standardfunktionen und gewisser
                 Nicht-Stan\-dard\-funk\-tion\-en} \toenglish {Further
                 Details on Pseudo-Division Procedures for Computation
                 of Standard Functions and Certain Nonstandard
                 Functions} \endtoenglish",
  journal =      j-Z-ANGE-MATH-MECH,
  volume =       "65",
  number =       "12",
  pages =        "605--612",
  year =         "1985",
  CODEN =        "ZAMMAX",
  ISSN =         "0044-2267 (print), 1521-4001 (electronic)",
  ISSN-L =       "0044-2267",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "{Zeitschrift f{\"u}r Angewandte Mathematik und
                 Mechanik}",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
  xxmonth =      "(none)",
}

@InProceedings{Bleher:1985:AHA,
  author =       "J. H. Bleher and A. E. Roeder and Siegfried M. Rump",
  title =        "{ACRITH}: High-accuracy arithmetic, an advanced tool
                 for numerical computation",
  crossref =     "Hwang:1985:PSC",
  pages =        "318--321",
  year =         "1985",
  bibdate =      "Sun May 28 18:31:07 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Bleher_Roeder_Rump.pdf",
  abstract =     "The High-Accuracy Arithmetic Subroutine Library
                 (ACRITH) is a program product for engineering /
                 scientific application. It consists of a subroutine
                 library for solving problems in numerical computation.
                 All results obtained have algorithmically verified
                 accuracy.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@InProceedings{Bohte:1985:GEF,
  author =       "Zvonimir Bohte and Marko Petkov{\v{s}}ek",
  title =        "{Gaussian} elimination in floating-point arithmetic",
  crossref =     "Vrdoljak:1985:ICA",
  pages =        "85--91",
  year =         "1985",
  MRclass =      "65F05 (65G05)",
  MRnumber =     "86m:65028",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Brent:1985:SAI,
  author =       "R. P. Brent and H. T. Kung",
  title =        "A Systolic Algorithm for Integer {GCD} Computation",
  crossref =     "Hwang:1985:PSC",
  pages =        "118--125",
  year =         "1985",
  bibdate =      "Wed Nov 14 18:06:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Brent_Kung.pdf",
  abstract =     "It is shown that the greatest common divisor of two
                 $n$-bit integers (given in the usual binary
                 representation) can be computed in time $ O(n) $ on a
                 linear systolic array of $ O(n) $ identical cells.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@Article{Burton:1985:SFE,
  author =       "C. G. Burton",
  title =        "The solution of finite element equations on the
                 floating point systems {FPS-164} attached processor",
  journal =      j-COMP-PHYS-COMM,
  volume =       "37",
  number =       "1-3",
  pages =        "171--180",
  year =         "1985",
  CODEN =        "CPHCBZ",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  MRclass =      "65N20 (65W05)",
  MRnumber =     "817 063",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@InProceedings{Cantoni:1985:PPA,
  author =       "V. Cantoni and M. Ferretti and S. Levialdi and R.
                 Stefanelli",
  title =        "{PAPIA}: {Pyramidal Architecture for Parallel Image
                 Analysis}",
  crossref =     "Hwang:1985:PSC",
  pages =        "237--242",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Cantoni_Ferretti_Levialdi_Stefanelli.pdf",
  abstract =     "In 1981 a national research program for the design,
                 simulation and construction of a multiprocessor image
                 processing system was started. After a first phase
                 devoted to the comparison of suggested and existing
                 systems and to the definition of a set of benchmarks
                 and to the evaluation of the performances of the major
                 classes of machines, a new system has been defined. The
                 structure of the new system is based on a pyramid of
                 processors and many applications in which this machine
                 may be exploited are highlighted. The multiprocessor
                 architecture has been fully designed and the chip will
                 be built by an Italian silicon foundry, the SGS
                 company, within the framework of the multichip national
                 project.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@Article{Cathey:1985:ISR,
  author =       "James Cathey",
  title =        "68000 Integer square root routine in {16BST}",
  journal =      j-DDJ,
  volume =       "10",
  number =       "5",
  pages =        "118--??",
  month =        may,
  year =         "1985",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@MastersThesis{Chen:1985:FPP,
  author =       "Jen-Chyun Chen",
  title =        "8087 floating point processor software utilities
                 development and evaluation",
  type =         "Thesis ({M.S.E.E.})",
  school =       "University of Alabama. Graduate School. Dept. of
                 Electrical and Engineering",
  address =      "Tuscaloosa, AL, USA",
  pages =        "x + 128",
  year =         "1985",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Programming (Electronic computers); Software
                 compatibility.",
}

@InProceedings{Chen:1985:MRS,
  author =       "Tien Chi Chen",
  title =        "Maximal Redundancy Signed-Digit Systems",
  crossref =     "Hwang:1985:PSC",
  pages =        "296--300",
  year =         "1985",
  bibdate =      "Wed Nov 14 18:06:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Chen.pdf",
  abstract =     "The maximal redundancy signed-digit (MAXSD) number
                 system has the highest redundancy within the
                 carry-absorbing signed-digit number system proposed by
                 Avizienis in 1961. The digital values for radix R lie
                 in $ [1 - R, R - 1] $.\par

                 Its compatibility with both standard nonredundant
                 systems and binary arithmetic makes it an excellent
                 choice for multiprecision arithmetic on binary
                 machines. The representations for finite numbers are
                 however nonunique and can even be unbounded in
                 wordlength; this is resolved by algorithms for partial
                 or complete conversion to standard nonredundant
                 notation without explicit carry propagation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@InProceedings{Cheng:1985:APF,
  author =       "H. D. Cheng and K. S. Fu",
  title =        "Algorithm Partition for a Fixed-Size {VLSI}
                 Architecture Using Space-Time Domain Expansion",
  crossref =     "Hwang:1985:PSC",
  pages =        "126--132",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Cheng_Fu.pdf",
  abstract =     "The space-time domain expansion method has recently
                 been used to transform a computational task with a
                 recursive formula into a VLSI architecture. In addition
                 to its simplicity and completeness, an important
                 advantage of this method is that it can easily solve
                 the problem of partitioning an algorithm to fit a fixed
                 size VLSI architecture. We propose a computational
                 model and a partition rule which can be easily used to
                 partition any recursive computation problem suited to
                 the space-time domain expansion method so it can be
                 solved on fixed-size VLSI architectures. Several
                 examples, such as partitioned vector inner product,
                 partitioned comparators in relational database
                 management, partitioned matrix multiplications. and
                 partitioned transitive closure computation, parallel
                 recognition of general context-free languages, string
                 matching and dynamic time-warp pattern-matching are
                 used to illustrate the proposed method.",
  acknowledgement = ack-nhfb,
  keywords =     "algorithm partition; ARITH-7; multiprocessing;
                 pipelining; recursive task; space-time domain
                 expansion; very large scale integration (VLSI)",
}

@InProceedings{Chiarulli:1985:DDR,
  author =       "Donald M. Chiarulli and W. G. Rudd and Duncan A.
                 Buell",
  title =        "{DRAFT}: a Dynamically Reconfigurable Processor for
                 Integer Arithmetic",
  crossref =     "Hwang:1985:PSC",
  pages =        "309--317",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Chiarulli_Rudd_Buell.pdf",
  abstract =     "A special computer for high-precision arithmetic
                 features an ALU that is dynamically reconfigurable
                 under program control. The 256-bit ALU consists of 8
                 32-bit slices each of which has its own ALU operation
                 code in each microinstruction. The slices can remain
                 logically separated from each other, or be dynamically
                 connected to either or both of their neighbors under
                 control of a segment control code that is part of each
                 microinstruction. The micro-assembly language designed
                 for the machine includes special features to assist in
                 the control of the segmentation, data addressing, and
                 control sequencing. Estimations of the times required
                 to execute arithmetic operations on the machine show
                 that it will be exceptionally fast for problems in
                 computational number theory and factoring of
                 integers.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@InProceedings{Chow:1985:PFD,
  author =       "Edward T. Chow and Dan I. Moldovan",
  title =        "Prime Factor {DFT} Parallel Processor Using Wafer
                 Scale Integration",
  crossref =     "Hwang:1985:PSC",
  pages =        "133--139",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Chow_Moldovan.pdf",
  abstract =     "A high speed, flexible, simple and regular Discrete
                 Fourier Transform (DFT) Array Processor architecture
                 based on the Prime Factor Algorithm (PFA) is presented
                 in this paper. The array processor is based only on one
                 type of VLSI cell and can compute an $N$ point DFT in
                 $N$ clock cycles throughput when $N$ is a composite
                 number of prime numbers. The high throughput rate is
                 achieved with only a small number of cells. With a
                 special indexing scheme presented in this paper, this
                 processor can use shift registers as the system memory
                 so that minimum global control and addressing is
                 achieved. This array processor architecture is also
                 highly tolerant to both semiconductor processing yield
                 and processor defects during run time. Thus, it can be
                 manufactured in large quantity with VLSI technology on
                 a single wafer and used in hazardous environments. With
                 these advantages, it is very attractive to satellite,
                 military and commercial applications.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@InProceedings{Ciminiera:1985:ESP,
  author =       "L. Ciminiera and A. Serra",
  title =        "Efficient Serial-Parallel Arrays for Multiplikation
                 and Addition",
  crossref =     "Hwang:1985:PSC",
  pages =        "28--35",
  year =         "1985",
  bibdate =      "Wed Nov 14 18:06:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Ciminiera_Serra.pdf",
  abstract =     "Three new arrays for unsigned and signed
                 multiplication, and for multiplication\slash addition
                 are presented. It is assumed that the factors are
                 expressed in 2's complement, while the addend (in the
                 latter array only) and the result are expressed in a
                 redundant notation. The arrays operate in
                 serial-parallel way since one factor is input in
                 parallel, while the second factor and the addend (in
                 the case of multiplication\slash addition) are entered
                 digit by digit starting from the most significant one;
                 the result is also produced serially with the most
                 significant digit first. Hence, the arithmetic unit
                 presented is suitable to be used as basic block of
                 special purpose processors performing functions such as
                 non-recursive digital filtering, signal correlation and
                 matrix multiplication. Indeed, they have the same speed
                 improvements as other similar units using redundant
                 representations for the result, with a cost: equivalent
                 to their counterparts based on full 2's complement
                 representation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@Article{Cody:1985:PRW,
  author =       "W. J. Cody and J. T. Coonen and D. M. Gay and K.
                 Hanson and D. Hough and W. Kahan and R. Karpinski and
                 J. Palmer and F. N. Ris and D. Stevenson",
  title =        "A Proposed Radix- and Word-length-independent Standard
                 for Floating-point Arithmetic",
  journal =      j-SIGNUM,
  volume =       "20",
  number =       "1",
  pages =        "37--51",
  month =        jan,
  year =         "1985",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Thu Sep 1 10:14:17 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}

@InProceedings{Conover:1985:AHS,
  author =       "B. Conover and D. L. Gustafson",
  title =        "An Algorithm for High Speed Square Roots",
  crossref =     "IEEE:1985:ERC",
  pages =        "19--21",
  year =         "1985",
  bibdate =      "Fri Jun 11 18:04:41 1999",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Cozzens:1985:CDF,
  author =       "J. Cozzens and L. Finkelstein",
  title =        "Computing the discrete {Fourier} transform using
                 residue number systems in a ring of algebraic
                 integers",
  journal =      j-IEEE-TRANS-INF-THEORY,
  volume =       "31",
  number =       "5",
  pages =        "580--588",
  month =        sep,
  year =         "1985",
  CODEN =        "IETTAW",
  DOI =          "https://doi.org/10.1109/TIT.1985.1057081",
  ISSN =         "0018-9448 (print), 1557-9654 (electronic)",
  ISSN-L =       "0018-9448",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=22750",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Information Theory",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A new method is described for computing an $N = R^{m}
                 = 2^{upsilon m}$-point complex discrete Fourier
                 transform that uses quantization within a dense ring of
                 algebraic integers in conjunction with a residue number
                 system over this ring. The \ldots{}",
}

@Article{Cuyt:1985:REA,
  author =       "Annie Cuyt and Paul Van der Cruyssen",
  title =        "Rounding error analysis for forward continued fraction
                 algorithms",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "11",
  number =       "6",
  pages =        "541--564",
  month =        jun,
  year =         "1985",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 19:00:53 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122185900379",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@InProceedings{Dadda:1985:FMT,
  author =       "Luigi Dadda",
  title =        "Fast Multipliers for Two's-Complement Numbers in
                 Serial Form",
  crossref =     "Hwang:1985:PSC",
  pages =        "57--63",
  year =         "1985",
  bibdate =      "Wed Nov 14 18:06:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Dadda.pdf",
  abstract =     "Schemes for designing multipliers of binary
                 two's-complement numbers in serial form are considered
                 with the condition of the least possible delay between
                 inputs and output.\par

                 Such schemes are composed by two parts: the first, the
                 array generator, produces the terms of the multiplier
                 array; the second, the summer, is fed by the array
                 generator and produces the product. Two classes of
                 multipliers are illustrated: the first generating the
                 multiplier array by diagonals and rows, the second by
                 columns.\par

                 The array generators are composed by and\slash or stack
                 registers and linear arrays of gates; the summer is
                 shown to be conveniently using parallel counters.",
  acknowledgement = ack-nhfb,
  author-dates = "29 April 1923--26 October 2012",
  keywords =     "ARITH-7",
}

@InProceedings{Dadda:1985:SBN,
  author =       "Luigi Dadda",
  title =        "Squares for Binary Numbers in Serial Form",
  crossref =     "Hwang:1985:PSC",
  pages =        "173--180",
  year =         "1985",
  bibdate =      "Wed Nov 14 18:06:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Dadda1.pdf",
  abstract =     "The problem of designing squarers for binary number[s]
                 in serial form (with the condition of the least
                 possible delay between input and output) is
                 treated.\par

                 Several schemes are illustrated, derived from fast
                 multipliers for binary numbers in serial form,
                 described in a previous paper.\par

                 It is shown that some of such multipliers offer a
                 considerable saving in components when they are reduced
                 to squarers. Some schemes are illustrated, both for
                 positive and for two's-complement numbers.",
  acknowledgement = ack-nhfb,
  author-dates = "29 April 1923--26 October 2012",
  keywords =     "ARITH-7",
}

@InProceedings{DeMori:1985:DRP,
  author =       "R. {De Mori} and R. Cardin",
  title =        "Design for a Recursive Parallel Multiplier",
  crossref =     "Hwang:1985:PSC",
  pages =        "44--50",
  year =         "1985",
  bibdate =      "Wed Nov 14 18:06:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Demori_Cardin.pdf",
  abstract =     "A network for performing multiplications of two two's
                 complement number's is proposed. The network can be
                 implemented in a synchronous or an asynchronous way. If
                 the factors to be multiplied have $N$ bits, the area
                 complexity of the network is $ O(N^2) $ for practical
                 values of $N$ as in the case of cellular multipliers.
                 Due to the design approach based on a recursive
                 algorithm, a time complexity $ O(\log N) $ is
                 achieved.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@InProceedings{Dongarra:1985:FAS,
  author =       "J. J. Dongarra and D. C. Sorensen",
  title =        "A Fast Algorithm for the Symmetric Eigenvalue
                 Problem",
  crossref =     "Hwang:1985:PSC",
  pages =        "338--342",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Dongarra_Sorensen.pdf",
  abstract =     "The symmetric eigenvalue problem is one of the most
                 fundamental problems of computational mathematics. It
                 arises in many applications, and therefore represents
                 an important area for algorithmic research. It is also
                 one of the first eigenvalue problems for which reliable
                 methods have been obtained. It would be surprising
                 therefore, if a new method were to be found that would
                 offer a significant improvement in execution time over
                 the fundamental algorithms available in standard
                 software packages such as EISPACK [7]. However, it is
                 reasonable to expect that eigenvalue calculations might
                 be accelerated through the use of parallel algorithms
                 for parallel computers that are emerging. We shall
                 present such an algorithm in this paper. The algorithm
                 is able to exploit parallelism at all levels of the
                 computation and is well suited to a variety of
                 architectures. However, a pleasant bonus of this
                 research is that the parallel algorithm, even when run
                 in serial mode, is significantly faster than the best
                 sequential algorithm on large problems, and is
                 effective on moderate size (order $ \geq 30 $) problems
                 when run in serial mode.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
  remark =       "Listed in table of contents as 276--277.",
}

@InProceedings{Dunham:1985:PFM,
  author =       "C. B. Dunham",
  title =        "Floating point with rounding before normalization",
  crossref =     "Meek:1985:PFM",
  pages =        "91--102",
  year =         "1985",
  MRclass =      "65G05",
  MRnumber =     "86f:65089",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Eldon:1985:FCF,
  author =       "John A. Eldon",
  title =        "A Family of {CMOS} Floating Point Arithmetic Chips",
  crossref =     "Hwang:1985:PSC",
  pages =        "101--109",
  year =         "1985",
  bibdate =      "Wed Nov 14 18:06:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Eldon.pdf",
  abstract =     "Although the advantages of floating point arithmetic
                 have long been recognized, hardware complexity and
                 expense have impeded its use in high speed digital
                 signal processing (DSP). Now, however, the availability
                 of a growing number of fast dedicated floating point
                 adder and multiplier chips is spurring renewed interest
                 in floating point for real time filtering and spectral
                 analysis.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@Article{Enzmann:1985:WDS,
  author =       "K. Enzmann",
  title =        "{Wurzelziehen durch sukzessive Approximation}
                 \toenglish {Root-Finding by Successive Approximation}
                 \endtoenglish",
  journal =      j-ELECTRONIK,
  volume =       "18",
  pages =        "92",
  year =         "1985",
  CODEN =        "EKRKAR",
  ISSN =         "0013-5658",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektronik",
}

@InProceedings{Ercegovac:1985:DAP,
  author =       "M. D. Ercegovac and T. Lang",
  title =        "A Division Algorithm with Prediction of Quotient
                 Digits",
  crossref =     "Hwang:1985:PSC",
  pages =        "51--56",
  year =         "1985",
  bibdate =      "Wed Nov 14 18:06:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Ercegovac_Lang.pdf",
  abstract =     "A division algorithm with a simple selection of
                 quotient digits including prediction is possible if the
                 divisor is restricted to a suitable range. The
                 condition that the divisor must satisfy to have the
                 quotient digit $ q_{i + 1} $ predicted while computing
                 $ R_{i + 1} $ are determined. Some implementation
                 considerations are also given.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@Book{Ercegovac:1985:DSH,
  author =       "Milo{\v{s}} D. Ercegovac and Tom{\'a}s Lang",
  title =        "Digital systems and hardware\slash firmware
                 algorithms",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xix + 838",
  year =         "1985",
  ISBN =         "0-471-88393-X",
  ISBN-13 =      "978-0-471-88393-7",
  LCCN =         "TK7868.D5 E73 1985",
  bibdate =      "Wed Nov 14 14:42:00 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "US\$32.95",
  URL =          "http://www.loc.gov/catdir/bios/wiley043/84021983.html;
                 http://www.loc.gov/catdir/description/wiley035/84021983.html;
                 http://www.loc.gov/catdir/toc/onix06/84021983.html",
  abstract =     "This modern treatment of digital system specification,
                 analysis, and design covers all topics from gates and
                 flip-flops to complex hardware and system software
                 algorithms. An upper-level undergraduate/graduate text,
                 it uses two complementary approaches --- system model
                 and algorithmic model --- in dealing with structured
                 analysis and design, and separates specification from
                 implementation to allow for the ready application of
                 concepts to practical system design. Extensive
                 illustrations and 500 exercises.",
  acknowledgement = ack-nhfb,
  subject =      "computer firmware; digital electronics",
  tableofcontents = "Combinational Systems \\
                 Specification of Combinational Systems \\
                 Implementation of Combinational Systems \\
                 Combinational Modules and Modular Networks \\
                 Sequential Systems \\
                 Specification of Sequential Systems \\
                 Implementation of Synchronous Sequential Systems \\
                 Standard Sequential Modules and Modular Networks \\
                 Hardware\slash Firmware Algorithmic Systems \\
                 Hardware\slash Firmware Algorithms and Their
                 Specification \\
                 Hardware\slash Firmware Implementation of
                 Group-Sequential Algorithms \\
                 Examples of Hardware\slash Firmware Systems \\
                 General-Purpose Microprogrammable Systems \\
                 Arithmetic Algorithms and Processors \\
                 Appendices \\
                 Bibliography \\
                 Index",
}

@InProceedings{Fandrianto:1985:VFP,
  author =       "Jan Fandrianto and B. Y. Woo",
  title =        "{VLSI} Floating-Point Processors",
  crossref =     "Hwang:1985:PSC",
  pages =        "93--100",
  year =         "1985",
  bibdate =      "Wed Nov 14 18:06:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Fandrianto_Woo.pdf",
  abstract =     "The advance of VLSI technology has been the enabling
                 factor in the appearance of VLSI circuits handling
                 floating-point arithmetics. These circuits have found
                 their way into many number-crunching applications such
                 as telecommunications, seismic energy exploration,
                 radar, medical imaging, graphics and simulation.
                 Because of the different requirements for different
                 applications, some processors have a rich repertoire of
                 functions but rather low performance, while some
                 processors aim at haying the highest throughput for the
                 most frequent operations such as multiply and add. This
                 paper will review the architecture, the technology, and
                 the design techniques for the current VLSI
                 floating-point processors; and it will also report a
                 high performance chipset (Weitek WTL1164\slash 1165)
                 implementing complete basic arithmetic functions.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@InProceedings{Ferguson:1985:RBA,
  author =       "Warren E. Ferguson and David W. Matula",
  title =        "Rationally Biased Arithmetic",
  crossref =     "Hwang:1985:PSC",
  pages =        "194--202",
  year =         "1985",
  bibdate =      "Wed Nov 14 18:06:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Ferguson_Matula.pdf",
  abstract =     "One can naively view a computer number system as a
                 pair $ (F, P) $ consisting of a finite set $F$ of real
                 numbers and a rounding rule $P$. One such number system
                 is a hyperbolic rational number system which has as $F$
                 a finite set of rational numbers and as $P$ the
                 so-called mediant rounding rule. In this paper we
                 demonstrate how one can simulate a hyperbolic rational
                 number system in any high level language that supports
                 floating point computation. From this simulation we
                 infer that hyperbolic rational number systems form
                 viable alternatives to traditional binary floating
                 point number systems. Many properties of hyperbolic
                 rational number systems are derived fran the
                 relationship of their rounding rule to the
                 well-developed theory of best rational approximation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@Book{Froberg:1985:NMT,
  author =       "Carl Erik Fr{\"o}berg",
  title =        "Numerical mathematics: theory and computer
                 applications",
  publisher =    pub-BENCUM,
  address =      pub-BENCUM:adr,
  pages =        "xi + 436",
  year =         "1985",
  ISBN =         "0-8053-2530-1",
  ISBN-13 =      "978-0-8053-2530-0",
  LCCN =         "QA297 .F6813 1985",
  bibdate =      "Fri Aug 20 09:03:54 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  remark =       "Revised edition of {\em Introduction to numerical
                 analysis, second edition, 1969}
                 \cite{Froberg:1969:INA}",
  subject =      "Numerical analysis; Data processing",
}

@InProceedings{Gal:1985:CEF,
  author =       "Shmuel Gal",
  title =        "Computing Elementary Functions: a New Approach for
                 Achieving High Accuracy and Good Performance",
  crossref =     "Miranker:1985:ASC",
  pages =        "1--16",
  year =         "1985",
  DOI =          "https://doi.org/10.1007/3-540-16798-6_1",
  bibdate =      "Thu Sep 01 12:27:23 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@InProceedings{Gannon:1985:SPH,
  author =       "Dennis Gannon",
  title =        "{On} the Structure of Parallelism in a Highly
                 Concurrent {PDE} Solver",
  crossref =     "Hwang:1985:PSC",
  pages =        "252--259",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Gannon.pdf",
  abstract =     "This paper studies a variation of a parallel multigrid
                 PDE solver originally due to John Van Rosendale. This
                 paper gives a detailed analysis of the method and
                 discusses the large scale parallel structure. It will
                 show that the method can be viewed as a data driven
                 ``large grain'' systolic structure. At a lower level
                 the algorithm is seen to be built from grid operators
                 that are, in turn, defined by expressions involving
                 vector functions.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@Article{Gnanasekaran:1985:FSP,
  author =       "R. Gnanasekaran",
  title =        "A Fast Serial-Parallel Binary Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "8",
  pages =        "741--744",
  month =        aug,
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.1676620",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 08:33:17 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676620",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Gomez:1985:PFA,
  author =       "Gustavo Rodr{\'\i}guez G{\'o}mez and David {Carrasco
                 Villareal}",
  title =        "Problems in floating-point arithmetic, and a method
                 for obtaining internal characteristics of digital
                 computers. ({Spanish})",
  journal =      "Miscel{\'a}nea Mat.",
  volume =       "15",
  pages =        "15--25",
  year =         "1985",
  MRclass =      "65G05",
  MRnumber =     "86h:65060",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "Spanish",
}

@Article{Goodman:1985:REF,
  author =       "R. H. Goodman and A. Feldstein and J. Bustoz",
  title =        "Relative error in floating-point multiplication",
  journal =      j-COMPUTING,
  volume =       "35",
  number =       "2",
  pages =        "127--139",
  year =         "1985",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65G05",
  MRnumber =     "87d:65052",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  reviewer =     "Luciano Biasini",
}

@MastersThesis{Gooley:1985:DFM,
  author =       "Markian Myron Gooley",
  title =        "Design of a floating-point multiplier with a recursive
                 fraction-unit",
  type =         "Thesis ({M.S.})",
  school =       "University of Illinois at Urbana-Champaign",
  address =      "Urbana-Champaign, IL 61801, USA",
  pages =        "vi + 54",
  year =         "1985",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@MastersThesis{Graham:1985:IFF,
  author =       "Douglas R. Graham",
  title =        "Implementation of {FORTH} with floating point
                 capabilities of an 8085 system",
  type =         "Thesis ({M.S.})",
  school =       "Ohio University",
  address =      "Athens, OH, USA",
  pages =        "v + 122",
  month =        mar,
  year =         "1985",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "FORTH (Computer program language)",
}

@Article{Grappel:1985:FSC,
  author =       "R. D. Grappel",
  title =        "Fast subroutine calculates exponentials",
  journal =      j-EDN,
  volume =       "30",
  number =       "10",
  pages =        "231",
  month =        may,
  year =         "1985",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 1 10:16:09 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}

@InProceedings{Gridley:1985:IPS,
  author =       "Curt Gridley",
  title =        "Improving the Performance of Scientific Applications
                 on a Supermicro Using a Custom Floating Point Processor
                 and An Optimizing Compiler",
  crossref =     "USENIX:1985:SCP",
  pages =        "597--610",
  year =         "1985",
  bibdate =      "Tue Feb 20 15:42:13 MST 1996",
  bibsource =    "ftp://ftp.uu.net/library/bibliography;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Massachusetts Computer Corp.",
}

@InProceedings{Gross:1985:FPA,
  author =       "Thomas Gross",
  title =        "Floating-Point Arithmetic on a Reduced-Instruction-Set
                 Processor",
  crossref =     "Hwang:1985:PSC",
  pages =        "86--92",
  year =         "1985",
  bibdate =      "Thu Sep 01 12:02:04 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Gross.pdf",
  abstract =     "Current single chip implementations of
                 reduced-instruction-set processors do not support
                 hardware floating-point operations. Instead, floating
                 point operations have to be provided either by a
                 co-processor or by software. This paper discusses
                 issues arising from a software implementation of
                 floating point arithmetic for the MIPS processor, an
                 experimental VLSI architecture. Measurements indicate
                 that an acceptable level of performance is achieved.
                 but this approach is no substitute for a hardware
                 accelerator if higher precision results are required,
                 This paper includes instruction profiles for the basic
                 floating point operations and evaluates the usefulness
                 of some aspects of the instruction set.",
  acknowledgement = ack-nj,
  keywords =     "ARITH-7",
}

@Article{Gross:1985:SIF,
  author =       "Thomas Gross",
  title =        "Software implementation of floating-point arithmetic
                 on a reduced-instruction-set processor",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "2",
  number =       "4",
  pages =        "362--375",
  month =        nov,
  year =         "1985",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliationaddress = "Carnegie-Mellon Univ, Pittsburgh, PA, USA",
  classification = "723; C5230 (Digital arithmetic methods); C6130 (Data
                 handling techniques); C6140B (Machine-oriented
                 languages)",
  corpsource =   "Department of Computer Science, Carnegie-Mellon
                 University, Pittsburgh, PA, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "computer metatheory; computer software; data handling;
                 digital arithmetic; floating-point arithmetic;
                 instruction profiles; instruction sets; integrated
                 circuits, VLSI; million instructions per minute; MIPS
                 processor; processors; reduced-instruction-set;
                 reduced-instruction-set processor; RISC; single chip
                 implementations; single-chip processors; software
                 implementation; Stanford MIPS processor; VLSI
                 architecture",
  treatment =    "P Practical",
}

@InProceedings{Gudenberg:1985:CID,
  author =       "R. Lohner and J. Wolff V. Gudenberg",
  title =        "Complex Interval Division with Maximum Accuracy",
  crossref =     "Hwang:1985:PSC",
  pages =        "332--336",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Lohner_Gudenberg.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
  xxabstract =   "n/a",
}

@TechReport{Hack:1985:RPS,
  author =       "James J. Hack",
  title =        "The relationship of peak to sustained performance in
                 highly concurrent vector machine organizations",
  type =         "Research report",
  number =       "RC 11094 (\#49829)",
  institution =  "IBM T.J. Watson Research Center",
  address =      "Yorktown Heights, NY, USA",
  pages =        "22",
  year =         "1985",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Performance.;
                 Supercomputers.",
}

@Article{Helyer:1985:SCC,
  author =       "R. Helyer",
  title =        "Sine and cosine calculations",
  journal =      j-MICROPROC-MICROSYS,
  volume =       "2",
  number =       "5",
  pages =        "284",
  month =        oct,
  year =         "1985",
  CODEN =        "MIMID5",
  ISSN =         "0141-9331 (print), 1872-9436 (electronic)",
  ISSN-L =       "0141-9331",
  bibdate =      "Thu Sep 1 10:15:56 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Microprocessors and Microsystems",
}

@Article{Hull:1985:NT,
  author =       "T. E. Hull and A. Abraham and M. S. Cohen and A. F. X.
                 Curley and C. B. Hall and D. A. Penny and J. T. M.
                 Sawchuk",
  title =        "{Numerical Turing}",
  journal =      j-SIGNUM,
  volume =       "20",
  number =       "3",
  pages =        "26--34",
  month =        jul,
  year =         "1985",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Sat Aug 13 17:16:02 MDT 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Numerical Turing is an extension of the Turing
                 programming language. Turing is a Pascal-like language
                 (with convenient string handling, dynamic arrays,
                 modules, and more general parameter lists) developed at
                 the University of Toronto. Turing has been in use since
                 May, 1983, and is now available on several
                 machines.\par

                 The Numerical Turing extension is especially designed
                 for numerical calculations. The important new features
                 are: (a) clean decimal arithmetic, along with
                 convenient functions for directed roundings and
                 exponent manipulation; (b) complete precision control
                 of variables and operations.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "decimal floating-point arithmetic; documentation;
                 languages",
  subject =      "D.3.3 Software, PROGRAMMING LANGUAGES, Language
                 Constructs, Procedures, functions, and subroutines \\
                 D.3.2 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, SUPERPILOT \\ G.1.0 Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Computer
                 arithmetic",
}

@Article{Hull:1985:PRV,
  author =       "T. E. Hull and A. Abrham",
  title =        "Properly Rounded Variable Precision Square Root",
  journal =      j-TOMS,
  volume =       "11",
  number =       "3",
  pages =        "229--237",
  month =        sep,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214408.214413",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D15 (65G05)",
  MRnumber =     "87a:65041",
  bibdate =      "Mon Dec 08 12:36:56 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p229-hull/",
  abstract =     "The square root function presented here returns a
                 properly rounded approximation to the square root of
                 its argument, or it raises an error condition if the
                 argument is negative. {\em Properly rounded} means
                 rounded to the nearest, or to nearest even in case of a
                 tie. It is {\em variable precision} in that it is
                 designed to return a $p$-digit approximation to a
                 $p$-digit argument, for any $ p > 0 $. (Precision $p$
                 means $p$ decimal digits.) The program and the analysis
                 are valid for all $ p > 0 $, but current
                 implementations place some restrictions on $p$.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; decimal floating-point arithmetic;
                 verification",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Certification and testing. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Verification. {\bf
                 G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Error analysis. {\bf G.1.0}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Numerical
                 algorithms.",
}

@Book{Hunter:1985:III,
  author =       "Colin B. Hunter and James F. Ready and Erin Farquhar",
  title =        "Introduction to the {Intel iAPX 432} Architecture",
  publisher =    pub-RESTON,
  address =      pub-RESTON:adr,
  pages =        "vii + 181",
  year =         "1985",
  ISBN =         "0-8359-3222-2",
  ISBN-13 =      "978-0-8359-3222-6",
  LCCN =         "QA76.8.I267 H86 1984",
  bibdate =      "Mon Feb 7 19:14:11 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$16.95",
  acknowledgement = ack-nhfb,
}

@Article{Hurson:1985:SMU,
  author =       "A. R. Hurson and B. Shirazi",
  title =        "A systolic multiplier unit and its {VLSI} design",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "13",
  number =       "3",
  pages =        "302--309",
  month =        jun,
  year =         "1985",
  CODEN =        "CANED2",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Fri May 12 09:40:54 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
}

@InProceedings{Hwang:1985:MEC,
  author =       "Kai Hwang and Zhiwei Xu",
  title =        "Multiprocessors for Evaluating Compound Arithmetic
                 Functions",
  crossref =     "Hwang:1985:PSC",
  pages =        "266--275",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Hwang_Xu.pdf",
  abstract =     "A dynamic network approach is proposed for designing
                 multifunctional arithmetic processors to support {\em
                 complex}, {\em interval}, {\em vector}, {\em matrix},
                 {\em polynomial}, and other {\em compound arithmetic}
                 operations. This arithmetic-network approach is
                 extended from the multipipeline chaining concept
                 implemented in Cray Research supercomputers. The
                 proposed design methodology offers a viable way of
                 developing very powerful and flexible arithmetic
                 multiprocessors for scientific supercomputing.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@InProceedings{Hwang:1985:SIS,
  author =       "Kai Hwang and Daniel D. Gajski and Ahmed Sameh",
  title =        "The {Seventh IEEE Symposium on Computer Arithmetic}:
                 Foreword",
  crossref =     "Hwang:1985:PSC",
  pages =        "iii--iii",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_contents.pdf;
                 http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Hwang_Gajski_Sameh.pdf;
                 http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_preface.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
  xxabstract =   "n/a",
}

@Book{IEEE:1985:AIS,
  author =       "{IEEE Task P754}",
  title =        "{ANSI\slash IEEE 754-1985, Standard for Binary
                 Floating-Point Arithmetic}",
  publisher =    pub-IEEE-STD,
  address =      pub-IEEE-STD:adr,
  pages =        "20",
  day =          "12",
  month =        aug,
  year =         "1985",
  ISBN =         "1-55937-653-8",
  ISBN-13 =      "978-1-55937-653-2",
  bibdate =      "Thu Mar 02 09:57:22 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Revised 1990. A preliminary draft was published in the
                 January 1980 issue of IEEE Computer, together with
                 several companion articles
                 \cite{Cody:1981:APF,Coonen:1981:UDN,Coonen:1980:IGP,Coonen:1981:EIG,Hough:1981:API,Stevenson:1981:PSBa,Stevenson:1981:PSBb}.
                 The final version was republished in
                 \cite{IEEE:1985:ISBa,IEEE:1985:ISBb}. See also
                 \cite{Waser:1982:IAD}. Also standardized as {{\em IEC
                 60559 (1989-01) Binary floating-point arithmetic for
                 microprocessor systems}}.",
  price =        "US\$35.00",
  URL =          "http://standards.ieee.org/reading/ieee/std/busarch/754-1985.pdf;
                 http://standards.ieee.org/reading/ieee/std_public/description/busarch/754-1985_desc.html;
                 http://www.iec.ch/cgi-bin/procgi.pl/www/iecwww.p?wwwlang=E&wwwprog=cat-det.p&wartnum=019113;
                 https://ieeexplore.ieee.org/iel1/2355/1316/00030711.pdf",
  acknowledgement = ack-nhfb,
}

@Manual{IEEE:1985:ASI,
  author =       "{IEEE Task P754}",
  title =        "{ANSI}\slash {IEEE 754}-1985, Standard for Binary
                 Floating-Point Arithmetic",
  organization = "IEEE, New York",
  month =        aug # " 12",
  year =         "1985",
  bibdate =      "Thu Nov 8 14:50:30 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "A preliminary draft was published in the January 1980
                 issue of IEEE Computer, together with several companion
                 articles
                 \cite{Cody:1981:APF,Coonen:1981:UDN,Coonen:1980:IGP,Coonen:1981:EIG,Hough:1981:API,Stevenson:1981:PSBa,Stevenson:1981:PSBb}.
                 Available from the IEEE Service Center, Piscataway, NJ,
                 USA.",
  acknowledgement = ack-nj,
}

@Article{IEEE:1985:ISBa,
  author =       "IEEE",
  title =        "{IEEE} Standard for Binary Floating-Point Arithmetic",
  journal =      j-SIGPLAN,
  volume =       "22",
  number =       "2",
  pages =        "9--25",
  month =        feb,
  year =         "1985",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun May 02 09:20:35 1999",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{IEEE:1985:AIS}.",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  xxnote =       "This reference is wrong; the volume 22 is from 1987,
                 and neither volume 20 (1985) nor 22 have this
                 article??",
}

@Book{IEEE:1985:ISBb,
  author =       "{IEEE Computer Society Standards Committee.Working
                 group of the Microprocessor Standards Subcommittee} and
                 {American National Standards Institute}",
  title =        "{IEEE} standard for binary floating-point arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "18",
  year =         "1985",
  bibdate =      "Sun May 02 09:20:47 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{IEEE:1985:AIS}.",
  series =       "ANSI/IEEE Std 754-1985.",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic and logic units --- Standards.;
                 Floating-point arithmetic --- Standards.",
}

@Book{Intel:1985:FPL,
  author =       "{Intel Staff}",
  title =        "Floating Point Library for {DOS} 8096 Systems Manual",
  publisher =    "Intel Corporation",
  address =      "Santa Clara",
  pages =        "60",
  month =        dec,
  year =         "1985",
  ISBN =         "0-917017-75-7",
  ISBN-13 =      "978-0-917017-75-9",
  LCCN =         "????",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$10.00",
  acknowledgement = ack-nhfb,
  keywords =     "(COMPUTER OPERATING SYSTEM); PC-DOS; TECHNOLOGY ---
                 COMPUTERS AND COMPUTER TECHNOLOGY",
  language =     "eng",
}

@Book{Intel:1985:PRM,
  author =       "Intel",
  title =        "The {iAPX} 286 Programmer's Reference Manual",
  publisher =    pub-INTEL,
  address =      pub-INTEL:adr,
  year =         "1985",
  bibdate =      "Sun May 2 09:20:57 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "The definitive statement of what the 80286 and 80287
                 are. A valuable reference for instruction definitions.
                 See also \cite{Intel:1983:HRM,Palmer:1984:P}.",
  acknowledgement = ack-nhfb,
}

@Manual{IntelCorporation:1985:FAL,
  author =       "{Intel Corporation}",
  title =        "The 8096 floating-point arithmetic library user's
                 guide for {DOS} systems",
  organization = "Intel Corporation",
  address =      "Santa Clara, CA.",
  pages =        "various",
  year =         "1985",
  ISBN =         "0-917017-75-7",
  ISBN-13 =      "978-0-917017-75-9",
  LCCN =         "????",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer programs.; Floating-point arithmetic.;
                 Operating systems (Computers)",
  remark =       "``Order number: 122366-001.'' On cover: Software
                 development tools. Cover title: 8096 floating point
                 library for DOS systems.",
}

@Article{Jankowski:1985:ASC,
  author =       "M. Jankowski and H. Wo{\'z}niakowski",
  title =        "The accurate solution of certain continuous problems
                 using only single precision arithmetic",
  journal =      j-BIT,
  volume =       "25",
  number =       "4",
  pages =        "635--651",
  year =         "1985",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65G05 (65L05)",
  MRnumber =     "87d:65053",
  MRreviewer =   "E. R. Hansen",
  bibdate =      "Thu Nov 12 18:12:56 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "accurate floating-point summation",
}

@InProceedings{Jenkins:1985:CDI,
  author =       "W. Jenkins and E. Davidson and D. Paul",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing, {ICASSP '85}",
  title =        "A custom-designed integrated circuit for the
                 realization of residue number digital filters",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "220--223",
  year =         "1985",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1049/el:19850252",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Results are presented on the design, layout, and
                 fabrication of a custom-designed integrated circuit for
                 a residue number system digital filter module. The
                 architecture is based on a ROM-ACCUMULATOR FIR
                 structure in which the modular arithmetic for
                 \ldots{}",
}

@InProceedings{Kahan:1985:AIA,
  author =       "W. Kahan and E. LeBlanc",
  title =        "Anomalies in the {IBM ACRITH} Package",
  crossref =     "Hwang:1985:PSC",
  pages =        "322--331",
  year =         "1985",
  bibdate =      "Thu Sep 08 00:10:49 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Kahan_LeBlanc.pdf",
  abstract =     "The IBM ACRITH package of numerical software is
                 advertised as reliable and easy to use; but sometimes
                 its results must astonish or confuse a naive user. This
                 report exhibits a few of the surprises. For instance, a
                 finite continued fraction, easy to evaluate in two
                 dozen keystrokes on a handheld calculator, causes
                 ACRITH to overflow either exponent range or 15
                 Megabytes of virtual memory. Lacking access to source
                 code, we must speculate to explain the anomalies. Some
                 seem attributable to small bugs in the code; some to
                 optimistic claims or oversimplifications in the code's
                 documentation; some to flaws in the doctrine underlying
                 the code. We conclude that different techniques than
                 used by ACRITH might have been about as accurate and
                 yet more economical, robust and perspicuous.",
  acknowledgement = ack-nj,
  keywords =     "ARITH-7",
}

@Article{Karpinski:1985:PFP,
  author =       "R. Karpinski",
  title =        "Paranoia: a Floating-Point Benchmark",
  journal =      j-BYTE,
  volume =       "10",
  number =       "2",
  pages =        "223--235",
  month =        feb,
  year =         "1985",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Thu Sep 1 10:15:07 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "BYTE Magazine",
}

@InProceedings{Kaushik:1985:MEC,
  author =       "Saroj Kaushik",
  title =        "Multiple Error Correction and Addictive Overflow
                 Detection with Magnitude Indices in Residue Code",
  crossref =     "Hwang:1985:PSC",
  pages =        "278--284",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Kaushik.pdf",
  abstract =     "A new approach for correcting multiple errors and
                 detecting an additive overflow in the Residue Number
                 System (RNS) is suggested. It works with the code whose
                 redundancy is in the form of magnitude indices. The
                 residue representation of a number with magnitude index
                 is reconsidered. The RNS with magnitude index were
                 first studied by Sasaki [16] and Rao [15] and then by
                 Barsi and Maestrini [5,6]. The range of a given RNS is
                 divided into intervals of equal width and the magnitude
                 of a number X is defined as a integer locating X into
                 one of such intervals. We have proposed algorithm which
                 detects and corrects multiple errors in residue number.
                 The algorithms for special cases viz., single burst
                 residue error and single residue error are also
                 suggested. Some of the advantages are pointed out over
                 the existing approaches.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@Article{Klatte:1985:ASS,
  author =       "R. Klatte and C. P. Ullrich and J. W. {Von
                 Gudenberg}",
  title =        "Arithmetic Specification for Scientific Computation in
                 {ADA}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "11",
  pages =        "996--1005",
  month =        nov,
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.1676532",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 08:33:34 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676532",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Kobayashi:1985:MTC,
  author =       "Hideaki Kobayashi",
  title =        "A Multioperand Two's Complement Addition Algorithm",
  crossref =     "Hwang:1985:PSC",
  pages =        "16--19",
  year =         "1985",
  bibdate =      "Wed Nov 14 18:06:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Kobayashi.pdf",
  abstract =     "This paper presents a novel algorithm for summing a
                 set of 2's complement numbers in parallel. The 2's
                 complement addition is converted to an equivalent
                 parallel summation of unsigned numbers. The conversion
                 is performed by simply complementing all the sign bits.
                 Only a few constant bits are required for sign
                 correction. This algorithm is suitable for
                 computer-aided design (CAD) of custom VLSI.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@Manual{Koopman:1985:FFP,
  author =       "Philip J. Koopman",
  title =        "{FORTH} floating point",
  volume =       "3",
  organization = "Mountain View Press",
  address =      "Mountain View, CA, USA",
  edition =      "Revised",
  pages =        "346",
  year =         "1985",
  ISBN =         "0-914699-28-8",
  ISBN-13 =      "978-0-914699-28-6",
  LCCN =         "????",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "MVP-FORTH books",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers --- Programming;
                 Floating-point arithmetic; FORTH (Computer program
                 language)",
  remark =       "Running title: MVP-FORTH integer and floating point
                 math. A complete glossary of MVP-FORTH math
                 extensions.",
}

@InProceedings{Kornerup:1985:FPL,
  author =       "Peter Kornerup and David W. Matula",
  title =        "Finite Precision Lexicographic Continued Fraction
                 Number Systems",
  crossref =     "Hwang:1985:PSC",
  pages =        "207--214",
  year =         "1985",
  bibdate =      "Wed Nov 14 18:06:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Kornerup_Matula.pdf",
  abstract =     "Lexicographic continued fraction binary (LCF)
                 representation provides an order preserving bitstring
                 representation of the non negative real numbers where
                 every rational number has a finite length bitstring
                 representation. We investigate the precision of $k$-bit
                 LCF approximation. The maximum gap size over $ [0, 1) $
                 for $ (k + 1) $-bit LCF representation is shown to be
                 less than $ 2^{0.81k} $, comparable to binary coded
                 decimal in worst case representation efficiency. The
                 distribution of gap sizes for $ (k + 1) $-bit LCF
                 representation over $ [0, 1] $ is shown on a
                 logarithmic scale to be bell shaped between $ 2^{0.81k}
                 $ and $ 2^{-1.39k} $, becoming more peaked near the
                 value corresponding to uniform spacing, $ 2^{-k} $,
                 with increasing $k$.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@InProceedings{Krishnan:1985:CDS,
  author =       "R. Krishnan and G. Jullien and W. Miller",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing, {ICASSP '85}",
  title =        "Complex digital signal processing using quadratic
                 residue number systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "764--767",
  year =         "1985",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1049/el:19850252",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Recently, the Quadratic Residue Number System (QRNS)
                 has been introduced [4,5,6], which allows the
                 multiplication of complex integers with two real
                 multiplications. Restrictions on the form of the moduli
                 can be removed if an increase in real \ldots{}",
}

@InProceedings{Kurokawa:1985:PT,
  author =       "Takakazu Kurokawa and Hideo Aiso",
  title =        "Polynomial Transformer",
  crossref =     "Hwang:1985:PSC",
  pages =        "153--158",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Kurokawa_Aiso.pdf",
  abstract =     "Any relations among finite fields can be transformed
                 to a unique polynomial of one variable using Galois
                 Fields. In this paper, we explain the design of a
                 ``Polynomial Transformer'' which executes the
                 transformation.\par

                 Polynomial Transformer consists of very simple and
                 iterative logic, and it is very suitable for parallel
                 and pipelined VLSI algorithm. Moreover, three
                 dimensional construction of a Polynomial Transformer is
                 possible. Thus, it serves as an example of a typical
                 three dimensional VLSI.\par

                 Its application can be found in Polynomial
                 Transformation, disturbance of data and so on.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@Article{Kwan:1985:MOW,
  author =       "Hon Kwan",
  title =        "A multi-output wave --- digital biquad using magnitude
                 truncation instead of controlled rounding",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "32",
  number =       "11",
  pages =        "1185--1187",
  month =        nov,
  year =         "1985",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 11:25:03 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "The use of magnitude truncation instead of controlled
                 rounding for the elimination of zero-input and
                 constant-input oscillations in the wave digital biquad
                 derived from the feedforwardRC-active configuration is
                 described. We also describe \ldots{}",
}

@Article{Lang:1985:ICL,
  author =       "J. H. Lang and C. A. Zukowski and R. O. Lamaire and
                 Chae Han",
  title =        "Integrated-Circuit Logarithmic Arithmetic Units",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "5",
  pages =        "475--483",
  month =        may,
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.1676588",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 08:32:33 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676588",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Li:1985:FCD,
  author =       "S.-Y. R. Li",
  title =        "Fast Constant Division Routines",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "9",
  pages =        "866--869",
  month =        sep,
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.1676646",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 08:33:33 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676646",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Li:1985:PAC,
  author =       "Xiaobo Li and Lionel M. Ni",
  title =        "A Pipeline Architecture for Computing Cumulative
                 Hypergeometric Distributions",
  crossref =     "Hwang:1985:PSC",
  pages =        "166--172",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Li_Ni.pdf",
  abstract =     "The hypergeometric distribution is a widely used
                 arithmetic function and is fundamental to many
                 statistical sampling and statistical pattern
                 recognition problems. Computation of the cumulative
                 hypergeometric distribution function, $ H(a) $, is
                 extremely time-consuming. As a result, many
                 approximation algorithms have been proposed to evaluate
                 the cumulative hypergeometric distribution. This paper
                 describes a two-level pipeline architecture for
                 computing $ H(a) $ with computation complexity reduced
                 to $ c + a $, where $c$ is a constant. The main part of
                 the design is a type of recurrence computation. A
                 modular and systematic approach is suggested to
                 implement the recurrence formula. The computation
                 complexity of the proposed architecture is also
                 compared with various other known methods. The highly
                 regular structure of the design can lead to efficient
                 VLSI implementation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@InProceedings{Ling:1985:NFL,
  author =       "Fuyun Ling and D. Manolakis and J. Proakis",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing: {ICASSP '85}",
  title =        "New forms of {LS} lattice algorithms and an analysis
                 of their round-off error characteristics",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1739--1742",
  year =         "1985",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "New formulas are presented for direct updating of the
                 reflection coefficients in the a priori and a
                 posteriori forms of the least squares (LS) lattice
                 algorithms. An analysis of the numerical
                 characteristics of the new LS lattice forms is given
                 and \ldots{}",
}

@InProceedings{Liu:1985:DVR,
  author =       "Wentai Liu and J. C. Duh and Daniel E. Atkins",
  title =        "The Design of a Vector-Radix {2DFFT} Chip",
  crossref =     "Hwang:1985:PSC",
  pages =        "231--236",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Liu_Duh_Atkins.pdf",
  abstract =     "Architectures based on the vector-radix 2DFFT
                 algorithm and hence can avoid the matrix transpose
                 problem have been proposed. The unique feature of the
                 proposed architectures is that the data can be driven
                 into the arithmetic processors in a pipeline fashion.
                 This paper presents a prototype chip, which has been
                 designed in $ 2 \mu $ m NMOS technology, for the
                 generalized butterfly unit. The chip is a two-stage
                 pipelined processor. The design experience, timing
                 information, and the chip features including four
                 multipliers, one adder\slash subtracter and PLA
                 controllers are presented.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@Article{Lohninger:1985:GF,
  author =       "H. Lohninger",
  title =        "{Gleitkommaarithmetik f{\"u}r den 68000} \toenglish
                 {Floating-point Arithmetic for the 68000}
                 \endtoenglish",
  journal =      j-MC,
  volume =       "2",
  pages =        "58--64",
  year =         "1985",
  ISSN =         "0720-4442, 0941-777x, 0943-5409",
  bibdate =      "Fri Sep 16 16:30:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "MC: Die Mikrocomputer-Zeitschrift",
}

@Article{Lorenz:1985:AIP,
  author =       "E. Lorenz",
  title =        "{Aspekte der Implementierung eines Programmpaketes zur
                 schnellen und flexiblen Ausf{\"u}hrung von
                 arithmetischen Operationen mit dem U880} \toenglish
                 {Aspects of the Implementation of a Software Package
                 for Fast and Flexible Execution of Arithmetic
                 Operations on the U880} \endtoenglish",
  journal =      j-NACH-ELEK,
  volume =       "35",
  number =       "5",
  pages =        "179--181",
  month =        "????",
  year =         "1985",
  CODEN =        "NTELAP",
  ISSN =         "0323-4657",
  bibdate =      "Fri Sep 16 16:30:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "The U880 is a Z80 clone microprocessor that was built
                 in the GDR (East Germany).",
  acknowledgement = ack-nj,
  fjournal =     "Nachrichtentechnik Elektronik",
}

@InProceedings{Luk:1985:PMC,
  author =       "Franklin T. Luk",
  title =        "A Parallel Method for Computing the Generalized
                 Singular Value Decomposition",
  crossref =     "Hwang:1985:PSC",
  pages =        "260--265",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Luk.pdf",
  abstract =     "We describe a new parallel algorithm for computing the
                 generalized singular value decomposition of two $ n
                 \times n $ matrices, one of which is nonsingular. Our
                 procedure requires $ O(n) $ e time and one triangular
                 array of $ O(n^2) $ processors.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@Article{Majerski:1985:SRA,
  author =       "S. Majerski",
  title =        "Square-Rooting Algorithms for High-Speed Digital
                 Circuits",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "8",
  pages =        "724--733",
  month =        aug,
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.1676618",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 08:33:17 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676618",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Matula:1985:FPR,
  author =       "David W. Matula and Peter Kornerup",
  title =        "Finite Precision Rational Arithmetic: Slash Number
                 Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "1",
  pages =        "3--18",
  month =        jan,
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.1676511",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 30 06:21:13 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  abstract =     "Fraction number systems characterized by fixed-slash
                 and floating-slash formats are specified. The structure
                 of arithmetic over such systems is prescribed by the
                 rounding obtained from ``best rational approximation.''
                 Multitiered precision hierarchies of both the
                 fixed-slash and floating-slash type are described and
                 analyzed with regards to their support of both exact
                 rational and approximate real computation.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Manual{ME:1985:FPS,
  title =        "Floating point and string listing",
  organization = "Microprocessor Engineering",
  address =      "Southampton, UK",
  edition =      "Second",
  pages =        "36",
  year =         "1985",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers --- Programming.;
                 Floating-point arithmetic.",
}

@Article{Mithani:1985:ASN,
  author =       "D. Mithani and S. Iyer",
  title =        "Algorithm speeds nonrestoring division in
                 microprogrammed systems",
  journal =      j-EDN,
  volume =       "30",
  number =       "4",
  pages =        "199--208",
  month =        feb,
  year =         "1985",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 15 18:42:21 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}

@Article{Modi:1985:AIS,
  author =       "J. J. Modi and J. S. Rollett",
  title =        "An algorithm for inverse square-roots",
  journal =      j-PARALLEL-COMPUTING,
  volume =       "2",
  number =       "1",
  pages =        "69--71",
  month =        mar,
  year =         "1985",
  CODEN =        "PACOEJ",
  DOI =          "https://doi.org/10.1016/0167-8191(85)90018-3",
  ISSN =         "0167-8191 (print), 1872-7336 (electronic)",
  ISSN-L =       "0167-8191",
  MRclass =      "65W05 (65D15)",
  MRnumber =     "86j:65195",
  bibdate =      "Mon Apr 14 12:07:40 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "An algorithm is presented for finding $ x^{ 1 / 2} $,
                 given $x$. The algorithm is designed to be particularly
                 suited for parallel computation, in which
                 floating-point multiplication, floating-point addition
                 and fixed-point arithmetic can be performed
                 simultaneously.",
  acknowledgement = ack-nhfb,
  classification = "C4290 (Other computer theory)",
  corpsource =   "Department of Eng., Cambridge University, UK",
  fjournal =     "Parallel Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01678191",
  keywords =     "fixed-point arithmetic; floating-point addition;
                 floating-point multiplication; inverse square roots
                 algorithm; parallel computation; parallel processing",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Moharir:1985:ESG,
  author =       "P. S. Moharir",
  title =        "Extending the Scope of {Golub}'s Method Beyond Complex
                 Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "5",
  pages =        "484--487",
  month =        may,
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.1676590",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 08:32:33 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676590",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Montgomery:1985:MMT,
  author =       "Peter L. Montgomery",
  title =        "Modular Multiplication Without Trial Division",
  journal =      j-MATH-COMPUT,
  volume =       "44",
  number =       "170",
  pages =        "519--521",
  month =        apr,
  year =         "1985",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11Y16",
  MRnumber =     "86e:11121",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2007970",
  abstract =     "Let $ N > 1 $. We present a method for multiplying two
                 integers (called $N$-residues) modulo $N$ while
                 avoiding division by $ N. N $-residues are represented
                 in a nonstandard way, so this method is useful only if
                 several computations are done modulo one $N$. The
                 addition and subtraction algorithms are unchanged.",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "C1160 (Combinatorial mathematics); C5230 (Digital
                 arithmetic methods); C6130 (Data handling techniques)",
  corpsource =   "Syst. Dev. Corp., Santa Monica, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "digital arithmetic; integer; integer arithmetic;
                 modular arithmetic; modular multiplication;
                 multiplication; N-residue; N-residue arithmetic; number
                 theory",
  treatment =    "T Theoretical or Mathematical",
}

@Manual{Motorola:1985:MFC,
  title =        "{MC68881} floating-point coprocessor user's manual",
  organization = "Motorola, Inc.",
  address =      "Phoenix, AZ, USA",
  pages =        "various",
  year =         "1985",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Microprocessors --- Handbooks, manuals, etc.",
  remark =       "Spine title: MC68881 user's manual. ``MC68881
                 UM/AD''--Cover.",
}

@Book{Motorola:1985:MFP,
  author =       "Motorola",
  title =        "{MC68881} Floating-Point Coprocessor User's Manual",
  publisher =    pub-MOTOROLA,
  address =      pub-MOTOROLA:adr,
  edition =      "Second",
  year =         "1985",
  bibdate =      "Fri Sep 02 23:38:03 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Muller:1985:DBC,
  author =       "Jean-Michel Muller",
  title =        "Discrete basis and computation of elementary
                 functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "9",
  pages =        "857--862",
  month =        sep,
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.1676643",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "65D20 (65V05)",
  MRnumber =     "87e:65016",
  MRreviewer =   "D. Zwick",
  bibdate =      "Sun Jul 10 08:33:33 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676643",
  abstract =     "We give necessary and sufficient conditions in order
                 that the infinite product or sum of the terms of a
                 positive decreasing sequence generates the reals in a
                 given interval.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Naseem:1985:MCA,
  author =       "Asif Naseem and P. David Fisher",
  title =        "The Modified {CORDIC} Algorithm",
  crossref =     "Hwang:1985:PSC",
  pages =        "144--152",
  year =         "1985",
  bibdate =      "Wed Sep 14 20:50:04 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Naseem_Fisher.pdf",
  abstract =     "A Modified CORDIC Algorithm (MCA) has been developed
                 for the evaluation of elementary arithmetic functions.
                 MCA incorporates increased parallelism over the
                 original CORDIC algorithm, thus, resulting in an
                 enhanced speed of computation. This has been
                 accomplished by decoupling the CORDIC iteration
                 equations, and transforming the sequential nature of
                 these equations. $n$-bit fixed point data operands are
                 assumed and the parameter $k$ relates to the level of
                 parallelism in the algorithm. The modified algorithm
                 employs a $ [k + 1]n^2 $-bit ROM for lookup tables that
                 enable elementary arithmetic functions to be evaluated
                 in no more than $ [3 n + 2] $ and no less than $2$ time
                 steps. The two bounds correspond to a pipelined and a
                 parallel implementation, respectively. The formulation
                 of the MCA can be manipulated to obtain implementations
                 with various speed\slash cost characteristics. This
                 compares to $ n(3 n + 1) / 2 $ time steps for the
                 original CORDIC algorithm. For example, 32-bit ALU has
                 $ k = 12 $ and $ n = 32 $; so, a 13,312-bit ROM is
                 required to store the lookup tables, and the
                 computation requires 98 time steps for a pipelined
                 implementation.",
  acknowledgement = ack-nj,
  keywords =     "ARITH-7",
}

@Article{Neumaier:1985:IPR,
  author =       "A. Neumaier",
  title =        "Inner Product Rounding Error Analysis in the Presence
                 of Underflow",
  journal =      j-COMPUTING,
  volume =       "34",
  number =       "4",
  pages =        "365--373",
  year =         "1985",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65G05",
  MRnumber =     "86j:65054",
  bibdate =      "Tue Oct 12 16:33:42 MDT 1999",
  bibsource =    "Compendex database;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ Freiburg, Inst f{\"u}r Angewandte Mathematik,
                 Freiburg, West Germany",
  classification = "723; 921",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Computing (Vienna/New York)",
  keywords =     "computer metatheory; inner product rounding error
                 analysis; inner products; mathematical techniques ---
                 error analysis; underflow",
}

@InProceedings{Ngai:1985:RAT,
  author =       "Tin-Fook Ngai and Mary Jane Irwin",
  title =        "Regular, area-time efficient carry-lookahead adders",
  crossref =     "Hwang:1985:PSC",
  pages =        "9--15",
  year =         "1985",
  bibdate =      "Fri Nov 16 10:05:44 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Ngai_Irwin.pdf",
  abstract =     "For fast binary addition, a carrylookahead (CLA)
                 design is the obvious choice [OnAt83, BaJM83]. However,
                 the direct implementation of a CLA adder in VLSI faces
                 some undesirable limitations. Either the design lacks
                 regularity, thus increasing the design and
                 implementation costs, or the interconnection wires are
                 too long, thus causing area-time inefficiency and
                 limits on the size of addition. Brent and Kung solved
                 the regularity problem by reformulating the carry chain
                 computation [BrKu82]. They showed that an $n$-bit
                 addition can be performed in time $ O(\log n) $, using
                 area $ O(n \log n) $ with maximum interconnection wire
                 length $ O(n) $. In this paper, we give an alternative
                 $ \log n $ stage design which is nearly optimum with
                 respect to regularity, area-time efficiency, and
                 maximum interconnection wire length.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@Article{Ni:1985:VRT,
  author =       "L. M. Ni and Kai Hwang",
  title =        "Vector-Reduction Techniques for Arithmetic Pipelines",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "5",
  pages =        "404--411",
  month =        may,
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.1676580",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 08:32:26 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676580",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Ohhashi:1985:HSC,
  author =       "M. Ohhashi and R. E. Schneider",
  title =        "High-Speed Computation of Unary Functions",
  crossref =     "Hwang:1985:PSC",
  pages =        "82--85",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Ohhashi_Schneider.pdf",
  abstract =     "This paper presents an architecture for fast
                 evaluation of unary functions such as reciprocal,
                 square root and reciprocal square root. The theory
                 behind the architecture has been presented in [1]. The
                 paper shows the results of extensive simulation that
                 have allowed us to implement the architecture with
                 minimum chip count and maximum accuracy. The accuracy
                 is about 8\% error rate in the LSB of the chosen
                 representation (IEEE 32-bit floating point format).
                 This architecture allows the computation of unary
                 functions in less than 200 nsec.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@InProceedings{Oklobdzija:1985:SOS,
  author =       "Vojin G. Oklobdzija and Earl R. Barnes",
  title =        "Some Optimal Schemes for {ALU} Implementations in
                 {VLSI} Technology",
  crossref =     "Hwang:1985:PSC",
  pages =        "2--8",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Oklobdzija_Barnes.pdf",
  abstract =     "An efficient scheme for carry propagation in an ALU
                 implemented in n-MOS technology is presented. An
                 algorithm that determines the optimum division of the
                 carry chain of a parallel adder for various data path
                 sizes is developed. This yields an implementation of a
                 fast ALU which due to its regular structure occupies a
                 modest amount of silicon. The speed of the
                 implementation described is comparable to the carry
                 look-ahead scheme. Our method is based on the
                 optimization of the carry path implemented in n-MOS
                 technology but the results can be applied to other
                 technologies.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@Book{Palmer:1985:MGN,
  author =       "John F. Palmer and Stephen P. Morse",
  title =        "{Die mathematischen Grundlagen der Numerik-Prozessoren
                 8087\slash 80287}",
  publisher =    pub-TEWI,
  address =      pub-TEWI:adr,
  pages =        "240",
  year =         "1985",
  ISBN =         "3-921803-33-0",
  ISBN-13 =      "978-3-921803-33-2",
  LCCN =         "????",
  bibdate =      "Wed Sep 07 21:14:32 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "German translation of {\em The 8087 Primer}
                 \cite{Palmer:1984:P}.",
  acknowledgement = ack-nj,
}

@Misc{Palmer:1985:PBS,
  author =       "John Palmer and Bruce Ravenel and Ravi Nave",
  title =        "Programmable Bidirectional Shifter",
  howpublished = "US Patent 4,509,144.",
  day =          "2",
  month =        apr,
  year =         "1985",
  bibdate =      "Sat Aug 23 06:44:00 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Filed 5 December 1983. See discussion
                 \cite{Shirriff:2020:AMC}.",
  URL =          "https://ieeemilestones.ethw.org/w/images/a/a4/Patent_Barrel_shifter_8087.pdf",
  abstract =     "A programmable bidirectional shifter is disclosed
                 comprised of a first bidirectional load and read
                 interface circuit selectively activated for left
                 shifts, and a similarly constituted second
                 bidirectional load and interface circuit which is
                 selectively activated for right shifts. The first
                 interface circuit is coupled to a byte shift matrix
                 while the second interface circuit is coupled to a bit
                 shift matrix. The byte shift matrix is arranged and con
                 figured to shift the input quantity by a multiple of
                 bytes, namely multiples of eight bits. The bit shift
                 matrix is similarly constituted to shift its input
                 quantity by a selected number of bit locations up to
                 seven consecutive places. The bit and byte shift
                 matrices are coupled to allow bidirectional flow of
                 signals there between. The bit and byte matrix are
                 controlled by a bit and byte shift control circuit
                 respectively which determines the number of bytes and
                 bit places each matrix will actually shift.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Papachristou:1985:MIR,
  author =       "Christos A. Papachristou",
  title =        "Multi-Input Residue Arithmetic Utilizing Read-Only
                 Associate Memory",
  crossref =     "Hwang:1985:PSC",
  pages =        "182--188",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Papachristou.pdf",
  abstract =     "In this paper an approach to residue arithmetic is
                 presented using Read-Only-Associative Memories (ROAMs),
                 such as PLAs. These memories have considerable
                 advantages for table lookup arithmetic processing over
                 the conventional ROMs in terms of their storage and
                 time efficiency. In residue arithmetic, the ROAM
                 storage required largely depends on the residue
                 recurrences in arithmetic tables modulo $M$. After
                 reviewing recent results on the computation of
                 recurrences, a scheme is proposed for implementing
                 residue arithmetic based on ROAMs. The efficiency of
                 the scheme is established by comparison to conventional
                 ROM-based table lookup techniques. Applications to
                 residue-to-binary number system conversion are also
                 discussed.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@Article{Parker:1985:GCI,
  author =       "J. R. Parker",
  title =        "A General Character to Integer Conversion Method",
  journal =      j-SPE,
  volume =       "15",
  number =       "8",
  pages =        "761--766",
  month =        aug,
  year =         "1985",
  CODEN =        "SPEXBL",
  DOI =          "https://doi.org/10.1002/spe.4380150804",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Sat May 31 13:36:16 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/spe.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Software --- Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  keywords =     "algorithms; integer overflow detection; languages;
                 programming techniques; type conversion",
  review =       "ACM CR 8603-0209",
  subject =      "D.1.m Software, PROGRAMMING TECHNIQUES,
                 Miscellaneous",
}

@InProceedings{Pellegrino:1985:RNS,
  author =       "J. M. Pellegrino and B. M. Sadler and S. D. Casey",
  editor =       "Bruce Ronald McAvoy",
  booktitle =    "{IEEE 1985 Ultrasonics Symposium: proceedings, October
                 16--18, 1985, Cathedral Hill Hotel, Van Ness at Geary,
                 San Francisco, CA}",
  title =        "A Residue Number System for Wideband Acousto-Optic
                 Spectrum Analysis",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "385--390",
  year =         "1985",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1049/el:19850252",
  ISSN =         "????",
  LCCN =         "A367 .U46 1985eb",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog number 85CH2209-5.",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
}

@PhdThesis{Peralta:1985:TRN,
  author =       "Rene Caupolican Peralta",
  title =        "Three results in number theory and cryptography: a new
                 algorithm to compute square roots modulo a prime
                 number; On the bit complexity of the discrete
                 logarithm; {A} framework for the study of
                 cryptoprotocols",
  type =         "Thesis ({Ph.D.})",
  school =       "Department of Computer Science, University of
                 California, Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "52",
  month =        dec,
  year =         "1985",
  LCCN =         "????",
  bibdate =      "Sat Oct 17 16:25:07 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "dissertations; dissertations, academic --- UCB ---
                 computer science --- 1981--1990; University of
                 California, Berkeley. computer science division --",
}

@Article{Raimi:1985:FDP,
  author =       "Ralph A. Raimi",
  title =        "The First Digit Phenomenon Again",
  journal =      j-PROC-AMER-PHIL-SOC,
  volume =       "129",
  number =       "2",
  pages =        "211--219",
  month =        jun,
  year =         "1985",
  CODEN =        "PAPCAA",
  ISSN =         "0003-049X (print), 2326-9243 (electronic)",
  ISSN-L =       "0003-049X",
  bibdate =      "Sat Nov 12 16:56:54 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "This paper contains strong criticism of a derivation
                 of Benford's Law \cite{Logan:1978:FDP}.",
  URL =          "http://www.jstor.org/stable/986989",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the {American Philosophical Society}
                 held at {Philadelphia} for promoting useful knowledge",
  journal-URL =  "http://www.jstor.org/journal/procamerphilsoci",
  remark =       "This paper contains mathematical derivations of both
                 Stigler's Law and Benford's Law. Raimi comments on p.
                 217: ``the Benford law itself as a conclusion to be
                 derived is by no means as firm as Kepler's planetary
                 curves. Indeed, it has been pointed out by Diaconis and
                 Freedman [D-F] [\cite{Diaconis:1979:RP}] that a
                 statistical analysis of Benford's announced data gives
                 a high probability to the conjecture that he did a bit
                 of rounding-off here and there, always in the direction
                 of his law. The license that a physicist often takes on
                 the path from his hypotheses to verified, observable,
                 and repeatable conclusion is not justified here.''.",
}

@Article{Ramnarayan:1985:LMR,
  author =       "R. Ramnarayan and F. Taylor",
  title =        "On large moduli residue number system recursive
                 digital filters",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "32",
  number =       "4",
  pages =        "349--359",
  month =        apr,
  year =         "1985",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23567",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The three moduli set{2^{n} - 1, 2^{n},2^{n} +
                 1}residue number system, or RNS, has recently been
                 shown to possess several attractive properties. In
                 particular, the problem of scaling is much simplified
                 through the use of an autoscale \ldots{}",
}

@InProceedings{Rao:1985:CCC,
  author =       "T. R. N. Rao and Kasem Vathanvit",
  title =        "A Class of {$ A(N + C) $} Codes and Its Properties",
  crossref =     "Hwang:1985:PSC",
  pages =        "293--295",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Rao_Vathanvit.pdf",
  abstract =     "We discuss here a new class of arithmetic codes,
                 called $ A(N + C) $ codes where $A$ and $C$ are
                 constant positive integers, $N$ is information to be
                 coded. $ A(N + C) $ codes are a special case of $ A N +
                 B $ arithmetic codes which were first studied by Brown.
                 $ A N $ codes are linear and cannot be used to detect
                 unidirectional multiple errors. $ A(N + C) $ codes are
                 non-linear and are useful for detecting and\slash or
                 correcting symmetric errors, arithmetic errors and
                 unidirectional errors. Furthermore, $ A(N + C) $ codes
                 can be constructed to provide constant-weight,
                 self-complementing and cyclic-code properties. It is
                 apparent that the codes with these properties have, in
                 some sense, broader capabilities of error detection and
                 error correction.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@InProceedings{Reed:1985:VRM,
  author =       "I. S. Reed and T. K. Truong and J. J. Chang and H. M.
                 Shao and I. S. Hsu",
  title =        "{VLSI} Residue Multiplier Modulo a {Fermat} Number",
  crossref =     "Hwang:1985:PSC",
  pages =        "203--206",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Reed_Truong_Chang_Shao_Hsu.pdf",
  abstract =     "Multiplication is central in the implementation of
                 Fermat number transforms (FNT) and other residue number
                 algorithms. There is need for a good multiplication
                 algorithm which can be realized easily on a VLSI chip.
                 In this paper, the Leibowitz multiplier [1] is modified
                 to realize multiplication in the ring of integers
                 modulo a Fermat number. The advantage of this new
                 algorithm over Leibowitz's algorithm is that
                 Leibowitz's algorithm takes modulo after the product of
                 multiplication is obtained. Hence time is wasted. In
                 this new algorithm, modulo is taken in every bit
                 operation when performing multiplication. Therefore no
                 time is wasted in this respect. Furthermore, this
                 algorithm requires only a sequence of cyclic shifts and
                 additions. The design[s] for this new multiplier are
                 regular, simple, expandable and therefore, suitable far
                 VLSI implementation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@InProceedings{Rump:1985:HOC,
  author =       "Siegfried M. Rump",
  title =        "Higher Order Computer Arithmetic",
  crossref =     "Hwang:1985:PSC",
  pages =        "302--308",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Rump.pdf",
  abstract =     "The floating-point arithmetic on computers is designed
                 to approximate the corresponding operations over the
                 real numbers as close as possible. In this paper it is
                 shown by means of counterexamples that this need not be
                 true for existing machines. For achieving good
                 numerical results a floating-point arithmetic
                 approximating the real operations as close as possible
                 is probably best. For achieving verifications on
                 computers, at least a precisely defined computer
                 arithmetic is indispensable.\par

                 In this paper we first introduce the Kulisch\slash
                 Miranker theory, which represents a sound basis for
                 computer arithmetic. Each operation is precisely
                 defined and, moreover, is of maximum accuracy. That
                 means, the computed result is the floating-point number
                 of the working precision closest to the infinite
                 precise result. The theory also covers directed
                 roundings allowing computations with intervals. These
                 properties hold true for the floating-point numbers of
                 single and double precision as well as for the vectors,
                 matrices and complex extensions over those.\par

                 In the second part of the paper we demonstrate the
                 theoretical basis for what we call 'Higher Order
                 Computer Arithmetic'. This is an inclusion theory
                 allowing the development of algorithms to compute
                 bounds for the solution of various problems in
                 numerical analysis. These bounds are automatically
                 verified to be correct and they are of high accuracy.
                 Very often they are of maximum accuracy, that means the
                 left and right bounds of all components of the solution
                 are adjacent in the floating-point screen. Moreover
                 existence and uniqueness of a solution within the
                 computed bounds is automatically verified by the
                 algorithm. If this verification is not possible, a
                 respective message is given. We develop the theory and
                 give algorithms for the solution of systems of linear
                 and nonlinear equations. As demonstrated by examples
                 even for extremely ill-conditioned problems existence
                 and uniqueness of the solution is verified within
                 bounds of least significant bit accuracy.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@Article{Salomon:1985:TGF,
  author =       "D. Salomon",
  title =        "Two generalized floating-point representations",
  journal =      j-BYTE,
  volume =       "10",
  number =       "9",
  pages =        "154--158",
  month =        sep,
  year =         "1985",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "BYTE Magazine",
  genterm =      "ALGORITHMS; DESIGN",
  guideno =      "03372",
}

@InProceedings{Schaeffer:1985:SPE,
  author =       "Jonathan Schaeffer and Darrell Makarenko",
  title =        "Systolic Polynomial Evaluation and Matrix
                 Multiplication with Multiple Precision",
  crossref =     "Hwang:1985:PSC",
  pages =        "110--117",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Schaeffer_Makarenko.pdf",
  abstract =     "The design and implementation of a systolic VLSI
                 multi-precision polynomial evaluator and matrix
                 multiplier is described. The use of bit-serial
                 arithmetic allows for a very simple cell design (two
                 registers and an accumulator) enabling a substantial
                 number of cells to be placed on a chip. A configuration
                 of $ N^2 $ cells can evaluate $N$ polynomials of $N$
                 coefficients at $N$ points and perform $N$-width band
                 matrix multiplication and $ N \times N $ full matrix
                 multiplication, each in linear time. Using current
                 technology, 100 polynomials of 100 coefficients can be
                 evaluated at 100 data points with 32 bit precision in
                 an estimated one millisecond.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@Article{Schoof:1985:ECF,
  author =       "Ren{\'e} Schoof",
  title =        "Elliptic Curves Over Finite Fields and the Computation
                 of Square Roots $ \operatorname {mod} p $",
  journal =      j-MATH-COMPUT,
  volume =       "44",
  number =       "170",
  pages =        "483--494",
  month =        apr,
  year =         "1985",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11Y16 (11G20 14G15)",
  MRnumber =     "86e:11122",
  MRreviewer =   "Karl Rubin",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "B0250 (Combinatorial mathematics); B0290D (Functional
                 analysis); C1160 (Combinatorial mathematics); C4120
                 (Functional analysis); C4240 (Programming and algorithm
                 theory)",
  corpsource =   "Amsterdam University, Netherlands",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "computational complexity; deterministic algorithm;
                 elliptic curve; F/sub q/-points; finite fields;
                 function evaluation; number theory; square roots mod p;
                 Weierstrass equation",
  treatment =    "T Theoretical or Mathematical",
}

@Book{Scott:1985:CNS,
  author =       "Norman R. Scott",
  title =        "Computer Number Systems and Arithmetic",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "x + 254",
  year =         "1985",
  ISBN =         "0-13-164211-1",
  ISBN-13 =      "978-0-13-164211-9",
  LCCN =         "QA76.9.C62 S38 1985",
  bibdate =      "Thu Sep 1 10:14:05 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Shah:1985:PHS,
  author =       "A. Shah and M. Sid-Ahmed and G. Jullien",
  title =        "A proposed hardware structure for two-dimensional
                 recursive digital filters using the residue number
                 system",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "32",
  number =       "3",
  pages =        "285--288",
  month =        mar,
  year =         "1985",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23566",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A hardware structure is proposed for implementing
                 two-dimensional ($2$-D) recursive digital filters based
                 on the residue number system (RNS). The parallel
                 pipelined structure arising from the use of RNS
                 arithmetic facilitates video bandwidth filtering.
                 \ldots{}",
}

@Article{Shimada:1985:NAC,
  author =       "R. Shimada and Y. Ohkura and J. Aoe",
  title =        "Nonbinary Arithmetic {AN} Codes Using Odd Radix
                 Expressions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "11",
  pages =        "1050--1056",
  month =        nov,
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.1676538",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 08:33:37 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676538",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Smith:1985:DFI,
  author =       "S. P. Smith and H. C. Torng",
  title =        "Design of a Faster Inner Product Processor",
  crossref =     "Hwang:1985:PSC",
  pages =        "38--43",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Smith_Torng.pdf",
  abstract =     "This paper presents the design of a fast inner product
                 processor, with appreciably reduced latency and cost.
                 The inner product processor is implemented with a tree
                 of carry propagate or carry save adders; this tree is
                 obtained with the incorporation of three innovations in
                 the conventional multiply/add tree:\par

                 (1) The leaf-multipliers are expanded into adder
                 subtrees, thus achieving an $ O(\log N b) $ latency,
                 where $N$ denotes the number of elements in a vector
                 and $b$ the number of bits in each element.\par

                 (2) The partial products, to be summed in producing an
                 inner product, are reordered according to their
                 ``minimum alignments'' bringing approximately a 20\%
                 saving in hardware.\par

                 (3) The reordering also truncates the carry propagation
                 chain in the final propagation stage by $ 2 \log b - 1
                 $ positions, significantly reducing the latency
                 further. A form of the Baugh and Wooley algorithm is
                 adopted to implement two's complement notation with
                 changes only in peripheral hardware.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@Article{Smith:1985:FIP,
  author =       "S. P. Smith and H. C. Torng",
  title =        "A fast inner product processor based on equal
                 alignments",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "2",
  number =       "4",
  pages =        "376--390",
  month =        nov,
  year =         "1985",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliationaddress = "Cornell Univ, Ithaca, NY, USA",
  classification = "713; 723; 921; B0290H (Linear algebra); B1265F
                 (Microprocessors and microcomputers); B2570
                 (Semiconductor integrated circuits); C4140 (Linear
                 algebra); C5130 (Microprocessor chips); C5230 (Digital
                 arithmetic methods)",
  corpsource =   "Sch. of Electr. Eng., Cornell University, Ithaca, NY,
                 USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "adder subtrees; Algorithms; alignments; Baugh and
                 Wooley algorithm; carry-; carry-propagate adder tree;
                 computer metatheory --- Boolean Algebra; computer
                 programming; computers --- Multiplying Circuits;
                 digital arithmetic; equal alignments; fast inner
                 product processor; free of carry-propagate or
                 carry-save adders; inner product processor; integrated
                 circuits, VLSI; leaf-multipliers; matrix algebra;
                 matrix multiplications; microprocessor chips; minimum;
                 satellite computers; save adders; special purpose
                 computers; two's complement notation; VLSI",
  treatment =    "P Practical",
}

@TechReport{Spafford:1985:RAS,
  author =       "Eugene Howard Spafford",
  title =        "A report on the accuracy of some floating point math
                 functions on selected computers",
  institution =  "School of Information and Computer Science, Georgia
                 Institute of Technology",
  address =      "Atlanta, GA, USA",
  pages =        "26",
  year =         "1985",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "GIT-ICS; 85/06",
  acknowledgement = ack-nhfb,
  keywords =     "Operating systems (Computers)",
}

@Article{Sreedharan:1985:ASS,
  author =       "J. Sreedharan and A. Dhurkadas",
  title =        "8086 algorithm solves square roots",
  journal =      j-EDN,
  volume =       "30",
  number =       "7",
  pages =        "272",
  month =        apr,
  year =         "1985",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 1 10:15:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}

@Article{Stewart:1985:NCD,
  author =       "G. W. Stewart",
  title =        "A Note on Complex Division",
  journal =      j-TOMS,
  volume =       "11",
  number =       "3",
  pages =        "238--241",
  month =        sep,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214408.214414",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Aug 26 23:38:15 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also \cite{Stewart:1986:CNC}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p238-stewart/",
  abstract =     "An algorithm for computing the quotient of two complex
                 numbers is modified to make it more robust in the
                 presence of underflows.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; complex arithmetic; computer arithmetic;
                 na",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Reliability and robustness.",
}

@Article{Stummel:1985:FEA,
  author =       "Friedrich Stummel",
  title =        "Forward error analysis of {Gaussian} elimination. {I}.
                 Error and residual estimates",
  journal =      j-NUM-MATH,
  volume =       "46",
  number =       "3",
  pages =        "365--395",
  year =         "1985",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65G05 (65F10)",
  MRnumber =     "87d:65054a",
  MRreviewer =   "Karl-Heinz Bachmann",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290B (Error analysis in numerical methods); C4110
                 (Error analysis in numerical methods)",
  corpsource =   "Fachbereich Math., Johann Wolfgang Goethe-University,
                 Frankfurt, West Germany",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "absolute errors; arithmetic floating-point operations;
                 associated optimal component-wise error; coefficient
                 matrices; condition numbers; data perturbations; error
                 analysis; error estimates; first order approximations;
                 forward error analysis; Gaussian elimination; general
                 linear algebraic systems; linearization method; matrix
                 norms; perturbation theory; residual estimates;
                 rounding errors; superposition; vector norms",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Swartzlander:1985:AHS,
  author =       "Earl {Swartzlander, Jr.} and John Eldon",
  title =        "Arithmetic for High Speed {FFT} Implementation",
  crossref =     "Hwang:1985:PSC",
  pages =        "223--230",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Swartzlander_Eldon.pdf",
  abstract =     "This paper describes recent progress in the
                 implementation of high speed spectrum analysis systems
                 with state-of-the-art commercial and semi-custom VLSI
                 circuits. Initial efforts are producing Fast Fourier
                 Transform (FFT) and inverse FFT processors that operate
                 at data rates of up to 40 MHz (complex). The current
                 implementation computes transforms of up to 16,384
                 points in length by means of the radix 4 pipeline FFT
                 algorithm. The interstage reordering is performed by
                 delay commutators implemented with semi-custom VLSI,
                 while the arithmetic is performed by commercial single
                 chip 22 bit floating point adders and multipliers. This
                 paper explains the pipeline FFT implementation and
                 focuses attention on the arithmetic used to realize the
                 design.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@Manual{Symbolics:1985:RGS,
  title =        "Reference Guide to {Symbolics-Lisp}",
  organization = "Symbolics, Inc.",
  address =      "Cambridge, MA, USA",
  month =        mar,
  year =         "1985",
  bibdate =      "Wed Jan 29 17:06:41 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "From \cite{Steele:2004:RHP}: ``The number of digits
                 printed is the `correct' number\ldots{}''",
}

@Article{Takagi:1985:HSV,
  author =       "N. Takagi and H. Yasuura and S. Yajima",
  title =        "High-speed {VLSI} multiplication algorithm with a
                 redundant binary addition tree",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "9",
  pages =        "789--796",
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.1676634",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Sep 16 16:29:25 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Takeda:1985:SCB,
  author =       "K. Takeda and F. Ishino and Y. Ito and T. Nakashima",
  title =        "A single-chip 80-bit floating point processor",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "20",
  number =       "5",
  pages =        "986--992",
  month =        oct,
  year =         "1985",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "A single-chip 80-bit floating point VLSI processor
                 capable of performing 5.6 million floating point
                 operations per second has been realized using
                 1.2-$\mu$m n-well CMOS technology. The processor
                 handles 80-bit double-extended floating point data
                 \ldots{}",
}

@InProceedings{Taniguchi:1985:TDI,
  author =       "Kenji Taniguchi",
  title =        "Three Dimensional {IC}'s and Application to High Speed
                 Image Processor",
  crossref =     "Hwang:1985:PSC",
  pages =        "216--222",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Taniguchi.pdf",
  abstract =     "Present state-of-the-art 3-D IC fabrication
                 technologies are reviewed. Both short interconnection
                 wiring inherent to 3-D structure and parallel
                 processing architecture offer high performance for 3-D
                 integrated circuit. An idea of a high speed image
                 sensor composed of six layers is proposed.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@Article{Taylor:1985:HFP,
  author =       "F. Taylor",
  title =        "A hybrid floating-point logarithmic number system
                 processor",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "32",
  number =       "1",
  pages =        "92--95",
  month =        jan,
  year =         "1985",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "The attributes of the traditional floating-point
                 processor and the logarithmic number system are
                 combined. The result is a hybrid system which offers
                 some advantages over the familiar floating-point
                 system. The new system, called the(FU)^{2}",
}

@InProceedings{Taylor:1985:MER,
  author =       "Fred J. Taylor",
  title =        "A More Efficient Residue Arithmetic Implementation of
                 the {FFT}",
  crossref =     "Hwang:1985:PSC",
  pages =        "243--250",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Taylor1.pdf",
  abstract =     "After 20 years, the FFT remains restricted in its real
                 time capabilities. To overcome this throughput
                 obstacle, fast residue arithmetic units are studied
                 based on several recent innovations in the field of
                 complex finite rings. A dedicated machine is designed
                 which makes use of these new results and is compared to
                 conventional FFT designs. Using high speed
                 semiconductor memory to implement the required residue
                 arithmetic mappings, speed and complexity metrics of a
                 basic FFT unit are shown to be improved. However, the
                 derived architecture and arithmetic introduce a new and
                 challenging set of magnitude scaling problems. They are
                 resolved with the result being an integrated residue
                 arithmetic FFT system capable of supporting very high
                 real time data rates.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@Article{Taylor:1985:RFU,
  author =       "F. J. Taylor and G. Papadourakis and A. Skavantzos and
                 A. Stouraitis",
  title =        "A Radix-4 {FFT} Using Complex {RNS} Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-34",
  number =       "6",
  pages =        "573--576",
  month =        jun,
  year =         "1985",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1985.5009414",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 10 08:32:52 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009414",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Taylor:1985:RSD,
  author =       "George S. Taylor",
  title =        "Radix 16 {SRT} dividers with overlapped quotient
                 selection stages: a 225 Nanosecond Double Precision
                 Divider for the {S-1 Mark IIB}",
  crossref =     "Hwang:1985:PSC",
  pages =        "64--71",
  year =         "1985",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Taylor.pdf",
  abstract =     "This paper compares the three simplest SRT division
                 methods by using them to design a divider that produces
                 four quotient bits per cycle (radix 16). The three
                 methods are distinguished by the number of bits found
                 per stage of quotient selection logic:\par

                 (a) one bit per stage (radix 2) with quotient digits
                 chosen from the set $ \{ - 1, 0, 1 \} $,\par

                 (b) two bits per stage (radix 4) with quotient digits $
                 \{ - 2, - 1, 0, 1, 2 \} $, or\par

                 (c) two bits per stage (radix 4) with quotient digits $
                 \{ - 3, - 2, - 1, 0, 1, 2, 3 \} $.\par

                 For each method, we compare several ways to overlap
                 multiple stages of quotient selection logic and we
                 consider both irredundant and redundant (carry-save)
                 representations for the remainder.\par

                 The cost and performance of each alternative is
                 evaluated in terms a specific ECL gate array
                 technology. We find that we can build a 15\% faster
                 divider with radix four stages than with radix two
                 stages, for about the same amount of hardware. Between
                 the two radix 4 alternatives, method (c) offers more
                 speed than method (b) at the cost of 20\% more
                 hardware.\par

                 A radix 16 divider using method (b) has been built for
                 the S-1 Mark IIB computer under development at Lawrence
                 Livermore Laboratory. This divider consists of eight
                 ECL gate arrays and has a 12.5 nanosecond cycle time.
                 It performs IEEE single and double precision floating
                 point division in 150 and 225 nanoseconds,
                 respectively, the shortest times reported for any
                 general purpose computer.",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  keywords =     "ARITH-7",
}

@MastersThesis{Tesnow:1985:IDS,
  author =       "Kurt Alan Tesnow",
  title =        "Implementation of the digital simulation of a
                 synchronous machine using a floating-point processor",
  type =         "Thesis ({M.S.})",
  school =       "Department of Electrical Engineering and Applied
                 Physics, Case Western Reserve University",
  address =      "Cleveland, OH 44106, USA",
  pages =        "vii + 255",
  year =         "1985",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{Thies:1985:NPE,
  author =       "Klaus-Dieter Thies",
  title =        "{Die 8087\slash 80287 numerischen Prozessor
                 Erweiterungen f{\"u}r 8086\slash 80286 Systeme}
                 \toenglish {The 8087\slash 80287 Numeric Processor
                 Extension for 8086\slash 80286 Systems} \endtoenglish",
  publisher =    pub-TEWI,
  address =      pub-TEWI:adr,
  pages =        "355",
  year =         "1985",
  ISBN =         "3-921803-53-5",
  ISBN-13 =      "978-3-921803-53-0",
  LCCN =         "????",
  bibdate =      "Sat Nov 09 10:08:28 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Tsuji:1985:REF,
  author =       "Kumiko Tsuji",
  title =        "Round-off errors in floating-point additions",
  journal =      j-MEM-FAC-SCI-KYUSHU-UNIV-A,
  volume =       "39",
  number =       "2",
  pages =        "209--225",
  year =         "1985",
  CODEN =        "MFKAAF",
  ISSN =         "0373-6385 (print), 1883-2172 (electronic)",
  ISSN-L =       "0373-6385",
  MRclass =      "65G05 (65-04)",
  MRnumber =     "86j:65056",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Memoirs of the Faculty of Science, Kyushu Imperial
                 University. Series A, Mathematics = Kyushu Teikoku
                 Daigaku Rigakubu kiyo",
  reviewer =     "Aur{\'e}l Gal{\'a}ntai",
}

@InProceedings{vonGudenberg:1985:FPC,
  author =       "J. W. von Gudenberg",
  title =        "Floating-point computation in {PASCAL-SC} with
                 verified results",
  crossref =     "Buchberger:1985:PEE",
  pages =        "322--324",
  year =         "1985",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G; G.1.0",
  CRclass =      "G.1.0 General; G.1.0 Computer arithmetic",
  descriptor =   "Mathematics of Computing, MATHEMATICAL SOFTWARE;
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Computer arithmetic",
  genterm =      "THEORY; VERIFICATION; ALGORITHMS",
  guideno =      "12475",
  subject =      "G. Mathematics of Computing; G.4 MATHEMATICAL
                 SOFTWARE; G. Mathematics of Computing; G.1 NUMERICAL
                 ANALYSIS",
}

@Article{Williamson:1985:NAB,
  author =       "D. Williamson and S. Sridharan and P. McCrea",
  title =        "A new approach for block floating-point arithmetic in
                 recursive filters",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "32",
  number =       "7",
  pages =        "719--722",
  month =        jul,
  year =         "1985",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "An approach to block floating-point arithmetic in
                 recursive second-order direct form digital filters is
                 proposed. Used in conjunction with residue (or error)
                 feedback, the method gives improved scaling and
                 roundoff noise properties compared to an \ldots{}",
}

@InProceedings{Yun:1985:BPS,
  author =       "David Y. Y. Yun and Chang N. Zhang",
  title =        "Binary Paradigm and Systolic Array Implementation for
                 Residue Arithmetic",
  crossref =     "Hwang:1985:PSC",
  pages =        "189--193",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Yun_Zhang.pdf",
  abstract =     "The problem of residue, or modular, arithmetic is
                 fundamental to symbolic and algebraic computation,
                 coding theory and applications, as well as to
                 error-free arithmetic computations. This paper
                 describes novel algorithms that can lead to efficient
                 hardware for arithmetic operations in residue domains.
                 One of the main achievements is in allowing the
                 flexibility of changing moduli. The technology of
                 systolic array has been used to implement one of the
                 most representative operations, the modular multiplier.
                 It is shown that a linear systolic array can compute
                 $N$ modular products in time $ O(N) $ with constant
                 number of cells.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@InProceedings{Zaccone:1985:INR,
  author =       "Richar J. Zaccone and Jesse L. Barlow",
  title =        "Improved Normalization Results for Digit On-Line
                 Arithmetic",
  crossref =     "Hwang:1985:PSC",
  pages =        "20--27",
  year =         "1985",
  bibdate =      "Wed Nov 14 18:06:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Zaccone_Barlow.pdf",
  abstract =     "In digit on-line arithmetic, operands are introduced 1
                 digit at a time. After the first few operand digits
                 have been introduced. the result begins to appear a
                 digit at a time. This feature of digit on-line
                 arithmetic allows a significant amount of overlapping
                 of arithmetic operations.\par

                 Digit on-line arithmetic can sometimes produce
                 unnormalized results. This can present a problem for
                 the divide and square root algorithms. If the divisor
                 and radicand are highly unnormalized, these algorithms
                 will not produce the correct results. Two advances in
                 overcoming this problem are presented. First, several
                 techniques for producing results that are closer to
                 being normalized are developed. Second, it is shown
                 that normalized results are not necessary for divide
                 and square root to work properly. Combining these
                 results yields algorithms that will always give the
                 correct results.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@InProceedings{Zadrozny:1985:AFP,
  author =       "W{\l}odzimierz Zadro{\'z}ny",
  title =        "Axiomatizations of Floating Point Arithmetics",
  crossref =     "Hwang:1985:PSC",
  pages =        "74--81",
  year =         "1985",
  bibdate =      "Fri Nov 16 08:47:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith7/papers/ARITH7_Zadrozny.pdf",
  abstract =     "We present a universal scheme for axiomatizing
                 floating point arithmetic. The schema can be used to
                 axiomatize any floating point arithmetic. It consists
                 of a labeled graph with vertices describing some
                 arithmetical properties and edges containing
                 appropriate axioms. The language of floating point
                 arithmetic is developed gradually in this scheme. The
                 scheme can provide a vehicle for studying and
                 implementing various versions of floating point
                 arithmetic.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-7",
}

@Article{Zorpette:1985:BBN,
  author =       "Glenn Zorpette",
  title =        "The beauty of 32 bits: This near-optimum bit width has
                 unprecedented potential for the well-informed designer
                 of microprocessor-based systems",
  journal =      j-IEEE-SPECTRUM,
  volume =       "22",
  number =       "9",
  pages =        "65--71",
  month =        sep,
  year =         "1985",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.1985.6370815",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Mon Jan 20 06:41:24 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "32 bit microprocessor chip; Companies; Computers;
                 dynamic RAM; floating-point arithmetic; mainframes;
                 memory management; microprocessor chips;
                 Microprocessors; Pipeline processing; pipelining;
                 processing rates; Random access memory; Registers; Sun;
                 very large scale integration; VLSI",
}

@TechReport{Adams:1986:FSSa,
  author =       "Glenn D. Adams",
  title =        "Functional specification and simulation of a floating
                 point co-processor for {SPUR} [1]",
  type =         "Report",
  number =       "UCB/CSD 87/311",
  institution =  "University of California. Computer Science Division",
  address =      "Berkeley, CA.",
  pages =        "52",
  year =         "1986",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer architecture.; Floating-point arithmetic.;
                 Integrated circuits --- Design and construction.",
  remark =       "Sponsored by DARPA. Monitored by Naval Electronic
                 Systems Command.",
}

@MastersThesis{Adams:1986:FSSb,
  author =       "Glenn D. Adams",
  title =        "Functional specification and simulation of a floating
                 point co-processor for {SPUR}: research project",
  type =         "{Master of Science, Plan II}",
  school =       "University of California, Berkeley. Dept. of
                 Electrical and Engineering and Computer Sciences",
  address =      "Berkeley, CA.",
  pages =        "various",
  year =         "1986",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Agarwal:1986:NSV,
  author =       "Ramesh C. Agarwal and James W. Cooley and Fred G.
                 Gustavson and James B. Shearer and Gordon Slishman and
                 Bryant Tuckerman",
  title =        "New Scalar and Vector Elementary Functions for the
                 {IBM System\slash 370}",
  journal =      j-IBM-JRD,
  volume =       "30",
  number =       "2",
  pages =        "126--144",
  month =        mar,
  year =         "1986",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.302.0126",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  MRclass =      "76W05",
  MRnumber =     "840 341",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
  note =         "See clarification \cite{Agarwal:1987:CNS}.",
  abstract =     "Algorithms have been developed to compute short-and
                 long-precision elementary functions: SIN, COS, TAN,
                 COTAN, LOG, LOG10, EXP, POWER, SQRT, ATAN, ASIN, ACOS,
                 ATAN2, and CABS, in scalar (28 functions) and vector
                 (22 functions) mode. They have been implemented as part
                 of the new VS FORTRAN library recently announced along
                 with the IBM 3090 Vector Facility. These algorithms are
                 essentially table-based algorithms. An important
                 feature of these algorithms is that they produce
                 bitwise-identical results on scalar and vector
                 System\slash 370 machines. Of these, for five functions
                 the computed value result is always the correctly
                 rounded value of the infinite-precision result. For the
                 rest of the functions, the value returned is one of the
                 two floating-point neighbors bordering the
                 infinite-precision result, which implies exact results
                 if they are machine-representable. For the five
                 correctly rounded elementary functions, scalar and
                 vector algorithms are designed independently to
                 optimize performance in each case.",
  accepted =     "2 December 1985",
  acknowledgement = ack-nhfb,
  ajournal =     "IBM J. Res. Develop.",
  classcodes =   "C6140D (High level languages); C7310 (Mathematics
                 computing)",
  classification = "723",
  corpsource =   "IBM Res. Div., Yorktown Heights, NY, USA",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  journalabr =   "IBM J Res Dev",
  keywords =     "ACOS; Algorithms; algorithms; ASIN; ATAN; ATAN2;
                 bitwise-identical results; CABS; computer metatheory;
                 computer programming; computer programming languages
                 --- fortran; COS; COTAN; design; elementary functions;
                 EXP; FORTRAN; fortran library; functions; IBM
                 computers; IBM System/370; infinite-precision result;
                 LOG; LOG10; mainframes; measurement; performance;
                 POWER; scalar elementary functions; SIN; SQRT;
                 subroutines; table-based algorithms; TAN; vector
                 elementary; VS FORTRAN library",
  received =     "5 November 1985",
  remark-1 =     "Numerous figures show errors in ulps, in either linear
                 or logarithmic scales, as dot plots over a range of
                 arguments, an idea that the authors credit to a
                 suggestion by Cleve Moler, then consulting with IBM
                 Palo Alto labs; such plots are used extensively in
                 \cite{Beebe:2017:MFC}.",
  remark-2 =     "From pages 128--129: ``A great deal of satisfaction
                 was obtained from the fact that five of the intrinsic
                 functions reported here always deliver correctly
                 rounded results; these are SQRT, DSQRT, CABS, CDABS,
                 and EXP. One important aspect of this is that correctly
                 rounded results were obtained with surprisingly little
                 sacrifice in performance.''",
  remark-3 =     "From page 132: ``Our CABS and CDABS functions satisfy
                 $\e/u < 0.5$ (this can also be called a half-ulp
                 criterion). They have best-possible rounding, except
                 that unavoidably there are cases when $| e/u | = 0.5$,
                 in which case it would be equally correct to round
                 downward or upward; we choose to round upward. This is
                 consistent with the System/370 definition of
                 rounding.''",
  remark-4 =     "From pages 134--135: ``Tuckerman's condition is of
                 historic significance, as its use allowed us to produce
                 IBM's first elementary function that delivered
                 correctly rounded results for all arguments.''",
  remark-5 =     "From page 137: ``X**2.0 usually produces a correctly
                 rounded value, while X*X always produces the truncated
                 value of $X^2$ .''",
  remark-6 =     "From page 139: ``Generating precise times is
                 difficult, since seemingly inconsequential changes in
                 the timing procedure may have a noticeable effect on
                 the measured times. For example, on the 3081KX the
                 performance of the STM [store multiple] and LM [load
                 multiple] instructions is severely degraded near page
                 boundaries. This means that in the rare event that the
                 save area of a subroutine is near a page boundary, the
                 speed of execution of the subroutine will be
                 substantially decreased.''",
  subject =      "C.4 Computer Systems Organization, PERFORMANCE OF
                 SYSTEMS \\ I.1.2 Computing Methodologies, ALGEBRAIC
                 MANIPULATION, Algorithms \\ F.3.3 Theory of
                 Computation, LOGICS AND MEANINGS OF PROGRAMS, Studies
                 of Program Constructs, Functional constructs \\ C.1.2
                 Computer Systems Organization, PROCESSOR ARCHITECTURES,
                 Multiple Data Stream Architectures (Multiprocessors),
                 Array and vector processors",
  treatment =    "N New Development; P Practical",
}

@Book{Apple:1986:ANM,
  author =       "{Apple Computer, Inc.} and Don Reed",
  title =        "{Apple} Numerics Manual",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "vii + 295",
  year =         "1986",
  ISBN =         "0-201-17741-2",
  ISBN-13 =      "978-0-201-17741-1",
  LCCN =         "QA297 .A66; QA76.8.A662 A59 1986",
  bibdate =      "Thu Nov 29 23:38:40 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  note =         "See also \cite{Apple:1988:ANM,Apple:1994:IMP}.",
  acknowledgement = ack-nhfb,
  keywords =     "SANE (Standard Apple Numeric Environment)",
  remark =       "Standard Apple Numeric Environment for all Macintosh
                 and Apple II computers.",
  subject =      "Numerical calculations; Computer programs; Apple
                 computer",
}

@Article{Ardalan:1986:FPE,
  author =       "S. Ardalan",
  title =        "Floating-point error analysis of recursive
                 least-squares and least-mean-squares adaptive filters",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "33",
  number =       "12",
  pages =        "1192--1208",
  month =        dec,
  year =         "1986",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "A floating-point error analysis of the Recursive Least
                 Squares (RLS) and Least-Mean-Squares (LMS) algorithms
                 is presented. Both the prewindowed growing memory RLS
                 algorithm (lambda = 1) for stationary systems and the
                 exponentially windowed RLS \ldots{}",
}

@Article{Bayoumi:1986:LBV,
  author =       "Magdy A. Bayoumi",
  title =        "Lower bounds for {VLSI} implementation of residue
                 number system architectures",
  journal =      j-INTEGRATION-VLSI-J,
  volume =       "4",
  number =       "3",
  pages =        "263--269",
  month =        sep,
  year =         "1986",
  CODEN =        "IVJODL",
  DOI =          "https://doi.org/10.1016/0167-9260(86)90004-0",
  ISSN =         "0167-9260 (print), 1872-7522 (electronic)",
  ISSN-L =       "0167-9260",
  bibdate =      "Thu Nov 18 09:57:37 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Since the number of components that can fit on a
                 single chip is large and rapidly growing, the
                 asymptotic analysis and computational complexity have
                 become applicable to the VLSI systems. We propose a
                 model of computation devoted to VLSI structures based
                 on Residue Number System (RNS). The developed model
                 employs the `cut theorem' which has been used by most
                 of the abstract VLSI models. It is not as general as
                 other reported models, but it gives tighter lower
                 bounds and more accurate measures of performance for
                 RNS structures. This computational model relates the
                 area and time complexities with the inherent properties
                 of RNS, the moduli size and the dynamic range. The
                 model supports the look-up table implementation
                 approach and it is technology-independent.",
  acknowledgement = ack-nhfb,
  fjournal =     "Integration, the VLSI journal",
  journal-URL =  "https://www.sciencedirect.com/journal/integration/issues",
  keywords =     "area-time complexity; lower bounds; RNS; VLSI",
}

@InProceedings{Beims:1986:FPP,
  author =       "B. Beims",
  title =        "The Floating-Point Performance Standard Gets Even
                 Faster!",
  crossref =     "Wescon:1986:WCR",
  pages =        "35/1/1--13",
  year =         "1986",
  bibdate =      "Wed Sep 14 19:13:54 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@InProceedings{Berger:1986:NNF,
  author =       "P. A. Berger",
  title =        "The {National NS32381} Floating Point Slave
                 Processor",
  crossref =     "Wescon:1986:WCR",
  pages =        "35/2/1--6",
  year =         "1986",
  bibdate =      "Mon Sep 12 08:32:02 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "",
  acknowledgement = ack-nj,
}

@Article{Bernstein:1986:MIC,
  author =       "Robert L. Bernstein",
  title =        "Multiplication by Integer Constants",
  journal =      j-SPE,
  volume =       "16",
  number =       "7",
  pages =        "641--652",
  month =        jul,
  year =         "1986",
  CODEN =        "SPEXBL",
  DOI =          "https://doi.org/10.1002/spe.4380160704",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Sat May 31 13:36:16 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Methods are given for finding a sequence of `add',
                 `subtract' and `shift' instructions to multiply the
                 contents of a register by an integer constant. Each
                 method generalizes the previous one and requires only a
                 few intermediate or scratch registers. A variation of
                 the last method is used in the PL.8 compiler and uses
                 an unnoticeable amount of the overall compile time.
                 Some statistics roughly indicating the effectiveness of
                 the methods are presented.",
  acknowledgement = ack-nhfb,
  fjournal =     "Software---Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
}

@Article{Campbell:1986:NSR,
  author =       "R. A. Campbell",
  title =        "{NS32000} Square Roots",
  journal =      j-DDJ,
  volume =       "11",
  number =       "3",
  pages =        "122--123, 106",
  month =        mar,
  year =         "1986",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Fri Dec 08 13:05:56 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@Article{Campbell:1986:SS,
  author =       "R. A. Campbell",
  title =        "In Search of a Sine",
  journal =      j-DDJ,
  volume =       "11",
  number =       "12",
  pages =        "30--32",
  month =        dec,
  year =         "1986",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Thu Sep 1 10:15:57 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@MastersThesis{Cao:1986:BFP,
  author =       "Hai Cao",
  title =        "A bit-slice floating point processor",
  type =         "Project ({M.S., Electrical and Electronic
                 Engineering})",
  school =       "California State University",
  address =      "Sacramento, CA, USA",
  pages =        "vii + 104",
  year =         "1986",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Karl E. Stoffers, Chairperson.",
  acknowledgement = ack-nhfb,
  keywords =     "Bit slice microprocessors.",
}

@Article{Cathey:1986:LEI,
  author =       "J. Cathey",
  title =        "Letter to the editor [Integer Square Root]",
  journal =      j-DDJ,
  volume =       "11",
  number =       "8",
  pages =        "14, 82--85",
  month =        aug,
  year =         "1986",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Thu Sep 08 07:59:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@InProceedings{Chadha:1986:IHP,
  author =       "K. Chadha",
  title =        "{Intel} 80387: high performance, single chip numerics
                 coprocessor for the 80386",
  crossref =     "Wescon:1986:WCR",
  pages =        "35/4/1--5",
  year =         "1986",
  bibdate =      "Wed Sep 7 22:31:45 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Chakraborti:1986:IMR,
  author =       "N. B. Chakraborti and J. S. Soundararajan and A. L. N.
                 Reddy",
  title =        "An Implementation of Mixed-Radix Conversion for
                 Residue Number Applications",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-35",
  number =       "8",
  pages =        "762--764",
  month =        aug,
  year =         "1986",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1986.1676829",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 14:09:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35258;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676829",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A method of residue number system (RNS) conversion to
                 mixed-radix (MR) representation is presented. This
                 method is found to be cost-effective and efficient,
                 particularly for moduli size 4/5 bits. A comparison of
                 conversion times and hardware \ldots{}",
}

@Article{Chowdary:1986:APR,
  author =       "N. Chowdary and W. Steenaart",
  title =        "Accumulation of product roundoff errors in modified
                 {FFT}'s",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "33",
  number =       "1",
  pages =        "103--107",
  month =        jan,
  year =         "1986",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "In this paper, expressions are derived for the mean
                 square error in modified radix-2 FFT algorithms. To
                 reduce the mean square error at the output of a special
                 purpose, high-speed low-order(n {leq} 32)FFT processor
                 implemented in fixed- \ldots{}",
}

@Article{Clenshaw:1986:GEL,
  author =       "C. W. Clenshaw and Daniel W. Lozier and F. W. J. Olver
                 and P. R. Turner",
  title =        "Generalized Exponential and Logarithmic Functions",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "12",
  number =       "5--6",
  pages =        "1091--1101",
  month =        sep # "\slash " # dec,
  year =         "1986",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(86)90233-6",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  MRclass =      "33A70 (39B10 65G05)",
  MRnumber =     "MR0871348 (88a:33027)",
  bibdate =      "Fri Jul 09 06:27:26 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Generalizations of the exponential and logarithmic
                 functions are defined and an investigation is made of
                 two possible versions of these functions. Some
                 applications are described, including computer
                 arithmetic, properties of very large and very small
                 numbers, and the determination of functional roots.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Clenshaw:1986:UAR,
  author =       "C. W. Clenshaw and F. W. J. Olver",
  title =        "Unrestricted algorithms for reciprocals and square
                 roots",
  journal =      j-BIT,
  volume =       "26",
  number =       "4",
  pages =        "475--492",
  month =        dec,
  year =         "1986",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01935054",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65D20",
  MRnumber =     "87k:65019",
  MRreviewer =   "Luciano Biasini",
  bibdate =      "Wed Jan 4 18:52:19 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=26&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=26&issue=4&spage=475",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  xxpages =      "476--492??",
}

@PhdThesis{Coonen:1986:CPS,
  author =       "Jerome Toby Coonen",
  title =        "Contributions to a proposed standard for binary
                 floating-point arithmetic",
  type =         "Thesis ({Ph.D.})",
  school =       "University of California, Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "various",
  year =         "1986",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Binary system (Mathematics)",
}

@MastersThesis{Crowell:1986:ECU,
  author =       "Deborah Susan Crowell",
  title =        "Error-free computation using multiple-modulus residue
                 arithmetic",
  type =         "Thesis ({M.S.})",
  school =       "University of Tennessee, Knoxville",
  address =      "Knoxville, TN, USA",
  pages =        "vi + 106",
  year =         "1986",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithms.; Approximation theory --- Data
                 processing.; Floating-point arithmetic.; Modular
                 arithmetic.",
}

@Article{Curtis:1986:CPL,
  author =       "T. W. Curtis and Paul Allison and James A. Howard",
  title =        "A {CORDIC} Processor for Laser Trimming",
  journal =      j-IEEE-MICRO,
  volume =       "6",
  number =       "3",
  pages =        "61--71",
  month =        may # "\slash " # jun,
  year =         "1986",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.1986.304680",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Sep 08 00:48:52 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  keywords =     "Computer errors; Computer interfaces; Control systems;
                 Error correction; Laser beam cutting; Optical control;
                 Weight control",
}

@InProceedings{Desrosiers:1986:CFP,
  author =       "B. Desrosiers and J.-L. Peter and C. Sitbon",
  title =        "Custom Floating Point Chip Designed with a Cohesive
                 Structured Method",
  crossref =     "IEEE:1986:PII",
  pages =        "402--405",
  year =         "1986",
  bibdate =      "Wed Sep 7 22:31:45 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@InProceedings{DuCroz:1986:FFP,
  author =       "J. Du Croz",
  title =        "{FPV} -- a Floating-Point Validation Package",
  crossref =     "Unicom:1986:SQA",
  pages =        "47--55",
  year =         "1986",
  bibdate =      "Thu Sep 01 11:58:18 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Dutka:1986:SRT,
  author =       "Jacques Dutka",
  title =        "On square roots and their representations",
  journal =      j-ARCH-HIST-EXACT-SCI,
  volume =       "36",
  number =       "1",
  pages =        "21--39",
  month =        mar,
  year =         "1986",
  CODEN =        "AHESAN",
  DOI =          "https://doi.org/10.1007/BF00357439",
  ISSN =         "0003-9519 (print), 1432-0657 (electronic)",
  ISSN-L =       "0003-9519",
  MRclass =      "01A05 (11-03 11A63)",
  MRnumber =     "863340 (87m:01003)",
  MRreviewer =   "Donald Cook",
  bibdate =      "Fri Feb 4 21:50:24 MST 2011",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=36&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=36&issue=1&spage=21",
  acknowledgement = ack-nhfb,
  fjournal =     "Archive for History of Exact Sciences",
  journal-URL =  "http://link.springer.com/journal/407",
  MRtitle =      "On square roots and their representations",
}

@Article{Dutta:1986:IMF,
  author =       "U. Dutta and D. Bhattacharya and A. D. Sarma",
  title =        "Implementation of Multibyte Floating Point Arithmetic
                 in 8-bit Microprocessor",
  journal =      j-MECH-ENG-BULL,
  volume =       "17",
  number =       "3",
  pages =        "104--113",
  month =        sep,
  year =         "1986",
  CODEN =        "MEGBBQ",
  ISSN =         "0379-5527",
  bibdate =      "Thu Sep 1 10:15:06 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Mechanical Engineering Bulletin",
}

@Article{Feldstein:1986:OUS,
  author =       "Alan Feldstein and Peter Turner",
  title =        "Overflow, underflow, and severe loss of significance
                 in floating-point addition and subtraction",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "6",
  number =       "2",
  pages =        "241--251",
  month =        apr,
  year =         "1986",
  CODEN =        "IJNADH",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65G05",
  MRnumber =     "89h:65065",
  bibdate =      "Sat Dec 23 14:52:49 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this paper it is shown that, under the assumption
                 of the logarithmic distribution of numbers,
                 floating-point addition and subtraction can result in
                 overflow or underflow with alarming frequency?--a
                 frequency that increases rapidly with machine speed
                 unless the range of the exponent is also increased. If
                 numbers are assumed to be distributed in accordance
                 with Sweeney's (1965) experiments, then severe loss of
                 significance occurs with large probability in floating
                 point subtraction. These results have implications for
                 computer design and lead to the suggestion of a long
                 word format which will reduce the risks to acceptable
                 levels.",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
  keywords =     "Benford's Law; Law of Anomalous Numbers; logarithmic
                 distribution; overflow; underflow; Zipf's Law",
}

@Article{Ferro:1986:DTF,
  author =       "F. Ferro",
  title =        "{DSP} tackles floating-point arithmetic",
  journal =      j-COMP-DESIGN,
  volume =       "25",
  number =       "15",
  pages =        "53--56",
  day =          "15",
  month =        aug,
  year =         "1986",
  CODEN =        "CMPDAM",
  ISSN =         "0010-4566",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  bibno =        "16915",
  catcode =      "B.7.1",
  CRclass =      "B.7.1 Types and Design Styles; B.7.1 Advanced
                 technologies",
  descriptor =   "Hardware, INTEGRATED CIRCUITS, Types and Design
                 Styles, Advanced technologies",
  fjournal =     "Computer Design",
  genterm =      "DESIGN",
  guideno =      "1986-04012",
  journalabbrev = "Comput. Des.",
  subject =      "B. Hardware; B.7 INTEGRATED CIRCUITS",
}

@Article{Gavrielov:1986:NFP,
  author =       "Moshe Gavrielov and Lev Epstein",
  title =        "The {NS32081} Floating-Point Unit --- Architecture and
                 Implementation",
  journal =      j-IEEE-MICRO,
  volume =       "6",
  number =       "2",
  pages =        "6--12",
  month =        mar # "\slash " # apr,
  year =         "1986",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.1986.304737",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Dec 14 06:08:58 MST 2000",
  bibsource =    "Compendex database;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Science Citation Index database (1980--2000)",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliationaddress = "Digital Equipment Corp, Hudson, MA, USA",
  classcodes =   "B1265F (Microprocessors and microcomputers); B2570F
                 (Other MOS integrated circuits); C5130 (Microprocessor
                 chips); C5220 (Computer architecture); C5230 (Digital
                 arithmetic methods)",
  classification = "713; 714; 721; 722; 723; 902",
  corpsource =   "Digital Equipment Corp., Hudson, MA, USA",
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  keywords =     "binary floating point arithmetic; binary floating-;
                 brand; carry propagation circuit; chip design; computer
                 architecture; computers, microcomputer; Construction;
                 data storage, semiconductor; digital arithmetic;
                 digital devices; field effect; floating-point
                 operations; high-speed; IEEE standard; integrated
                 circuits; internal structure; logic circuit
                 implementations; microcode; microprocessor chips; NMOS
                 processor; ns32081 floating-point processor; NS32081
                 floating-point unit; parallel multiway-; point
                 arithmetic; processor concept; semiconductor devices,
                 MOS; slave; slave processor; software package;
                 standards",
  treatment =    "P Practical; R Product Review",
  xxtitle =      "The {NS32081} Floating-point Unit",
}

@Article{Grappel:1986:SRA,
  author =       "R. D. Grappel",
  title =        "Square-root algorithm is fast and simple",
  journal =      j-EDN,
  volume =       "31",
  number =       "8",
  pages =        "248--248",
  month =        apr,
  year =         "1986",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Thu Sep 1 10:15:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}

@Article{Gustafson:1986:AHV,
  author =       "John L. Gustafson and Stuart Hawkinson and Ken Scott",
  title =        "The architecture of a homogeneous vector
                 supercomputer",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "3",
  number =       "3",
  pages =        "297--304",
  month =        sep,
  year =         "1986",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliationaddress = "Floating Point Systems Inc, Beaverton, OR, USA",
  classification = "722; 723; C5220 (Computer architecture); C5440
                 (Multiprocessor systems and techniques); C6110 (Systems
                 analysis and programming)",
  corpsource =   "Floating Point Syst. Inc., Beaverton, OR, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "12 MFLOPS; 64-bit floating-point; 96 MFLOPS;
                 arithmetic; binary n-cube; computer architecture;
                 computer systems, digital; dual-ported memory design;
                 Floating Point; homogeneous vector supercomputer;
                 interconnection scheme; multiprocessing; parallel;
                 parallel architecture; parallel architectures; parallel
                 machines; Parallel Processing; pipeline processing;
                 pipeline vector arithmetic; pipelined vector
                 arithmetic; programming; software development;
                 supercomputer; Systems; technology; vector processing;
                 VLSI",
  treatment =    "P Practical",
}

@Book{Hamming:1986:NMS,
  author =       "R. W. (Richard Wesley) Hamming",
  title =        "Numerical methods for scientists and engineers",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  edition =      "Second",
  pages =        "ix + 721",
  year =         "1986",
  ISBN =         "0-486-65241-6 (paperback)",
  ISBN-13 =      "978-0-486-65241-2 (paperback)",
  LCCN =         "QA297 .H28 1986",
  bibdate =      "Fri Aug 20 09:12:08 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "US\$14.95",
  URL =          "http://www.loc.gov/catdir/description/dover032/86016226.html",
  acknowledgement = ack-nhfb,
  remark =       "Reprint of \cite{Hamming:1973:NMS}.",
  subject =      "numerical analysis; data processing",
}

@Article{Heath:1986:NRD,
  author =       "J. Heath",
  title =        "A note on {``Realization of digital filters using
                 input-scaled floating-point arithmetic''}",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "34",
  number =       "4",
  pages =        "995--995",
  month =        aug,
  year =         "1986",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Heath:1979:RDF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  summary =      "In [1] and [2], a theoretical Bode plot with
                 experimental data points is shown. The experimental
                 data points on the Bode plot are not correct \ldots{}",
}

@Article{Henning:1986:KBD,
  author =       "D. Henning",
  title =        "{Konvertierung bin{\"a}rer in dezimale
                 Gleitkommazahlen f{\"u}r me{\ss}technische Anwendungen}
                 \toenglish {Conversion of Binary [Numbers] to Decimal
                 Floating-Point Numbers for Measurement Applications}
                 \endtoenglish",
  journal =      "Radio Fernsehen Elektronik",
  volume =       "35",
  number =       "11",
  pages =        "731--733",
  month =        "????",
  year =         "1986",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  keywords =     "decimal floating-point arithmetic",
}

@Article{Higginbotham:1986:AF,
  author =       "T. F. Higginbotham",
  title =        "Another factor of $ (10^{31} - 1) / 9 $",
  journal =      j-SIGNUM,
  volume =       "21",
  number =       "3",
  pages =        "12--12",
  month =        jul,
  year =         "1986",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/1057958.1057960",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Thu Aug 07 18:41:01 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A second factor of $ (10^{31} - 1) / 9 $ was found to
                 be 6943319 with the use of an eight spoke wheel [1].
                 The spokes D(i) were 1, 7, 11, 13, 17, 19, 23, and 29.
                 The possible factors 2, 3, and 5 were tested prior to
                 starting the wheel. The constant multiplier was 30. The
                 possible divisors were of the form $ 30 \times K +
                 D(i), K = 0, 1, 2, 3, \ldots {} $. The program was
                 written in COBOL for the Honeywell DPS 8, running under
                 CP-6. The picture clauses were selected such that
                 31-digit decimal arithmetic was used. Execution time
                 was about forty-five minutes.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "decimal arithmetic",
  remark =       "Maple 8 reports in 2 sec on a 1400 MHz Itanium IA-64:
                 ifactor((10^31 - 1)/9) = (57336415063790604359)
                 (6943319) (2791).",
}

@Article{Hill:1986:DDS,
  author =       "Mark Hill and Susan Eggers and Jim Larus and George
                 Taylor and Glenn Adams and B. K. Bose and Garth Gibson
                 and Paul Hansen and Jon Keller and Shing Kong and
                 Corinna Lee and Daebum Lee and Joan Pendleton and Scott
                 Ritchie and David Wood and Ben Zorn and Paul Hilfinger
                 and Dave Hodges and Randy Katz and John Ousterhout and
                 Dave Patterson",
  key =          "C.0.B RISC",
  title =        "Design decisions in {SPUR}",
  journal =      j-COMPUTER,
  volume =       "19",
  number =       "11",
  pages =        "8--22",
  month =        nov,
  year =         "1986",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "University of California, Berkeley",
  bibno =        "9486",
  catcode =      "C.1.2; C.2.4; D.4.3; C.0; D.3.0; B.3.2; D.3.2",
  content =      "SPUR (Symbolic Processing Using RISCs) is a
                 multiprocessor workstation under development at the
                 University of California at Berkeley for parallel
                 processing research. Its development is part of a
                 long-term effort to study hardware and software issues
                 in multiprocessing, in general, and parallel processing
                 in LISP, in particular. This paper concentrates on the
                 initial architectural research and development of SPUR.
                 A SPUR processor is a general-purpose RISC processor
                 that provides support for Common LISP and IEEE
                 floating-point. A processor is implemented on a single
                 board with about 200 standard chips and three custom
                 two-micron CMOS chips: the cache controller, the CPU,
                 and the floating-point coprocessor. The chip that
                 manages the cache handles cache access by the CPU,
                 performing address translation, accessing shared memory
                 over the SPUR bus, and maintaining cache consistency.
                 Operating systems researchers are investigating network
                 file systems, network page servers, the effects of
                 large physical memories on virtual memory
                 implementations, and workload distribution. Programming
                 languages researchers ar",
  CRclass =      "C.1.2 Multiple Data Stream Architectures
                 (Multiprocessors); C.1.2 Parallel processors; C.2.4
                 Distributed Systems; D.4.3 File Systems Management; C.0
                 Instruction set design; D.3.0 General; B.3.2 Design
                 Styles; B.3.2 Cache memories; D.3.2 Language
                 Classifications; D.3.2 LIS-11",
  CRnumber =     "8710-0848",
  descriptor =   "Computer Systems Organization, PROCESSOR
                 ARCHITECTURES, Multiple Data Stream Architectures
                 (Multiprocessors), Parallel processors; Computer
                 Systems Organization, COMPUTER-COMMUNICATION NETWORKS,
                 Distributed Systems; Software, OPERATING SYSTEMS, File
                 Systems Management; Computer Systems Organization,
                 GENERAL, Instruction set design; Software, PROGRAMMING
                 LANGUAGES, General; Hardware, MEMORY STRUCTURES, Design
                 Styles, Cache memories; Software, PROGRAMMING
                 LANGUAGES, Language Classifications, LIS-11",
  fjournal =     "Computer",
  genterm =      "DESIGN; HUMAN FACTORS; PERFORMANCE; EXPERIMENTATION",
  guideno =      "1986-03762",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
  journalabbrev = "Computer",
  reviewer =     "P. C. Patton",
  subject =      "C. Computer Systems Organization; C.1 PROCESSOR
                 ARCHITECTURES; C. Computer Systems Organization; C.2
                 COMPUTER-COMMUNICATION NETWORKS; D. Software; D.4
                 OPERATING SYSTEMS; C. Computer Systems Organization;
                 C.0 GENERAL; D. Software; D.3 PROGRAMMING LANGUAGES; B.
                 Hardware; B.3 MEMORY STRUCTURES; D. Software; D.3
                 PROGRAMMING LANGUAGES",
}

@Article{Hongyuan:1986:CSL,
  author =       "Wang Hongyuan and S. C. Lee",
  title =        "Comments on {``Sign\slash Logarithm Arithmetic for FFT
                 Implementation''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-35",
  number =       "5",
  pages =        "482--484",
  month =        may,
  year =         "1986",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1986.1676792",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 14:09:48 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  note =         "See \cite{Swartzlander:1983:SLA}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676792",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Hull:1986:VPE,
  author =       "T. E. Hull and A. Abrham",
  title =        "Variable Precision Exponential Function",
  journal =      j-TOMS,
  volume =       "12",
  number =       "2",
  pages =        "79--91",
  month =        jun,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/6497.6498",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D15 (65D20)",
  MRnumber =     "863 786",
  bibdate =      "Sun Sep 04 21:17:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-2/p79-hull/",
  abstract =     "The exponential function presented here returns a
                 result which differs from $ e^x $ by less than one unit
                 in the last place, for any representable value of $x$
                 which is not too close to values for which $ e^x $
                 would overflow or underflow. (For values of $x$ which
                 are not within this range, an error condition is
                 raised.) It is a ``variable precision'' function in
                 that it returns a $p$-digit approximation for a
                 $p$-digit argument, for any $ p > 0 $ ($p$-digit means
                 $p$-decimal-digit). The program and analysis are valid
                 for all $ p > 0 $, but current implementations place a
                 restriction on $p$. The program is presented in a
                 Pascal-like programming language called Numerical
                 Turing which has special facilities for scientific
                 computing, including precision control, directed
                 roundings, and built-in functions for getting and
                 setting exponents.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; decimal floating-point arithmetic; theory;
                 verification",
  review =       "ACM CR 8702-0091",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Certification and testing. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Verification.",
}

@TechReport{IBM:1986:IHA,
  author =       "{IBM Corporation}",
  title =        "{IBM High-Accuracy Arithmetic Subroutine Library
                 (ACRITH)}",
  type =         "Technical Report",
  number =       "GC 33-6163-02, SC 33-6164-02, GX 33-9009-02",
  institution =  pub-IBM,
  address =      pub-IBM:adr,
  edition =      "Third",
  year =         "1986",
  bibdate =      "Thu Jan 21 17:27:09 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "1. General Information Manual \\
                 2. Program Description and User's Guide \\
                 3. Reference Summary",
}

@Book{IBM:1986:IRP,
  author =       "{IBM}",
  title =        "{IBM RT} Personal Computer Technology, publication
                 {SA23-1057}",
  publisher =    pub-IBM,
  address =      pub-IBM:adr,
  year =         "1986",
  bibdate =      "Sat Oct 28 08:16:44 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Iiguni:1986:REA,
  author =       "Y. Iiguni and H. Sakai and H. Tokumaru",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing: {ICASSP '86}",
  title =        "Rounding error analysis of the triangular lattice and
                 escalator algorithms",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2119--2122",
  year =         "1986",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "In this paper, first, the normalized Triangular
                 Lattice and Escalator algorithms for recursive least
                 squares estimation are presented. Next, roundoff errors
                 of both algorithms in fixed point arithmetic are
                 analyzed and compared. Expressions are \ldots{}",
}

@Article{Jansen:1986:HAA,
  author =       "Paul Jansen and Peter Weidner",
  title =        "High-Accuracy Arithmetic Software --- Some Tests of
                 the {ACRITH} Problem-Solving Routines",
  journal =      j-TOMS,
  volume =       "12",
  number =       "1",
  pages =        "62--70",
  month =        mar,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/5960.5962",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65Dxx",
  MRnumber =     "868 096",
  bibdate =      "Sat Aug 13 17:26:53 MDT 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://doi.acm.org/10.1145/5960.5962;
                 http://www.acm.org/pubs/citations/journals/toms/1986-12-1/p62-jansen/",
  abstract =     "The program package ACRITH (High-Accuracy Arithmetic
                 Subroutine Library) provides FORTRAN subroutines for
                 the solution of several standard mathematical problems.
                 The routines use floating point operations with
                 extended precision and interval arithmetic and are
                 designated especially for the solution of
                 ill-conditioned problems. Test results for most of the
                 routines are presented with emphasis on the practical
                 usability of the package. It turns out that not all
                 routines are of equal high quality and reliability; in
                 the documentation, hints to the implemented numerical
                 algorithms are completely missing, and the error
                 messages are not always concise. Some possible
                 alternatives like symbolic algebra systems or multiple
                 precision packages are mentioned.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; floating-point testing",
  review =       "ACM CR 8612-1110",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, ACRITH. {\bf G.1.0}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Numerical
                 algorithms. {\bf I.1.3}: Computing Methodologies,
                 ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
                 {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Reliability and
                 robustness.",
}

@InProceedings{Johnson:1986:TRH,
  author =       "T. Johnson and G. Clark",
  title =        "Techniques for realization of high-speed recursive
                 digital filters using residue number system
                 arithmetic",
  crossref =     "IEEE:1986:III",
  volume =       "11",
  pages =        "2623--2626",
  month =        apr,
  year =         "1986",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Residue-number-arithmetic digital filters offer major
                 cost and speed advantages over binary-arithmetic
                 digital filters but suffer one major drawback. The
                 filter coefficients must remain constant because
                 efficient means of updating by fractional arithmetic in
                 residue number systems involves time consuming
                 overhead. To maintain high speed in the system the
                 choices are to use RNS in the adders and multipliers
                 with scaling done in ROM, to do RNS multiplies and
                 additions and scale as part of CRT conversion at the
                 output, or to apply a new fractional NTT interpretation
                 of multiplier output and use RNS throughout. These
                 methods are discussed in this paper.",
}

@InProceedings{Kabal:1986:PFP,
  author =       "P. Kabal and B. Sayar",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing: {ICASSP '86}",
  title =        "Performance of fixed-point {FFT}'s: Rounding and
                 scaling considerations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "221--224",
  year =         "1986",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The calculation of the discrete Fourier transform
                 using a fast Fourier transform (FFT) algorithm with
                 fixed-point arithmetic is considered. The input data is
                 scaled to prevent overflow and to maintain accuracy.
                 The implementation uses 16-bit fixed- \ldots{}",
}

@TechReport{Kahan:1986:RAF,
  author =       "W. Kahan",
  title =        "Rational Arithmetic in Floating-Point",
  type =         "Technical Report",
  number =       "PAM-343",
  institution =  inst-BERKELEY-CPAM,
  address =      inst-BERKELEY-CPAM:adr,
  pages =        "8",
  month =        sep,
  year =         "1986",
  bibdate =      "Sun Dec 18 15:33:08 GMT 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1986:S,
  author =       "W. Kahan and K. C. Ng",
  title =        "{SQRT}",
  howpublished = "Web document.",
  pages =        "11",
  day =          "6",
  month =        may,
  year =         "1986",
  bibdate =      "Sat Dec 13 10:38:09 2025",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://adampunk.com/documents/softsqrt.pdf",
  abstract =     "Two algorithms are given in this document to implement
                 $ \sqrt {x} $ in software. Both supply $ \sqrt {x} $
                 correctly rounded. The first algorithm (in Section A)
                 uses Newton iterations and involves four divisions. The
                 second one uses reciproot iterations to avoid division,
                 but requires more multiplications. Both algorithms need
                 the ability to chop results of arithmetic operations
                 instead of round them, and the INEXACT flag to indicate
                 when an arithmetic operation is executed exactly with
                 no roundoff error, all part of the standard. The
                 ability to perform shift, add, subtract and logical AND
                 operations upon 32-bit words is needed too, though not
                 part of the standard.",
  acknowledgement = ack-nhfb,
  remark =       "See \cite{Hyland:20xx:FIS} for later developments that
                 were influenced by this report.",
}

@TechReport{Kreithen:1986:FPC,
  author =       "Daniel E. Kreithen",
  title =        "Floating point calculation speeds for the image
                 processing workstation",
  institution =  "Brown University, Division of Engineering",
  address =      "Providence, RI, USA",
  pages =        "23",
  year =         "1986",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Krishnan:1986:CCN,
  author =       "R. Krishnan and G. Jullien and W. Miller",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing, {ICASSP '86}",
  title =        "Computation of complex number theoretic transforms
                 using quadratic residue number systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "233--236",
  year =         "1986",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Very recently, the Quadratic Residue Number System
                 (QRNS) has been introduced [4,5]. The QRNS is obtained
                 from a mapping of Gaussian integers over a finite ring
                 to a ring of conjugate elements. The conjugate ring has
                 the remarkable property that \ldots{}",
}

@Article{Krishnan:1986:CDS,
  author =       "R. Krishnan and G. Jullien and W. Miller",
  title =        "Complex digital signal processing using quadratic
                 residue number systems",
  journal =      "Acoustics, Speech, and Signal Processing [see also
                 IEEE Transactions on Signal Processing], IEEE
                 Transactions on",
  volume =       "34",
  number =       "1",
  pages =        "166--177",
  month =        feb,
  year =         "1986",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26196",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Recently, the quadratic residue number system (QRNS)
                 has been introduced [6], [7] which allows the
                 multiplication of complex integers with two real
                 multiplications. The restriction is that the number
                 system has either all prime moduli of the form 4K
                 \ldots{}",
}

@Article{Krishnan:1986:ICN,
  author =       "R. Krishnan and G. Jullien and W. Miller",
  title =        "Implementation of complex number theoretic transforms
                 using quadratic residue number systems",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "33",
  number =       "8",
  pages =        "759--766",
  month =        aug,
  year =         "1986",
  CODEN =        "ICSYBT",
  DOI =          "https://doi.org/10.1049/el:19850252",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23583",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Very recently, the Quadratic Residue Number System
                 (QRNS) has been introduced [6], [7]. The QRNS is
                 obtained from a mapping of Gaussian integers over a
                 finite ring to a ring of conjugate elements. The
                 conjugate ring has the remarkable property that
                 \ldots{}",
}

@Article{Krishnan:1986:MQR,
  author =       "R. Krishnan and G. Jullien and W. Miller",
  title =        "The modified quadratic residue number system ({MQRNS})
                 for complex high-speed signal processing",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "33",
  number =       "3",
  pages =        "325--327",
  month =        mar,
  year =         "1986",
  CODEN =        "ICSYBT",
  DOI =          "https://doi.org/10.1049/el:19850252",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23578",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Recently, the Quadratic Residue Number System,(QRNS)
                 has been introduced [5], [6], which allows the
                 multiplication of complex integers with two real
                 multiplications. The restriction is that this special
                 residue number system has all moduli with \ldots{}",
}

@Article{Kulisch:1986:ADC,
  author =       "Ulrich W. Kulisch and Willard L. Miranker",
  title =        "The Arithmetic of the Digital Computer: a New
                 Approach",
  journal =      j-SIAM-REVIEW,
  volume =       "28",
  number =       "1",
  pages =        "1--40",
  month =        mar,
  year =         "1986",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1028001",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "65G10 (68M15)",
  MRnumber =     "87e:65030",
  MRreviewer =   "G. Blanch",
  bibdate =      "Sat Mar 29 09:54:03 MDT 2014",
  bibsource =    "Compendex database;
                 http://epubs.siam.org/toc/siread/28/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  abstract =     "A new approach to the arithmetic of the digital
                 computer is surveyed. The methodology for defining and
                 implementing floating-point arithmetic is described.
                 Shortcomings of elementary floating-point arithmetic
                 are revealed through sample problems. The development
                 of automatic computation with emphasis on the user
                 control of errors is reviewed. The limitations of
                 conventional rule-of-thumb procedures for error control
                 in scientific computation are demonstrated by means of
                 examples. Computer arithmetic is extended so that the
                 arithmetic operations in the linear spaces and their
                 interval correspondents which are most commonly used in
                 computation can be performed with maximum accuracy on
                 digital computers. A new fundamental computer
                 operation, the scalar product, is introduced to develop
                 this advanced computer arithmetic.",
  acknowledgement = ack-nhfb,
  affiliationaddress = "Univ of California, Computer Science Dep, Santa
                 Barbara, CA, USA",
  classification = "723",
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  journalabr =   "SIAM Rev",
  keywords =     "accurate floating-point summation; computer
                 arithmetic; computer metatheory; computer programming
                 languages; computers, digital; floating-point
                 arithmetic",
  onlinedate =   "March 1986",
  referred =     "[Layn91a].",
}

@Misc{Kulisch:1986:CGS,
  author =       "Ulrich Kulisch",
  title =        "Circuitry for generating scalar products and sums of
                 floating point numbers with maximum accuracy",
  howpublished = "US Patent 4622650",
  day =          "11",
  month =        nov,
  year =         "1986",
  bibdate =      "Mon Dec 29 16:20:01 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/4622650/fulltext.html",
  abstract =     "Circuitry for generating scalar products and sums of
                 floating point numbers with maximum accuracy and
                 circuitry and a method for electronic computers by
                 which scalar products of floating point numbers of the
                 type pi, qi, ES(b,l,e1,e2) are summed with full
                 precision in a fixed point representation by means of a
                 summing unit (ALU) and one or more accumulator
                 registers (ARC1, ARC2) with cells (Ai, j) for storing
                 of codes of a base b having a length (2l + 2 e1 + 2e2)
                 for fixed point representation and certain overflow
                 positions. By control means (SHR, E, Contr) the
                 mantissas of products are delivered depending on the
                 value of the respective exponents into the summing unit
                 (ALU). By control means (RD, Contro), rounding
                 operations demanded by the higher level computer are
                 performed, and a rounded floating point number and
                 overflow (OF) and underflow (UF) criteria are
                 delivered. Parallel, serial and word organized summing
                 units (ALU) and accumulator registers (ACR) are usable
                 and in another embodiment, the multiplication of the
                 factors (pi, qi) is performed using a table of
                 multiples store.",
  acknowledgement = ack-nhfb,
}

@Article{Lorang:1986:SD,
  author =       "O. Lorang",
  title =        "{Schnelle Division} \toenglish {Fast Division}
                 \endtoenglish",
  journal =      j-ELECTRONIK,
  volume =       "22",
  pages =        "167--168",
  year =         "1986",
  CODEN =        "EKRKAR",
  ISSN =         "0013-5658",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektronik",
}

@Article{MacIntyre:1986:UOS,
  author =       "Ferren MacIntyre and Thomas Dowling",
  title =        "User-oriented suggestions for floating-point and
                 complex-arithmetic {Forth} standard extensions",
  journal =      j-J-FORTH-APPL-RES,
  volume =       "3",
  number =       "4",
  pages =        "65--84",
  year =         "1986",
  CODEN =        "JFAREL",
  ISSN =         "0738-2022",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  bibno =        "11736",
  catcode =      "D.3.2; D.3.0; H.1.2; G.1.0",
  CRclass =      "D.3.2 Language Classifications; D.3.2 FORTH; D.3.0
                 General; D.3.0 Standards; H.1.2 User/Machine Systems;
                 H.1.2 Human factors; G.1.0 General; G.1.0 Computer
                 arithmetic",
  descriptor =   "Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTH; Software, PROGRAMMING
                 LANGUAGES, General, Standards; Information Systems,
                 MODELS AND PRINCIPLES, User/Machine Systems, Human
                 factors; Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Computer arithmetic",
  fjournal =     "Journal of FORTH Application and Research",
  genterm =      "LANGUAGES; THEORY; HUMAN FACTORS; STANDARDIZATION",
  guideno =      "1986-08466",
  journalabbrev = "J. FORTH Appl. Res.",
  subject =      "D. Software; D.3 PROGRAMMING LANGUAGES; D. Software;
                 D.3 PROGRAMMING LANGUAGES; H. Information Systems; H.1
                 MODELS AND PRINCIPLES; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS",
}

@Article{Marrin:1986:MBF,
  author =       "K. Marrin",
  title =        "Microprocessor brings floating-point capability to
                 32-bit market",
  journal =      j-COMP-DESIGN,
  volume =       "25",
  number =       "9",
  pages =        "31--38",
  day =          "1",
  month =        may,
  year =         "1986",
  CODEN =        "CMPDAM",
  ISSN =         "0010-4566",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  bibno =        "20530",
  catcode =      "B.7.1",
  CRclass =      "B.7.1 Types and Design Styles; B.7.1 Advanced
                 technologies",
  descriptor =   "Hardware, INTEGRATED CIRCUITS, Types and Design
                 Styles, Advanced technologies",
  fjournal =     "Computer Design",
  genterm =      "DESIGN",
  guideno =      "1986-03960",
  journalabbrev = "Comput. Des.",
  subject =      "B. Hardware; B.7 INTEGRATED CIRCUITS",
}

@Article{Marrin:1986:PBT,
  author =       "K. Marrin",
  title =        "Plug-in boards transform {PCs} into floating-point
                 workstations",
  journal =      j-COMP-DESIGN,
  volume =       "25",
  number =       "4",
  pages =        "31--34",
  day =          "15",
  month =        feb,
  year =         "1986",
  CODEN =        "CMPDAM",
  ISSN =         "0010-4566",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  bibno =        "19192",
  catcode =      "K.8; C.1.2; C.4",
  CRclass =      "C.1.2 Multiple Data Stream Architectures
                 (Multiprocessors); C.1.2 Array and vector processors",
  descriptor =   "Computing Milieux, PERSONAL COMPUTING; Computer
                 Systems Organization, PROCESSOR ARCHITECTURES, Multiple
                 Data Stream Architectures (Multiprocessors), Array and
                 vector processors; Computer Systems Organization,
                 PERFORMANCE OF SYSTEMS",
  fjournal =     "Computer Design",
  genterm =      "DESIGN; PERFORMANCE; MEASUREMENT",
  guideno =      "1986-03913",
  journalabbrev = "Comput. Des.",
  subject =      "K. Computing Milieux; K.8 PERSONAL COMPUTING; C.
                 Computer Systems Organization; C.1 PROCESSOR
                 ARCHITECTURES; C. Computer Systems Organization; C.4
                 PERFORMANCE OF SYSTEMS",
}

@InProceedings{Melear:1986:HSM,
  author =       "C. Melear and D. Tietjen",
  title =        "High Speed Math Using a Floating Point Coprocessor",
  crossref =     "Mini-Micro:1986:EMM",
  pages =        "14/3/1--8",
  year =         "1986",
  bibdate =      "Wed Sep 7 22:31:45 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@MastersThesis{Moore:1986:PFS,
  author =       "Brian A. Moore",
  title =        "A pipelined floating-point systolic array arithmetic
                 processor",
  type =         "Thesis ({M.S.})",
  school =       "Brigham Young University. Department of Electrical
                 Engineering",
  address =      "Provo, UT, USA",
  pages =        "vi + 58",
  year =         "1986",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer architecture.; Computer arithmetic and logic
                 units.; Computers, Pipeline.",
}

@Article{Moshier:1986:CA,
  author =       "S. L. Moshier",
  title =        "Computer Approximations",
  journal =      j-BYTE,
  volume =       "11",
  number =       "4",
  pages =        "161--178",
  month =        apr,
  year =         "1986",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Thu Sep 1 10:15:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "BYTE Magazine",
}

@Article{Ngai:1986:RAT,
  author =       "Tin-Fook Ngai and Mary Jane Irwin and Shishpal Rawat",
  title =        "Regular, Area-Time Efficient Carry-Lookahead Adders",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "3",
  number =       "1",
  pages =        "92--105",
  month =        mar,
  year =         "1986",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Mon Apr 14 07:47:57 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliationaddress = "Stanford Univ, Stanford, CA, USA",
  classification = "723; 921; C5230 (Digital arithmetic methods)",
  corpsource =   "Department of Electr. Eng., Stanford University, CA,
                 USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "adders; Adders; area-time efficiency; carry chain
                 computation; carry logic; carry-lookahead adders;
                 carry-lookahead adders (cla); computers; digital
                 arithmetic; fast binary addition; integrated circuits,
                 VLSI --- Electric Wiring; interconnection wire length;
                 log n; log N stage design; maximum; regularity; stage
                 design; VLSI",
  treatment =    "P Practical",
}

@Article{Nowak:1986:HBU,
  author =       "M. Nowak",
  title =        "{Hex-BCD-Um\-wand\-lung} \toenglish {Hexadecimal-BCD
                 Conversion} \endtoenglish",
  journal =      j-MC,
  volume =       "10",
  pages =        "68",
  year =         "1986",
  ISSN =         "0720-4442, 0941-777x, 0943-5409",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "MC: Die Mikrocomputer-Zeitschrift",
}

@PhdThesis{Paez-Monzon:1986:ERC,
  author =       "Gerard Paez-Monzon",
  title =        "{{\'E}}tude et {R}{\'e}alisation d'un Co-processeur
                 Arithm{\'e}tique en Virgule Flottante. ({French})
                 [{Study} and Implementation of a Floating-Point
                 Coprocessor]",
  type =         "Doctorat d'{\'E}tat",
  school =       "Sciences Appliqu{\'e}es, Universit{\'e} Paris 6",
  address =      "Paris, France",
  pages =        "229",
  year =         "1986",
  bibdate =      "Thu May 09 09:55:31 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Sous la direction de Gerard Noguez.",
  abstract =     "Le premier chapitre d'introduction d{\'e}crit
                 l'{\'e}tat de l'art dans le domaine des
                 algorithmes-cabl{\'e}s {\'e}l{\'e}mentaires
                 utilis{\'e}s dans l'arithm{\'e}tique flottante. Nous y
                 pr{\'e}sentons une classification architecturale des
                 coprocesseurs arithm{\'e}tiques en virgule flottante.
                 {\`A} partir d'une comparaison de trois standards de
                 virgule flottante orient{\'e}s vers les syst{\`e}mes
                 bases sur microprocesseurs: IEEE-P754, VAX-DEC, et
                 Hewlett--Packard, le deuxi{\`e}me chapitre explique le
                 choix de l'architecture externe de coprocesseur. Le
                 troisi{\`e}me chapitre pr{\'e}sente l'architecture
                 interne microprogramm{\'e}e et l'organisation du
                 coprocesseur d{\'e}velopp{\'e} dans l'{\'e}tude,
                 nomm{\'e}e FPU-IP6. Dans le quatri{\`e}me chapitre,
                 nous proposons une nouvelle m{\'e}thode pour le
                 d{\'e}veloppement des microprogrammes. La cle de la
                 m{\'e}thode est la visualisation de la s{\'e}paration
                 des phases de planification et d'implantation. Le
                 cinqui{\`e}me chapitre pr{\'e}sente les microprogrammes
                 d{\'e}velopp{\'e}s pour notre coprocesseur. Nous
                 analysons les diff{\'e}rents micro-algorithmes selon le
                 type d'instruction (E/S, arith, etc) et la
                 pr{\'e}cision (simple, double). L'organisation de
                 l'espace de la microm{\'e}moire est present{\'e}e. Le
                 sixi{\`e}me chapitre d{\'e}crit l'{\'e}tude
                 realis{\'e}e pour l'int{\'e}gration du coprocesseur
                 dans le compilateur C et le syst{\`e}me UNIX de la
                 machine SM90.",
  acknowledgement = ack-nhfb,
  language =     "French",
}

@Article{Payne:1986:PTF,
  author =       "Mary H. Payne",
  title =        "Proposal for the transfer of floating point data",
  journal =      j-SIGNUM,
  volume =       "21",
  number =       "3",
  pages =        "25--26",
  month =        jul,
  year =         "1986",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Mon Apr 25 11:24:15 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}

@Article{Petkovic:1986:SIS,
  author =       "M. S. Petkovi{\'c} and L. V. Stefanovi{\'c}",
  title =        "On some improvements of square root iteration for
                 polynomial complex zeros",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "15",
  number =       "1",
  pages =        "13--25",
  month =        may,
  year =         "1986",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/0377-0427(86)90235-9",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 11:59:55 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042786902359",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "polynomial root finding",
}

@Article{Pfenninger:1986:SQA,
  author =       "E. Pfenninger",
  title =        "{Schneller Quadratwurzel-Algorithmus} \toenglish {Fast
                 Square-Root Algorithms} \endtoenglish",
  journal =      j-ELECTRONIK,
  volume =       "22",
  pages =        "179--180",
  year =         "1986",
  CODEN =        "EKRKAR",
  ISSN =         "0013-5658",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektronik",
}

@Article{Porter:1986:FPM,
  author =       "K. Porter and J. Kath",
  title =        "Floating-point methods combine to boost performance",
  journal =      j-COMP-DESIGN,
  volume =       "25",
  number =       "3",
  pages =        "75--80",
  month =        feb,
  year =         "1986",
  CODEN =        "CMPDAM",
  ISSN =         "0010-4566",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  bibno =        "18468",
  catcode =      "G.1.0; K.1",
  CRclass =      "G.1.0 General; G.1.0 Computer arithmetic; K.1
                 Standards",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Computer arithmetic; Computing Milieux, THE COMPUTER
                 INDUSTRY, Standards",
  fjournal =     "Computer Design",
  genterm =      "DESIGN; THEORY; ALGORITHMS; PERFORMANCE;
                 STANDARDIZATION",
  guideno =      "1986-03910",
  journalabbrev = "Comput. Des.",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 K. Computing Milieux; K.1 THE COMPUTER INDUSTRY",
}

@Article{Quong:1986:FPI,
  author =       "D. Quong",
  title =        "Floating-point $ \mu {P} $ implements high-speed math
                 functions",
  journal =      j-EDN,
  volume =       "31",
  number =       "3",
  pages =        "143--150",
  month =        feb,
  year =         "1986",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Wed Sep 7 22:31:45 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "EDN",
}

@Article{Ramnarayan:1986:LCL,
  author =       "R. Ramnarayan and F. Taylor",
  title =        "Limit cycles in large moduli residue number system
                 digital filters",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "33",
  number =       "9",
  pages =        "912--915",
  month =        sep,
  year =         "1986",
  CODEN =        "ICSYBT",
  DOI =          "https://doi.org/10.1049/el:19850252",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23584",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
}

@Article{Rhyne:1986:SBS,
  author =       "T. Rhyne and N. R. {Strader II}",
  title =        "A Signed Bit-Sequential Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-35",
  number =       "10",
  pages =        "896--901",
  month =        oct,
  year =         "1986",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1986.1676680",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 14:09:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  note =         "See comments \cite{Smith:1989:CSB}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676680",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@TechReport{Robertson:1986:NQD,
  author =       "James Evans Robertson",
  title =        "Normalization and quotient digit selection for a
                 variable precision arithmetic unit",
  type =         "Report",
  number =       "UIUCDCS-R-86-1229",
  institution =  "Department of Computer Science, University of Illinois
                 at Urbana-Champaign",
  address =      "Urbana, IL, USA",
  pages =        "14",
  year =         "1986",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.",
  remark =       "``April 1986.''--Cover. ``UILU-ENG-86-1723.''--Cover.
                 Bibliography: p. 13.",
}

@Article{Rump:1986:SER,
  author =       "Siegfried M. Rump",
  title =        "{Sichere Ergebnisse auf Rechenanlagen} \toenglish
                 {Safe Results from Computers} \endtoenglish",
  journal =      j-INFORMATIK-SPEKTRUM,
  volume =       "9",
  number =       "3",
  pages =        "174--183",
  month =        jun,
  year =         "1986",
  CODEN =        "INSKDW",
  ISSN =         "0170-6012 (print), 1432-122X (electronic)",
  ISSN-L =       "0170-6012",
  bibdate =      "Fri Sep 16 16:30:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Informatik Spektrum",
  journal-URL =  "http://link.springer.com/journal/287",
}

@Article{Schatte:1986:ALD,
  author =       "Peter Schatte",
  title =        "On the asymptotic logarithmic distribution of the
                 floating-point mantissas of sums",
  journal =      j-MATH-NACHR,
  volume =       "127",
  pages =        "7--20",
  year =         "1986",
  CODEN =        "MTMNAQ",
  ISSN =         "0025-584X",
  MRclass =      "60F05",
  MRnumber =     "87m:60059",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
  reviewer =     "A. Fuchs",
}

@TechReport{Schmickley:1986:CCP,
  author =       "Ronald D. Schmickley and David H. Bailey",
  title =        "A comparison of the {Cray-2} performance before and
                 after the installation of memory psudo-banking",
  type =         "{NASA} contractor report",
  number =       "NASA CR-177462",
  institution =  "National Aeronautics and Space Administration, Ames
                 Research Center; National Technical Information
                 Service, distributor",
  address =      "Moffett Field, CA, USA",
  pages =        "????",
  year =         "1986",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  govtdocnumber = "NAS 1.26:177462 0830-H-14 (MF)",
  keywords =     "Accounting.; Computer systems performance.; Cray
                 computers.; Floating point arithmetic.; Memory
                 (Computers); Response time (Computers)",
  remark =       "Distributed to depository libraries in microfiche.
                 Microfiche. [Washington, D.C.: National Aeronautics and
                 Space Administration, 1988] 1 microfiche.",
}

@Article{Semba:1986:ADL,
  author =       "I. Semba",
  title =        "An Algorithm for Division of Large Integers",
  journal =      j-INFO-PROC,
  volume =       "9",
  number =       "3",
  pages =        "145--147",
  month =        "????",
  year =         "1986",
  bibdate =      "Thu Sep 1 10:15:09 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@MastersThesis{Shukla:1986:IMN,
  author =       "Pankaj N. Shukla",
  title =        "An implementation on a {MC68000\slash NS32081}
                 microcomputer of binary floating-point arithmetic based
                 on the {IEEE 754} standard",
  type =         "Thesis ({M.S.})",
  school =       "Michigan Technological University",
  address =      "1400 Townsend Drive, Houghton, MI 49931-1295, USA",
  pages =        "vii + 166",
  year =         "1986",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Michigan Technological University. --- Theses
                 ({M.S.}).; MTU Electrical Engineering. --- Thesis
                 ({M.S.}).",
}

@InProceedings{Simcoe:1986:MFP,
  author =       "R. J. Simcoe and A. Fisher and B. M. Leary and W. R.
                 Bidermann and W. R. Wheeler",
  title =        "The {MicroVAX} 78132 Floating Point Chip",
  crossref =     "IEEE:1986:PII",
  pages =        "420--425",
  year =         "1986",
  bibdate =      "Wed Sep 07 23:14:42 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Book{Soderstrand:1986:RNS,
  editor =       "Michael A. Soderstrand and W. K. Jenkins and G. A.
                 Graham and F. J. Taylor",
  title =        "Residue number system arithmetic: modern applications
                 in digital signal processing",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "vii + 418",
  year =         "1986",
  ISBN =         "0-87942-205-X",
  ISBN-13 =      "978-0-87942-205-9",
  LCCN =         "QA247.35 .R45 1986",
  bibdate =      "Wed Nov 14 14:28:02 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "IEEE Press selected reprint series",
  acknowledgement = ack-nhfb,
  subject =      "modular arithmetic; signal processing; digital
                 techniques; computer programming",
}

@Article{Soderstrand:1986:VIM,
  author =       "M. Soderstrand and R. Escott",
  title =        "{VLSI} implementation in multiple-valued logic of an
                 {FIR} digital filter using residue number system
                 arithmetic",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "33",
  number =       "1",
  pages =        "5--25",
  month =        jan,
  year =         "1986",
  CODEN =        "ICSYBT",
  DOI =          "https://doi.org/10.1049/el:19850252",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=23573",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Computer simulations using SPICE establish the
                 feasibility of implementing a highly pipelined
                 high-speed FIR digital filter using Multiple-Valued
                 Logic (MVL) Read-Only Memories (ROM's) to implement
                 Residue Number System (RNS) Arithmetic in VLSI
                 \ldots{}",
}

@TechReport{Spafford:1986:RASa,
  author =       "E. H. Spafford and J. C. Flaspohler",
  title =        "A Report on the Accuracy of Some Floating-Point Math
                 Functions on Selected Computers",
  type =         "Technical Report",
  number =       "GIT-SERC-86/02, GIT-ICS-85/06",
  institution =  "Georgia Institute of Technology",
  pages =        "??",
  year =         "1986",
  bibdate =      "Mon Sep 12 23:54:04 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Spafford:1986:RASb,
  author =       "Eugene H. Spafford and John C. Flaspohler",
  title =        "A Report on the Accuracy of Some Floating Point Math
                 Functions on Selected Computers",
  journal =      j-LOGIN,
  volume =       "11",
  number =       "2",
  pages =        "31--56",
  month =        mar # "\slash " # apr,
  year =         "1986",
  CODEN =        "LOGNEM",
  ISSN =         "1044-6397 (print), 2169-9364 (electronic)",
  bibdate =      "Tue Feb 20 15:42:13 MST 1996",
  bibsource =    "ftp://ftp.uu.net/library/bibliography;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Georgia Institute of Technology",
  fjournal =     ";login: the USENIX Association newsletter",
}

@Article{Stewart:1986:CNC,
  author =       "G. W. Stewart",
  title =        "Corrigendum: ``{A} Note on Complex Division''",
  journal =      j-TOMS,
  volume =       "12",
  number =       "3",
  pages =        "285",
  month =        sep,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/7921.356182",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 21:20:12 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Stewart:1985:NCD}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@InProceedings{Strobach:1986:NFL,
  author =       "P. Strobach",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing: {ICASSP '86}",
  title =        "New forms of least squares lattice algorithms and a
                 comparison of their round-off error characteristics",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "573--576",
  year =         "1986",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Two versions of the most recently introduced ``pure
                 order recursive'' LS lattice algorithm are discussed in
                 this paper. An analysis of the round-off error
                 characteristics of the new order recursive lattice
                 method is performed and a comparison is made \ldots{}",
}

@Article{Stummel:1986:SOP,
  author =       "F. Stummel",
  title =        "Strict optimal a posteriori error and residual bounds
                 for {Gaussian} elimination in floating-point
                 arithmetic",
  journal =      j-COMPUTING,
  volume =       "37",
  number =       "2",
  pages =        "103--124",
  year =         "1986",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65F05 (65G05)",
  MRnumber =     "88b:65047",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  reviewer =     "Alfonso Laratta",
}

@Manual{Sun:1986:FPG,
  title =        "Floating-point programmer's guide for the {Sun}
                 workstation",
  publisher =    "Sun Microsystems, Inc.",
  address =      "Mountain View, CA, USA",
  edition =      "Revision {A} of 19 {September} 1986.",
  pages =        "various",
  year =         "1986",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic and logic units.; Floating-point
                 arithmetic.",
  remark =       "``Part Number 800-1552-10.''",
}

@Article{Thun:1986:RNS,
  author =       "R. Thun",
  title =        "On residue number system decoding",
  journal =      "Acoustics, Speech, and Signal Processing [see also
                 IEEE Transactions on Signal Processing], IEEE
                 Transactions on",
  volume =       "34",
  number =       "5",
  pages =        "1346--1347",
  month =        oct,
  year =         "1986",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26200",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The use of a residue number system (RNS) in digital
                 systems and especially filter designs is facilitated by
                 efficient algorithms for the conversion from RNS to
                 binary numbers. The conversion is generally based on
                 the Chinese remainder theorem or the \ldots{}",
}

@Article{Troutman:1986:DSF,
  author =       "W. W. Troutman and P. W. Diodato and A. K. Goksel and
                 Mean-Sea Tsay and R. H. Krambeck",
  title =        "Design of a Standard Floating-Point Chip",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "21",
  number =       "3",
  pages =        "396--399",
  month =        jun,
  year =         "1986",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:53 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "Some aspects of design of a VLSI floating-point chip,
                 which provides the WE{\reg}32100 microprocessor with
                 math acceleration capabilities, are described. The chip
                 is implemented in 1.75-$\mu$m twin-tub CMOS II
                 technology [2] and contains \ldots{}",
}

@Article{Truong:1986:TCD,
  author =       "T. K. Truong and J. J. Chang and I. S. Hsu and D. Y.
                 Pei and I. S. Reed",
  title =        "Techniques for Computing the Discrete {Fourier}
                 Transform Using the Quadratic Residue {Fermat} Number
                 Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-35",
  number =       "11",
  pages =        "1008--1012",
  month =        nov,
  year =         "1986",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1986.1676704",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 14:09:53 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676704",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Twaddell:1986:HPM,
  author =       "W. Twaddell",
  title =        "Higher performance marks floating-point chips",
  journal =      j-COMP-DESIGN,
  volume =       "25",
  number =       "8",
  pages =        "24--30",
  day =          "15",
  month =        apr,
  year =         "1986",
  CODEN =        "CMPDAM",
  ISSN =         "0010-4566",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  bibno =        "19171",
  catcode =      "B.7.1; C.4",
  CRclass =      "B.7.1 Types and Design Styles; B.7.1 Advanced
                 technologies",
  descriptor =   "Hardware, INTEGRATED CIRCUITS, Types and Design
                 Styles, Advanced technologies; Computer Systems
                 Organization, PERFORMANCE OF SYSTEMS",
  fjournal =     "Computer Design",
  genterm =      "DESIGN; PERFORMANCE",
  guideno =      "1986-03952",
  journalabbrev = "Comput. Des.",
  subject =      "B. Hardware; B.7 INTEGRATED CIRCUITS; C. Computer
                 Systems Organization; C.4 PERFORMANCE OF SYSTEMS",
}

@InProceedings{Vaccaro:1986:SDF,
  author =       "J. Vaccaro and B. Johnson and C. Nowacki",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing, {ICASSP '86}",
  title =        "A systolic discrete {Fourier} transform using residue
                 number systems over the ring of {Gaussian} integers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1157--1160",
  month =        aug,
  year =         "1986",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A VLSI implementation of a bit-serial systolic
                 architecture for a DFT processor has been developed
                 which performs residue number system (RNS) processing
                 over the ring of Gaussian integers. An architecture for
                 a 128-point DFT using the chirp z-transform algorithm
                 is described, and its use in an R2FFT architecture to
                 obtain a 16,384-point transform is illustrated. Based
                 on three custom-designed chips, the processor is
                 capable of transforming data at a continuous 2 MHz
                 rate. The use of RNS techniques and systolic arrays
                 provides two dimensions of parallelism, resulting in
                 hardware of low complexity and high speed. The overall
                 system has great flexibility in dynamic range, and can
                 be used in many signal processing applications.",
}

@MastersThesis{Verma:1986:DEF,
  author =       "Deepak Verma",
  title =        "Design of an efficient floating point vector
                 coprocessor of an advanced microcomputer system",
  type =         "Thesis ({M.S.})",
  school =       "Department of Computer Engineering and Science, Case
                 Western Reserve University",
  address =      "Cleveland, OH 44106, USA",
  pages =        "viii + 121",
  year =         "1986",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Waterhouse:1986:TMW,
  author =       "William C. Waterhouse",
  title =        "The Teaching of Mathematics: Why Square Roots are
                 Irrational",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "93",
  number =       "3",
  pages =        "213--214",
  month =        mar,
  year =         "1986",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:38:15 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@TechReport{Weitek:1986:WSW,
  author =       "{Weitek Corporation}",
  title =        "{WTL} 1164\slash {WTL} 1165 64-bit {IEEE}
                 Float\-ing-Point Multiplier\slash Divider and {ALU}",
  institution =  pub-WEITEK,
  address =      pub-WEITEK:adr,
  month =        jul,
  year =         "1986",
  bibdate =      "Thu Nov 8 14:50:32 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@TechReport{Wichmann:1986:FPI,
  author =       "Brian A. Wichmann",
  title =        "Floating point interval arithmetic for validation",
  institution =  "National Physical Laboratory, Division of Information
                 Technology and Computing",
  address =      "Teddington Middlesex",
  pages =        "i + 12",
  year =         "1986",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "NPL report; DITC 76/86",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithms.; Floating-point arithmetic.",
}

@Article{Wollenberg:1986:SRD,
  author =       "R. Wollenberg and R. Milnikel",
  title =        "{Schnelles Radizierverfahren durch Tabellenzugriff}
                 \toenglish {Fast Square-rooting Method by Means of
                 Table Lookup} \endtoenglish",
  journal =      j-ELECTRONIK,
  volume =       "6",
  pages =        "79--82",
  year =         "1986",
  CODEN =        "EKRKAR",
  ISSN =         "0013-5658",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektronik",
}

@Article{Agarwal:1987:CNS,
  author =       "Ramesh C. Agarwal and James W. Cooley and Fred G.
                 Gustavson and James B. Shearer and Gordon Slishman and
                 Bryant Tuckerman",
  title =        "Clarification: {``New scalar and vector elementary
                 functions for the IBM System\slash 370''} [{IBM J. Res.
                 Develop. {\bf 30} (1986), no. 2, 126--144}]",
  journal =      j-IBM-JRD,
  volume =       "31",
  number =       "2",
  pages =        "274--274",
  month =        mar,
  year =         "1987",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.312.0274",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  MRclass =      "76W05",
  MRnumber =     "MR894626",
  bibdate =      "Mon Feb 12 08:07:08 2001",
  bibsource =    "http://www.research.ibm.com/journal/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
  note =         "See \cite{Agarwal:1986:NSV}.",
  acknowledgement = ack-nhfb,
  ajournal =     "IBM J. Res. Develop.",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}

@InProceedings{Agrawal:1987:CEF,
  author =       "J. C. Agrawal and P. S. Sehdev",
  title =        "Comparison and Evaluation of Floating Point
                 Representations in {IBM\slash 370} and {VAX-11\slash
                 780}",
  crossref =     "Zunde:1987:EFI",
  pages =        "353--369",
  year =         "1987",
  bibdate =      "Wed Sep 14 20:23:44 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Ahmad:1987:IDA,
  author =       "M. Ahmad",
  title =        "Implementable Decimal Arithmetic Algorithms for
                 Micro\slash Minicomputers",
  journal =      j-MICROPROC-MICROPROG,
  volume =       "19",
  number =       "2",
  pages =        "119--128",
  month =        feb,
  year =         "1987",
  CODEN =        "MMICDT",
  ISSN =         "0165-6074 (print), 1878-7061 (electronic)",
  ISSN-L =       "0165-6074",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Microprocessing and Microprogramming",
  journal-URL =  "https://www.sciencedirect.com/journal/microprocessing-and-microprogramming/issues",
  keywords =     "decimal floating-point arithmetic",
}

@Article{Anonymous:1987:BRCe,
  author =       "Anonymous",
  title =        "Book Review: {{\booktitle{Computer arithmetic ---
                 scientific computation and programming languages}}: E.
                 Kaucher, U. Kulisch and Ch. Ullrich (Eds): B. G.
                 Teubner, Stuttgart, 1987, 456 pages, DM 28.00, ISBN
                 3-519- 02448-9}",
  journal =      j-MATH-COMPUT-SIMUL,
  volume =       "29",
  number =       "5",
  pages =        "448--449",
  month =        oct,
  year =         "1987",
  CODEN =        "MCSIDR",
  DOI =          "https://doi.org/10.1016/0378-4754(87)90086-3",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  bibdate =      "Mon Aug 18 16:03:53 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomputsimul1980.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/0378475487900863",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput. Simul.",
  fjournal =     "Mathematics and Computers in Simulation",
  journal-URL =  "https://www.sciencedirect.com/science/journal/03784754",
}

@Article{Anonymous:1987:MAU,
  author =       "Anonymous",
  title =        "Multiply-Addition --- An Ultra High Performance
                 Dataflow",
  journal =      j-IBM-TDB,
  volume =       "30",
  number =       "3",
  pages =        "982--987",
  month =        aug,
  year =         "1987",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Thu Oct 17 12:06:22 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Technical Disclosure Bulletin",
  keywords =     "FMA; fused multiply-add",
  remark =       "Author(s) unknown; I cannot find an online copy of
                 this paper. This may be the first publication on the
                 fused multiply-add operation, first implemented in
                 hardware in early 1990 on the IBM POWER CPU, and
                 standardized in IEEE 754-2008.",
}

@Book{ANSI:1987:AIS,
  author =       "{ANSI\slash IEEE}",
  title =        "{ANSI\slash IEEE Std 854-1987: An American National
                 Standard: IEEE Standard for Radix-Independent
                 Floating-Point Arithmetic}",
  publisher =    pub-IEEE-STD,
  address =      pub-IEEE-STD:adr,
  pages =        "v + 14",
  day =          "5",
  month =        oct,
  year =         "1987",
  ISBN =         "0-7381-1167-8",
  ISBN-13 =      "978-0-7381-1167-4",
  bibdate =      "Thu Mar 02 09:40:18 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Revised 1994. INSPEC Accession Number: 3095617.",
  price =        "US\$44.00",
  URL =          "http://ieeexplore.ieee.org/xpl/standardstoc.jsp?isnumber=1121&isYear=1987;
                 https://ieeexplore.ieee.org/iel1/2502/1121/00027840.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Ardalan:1987:FPR,
  author =       "S. Ardalan and S. Alexander",
  title =        "Fixed-point roundoff error analysis of the
                 exponentially windowed {RLS} algorithm for time-varying
                 systems",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "35",
  number =       "6",
  pages =        "770--783",
  month =        jun,
  year =         "1987",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  summary =      "A fixed-point roundoff error analysis of the
                 exponentially windowed RLS algorithm is presented. It
                 is shown that a tradeoff exists in the choice of the
                 forgetting factor {\lambda}. In order to reduce the
                 sensitivity of the algorithm to additive noise, {\&}
                 \ldots{}",
}

@MastersThesis{Azmi:1987:FPS,
  author =       "Aqil M. Azmi",
  title =        "A floating point system with variable-length
                 exponent",
  type =         "Thesis ({M.S.})",
  school =       "University of Colorado",
  address =      "Boulder, CO, USA",
  pages =        "viii + 73",
  year =         "1987",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic.; Floating-point arithmetic.",
}

@InProceedings{Balsara:1987:SSS,
  author =       "Paras T. Balsara and Robert M. Owens",
  title =        "Systolic and Semi-Systolic Digit Serial Multipliers",
  crossref =     "Irwin:1987:PSC",
  pages =        "169--173",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158682",
  bibdate =      "Wed Nov 14 18:22:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Balsara_Owens.pdf",
  abstract =     "Digit serial data transmission can be used to an
                 advantage in the design of special purpose processors
                 where communication issues dominate and where digit
                 pipelining can be used to maintain high data rates.
                 VLSI signal processing is one such problem domain. We
                 propose designs of systolic and semi-systolic digit
                 serial multipliers. These multipliers are programmable
                 i.e., one operand is pre-stored in the multiplier and
                 the other operand is fed in a digit serial fashion..
                 The VLSI implementation of the systolic multiplier is
                 also given. This systolic multiplier is used in our
                 VLSI signal processing system.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@MastersThesis{Baranyk:1987:EBP,
  author =       "Michael L. Baranyk",
  title =        "Extensions beyond the proposed {IEEE} standard number
                 754 for binary floating point arithmetic",
  type =         "Thesis ({M.S.})",
  school =       "Marquette University",
  address =      "Milwaukee, WI, USA",
  pages =        "various",
  year =         "1987",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Binary system (Mathematics); Floating-point
                 arithmetic.; Institute of Electrical and Electronics
                 Engineers. --- IEEE; standard 754.",
}

@InProceedings{Barrett:1987:FAR,
  author =       "Geoff Barrett",
  title =        "A formal approach to rounding",
  crossref =     "Irwin:1987:PSC",
  pages =        "247--254",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158683",
  bibdate =      "Wed Nov 24 12:49:55 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Barrett.pdf",
  abstract =     "This paper presents a formal description of rounding,
                 as specified in the IEEE Standard, and an algorithm to
                 perform the task along with its proof of correctness.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@TechReport{Barrett:1987:FMA,
  author =       "Geoff Barrett",
  title =        "Formal methods applied to a floating point number
                 system",
  type =         "Technical monograph",
  number =       "PRG 58",
  institution =  "Oxford University Computing Laboratory",
  address =      "Oxford, England",
  pages =        "47",
  year =         "1987",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Binary system (Mathematics).; Floating-point
                 arithmetic.; Formal languages.",
}

@Article{Boettner:1987:QA,
  author =       "H. B{\"o}ttner",
  title =        "{Quadratwurzel-Algorithmus} \toenglish {Square-Root
                 Algorithms} \endtoenglish",
  journal =      j-MC,
  volume =       "5",
  pages =        "58",
  year =         "1987",
  ISSN =         "0720-4442, 0941-777x, 0943-5409",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "MC: Die Mikrocomputer-Zeitschrift",
}

@InCollection{Bohlender:1987:DFP,
  author =       "G. Bohlender and T. Teufel",
  title =        "A Decimal Floating-Point Processor for Optimal
                 Arithmetic",
  crossref =     "Kaucher:1987:CAS",
  pages =        "31--58",
  year =         "1987",
  bibdate =      "Fri Nov 28 11:46:56 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@Article{Boisvert:1987:AAH,
  author =       "Ronald F. Boisvert",
  title =        "{Algorithm 651}: Algorithm {HFFT}\emdash High-Order
                 Fast-Direct Solution of the {Helmholtz} Equation",
  journal =      j-TOMS,
  volume =       "13",
  number =       "3",
  pages =        "235--249",
  month =        sep,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/29380.214342",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65V05",
  MRnumber =     "918 578",
  bibdate =      "Sun Sep 4 21:40:33 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also \cite{Johnson:1987:CES}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1987-13-3/p235-boisvert/",
  abstract =     "HFFT is a software package for solving the Helmholtz
                 equation on bounded two- and three-dimensional
                 rectangular domains with Dirichlet, Neumann, or
                 periodic boundary conditions. The software is the
                 result of combining new fourth-order accurate compact
                 finite difference (HODIE) discretizations and a
                 fast-direct solution technique (the Fourier method). In
                 this paper we briefly describe the user interface to
                 HFFT and present an example of its usage and several
                 details of its implementation.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory; verification",
  subject =      "{\bf G.1.8}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Partial Differential Equations, Elliptic
                 equations. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis.",
}

@Article{Bose:1987:DAR,
  author =       "B. Bose",
  title =        "$2$-dimensional arithmetic residue check codes",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "13",
  number =       "5--6",
  pages =        "547--554",
  month =        "????",
  year =         "1987",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 19:01:00 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122187900824",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@InProceedings{Bose:1987:FMD,
  author =       "B. K. Bose and L. Pei and G. S. Taylor and D. A.
                 Patterson",
  title =        "Fast Multiply and Divide for a {VLSI} Floating-Point
                 Unit",
  crossref =     "Irwin:1987:PSC",
  pages =        "87--93",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158684",
  bibdate =      "Wed Nov 14 18:22:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Bose_Pei_Taylor_Patterson.pdf",
  abstract =     "This paper presents the design of a fast and
                 area-efficient multiply-divide unit used in building a
                 VLSI floating-point processor (FPU), conforming to the
                 IEEE standard 754. Details of the algorithms,
                 implementation techniques and design tradeoffs are
                 presented. The multiplier and divider are implemented
                 in 2 micron CMOS technology with two layers of metal,
                 and occupy 23 square mm (23\% of the entire FPU). We
                 expect to perform extended-precision multiplication and
                 division in 1.1 and 2.8 microseconds, respectively.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@PhdThesis{Braune:1987:HSF,
  author =       "K. Braune",
  title =        "{Hochgenaue Standardfunktionen f{\"u}r reelle und
                 komplexe Punkte und Intervalle in beliebigen
                 Gleitpunktrastern} \toenglish {High-Accuracy Elementary
                 Functions for Real and Complex Points and Intervals in
                 Arbitrary Floating-Point Systems} \endtoenglish",
  type =         "Dissertation",
  school =       "Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "??",
  year =         "1987",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@InCollection{Breuer:1987:NMR,
  author =       "P. T. Breuer",
  title =        "A New Method for Real Rational Uniform Approximation",
  crossref =     "Mason:1987:AAB",
  pages =        "265--284",
  year =         "1987",
  bibdate =      "Thu Sep 01 12:25:00 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@InProceedings{Carter:1987:SAT,
  author =       "Tony M. Carter",
  title =        "Structured Arithmetic Tiling of Integrated Circuits",
  crossref =     "Irwin:1987:PSC",
  pages =        "41--48",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158685",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Carter.pdf",
  abstract =     "Robertson's Theory of Decomposition and Structured
                 Tiling (an IC design technique) are combined in a
                 structured arithmetic circuit design method. This
                 method, extended by a set of inverse operators and a
                 set of multiply operators, is used with computer-aided
                 design tools to automate the design of arithmetic
                 circuits.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@InProceedings{Cavallaro:1987:CAS,
  author =       "Joseph R. Cavallaro and Franklin T. Luk",
  title =        "{CORDIC} Arithmetic for an {SVD} Processor",
  crossref =     "Irwin:1987:PSC",
  pages =        "113--120",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158686",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Cavallaro_Luk.pdf",
  abstract =     "Arithmetic issues in the calculation of the Singular
                 Value Decomposition (SVD) are discussed. Traditional
                 algorithms using hardware division and square root are
                 replaced with the special purpose CORDIC algorithms for
                 computing vector rotations and inverse tangents. The
                 CORDIC $ 2 \times 2 $ SVD processor can be twice as
                 fast as one assembled from traditional hardware units.
                 A prototype VISI implementation of a CORDIC SVD
                 processor array is planned for use in real-time signal
                 processing applications.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@Article{Chandra:1987:ACR,
  author =       "D. V. Chandra",
  title =        "Accumulation of coefficient roundoff error in fast
                 {Fourier} transforms implemented with logarithmic
                 number system",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "35",
  number =       "11",
  pages =        "1633--1636",
  month =        nov,
  year =         "1987",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  summary =      "When a fast Fourier transform (FFT) is implemented on
                 a digital computer or with special-purpose hardware,
                 quantization errors will arise due to finite word
                 lengths in the digital system. This correspondence
                 presents an analysis of error \ldots{}",
}

@Article{Chen:1987:MFP,
  author =       "Chang-Fuu Chen",
  title =        "A modified floating-point code for voice coding and
                 its applications",
  journal =      j-J-CHINESE-INST-ENG,
  volume =       "10",
  number =       "4",
  pages =        "421--427",
  month =        jul,
  year =         "1987",
  CODEN =        "CKCKDZ",
  ISSN =         "0253-3839",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Tatung Institute of Technology, Taipei, Taiwan",
  bibno =        "43559",
  catcode =      "E.4; I.2.7; I.2.10; I.5.4",
  CRclass =      "E.4 Data compaction and compression; I.2.7 Natural
                 Language Processing; I.2.7 Speech recognition and
                 understanding; I.2.10 Vision and Scene Understanding;
                 I.2.10 Modeling and recovery of physical attributes;
                 I.5.4 Applications; I.5.4 Signal processing",
  descriptor =   "Data, CODING AND INFORMATION THEORY, Data compaction
                 and compression; Computing Methodologies, ARTIFICIAL
                 INTELLIGENCE, Natural Language Processing, Speech
                 recognition and understanding; Computing Methodologies,
                 ARTIFICIAL INTELLIGENCE, Vision and Scene
                 Understanding, Modeling and recovery of physical
                 attributes; Computing Methodologies, PATTERN
                 RECOGNITION, Applications, Signal processing",
  fjournal =     "Journal of the Chinese Institute of Engineers =
                 Chung-kuo kung ch'eng hsueh kan",
  genterm =      "THEORY; ALGORITHMS; HUMAN FACTORS; DESIGN",
  guideno =      "1988-11733",
  journalabbrev = "J. Chin. Inst. Eng.",
  subject =      "E. Data; E.4 CODING AND INFORMATION THEORY; I.
                 Computing Methodologies; I.2 ARTIFICIAL INTELLIGENCE;
                 I. Computing Methodologies; I.2 ARTIFICIAL
                 INTELLIGENCE; I. Computing Methodologies; I.5 PATTERN
                 RECOGNITION",
}

@InProceedings{Ciminiera:1987:PMB,
  author =       "Luigi Ciminiera",
  title =        "Parallel Multipliers Based on Horizontal Compressors",
  crossref =     "Irwin:1987:PSC",
  pages =        "63--69",
  month =        may,
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158687",
  bibdate =      "Wed Nov 14 18:22:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Ciminiera.pdf",
  abstract =     "Two new implementations of parallel multipliers, based
                 on iterative arrays of logic cells are presented in
                 this paper. Both are able to compute the product of two
                 $n$ bit numbers with a delay of $n$ cells, rather $ 2 n
                 - 1 $ as in classical structures. The high speed
                 operation is obtained by using pure horizontal
                 compressors, to accelerate the horizontal signal
                 propagation, and by adopting a suitable array
                 structure, to shorten the vertical signal propagation.
                 The cost and performance advantages over similar
                 structures based on vertical compressors are
                 discussed.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@Article{Clenshaw:1987:LIA,
  author =       "C. W. Clenshaw and Frank W. J. Olver",
  title =        "Level-Index Arithmetic Operations",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "24",
  number =       "2",
  pages =        "470--485",
  month =        apr,
  year =         "1987",
  CODEN =        "SJNAAM",
  DOI =          "https://doi.org/10.1137/0724034",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65G05 (65G99)",
  MRnumber =     "881377",
  MRreviewer =   "F. Szidarovszky",
  bibdate =      "Sun Nov 12 06:18:24 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In a recent paper the authors described a system for
                 the internal representation of numbers in a computer,
                 based on repeated exponentiations. The main objective
                 in introducing this system is to eradicate the problems
                 of overflow and underflow. The present paper supplies
                 algorithms for performing the four basic arithmetical
                 operations in the new system. The algorithm are
                 accompanied by error analyses, which show that the
                 algorithms can be executed with fixed-point arithmetic.
                 Illustrative examples are included.",
  acknowledgement = ack-nhfb,
  author-dates = "Charles William Clenshaw (15 March 1926--23 September
                 2004); Frank William John Olver (15 December 1924--23
                 April 2013)",
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
}

@InProceedings{Colagrossi:1987:NAT,
  author =       "A. Colagrossi and A. Miola",
  title =        "A Normalization Algorithm for Truncated $p$-{ADIC}
                 Arithmetic",
  crossref =     "Irwin:1987:PSC",
  pages =        "212--216",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158688",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Colagrossi_Miola.pdf",
  abstract =     "This paper presents a new algorithmic approach to cope
                 with the problems related to the generation and the
                 manipulation of the pseudo-Hensel-codes in the p-adic
                 arithmetic. After reviewing some classical properties
                 and the results of the Hensel code arithmetic, a new
                 algorithm to manipulate pseudo-Hensel-codes is
                 presented, discussed and compared with two existing
                 methods. The lower cost of the proposed new algorithm
                 will result from the comparison.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@InProceedings{Cosnard:1987:FAC,
  author =       "M. Cosnard and A. Guyot and B. Hochet and Jean-Michel
                 Muller and H. Ouaouicha and P. Paul and E. Zysman",
  title =        "The {FELIN} Arithmetic Coprocessor Chip",
  crossref =     "Irwin:1987:PSC",
  pages =        "107--112",
  month =        may,
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158691",
  bibdate =      "Wed Nov 14 18:22:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Cosnard_Guyot_Hochet_Muller_Ouaouicha_Paul_Zysman.pdf",
  abstract =     "We describe a general VLSI architecture for the
                 computation of arithmetic expressions including
                 floating-point transcendental functions. This
                 architecture, is divided in three parts: a
                 communication machine, the control part of a
                 computation machine and the operative part of this
                 computation machine. In order to compute the most usual
                 transcendental functions, we introduced some general
                 algorithms, presented briefly here, including as a
                 particular case the CORDIC scheme. Our major
                 architecture goals were regularity, parametrization and
                 automatic design. The final chip is designed in a 2-Alu
                 CMOS technology, and its name is FELIN (``Fonctions
                 EL{\'e}mentaires INt{\'e}gr{\'e}es'' is the French for
                 ``integrated elementary functions'').",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@TechReport{Crockett:1987:PFF,
  author =       "Thomas W. Crockett",
  title =        "Performance of {Fortran} Floating-Point Operations on
                 the {Flex\slash 32} Multicomputer",
  type =         "{ICASE} Interim Report",
  number =       "4",
  institution =  "ICASE, NASA Langley Research Center",
  address =      "Hampton, VA, USA",
  pages =        "????",
  year =         "1987",
  bibdate =      "Wed Sep 14 20:24:43 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran2.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ovr.bib;
                 Parallel/ovr.bib",
  series =       "NASA contractor report; 178364 ICASE interim report; 4
                 NASA contractor report; NASA CR-178364.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  govtdocnumber = "NAS 1.26:178364 830-H-14 (MF)",
  keywords =     "Computer networks; FORTRAN (Computer program
                 language)",
  remark =       "Distributed to depository libraries in microfiche.
                 Microfiche. [Washington, D.C.?: National Aeronautics
                 and Space Administration], 1987. 1 microfiche.",
}

@InCollection{Crowell:1987:FPA,
  author =       "Charles Crowell",
  title =        "Floating-point arithmetic with the {TMS32020}",
  crossref =     "Lin:1987:DSP",
  pages =        "245--268",
  year =         "1987",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$30.67",
  acknowledgement = ack-nhfb,
  bibno =        "42623",
  catcode =      "J.2; C.5.3; G.1.0",
  CRclass =      "J.2 Mathematics and statistics; C.5.3 Microcomputers;
                 C.5.3 TMS 32010; G.1.0 General; G.1.0 Computer
                 arithmetic",
  descriptor =   "Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Mathematics and statistics; Computer
                 Systems Organization, COMPUTER SYSTEM IMPLEMENTATION,
                 Microcomputers, TMS 32010; Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Computer arithmetic",
  genterm =      "MEASUREMENT; ALGORITHMS",
  guideno =      "1988-01737",
  subject =      "J. Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING; C. Computer Systems Organization; C.5
                 COMPUTER SYSTEM IMPLEMENTATION; G. Mathematics of
                 Computing; G.1 NUMERICAL ANALYSIS",
}

@InProceedings{Demmel:1987:EAA,
  author =       "James W. Demmel",
  title =        "On error analysis in arithmetic with varying relative
                 precision",
  crossref =     "Irwin:1987:PSC",
  pages =        "148--152",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158694",
  bibdate =      "Thu Aug 23 06:14:44 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.netlib.org/na-digest/91/v91n39",
  abstract =     "Recently Clenshaw\slash Olver and Iri\slash Matsui
                 proposed new floating point arithmetics which seek to
                 eliminate overflows and underflows from most
                 computations. Their common approach is to redistribute
                 the available numbers to spread out the largest and
                 smallest numbers much more thinly than in standard
                 floating point, thus achieving a larger range at the
                 cost of lower precision at the ends of the range. The
                 goal of these arithmetics is to eliminate much of the
                 effort needed to write code which is reliable despite
                 over\slash underflow. In this paper we argue that for
                 many codes this eliminated effort will reappear in the
                 error analyses needed to ascertain or guarantee the
                 accuracy of the computed solution. Thus reliability
                 with respect to over\slash underflow has been traded
                 for reliability with respect to roundoff. We also
                 propose a hardware flag, analogous to the ``sticky
                 flags'' of the IEEE binary floating point standard, to
                 do some of this extra error analysis automatically.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
  remark =       "Comments on SLI arithmetic proposed by Olver, Lozier,
                 and Turner, and on Kulisch and Miranker's interval
                 arithmetic and its implementation in IBM's ACRITH
                 product.",
}

@TechReport{Dion:1987:MFA,
  author =       "Jeremy Dion and David Reeves Boggs and Norman P.
                 Jouppi",
  title =        "{MultiTitan}: four architecture papers",
  institution =  "Digital, Western Research Laboratory",
  address =      "Palo Alto, CA, USA",
  pages =        "various",
  year =         "1987",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "WRL research report. Digital Equipment Corporation.
                 Western Research Laboratory; 87-8 Digital Equipment
                 Corporation. Western Research Laboratory. WRL research
                 report; 87/8.",
  acknowledgement = ack-nhfb,
  keywords =     "Titan (Computer)",
}

@InProceedings{DuCroz:1987:DFP,
  author =       "J. {Du Croz} and M. Pont",
  title =        "The Development of a Floating-Point Validation
                 Package",
  crossref =     "Irwin:1987:PSC",
  pages =        "255--255",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158693",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
  remark =       "Paper not received in time for publication.",
}

@Article{Duff:1987:EAP,
  author =       "Iain S. Duff and Jacques Laminie and Alain Lichnewsky
                 and Fran{\c{c}}ois Thomasset",
  title =        "An experiment with arithmetic precision in linear
                 algebra computations",
  journal =      j-INT-J-NUM-METH-FLUIDS,
  volume =       "7",
  number =       "????",
  pages =        "1077--1092",
  year =         "1987",
  bibdate =      "Mon Jan 02 17:53:34 2006",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0363",
}

@Manual{Duhamel:1987:ASR,
  author =       "Bob Duhamel",
  title =        "{Atari} System Reference Manual",
  address =      "6915 Casselberry Way, San Diego, CA 92119, USA",
  year =         "1987",
  bibdate =      "Sat Mar 04 16:04:10 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See Chapter 11: The Floating Point Arithmetic
                 Package.",
  URL =          "http://atrey.karlin.mff.cuni.cz/~pavel/atari/atr11.html;
                 http://web.archive.org/web/20040606074520/trident.mcs.kent.edu/~clisowsk/8bit/atrpref.html",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
  remark =       "The ROM O/S on the Atari 6502 handles decimal
                 floating-point values stored in six-byte fields. The
                 first byte contains the sign and an excess-64 exponent,
                 followed by five bytes containing ten BCD digits. The
                 O/S provides for conversion to and from ASCII string
                 representation, to and from binary integers, add,
                 subtract, multiple, divide, log(), log10(), exp(),
                 exp10(), and polynomial evaluation.",
}

@Article{Dunham:1987:PMA,
  author =       "C. B. Dunham",
  title =        "Provably Monotone Approximations {II}",
  journal =      j-SIGNUM,
  volume =       "22",
  number =       "3",
  pages =        "30--31",
  month =        jul,
  year =         "1987",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Sep 13 09:01:31 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "theory",
  subject =      "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation",
}

@Article{Ercegovac:1987:FCR,
  author =       "M. D. Ercegovac and T. Lang",
  title =        "On-the-fly conversion of redundant into conventional
                 representations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "7",
  pages =        "895--897",
  month =        jul,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.1676986",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Ercegovac:1987:LSC,
  author =       "Milo{\v{s}} D. Ercegovac and Tomas Lang",
  title =        "On-Line Scheme for Computing Rotation Factors",
  crossref =     "Irwin:1987:PSC",
  pages =        "196--203",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158695",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Ercegovac_Lang.pdf",
  abstract =     "An integrated radix-2 on-line algorithm for computing
                 rotation factors for matrix transformations is
                 presented. The inputs and outputs are in parallel form,
                 conventional 2's complement, floating-point
                 representation. The exponents are computed using
                 conventional arithmetic while the significands are
                 processed using on-line algorithms. The conventional
                 result is obtained by using an on-the-fly conversion
                 scheme. The rotation factors are computed in $ 9 + n $
                 clock cycles for $n$-bit significands. The clock period
                 is kept small by the use of carry-save adder schemes.
                 The implementation and performance of the algorithm are
                 discussed.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@InProceedings{Fandrianto:1987:AHS,
  author =       "Jan Fandrianto",
  title =        "Algorithms for High Speed Shared Radix 4 Division and
                 Radix 4 Square-Root",
  crossref =     "Irwin:1987:PSC",
  pages =        "73--79",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158696",
  bibdate =      "Wed Nov 14 18:22:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Fandrianto.pdf",
  abstract =     "An algorithm to implement radix four division and
                 radix four square-root in a shared hardware for IEEE
                 standard for binary floating point format will be
                 described. The algorithm is best suited to be
                 implemented in either off-the-shelf components or being
                 a portion of a VLSI floating-point chip. Division and
                 square-root bits are generated by a non-restoring
                 method while keeping the partial remainder, partial
                 radicand, quotient and root all in redundant forms. The
                 core iteration involves a 8-bit carry look-ahead adder,
                 a multiplexer to convert two's complement to sign
                 magnitude, a 19-term next quotient\slash root
                 prediction PLA, a divisor\slash root multiple selector,
                 and a carry save adder. At the end, two iterations of
                 carry look-ahead adder across the length of th,e
                 mantissa are required to generate the quotient\slash
                 root in a correctly rounded form. Despite its
                 simplicity in the hardware requirement, the algorithm
                 takes only about 30 cycles to compute double precision
                 division or square-root. Finally, extending the
                 algorithm to radix eight or higher division\slash
                 square-root will be discussed.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8; correct rounding; floating-point arithmetic",
}

@Periodical{FPS:1987:AR,
  author =       "{Floating Point Systems, Inc.}",
  key =          "FPS",
  title =        "Annual report",
  publisher =    "Floating Point Systems, Inc.",
  address =      "Portland, OR, USA",
  pages =        "various",
  year =         "1987",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer industry --- United States --- Periodicals.;
                 Floating Point Systems, Inc. --- Periodicals.",
  remark =       "Description based on: 1987.",
}

@Article{Froggatt:1987:FPC,
  author =       "Terry Froggatt",
  title =        "Fixed-point conversion, multiplication, and division
                 in {Ada}",
  journal =      j-SIGADA-LETTERS,
  volume =       "7",
  number =       "1",
  pages =        "71--81",
  month =        jan # "\slash " # feb,
  year =         "1987",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Sat Aug 9 09:05:24 MDT 2003",
  bibsource =    "ftp://ftp.uu.net/library/bibliography;
                 http://portal.acm.org/;
                 http://www.adahome.com/Resources/Bibliography/articles.ref;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "languages; theory",
  subject =      "D.3.2 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Ada \\ G.1.0 Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Computer arithmetic",
}

@Article{Grosse:1987:UCB,
  author =       "Eric Grosse and Cleve Moler",
  title =        "Underflow can be Harmful",
  journal =      j-SIAM-NEWS,
  volume =       "20",
  number =       "6",
  pages =        "1",
  year =         "1987",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibdate =      "Sat Feb 8 10:30:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/grosse-eric.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM News",
  journal-URL =  "https://sinews.siam.org/",
}

@Article{Guyot:1987:WBE,
  author =       "Alain Guyot and Bertrand Hochet and Jean-Michel
                 Muller",
  title =        "A Way to Build Efficient Carry-Skip Adders",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "10",
  pages =        "1144--1152",
  month =        oct,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.1676855",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 09:28:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676855",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Hamada:1987:NRN,
  author =       "Hozumi Hamada",
  title =        "A New Real Number Representation and Its Operation",
  crossref =     "Irwin:1987:PSC",
  pages =        "153--157",
  month =        may,
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158698",
  bibdate =      "Wed Nov 14 18:22:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Hamada.pdf",
  abstract =     "A new internal representation is proposed for real
                 numbers. It has been named URR for universal
                 representation of real numbers. This approach is based
                 on a bisection method which is applied to real number
                 intervals. With this method, the point of division
                 increases or decreases in a double exponential manner
                 in the global range. The main characteristics of the
                 method are as follows. First, overflow\slash underflow
                 does not, in practice, occur. Second, since the data
                 format does not depend on the length but on the value
                 of the data, a transformation operation is virtually
                 not needed between systems of long and short data.
                 Finally, only one bit of resolution is lost compared
                 with the fixed point form. In addition, arithmetic
                 operations are slightly complicated compared with
                 conventional representation, but they present no
                 special difficulties. This new method is thus the most
                 suitable internal form as an interface not only between
                 computers but also between computers and digital
                 systems which deal with real numbers or physical
                 (scalar) values.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@InProceedings{Han:1987:FAE,
  author =       "Tackdon Han and David A. Carlson",
  title =        "Fast Area-Efficient {VLSI} Adders",
  crossref =     "Irwin:1987:PSC",
  pages =        "49--56",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158699",
  bibdate =      "Wed Nov 14 18:22:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Han_Carlson.pdf",
  abstract =     "In this paper, we study area-time tradeoffs in VLSI
                 for prefix computation using graph representations of
                 this problem. Since the problem is intimately related
                 to binary addition the results we obtain lead to the
                 design of area-time efficient VLSI adders. This is a
                 major goal of our work: to design {\em very low
                 latency\/} addition circuitry that is also {\em area
                 efficient}. To this end, we present a new graph
                 representation for prefix computation that leads to the
                 design of a fast, area-efficient binary adder. The new
                 graph is a combination of previously known graph
                 representations for prefix computation, and its area is
                 close to known lower bounds on the VLSI area of
                 parallel prefix graphs. Using it, we are able to design
                 VLSI adders having area $ A = O(n \log n) $ whose delay
                 time is the lowest possible value, i.e., the fastest
                 possible area-efficient VLSI adder.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@Book{Herz-Fischler:1987:MHD,
  author =       "Roger Herz-Fischler",
  title =        "A mathematical history of division in extreme and mean
                 ratio",
  publisher =    "Wilfrid Laurier University Press",
  address =      "Waterloo, ON, Canada",
  pages =        "xvi + 191",
  year =         "1987",
  ISBN =         "0-88920-152-8",
  ISBN-13 =      "978-0-88920-152-1",
  LCCN =         "A481.H47 1987",
  bibdate =      "Thu Jul 10 08:02:28 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$65.00",
  acknowledgement = ack-nhfb,
  libnote =      "Not yet in my library.",
}

@Book{Hildebrand:1987:INA,
  author =       "Francis Begnaud Hildebrand",
  title =        "Introduction to numerical analysis",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  edition =      "Second",
  pages =        "xiii + 669",
  year =         "1987",
  ISBN =         "0-486-65363-3 (paperback)",
  ISBN-13 =      "978-0-486-65363-1 (paperback)",
  LCCN =         "QA297 .H54 1987",
  bibdate =      "Fri Aug 20 09:19:58 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/description/dover032/87005370.html",
  acknowledgement = ack-nhfb,
  remark =       "Unabridged, slightly corrected republication of
                 \cite{Hildebrand:1974:INA}.",
  subject =      "Numerical analysis",
}

@Article{Himmeroeder:1987:CKC,
  author =       "H.-J. Himmer{\"o}der and R. M. Toschke",
  title =        "{c't-KAT-Ce. Ein 68000-Einplatinenrechner, Teil 3:
                 REAL-Arithmetik} \toenglish {c't-KAT-Ce. A 68000
                 Single-Board Computer} \endtoenglish",
  journal =      j-CT,
  volume =       "1",
  pages =        "152--158",
  year =         "1987",
  ISSN =         "0724-8679",
  bibdate =      "Sat Feb 24 09:05:58 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "C T: Magazin f{\"u}r Computer Technik (Hannover)",
}

@InProceedings{Hochet:1987:SSL,
  author =       "Bertrand Hochet and Patrice Quinton and Yves Robert",
  title =        "Systolic Solution of Linear Systems over {$ \mathrm
                 {GF}(p) $} with Partial Pivoting",
  crossref =     "Irwin:1987:PSC",
  pages =        "161--168",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158700",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Hochet_Quinton_Robert.pdf",
  abstract =     "We propose two systolic architectures for the Gaussian
                 triangularization and the Gauss--Jordan diagonalization
                 of large dense $ n \times n $ matrices over $ \mathrm
                 {GF}(p) $, where $p$ is a prime number. The solution of
                 large dense linear systems over $ \mathrm {GF}(p) $ is
                 the major computational step in various algorithms
                 issued from arithmetic number theory and computer
                 algebra. The two proposed architectures implement the
                 elimination with partial pivoting, although the
                 operation of the array remains purely systolic. The
                 last section is devoted to the design and layout of a
                 CMOS 8 by 8 Gauss--Jordan diagonalization systolic chip
                 over $ \mathrm {GF}(2) $.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@Article{Homewood:1987:ITT,
  author =       "Mark Homewood and David May and David Shepherd and
                 Roger Shepherd",
  title =        "The {IMS T800} Transputer",
  journal =      j-IEEE-MICRO,
  volume =       "7",
  number =       "5",
  pages =        "10--26",
  month =        sep # "\slash " # oct,
  year =         "1987",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.1987.305012",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Dec 14 06:08:58 MST 2000",
  bibsource =    "Compendex database;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Parallel/transputer.bib; Science Citation Index
                 database (1980--2000)",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliationaddress = "Inmos Ltd, Bristol, Engl",
  classcodes =   "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips)",
  classification = "714; 722; 723; 921",
  corpsource =   "Inmos Ltd., Bristol, UK",
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  keywords =     "architecture; capability; communication links;
                 computer architecture; computer graphics; computer
                 programming languages; computers, microcomputer;
                 Design; floating-point arithmetic; floating-point unit
                 design; graphics; IMS T800 transputer; integrated
                 circuits, VLSI; microprocessor chips; performance;
                 scientific computer; supercomputers; telecommunication
                 links",
  treatment =    "P Practical; R Product Review",
}

@InCollection{HP:1987:IPH,
  author =       "{Hewlett Packard}",
  booktitle =    "{HP-71} Reference Manual",
  title =        "The {IEEE} Proposal for Handling Math Exceptions",
  publisher =    "Hewlett Packard Company",
  address =      "Palo Alto, CA, USA",
  pages =        "338--345",
  month =        oct,
  year =         "1987",
  bibdate =      "Fri Nov 28 17:12:16 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Mfg. \#0071-90110, Reorder \#0071-90010. First edition
                 October 1983. Manual available from {\em The Museum of
                 HP Calculators}.",
  URL =          "http://www.hpmuseum.org/",
  abstract =     "The IEEE Radix Independent Floating-Point Proposal
                 divides all of the floating-point ``exceptional
                 events'' encountered in calculations into five classes
                 of {\em math exceptions\/}: invalid operation, division
                 by zero, overflow, underflow, and inexact result.
                 Associated with each math exception is a flag that is
                 set by the HP-71 whenever an exception is encountered.
                 These flags remain set until you clear them. Each of
                 these flags can be accessed by its number or its
                 name.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}

@MastersThesis{Hu:1987:CDT,
  author =       "Timothy Hu",
  title =        "Circuit design techniques for a floating-point
                 processor: research project",
  type =         "{Master of Science, Plan II}",
  school =       "University of California, Berkeley. Dept. of
                 Electrical Engineering and Computer Sciences",
  address =      "Berkeley, CA, USA",
  pages =        "70",
  year =         "1987",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hull:1987:TIC,
  author =       "T. E. Hull and M. S. Cohen",
  title =        "Toward an Ideal Computer Arithmetic",
  crossref =     "Irwin:1987:PSC",
  pages =        "131--138",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158701",
  bibdate =      "Fri Nov 28 11:41:31 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Hull_Cohen.pdf",
  abstract =     "A new computer arithmetic is described. Closely
                 related built-in functions are included. A user's point
                 of view is taken, so that the emphasis is on what
                 language features are available to a user. The main new
                 feature is flexible precision control of decimal
                 floating-point arithmetic. It is intended that the
                 language facilities be sufficient for describing
                 numerical processes one might want to implement, while
                 at the same time being simple to use, and implementable
                 in a reasonably efficient manner. Illustrative examples
                 are based on experience with an existing software
                 implementation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8; decimal floating-point arithmetic",
}

@Article{IEEE:1987:ISB,
  author =       "{IEEE}",
  title =        "{IEEE} Standard for Binary Floating-Point Arithmetic",
  journal =      j-SIGPLAN,
  volume =       "22",
  number =       "2",
  pages =        "9--25",
  month =        feb,
  year =         "1987",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1109/IEEESTD.1985.82928",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Fri Sep 09 12:55:55 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}

@Book{IEEE:1987:RIS,
  editor =       "{IEEE}",
  title =        "{854-1987 (R1994) IEEE Standard for Radix-Independent
                 Floating-Point Arithmetic}",
  publisher =    pub-IEEE-STD,
  address =      pub-IEEE-STD:adr,
  pages =        "16",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/IEEESTD.1987.81037",
  ISBN =         "1-55937-859-X",
  ISBN-13 =      "978-1-55937-859-8",
  bibdate =      "Mon Apr 24 07:02:34 2000",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Revised 1994.",
  price =        "US\$44.00",
  URL =          "http://standards.ieee.org/reading/ieee/std_public/description/busarch/854-1987_desc.html",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  keywords =     "floating point arithmetic; Floating-point arithmetic.;
                 Standards",
  remark =       "At head of title: An American National Standard.
                 ``Approved March 12, 1987 IEEE Standards Board;
                 Approved September 10, 1987 American National Standards
                 Institute.''",
}

@MastersThesis{Jensen:1987:CIS,
  author =       "Debby Jensen",
  title =        "Control implementation for the {SPUR} floating point
                 coprocessor: research project",
  type =         "{Master of Science, Plan II}",
  school =       "University of California, Berkeley. Dept. of
                 Electrical Engineering and Computer Sciences",
  address =      "Berkeley, CA, USA",
  pages =        "76",
  year =         "1987",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Johnson:1987:AES,
  author =       "Kenneth C. Johnson",
  title =        "{Algorithm 650}: Efficient Square Root Implementation
                 on the 68000",
  journal =      j-TOMS,
  volume =       "13",
  number =       "2",
  pages =        "138--151",
  month =        jun,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/328512.328520",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D15",
  MRnumber =     "898 489",
  bibdate =      "Thu Sep 1 10:15:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also \cite{Johnson:1987:CES}.",
  acknowledgement = ack-nj,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Johnson:1987:CES,
  author =       "Kenneth C. Johnson",
  title =        "Corrigendum: {``Algorithm 650: efficient square root
                 implementation on the 68000'' [ACM Trans. Math.
                 Software {\bf 13} (1987), no. 2, 138--151]}",
  journal =      j-TOMS,
  volume =       "13",
  number =       "3",
  pages =        "320--320",
  month =        sep,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/29380.356210",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "320. 65D15",
  MRnumber =     "918 582",
  bibdate =      "Sat Feb 8 10:30:18 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See
                 \cite{Johnson:1987:AES,Monahan:1987:AGC,Boisvert:1987:AAH}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@InProceedings{Kahan:1987:BCC,
  author =       "W. Kahan",
  title =        "Branch Cuts for Complex Elementary Functions or Much
                 Ado About Nothing's Sign Bit",
  crossref =     "Iserles:1987:SAN",
  volume =       "9",
  pages =        "165--211",
  year =         "1987",
  MRclass =      "65E05",
  MRnumber =     "88k:65027",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Inst. Math. Appl. Conf. Ser. New Ser.",
  URL =          "http://people.freebsd.org/~das/kahan86branch.pdf;
                 http://www.cs.berkeley.edu/~dbindel/class/cs279/",
  acknowledgement = ack-nhfb # " and " # ack-nj,
}

@Unpublished{Kahan:1987:CWF,
  author =       "W. Kahan",
  title =        "Checking whether floating-point division is correctly
                 rounded",
  year =         "1987",
  bibdate =      "Mon Apr 25 05:40:03 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Lecture notes.",
  acknowledgement = ack-nhfb,
  keywords =     "correct rounding; floating-point arithmetic; rounding
                 errors",
}

@Misc{Kahan:1987:DPI,
  author =       "W. Kahan",
  title =        "Doubled-precision {IEEE Standard 754} floating-point
                 arithmetic",
  howpublished = "Manuscript",
  month =        feb,
  year =         "1987",
  bibdate =      "Thu May 09 07:25:40 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
  remark =       "Cited in \cite{Higham:1993:AFP}.",
}

@TechReport{Kahan:1987:HAE,
  author =       "W. Kahan",
  title =        "Handling Arithmetic Exceptions",
  type =         "Report",
  institution =  inst-BERKELEY-MATH-EECS,
  address =      inst-BERKELEY-MATH-EECS:adr,
  day =          "14",
  month =        may,
  year =         "1987",
  bibdate =      "Mon Aug 26 10:42:10 2024",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.arithmazium.org/classroom/lib//Kahan_Handling_Arithmetic_Exceptions.pdf",
  abstract =     "An {\em Exception\/} arises when an operation
                 performed by a computer has to produce a result to
                 which some people might reasonably take exception.
                 Examples are {\em Division by Zero}, {\em Overflow\/ }
                 and Floating-Point {\em Underflow}. Though most (but
                 not all) exceptions must be rare, too rare to be topics
                 cf everyday conversation, they are not so rare that
                 computer programmers and users can ignore them
                 altogether. This paper presents proposals, many of them
                 now implemented on a few computers, to handle
                 arithmetic exceptions in a generally satisfactory way
                 at a tolerable cost. The proposals are designed to be
                 fully compatible with concurrent, overlapped, parallel,
                 pipelined and vectorized computing on new hardware that
                 will be designed to support them without {\em precise
                 interrupts}. {\em Flags\/} and {\em Modes\/} are
                 proposed to help programmers cope with exceptions; {\em
                 Retrospective Diagnostics\/} are proposed to help most
                 of the rest of us, who aspire to use computers without
                 having to program them. The features of IEEE Standards
                 754 and 854 are supported by but not obligatory for the
                 proposals.",
  acknowledgement = ack-nhfb,
}

@Book{Kane:1987:MRR,
  author =       "Gerry Kane",
  title =        "{MIPS R2000 RISC} Architecture",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  year =         "1987",
  ISBN =         "0-13-584749-4",
  ISBN-13 =      "978-0-13-584749-7",
  LCCN =         "QA76.8.M52 K36 1987",
  bibdate =      "Wed Dec 15 17:51:38 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kao:1987:ISM,
  author =       "Rom-Shen Kao and Fred J. Taylor",
  title =        "Implementation of the Single Modulus Complex {ALU}",
  crossref =     "Irwin:1987:PSC",
  pages =        "21--27",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158703",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Kao_Taylor.pdf",
  abstract =     "Recently the complex residue number system, or RNS,
                 has been a subject of intense study. One special
                 embodiment of this theory is the single modulus complex
                 RNS processor which suggests both implementation and
                 performance advantages. In this paper these conjectures
                 are tested in the context of a CMOS gate array design
                 and are found to be valid.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@InProceedings{Kirchner:1987:AVP,
  author =       "R. Kirchner and U. Kulisch",
  title =        "Arithmetic for Vector Processors",
  crossref =     "Irwin:1987:PSC",
  pages =        "256--269",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158704",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Kirchner_Kulisch.pdf",
  abstract =     "In electronic computers the elementary arithmetic
                 operations are these days generally approximated by
                 floating-point operations of highest accuracy. Vector
                 processors and parallel computers often provide
                 additional operations like ``multiply and add'',
                 ``accumulate'' or ``multiply and accumulate''. Also
                 these operations shall always deliver the correct
                 answer whatever the data are. The user should not be
                 obliged to execute an error analysis for operations
                 predefined by the manufacturer. In the first part of
                 this paper we discuss circuits which allow a fast and
                 correct computation of sums and scalar products making
                 use of a matrix shaped arrangement of adders and
                 pipeline technology. In the second part a variant is
                 discussed which permits a drastic reduction in the
                 number of adders required. The methods discussed in
                 this paper can also be used to build a fast arithmetic
                 unit for micro computers in VLSI-technology.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@Article{Kirchner:1987:SVS,
  author =       "Reinhard Kirchner and Ulrich Kulisch",
  title =        "{Schaltungsanordnung und Verfahren zur schnellen
                 Berechnung von Summen und Skalarprodukten von
                 Gleitkommazahlen mit maximaler Genauigkeit mittels
                 Pipelinetechnik}. ({German}) [Circuit diagrams and
                 methods for fast computation of sums and scalar
                 products of floating point numbers with maximal
                 accuracy via pipeline technique]",
  journal =      "Beitr{\"a}ge zur angewandten Mathematik und
                 Statistik",
  publisher =    pub-HANSER,
  address =      pub-HANSER:adr,
  pages =        "139--177",
  year =         "1987",
  MRclass =      "68Q25 (68Q10)",
  MRnumber =     "986 782",
  bibdate =      "Fri Dec 08 12:20:44 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Koopman:1987:TF,
  author =       "P. Koopman",
  title =        "Transcendental Functions",
  journal =      j-FORTH-DIMENSIONS,
  volume =       "9",
  number =       "4",
  pages =        "21--22",
  month =        dec,
  year =         "1987",
  CODEN =        "FODMD5",
  ISSN =         "0884-0822",
  bibdate =      "Thu Sep 1 10:15:30 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Forth Dimensions",
}

@InProceedings{Kornerup:1987:BSA,
  author =       "Peter Kornerup and David W. Matula",
  title =        "A Bit-Serial Arithmetic Unit for Rational Arithmetic",
  crossref =     "Irwin:1987:PSC",
  pages =        "204--211",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158705",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Kornerup_Matula.pdf",
  abstract =     "We describe a binary implementation of an algorithm of
                 Gosper to compute the sum, difference, product,
                 quotient and certain rational functions of two rational
                 operands applicable to integrated approximate and exact
                 rational computation. The arithmetic unit we propose is
                 an eight register computation cell with bit, serial
                 input and output employing the binary lexicographic
                 continued fraction (LCF) representation of the rational
                 operands., The operands and results are processed in a
                 most-significant-bit first on-line fashion with bit
                 level logic leading to less delay in the computation
                 cell when compared to operation on the full partial
                 quotients of the standard continued fraction
                 representation. Minimization of delay is investigated
                 with the aim of supporting greater throughput in
                 cascaded parallel computation with such computation
                 cells.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@PhdThesis{Kraemer:1987:ISF,
  author =       "W. Kr{\"a}mer",
  title =        "Inverse Standardfunktionen f{\"u}r reelle und komplexe
                 Intervallargumente mit a priori Fehlerabsch{\"a}tzungen
                 f{\"u}r beliebige Datenformate \toenglish {Inverse
                 Elementary Functions for Real and Complex Interval
                 Arguments with A-Priori Error Estimates for Arbitrary
                 Data Formats} \endtoenglish",
  type =         "Dissertation",
  school =       "Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "??",
  year =         "1987",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  author-dates = "1952--2014",
}

@InProceedings{Kuninobu:1987:DHS,
  author =       "Shigeo Kuninobu and Tamotsu Nishiyama and Hisakazu
                 Edamatsu and Takashi Taniguchi and Naofumi Takagi",
  key =          "KNE87",
  title =        "Design of High Speed {MOS} Multiplier and Divider
                 Using Redundant Binary Representation",
  crossref =     "Irwin:1987:PSC",
  pages =        "80--86",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158706",
  bibdate =      "Wed Nov 14 18:22:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Kuninobu_Nishiyama_Edamatsu_Taniguchi_Takagi.pdf",
  abstract =     "A high speed multiplier and divider for MOS LSI based
                 on a new algorithm is presented. When we implement the
                 multiplier and the divider in LSI. the features such as
                 high speed operation, small number of transistors and
                 easy layout are the most important factors. A
                 computational algorithm using a redundant binary
                 representation has several excellent features such as
                 high speed addition operations. We improved the
                 algorithm and the method of implementation. and
                 designed an advanced multiplier and divider with the
                 above mentioned features. We expect that our multiplier
                 and divider are excellent compared with multipliers
                 using the Booth algorithm and the Wallace tree. and
                 with divider using the SRT method, respectively.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@Article{Lange:1987:ITA,
  author =       "Eberhard Lange",
  title =        "Implementation and Test of the {ACRITH} Facility in a
                 {System}\slash 370",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "9",
  pages =        "1088--1096",
  month =        sep,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.5009539",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 09:28:55 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009539",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "floating-point testing",
}

@Article{Leavitt:1987:APF,
  author =       "Randal Leavitt",
  title =        "Adjustable Precision Floating Point Arithmetic in
                 {Ada}",
  journal =      j-SIGADA-LETTERS,
  volume =       "7",
  number =       "5",
  pages =        "63--78",
  month =        sep # "\slash " # oct,
  year =         "1987",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Sat Aug 9 09:05:26 MDT 2003",
  bibsource =    "ftp://ftp.uu.net/library/bibliography;
                 http://portal.acm.org/;
                 http://www.adahome.com/Resources/Bibliography/articles.ref;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "design; performance; theory",
  subject =      "D.3.2 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Ada \\ G.1.0 Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Computer arithmetic",
}

@Article{Lien:1987:RCI,
  author =       "B. Lien and G. Tang",
  title =        "Reversed {Chebyshev} implementation of {McClellan}
                 transform and its roundoff error",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "35",
  number =       "10",
  pages =        "1435--1439",
  month =        oct,
  year =         "1987",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  summary =      "A new structure, called the reversed Chebyshev
                 structure, for the fixed point implementation of the
                 FIR filters designed with the McClellan transformation
                 is presented. It shows the best roundoff noise
                 performance among the existing ones for both \ldots{}",
}

@InProceedings{Lin:1987:NFP,
  author =       "Haixiang X. Lin and Henk J. Sips",
  title =        "A Novel Floating-Point Online Division Algorithm",
  crossref =     "Irwin:1987:PSC",
  pages =        "188--195",
  month =        may,
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158707",
  bibdate =      "Wed Nov 14 18:22:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Lin_Sips.pdf",
  abstract =     "This paper describes a new online division
                 (reciprocal) algorithm for (maximally) redundant
                 floating-point numbers of arbitrary radix. The
                 algorithm works for normalized, quasi-normalized, and
                 pseudo-normalized numbers and can therefore be applied
                 in chained online computations. The online delay of the
                 proposed algorithm is the smallest reported so far. The
                 algorithm consists of two steps: the first $m$ digits
                 of the result are generated by a simple table lookup
                 method; the remaining $ n - m $ digits are generated by
                 using an adapted Newton--Raphson iteration method. In
                 the second step, the online digits are created by using
                 a fast and simple selection mechanism.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@MastersThesis{Liu:1987:BEF,
  author =       "Zhi-Shun Alex Liu",
  title =        "{Berkeley} Elementary Function Test Suite: Research
                 Project",
  type =         "{Master of Science, Plan II}",
  school =       "Computer Science Division, Department of Electrical
                 Engineering and Computer Science, Univerity of
                 California at Berkeley",
  address =      "Berkeley, CA, USA",
  month =        dec,
  year =         "1987",
  bibdate =      "Mon Sep 12 23:52:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  keywords =     "BeEF test suite; floating-point testing",
}

@Article{Lo:1987:HGA,
  author =       "H.-Y. Lo and J.-L. Chen",
  title =        "A Hardwired Generalized Algorithm for Generating the
                 Logarithm Base-$k$ by Iteration",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "11",
  pages =        "1363--1367",
  month =        nov,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.5009477",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 08 08:08:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Maenner:1987:FIB,
  author =       "R. Maenner",
  title =        "A Fast Integer Binary Logarithm of Large Arguments",
  journal =      j-IEEE-MICRO,
  volume =       "7",
  number =       "6",
  pages =        "41--45",
  month =        nov # "\slash " # dec,
  year =         "1987",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.1987.304914",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Sep 1 10:16:09 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}

@Article{Magenheimer:1987:IMD,
  author =       "Daniel J. Magenheimer and Liz Peters and Karl Pettis
                 and Dan Zuras",
  title =        "Integer multiplication and division on the {HP
                 Precision Architecture}",
  journal =      j-SIGPLAN,
  volume =       "22",
  number =       "10",
  pages =        "90--99",
  month =        oct,
  year =         "1987",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:15:15 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}

@Article{Makarenko:1987:VMM,
  author =       "Darrell Makarenko and Jonathan Schaeffer",
  title =        "A {VLSI} multiprecision matrix multiplier and
                 polynomial evaluator",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "4",
  number =       "6",
  pages =        "619--628",
  month =        dec,
  year =         "1987",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliationaddress = "Univ of Alberta, Edmonton, Alberta, Can",
  classification = "713; 722; C4140 (Linear algebra); C4240 (Programming
                 and algorithm theory); C5230 (Digital arithmetic
                 methods)",
  corpsource =   "Department of Computer Science, Alberta University,
                 Edmonton, Alta., Canada",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "32 bit; 32-bit multiplication; algebra; band-matrix
                 multiplication; bit-serial; computational complexity;
                 computers --- Multiplying Circuits; Design; digital
                 arithmetic; evaluations; full-matrix multiplication;
                 integrated circuits, VLSI; linear-space evaluations;
                 linear-time; mathematical techniques --- Polynomials;
                 matrix; matrix multiplier; multiply and accumulate
                 cells; multiprecision matrix multiplier; polynomial
                 evaluator; polynomials; two dimensional array; two's
                 complement numbers; VLSI; VLSI multiprecision; VLSI
                 multiprecision polynomial evaluator",
  treatment =    "P Practical",
}

@InProceedings{Manzoul:1987:QCN,
  author =       "Mahmoud A. Manzoul",
  title =        "A quaternary complex number {CCD} adder (abstract
                 only)",
  crossref =     "Davis:1987:PAC",
  pages =        "434--434",
  year =         "1987",
  DOI =          "https://doi.org/10.1145/322917.323095",
  bibdate =      "Sat Aug 22 09:06:07 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Complex number arithmetic occurs frequently in digital
                 signal processing and power systems analysis. Normally,
                 complex numbers are given two binary words, with one
                 word for each component (real and imaginary).
                 Therefore, the standard binary implementation of
                 complex numbers requires several real arithmetic
                 operations. Besides, the two components of each complex
                 number must be tracked down at every stage of the
                 computation. Different digital representations for
                 complex numbers have been proposed in an effort to
                 reduce these problems. Knuth [1] has proposed an
                 unconventional single component representation of
                 complex numbers whereby the radix is chosen to be (2j)
                 with the digit set comprised of the first four positive
                 integers (0, 1, 2, 3). This is in contrast with the
                 conventional two components representation with binary
                 radix whether in Cartesian or Polar coordinates.
                 Knuth's representation leads to simple and interesting
                 arithmetic in the complex field [2] [3].",
  acknowledgement = ack-nhfb,
}

@Article{Mariella:1987:IDF,
  author =       "Ray Mariella",
  title =        "Integers Don't Float",
  journal =      j-DDJ,
  volume =       "12",
  number =       "12",
  pages =        "48--??",
  month =        dec,
  year =         "1987",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@Article{Mays:1987:IDA,
  author =       "Michael E. Mays",
  title =        "Iterating the Division Algorithm",
  journal =      j-FIB-QUART,
  volume =       "25",
  number =       "3",
  pages =        "204--213",
  month =        aug,
  year =         "1987",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:00:58 MDT 2011",
  bibsource =    "http://www.fq.math.ca/25-3.html;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.fq.math.ca/Scanned/25-3/mays.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Book{McMcusersmanual:1987:MMF,
  author =       "{Motorola, Inc.}",
  title =        "{MC68881\slash MC68882} floating-point coprocessor
                 user's manual",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "various",
  year =         "1987",
  ISBN =         "0-13-566936-7 (pbk.)",
  ISBN-13 =      "978-0-13-566936-5 (pbk.)",
  LCCN =         "????",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Motorola 68881
                 (Microprocessor); Motorola 68882 (Microprocessor)",
  remark =       "Spine title: MC68881/MC68882 user's manual.
                 ``MC68881UM/AD REV 1''--Cover.",
}

@Article{Monahan:1987:AGC,
  author =       "John F. Monahan",
  title =        "An Algorithm for Generating Chi Random Variables",
  journal =      j-TOMS,
  volume =       "13",
  number =       "2",
  pages =        "168--172",
  month =        jun,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/328512.328522",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65C10",
  MRnumber =     "88d:65013",
  bibdate =      "Sat Nov 19 13:08:24 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also \cite{Johnson:1987:CES,Monahan:1988:CAG}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Montgomery:1987:SPE,
  author =       "Peter L. Montgomery",
  title =        "Speeding the {Pollard} and elliptic curve methods of
                 factorization",
  journal =      j-MATH-COMPUT,
  volume =       "48",
  number =       "177",
  pages =        "243--264",
  month =        jan,
  year =         "1987",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11Y05 (11A51 68Q40)",
  MRnumber =     "88e:11130",
  MRreviewer =   "Kevin S. McCurley",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
                 JSTOR database",
  note =         "See improvement \cite{Kim:2024:MCA}.",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "C1160 (Combinatorial mathematics); C4240 (Programming
                 and algorithm theory)",
  corpsource =   "Syst. Dev. Corp., Santa Monica, CA, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "computational complexity; elliptic curve; elliptic
                 curve method; elliptic curve methods; factorization;
                 Lenstra method; Monte Carlo methods; number; number
                 theory; parametrisation; Pollard methods; polynomial
                 preconditioning; theory; Williams method",
  treatment =    "T Theoretical or Mathematical",
}

@TechReport{Motorola:1987:MFP,
  author =       "{Motorola, Inc.}",
  title =        "{MC68881} Floating-Point Coprocessor as a Peripheral
                 in an {M68000} System",
  type =         "Motorola Semiconductor Application Note",
  number =       "AN947/D",
  institution =  "Motorola, Inc.",
  address =      "Phoenix, AZ, USA",
  pages =        "37",
  year =         "1987",
  bibdate =      "Thu Nov 13 09:51:10 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.bitsavers.org/components/motorola/_appNotes/AN-0947_MC68881_Floating-Point_Coprocessor_as_a_Peripheral_in_a_M68000_System_%5BMotorola_1987_37p%5D.pdf",
  abstract =     "The MC68881 floating-point coprocessor is a complete
                 implementation of the proposed IEEE Standard for Binary
                 Floating-Point Arithmetic (Task P754, Draft 10.0). All
                 data formats, data types, operations, modes,
                 conversions, and exception handling required in a
                 conforming implementation of the proposed standard are
                 supported entirely in hardware. Additionally, a full
                 library of fast elementary transcendental functions is
                 implemented in the hardware.",
  acknowledgement = ack-nhfb,
}

@Book{Motorola:1987:MMF,
  author =       "{Motorola, Inc.}",
  title =        "{MC68881\slash MC68882} Floating-Point Coprocessor
                 User's Manual",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "various",
  year =         "1987",
  ISBN =         "0-13-566936-7",
  ISBN-13 =      "978-0-13-566936-5",
  LCCN =         "QA76.8.M69 M3 1987",
  bibdate =      "Fri Dec 08 13:03:15 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Mutrie:1987:FEA,
  author =       "Mark P. W. Mutrie and Richard H. Bartels and Bruce W.
                 Char",
  title =        "Floating-point error analysis using symbolic algebraic
                 computation",
  type =         "Research report",
  number =       "CS-87-08",
  institution =  "University of Waterloo, Faculty of Mathematics",
  address =      "Waterloo, Ont., Canada",
  pages =        "13",
  year =         "1987",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Roundoff errors.",
  remark =       "Supported in part by the Natural Sciences and
                 Engineering Research Council of Canada.",
}

@Misc{Nakano:1987:MAD,
  author =       "Hiraku Nakano",
  title =        "Method and apparatus for division using interpolation
                 approximation",
  howpublished = "United States Patent 4,707,798",
  day =          "17",
  month =        nov,
  year =         "1987",
  bibdate =      "Tue Jan 08 22:36:28 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.freepatentsonline.com/4707798.html",
  abstract =     "A divide method and a divide apparatus for use in a
                 data processing system. The divisor and dividend are
                 normalized in a normalization circuit. A table unit
                 stores a plurality of approximate reciprocal divisors
                 and differences between adjacent approximate reciprocal
                 divisors and is addressed by the high-order bits of the
                 normalized divisor. The approximate reciprocal divisor
                 read out from the table unit is, in an interpolation
                 approximation circuit, changed into an interpolation
                 approximated approximate reciprocal divisor in
                 accordance with a plurality of bits following the
                 high-order bits and the difference. A multiplication
                 unit multiplies the interpolation approximated
                 approximate reciprocal divisor by the normalized
                 dividend to output a quotient.",
  acknowledgement = ack-nhfb,
}

@Article{Nelsen:1987:PSR,
  author =       "Roger B. Nelsen and James E. Schultz",
  title =        "The Probability that the {``Sum} of the Rounds''
                 Equals the {``Round} of the Sum''",
  journal =      j-COLLEGE-MATH-J,
  volume =       "18",
  number =       "5",
  pages =        "390--396",
  month =        nov,
  year =         "1987",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/07468342.1987.11973061",
  ISSN =         "0746-8342 (print), 1931-1346 (electronic)",
  ISSN-L =       "0746-8342",
  bibdate =      "Thu Feb 14 09:50:35 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/collegemathj.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib",
  URL =          "http://www.jstor.org/stable/2686963;
                 http://www.tandfonline.com/doi/abs/10.1080/07468342.1987.11973061",
  acknowledgement = ack-nhfb,
  fjournal =     "College Mathematics Journal",
  journal-URL =  "https://maa.tandfonline.com/loi/ucmj20;
                 https://www.jstor.org/journal/collmathj",
  keywords =     "rounding in fixed-point addition",
  onlinedate =   "30 Jan 2018",
  remark =       "See also \cite{Hopkins:2016:WMN} for a later
                 independent derivation of part of this work.",
}

@Article{Obermaier:1987:SCI,
  author =       "A. Obermaier",
  title =        "{Sin und cosin mit Integerarithmetik} \toenglish {Sine
                 and Cosine with Integer Arithmetic} \endtoenglish",
  journal =      j-MC,
  volume =       "6",
  pages =        "108--112",
  year =         "1987",
  ISSN =         "0720-4442, 0941-777x, 0943-5409",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "MC: Die Mikrocomputer-Zeitschrift",
}

@InProceedings{Olver:1987:CCA,
  author =       "F. W. J. Olver",
  title =        "A Closed Computer Arithmetic",
  crossref =     "Irwin:1987:PSC",
  pages =        "139--143",
  month =        may,
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158708",
  bibdate =      "Wed Nov 14 18:22:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Olver.pdf",
  abstract =     "Two closely related new systems of computer arithmetic
                 are proposed. It is shown that both are closed under
                 arithmetic operations in finite-precision arithmetic,
                 thereby offering a permanent solution to the problems
                 of overflow and underflow. Other advantages of the new
                 systems pertaining to precision are described, and
                 there is also a brief discussion of possible ways of
                 hardware implementation.",
  acknowledgement = ack-nhfb,
  author-dates = "Frank William John Olver (15 December 1924--23 April
                 2013)",
  keywords =     "ARITH-8",
  remark =       "Reprinted in \cite{Olver:1990:CCA}.",
}

@InProceedings{Olver:1987:ILI,
  author =       "F. W. J. Olver and P. R. Turner",
  title =        "Implementation of Level-Index Arithmetic Using Partial
                 Table Look-Up",
  crossref =     "Irwin:1987:PSC",
  pages =        "144--147",
  month =        may,
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158709",
  bibdate =      "Wed Nov 14 18:22:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Olver_Turner.pdf",
  abstract =     "This paper is concerned with finding fast efficient
                 algorithms for performing level-index arithmetic. The
                 approach used combines the advantages of parallel
                 processing with the use of table look-up. The latter is
                 used only for short words and the result is a potential
                 implementation with $ \li $ operation times comparable
                 with floating-point long multiplications.",
  acknowledgement = ack-nhfb,
  author-dates = "Frank William John Olver (15 December 1924--23 April
                 2013)",
  keywords =     "ARITH-8",
}

@Article{Owens:1987:AC,
  author =       "Robert Michael Owens and Mary Jane Irwin",
  title =        "The Arithmetic Cube",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "11",
  pages =        "1342--1348",
  month =        nov,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.5009473",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 09:28:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009473",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Papachristou:1987:ATL,
  author =       "Christos A. Papachristou",
  title =        "Associative Table Lookup Processing for Multioperand
                 Residue Arithmetic",
  journal =      j-J-ACM,
  volume =       "34",
  number =       "2",
  pages =        "376--396",
  month =        apr,
  year =         "1987",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Sat Oct 22 00:20:03 1994",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Misc/IMMD_IV.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}

@Article{Parhami:1987:CTL,
  author =       "B. Parhami",
  title =        "On the Complexity of Table Lookup for Iterative
                 Division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "10",
  pages =        "1233--1236",
  month =        oct,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.1676863",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 09:28:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676863",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Parhami:1987:SUC,
  author =       "Behrooz Parhami",
  title =        "Systolic Up\slash Down Counters with Zero and Sign
                 Detection",
  crossref =     "Irwin:1987:PSC",
  pages =        "174--178",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158710",
  bibdate =      "Wed Nov 14 18:22:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Parhami.pdf",
  abstract =     "Although a state encoding scheme for systolic counters
                 has been presented earlier, several important practical
                 problems such as zero test, sign detection, overflow,
                 underflow, and modulo-$n$ (cyclic) counting have not
                 been dealt with adequately. In this paper, design
                 principles for unary and binary systolic up\slash down
                 counters are presented. The unary counters, which are
                 attractive when dealing with relatively small counts,
                 are based on the systolic stack concept. The binary
                 counters use conventional binary number representation,
                 with several tags associated with each bit position.
                 The binary counter design presented can be generalized
                 to counters with higher-radix state encodings.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@InProceedings{Peng:1987:ISM,
  author =       "Victor Peng and Sridhar Samudrala and Moshe
                 Gavrielov",
  title =        "On the Implementation of Shifters, Multipliers, and
                 Dividers in {VLSI} Floating Point Units",
  crossref =     "Irwin:1987:PSC",
  pages =        "95--102",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158711",
  bibdate =      "Wed Nov 14 18:22:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Peng_Samudrala_Gavrielov.pdf",
  abstract =     "Several options for the implementation of
                 combinatorial shifters, multipliers, and dividers for a
                 VLSI floating point unit are presented and compared.
                 The comparisons are made in the context of a single
                 chip implementation in light of the constraints imposed
                 by currently available MOS technology.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@Article{Perlmutter:1987:A,
  author =       "D. Perlmutter and A. K.-W. Yuen",
  title =        "The 80387 and its Applications",
  journal =      j-IEEE-MICRO,
  volume =       "7",
  number =       "4",
  pages =        "42--57",
  month =        jul # "\slash " # aug,
  year =         "1987",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.1987.304880",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Wed Sep 7 22:32:00 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}

@Article{Pfeiffer:1987:ADP,
  author =       "F. W. Pfeiffer",
  title =        "Automatic differentiation in {PROSE}",
  journal =      j-SIGNUM,
  volume =       "22",
  number =       "1",
  pages =        "2--8",
  month =        jan,
  year =         "1987",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:14 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A programming language is presented in which has the
                 feature that first and second order partial derivatives
                 of a function can be calculated using differentiation
                 arithmetic. The language syntax allows the user to
                 specify which variables each function is required to be
                 differentiated with respect to. Model examples are
                 provided.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "differentiation arithmetic; languages; point
                 algorithm; program transformation; theory",
  subject =      "D.3.2 Software, PROGRAMMING LANGUAGES, Language
                 Classifications \\ F.4.3 Theory of Computation,
                 MATHEMATICAL LOGIC AND FORMAL LANGUAGES, Formal
                 Languages, Algebraic language theory",
}

@InProceedings{Piuri:1987:FTS,
  author =       "Vincenzo Piuri",
  title =        "Fault-Tolerant Systolic Arrays: An Approach Based upon
                 Residue Arithmetic",
  crossref =     "Irwin:1987:PSC",
  pages =        "230--238",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158712",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Piuri.pdf",
  abstract =     "Much attention has been recently given to VLSI and WSI
                 processing arrays: systolic arrays are often adopted to
                 execute a wide class of algorithms, e.g., for matrix
                 arithmetic or signal and image processing. In this
                 paper a fault-tolerant architecture is proposed to
                 allow reliable computation of systolic arrays by using
                 physical redundancy and residue number coding. Such
                 architecture supplies also information for fast
                 reconfiguration.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@Article{Prado:1987:FSR,
  author =       "J. Prado and R. Alcantara",
  title =        "A fast square-rooting algorithm using a digital signal
                 processor",
  journal =      j-PROC-IEEE,
  volume =       "75",
  number =       "2",
  pages =        "262--264",
  month =        feb,
  year =         "1987",
  CODEN =        "IEEPAD",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
  summary =      "The computation of square roots is required in signal
                 processing applications, such as adaptive filtering
                 using transversal filters or lattice filters, spectral
                 estimation, and many other fields of engineering
                 sciences. Actually, all the existing \ldots{}",
}

@Article{Purdy:1987:IDL,
  author =       "C. N. Purdy and G. B. Purdy",
  title =        "Integer Division in Linear Time with Bounded Fan-In",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "5",
  pages =        "640--644",
  month =        may,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.1676952",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 09:28:52 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676952",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Rall:1987:ISC,
  author =       "L. B. Rall",
  title =        "An introduction to the scientific computing language
                 {Pascal-SC}",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "14",
  number =       "1",
  pages =        "53--69",
  year =         "1987",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(87)90181-7",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Oct 13 22:36:01 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Microcomputers are now widely used for small-scale
                 scientific, engineering, and statistical computing.
                 Pascal-SC (Pascal for Scientific Computing) is a
                 language developed specifically for this purpose. Its
                 most important features are: (i) accurate
                 floating-point arithmetic for real, complex, and
                 interval numbers, vectors, and matrices, with
                 controlled rounding if desired; (ii) the convenience of
                 operator notation for numerical data types and the
                 ability to accept user-defined operators for
                 nonstandard data types to make programs easier to
                 write, read, and document; and (iii) compatibility with
                 ordinary Pascal, so that Pascal programming techniques
                 and programs already written in Pascal can be used
                 immediately. In PascalSC, solutions of linear systems
                 of equations, inverses of matrices, and eigenvalues and
                 eigenvectors are computed with guaranteed error bounds,
                 and scalar products of vectors and sums of arbitrary
                 length of floating-point numbers are computed to the
                 closest floating-point number, or rounded upward or
                 downward as desired. These basic features of Pascal-SC
                 will be described, together with some applications.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Rauch:1987:MCH,
  author =       "K. Rauch",
  title =        "Math chips: How they work: Augmenting microprocessors,
                 they speed up math operations while giving systems
                 designers a variety of performance, cost, and
                 integration options",
  journal =      j-IEEE-SPECTRUM,
  volume =       "24",
  number =       "7",
  pages =        "25--30",
  month =        jul,
  year =         "1987",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.1987.6448961",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Mon Jan 20 06:41:24 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "computer architecture; Coprocessors; desktop
                 computers; digital arithmetic; math chips; mathematics
                 coprocessors; microprocessor chips; numeric processors;
                 operation speed; Process control; Program processors;
                 satellite computers; standard building blocks;
                 Standards; Workstations; workstations",
}

@MastersThesis{Reddy:1987:STF,
  author =       "Chakradher Ayyalaper Reddy",
  title =        "A self-testing and testable floating point divider",
  type =         "Thesis ({M.S.})",
  school =       "Mississippi State University. Department of Electrical
                 Engineering",
  address =      "Mississippi State, MS 39762, USA",
  pages =        "viii + 103",
  year =         "1987",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point testing; Integrated circuits;
                 Mississippi State University; Testing.; Very large
                 scale integration",
}

@InProceedings{Redinbo:1987:PCT,
  author =       "G. Robert Redinbo",
  title =        "Protecting Convolution-Type Arithmetic Array
                 Calculations with Generalized Cyclic Codes",
  crossref =     "Irwin:1987:PSC",
  pages =        "219--225",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158713",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Redinbo.pdf",
  abstract =     "Fault-tolerance in dense high-speed arithmetic units
                 that calculate convolutions between arrays of data is
                 introduced through cyclic codes which are defined over
                 the rings and fields commonly employed by such units.
                 New systematic encoding and data manipulation
                 techniques make the application of these generalized
                 cyclic codes to error detection straightforward and
                 efficient. The necessary overhead parity computations
                 have complexity proportional to the number of parity
                 symbols squared, whereas the error-detecting capability
                 for both random and burst errors is directly related to
                 this parity number'.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@Article{Rehmer:1987:DIM,
  author =       "Karl Rehmer",
  title =        "Development and Implementation of the {Magnavox}
                 Generic {Ada} Basic Mathematics Package",
  journal =      j-SIGADA-LETTERS,
  volume =       "7",
  number =       "3",
  pages =        "73--83",
  month =        may # "\slash " # jun,
  year =         "1987",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Sat Aug 9 09:05:25 MDT 2003",
  bibsource =    "ftp://ftp.uu.net/library/bibliography;
                 http://portal.acm.org/;
                 http://www.adahome.com/Resources/Bibliography/articles.ref;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "design; floating point, real arithmetic; languages;
                 theory; verification",
  subject =      "D.2.2 Software, SOFTWARE ENGINEERING, Tools and
                 Techniques, Software libraries \\ D.3.2 Software,
                 PROGRAMMING LANGUAGES, Language Classifications, Ada
                 \\
                 G.4 Mathematics of Computing, MATHEMATICAL SOFTWARE",
}

@InProceedings{Robertson:1987:EDC,
  author =       "James E. Robertson",
  title =        "Error-Detection and Correction for Addition and
                 Subtraction through Use of Higher Radix Extensions of
                 {Hamming} Codes",
  crossref =     "Irwin:1987:PSC",
  pages =        "226--229",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158714",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Robertson.pdf",
  abstract =     "The properties of Hamming codes for error detection
                 and correction can be extended from the binary parity
                 check to addition, modulo $ 2 r $. Malfunctions in
                 hardware during addition, modulo $ 2 r $, can be
                 detected and corrected. Since carry-save and
                 signed-digit addition, radix $r$, are included in
                 addition, modulo $ 2 r $, this extension of Hamming
                 codes makes possible new techniques for detection and
                 correction of hardware malfunctions during signed-digit
                 and carry-save addition.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@Article{Rolfe:1987:FIS,
  author =       "Timothy J. Rolfe",
  title =        "On a Fast Integer Square Root Algorithm",
  journal =      j-SIGNUM,
  volume =       "22",
  number =       "4",
  pages =        "6--11",
  month =        oct,
  year =         "1987",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Thu Sep 1 10:15:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "algorithms; performance; theory",
  subject =      "F.2.1 Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Number-theoretic computations",
}

@Article{Rysavy:1987:MSC,
  author =       "M. Rysav{\'y}",
  title =        "{MISHA} --- a system for calculations with arbitrary
                 arithmetic precision",
  journal =      j-COMP-PHYS-COMM,
  volume =       "47",
  number =       "2--3",
  pages =        "351--359",
  month =        nov # "\slash " # dec,
  year =         "1987",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(87)90120-2",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 10:28:21 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0010465587901202",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Scheidt:1987:DFP,
  author =       "J. K. Scheidt and C. W. Schelin",
  title =        "Distributions of floating point numbers",
  journal =      j-COMPUTING,
  volume =       "38",
  number =       "4",
  pages =        "315--324",
  year =         "1987",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65G10",
  MRnumber =     "88g:65046",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  reviewer =     "J. A. Grant",
}

@InProceedings{Scherson:1987:VCO,
  author =       "Isaac D. Scherson and Yiming Ma",
  title =        "Vector Computations on Orthogonal Memory Access
                 Multiprocessor System",
  crossref =     "Irwin:1987:PSC",
  pages =        "28--36",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158715",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Scherson_Ma.pdf",
  abstract =     "An Orthogonal Memory Access system allows a
                 multiplicity of processors to concurrently access
                 distinct rows or columns of a rectangular array of data
                 elements. The resulting tightly-coupled
                 multi-processing system is feasible with current
                 technology and has even been suggested for VLSI as a
                 ``reduced mesh''. In this paper we introduce the
                 architecture and concentrate on its application to a
                 number of basic vector and. numerical computations.
                 Matrix multiplication, L-U decomposition. polynomial
                 evaluation and solutions to linear systems and partial
                 differential equations, all show a speed-up of $ O(n) $
                 for a $n$-processor system. The flexibility in the
                 choice of the number of PEs makes the architecture a
                 strong competitor in the world of special-purpose
                 parallel systems. Actually, we prove that the machine
                 exhibits the same performance as any other system with
                 the same number of processors within a factor of 3.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8; numerical analysis; parallel algorithms;
                 parallel architecture; performance analysis; time
                 complexity",
}

@InProceedings{Schumacher:1987:CAI,
  author =       "G{\"u}nter Schumacher",
  title =        "Computer Arithmetic and Ill-Conditioned Algebraic
                 Problems",
  crossref =     "Irwin:1987:PSC",
  pages =        "270--276",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158716",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Schumacher.pdf",
  abstract =     "n/a",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
  remark =       "Text illegible because of large white streak on each
                 page.",
}

@InProceedings{Sharma:1987:ATE,
  author =       "Ramautar Sharma",
  title =        "Area-Time Efficient Arithmetic Elements for {VLSI}
                 Systems",
  crossref =     "Irwin:1987:PSC",
  pages =        "58--62",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158717",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Sharma.pdf",
  abstract =     "Algorithms for the high speed binary arithmetic
                 operations of addition and multiplication in a VLSI
                 environment are analyzed for area-time efficiency. It
                 is shown that some schemes for addition and
                 multiplication, although good for stand-alone designs,
                 fail to provide both area and time efficiencies
                 simultaneously. Solutions that yield area-time
                 efficient practical implementations of these arithmetic
                 functions are described.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@InProceedings{Shenoy:1987:AST,
  author =       "A. Shenoy and R. Kumaresan",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing, {ICASSP '87}",
  title =        "An accurate scaling technique in improved residue
                 number system arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1414--1417",
  month =        "????",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/TC.1987.1676868",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A fast and accurate magnitude scaling technique in the
                 residue number system (RNS) is proposed. This technique
                 obtains the residues of the scaled integer, when scaled
                 by a product of a subset of the moduli, in
                 approximately log n cycles, where n is \ldots{}",
}

@Article{Shyu:1987:CIM,
  author =       "H. C. Shyu and T. K. Truong and I. S. Reed",
  title =        "A Complex Integer Multiplier Using the
                 Quadratic-Polynomial Residue Number System with Numbers
                 of Form $ 22 n + 1 $",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "10",
  pages =        "1255--1258",
  month =        oct,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.1676868",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 09:28:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12;
                 http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=35260;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676868",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A quadratic-polynomial Fermat residue number system
                 (QFNS) can be used to compute the complex
                 multiplications needed to perform a DFT. The advantage
                 of such a QFNS is that complex multiplication can be
                 accomplished with only two integer \ldots{}",
}

@InCollection{Simar:1987:FPA,
  author =       "R. {Simar, Jr.}",
  title =        "Floating-point arithmetic with the {TMS32010}",
  crossref =     "Lin:1987:DSP",
  pages =        "213--244",
  year =         "1987",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  bibno =        "42622",
  catcode =      "J.2; C.5.3; G.1.0",
  CRclass =      "J.2 Mathematics and statistics; C.5.3 Microcomputers;
                 C.5.3 TMS 32010; G.1.0 General; G.1.0 Computer
                 arithmetic",
  descriptor =   "Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Mathematics and statistics; Computer
                 Systems Organization, COMPUTER SYSTEM IMPLEMENTATION,
                 Microcomputers, TMS 32010; Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Computer arithmetic",
  genterm =      "MEASUREMENT; ALGORITHMS",
  guideno =      "1988-01736",
  pubcite =      "Englewood Cliffs, NJ",
  pubname =      "Prentice-Hall, Inc.",
  subject =      "J. Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING; C. Computer Systems Organization; C.5
                 COMPUTER SYSTEM IMPLEMENTATION; G. Mathematics of
                 Computing; G.1 NUMERICAL ANALYSIS",
}

@InProceedings{Smith:1987:SAE,
  author =       "S. G. Smith and P. B. Denyer",
  title =        "Synthesis of Area-Efficient {VLSI} Architectures for
                 Vector and Matrix Multiplication",
  crossref =     "Irwin:1987:PSC",
  pages =        "13--20",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158718",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Smith_Denyer.pdf",
  abstract =     "A methodology is presented for synthesis of
                 area-efficient, high-performance VLSI modules for
                 vector and matrix multiplication. Three fundamental
                 computational elements are employed in the composition
                 of these architectures: memory register, multiplexer
                 (1-from-2 data selector), and carry-save add-shift
                 computer. Two's complement serial\slash parallel
                 carry-save accumulation provides performance, while the
                 use of symmetric-coded distributed arithmetic
                 eliminates redundant computation to effect
                 area-savings.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@InCollection{Spangler:1987:RMM,
  author =       "R. A. Spangler",
  title =        "Revealing the mystery---the machine and how it
                 functions",
  crossref =     "Anbar:1987:CM",
  pages =        "9--46",
  year =         "1987",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "State University of New York at Buffalo, Buffalo",
  bibno =        "22925",
  catcode =      "C.0; B.0",
  content =      "In this paper, the author tries to describe the way a
                 digital computer works: from gates, through
                 instructions, data encoding, and interrupts, to
                 peripherals of more than a dozen types. He tries to do
                 this in 29 pages plus a nine-page appendix on
                 semiconductor technology. He tries to do it for an
                 audience described in the book's foreword as \par

                 (1) physicians who were educated in the pre-computer
                 era, (2) medical students and house staff being
                 educated now, (3) computer professionals interested in
                 medical applications, and (4) readers outside of the
                 medical profession and the computer science community
                 who are interested in the role of automation in health
                 care.\par

                 This is a tall order. The paper comes impressively
                 close to filling it. In clearly-written prose, Spangler
                 takes the reader through the overall structure of a
                 computer; its major components; information, binary
                 numbers (including floating point), and character
                 codes; word length issues; gates, combinatorial
                 circuits and flip-flops; instruction sets, including
                 subroutines and interrupts; and peripheral devices,
                 with emphasis on mass storage.\par

                 A necessary byproduct of covering all this material in
                 such a short space is a condensed, economical writing
                 style. Statements are made and concept",
  CRnumber =     "8802-0079",
  descriptor =   "Computer Systems Organization, GENERAL; Hardware,
                 GENERAL",
  genterm =      "DESIGN",
  pubcite =      "Rockville, MD",
  pubname =      "Computer Science Press, Inc.",
  reviewer =     "E. Mallach",
  subject =      "C. Computer Systems Organization; C.0 GENERAL; B.
                 Hardware; B.0 GENERAL",
  waffil =       "State University of New York at Buffalo, Buffalo",
}

@Manual{Sun:1987:SAM,
  key =          "Sun Microsystems",
  title =        "The {SPARC} Architecture Manual",
  organization = pub-SUN,
  address =      pub-SUN:adr,
  edition =      "Part No: 800-1399-07",
  month =        aug # " 8",
  year =         "1987",
  bibdate =      "Wed Sep 14 23:02:18 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Takagi:1987:LED,
  author =       "Naofumi Takagi and Shuzo Yajima",
  title =        "On-Line Error-Detectable High-Speed Multiplier Using
                 Redundant Binary Representation and Three-Rail Logic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "11",
  pages =        "1310--1317",
  month =        nov,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.5009470",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 09:28:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009470",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@PhdThesis{Takagi:1987:SHA,
  author =       "Naofumi Takagi",
  title =        "Studies on Hardware Algorithms for Arithmetic
                 Operations with a Redundant Binary Adder",
  type =         "{PhD} dissertation",
  school =       "Department of Information Sciences, Faculty of
                 Engineering, Kyoto University",
  address =      "Kyoto, Japan",
  pages =        "vii + 150",
  month =        aug,
  year =         "1987",
  bibdate =      "Thu Nov 13 06:14:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://hdl.handle.net/2433/154053;
                 https://repository.kulib.kyoto-u.ac.jp/server/api/core/bitstreams/b38960be-ee22-458e-9899-ed77db01155e/content;",
  acknowledgement = ack-nhfb,
  tableofcontents = "Abstract / i \\
                 Table of Contents / v \\
                 \\
                 1: Introduction / 1 \\
                 1.1 Backgrounds / 1 \\
                 1.2 Outline of the Thesis / 4 \\
                 \\
                 2: Preliminaries / 8 \\
                 2.1 Binary Number System / 8 \\
                 2.2 Computation Model / 8 \\
                 2.3 Redundant Binary Representation \\
                 2.3.1 Redundant Binary Representation / 10 \\
                 2.3.2 Carry-Propagation-Free Addition / 11 \\
                 2.3.3 Redundant Binary to Binary Conversion / 15 \\
                 2.3.4 Special Redundant Binary Numbers / 16 \\
                 \\
                 3: A Multiplication Hardware Algorithm with a Redundant
                 Binary Addition Tree / 19 \\
                 3.1 Introduction / 19 \\
                 3.2 A Multiplication Hardware Algorithm / 19 \\
                 3.2.1 Algorithm / 21 \\
                 3.2.2 Analysis of the Algorithm / 25 \\
                 3.3 A Multiplier Based on the Algorithm \\
                 3.3.1 Multiplier Recoding and Partial Product
                 Generation / 27 \\
                 3.3.2 A Multiplier Based on the Algorithm / 30 \\
                 3.3.3 The Depth and the Gate Count of the Multiplier /
                 33 \\
                 3.4 Computation of Other Arithmetic Functions Using the
                 Multiplier \\
                 3.4.1 Redundant Binary Multiplier Receding / 35 \\
                 3.4.2 Computation of Other Arithmetic Functions / 36
                 \\
                 3.5 Remarks and Discussions / 39 \\
                 \\
                 4: A Subtract-and-Shift Division Hardware Algorithm /
                 42 \\
                 4.1 Introduction / 42 \\
                 4.2 A Division Hardware Algorithm / 44 \\
                 4.2.1 Algorithm / 44 \\
                 4.2.2 Analysis of the Algorithm / 47 \\
                 4.3 A Divider Based on the Algorithm / 51 \\
                 4.4 Remarks and Discussions / 56 \\
                 4.A A Proof of the Correctness of the Algorithm / 57
                 \\
                 \\
                 5: A Subtract-and-Shift Square Root Hardware Algorithm
                 / 60 \\
                 5.1 Introduction / 60 \\
                 5.2 A Square Root Hardware Algorithm / 62 \\
                 5.2.1 Algorithm / 62 \\
                 5.2.2 Analysis of the Algorithm / 67 \\
                 5.3 A Square Root Circuit Based on the Algorithm / 69
                 \\
                 5.4 Remarks and Discussions / 70 \\
                 5.A A Proof of the Correctness of the Algorithm / 71
                 \\
                 \\
                 6: Hardware Algorithms for Elementary Functions / 75
                 \\
                 6.1 Introduction / 75 \\
                 6.2 Hardware Algorithms Based on the CORDIC Method / 77
                 \\
                 6.2.1 Principle of the CORDIC Method / 77 \\
                 6.2.2 A Hardware Algorithm for Computing Sines and
                 Cosines / 80 \\
                 6.2.3 A Hardware Algorithm for Computing Arctangents /
                 87 \\
                 6.3 Hardware Algorithms Based on the STL Method / 91
                 \\
                 6.3.1 Principle of the STL Method / 91 \\
                 6.3.2 A Hardware Algorithm for Computing Logarithms /
                 92 \\
                 6.3.3 A Hardware Algorithm for Computing Exponentials /
                 97 \\
                 6.4 Remarks and Discussions / 101 \\
                 \\
                 7: Design of Self-Checking Arithmetic Circuits by Means
                 of the Three-Rail Logic / 103 \\
                 7.1 Introduction / 103 \\
                 7.2 Design of Self-Checking Arithmetic Circuits / 106
                 \\
                 7.3 A Design of a Self-Checking Multiplier / 112 \\
                 7.4 Remarks and Discussions / 119 \\
                 \\
                 8: Redundant Coding Schemes for Several Algebraic
                 Systems / 121 \\
                 8.1 Introduction / 121 \\
                 8.2 Coding Schemes and Local Computability / 122 \\
                 8.3 A Redundant Coding Scheme for a Residue Class and a
                 Hardware Algorithm for Modular Addition / 124 \\
                 8.4 Redundant Coding Schemes for Other Algebraic
                 Systems / 129 \\
                 8.5 Remarks and Discussions / 132 \\
                 \\
                 9: Conclusion / 135 \\
                 Acknowledgments / 138",
}

@Article{Taylor:1987:RAI,
  author =       "Fred J. Taylor",
  title =        "A residue arithmetic implementation of the {FFT}",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "4",
  number =       "2",
  pages =        "191--208",
  month =        apr,
  year =         "1987",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliationaddress = "Univ of Florida, Gainesville, FL, USA",
  classification = "723; 921; C4190 (Other numerical methods); C4240
                 (Programming and algorithm theory); C5230 (Digital
                 arithmetic methods); C5260 (Digital signal processing);
                 C5470 (Performance evaluation and testing)",
  corpsource =   "Department of Electr. Eng., Coll. of Eng., Florida
                 University, Gainesville, FL, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "complex arithmetic; complexity; computational
                 complexity; computer metatheory; computerised signal
                 processing; digital arithmetic; discrete Fourier
                 transform (DFT); evaluation; Fast Fourier Transforms;
                 fast Fourier transforms; FFT; FFT system; management
                 system; mathematical techniques; mathematical
                 transformations; performance; residue arithmetic;
                 residue arithmetic number system; sign; sign
                 management; single-modulus complex residue number
                 system; speed",
  treatment =    "T Theoretical or Mathematical; X Experimental",
}

@Article{Thompson:1987:FME,
  author =       "T. Thompson",
  title =        "Fast Math --- a first look at {Motorola}'s 68882 math
                 coprocessor",
  journal =      j-BYTE,
  volume =       "12",
  number =       "12",
  pages =        "120--121",
  month =        dec,
  year =         "1987",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Wed Sep 7 22:32:00 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "BYTE Magazine",
}

@Article{Thompson:1987:IEF,
  author =       "P. Thompson",
  title =        "Implementing an Elementary Function Library",
  journal =      j-SIGNUM,
  volume =       "22",
  number =       "2",
  pages =        "2--5",
  month =        apr,
  year =         "1987",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Thu Sep 1 10:15:30 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}

@InProceedings{Tu:1987:RLD,
  author =       "Paul K. G. Tu and Milo{\v{s}} D. Ercegovac",
  title =        "A Radix-4 On-Line Division Algorithm",
  crossref =     "Irwin:1987:PSC",
  pages =        "181--187",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158719",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Tu_Ercegovac.pdf",
  abstract =     "We present an on-line algorithm for radix-4 floating
                 point division. The divisor is first transformed in to
                 a range such that the quotient digits are computed as a
                 function of the scaled partial remainder only.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@Article{Turner:1987:DDI,
  author =       "Peter R. Turner",
  title =        "The Distribution of l.s.d. and Its Implications for
                 Computer Design",
  journal =      j-MATH-GAZ,
  volume =       "71",
  number =       "455",
  pages =        "26--31",
  month =        mar,
  year =         "1987",
  CODEN =        "MAGAAS",
  DOI =          "https://doi.org/10.2307/3616283",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  bibdate =      "Tue Oct 30 23:36:58 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Gazette",
  journal-URL =  "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
  keywords =     "Benford's Law; Law of Anomalous Numbers; logarithmic
                 distribution; overflow; underflow; Zipf's Law",
}

@InProceedings{Umeo:1987:DTO,
  author =       "Hiroshi Umeo",
  title =        "A Design of Time-Optimum and Register-Number-Minimum
                 Systolic Convolver",
  crossref =     "Irwin:1987:PSC",
  pages =        "5--12",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158720",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Umeo.pdf",
  abstract =     "We present an optimum bit-parallel\slash
                 word-sequential systolic convolver. Our design is the
                 best one among the previous many convolvers in the
                 sense that its optimality in time and space
                 performances is simultaneously attained without
                 augmenting any global control, broadcasting,
                 preloading, and\slash or multi sequential or parallel
                 I/O ports, which were allowed in most of the previous
                 designs. As an application of our convolver we give a
                 systolic polynomial divider which can compute the
                 polynomial division in exactly $ n + O(1) $ steps on $
                 [\min (n - m, m) / 2] + O(1) $ systolic cells, for the
                 division of any degree n polynomial by any degree $m$
                 polynomial ($ n \geq m $).",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@Article{Ushio:1987:CRE,
  author =       "T. Ushio and C. Hsu",
  title =        "Chaotic rounding error in digital control systems",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "34",
  number =       "2",
  pages =        "133--139",
  month =        feb,
  year =         "1987",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 11:25:03 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "Chaotic behavior due to the round-off effect in
                 digital control systems is called the chaotic rounding
                 error. First, we model digital control systems with
                 finite-wordlength digital compensators by mixed
                 mappings. A mixed mapping system is described
                 \ldots{}",
}

@Article{Vachss:1987:CMF,
  author =       "R. Vachss",
  title =        "The {Cordic} Magnification Function",
  journal =      j-IEEE-MICRO,
  volume =       "7",
  number =       "5",
  pages =        "83--84",
  month =        sep # "\slash " # oct,
  year =         "1987",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.1987.305021",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Sep 1 10:15:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}

@Article{Vitek:1987:EFA,
  author =       "V. Vitek",
  title =        "Enumeration in floating-point arithmetic",
  journal =      "ASR - Bulletin INORGA",
  volume =       "21",
  number =       "6",
  pages =        "301--305",
  month =        "????",
  year =         "1987",
  ISSN =         "0231-8954",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The paper studies the computer representation of
                 numbers in floating-point arithmetic and algebraic
                 operations with these numbers with respect to the
                 validity of basic algebraic laws. Methods for the
                 handling of emergency situations are given: overflow
                 and underflow, illustrated using the example of the
                 computation of a member of the binomial expansion. (6
                 Refs.)",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods)",
  keywords =     "Algebraic operations; Computer representation;
                 Floating-point arithmetic; Overflow; Underflow",
  pubcountry =   "Czechoslovakia",
  thesaurus =    "Carry logic; Digital arithmetic; Error handling",
}

@InProceedings{Wang:1987:EEF,
  author =       "Kai Hwang and H. C. Wang and Z. Xu",
  title =        "Evaluating Elementary Functions with {Chebyshev}
                 Polynomials on Pipeline Nets",
  crossref =     "Irwin:1987:PSC",
  pages =        "121--128",
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH.1987.6158702",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Hwang_Wang_Xu.pdf",
  abstract =     "Fast evaluation of vector-valued elementary functions
                 plays a vital role in many real-time applications. In
                 this paper, we present a pipeline networking approach
                 to designing a Chebyshev polynomial evaluator for the
                 fast evaluation of elementary functions over a string
                 of arguments. In particular, pipeline nets are employed
                 to perform the preprocessing and postprocessing of
                 various elementary functions to boost the overall
                 system performance. Design tradeoffs are analyzed among
                 representational accuracy, processing speed and
                 hardware complexity.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@Manual{WeitekCorporation:1987:WFP,
  title =        "{WTL} 1167 floating point coprocessor: preliminary
                 data",
  organization = "{Weitek Corporation}",
  address =      "Sunnyvale, CA, USA",
  pages =        "54",
  year =         "1987",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Intel 80386
                 (Microprocessor) --- Programming.",
  remark =       "August 1988.",
}

@MastersThesis{Williams:1987:FPL,
  author =       "Robert Leslie Williams",
  title =        "A floating point loop engine architecture using
                 pattern generation",
  type =         "Thesis ({M.S.})",
  school =       "University of New Mexico",
  address =      "Albuquerque, NM, USA",
  pages =        "ix + 92",
  year =         "1987",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer architecture.; Computer engineering.",
}

@InProceedings{Williams:1987:STC,
  author =       "T. E. Williams and M. Horowitz and R. L. Alverson and
                 T. S. Yang",
  title =        "A self-timed chip for division",
  crossref =     "Losleben:1987:ARV",
  pages =        "75--96",
  year =         "1987",
  bibdate =      "Mon Sep 16 16:35:03 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Wu:1987:FDS,
  author =       "I-Chen Wu",
  title =        "A Fast {$1$-D} Serial-Parallel Systolic Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "10",
  pages =        "1243--1247",
  month =        oct,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.1676865",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 09:28:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1676865",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Wu:1987:TRF,
  author =       "Chwan-Ghia Wu and Lih-Ren Tzeng and Tien-Shou Wu",
  title =        "Time-Redundant Fault-Masking in {ALUs}",
  crossref =     "Irwin:1987:PSC",
  pages =        "239--243",
  year =         "1987",
  bibdate =      "Fri Nov 16 21:39:46 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith8/papers/ARITH8_Wu_Cheng_Wu.pdf",
  abstract =     "A new error correction scheme for bit-sliced ALUs is
                 presented. The method adopted for fault location is an
                 extension of a concurrent error detection scheme called
                 RESO (Recomputing with Shifted Operands). The term
                 bit-slice is used in the generic sense and the length
                 of the slice may be one or more bits. The proposed
                 scheme requires two consecutive computation steps for
                 normal operations and the possible locations of faults,
                 if any, can be located provided that the failures are
                 confined to a certain number of adjacent bit-slices.
                 The fault-free bit-slices of the ALU are thus figured
                 out. The final and effective computation is then
                 carried out through those identified fault-free
                 bit-slices. A circular structure is proposed to realize
                 this concept.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
  remark =       "This paper is missing from the IEEE Xplore database,
                 so its DOI and text are not available there.",
}

@Article{Zaccone:1987:ENP,
  author =       "Richard J. Zaccone and Jesse L. Barlow",
  title =        "Eliminating the Normalization Problem in Digit On-Line
                 Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "1",
  pages =        "36--46",
  month =        jan,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.5009447",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 09:28:49 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009447",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Zurawski:1987:DHS,
  author =       "J. H. P. Zurawski and J. B. Gosling",
  title =        "Design of a High-Speed Square Root Multiply and Divide
                 Unit",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-36",
  number =       "1",
  pages =        "13--23",
  month =        jan,
  year =         "1987",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1987.5009445",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 09:28:49 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5009445",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Book{Aberth:1988:PNA,
  author =       "Oliver Aberth",
  title =        "Precise Numerical Analysis",
  publisher =    pub-WCB,
  address =      pub-WCB:adr,
  pages =        "x + 225",
  year =         "1988",
  ISBN =         "0-697-06760-2",
  ISBN-13 =      "978-0-697-06760-9",
  LCCN =         "QA297 .A28 1988",
  bibdate =      "Thu Nov 8 14:50:32 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Aberth addresses elementary issues of precise floating
                 point computations using variable precision range
                 arithmetic. Numbers are represented as a variable
                 precision number $ \pm $ a range. Rational arithmetic
                 is also considered. Chapters are devoted to
                 \begin{enumerate} \item rootfinding, \item polynomial
                 rootfinding, \item numerical linear algebra, \item
                 differentiation and integration, and \item ordinary
                 differential equations. \end{enumerate} Differentiation
                 is handled by a codelist approach like [Rall81a], and
                 applications to Taylor series are given. Interval
                 techniques for ordinary differential equations are
                 based on using an {\it a priori\/} bound to capture
                 remainder terms. Several methods are illustrated,
                 including Taylor series methods.",
  acknowledgement = ack-nj,
  comment =      "Text for a one semester, junior level course in
                 numerical analysis. Includes PC disk with software
                 written in PBASIC. Sound introductory level discussion
                 of code lists and error capture techniques.",
  keywords =     "differentiation; differentiation arithmetic; general
                 numerical analysis; integration; interval techniques;
                 linear algebra; ordinary differential equations.;
                 variable precision arithmetic",
}

@Article{Alt:1988:FEP,
  author =       "Ren{\'e} Alt",
  title =        "Floating-point error propagation in iterative methods.
                 Stochastic methods in round-off error analysis",
  journal =      j-MATH-COMPUT-SIMUL,
  volume =       "30",
  number =       "6",
  pages =        "505--517",
  year =         "1988",
  CODEN =        "MCSIDR",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  MRclass =      "65G05 (65F10)",
  MRnumber =     "90f:65067",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics and Computers in Simulation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784754",
  reviewer =     "D. Bini",
}

@Article{Alt:1988:FPE,
  author =       "R. Alt",
  title =        "Floating-point error propagation in iterative
                 methods",
  journal =      j-MATH-COMPUT-SIMUL,
  volume =       "30",
  number =       "6",
  pages =        "505--517",
  month =        dec,
  year =         "1988",
  CODEN =        "MCSIDR",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  bibno =        "56847",
  catcode =      "G.1.0",
  CRclass =      "G.1.0 General; G.1.0 Computer arithmetic",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Computer arithmetic",
  fjournal =     "Mathematics and Computers in Simulation",
  genterm =      "THEORY; ALGORITHMS",
  guideno =      "1988-12109",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784754",
  journalabbrev = "Math. Comput. Simul.",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
}

@Article{AMD:1988:IFP,
  author =       "{Advanced Micro Devices}",
  title =        "{IEEE} floating-point format",
  journal =      j-MICROPROC-MICROSYS,
  volume =       "12",
  number =       "1",
  pages =        "13--23",
  month =        jan # "\slash " # feb,
  year =         "1988",
  CODEN =        "MIMID5",
  ISSN =         "0141-9331 (print), 1872-9436 (electronic)",
  ISSN-L =       "0141-9331",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  bibno =        "23",
  categories =   "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 K. Computing Milieux; K.1 THE COMPUTER INDUSTRY; G.1.0
                 General; G.1.0 Computer arithmetic; K.1 Standards",
  content =      "DESIGN; STANDARDIZATION; THEORY",
  CRnumber =     "1988-12470",
  fjournal =     "Microprocessors and Microsystems",
  guideno =      "1",
  subject =      "mathematics of computing, numerical analysis, general,
                 computer arithmetic; computing milieux, the computer
                 industry, standards",
  wsub =         "Jesse L. Barlow",
}

@Article{An:1988:CRE,
  author =       "S. H. An and K. Yao",
  title =        "Convergent and roundoff error properties of reflection
                 coefficients in adaptive spatial recursive least
                 squares lattice algorithm",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "35",
  number =       "2",
  pages =        "241--246",
  month =        feb,
  year =         "1988",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "The spatial recursive least-squares lattice (RLSL)
                 algorithm is considered and the convergent properties
                 as well as the finite-precision roundoff effects of the
                 reflection coefficients are studied in detail. It is
                 shown that when the forgetting \ldots{}",
}

@Article{Anderson:1988:MRE,
  author =       "Ned Anderson",
  title =        "Minimum relative error approximations for $ 1 / t $",
  journal =      j-NUM-MATH,
  volume =       "54",
  number =       "2",
  pages =        "117--124",
  month =        nov,
  year =         "1988",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01396969",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65D15",
  MRnumber =     "90a:65037",
  MRreviewer =   "Mariano Gasca",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  corpsource =   "Corp. Res., Digital Equipment Corp., Hudson, MA, USA",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "approximation theory; functional equation; geometric
                 convergence rates; iterative methods; minimum relative
                 error approximations; polynomial approximations;
                 polynomials",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Anonymous:1988:IGI,
  author =       "Anonymous",
  title =        "{IMACS-GAMM} international symposium on computer
                 arithmetic and self-validating numerical methods",
  journal =      j-MATH-COMPUT-SIMUL,
  volume =       "30",
  number =       "6",
  pages =        "572--572",
  month =        dec,
  year =         "1988",
  CODEN =        "MCSIDR",
  DOI =          "https://doi.org/10.1016/0378-4754(88)90091-2",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  bibdate =      "Mon Aug 18 16:03:57 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomputsimul1980.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/0378475488900912",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput. Simul.",
  fjournal =     "Mathematics and Computers in Simulation",
  journal-URL =  "https://www.sciencedirect.com/science/journal/03784754",
}

@Book{Apple:1988:ANM,
  author =       "{Apple Computer, Inc.}",
  title =        "{Apple} Numerics Manual",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Second",
  pages =        "xxvi + 294",
  year =         "1988",
  ISBN =         "0-201-17738-2",
  ISBN-13 =      "978-0-201-17738-1",
  LCCN =         "QA76.8.A662 A767 1988",
  bibdate =      "Wed Sep 07 21:06:52 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$29.95",
  series =       "The Apple technical library",
  acknowledgement = ack-nhfb,
  keywords =     "Apple II (computer) --- programming; computation by
                 computer systems --- floating point representation;
                 Macintosh (computer) --- programming; numerical
                 calculations --- data processing; SANE (Standard Apple
                 Numeric Environment)",
}

@Article{Bailey:1988:EHS,
  author =       "David H. Bailey",
  title =        "Extra high speed matrix multiplication on the
                 {Cray-2}",
  journal =      j-SIAM-J-SCI-STAT-COMP,
  volume =       "9",
  number =       "3",
  pages =        "603--607",
  month =        may,
  year =         "1988",
  CODEN =        "SIJCD4",
  DOI =          "https://doi.org/10.1137/0909040",
  ISSN =         "0196-5204",
  ISSN-L =       "0196-5204",
  MRclass =      "65F30 (65G05 65W05)",
  MRnumber =     "937 496",
  bibdate =      "Mon Mar 31 10:00:04 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscistatcomp.bib",
  acknowledgement = ack-nhfb,
  classification = "C7310 (Mathematics)",
  corpsource =   "Ames Res. Center, NASA, Moffett Field, CA, USA",
  fjournal =     "SIAM Journal on Scientific and Statistical Computing",
  journal-URL =  "http://epubs.siam.org/loi/sijcd4",
  keywords =     "Cray-2; floating-point operations; library routines;
                 mathematics computing; matrix algebra; matrix
                 multiplication; memory bank contention; numerical
                 stability",
  onlinedate =   "May 1988",
  treatment =    "P Practical",
}

@InProceedings{Bandyopadhyay:1988:SAF,
  author =       "S. Bandyopadhyay and G. A. Jullien and A. Sengupta",
  booktitle =    "Proceedings of the International Conference on
                 Systolic Arrays, 1988. 25--27 May 1988",
  title =        "A systolic array for fault tolerant digital signal
                 processing using a residue number system approach",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "577--586",
  year =         "1988",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ARRAYS.1988.18094",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Fault detection and correction using the Chinese
                 remainder theorem for decoding is investigated. It is
                 shown that this approach is well suited for
                 implementation by VLSI circuits for digital signal
                 processing using systolic architectures. A systolic
                 \ldots{}",
}

@Article{Banning:1988:PRF,
  author =       "Craig Banning",
  title =        "Perfectly Rounded Floats",
  journal =      j-CUJ,
  volume =       "6",
  number =       "2",
  pages =        "14--??",
  month =        feb,
  year =         "1988",
  ISSN =         "0898-9788",
  bibdate =      "Fri Aug 30 16:52:23 MDT 1996",
  bibsource =    "http://www.cuj.com/cbklist.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "C Users Journal",
}

@Article{Barany:1988:FEI,
  author =       "T. E. Barany",
  title =        "Fast evaluation of integer roots in microcontroller
                 systems",
  journal =      j-MICROPROC-MICROSYS,
  volume =       "12",
  number =       "6",
  pages =        "341--344",
  month =        jul # "--" # aug,
  year =         "1988",
  CODEN =        "MIMID5",
  ISSN =         "0141-9331 (print), 1872-9436 (electronic)",
  ISSN-L =       "0141-9331",
  bibdate =      "Fri Dec 08 13:06:02 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Microprocessors and Microsystems",
}

@TechReport{Barlow:1988:EAU,
  author =       "Jesse Louis Barlow and Richard J. Zaccone",
  title =        "Error analysis in unnormalized floating point
                 arithmetic",
  type =         "Technical report",
  number =       "CS-88-33",
  institution =  "Pennsylvania State University, Department of Computer
                 Science",
  address =      "University Park, PA, USA",
  pages =        "12",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.",
  remark =       "Supported by the National Science Foundation.
                 Supported by the Office of Naval Research.",
}

@TechReport{Barlowe:1988:EAU,
  author =       "Jesse L. Barlowe",
  title =        "Error analysis in unnormalized floating point
                 arithmetic",
  type =         "Technical report",
  number =       "CS-88-10",
  institution =  "Pennsylvania State University, Department of Computer
                 Science",
  address =      "University Park, PA, USA",
  pages =        "14",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic.; Errors.",
  remark =       "Supported by the National Science Foundation.
                 Supported by the Office of Naval Research.",
}

@InProceedings{BenChorin:1988:NPC,
  author =       "S. Ben-Chorin",
  title =        "{NS32532-NS32580} processor cluster delivers high
                 floating-point performance",
  crossref =     "Midcon:1988:MCP",
  pages =        "243--248",
  year =         "1988",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The NS32580 Floating-Point Controller (FPC) teams with
                 Weitek's WTL3164 Floating-Point Data Path (FPDP) device
                 and the NS32532 CPU to achieve a floating-point
                 performance that complements the NS32532's 15 MIPS
                 peak-integer performance. Due to a pipelined
                 coprocessor interface and the floating-point controller
                 design, this processor cluster achieves a peak
                 floating-point performance of 15 MFLOPs for both
                 single-precision (32-bit) and double-precision (64-bit)
                 floating-point instructions, such as add, subtract and
                 multiply. This high-performance is accomplished without
                 sacrificing software compatibility with the previous
                 Series 32000 processor clusters, including precise
                 floating-point exceptions.",
  acknowledgement = ack-nhfb,
  affiliation =  "Nat. Semicond. Corp., Santa Clara, CA, USA",
  classification = "C5130 (Microprocessor chips); C5220 (Computer
                 architecture)",
  keywords =     "Floating-Point Controller; Floating-Point Data Path;
                 Floating-point performance; NS32532 CPU; NS32580;
                 Pipelined coprocessor interface; Processor cluster;
                 WTL3164",
  thesaurus =    "Computer architecture; Microprocessor chips",
}

@InProceedings{Bewick:1988:ANB,
  author =       "G. Bewick and P. Song and G. De Micheli and M. Flynn",
  title =        "Approaching a nanosecond: a 32-bit adder",
  crossref =     "IEEE:1988:PII",
  pages =        "221--226",
  year =         "1988",
  DOI =          "https://doi.org/10.1109/ICCD.1988.25695",
  bibdate =      "Mon Dec 24 09:52:15 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Birman:1988:DHS,
  author =       "M. Birman and G. Chu and L. Hu and J. McLeod and N.
                 Bedard and F. Ware and L. Torban and C. M. Lim",
  title =        "Design of a high-speed arithmetic datapath",
  crossref =     "IEEE:1988:PII",
  pages =        "214--216",
  year =         "1988",
  bibdate =      "Wed Sep 7 22:32:00 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@MastersThesis{Blaker:1988:FPB,
  author =       "David Mark Blaker",
  title =        "Floating point bit-sequential arithmetic units",
  type =         "Thesis ({M.S.})",
  school =       "Lehigh University",
  address =      "Bethlehem, PA, USA",
  pages =        "vi + 73",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic.; Floating-point arithmetic.",
}

@Article{Bohlender:1988:IFA,
  author =       "Gerd Bohlender",
  title =        "Is floating-point arithmetic still adequate?",
  journal =      "Systems analysis and simulation",
  volume =       "46",
  publisher =    "Akademie-Verlag",
  address =      "Berlin, Germany",
  pages =        "105--108",
  year =         "1988",
  MRclass =      "68N15 (65G99)",
  MRnumber =     "976 389",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  xxjournal =    "Math. Res.",
  xxx =          "I (Berlin, 1988)",
}

@TechReport{Bose:1988:VDT,
  author =       "Bidyut Kumar Bose",
  title =        "{VLSI} design techniques for floating-point
                 computation",
  type =         "Report",
  number =       "UCB/CSD 88/469",
  institution =  "University of California, Berkeley, Computer Science
                 Division",
  address =      "Berkeley, CA, USA",
  pages =        "vi + 173",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Integrated circuits ---
                 Very large scale integration.",
}

@MastersThesis{Brooks:1988:VIF,
  author =       "Kelvin R. Brooks",
  title =        "The {VLSI} implementation of a floating-point
                 multiplier",
  type =         "Thesis ({M.S.})",
  school =       "North Carolina A\&T State University",
  address =      "Greensboro, NC, USA",
  pages =        "x + 78",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electric engineering.; Integrated circuits --- Very
                 large scale integration.",
}

@Article{Brosnan:1988:MED,
  author =       "T. J. Brosnan and N. R. {Strader II}",
  title =        "Modular error detection for bit-serial
                 multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "37",
  number =       "9",
  pages =        "1043--1052",
  month =        sep,
  year =         "1988",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.2255",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 08:33:28 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2255",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Byington:1988:HGB,
  author =       "Carl Byington",
  title =        "How to get better floating-point results",
  journal =      j-BYTE,
  volume =       "13",
  number =       "3",
  pages =        "229--236",
  month =        mar,
  year =         "1988",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  bibno =        "44973",
  catcode =      "C.5.3; G.1.0; D.1.m",
  CRclass =      "C.5.3 Microcomputers; G.1.0 General; G.1.0 Computer
                 arithmetic; D.1.m Miscellaneous",
  descriptor =   "Computer Systems Organization, COMPUTER SYSTEM
                 IMPLEMENTATION, Microcomputers; Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Computer
                 arithmetic; Software, PROGRAMMING TECHNIQUES,
                 Miscellaneous",
  fjournal =     "BYTE Magazine",
  genterm =      "DESIGN; RELIABILITY",
  guideno =      "1988-05276",
  subject =      "C. Computer Systems Organization; C.5 COMPUTER SYSTEM
                 IMPLEMENTATION; G. Mathematics of Computing; G.1
                 NUMERICAL ANALYSIS; D. Software; D.1 PROGRAMMING
                 TECHNIQUES",
}

@Article{Callahan:1988:EII,
  author =       "D. Callahan and J. Cocke and K. Kennedy",
  title =        "Estimating interlock and improving balance for
                 pipelined architectures",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "5",
  number =       "4",
  pages =        "334--358",
  month =        aug,
  year =         "1988",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 17:13:17 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C5220 (Computer architecture); C5230 (Digital
                 arithmetic methods)",
  corpsource =   "Department of Computer Science, Rice University,
                 Houston, TX, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "arithmetic; bandwidth; digital arithmetic; DO loops;
                 execution order constraints; fine-grain parallelism;
                 floating-point; memory; parallel architectures;
                 pipeline; pipeline balance; pipeline interlock;
                 pipelined architectures; processing",
  treatment =    "P Practical",
}

@Article{Capocelli:1988:EVN,
  author =       "R. M. Capocelli and R. Giancarlo",
  title =        "Efficient {VLSI} networks for converting an integer
                 from binary system to residue number system and vice
                 versa",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "35",
  number =       "11",
  pages =        "1425--1430",
  month =        nov,
  year =         "1988",
  CODEN =        "ICSYBT",
  DOI =          "https://doi.org/10.1109/31.14466",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=565",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
  summary =      "VLSI networks for converting integers from binary to
                 residue number systems are presented Both direct and
                 reverse conversion are treated. The networks are
                 improvements, with respect to area or time or both, of
                 previously proposed \ldots{}",
}

@TechReport{Cappello:1988:SSSa,
  author =       "Peter R. Cappello and Willard L. Miranker",
  title =        "Systolic super summation with reduced hardware",
  type =         "Technical report",
  number =       "TRCS88-27",
  institution =  "University of California, Santa Barbara, College of
                 Engineering Department of Computer Science",
  address =      "Santa Barbara, CA, USA",
  pages =        "8",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation; computer science
                 --- mathematics; floating-point arithmetic",
  remark =       "``A principle limitation in accuracy for scientific
                 computation performed with floating-point arithmetic
                 may be traced to the computation of repeated sums, such
                 as those which arise in inner products. A design is
                 proposed for a systolic super summer, a cellular piece
                 of hardware for the summation of floating-point
                 numbers. The apparatus receives floating-point
                 summands, converting them into a fixed-point form by a
                 sieve-like cellular array. The emerging fixed-point
                 numbers then are summed in a pipelined array of long
                 accumulators. The architectural regularity of the sieve
                 makes it ideal for implementation in VLSI circuit
                 technology.'' Supported by the Office of Naval
                 Research.",
}

@Misc{Cappello:1988:SSSb,
  author =       "Peter R. Cappello and Willard L. Miranker",
  title =        "Systolic super summation device",
  howpublished = "US Patent 4751665",
  day =          "14",
  month =        jun,
  year =         "1988",
  bibdate =      "Mon Dec 29 16:20:01 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/4751665/fulltext.html",
  abstract =     "A cellular architecture for a systolic super summer
                 for high throughput performance of repeated sums of
                 floating-point numbers. The summer receives pipelined
                 inputs of streams of summands, converts the
                 floating-point summands into a fixed-point form by a
                 sieve-like pipelined cellular network, and sums the
                 emerging fixed-point numbers in a corresponding network
                 of extremely long accumulators. The throughput per unit
                 area of the hardware approaches that of a tree network,
                 but without the long wires and signal propagation that
                 are intrinsic to tree networks.",
  acknowledgement = ack-nhfb,
}

@Article{Capps:1988:OAL,
  author =       "C. David Capps and R. Aaron Falk and Theodore L.
                 Houk",
  title =        "Optical Arithmetic\slash Logic Unit Based on Residue
                 Arithmetic and Symbolic Substitution",
  journal =      j-APPL-OPTICS,
  volume =       "27",
  number =       "9",
  pages =        "1682--1686",
  month =        may,
  year =         "1988",
  CODEN =        "APOPAI",
  ISSN =         "0003-6935",
  bibdate =      "Fri Jun 24 18:13:20 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "There has been difficulty in achieving a fully
                 parallel, digital optical adder or multiplier. The
                 primary obstacle is the carry operation inherent in any
                 fixed-radix number system. The concepts of residue
                 number representation and symbolic substitution can be
                 combined to produce a parallel optical arithmetic/logic
                 unit.",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Optics",
  journal-URL =  "http://www.osapublishing.org/ao/browse.cfm",
}

@Article{Cardarilli:1988:SPD,
  author =       "G. C. Cardarilli and R. Lojacono and G. Martinelli and
                 M. Salerno",
  title =        "Structurally passive digital filters in residue number
                 systems",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "35",
  number =       "2",
  pages =        "149--158",
  month =        feb,
  year =         "1988",
  CODEN =        "ICSYBT",
  DOI =          "https://doi.org/10.1109/31.1716",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=107",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The possibility of realizing structural passive
                 digital filters in terms of residue number systems
                 (RNS) is considered. For this purpose, an algorithm is
                 proposed for realizing the RNS rotator, which
                 represents the basic element of these filters.
                 \ldots{}",
}

@Article{Cavallaro:1988:CAS,
  author =       "Joseph R. Cavallaro and Franklin T. Luk",
  title =        "{CORDIC} arithmetic for an {SVD} processor",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "5",
  number =       "3",
  pages =        "271--290",
  month =        jun,
  year =         "1988",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliationaddress = "Cornell Univ, Ithaca, NY, USA",
  classification = "721; 722; 723; 921; C5230 (Digital arithmetic
                 methods); C5440 (Multiprocessor systems and
                 techniques)",
  corpsource =   "Sch. of Electr. Eng., Cornell University, NY, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "Algorithms; computer architecture; computer
                 programming; computers, digital --- Computational
                 Methods; CORDIC arithmetic; Decomposition; digital
                 arithmetic; hardware division; inverse tangents;
                 mathematical techniques --- Algorithms; parallel
                 processing; real-time; rotations; signal processing
                 applications; Singular Value; singular value
                 decomposition; special-purpose arithmetic techniques;
                 square root; SVD processor; vector; vector rotations;
                 VLSI implementation",
  treatment =    "P Practical",
}

@InProceedings{Cavallaro:1988:FPC,
  author =       "J. R. Cavallaro and F. T. Luk",
  booktitle =    "{Proceedings 1988 IEEE International Conference on
                 Computer Design: VLSI}",
  title =        "Floating point {CORDIC} for matrix computations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "40--42",
  year =         "1988",
  DOI =          "https://doi.org/10.1109/ICCD.1988.25655",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; Equations; Floating-point arithmetic;
                 Hardware; Matrix decomposition; Read only memory;
                 Registers; Signal processing algorithms; Singular value
                 decomposition; Very large scale integration",
}

@Article{Chaitin:1988:RA,
  author =       "Gregory J. Chaitin",
  title =        "Randomness in Arithmetic",
  journal =      j-SCI-AMER,
  volume =       "259",
  number =       "1",
  pages =        "80--85 (Intl. ed. 52--57)",
  month =        jul,
  year =         "1988",
  CODEN =        "SCAMAC",
  DOI =          "https://doi.org/10.1038/scientificamerican0788-80",
  ISSN =         "0036-8733 (print), 1946-7087 (electronic)",
  ISSN-L =       "0036-8733",
  bibdate =      "Wed May 22 15:04:14 MDT 2013",
  bibsource =    "Distributed/QLD/1988.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sciam1980.bib",
  URL =          "http://www.nature.com/scientificamerican/journal/v259/n1/pdf/scientificamerican0788-80.pdf",
  acknowledgement = ack-nhfb,
  country =      "USA",
  date =         "01/07/93",
  descriptors =  "Randomness; Arithmetic",
  enum =         "9449",
  fjournal =     "Scientific American",
  journal-URL =  "http://www.nature.com/scientificamerican",
  keywords =     "algorithmic information theory; computability theory;
                 halting problem; incompleteness theorem; number theory;
                 Pascal's triangle; randomness",
  remark =       "(VBI-001989)",
  xxnewdata =    "1998.01.30",
}

@Article{Chen:1988:GCM,
  author =       "M. C. Chen",
  title =        "The generation of a class of multipliers: synthesizing
                 highly parallel algorithms in {VLSI}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "37",
  number =       "3",
  pages =        "329--338",
  month =        mar,
  year =         "1988",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.2170",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 08:33:25 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2170",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@TechReport{Cheng:1988:ATM,
  author =       "Kuo-kuang Cheng and Robert R. Seban",
  title =        "Algorithm theory and the microarchitecture of an
                 optimal {VLSI} floating point divider",
  institution =  "Department of Computer Science, College of Engineering
                 and Applied Sciences, Arizona State University",
  address =      "Tempe, AZ, USA",
  pages =        "17",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "CR-R; 89028 TR; 88-032 Report (Arizona State
                 University. College of Engineering and Applied
                 Sciences); 89:28. Technical report (Arizona State
                 University. Department of Computer Science); 88-032.",
  acknowledgement = ack-nhfb,
  remark =       "``December 22, 1988.''",
}

@Article{Cody:1988:AMS,
  author =       "W. J. Cody",
  title =        "{Algorithm 665}: {MACHAR}: a Subroutine to Dynamically
                 Determine Machine Parameters",
  journal =      j-TOMS,
  volume =       "14",
  number =       "4",
  pages =        "303--311",
  month =        dec,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/50063.51907",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 22:33:58 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-4/p303-cody/",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Portability. {\bf G.1.0}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Computer
                 arithmetic.",
}

@InCollection{Cody:1988:FPS,
  author =       "W. J. Cody",
  title =        "Floating-point standards --- theory and practice",
  crossref =     "Moore:1988:RCR",
  pages =        "99--107",
  year =         "1988",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Argonne National Laboratory, Argonne, IL",
  bibno =        "60186",
  catcode =      "B.7.1; K.1",
  CRclass =      "B.7.1 Types and Design Styles; K.1 Standards",
  descriptor =   "Hardware, INTEGRATED CIRCUITS, Types and Design
                 Styles; Computing Milieux, THE COMPUTER INDUSTRY,
                 Standards",
  genterm =      "THEORY; RELIABILITY; STANDARDIZATION; RELIABILITY",
  guideno =      "1988-01977",
  subject =      "B. Hardware; B.7 INTEGRATED CIRCUITS; K. Computing
                 Milieux; K.1 THE COMPUTER INDUSTRY",
  waffil =       "Ohio State University, Columbus",
}

@Article{Cosentino:1988:FTS,
  author =       "R. J. Cosentino",
  title =        "Fault tolerance in a systolic residue arithmetic
                 processor array",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "37",
  number =       "7",
  pages =        "886--890",
  month =        jul,
  year =         "1988",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.2239",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 08:33:27 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2239",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Davila:1988:FPA,
  author =       "J. M. Davila and A. J. Phillips and D. Tabak",
  title =        "Floating Point Arithmetic on a {RISC}",
  journal =      j-MICROPROC-MICROPROG,
  volume =       "23",
  number =       "1--5",
  pages =        "179--184",
  month =        mar,
  year =         "1988",
  CODEN =        "MMICDT",
  ISSN =         "0165-6074 (print), 1878-7061 (electronic)",
  ISSN-L =       "0165-6074",
  bibdate =      "Thu Sep 1 10:15:06 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Microprocessing and Microprogramming",
  journal-URL =  "https://www.sciencedirect.com/journal/microprocessing-and-microprogramming/issues",
}

@InProceedings{deLange:1988:OFP,
  author =       "A. A. J. de Lange and A. J. van der Hoeven and E. F.
                 Deprettere and J. Bu",
  booktitle =    "{1988., IEEE International Symposium on Circuits and
                 Systems}",
  title =        "An optimal floating-point pipeline {CMOS} {CORDIC}
                 processor",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2043--2047 (vol. 3)",
  year =         "1988",
  DOI =          "https://doi.org/10.1109/ISCAS.1988.15343",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithm design and analysis; Analytical models;
                 Circuit simulation; CMOS process; Design methodology;
                 Macrocell networks; Pipelines; Signal processing
                 algorithms; Silicon compiler; Very large scale
                 integration",
}

@MastersThesis{Duerksen:1988:CAP,
  author =       "Joel L. Duerksen",
  title =        "A comparative analysis of the performance of floating
                 point and integer based line drawing algorithms for
                 raster displays",
  type =         "Thesis ({M.S.})",
  school =       "Department of Computer Science, Ball State
                 University",
  address =      "Muncie, IN 47306, USA",
  pages =        "ix + 206",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithms.; Computer graphics.",
}

@Article{Dunham:1988:PMA,
  author =       "C. B. Dunham",
  title =        "Provably Monotone Approximations {III}",
  journal =      j-SIGNUM,
  volume =       "23",
  number =       "1",
  pages =        "10--10",
  month =        jan,
  year =         "1988",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Sep 13 09:05:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "theory",
  subject =      "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation",
}

@Article{Duprat:1988:HPE,
  author =       "Jean Duprat and Jean-Michel Muller",
  title =        "Hardwired polynomial evaluation",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "5",
  number =       "3",
  pages =        "291--309",
  month =        jun,
  year =         "1988",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliationaddress = "CNRS, Grenoble, Fr",
  classification = "721; 722; 723; 921; C4130 (Interpolation and
                 function approximation); C5230 (Digital arithmetic
                 methods)",
  corpsource =   "Inst. Nat. Polytech. de Grenoble, France",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "computer architecture; computers, digital ---
                 Circuits; digital arithmetic; elementary functions;
                 hardwired polynomial evaluation; mathematical
                 functions; mathematical techniques; Polynomials;
                 polynomials; special-purpose circuits; VLSI
                 implementation",
  treatment =    "P Practical",
}

@InProceedings{Ercegovac:1988:LAD,
  author =       "M. D. Ercegovac and T. Lang",
  title =        "On-Line Arithmetic: a Design Methodology and
                 Applications in Digital Signal Processing",
  crossref =     "Brodersen:1988:VSP",
  volume =       "3",
  pages =        "252--263",
  year =         "1988",
  bibdate =      "Fri Dec 08 10:42:22 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[66--77]{Swartzlander:1990:CAb}.",
  acknowledgement = ack-nhfb,
}

@Article{Ercegovac:1988:LSC,
  author =       "Milo{\v{s}} D. Ercegovac and Tomas Lang",
  title =        "On-line scheme for computing rotation factors",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "5",
  number =       "3",
  pages =        "209--227",
  month =        jun,
  year =         "1988",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliationaddress = "Univ of California, Los Angeles, CA, USA",
  classification = "721; 722; 723; 921; C5230 (Digital arithmetic
                 methods)",
  corpsource =   "Department of Computer Science, California University,
                 Los Angeles, CA, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "algorithm; Algorithms; clock period; computer
                 programming; computers, digital --- Computational
                 Methods; computing rotation factors; digital
                 arithmetic; floating-point; low-precision estimates;
                 mathematical techniques --- Algorithms; matrix
                 transformations; on-line algorithm; online scheme;
                 radix-2 online; representation; rotation factors
                 computing; systolic arrays",
  treatment =    "P Practical; T Theoretical or Mathematical",
}

@Article{Fam:1988:ECM,
  author =       "A. T. Fam",
  title =        "Efficient complex matrix multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "37",
  number =       "7",
  pages =        "877--879",
  month =        jul,
  year =         "1988",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.2236",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 08:33:27 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2236",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Farnum:1988:CSF,
  author =       "Charles Farnum",
  title =        "Compiler Support for Floating-Point Computation",
  journal =      j-SPE,
  volume =       "18",
  number =       "7",
  pages =        "701--709",
  month =        jul,
  year =         "1988",
  CODEN =        "SPEXBL",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Sat May 24 19:46:39 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Software---Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
}

@Article{Fiske:1988:RAP,
  author =       "S. Fiske and W. J. Dally",
  title =        "The reconfigurable arithmetic processor",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "16",
  number =       "2",
  pages =        "30--36",
  month =        may,
  year =         "1988",
  CODEN =        "CANED2",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Fri May 12 09:40:45 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
}

@Article{Fitzpatrick:1988:PVF,
  author =       "S. Fitzpatrick",
  title =        "Processeur {\`a} virgule flottante {\`a} 33 {Mflops}
                 \toenglish {33 Mflops Floating-Point Processor}
                 \endtoenglish",
  journal =      "Electronique Industrielle",
  volume =       "148",
  pages =        "30--32",
  day =          "15",
  month =        sep,
  year =         "1988",
  bibdate =      "Sat Oct 24 15:01:51 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Fuccio:1988:DAS,
  author =       "M. L. Fuccio and R. N. Gadenz and C. J. Garen and J.
                 M. Huser and B. Ng and S. P. Pekarich and K. D. Ulery",
  title =        "The {DSP32C}: {AT\&T}'s Second-Generation
                 Floating-Point Digital Signal Processor",
  journal =      j-IEEE-MICRO,
  volume =       "8",
  number =       "6",
  pages =        "30--48",
  month =        nov # "\slash " # dec,
  year =         "1988",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/40.16779",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  summary =      "The WEDSP32C high-performance, programmable digital
                 signal processor supports 32-bit floating-point
                 arithmetic and is upwardly compatible with its
                 predecessor, the WEDSP32. Because it is implemented in
                 0.75-$\mu$m (effective channel length) CMOS technology
                 \ldots{}",
}

@Article{Gibson:1988:GBA,
  author =       "J. K. Gibson",
  title =        "A generalisation of {Brickell}'s algorithm for fast
                 modular multiplication",
  journal =      j-BIT,
  volume =       "28",
  number =       "4",
  pages =        "755--763",
  month =        dec,
  year =         "1988",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01954895",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "68Q25 (68P25 68U99)",
  MRnumber =     "89m:68058",
  MRreviewer =   "Ricardo Baeza-Yates",
  bibdate =      "Wed Jan 4 18:52:20 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=28&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=28&issue=4&spage=755",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Grehan:1988:BBL,
  author =       "R. Grehan and T. Thompson",
  title =        "{Borland} beefs up its languages",
  journal =      j-BYTE,
  volume =       "13",
  number =       "10",
  pages =        "151--154",
  month =        oct,
  year =         "1988",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Thu Sep 12 17:54:09 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C6140D (High level languages); C6150C (Compilers,
                 interpreters and other processors); C6150G (Diagnostic,
                 testing, debugging and evaluating systems)",
  fjournal =     "BYTE Magazine",
  keywords =     "Borland International; Built-in source-level
                 debuggers; Command-line interface version; Expanded
                 memory; Floating-point emulation; High-speed assembler;
                 In-line assembly language support; Integrated
                 development environment; Line-oriented environment;
                 Premier development languages; Stand-alone debugger;
                 TASM; Turbo Assembler; Turbo C; Turbo Debugger; Turbo
                 language; Turbo Pascal",
  thesaurus =    "C language; Pascal; Program assemblers; Program
                 compilers; Program debugging; Software packages",
}

@Article{Grehan:1988:FPCa,
  author =       "Rick Grehan",
  title =        "Floating-Point Without a Coprocessor",
  journal =      j-BYTE,
  volume =       "13",
  number =       "9",
  pages =        "313--319",
  month =        sep,
  year =         "1988",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  bibno =        "47602",
  catcode =      "C.3; G.0",
  descriptor =   "Computer Systems Organization, SPECIAL-PURPOSE AND
                 APPLICATION-BASED SYSTEMS; Mathematics of Computing,
                 GENERAL",
  fjournal =     "BYTE Magazine",
  genterm =      "DESIGN; THEORY; MANAGEMENT",
  guideno =      "1988-05346",
  subject =      "C. Computer Systems Organization; C.3 SPECIAL-PURPOSE
                 AND APPLICATION-BASED SYSTEMS; G. Mathematics of
                 Computing; G.0 GENERAL",
}

@Article{Grehan:1988:FPCb,
  author =       "R. Grehan",
  title =        "Floating-Point Without a Coprocessor, Part 2",
  journal =      j-BYTE,
  volume =       "13",
  number =       "10",
  pages =        "293--297 (or 293--298??)",
  month =        oct,
  year =         "1988",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Thu Sep 12 17:54:09 MDT 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  classification = "C1160 (Combinatorial mathematics); C6110 (Systems
                 analysis and programming); C7310 (Mathematics)",
  fjournal =     "BYTE Magazine",
  keywords =     "Addition; Binary floating-point mathematics package;
                 Division; Floating-point accumulators; Floating-point
                 number manipulation; Maths chip emulation;
                 Multiplication; Number input/output; Primary math
                 operations; Pseudocode routines; Subtraction",
  thesaurus =    "Input-output programs; Mathematics computing; Number
                 theory; Programming; Software packages",
}

@MastersThesis{Helminen:1988:AFP,
  author =       "Brenda K. Helminen",
  title =        "An analysis of the floating point and communication
                 performance of the {FPS} {T-Series} hypercube",
  type =         "Thesis ({M.S.})",
  school =       "Michigan Technological University",
  address =      "Houghton, MI, USA",
  pages =        "viii + 69",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Michigan Technological University. --- Theses
                 ({M.S.}).; MTU Computer Science. --- Thesis ({M.S.}).",
}

@MastersThesis{Ho:1988:ADI,
  author =       "Naven Chuen Wing Ho",
  title =        "Analysis and design of an instantaneous floating point
                 amplifier",
  type =         "Thesis ({M.S.})",
  school =       "Department of Electrical Engineering, Cullen College
                 of Engineering, University of Houston",
  address =      "Houston, TX, USA",
  pages =        "xv + 185",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Amplifiers (Electronics); Seismic waves --- Data
                 processing.",
}

@Book{Holt:1988:BR,
  editor =       "Wayne E. Holt and Steven M. Cooper and Jason M. Goertz
                 and Scott E. Levine and Joanna L. Mosher and Stanley R.
                 {Sieler, Jr.} and Jacques {Van Damme}",
  title =        "Beyond {RISC}\emdash An Essential Guide to
                 Hewlett--Packard Precision Architecture",
  publisher =    pub-SRNI,
  address =      pub-SRNI:adr,
  pages =        "xvii + 342",
  year =         "1988",
  ISBN =         "0-9618813-7-2",
  ISBN-13 =      "978-0-9618813-7-5",
  LCCN =         "QA76.8.H66 B49 1988",
  bibdate =      "Thu Sep 15 11:34:06 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Hsu:1988:CVA,
  author =       "I. S. Hsu and T. K. Truong and L. J. Deutsch and I. S.
                 Reed",
  title =        "A comparison of {VLSI} architecture of finite field
                 multipliers using dual, normal, or standard bases",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "37",
  number =       "6",
  pages =        "735--739",
  month =        jun,
  year =         "1988",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.2212",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 08:33:27 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2212",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Iacobovici:1988:HFC,
  author =       "S. Iacobovici",
  title =        "High-performance floating-point coprocessor for the
                 {NS32532 CPU}",
  crossref =     "Wescon:1988:WCR",
  pages =        "1.3/1--6",
  year =         "1988",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The need to match the integer processing performance
                 of the NS32532 CPU with the floating-point performance
                 teams the NS32580 floating-point controller with
                 Weitek's WTL3164 floating-point data path to achieve a
                 peak performance of 15 MFLOPS for single- or
                 double-precision. Using a pipelined slave protocol this
                 solution is software compatible with existing Series
                 32000 software base and supports precise exception
                 handling. Together, NS32532-NS32580-WTL3164 provide a
                 high-performance, well-balanced solution for scientific
                 applications, as well as number crunching, graphics and
                 image processing.",
  acknowledgement = ack-nhfb,
  affiliation =  "National Semicond. Corp., Santa Clara, CA, USA",
  classification = "C5130 (Microprocessor chips); C5230 (Digital
                 arithmetic methods)",
  keywords =     "15 MFLOPS; Double-precision; Exception handling;
                 Floating-point coprocessor; Graphics; Image processing;
                 NS32532 CPU; NS32580 floating-point controller;
                 Pipelined slave protocol; Processing performance;
                 Scientific applications; Series 32000 software; Single
                 precision arithmetic; WTL3164 floating-point data
                 path",
  numericalindex = "Computer speed 1.5E+07 FLOPS",
  thesaurus =    "Digital arithmetic; Microprocessor chips",
}

@Article{Iacobovici:1988:PIH,
  author =       "S. Iacobovici",
  title =        "A pipelined interface for high floating-point
                 performance with precise exceptions",
  journal =      j-IEEE-MICRO,
  volume =       "8",
  number =       "3",
  pages =        "77--87",
  month =        may # "\slash " # jun,
  year =         "1988",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/40.542",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  summary =      "Two options are presented that were considered for a
                 pipelined interface between a central processing unit
                 (CPU) and a floating-point coprocessor (FPU), along
                 with the CPU recovery mechanisms that provide precise
                 floating-point exceptions for each \ldots{}",
}

@Article{Irwin:1988:SIP,
  author =       "M. J. Irwin",
  title =        "Special issue on parallelism in computer arithmetic",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "5",
  number =       "3",
  pages =        "205--208",
  month =        jun,
  year =         "1988",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 17:13:17 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods); C5440
                 (Multiprocessor systems and techniques)",
  corpsource =   "Pennsylvania State University, University Park, PA,
                 USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "computer arithmetic; digital arithmetic; lookahead
                 adders; parallel processing; parallelism; pipelined
                 arithmetic processors; VLSI systems",
  treatment =    "G General Review; P Practical",
}

@Article{Jenkins:1988:SCP,
  author =       "W. K. Jenkins and E. J. Altman",
  title =        "Self-checking properties of residue number error
                 checkers based on mixed radix conversion",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "35",
  number =       "2",
  pages =        "159--167",
  month =        feb,
  year =         "1988",
  CODEN =        "ICSYBT",
  DOI =          "https://doi.org/10.1109/31.1717",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=107",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "residue arithmetic; residue number system",
  summary =      "It has been shown previously that a mixed-radix
                 converter can be modified to perform all the essential
                 functions of an error checker for error detection and
                 correction in residue number system hardware
                 architectures. Since the computations in a \ldots{}",
}

@PhdThesis{Johnstone:1988:DFP,
  author =       "Paul Johnstone",
  title =        "Decimal floating point representation",
  type =         "Thesis ({Ph.D.})",
  school =       "Tulane University",
  address =      "New Orleans, LA 70118, USA",
  pages =        "vi + 101",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Binary system (Mathematics); decimal floating-point
                 arithmetic; Floating-point arithmetic.",
}

@TechReport{Jouppi:1988:MFA,
  author =       "Norman Paul Jouppi and Jeremy Dion and David Reeves
                 Boggs and Michael J. K. Nielsen",
  title =        "{MultiTitan}: four architecture papers",
  institution =  "Digital Western Research Laboratory",
  address =      "Palo Alto, CA, USA",
  edition =      "[Revised]",
  pages =        "various",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "WRL research report; 87/8",
  acknowledgement = ack-nhfb,
  keywords =     "Computer architecture.; MultiTitan (Computer)",
  remark =       "``April 10, 1988.'' MultiTitan central processor unit
                 / Norman P. Jouppi --- MultiTitan floating point unit /
                 Norman P. Jouppi --- MultiTitan cache control unit /
                 Jeremy Dion --- MultiTitan intra-processor bus / David
                 Boggs, Jeremy Dion, Michael J. K. Nielsen.",
}

@TechReport{Jouppi:1988:UVS,
  author =       "Norman P. Jouppi and Jonathan Bertoni and David W.
                 Wall",
  title =        "A unified vector\slash scalar floating-point
                 architecture",
  type =         "Report",
  number =       "WRL TN-3",
  institution =  "Digital Western Research Laboratory",
  address =      "Palo Alto, CA, USA",
  pages =        "19",
  year =         "1988",
  bibdate =      "Thu May 09 08:38:06 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Joy:1988:OCT,
  author =       "Edward Bennett Joy and Paul R. Beaudet and Pankaj K.
                 Das",
  title =        "Optical communications techniques\slash floating point
                 residue number system",
  institution =  "School of Electrical Engineering, Georgia Institute of
                 Technology",
  address =      "Atlanta, GA, USA",
  pages =        "17",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer network architectures.; Computers --- Optical
                 equipment.",
  remark =       "Issued as R and D status reports [nos. 1--7], Contract
                 funds status reports [nos. 1--8], Final technical
                 report, and Final report, Project E-21-T01. Final
                 technical report has author: Paul R. Beaudet. Final
                 report has author: Pankaj K. Das. Final technical
                 report has title: Floating point residue number system.
                 Final report has title: New techniques in optical
                 communications and signal processing.",
}

@Article{Juffa:1988:SAF,
  author =       "N. Juffa",
  title =        "{Schnelle Algorithmen f{\"u}r Sin und Cos} \toenglish
                 {Fast Algorithms for Sin and Cos} \endtoenglish",
  journal =      j-MC,
  volume =       "5",
  pages =        "105--107",
  year =         "1988",
  ISSN =         "0720-4442, 0941-777x, 0943-5409",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "MC: Die Mikrocomputer-Zeitschrift",
}

@Misc{Kahan:1988:AFP,
  author =       "William Kahan",
  title =        "Arithmazium: The Floating Point Expos{\'e}",
  howpublished = "Web site",
  month =        may # "\slash " # jul,
  year =         "1988",
  bibdate =      "Wed Jun 05 09:50:01 2024",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "This site includes 27 lectures with notes and videos
                 for CS 279 (Computer System Support for Scientific and
                 Engineering Computation). The class handouts amount to
                 more than 2000 pages.",
  URL =          "https://www.arithmazium.org/classroom/wk88_toc.html",
  acknowledgement = ack-nhfb,
}

@TechReport{Kahan:1988:CSS,
  author =       "W. Kahan and David Goldberg",
  title =        "Computer System Support for Scientific and Engineering
                 Computation",
  type =         "Report",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  day =          "26",
  month =        jul,
  year =         "1988",
  bibdate =      "Mon Aug 26 10:39:23 2024",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Revised 14 June 1990.",
  URL =          "http://www.arithmazium.org/classroom/lib//Lecture_25_notes_slides.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Kahaner:1988:BRP,
  author =       "D. K. Kahaner",
  title =        "Benchmarks for `real' programs",
  journal =      j-SIAM-NEWS,
  pages =        "A-61",
  month =        nov,
  year =         "1988",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibdate =      "Mon Sep 16 16:15:31 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM News",
  journal-URL =  "https://sinews.siam.org/",
}

@InProceedings{Kanada:1988:VMA,
  author =       "Yasumasa Kanada",
  title =        "Vectorization of multiple-precision arithmetic program
                 and 201,326,000 decimal digits of {$ \pi $}
                 calculation",
  crossref =     "Martin:1988:SPN",
  volume =       "2",
  pages =        "117--128",
  year =         "1988",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:53:44 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  abstract =     "More than 200 million decimal places of {$ \pi $} were
                 calculated using an arithmetic geometric mean formula
                 independently discovered by E. Salamin and R. P. Brent
                 in 1976. Correctness of the calculation was verified
                 through Borwein's quartic convergent formula developed
                 in 1983. The computation took CPU times of 5 hours 57
                 minutes for the main calculation and 7 hours 30 minutes
                 for the verification calculation on the HITAC S-820
                 model 80 supercomputer with 256 MB of main memory and 3
                 GB of high speed semiconductor storage, Extended
                 Storage, to shorten I/O time.\par Computation was
                 completed in 27th of January 1988. At that day two
                 programs generated values up to $ 3 \times 2^{26} $,
                 about 201 million. The two results agreed except for
                 the last 21 digits. These results also agree with the
                 133,554,000 places of calculation of $ \pi $ which was
                 done by the author in January 1987. Compare to the
                 record in 1987, 50\% more decimal digits were
                 calculated with about $ 1 / 6 $ of CPU time.\par
                 Computation was performed with real arithmetic based
                 vectorized Fast Fourier Transform (FFT) multiplier and
                 newly vectorized multiple-precision add, subtract and
                 (single word) constant multiplication programs.
                 Vectorizations for the later cases were realized
                 through first order linear recurrence vector
                 instruction on the S-820. Details of the computation
                 and statistical tests on the first 200 million digits
                 of $ \pi - 3 $ are reported.",
  acknowledgement = ack-nhfb,
  classification = "C4190 (Other numerical methods); C7310
                 (Mathematics)",
  corpsource =   "Comput. Centre, Tokyo University, Japan",
  keywords =     "arithmetic geometric mean formula; Borwein's quartic
                 convergent formula; fast Fourier transform; fast
                 Fourier transforms; first order linear recurrence
                 vector instruction; HITAC S-820 model 80 supercomputer;
                 mathematics computing; multiple-precision arithmetic
                 program; multiplier; parallel processing; pi
                 calculation; S-820; vectorization",
  sponsororg =   "IEEE; ACM SIGARCH",
  treatment =    "P Practical",
}

@InProceedings{Kanada:1988:VMP,
  author =       "Yasumasa Kanada",
  booktitle =    "Proceedings of Supercomputing 88. Vol. {II}: Science
                 and Applications",
  title =        "Vectorization of multiple-precision arithmetic program
                 and 201,326,000 decimal digits of {$ \pi $}
                 calculation",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "117--128",
  year =         "1988",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:53:44 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "More than 200 million decimal places of {\pi} were
                 calculated using an arithmetic geometric mean formula
                 independently discovered by E. Salamin and R. P. Brent
                 in 1976. Correctness of the calculation was verified
                 through Borwein's quartic convergent formula developed
                 in 1983. The computation took CPU times of 5 hours 57
                 minutes for the main calculation and 7 hours 30 minutes
                 for the verification calculation on the HITAC S-820
                 model 80 supercomputer with 256 MB of main memory and 3
                 GB of high speed semiconductor storage, Extended
                 Storage, to shorten I/O time.\par

                 Computation was completed in 27th of January 1988. At
                 that day two programs generated values up to $ 3 \times
                 2^{26} $, about 201 million. The two results agreed
                 except for the last 21 digits. These results also agree
                 with the 133,554,000 places of calculation of $ \pi $
                 which was done by the author in January 1987. Compare
                 to the record in 1987, 50\% more decimal digits were
                 calculated with about $ 1 / 6 $ of CPU
                 time.\par

                 Computation was performed with real arithmetic based
                 vectorized Fast Fourier Transform (FFT) multiplier and
                 newly vectorized multiple-precision add, subtract and
                 (single word) constant multiplication programs.
                 Vectorizations for the later cases were realized
                 through first order linear recurrence vector
                 instruction on the S-820. Dertails of the computation
                 and statistical tests on the first 200 million digits
                 of $ \pi - 3 $ are reported.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kida:1988:FPP,
  author =       "H. Kida and M. Watabe and T. Nakamikawa and S.
                 Morinaga and S. Kawasaki and H. Inayoshi",
  title =        "A floating point processing unit for the {GMICRO}
                 {CPU}",
  crossref =     "Sakamura:1988:TPO",
  bookpages =    "xi + 384",
  pages =        "301--316",
  year =         "1988",
  DOI =          "https://doi.org/10.1007/978-4-431-68081-9_21",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Describes the architecture and implementation of a
                 newly developed floating point processing unit (FPU).
                 It was developed as a high performance 32-bit
                 coprocessor of the 32-bit GMICRO microprocessor, which
                 satisfies the IEEE 754 Standard for Binary
                 Floating-Point Arithmetic. High performance was
                 achieved by the high speed coprocessor's interface with
                 the GMICRO CPU and the pipeline processing. The
                 coprocessor's interface was designed to minimize
                 CPU-FPU communication overhead caused by transferring
                 commands, operands and coprocessor information.
                 Furthermore, to improve operation speed, the FPU
                 performs pipeline processing named command pipeline.
                 The FPU has three main elements, the bus control unit,
                 format conversion unit, and execution control unit. In
                 order to perform high speed calculations, each element
                 in the chip is designed to operate in parallel. (5
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "Hitachi Ltd., Tokyo, Japan",
  classification = "C5220 (Computer architecture)",
  confdate =     "1988",
  conflocation = "Japan",
  keywords =     "32 Bit; Coprocessor; Floating point processing unit;
                 FPU; GMICRO CPU; GMICRO microprocessor; IEEE 754;
                 Standard for Binary Floating-Point Arithmetic",
  numericalindex = "Word length 3.2E+01 bit",
  pubcountry =   "Japan",
  thesaurus =    "Computer architecture; Microprocessor chips",
}

@Article{Kirchner:1988:AAV,
  author =       "R. Kirchner and U. Kulisch",
  title =        "Accurate arithmetic for vector processors",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "5",
  number =       "3",
  pages =        "250--270",
  month =        jun,
  year =         "1988",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliationaddress = "Univ Kaiserslautern, West Ger",
  classification = "721; 722; 723; C5230 (Digital arithmetic methods);
                 C5440 (Multiprocessor systems and techniques)",
  corpsource =   "Fachbereich Inf., Kaiserslautern University, West
                 Germany",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "arithmetic operations; Computational Methods; computer
                 systems, digital --- Parallel Processing; computers;
                 computers, digital; computers, microcomputer; digital
                 arithmetic; dot products; implementation techniques;
                 local memory; microcomputers; parallel; parallel
                 processing; pipelined compound operations; sums; vector
                 processors; VLSI technology",
  treatment =    "P Practical",
}

@Article{Knuth:1988:FM,
  author =       "Donald E. Knuth",
  title =        "{Fibonacci} multiplication",
  journal =      j-APPL-MATH-LETT,
  volume =       "1",
  number =       "1",
  pages =        "57--60",
  year =         "1988",
  CODEN =        "AMLEEL",
  ISSN =         "0893-9659 (print), 1873-5452 (electronic)",
  ISSN-L =       "0893-9659",
  MRclass =      "11B39",
  MRnumber =     "89f:11031",
  MRreviewer =   "W. Herget",
  bibdate =      "Fri Mar 22 18:03:29 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08939659",
}

@Article{Kornerup:1988:LAU,
  author =       "Peter Kornerup and David W. Matula",
  title =        "An on-line arithmetic unit for bit-pipelined rational
                 arithmetic",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "5",
  number =       "3",
  pages =        "310--330",
  month =        jun,
  year =         "1988",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliationaddress = "Odense Univ, Odense, Den",
  classification = "722; 723; 921; C5230 (Digital arithmetic methods)",
  corpsource =   "Odense University, Denmark",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "algorithm of Gosper; Algorithms; binary version;
                 bit-pipelined rational arithmetic; computer metatheory
                 --- Binary Sequences; computer programming; computers,
                 digital --- Computational Methods; difference; digital
                 arithmetic; functions; mathematical techniques ---
                 Algorithms; on-line arithmetic unit; online arithmetic
                 unit; product; quotient; rational; sum",
  treatment =    "P Practical",
}

@InProceedings{Krishnan:1988:IRN,
  author =       "R. Krishnan",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, 7--9 June 1988",
  title =        "Implementation of recursive and nonrecursive digital
                 filters using the single multiplexed {ROM} in the
                 quadratic residue number system",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1297--1300",
  year =         "1988",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1988.15166",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Recursive and nonrecursive digital filters have been
                 implemented using the proposed single-multiplexed
                 dual-clock computational module (SDCM) in the bit-slice
                 architecture. The amount of memory requirements has
                 been reduced to 50\% required for the \ldots{}",
}

@InProceedings{Krishnan:1988:SCR,
  author =       "R. Krishnan",
  booktitle =    "International Conference on Acoustics, Speech, and
                 Signal Processing, {ICASSP-88, 11--14} April 1988",
  title =        "A single-channel {ROM}-based complex digital filter
                 implementation in the quadratic residue number
                 systems",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1842--1845",
  year =         "1988",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICASSP.1988.196981",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The implementation of complex digital filters using
                 the quadratic residue number system (QRNs) and modified
                 quadratic residue number system (MQRNS) is considered.
                 These QRNS/MQRNS-based filter architectures are
                 memory-intensive because the lookup- \ldots{}",
}

@InProceedings{Lai:1988:FAI,
  author =       "K. Lai and J. Valerio",
  title =        "The floating-point architecture of {Intel's 80960}",
  crossref =     "Wescon:1988:WCR",
  pages =        "1.5/1--3",
  year =         "1988",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Intel 80960KB is a microprocessor with hardware
                 floating-point support integrated on-chip. In a
                 departure from previous microprocessors, the 80960KB
                 incorporates full floating-point support within the
                 processor instead of relying on a coprocessor. As
                 floating-point speeds increase, the off-chip
                 coprocessor interface becomes a significant performance
                 bottleneck. Additionally, component and system cost,
                 board space, and cleanliness of architecture are other
                 good reasons to have on-chip floating-point support.
                 The implementation delivers accurate results with good
                 performance: 1.1 single-precision Linpack MFLOPS, and
                 4.1 single-precision mega-Whetstones per second. (0
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "Intel Corp., Hillsboro, OR, USA",
  classification = "C5130 (Microprocessor chips); C5220 (Computer
                 architecture); C5230 (Digital arithmetic methods)",
  keywords =     "1.1 MFLOPS; Board space; Cleanliness; Component costs;
                 Floating-point architecture; Intel 80960KB; Linpack;
                 Microprocessor; On-chip floating-point support;
                 Performance; System cost",
  numericalindex = "Computer speed 1.1E+06 FLOPS",
  thesaurus =    "Computer architecture; Digital arithmetic;
                 Microprocessor chips",
}

@InProceedings{Lai:1988:IFS,
  author =       "K. Lai and J. Valerio",
  title =        "Integrated floating-point solution for the {Intel
                 80960KB}",
  crossref =     "Midcon:1988:MCP",
  pages =        "249--251",
  year =         "1988",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Intel 80960KB is a microprocessor with hardware
                 floating-point support integrated on-chip. In a
                 departure from previous microprocessors, the 80960KB
                 incorporates full floating-point support within the
                 processor instead of relying on a coprocessor. As
                 floating-point speeds increase, the off-chip
                 coprocessor interface becomes a significant performance
                 bottleneck. Additionally, component and system cost,
                 board space, and cleanliness of architecture are other
                 good reasons to have on-chip floating-point support.
                 The implementation delivers accurate results with good
                 performance: 1.1 single precision Linpack MFLOPS, and
                 4.1 single precision mega Whetstones per second. (0
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "Intel Corp., Hillsboro, OR, USA",
  classification = "C5130 (Microprocessor chips)",
  keywords =     "Floating-point support; Integrated floating point;
                 Intel 80960KB; Microprocessor; Onchip floating point",
  thesaurus =    "Digital arithmetic; Microprocessor chips",
}

@Article{Lawson:1988:SRR,
  author =       "Charles L. Lawson",
  title =        "Series reversion as the reversed chain rule",
  journal =      j-SIGNUM,
  volume =       "23",
  number =       "1",
  pages =        "7--9",
  month =        jan,
  year =         "1988",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:16 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Lawson gives Fortran subroutines for differentiation
                 arithmetic. A subroutine SWPRO for products corresponds
                 to Chang's ATS [Chang74a]. The chain rule is
                 implemented by repeated calls to SWPRO. Series
                 reversion for implicit functions is implemented by
                 reversing the chain rule. An application is given to
                 Keppler's equation, $ M - E + e \sin (E) = 0 $.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "design; differentiation arithmetic; implicit
                 functions; languages; theory",
  subject =      "D.3.3 Software, PROGRAMMING LANGUAGES, Language
                 Constructs, Modules, packages \\ G.4 Mathematics of
                 Computing, MATHEMATICAL SOFTWARE \\ D.3.3 Software,
                 PROGRAMMING LANGUAGES, Language Constructs, Procedures,
                 functions, and subroutines",
}

@TechReport{Liu:1988:BEF,
  author =       "Zhi-Shun Alex Liu",
  title =        "{Berkeley} Elementary Function Test Suite",
  institution =  "Computer Science Division, Department of Electrical
                 Engineering and Computer Science, Univerity of
                 California at Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "ii + 59",
  day =          "30",
  month =        dec,
  year =         "1988",
  bibdate =      "Mon Sep 12 23:52:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.netlib.org/fp/ucbtest.tgz;
                 http://www.ucbtest.org/zaliu-papers/zaliu-beef-doc.pdf",
  abstract =     "A suite of programs is presented to test how
                 accurately the elementary transcendental functions exp,
                 log, sin, cos and atan have been implemented in a
                 computer's run-time library. The suite is written in
                 the language C and designed to run on any computer with
                 binary floating-point arithmetic rounded in a
                 reasonable way. The suite makes no appeal to
                 extra-precise arithmetic; the tests use only whatever
                 arithmetic capabilities are present in the environment
                 where the transcendental functions are to be used.
                 Despite this limitation, the tests run fast and deliver
                 indication of accuracy to within a small fraction of an
                 ULP (Unit in the Last Place) of the functions under
                 test. This account includes the proofs of the test
                 suite's claims to accuracy.",
  acknowledgement = ack-nj,
  keywords =     "BeEF test suite; floating-point testing",
}

@InProceedings{Lu:1988:MCF,
  author =       "P. Y. Lu and A. Jain and J. Kung and P. H. Ang",
  title =        "A 30-{MFLOP} 32b {CMOS} Floating-Point Processor",
  crossref =     "IEEE:1988:IIS",
  pages =        "28, 29, 285",
  year =         "1988",
  bibdate =      "Fri Dec 08 13:04:40 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Luk:1988:AAB,
  author =       "Franklin T. Luk and Haesun Park",
  title =        "An analysis of algorithm-based fault tolerance
                 techniques",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "5",
  number =       "2",
  pages =        "172--184",
  month =        apr,
  year =         "1988",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliationaddress = "Cornell Univ, Ithaca, NY, USA",
  classification = "722; 723; C4110 (Error analysis in numerical
                 methods); C4140 (Linear algebra); C5230 (Digital
                 arithmetic methods); C5470 (Performance evaluation and
                 testing)",
  corpsource =   "Sch. of Electr. Eng., Cornell University, Ithaca, NY,
                 USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "algorithm-based fault tolerance; analysis;
                 computation; computer programming --- Algorithms;
                 computer systems, digital; decomposition; error
                 analysis; Fault Tolerant Capability; fault tolerant
                 computing; floating point error; Gaussian elimination;
                 Gaussian elimination with pairwise pivoting; LU; lu
                 decomposition; matrix algebra; pairwise pivoting; qr
                 decomposition; QR decomposition; rank-one perturbation;
                 rounding errors; roundoff errors; systolic array;
                 transient error; unified checksum scheme",
  treatment =    "T Theoretical or Mathematical",
}

@MastersThesis{Lyu:1988:PFP,
  author =       "Chung-nan Lyu",
  title =        "Pipelined floating point divider with built-in testing
                 circuits",
  type =         "Thesis ({M.S.})",
  school =       "Ohio University",
  address =      "Athens, OH, USA",
  pages =        "90",
  month =        jun,
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point testing; parallel processing
                 (electronic computers)",
}

@Article{Magenheimer:1988:IMD,
  author =       "Daniel J. Magenheimer and Liz Peters and Karl W.
                 Peters and Dan Zuras",
  title =        "Integer Multiplication and Division on the {HP
                 Precision Architecture}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "37",
  number =       "8",
  pages =        "980--990",
  month =        aug,
  year =         "1988",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.2248",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Aug 04 16:38:15 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Marchyulaitis:1988:SRN,
  author =       "Saulyus Marchyula{\u\i}tis",
  title =        "Summation of real numbers in arithmetic with a
                 floating point. {A} probability approach to determining
                 the variance of absolute round-off error. ({Russian})",
  journal =      "Statist. Problemy Upravleniya",
  volume =       "82",
  pages =        "57--68",
  year =         "1988",
  MRclass =      "65G05 (65C20)",
  MRnumber =     "89k:65056",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
  language =     "Russian",
}

@Article{Maurer:1988:DVW,
  author =       "P. M. Maurer",
  title =        "Design Verification of the {WE} 32106 Math Accelerator
                 Unit",
  journal =      j-IEEE-DES-TEST-COMPUT,
  volume =       "5",
  number =       "3",
  pages =        "11--21",
  month =        jun,
  year =         "1988",
  ISSN =         "0740-7475 (print), 1558-1918 (electronic)",
  ISSN-L =       "0740-7475",
  bibdate =      "Wed Sep 7 22:32:00 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IEEE Design \& Test of Computers",
}

@Article{McLellan:1988:DCF,
  author =       "E. J. McLellan and G. M. Wolrich and R. A. J.
                 Yodlowski",
  title =        "Development of the {CVAX} floating-point chip",
  journal =      j-DEC-TECH-J,
  volume =       "??",
  number =       "7",
  pages =        "109--120",
  month =        aug,
  year =         "1988",
  CODEN =        "DTJOEL",
  ISSN =         "0898-901X",
  bibdate =      "Wed Sep 7 22:32:00 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Digital Technical Journal",
}

@InProceedings{Melear:1988:IFP,
  author =       "C. Melear",
  title =        "An integrated floating point unit for a {RISC}
                 architecture",
  crossref =     "Wescon:1988:WCR",
  pages =        "1.2/1--8",
  year =         "1988",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "RISC architectures require multiple bus structures
                 that allow for instructions, operands, and results to
                 all travel about the processor on each clock cycle.
                 Thus, by putting the floating point unit on these
                 multiple bus structures, it can receive instructions
                 and operands on each clock cycle. Some number of cycles
                 later, as more floating point instructions are issued,
                 floating point results can also be sent out on the
                 destination bus, yielding burst execution rates equal
                 to the clock rate. The present clock rate is 20 MHz and
                 will be increased eventually to the 40 MHz area. At 20
                 MHz, sustained execution rates of 7 MFLOPS are typical.
                 Performance rates of 10.5 MWhetstones have also been
                 demonstrated (20 MHz clock). The floating point unit is
                 only one part of the RISC processor. By combining all
                 the aspects of software, memory system interfacing and
                 high performance hardware like the 88100 floating point
                 unit, mainframe performance moves one step closer to
                 the desktop computer world.",
  acknowledgement = ack-nhfb,
  affiliation =  "Motorola, Austin, TX, USA",
  classification = "C5130 (Microprocessor chips); C5220 (Computer
                 architecture); C5230 (Digital arithmetic methods)",
  keywords =     "20 MHz; 7 MFLOPS; 88100 Floating point unit; Burst
                 execution rates; Clock cycle; Clock rate; Desktop
                 computer; Execution rates; Memory system interfacing;
                 Multiple bus structures; Performance rates; RISC
                 architecture",
  numericalindex = "Frequency 2.0E+07 Hz; Computer speed 7.0E+06 FLOPS",
  thesaurus =    "Digital arithmetic; Microprocessor chips; Reduced
                 instruction set computing",
}

@Article{Milnikel:1988:SRF,
  author =       "R. Milnikel and R. Wollenberg",
  title =        "{Schnelles Radizierverfahren f{\"u}r Gleitkommazahlen
                 im IEEE-Format} \toenglish {Fast Square-rooting method
                 for Floating-point Numbers in IEEE Format}
                 \endtoenglish",
  journal =      j-ELECTRONIK,
  volume =       "8",
  pages =        "114--1122",
  year =         "1988",
  CODEN =        "EKRKAR",
  ISSN =         "0013-5658",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektronik",
}

@Article{Monahan:1988:CAG,
  author =       "John F. Monahan",
  title =        "Corrigendum: ``{An} Algorithm for Generating Chi
                 Random Variables''",
  journal =      j-TOMS,
  volume =       "14",
  number =       "1",
  pages =        "111--111",
  month =        mar,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/42288.356228",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "111. 65C10",
  MRnumber =     "89d:65006, 88d:65013",
  bibdate =      "Fri Mar 28 10:45:16 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Monahan:1987:AGC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Manual{Motorola:1988:GPF,
  title =        "96-bit general purpose floating-point digital-signal
                 processor technical summary",
  organization = "Motorola, Inc.",
  address =      "Phoenix, AZ, USA",
  pages =        "23",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Motorola semiconductor technical data",
  acknowledgement = ack-nhfb,
  keywords =     "Integrated circuits.; Signal processing --- Digital
                 techniques.",
  remark =       "Caption title. ``BR574/D.''",
}

@Book{Motorola:1988:MFP,
  author =       "{Motorola, Inc.}",
  title =        "{MC68881\slash MC68882} Floating-Point Coprocessor
                 User's Manual",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  month =        feb,
  year =         "1988",
  ISBN =         "0-13-566936-7",
  ISBN-13 =      "978-0-13-566936-5",
  LCCN =         "????",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$22.50",
  acknowledgement = ack-nhfb,
  language =     "eng",
}

@Article{Nakamura:1988:SCP,
  author =       "S. Nakamura and K.-Y. Chu",
  title =        "A single chip parallel multiplier by {MOS}
                 technology",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "37",
  number =       "3",
  pages =        "274--282",
  month =        mar,
  year =         "1988",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.2164",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 08:33:25 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2164",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Nikolos:1988:EDT,
  author =       "D. Nikolos and A. M. Paschalis and G. Philokyprou",
  title =        "Efficient design of totally self-checking checkers for
                 all low-cost arithmetic codes",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "37",
  number =       "7",
  pages =        "807--814",
  month =        jul,
  year =         "1988",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.2226",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 08:33:27 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2226",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Normand:1988:PSP,
  author =       "J. M. Normand",
  title =        "{Percola}: a special purpose programmable 64-bit
                 floating-point processor",
  crossref =     "ACM:1988:ICS",
  pages =        "55--65",
  year =         "1988",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$49.00",
  URL =          "http://doi.acm.org/10.1145/55364.55370",
  acknowledgement = ack-nhfb,
  affiliation =  "Centre d'Etudes Nucl{\'e}aires, Saclay, France",
  bibno =        "55370",
  catcode =      "G.3; C.5.1; C.5.3; J.2; G.3; B.6.3",
  CRclass =      "G.3 Random number generation; C.5.1 Large and Medium
                 (``Mainframe'') Computers; C.5.1 Super (very large)
                 computers; C.5.3 Microcomputers; C.5.3 Motorola 68000;
                 J.2 Physics; G.3 Statistical computing; B.6.3 Design
                 Aids; B.6.3 Optimization",
  descriptor =   "Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Random number generation; Computer Systems
                 Organization, COMPUTER SYSTEM IMPLEMENTATION, Large and
                 Medium (``Mainframe'') Computers, Super (very large)
                 computers; Computer Systems Organization, COMPUTER
                 SYSTEM IMPLEMENTATION, Microcomputers, Motorola 68000;
                 Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Physics; Mathematics of Computing,
                 PROBABILITY AND STATISTICS, Statistical computing;
                 Hardware, LOGIC DESIGN, Design Aids, Optimization",
  genterm =      "ALGORITHMS; DESIGN",
  guideno =      "1988-15563",
  subject =      "G. Mathematics of Computing; G.3 PROBABILITY AND
                 STATISTICS; C. Computer Systems Organization; C.5
                 COMPUTER SYSTEM IMPLEMENTATION; C. Computer Systems
                 Organization; C.5 COMPUTER SYSTEM IMPLEMENTATION; J.
                 Computer Applications; J.2 PHYSICAL SCIENCES AND
                 ENGINEERING; G. Mathematics of Computing; G.3
                 PROBABILITY AND STATISTICS; B. Hardware; B.6 LOGIC
                 DESIGN",
  waffil =       "Rennes",
  wauthedit =    "Lenfant, J.",
  wsub =         "Conference Proceedings",
}

@Article{Oklobdzija:1988:IAV,
  author =       "Vojin G. Oklobdzija and Earl R. Barnes",
  title =        "On implementing addition in {VLSI} technology",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "5",
  number =       "6",
  pages =        "716--728",
  month =        dec,
  year =         "1988",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliationaddress = "Yorktown Heights, NY, USA",
  classification = "713; 714; 723; B1265B (Logic circuits); B2570D (CMOS
                 integrated circuits); C5210 (Logic design methods);
                 C5230 (Digital arithmetic methods)",
  corpsource =   "IBM Thomas J. Watson Res. Center, Yorktown Heights,
                 NY, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "addition; Arithmetic Algorithms; arithmetic
                 algorithms; carry-lookahead; CMOS integrated circuits;
                 CMOS technology; Computer Aided Design; Computer
                 Programming--Algorithms; digital arithmetic; estimates;
                 integrated; Integrated Circuits, VLSI; logic circuits;
                 logic design; Logic Levels; logic levels; quick;
                 recurrence solver schemes; Semiconductor Devices, MOS;
                 Single-chip VLSI Processor; VLSI; VLSI Implementation;
                 VLSI technology; VLSI-; VLSI-cmos Technology",
  treatment =    "P Practical",
}

@InProceedings{Papadourakis:1988:VDP,
  author =       "G. M. Papadourakis and J. Condorodis",
  booktitle =    "1988 International Conference on Acoustics, Speech,
                 and Signal Processing: {ICASSP-88, 11--14} April 1988",
  title =        "A {VLSI} design of processing element for
                 reconfigurable systolic architectures based on {LNS}",
  volume =       "4",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2080--2083",
  year =         "1988",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The design and development of a processing element
                 (PE) in an orthogonal systolic architecture, using the
                 state of the art in VLSI technology, is presented. The
                 goal was to create a high-speed, high-precision PE
                 which would be adaptive to a highly \ldots{}",
}

@Article{Papamichalis:1988:TFP,
  author =       "P. Papamichalis and R. {Simar, Jr.}",
  title =        "The {TMS320C30} Floating-Point Digital Signal
                 Processor",
  journal =      j-IEEE-MICRO,
  volume =       "8",
  number =       "6",
  pages =        "13--29",
  month =        nov # "\slash " # dec,
  year =         "1988",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/40.16778",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  summary =      "The 320C30 is a fast processor with a large memory
                 space and floating-point-arithmetic capabilities. The
                 authors describe the 320C30 architecture in detail,
                 discussing both the internal organization of the device
                 and the external interfaces. They also \ldots{}",
}

@InProceedings{Perlman:1988:AFP,
  author =       "R. M. Perlman",
  title =        "The {Am29027} --- a floating-point accelerator for the
                 {Am29000} streamlined instruction processor",
  crossref =     "Wescon:1988:WCR",
  pages =        "1.4/1--7",
  year =         "1988",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Am29000, a 32-bit RISC processor, sets new
                 standards of performance for integer processing. A 25
                 MHz Am29000 with cache can achieve in excess of 35600
                 Dhrystones. Even with simple video DRAM memory, the
                 Am29000 has a performance of 24300 Dhrystones. Although
                 the Am29000 contains no hardware dedicated to
                 floating-point computation, it can emulate
                 floating-point operations in software at speeds that
                 were heretofore achieved only by dedicated
                 floating-point coprocessors. For numerically-intensive
                 applications, the Am29000 can be augmented with the
                 Am29027 arithmetic accelerator. The Am29027 is a
                 single-chip floating-point unit that performs single-,
                 double-, and mixed-precision operations, and completely
                 implements IEEE standard 754 for those operations
                 supported. The Am29027 offers two operating modes: a
                 low-latency mode, for scalar operations, and a pipeline
                 mode, for vector and matrix calculations. When
                 configured in pipeline mode, the AM29027 can achieve a
                 peak throughput of 16 MFLOPS.",
  acknowledgement = ack-nhfb,
  affiliation =  "Adv. Micro Devices, Sunnyale, CA, USA",
  classification = "C5130 (Microprocessor chips); C5230 (Digital
                 arithmetic methods)",
  keywords =     "16 MFLOPS; 32 Bit; Am29000 streamlined instruction
                 processor; Am29027 arithmetic accelerator; Cache;
                 Floating-point operations; IEEE standard 754;
                 Low-latency mode; Matrix calculations; Mixed-precision
                 operations; Pipeline mode; RISC processor; Scalar
                 operations; Vector calculations; Video DRAM memory",
  numericalindex = "Word length 3.2E+01 bit; Computer speed 1.6E+07
                 FLOPS",
  thesaurus =    "Digital arithmetic; Microprocessor chips; Pipeline
                 processing; Reduced instruction set computing",
}

@Article{Pichat:1988:APC,
  author =       "M. A. Pichat",
  title =        "All possible computed results in correct
                 floating-point summation. Stochastic methods in
                 round-off error analysis",
  journal =      j-MATH-COMPUT-SIMUL,
  volume =       "30",
  number =       "6",
  pages =        "541--552",
  year =         "1988",
  CODEN =        "MCSIDR",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  MRclass =      "65G05",
  MRnumber =     "90d:65090",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics and Computers in Simulation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784754",
  reviewer =     "Luciano Biasini",
}

@MastersThesis{Pier:1988:IPA,
  author =       "Richard Michael Pier",
  title =        "An {IBM PC\slash AT}-based floating point imaging
                 workstation architecture",
  type =         "Thesis ({M.S.E.E.})",
  school =       "University of Washington",
  address =      "Seattle, WA, USA",
  pages =        "vi + 35",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer architecture.; IBM Personal Computer AT.;
                 Image processing --- Equipment and supplies.;
                 Microcomputer workstations.",
}

@Article{Pitas:1988:FPE,
  author =       "I. Pitas and M. G. Strintzis",
  title =        "Floating point error analysis of two-dimensional, fast
                 {Fourier} transform algorithms",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "35",
  number =       "1",
  pages =        "112--115",
  month =        jan,
  year =         "1988",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "Floating-point error is conducted for three algorithms
                 commonly used for the calculation of two-dimensional
                 fast Fourier transforms (FFTs), namely, the
                 conventional row-column FFT, the vector-radix FFT, and
                 the polynomial-transform FFT. The respective \ldots{}",
}

@Article{Plauger:1988:PFP,
  author =       "P. J. Plauger",
  title =        "Properties of floating-point arithmetic",
  journal =      j-COMP-LANG-MAG,
  volume =       "5",
  number =       "3",
  pages =        "17--22",
  month =        mar,
  year =         "1988",
  CODEN =        "COMLEF",
  ISSN =         "0749-2839",
  bibdate =      "Thu Sep 1 10:14:15 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computer Language Magazine",
}

@InProceedings{Prandolini:1988:VIB,
  author =       "R. Prandolini and S. Sridharan",
  title =        "{VLSI} implementation of a block floating point
                 coprocessor for the {TMS320} fixed point digital signal
                 processor",
  crossref =     "IREE:1988:AMC",
  pages =        "33--40",
  year =         "1988",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The design of a co-processor which can be interfaced
                 to the TMS32020 fixed-point digital signal processor is
                 described. The co-processor enables efficient
                 implementation of block floating-point arithmetic for
                 digital filtering using the TMS32020.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sch. of Electr. and Electron. Syst. Eng., Queensland
                 Inst. of Technol., Brisbane, Qld., Australia",
  classification = "B1265F (Microprocessors and microcomputers); B1270F
                 (Digital filters); B2570 (Semiconductor integrated
                 circuits); C5130 (Microprocessor chips); C5240 (Digital
                 filters); C5260 (Digital signal processing)",
  keywords =     "Block floating point coprocessor; Block floating-point
                 arithmetic; Digital filtering; TMS320 fixed point
                 digital signal processor; VLSI implementation",
  thesaurus =    "Digital filters; Digital signal processing chips;
                 VLSI",
}

@Article{Prather:1988:CET,
  author =       "R. E. Prather",
  title =        "Comparison and Extension of Theories of {Zipf} and
                 {Halstead}",
  journal =      j-COMP-J,
  volume =       "31",
  number =       "3",
  pages =        "248--252",
  month =        jun,
  year =         "1988",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "Compendex database;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/248.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/249.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/250.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/251.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/252.tif",
  acknowledgement = ack-nhfb,
  affiliation =  "Trinity Univ, San Antonio, TX, USA",
  affiliationaddress = "Trinity Univ, San Antonio, TX, USA",
  classcodes =   "C6110B (Software engineering techniques)",
  classification = "723",
  corpsource =   "Comput. and Inf. Sci., Trinity University, San
                 Antonio, TX, USA",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "behavioural psychology; computer programming; computer
                 software; empirical law; Halstead metrics; Halstead's
                 hypothesis; length estimates; Measurements;
                 probabilistic hypothesis; process; programming;
                 software engineering; software metrication; software
                 science; Zipf metrics; Zipf's law",
  treatment =    "T Theoretical or Mathematical",
}

@Book{Press:1988:NRC,
  author =       "W. H. Press and B. P. Flannery and S. A. Teukolsky and
                 W. T. Vetterling",
  title =        "Numerical Recipes in {C}: The Art of Scientific
                 Computing",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xxii + 735",
  year =         "1988",
  ISBN =         "0-521-43724-5",
  ISBN-13 =      "978-0-521-43724-0",
  LCCN =         "QA76.73.C15 N865 1988",
  bibdate =      "Thu Sep 01 10:34:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@MastersThesis{Rajanala:1988:ISP,
  author =       "Arunkumar V. Rajanala",
  title =        "{IEEE 754} single precision standard compatible
                 floating point processor implemented using silicon
                 compiler technology",
  type =         "Thesis ({M.S.})",
  school =       "Oregon State University",
  address =      "Corvallis, OR, USA",
  pages =        "77",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Microprocessors.",
}

@InProceedings{Randal:1988:FPC,
  author =       "V. T. Randal and J. L. Schmalzel and A. P. Shepherd",
  title =        "Floating-Point Computation Using a Microcontroller",
  crossref =     "Harris:1988:PAI",
  pages =        "1243--1244",
  year =         "1988",
  bibdate =      "Wed Sep 07 22:02:38 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Razaz:1988:TPM,
  author =       "M. Razaz and J. L. Schonfelder",
  title =        "Test Procedures for Measurement of Floating-Point
                 Characteristics of Computing Environments",
  journal =      j-COMP-J,
  volume =       "31",
  number =       "1",
  pages =        "12--16",
  month =        feb,
  year =         "1988",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ of Birmingham, Birmingham, Engl",
  affiliationaddress = "Univ of Birmingham, Birmingham, Engl",
  classcodes =   "C5470 (Performance evaluation and testing)",
  classification = "723",
  corpsource =   "Department of Electron. and Electr. Eng., Birmingham
                 University, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "arithmetic; arithmetic processors; CDC; computer
                 testing; computers, digital; computing environments;
                 conversion test; DEC; digital arithmetic;
                 floating-point arithmetic; floating-point
                 characteristics; floating-point testing; IBM; ICL;
                 mantissa; minimum representable number; nominal
                 decimal; normalisation base; number representation;
                 operations; parameters; performance evaluation;
                 precision; precision-dependent; procedures;
                 representation test; test; Testing",
  treatment =    "P Practical",
}

@InProceedings{Ries:1988:MFP,
  author =       "P. S. Ries",
  title =        "An 8 {MFLOP} Floating-Point Coprocessor for a {RISC}
                 Microprocessor",
  crossref =     "Electro:1988:ECR",
  pages =        "48/1/1--8",
  year =         "1988",
  bibdate =      "Wed Sep 7 22:32:00 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Robertazzi:1988:BOF,
  author =       "T. G. Robertazzi and S. C. Schwartz",
  title =        "Best {``Ordering''} for Floating-Point Addition",
  journal =      j-TOMS,
  volume =       "14",
  number =       "1",
  pages =        "101--110",
  month =        mar,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/42288.42343",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65G99 (65V05)",
  MRnumber =     "89b:65117",
  bibdate =      "Sat Nov 19 13:08:22 1994",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-1/p101-robertazzi/",
  acknowledgement = ack-nhfb,
  affiliation =  "State University of New York at Stony Brook, Stony
                 Brook; Princeton University, Princeton, NJ",
  bibno =        "42343",
  catcode =      "G.1.0",
  content =      "This paper compares a variety of methods for
                 accumulating a floating-point sum. Wilkinson pointed
                 out that if we compute the $\sum^n_{i = 1} x_i$ in
                 strictly increasing order in magnitude of the $x_i$,
                 then we obtain a better bound on the rounding error
                 than if the sum is computed in random order
                 [1].\par

                 The authors discuss five different accumulation
                 strategies. They compare these accumulation strategies
                 for when the $x_i$ are uniformly distributed and for
                 when they are exponentially distributed. First they
                 compare a random order for summing the $x_i$, summing
                 in decreasing order of magnitude, and summing in
                 increasing order of magnitude. Not surprisingly,
                 summing in increasing order of magnitude is the best
                 and summing in decreasing order of magnitude is the
                 worst. In fact, it is not difficult to show this for
                 any class of distributions where the mean and variance
                 exist.\par

                 The interesting results in the paper concern two other
                 accumulation strategies. Both of these are shown to be
                 better than summing in increasing order of magnitude
                 for both the uniform and exponential distribution.
                 Fortunately, one of these strategies is the tree sum
                 (or fan-in sum) that is often used in parallel
                 computation. The paper calls this strategy the
                 ``adjacency'' ordering.",
  CRclass =      "G.1.0 General; G.1.0 Computer arithmetic",
  CRnumber =     "8810-0794",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Computer arithmetic",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  genterm =      "ALGORITHMS; PERFORMANCE",
  journal-URL =  "https://dl.acm.org/loi/toms",
  journalabbrev = "ACM Trans. Math. Softw.",
  keywords =     "accurate floating-point summation; algorithms;
                 performance",
  review =       "ACM CR 8810-0794",
  reviewer =     "Jesse L. Barlow",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Computer arithmetic",
}

@Article{Rowen:1988:MRF,
  author =       "Chris Rowen and Mark Johnson and Paul Ries",
  title =        "The {MIPS R3010} Floating-Point Coprocessor",
  journal =      j-IEEE-MICRO,
  volume =       "8",
  number =       "3",
  pages =        "53--62",
  month =        may # "\slash " # jun,
  year =         "1988",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/40.540",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "Compendex database;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Science Citation Index database (1980--2000)",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliationaddress = "MIPS Computer Systems, Sunnyvale, CA, USA",
  classcodes =   "B1265F (Microprocessors and microcomputers); B2570
                 (Semiconductor integrated circuits); C5130
                 (Microprocessor chips); C5220 (Computer architecture);
                 C5230 (Digital arithmetic methods)",
  classification = "714; 722; 723",
  corpsource =   "MIPS Comput. Syst., Sunnyvale, CA, USA",
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  keywords =     "32-bit R31010 floating-point coprocessor; accelerator
                 chip; computer architecture; computer systems, digital
                 --- Parallel Processing; computers, microcomputer;
                 Design; design techniques; digital arithmetic;
                 floating-point; instruction set computing; integrated
                 circuits, VLSI; microprocessor chips; million
                 instruction per second (MIPS) processor; MIPS R3010
                 floating-point coprocessor; reduced;
                 reduced-instruction-set-computer;
                 reduced-instruction-set-computer (RISC); VLSI",
  summary =      "A description is given of the R3010 floating-point
                 accelerator chip, a coprocessor that is based on
                 advanced reduced-instruction-set-computer (RISC)
                 architecture and VLSI design techniques and provides
                 high-speed floating-point operation. The 75000-
                 \ldots{}",
  treatment =    "P Practical",
  xxauthor =     "C. Rowen and P. Ries and M. Johnson",
}

@InProceedings{Roylance:1988:EMS,
  author =       "G. Roylance",
  title =        "Expressing Mathematical Subroutines Constructively",
  crossref =     "ACM:1988:PAC",
  pages =        "8--13",
  year =         "1988",
  bibdate =      "Thu Sep 01 11:52:13 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@InProceedings{Santoro:1988:PIA,
  author =       "M. Santoro and M. Horowitz",
  booktitle =    "Digest of Technical Papers, {IEEE} International
                 Solid-State Circuits Conference",
  title =        "A pipelined $ 64 \times 64 $ b iterative array
                 multiplier",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "35--36",
  month =        feb,
  year =         "1988",
  bibdate =      "Mon Dec 24 10:19:42 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Schatte:1988:ASC,
  author =       "Peter Schatte",
  title =        "On the almost sure convergence of floating-point
                 mantissas and {Benford}'s law",
  journal =      j-MATH-NACHR,
  volume =       "135",
  pages =        "79--83",
  year =         "1988",
  CODEN =        "MTMNAQ",
  ISSN =         "0025-584X",
  MRclass =      "60F15 (11K31)",
  MRnumber =     "89g:60114",
  bibdate =      "Fri Dec 08 12:49:25 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  reviewer =     "S. A. Book",
}

@Article{Schatte:1988:MDC,
  author =       "P. Schatte",
  title =        "On Mantissa Distribution in Computing and {Benford}'s
                 Law",
  journal =      j-J-INFO-PROC-CYBERNETICS-EIK,
  volume =       "24",
  number =       "9",
  pages =        "443--455",
  month =        "????",
  year =         "1988",
  CODEN =        "JICYE5",
  ISSN =         "0863-0593",
  bibdate =      "Thu Sep 1 10:14:16 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Journal of Information Processing and Cybernetics:
                 EIK",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Scherson:1988:MOA,
  author =       "Isaac D. Scherson and Smil Ruhman",
  title =        "Multi-operand arithmetic in a partitioned associative
                 architecture",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "5",
  number =       "6",
  pages =        "655--668",
  month =        dec,
  year =         "1988",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliationaddress = "Princeton, NJ, USA",
  classification = "722; 723; 921; C5220 (Computer architecture); C5230
                 (Digital arithmetic methods)",
  corpsource =   "Department of Electr. Eng., Princeton University, NJ,
                 USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "16-bit precision; Analysis; Associative
                 Multiplication; associative multiplication; common
                 filter vector; Computer Architecture; Computer
                 Metatheory; concurrency; Convolution; convolution; Data
                 Storage, Digital--Associative; digital arithmetic;
                 Disjoint Data Sets; disjoint data sets; Filter Vectors;
                 Mathematical Techniques; Multi-operand Arithmetic;
                 multioperand arithmetic; multiplier bits; parallel
                 architectures; parallel processing; Partitioned
                 Associative Architecture; partitioned associative
                 architecture",
  treatment =    "P Practical",
}

@InProceedings{Schwarz:1988:CLI,
  author =       "Jerry Schwarz",
  title =        "A {C++} Library for Infinite Precision Floating
                 Point",
  crossref =     "USENIX:1988:UPC",
  bookpages =    "362",
  pages =        "271--281",
  year =         "1988",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "ftp://ftp.uu.net/library/bibliography;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Real library supports infinite precision floating
                 point computation in C++. Arbitrary precision rational
                 arithmetic and transcendental functions are
                 supported.",
  acknowledgement = ack-nhfb,
  affiliation =  "AT\&T Bell Laboratories, Murray Hill",
  classification = "C5230 (Digital arithmetic methods); C6130 (Data
                 handling techniques)",
  confdate =     "17--21 Oct. 1988",
  conflocation = "Denver, CO, USA",
  keywords =     "C++ library; Infinite precision floating point;
                 Rational arithmetic; Real library; Transcendental
                 functions",
  thesaurus =    "C language; Digital arithmetic; Object-oriented
                 programming; Subroutines",
}

@Article{Scott:1988:CMM,
  author =       "Michael Scott",
  title =        "{CUG247} --- {M.I.R.A.C.L.} --- a Multi-Pre\-ci\-sion
                 Arithmetic Library",
  journal =      j-CUJ,
  volume =       "6",
  type =         "{CUG} New Release",
  number =       "5",
  pages =        "76--??",
  month =        may,
  year =         "1988",
  ISSN =         "0898-9788",
  bibdate =      "Fri Aug 30 16:52:23 MDT 1996",
  bibsource =    "http://www.cuj.com/cbklist.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "C Users Journal",
}

@Article{Shepherd:1988:LEC,
  author =       "Roger Shepherd and Charles Farnum",
  title =        "Letter to the {Editor}: Compiler support for
                 floating-point computation",
  journal =      j-SPE,
  volume =       "18",
  number =       "12",
  pages =        "1193--1194",
  month =        dec,
  year =         "1988",
  CODEN =        "SPEXBL",
  DOI =          "https://doi.org/10.1002/spe.4380181208",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Wed Sep 10 12:36:39 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/spe.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Software --- Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  onlinedate =   "30 Oct 2006",
}

@Article{Simon:1988:SP,
  author =       "Barry Simon and Richard M. Wilson",
  title =        "Supercalculators on the {PC}",
  journal =      j-NAMS,
  volume =       "35",
  number =       "7",
  pages =        "978--1001",
  month =        sep,
  year =         "1988",
  CODEN =        "AMNOAN",
  ISSN =         "0002-9920 (print), 1088-9477 (electronic)",
  ISSN-L =       "0002-9920",
  bibdate =      "Wed Jun 12 16:56:18 2024",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Notices Amer. Math. Soc.",
  fjournal =     "Notices of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/notices/",
  mynote =       "September",
}

@Article{Smith:1988:ASD,
  author =       "S. G. Smith and P. B. Denyer",
  title =        "Advanced serial-data computation",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "5",
  number =       "3",
  pages =        "228--249",
  month =        jun,
  year =         "1988",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliationaddress = "Univ of Edinburgh, Edinburgh, Scotl",
  classification = "716; 718; 721; 722; 723; C5230 (Digital arithmetic
                 methods)",
  corpsource =   "Department of Electr. Eng., Edinburgh University, UK",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "arithmetic operations; bit-parallel architectures;
                 Computational Methods; computational modules; computer
                 architecture; computers, digital; digital arithmetic;
                 dynamic range; high-; multiwire; multiwire techniques;
                 performance computer arithmetic; serial data
                 architectures; serial data computation; serial-data
                 architectures; signal processing --- Digital
                 Techniques; symmetric-coded distributed arithmetic;
                 techniques",
  treatment =    "P Practical",
}

@Article{Sohie:1988:DSP,
  author =       "G. R. L. Sohie and K. L. Kloker",
  title =        "A Digital Signal Processor with {IEEE} Floating-Point
                 Arithmetic",
  journal =      j-IEEE-MICRO,
  volume =       "8",
  number =       "6",
  pages =        "49--67",
  month =        nov # "\slash " # dec,
  year =         "1988",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/40.16780",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  summary =      "A overview is given of Motorola's DSP96002, a digital
                 signal processor that implements IEEE-standard
                 floating-point arithmetic. It is designed for graphics,
                 image processing, spectral analysis and scientific
                 computing applications. Performance peaks \ldots{}",
}

@Article{Sridharan:1988:BFP,
  author =       "S. Sridharan and G. Dickman",
  title =        "Block floating-point implementation of digital filters
                 using the {DSP56000}",
  journal =      j-MICROPROC-MICROSYS,
  volume =       "12",
  number =       "6",
  pages =        "299--308",
  month =        aug,
  year =         "1988",
  CODEN =        "MIMID5",
  ISSN =         "0141-9331 (print), 1872-9436 (electronic)",
  ISSN-L =       "0141-9331",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Queensland Institute of Technology, Queensland,
                 Australia; Queensland Institute of Technology,
                 Queensland, Australia",
  bibno =        "49397",
  catcode =      "G.m; I.5.4; C.3; C.5.3",
  CRclass =      "I.5.4 Applications; I.5.4 Signal processing; C.3
                 Signal processing systems; C.5.3 Microcomputers; C.5.3
                 Microprocessors",
  descriptor =   "Mathematics of Computing, MISCELLANEOUS; Computing
                 Methodologies, PATTERN RECOGNITION, Applications,
                 Signal processing; Computer Systems Organization,
                 SPECIAL-PURPOSE AND APPLICATION-BASED SYSTEMS, Signal
                 processing systems; Computer Systems Organization,
                 COMPUTER SYSTEM IMPLEMENTATION, Microcomputers,
                 Microprocessors",
  fjournal =     "Microprocessors and Microsystems",
  genterm =      "ALGORITHMS; DESIGN",
  guideno =      "1988-12500",
  journalabbrev = "Microprocess. Microsyst.",
  subject =      "G. Mathematics of Computing; G.m MISCELLANEOUS; I.
                 Computing Methodologies; I.5 PATTERN RECOGNITION; C.
                 Computer Systems Organization; C.3 SPECIAL-PURPOSE AND
                 APPLICATION-BASED SYSTEMS; C. Computer Systems
                 Organization; C.5 COMPUTER SYSTEM IMPLEMENTATION",
}

@Book{Startz:1988:IPC,
  author =       "Richard Startz",
  title =        "8087\slash 80287\slash 80387 for the {IBM PC} and
                 Compatibles: Applications and Programming with
                 {Intel}'s Math Coprocessors",
  publisher =    pub-BRADY,
  address =      pub-BRADY:adr,
  edition =      "Third",
  pages =        "xviii + 296",
  year =         "1988",
  ISBN =         "0-13-246604-X",
  ISBN-13 =      "978-0-13-246604-2",
  LCCN =         "QA76.8.I2923 S79 1988",
  bibdate =      "Wed Sep 14 20:23:49 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@InProceedings{Stasinski:1988:MRE,
  author =       "R. Stasinski and E. Lukasik",
  booktitle =    "Acoustics, Speech, and Signal Processing, 1988.
                 {ICASSP-88., 1988} International Conference on. 11--14
                 April 1988",
  title =        "Minimization of rounding errors in {WFTA} programs",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1423--1426",
  year =         "1988",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:03 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Two ideas linked with high-precision computation of
                 WFTAs (Winograd-Fourier transform algorithm) using
                 fixed-point arithmetic are analyzed. Use of the best,
                 optimized small-N DFT (discrete Fourier transform)
                 modules is considered. The sizes \ldots{}",
}

@Article{Stouraitis:1988:FPL,
  author =       "Thanos Stouraitis and Fred J. Taylor",
  title =        "Floating-point to logarithmic encoder error analysis",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "37",
  number =       "7",
  pages =        "858--863",
  month =        jul,
  year =         "1988",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.2232",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Ohio State University of University, Columbus;
                 University of Florida, Gainesville",
  ajournal =     "IEEE Trans. Comput.",
  bibno =        "48698",
  catcode =      "F.2.1; G.m; C.1.m",
  CRclass =      "F.2.1 Numerical Algorithms and Problems; F.2.1
                 Number-theoretic computations; C.1.m Miscellaneous",
  descriptor =   "Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Number-theoretic computations; Mathematics of
                 Computing, MISCELLANEOUS; Computer Systems
                 Organization, PROCESSOR ARCHITECTURES, Miscellaneous",
  fjournal =     "IEEE Transactions on Computers",
  genterm =      "DESIGN; THEORY; VERIFICATION",
  guideno =      "1988-08687",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  journalabbrev = "IEEE Trans. Comput.",
  subject =      "F. Theory of Computation; F.2 ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY; G. Mathematics of Computing;
                 G.m MISCELLANEOUS; C. Computer Systems Organization;
                 C.1 PROCESSOR ARCHITECTURES",
  summary =      "The logarithmic number (LNS), which supports
                 high-speed, high-precision arithmetic, is envisioned as
                 a possible arithmetic coprocessor attachment to a
                 floating-point (FLP) processor. An error analysis of an
                 FLP-to-LNS encoder is presented. Analytic \ldots{}",
}

@Manual{Sun:1988:PG,
  title =        "Programmer's guides",
  publisher =    "Sun Microsystems",
  address =      "Mountain View, CA, USA",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "12 volumes in 1 case.",
  acknowledgement = ack-nhfb,
  keywords =     "Operating systems (Computers); Sun computers ---
                 Programming.; SunOS (Computer operating system)",
  remark =       "Title from container. Contents sheet has title: 4.0
                 programmer's guides minibox. ``Revision A, of 9 May
                 1988.''--Contents. ``825-1050-10.''--Contents. C
                 programmer's guide --- Assembly language reference for
                 the Sun-2 and Sun-3 --- Programming utilities and
                 libraries --- Debugging tools --- Network programming
                 --- Writing device drivers --- Floating point
                 programmer's guide --- SunView 1 programmer's guide ---
                 SunView 1 system programmer's guide --- Pixrect
                 reference manual --- SunCGI reference manual ---
                 SunCore reference manual.",
}

@TechReport{Takagi:1988:SHA,
  author =       "Naofumi Takagi",
  title =        "Studies on Hardware Algorithms for Arithmetic
                 Operations with a Redundant Binary Representation",
  type =         "Report",
  institution =  "Department of Information Sciences, Faculty of
                 Engineering, Kyoto University",
  address =      "Kyoto, Japan",
  pages =        "vii + 150",
  day =          "23",
  month =        jan,
  year =         "1988",
  bibdate =      "Thu Nov 13 06:14:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://hdl.handle.net/2433/154053;
                 https://repository.kulib.kyoto-u.ac.jp/server/api/core/bitstreams/b38960be-ee22-458e-9899-ed77db01155e/content;",
  acknowledgement = ack-nhfb,
  remark =       "Wrapper around \cite{Takagi:1987:SHA}.",
}

@Article{Taylor:1988:BLN,
  author =       "F. J. Taylor and R. Gill and J. Joseph and J. Radke",
  title =        "A 20 Bit Logarithmic Number System Processor",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-37",
  number =       "2",
  pages =        "190--199",
  year =         "1988",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.2148",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jun 24 19:49:19 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  abstract =     "The architecture and performance of a 20-bit
                 arithmetic processor based on the logarithmic number
                 system (LNS) is described. The processor performed LNS
                 multiplication and division rapidly and with a low
                 hardware complexity. Addition and subtraction in the
                 LNS require the support of a table lookup unit. A
                 scheme is proposed to minimize this complexity using a
                 partitioned memory (ROM) and a PLA (programmable logic
                 array). For performance evaluation, the target
                 technology is integrated Schottky logic. The processor
                 is shown to compare well with, if not to outperform,
                 existing floating point (FLP) processors of equivalent
                 range and precision. The speed-power-product ratio of
                 an equivalent FLP processor, compared with that of the
                 LNS processor, is reported to be 20 to 1 in the case of
                 the square and square-root operation and 1 to 1 in the
                 case of addition and subtraction. For multiplication
                 and division, this ratio is about 5 to 1.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Misc{Taylor:1988:HFP,
  author =       "Fred J. Taylor",
  title =        "Hybrid floating point\slash logarithmic number system
                 arithmetic processor",
  howpublished = "United States Patent 4,720,809",
  day =          "19",
  month =        jan,
  year =         "1988",
  bibdate =      "Tue Jan 08 21:48:35 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.freepatentsonline.com/4720809.html",
  abstract =     "A hybrid arithmetic processor which combines
                 attributes of conventional floating point (F.P.)
                 arithmetic with logarithmic number system (LNS)
                 arithmetic. The arithmetic processor includes an input
                 section (forward code converter) for converting input
                 operands in F.P. format to intermediate operands in LNS
                 format, an LNS arithmetic section for performing an
                 arithmetic operation on the LNS intermediate operands
                 and providing an intermediate output in LNS format, and
                 an output section (inverse code converter) for
                 converting the LNS intermediate output to an output in
                 F.P. format. Significantly, output is provided in
                 normalized floating point format but without the need
                 for a time-consuming exponent alignment operation.
                 Arithmetic operations, including addition and
                 multiplication, are accomplished at a high speed, which
                 speed moreover is constant and independent of the data.
                 An efficient accumulator structure and the structure of
                 an ultra-fast numeric processor are disclosed.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Thistle:1988:PAH,
  author =       "M. R. Thistle and B. J. Smith",
  title =        "A processor architecture for {Horizon}",
  crossref =     "IEEE:1988:PSN",
  volume =       "1",
  pages =        "35--41",
  year =         "1988",
  bibdate =      "Thu Apr 16 07:55:03 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C5220 (Computer architecture); C5440 (Multiprocessor
                 systems and techniques)",
  corpsource =   "Supercomput. Res. Center, Lanham, MD, USA",
  keywords =     "floating-point operations; Horizon; horizontal
                 instruction set; parallel architectures; parallel
                 machines; processor architecture; scalable
                 shared-memory MIMD computer; scalable shared-memory
                 multiple-instruction-stream-multiple-data-stream
                 computer; scalar processors; three-dimensional
                 nearest-neighbor network",
  sponsororg =   "IEEE; ACM",
  treatment =    "P Practical",
}

@Article{Ton-That:1988:NAC,
  author =       "Long Ton-That",
  title =        "Numerical accuracy control in fixed-point arithmetic",
  journal =      j-MATH-COMPUT-SIMUL,
  volume =       "30",
  number =       "6",
  pages =        "553--561",
  month =        dec,
  year =         "1988",
  CODEN =        "MCSIDR",
  DOI =          "https://doi.org/10.1016/0378-4754(88)90076-6",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  bibdate =      "Mon Aug 18 16:03:57 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomputsimul1980.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/0378475488900766",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput. Simul.",
  fjournal =     "Mathematics and Computers in Simulation",
  journal-URL =  "https://www.sciencedirect.com/science/journal/03784754",
}

@TechReport{Tsao:1988:AST,
  author =       "Nai-kuan Tsao",
  title =        "On the accuracy of solving triangular systems in
                 parallel",
  institution =  "National Aeronautics and Space Administration; For
                 sale by the National Technical Information Service",
  address =      "Washington, DC, USA",
  pages =        "????",
  year =         "1988",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "NASA technical memorandum; 101384 ICOMP; 88-19",
  acknowledgement = ack-nhfb,
  govtdocnumber = "NAS 1.15:101384 0830-D (MF)",
  keywords =     "Algorithms.; Error analysis.; Errors.; Floating point
                 arithmetic.",
  remark =       "Distributed to depository libraries in microfiche.
                 Microfiche. [Washington, D.C.: National Aeronautics and
                 Space Administration, 1989] 1 microfiche.",
}

@Article{Venkaiah:1988:CMS,
  author =       "V. Ch Venkaiah and S. K. Sen",
  title =        "Computing a matrix symmetrizer exactly using modified
                 multiple modulus residue arithmetic",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "21",
  number =       "1",
  pages =        "27--40",
  month =        jan,
  year =         "1988",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:37 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1980.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042788903858",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Voelzke:1988:FSAa,
  author =       "H. V{\"o}lzke",
  title =        "{Flie{\ss}komma-Arithmetik und
                 IEEE-Spez\-i\-fi\-ka\-tion\-en. Teil 1: Standards und
                 Strukturen} \toenglish {Floating-point Arithmetic and
                 its IEEE Specification. Part 1: Standards and
                 Structures} \endtoenglish",
  journal =      j-MC,
  volume =       "10",
  pages =        "123--129",
  year =         "1988",
  ISSN =         "0720-4442, 0941-777x, 0943-5409",
  bibdate =      "Fri Sep 16 16:30:39 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "MC: Die Mikrocomputer-Zeitschrift",
}

@Article{Voelzke:1988:FSAb,
  author =       "H. V{\"o}lzke",
  title =        "{Flie{\ss}komma-Arithmetik und
                 IEEE-Spez\-i\-fi\-ka\-tion\-en. Teil 2: Entwurf eines
                 Flie{\ss}kommapakets} \toenglish {Floating-point
                 Arithmetic and its IEEE Specification. Part 2: Design
                 of a Floating-Point Package} \endtoenglish",
  journal =      j-MC,
  volume =       "11",
  pages =        "78--95",
  year =         "1988",
  ISSN =         "0720-4442, 0941-777x, 0943-5409",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "MC: Die Mikrocomputer-Zeitschrift",
}

@Article{Voelzke:1988:FSAc,
  author =       "H. V{\"o}lzke",
  title =        "{Flie{\ss}komma-Arithmetik und
                 IEEE-Spez\-i\-fi\-ka\-tion\-en. Teil 3: Die verwendeten
                 Algorithmen} \toenglish {Floating-point Arithmetic and
                 its IEEE Specification. Part 3: The Algorithms Used}
                 \endtoenglish",
  journal =      j-MC,
  volume =       "12",
  pages =        "95--108",
  year =         "1988",
  ISSN =         "0720-4442, 0941-777x, 0943-5409",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "MC: Die Mikrocomputer-Zeitschrift",
}

@Article{Weyland:1988:LCS,
  author =       "Nicholas J. Weyland and Edward A. Puckett",
  title =        "Lossless coding for sources of floating-point and
                 fixed-precision numbers",
  journal =      j-IEEE-TRANS-INF-THEORY,
  volume =       "34",
  number =       "4",
  pages =        "882--888",
  month =        jul,
  year =         "1988",
  CODEN =        "IETTAW",
  DOI =          "https://doi.org/10.1109/18.9791",
  ISSN =         "0018-9448 (print), 1557-9654 (electronic)",
  ISSN-L =       "0018-9448",
  MRclass =      "94A29",
  MRnumber =     "89i:94023",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Information Theory",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
  summary =      "A procedure for constructing binary models for sources
                 of floating-point and fixed-precision numbers is given
                 and used together with the minimum description length
                 principle to find optimal models. These models are used
                 to design noiseless source code \ldots{}",
}

@Article{Wilson:1988:FPS,
  author =       "Pete Wilson",
  title =        "Floating-Point Survival Kit",
  journal =      j-BYTE,
  volume =       "13",
  number =       "3",
  pages =        "217--217",
  month =        mar,
  year =         "1988",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Thu Oct 31 18:51:38 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "BYTE Magazine",
}

@Article{Wilson:1988:NDP,
  author =       "Fred Wilson",
  title =        "A Note on Division of Positive Integers",
  journal =      j-SIGMICRO,
  volume =       "19",
  number =       "1--2",
  pages =        "4--4",
  month =        jun,
  year =         "1988",
  CODEN =        "SIGMDJ",
  DOI =          "https://doi.org/10.1145/62197.1096672",
  ISSN =         "0163-5751, 1050-916X",
  ISSN-L =       "0163-5751",
  bibdate =      "Fri Apr 16 10:27:39 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigmicro.bib",
  URL =          "https://dl.acm.org/doi/10.1145/62197.1096672",
  abstract =     "At the risk of flaunting a marginal grasp of the
                 obvious I would like to make a few observations on the
                 division of fixed point numbers.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMICRO Newsletter",
  journal-URL =  "https://dl.acm.org/loi/sigmicro",
}

@Article{Wilson:1988:NFP,
  author =       "R. Wilson",
  title =        "Newest floating-point processors blur architectural
                 distinctions",
  journal =      j-COMP-DESIGN,
  volume =       "27",
  number =       "8",
  pages =        "32--43",
  day =          "15",
  month =        apr,
  year =         "1988",
  CODEN =        "CMPDAM",
  ISSN =         "0010-4566",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  bibno =        "44373",
  catcode =      "B.7.1; C.1.1; C.1.1",
  CRclass =      "B.7.1 Types and Design Styles; B.7.1 Memory
                 technologies; C.1.1 Single Data Stream Architectures;
                 C.1.1 RISC; C.1.1 Single Data Stream Architectures;
                 C.1.1 CISC",
  descriptor =   "Hardware, INTEGRATED CIRCUITS, Types and Design
                 Styles, Memory technologies; Computer Systems
                 Organization, PROCESSOR ARCHITECTURES, Single Data
                 Stream Architectures, RISC; Computer Systems
                 Organization, PROCESSOR ARCHITECTURES, Single Data
                 Stream Architectures, CISC",
  fjournal =     "Computer Design",
  genterm =      "PERFORMANCE; DESIGN",
  guideno =      "1988-05955",
  journalabbrev = "Comput. Des.",
  subject =      "B. Hardware; B.7 INTEGRATED CIRCUITS; C. Computer
                 Systems Organization; C.1 PROCESSOR ARCHITECTURES; C.
                 Computer Systems Organization; C.1 PROCESSOR
                 ARCHITECTURES",
}

@Article{Wollard:1988:TSS,
  author =       "K. Wollard",
  title =        "Technology '88: Solid state",
  journal =      j-IEEE-SPECTRUM,
  volume =       "25",
  number =       "1",
  pages =        "44--46",
  month =        jan,
  year =         "1988",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/6.4483",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Mon Jan 20 06:41:24 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "16 Mbit; 4 Mbit; application-specific ICs; Consumer
                 electronics; digital integrated circuits; Electronics
                 industry; EPROM; floating-point digital signal
                 processors; GaAs-Si; Government; high-density
                 packaging; integrated circuit technology; Japan;
                 Manufacturing industries; Microprocessors; Production;
                 Semiconductor device manufacture; solid state; Solid
                 state circuits; Trade agreements; US",
}

@Book{Young:1988:SNMa,
  author =       "David M. Young and Robert Todd Gregory",
  title =        "A Survey of Numerical Mathematics",
  volume =       "I",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "x + 492 + A22 + B16 + I18",
  year =         "1988",
  ISBN =         "0-486-65691-8",
  ISBN-13 =      "978-0-486-65691-5",
  LCCN =         "QA297.Y63 1972",
  MRclass =      "65-02",
  MRnumber =     "92b:65005b",
  bibdate =      "Wed Jan 17 10:30:33 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/matrix-analysis-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Corrected reprint of the 1973 original.",
  URL =          "http://www.zentralblatt-math.org/zmath/en/search/?an=0732.65002",
  ZMnumber =     "0732.65002",
  acknowledgement = ack-nhfb,
  tableofcontents = "1: Numerical Analysis as a Subject Area \\
                 1.1 Introduction \\
                 1.2 Some pitfalls in computation \\
                 1.3 Mathematical and computer aspects of an algorithm
                 \\
                 1.4 Numerical instability of algorithms and
                 ill-conditioned problems \\
                 1.5 Typical problems of interest to the numerical
                 analyst \\
                 1.6 Iterative methods \\
                 2: Elementary Operations with Automatic Digital
                 Computers \\
                 2.1 Introduction \\
                 2.2 Binary arithmetic \\
                 2.3 Conversion from base $D$ to base $B$ representation
                 \\
                 2.4 Representation of integers on a binary computer \\
                 2.5 Floating-point representations \\
                 2.6 Computer-representable numbers \\
                 2.7 Floating-point arithmetic operations \\
                 2.8 Fortran analysis of a floating-point number \\
                 2.9 Calculation of elementary functions \\
                 3: Surveillance of Number Ranges \\
                 3.1 Introduction \\
                 3.2 Allowable number ranges \\
                 3.3 Basic real arithmetic operations \\
                 3.4 The quadratic equation \\
                 3.5 Complex arithmetic operations \\
                 4: Solution of Equations \\
                 4.1 Introduction \\
                 4.2 Attainable accuracy \\
                 4.3 Graphical methods \\
                 4.4 The method of bisection \\
                 4.5 The method of false position \\
                 4.6 The secant method \\
                 4.7 General properties of iterative methods \\
                 4.8 Generation of iterative methods \\
                 4.9 The Newton method \\
                 4.10 Muller's method \\
                 4.11 Orders of convergence of iterative methods \\
                 4.12 Acceleration of the convergence \\
                 4.13 Systems of nonlinear equations \\
                 5: Roots of Polynomial Equations \\
                 5.1 Introduction \\
                 5.2 General properties of polynomials \\
                 5.3 The Newton method and related methods \\
                 5.4 Muller's method and Cauchy's method \\
                 5.5 Location of the roots \\
                 5.6 Root acceptance and refinement \\
                 5.7 Matrix related methods: the modified Bernoulli
                 method \\
                 5.8 Matrix related methods: the IP method \\
                 5.9 Polyalgorithms \\
                 5.10 Other methods \\
                 6: Interpolation and Approximation \\
                 6.1 Introduction \\
                 6.2 Linear interpolation \\
                 6.3 Convergence and accuracy of linear interpolation
                 \\
                 6.4 Lagrangian interpolation \\
                 6.5 Convergence and accuracy of Lagrangian
                 interpolation \\
                 6.6 Interpolation with equal intervals \\
                 6.7 Hermite interpolation \\
                 6.8 Limitations on polynomial interpolation: smooth
                 interpolation \\
                 6.9 Inverse interpolation \\
                 6.10 Approximation by polynomials \\
                 6.11 Least squares approximation by polynomials \\
                 6.12 Rational approximation \\
                 6.13 Trigonometric interpolation and approximation \\
                 6.14 Interpolation in two variables \\
                 7: Numerical Differentiation and Quadrature \\
                 7.1 Introduction \\
                 7.2 The method of undetermined weights \\
                 7.3 Numerical differentiation \\
                 7.4 Numerical quadrature --- equal intervals \\
                 7.5 The Euler--MacLaurin formula \\
                 7.6 Romberg integration \\
                 7.7 Error determination \\
                 7.8 Numerical quadrature --- unequal intervals \\
                 8: Ordinary Differential Equations \\
                 8.1 Introduction \\
                 8.2 Existence and uniqueness \\
                 8.3 Analytic methods \\
                 8.4 Integral equation formulation --- the Picard method
                 of successive approximations \\
                 8.5 The Euler method \\
                 8.6 Methods based on numerical quadrature \\
                 8.7 Error estimation for predictor-corrector methods
                 \\
                 8.8 A numerical example \\
                 8.9 Runge--Kutta methods \\
                 8.10 Methods based on numerical differentiation \\
                 8.11 Higher-order equations and systems of first-order
                 equations \\
                 8.12 The use of high-speed computers \\
                 Appendix A \\
                 Appendix B \\
                 Appendix C \\
                 Bibliography \\
                 Index",
}

@InProceedings{Yuen:1988:IFP,
  author =       "A. K. Yuen",
  title =        "{Intel}'s floating-point processors",
  crossref =     "Electro:1988:ECR",
  pages =        "48/5/1--7",
  year =         "1988",
  bibdate =      "Wed Sep 7 22:32:00 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Zhou:1988:NBS,
  author =       "B. B. Zhou",
  title =        "A new bit-serial systolic multiplier over {$ \mathrm
                 {GF}(2^m) $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "37",
  number =       "6",
  pages =        "749--751",
  month =        jun,
  year =         "1988",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.2216",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 9 08:33:27 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=2216",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Zoicas:1988:PBG,
  author =       "A. Zoicas and K. Grohe and C. Kellerhoff",
  title =        "{PC} based general-purpose floating-point {DSP $ \mu
                 $PD77230} board with various analog front end options
                 and application software packages",
  crossref =     "Lacoume:1988:SPI",
  pages =        "1233--1236 vol.3",
  year =         "1988",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "3 vol.",
  abstract =     "The EBIBM-77230 FFT is a software and hardware DSP
                 engineering environment incorporated in a PC in the
                 form of a plug-in board. It offers no downgrade from
                 the ideal in terms of its processing power, which
                 amounts of 27 MFLOPs, its open architecture, standard
                 cross-software support and interfaces to popular
                 commercial DSP packages. A variety of analog front-end
                 options and supervisor modules (for stand-alone
                 operation) can be hooked onto the board itself thereby
                 opening its application to most DSP areas. A math
                 library, which features interfaces to most high level
                 languages (C, Fortran, Pascal, Basic), brings
                 workstation computational power to the PC. The
                 EBIBM-77230 FFT bridges the gap between fast high
                 precision number crunching and an accessible
                 user-friendly environment. The turn-around time from an
                 idea to its real-time execution is thus minimised and
                 cost-wise it is an economic solution in relation to
                 most DSP working environments.",
  acknowledgement = ack-nhfb,
  affiliation =  "NEC Electron. GmbH, Dusseldorf, West Germany",
  classification = "B1265F (Microprocessors and microcomputers); B6140
                 (Signal processing and detection); C5130
                 (Microprocessor chips); C5150 (Other circuits for
                 digital computers); C7410F (Communications)",
  keywords =     "27 MFLOPS; Analog front end; Application software
                 packages; Basic; C; DSP engineering environment;
                 EBIBM-77230 FFT; Fortran; General purpose floating
                 point DSP; High level languages; Interfaces; Math
                 library; Microprocessor D77230 board; Open
                 architecture; Pascal; PC; Personal computer; Plug-in
                 board; Supervisor modules",
  numericalindex = "Computer speed 2.7E+07 FLOPS",
  thesaurus =    "Add-on boards; Computerised signal processing;
                 Microcomputer applications; Microprocessor chips;
                 Software packages",
}

@InProceedings{Ahmed:1989:EEF,
  author =       "Hassan M. Ahmed",
  title =        "Efficient Elementary Function Generation with
                 Multipliers",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "52--59",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Ahmed.pdf",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  keywords =     "ARITH-9",
}

@Article{Amit:1989:MRE,
  author =       "G. Amit and U. Shaked",
  title =        "Minimization of roundoff errors in digital
                 realizations of {Kalman} filters",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "37",
  number =       "12",
  pages =        "1980--1982",
  month =        dec,
  year =         "1989",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  summary =      "A comparison between D. Williamson's method (IEEE
                 Trans. Autom. Contr., vol.AC-30, p.930-9, 1985) and the
                 0-1 method for the design of the digital Kalman filter
                 is made. The 0-1 method is shown to be much better than
                 Williamson's method and the \ldots{}",
}

@TechReport{Anonymous:1989:FAR,
  author =       "Anonymous",
  title =        "{FasMath} Accuracy Report",
  type =         "Report",
  institution =  "Cyrix Corporation",
  address =      "Richardson, TX, USA",
  pages =        "????",
  month =        aug,
  year =         "1989",
  bibdate =      "Thu Nov 13 05:50:51 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Cyrix FasMath 83D87 (floating-point coprocessor chip
                 pin-compatible with) Intel 80387",
}

@InProceedings{Arison:1989:SAN,
  author =       "D. Arison and A. Genusov and L. Gerzberg",
  title =        "System applications of a new 32-bit floating-point
                 {DSP} processor",
  crossref =     "Chen:1989:TSA",
  pages =        "890--897 vol.2",
  year =         "1989",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The authors present the ZR34325, a novel
                 floating-point vector signal processor in the context
                 of system applications. The ZR34325 represents the
                 first full IEEE floating-point integrated array
                 processor on silicon, supplemented with the pertinent
                 scalar and control flow capabilities. The ZR34325
                 directly executes embedded DSP (digital signal
                 processing) and array processing primitives on
                 multidimensional arrays. Furthermore, an integrated
                 development environment which includes a system
                 software simulation, vectorized and parametric DSP,
                 arithmetic and matrix library, C-based
                 assembler/linker, and hardware development tools
                 facilities top-down complete application development.
                 The ZR34325 enables very efficient multiprocessor
                 multitasking schemes for tasks where execution time is
                 either data independent or data dependent. The authors
                 show the top-down integrated design methodology via
                 sample signal/image processing application examples
                 such as Kalman filtering, spectral analysis, and
                 constant false alarm rate processing for radar
                 applications as well as two-dimensional image
                 filtering.",
  acknowledgement = ack-nhfb,
  affiliation =  "Zoran Corp., Santa Clara, CA, USA",
  classification = "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5260 (Digital signal
                 processing)",
  keywords =     "32 Bit; Arithmetic library; C-based assembler/linker;
                 Digital signal processing; False alarm rate processing;
                 Floating-point DSP processor; Image filtering; Kalman
                 filtering; Matrix library; Multidimensional arrays;
                 Radar; Spectral analysis; Vector signal processor;
                 ZR34325",
  numericalindex = "Word length 3.2E+01 bit",
  thesaurus =    "Computerised signal processing; Digital signal
                 processing chips; Parallel processing",
}

@InProceedings{Arnold:1989:RLN,
  author =       "M. G. Arnold and T. A. Bailey and J. R. Cowles and J.
                 J. Cupal",
  title =        "Redundant logarithmic number systems",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "144--151",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Arnold.pdf",
  abstract =     "A new number system that offers advantages over
                 conventional floating-point and sign/logarithm number
                 systems is described. Called redundant logarithmic
                 arithmetic, it relies, like conventional logarithmic
                 arithmetic, on table lookups to make the arithmetic
                 unit simpler than an equivalent floating-point unit.
                 The cost of 32-b subtraction in a redundant logarithmic
                 number system is lower than that of previously
                 published logarithmic subtraction methods. Another
                 advantage of a redundant logarithmic number system is
                 that a single arithmetic unit can use the same hardware
                 to add, subtract, or multiply in similar times. (25
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "Wyoming University, Laramie, WY, USA",
  classification = "C5230 (Digital arithmetic methods)",
  keywords =     "Add; ARITH-9; Floating-point; Multiply; Number system;
                 Redundant logarithmic arithmetic; Sign/logarithm number
                 systems; Subtract; Table lookups",
  thesaurus =    "Digital arithmetic; Table lookup",
}

@Article{Ashton:1989:AFP,
  author =       "C. Ashton",
  title =        "The {Am29C327} floating point processor",
  journal =      "Electronic Product Design",
  volume =       "10",
  number =       "3",
  pages =        "51--59",
  month =        mar,
  year =         "1989",
  bibdate =      "Wed Sep 7 22:32:01 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@InProceedings{Azmi:1989:TFP,
  author =       "A. M. Azmi and F. Lombardi",
  title =        "On a tapered floating point system",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "2--9",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Azmi.pdf",
  abstract =     "R. Morris (see IEEE Trans. Comput., vol. TC-20, p.
                 1578--1579, 1971), suggested adding an extra field to
                 the fixed floating point system, so that exponents can
                 be stored more efficiently. The exponents are stored in
                 the smallest possible space, passing the extra bits to
                 the mantissa. The extra field is used to monitor the
                 current length of the exponent. The gain in precision
                 and/or exponent range outweighs the overhead of the
                 extra field and the processing speed. The authors
                 provide implementation details, error analysis, and
                 some future research ideas. Simulation results are
                 provided for comparison purposes.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Electr. and Comput. Eng., Colorado
                 University, Boulder, CO, USA",
  classification = "C5230 (Digital arithmetic methods)",
  keywords =     "ARITH-9; Error analysis; Exponents; Tapered floating
                 point system",
  thesaurus =    "Digital arithmetic",
}

@Article{Bailey:1989:FPA,
  author =       "D. H. Bailey and H. D. Simon and J. T. Barton",
  title =        "Floating Point Arithmetic in Future Supercomputers",
  journal =      j-IJSA,
  volume =       "3",
  number =       "3",
  pages =        "86--90",
  month =        "Fall",
  year =         "1989",
  CODEN =        "IJSAE9",
  ISSN =         "0890-2720",
  bibdate =      "Thu Aug 22 17:56:36 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 UnCover library database",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Supercomputer Applications",
  journal-URL =  "http://hpc.sagepub.com/content/by/year",
}

@Article{Baran:1989:MST,
  author =       "N. Baran",
  title =        "The {Mac SE} takes off",
  journal =      j-BYTE,
  volume =       "14",
  number =       "2",
  pages =        "113--116",
  month =        feb,
  year =         "1989",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Thu Sep 12 17:54:09 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C5430 (Microcomputers)",
  fjournal =     "BYTE Magazine",
  keywords =     "16 MHz; 2 MBytes; 4 MBytes; 68030 CPU; 68882
                 Floating-point unit; Apple Macintosh SE/30; Built-in
                 memory management unit; FPU; Logic board; Mac SE/30;
                 MMU; Motorola 68030 processor; SIMM-mounted ROMs;
                 Single in-line memory module RAM chips",
  numericalindex = "Frequency 1.6E+07 Hz; Memory size 2.1E+06 Byte;
                 Memory size 4.2E+06 Byte",
  thesaurus =    "Apple computers; Microcomputers",
}

@Article{Bardin:1989:IUI,
  author =       "B. Bardin and C. Colket and D. Smith",
  title =        "Implementation of unsigned integers in {Ada}",
  journal =      j-SIGADA-LETTERS,
  volume =       "9",
  number =       "1",
  pages =        "47--70",
  month =        jan # "\slash " # feb,
  year =         "1989",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Thu Mar 20 07:41:09 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages); C6130 (Data handling
                 techniques)",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "Ada; address arithmetic; digital arithmetic; full
                 range; logical operations; modular arithmetic; numeric
                 literals; symbol manipulation; unsigned integers",
  treatment =    "P Practical",
}

@Article{Barrett:1989:FMA,
  author =       "Geoff Barrett",
  title =        "Formal methods applied to a floating-point number
                 system",
  journal =      j-IEEE-TRANS-SOFTW-ENG,
  volume =       "15",
  number =       "5",
  pages =        "611--621",
  month =        may,
  year =         "1989",
  CODEN =        "IESEDJ",
  DOI =          "https://doi.org/10.1109/32.24710",
  ISSN =         "0098-5589 (print), 1939-3520 (electronic)",
  ISSN-L =       "0098-5589",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A formalization of the IEEE standard for binary
                 floating-point arithmetic (ANSI/IEEE Std. 754-1985) is
                 presented in the set-theoretic specification language
                 Z. The formal specification is refined into four
                 sequential components, which unpack the operands,
                 perform the arithmetic, and pack and round the result.
                 This refinement follows proven rules and so
                 demonstrates a mathematically rigorous method of
                 program development. In the course of the proofs,
                 useful internal representations of floating-point
                 numbers are specified. The procedures presented form
                 the basis for the floating-point unit of the Inmos IMS
                 T800 transputer.",
  acknowledgement = ack-nhfb,
  affiliation =  "Oxford University, Oxford, UK",
  bibno =        "65476",
  catcode =      "F.3.1; C.5.3; D.2.1; D.2.0; B.2.0; B.5.1",
  content =      "It is paradoxical that no programming language can be
                 completely defined unless it has a formally defined
                 syntax, yet at the same time, languages have informal
                 semantic descriptions. This is most evident in
                 arithmetic, in which the closest thing to a formal
                 description lies in the IEEE standard for binary
                 floating point arithmetic adopted by ANSI in 1985. The
                 standard is written in natural language, with the
                 attendant possibility of ambiguity and inconsistency.
                 The author of this paper has given a formal version of
                 the standard in the Z specification language, which can
                 be thought of as a structured version of predicate
                 logic. After giving a cogent argument for the use of
                 formal methods in standardization, the author presents
                 a stage-by-stage development of the formal description
                 of the standard; while doing this, he stresses the
                 modularity of the description, as exemplified by the
                 separation of normal and exceptional conditions.\par

                 As he introduces the concepts of Z, the author gives
                 brief explanations of the notation, but for a beginner
                 in the field, the paper is best read in conjunction
                 with the original standard and a description of
                 Z.\par

                 A very powerful argument for the formal approach lies
                 in the specification's use. The INMOS T800 floating
                 point unit was developed by means of a series of
                 refinements of the formal specification; the",
  CRclass =      "F.3.1 Specifying and Verifying and Reasoning about
                 Programs; F.3.1 Specification techniques; C.5.3
                 Microcomputers; C.5.3 INMOS Transputer; D.2.1
                 Requirements/Specifications; D.2.1 Z; D.2.0 General;
                 D.2.0 Standards; B.2.0 General; B.5.1 Design; B.5.1
                 Arithmetic and logic units",
  CRnumber =     "9004-0316",
  descriptor =   "Theory of Computation, LOGICS AND MEANINGS OF
                 PROGRAMS, Specifying and Verifying and Reasoning about
                 Programs, Specification techniques; Computer Systems
                 Organization, COMPUTER SYSTEM IMPLEMENTATION,
                 Microcomputers, INMOS Transputer; Software, SOFTWARE
                 ENGINEERING, Requirements/Specifications, Z; Software,
                 SOFTWARE ENGINEERING, General, Standards; Hardware,
                 ARITHMETIC AND LOGIC STRUCTURES, General; Hardware,
                 REGISTER-TRANSFER-LEVEL IMPLEMENTATION, Design,
                 Arithmetic and logic units",
  fjournal =     "IEEE Transactions on Software Engineering",
  genterm =      "ALGORITHMS; DOCUMENTATION; LANGUAGES; STANDARDIZATION;
                 THEORY",
  guideno =      "1989-06803",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=32",
  journalabbrev = "IEEE Trans. Softw. Eng.",
  reviewer =     "Simon Thompson",
  subject =      "F. Theory of Computation; F.3 LOGICS AND MEANINGS OF
                 PROGRAMS; C. Computer Systems Organization; C.5
                 COMPUTER SYSTEM IMPLEMENTATION; D. Software; D.2
                 SOFTWARE ENGINEERING; D. Software; D.2 SOFTWARE
                 ENGINEERING; B. Hardware; B.2 ARITHMETIC AND LOGIC
                 STRUCTURES; B. Hardware; B.5 REGISTER-TRANSFER-LEVEL
                 IMPLEMENTATION",
}

@InProceedings{Bedard:1989:WFD,
  author =       "N. Bedard and M. Birman and G. Chu and L. Hu and C. M.
                 Lim and J. McLeod and L. Torban and F. Ware",
  title =        "The {Weitek} 64-bit floating-point datapath unit",
  crossref =     "Chen:1989:TSA",
  pages =        "898--902 (vol. 2)",
  year =         "1989",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The authors describe the WTL 3165 and WTL 3364,
                 jointly referred to as the WTL 3X64, which are each
                 64-bit floating-point data path units designed for
                 high-speed operation in pipelined environment while
                 making possible full compliance with the IEEE standard
                 for binary floating-point arithmetic. It also provides
                 full interruptibility, even in a pipelined environment.
                 The architecture and performance of the 3X64 are
                 described, and a detailed block diagram is presented.",
  acknowledgement = ack-nhfb,
  affiliation =  "Weitek Corp., Sunnyvale, CA, USA",
  classification = "B1265F (Microprocessors and microcomputers); B2570D
                 (CMOS integrated circuits); C5130 (Microprocessor
                 chips); C5220 (Computer architecture); C5230 (Digital
                 arithmetic methods); C5260 (Digital signal
                 processing)",
  keywords =     "64 Bit; Architecture; Binary floating-point
                 arithmetic; Computerised signal processing; DSP chip;
                 Floating-point data path units; Interruptibility;
                 Pipelined environment; Weitek; WTL 3165; WTL 3364; WTL
                 3X64",
  numericalindex = "Word length 6.4E+01 bit",
  thesaurus =    "CMOS integrated circuits; Computerised signal
                 processing; Digital arithmetic; Digital signal
                 processing chips; Parallel architectures; Pipeline
                 processing",
}

@Book{Beliankov:1989:NPO,
  author =       "A. Ia Beliankov",
  title =        "Nekotorye primeneniia otsenochnoi (``gruboi'')
                 arifmetiki",
  publisher =    "VTS AN SSSR",
  address =      "Moskva, Russia",
  pages =        "35",
  year =         "1989",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Soobshcheniia po vychislitelnoi matematike",
  acknowledgement = ack-nhfb,
  keywords =     "Algebras, Linear.; Computer arithmetic.;
                 Floating-point arithmetic.",
  remark =       "At head of title: Akademiia nauk SSSR. Vychislitelnyi
                 tsentr.",
}

@InProceedings{Benschneider:1989:MUP,
  author =       "B. J. Benschneider and W. J. Bowhill and E. M. Cooper
                 and M. N. Gavrielov and P. E. Gronowski and V. K.
                 Maheshwari and V. Peng and J. D. Pickholtz and S.
                 Samudrala",
  title =        "A 50 {MHz} Uniformly Pipelined 64b Floating-Point
                 Arithmetic Processor",
  crossref =     "Wuorinen:1989:DTP",
  pages =        "50--51, 288",
  year =         "1989",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A description is given of a uniformly pipelined,
                 50-MHz, 64-b floating-point arithmetic processor
                 implemented in a 1.5- mu m (drawn) CMOS technology
                 which performs single- and double-precision
                 floating-point operations and integer multiplication as
                 defined by a superminicomputer architecture standard.
                 The chip is composed of an interface section and a
                 five-segment execution core. The core insists of a
                 divider, bypassed in all instruction except division,
                 and four fully pipelined stages that are uniformly
                 utilized in the execution of all instructions. The
                 performance is summarized. First pass silicon has been
                 functionally verified at 50 MHz with a set of over one
                 million vectors.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Digital Equipment Corp., Hudson, MA, USA",
  classification = "B1265F (Microprocessors and microcomputers); B2570D
                 (CMOS integrated circuits); C5130 (Microprocessor
                 chips); C5220 (Computer architecture); C5230 (Digital
                 arithmetic methods)",
  confdate =     "15-17 Feb. 1989",
  conflocation = "New York, NY, USA",
  confsponsor =  "IEEE; University of Pennsylvania",
  keywords =     "1.5 Micron; 50 MHz; 64 Bit; CMOS technology; Divider;
                 Double-precision floating-point operations;
                 Five-segment execution core; Floating-point arithmetic
                 processor; Fully pipelined stages; Integer
                 multiplication; Interface section; Single-precision
                 floating point; Superminicomputer architecture
                 standard",
  numericalindex = "Frequency 5.0E+07 Hz; Word length 6.4E+01 bit; Size
                 1.5E-06 m",
  thesaurus =    "CMOS integrated circuits; Digital arithmetic;
                 Microprocessor chips; Pipeline processing",
}

@Article{Benschneider:1989:PMC,
  author =       "Bradley J. Benschneider and William J. Bowhill and
                 Elizabeth M. Cooper and Moshe N. Gavrielov and Paul E.
                 Gronowski and Vijay K. Maheshwari and Victor Peng and
                 Jeffrey D. Pickholtz and Sridhar Samudrala",
  title =        "A pipelined {50-MHz} {CMOS} 64-bit floating-point
                 arithmetic processor",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "24",
  number =       "5",
  pages =        "1317--1323",
  month =        oct,
  year =         "1989",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A 135K transistor, uniformly pipelined 50-MHz CMOS
                 64-bit floating-point arithmetic processor chip is
                 described. The execution unit is capable of sustaining
                 pipelined performance of one 32-bit or 64-bit result
                 every 20 ns for all operations except double-precision
                 multiply (40 ns) and divide. The chip employs an
                 exponent difference prediction scheme and a unified
                 leading-one and sticky-bit computation logic for the
                 addition and subtraction operations. A hardware
                 multiplier using a radix-8 modified Booth algorithm and
                 a divider using a radix-2 SRT algorithm are employed.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Digital Equipment Corp., Hudson, MA, USA",
  classification = "B1265F (Microprocessors and microcomputers); B2570D
                 (CMOS integrated circuits); C5130 (Microprocessor
                 chips); C5230 (Digital arithmetic methods)",
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "20 Ns; 40 Ns; 50 MHz; 64 Bit; Addition; CMOS; Divider;
                 Execution unit; Exponent difference prediction scheme;
                 Floating-point arithmetic processor; Hardware
                 multiplier; Microprocessor; Processor chip; Radix-2 SRT
                 algorithm; Radix-8 modified Booth algorithm; Sticky-bit
                 computation logic; Subtraction; Unified leading-one;
                 Uniformly pipelined",
  numericalindex = "Word length 6.4E+01 bit; Frequency 5.0E+07 Hz; Time
                 2.0E-08 s; Time 4.0E-08 s",
  summary =      "A 135K transistor, uniformly pipelined 50-MHz CMOS
                 64-bit floating-point arithmetic processor chip is
                 described. The execution unit is capable of sustaining
                 pipelined performance of one 32-bit or 64-bit result
                 every 20 ns for all operations except \ldots{}",
  thesaurus =    "CMOS integrated circuits; Digital arithmetic;
                 Microprocessor chips; Pipeline processing",
}

@Misc{Bleher:1989:MCA,
  author =       "J. Hartmut Bleher and Axel T. Gerlicher and Siegfried
                 M. Rump and Dieter K. Unkauf",
  title =        "Method and circuit arrangement for adding floating
                 point numbers",
  howpublished = "US Patent 4866651",
  day =          "12",
  month =        sep,
  year =         "1989",
  bibdate =      "Mon Dec 29 16:18:28 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/4866651/fulltext.html",
  abstract =     "For successively adding a series of floating point
                 numbers, a floating point adder stage (FIG. 2) is used
                 which, in addition to the sum of two floating point
                 operands, emits the remainder, truncated from the
                 smaller operand, as a floating point number. For
                 obtaining an exact sum of the operands, these
                 remainders are summed in the form of intermediate sums.
                 A circuit arrangement for parallel operation comprises
                 series-connected floating point adder stages (FIG. 6),
                 the intermediate sum occurring at the output of each
                 stage and the intermediate remainder being buffered.
                 Remainders are in each case passed on to the next
                 stage, their value decreasing until they are zero. A
                 serially operating arrangement (FIG. 8) comprises a
                 single adder stage (30) and a register stack (34) for
                 buffering the intermediate sums and the final result. A
                 remainder occurring is stored in a remainder register
                 (32) at the output of the adder stage and added to the
                 intermediate sums until the remainder is zero.
                 Subsequently, a fresh operand is applied to the input
                 of the adder stage.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Boddie:1989:FDC,
  author =       "J. R. Boddie and R. N. Gadenz and C. J. Garen and J.
                 M. Huser and B. Ng and S. P. Pekarich",
  title =        "A 32-bit floating-point {DSP} with {C} compiler",
  crossref =     "Chen:1989:TSA",
  pages =        "880--884 vol.2",
  year =         "1989",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A novel digital signal processor (the DSP32C) has been
                 developed which performs 32-bit floating point
                 operations at a rate of 25 MFLOPS (million
                 floating-point operations per second) and can be
                 programmed using a standard C compiler. The authors
                 present an overview of the architecture and instruction
                 set with emphasis on the enhancements over its
                 predecessor, the DSP32. The performance is expressed
                 with common signal processor benchmarks. The
                 application development environment is described which
                 highlights the C compiler and hardware development
                 system. Finally, an application example illustrates the
                 power and ease of this DSP.",
  acknowledgement = ack-nhfb,
  affiliation =  "AT\&T Bell Lab., Holmdel, NJ, USA",
  classification = "B1265F (Microprocessors and microcomputers); B2570D
                 (CMOS integrated circuits); C5130 (Microprocessor
                 chips); C5260 (Digital signal processing); C6150C
                 (Compilers, interpreters and other processors)",
  keywords =     "25 MFLOPS; 32 Bit; Architecture; C compiler;
                 Computerised signal processing; DSP32C; Floating point
                 digital signal processor; Instruction set",
  numericalindex = "Word length 3.2E+01 bit; Computer speed 2.5E+07
                 FLOPS",
  thesaurus =    "CMOS integrated circuits; Computerised signal
                 processing; Digital signal processing chips; Program
                 compilers",
}

@TechReport{Bohlender:1989:FST,
  author =       "Gerd Bohlender and Gudenberg, J. Wolff von (Jurgen
                 Wolff) and Willard L. Miranker",
  title =        "Floating-point systems for theorem proving",
  type =         "Research report",
  number =       "RC 15101 (\#67356)",
  institution =  "IBM T.J. Watson Research Center",
  address =      "Yorktown Heights, NY, USA",
  pages =        "14",
  day =          "2",
  month =        nov,
  year =         "1989",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "There are a number of existing floating-point systems
                 (programming languages and libraries) which allow the
                 computer user to produce computation with guarantees.
                 These systems may be conveniently used as a component
                 in theorem proving. Following a brief description of
                 the methodology which underlies these systems, we
                 tabulate them, indicating some properties and noting
                 where they may be obtained for use. A brief appendix
                 supplies an introduction to the formalism of the
                 methodology.",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers --- Programming.;
                 Floating-point arithmetic.",
}

@InProceedings{Brackert:1989:DLM,
  author =       "R. H. {Brackert, Jr.} and M. D. Ercegovac and A. N.
                 {Willson, Jr.}",
  title =        "Design of an on-line multiply-add module for recursive
                 digital filters",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "34--41",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Brackert.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9",
}

@Article{Brightman:1989:ASF,
  author =       "T. Brightman",
  title =        "Advancing the Standard in Floating-Point Performance",
  journal =      j-HIGH-PERFORM-SYST,
  volume =       "10",
  number =       "11",
  pages =        "59, 62--64",
  month =        nov,
  year =         "1989",
  CODEN =        "HPSYEA",
  ISSN =         "0279-2834",
  bibdate =      "Wed Dec 13 18:25:43 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Cyrix FasMath 83D87 is a floating-point
                 coprocessor chip that combines Intel 80387 socket and
                 software compatibility with the high performance of
                 Weitek's industry-leading coprocessor. The chip is a
                 VLSI CMOS integrated circuit built initially using
                 1.2-micron double-layer-metal, single-layer-polysilicon
                 process technology. It was designed to minimize
                 complications in the design of high-performance desktop
                 and laptop computer systems.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Cyrix Corp., Richardson, TX, USA",
  chemicalindex = "Si/int Si/el",
  classification = "B1265F (Microprocessors and microcomputers); B2570D
                 (CMOS integrated circuits); C5130 (Microprocessor
                 chips)",
  fjournal =     "High performance systems",
  keywords =     "Cyrix FasMath 83D87; Desktop computer systems;
                 Double-layer-metal; Floating-point coprocessor chip;
                 Intel 80387; Laptop computer systems; Math coprocessor;
                 Si; Single-layer-polysilicon process technology; Socket
                 compatibility; Software compatibility; VLSI CMOS
                 integrated circuit",
  thesaurus =    "CMOS integrated circuits; Digital arithmetic;
                 Microprocessor chips; Satellite computers; VLSI",
}

@Article{Buell:1989:MIA,
  author =       "D. Buell and R. Ward",
  title =        "A Multiprecise Integer Arithmetic Package",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "3",
  number =       "??",
  pages =        "89--107",
  month =        "????",
  year =         "1989",
  CODEN =        "JOSUED",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Sun Sep 11 21:56:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
}

@InProceedings{Carter:1989:CHH,
  author =       "T. M. Carter",
  title =        "{Cascade}: hardware for high\slash variable precision
                 arithmetic",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "184--191",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Carter.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9",
}

@InProceedings{Chan:1989:ADC,
  author =       "P. K. Chan and M. D. F. Schlag",
  title =        "Analysis and design of {CMOS Manchester} adders with
                 variable carry-skip",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "86--95",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Chan.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9",
}

@InProceedings{Chen:1989:DRN,
  author =       "J. T. Chen and W. K. Jenkins",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, 8--11 May 1989",
  title =        "Design of a residue number system digital correlator
                 for real-time processing in ultrasonic blood flow
                 measurements",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "208--211",
  year =         "1989",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1989.100328",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The design of a high-speed digital correlator for
                 implementing the real-time correlation function
                 required in an ultrasonic blood flowmeter is presented.
                 In order to achieve the necessary real-time processing
                 rates, a residue number system (RNS) \ldots{}",
}

@Article{Chen:1989:FCN,
  author =       "S. G. Chen and P. Y. Hsieh",
  title =        "Fast Computation of the {$N$ th} Root",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "17",
  number =       "10",
  pages =        "1423--1427",
  year =         "1989",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Thu Sep 15 18:41:31 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  xxmonth =      "(none)",
}

@Article{Chen:1989:FCTa,
  author =       "S.-G. Chen and P. Y. Hsieh",
  title =        "Fast computation of the {$N$}-th root",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "17",
  number =       "10",
  pages =        "1423--1427",
  month =        "????",
  year =         "1989",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(89)90024-2",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 19:01:11 MST 2017",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/computmathappl1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122189900242",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  remark =       "From the abstract: ``A new class of iterative methods
                 for computing a differentiable function is proposed,
                 which is based on Pad{\'e} approximation to Taylor's
                 series of the function. It leads to a faster algorithm
                 than Newton's method for $ x^{1 / N} $ and a different
                 interpretation of Newton's method.''",
}

@MastersThesis{Chinn:1989:DIA,
  author =       "Patty Chinn",
  title =        "The design, implementation, and applications of an
                 {ACT8837} floating point processor in an image
                 processing hardware subsystem",
  type =         "Thesis ({M.S.E.E.})",
  school =       "University of Washingto",
  address =      "Seattle, WA, USA",
  pages =        "vi + 45 + 1",
  year =         "1989",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Image processing --- Digital techniques.",
}

@Book{Chow:1989:MXR,
  editor =       "Paul Chow",
  title =        "The {MIPS-X RISC} Microprocessor",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "xxiv + 231",
  year =         "1989",
  ISBN =         "0-7923-9045-8",
  ISBN-13 =      "978-0-7923-9045-9",
  LCCN =         "QA76.8.M524 M57 1989",
  bibdate =      "Tue Dec 14 23:27:43 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/microchip.bib",
  series =       "The Kluwer international series in engineering and
                 computer science",
  ZMnumber =     "0706.68010",
  acknowledgement = ack-nhfb,
  keywords =     "MIPS-X (microprocessor); VLSI, computer architecture,
                 and digital signal processing SECS 81",
}

@InProceedings{Clenshaw:1989:LIA,
  author =       "C. W. Clenshaw and F. W. J. Olver and Peter R.
                 Turner",
  title =        "Level-index arithmetic: an introductory survey",
  crossref =     "Turner:1989:NAP",
  pages =        "95--168",
  year =         "1989",
  DOI =          "https://doi.org/10.1007/BFb0085718",
  MRclass =      "65Q05",
  MRnumber =     "1022263",
  bibdate =      "Tue Oct 09 09:58:20 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Charles William Clenshaw (15 March 1926--23 September
                 2004); Frank William John Olver (15 December 1924--23
                 April 2013)",
}

@Article{Clenshaw:1989:RSU,
  author =       "C. W. Clenshaw and Peter R. Turner",
  title =        "Root squaring using level-index arithmetic",
  journal =      j-COMPUTING,
  volume =       "43",
  number =       "2",
  pages =        "171--185",
  month =        jun,
  year =         "1989",
  CODEN =        "CMPTA2",
  DOI =          "https://doi.org/10.1007/BF02241860",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65G99 (65H05)",
  MRnumber =     "1 034 362",
  bibdate =      "Sun Nov 12 06:18:24 2023",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  author-dates = "Charles William Clenshaw (15 March 1926--23 September
                 2004)",
  fjournal =     "Computing. Archives for Scientific Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  subject-dates = "Frank William John Olver (15 December 1924--23 April
                 2013)",
  xxtitle =      "{Das Graeffe-Verfahren mit H{\"o}henindexarithmetik}",
}

@TechReport{Cody:1989:AXF,
  author =       "W. J. Cody",
  title =        "Algorithm {XXX}: Functions to Support the {IEEE}
                 Standard for Binary Floating-Point Arithmetic",
  number =       "MCS-P90-0789",
  institution =  "Mathematics and Computer Science Division, Argonne
                 National Laboratory",
  address =      "Argonne, IL, USA",
  pages =        "??",
  month =        jul,
  year =         "1989",
  bibdate =      "Thu Sep 01 10:38:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@InProceedings{Dadda:1989:PC,
  author =       "Luigi Dadda",
  title =        "Polyphase convolvers",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "78--85",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Dadda.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "29 April 1923--26 October 2012",
  keywords =     "ARITH-9",
}

@Article{Dadda:1989:SIM,
  author =       "Luigi Dadda",
  title =        "On serial-input multipliers for two's complement
                 numbers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "38",
  number =       "9",
  pages =        "1341--1345",
  month =        sep,
  year =         "1989",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.29478",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jul 8 19:00:41 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=29478",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  author-dates = "29 April 1923--26 October 2012",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Dally:1989:MOF,
  author =       "W. J. Dally",
  title =        "Micro-optimization of floating-point operations",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "17",
  number =       "2",
  pages =        "283--289",
  month =        apr,
  year =         "1989",
  CODEN =        "CANED2",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Fri May 12 09:40:39 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
}

@Article{DAngelo:1989:DEA,
  author =       "S. D'Angelo and G. R. Sechi",
  title =        "Definition of elementary arithmetic operations by
                 using {ACM}",
  journal =      j-SIGMICRO,
  volume =       "20",
  number =       "3",
  pages =        "160--162",
  month =        aug,
  year =         "1989",
  CODEN =        "SIGMDJ",
  DOI =          "https://doi.org/10.1145/75395.75414",
  ISSN =         "0163-5751, 1050-916X",
  ISSN-L =       "0163-5751",
  bibdate =      "Fri Apr 16 10:27:41 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigmicro.bib",
  URL =          "https://dl.acm.org/doi/10.1145/75395.75414",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMICRO Newsletter",
  journal-URL =  "https://dl.acm.org/loi/sigmicro",
}

@Misc{Darley:1989:FPI,
  author =       "Henry M. Darley and Michael C. Gill and Dale C. Earl
                 and Dinh T. Ngo and Paul C. Wang and Maria B. L. Hipona
                 and Jim Dodrill",
  title =        "Floating Point\slash Integer Processor with Divide and
                 Square Root Functions",
  day =          "31",
  month =        oct,
  year =         "1989",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "U.S. Patent No. 4,878,190 held by Texas Instruments.
                 Expired 2008-01-29.",
  URL =          "https://patentimages.storage.googleapis.com/bb/ca/c5/ed5ce0fc874200/US4878190.pdf",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}

@InProceedings{deLange:1989:DMA,
  author =       "A. A. J. de Lange and A. J. van der Hoeven and E. F.
                 Deprettere and P. Dewilde and J. Bu",
  title =        "The design of a 50 Mflop arithmetic chip for massively
                 parallel pipelined {DSP} algorithms: the floating point
                 pipeline {CORDIC} processor",
  crossref =     "IEE:1989:EEC",
  pages =        "410--414",
  year =         "1989",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The paper describes a high performance VLSI CORDIC
                 arithmetic chip. It performs 15 10/sup 6/ rotations/sec
                 (50 Mflops) and can be applied as a processing element
                 in parallel/pipelined processor structures (systolic
                 and wavefront arrays) for real time/high speed signal
                 processing algorithms and matrix computation
                 applications. The authors present a novel optimized
                 (floating point) CORDIC algorithm, and architecture,
                 its performance and layout. Algorithm, architecture,
                 performance and layout are parametrized which allows
                 automatic generation of the chip layout for any
                 required chip performance, accuracy and dynamic range
                 of arithmetic operations.",
  acknowledgement = ack-nhfb,
  affiliation =  "Delft University of Technol., Netherlands",
  classification = "B1265F (Microprocessors and microcomputers); B2570
                 (Semiconductor integrated circuits); C5220 (Computer
                 architecture); C5230 (Digital arithmetic methods);
                 C5260 (Digital signal processing)",
  keywords =     "50 MFLOPS; Chip layout automatic generation; Dynamic
                 range; Floating point pipeline CORDIC processor; High
                 speed signal processing algorithm; Matrix computation
                 applications; Parallel structure; Pipelined processor
                 structure; Real time signal processing; Systolic
                 arrays; VLSI CORDIC arithmetic chip; Wavefront arrays",
  numericalindex = "Computer speed 5.0E+07 FLOPS",
  thesaurus =    "Digital arithmetic; Digital signal processing chips;
                 Parallel architectures; Pipeline processing; VLSI",
}

@TechReport{Demmel:1989:FPE,
  author =       "J. Demmel",
  title =        "On Floating Point Errors in {Cholesky}",
  type =         "{LAPACK} Working Note",
  number =       "14",
  institution =  inst-UT-CS,
  address =      inst-UT-CS:adr,
  month =        oct,
  year =         "1989",
  bibdate =      "Fri Apr 22 17:06:37 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "UT-CS-89-87, October 1989.",
  URL =          "http://www.netlib.org/lapack/lawns/lawn14.ps;
                 http://www.netlib.org/lapack/lawnspdf/lawn14.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dennis:1989:AAD,
  author =       "A. M. Dennis and C. B. Marshall and I. A. Burgess",
  booktitle =    "{IEE} Colloquium on Signal Processing Applications of
                 Finite Field Mathematics, 1 June 1989",
  title =        "Algorithm and architecture design for the
                 implementation of high order {FIR} filters using the
                 residue number system",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1/1--1/5",
  year =         "1989",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICASSP.1989.266615",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The computational speed requirements of future signal
                 processing algorithms necessitate the use of special
                 purpose multiprocessor systems implemented using VLSI
                 technology. Finite field arithmetic and algorithms
                 offer an extra degree of freedom in \ldots{}",
}

@InProceedings{Dowling:1989:MVF,
  author =       "E. Dowling and M. Griffin and M. Lynch and F. Taylor",
  title =        "A multi-purpose {VLSI} floating-point array
                 processor",
  crossref =     "Chen:1989:TSA",
  pages =        "730--734 vol.2",
  year =         "1989",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A 3*3 single-instruction multiple-data (SIMD) array
                 processor for the IBM PC/AT is described. This array
                 processor is a modified bus-connected architecture
                 (MBCA) using TI's SN74ACT8847 64-bit VLSI
                 floating-point units for processing elements. The array
                 processor can operate four different modes of
                 operation: scalar, vector processor, full utilization,
                 and simulated systolic. In full utilization mode, this
                 array processor can sustain a 90-MFLOP computational
                 rate. System software is also discussed, and attention
                 is given to how it will be used with the SIGLAB
                 programming environment.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Electr. Eng., Florida University,
                 Gainesville, FL, USA",
  classification = "B1265F (Microprocessors and microcomputers); B2570D
                 (CMOS integrated circuits); C5130 (Microprocessor
                 chips); C5220 (Computer architecture); C5430
                 (Microcomputers); C5440 (Multiprocessor systems and
                 techniques)",
  keywords =     "64 Bit; 90 MFLOPS; Full utilization mode; IBM PC/AT;
                 Modes of operation; Modified bus-connected
                 architecture; SIGLAB programming environment; SIMD;
                 Single-instruction multiple-data; SN74ACT8847; VLSI
                 floating-point array processor",
  numericalindex = "Word length 6.4E+01 bit; Computer speed 9.0E+07
                 FLOPS",
  thesaurus =    "CMOS integrated circuits; IBM computers;
                 Microcomputers; Microprocessor chips; Parallel
                 architectures; Parallel processing; VLSI",
}

@TechReport{Dritz:1989:RPS,
  author =       "K. W. Dritz",
  title =        "Rationale for the Proposed Standard for a Generic
                 Package of Elementary Functions for {Ada}",
  type =         "Report",
  number =       "ANL-89/2 Rev. 1",
  institution =  "Argonne National Laboratory, Mathematics and Computer
                 Science Division",
  address =      "Argonne, IL, USA",
  pages =        "??",
  month =        oct,
  year =         "1989",
  bibdate =      "Thu Sep 01 12:08:24 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Dunham:1989:ICA,
  author =       "C. B. Dunham",
  title =        "Improvement of complex arithmetic by use of double
                 elements",
  journal =      j-SIGNUM,
  volume =       "24",
  number =       "4",
  pages =        "3--7",
  month =        oct,
  year =         "1989",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:18 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "algorithms; theory",
  subject =      "G.1.3 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Numerical Linear Algebra, Matrix inversion \\ G.1.0
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Computer arithmetic",
}

@Article{Dunham:1989:PAH,
  author =       "C. B. Dunham",
  title =        "Perturbation Analysis of {Horner}'s Method for Nice
                 Cases",
  journal =      j-SIGNUM,
  volume =       "24",
  number =       "2 and 3",
  pages =        "8--9",
  month =        apr # "/" # jul,
  year =         "1989",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Thu Sep 1 10:15:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}

@Article{Dunham:1989:S,
  author =       "C. B. Dunham",
  title =        "Summation",
  journal =      j-SIGNUM,
  volume =       "24",
  number =       "1",
  pages =        "14--15",
  month =        jan,
  year =         "1989",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Sep 13 08:58:48 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "accurate floating-point summation",
}

@InProceedings{Duprat:1989:SRA,
  author =       "Jean Duprat and Yves Herreros and Jean-Michel Muller",
  title =        "Some results about on-line computation of functions",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "112--118",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Duprat.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9",
}

@InProceedings{Elleithy:1989:ARA,
  author =       "K. M. Elleithy and M. A. Bayoumi and K. P. Lee",
  title =        "{$ \theta (\log N) $} architectures for {RNS}
                 arithmetic decoding",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "202--209",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Elleithy.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9",
}

@InProceedings{Ercegovac:1989:FRD,
  author =       "M. D. Ercegovac and T. Lang",
  title =        "On-the-fly rounding for division and square root",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "169--173",
  year =         "1989",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Ercegovac_rounding.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9",
  summary =      "In division and square root implementation based on
                 digit-recurrence algorithms, the result is obtained in
                 digit-serial form, from most significant digit to least
                 significant. To reduce the complexity of the
                 result-digit selection and to allow the \ldots{}",
}

@InProceedings{Ercegovac:1989:FSC,
  author =       "Milo{\v{s}} D. Ercegovac and Algirdas Avi{\v{z}}ienis
                 and Earl Swartzlander",
  title =        "Foreword: {9th Symposium on Computer Arithmetic
                 (ARITH9)}",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "v--v",
  year =         "1989",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_contents.pdf;
                 http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_foreword.pdf;
                 http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_preface.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9",
}

@InProceedings{Ercegovac:1989:IMC,
  author =       "M. D. Ercegovac and T. Lang",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, 8--11 May 1989",
  title =        "Implementation of module combining multiplication,
                 division, and square root",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "150--153",
  year =         "1989",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The implementation of a module that performs radix-$2$
                 multiplication, division, and square root is presented.
                 The module is compact because most of the components
                 are shared by all three operations, the complexity
                 being similar to that of a radix-$2$ \ldots{}",
}

@InProceedings{Ercegovac:1989:RSR,
  author =       "Milo{\v{s}} D. Ercegovac and Tomas Lang",
  title =        "Radix-4 square root without initial {PLA}",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "162--168",
  year =         "1989",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Ercegovac_radix4.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9",
  summary =      "A systematic derivation of a radix-$4$ square root
                 algorithm using redundance in the partial residuals and
                 the result is presented. Unlike other similar schemes,
                 the algorithm does not use a table-lookup or
                 programmable logic array (PLA) for the \ldots{}",
}

@InProceedings{Fandrianto:1989:AHS,
  author =       "Jan Fandrianto",
  title =        "Algorithms for high-speed shared radix 8 division and
                 radix 8 square root",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "68--75",
  year =         "1989",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Fandrianto.pdf",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  keywords =     "ARITH-9",
  summary =      "An algorithm for performing radix-$8$ division and
                 square root in a shared hardware is described. To
                 achieve short iteration cycle time, it utilizes an
                 optimized `next quotient/root prediction PLA' generally
                 used in a radix-$4$ SRT division with minimal
                 \ldots{}",
}

@InBook{Feldstein:1989:NAP,
  author =       "Alan Feldstein and Richard H. Goodman",
  title =        "Some aspects of floating point computation",
  crossref =     "Turner:1989:NAP",
  pages =        "169--181",
  year =         "1989",
  DOI =          "https://doi.org/10.1007/BFb0085718",
  MRclass =      "65G05",
  MRnumber =     "022 264",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The floating point format is widely used in computing
                 because it allows for the representation of numbers
                 with greatly varying magnitude. This paper introduces
                 some general aspects of floating point representation
                 and includes a discussion of the implications of
                 balanced and unbalanced exponent ranges. A statistical
                 approach is presented in order to analyze the error in
                 floating point computations. The shortening of computer
                 words is discussed and is applied to study aspects of
                 the fraction error and the relative error.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Fowler:1989:AHS,
  author =       "D. L. Fowler and J. E. Smith",
  title =        "An accurate, high speed implementation of division by
                 reciprocal approximation",
  crossref =     "Ercegovac:1989:PSC",
  bookpages =    "xv + 247",
  pages =        "60--67",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Fowler.pdf",
  abstract =     "While unlimited accuracy is theoretically possible, it
                 is very important to minimize the number of iteration
                 steps to improve performance and/or to reduce hardware
                 requirements. Consequently, there is an important
                 accuracy/speed/cost tradeoff in reciprocal
                 approximation implementations. A reciprocal
                 approximation implementation is discussed, with special
                 attention given to these tradeoffs. An interpolation
                 method is used to ensure that an initial approximation,
                 held in a ROM table, is as accurate as possible. A
                 method for implementing the iteration steps is given.
                 Special instructions are used so that maximum accuracy
                 can be carried between iteration operations. For 64-b
                 floating-point operands (53-b mantissa), a table lookup
                 and only two iterations are required, and high accuracy
                 is maintained. The rounded reciprocal rarely differs
                 from a true round-to-nearest value based on an infinite
                 precision result. When the results do differ (less than
                 once every 1000 calculations), the difference in
                 accuracy is shown to be less than 0.025 of a least
                 significant bit (LSB).",
  acknowledgement = ack-nhfb,
  affiliation =  "Astronaut. Corp. of America, Madison, WI, USA",
  classification = "C4130 (Interpolation and function approximation);
                 C5230 (Digital arithmetic methods); C6130 (Data
                 handling techniques)",
  confdate =     "6-8 Sept. 1989",
  conflocation = "Santa Monica, CA, USA",
  confsponsor =  "IEEE; IFIP; University of California",
  keywords =     "ARITH-9; Division; Hardware requirements; High speed
                 implementation; Interpolation; Reciprocal
                 approximation; ROM table; Rounded reciprocal; Table
                 lookup",
  thesaurus =    "Digital arithmetic; Interpolation; Table lookup",
}

@Article{Fried:1989:ONC,
  author =       "S. Fried",
  title =        "Optimizing numeric coprocessing",
  journal =      j-BYTE,
  volume =       "14",
  number =       "11",
  pages =        "221--224",
  month =        "????",
  year =         "1989",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Thu Sep 12 17:47:21 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods); C5470
                 (Performance evaluation and testing)",
  fjournal =     "BYTE Magazine",
  keywords =     "Addition; Compiler optimizations; CPU code;
                 Floating-point operations; Multiplication; Numeric
                 coprocessing; Optimisation; Weitek 3167",
  thesaurus =    "Computer testing; Digital arithmetic; Performance
                 evaluation; Satellite computers",
}

@InProceedings{Fu:1989:PMI,
  author =       "B. Fu and A. Saini and P. P. Gelsinger",
  title =        "Performance and Microarchitecture of the i486{\TM}
                 Processor",
  crossref =     "IEEE:1989:PII",
  pages =        "182--187",
  year =         "1989",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The i486 microprocessor includes a carefully tuned,
                 five-stage pipeline with an integrated 8-kB cache. A
                 variety of techniques previously associated only with
                 RISC (reduced-instruction-set computer) processors are
                 used to execute the average instruction in 1.8 clocks.
                 This represents a 2.5* reduction from its predecessor,
                 the 386 microprocessor. The pipeline and clock count
                 comparisons are described in detail. In addition, an
                 onchip floating-point unit is included which yields a
                 4* clock count reduction from the 387 numeric
                 coprocessor. The microarchitecture enhancements and
                 optimizations used to achieve this goal, most of which
                 are non-silicon-intensive, are discussed. All
                 instructions of the 386 microprocessor and the 387
                 numeric coprocessor are implemented in a completely
                 compatible fashion.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Intel Corp., Santa Clara, CA, USA",
  classification = "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips)",
  confdate =     "2-4 Oct. 1989",
  conflocation = "Cambridge, MA, USA",
  confsponsor =  "IEEE",
  keywords =     "386 Microprocessor; 387 Numeric coprocessor; Clock
                 count; Five-stage pipeline; I486 processor; Intel;
                 Microarchitecture; Onchip floating-point unit;
                 Performance",
  thesaurus =    "Microprocessor chips",
}

@Article{Fujiyama:1989:FD,
  author =       "T. Fujiyama and Y. Shimazu and T. Tokuda and S.
                 Tsujimichi",
  title =        "A 24-bit floating-point {DSP}",
  journal =      "Mitsubishi Denki Giho",
  volume =       "63",
  number =       "12",
  pages =        "59--62",
  month =        "????",
  year =         "1989",
  ISSN =         "0369-2302",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The authors report on a new high-speed 24-bit floating
                 point DSP (digital signal processor) and its
                 development tools. The DSP features a short 75 ns
                 instruction cycle and low 750 mW power dissipation.
                 Other features include a large memory space, internal
                 RAM that can be configured as a cache, and speed
                 control via an internal clock prescaler that is
                 accessed by a special instruction. The DSP is suitable
                 for application in audio and image processing,
                 communications and numerical control.",
  acknowledgement = ack-nhfb,
  affiliation =  "Mitsubishi Electr. Corp., Tokyo, Japan",
  classification = "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5260 (Digital signal
                 processing)",
  keywords =     "24 Bit; 24-Bit floating-point DSP; 75 Ns; 750 MW;
                 Audio processing; Communications; Development; Digital
                 signal processor; DSP chips; Image processing;
                 Instruction cycle; Internal clock prescaler; Memory;
                 Numerical control; Power dissipation; RAM; Speed
                 control",
  language =     "Japanese",
  numericalindex = "Power 7.5E-01 W; Time 7.5E-08 s; Word length 2.4E+01
                 bit",
  pubcountry =   "Japan",
  thesaurus =    "Computerised signal processing; Digital signal
                 processing chips",
}

@InProceedings{Gamberger:1989:ISN,
  author =       "D. Gamberger",
  title =        "Incompletely specified numbers in the residue number
                 system-definition and applications",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "210--215",
  year =         "1989",
  DOI =          "https://doi.org/10.1109/ARITH.1989.72828",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Gamberger.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9; residue arithmetic; residue number system",
  summary =      "Incompletely specified numbers in the residue number
                 system (RNS) are defined in order to make
                 multiplicative inverse computation of a number
                 regardless of its magnitude possible. Incompletely
                 specified RNS is the general RNS model in which
                 \ldots{}",
}

@InProceedings{Games:1989:AIQ,
  author =       "R. A. Games and D. Moulin and S. D. O'Neil and J. J.
                 Rushanan",
  booktitle =    "International Conference on Acoustics, Speech, and
                 Signal Processing, {ICASSP-89, 23--26} May 1989",
  title =        "Algebraic-integer quantization an residue number
                 system processing",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "948--951",
  year =         "1989",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICASSP.1989.266586",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The algebraic-integer number representation, in which
                 the signal sample is represented by a set of (typically
                 four to eight) small integers, combines with residue
                 number system (RNS) processing to produce processors
                 composed of simple parallel \ldots{}",
}

@InProceedings{Goel:1989:RTA,
  author =       "B. D. Goel and M. M. Jamali and S. C. Kwatra",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, 8--11 May 1989",
  title =        "Real time architecture for vector quantization in
                 residue number system",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "204--207",
  year =         "1989",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1989.100327",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A fast and simplified systolic array architecture for
                 real-time implementation of vector quantization is
                 proposed. The proposed architecture uses the residue
                 number system (RNS) for arithmetic operations. The
                 arithmetic operations can be precomputed \ldots{}",
}

@TechReport{Goldberg:1989:FCS,
  author =       "David Goldberg",
  title =        "Floating-point and computer systems",
  type =         "Technical report",
  number =       "CSL-89-9",
  institution =  "Xerox Corp., Palo Alto Research Center",
  address =      "Palo Alto, CA, USA",
  pages =        "58",
  year =         "1989",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.",
  remark =       "``August 1989.'' ``A version of this paper will appear
                 in Computing Surveys.''",
}

@InProceedings{Gonnella:1989:ACF,
  author =       "J. Gonnella and J. Periard",
  booktitle =    "{IEEE} Military Communications Conference, 1989.
                 {MILCOM '89}. Conference Record. Bridging the Gap.
                 Interoperability, Survivability, Security, 1989",
  title =        "The application of core functions to residue number
                 system signal processing",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "604--608",
  year =         "1989",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MILCOM.1989.103996",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The authors briefly outline core-based residue number
                 system (RNS) processing. An RNS adaptive array
                 processor using Choleski decomposition and forward
                 elimination/back substitution is described as an
                 example. The RNS adaptive processor was \ldots{}",
}

@MastersThesis{Gordon:1989:RDF,
  author =       "Stephen E. Gordon",
  title =        "Recursive digital filtering with digital differential
                 analyzers and floating point incremental coders",
  type =         "Thesis ({M.S.E.C.E.})",
  school =       "University of Massachusetts at Amherst",
  address =      "Amherst, MA, USA",
  pages =        "xi + 123",
  year =         "1989",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Digital filters (Mathematics)",
}

@Article{Grassmann:1989:PAR,
  author =       "Winfried K. Grassmann",
  title =        "A probabilistic analysis of rounding errors of
                 floating point numbers. {Eighteenth Manitoba Conference
                 on Numerical Mathematics and Computing (Winnipeg, MB,
                 1988)}",
  journal =      j-CONG-NUM,
  volume =       "68",
  pages =        "171--182",
  year =         "1989",
  ISSN =         "0384-9864",
  MRclass =      "65G05",
  MRnumber =     "90d:65089",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Congressus Numerantium",
}

@Article{Grehan:1989:FPR,
  author =       "R. Grehan",
  title =        "Floating-Point Revisited",
  journal =      j-BYTE,
  volume =       "14",
  number =       "4",
  pages =        "311--318",
  month =        apr,
  year =         "1989",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Thu Sep 1 10:15:05 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "BYTE Magazine",
}

@InProceedings{Griffin:1989:ESR,
  author =       "M. Griffin and M. Sousa and F. Taylor",
  booktitle =    "International Conference on Acoustics, Speech, and
                 Signal Processing, {ICASSP-89, 23--26} May 1989",
  title =        "Efficient scaling in the residue number system",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1075--1078",
  year =         "1989",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICASSP.1989.266618",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A unified residue number system scaling technique that
                 allows the designer a great deal of flexibility in
                 choosing the scale factor is presented. The technique
                 is based on the L({\&}epsi;+{\delta})-CRT (Chinese
                 remainder theorem). By embedding \ldots{}",
}

@InProceedings{Griffin:1989:RNS,
  author =       "M. F. Griffin and F. J. Taylor",
  booktitle =    "International Conference on Acoustics, Speech, and
                 Signal Processing, {ICASSP-89, 23--26} May 1989",
  title =        "A residue number system reduced instruction set
                 computer ({RISC}) concept",
  volume =       "4",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2581--2584",
  year =         "1989",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICASSP.1989.266995",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A reduced-instruction-set RNS (residue number system)
                 processor is proposed for digital signal processing
                 algorithms. Issues leading toward a RNS RISC are
                 examined, namely suitable RNS algorithms. It is argued
                 that this is a reasonable next step in \ldots{}",
}

@Article{Groeger:1989:DRG,
  author =       "Detlef Gr{\"o}ger",
  title =        "{Zur Division mit Rest auf Gleitkommarechnern.
                 (German)} [{On} division with remainder on floating
                 point computers]",
  journal =      j-MATH-SEMESTERBER,
  volume =       "36",
  number =       "1",
  pages =        "106--111",
  year =         "1989",
  ISSN =         "0720-728x (print), 1432-1815 (electronic)",
  ISSN-L =       "0720-728X",
  MRclass =      "65G99 (11Y16)",
  MRnumber =     "90g:65070",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Semesterberichte",
  language =     "German",
}

@InProceedings{Guyot:1989:JLM,
  author =       "Alain Guyot and Bertrand Hochet and Jean-Michel
                 Muller",
  title =        "{JANUS}, an on-line multiplier\slash divider for
                 manipulating large numbers",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "106--111",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Guyot.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9",
}

@Article{Hoffmann:1989:PAR,
  author =       "C. M. Hoffmann",
  title =        "The Problems of Accuracy and Robustness in Geometric
                 Computation",
  journal =      j-COMPUTER,
  volume =       "22",
  number =       "3",
  institution =  "Purdue U",
  pages =        "31--39, 41",
  month =        mar,
  year =         "1989",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Sat Sep 14 07:29:35 MDT 1996",
  bibsource =    "Graphics/rosenfeld/1989.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Misc/IMMD_IV.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Computer Science Dept., Purdue University, West
                 Lafayette, IN, USA",
  classification = "C1160 (Combinatorial mathematics); C4190 (Other
                 numerical methods); C4290 (Other computer theory)",
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
  keywords =     "Accuracy; Degeneracies avoidance; Degenerate
                 positions; Floating-point computation; Geometric
                 computation; Geometric operations; Interacting numeric
                 data; Interacting symbolic data; Limited-precision
                 rational arithmetic; Linear elements; Model, IMAGE PART
                 MEASUREMENT; Numerical precision; Perturbation-free
                 methods; Purely symbolic representations;
                 Representation; Robustness; Symbolic data alteration",
  thesaurus =    "Computational geometry",
}

@InProceedings{Hohne:1989:PHP,
  author =       "R. A. Hohne and R. Siferd",
  booktitle =    "Proceedings of the {IEEE 1989} National Aerospace and
                 Electronics Conference, {NAECON 1989}, 22--26 May
                 1989",
  title =        "A programmable high performance processor using the
                 residue number system and {CMOS} {VLSI} technology",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "41--43",
  year =         "1989",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/NAECON.1989.40188",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The authors describe the general architecture of RNS
                 (residue number system) processors, the VLSI
                 implementation of the associated hardware, and finally,
                 an RNS processor designed by the authors. The 2-{\mu}m
                 CMOS implementation of the processor \ldots{}",
}

@Article{Hollingsworth:1989:CPI,
  author =       "Walter Hollingsworth and Howard Sachs and Alan Jay
                 Smith",
  title =        "The {Clipper\TM} Processor: Instruction Set
                 Architecture and Implementation",
  journal =      j-CACM,
  volume =       "32",
  number =       "2",
  pages =        "200--219",
  month =        feb,
  year =         "1989",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Sep 26 13:49:15 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "design; measurement; performance",
  review =       "ACM CR 9002-0119",
  subject =      "C.5.3 Computer Systems Organization, COMPUTER SYSTEM
                 IMPLEMENTATION, Microcomputers, CLIPPER \\ C.1.1
                 Computer Systems Organization, PROCESSOR ARCHITECTURES,
                 Single Data Stream Architectures,
                 Single-instruction-stream, single-data-stream
                 processors (SISD) \\ C.4 Computer Systems Organization,
                 PERFORMANCE OF SYSTEMS \\ C.0 Computer Systems
                 Organization, GENERAL, Instruction set design",
}

@Article{Hoshi:1989:RPV,
  author =       "T. Hoshi and K. Koya and A. Kuwata and T. Uno and M.
                 Kashimura and T. Kuwata and T. Nishigouri and K. Obuchi
                 and N. Morikawa",
  title =        "{RISC} processor {V}/sub {R}/3000",
  journal =      j-NEC-TECH-J,
  volume =       "42",
  number =       "11",
  pages =        "34--38",
  month =        dec,
  year =         "1989",
  CODEN =        "NECGEZ",
  ISSN =         "0285-4139",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Outlines NEC's first RISC type microprocessor, the
                 V/sub R/3000 and its developmental environment. V/sub
                 R/3000 is fully compatible with the R3000 developed by
                 MIPS Computer Systems, USA. It offers one of the
                 fastest microprocessor systems in the world, together
                 with a floating point processor V/sub R/3010 that is
                 fully compatible with the R3010.",
  acknowledgement = ack-nhfb,
  classification = "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5220 (Computer architecture)",
  fjournal =     "NEC Technical Journal = NEC giho",
  keywords =     "Floating point processor; NEC; RISC type
                 microprocessor; V/sub R/3000; V/sub R/3010",
  language =     "Japanese",
  pubcountry =   "Japan",
  thesaurus =    "Microprocessor chips; Reduced instruction set
                 computing",
}

@InProceedings{Hu:1989:ARM,
  author =       "Y. H. Hu and S. Naganathan",
  title =        "Angle Recoding Method for Efficient Implementation of
                 the {CORDIC} Algorithm",
  crossref =     "IEEE:1989:IISa",
  pages =        "175--178 (Vol. 1)",
  year =         "1989",
  bibdate =      "Thu Sep 01 11:41:20 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@PhdThesis{Hu:1989:SCD,
  author =       "Xiaobo Hu",
  title =        "A silicon compiler for dedicated mathematical systems
                 based on {CORDIC} arithmetic processors",
  type =         "{Ph.D.} thesis",
  school =       "Purdue University",
  address =      "West Lafayette, IN, USA",
  pages =        "184",
  year =         "1989",
  ISBN-13 =      "979-82-07-65496-6",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://login.ezproxy.lib.utah.edu/login?url=https://www.proquest.com/dissertations-theses/silicon-compiler-dedicated-mathematical-systems/docview/303729399/se-2",
  acknowledgement = ack-nhfb,
  advisor =      "Steven C. Bass",
  keywords =     "0544:Electrical engineering; 0984:Computer science;
                 Applied sciences; Compiler; Computer science;
                 Electrical engineering; Mathematical systems",
  ris-m1 =       "9018840",
}

@Book{Huck:1989:ACA,
  author =       "Jerome C. Huck and Michael J. Flynn",
  title =        "Analyzing Computer Architectures",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiii + 188",
  year =         "1989",
  ISBN =         "0-8186-8857-2, 0-8186-4857-0 (microfiche),
                 0-8186-8857-2 (casebound)",
  ISBN-13 =      "978-0-8186-8857-7, 978-0-8186-4857-1 (microfiche),
                 978-0-8186-8857-7 (casebound)",
  LCCN =         "QA76.9.A73 H83 1989",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE Computer Society order number 857. IEEE catalog
                 number EH0285-7. SAN 264-620X.",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}

@Article{Husby:1989:FPE,
  author =       "D. Husby and R. Atac and A. Cook and J. Deppe and M.
                 Fischler and I. Gaines and T. Nash and T. Pham and T.
                 Zmuda and E. Eichten and G. M. Hockney and P. B.
                 Mackenzie and H. B. Thacker and D. Toussaint",
  title =        "A floating point engine for lattice gauge
                 calculations",
  journal =      j-IEEE-TRANS-NUCL-SCI,
  volume =       "36",
  number =       "1",
  pages =        "734--737",
  month =        feb,
  year =         "1989",
  CODEN =        "IRNSAM",
  ISSN =         "0018-9499 (print), 1558-1578 (electronic)",
  ISSN-L =       "0018-9499",
  LCCN =         "TK6540 .I573 Jan-June 1988",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://weblib.cern.ch/format/showfull?uid=1451323_18194&base=CERCER&sysnb=0105825",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Nuclear Science",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=23",
  summary =      "The Fermilab Advanced Computer Program Multiple Array
                 Processor System, which dedicated to solving problems
                 in the field of quantum chromodynamics, is discussed. A
                 typical system with 256 processors, 2.5 Gb of memory,
                 and 64 Gb of online tape storage \ldots{}",
}

@InProceedings{Hwang:1989:OAU,
  author =       "Kai Hwang and D. K. Panda",
  title =        "Optical arithmetic using high-radix symbolic
                 substitution rules",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "226--232",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Hwang.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9",
}

@Book{IEC:1989:IBF,
  author =       "{IEC}",
  title =        "{IEC 60559 (1989-01)}: Binary floating-point
                 arithmetic for microprocessor systems",
  publisher =    pub-IEC,
  address =      pub-IEC:adr,
  pages =        "45",
  year =         "1989",
  bibdate =      "Mon Apr 24 06:17:57 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "This Standard was formerly known as IEEE 754.",
  price =        "US\$86.00",
  URL =          "http://www.iec.ch/cgi-bin/procgi.pl/www/iecwww.p?wwwlang=E&wwwprog=cat-det.p&wartnum=019113",
  acknowledgement = ack-nhfb,
  remark =       "Working Draft, 1997-11-21, WG14/N794 J11/97-158 of the
                 ISO C9X Standard references ``Binary floating-point
                 arithmetic for microprocessor systems, second edition
                 (IEC 559:1993)''. However, I cannot locate that edition
                 at the IEC Web site. The 1997 renumbering of IEC
                 Standards by the addition of 60000 indicates that this
                 document should now be IED 60559:1993, but only the
                 1989 version is listed in the IEC catalog.",
}

@MastersThesis{Intwala:1989:BFP,
  author =       "Jaiprakash D. Intwala",
  title =        "{8085A} based floating point arithmetic system",
  type =         "Thesis ({M.S.})",
  school =       "California State University, Northridge",
  address =      "Northridge, CA, USA",
  pages =        "viii + 81",
  year =         "1989",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Jain:1989:SLU,
  author =       "V. K. Jain and D. L. Landia and C. E. Alvarez",
  title =        "Systolic {L-U} Decomposition Array With a New
                 Reciprocal Cell",
  crossref =     "IEEE:1989:PII",
  pages =        "460--465",
  year =         "1989",
  bibdate =      "Sun Sep 11 20:59:19 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Jamieson:1989:SNR,
  author =       "M. J. Jamieson",
  title =        "Short Notes: Rapidly Converging Iterative Formulae for
                 Finding Square Roots and their Computational
                 Efficiencies",
  journal =      j-COMP-J,
  volume =       "32",
  number =       "1",
  pages =        "93--94",
  month =        feb,
  year =         "1989",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/32.1.93",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  MRclass =      "65H05",
  MRnumber =     "89k:65063",
  bibdate =      "Tue Dec 4 14:48:26 MST 2012",
  bibsource =    "Compendex database;
                 http://comjnl.oxfordjournals.org/content/32/1.toc;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_32/Issue_01/;
                 https://www.math.utah.edu/pub/tex/bib/compj1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "This work generalizes the Pythagorean sums in
                 \cite{Dubrulle:1983:CNM,Moler:1983:RSR}.",
  URL =          "http://comjnl.oxfordjournals.org/content/32/1/93.full.pdf+html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_32/Issue_01/tiff/93.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_32/Issue_01/tiff/94.tif",
  abstract =     "A derivation is given of rapidly converging iterative
                 formulae for finding square roots which include, as
                 special cases, some recently published examples. Their
                 computational efficiencies are investigated for
                 sequential and parallel implementation. It is concluded
                 that the most efficient method is equivalent to
                 sequential application of the Newton Raphson formula; a
                 simple modification is suggested which brings the
                 advantage of root bracketing at little extra
                 computational cost.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, Glasgow University,
                 UK",
  affiliationaddress = "Glasgow, Scotl",
  classcodes =   "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation)",
  classification = "723; 921; B0290F (Interpolation and function
                 approximation); C4130 (Interpolation and function
                 approximation)",
  corpsource =   "Department of Computer Science, Glasgow University,
                 UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "computational; Computational efficiencies;
                 Computational Efficiency; Computer Metatheory;
                 Convergence; convergence of numerical methods;
                 Converging iterative formulae; converging iterative
                 formulae; efficiencies; formula; function
                 approximation; Iterative Methods; iterative methods;
                 Newton Raphson; Newton Raphson formula, Mathematical
                 Techniques; Parallel implementation; parallel
                 implementation; Square Roots; Square roots; square
                 roots",
  thesaurus =    "Convergence of numerical methods; Function
                 approximation; Iterative methods",
  treatment =    "P Practical",
}

@InProceedings{Jenkins:1989:AFP,
  author =       "W. K. Jenkins and J. K. Yun",
  booktitle =    "European Conference on Circuit Theory and Design, 5--8
                 Sep 1989",
  title =        "Analysis of fixed point roundoff effects in transform
                 domain {LMS} adaptive filters",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "228--232",
  year =         "1989",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "One of the disadvantages of the well known LMS FIR
                 adaptive digital filter is that, for a colored noise
                 input signals, the filter tends to converge slowly. One
                 way to improve the convergence rate is to prefilter the
                 input signal with an \ldots{}",
}

@Article{Johnson:1989:IMA,
  author =       "K. R. Johnson",
  title =        "An Iterative Method for Approximating Square Roots",
  journal =      j-MATH-MAG,
  volume =       "62",
  number =       "4",
  pages =        "253--259",
  month =        oct,
  year =         "1989",
  CODEN =        "MAMGA8",
  ISSN =         "0025-570X",
  bibdate =      "Thu Sep 1 10:15:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Mathematics Magazine",
  journal-URL =  "http://www.maa.org/pubs/mathmag.html",
}

@InProceedings{Johnstone:1989:HRF,
  author =       "Paul Johnstone and Frederick E. Petry",
  title =        "Higher Radix Floating Point Representations",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "128--135",
  year =         "1989",
  DOI =          "https://doi.org/10.1109/ARITH.1989.72818",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Johnstone.pdf",
  abstract =     "An examination is made of the feasibility of
                 higher-radix floating-point representations and, in
                 particular, decimal-based representations. Traditional
                 analyses of such representations have assumed the
                 format of a floating-point datum to be roughly
                 identical to that of traditional binary floating-point
                 encodings such as the IEEE P754 task group standard
                 representations. The authors relax this restriction and
                 propose a method of encoding higher-radix
                 floating-point data with range, precision, and storage
                 requirements comparable to those exhibited by
                 traditional binary representations. The results of
                 other authors are extended to accommodate the proposed
                 representation. A decimal alternative to traditional
                 binary representations is proposed, and the behavior of
                 such a system is contrasted with that of a comparable
                 binary system.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Telerate Syst. Inc., New Orleans, LA, USA",
  classification = "C5230 (Digital arithmetic methods)",
  confdate =     "6-8 Sept. 1989",
  conflocation = "Santa Monica, CA, USA",
  confsponsor =  "IEEE; IFIP; University of California",
  keywords =     "ARITH-9; Binary representations; decimal
                 floating-point arithmetic; Decimal-based
                 representations; encodings; higher radix floating point
                 representation; IEEE P754 task group standard
                 representations",
  thesaurus =    "Digital arithmetic",
}

@Article{Jones:1989:EDC,
  author =       "Tom Jones",
  key =          "C.5.1 Convex C2",
  title =        "Engineering design of the {Convex C2}",
  journal =      j-COMPUTER,
  volume =       "22",
  number =       "1",
  pages =        "36--44",
  month =        jan,
  year =         "1989",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Convex Computer Corp., Richardson, TX",
  bibno =        "58556",
  catcode =      "C.5.1; C.5.1; B.4.3; B.7.1; C.1.2",
  content =      "The Convex C220 and C240 supercomputers are 64-bit
                 multiprocessors that are tightly coupled through a
                 shared main memory. Each processor contains an
                 integrated vector processor. A microcoded instruction
                 set controls all processor features, including the
                 vector processor. The system is implemented in 100K
                 emitter-coupled logic with a cycle time of 40
                 nanoseconds. The C220 contains two processors, an I/O
                 system, and memory. The C240 contains four processors,
                 a larger I/O system, and memory. This paper describes
                 the design process of this computer family and tries to
                 illuminate the methods and rationale behind
                 project-related decisions.\par

                 The original C1 system was designed in early 1983 using
                 transistor-transistor logic and complementary
                 metal-oxide semiconductor (CMOS) technologies. The bulk
                 of the machine consisted of medium- and
                 small-scale-integration logic, and the vector
                 functional units were built with 8,000-gate CMOS
                 arrays. The original C1 (later dubbed the C1-XL) had no
                 scalar floating-point hardware but sent the operands to
                 the vector processor. In 1984, floating-point
                 add-and-multiply functional units were designed in
                 20,000-gate CMOS arrays, and the C1 was upgraded to the
                 C1-XP. That machine, with minor changes, became the
                 C120 when the C2 was announced.\par

                 This paper is unusually frank for a retrospective
                 design trade-off study. The author describes",
  CRclass =      "C.5.1 Large and Medium (``Mainframe'') Computers;
                 C.5.1 Super (very large) computers; C.5.1 Large and
                 Medium (``Mainframe'') Computers; C.5.1 Convex C2;
                 B.4.3 Interconnections (subsystems); B.7.1 Types and
                 Design Styles; B.7.1 Gate arrays; C.1.2 Multiple Data
                 Stream Architectures (Multiprocessors); C.1.2
                 Interconnection architectures",
  CRnumber =     "8909-0654",
  descriptor =   "Computer Systems Organization, COMPUTER SYSTEM
                 IMPLEMENTATION, Large and Medium (``Mainframe'')
                 Computers, Super (very large) computers; Computer
                 Systems Organization, COMPUTER SYSTEM IMPLEMENTATION,
                 Large and Medium (``Mainframe'') Computers, Convex C2;
                 Hardware, INPUT/OUTPUT AND DATA COMMUNICATIONS,
                 Interconnections (subsystems); Hardware, INTEGRATED
                 CIRCUITS, Types and Design Styles, Gate arrays;
                 Computer Systems Organization, PROCESSOR ARCHITECTURES,
                 Multiple Data Stream Architectures (Multiprocessors),
                 Interconnection architectures",
  fjournal =     "Computer",
  genterm =      "DESIGN; MANAGEMENT; PERFORMANCE; ECONOMICS",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
  journalabbrev = "Computer",
  reviewer =     "P. C. Patton",
  subject =      "C. Computer Systems Organization; C.5 COMPUTER SYSTEM
                 IMPLEMENTATION; C. Computer Systems Organization; C.5
                 COMPUTER SYSTEM IMPLEMENTATION; B. Hardware; B.4
                 INPUT/OUTPUT AND DATA COMMUNICATIONS; B. Hardware; B.7
                 INTEGRATED CIRCUITS; C. Computer Systems Organization;
                 C.1 PROCESSOR ARCHITECTURES",
}

@Book{Jorke:1989:AAM,
  author =       "G{\"u}nter Jorke and Bernhard Lampe and Norbert
                 Wengel",
  title =        "{Arithmetische Algorithmen der Mikrorechentechnik}
                 \toenglish {Arithmetic Algorithms of Microcomputing}
                 \endtoenglish",
  publisher =    pub-VEB-VERLAG-TECHNIK,
  address =      pub-VEB-VERLAG-TECHNIK:adr,
  pages =        "323",
  year =         "1989",
  ISBN =         "3-341-00515-3",
  ISBN-13 =      "978-3-341-00515-6",
  LCCN =         "????",
  bibdate =      "Fri Sep 16 16:30:36 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  xxnote =       "fpbiblio.txt 1.8 has order Lampe, Jorke, Wengel, but
                 RLIN catalog has Jorke, Lampe, Wengel.",
}

@Article{Joslin:1989:EPN,
  author =       "David A. Joslin",
  title =        "Extended {Pascal} --- numerical features",
  journal =      j-SIGPLAN,
  volume =       "24",
  number =       "6",
  pages =        "77--80",
  month =        jun,
  year =         "1989",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:15:40 MST 2003",
  bibsource =    "Compendex database; http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Extended Pascal standard, drafted by the Joint
                 X3J9\slash IEEE-770 Pascal Standards Committee (JPC) in
                 conjunction with the ISO Pascal working group
                 (ISO\slash IEC JTC1\slash SC22\slash WG2), completed
                 its second public comment period at the end of 1988.
                 The comments received have been considered by JPC and
                 the ISO group, and the standard is now almost certainly
                 in its final form. Earlier papers by this author
                 described the main features of the standard by means of
                 illustrative examples. This is now the first in an
                 occasional series of articles, by this author and other
                 JPC \& WG2 members, describing in more detail various
                 extensions which have been made to the Pascal language;
                 rationale is given where appropriate. This paper
                 describes the predefined type COMPLEX, the range and
                 precision of type REAL, and the EXPONENTIATION
                 operators.",
  acknowledgement = ack-nhfb,
  affiliationaddress = "Middlesbrough, Engl",
  classification = "723; 902",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  journalabr =   "SIGPLAN Not",
  keywords =     "Complex Arithmetic; Computer Operating
                 Systems--Program Compilers; Computer Programming
                 Languages; design; Extended Pascal; languages; pascal;
                 standardization; Standards",
  subject =      "D.2.1 Software, SOFTWARE ENGINEERING,
                 Requirements/Specifications \\ D.3.2 Software,
                 PROGRAMMING LANGUAGES, Language Classifications,
                 Pascal",
}

@TechReport{Jouppi:1989:UVSa,
  author =       "Norman Paul Jouppi and Jonathan Bertoni and David
                 Wayne Wall",
  title =        "A unified vector\slash scalar floating-point
                 architecture",
  institution =  "Digital Western Research Laboratory",
  address =      "Palo Alto, CA, USA",
  pages =        "v + 23",
  month =        jul,
  year =         "1989",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "WRL research report; 89/8",
  acknowledgement = ack-nhfb,
  keywords =     "Computer architecture.; Floating-point arithmetic.;
                 MultiTitan (Computer); Scalar field theory.;
                 Supercomputers.; Vector processing (Computer science)",
}

@Article{Jouppi:1989:UVSb,
  author =       "N. P. Jouppi and J. Bertoni and D. W. Wall",
  title =        "A unified vector\slash scalar floating-point
                 architecture",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "17",
  number =       "2",
  pages =        "134--143",
  month =        apr,
  year =         "1989",
  CODEN =        "CANED2",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Fri May 12 09:40:39 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
}

@Misc{Kahan:1989:PCA,
  author =       "W. Kahan",
  title =        "Paradoxes in Concepts of Accuracy",
  howpublished = "Lecture notes from Joint Seminar on Issues and
                 Directions in Scientific Computation, Berkeley",
  year =         "1989",
  bibdate =      "Sat Sep 17 18:40:08 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kak:1989:BAS,
  author =       "S. C. Kak and A. O. Barbir",
  booktitle =    "Proceedings of the Twenty-First Southeastern Symposium
                 on System Theory, 26--28 March 1989",
  title =        "The {Brahmagupta} algorithm for square rooting",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "456--459",
  year =         "1989",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "An algorithm for square root evaluation is introduced.
                 Novel features of the algorithm include suitability for
                 parallel processing and multi-initial guesses of the
                 root. An extension of the algorithm to the nth rooting
                 is provided. A VLSI \ldots{}",
}

@Article{Kaneko:1989:VRM,
  author =       "K. Kaneko and T. Okamoto and M. Nakajima and Y.
                 Nakakura and S. Gokita and J. Nishikawa and Y. Tanikawa
                 and H. Kadota",
  title =        "A {VLSI RISC} with {20-MFLOPS} peak, 64-bit
                 floating-point unit",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "24",
  number =       "5",
  pages =        "1331--1340",
  month =        oct,
  year =         "1989",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "A microprocessor designed as a processing element of a
                 scientific parallel computer system is described. This
                 chip consists of a simple integer processor core and
                 dedicated floating-point hardware and executes 64-bit
                 floating-point addition, subtraction \ldots{}",
}

@Article{Kaneko:1989:VRP,
  author =       "K. Kaneko and T. Okamoto and M. Nakajima and Y.
                 Nakakura and S. Gokita and J. Nishikawa and Y. Tanikawa
                 and H. Kadota",
  title =        "A {VLSI RISC} with 20-{MFLOPS} peak, 64-bit
                 floating-point unit",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "24",
  number =       "5",
  pages =        "1331--1340",
  month =        oct,
  year =         "1989",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A microprocessor designed as a processing element of a
                 scientific parallel computer system is described. This
                 chip consists of a simple integer processor core and
                 dedicated floating-point hardware and executes 64-bit
                 floating-point addition, subtraction, and
                 multiplication at a rate of every 50 ns and division
                 every 350 ns. The processor, which employs RISC
                 architecture and Harvard-style bus organization,
                 executes most of the 47 instructions in one 50-ns
                 cycle. The chip is fabricated in 1.2- mu m n-well CMOS
                 technology, containing 440K transistors in a
                 14.4*13.5-mm/sup 2/ die. The authors provide an
                 overview of the processor, especially focusing on the
                 functions for a parallel system, floating-point
                 hardware, and the new divide algorithm.",
  acknowledgement = ack-nhfb,
  affiliation =  "Semicond. Research Center, Matsushita Electr. Ind.
                 Co., Ltd., Osaka, Japan",
  classification = "B1265F (Microprocessors and microcomputers); B2570D
                 (CMOS integrated circuits); C5130 (Microprocessor
                 chips); C5230 (Digital arithmetic methods)",
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "1.2 Micron; 20 MFLOPS; 350 Ns; 50 Ns; 64 Bit;
                 Addition; Dedicated floating-point hardware; Division;
                 Floating-point unit; Harvard-style bus organization;
                 Integer processor core; Microprocessor; Multiplication;
                 N-well CMOS technology; RISC architecture; Scientific
                 parallel computer system; Subtraction; VLSI",
  numericalindex = "Computer speed 2.0E+07 FLOPS; Word length 6.4E+01
                 bit; Time 5.0E-08 s; Time 3.5E-07 s; Size 1.2E-06 m",
  thesaurus =    "CMOS integrated circuits; Digital arithmetic;
                 Microprocessor chips; Parallel processing; Reduced
                 instruction set computing; VLSI",
}

@InProceedings{Kawarai:1989:OPM,
  author =       "S. Kawarai and T. Murakami",
  booktitle =    "Acoustics, Speech, and Signal Processing, 1989.
                 {ICASSP-89., 1989} International Conference on. 23--26
                 May 1989",
  title =        "An optimization procedure to minimize the roundoff
                 noise in cascade floating-point digital filters",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "884--887",
  year =         "1989",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The authors study the roundoff errors in
                 floating-point arithmetic and present an optimization
                 procedure for cascade floating-point digital filters.
                 Applying the isosceles trapezoidal distribution to the
                 error analysis of cascade floating-point \ldots{}",
}

@Article{Kawasaki:1989:FPV,
  author =       "S. Kawasaki and M. Watabe and S. Morinaga",
  title =        "A floating-point {VLSI} chip for the {TRON}
                 architecture: an architecture for reliable numerical
                 programming",
  journal =      j-IEEE-MICRO,
  volume =       "9",
  number =       "3",
  pages =        "26--44",
  month =        may # "\slash " # jun,
  year =         "1989",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/40.31476",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  summary =      "A description is given of the Gmicro/FPU
                 (floating-point unit), a chip that provides
                 floating-point instructions for both the Gmicro/200 and
                 the Gmicro/300 microprocessors. The VLSI
                 central-processing-unit architecture, for which it is
                 designed, \ldots{}",
}

@InProceedings{Koc:1989:SAI,
  author =       "{\c{C}}. K. Ko{\c{c}} and P. R. Cappello",
  title =        "Systolic arrays for integer {Chinese} remaindering",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "216--223",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Koc.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9",
}

@InProceedings{Kohn:1989:ISM,
  author =       "L. Kohn and N. Margulis",
  title =        "The {i860} 64-bit supercomputing microprocessor",
  crossref =     "ACM:1989:PSN",
  pages =        "450--456",
  year =         "1989",
  bibdate =      "Wed Apr 15 19:32:44 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5220 (Computer architecture)",
  corpsource =   "Intel Corp., Santa Clara, CA, USA",
  keywords =     "64 bit; caches; floating point unit; i860 64-bit
                 supercomputing microprocessor; Intel; memory
                 management; microprocessor chips; multiplier units;
                 parallel architectures; parallelism; pipelined adder;
                 pipelining; reduced instruction set computing; RISC
                 based microprocessor; three-dimensional graphics",
  sponsororg =   "ACM; IEEE",
  treatment =    "P Practical",
}

@InProceedings{Kohn:1989:TM,
  author =       "L. Kohn and S.-W. Fu",
  title =        "A 1,000,000 Transistor Microprocessor",
  crossref =     "Wuorinen:1989:DTP",
  pages =        "54--55, 290",
  year =         "1989",
  bibdate =      "Wed Sep 7 22:32:01 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Komori:1989:FPE,
  author =       "S. Komori and H. Takata and T. Tamura and F. Asai and
                 T. Ohno and O. Tomisawa and T. Yamasaki and K. Shima
                 and H. Nishikawa and H. Terada",
  title =        "A 40-{MFLOPS} 32-bit floating-point processor with
                 elastic pipeline scheme",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "24",
  number =       "5",
  pages =        "1341--1347",
  month =        oct,
  year =         "1989",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The authors present a 40-MFLOPS 32-bit floating-point
                 processor (FP) which is a component chip for a
                 data-driven single-board processor. The FP is the first
                 practical LSI chip which has introduced the elastic
                 pipeline scheme. All parts in the FP are autonomously
                 controlled by self-timed circuits, and no system clock
                 is needed for processing. The elastic pipeline scheme
                 provides data buffering capability and stabilization of
                 circuit operation at the same time. Pipelining has been
                 extensively utilized so that high throughput over
                 40-MFLOPS can be achieved. An automatic power
                 conservation technique, called `latch mode control', is
                 also described.",
  acknowledgement = ack-nhfb,
  affiliation =  "LSI Res. and Dev. Lab., Misubishi Electr. Corp.,
                 Hyogo, Japan",
  classification = "B1265F (Microprocessors and microcomputers); B2570
                 (Semiconductor integrated circuits); C5130
                 (Microprocessor chips)",
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "32 Bit; 40 MFLOPS; Automatic power conservation;
                 Component chip; Data buffering capability; Data-driven
                 single-board processor; Elastic pipeline scheme;
                 Floating-point processor; Latch mode control; LSI chip;
                 Microprocessor; Self-timed circuits; Stabilization",
  numericalindex = "Computer speed 4.0E+07 FLOPS; Word length 3.2E+01
                 bit",
  thesaurus =    "Large scale integration; Microprocessor chips;
                 Pipeline processing",
}

@InProceedings{Komori:1989:MBFa,
  author =       "S. Komori and H. Takata and T. Tamura and F. Asai and
                 T. Ohno and O. Tomisawa and T. Yamasaki and K. Shima
                 and H. Nishikawa and H. Terada",
  title =        "A 40 {MFLOPS} 32-bit Floating-Point Processor",
  crossref =     "Wuorinen:1989:DTP",
  pages =        "46--47, 286",
  year =         "1989",
  bibdate =      "Wed Sep 7 22:32:01 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Komori:1989:MBFb,
  author =       "S. Komori and H. Takata and T. Tamura and F. Asai and
                 T. Ohno and O. Tomisawa and T. Yamasaki and K. Shima
                 and H. Nishikawa and H. Terada",
  title =        "A {40-MFLOPS} 32-bit floating-point processor with
                 elastic pipeline scheme",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "24",
  number =       "5",
  pages =        "1341--1347",
  month =        oct,
  year =         "1989",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "The authors present a 40-MFLOPS 32-bit floating-point
                 processor (FP) which is a component chip for a
                 data-driven single-board processor. The FP is the first
                 practical LSI chip which has introduced the elastic
                 pipeline scheme. All parts in the FP are \ldots{}",
}

@InProceedings{Komori:1989:MFP,
  author =       "S. Komori and H. Takata and T. Tamura and F. Asai and
                 T. Ohno and O. Tomisawa and T. Yamasaki and K. Shima
                 and H. Nishikawa and H. Terada",
  title =        "A 40 {MFLOPS} 32-bit floating-point processor",
  crossref =     "Wuorinen:1989:DTP",
  pages =        "46--47, 286",
  year =         "1989",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A 40 MFLOPS (million floating-point operations per
                 second), 32-bit floating-point processor (FP) for a
                 single-board data-driven processor is developed using a
                 pipeline configuration called the elastic pipeline
                 structure. Because there is no need to add controls for
                 pipeline flushing by virtue of the data-driven
                 processing principle, it is possible to employ
                 extensively subdivided pipeline stages. The elastic
                 mode of data transfer between pipeline stages and
                 distributed execution controls along the pipeline
                 result in minimum deterioration of the inherent logic
                 switching speed. The structure of the FP is shown
                 together with details of the ALU (arithmetic logic
                 unit) block. The fabrication process and chip
                 specifications are summarized.",
  acknowledgement = ack-nhfb,
  affiliation =  "Mitsubishi Electr. Corp., Hyogo, Japan",
  classification = "B1265F (Microprocessors and microcomputers); B2570D
                 (CMOS integrated circuits); C5130 (Microprocessor
                 chips); C5220 (Computer architecture); C5230 (Digital
                 arithmetic methods)",
  keywords =     "32 Bit; 40 MFLOPS; ALU; Chip specifications; CMOS
                 chip; Data transfer; Distributed execution controls;
                 Elastic pipeline structure; Fabrication process;
                 Floating-point processor; Logic switching speed;
                 Pipeline configuration; Single-board data-driven
                 processor; Subdivided pipeline stages",
  numericalindex = "Computer speed 4.0E+07 FLOPS; Word length 3.2E+01
                 bit",
  thesaurus =    "CMOS integrated circuits; Digital arithmetic;
                 Microprocessor chips; Pipeline processing",
}

@InProceedings{Kornerup:1989:ERB,
  author =       "Peter Kornerup and David W. Matula",
  title =        "Exploiting Redundancy in Bit-Pipelined Rational
                 Arithmetic",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "119--126",
  year =         "1989",
  DOI =          "https://doi.org/10.1109/ARITH.1989.72817",
  bibdate =      "Wed Nov 14 18:29:43 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Kornerup.pdf",
  abstract =     "The authors develop and analyze a redundant
                 continued-fraction representation of the rationals in
                 the implementation of an arithmetic unit for computing
                 the sum, difference, product, quotient, and other
                 useful functions of two rational operands. Their
                 representation of operands and results allows the
                 computations of the unit to be performed in a signed
                 bit-serial, online fashion. Several such units can then
                 be interconnected for the computation of more
                 complicated expressions in a pipelined manner.
                 Redundancy is used to help achieve a small bounded
                 online delay and uniform throughput",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9",
}

@InProceedings{Krishna:1989:NAC,
  author =       "H. Krishna and Kuo Yu Lin",
  booktitle =    "Twenty-Third Asilomar Conference on Signals, Systems
                 and Computers, 1989",
  title =        "New algorithms for correcting errors in redundant
                 residue number systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "653--657",
  year =         "1989",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICASSP.1989.266586",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
}

@InProceedings{Krishnan:1989:CBN,
  author =       "R. Krishnan",
  booktitle =    "Twenty-Third Asilomar Conference on Signals, Systems
                 and Computers, 1989",
  title =        "Conventional binary number system ({BNS}) versus
                 residue number system ({RNS}) digital signal processing
                 architecture suitable for complex digital filtering",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "873--877",
  year =         "1989",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICASSP.1989.266586",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
}

@InProceedings{Krishnan:1989:ESA,
  author =       "R. Krishnan",
  booktitle =    "International Conference on Acoustics, Speech, and
                 Signal Processing, {ICASSP-89, 23--26} May 1989",
  title =        "An efficient systolic array {VLSI} cell architecture
                 for the implementation of transversal filter based on
                 the quadratic residue number systems",
  volume =       "4",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2585--2588",
  year =         "1989",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICASSP.1989.266996",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The author presents efficient direct and indirect
                 implementations of transversal filter architectures
                 using the quadratic residue number system (QRNS). In
                 the case of the direct transversal filter, a systolic
                 array architecture has been developed \ldots{}",
}

@Misc{Kulisch:1989:CGS,
  author =       "Ulrich Kulisch and Reinhard Kirchner",
  title =        "Circuitry for generating sums, especially scalar
                 products",
  howpublished = "US Patent 4866653",
  day =          "12",
  month =        sep,
  year =         "1989",
  bibdate =      "Mon Dec 29 16:20:01 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/4866653/fulltext.html",
  abstract =     "Circuitry for the summation, especially for
                 generation, of scalar products, to which one summand in
                 floating-point representation is conveyed per machine
                 cycle (ZT), in which, after conversion into fixed point
                 representation, it is received in a summing unit with
                 an accumulator (AS1,-AS4) comprising the whole exponent
                 range. The accumulator is subdivided into row sections,
                 which are longer than the mantissa of the summands.
                 Partial exponents (EPK1,-EPK4) generated in an exponent
                 analyzer (EXA) control the mantissa positioner (PM) or
                 are allocated to the mantissas and delivered
                 continuously and cycle-wise to transfer registers
                 (RE1,-RE4; RVS1,-RVS4; RNS1, RNS4), controlling
                 summation row-wise. The carriers are allocated to the
                 accumulator sections and intermediately stored in carry
                 memory sections (CS1,-CS4) and are not added digit
                 positionwise to the contents of each adjacent memory
                 section until the sum is output, further carries being
                 continuously processed. Afterwards the rounded result
                 mantissa (ME) is generated in transfer registers (RA1,
                 RA2, RPR) arranged downstream and the result exponent
                 (EE) is generated in an exponent generator (EXG).",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lai:1989:HNS,
  author =       "F. S. Lai and C. E. Wu",
  title =        "A hybrid number system multiplier for graphics and
                 complex arithmetic applications",
  crossref =     "IEEE:1989:ISV",
  pages =        "352--356",
  year =         "1989",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A hybrid multiplier design which supports 32-bit
                 floating-point, 24-bit fixed-point and 32-bit
                 logarithmic number systems is described. Except for
                 additions and subtractions, floating-point operations
                 such as multiplication, division, and square root are
                 all performed in the logarithmic number system domain.
                 A modified squaring approach is adopted for fixed-point
                 multiplications with little extra hardware. The
                 performance of this multiplier is shown to be superior
                 to that of conventional binary multipliers for most
                 graphics and digital signal processing applications,
                 and the size of the multiplier is comparable to that of
                 conventional multipliers in terms of silicon area.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Thomas J. Watson Res Center, Yorktown-Heights, NY,
                 USA",
  classification = "B1265B (Logic circuits); C5230 (Digital arithmetic
                 methods); C5260 (Digital signal processing); C5540
                 (Terminals and graphic displays)",
  keywords =     "Complex arithmetic; Digital signal processing;
                 Division; Fixed-point multiplications; Floating-point
                 operations; Graphics; Hybrid number system multiplier;
                 Logarithmic number; Modified squaring approach;
                 Multiplication; Square root",
  thesaurus =    "Computer graphic equipment; Computerised signal
                 processing; Digital arithmetic; Multiplying circuits",
}

@InProceedings{Langston:1989:DBT,
  author =       "J. L. Langston and K. Hinman",
  booktitle =    "{IEEE} Military Communications Conference, 1989.
                 {MILCOM '89}. Conference Record. Bridging the Gap.
                 Interoperability, Survivability, Security, 1989",
  title =        "Digital beamforming techniques and processors based on
                 quadratic residue number system techniques",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "609--614",
  year =         "1989",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MILCOM.1989.103997",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A very-high-performance digital beamforming processor
                 has been implemented using ASICs (application-specific
                 integrated circuits) fabricated in readily available
                 commercial CMOS process technology by using QRNS
                 (quadratic residue number system) \ldots{}",
}

@TechReport{Lee:1989:FIR,
  author =       "Jeong-A Lee and Tomas Lang",
  title =        "Floating-point implementation of redundant {CORDIC}
                 for {QR} decomposition",
  type =         "Technical report",
  number =       "CSD-890044",
  institution =  "Computer Science Dept., University of California",
  address =      "Los Angeles, CA, USA",
  pages =        "15 + 8",
  year =         "1989",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Decomposition method.; Matrices.",
  remark =       "``July 1989.'' Supported by the National Science
                 Foundation.",
}

@Article{Lee:1989:MGR,
  author =       "Corinna Lee",
  title =        "Multistep Gradual Rounding",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "38",
  number =       "4",
  pages =        "595--600",
  month =        apr,
  year =         "1989",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.21152",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jul 8 19:00:39 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "http://dlib.computer.org/tc/books/tc1989/pdf/t0593.pdf;
                 http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=21152;
                 http://www.computer.org/tc/tc1989/t0595abs.htm",
  abstract =     "A value $V$ is to be rounded to an arbitrary precision
                 resulting in the value $ V' $. Conventional rounding
                 technique uses one step to accomplish this.
                 Alternatively, {\em multistep rounding\/} uses several
                 steps to round the value $V$ to successively shorter
                 precisions with the final rounding step producing the
                 desired value $ V' $. This alternate rounding method is
                 one way to implement, with the minimum of hardware, the
                 denormalization process that the IEEE Floating-Point
                 Standard 754 requires when underflow occurs. There are
                 certain cases for which multistep rounding produces a
                 different result than single-step rounding. To prevent
                 such a {\em step error}, the author introduces a
                 rounding procedure called {\em gradual rounding} that
                 is very similar to conventional rounding with the
                 addition of two tag bits associated with each
                 floating-point register.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "double rounding",
}

@Article{Lee:1989:QCC,
  author =       "Jon Lee",
  title =        "A quirk of the {CRAY CFT77} compiler: {IF} (logical)
                 in lieu of {IF} (arithmetic)",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "3",
  number =       "4",
  pages =        "351--355",
  month =        dec,
  year =         "1989",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1007/BF00128170",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Wed Jul 6 11:13:01 MDT 2005",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0920-8542&volume=3&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0920-8542&volume=3&issue=4&spage=351",
  acknowledgement = ack-nhfb,
  affiliation =  "Flight Dynamics Lab., Wright-Patterson AFB, OH, USA",
  classification = "C5440 (Multiprocessor systems and techniques); C6110
                 (Systems analysis and programming); C6150C (Compilers,
                 interpreters and other processors); C7440 (Civil and
                 mechanical engineering)",
  corpsource =   "Flight Dynamics Lab., Wright-Patterson AFB, OH, USA",
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
  keywords =     "CFT77 compiler; CIVIC; computational fluid dynamics
                 code; conditional IF exit; DO-loops; homogeneous
                 turbulence; optimised code; parallel programming;
                 program compilers; vectorization",
  treatment =    "X Experimental",
}

@Book{Levy:1989:CPA,
  author =       "Henry M. Levy and Richard H. {Eckhouse, Jr.}",
  title =        "Computer programming and architecture: the {VAX}",
  publisher =    pub-DP,
  address =      pub-DP:adr,
  edition =      "Second",
  pages =        "xix + 444",
  year =         "1989",
  ISBN =         "1-55558-015-7",
  ISBN-13 =      "978-1-55558-015-5",
  LCCN =         "QA76.8.V32 L48 1989",
  bibdate =      "Wed Sep 14 22:51:31 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lewis:1989:ADB,
  author =       "D. M. Lewis and L. K. Yu",
  title =        "Algorithm design for a 30-bit integrated logarithmic
                 processor",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "192--199",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Lewis.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9",
}

@InProceedings{Lin:1989:LCA,
  author =       "H. Lin and H. J. Sips",
  title =        "On-line {CORDIC} algorithms",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "26--33",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Lin.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9",
}

@InProceedings{Lo:1989:CED,
  author =       "J.-C. Lo and S. Thanawastien and T. R. N. Rao",
  title =        "Concurrent error detection in arithmetic and logical
                 operations using {Berger} codes",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "233--240",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Lo.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9",
}

@InProceedings{Lu:1989:VMI,
  author =       "P. Y. Lu and K. Dawallu",
  title =        "A {VLSI} Module for {IEEE} Floating-Point
                 Multiplication\slash Division\slash Square Root",
  crossref =     "IEEE:1989:PII",
  bookpages =    "xvii + 587",
  pages =        "366--368",
  year =         "1989",
  bibdate =      "Wed Nov 06 12:08:38 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The major objective of this VLSI module design is to
                 determine how to modify a fast floating-point
                 multiplier so that it can perform division and square
                 root in accordance with IEEE standards. This has been
                 achieved by applying the Newton-Ralphson iteration only
                 on the mantissa and adjusting the iterated result by a
                 rounding algorithm. Using 1.0- mu m CMOS standard cell
                 technology, the total area of this module is
                 approximately 7.0 mm*6.5 mm, which is just 25\% larger
                 than the floating-point multiplier. The module can
                 compute multiplication, division, and square root in 3,
                 31, and 43 cycles, respectively. The cycle time, under
                 nominal conditions, is expected to be 20 ns. (2
                 Refs.)",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "LSI Logic Corp., Menlo Park, CA, USA",
  classification = "B1265B (Logic circuits); B2570D (CMOS integrated
                 circuits); C4130 (Interpolation and function
                 approximation); C5230 (Digital arithmetic methods)",
  keywords =     "1 Micron; 20 Ns; 7 To 6.5 mm; CMOS standard cell
                 technology; Cycle time; Fast floating-point multiplier;
                 Floating point division; Floating point square root;
                 IEEE standards; Iterated result; Mantissa; Multiplier
                 modification; Newton-Ralphson iteration; Rounding
                 algorithm; VLSI module design",
  numericalindex = "Time 2.0E-08 s; Size 1.0E-06 m; Size 6.5E-03 to
                 7.0E-03 m",
  thesaurus =    "Cellular arrays; CMOS integrated circuits; Digital
                 arithmetic; Dividing circuits; Iterative methods;
                 Modules; Multiplying circuits; VLSI",
}

@InProceedings{Malarkey:1989:RNS,
  author =       "E. C. Malarkey and G. E. Marx and J. D. Fogarty and D.
                 Mergerian and H. K. Hahn and J. C. Bradley and P. R.
                 Beaudet and R. Fenton",
  booktitle =    "{IEEE} Military Communications Conference, 1989.
                 {MILCOM '89}. Conference Record. Bridging the Gap.
                 Interoperability, Survivability, Security, 1989",
  title =        "Residue-number-system-based optical adaptive
                 processor",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "620--623",
  year =         "1989",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MILCOM.1989.103999",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "An optical adaptive processor with 4 degrees of
                 freedom is under development. This processor is based
                 upon the use of optical lookup tables and operates
                 within the residue number system to provide adaptive
                 tap weights for nulling applications. The \ldots{}",
}

@InProceedings{Mansour:1989:CAS,
  author =       "Y. Mansour and B. Schieber and P. Tiwari",
  booktitle =    "30th Annual Symposium on Foundations of Computer
                 Science, 1989",
  title =        "The complexity of approximating the square root",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "325--330",
  year =         "1989",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The authors prove upper and lower bounds for
                 approximately computing the square root using a given
                 set of operations. The bounds are extended to hold for
                 approximating the kth root, for any fixed k. Several
                 tools from approximation \ldots{}",
}

@Article{Marshall:1989:TUT,
  author =       "Mark Marshall",
  title =        "Techniques for user testing of the 68882",
  journal =      j-MICROPROC-MICROSYS,
  volume =       "13",
  number =       "6",
  pages =        "382--386",
  month =        jul # "\slash " # aug,
  year =         "1989",
  CODEN =        "MIMID5",
  ISSN =         "0141-9331 (print), 1872-9436 (electronic)",
  ISSN-L =       "0141-9331",
  bibdate =      "Sat Nov 9 08:26:18 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "NCR Corp., Wichita, KS",
  bibno =        "72545",
  catcode =      "B.5.3; C.5.3; B.5.1",
  content =      "This short, clearly written paper describes how NCR
                 Corporation developed a series of programs to test the
                 Motorola 68882 floating-point coprocessor for
                 Motorola's 68020 and 68030 microprocessors. Integrated
                 circuits are tested for two reasons: to ensure that a
                 properly working unit meets its specifications, and to
                 ensure that a particular unit works properly. As
                 Marshall points out, manufacturers cannot always be
                 relied upon to perform either of these tests perfectly.
                 The programs described in this paper have been used
                 both to monitor the quality of incoming parts and to
                 verify that device mask or specification changes do not
                 effect the part's usability for NCR's
                 purposes.\par

                 This paper describes the methods by which NCR's
                 2700-instruction, 550,000-clock cycle test program was
                 developed and how it works. Since the internal workings
                 of the 68882 are not visible to the user, NCR adopted
                 the functional testing approach. Of particular interest
                 is NCR's sequential approach to the testing proper,
                 which assumes that ``no element is functional unless
                 previously tested.'' While the specifics of each step
                 vary from one microprocessor to another, the principles
                 still apply.\par

                 This is not a research paper. It does not disclose
                 startling new results or advance the frontiers of human
                 knowledge. It does show how state-of-the-art
                 engineering practice can achieve desirable \ldots{}",
  CRclass =      "B.5.3 Reliability and Testing; B.5.3 Test generation;
                 C.5.3 Microcomputers; B.5.1 Design",
  CRnumber =     "9006-0473",
  descriptor =   "Hardware, REGISTER-TRANSFER-LEVEL IMPLEMENTATION,
                 Reliability and Testing, Test generation; Computer
                 Systems Organization, COMPUTER SYSTEM IMPLEMENTATION,
                 Microcomputers; Hardware, REGISTER-TRANSFER-LEVEL
                 IMPLEMENTATION, Design",
  fjournal =     "Microprocessors and Microsystems",
  genterm =      "ALGORITHMS; DESIGN; VERIFICATION",
  guideno =      "1989-09211",
  journalabbrev = "Microprocess. Microsyst.",
  keywords =     "floating-point testing",
  reviewer =     "E. Mallach",
  subject =      "B. Hardware; B.5 REGISTER-TRANSFER-LEVEL
                 IMPLEMENTATION; C. Computer Systems Organization; C.5
                 COMPUTER SYSTEM IMPLEMENTATION; B. Hardware; B.5
                 REGISTER-TRANSFER-LEVEL IMPLEMENTATION",
}

@Article{Mastrovito:1989:VDM,
  author =       "E. D. Mastrovito",
  title =        "{VLSI} designs for multiplication over finite fields
                 {$ \mathrm {GF}(2^m) $}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "357",
  pages =        "397--309",
  year =         "1989",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Fri Jun 24 21:09:00 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Maytal:1989:DCG,
  author =       "B. Maytal and S. Iacobovici and D. B. Alpert and D.
                 Biran and J. Levy and S. Y. Tov",
  title =        "Design considerations for a general-purpose
                 microprocessor",
  journal =      j-COMPUTER,
  volume =       "22",
  number =       "1",
  pages =        "66--76",
  month =        jan,
  year =         "1989",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Sat Sep 14 07:29:35 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Misc/IMMD_IV.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Nat. Semicond., Santa Clara, CA, USA",
  classification = "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5220 (Computer architecture)",
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
  keywords =     "32 Bit; Clock frequency; Data-flow monitoring
                 mechanisms; Floating-point operations; General-purpose
                 microprocessor; Instruction-flow; Market requirements;
                 Memory hierarchy; Memory reference transactions;
                 Microarchitecture; Multiprocessing support; NS 32532;
                 On-chip caches; Packaging technologies; Pipeline;
                 System interface; Target applications; VLSI",
  numericalindex = "Word length 3.2E+01 bit",
  thesaurus =    "Computer architecture; Microcomputers; Microprocessor
                 chips",
}

@InProceedings{Milenkovic:1989:DPG,
  author =       "V. Milenkovic",
  booktitle =    "30th Annual Symposium on Foundations of Computer
                 Science, 1989",
  title =        "Double precision geometry: a general technique for
                 calculating line and segment intersections using
                 rounded arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "500--505",
  year =         "1989",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:03 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "For the first time it is shown how to reduce the cost
                 of performing specific geometric constructions by using
                 rounded arithmetic instead of exact arithmetic. By
                 exploiting a property of floating-point arithmetic
                 called monotonicity, a technique \ldots{}",
}

@Article{Milutinovic:1989:MSD,
  author =       "V. Milutinovic and M. Bettinger and W. Helbig",
  title =        "Multiplier\slash shifter design tradeoffs in a 32-bit
                 microprocessor",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "38",
  number =       "6",
  pages =        "874--880",
  month =        jun,
  year =         "1989",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.24298",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jul 8 19:00:40 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=24298",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Molnar:1989:MBF,
  author =       "K. Molnar and C.-Y. Ho and D. Staver and B. Davis and
                 R. Jerdonek",
  title =        "A 40 {MHz} 64-Bit Floating-Point Co-Processor",
  crossref =     "Wuorinen:1989:DTP",
  pages =        "48--49, 287",
  year =         "1989",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "An arithmetic coprocessor capable of executing 64-bit
                 double-precision floating-point, 32-bit
                 single-precision floating-point, and 32-bit integer
                 instructions has been integrated onto a 1.0-cm*1.1-cm
                 chip in a 1.2- mu m, single-poly, double-metal bulk
                 CMOS process. The chip contains 17000 transistors and
                 includes a register file, two accumulators, and
                 separate interface, multiplication, and addition
                 subprocessors. The coprocessor which is the arithmetic
                 unit for a multichip microprocessor system, is packaged
                 in a 132-pin leadless ceramic chip carrier. The
                 coprocessor can be issued a new instruction each 25-ns
                 clock cycle, and 64-bit double-precision arithmetic
                 with full IEEE rounding is executed at a peak rate of
                 26.7 MFLOPs (million floating-point operations per
                 second). The waveforms of a store instruction operating
                 at 40 MHz are shown.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Gen. Electr. Corp. Res. and Dev. Center, Schenectady,
                 NY, USA",
  classification = "B1265F (Microprocessors and microcomputers); B2570D
                 (CMOS integrated circuits); C5130 (Microprocessor
                 chips); C5230 (Digital arithmetic methods)",
  keywords =     "1.2 Micron; 26.7 MFLOPS; 32-Bit integer instructions;
                 40 MHz; 64 Bit; Accumulators; Addition subprocessors;
                 Arithmetic coprocessor; Double-metal bulk CMOS process;
                 Double-precision floating-point; Floating point
                 coprocessor; Interface subprocessor; Leadless ceramic
                 chip carrier; Multichip microprocessor system;
                 Multiplication subprocessor; Peak rate; Register file;
                 Single-precision floating-point; Store instruction;
                 Waveforms",
  numericalindex = "Frequency 4.0E+07 Hz; Word length 6.4E+01 bit; Size
                 1.2E-06 m; Computer speed 2.67E+07 FLOPS",
  thesaurus =    "CMOS integrated circuits; Digital arithmetic;
                 Microprocessor chips",
}

@InProceedings{Montuschi:1989:EIH,
  author =       "Paolo Montuschi and Luigi Cinimera",
  title =        "On the efficient implementation of higher radix square
                 root algorithms",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "154--161",
  year =         "1989",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Montuschi.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9",
  summary =      "Square root nonrestoring algorithms operating with a
                 radix higher than two (but power of 2) are discussed.
                 Formulas are derived delimiting the feasibility space
                 of the class of algorithms considered as a function of
                 the different parameters. This \ldots{}",
}

@Book{Moshier:1989:MPM,
  author =       "Stephen L. B. Moshier",
  title =        "Methods and Programs for Mathematical Functions",
  publisher =    pub-ELLIS-HORWOOD,
  address =      pub-ELLIS-HORWOOD:adr,
  pages =        "vii + 415",
  year =         "1989",
  ISBN =         "0-7458-0289-3",
  ISBN-13 =      "978-0-7458-0289-3",
  LCCN =         "QA331 .M84 1989",
  MRclass =      "*65D20, 26-04, 33-04, 65-02, 65C99",
  bibdate =      "Thu Sep 01 10:33:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\pounds 48.00",
  URL =          "http://www.moshier.net/;
                 http://www.netlib.org/cephes",
  ZMnumber =     "0701.65011",
  acknowledgement = ack-nj,
  shorttableofcontents = "Preface / vii \\
                 1: Floating Point Arithmetic / 1 \\
                 2: Approximation Methods / 75 \\
                 3: Software Notes / 129 \\
                 4: Elementary Functions / 143 \\
                 5: Probability Distributions and Related Functions /
                 201 6: Bessel Functions / 263 \\
                 7: Other Special Functions / 333 \\
                 Bibliography / 411 \\
                 Index / 413",
  tableofcontents = "Preface / vii \\
                 1: Floating Point Arithmetic / 1 \\
                 1.1 Numeric Data Structures / 1 \\
                 1.2 Rounding / 5 \\
                 1.3 Addition and Subtraction / 6 \\
                 1.4 Multiplication / 7 \\
                 1.4.1 Long Multiplication in Binary Radix / 8 \\
                 1.4.2 Multiplication in Word Integer Radix / 8 \\
                 1.4.3 Fast Multiplication / 9 \\
                 1.5 Division / 10 \\
                 1.5.1 Long Division / 10 \\
                 1.5.2 Division by Taylor Series / 11 \\
                 1.5.3 Newton--Raphson Division / 11 \\
                 1.6 C Language / 12 \\
                 1.7 An Extended Double Arithmetic: ieee.c / 13 \\
                 1.8 Binary - Decimal Conversion / 46 \\
                 1.8.1 etoasc.c / 47 \\
                 1.8.2 asctoe.c / 54 \\
                 1.9 Analysis of Error / 58 \\
                 1.9.1 Roundoff and Cancellation / 58 \\
                 1.9.2 Error Propagation / 60 \\
                 1.9.3 Error as a Random Variable / 61 \\
                 1.9.4 Order of Summation / 62 \\
                 1.10 Complex Arithmetic / 62 \\
                 1.10.1 cmplx.c / 64 \\
                 1.10.2 Absolute Value: cabs.c / 67 \\
                 1.11 Rational Arithmetic / 69 \\
                 1.11.1 euclid.c / 70 \\
                 2: Approximation Methods / 75 \\
                 2.1 Power Series / 75 \\
                 2.2 Chebyshev Expansions / 76 \\
                 2.2.1 chbevl.c / 79 \\
                 2.3 Pad{\'e} Approximations / 80 \\
                 2.4 Least Maximum Approximations / 82 \\
                 2.4.1 Best Polynomial Approximations / 82 \\
                 2.4.2 Best Rational Approximations / 85 \\
                 2.4.3 Special Rational Forms / 87 \\
                 2.5 A Program to Find Best Approximations: remes.c / 88
                 \\
                 2.6 Forms of Approximation / 111 \\
                 2.7 Asymptotic Expansions / 113 \\
                 2.8 Continued Fractions / 114 \\
                 2.8.1 Continued Fractions from Recurrences / 115 \\
                 2.8.2 Recurrences from Differential Equations / 116 \\
                 2.8.3 Computing Continued Fractions / 117 \\
                 2.9 Polynomials / 117 \\
                 2.9.1 polevl.c / 118 \\
                 2.10 Newton--Raphson Iterations / 119 \\
                 2.10.1 Division / 120 \\
                 2.10.2 Exponent Separation / 121 \\
                 2.10.3 Square Root / 122 \\
                 2.10.4 sqrt.c / 123 \\
                 2.10.5 Longhand Square Root / 124 \\
                 2.10.6 esqrt.c / 124 \\
                 2.10.7 Cube Root / 126 \\
                 2.10.8 cbrt.c / 127 \\
                 3: Software Notes / 129 \\
                 3.1 Design Strategy / 129 \\
                 3.2 Testing / 131 \\
                 3.3 System Utilities / 132 \\
                 3.3.1 mconf.h / 132 \\
                 3.3.2 mtherr.c / 134 \\
                 3.3.3 const.c / 136 \\
                 3.4 Arithmetic Utilities / 137 \\
                 3.4.1 efloor.c / 138 \\
                 3.4.2 efrexp.c / 140 \\
                 3.4.3 eldexp.c / 140 \\
                 4: Elementary Functions / 143 \\
                 4.1 $e^x$ / 143 \\
                 4.1.1 exp.c / 145 \\
                 4.2 $\ln x$ / 147 \\
                 4.2.1 log.c / 149 \\
                 4.3 Argument Transformation for Circular Functions /
                 152 \\
                 4.4 Sine and cosine / 153 \\
                 4.4.1 sin.c / 154 \\
                 4.4.2 cos.c / 156 \\
                 4.5 Tangent and Cotangent / 157 \\
                 4.5.1 tan.c / 158 \\
                 4.6 Complex Circular Functions / 161 \\
                 4.7 $\sin^{-1} x $ / 162 \\
                 4.7.1 asin.c / 163 \\
                 4.8 $\cos^{-1} x $ / 165 \\
                 4.8.1 acos.c / 165 \\
                 4.9 $\tan^{-1} x$ / 166 \\
                 4.9.1 atan.c / 168 \\
                 4.9.2 atan2.c / 169 \\
                 4.10 Complex Inverse Circular Functions / 170 \\
                 4.11 $\sinh x$ / 170 \\
                 4.11.1 sinh.c / 171 \\
                 4.12 $\cosh x$ / 172 \\
                 4.12.1 cosh.c / 173 \\
                 4.13 $\tanh x$ / 173 \\
                 4.13.1 tanh.c / 174 \\
                 4.14 $\sinh^{-1} x $ / 175 \\
                 4.14.1 asinh.c / 176 \\
                 4.15 $\cosh^{-1} x $ / 177 \\
                 4.15.1 acosh.c / 178 \\
                 4.16 $\tanh^{-1} x$ / 179 \\
                 4.16.1 atanh.c / 180 \\
                 4.17 Power Function / 181 \\
                 4.17.1 Real Exponent / 182 \\
                 4.17.2 pow.c / 182 \\
                 4.17.3 Integer Exponent / 189 \\
                 4.17.4 powi.c / 190 \\
                 4.18 Testing / 192 \\
                 4.19 Single Precision Polynomial Approximations / 193
                 \\
                 4.19.1 $\cos x$ / 193 \\
                 4.19.2 $\cosh^{-1} x $ / 193 \\
                 4.19.3 $\exp x$ / 196 \\
                 4.19.4 $\ln x$ / 196 \\
                 4.19.5 $\sin x$ / 197 \\
                 4.19.6 $\sin^{-1} x $ / 197 \\
                 4.19.7 Square Root / 197 \\
                 4.19.8 $\tan x$ / 198 \\
                 4.19.9 $\tan^{-1} x$ / 198 \\
                 4.19.10 $\tanh x$ / 199 \\
                 4.19.11 $tanh^{-1} x$ / 199 \\
                 5: Probability Distributions and Related Functions /
                 201 \\
                 5.1 $n!$ / 202 \\
                 5.1.1 fac.c / 204 \\
                 5.2 $\Gamma(x)$ / 206 \\
                 5.2.1 gamma.c / 210 \\
                 5.2.2 lgam.c / 214 \\
                 5.3 Incomplete Gamma Integral / 217 \\
                 5.3.1 igamc.c / 218 \\
                 5.3.2 igam.c / 220 \\
                 5.3.3 Functional Inverse of Incomplete Gamma Integral /
                 221 \\
                 5.3.4 igami.c / 221 \\
                 5.4 Gamma Distribution / 222 \\
                 5.4.1 gdtr c / 222 \\
                 5.4.2 gdtrc.c / 223 \\
                 5.5 $\chi^2$ Distribution / 223 \\
                 5.5.1 chdtrc.c / 224 \\
                 5.5.2 chdtr.c / 224 \\
                 5.5.3 chdtrl.c / 224 \\
                 5.6 Poisson Distribution / 225 \\
                 5.6.1 pdtrc.c / 225 \\
                 5.6.2 pdtr.c / 226 \\
                 5.6.3 pdtri.c / 226 \\
                 5.7 Beta Function / 227 \\
                 5.7.1 beta.c / 227 \\
                 5.8 Incomplete Beta Integral / 229 \\
                 5.8.1 ibet.c / 231 \\
                 5.8.2 Functional Inverse of Incomplete Beta Integral /
                 238 \\
                 5.9 Beta Distribution / 241 \\
                 5.9.1 btdtr.c / 241 \\
                 5.10 Binomial Distribution / 241 \\
                 5.10.1 bdtrc.c / 242 \\
                 5.10.2 bdtr.c / 243 \\
                 5.10.3 bdtri.c / 244 \\
                 5.11 Negative Binomial Distribution / 244 \\
                 5.11.1 nbdtr.c / 245 \\
                 5.11.2 nbdtrc.c / 245 \\
                 5.12 F Distribution / 246 \\
                 5.12.1 fdtrc.c / 247 \\
                 5.12.2 fdtr.c / 247 \\
                 5.12.3 fdtrci.c / 248 \\
                 5.13 Student's $t$ distribution / 249 \\
                 5.13.1 stdtr.c / 250 \\
                 5.14 Gaussian Distribution / 252 \\
                 5.14.1 ndtr.c / 254 \\
                 5.14.2 erfc.c / 256 \\
                 5.14.3 erf.c / 257 \\
                 5.14.4 Functional Inverse of Gaussian Distribution /
                 258 \\
                 5.14.5 ndtri.c / 259 \\
                 6: Bessel Functions / 263 \\
                 6.1 $J_0(x)$ / 263 \\
                 6.1.1 jO.c / 265 \\
                 6.2 $Y_0(x)$ / 268 \\
                 6.2.1 yO.c / 269 \\
                 6.3 Modulus and Phase / 270 \\
                 6.4 $J_1(x)$ / 271 \\
                 6.4.1 jl.c / 272 \\
                 6.5 $Y_1(x)$ / 275 \\
                 6.5.1 yl.c / 275 \\
                 6.6 $J_n(x)$ / 276 \\
                 6.1 $I_0(x)$ / 277 \\
                 6.7.1 i0.c / 278 \\
                 6.8 $I_1(x)$ / 281 \\
                 6.8.1 i1.c / 283 \\
                 6.9 $I_\nu(x)$ / 285 \\
                 6.9.1 iv.c / 286 \\
                 6.10 $K_0(x)$ / 287 \\
                 6.10.1 kO.c / 287 \\
                 6.11 $K_1(x)$ / 291 \\
                 6.11.1 kl.c / 291 \\
                 6.12 $K_n(x)$ / 294 \\
                 6.12.1 kn.c / 295 \\
                 6.13 $J_\nu(x)$ / 299 \\
                 6.13.1 jv.c / 301 \\
                 6.14 Airy Functions / 315 \\
                 6.14.1 airy.c / 322 \\
                 6.15 $Y_n(x)$ / 328 \\
                 6.15.1 yn.c / 329 \\
                 6.16 Testing / 330 \\
                 7: Other Special Functions / 333 \\
                 7.1 Hypergeometric Functions / 333 \\
                 7.1.1 $_2F_1$ / 334 \\
                 7.1.2 hyp2fi.c / 335 \\
                 7.1.3 $_1F_1$ / 341 \\
                 7.1.4 hyplfi.c / 342 \\
                 7.1.5 $_2F_0$ / 346 \\
                 7.1.6 hyp2ffi.c / 346 \\
                 7.2 Struve Functions / 348 \\
                 7.2.1 hypl1f2.c / 348 \\
                 7.2.2 hyp3f0.c / 349 \\
                 7.2.3 yv.c / 351 \\
                 7.2.4 struve.c / 351 \\
                 7.3 $\psi(x)$ / 352 \\
                 7.3.1 psi.c / 354 \\
                 7.4 Exponential Integral / 355 \\
                 7.4.1 en.c / 356 \\
                 7.5 Sine and Cosine Integrals / 360 \\
                 7.5.1 sici.c / 362 \\
                 7.5.2 Hyperbolic Sine and Cosine Integrals / 367 \\
                 7.5.3 shichi.c / 370 \\
                 7.6 Dilogarithm / 374 \\
                 7.6.1 spence.c / 375 \\
                 7.7 Dawson's Integral / 377 \\
                 7.7.1 dawsn.c / 378 \\
                 7.8 Fresnel Integrals / 381 \\
                 7.8.1 fresnl.c / 383 \\
                 7.9 Elliptic Functions / 387 \\
                 7.9.1 $K(m)$ / 387 \\
                 7.9.2 ellpk.c / 388 \\
                 7.9.3 $F(\phi|m)$ / 389 \\
                 7.9.4 ellik.c / 390 \\
                 7.9.5 $E(m)$ / 392 \\
                 7.9.6 ellpe.c / 392 \\
                 7.9.7 $E(\phi|m)$ / 393 \\
                 7.9.8 ellie.c / 394 \\
                 7.9.9 Jacobian Elliptic Functions / 396 \\
                 7.9.10 ellpj.c / 398 \\
                 7.10 Zeta Functions / 400 \\
                 7.10.1 hurwiz.c / 400 \\
                 7.10.2 Riemann Zeta Function / 402 \\
                 7.10.3 zetac.c / 405 \\
                 Bibliography / 411 \\
                 Index / 413",
}

@Manual{Motorola:1989:DIF,
  title =        "{DSP96002}: {IEEE} floating-point dual-port processor:
                 user's manual",
  organization = "{Motorola, Inc.}",
  address =      "Phoeniz, AZ, USA",
  pages =        "various",
  year =         "1989",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Signal processing.",
  remark =       "Cover title. Spine title: DSP96002 user's manual.
                 ``DSP96002UM/AD''--Cover.",
}

@Book{Motorola:1989:MMF,
  author =       "{Motorola, Inc.}",
  title =        "{MC68881\slash MC68882} Floating-Point Coprocessor
                 User's Manual",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  edition =      "Second",
  pages =        "409 (various paging)",
  month =        aug,
  year =         "1989",
  ISBN =         "0-13-567009-8 (paperback)",
  ISBN-13 =      "978-0-13-567009-5 (paperback)",
  LCCN =         "????",
  bibdate =      "Fri Dec 08 13:02:55 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.nxp.com/docs/en/reference-manual/MC68881UM.pdf",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  keywords =     "Floating-point arithmetic.; microprocessors;
                 Microprocessors --- Handbooks, manuals, etc.; Motorola
                 68881 (Microprocessor); Motorola 68882
                 (Microprocessor); technology --- computers and computer
                 technology",
  remark =       "Spine title: MC68881/882 user's manual. ``MC68881UM/AD
                 REV 2''--Cover.",
}

@Book{Motorola:1989:MRM,
  author =       "Motorola",
  title =        "{MC88100} {RISC} Microprocessor User's Manual",
  publisher =    pub-MOTOROLA,
  address =      pub-MOTOROLA:adr,
  edition =      "Second",
  year =         "1989",
  ISBN =         "0-13-567090-X",
  ISBN-13 =      "978-0-13-567090-3",
  LCCN =         "QA76.8.M75 M3 1990",
  bibdate =      "Wed Jul 6 14:23:15 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/microchip.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "Overview \\
                 Features \\
                 Introduction \\
                 Execution Units and Register File \\
                 Execution Model \\
                 Programming Model \\
                 Processor States \\
                 Reset State \\
                 Flow-Control Instructions \\
                 Register with 9-Bit Vector Table Index \\
                 Instruction Categories \\
                 Programming Tips \\
                 Instruction Set \\
                 Opcode Summary \\
                 Signal Description \\
                 Data Processor Bus Signals \\
                 Exceptions \\
                 Exception Overview \\
                 Exception Vectors and Vector Base Register (VBR) \\
                 Exception Priority \\
                 Exception Processing \\
                 Instruction Unit Exceptions \\
                 Integer Overflow Exception (Vector Offset \$48) \\
                 Memory Access Exceptions \\
                 FPU Exception Processing \\
                 FPU Exception Processing Registers \\
                 Timing Factors \\
                 Execution Example \\
                 Instruction Set Timing Summary \\
                 Applications Information \\
                 Cache Memory Management Units \\
                 Power and Ground Considerations \\
                 Master/Checker Operations \\
                 Synchronization Operations \\
                 Electrical Characteristics",
}

@Article{Mulcahy:1989:FPR,
  author =       "L. P. Mulcahy",
  title =        "On fixed-point roundoff error analysis",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "37",
  number =       "10",
  pages =        "1623",
  month =        oct,
  year =         "1989",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  summary =      "The author points out the existence of work published
                 by the author (US Department of Commerce, Tech. Rep.
                 AD-A086826, 57 pp., Apr. 1980) prior to the appearance
                 of the paper by Barnes et al. (ibid., vol.ASSP-33,
                 p.595-606, June 1985) covering the same \ldots{}",
}

@InProceedings{Nakayama:1989:BMF,
  author =       "T. Nakayama and S. Kojima and H. Harigai and H.
                 Igarashi and K. Tamada and T. Toba",
  title =        "An 80 b, 6.7 {MFLOPS} floating-point processor with
                 vector\slash matrix instructions",
  crossref =     "Wuorinen:1989:DTP",
  pages =        "52--53, 289",
  year =         "1989",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A description is given of an 80-b CMOS VLSI
                 floating-point processor (FPP) in 1.2- mu m
                 double-metal layer CMOS which contains 433000
                 transistors on an 11.6-mm*14.9-mm die. It operates at
                 20 MHz, dissipates 1.5 W, and is assembled in a 68-lead
                 pin-grid-array package. The FPP is designed as a
                 coprocessor for 32-b microprocessors. It implements
                 data formats, arithmetic rounding modes, and exception
                 types which are defined by the IEEE 754 standard. The
                 chip can handle single (32 b), double (64 b), and
                 double-extended (80 b) floating-point data formats. The
                 complex-instruction-set-computer- (CISC-) like
                 78-instruction set includes 22 mathematical functions
                 such as sin, cos, arctan, exp, and log, and 24
                 vector/matrix operations such as add, multiply, and
                 inner product. The features and performance of the
                 device are summarized.",
  acknowledgement = ack-nhfb,
  affiliation =  "NEC, Kawasaki, Japan",
  classification = "B1265F (Microprocessors and microcomputers); B2570D
                 (CMOS integrated circuits); C5130 (Microprocessor
                 chips); C5230 (Digital arithmetic methods)",
  keywords =     "1.2 Micron; 1.5 W; 20 MHz; 6.7 MFLOPS; 80 Bit;
                 Arithmetic rounding modes; CMOS VLSI floating-point
                 processor; Complex instruction set computer; Data
                 formats; Double-metal layer CMOS; Exception types;
                 Mathematical functions; Pin-grid-array package; Power
                 dissipation; Vector/matrix instructions",
  numericalindex = "Word length 8.0E+01 bit; Computer speed 6.7E+06
                 FLOPS; Size 1.2E-06 m; Frequency 2.0E+07 Hz; Power
                 1.5E+00 W",
  thesaurus =    "CMOS integrated circuits; Digital arithmetic;
                 Microprocessor chips; VLSI",
}

@Article{Nakayama:1989:FCV,
  author =       "T. Nakayama and H. Harigai and S. Kojima and H. Kaneko
                 and H. Igarashi and T. Toba and Y. Yamagami and Y.
                 Yano",
  title =        "A 6.7-{MFLOPS} floating-point coprocessor with
                 vector\slash matrix instructions",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "24",
  number =       "5",
  pages =        "1324--1330",
  month =        oct,
  year =         "1989",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "An 80-bit floating-point coprocessor which implements
                 24 vector/matrix instructions and 22 mathematical
                 functions is described. This processor can execute
                 floating-point addition/rounding and pipelined
                 multiplication concurrently, under the control of
                 horizontal-type microinstructions. The SRT division
                 method and CORDIC trigonometrical algorithm are used
                 for a favorable cost/performance implementation. The
                 performance of 6.7 MFLOPS in the vector-matrix
                 multiplication at 20 MHz has been attained by the use
                 of parallel operations. The vector/matrix instruction
                 is about three times faster than conventional add and
                 multiply instructions. The chip has been fabricated in
                 1.2- mu m double-metal layer CMOS process containing
                 433000 transistors on a 11.6*14.9-mm/sup 2/ die size.",
  acknowledgement = ack-nhfb,
  classification = "B1265F (Microprocessors and microcomputers); B2570D
                 (CMOS integrated circuits); C5130 (Microprocessor
                 chips); C5230 (Digital arithmetic methods)",
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "1.2 Micron; 20 MHz; 6.7 MFLOPS; 80 Bit; CMOS process;
                 CORDIC trigonometrical algorithm; Double-metal layer;
                 Floating-point coprocessor; Horizontal-type
                 microinstructions; Mathematical functions; Parallel
                 operations; Pipelined multiplication; SRT division
                 method; Vector/matrix instructions; VLSI
                 microprocessor",
  numericalindex = "Word length 8.0E+01 bit; Size 1.2E-06 m; Computer
                 speed 6.7E+06 FLOPS; Frequency 2.0E+07 Hz",
  thesaurus =    "CMOS integrated circuits; Digital arithmetic;
                 Instruction sets; Microprocessor chips; Parallel
                 architectures; Pipeline processing; Satellite
                 computers; VLSI",
}

@InProceedings{Nakayama:1989:MFPa,
  author =       "T. Nakayama and S. Kojima and H. Harigai and H.
                 Igarashi and K. Tamada and T. Toba",
  title =        "An 80b, 6.7 {MFLOPS} Floating-Point Processor with
                 Vector\slash Matrix Instructions",
  crossref =     "Wuorinen:1989:DTP",
  pages =        "52--53, 289",
  year =         "1989",
  bibdate =      "Fri Dec 08 13:04:53 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Nakayama:1989:MFPb,
  author =       "T. Nakayama and H. Harigai and S. Kojima and H. Kaneko
                 and H. Igarashi and T. Toba and Y. Yamagami and Y.
                 Yano",
  title =        "A 6.7-{MFLOPS} Floating-Point Coprocessor with
                 Vector\slash Matrix Instructions",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "24",
  number =       "5",
  pages =        "1324--1330",
  month =        oct,
  year =         "1989",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "An 80-bit floating-point coprocessor which implements
                 24 vector/matrix instructions and 22 mathematical
                 functions is described. This processor can execute
                 floating-point addition/rounding and pipelined
                 multiplication concurrently, under the control
                 \ldots{}",
}

@InProceedings{Nowacki:1989:ABQ,
  author =       "C. L. Nowacki and J. D. Harris and M. N. Richard",
  booktitle =    "{IEEE} Military Communications Conference, 1989.
                 {MILCOM '89}. Conference Record. Bridging the Gap.
                 Interoperability, Survivability, Security, 1989",
  title =        "Adaptive beamforming in quadratic residue number
                 systems on a cluster array processor",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "624--628",
  year =         "1989",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MILCOM.1989.104000",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The authors describe a quadratic residue number system
                 (QRNS) implementation of the Leverrier algorithm for
                 computing the adjoint and determinant of a matrix on a
                 prototype parallel signal processor, called the cluster
                 array processor (CAP). Some \ldots{}",
}

@Article{Ochs:1989:TPF,
  author =       "T. Ochs",
  title =        "Theory and practice (floating point arithmetic)",
  journal =      j-COMP-LANG-MAG,
  volume =       "6",
  number =       "3",
  pages =        "67--70, 72, 74, 77--78, 80--81",
  month =        mar,
  year =         "1989",
  CODEN =        "COMLEF",
  ISSN =         "0749-2839",
  bibdate =      "Tue Dec 12 09:20:14 MST 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The IEEE-754 standard for floating point arithmetic
                 has inherent limits. The author presents a guide to
                 NaNs, unnormals, underflows and signal infinite
                 quantities.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  classification = "C5230 (Digital arithmetic methods); C6150C
                 (Compilers, interpreters and other processors)",
  fjournal =     "Computer Language Magazine",
  keywords =     "Compilers; Floating point arithmetic; IEEE-754
                 standard; NaNs; Signal infinite quantities; Underflows;
                 Unnormals",
  thesaurus =    "Digital arithmetic; Program compilers",
}

@InProceedings{Petkovsek:1989:CDS,
  author =       "M. Petkovsek",
  title =        "Contiguous digit sets and local roundings",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "136--143",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Petkovsek.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9",
}

@Article{Pincin:1989:NAM,
  author =       "A. Pincin",
  title =        "A new algorithm for multiplication in finite fields",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "38",
  number =       "7",
  pages =        "1045--1049",
  month =        jul,
  year =         "1989",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.30855",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jul 8 19:00:40 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=30855",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Prince:1989:FTF,
  author =       "Timothy Prince",
  title =        "Float Trig Functions For The {C} Preprocessor",
  journal =      j-CUJ,
  volume =       "7",
  number =       "8",
  pages =        "103--??",
  month =        aug,
  year =         "1989",
  ISSN =         "0898-9788",
  bibdate =      "Fri Aug 30 16:52:23 MDT 1996",
  bibsource =    "http://www.cuj.com/cbklist.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "C Users Journal",
}

@InProceedings{Ramamoorthy:1989:HSA,
  author =       "P. A. Ramamoorthy and B. Potu",
  booktitle =    "International Conference on Acoustics, Speech, and
                 Signal Processing, {ICASSP-89, 23--26} May 1989",
  title =        "High-speed {ADC} using residue number system",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1063--1066",
  year =         "1989",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICASSP.1989.266615",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "An ADC (analog/digital converter) architecture based
                 on a residue number system (RNS) and multiple folding
                 of the input signal is described. The number of
                 comparators used is equal to the sum of moduli for
                 obtaining the dynamic range desired. An \ldots{}",
}

@InProceedings{Rao:1989:RNF,
  author =       "B. D. Rao",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, 8--11 May 1989",
  title =        "Roundoff noise in floating point state space digital
                 filters",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "724--727",
  year =         "1989",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The roundoff noise properties of floating-point
                 state-space digital filters are examined. It is shown
                 that the roundoff noise behavior of these filters is
                 related to their coefficient sensitivity. Expressions
                 for the variance of the output roundoff \ldots{}",
}

@InProceedings{Ray:1989:MCA,
  author =       "G. A. Ray",
  booktitle =    "Proceedings of the 32nd Midwest Symposium on Circuits
                 and Systems, 1989",
  title =        "Multiple core algorithms for residue number systems",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "833--836",
  year =         "1989",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1989.101984",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The core function provides an easily implemented and
                 efficient means for performing the traditionally
                 difficult residue operations. However, two problems
                 with core algorithms are the difficulty in choosing
                 core coefficients and the many iterations \ldots{}",
}

@InProceedings{Rishe:1989:LEN,
  author =       "Naphtali Rishe",
  title =        "Lexicographic Encoding of Numeric Data Fields",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "241--246",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Rishe.pdf",
  abstract =     "This paper proposes a method of variable-radix
                 representation of numeric data. The method allows
                 compact representation of arbitrary numbers. Among its
                 properties is that bitwise lexicographic comparison
                 ($<$, $>$) is consistent with correct numeric
                 comparison of numbers.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9",
}

@Book{Robbins:1989:CXM,
  author =       "Kay A. Robbins and Steven Robbins",
  title =        "The {Cray X-MP}\slash {Model} 24",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "vi + 165",
  year =         "1989",
  ISBN =         "0-387-97089-4, 3-540-97089-4",
  ISBN-13 =      "978-0-387-97089-9, 978-3-540-97089-7",
  LCCN =         "QA76.8 C72 R63 1989",
  bibdate =      "Sat Jan 29 18:17:38 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Saffari:1989:PDW,
  author =       "B. Saffari",
  title =        "Putting {DSPs} to work",
  journal =      j-BYTE,
  volume =       "14",
  number =       "13",
  pages =        "259--272",
  month =        dec,
  year =         "1989",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Thu Sep 12 17:47:21 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "B1265F (Microprocessors and microcomputers); B2570
                 (Semiconductor integrated circuits); B6140 (Signal
                 processing and detection); C5130 (Microprocessor
                 chips); C5260 (Digital signal processing)",
  fjournal =     "BYTE Magazine",
  keywords =     "Digital filters; Feature extraction; Floating-point
                 application-specific-IC DSPs; Image processing;
                 Moments; Pattern recognition architecture; Sound; Space
                 correction; Time",
  thesaurus =    "Application specific integrated circuits; Computerised
                 signal processing; Digital signal processing chips",
}

@InProceedings{Santoro:1989:RAI,
  author =       "M. R. Santoro and G. Bewick and M. A. Horowitz",
  title =        "Rounding Algorithms for {IEEE} Multipliers",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "176--183",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Santoro.pdf",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  keywords =     "ARITH-9",
  summary =      "Several technology independent rounding algorithms for
                 multiplying normalized numbers are presented. The first
                 is a simple rounding algorithm suitable for software
                 simulation or moderate performance hardware
                 multipliers. The next two algorithms are \ldots{}",
}

@Article{Sasaki:1989:AAD,
  author =       "Tateaki Sasaki and Mutsuko Sasaki",
  title =        "Analysis of accuracy decreasing in polynomial
                 remainder sequence with floating-point number
                 coefficients",
  journal =      "J. Inform. Process.",
  volume =       "12",
  number =       "4",
  pages =        "394--403",
  year =         "1989",
  MRclass =      "65G05 (65Y20)",
  MRnumber =     "91h:65069",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Schwarz:1989:IIP,
  author =       "Jerry Schwarz",
  title =        "Implementing infinite precision arithmetic",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "10--17",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Schwarz.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9",
}

@Article{Scott:1989:FRM,
  author =       "M. Scott",
  title =        "Fast rounding in multiprecision floating-slash
                 arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "38",
  number =       "7",
  pages =        "1049--1052",
  month =        jul,
  year =         "1989",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.30856",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 11:25:03 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "A computational algorithm is described which quickly
                 rounds large fractions into a fixed-length
                 multiprecision floating-slash representation, using
                 single-precision operations where possible. An easily
                 calculated criterion for terminating the \ldots{}",
}

@Article{Shenoy:1989:FBE,
  author =       "A. P. Shenoy and R. Kumaresan",
  title =        "Fast base extension using a redundant modulus in
                 {RNS}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "38",
  number =       "2",
  pages =        "292--297",
  month =        feb,
  year =         "1989",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.16508",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jul 8 19:00:38 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=16508",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Shimazu:1989:MFP,
  author =       "Y. Shimazu and T. Kengaku and T. Fujiyama and E.
                 Teraoka and T. Ohno and T. Tokuda and O. Tomisawa and
                 S. Tsujimichi",
  title =        "A 50 {MHz} 24b Floating-Point {DSP}",
  crossref =     "Wuorinen:1989:DTP",
  pages =        "44--45, 285",
  year =         "1989",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A 24-bit floating-point digital signal processor (DSP)
                 has been developed primarily for speech processing and
                 communication applications. The chip uses 1.0- mu m
                 double-metal CMOS with tungsten silicide technology.
                 The instruction set is upward compatible with an 18-bit
                 DSP. Novel circuit design techniques allowing 40-ns
                 machine cycle time at 50-MHz clock and less than 600-mW
                 power dissipation are described. A built-in self-test
                 is prepared using on-chip IROM and the two 24-bit
                 linear feedback shift registers which are included in
                 I/O registers such as the data register, the serial
                 input registers, and the serial output registers. The
                 DSP design features are summarized.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  affiliation =  "Mitsubishi, Hyogo, Japan",
  chemicalindex = "WSi2/int Si2/int Si/int W/int WSi2/bin Si2/bin Si/bin
                 W/bin",
  classification = "B1265F (Microprocessors and microcomputers); B2570D
                 (CMOS integrated circuits); B6130 (Speech analysis and
                 processing techniques); C5130 (Microprocessor chips);
                 C5230 (Digital arithmetic methods); C5260 (Digital
                 signal processing)",
  keywords =     "1 Micron; 24 Bit; 40 Ns; 50 MHz; 600 MW; Built-in
                 self-test; Circuit design techniques; Clock frequency;
                 Communication applications; Data register; Double-metal
                 CMOS; Floating-point digital signal processor; I/O
                 registers; Instruction set; Linear feedback shift
                 registers; Machine cycle time; On-chip IROM; Power
                 dissipation; Serial input registers; Serial output
                 registers; Speech processing; WSi/sub 2/ technology",
  numericalindex = "Frequency 5.0E+07 Hz; Word length 2.4E+01 bit; Time
                 4.0E-08 s; Power 6.0E-01 W; Size 1.0E-06 m",
  thesaurus =    "CMOS integrated circuits; Digital arithmetic; Digital
                 signal processing chips; Speech analysis and
                 processing",
}

@Article{Sinha:1989:FPA,
  author =       "B. P. Sinha and P. K. Srimani",
  title =        "Fast parallel algorithms for binary multiplication and
                 their implementation on systolic architectures",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "38",
  number =       "3",
  pages =        "424--431",
  month =        mar,
  year =         "1989",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.21128",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jul 8 19:00:38 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=21128",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Sit:1989:MFP,
  author =       "H. P. Sit and M. R. Nofal and S. Kimn",
  title =        "An 80 {MFLOPS} Floating-point Engine in the {Intel}
                 i860{\TM} Processor",
  crossref =     "IEEE:1989:PII",
  pages =        "374--379",
  year =         "1989",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The i860 processor is a 64-b microprocessor with 1.02
                 million transistors. It has a 64-b external data bus
                 and a 32-b external address bus. It is fabricated with
                 Intel's CHMOS IV technology (a 1- mu m double-metal
                 process). The die size is approximately 10 mm*15 mm.
                 First silicon is functional over commercial temperature
                 and voltage ranges with an execution speed of 40 MHz.
                 The floating-point engine consists of a pipelined adder
                 and a pipelined multiplier, incorporates a special
                 hardware to support the dual operation instructions,
                 and operates synchronously with the RISC
                 (reduced-instruction-set computer) core to execute up
                 to three operations per clock. Its high performance
                 lends itself well to a numeric-intensive computation
                 environment, including vector processing.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  affiliation =  "Intel Corp., Santa Clara, CA, USA",
  classification = "B1265F (Microprocessors and microcomputers); B2570D
                 (CMOS integrated circuits); C5130 (Microprocessor
                 chips)",
  keywords =     "1 Micron; 10 Mm; 15 Mm; 32 Bit; 40 MHz; 64 Bit; 80
                 MFLOPS; 80 MFLOPS floating-point engine; CHMOS IV
                 technology; CMOS; Commercial temperature; Die size;
                 Double-metal process; Dual operation instructions;
                 Execution speed; Floating-point engine; Intel i860
                 processor; Numeric-intensive computation environment;
                 Pipelined adder; Pipelined multiplier;
                 Reduced-instruction-set computer; RISC core; Three
                 operations per clock; Vector processing",
  numericalindex = "Word length 6.4E+01 bit; Frequency 4.0E+07 Hz; Word
                 length 3.2E+01 bit; Computer speed 8.0E+07 FLOPS; Size
                 1.0E-06 m; Size 1.0E-02 m; Size 1.5E-02 m",
  thesaurus =    "CMOS integrated circuits; Digital arithmetic;
                 Microprocessor chips; Reduced instruction set
                 computing",
}

@InProceedings{Skavantzos:1989:DFC,
  author =       "A. Skavantzos",
  booktitle =    "Twenty-Third Asilomar Conference on Signals, Systems
                 and Computers, 1989",
  title =        "Designing fast convolvers for residue number systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "497--501",
  year =         "1989",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICASSP.1989.266586",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
}

@Article{Smith:1989:CSB,
  author =       "S. G. Smith",
  title =        "Comments on {``A signed bit-sequential multiplier''}
                 by {T. Rhyne} and {N. R. Strader II}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "38",
  number =       "9",
  pages =        "1328--1330",
  month =        sep,
  year =         "1989",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.29473",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jul 8 19:00:41 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  note =         "See \cite{Rhyne:1986:SBS}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=29473",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Spaderna:1989:IFP,
  author =       "D. Spaderna and P. Green and K. Tam and T. Datta and
                 M. Kumar",
  title =        "An integrated floating point vector processor for
                 {DSP} and scientific computing",
  crossref =     "IEEE:1989:PII",
  pages =        "8--13",
  year =         "1989",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The architecture of a high-performance floating-point
                 microprocessor intended for computation-intensive
                 applications is presented. Utilizing a massively
                 parallel execution unit, very high bandwidth onchip
                 memory, and extensive parallel address calculation
                 hardware, the processor is expected to achieve peak
                 execution rates of 400 MFLOPS for single-precision
                 floating-point numbers. This type of performance is
                 competitive with that of popular mainframe vector
                 processors.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sharp Microelectron. Technol. Inc., Vancouver, WA,
                 USA",
  classification = "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5220 (Computer architecture);
                 C5260 (Digital signal processing)",
  keywords =     "400 MFLOPS; Computation-intensive applications; DSP;
                 Floating-point microprocessor; Integrated floating
                 point vector processor; Mainframe vector processors;
                 Massively parallel execution unit; Onchip memory;
                 Parallel address calculation hardware; Peak execution
                 rates; Scientific computing; Single-precision
                 floating-point numbers",
  numericalindex = "Computer speed 4.0E+08 FLOPS",
  thesaurus =    "Digital signal processing chips; Parallel
                 architectures",
}

@InProceedings{Stearns:1989:SFD,
  author =       "C. C. Stearns",
  title =        "Subtractive floating-point division and square root
                 for {VLSI DSP}",
  crossref =     "IEE:1989:EEC",
  pages =        "405--409",
  year =         "1989",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper describes recent architectural developments
                 in VLSI design for real-time digital signal processing.
                 In particular, floating point division and floating
                 point square root architectures applicable to both
                 adaptive filtering, standard deviation computations,
                 and general purpose processing are discussed. Emphasis
                 here is on the internal architectures of the arithmetic
                 units not on their applications. The research presented
                 in this paper has been proven feasible and reliable
                 from extensive gate-level simulation and fabrication in
                 silicon.",
  acknowledgement = ack-nhfb,
  classification = "B1265F (Microprocessors and microcomputers); B1270F
                 (Digital filters); B2570D (CMOS integrated circuits);
                 C5230 (Digital arithmetic methods); C5240 (Digital
                 filters); C5260 (Digital signal processing)",
  keywords =     "Adaptive filtering; Arithmetic units; CMOS technology;
                 Floating point division; Floating point square root
                 architectures; Gate-level simulation; General purpose
                 processing; Real-time digital signal processing;
                 Semiconductor; Standard deviation computations; VLSI
                 DSP",
  thesaurus =    "Adaptive filters; CMOS integrated circuits; Digital
                 arithmetic; Digital signal processing chips; VLSI",
}

@InProceedings{Stearns:1989:SFP,
  author =       "C. C. Stearns",
  booktitle =    "European Conference on Circuit Theory and Design, 5--8
                 Sep 1989",
  title =        "Subtractive floating-point division and square root
                 for {VLSI} {DSP}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "405--409",
  year =         "1989",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper describes recent architectural developments
                 in VLSI design for real-time digital signal processing.
                 In particular, floating point division and floating
                 point square root architectures applicable to both
                 adaptive filtering, standard \ldots{}",
}

@TechReport{Tang:1989:TCA,
  author =       "P. T. P. Tang",
  title =        "Testing Computer Arithmetic by Elementary Number
                 Theory",
  institution =  "Mathematics and Computer Science Division, Argonne
                 National Laboratory",
  pages =        "??",
  month =        aug,
  year =         "1989",
  bibdate =      "Thu Sep 01 11:57:30 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  keywords =     "floating-point testing",
}

@Article{Tang:1989:TDI,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Driven Implementation of the Exponential
                 Function in {IEEE} Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "15",
  number =       "2",
  pages =        "144--157",
  month =        jun,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/63522.214389",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 22:47:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-2/p144-tang/",
  abstract =     "Algorithms and implementation details for the
                 exponential function in both single- and
                 double-precision of IEEE 754 arithmetic are presented
                 here. With a table of moderate size, the
                 implementations need only working-precision arithmetic
                 and are provably accurate to within 0.54 ulp as long as
                 the final result does not underflow. When the final
                 result suffers gradual underflow, the error is still no
                 worse than 0.77 ulp.",
  acknowledgement = ack-nj,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis. {\bf G.1.0}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis.",
}

@Book{Thies:1989:PXA,
  author =       "Klaus-Dieter Thies",
  title =        "{PC\slash {XT}\slash {AT} Numerik Buch} \toenglish
                 {PC\slash XT\slash AT Numeric Book} \endtoenglish",
  publisher =    pub-TEWI,
  address =      pub-TEWI:adr,
  pages =        "xiii + 707",
  year =         "1989",
  ISBN =         "3-89362-033-8",
  ISBN-13 =      "978-3-89362-033-3",
  LCCN =         "????",
  bibdate =      "Sat Nov 09 10:09:41 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@InProceedings{Tu:1989:DLD,
  author =       "Paul K. Tu and M. D. Ercegovac",
  title =        "Design of on-line division unit",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "42--49",
  year =         "1989",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Tu.pdf",
  abstract =     "A gate array implementation of a radix-2
                 floating-point online division algorithm is presented.
                 The design requires 111 equivalent gates per bit and
                 has a cycle time of 24 ns. For 8-b exponent and 24-b
                 mantissa, the design requires 2497 equivalent gates and
                 can fit on an LSI Logic LL9320P chip with a utilization
                 factor 78\%.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, California University,
                 Los Angeles, CA, USA",
  classification = "B1265B (Logic circuits); B2570 (Semiconductor
                 integrated circuits); C5120 (Logic and switching
                 circuits); C5230 (Digital arithmetic methods)",
  keywords =     "24 Ns Cycle time; ARITH-9; Gate array implementation;
                 LSI Logic LL9320P chip; Online division unit design;
                 Radix-2 floating-point online division algorithm;
                 Utilization factor",
  numericalindex = "Time 2.4E-08 s",
  thesaurus =    "Digital arithmetic; Large scale integration; Logic
                 arrays",
}

@InProceedings{Turner:1989:SIS,
  author =       "Peter R. Turner",
  title =        "A software implementation of {SLI} arithmetic",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "18--24",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Turner.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9",
}

@InProceedings{Turrini:1989:OGD,
  author =       "Silvio Turrini",
  title =        "Optimal group distribution in carry-skip adders",
  crossref =     "Ercegovac:1989:PSC",
  pages =        "96--103",
  year =         "1989",
  bibdate =      "Sat Nov 27 14:19:10 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith9/papers/ARITH9_Turrini.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-9",
}

@Article{Unguru:1989:BRB,
  author =       "Sabetai Unguru",
  title =        "Book Review: {{\booktitle{A Mathematical History of
                 Division in Extreme and Mean Ratio}} by Roger
                 Herz-Fischler}",
  journal =      j-ISIS,
  volume =       "80",
  number =       "2",
  pages =        "298--299",
  month =        jun,
  year =         "1989",
  CODEN =        "ISISA4",
  ISSN =         "0021-1753 (print), 1545-6994 (electronic)",
  ISSN-L =       "0021-1753",
  bibdate =      "Tue Jul 30 21:23:50 MDT 2013",
  bibsource =    "http://www.jstor.org/action/showPublication?journalCode=isis;
                 http://www.jstor.org/stable/i211193;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/isis1980.bib",
  URL =          "http://www.jstor.org/stable/234607",
  acknowledgement = ack-nhfb,
  fjournal =     "Isis",
  journal-URL =  "http://www.jstor.org/journal/isis",
}

@Article{VanVeen:1989:MBC,
  author =       "B. D. {Van Veen} and R. Baraniuk",
  title =        "Matrix based computation of floating-point roundoff
                 noise",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "37",
  number =       "12",
  pages =        "1995--1998",
  month =        dec,
  year =         "1989",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  summary =      "A matrix-based procedure is presented for computing
                 the output roundoff power for filters implemented with
                 floating-point arithmetic. The filter's computational
                 structure is represented in terms of a product of
                 matrices, known as a factored state \ldots{}",
}

@Article{Vassiliadis:1989:GPO,
  author =       "S. Vassiliadis and E. M. Schwarz and D. J. Hanrahan",
  title =        "A General Proof for Overlapped Multiple-Bit Scanning
                 Multiplications",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "38",
  number =       "2",
  pages =        "172--183",
  month =        feb,
  year =         "1989",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.16494",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jul 8 19:00:37 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=16494",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Vassiliadis:1989:SMF,
  author =       "S. Vassiliadis and D. S. Lemon and M. Putrino",
  title =        "{S/370} sign-magnitude floating-point adder",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "24",
  number =       "4",
  pages =        "1062--1070",
  month =        aug,
  year =         "1989",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A 56-bit S/370 sign-magnitude adder for floating-point
                 operations implemented in a four-level metal (4LM)
                 bipolar master-slice technology is described. The
                 design of the two-to-one adder is based on a carry
                 lookahead scheme with implicit calculation of the
                 end-around carry. The implementation of the
                 floating-point adder and the error-detecting logic
                 requires one chip of 7500 automatically placed and
                 wired NAND gates. The chip die size is 7.39 x 7.39 mm
                 super(2) and it is mounted on a metalized ceramic (MC)
                 substrate. The floating-point sign-magnitude adder chip
                 is used in the IBM 9370 model 60 (9375) Engineering
                 Scientific Accelerator (ESA) card.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Corp., Endicott, NY, USA",
  classification = "B1265B (Logic circuits); B2570B (Bipolar integrated
                 circuits); C5120 (Logic and switching circuits)",
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "algorithms; arithmetic circuits; Carry lookahead
                 scheme; Chip die size; design; End-around carry;
                 Engineering scientific accelerator card;
                 Error-detecting logic; floating point arithmetic;
                 Four-level metal bipolar master-slice technology; IBM
                 9370 Model 60; logic circuits; Metallized ceramic
                 substrate; NAND gates; S/370; Sign-magnitude
                 floating-point adder",
  summary =      "A 56 bit S/370 sign-magnitude adder for floating-point
                 operations implemented in a four-level metal bipolar
                 master-slice technology is described. The design of the
                 two-to-one adder is based on a carry lookahead scheme
                 with implicit calculation of the \ldots{}",
  thesaurus =    "Adders; Bipolar integrated circuits; Carry logic;
                 Integrated logic circuits; NAND circuits",
}

@Article{Voelzke:1989:FSAa,
  author =       "H. V{\"o}lzke",
  title =        "{Flie{\ss}komma-Arithmetik und
                 IEEE-Spez\-i\-fi\-ka\-tion\-en. Teil 4: Die
                 Konvertierungsroutinen} \toenglish {Floating-point
                 Arithmetic and its IEEE Specification. Part 4:
                 Conversion Routines} \endtoenglish",
  journal =      j-MC,
  volume =       "1",
  pages =        "66--73",
  year =         "1989",
  ISSN =         "0720-4442, 0941-777x, 0943-5409",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "MC: Die Mikrocomputer-Zeitschrift",
}

@Article{Voelzke:1989:FSAb,
  author =       "H. V{\"o}lzke",
  title =        "{Flie{\ss}komma-Arithmetik und
                 IEEE-Spez\-i\-fi\-ka\-tion\-en. Teil 5: Ein- und
                 Ausgabefunktionen} \toenglish {Floating-point
                 Arithmetic and its IEEE Specification. Part 5: Input
                 and Output Functions} \endtoenglish",
  journal =      j-MC,
  volume =       "2",
  pages =        "65--71",
  year =         "1989",
  ISSN =         "0720-4442, 0941-777x, 0943-5409",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "MC: Die Mikrocomputer-Zeitschrift",
}

@Article{Vulchanov:1989:SCR,
  author =       "N. L. Vulchanov and M. M. Konstantinov",
  title =        "Safe calculation of the relative machine precision in
                 floating-point computing environments",
  journal =      j-C-R-ACAD-BULGARE-SCI,
  volume =       "42",
  number =       "2",
  pages =        "45--48",
  year =         "1989",
  CODEN =        "DBANAD",
  ISSN =         "0366-8681",
  MRclass =      "65G99",
  MRnumber =     "991 451",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Comptes rendus de l'Acad{\'e}mie bulgare des
                 sciences",
}

@Article{Wagner:1989:EDD,
  author =       "Neal R. Wagner and Paul Putter",
  title =        "Error detecting decimal digits",
  journal =      j-CACM,
  volume =       "32",
  number =       "1",
  pages =        "106--110",
  month =        jan,
  year =         "1989",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/63238.63246",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu May 30 09:41:10 MDT 1996",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Misc/IMMD_IV.bib;
                 http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/0001-0782/63246.html",
  abstract =     "We were recently engaged by a large mail-order house
                 to act as consultants on their use of check digits for
                 detecting errors in account numbers. Since we were not
                 experts in coding theory, we looked in reference books
                 such as Error Correcting Codes [7] and asked colleagues
                 who were familiar with coding theory. Uniformly, the
                 answer was: There is no field of order 10; the theory
                 only works over a field. This article relates our
                 experiences and presents several of the simple
                 decimal-oriented error detection schemes that are
                 available, but not widely known.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "decimal floating-point arithmetic; reliability",
  review =       "ACM CR 9002-0109",
  subject =      "{\bf B.4.5}: Hardware, INPUT/OUTPUT AND DATA
                 COMMUNICATIONS, Reliability, Testing, and
                 Fault-Tolerance, Error-checking. {\bf E.4}: Data,
                 CODING AND INFORMATION THEORY, Nonsecret encoding
                 schemes.",
}

@Article{Wang:1989:ADF,
  author =       "C. C. Wang",
  title =        "An algorithm to design finite field multipliers using
                 a self-dual normal basis",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "38",
  number =       "10",
  pages =        "1457--1460",
  month =        oct,
  year =         "1989",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.35840",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jul 8 19:00:42 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1980.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=35840",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Wang:1989:MBC,
  author =       "Song-Tine Wang and Chi-Suan Wang and Morries Wang and
                 Shyh-Rurong Wang and Jhy-Kun Wang and Ching-Lu Hon and
                 Row-Ming Yang and Wei-Hsiung Chuang and Te-Tsoung Tsai
                 and Ming-Yuan Jang and Gwo-Jeng Pun",
  title =        "A 34-{MFLOP} 32-bit {CMOS} floating point processor",
  crossref =     "IEEE:1989:ISV",
  pages =        "361--364",
  year =         "1989",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A 34-MFLOP 32-bit floating-point processor in 2- mu m
                 CMOS technology is presented. In order to achieve the
                 high speed of floating-point operation, the authors use
                 such techniques as hierarchical design parallel
                 circuits, and a three-stage pipeline that has been
                 optimized with equal delay in each stage. It is shown
                 that the CIC81232Y (multiplier) and CIC81233Y
                 (arithmetic and logic circuit) are fully compatible
                 with WTL1232 and WTL1233 in function, but the speeds
                 are 1.7 times faster.",
  acknowledgement = ack-nhfb,
  affiliation =  "Electron. Res and Service Organ., Hsing-Chu, Taiwan",
  classification = "B1265F (Microprocessors and microcomputers); B2570D
                 (CMOS integrated circuits); C5130 (Microprocessor
                 chips); C5220 (Computer architecture); C5230 (Digital
                 arithmetic methods)",
  keywords =     "32 Bit; 32-Bit floating-point processor; 34 MFLOPS;
                 Arithmetic circuit; CIC81232Y; CIC81233Y; CMOS
                 technology; Hierarchical design parallel circuits;
                 Logic circuit; Multiplier; Three-stage pipeline",
  numericalindex = "Word length 3.2E+01 bit; Computer speed 3.4E+07
                 FLOPS",
  thesaurus =    "CMOS integrated circuits; Digital arithmetic;
                 Microprocessor chips; Pipeline processing",
}

@MastersThesis{Ward:1989:BFP,
  author =       "Kenneth L. Ward",
  title =        "A block floating point distributed arithmetic finite
                 impulse response filter",
  type =         "Thesis ({M.S.})",
  school =       "University of Florida",
  address =      "Gainesville, FL, USA",
  year =         "1989",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Digital filters (Mathematics); Filters (Mathematics);
                 Floating-point arithmetic.",
}

@Article{Wichmann:1989:SPI,
  author =       "B. A. Wichmann",
  title =        "Scientific processing in {ISO-Pascal}: a proposal to
                 get the benefits of mixed precision floating-point",
  journal =      j-SIGPLAN,
  volume =       "24",
  number =       "6",
  pages =        "20--22",
  month =        jun,
  year =         "1989",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:15:40 MST 2003",
  bibsource =    "Compendex database; http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Although Pascal is a very popular language for
                 teaching and for use on microprocessors, it has not
                 been very successful for scientific calculations. Apart
                 from the pre-eminence of FORTRAN in this application
                 area, several technical defects in Pascal have
                 inhibited its use. One defect has been the problem in
                 Pascal as defined by Jensen and Wirth of the inability
                 to handle arrays of varying size as parameters to
                 procedures. The level 1 option in ISO-Pascal addressed
                 this defect by means of conformant arrays, albeit in a
                 somewhat inelegant fashion. Array handling in
                 ISO-Pascal can now be regarded as adequate since level
                 1 validated compilers are available for the majority of
                 widely available machines. This note addresses another
                 defect of Pascal, that no facility is provided to
                 handle floating point types of more than one
                 precision.",
  acknowledgement = ack-nhfb,
  affiliationaddress = "Teddington, Engl",
  classification = "723; 902",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  journalabr =   "SIGPLAN Not",
  keywords =     "algorithms; Computer Programming Languages; design;
                 Floating Point Computation; iso-pascal; languages;
                 pascal; Scientific Computing; standardization;
                 Standards",
  subject =      "D.2.1 Software, SOFTWARE ENGINEERING,
                 Requirements/Specifications \\ D.3.2 Software,
                 PROGRAMMING LANGUAGES, Language Classifications, Pascal
                 \\ E.1 Data, DATA STRUCTURES, Arrays",
}

@Article{Wichmann:1989:TFS,
  author =       "B. A. Wichmann",
  title =        "Towards a formal specification of floating point",
  journal =      j-COMP-J,
  volume =       "32",
  number =       "5",
  pages =        "432--436",
  month =        oct,
  year =         "1989",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  MRclass =      "65G99 (65Y10)",
  MRnumber =     "91b:65055",
  bibdate =      "Wed Dec 13 18:44:32 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Although the concept of floating point is well
                 understood, a formal mathematical treatment appears to
                 be new. The paper presents a formal definition of
                 floating point using the Vienna Development Method
                 (VDM). The relationship between this definition and the
                 informal definition in the Ada Standard and the work of
                 W. S. Brown (1981) is discussed.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Trade and Ind., NPL, Teddington, UK",
  classification = "C5230 (Digital arithmetic methods); C6110B (Software
                 engineering techniques)",
  corpsource =   "Department of Trade and Ind., NPL, Teddington, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "digital arithmetic; Floating point; floating point;
                 Formal specification; formal specification; Method;
                 Vienna Development; Vienna Development Method",
  pubcountry =   "UK",
  thesaurus =    "Digital arithmetic; Formal specification",
  treatment =    "P Practical",
}

@MastersThesis{Wittman:1989:SCU,
  author =       "Susan Jean Wittman",
  title =        "Servo compensation using a floating point digital
                 signal processor",
  type =         "Thesis ({M.S.})",
  school =       "Massachusetts Institute of Technology, Dept. of
                 Aeronautics and Astronautics",
  address =      "Cambridge, MA, USA",
  pages =        "60",
  year =         "1989",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Supervised by James K. Roberge",
  acknowledgement = ack-nhfb,
}

@InProceedings{Zeng:1989:RNP,
  author =       "B. Zeng and Y. Neuvo",
  booktitle =    "European Conference on Circuit Theory and Design, 5--8
                 Sep 1989",
  title =        "Roundoff noise properties of lattice filters employing
                 floating-point arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "233--237",
  year =         "1989",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The roundoff noise properties of general lattice
                 filters are studied for floating-point implementations
                 using the concept of dummy multipliers. The main
                 efforts are devoted to the Gray-Markel recursive
                 structures. It is shown that the roundoff noise
                 \ldots{}",
}

@Article{Zorpette:1989:PGD,
  author =       "Glenn Zorpette",
  title =        "{Parkinson}'s gun director",
  journal =      j-IEEE-SPECTRUM,
  volume =       "26",
  number =       "4",
  pages =        "43--43",
  month =        apr,
  year =         "1989",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/6.24154",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Mon Jan 20 06:41:24 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum1980.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "antiaircraft guns; Arithmetic; Automatic control;
                 Cities and towns; controllers; Crystallization;
                 electromechanical system; gun director; Guns;
                 Laboratories; M-9; magnetic clutches; operational
                 amplifiers; Operational amplifiers; position control;
                 potentiometer; Psychology; Springs; Telephony;
                 weapons",
}

@Article{Alsup:1990:MFA,
  author =       "M. Alsup",
  title =        "{Motorola}'s 88000 Family Architecture",
  journal =      j-IEEE-MICRO,
  volume =       "10",
  number =       "3",
  pages =        "48--66",
  month =        may # "\slash " # jun,
  year =         "1990",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/40.56325",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Wed Sep 7 22:32:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}

@Article{Anonymous:1990:MUF,
  author =       "Anonymous",
  title =        "{Motorola} unveils 96002 floating point processor",
  journal =      "Integrated circuits international",
  pages =        "3--??",
  month =        jul,
  year =         "1990",
  ISSN =         "0263-6522",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@MastersThesis{Ansari:1990:MBF,
  author =       "Ahmad Ansari",
  title =        "A $ 3 \times 3 $ multipurpose bus-connected
                 floating-point array processor",
  type =         "Thesis ({M.S.})",
  school =       "University of Florida",
  address =      "Gainesville, FL, USA",
  pages =        "vi + 127",
  year =         "1990",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Arnold:1990:RLA,
  author =       "M. G. Arnold and T. A. Bailey and J. R. Cowles and J.
                 J. Cupal",
  title =        "Redundant logarithmic arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "8",
  pages =        "1077--1086",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57046",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:03 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57046",
  abstract =     "A number system that offers advantages in some
                 situations over conventional floating point and
                 sign/logarithmic number systems is described. Redundant
                 logarithmic arithmetic, like conventional logarithmic
                 arithmetic, relies on table lookups to make the
                 arithmetic unit simpler than an equivalent floating
                 point unit. The cost of 32 bit subtraction in a
                 redundant logarithmic number system is lower than
                 previously published logarithmic subtraction methods.
                 The total memory requirement for a 29-bit redundant
                 logarithmic unit is 16 K words compared to 22 K words
                 by the best previously published conventional sign
                 logarithm unit, assuming similar addition techniques
                 are employed. A redundant logarithmic number system can
                 be implemented with online arithmetic, which would be
                 impractical for a conventional sign logarithm number
                 system. The disadvantages of redundant arithmetic are
                 typical of redundant number systems. First, the
                 redundancy doubles the storage requirements for data
                 values. Second, the representation can become
                 ill-conditioned, especially as a result of iterated
                 multiplications. Third, division and square root
                 operations are more difficult to implement in redundant
                 logarithmic arithmetic.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, Wyoming University,
                 Laramie, WY, USA",
  ajournal =     "IEEE Trans. Comput.",
  classification = "C1160 (Combinatorial mathematics); C1210B
                 (Reliability theory); C5230 (Digital arithmetic
                 methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "29-Bit redundant logarithmic unit; 32 Bit subtraction;
                 Arithmetic unit; Data values; Division;
                 Ill-conditioned; Iterated multiplications; Memory
                 requirement; Online arithmetic; Redundant logarithmic
                 arithmetic; Redundant logarithmic number system; Square
                 root; Storage requirements; Table lookups",
  thesaurus =    "Digital arithmetic; Number theory; Redundancy; Table
                 lookup",
}

@Article{Aspray:1990:BBS,
  author =       "William Aspray",
  title =        "Back to Basics: The Stored Program Concept",
  journal =      j-IEEE-SPECTRUM,
  volume =       "27",
  number =       "9",
  pages =        "51--51",
  month =        sep,
  year =         "1990",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/6.58457",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Wed Jan 15 12:40:28 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum1990.bib",
  abstract =     "The history and early development of the stored
                 program concept are briefly described. This refers to
                 the ability of a calculating machine to store its
                 instructions in its internal memory and process them in
                 its arithmetic unit, so that in the course of a
                 computation they may be not just executed but also
                 modified at electronic speeds. John von Neumann, a
                 faculty member of the Institute for Advanced Study in
                 Princeton, NJ, participated in the discussions in which
                 the idea was elaborated, wrote the first report of the
                 concept, placed it in a theoretical context, and built
                 his own computer, which was the early model for a
                 number of others, including the important commercially
                 manufactured IBM 701. J. Presper Eckert and John
                 Mauchly perhaps first conceived of the stored program
                 concept and developed most of the plans for
                 implementing it in the Edvac, and later incorporated it
                 in the Univac and other computers produced by their
                 company. Several British computer scientists, notably
                 Maurice Wilkes, were the first to implement the idea in
                 machines initially designed to embody this feature.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "arithmetic unit; calculating machine; Computer aided
                 instruction; Computer aided manufacturing; Computer
                 architecture; Context modeling; Digital arithmetic;
                 file organisation; history; History; internal memory;
                 Laboratories; Military computing; Prototypes; storage
                 allocation; stored program concept; Virtual
                 manufacturing",
}

@InProceedings{Bajwa:1990:FFP,
  author =       "A. Bajwa and R. Steck",
  title =        "A fast floating point unit in the i960 general-purpose
                 embedded processor family",
  crossref =     "Wescon:1990:WCR",
  pages =        "218--222",
  year =         "1990",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Fast, cheap floating point arithmetic is required in
                 many embedded processor applications. This paper
                 describes a next-generation floating point unit
                 designed as an integrated functional unit on Intel's
                 i960 family of 32-bit embedded RISC processors. High
                 performance is achieved by utilizing two separate,
                 concurrent floating point execution units with wide
                 datapaths, both internally and to general-purpose
                 registers. Hardware system cost is reduced by
                 integrating the FPU on the main processor while
                 software development cost is minimized by using the
                 i960 Numerics Architecture supported by standard i960
                 family development tools.",
  acknowledgement = ack-nhfb,
  affiliation =  "Intel Corp., Hillsboro, OR, USA",
  availability = "Western Periodicals Co., 13000 Rayner Street, North
                 Hollywood, CA 91605, USA",
  classification = "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5220 (Computer architecture);
                 C5230 (Digital arithmetic methods)",
  keywords =     "32 Bit; 32-Bit embedded RISC processors; Concurrent
                 floating point execution units; Embedded processor
                 applications; Fast floating point unit; Floating point
                 arithmetic; FPU; General-purpose embedded processor
                 family; General-purpose registers; I960; I960 family;
                 I960 Numerics Architecture; Integrated functional unit;
                 Intel; Wide datapaths",
  numericalindex = "Word length 3.2E+01 bit",
  thesaurus =    "Computer architecture; Digital arithmetic;
                 Microprocessor chips; Reduced instruction set
                 computing",
}

@TechReport{Barlow:1990:EAU,
  author =       "Jesse Louis Barlow and Richard J. Zaccone",
  title =        "Error analysis in unnormalized floating point
                 arithmetic",
  type =         "Technical report",
  number =       "CS-90-23",
  institution =  "Pennsylvania State University, Department of Computer
                 Science",
  address =      "University Park, PA, USA",
  pages =        "9",
  month =        apr,
  year =         "1990",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Supported by the Air Force Office of Scientific
                 Research. Supported by the National Science Foundation.
                 Supported by the Office of Naval Research.",
  abstract =     "The need to construct architectures in VLSI has
                 focused attention on unnormalized floating point
                 arithmetic. Certain unnormalized arithmetics allow one
                 to `pipe on digits,' thus producing significant speed
                 up in computation and making the input problems of
                 special purpose devices such as systolic arrays easier
                 to solve. We consider the error analysis implications
                 of using unnormalized arithmetic in numerical
                 algorithms. We also give specifications for its
                 implementation. Our discussion centers on the example
                 of Gaussian elimination. We show that the use of
                 unnormalized arithmetic requires changes in the
                 analysis of this algorithm. We will show that only for
                 certain classes of matrices that include diagonally
                 dominant matrices (either row or column), Gaussian
                 elimination is as stable in unnormalized arithmetic as
                 in normalized arithmetic. However, if the diagonal
                 elements of the upper triangular matrix are post
                 normalized, then Gaussian elimination is as stable in
                 unnormalized arithmetic as in normalized arithmetic for
                 all matrices.",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic.; Floating-point arithmetic.",
}

@MastersThesis{Bhargava:1990:DFP,
  author =       "Ish Kumar Bhargava",
  title =        "Design of a floating point data acquisition system and
                 a development system for the {NC} 4016",
  type =         "Electrical Engineering Thesis ({M.S.})",
  school =       "University of Missouri--Rolla",
  address =      "Rolla, MO, USA",
  pages =        "ix + 107",
  year =         "1990",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Birman:1990:DWS,
  author =       "Mark Birman and Allen Samuels and George Chu and Chuk
                 Ting and Larry Hu and John McLeod and John Barnes",
  title =        "Developing the {WTL3170\slash 3171 Sparc}
                 Floating-Point Coprocessors",
  journal =      j-IEEE-MICRO,
  volume =       "10",
  number =       "1",
  pages =        "55--64",
  month =        jan # "\slash " # feb,
  year =         "1990",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/40.46769",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Contending with dual floating-point interfaces at both
                 25 and 40 MHz posed an extraordinary challenge in
                 coprocessor development.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  summary =      "The development of the first two members in a family
                 of scalable-processor-architecture (Sparc)-compatible
                 parts is described. With varying frequency and latency
                 performance, the chips work with the first two integer
                 unit (IU) implementations from \ldots{}",
}

@Article{Blevins:1990:BHI,
  author =       "D. W. Blevins and E. W. Davis and R. A. Heaton and J.
                 H. Feif",
  title =        "{BLITZEN}: a Highly Integrated Massively Parallel
                 Machine",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "8",
  number =       "2",
  pages =        "150--160",
  month =        feb,
  year =         "1990",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 17:13:17 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "B1265F (Microprocessors and microcomputers); B2570D
                 (CMOS integrated circuits); C5130 (Microprocessor
                 chips); C5220 (Computer architecture); C5440
                 (Multiprocessor systems and techniques)",
  corpsource =   "Microelectron. Center of North Carolina, Research
                 Triangle Park, NC, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "1.25 micron; 20 MHz; architecture; BLITZEN; CMOS
                 design rules; CMOS integrated circuits; computer
                 architecture; global; highly integrated massively
                 parallel machine; IEEE standard 32-bit floating point;
                 local control features; memory address; microprocessor
                 chips; multiplication; parallel processing; static RAM;
                 VLSI",
  treatment =    "P Practical",
}

@InBook{Branham:1990:PFP,
  author =       "Richard L. Branham",
  booktitle =    "Scientific Data Analysis: An Introduction to
                 Overdetermined Systems",
  title =        "Properties of Floating-Point Numbers",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "x + 237 + 36",
  pages =        "1--19",
  year =         "1990",
  DOI =          "https://doi.org/10.1007/978-1-4612-3362-6_1",
  ISBN =         "1-4612-3362-3 (e-book), 1-4612-7981-X",
  ISBN-13 =      "978-1-4612-3362-6 (e-book), 978-1-4612-7981-5",
  LCCN =         "QA76.9.D35",
  bibdate =      "Sat Dec 31 11:59:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
  remark =       "This introductory chapter discusses floating-point
                 arithmetic in VAX binary, IBM System\slash 360
                 hexadecimal, and Sharp pocket calculator decimal
                 formats, but has no mention of IEEE 754 arithmetic. It
                 discusses the failure in floating-point arithmetic of
                 the associative, cancellation, and distributive laws of
                 exact arithmetic. In the context of accurate
                 floating-point summation, it describes Kahan's
                 compensated summation algorithm, Linz'
                 binary-subdivision summation algorithm, and Wolfe's
                 cascaded accumulator algorithm, all implemented in
                 Fortran code given in the chapter figures. It also
                 treats the error in summation in rounded and truncated
                 arithmetic, and mentions the importance of guard
                 digits.",
  tableofcontents = "Properties of Floating-Point Numbers \\
                 Matrices, Norms, and Condition Numbers \\
                 Sparse Matrices \\
                 Introduction to Overdetermined Systems \\
                 Linear Least Squares \\
                 The L1 Method \\
                 Nonlinear Methods \\
                 The Singular Value Decomposition \\
                 Index",
}

@InProceedings{Buck:1990:PAN,
  author =       "P. D. Buck and S. L. Day and D. Gonzalez",
  title =        "Problems with {Ada} numeric routines",
  crossref =     "Anonymous:1990:PAN",
  pages =        "195--204",
  year =         "1990",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Computer programmers believe that their systems will
                 always perform as expected. Standardization of computer
                 languages has been a major advance towards this goal.
                 The Ada language was intended to further advance this
                 goal by rigorously defining the language. In addition
                 the language was intended to improve the portability of
                 programs. The authors' experience shows that the
                 definition of the Ada language does not ensure
                 mathematical algorithms will function consistently
                 across multiple hardware environments. The method used
                 by the language designers to specify the floating point
                 data types appears to be the cause of the problem.",
  acknowledgement = ack-nhfb,
  affiliation =  "Nat. University, San Diego, CA, USA",
  classification = "C6120 (File organisation); C6130 (Data handling
                 techniques); C6140D (High level languages)",
  keywords =     "Ada; Floating point data types; Mathematical
                 algorithms; Multiple hardware environments; Numeric
                 routines; Portability",
  thesaurus =    "Ada; Data structures; Digital arithmetic; Software
                 portability; Symbol manipulation",
}

@Article{Bursky:1990:FMC,
  author =       "D. Bursky",
  title =        "Floating-point math chip delivers 200 mflops peak",
  journal =      j-ELECTRONIC-DESIGN,
  volume =       "38",
  number =       "4",
  pages =        "51--52, 54, 55",
  month =        feb,
  year =         "1990",
  CODEN =        "ELODAW",
  ISSN =         "0013-4872 (print), 1944-9550 (electronic)",
  ISSN-L =       "0013-4872",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "By exploiting its latest process improvements and a
                 three-layer metal interconnection capability, Bipolar
                 Integrated Technology has managed to boost
                 floating-point throughput three- to five-fold over its
                 previous-generation circuits. The new B3130, a
                 single-chip double-precision floating-point processor
                 with 64-bit data buses, can deliver up to 200 MFLOPS of
                 peak throughput. With more than 55000 equivalent gates
                 and multiple 64-bit data buses (plus eight parity bits
                 on each bus), the chip is the highest-complexity ECL
                 chip to be sold commercially. By employing a high
                 degree of integration, the single chip packs a 64-bit
                 ALU, a 54-bit parallel multiplier (for the mantissa),
                 and a 64-bit divide/square root unit. The chip's
                 architecture is optimized for vector processing, but it
                 can also perform scalar calculations. In addition, the
                 wide data buses and pipelining support eliminate the
                 loading and unloading bottlenecks that frequently
                 degrade chip performance.",
  acknowledgement = ack-nhfb,
  classification = "B1265F (Microprocessors and microcomputers); B2570B
                 (Bipolar integrated circuits); C5130 (Microprocessor
                 chips); C5230 (Digital arithmetic methods)",
  fjournal =     "Electronic Design",
  keywords =     "200 MFLOPS; 64 Bit; ALU; B3130; Bipolar Integrated
                 Technology; Bipolar microprocessor; Divide/square root
                 unit; Double-precision; ECL chip; Floating-point
                 processor; Multiple data buses; Parallel multiplier;
                 Pipelining support; Scalar calculations; Three-layer
                 metal interconnection; Vector processing",
  numericalindex = "Computer speed 2.0E+08 FLOPS; Word length 6.4E+01
                 bit",
  thesaurus =    "Bipolar integrated circuits; Digital arithmetic;
                 Emitter-coupled logic; Microprocessor chips; Parallel
                 architectures; Parallel machines; Pipeline processing;
                 VLSI",
}

@Article{Carter:1990:RSD,
  author =       "T. M. Carter and J. E. Robertson",
  title =        "Radix-$ 16 $ signed-digit division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "12",
  pages =        "1424--1433",
  month =        dec,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.61063",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:05 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=61063",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Carter:1990:STA,
  author =       "T. M. Carter and J. E. Robertson",
  title =        "The set theory of arithmetic decomposition",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "8",
  pages =        "993--1005",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57037",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:03 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57037",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Chen:1990:DIH,
  author =       "J. T. Chen and W. K. Jenkins and I. A. Hein and W. D.
                 {O'Brien, Jr.}",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, 1--3 May 1990",
  title =        "Design and implementation of a high speed residue
                 number system correlator for ultrasonic time domain
                 blood flow measurement",
  volume =       "4",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2893--2896",
  year =         "1990",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1990.112615",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The design and operation of a high-speed residue
                 number system (RNS) digital correlator is presented for
                 implementing the correlation function in a real-time
                 ultrasonic blood flow measurement system. This
                 architecture allows for both high-speed \ldots{}",
}

@Article{Chren:1990:NRN,
  author =       "W. A. {Chren, Jr.}",
  title =        "A new residue number system division algorithm",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "19",
  number =       "7",
  pages =        "13--29",
  month =        "????",
  year =         "1990",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 19:01:19 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/089812219090190U",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Ciminiera:1990:HRS,
  author =       "L. Ciminiera and P. Montuschi",
  title =        "Higher radix square rooting",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "10",
  pages =        "1220--1231",
  month =        oct,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.59853",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:04 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=59853",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "A general discussion on nonrestoring square root
                 algorithms is presented, showing bounds and constraints
                 delimiting the space of feasible algorithms, for all
                 the choices of radix, digit set and representation of
                 the partial remainder. Two classes of \ldots{}",
}

@Article{Clinger:1990:HRF,
  author =       "William D. Clinger",
  title =        "How to Read Floating Point Numbers Accurately",
  journal =      j-SIGPLAN,
  volume =       "25",
  number =       "6",
  pages =        "92--101",
  month =        jun,
  year =         "1990",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/93548.93557",
  ISBN =         "0-89791-364-7",
  ISBN-13 =      "978-0-89791-364-5",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:15:53 MST 2003",
  bibsource =    "Compendex database;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbiblio.txt;
                 http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/proceedings/pldi/93542/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigplan1990.bib",
  note =         "See also output algorithms in
                 \cite{Knuth:1990:SPW,Steele:1990:HPF,Burger:1996:PFP,Abbott:1999:ASS,Steele:2004:RHP}.",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/pldi/93542/p92-clinger/",
  abstract =     "Consider the problem of converting decimal scientific
                 notation for a number into the best binary floating
                 point approximation to that number, for some fixed
                 precision. This problem cannot be solved using
                 arithmetic of any fixed precision. Hence the IEEE
                 Standard for Binary Floating-Point Arithmetic does not
                 require the result of such a conversion to be the best
                 approximation. This paper presents an efficient
                 algorithm that always finds the best approximation. The
                 algorithm uses a few extra bits of precision to compute
                 an IEEE-conforming approximation while testing an
                 intermediate result to determine whether the
                 approximation could be other than the best. If the
                 approximation might not be the best, then the best
                 approximation is determined by a few simple operations
                 on multiple-precision integers, where the precision is
                 determined by the input. When using 64 bits of
                 precision to compute IEEE double precision results, the
                 algorithm avoids higher-precision arithmetic over 99\%
                 of the time.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Oregon University, Eugene, OR, USA",
  annote =       "Published as part of the Proceedings of PLDI'90.",
  classification = "722; 723; C1160 (Combinatorial mathematics); C5230
                 (Digital arithmetic methods); C7310 (Mathematics)",
  confdate =     "20-22 June 1990",
  conference =   "Proceedings of the ACM SIGPLAN '90 Conference on
                 Programming Language Design and Implementation",
  conferenceyear = "1990",
  conflocation = "White Plains, NY, USA",
  confsponsor =  "ACM",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  journalabr =   "SIGPLAN Not",
  keywords =     "algorithms; Best binary floating point approximation;
                 Computer Programming Languages; Computers, Digital ---
                 Computational Methods; Decimal scientific notation;
                 Design; Efficient algorithm; experimentation; Fixed
                 precision; Floating point numbers; Floating Point
                 Numbers; Higher-precision arithmetic; IEEE double
                 precision results; IEEE Standard; IEEE-conforming
                 approximation; Intermediate result; Multiple-precision
                 integers",
  meetingaddress = "White Plains, NY, USA",
  meetingdate =  "Jun 20--22 1990",
  meetingdate2 = "06/20--22/90",
  sponsor =      "Assoc for Computing Machinery, Special Interest Group
                 on Programming Languages",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems. {\bf G.1.0} Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf
                 G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation.",
  thesaurus =    "Digital arithmetic; Mathematics computing; Number
                 theory; Standards",
}

@Article{Codenotti:1990:ATT,
  author =       "B. Codenotti and G. Lotti and F. Romani",
  title =        "Area-time trade-offs for matrix-vector
                 multiplication",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "8",
  number =       "1",
  pages =        "52--59",
  month =        jan,
  year =         "1990",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst di Elaborazione dell'Informazione-CNR",
  affiliationaddress = "Pisa, Italy",
  classification = "722; 723; 921; B0290H (Linear algebra); B1265B
                 (Logic circuits); C4140 (Linear algebra); C4240
                 (Programming and algorithm theory)",
  corpsource =   "Istituto di Elaborazione dell'Inf., CNR, Pisa, Italy",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "algebra; area-time complexity; Area-Time Trade-Offs;
                 arithmetic; computation; computational complexity;
                 Computer Systems, Digital; Computers,
                 Digital--Computational Methods; I/O conventions;
                 information flow; integrated logic circuits;
                 Mathematical Techniques--Matrix Algebra; matrix;
                 Matrix-Vector Multiplication; matrix-vector
                 multiplication; operations; Parallel Processing; sparse
                 matrix; VLSI",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Cosnard:1990:STF,
  author =       "Michel Cosnard and Jean Duprat and Yves Robert",
  title =        "Systolic triangularization over finite fields",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "9",
  number =       "3",
  pages =        "252--260",
  month =        jul,
  year =         "1990",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Ecole Normale Superieure de Lyon Lab LIP-IMAG",
  affiliationaddress = "Lyon, Fr",
  classification = "722; 723; 921; C4140 (Linear algebra); C5220
                 (Computer architecture); C5230 (Digital arithmetic
                 methods)",
  corpsource =   "IMAG, Ecole Normale Superieure de Lyon, France",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "architecture; arithmetic number; computer algebra;
                 Computer Programming--Algorithms; Computer Systems,
                 Digital--Parallel Processing; Computers, Digital;
                 digital arithmetic; finite fields; Gaussian
                 Elimination; Gaussian elimination; large dense linear
                 systems; linear algebra; Mathematical
                 Techniques--Linear Algebra; Modular Multiplication
                 Algorithm; parallel architectures; partial; pivoting;
                 Special Purpose Application; systolic; Systolic Arrays;
                 Systolic Triangularization; systolic triangularization;
                 theory",
  treatment =    "P Practical; T Theoretical or Mathematical",
}

@Manual{Cyrix:1990:FCU,
  title =        "{FasMath CX-83D87} User's Manual: High Performance
                 {CMOS} Math Processor",
  publisher =    "Cyrix Corp.",
  address =      "Richardson, TX, USA",
  pages =        "115 + 5 + 3",
  year =         "1990",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.ardent-tool.com/CPU/docs/Cyrix/387/83d87.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Cyrix CX-83D87 (Microprocessor); Cyrix CX-83S87
                 (Microprocessor); Floating-point arithmetic; Integrated
                 circuits --- Very large scale integration; Metal oxide
                 semiconductors, Complementary",
}

@Article{Darley:1990:TFC,
  author =       "Merrick Darley and Bill Kronlage and David Bural and
                 Bob Churchill and David Pulling and Paul Wang and Rick
                 Iwamoto and Larry Yang",
  title =        "The {TMS390C602A} Floating-Point Coprocessor for
                 {Sparc} Systems",
  journal =      j-IEEE-MICRO,
  volume =       "10",
  number =       "3",
  pages =        "36--47",
  month =        may # "\slash " # jun,
  year =         "1990",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/40.56324",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/microchip.bib",
  abstract =     "A recent Sparc (scalable processor architecture)
                 processor consists of a two-chip configuration,
                 containing the TMS390C601 integer unit (IU) and the
                 TMS390C602A floating-point unit (FPU). The second
                 device, an innovative coprocessor that lets the
                 processor execute single- or double-precision
                 floating-point instructions concurrently with IU
                 operations is described. Dedicated floating-point
                 hardware in the FPU increases the performance of the
                 system. Running at clock periods as small as 20 ns, the
                 chip should deliver 5.5 million double-precision
                 floating-point operations per second under the Linpack
                 benchmark (50-MHz clock rate). The FPU provides single-
                 and double-precision arithmetic functions: addition,
                 subtraction, multiplication, division, square root,
                 compare, and convert. To minimize its math unit's
                 latency, the FPU uses a highly parallel architecture
                 requiring separate math units to optimize additions and
                 multiplications. Traps stop the execution of a program
                 to jump to software routine for handling data-dependent
                 errors or to execute instructions not implemented in
                 the hardware. Benchmark results are presented. (4
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "Texas Instrum. Inc., Dallas, TX, USA",
  classification = "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5230 (Digital arithmetic
                 methods)",
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  keywords =     "Addition; Compare; Convert; Division; Linpack
                 benchmark; Multiplication; Sparc systems; Square root;
                 Subtraction; TMS390C601 integer unit; TMS390C602A
                 floating-point coprocessor; TMS390C602A floating-point
                 unit; Two-chip configuration",
  language =     "English",
  pubcountry =   "USA",
  thesaurus =    "Digital arithmetic; Microprocessor chips",
}

@Article{Darley:1990:TFP,
  author =       "Merrick Darley and Bill Kronlage and David Bural and
                 Bob Churchill and David Pulling and Paul Wang and Rick
                 Iwamoto and Larry Yang",
  title =        "The {TMS390C602A} Floating-Point Coprocessor for
                 {Sparc} Systems",
  journal =      j-IEEE-MICRO,
  volume =       "10",
  number =       "3",
  pages =        "36--47",
  month =        may # "\slash " # jun,
  year =         "1990",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/40.56324",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A recent Sparc (scalable processor architecture)
                 processor consists of a two-chip configuration,
                 containing the TMS390C601 integer unit (IU) and the
                 TMS390C602A floating-point unit (FPU). The second
                 device, an innovative coprocessor that lets the
                 processor execute single- or double-precision
                 floating-point instructions concurrently with IU
                 operations is described. Dedicated floating-point
                 hardware in the FPU increases the performance of the
                 system. Running at clock periods as small as 20 ns, the
                 chip should deliver 5.5 million double-precision
                 floating-point operations per second under the Linpack
                 benchmark (50-MHz clock rate). The FPU provides single-
                 and double-precision arithmetic functions: addition,
                 subtraction, multiplication, division, square root,
                 compare, and convert. To minimize its math unit's
                 latency, the FPU uses a highly parallel architecture
                 requiring separate math units to optimize additions and
                 multiplications. Traps stop the execution of a program
                 to jump to software routine for handling data-dependent
                 errors or to execute instructions not implemented in
                 the hardware. Benchmark results are presented. (4
                 Refs.)",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  affiliation =  "Texas Instrum. Inc., Dallas, TX, USA",
  classification = "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5230 (Digital arithmetic
                 methods)",
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  keywords =     "Addition; Compare; Convert; Division; Linpack
                 benchmark; Multiplication; Sparc systems; Square root;
                 Subtraction; TMS390C601 integer unit; TMS390C602A
                 floating-point coprocessor; TMS390C602A floating-point
                 unit; Two-chip configuration",
  summary =      "A recent Sparc (scalable processor architecture)
                 processor consists of a two-chip configuration,
                 containing the TMS390C601 integer unit (IU) and the
                 TMS390C602A floating-point unit (FPU). The second
                 device, an innovative coprocessor that lets the
                 \ldots{}",
  thesaurus =    "Digital arithmetic; Microprocessor chips",
}

@InProceedings{deLange:1990:ASI,
  author =       "A. A. J. de Lange and A. J. van der Hoeven and E. F.
                 Deprettere and P. Dewilde",
  booktitle =    "{[Proceedings] EURO ASIC `90}",
  title =        "An application specific {IC} for digital signal
                 processing: the floating point pipeline {CORDIC}
                 processor",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "62--67",
  year =         "1990",
  DOI =          "https://doi.org/10.1109/EASIC.1990.207911",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Application specific integrated circuits; Array signal
                 processing; Digital integrated circuits; Digital signal
                 processing; Hardware; Pipelines; Radar antennas; Radar
                 signal processing; Signal processing algorithms;
                 Vectors",
}

@InProceedings{deLange:1990:RTA,
  author =       "A. A. J. de Lange and E. F. Deprettere and A. J. van
                 der Veen and J. Bu",
  editor =       "????",
  booktitle =    "{Proceedings of the ICASSP International Conference on
                 Acoustic, Speech, and Signal Processing April 1990}",
  title =        "Real Time Applications of the Floating Point Pipeline
                 {CORDIC} Processor in Massive-Parallel Pipelined {DSP}
                 Algorithms",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1013--1016 (vol. 2)",
  year =         "1990",
  DOI =          "https://doi.org/10.1109/ICASSP.1990.116062",
  ISBN =         "",
  ISBN-13 =      "",
  LCCN =         "",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1109/ICASSP.1990",
  keywords =     "Application software; Array signal processing;
                 Computer graphics; Digital arithmetic; Multiprocessing
                 systems; Pipelines; Speech processing; System testing;
                 Very large scale integration",
}

@Book{Dewar:1990:MPV,
  author =       "Robert B. K. Dewar and Matthew Smosna",
  title =        "Microprocessors: a programmer's view",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "xvii + 462",
  year =         "1990",
  ISBN =         "0-07-016638-2, 0-07-016639-0 (soft)",
  ISBN-13 =      "978-0-07-016638-7, 978-0-07-016639-4 (soft)",
  LCCN =         "????",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Microprocessors --- Programming.",
  remark =       "Microprocessors --- Introduction to the 80386 ---
                 Addressing and memory on the 80386 --- Tasking, virtual
                 memory, and exceptions to the 80386 --- Microprocessors
                 and floating-point arithmetic --- 68030 user
                 programming model --- 68030 supervisor state ---
                 Introduction to RISC architectures --- MIPS processors
                 --- SPARC architecture --- Intel i860 --- IBM RISC
                 chips --- INMOS transputer - - Future of microprocessor
                 design.",
}

@InProceedings{Dixon:1990:HPB,
  author =       "G. Dixon",
  title =        "A high performance block floating point {DSP}
                 chip-set",
  crossref =     "IEE:1990:ICV",
  pages =        "9/1--7",
  year =         "1990",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper describes the design and development of two
                 ASICs which form the processing kernel of a high
                 performance sonar signal processor; namely a 24-bit
                 Block Floating Point Arithmetic Unit (BFPAU), and a
                 Table Memory And Address Modifier (TMAAM). The system
                 is based upon a 24-bit block floating point data format
                 which is a compromise between fixed and floating point
                 data; possessing the advantage of reducing the data
                 storage requirement compared to true floating point
                 while allowing arithmetic to be performed in the faster
                 fixed-point format whilst retaining the extended
                 dynamic range provided by floating point. The BFPAU and
                 TMAAM perform the arithmetic processing; the BFPAU is
                 the central arithmetic processor aimed at sonar signal
                 processing in general and beamforming in particular,
                 while the TMAAM provides a range of essential support
                 functions such as look-up tables for trigonometric
                 functions, address generation, exponent control and
                 normalisation and program sequencing. Two blocks of
                 dual-port RAM provide storage for system I/O data
                 transfers, together with two blocks of RAM providing
                 working data storage for the BFPAU. A block of video
                 RAM is used to store address and control sequences for
                 the processing element.",
  acknowledgement = ack-nhfb,
  affiliation =  "Plessey Res. Caswell, Towcester, UK",
  classification = "B1265F (Microprocessors and microcomputers); B6320E
                 (Sonar and acoustic radar)",
  keywords =     "Address generation; Arithmetic processing; ASICs;
                 Beamforming; Block floating point DSP chip-set; Data
                 format; Data storage requirement; Dual-port RAM;
                 Dynamic range; Exponent control; Fixed-point format;
                 Look-up tables; Normalisation; Program sequencing;
                 Sonar signal processor; System I/O data transfers;
                 Video RAM; Working data storage",
  thesaurus =    "Application specific integrated circuits; Digital
                 signal processing chips; Random-access storage; Sonar",
}

@Article{Dotzel:1990:DMG,
  author =       "G{\"u}nter Dotzel",
  title =        "Does {Modula-2} generate racehorses? {Comparison} of
                 compiler generated code quality for floating point
                 arithmetic",
  journal =      j-SIGPLAN,
  volume =       "25",
  number =       "12",
  pages =        "85--88",
  month =        dec,
  year =         "1990",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:16:00 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A simple example serves to demonstrate the code
                 quality generated by two different Modula-2 compilers.
                 The two compilers are called the Zurich/Hamburger and
                 the Erlanger. The author lists the Modula-2 source
                 program, shows an excerpt of the machine code listing
                 generated by the Erlanger and presents that of the
                 Zurich/Hamburger. The differences in code quality
                 concerning instruction count, code size and execution
                 speed are discussed and summarized. The author also
                 presents the main program module used for the
                 benchmarks and a short description of the development
                 history of Modula-2 and Modula/R.",
  acknowledgement = ack-nhfb,
  affiliation =  "ModulaWare GmbH, Erlangen, West Germany",
  classification = "C6140D (High level languages); C6150C (Compilers,
                 interpreters and other processors); C6150G (Diagnostic,
                 testing, debugging and evaluating systems)",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "Benchmarks; Code size; Compiler generated code
                 quality; Development history; Erlanger; Execution
                 speed; Floating point arithmetic; Instruction count;
                 Machine code listing; Main program module; Modula-2
                 compilers; Modula-2 source program; Modula/R;
                 Zurich/Hamburger",
  thesaurus =    "Modula; Modula listings; Program compilers; Program
                 testing",
}

@Article{Dunham:1990:FFE,
  author =       "C. B. Dunham",
  title =        "Feasibility of `Perfect' Function Evaluation",
  journal =      j-SIGNUM,
  volume =       "25",
  number =       "4",
  pages =        "25--26",
  month =        oct,
  year =         "1990",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Thu Sep 1 10:15:30 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}

@Article{Edenfield:1990:PPD,
  author =       "R. W. Edenfield and M. G. Gallup and W. B. {Ledbetter,
                 Jr.} and R. C. McGarity and E. E. Quintana and R. A.
                 Reininger",
  title =        "The 68040 Processor. {Part} 1, Design and
                 Implementation",
  journal =      j-IEEE-MICRO,
  volume =       "10",
  number =       "1",
  pages =        "66--78",
  month =        jan # "\slash " # feb,
  year =         "1990",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/40.46770",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Wed Sep 7 22:32:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}

@Article{Ercegovac:1990:FMC,
  author =       "M. D. Ercegovac and T. Lang",
  title =        "Fast multiplication without carry-propagate addition",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "11",
  pages =        "1385--1390",
  month =        nov,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.61047",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:05 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=61047",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Ercegovac:1990:RSR,
  author =       "M. D. Ercegovac and T. Lang",
  title =        "Radix-$4$ square root without initial {PLA}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "8",
  pages =        "1016--1024",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57040",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:03 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57040",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Ercegovac:1990:SRD,
  author =       "M. D. Ercegovac and T. Lang",
  title =        "Simple radix-$4$ division with operands scaling",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "9",
  pages =        "1204--1208",
  month =        sep,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57060",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:04 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57060",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Fussichen:1990:GAM,
  author =       "Kenneth Fussichen",
  title =        "Getting {Ada} into the mainstream in the 1990's",
  crossref =     "ACM:1990:PDB",
  pages =        "428--428",
  year =         "1990",
  DOI =          "https://doi.org/10.1145/255471.255572",
  bibdate =      "Thu Aug 07 18:17:35 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Ada offers a great deal to the MIS community. There
                 are a number of language features that provide
                 attractive tools to the programmer. Ada's support for
                 Object Orientation is far superior to that currently
                 afforded by IBM mainframe languages such as COBOL and
                 PL/1. This translates into more maintainable code,
                 which is the key to MIS Ada
                 acceptance.\par

                 Unfortunately, Ada introduces problems that do not
                 currently exist in MIS. Decimal arithmetic and string
                 manipulation adequate to support reporting are
                 inherently non-existent. I/O support is inadequate as
                 are DBMS bindings. Conversions are forced on non-ASCII
                 hosts. The compiler has the option of reordering fields
                 within records, rendering non-Ada utilities useless.
                 There is an inexcusable lack of understanding of the
                 targeted market.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@Article{Gallant:1990:MCI,
  author =       "John Gallant and Bill Travis",
  title =        "Math coprocessor {ICs}: Floating-point chips boost
                 {muP} performance",
  journal =      j-EDN,
  volume =       "35",
  number =       "12",
  pages =        "63--??",
  month =        jun,
  year =         "1990",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Floating-point arithmetic exacts huge penalties in CPU
                 computation time. Dedicated coprocessor ICs execute
                 this onerous task automatically and efficiently.",
  acknowledgement = ack-nhfb,
  fjournal =     "EDN",
}

@TechReport{Gay:1990:CRB,
  author =       "David M. Gay",
  title =        "Correctly Rounded Binary---Decimal and Decimal--Binary
                 Conversions",
  type =         "Numerical Analysis Manuscript",
  number =       "90-10",
  institution =  pub-ATT-BELL,
  address =      pub-ATT-BELL:adr,
  pages =        "16",
  day =          "30",
  month =        nov,
  year =         "1990",
  bibdate =      "Sat Apr 28 18:42:55 2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/gay-david-m.bib",
  URL =          "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://cm.bell-labs.com/cm/cs/doc/90/4-10.ps.gz;
                 http://cm.bell-labs.com/cm/cs/what/ampl/REFS/rounding.ps.gz;
                 http://www.ampl.com/ampl/REFS/rounding.ps.gz;
                 http://www.netlib.org/fp/dtoa.c;
                 http://www.netlib.org/fp/g_fmt.c;
                 http://www.netlib.org/fp/gdtoa.tgz;
                 http://www.netlib.org/fp/rnd_prod.s;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This note discusses the main issues in performing
                 correctly rounded decimal-to-binary and
                 binary-to-decimal conversions. It reviews recent work
                 by Clinger and by Steele and White on these conversions
                 and describes some efficiency enhancements.
                 Computational experience with several kinds of
                 arithmetic suggests that the average computational cost
                 for correct rounding can be small for typical
                 conversions. Source for conversion routines that
                 support this claim is available from netlib.",
  acknowledgement = ack-nj,
  keywords =     "correct rounding; decimal floating-point arithmetic",
}

@InProceedings{Gibson:1990:CII,
  author =       "D. H. Gibson",
  title =        "Considerations for including {IEEE} floating point in
                 large systems",
  crossref =     "SHARE:1990:PSE",
  pages =        "47--62",
  year =         "1990",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "International standards such as ANSI/IEEE Std 754-1985
                 floating-point arithmetic provide the potential for
                 application portability. The paper, beginning with a
                 1984 SHARE requirements statement, sets forth certain
                 considerations for including IEEE Std 754 floating
                 point in large systems. A tutorial is presented on IEEE
                 Std 754 floating-point arithmetic. The considerations
                 for integrating IEEE into a large system along with an
                 existing floating point representation are discussed in
                 three categories: architectural; implementation; usage.
                 Related topics are identified and discussed. The paper
                 concludes with a summary of the considerations. (11
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Corp., Poughkeepsie, NY, USA",
  classification = "C5230 (Digital arithmetic methods)",
  keywords =     "Application portability; Floating-point arithmetic;
                 IEEE Std 754 floating point; SHARE",
  thesaurus =    "Digital arithmetic; Standards",
}

@Article{Glass:1990:MC,
  author =       "L. B. Glass",
  title =        "Math coprocessors",
  journal =      j-BYTE,
  volume =       "15",
  number =       "1",
  pages =        "337--348",
  month =        jan,
  year =         "1990",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Thu Sep 12 17:47:21 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "B1265B (Logic circuits); B1265F (Microprocessors and
                 microcomputers); C5130 (Microprocessor chips); C5230
                 (Digital arithmetic methods)",
  fjournal =     "BYTE Magazine",
  keywords =     "Cyrix 83D87; Floating-point maths; IEEE 754
                 floating-point standard; Integrated Information
                 Technology; Intel 80287; Intel 80387; Intel 8087; Maths
                 coprocessors; Motorola 68881; Motorola 68882; NP-3C87;
                 Weitek Abacus 3167",
  thesaurus =    "Digital arithmetic; Microprocessor chips; Satellite
                 computers",
}

@InCollection{Goldberg:1990:CA,
  author =       "D. Goldberg",
  title =        "Computer Arithmetic",
  crossref =     "Hennessy:1990:CAQ",
  chapter =      "A",
  pages =        "A-1--A-66",
  year =         "1990",
  bibdate =      "Fri Dec 08 13:04:21 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Goodman:1990:SMR,
  author =       "R. H. Goodman",
  title =        "Some Models of Relative Error in Products",
  journal =      j-APPL-NUM-MATH,
  volume =       "6",
  number =       "3",
  pages =        "209--220",
  month =        mar,
  year =         "1990",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Thu Sep 1 10:14:16 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274",
}

@MastersThesis{Goodreau:1990:DIF,
  author =       "Michael S. Goodreau",
  title =        "The design and implementation of a floating-point
                 format conversion integrated circuit",
  type =         "Thesis ({M.S.E.E.})",
  school =       "University of Washington",
  address =      "Seattle, WA, USA",
  pages =        "ix + 113",
  year =         "1990",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers --- Programming.;
                 Floating-point arithmetic.; Integrated circuits ---
                 Design and construction.",
}

@InCollection{Gries:1990:BDO,
  author =       "David Gries",
  title =        "Binary to Decimal, One More Time",
  crossref =     "Feijen:1990:BOB",
  chapter =      "16",
  pages =        "141--148",
  year =         "1990",
  DOI =          "https://doi.org/10.1007/978-1-4612-4476-9_17",
  bibdate =      "Sat Sep 03 09:41:32 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/texbook3.bib",
  note =         "This paper presents an alternate proof of Knuth's
                 algorithm \cite{Knuth:1990:SPW} for conversion between
                 decimal and fixed-point binary numbers.",
  URL =          "https://link.springer.com/chapter/10.1007/978-1-4612-4476-9_17",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@Article{Gu:1990:TIT,
  author =       "Li Zhen Gu and Xing Yuan Chen",
  title =        "Table-driven implementation of the trigonometric
                 functions using {IEEE} floating point operations.
                 ({Chinese})",
  journal =      "Journal of Tsinghua University",
  volume =       "30",
  number =       "3",
  pages =        "31--38",
  year =         "1990",
  MRclass =      "65D20 (65-04)",
  MRnumber =     "92a:65070",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Tsinghua Univ.",
}

@Book{Hamacher:1990:CO,
  author =       "V. Carl Hamacher and Zvonko G. Vranesic and Safwat G.
                 Zaky",
  title =        "Computer organization",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  edition =      "Third",
  pages =        "xx + 617",
  year =         "1990",
  ISBN =         "0-07-025685-3",
  ISBN-13 =      "978-0-07-025685-9",
  LCCN =         "QA76.9.A73 H351 1990",
  bibdate =      "Sat May 18 14:24:11 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "McGraw-Hill series in computer organization and
                 architecture",
  acknowledgement = ack-nhfb,
}

@Article{Hashemian:1990:SRA,
  author =       "R. Hashemian",
  title =        "Square Rooting Algorithms for Integer and
                 Floating-Point Numbers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "8",
  pages =        "1025--1029",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57041",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:03 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57041",
  abstract =     "An algorithm for evaluating the square root of
                 integers and real numbers is developed. The procedure
                 consists of two parts: one to obtain a close estimate
                 of the square root and the other to modify the initial
                 value, iteratively, until a precise root is evaluated.
                 The major effort in this development has been
                 concentrated on two objectives: high speed and no
                 division operation other than division by 2. The first
                 objective is achieved through a simple two-step
                 procedure for getting the first estimate, and then
                 modifying it by employing a fast converging iteration
                 technique. The second objective is also fulfilled
                 through applying bit-shift operation rather than
                 division operation. The algorithm is simulated for both
                 integer and real numbers, and the results are compared
                 to two methods being widely used. The results
                 (tabulated) show considerable improvement in speed
                 compared to these other two methods.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Department of Electr. Eng., Northern Illinois
                 University, Dekalb, IL, USA",
  ajournal =     "IEEE Trans. Comput.",
  classification = "C1160 (Combinatorial mathematics); C4130
                 (Interpolation and function approximation); C5230
                 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Bit-shift operation; Close estimate; Division by 2;
                 Fast converging iteration; Floating-point numbers;
                 Initial value modification; Integer numbers; Precise
                 root; Real numbers; Square rooting algorithms",
  summary =      "An algorithm for evaluating the square root of
                 integers and real numbers is developed. The procedure
                 consists of two parts: one to obtain a close estimate
                 of the square root and the other to modify the initial
                 value, iteratively, until a precise \ldots{}",
  thesaurus =    "Digital arithmetic; Iterative methods; Number theory",
}

@Article{Hokenek:1990:LZA,
  author =       "E. Hokenek and R. K. Montoye",
  title =        "Leading-zero anticipator ({LZA}) in the {IBM RISC
                 System\slash 6000} floating-point execution unit",
  journal =      j-IBM-JRD,
  volume =       "34",
  number =       "1",
  pages =        "71--77",
  month =        jan,
  year =         "1990",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Presents a novel technique used in the
                 multiply-add-fused (MAF) unit of the IBM RISC
                 System/6000 (RS/6000) processor for normalizing the
                 floating-point results. Unlike the conventional
                 procedures applied thus far, the so-called leading-zero
                 anticipator (LZA) of the RS/6000 carries out processing
                 of the leading zeros and ones in parallel with
                 floating-point addition. Therefore, the new circuitry
                 reduces the total latency of the MAF unit by enabling
                 the normalization and addition to take place in a
                 single cycle.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Res. Div., Thomas J. Watson Res. Center, Yorktown
                 Heights, NY, USA",
  classification = "B1265B (Logic circuits); C5230 (Digital arithmetic
                 methods)",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "Circuitry; Floating-point addition; IBM RISC
                 System/6000 floating-point execution unit; Latency;
                 Leading-zero anticipator; Multiply-add-fused;
                 Normalization; Parallel",
  thesaurus =    "Digital arithmetic; IBM computers; Reduced instruction
                 set computing",
}

@Article{Hokenek:1990:SGR,
  author =       "E. Hokenek and R. K. Montoye and P. W. Cook",
  title =        "Second-Generation {RISC} Floating Point with
                 Multiply-Add Fused",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "25",
  number =       "5",
  pages =        "1207--1213",
  month =        oct,
  year =         "1990",
  CODEN =        "IJSCBC",
  DOI =          "https://doi.org/10.1109/4.62143",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A 440000-transistor second-generation RISC (reduced
                 instruction set computer) floating-point chip is
                 described. The pipeline latency is only two cycles, and
                 a double-precision result is produced every cycle.
                 System throughput and accuracy are increased by using a
                 floating-point multiply-add-fused unit, which carries
                 out a double-precision accumulate as a two-cycle
                 pipelined execution with only one rounding error. While
                 the cycle time (40 ns) is competitive with other CMOS
                 RISC systems, the floating-point performance stretches
                 to the range of bipolar RISC systems (7.4-13 MFLOPS
                 LINPACK). Leading zero anticipation makes the two-cycle
                 pipeline possible by nearly eliminating the additional
                 postnormalization time, and it allows for reduced
                 overall system latency. Partial decode shifters allow
                 complete time sharing for the multiply and data
                 alignment. Improved design techniques for logarithmic
                 addition and higher order counters for multiplication
                 complete this second-generation RISC floating-point
                 unit design.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "IBM Thomas J. Watson Res. Center, Yorktown Heights,
                 NY, USA",
  classification = "B1265F (Microprocessors and microcomputers); B2570D
                 (CMOS integrated circuits); C5130 (Microprocessor
                 chips)",
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "40 Ns; 7.4 To 13 MFLOPS; Double-precision accumulate;
                 Double-precision result; Floating-point chip; Higher
                 order counters; Logarithmic addition; Multiplication;
                 Multiply-add-fused unit; Partial decode shifters;
                 Pipeline latency; Reduced instruction set computer;
                 RISC; Two-cycle pipelined execution",
  numericalindex = "Time 4.0E-08 s; Computer speed 7.4E+06 to 1.3E+07
                 FLOPS",
  summary =      "A 440000-transistor second-generation RISC (reduced
                 instruction set computer) floating-point chip is
                 described. The pipeline latency is only two cycles, and
                 a double-precision result is produced every cycle.
                 System throughput and accuracy are increased \ldots{}",
  thesaurus =    "CMOS integrated circuits; Microprocessor chips;
                 Pipeline processing; Reduced instruction set
                 computing",
}

@Article{Hong:1990:DTP,
  author =       "S. J. Hong",
  title =        "The design of a testable parallel multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "3",
  pages =        "411--416",
  month =        mar,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.48874",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=48874",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Horiguchi:1990:FNR,
  author =       "Hiroshi Horiguchi",
  title =        "Floating-Point Numbers and Real Numbers",
  journal =      j-ADV-SOFT-SCI-TECH,
  volume =       "1",
  number =       "??",
  pages =        "157--??",
  year =         "1990",
  ISSN =         "1044-7997",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Advances in software science and technology",
}

@TechReport{IBM:1990:AXI,
  author =       "{IBM Corporation}",
  title =        "{ACRITH-XSC}: {IBM} High Accuracy Arithmetic ---
                 Extended Scientific Computation",
  type =         "Technical Report",
  number =       "GC33-6461-01, SC33-6462-00, SC33-6463-00,
                 SC33-6464-00, SC33-6466-00.",
  institution =  pub-IBM,
  address =      pub-IBM:adr,
  year =         "1990",
  bibdate =      "Thu Jan 21 17:27:09 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "1. General Information \\
                 2. Reference \\
                 3. Sample Programs \\
                 4. How To Use \\
                 5. Syntax Diagrams",
}

@Book{IBM:1990:IRS,
  editor =       "Mamata Misra",
  title =        "{IBM RISC System\slash 6000 Technology, publication
                 SA23-2619-00}",
  publisher =    pub-IBM,
  address =      pub-IBM:adr,
  year =         "1990",
  bibdate =      "Wed Sep 14 23:02:26 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Jarvis:1990:ICA,
  author =       "P. Jarvis",
  title =        "Implementing {Cordic} Algorithms",
  journal =      j-DDJ,
  volume =       "15",
  number =       "10",
  pages =        "152--158",
  month =        oct,
  year =         "1990",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Thu Sep 1 10:15:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@InProceedings{Kahan:1990:HCA,
  author =       "W. Kahan",
  title =        "How {Cray}'s arithmetic hurts scientific computation
                 (and what might be done about it)",
  crossref =     "CUG:1990:PSC",
  pages =        "42",
  day =          "14",
  month =        jun,
  year =         "1990",
  bibdate =      "Tue Jan 03 18:17:16 2006",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Manuscript prepared for the Cray User Group meeting in
                 Toronto, Canada, April 10, 1990.",
  URL =          "http://754r.ucbtest.org/issues/cray-hurts-uk.pdf;
                 http://754r.ucbtest.org/issues/cray-hurts-ut.pdf;
                 http://754r.ucbtest.org/issues/cray-hurts.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1990:PCA,
  author =       "William Kahan",
  title =        "Paradoxes in concepts of accuracy",
  publisher =    "Carnegie Mellon University",
  address =      "Pittsburgh, PA, USA",
  year =         "1990",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "1 videocassette (60 min.)",
  series =       "Distinguished lecture series",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic.; Floating-point arithmetic ---
                 Data processing.",
  remark =       "Lecture given February 15, 1990. VHS format. Lecturer,
                 William Kahan. Paradoxes expose errors in conventional
                 wisdom about floating-point arithmetic.",
}

@Article{Kalbasi:1990:CYT,
  author =       "K. Kalbasi",
  title =        "Can you trust your computer?",
  journal =      j-IEEE-POT,
  volume =       "9",
  number =       "2",
  pages =        "15--18",
  month =        apr,
  year =         "1990",
  CODEN =        "IEPTDF",
  ISSN =         "0278-6648 (print), 1558-1772 (electronic)",
  ISSN-L =       "0278-6648",
  bibdate =      "Wed Sep 14 19:14:21 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IEEE Potentials",
}

@Article{Katsuno:1990:BFP,
  author =       "A. Katsuno and H. Takahashi and H. Kubosawa and T.
                 Sato and A. Suga and G. Goto",
  title =        "A 64-bit Floating-Point Processing Unit with a
                 Horizontal Instruction Code for Parallel Operations",
  crossref =     "IEEE:1990:PII",
  pages =        "347--350",
  year =         "1990",
  bibdate =      "Wed Sep 7 22:32:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@InProceedings{Khan:1990:FPA,
  author =       "A. Khan",
  title =        "Floating point architecture and implementation",
  crossref =     "Wescon:1990:WCR",
  pages =        "205--213",
  year =         "1990",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Analyzes various requirements of efficient floating
                 point architecture and implementation. The basic
                 elements of architecture such as latency, repeat rate
                 and issue rate are defined. Handling various exceptions
                 in a precise manner is described. Finally, a
                 description of one example (MIPS R3010) is provided. (0
                 Refs.)",
  acknowledgement = ack-nhfb,
  availability = "Western Periodicals Co., 13000 Rayner Street, North
                 Hollywood, CA 91605, USA",
  classification = "C5130 (Microprocessor chips); C5220 (Computer
                 architecture); C5230 (Digital arithmetic methods)",
  keywords =     "Elements of architecture; Floating point architecture;
                 Issue rate; Latency; MIPS R3010; Repeat rate;
                 Requirements",
  thesaurus =    "Computer architecture; Digital arithmetic",
}

@InProceedings{Kiernan:1990:FAE,
  author =       "J. M. Kiernan and T. B. Blachowiak",
  title =        "Fast, Accurate Elementary Functions For the {Cray
                 Y-MP} Computer",
  crossref =     "CUG:1990:PSC",
  pages =        "243--252",
  year =         "1990",
  bibdate =      "Thu Sep 1 10:15:30 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@InCollection{Knuth:1990:SPW,
  author =       "Donald E. Knuth",
  title =        "A Simple Program Whose Proof Isn't",
  crossref =     "Feijen:1990:BOB",
  chapter =      "27",
  pages =        "233--242",
  year =         "1990",
  bibdate =      "Mon Feb 03 07:07:55 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprinted in \cite[Chapter 11]{Knuth:2010:SPD}. This
                 paper discusses the algorithm used in {\TeX} for
                 converting between decimal and scaled fixed-point
                 binary values, and for guaranteeing a minimum number of
                 digits in the decimal representation. See also
                 \cite{Clinger:1990:HRF,Clinger:2004:RHR} for decimal to
                 binary conversion,
                 \cite{Steele:1990:HPF,Steele:2004:RHP} for binary to
                 decimal conversion, and \cite{Gries:1990:BDO} for an
                 alternate proof of Knuth's algorithm.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@Article{Koren:1990:EEF,
  author =       "I. Koren and O. Zinaty",
  title =        "Evaluating Elementary Functions in a Numerical
                 Coprocessor Based on Rational Approximations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-39",
  number =       "8",
  pages =        "1030--1037",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57042",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:15:30 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Kornerup:1990:ARB,
  author =       "Peter Kornerup and David W. Matula",
  title =        "An algorithm for redundant binary bit-pipelined
                 rational arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "8",
  pages =        "1106--1115",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57048",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:04 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57048",
  abstract =     "The authors introduce a redundant binary
                 representation of the rationals and an associated
                 algorithm for computing the sum, difference, product,
                 quotient, and other useful functions of two rational
                 operands, using this representation. The algorithm
                 extends R. W. Gosper's (1972) partial quotient
                 arithmetic algorithm and allows the design of an online
                 arithmetic unit with computations granularized at the
                 signed bit level. Each input or output port can be
                 independently set to receive/produce operands/result in
                 either binary radix or the binary rational
                 representation. The authors investigate by simulation
                 the interconnection of several such units for the
                 parallel computation of more complicated expressions in
                 a tree-pipelined manner, with particular regard to
                 measuring individual and compounded online delays",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Laakso:1990:RFP,
  author =       "T. Laakso and B. Zeng and I. Hartimo and Y. Neuvo",
  booktitle =    "{IEEE} International Conference on Systems
                 Engineering, 1990",
  title =        "Reduction of floating-point roundoff noise in
                 recursive digital filters with error feedback",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "244--247",
  year =         "1990",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The reduction of roundoff noise in floating-point
                 recursive digital filters by means of error feedback is
                 discussed. Optimal (minimum-noise) error feedback is
                 formulated, and it is shown to be different from the
                 optimal solution in the fixed-point \ldots{}",
}

@Article{Lee:1990:OPC,
  author =       "Vernon A. {Lee, Jr.} and Hans-J. Boehm",
  title =        "Optimizing programs over the constructive reals",
  journal =      j-SIGPLAN,
  volume =       "25",
  number =       "6",
  pages =        "102--111",
  month =        jun,
  year =         "1990",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/93542.93558",
  ISBN =         "0-89791-364-7",
  ISBN-13 =      "978-0-89791-364-5",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:15:53 MST 2003",
  bibsource =    "Compendex database; http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/proceedings/pldi/93542/index.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/pldi/93542/p102-lee/",
  abstract =     "The constructive reals provide programmers with a
                 useful mechanism for prototyping numerical programs,
                 and for experimenting with numerical algorithms.
                 Unfortunately, the performance of current
                 implementations is inadequate for some potential
                 applications. In particular, these implementations tend
                 to be space inefficient, in that they essentially
                 require a complete computation history to be
                 maintained. Some numerical analysts propose that the
                 programmer instead be provided with variable precision
                 interval arithmetic, and then be required to write code
                 to restart a computation when the intervals become too
                 inaccurate. Though this model is no doubt appropriate
                 at times, it is not an adequate replacement for exact
                 arithmetic. The correct transformation from a program
                 operating on the constructive reals to a reasonable
                 program using iterated interval arithmetic can be
                 nontrivial and error prone. Here we present a technique
                 based on program slicing to both automate this process
                 and reduce the amount of reexecution. Thus the
                 programmer is still free to use the simpler abstraction
                 of exact real arithmetic, but we can provide a more
                 efficient interval arithmetic based implementation.
                 Some preliminary empirical results are presented.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, Rice University",
  affiliationaddress = "Houston, TX, USA",
  annote =       "Published as part of the Proceedings of PLDI'90.",
  classification = "722; 723; C6110 (Systems analysis and programming);
                 C6120 (File organisation); C7310 (Mathematics)",
  confdate =     "20-22 June 1990",
  conference =   "Proceedings of the ACM SIGPLAN '90 Conference on
                 Programming Language Design and Implementation",
  conferenceyear = "1990",
  conflocation = "White Plains, NY, USA",
  confsponsor =  "ACM",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  journalabr =   "SIGPLAN Not",
  keywords =     "algorithms; Computer Operating Systems; Computer
                 Programming Languages --- Design; Constructive reals;
                 Efficient interval arithmetic based implementation;
                 Empirical results; Exact real arithmetic; Numerical
                 algorithms; Numerical analysts; Numerical programs;
                 Optimizing Compilers; performance; Performance; Program
                 Compilers; Program slicing; Reexecution; Variable
                 precision interval arithmetic",
  meetingaddress = "White Plains, NY, USA",
  meetingdate =  "Jun 20--22 1990",
  meetingdate2 = "06/20--22/90",
  sponsor =      "Assoc for Computing Machinery, Special Interest Group
                 on Programming Languages",
  subject =      "{\bf D.3.4} Software, PROGRAMMING LANGUAGES,
                 Processors, Optimization. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems. {\bf
                 G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Computer arithmetic. {\bf F.2.2} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Computations on discrete structures.",
  thesaurus =    "Data structures; Mathematics computing; Programming",
}

@Article{Ling:1990:AIM,
  author =       "H. Ling",
  title =        "An approach to implementing multiplication with small
                 tables",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "5",
  pages =        "717--718",
  month =        may,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.53588",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=53588",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Lozier:1990:CPL,
  author =       "D. W. Lozier and F. W. J. Olver",
  title =        "Closure and Precision in Level-Index Arithmetic",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "27",
  number =       "5",
  pages =        "1295--1304",
  month =        oct,
  year =         "1990",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65-04 (65G05)",
  MRnumber =     "91f:65002",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
}

@Article{MacDonald:1990:IFP,
  author =       "Tom MacDonald",
  title =        "{IEEE} Floating-Point Arithmetic and {C}",
  journal =      j-JCLT,
  volume =       "2",
  number =       "2",
  pages =        "102--112",
  month =        sep,
  year =         "1990",
  ISSN =         "1042-5721",
  bibdate =      "Thu Nov 8 14:50:33 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "The Journal of {C} Language Translation",
}

@Article{Mandelbaum:1990:SMD,
  author =       "D. M. Mandelbaum",
  title =        "A systematic method for division with high average bit
                 skipping",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "1",
  pages =        "127--130",
  month =        jan,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.46287",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:19:59 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=46287",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@PhdThesis{MangaEbongue:1990:PBV,
  author =       "Charles {Manga Ebongue}",
  title =        "Processeur 32 Bits en Virgule Flottante: Techniques de
                 Validation Fonctionnelle, {{\'E}}lectrique et Test
                 {\`a} la Conception. ({French}) [32-bit Floating-Point
                 Processor: Techniques of Functional and Electrical
                 Validation and Test in the Design]",
  type =         "Th{\`e}se Doctoral",
  school =       "Sciences Appliqu{\'e}es, Universit{\'e} Paris 6",
  address =      "Paris, France",
  year =         "1990",
  bibdate =      "Thu May 09 10:03:41 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Sous la direction de Alain Greiner.",
  abstract =     "Cette th{\`e}se d{\'e}veloppe deux aspects de la
                 conception des circuits integr{\'e}s: (1) le premier
                 aspect correspond {\`a} la m{\'e}thodologie
                 d'implantation du processeur de calcul en virgule
                 flottante d{\'e}velopp{\'e} au laboratoire MASI par
                 l'{\'e}quipe de Cao \& VLSI de l'Universit{\'e} Pierre
                 et Marie Curie, (2) le deuxi{\'e}me aspect pr{\'e}sente
                 les travaux concernant une m{\'e}thodologie de test
                 {\`a} la conception conduisant aussi bien {\`a} la
                 validation fonctionnelle et {\'e}lectrique au cours de
                 la conception qu'{\`a} la testabilit{\'e} apr{\`e}s
                 fabrication. Le premier aspect a des implications {\`a}
                 diff{\'e}rents niveaux: (1) au niveau assemblage par
                 l'introduction d'une m{\'e}thodologie de conception
                 sp{\'e}cifique au circuit, (2) au niveau {\'e}lectrique
                 pour le choix et la conception d'une biblioth{\`e}que
                 de cellules standards qui tient compte des
                 caract{\'e}ristiques dynamiques des signaux sur chaque
                 nud du circuit. Le deuxi{\`e}me aspect a pour
                 r{\'e}sultat l'introduction d'une technique originale
                 de recherche de vecteurs de test. De m{\^e}me, la
                 validation fonctionnelle de ce circuit sera
                 invoqu{\^e}e en r{\^e}solvant les principaux
                 probl{\`e}mes de coh{\'e}rence entre les masques
                 d{\'e}ssin{\'e}s et la liste des interconnexions.",
  acknowledgement = ack-nhfb,
  language =     "French",
}

@Book{Mar:1990:DSP,
  editor =       "Amy Mar",
  title =        "Digital signal processing applications using the
                 {ADSP-2100} family",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xvi + 611",
  year =         "1990",
  ISBN =         "0-13-212978-7",
  ISBN-13 =      "978-0-13-212978-7",
  LCCN =         "TK5102.5 .D44824 1990",
  bibdate =      "Sat Jan 15 05:58:58 MST 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  remark =       "System requirements for computer disks: IBM PC; PC-DOS
                 3.0.",
  subject =      "Signal processing; Digital techniques;
                 Microprocessors",
}

@Article{Margulis:1990:IMI,
  author =       "N. Margulis",
  title =        "i860 microprocessor internal architecture",
  journal =      j-MICROPROC-MICROSYS,
  volume =       "14",
  number =       "2",
  pages =        "89--96",
  month =        mar,
  year =         "1990",
  CODEN =        "MIMID5",
  ISSN =         "0141-9331 (print), 1872-9436 (electronic)",
  ISSN-L =       "0141-9331",
  bibdate =      "Wed Sep 7 22:32:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Microprocessors and Microsystems",
}

@Article{Markstein:1990:CEF,
  author =       "P. W. Markstein",
  title =        "Computation of elementary functions on the {IBM RISC
                 System\slash 6000} processor",
  journal =      j-IBM-JRD,
  volume =       "34",
  number =       "1",
  pages =        "111--119",
  month =        jan,
  year =         "1990",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  MRclass =      "65-04 (65D20)",
  MRnumber =     "1 057 659",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The additional speed and precision of the IBM RISC
                 System\slash 6000 floating-point unit have motivated
                 reexamination of algorithms to perform division, square
                 root, and the elementary functions. New results are
                 obtained which avoid the necessity of doing special
                 testing to get the last bit rounded correctly in
                 accordance with all of the IEEE rounding modes in the
                 case of division and square root. For the elementary
                 function library, a technique is described for always
                 getting the last bit rounded correctly in the selected
                 IEEE rounding mode.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Res. Div., Austin, TX, USA",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "correct rounding; Division; Elementary functions;
                 Floating-point unit; IBM RISC System\slash 6000
                 processor; IEEE rounding modes; IEEE rounding modes,
                 IBM RISC System/6000 processor; Square root",
  thesaurus =    "Digital arithmetic; IBM computers; Reduced instruction
                 set computing",
}

@InProceedings{Matula:1990:HPD,
  author =       "D. Matula",
  title =        "Highly parallel divide and square root algorithms for
                 a new generation floating point processor",
  crossref =     "Ullrich:1990:CCA",
  pages =        "??--??",
  year =         "1990",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}

@InProceedings{McCloud:1990:FPU,
  author =       "S. McCloud and D. Anderson and C. DeWitt and C. Hinds
                 and Y. W. Ho and D. Marquette and E. Quintana",
  title =        "A Floating Point Unit for the 68040",
  crossref =     "IEEE:1990:PII",
  pages =        "187--190",
  year =         "1990",
  bibdate =      "Wed Sep 7 22:32:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Metafas:1990:DPP,
  author =       "Dimitris E. Metafas and Costas E. Goutis",
  title =        "A {DSP} processor with a powerful set of elementary
                 arithmetic operations based on {CORDIC} and {CCM}
                 algorithms",
  journal =      j-MICROPROC-MICROPROG,
  volume =       "30",
  number =       "1",
  pages =        "51--57",
  year =         "1990",
  CODEN =        "MMICDT",
  DOI =          "https://doi.org/10.1016/0165-6074(90)90217-W",
  ISSN =         "0165-6074 (print), 1878-7061 (electronic)",
  ISSN-L =       "0165-6074",
  bibdate =      "Wed Oct 29 14:21:46 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Proceedings Euromicro 90: Hardware and Software in
                 System Engineering",
  URL =          "https://www.sciencedirect.com/science/article/pii/016560749090217W",
  acknowledgement = ack-nhfb,
  fjournal =     "Microprocessing and Microprogramming",
  journal-URL =  "https://www.sciencedirect.com/journal/microprocessing-and-microprogramming/issues",
}

@MastersThesis{Mills:1990:DIH,
  author =       "Karl Scott Mills",
  title =        "The design and implementation of a high performance
                 floating-point image processing and graphics subsystem
                 for the {NeXT} computer",
  type =         "Thesis ({M.S.E.E.})",
  school =       "University of Washington",
  address =      "Seattle, WA, USA",
  pages =        "v + 60 + 3",
  year =         "1990",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer graphics.; Image processing --- Digital
                 techniques.",
}

@Article{Montoye:1990:DIR,
  author =       "R. K. Montoye and E. Hokenek and S. L. Runyon",
  title =        "Design of the {IBM RISC System\slash 6000}
                 floating-point execution unit",
  journal =      j-IBM-JRD,
  volume =       "34",
  number =       "1",
  pages =        "59--70",
  month =        jan,
  year =         "1990",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.341.0059",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Tue Mar 25 14:26:59 MST 1997",
  bibsource =    "http://www.research.ibm.com/journal/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
  URL =          "http://www.research.ibm.com/journal/rd/341/ibmrd3401G.pdf",
  abstract =     "The IBM RISC System\slash 6000 (RS\slash 6000)
                 floating-point unit (FPU) exemplifies a
                 second-generation RISC CPU architecture and an
                 implementation which greatly increases floating-point
                 performance and accuracy. The key feature of the FPU is
                 a unified floating-point multiply-add-fused unit (MAF)
                 which performs the accumulate operation (A*B)+C as an
                 indivisible operation. The paper first discusses the
                 motivation for MAF, explaining in some detail why it is
                 an appropriate addition to the floating-point
                 architecture in VLSI. A summary of floating-point
                 operations is then given, with a discussion to
                 demonstrate the parallelism that is possible when the
                 multiply and add are fused. This is followed by a
                 description of the two-stage pipeline used for the
                 version of IEEE double-precision floating-point
                 arithmetic used in the RS\slash 6000 processor, with
                 delays consistent with its over-all superscalar
                 second-generation RISC architecture. Then the paper
                 describes the interaction of logical and physical
                 design required to incorporate several advances in VLSI
                 arithmetic while accommodating required delay and
                 technological (physical) constraints. The results are
                 then summarized.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Res. Div., Thomas J. Watson Res. Center, Yorktown
                 Heights, NY, USA",
  classcodes =   "B1265B (Logic circuits); B1130B (Computer-aided
                 circuit analysis and design); B1265F (Microprocessors
                 and microcomputers); C5230 (Digital arithmetic
                 methods); C5220 (Computer architecture); C5210B
                 (Computer-aided logic design)C7410D (Electronic
                 engineering)",
  classification = "B1130B (Computer-aided circuit analysis and design);
                 B1265B (Logic circuits); B1265F (Microprocessors and
                 microcomputers); C5210B (Computer-aided logic design);
                 C5220 (Computer architecture); C5230 (Digital
                 arithmetic methods); C7410D (Electronic engineering)",
  corpsource =   "IBM Res. Div., Thomas J. Watson Res. Center, Yorktown
                 Heights, NY, USA",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "Accumulate operation; accumulate operation;
                 arithmetic; CAD; circuit layout CAD; digital
                 arithmetic; floating-point architecture; Floating-point
                 architecture; generation RISC CPU architecture; IBM
                 computers; IBM RISC System/6000 floating-point
                 execution unit; IBM RISC System\slash 6000
                 floating-point execution unit; IEEE double-precision
                 floating-point; IEEE double-precision floating-point
                 arithmetic; indivisible; Indivisible operation; logic;
                 multiply-add-fused unit; operation; Parallelism;
                 parallelism; reduced instruction set computing;
                 second-; Second-generation RISC CPU architecture; stage
                 pipeline; Superscalar second-generation RISC
                 architecture; superscalar second-generation RISC
                 architecture; two-; Two-stage pipeline; unified
                 floating-point; Unified floating-point
                 multiply-add-fused unit; VLSI arithmetic; VLSI
                 arithmetic, IBM RISC System/6000 floating-point
                 execution unit",
  thesaurus =    "Circuit layout CAD; Digital arithmetic; IBM computers;
                 Logic CAD; Reduced instruction set computing",
  treatment =    "P Practical",
}

@Article{Montuschi:1990:SSR,
  author =       "P. Montuschi and P. M. Mezzalama",
  title =        "Survey of square rooting algorithms",
  journal =      j-IEE-PROC-COMPUT-DIGIT-TECH,
  volume =       "137",
  number =       "1",
  pages =        "31--40",
  month =        jan,
  year =         "1990",
  CODEN =        "ICDTEA",
  ISSN =         "1350-2387 (print), 1359-7027 (electronic)",
  ISSN-L =       "1350-2387",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEE Proceedings. Computers and Digital Techniques",
  summary =      "The paper reviews the algorithms for the computation
                 of square roots for binary machines. After an initial
                 classification, the algorithms are analysed in detail
                 by considering their specific peculiarities and
                 properties. Finally, some comments are \ldots{}",
}

@Article{Morita:1990:FMM,
  author =       "Hikaru Morita",
  title =        "A Fast Modular-Multiplication Algorithm Based on a
                 Higher Radix",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "435",
  pages =        "387--??",
  year =         "1990",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Mon Feb 4 12:01:59 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t0435.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/0435/04350387.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/0435/04350387.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@MastersThesis{Muller:1990:HCA,
  author =       "Volker M{\"u}ller",
  title =        "{Hochgenaue CORDIC-Algorithmen f{\"u}r reelle
                 Standardfunktionen mittels dynamischer
                 Defektberechnung}. ({German}) [{High}-accuracy {CORDIC}
                 Algorithms for Real Elementary Functions by Means of
                 Dynamic Error Computation]",
  type =         "{Diplomarbeit}",
  school =       "Institut f{\"u}r angewandte Mathematik,
                 Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "????",
  month =        dec,
  year =         "1990",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  language =     "German",
}

@Article{Murthy:1990:MPA,
  author =       "Narayan Murthy and Allen Stix",
  title =        "Multiple precision arithmetic: a programming
                 assignment in {CS2} applying linked lists",
  journal =      j-SIGCSE,
  volume =       "22",
  number =       "1",
  pages =        "129--133",
  month =        feb,
  year =         "1990",
  CODEN =        "SIGSD3",
  DOI =          "https://doi.org/10.1145/319059.323431",
  ISSN =         "0097-8418 (print), 2331-3927 (electronic)",
  ISSN-L =       "0097-8418",
  bibdate =      "Sat Nov 17 18:57:12 MST 2012",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigcse1990.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGCSE Bulletin (ACM Special Interest Group on
                 Computer Science Education)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J688",
}

@Article{Ohtomo:1990:FPD,
  author =       "Hiroyasu Ohtomo and Hisao Ishizuka and Masahiko
                 Kashimura and Akio Nakajima and Tetsuhiro Hira",
  title =        "A 32-bit Floating Point Digital Signal Processor for
                 Graphics Application",
  journal =      j-NEC-RES-DEV,
  volume =       "??",
  number =       "99",
  pages =        "47--??",
  month =        oct,
  year =         "1990",
  CODEN =        "NECRAU",
  ISSN =         "0048-0436",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Nippon Electric Company research and development",
}

@InProceedings{Olson:1990:FAA,
  author =       "T. Olson and B. Stewart",
  title =        "Floating-point architecture of the Am29050",
  crossref =     "Wescon:1990:WCR",
  pages =        "214--217",
  year =         "1990",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Am29050 is the newest member of Advanced Micro
                 Devices' 29K family of RISC microprocessors. It is both
                 binary and pin compatible with the Am29000, and also
                 incorporates a high-performance floating-point unit
                 (FPU) on chip. The FPU, which complies with the IEEE
                 754 standard, consists of parallel add, multiply, and
                 divide/square-root units, operating on single-precision
                 and double-precision values. In addition to the
                 standard operations, the FPU implements two types of
                 multiply-add functions, which take three operands and
                 produce one result. A single register file, which is
                 shared between the integer and floating-point units,
                 can supply two 64-bit operands and write back both a
                 32-bit integer result and a 64-bit floating-point
                 result in a single cycle.",
  acknowledgement = ack-nhfb,
  affiliation =  "Adv. Micro Devices, Austin, TX, USA",
  availability = "Western Periodicals Co., 13000 Rayner Street, North
                 Hollywood, CA 91605, USA",
  classification = "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5220 (Computer architecture);
                 C5230 (Digital arithmetic methods)",
  keywords =     "29K family; 64 Bit; Advanced Micro Devices; Am29050;
                 Double-precision; Floating point architecture; Floating
                 point arithmetic; Floating-point unit; FPU; IEEE 754
                 standard; Multiply-add functions; Parallel add; RISC
                 microprocessors; Single-precision",
  numericalindex = "Word length 6.4E+01 bit",
  thesaurus =    "Computer architecture; Digital arithmetic;
                 Microprocessor chips; Reduced instruction set
                 computing",
}

@Article{Owens:1990:BSM,
  author =       "R. M. Owens and M. J. Irwin",
  title =        "Being stingy with multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "6",
  pages =        "809--818",
  month =        jun,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.53602",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=53602",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Palmore:1990:CAC,
  author =       "J. Palmore and C. Herring",
  title =        "Computer arithmetic, chaos and fractals",
  journal =      j-PHYSICA-D,
  volume =       "42",
  number =       "1-3",
  pages =        "99--110",
  month =        jun,
  year =         "1990",
  CODEN =        "PDNPDT",
  ISSN =         "0167-2789 (print), 1872-8022 (electronic)",
  ISSN-L =       "0167-2789",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Ninth Annual International Conference of the Center
                 for Nonlinear Studies on Self-Organizing, Collective
                 and Cooperative Phenomena in Natural and Artificial
                 Networks",
  abstract =     "The authors explore aspects of computer arithmetic
                 from the viewpoint of dynamical systems. They
                 demonstrate the effects of finite precision arithmetic
                 in three uniformly hyperbolic chaotic dynamical
                 systems: Bernoulli shifts, cat maps, and pseudorandom
                 number generators. They show that elementary
                 floating-point operations in binary computer arithmetic
                 possess an inherently fractal structure. Each of these
                 dynamical systems allows us to compare the exact
                 results in integer arithmetic with those obtained by
                 using floating-point arithmetic.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Math., Illinois University, Urbana, IL,
                 USA",
  classification = "C1160 (Combinatorial mathematics); C5230 (Digital
                 arithmetic methods)",
  confdate =     "22-26 May 1989",
  conflocation = "Los Alamos, NM, USA",
  fjournal =     "Physica. D, Nonlinear phenomena",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01672789",
  keywords =     "Bernoulli shifts; Binary computer arithmetic; Cat
                 maps; Chaos; Computer arithmetic; Dynamical systems;
                 Elementary floating-point operations; Finite precision
                 arithmetic; Floating-point arithmetic; Fractal
                 structure; Integer arithmetic; Pseudorandom number
                 generators; Self-similar structure; Uniformly
                 hyperbolic chaotic dynamical systems",
  pubcountry =   "Netherlands",
  thesaurus =    "Chaos; Digital arithmetic; Fractals; Random number
                 generation; Roundoff errors",
}

@InProceedings{Pan:1990:FSI,
  author =       "J. Pan and K. N. Levitz",
  title =        "A Formal Specification of the {IEEE Floating-Point
                 Standard} with Application to the Verification of
                 Floating-Point Coprocessors",
  crossref =     "Chen:1990:CRT",
  pages =        "505--510",
  year =         "1990",
  bibdate =      "Wed Dec 13 18:41:54 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A description is given of work in progress on
                 verifying a floating-point coprocessor based on the
                 MC68881/82, with respect to the IEEE standard
                 floating-point arithmetic (ANSI-IEEE Std 754-1985). A
                 complete formalization of the IEEE floating-point
                 standard using the HOL (high-order-logic) specification
                 and verification system is presented. The specification
                 of floating-point numbers, floating-point arithmetic
                 functions, rounding schemes and post-normalization is
                 described. In order for the specification to be
                 adaptable to different implementation, several model
                 parameters are used in specifying all the functions.
                 The floating-point coprocessor is specified as a
                 hierarchy of interpreters. The communication with the
                 CPU is modeled as standard interprocessor
                 communication. A technique for verifying hierarchies of
                 communicating hardware interpreters is described. (11
                 Refs.)",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Div. of Computer Science, California University,
                 Berkeley, CA, USA",
  availability = "IEEE Computer Society Press, Los Alamitos, CA, USA",
  classification = "C5130 (Microprocessor chips); C5230 (Digital
                 arithmetic methods)",
  keywords =     "ANSI-IEEE Std 754-1985; Communicating hardware
                 interpreters; CPU communication; Floating-point
                 coprocessors; Higher order logic specification; HOL;
                 IEEE standard floating-point arithmetic; Interpreter
                 hierarchy; Interprocessor communication; MC68881/82;
                 Post-normalization; Rounding schemes; Standard
                 formalization; Verification system",
  thesaurus =    "Digital arithmetic; Formal specification;
                 Microprocessor chips; Satellite computers; Standards",
}

@Article{Parhami:1990:GSD,
  author =       "Behrooz Parhami",
  title =        "Generalized Signed-Digit Number Systems: a Unifying
                 Framework for Redundant Number Representations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "1",
  pages =        "89--98",
  month =        jan,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.46283",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Feb 15 15:47:08 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  abstract =     "Signed-digit (SD) number representation systems have
                 been defined for any radix r ?? 3 with digit values
                 ranging over the set $ ( - \alpha, \ldots {}, - 1, 0,
                 1, \ldots {}, \alpha) $, where $ \alpha $ is an
                 arbitrary integer in the range $ 1 / 2 r > \alpha > r
                 $. Such number representation systems possess
                 sufficient redundancy to allow for the annihilation of
                 carry or borrow chains and hence result in fast
                 propagation-free addition and subtraction. The author
                 refers to the above as ordinary SD number systems and
                 defines generalized SD number systems which contain
                 them as a special symmetric subclass. It is shown that
                 the generalization not only provides a unified view of
                 all redundant number systems which have proven useful
                 in practice (including stored-carry and stored-borrowed
                 systems), but also leads to new number systems not
                 examined before. Examples of such new number systems
                 are stored-carry-or-borrow systems, stored-double-carry
                 systems, and certain redundant decimal
                 representations.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Payne:1990:PLCa,
  author =       "M. Payne and C. Schaffert and B. Wichmann",
  title =        "Proposal for a language compatible arithmetic
                 standard",
  journal =      j-SIGNUM,
  volume =       "25",
  number =       "1",
  pages =        "2--43",
  month =        jan,
  year =         "1990",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Describes the proposal for an arithmetic standard
                 which has been submitted to the American National
                 Standards Institute and the International Organization
                 for Standardization. It is being processed by the ANSI
                 X3T2 committee and the ISO/IEC JTC1/SC22/WG11 working
                 group. The specifications cover both integer and
                 floating point arithmetic.",
  acknowledgement = ack-nhfb,
  affiliation =  "Digital Equipment Corp, Maynard, MA, USA",
  classification = "C7310 (Mathematics)",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "American National Standards Institute; ANSI X3T2
                 committee; Floating point arithmetic; Integer
                 arithmetic; International Organization for
                 Standardization; Language compatible arithmetic
                 standard",
  thesaurus =    "Digital arithmetic; Mathematics computing; Standards",
}

@Article{Payne:1990:PLCb,
  author =       "M. Payne and C. Schaffert and B. Wichmann",
  title =        "Proposal for a language compatible arithmetic
                 standard",
  journal =      j-SIGPLAN,
  volume =       "25",
  number =       "1",
  pages =        "59--86",
  month =        jan,
  year =         "1990",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:15:49 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The proposal for an arithmetic standard has been
                 submitted to the American National Standard Institute
                 and the International Organization for Standardization.
                 The proposal covers both integer and floating point
                 arithmetic. The underlying goal is to expedite the
                 production of robust numerical software which is
                 portable among the diverse arithmetic implementations
                 currently in wide-spread use. The proposal requires
                 that a complying system provide error detection
                 capabilities beyond those currently required by many
                 language standards. The proposal requires that a
                 conforming system makes the values of certain
                 parameters known to users, although the method for
                 doing so is not specified. It also required a number of
                 useful operations, beyond those usually implemented. It
                 is acceptable to implement them by subroutine calls.",
  acknowledgement = ack-nhfb,
  affiliation =  "Digital Equipment Corp., Maynard, MA, USA",
  classification = "C5230 (Digital arithmetic methods); C6140D (High
                 level languages)",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "American National Standard Institute; Error detection
                 capabilities; Floating point arithmetic; International
                 Organization for Standardization; Language compatible
                 arithmetic standard; Robust numerical software;
                 Subroutine calls",
  thesaurus =    "Digital arithmetic; High level languages; Standards",
}

@Article{Peter:1990:PZW,
  author =       "O. Peter",
  title =        "{Prozessor zieht Wurzeln} \toenglish {Processor
                 Extracts Roots} \endtoenglish",
  journal =      j-CT,
  volume =       "1",
  pages =        "300--306",
  year =         "1990",
  ISSN =         "0724-8679",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "C T: Magazin f{\"u}r Computer Technik (Hannover)",
}

@Article{Piestrak:1990:DHS,
  author =       "S. J. Piestrak",
  title =        "Design of high-speed and cost-effective self-testing
                 checkers for low-cost arithmetic codes",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "3",
  pages =        "360--374",
  month =        mar,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.48866",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=48866",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Popov:1990:AFA,
  author =       "Wladimir Popov",
  title =        "On the axiomatizations of floating-point arithmetics.
                 Contributions to computer arithmetic and
                 self-validating numerical methods ({Basel, 1989})",
  journal =      "IMACS Ann. Comput. Appl. Math.",
  volume =       "7",
  publisher =    pub-BALTZER,
  address =      pub-BALTZER:adr,
  pages =        "55--66",
  year =         "1990",
  MRclass =      "03B70 (65G05)",
  MRnumber =     "93g:03024",
  bibdate =      "Fri Dec 08 12:21:25 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Preparata:1990:PCD,
  author =       "F. P. Preparata and Jean E. Vuillemin",
  title =        "Practical cellular dividers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "5",
  pages =        "605--614",
  month =        may,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.53574",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:01 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=53574",
  abstract =     "A discussion is presented of parallel division
                 algorithms that can be classified among modified higher
                 radix nonrestoring online division methods, where
                 redundant representations are extensively utilized to
                 speed up the operation. The network realizations of
                 these algorithms are cellular, or even systolic with
                 exclusively local control; they have both size (area)
                 and time of $ O(n) $, where $n$ is the length of the
                 dividend representation. The same structures can also
                 be used as a signed, digit-serial multiplier. When
                 suitably equipped with some control and a few
                 registers, the divider\slash multiplier brings
                 remarkable performance to large modular arithmetic, RSA
                 cryptography, and greatest common divisor computations.
                 They are also of interest for the design of
                 floating-point units and signal processing
                 applications.",
  acknowledgement = ack-nhfb,
  affiliation =  "Ecole Normale Superieure, Paris, France",
  ajournal =     "IEEE Trans. Comput.",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Digit-serial multiplier; Divider/multiplier;
                 Floating-point units; Greatest common divisor
                 computations; Modular arithmetic; Nonrestoring online
                 division methods; Parallel division algorithms;
                 Redundant representations; RSA cryptography; Signal
                 processing; Signed; Systolic",
  language =     "English",
  pubcountry =   "USA",
  thesaurus =    "Digital arithmetic; Dividing circuits; Parallel
                 algorithms",
}

@Article{Prince:1990:GST,
  author =       "Timothy Prince",
  title =        "Generating Source For {{\tt <float.h>}}",
  journal =      j-CUJ,
  volume =       "8",
  number =       "6",
  pages =        "119--??",
  month =        jun,
  year =         "1990",
  ISSN =         "0898-9788",
  bibdate =      "Fri Aug 30 16:52:23 MDT 1996",
  bibsource =    "http://www.cuj.com/cbklist.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "C Users Journal",
}

@Article{Pugh:1990:CBF,
  author =       "Kenneth Pugh",
  title =        "Converting {BASIC} Floating Point Files to {C}",
  journal =      j-CUJ,
  volume =       "8",
  type =         "Questions and Answers",
  number =       "5",
  pages =        "69--??",
  month =        may,
  year =         "1990",
  ISSN =         "0898-9788",
  bibdate =      "Fri Aug 30 16:52:23 MDT 1996",
  bibsource =    "http://www.cuj.com/cbklist.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "C Users Journal",
}

@TechReport{Quach:1990:IAH,
  author =       "N. T. Quach and M. J. Flynn",
  title =        "An improved algorithm for high-speed floating-point
                 addition",
  type =         "Technical Report",
  number =       "CSL-TR-90-442",
  institution =  "Computer Systems Laboratory, Stanford University",
  address =      "Stanford, CA, USA",
  month =        aug,
  year =         "1990",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}

@Article{Quinn:1990:REL,
  author =       "T. Quinn and S. Tremaine",
  title =        "Roundoff error in long-term planetary orbit
                 integrations",
  journal =      j-ASTRON-J,
  volume =       "99",
  number =       "3",
  pages =        "1016--1023",
  month =        mar,
  year =         "1990",
  CODEN =        "ANJOAA",
  ISSN =         "0004-6256 (print), 1538-3881 (electronic)",
  ISSN-L =       "0004-6256",
  bibdate =      "Tue Dec 12 09:17:24 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The dominant source of error in most long-term
                 integrations of the solar system is roundoff, which
                 leads to a fractional energy error of order $ n i_n $
                 where $n$ is the number of steps and $ i_n $ is the
                 precision of the floating-point arithmetic. The most
                 accurate computers are those with optimal
                 floating-point arithmetic, that is, arithmetic in which
                 the result of evaluating in arithmetic expression is
                 the representable number closest to the true value of
                 that expression. The authors argue that when
                 floating-point arithmetic is optimal, most of the
                 roundoff error arises from two sources: the approximate
                 representation of the numerical coefficients used in
                 multistep integration formulas, and the additions
                 required to evaluate these formulas. The authors
                 present an algorithm that removes these two sources of
                 error in computers with optimal arithmetic, and appears
                 to reduce the fractional energy error to of order $
                 n^{0.5i}_n $ (at least for $ n < $ or approximately $ =
                 10^7 $), at the cost of less than a factor of $2$
                 increase in computing time.",
  acknowledgement = ack-nhfb,
  affiliation =  "Canadian Inst. for Theor. Astrophys., Toronto
                 University, Ont., Canada",
  classification = "A9510C (Celestial mechanics); A9575P (Mathematical
                 and computer techniques); A9630 (Planets and
                 satellites); C7350 (Astronomy and astrophysics)",
  fjournal =     "Astronomical Journal",
  journal-URL =  "http://iopscience.iop.org/1538-3881",
  keywords =     "Addition error; Approximate representation; Arithmetic
                 expression; Celestial mechanics; Computing time;
                 Floating-point arithmetic precision; Fractional energy
                 error; Integration steps number; Long-term planetary
                 orbit integrations; Multistep integration formulas;
                 Numerical coefficients; Optimal floating-point
                 arithmetic; Representable number; Roundoff error; Solar
                 system long-term stability; True value",
  thesaurus =    "Astronomical techniques; Astronomy computing;
                 Celestial mechanics; Error correction; Planets; Solar
                 system; Stability",
}

@InProceedings{Ramamoorthy:1990:MRN,
  author =       "P. A. Ramamoorthy and P. E. Pace and D. Styer",
  booktitle =    "Proceedings of the 33rd Midwest Symposium on Circuits
                 and Systems, 1990",
  title =        "A modified residue number system with applications to
                 signal processing",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1018--1021",
  year =         "1990",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1990.140897",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The authors have developed a number system, the
                 modified residue number system (MRNS), which is a
                 direct consequence of considering the need for a more
                 convenient folding waveform that can be implemented
                 easily. Through various arrangements of the \ldots{}",
}

@InProceedings{Rao:1990:SAA,
  author =       "B. D. Rao",
  booktitle =    "Signals, Systems and Computers, 1990. 1990 Conference
                 Record Twenty-Fourth Asilomar Conference on. 5--7 Nov
                 1990",
  title =        "A systematic approach for the analysis of roundoff
                 noise in floating point digital filters",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "495",
  year =         "1990",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Not \ldots{}",
}

@Article{Rauchwerger:1990:MFPa,
  author =       "Lawrence Rauchwerger and Michael P. Farmwald",
  title =        "A multiple floating point coprocessor architecture",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "18",
  number =       "2",
  pages =        "15--24",
  month =        jun,
  year =         "1990",
  CODEN =        "CANED2",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Fri May 12 09:40:46 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
}

@InProceedings{Rauchwerger:1990:MFPb,
  author =       "L. Rauchwerger and P. M. Farmwald",
  title =        "A multiple floating point coprocessor architecture",
  crossref =     "IEEE:1990:MMM",
  pages =        "216--222",
  year =         "1990",
  bibdate =      "Tue Dec 12 09:26:54 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "General purpose microprocessor based computers usually
                 speed their arithmetic processing performance by using
                 a floating point co-processor. Because adding more
                 co-processors represents neither a technological nor a
                 cost problem, the authors investigated a system based
                 on a MIPS R2000 and 4 floating point units. They show a
                 block diagram of such an implementation and how two
                 important scientific operations can be accelerated
                 using a single unmodified data bus. A large percentage
                 of the engineering applications are solved with the
                 help of linear algebra methods like BLAS3 algorithms;
                 it is precisely for these primitives that the proposed
                 architecture brings significant performance gains. The
                 first operation described is a matrix multiplication
                 algorithm, its timing diagram and some results. Next a
                 polynomial evaluation technique is examined. Finally
                 they show how to use the same ideas with various other
                 microprocessors.",
  acknowledgement = ack-nhfb,
  affiliation =  "Center for Supercomput. Res. and Dev., Illinois
                 University, Urbana-Champaign, IL, USA",
  classification = "C5220 (Computer architecture); C5230 (Digital
                 arithmetic methods)",
  keywords =     "Arithmetic processing performance; BLAS3; Engineering
                 applications; Matrix multiplication algorithm;
                 Microprocessors; MIPS R2000; Multiple floating point
                 coprocessor architecture; Polynomial evaluation; RISC",
  thesaurus =    "Computer architecture; Digital arithmetic; Satellite
                 computers",
}

@Article{Reemtsen:1990:MFR,
  author =       "Rembert Reemtsen",
  title =        "Modifications of the First {Remez} Algorithm",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "27",
  number =       "2",
  pages =        "507--518",
  month =        apr,
  year =         "1990",
  CODEN =        "SJNAAM",
  DOI =          "https://doi.org/10.1137/0727031",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65D15",
  MRnumber =     "91a:65039",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
}

@Article{Reif:1990:OSI,
  author =       "John H. Reif and Stephen R. Tate",
  title =        "Optimal Size Integer Division Circuits",
  journal =      j-SIAM-J-COMPUT,
  volume =       "19",
  number =       "5",
  pages =        "912--924",
  month =        oct,
  year =         "1990",
  CODEN =        "SMJCAT",
  ISSN =         "0097-5397 (print), 1095-7111 (electronic)",
  ISSN-L =       "0097-5397",
  MRclass =      "68Q40 (68Q15 68Q25)",
  MRnumber =     "91h:68092",
  MRreviewer =   "Helmut Alt",
  bibdate =      "Mon Nov 29 11:01:37 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/19/5;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Computing",
  journal-URL =  "http://epubs.siam.org/sicomp",
}

@PhdThesis{Rowan:1990:FSA,
  author =       "Thomas Harvey Rowan",
  title =        "Functional stability analysis of numerical
                 algorithms",
  type =         "{Ph.D.} thesis",
  school =       "University of Texas at Austin",
  address =      "Austin, TX, USA",
  pages =        "xii + 206",
  month =        may,
  year =         "1990",
  bibdate =      "Mon Oct 21 18:08:52 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://search.proquest.com/pqdtglobal/docview/303865032",
  abstract =     "The standard technique for detecting instability in
                 numerical algorithms is backward error analysis. The
                 analysis is difficult and tedious when performed by
                 hand, while attempts to automate it have always placed
                 severe restrictions on the tested numerical algorithms.
                 A new approach for detecting instability, functional
                 stability analysis, removes these restrictions by
                 treating numerical algorithms as black boxes. The
                 approach consists of two parts. The first part uses the
                 relationship between the forward error, the backward
                 error, and a problem's condition to define a function
                 that estimates a lower bound on the backward error. In
                 the second part, a new optimization method maximizes
                 the function. A numerical algorithm is unstable if the
                 maximization shows that the backward error can become
                 large. Since numerical algorithms are treated as black
                 boxes, functional stability analysis normally requires
                 little more than an executable version of a numerical
                 algorithm to determine if it is unstable.",
  acknowledgement = ack-nhfb,
  advisor =      "Alan K. Cline",
}

@Article{Sam:1990:GMR,
  author =       "H. Sam and A. Gupta",
  title =        "A generalized multibit recoding of two's complement
                 binary numbers and its proof with application in
                 multiplier implementations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "8",
  pages =        "1006--1015",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57039",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:03 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57039",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Schatte:1990:SBF,
  author =       "Peter Schatte",
  title =        "On the stochastic behaviour of the floating point
                 mantissas of sums",
  journal =      "J. Inform. Process. Cybernet.",
  volume =       "26",
  number =       "4",
  pages =        "249--254",
  year =         "1990",
  MRclass =      "60F99 (11K99)",
  MRnumber =     "91m:60065",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  reviewer =     "Eugenijus Manstavi{\v{c}}ius",
}

@Article{Schimandle:1990:MBC,
  author =       "James Schimandle",
  title =        "{Microsoft BASIC}'s and {C}'s Floating Point Formats",
  journal =      j-CUJ,
  volume =       "8",
  type =         "Letter",
  number =       "7",
  pages =        "139--??",
  month =        jul,
  year =         "1990",
  ISSN =         "0898-9788",
  bibdate =      "Fri Aug 30 16:52:23 MDT 1996",
  bibsource =    "http://www.cuj.com/cbklist.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "C Users Journal",
}

@Article{Sheppard:1990:EYF,
  author =       "Gene Sheppard",
  title =        "Evaluating Your Floating Point Library",
  journal =      j-CUJ,
  volume =       "8",
  number =       "8",
  pages =        "121--??",
  month =        aug,
  year =         "1990",
  ISSN =         "0898-9788",
  bibdate =      "Fri Aug 30 16:52:23 MDT 1996",
  bibsource =    "http://www.cuj.com/cbklist.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "C Users Journal",
}

@Article{Silverman:1990:PPA,
  author =       "Robert D. Silverman",
  title =        "Parallel polynomial arithmetic over finite rings",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "10",
  number =       "3",
  pages =        "265--270",
  month =        nov,
  year =         "1990",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "MITRE Corp",
  affiliationaddress = "Bedford, Ma, USA",
  classification = "723; 921; C4130 (Interpolation and function
                 approximation); C4240 (Programming and algorithm
                 theory); C5230 (Digital arithmetic methods)",
  corpsource =   "Mitre Corp., Bedford, MA, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "Alliant FX/8; Chinese remainder; Chinese Remainder
                 Theorem; Computer Systems, Digital--Parallel
                 Processing; Computers, Digital--Computational Methods;
                 Convolution Algorithms; digital arithmetic; Finite
                 Rings; finite rings; Mathematical Techniques; message
                 passing; message passing parallel computer;
                 multiplication; parallel algorithms; parallel
                 computers; parallel polynomial arithmetic; performance;
                 polynomial; Polynomial Arithmetic; Polynomials;
                 polynomials; residue number systems; shared memory;
                 Symult S2010; theorem",
  treatment =    "P Practical",
}

@InProceedings{Silverstein:1990:USM,
  author =       "Joel D. Silverstein and Steven E. Sommars and
                 Yio-Chian Tao",
  title =        "The {UNIX} System Math Library, a Status Report",
  crossref =     "USENIX:1990:PWU",
  pages =        "117--131",
  year =         "1990",
  bibdate =      "Thu Sep 01 11:51:21 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Sips:1990:NML,
  author =       "Henk J. Sips and Hai Xiang Lin",
  title =        "A new model for on-line arithmetic with an application
                 to the reciprocal calculation",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "8",
  number =       "3",
  pages =        "218--230",
  month =        mar,
  year =         "1990",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Delft Univ of Technology",
  affiliationaddress = "Delft, Neth",
  classification = "722; 723; 921; C4130 (Interpolation and function
                 approximation); C5230 (Digital arithmetic methods)",
  corpsource =   "Delft University of Technol., Netherlands",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "adapted Newton--Raphson; approximation method;
                 Approximation Theory; arithmetic; attainable on-;
                 computation pipelining; Computational Models; Computer
                 Systems, Digital--On Line Operation; conditional
                 on-line; cycle times; delay; delays; Digital
                 Arithmetic; digital arithmetic; exact function value;
                 functions; iteration; iteration method; iterative;
                 Iterative Methods; iterative methods; line delay;
                 Mathematical Techniques; on-line arithmetic; on-line
                 computation; on-line digits; online arithmetic;
                 overlapping computation; pipeline; processing;
                 reciprocal calculation; seed table; step; table
                 look-up",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Skelton:1990:GSE,
  author =       "R. E. Skelton and D. Williamson",
  booktitle =    "Proceedings of the 29th {IEEE} Conference on Decision
                 and Control, 1990",
  title =        "Guaranteed state estimation accuracies with roundoff
                 error",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "297--298",
  year =         "1990",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Kalman filter theory is modified to accommodate
                 roundoff errors in state computation. Two problems are
                 solved: (i) choosing the wordlength required for each
                 state computation to guarantee specified estimation
                 accuracies of multiple output variables \ldots{}",
}

@TechReport{Slishman:1990:FPR,
  author =       "G. Slishman",
  title =        "Fast and Perfectly Rounding Decimal\slash Hexadecimal
                 Conversions",
  type =         "Research Report",
  number =       "RC-15683",
  institution =  pub-IBM-WATSON,
  address =      pub-IBM-WATSON:adr,
  year =         "1990",
  bibdate =      "Fri Apr 21 07:04:09 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@Article{Steele:1990:HPF,
  author =       "Guy L. {Steele Jr.} and Jon L. White",
  title =        "How to Print Floating-Point Numbers Accurately",
  journal =      j-SIGPLAN,
  volume =       "25",
  number =       "6",
  pages =        "112--126",
  month =        jun,
  year =         "1990",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/93548.93559",
  ISBN =         "0-89791-364-7",
  ISBN-13 =      "978-0-89791-364-5",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:15:53 MST 2003",
  bibsource =    "Compendex database; http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/proceedings/pldi/93542/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigplan1990.bib",
  note =         "See also input algorithm in
                 \cite{Clinger:1990:HRF,Clinger:2004:RHR}, and a faster
                 output algorithm in \cite{Burger:1996:PFP} and
                 \cite{Knuth:1990:SPW}, IBM S/360 algorithms in
                 \cite{Abbott:1999:ASS} for both IEEE 754 and S/360
                 formats, and a twenty-year retrospective in
                 \cite{Steele:2004:RHP}. In electronic mail dated Wed,
                 27 Jun 1990 11:55:36 EDT, Guy Steele reported that an
                 intrepid pre-SIGPLAN 90 conference implementation of
                 what is stated in the paper revealed 3 mistakes:
                 \begin{itemize} \item[1.] Table~5 (page 124):\par
                 \noindent insert {\tt k <-- 0} after assertion, and
                 also delete {\tt k <-- 0} from Table~6. \item[2.]
                 Table~9 (page 125):\par \noindent \begin{tabular} {ll}
                 for & {\tt -1:USER!({"}{"});} \\
                 substitute & {\tt -1:USER!({"}0{"});} \end{tabular}\par
                 \noindent and delete the comment. \item[3.] Table~10
                 (page 125):\par \noindent \begin{tabular}{ll} for &
                 {\tt fill(-k, "0")}\\
                 substitute & {\tt fill(-k-1, "0")} \end{tabular}
                 \end{itemize}
                 \def\EatBibTeXPeriod#1{\ifx#1.\else#1\fi}\EatBibTeXPeriod",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/pldi/93542/p112-steele/",
  abstract =     "Algorithms are presented for accurately converting
                 floating-point numbers to decimal representation. The
                 key idea is to carry along with the computation an
                 explicit representation of the required rounding
                 accuracy. The authors begin with the simpler problem of
                 converting fixed-point fractions. A modification of the
                 well-known algorithm for radix-conversion of
                 fixed-point fractions by multiplication explicitly
                 determines when to terminate the conversion process; a
                 variable number of digits are produced. They derive two
                 algorithms for free-format output of floating-point
                 numbers. Finally, they modify the free-format
                 conversion algorithm for use in fixed-format
                 applications. Information may be lost if the fixed
                 format provides too few digit positions, but the output
                 is always correctly rounded. On the other hand, no
                 `garbage digits' are ever produced, even if the fixed
                 format specifies too many digit positions (intuitively,
                 the `4/3 prints as 1.333333328366279602' problem does
                 not occur).",
  acknowledgement = ack-nhfb,
  affiliation =  "Thinking Machines Corp",
  affiliationaddress = "Cambridge, MA, USA",
  classification = "722; 723; C5230 (Digital arithmetic methods); C7310
                 (Mathematics)",
  confdate =     "20-22 June 1990",
  conference =   "Proceedings of the ACM SIGPLAN '90 Conference on
                 Programming Language Design and Implementation",
  conferenceyear = "1990",
  conflocation = "White Plains, NY, USA",
  confsponsor =  "ACM",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  journalabr =   "SIGPLAN Not",
  keywords =     "algorithms; computer programming languages; computers,
                 digital --- computational methods; conversion process;
                 correct rounding; decimal decimal representation;
                 design; digit positions; explicit representation;
                 fixed-format applications; fixed-point fractions;
                 floating point numbers; floating-point arithmetic;
                 floating-point numbers; free-format conversion
                 algorithm; free-format output; garbage digits;
                 performance; radix-conversion; rounding accuracy;
                 verification",
  remark =       "Published as part of the Proceedings of PLDI'90.",
  sponsor =      "Assoc for Computing Machinery, Special Interest Group
                 on Programming Languages",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems. {\bf G.1.0} Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Computer arithmetic.",
  thesaurus =    "Digital arithmetic; Mathematics computing",
  xxabstract =   "We present algorithms for accurately converting
                 floating-point numbers to decimal representation. The
                 key idea is to carry along with the computation an
                 explicit representation of the required rounding
                 accuracy. We begin with the simpler problem of
                 converting fixed-point fractions. A modification of the
                 well-known algorithm for radix-conversion of
                 fixed-point fractions by multiplication explicitly
                 determines when to terminate the conversion process; a
                 variable number of digits are produced. We then derive
                 two algorithms for free-format output of floating-point
                 numbers. Finally, we modify the free-format conversion
                 algorithm for use in fixed-format applications.",
}

@Article{Stewart:1990:SPT,
  author =       "G. W. Stewart",
  title =        "Stochastic Perturbation Theory",
  journal =      j-SIAM-REVIEW,
  volume =       "32",
  number =       "4",
  pages =        "579--610",
  month =        dec,
  year =         "1990",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1032121",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "15A06 (15A09 15A12 15A18 15A52 15A60)",
  MRnumber =     "91m:15007",
  MRreviewer =   "James Weldon Demmel",
  bibdate =      "Sat Mar 29 09:54:48 MDT 2014",
  bibsource =    "Compendex database;
                 http://epubs.siam.org/toc/siread/32/4;
                 https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  abstract =     "In this paper classical matrix perturbation theory is
                 approached from a probabilistic point of view. The
                 perturbed quantity is approximated by a first-order
                 perturbation expansion, in which the perturbation is
                 assumed to be random. This permits the computation of
                 statistics estimating the variation in the perturbed
                 quantity. Up to the higher-order terms that are ignored
                 in the expansion, these statistics tend to be more
                 realistic than perturbation bounds obtained in terms of
                 norms. The technique is applied to a number of problems
                 in matrix perturbation theory, including least squares
                 and the eigenvalue problem.",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ of Maryland",
  affiliationaddress = "College Park, MD, USA",
  classification = "921; 922",
  fjournal =     "SIAM Review",
  GWS-number =   "J69",
  journal-URL =  "http://epubs.siam.org/sirev",
  journalabr =   "SIAM Rev",
  keywords =     "Mathematical Techniques; Perturbation Techniques;
                 Probability --- Random Processes; Stochastic
                 Perturbation Theory",
  mynote =       "Maryland CS-TR-2129, October 88",
  onlinedate =   "December 1990",
}

@Article{Su:1990:ASS,
  author =       "C.-C. Su and H.-Y. Lo",
  title =        "An algorithm for scaling and single residue error
                 correction in residue number systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "8",
  pages =        "1053--1064",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57044",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:03 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2065;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57044",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "An algorithm for scaling and single residue digit
                 error correction is proposed. This algorithm is fully
                 based on mixed radix conversion (MRC). The redundant
                 digits of MRC can be used to establish a lookup table
                 to correct single residue digit \ldots{}",
}

@InProceedings{Sun:1990:FAM,
  author =       "Jenn-Dong Sun and H. Krishna",
  booktitle =    "Conference Record Twenty-Fourth Asilomar Conference on
                 Signals, Systems and Computers, 5--7 Nov 1990",
  title =        "Fast Algorithms for Multiple Errors Detection and
                 Correction in Redundant Residue Number Systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "831",
  year =         "1990",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1990.140897",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
}

@Book{Tabak:1990:RS,
  author =       "Daniel Tabak",
  title =        "{RISC} Systems",
  publisher =    pub-JW,
  address =      pub-JW:adr,
  pages =        "xii + 300",
  year =         "1990",
  ISBN =         "0-471-92694-9",
  ISBN-13 =      "978-0-471-92694-8",
  LCCN =         "QA76.9.A73.T294 1990",
  bibdate =      "Wed Aug 10 11:51:06 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$49.95",
  acknowledgement = ack-nhfb,
  libnote =      "Not yet in my library.",
}

@Article{Tang:1990:AET,
  author =       "Ping Tak Peter Tang",
  title =        "Accurate and Efficient Testing of the Exponential and
                 Logarithm Functions",
  journal =      j-TOMS,
  volume =       "16",
  number =       "3",
  pages =        "185--200",
  month =        sep,
  year =         "1990",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65G99)",
  MRnumber =     "1 070 797",
  bibdate =      "Sun Sep 04 23:14:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://doi.acm.org/10.1145/79505.79506;
                 http://www.acm.org/pubs/citations/journals/toms/1990-16-3/p185-tang/",
  abstract =     "Table-driven techniques can be used to test highly
                 accurate implementation of EXP LOG. The largest error
                 observed in EXP and LOG accurately to within 1/500 unit
                 in the last place are reported in our tests. Methods to
                 verify the tests' reliability are discussed. Results of
                 applying the tests to our own as well as to a number of
                 other implementations of EXP and LOG are presented.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; languages; verification",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Certification and testing. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Portability.",
}

@TechReport{Tang:1990:SSI,
  author =       "P. T. P. Tang",
  title =        "Some Software Implementations of the Functions Sine
                 and Cosine",
  number =       "Report ANL-90/3",
  institution =  "Argonne National Laboratory",
  address =      "Argonne, IL, USA",
  pages =        "27",
  month =        apr,
  year =         "1990",
  bibdate =      "Mon Sep 12 23:55:17 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Tang:1990:TDIa,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Driven Implementation of the Logarithm Function
                 in {IEEE} Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "16",
  number =       "4",
  pages =        "378--400",
  month =        dec,
  year =         "1990",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:26:09 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p378-tang/",
  abstract =     "Algorithms and implementation details for the
                 logarithm functions in both single and double precision
                 of IEEE 754 arithmetic are presented here. With a table
                 of moderate size, the implementation need only working-
                 precision arithmetic and are provably accurate to
                 within 0.57 ulp.",
  acknowledgement = ack-nj,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design; performance; reliability;
                 standardization; theory; verification",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis. {\bf G.1.0}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis.",
}

@TechReport{Tang:1990:TDIb,
  author =       "P. T. P. Tang",
  title =        "Table-driven Implementation of the Expm1 Function in
                 {IEEE} Floating-Point Arithmetic",
  number =       "Preprint MCS-P144-0390",
  institution =  "Argonne National Laboratory",
  address =      "Argonne, IL, USA",
  pages =        "??",
  month =        mar,
  year =         "1990",
  bibdate =      "Mon Sep 12 23:55:14 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@TechReport{Teetz:1990:SNS,
  author =       "Ingo Teetz and Thomas Fischer and Walter Issel",
  title =        "{Die Sprache NBSF fur die strukturelle Beschreibung
                 von Schaltkreisen.: Eine Darstellung am Beispiel eines
                 Gleitkomma-Prozessors}",
  type =         "Report",
  number =       "R-Math-01/90 0233-2876",
  institution =  "Akademie der Wissenschaften der DDR,
                 Karl-Weierstrass-Institut fur Mathematik",
  address =      "Berlin, Germany",
  pages =        "vii + 79",
  year =         "1990",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer hardware description languages.;
                 Floating-point arithmetic.; NBSF (Computer hardware
                 description language)",
  remark =       "Summary in English and German.",
}

@InCollection{Trefethen:1990:PSP,
  author =       "L. N. Trefethen and M. H. Gutknecht",
  title =        "{Pad{\'e}}, Stable {Pad{\'e}}, and
                 {Chebyshev--Pad{\'e}} Approximation",
  crossref =     "Mason:1990:AAI",
  pages =        "??--??",
  year =         "1990",
  bibdate =      "Thu Sep 01 12:23:25 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Tricker:1990:ERP,
  author =       "A. R. Tricker",
  title =        "The effect of rounding on the power level of certain
                 normal test statistics",
  journal =      j-J-APPL-STAT,
  volume =       "17",
  number =       "2",
  pages =        "219--228",
  year =         "1990",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/757582833",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  bibdate =      "Tue Sep 6 11:16:18 MDT 2011",
  bibsource =    "http://www.tandf.co.uk/journals/routledge/02664763.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
  onlinedate =   "5 Jun 2011",
}

@Article{Tricker:1990:ERSa,
  author =       "A. R. Tricker",
  title =        "The effect of rounding on the significance level of
                 certain normal test statistics",
  journal =      j-J-APPL-STAT,
  volume =       "17",
  number =       "1",
  pages =        "31--38",
  year =         "1990",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/757582644",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  bibdate =      "Tue Sep 6 11:16:16 MDT 2011",
  bibsource =    "http://www.tandf.co.uk/journals/routledge/02664763.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
  onlinedate =   "18 Jul 2011",
}

@Article{Tricker:1990:ERSb,
  author =       "A. R. Tricker",
  title =        "The effect of rounding on the significance level and
                 power of certain test statistics for non-normal data",
  journal =      j-J-APPL-STAT,
  volume =       "17",
  number =       "3",
  pages =        "329--340",
  year =         "1990",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/02664769000000005",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  bibdate =      "Tue Sep 6 11:16:20 MDT 2011",
  bibsource =    "http://www.tandf.co.uk/journals/routledge/02664763.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
  onlinedate =   "28 Jul 2006",
}

@Article{vanderVorst:1990:CBP,
  author =       "H. A. {van der Vorst}",
  title =        "The convergence behaviour of preconditioned {CG} and
                 {CG-S} in the presence of rounding errors",
  journal =      j-LECT-NOTES-MATH,
  volume =       "1457",
  pages =        "126--136",
  year =         "1990",
  CODEN =        "LNMAA2",
  DOI =          "https://doi.org/10.1007/BFb0090905",
  ISBN =         "3-540-53515-2 (print), 3-540-46746-7 (e-book)",
  ISBN-13 =      "978-3-540-53515-7 (print), 978-3-540-46746-5
                 (e-book)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  ISSN-L =       "0075-8434",
  MRclass =      "65F35",
  MRnumber =     "1101632 (92a:65141)",
  MRreviewer =   "Seymour Bachmuth",
  bibdate =      "Fri May 9 19:07:18 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lnm1990.bib;
                 MathSciNet database",
  URL =          "http://link.springer.com/chapter/10.1007/BFb0090905/",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/BFb0090897",
  book-URL =     "http://www.springerlink.com/content/978-3-540-46746-5",
  fjournal =     "Lecture Notes in Mathematics",
  journal-URL =  "http://link.springer.com/bookseries/304",
  MRauthor =     "H. A. {van der Vorst}",
  mynote =       "Not copied. No actual error analysis. Just
                 explanations based on his paper with van der Sluis
                 (don't reference Greenbaum!).",
}

@MastersThesis{VanElsen:1990:OCL,
  author =       "Lucien William {Van Elsen}",
  title =        "An optimizing compiler for low-level floating point
                 operations",
  type =         "Thesis ({B.S.})",
  school =       "Massachusetts Institute of Technology, Dept. of
                 Electrical Engineering and Computer Science",
  address =      "Cambridge, MA, USA",
  pages =        "v + 56",
  year =         "1990",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Supervised by William J. Dally.",
  acknowledgement = ack-nhfb,
}

@Article{Vuillemin:1990:ERC,
  author =       "Jean E. Vuillemin",
  title =        "Exact real computer arithmetic with continued
                 fractions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "8",
  pages =        "1087--1105",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57047",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:04 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57047",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Book{Wallis:1990:IFP,
  editor =       "Peter J. L. Wallis",
  title =        "Improving Floating-Point Programming",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xvi + 191",
  year =         "1990",
  ISBN =         "0-471-92437-7",
  ISBN-13 =      "978-0-471-92437-1",
  LCCN =         "QA76.6 .I446 1990",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$60.00",
  abstract =     "This contributed work covers, in precise detail, the
                 potential sources of error in floating-point
                 programming and how these trouble spots can be
                 controlled. Explains several methods for improving the
                 accuracy of floating-point programming, concentrating
                 on those methods that are relevant to the exploitation
                 of the Karlsruhe Accurate Arithmetic.",
  acknowledgement = ack-nhfb,
  keywords =     "Computation by computer systems --- Floating point
                 representation; Electronic digital computers ---
                 Programming; Floating-point arithmetic; Floating-point
                 arithmetic, Compiling (Electronic computers)",
  tableofcontents = "Fundamentals \\
                 Basic Concepts \\
                 Machine Arithmetic \\
                 Model Arithmetic \\
                 \\
                 Error control \\
                 Sources of Error \\
                 Different Approaches to Interval Arithmetic / C.
                 Ullrich and J. Wolff von Gudenberg \\
                 The Karlsruhe Accurate Arithmetic Approach / J. Wolff
                 von Gudenberg \\
                 \\
                 Embedding Of Karlsruhe Arithmetic / J. Wolff von
                 Gudenberg \\
                 The Embedding of Accurate Arithmetic in PASCAL-SC / J.
                 Wolff von Gudenberg \\
                 The Embedding of Accurate Arithmetic in Ada / J. Kok
                 \\
                 \\
                 Improving Accuracy \\
                 Automatic Identification of Scalar Products / D. Winter
                 \\
                 Guidelines for Selected Transformations of Existing
                 Programs / L. Bamberger \\
                 Manipulation of Expressions / J. Davenport and H.
                 Fischer \\
                 E-Methods for Improving Accuracy / G. Schumacher and J.
                 Wolff von Gudenberg \\
                 \\
                 References \\
                 Index",
}

@Article{Weber:1990:EHP,
  author =       "Ken Weber",
  title =        "An experiment in high-precision arithmetic on shared
                 memory multiprocessors",
  journal =      j-SIGSAM,
  volume =       "24",
  number =       "2",
  pages =        "22--40",
  month =        apr,
  year =         "1990",
  CODEN =        "SIGSBZ",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Wed Oct 5 08:31:59 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGSAM Bulletin",
  issue =        "??",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}

@Article{Wigley:1990:MRR,
  author =       "N. M. Wigley and G. A. Jullien",
  title =        "On modulus replication for residue arithmetic
                 computations of complex inner products",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "8",
  pages =        "1065--1076",
  month =        aug,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.57045",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:03 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=57045",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Wingler:1990:TMI,
  author =       "Eric Wingler",
  title =        "The Teaching of Mathematics: An Infinite Product
                 Expansion for the Square Root Function",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "97",
  number =       "9",
  pages =        "836--839",
  month =        nov,
  year =         "1990",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:36:09 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@MastersThesis{Wong:1990:PFP,
  author =       "Kar-pang Wong",
  title =        "The precision of floating point computation in digital
                 computer",
  type =         "Thesis ({M.S. in Computer Science})",
  school =       "University of Wisconsin, Milwaukee",
  address =      "Milwaukee, WI, USA",
  pages =        "vii + 45",
  year =         "1990",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Electronic digital computers --- Programming.;
                 Floating-point arithmetic.",
}

@Article{Wong:1990:QNF,
  author =       "P. W. Wong",
  title =        "Quantization noise, fixed-point multiplicative
                 roundoff noise, and dithering",
  journal =      j-IEEE-TRANS-ACOUST-SPEECH,
  volume =       "38",
  number =       "2",
  pages =        "286--300",
  month =        feb,
  year =         "1990",
  CODEN =        "IETABA",
  ISSN =         "0096-3518",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Acoustics, Speech, and Signal
                 Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=29",
  summary =      "The author considers the characteristics of the error
                 resulting when a continuous amplitude signal $x_n$ is
                 quantized and then multiplied by a constant multiplier
                 a under fixed-point roundoff arithmetic. It is shown
                 that \ldots{}",
}

@Article{Yager:1990:SNM,
  author =       "T. Yager",
  title =        "{Sony NeWS} and {MIPS Magnum}: a double shot of
                 {RISC}",
  journal =      j-BYTE,
  volume =       "15",
  number =       "13",
  pages =        "172--175",
  month =        dec,
  year =         "1990",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Thu Sep 12 18:39:30 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C5430 (Microcomputers)",
  fjournal =     "BYTE Magazine",
  keywords =     "20 MHz; 25 MHz; Fast color graphics; Floating-point
                 acceleration; High-density 3/sup 1///sub 2/-inch floppy
                 disk; MIPS Magnum 3000; MIPS R3000 RISC CPU chip set;
                 Quarter-inch cartridge tape drives; RISC/OS; Sony NeWS
                 3710; System V release 4; Thick-wire Ethernet port;
                 Unix workstations; X Window System",
  numericalindex = "Frequency 2.0E+07 Hz; Frequency 2.5E+07 Hz",
  thesaurus =    "Computer evaluation; Microcomputers; Workstations",
}

@MastersThesis{Yang:1990:PRN,
  author =       "George Chia-Jin Yang",
  title =        "A parametric roundoff noise analysis of second-order
                 state-space digital filters with floating-point
                 arithmetic",
  type =         "Thesis ({M.S.})",
  school =       "University of Tennessee, Knoxville",
  address =      "Knoxville, TN, USA",
  pages =        "vii + 67",
  year =         "1990",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Digital filters (Mathematics).; Floating-point
                 arithmetic.",
}

@Article{Yeh:1990:RTI,
  author =       "H.-G. Yeh",
  title =        "Real-Time Implementation of a Narrow-Band {Kalman}
                 Filter with a Floating-Point Processor {DSP32}",
  journal =      j-IEEE-TRANS-IND-ELECTRON,
  volume =       "37",
  number =       "1",
  pages =        "13--18",
  month =        feb,
  year =         "1990",
  CODEN =        "ITIED6",
  DOI =          "https://doi.org/10.1109/41.45838",
  ISSN =         "0278-0046 (print), 1557-9948 (electronic)",
  ISSN-L =       "0278-0046",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Industrial Electronics",
  summary =      "The author presents experimental results from two
                 studies. First, a real-time narrowband Kalman filter is
                 implemented with a floating-point digital processor
                 DSP32. The real-time capability of this narrowband
                 filter is investigated by varying parameters \ldots{}",
}

@Article{Yoon:1990:MTP,
  author =       "Hyunsoo Yoon and Kyungsook Y. Lee and Amos Bahiri",
  title =        "On the modulo {$M$} translators for the prime memory
                 system",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "8",
  number =       "1",
  pages =        "72--76",
  month =        jan,
  year =         "1990",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Ohio State Univ",
  affiliationaddress = "Columbus, OH, USA",
  classification = "722; 723; C5230 (Digital arithmetic methods)",
  corpsource =   "Department of Comput. and Inf. Sci., Ohio State
                 University, Columbus, OH, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "array processor; binary number system; Burroughs
                 Scientific Processor; Burroughs Scientific Processor
                 (bsp); casting out nine rule; Computer Operating
                 Systems; Computer Systems Programming--Utility
                 Programs; Computer Systems, Digital--Parallel
                 Processing; conflict-free access; decimal
                 floating-point arithmetic; decimal number system;
                 digital arithmetic; Modulo M Computation; modulo M
                 translators; parallel algorithms; prime memory system;
                 Program Translators; SIMD Architecture; SIMD shared
                 memory parallel processor",
  treatment =    "P Practical",
}

@Article{Zarowski:1990:AMH,
  author =       "C. J. Zarowski and H. C. Card",
  title =        "On addition and multiplication with {Hensel} codes",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "39",
  number =       "12",
  pages =        "1417--1423",
  month =        dec,
  year =         "1990",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.61062",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 14:20:05 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=61062",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Zelniker:1990:PBD,
  author =       "G. S. Zelniker and F. J. Taylor",
  booktitle =    "Conference Record Twenty-Fourth Asilomar Conference on
                 Signals, Systems and Computers, 5--7 Nov 1990",
  title =        "Prime Blocklength Discrete {Fourier} Transforms
                 Utilising the Polynomial Residue Number System",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "314",
  year =         "1990",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1990.140897",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
}

@InCollection{Aberth:1991:CHO,
  author =       "Oliver Aberth",
  title =        "The Conversion of a High Order Programming Language
                 from Floating-Point Arithmetic to Range Arithmetic",
  crossref =     "Meyer:1991:CAP",
  pages =        "1--4",
  year =         "1991",
  DOI =          "https://doi.org/10.1007/978-1-4613-9092-3_1",
  bibdate =      "Fri Sep 22 18:54:58 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Adali:1991:FPR,
  author =       "T. Adali and S. H. Ardalan",
  booktitle =    "Acoustics, Speech, and Signal Processing, 1991.
                 {ICASSP-91., 1991} International Conference on. 14--17
                 April 1991",
  title =        "Fixed-point roundoff error analysis of the {RLS}
                 algorithm with time-varying channels",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1865--1868",
  year =         "1991",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The authors derive the steady-state mean square
                 prediction error expression for the fixed-point RLS
                 (recursive least squares) algorithm for the case of
                 time-varying channel estimation, which is modeled as a
                 first-order Markov tapped delay line. It \ldots{}",
}

@Article{Alia:1991:VMM,
  author =       "G. Alia and E. Martinelli",
  title =        "A {VLSI} modulo $m$ multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "40",
  number =       "7",
  pages =        "873--878",
  month =        jul,
  year =         "1991",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.83626",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 12:52:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=83626",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Alverson:1991:IDU,
  author =       "Robert Alverson",
  title =        "Integer Division Using Reciprocals",
  crossref =     "Kornerup:1991:PIS",
  pages =        "186--190",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Alverson.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10; correct rounding; floating-point
                 arithmetic",
  remark =       "Demonstrates a correctly-rounded algorithm for integer
                 division that requires six floating-point
                 multiplications and a table lookup. For comparison,
                 \cite{Markstein:2000:IEF} shows an algorithm that needs
                 seven multiply-adds and a reciprocal approximation.",
}

@Article{Anido:1991:IDI,
  author =       "M. Lois Anido",
  title =        "Improving the division instruction of
                 application-specific {RISCs}",
  journal =      j-MICROPROC-MICROPROG,
  volume =       "32",
  number =       "1-5",
  pages =        "13--21",
  month =        aug,
  year =         "1991",
  CODEN =        "MMICDT",
  ISSN =         "0165-6074 (print), 1878-7061 (electronic)",
  ISSN-L =       "0165-6074",
  bibdate =      "Tue Dec 12 09:26:54 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "17th EUROMICRO Symposium on Microprocessing and
                 Microprogramming. Hardware and Software Design
                 Automation.",
  abstract =     "Presents the development and application of a signed
                 radix-4 division algorithm to a RISC architecture,
                 where the internal ALU Manchester carry adder is used
                 to maintain the partial remainder in irredundant form.
                 There are division algorithms which are faster than the
                 one described in this paper, however they usually make
                 use of a redundant representation of the partial
                 remainder and require carry-save adders which are not
                 normally used in the integer execution unit of RISCs.
                 The method presented in this contribution employs 3x
                 divisor multiples and uses a reduced next divisor
                 multiple estimate table which is implemented by a small
                 and fast logic. Alternative radix-4 schemes with
                 quotient digits (-2,-1,0,1,2) require large and slow
                 PLAs for quotient digit generation. Additionally, there
                 is no need for positive and negative quotient registers
                 because quotient bits are generated on-the-fly by a
                 small-sized logic, concurrently with partial remainder
                 formation. This method also deals directly with signed
                 two's complement numbers, eliminating the need for
                 additional instructions for sign conversion. The
                 application of this radix-4 division algorithm provides
                 a two-bits-at-a-time division instruction, instead of
                 the traditional single bit approach used in some RISCs.
                 The speedup achieved can be very important in many
                 numerically intensive applications, in which the use of
                 floating-point units is not essential.",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ. Federal do Rio de Janeiro, Brazil",
  classification = "C5220 (Computer architecture); C5230 (Digital
                 arithmetic methods)",
  confdate =     "2-5 Sept. 1991",
  conflocation = "Vienna, Austria",
  fjournal =     "Microprocessing and Microprogramming",
  journal-URL =  "https://www.sciencedirect.com/journal/microprocessing-and-microprogramming/issues",
  keywords =     "3X divisor multiples; Application-specific RISCs;
                 Binary division; Division instruction; Internal ALU
                 Manchester carry adder; Irredundant form; Logic;
                 Numerically intensive applications; Partial remainder;
                 Quotient bits; Quotient digits; Reduced next divisor
                 multiple estimate table; RISC architecture; Signed
                 radix-4 division algorithm; Signed two's complement
                 numbers; Speedup",
  pubcountry =   "Netherlands",
  thesaurus =    "Application specific integrated circuits; Digital
                 arithmetic; Reduced instruction set computing",
}

@Article{Anonymous:1991:FDC,
  author =       "Anonymous",
  title =        "{60M-flops}, floating-point {DSP} chip",
  journal =      j-EDN,
  volume =       "36",
  number =       "13",
  pages =        "80--??",
  month =        jun,
  year =         "1991",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "EDN",
}

@Article{Anonymous:1991:SIS,
  author =       "Anonymous",
  title =        "{SCAN-1991: International Symposium on Computer
                 Arithmetic and Scientific Computation}",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "34",
  number =       "2",
  pages =        "N13--N14",
  day =          "4",
  month =        apr,
  year =         "1991",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:20:48 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037704279190071Q",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Arambepola:1991:CVA,
  author =       "B. Arambepola",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, 11--14 June 1991",
  title =        "Common {VLSI} architecture for a practically useful
                 residue number system",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2951--2954",
  year =         "1991",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1991.176164",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "An architecture is presented for carrying out modulo
                 arithmetic in a practically useful residue number
                 system. An important feature of this is that it allows
                 a single hardware design to be used for all moduli. An
                 application of this architecture is \ldots{}",
}

@Book{Arvo:1991:GGI,
  author =       "James Arvo",
  title =        "Graphics gems {II}",
  volume =       "2",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xxxii + 643",
  year =         "1991",
  ISBN =         "0-12-064480-0",
  ISBN-13 =      "978-0-12-064480-3",
  LCCN =         "T385 .G6972 1991",
  bibdate =      "Mon Aug 24 17:12:23 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  series =       "Graphics Gems",
  URL =          "http://www.sciencedirect.com/science/book/9780080507545",
  ZMnumber =     "0774.68010",
  abstract =     "\booktitle{Graphics Gems II} is a collection of
                 articles shared by a diverse group of people that
                 reflect ideas and approaches in graphics programming
                 which can benefit other computer graphics programmers.
                 This volume presents techniques for doing well-known
                 graphics operations faster or easier. The book contains
                 chapters devoted to topics on two-dimensional and
                 three-dimensional geometry and algorithms, image
                 processing, frame buffer techniques, and ray tracing
                 techniques. The radiosity approach, matrix techniques,
                 and numerical and programming techniques are likewise
                 discussed.",
  acknowledgement = ack-nhfb,
  libnote =      "Not yet in my library.",
  tableofcontents = "Foreword / Andrew Glassner \\
                 The Area of a Simple Polygon / Jon Rokne \\
                 Intersection of Line Segments / Mukesh Prasad \\
                 Distance from a Point to a Line / Jack C. Morrison \\
                 An Easy Bounding Circle / Jon Rokne \\
                 The Smallest Circle Containing the Intersection of Two
                 Circles / Jon Rokne \\
                 Appolonius's 10th Problem / Jon Rokne \\
                 A Peano Curve Generation Algorithm / Ken Musgrave \\
                 Space-Filling Curves and a Measure of Coherence /
                 Douglas Voorhies \\
                 Scanline Coherent Shape Algebra / Jonathan E. Steinhart
                 \\
                 Image Smoothing and Sharpening by Discrete Convolution
                 / Dale A. Schumacher \\
                 A Comparison of Digital Halftoning Techniques / Dale A.
                 Schumacher \\
                 Color Dithering / Spencer W. Thomas and Rod G. Bogart
                 \\
                 Fast Anamorphic Image Scaling / Dale A. Schumacher \\
                 Real Pixels / Greg Ward \\
                 A Fast 90-Degree Bitmap Rotator / Sue-Ken Yap \\
                 Rotation of Run-Length Encoded Image Data / Jeff Holt
                 \\
                 Adaptive Run-Length Encoding / Andrew S. Glassner \\
                 Image File Compression Made Easy / Alan W. Paeth \\
                 An Optimal Filter for Image Reconstruction / Nelson Max
                 \\
                 Noise Thresholding in Edge Images / John Schlag \\
                 Computing the Area, the Circumference, and the Genus of
                 a Binary Digital Image / Hanspeter Bieri and Andreas
                 Kohler \\
                 Efficient Inverse Color Map Computation / Spencer W.
                 Thomas \\
                 Efficient Statistical Computations for Optimal Color
                 Quantization / Xiaolin Wu \\
                 A Random Color Map Animation Algorithm / Ken Musgrave
                 \\
                 A Fast Approach to PHIGS PLUS Pseudo Color Mapping /
                 James Hall and Terence Lindgren \\
                 Mapping RGB Triples onto 16 Distinct Values / Alan W.
                 Paeth \\
                 Television Color Encoding and ``Hot'' Broadcast Colors
                 / David Martindale and Alan W. Paeth \\
                 An Inexpensive Method of Setting the Monitor White
                 Point / Gary W. Meyer \\
                 Some Tips for Making Color Hardcopy / Ken Musgrave \\
                 Area of Planar Polygons and Volume of Polyhedra /
                 Ronald N. Goldman \\
                 Getting Around on a Sphere / Clifford A. Shaffer \\
                 Exact Dihedral Metrics for Common Polyhedra / Alan W.
                 Paeth \\
                 A Simple Viewing Geometry / Andrew S. Glassner \\
                 View Correlation / Rod G. Bogart \\
                 Maintaining Winged-Edge Models / Andrew S. Glassner \\
                 Quadtree\slash Octree-to-Boundary Conversion / Claudio
                 Montani and Roberto Scopigno \\
                 Three-Dimensional Homogeneous Clipping of Triangle
                 Strips / Patrick-Gilles Maillot \\
                 InterPhong Shading / Nadia Magnenat Thalmann, Daniel
                 Thalmann and Hong Tong Minh \\
                 Fast Ray-Convex Polyhedron Intersection / Eric Haines
                 \\
                 Intersecting a Ray with an Elliptical Torus / Joseph M.
                 Cychosz \\
                 Ray-Triangle Intersection Using Binary Recursive
                 Subdivision / Douglas Voorhies and David Kirk \\
                 Improved Ray Tagging for Voxel-Based Ray Tracing /
                 David Kirk and James Arvo \\
                 Efficiency Improvements for Hierarchy Traversal in Ray
                 Tracing / Eric Haines \\
                 A Recursive Shadow Voxel Cache for Ray Tracing / Andrew
                 Pearce \\
                 Avoiding Incorrect Shadow Intersections for Ray Tracing
                 / Andrew Pearce \\
                 A Body Color Model: Absorption of Light through
                 Translucent Media / Mark E. Lee and Samuel P. Uselton
                 \\
                 More Shadow Attenuation for Ray Tracing Transparent or
                 Translucent Objects / Mark E. Lee and Samuel P. Uselton
                 \\
                 Implementing Progressive Radiosity with User-Provided
                 Polygon Display Routines / Shenchang Eric Chen \\
                 A Cubic Tetrahedral Adaptation of the Hemi-Cube
                 Algorithm / Jeffrey C. Beran-Koehn and Mark J. Pavicic
                 \\
                 Fast Vertex Radiosity Update / Filippo Tampieri \\
                 Radiosity via Ray Tracing / Peter Shirley \\
                 Detection of Shadow Boundaries for Adaptive Meshing in
                 Radiosity / Fran{\c{c}}ois Sillion \\
                 Decomposing a Matrix into Simple Transformations /
                 Spencer W. Thomas \\
                 Recovering the Data from the Transformation Matrix /
                 Ronald N. Goldman \\
                 Transformations as Exponentials / Ronald N. Goldman \\
                 More Matrices and Transformations: Shear and
                 Pseudo-Perspective / Ronald N. Goldman \\
                 Fast Matrix Inversion / Kevin Wu \\
                 Quaternions and $4 \times 4$ Matrices / Ken Shoemake
                 \\
                 Random Rotation Matrices / James Arvo \\
                 Classifying Small Sparse Matrices / James Arvo \\
                 Bit Picking / Ken Shoemake \\
                 Faster Fourier Transform / Ken Shoemake \\
                 Of Integers, Fields, and Bit Counting / Alan W. Paeth
                 and David Schilling \\
                 Using Geometric Constructions to Interpolate
                 Orientation with Quaternions / John Schlag \\
                 A Half-Angle Identity for Digital Computation: The Joys
                 of the Halved Tangent / Alan W. Paeth \\
                 An Integer Square Root Algorithm / Christopher J.
                 Musial \\
                 Fast Approximation to the Arctangent / Ron Capelli \\
                 Fast Sign of Cross Product Calculation / Jack Ritter
                 \\
                 Interval Sampling / Ken Shoemake \\
                 A Recursive Implementation of the Perlin Noise Function
                 / Greg Ward \\
                 Least-Squares Approximations to B{\'e}zier Curves and
                 Surfaces / Doug Moore and Joe Warren \\
                 Beyond B{\'e}zier Curves / Ken Shoemake \\
                 A Simple Formulation for Curve Interpolation with
                 Variable Control Point Approximation / John Schlag \\
                 Symmetric Evaluation of Polynomials / Terence Lindgren
                 \\
                 Menelaus's Theorem / Hans-Peter Seidel \\
                 Geometrically Continuous Cubic B{\'e}zier Curves /
                 Hans-Peter Siedel \\
                 A Good Straight-Line Approximation of a Circular Arc /
                 Christopher J. Musial \\
                 Great Circle Plotting / Alan W. Paeth \\
                 Fast Anti-Aliased Circle Generation / Xiaolin Wu \\
                 Graphics Gems C Header File \\
                 2D and 3D Vector C Library \\
                 Corrected and Indexed \\
                 Useful C Macros for Vector Operations / Steve
                 Hollasch",
  xxtableofcontents = "Foreword \\
                 Preface \\
                 Mathematical Notation \\
                 Pseudo-Code \\
                 Contributors \\
                 I: 2D Geometry and Algorithms \\
                 Introduction \\
                 1: The Area of a Simple Polygon \\
                 2: Intersection of Line Segments \\
                 3: Distance from a Point to a Line \\
                 4: An Easy Bounding Circle \\
                 5: The Smallest Circle Containing the Intersection of
                 Two Circles \\
                 6: Appolonius's 10th Problem \\
                 7: A Peano Curve Generation Algorithm \\
                 8: Space-Filling Curves and a Measure of Coherence \\
                 9: Scanline Coherent Shape Algebra \\
                 II: Image Processing \\
                 Introduction \\
                 1: Image Smoothing and Sharpening by Discrete
                 Convolution \\
                 2: A Comparison of Digital Halftoning Techniques \\
                 3: Color Dithering \\
                 4: Fast Anamorphic Image Scaling \\
                 5: Real Pixels \\
                 6: A Fast 90-Degree Bitmap Rotator \\
                 7: Rotation of Run-Length Encoded Image Data \\
                 8: Adaptive Run-Length Encoding \\
                 9: Image File Compression Made Easy \\
                 10: An Optimal Filter for Image Reconstruction \\
                 11: Noise Thresholding in Edge Images \\
                 12: Computing the Area, the Circumference, and the
                 Genus of a Binary Digital Image \\
                 III: Frame Buffer Techniques \\
                 Introduction \\
                 1: Efficient Inverse Color Map Computation \\
                 2. Efficient Statistical Computations for Optimal Color
                 Quantization \\
                 3: A Random Color Map Animation Algorithm \\
                 4: A Fast Approach to PHIGS PLUS Pseudo Color Mapping
                 \\
                 5: Mapping RGB Triples onto 16 Distinct Values \\
                 6: Television Color Encoding and ``Hot'' Broadcast
                 Colors \\
                 7: An Inexpensive Method of Setting the Monitor White
                 Point \\
                 8: Some Tips for Making Color Hardcopy \\
                 IV: 3D Geometry and Algorithms \\
                 Introduction \\
                 1: Area of Planar Polygons and Volume of Polyhedra \\
                 2: Getting Around on a Sphere \\
                 3: Exact Dihedral Metrics for Common Polyhedra \\
                 4: A Simple Viewing Geometry \\
                 5: View Correlation \\
                 6: Maintaining Winged-Edge Models \\
                 7: Quadtree\slash Octree-to-Boundary Conversion \\
                 8: Three-Dimensional Homogeneous Clipping of Triangle
                 Strips \\
                 9: InterPhong Shading \\
                 V: Ray Tracing \\
                 Introduction \\
                 1: Fast Ray-Convex Polyhedron Intersection \\
                 2: Intersecting a Ray with an Elliptical Torus \\
                 3: Ray-Triangle Intersection Using Binary Recursive
                 Subdivision \\
                 4: Improved Ray Tagging for Voxel-Based Ray Tracing \\
                 5: Efficiency Improvements for Hierarchy Traversal in
                 Ray Tracing \\
                 6: A Recursive Shadow Voxel Cache for Ray Tracing \\
                 7: Avoiding Incorrect Shadow Intersections for Ray
                 Tracing \\
                 8: A Body Color Model: Absorption of Light through
                 Translucent Media \\
                 9: More Shadow Attenuation for Ray Tracing Transparent
                 or Translucent Objects \\
                 VI: Radiosity \\
                 Introduction \\
                 1: Implementing Progressive Radiosity with
                 User-Provided Polygon Display Routines \\
                 2: A Cubic Tetrahedral Adaptation of the Hemi-Cube
                 Algorithm \\
                 3: Fast Vertex Radiosity Update \\
                 4: Radiosity via Ray Tracing \\
                 5: Detection of Shadow Boundaries for Adaptive Meshing
                 in Radiosity \\
                 [data unavailable] \ldots{}",
}

@Article{Balsara:1991:DSM,
  author =       "Poras T. Balsara and Robert M. Owens and Mary Jane
                 Irwin",
  title =        "Digit serial multipliers",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "11",
  number =       "2",
  pages =        "156--162",
  month =        feb,
  year =         "1991",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ of Texas at Dallas",
  affiliationaddress = "Richardson, TX, USA",
  classification = "713; 723; B2570 (Semiconductor integrated circuits);
                 C5120 (Logic and switching circuits); C5230 (Digital
                 arithmetic methods)",
  corpsource =   "Erik Jonsson Sch. of Eng. and Computer Science, Texas
                 University, Richardson, TX, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "communication; Computers, Digital; data; digit
                 pipelined multipliers; digit pipelining; digit serial
                 multipliers; digital arithmetic; Integrated Circuits,
                 VLSI; Multiplying Circuits; multiplying circuits;
                 parallel; pipeline processing; Pipelined Multipliers;
                 processing; programmable multipliers; semisystolic;
                 Signal Processing --- Digital Techniques; special
                 purpose computers; special purpose processors;
                 systolic; systolic multiplier; Systolic Multipliers;
                 transmission; VLSI; VLSI signal processing",
  treatment =    "P Practical",
}

@Article{Barrenechea:1991:NEH,
  author =       "M. J. Barrenechea",
  title =        "Numeric exception handling",
  journal =      j-PROGRAM-J,
  volume =       "9",
  number =       "3",
  pages =        "40--42, 44--49",
  month =        may # "--" # jun,
  year =         "1991",
  ISSN =         "0747-5861",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Numeric exception handling is a facet of compiler
                 runtime support that is not well understood by many
                 application programmers, or even by some compiler
                 vendors. Floating-point errors have puzzled programmers
                 for too long. The author demystifies the IEEE 754 and
                 854 floating-point standards and explains how the Intel
                 80287/80387 and i860 chips fit into the puzzle. He
                 gives some techniques for handling numeric exceptions
                 in C++.",
  acknowledgement = ack-nhfb,
  affiliation =  "Microway Inc., Plymouth, MA, USA",
  classification = "C6110 (Systems analysis and programming)",
  fjournal =     "Programmer's Journal",
  keywords =     "C++; Compiler runtime support; Floating point errors;
                 Floating-point standards; I860 chips; IEEE 754; IEEE
                 854; Intel 80287/80387; Numeric exceptions",
  thesaurus =    "C language; C listings; Standards",
}

@Article{Barsi:1991:MAB,
  author =       "Ferruccio Barsi",
  title =        "Mod $m$ arithmetic in binary systems",
  journal =      j-INFO-PROC-LETT,
  volume =       "40",
  number =       "6",
  pages =        "303--309",
  year =         "1991",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  MRclass =      "68M07 (68Q35)",
  MRnumber =     "MR1156823 (92m:68009)",
  bibdate =      "Thu Nov 8 14:50:34 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}

@Article{Bartholomew-Biggs:1991:AST,
  author =       "M. C. Bartholomew-Biggs",
  title =        "{Ada} Software for Teaching Modern Computer
                 Arithmetic",
  journal =      j-SIGNUM,
  volume =       "26",
  number =       "3",
  pages =        "17--26",
  month =        jul,
  year =         "1991",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/122649.122651",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:20 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Describes three Ada packages which support the
                 teaching of some recent and important ideas in
                 numerical computation. The first is designed to enable
                 students to write and use applications programs
                 demonstrating the behavior of floating point arithmetic
                 with different precisions and roundings. It also
                 underpins the other two packages which provide simple
                 computational tools for interval arithmetic and for
                 accurate arithmetic.",
  acknowledgement = ack-nhfb,
  affiliation =  "Numerical Optimisation Centre, Hatfield Polytech.,
                 UK",
  classification = "C0220 (Education and training); C5230 (Digital
                 arithmetic methods); C7430 (Computer engineering);
                 C7810C (Computer-aided instruction)",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "Accurate arithmetic; Ada software; Computer
                 arithmetic; Floating point arithmetic; Interval
                 arithmetic; Numerical computation; Precisions;
                 Roundings; Students; Teaching",
  thesaurus =    "Computer aided instruction; Computer science
                 education; Digital arithmetic; Numerical analysis;
                 Software packages; Teaching",
  xxpages =      "16--26",
}

@Article{BartholomewBiggs:1991:AST,
  author =       "M. C. Bartholomew-Biggs",
  title =        "{Ada} software for teaching modern computer
                 arithmetic",
  journal =      j-SIGNUM,
  volume =       "26",
  number =       "3",
  pages =        "16--26",
  month =        jul,
  year =         "1991",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Wed Dec 13 13:13:34 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Describes three Ada packages which support the
                 teaching of some recent and important ideas in
                 numerical computation. The first is designed to enable
                 students to write and use applications programs
                 demonstrating the behavior of floating point arithmetic
                 with different precisions and roundings. It also
                 underpins the other two packages which provide simple
                 computational tools for interval arithmetic and for
                 accurate arithmetic.",
  acknowledgement = ack-nhfb,
  affiliation =  "Numerical Optimisation Centre, Hatfield Polytech.,
                 UK",
  classification = "C0220 (Education and training); C5230 (Digital
                 arithmetic methods); C7430 (Computer engineering);
                 C7810C (Computer-aided instruction)",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "Accurate arithmetic; Ada software; Computer
                 arithmetic; Floating point arithmetic; Interval
                 arithmetic; Numerical computation; Precisions;
                 Roundings; Students; Teaching",
  thesaurus =    "Computer aided instruction; Computer science
                 education; Digital arithmetic; Numerical analysis;
                 Software packages; Teaching",
}

@Article{Bartoloni:1991:MFU,
  author =       "A. Bartoloni and C. Battista and S. Cabasino and N.
                 Cabibbo and F. Del Prete and F. Marzano and P. S.
                 Paolucci and R. Sarno and G. Salina and G. M. Todesco
                 and M. Torelli and R. Tripiccione and W. Tross and E.
                 Zanetti",
  title =        "{MAD}, a floating-point unit for massively-parallel
                 processors",
  journal =      "Particle World",
  volume =       "2",
  number =       "3",
  pages =        "65--73",
  month =        "????",
  year =         "1991",
  ISSN =         "1043-6790",
  bibdate =      "Tue Dec 12 09:26:54 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The authors describe in detail the architecture and
                 implementation of the MAD chip. It is a floating point
                 unit, used as the elementary processing element of the
                 APE100 array processor. The design has been accurately
                 tailored to the requirements of a SIMD floating point
                 intensive machine.",
  acknowledgement = ack-nhfb,
  affiliation =  "Roma University, Italy",
  classification = "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5220P (Parallel architecture);
                 C5230 (Digital arithmetic methods); C7320 (Physics and
                 Chemistry)",
  keywords =     "APE100 array processor; Architecture; Elementary
                 processing element; Floating-point unit;
                 Massively-parallel processors; SIMD floating point
                 intensive machine",
  pubcountry =   "UK",
  thesaurus =    "Digital arithmetic; Microprocessor chips; Parallel
                 architectures; Physics computing",
}

@InProceedings{Bass:1991:BSF,
  author =       "S. C. Bass and G. M. Butler and R. L. Williams and F.
                 Barlos and D. R. Miller",
  booktitle =    "{[Proceedings] ICASSP 91: 1991 International
                 Conference on Acoustics, Speech, and Signal
                 Processing}",
  title =        "A bit-serial, floating point {CORDIC} processor in
                 {VLSI}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1165--1168 (vol. 2)",
  year =         "1991",
  DOI =          "https://doi.org/10.1109/ICASSP.1991.150583",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Application software; Circuits; CMOS technology;
                 Computer architecture; Equations; Hardware; Process
                 design; Signal processing; Signal processing
                 algorithms; Very large scale integration",
}

@InProceedings{Beal:1991:GAP,
  author =       "D. Beal and C. Lambrinoudakis",
  title =        "{GPFP}: an array processing element for the next
                 generation of massively parallel supercomputer
                 architectures",
  crossref =     "IEEE:1991:PSA",
  pages =        "348--357",
  year =         "1991",
  bibdate =      "Wed Apr 15 16:28:01 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "B1265F (Microprocessors and microcomputers); B2570D
                 (CMOS integrated circuits); C5130 (Microprocessor
                 chips); C5220P (Parallel architecture); C5230 (Digital
                 arithmetic methods)",
  corpsource =   "Department of Computer Science, Queen Mary and
                 Westfield Coll., London University, UK",
  keywords =     "1.6 micron; 2.5 GFLOPS; 50 MHz; 50-MHz clock; ALU;
                 arithmetic and logic unit; array processing element;
                 CMOS integrated circuits; CMOSIC; cost-effective extra
                 functionality; digital arithmetic; floating point
                 arithmetic; general purpose with floating point
                 support; GPFP; MasPar; massively parallel SIMD arrays;
                 massively parallel supercomputer architectures;
                 microprocessor chips; on-chip memory; parallel
                 architectures; processing element; VLSI",
  sponsororg =   "IEEE; ACM",
  treatment =    "P Practical",
}

@TechReport{Beebe:1991:ASR,
  author =       "Nelson H. F. Beebe",
  title =        "Accurate Square Root Computation",
  institution =  inst-CSC,
  address =      inst-CSC:adr,
  pages =        "23",
  day =          "4",
  month =        feb,
  year =         "1991",
  bibdate =      "Sat Feb 8 10:28:55 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Supplemental class notes prepared for Mathematics
                 118.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bohlender:1991:DFP,
  author =       "G. Bohlender",
  title =        "Decimal floating-point arithmetic in binary
                 representation",
  crossref =     "Kaucher:1991:CAS",
  pages =        "13--27",
  year =         "1991",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The binary representation of decimal floating-point
                 numbers permits an efficient implementation of the
                 proposed radix independent IEEE standard for
                 floating-point arithmetic, as far as storage space is
                 concerned. Unfortunately the left and right shifts
                 occurring in the arithmetic operations are very
                 complicated and slow in this representation. The paper
                 proposes methods which speed up these shifts; in
                 particular a kind of carry look-ahead technique is used
                 for division. These methods can be combined to
                 construct a decimal shifter which is needed in an ALU
                 for decimal arithmetic.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliation =  "Inst. fur Angewandte Math., Karlsruhe University,
                 Germany",
  classification = "C5230 (Digital arithmetic methods)",
  keywords =     "ALU; Binary representation; Carry look-ahead; Decimal
                 arithmetic; decimal floating-point arithmetic; Decimal
                 floating-point numbers; Decimal shifter; Division;
                 Floating-point arithmetic; IEEE standard; Left shifts;
                 Radix independent; Right shifts; Storage space",
  thesaurus =    "Digital arithmetic; Standards",
}

@InProceedings{Bohlender:1991:SEF,
  author =       "G. Bohlender and W. Walter and P. Kornerup and D. W.
                 Matula",
  title =        "Semantics for exact floating point operations",
  crossref =     "Kornerup:1991:PIS",
  pages =        "22--26",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Boldo:2003:RCT} for some special cases that
                 this paper may have overlooked.",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Bohlender.pdf",
  abstract =     "Semantics are given for the four elementary arithmetic
                 operations and the square root, to characterize what
                 are termed exact floating point operations. The
                 operands of the arithmetic operations and the argument
                 of the square root are all floating point numbers in
                 one format. In every case, the result is a pair of
                 floating point numbers in the same format with no
                 accuracy lost in the computation. These semantics make
                 it possible to realize the following principle: it
                 shall be a user option to discard any information in
                 the result of a floating point arithmetic operation.
                 The reliability and portability previously associated
                 with only mathematical software implementations in
                 integer arithmetic can thus be attained exploiting the
                 generally higher efficiency of floating point
                 hardware.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Angewandte Math., Karlsruhe University,
                 Germany",
  classification = "C1160 (Combinatorial mathematics); C5230 (Digital
                 arithmetic methods)",
  keywords =     "accurate floating-point summation; argument; ARITH-10;
                 elementary arithmetic operations; exact floating point
                 operations; floating point arithmetic; floating point
                 hardware; floating point numbers; integer arithmetic;
                 mathematical software; operands; portability;
                 reliability; semantics; square root",
  thesaurus =    "Digital arithmetic; Number theory",
}

@InProceedings{Bohlender:1991:SPH,
  author =       "Gerd Bohlender and Andreas Kn{\"o}fel",
  title =        "A Survey of Pipelined Hardware Support for Accurate
                 Scalar Products",
  crossref =     "Kaucher:1991:CAS",
  pages =        "29--43",
  year =         "1991",
  bibdate =      "Sat Sep 17 19:05:23 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bohlender:1991:VEI,
  author =       "Gerd Bohlender",
  title =        "A Vector Extension of the {IEEE} Standard for
                 Floating-Point Arithmetic",
  crossref =     "Kaucher:1991:CAS",
  pages =        "3--12",
  year =         "1991",
  bibdate =      "Wed Dec 13 18:41:16 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The IEEE standard for floating-point arithmetic aims
                 at improving security, accuracy, reliability, and
                 compatibility of floating-point computations. However,
                 the standard only specifies single, double, and
                 extended precision operations for real operands.
                 Therefore, often only these operations are available in
                 hardware on customary floating-point processors. Vector
                 and matrix operations, complex operations, and interval
                 operations, in contrast have to be simulated in the
                 traditional way, using sequences of rounded operations.
                 This method leads to an unnecessary loss of accuracy
                 and efficiency. As floating-point processors more and
                 more evolve into vector processors for sophisticated
                 numerical applications, the same aims should be
                 satisfied for all operations on the customary numerical
                 data types. The paper proposes a vector extension of
                 the IEEE standard which leads to improved operations in
                 higher numerical spaces.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Angewandte Math., Karlsruhe University,
                 Germany",
  classification = "C5220P (Parallel architecture); C5230 (Digital
                 arithmetic methods)",
  keywords =     "Floating-point arithmetic; Floating-point processors;
                 IEEE standard; Numerical data types; Vector
                 processors",
  thesaurus =    "Digital arithmetic; Standards; Vector processor
                 systems",
}

@TechReport{Boughton:1991:CSG,
  author =       "G. A. {Boughton (editor)}",
  title =        "{Computation Structures Group} Progress Report
                 1990--91",
  type =         "{CSG} Memo",
  number =       "337",
  institution =  "MIT Laboratory for Computer Science",
  address =      "Cambridge, MA, USA",
  month =        jun,
  year =         "1991",
  bibdate =      "Wed Jan 29 16:27:14 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Utilities for accurate reading and printing of double
                 precision floating point numbers (cited in
                 \cite{Steele:2004:RHP}).",
}

@Article{Briggs:1991:PCF,
  author =       "Keith Briggs",
  title =        "A Precise Calculation of the {Feigenbaum} Constants",
  journal =      j-MATH-COMPUT,
  volume =       "57",
  number =       "195",
  pages =        "435--439",
  month =        jul,
  year =         "1991",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11Y60 (39B12 58F14 65Q05)",
  MRnumber =     "91j:11117",
  MRreviewer =   "Jeffrey O. Shallit",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "B0290F (Interpolation and function approximation);
                 B0290K (Nonlinear and functional equations); C4130
                 (Interpolation and function approximation); C4150
                 (Nonlinear and functional equations)",
  corpsource =   "Department of Math., La Trobe University, Bundoora,
                 Vic., Australia",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Feigenbaum constants; Feigenbaum functional equation;
                 functional equations; iteration; iterative methods;
                 multiple precision floating point; period-doubling
                 bifurcations; real functions",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Bromley:1991:FAT,
  author =       "Mark Bromley and Steven Heller and Tim McNerney and
                 Guy L. {Steele Jr.}",
  title =        "{Fortran} at ten gigaflops: the {Connection Machine}
                 convolution compiler",
  journal =      j-SIGPLAN,
  volume =       "26",
  number =       "6",
  pages =        "145--156",
  month =        jun,
  year =         "1991",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Thu May 13 12:37:27 MDT 1999",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/pldi/113445/index.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/pldi/113445/p145-bromley/",
  abstract =     "The authors have implemented a prototype of a
                 specialized compiler module and associated run-time
                 support that allows a Fortran user to achieve sustained
                 floating-point performance of over 10 gigaflops on the
                 Connection Machine Model CM-2. This improves
                 substantially over the previous record of 5.6
                 gigaflops, which was achieved by means of hand-crafted
                 low-level coding techniques. The compiler module
                 processes array assignment statements of a certain
                 form: the right-hand side must be a sum of products and
                 the products must use the Fortran 90 array shifting
                 intrinsics in a certain stylized pattern. Such
                 assignment statements are suitable for expressing array
                 convolution (stencil) computations and can be executed
                 efficiently by chained multiply-add operations.",
  acknowledgement = ack-nhfb,
  affiliation =  "Thinking Machines Corp., Cambridge, MA, USA",
  classification = "C5440 (Multiprocessor systems and techniques); C6110
                 (Systems analysis and programming); C6140D (High level
                 languages); C6150C (Compilers, interpreters and other
                 processors)",
  confdate =     "26-28 June 1991",
  conflocation = "Toronto, Ont., Canada",
  confsponsor =  "ACM",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "Array assignment statements; Array convolution;
                 Chained multiply-add operations; Connection Machine
                 convolution compiler; Connection Machine Model CM-2;
                 Fortran 90 array shifting intrinsics; Fortran user;
                 Hand-crafted low-level coding techniques; languages;
                 performance; Run-time support; Specialized compiler
                 module; Sustained floating-point performance",
  subject =      "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf D.3.4} Software,
                 PROGRAMMING LANGUAGES, Processors, Compilers.",
  thesaurus =    "FORTRAN; Parallel machines; Parallel programming;
                 Program compilers",
}

@Book{Brunner:1991:VAR,
  editor =       "Richard A. Brunner and Dileep P. Bhandarkar and
                 others",
  title =        "{VAX} Architecture Reference Manual",
  publisher =    pub-DP # " and " # pub-PH,
  address =      pub-DP:adr # " and " # pub-PH:adr,
  pages =        "xv + 560",
  year =         "1991",
  ISBN =         "1-55558-057-2 (Digital Press), 0-13-929522-4
                 (Prentice-Hall)",
  ISBN-13 =      "978-1-55558-057-5 (Digital Press), 978-0-13-929522-5
                 (Prentice-Hall)",
  LCCN =         "QA76.8.V32 V39 1991",
  bibdate =      "Wed Nov 01 08:09:54 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{Bruss:1991:RMF,
  author =       "Rolf-J{\"u}rgen Br{\"u}{\ss}",
  title =        "{RISC}\emdash The {MIPS-R3000} Family",
  publisher =    pub-SIEMENS,
  address =      pub-SIEMENS:adr,
  pages =        "340",
  year =         "1991",
  ISBN =         "3-8009-4103-1",
  ISBN-13 =      "978-3-8009-4103-2",
  LCCN =         "QA76.5 R48 1991",
  bibdate =      "Sat Jan 29 23:10:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Bryant:1991:CVI,
  author =       "R. E. Bryant",
  title =        "On the complexity of {VLSI} implementations and graph
                 representations of {Boolean} functions with application
                 to integer multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "40",
  number =       "2",
  pages =        "205--213",
  month =        feb,
  year =         "1991",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.73590",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 12:52:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=73590",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Calvetti:1991:REF,
  author =       "Daniela Calvetti",
  title =        "Roundoff error for floating point representation of
                 real data",
  journal =      j-COMMUN-STAT-THEORY-METH,
  volume =       "20",
  number =       "8",
  pages =        "2687--2695",
  year =         "1991",
  CODEN =        "CSTMDC",
  DOI =          "https://doi.org/10.1080/03610929108830658",
  ISSN =         "0361-0926 (print), 1532-415X (electronic)",
  ISSN-L =       "0361-0926",
  MRclass =      "62E99 (65C20)",
  MRnumber =     "93d:62031",
  bibdate =      "Wed Jan 27 05:39:04 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/communstattheorymeth1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications in Statistics: Theory and Methods",
  journal-URL =  "http://www.tandfonline.com/loi/lsta20",
  reviewer =     "Evdokia Xekalaki",
}

@Article{Calvetti:1991:SRE,
  author =       "Daniela Calvetti",
  title =        "A stochastic roundoff error analysis for the {Fast
                 Fourier Transform}",
  journal =      j-MATH-COMPUT,
  volume =       "56",
  number =       "194",
  pages =        "755--774",
  month =        apr,
  year =         "1991",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65T20 (65G05)",
  MRnumber =     "91m:65341",
  MRreviewer =   "Harald E. Krogstad",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "B0290Z (Other numerical methods); B0290B (Error
                 analysis in numerical methods); C4190 (Other numerical
                 methods); C4110 (Error analysis in numerical methods)",
  corpsource =   "Dept. of Math., Southern Colorado Univ., Pueblo, CO,
                 USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "addition; discrete Fourier transform; error analysis;
                 expected value; fast Fourier transform; fast Fourier
                 transforms; linear forms; multiplication; stochastic
                 roundoff error analysis; variance",
  treatment =    "T Theoretical or Mathematical",
}

@Book{Catanzaro:1991:STP,
  editor =       "Ben J. Catanzaro",
  title =        "The {SPARC} Technical Papers",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xvi + 501",
  year =         "1991",
  ISBN =         "0-387-97634-5, 3-540-97634-5",
  ISBN-13 =      "978-0-387-97634-1, 978-3-540-97634-9",
  LCCN =         "QA76.9.A73 S65 1991",
  bibdate =      "Wed Feb 9 01:57:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Celarier:1991:AML,
  author =       "Donald A. Celarier and Donald W. Sando",
  title =        "An {Ada} math library for real-time avionics",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "274--284",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Sat Aug 9 09:05:43 MDT 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C7460 (Aerospace engineering); C7150 (Military); C7310
                 (Mathematics); C6140D (High level languages)",
  corpsource =   "Boeing Defense and Space Group, Seattle, WA, USA",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "accuracy testing; Ada; Ada math library; aerospace
                 computing; applications; avionics; computing;
                 implementation; library; mathematics computing;
                 military; military avionics processor; real-time
                 avionics; real-time systems; subroutines",
  treatment =    "P Practical",
}

@Article{Chai:1991:MCF,
  author =       "P. Chai and T. Chuk and Y. H. Fong and L. Hu and K. Ng
                 and J. Prabhu and A. Quek and A. Samuels and J. Yeun",
  title =        "A 120 {MFLOPS CMOS} Floating-Point Processor",
  crossref =     "IEEE:1991:PIC",
  pages =        "15.1/1--4",
  year =         "1991",
  bibdate =      "Wed Sep 7 22:32:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@InProceedings{Chan:1991:DOC,
  author =       "Pak K. Chan and Martine D. F. Schlag and Clark D.
                 Thomborson and Vojin G. Oklobdzija",
  title =        "Delay optimization of carry-skip adders and block
                 carry-lookahead adders",
  crossref =     "Kornerup:1991:PIS",
  pages =        "154--164",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Chan.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}

@Article{Chance:1991:EPA,
  author =       "R. J. Chance",
  title =        "The effect of processor architecture on an efficient
                 floating point table look-up algorithm",
  journal =      j-MICROPROC-MICROSYS,
  volume =       "15",
  number =       "8",
  pages =        "411--416 (or 411--415??)",
  month =        oct,
  year =         "1991",
  CODEN =        "MIMID5",
  ISSN =         "0141-9331 (print), 1872-9436 (electronic)",
  ISSN-L =       "0141-9331",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "R J Chance investigates the performance that can be
                 achieved using linear interpolation and partitioning
                 techniques in look-up tables",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Microprocessors and Microsystems",
}

@Article{Chang:1991:PLA,
  author =       "Yuh-Huu Chang and Ching-Kae Tzou and N. J. Bershad",
  title =        "Postsmoothing for the {LMS} algorithm and a fixed
                 point roundoff error analysis",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "39",
  number =       "4",
  pages =        "959--962",
  month =        apr,
  year =         "1991",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "The effect of post-algorithm smoothing on digital
                 implementations of the least mean square (LMS)
                 algorithm is studied. An expression is derived for the
                 mean square error (MSE) with post-algorithm (PA)
                 smoothing but without finite wordlength effects.
                 \ldots{}",
}

@Article{Chassaing:1991:DSP,
  author =       "Chassaing and Horning",
  title =        "Digital Signal Processing with Fixed- and
                 Floating-Point Processors",
  journal =      j-COED,
  volume =       "II",
  number =       "1",
  pages =        "1--4",
  month =        jan,
  year =         "1991",
  CODEN =        "CWLJDP",
  ISSN =         "0736-8607",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "CoED",
}

@InProceedings{Chatelin:1991:AAA,
  author =       "F. Chatelin and V. Frayss{\'e}",
  title =        "Analysis of arithmetic algorithms: a statistical
                 study",
  crossref =     "Kornerup:1991:PIS",
  pages =        "10--16",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Chatelin.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}

@Article{Chen:1991:BDR,
  author =       "F. Chen and C. S. Chen",
  title =        "A {20~b} dynamic-range floating-point data acquisition
                 system",
  journal =      j-IEEE-TRANS-IND-ELECTRON,
  volume =       "38",
  number =       "1",
  pages =        "10--14",
  month =        feb,
  year =         "1991",
  CODEN =        "ITIED6",
  DOI =          "https://doi.org/10.1109/41.103477",
  ISSN =         "0278-0046 (print), 1557-9948 (electronic)",
  ISSN-L =       "0278-0046",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Industrial Electronics",
  summary =      "The design and engineering of a floating-point
                 data-acquisition system are described. The system has
                 both automatic gain and software-programmable gain
                 adjustment features. In automatic gain adjustment mode,
                 the gain is set automatically dependent on \ldots{}",
}

@Article{Chiang:1991:FNR,
  author =       "Jen-Shiun Chiang and Mi Lu",
  title =        "Floating-point numbers in residue number systems",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "22",
  number =       "10",
  pages =        "127--140",
  month =        "????",
  year =         "1991",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  MRclass =      "65Y10",
  MRnumber =     "92h:65212",
  bibdate =      "Wed Dec 13 18:13:40 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Introduce a new type of the residue number system
                 (RNS), floating-point RNS, which can significantly
                 increase the range of the numbers represented by RNS.
                 The concept of the RNS floating-point arithmetics are
                 presented, and the approaches to perform these
                 arithmetic operations are proposed. The introduced
                 methods are simple, efficient and easy to implement. (6
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Electr. Eng., Texas A\&M University,
                 College Station, TX, USA",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  keywords =     "Floating-point RNS; Residue number system; RNS",
  pubcountry =   "UK",
  thesaurus =    "Digital arithmetic",
}

@Article{Chiang:1991:FPNa,
  author =       "Jen-Shiun Chiang and Mi Lu",
  title =        "Floating-point numbers in residue number systems",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "22",
  number =       "10",
  pages =        "127--140",
  month =        "????",
  year =         "1991",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  MRclass =      "65Y10",
  MRnumber =     "92h:65212",
  bibdate =      "Wed Dec 13 18:13:40 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Introduce a new type of the residue number system
                 (RNS), floating-point RNS, which can significantly
                 increase the range of the numbers represented by RNS.
                 The concept of the RNS floating-point arithmetics are
                 presented, and the approaches to perform these
                 arithmetic operations are proposed. The introduced
                 methods are simple, efficient and easy to implement. (6
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Electr. Eng., Texas A\&M University,
                 College Station, TX, USA",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  keywords =     "Floating-point RNS; Residue number system; RNS",
  pubcountry =   "UK",
  thesaurus =    "Digital arithmetic",
}

@Article{Chiang:1991:FPNb,
  author =       "Jen-Shiun Chiang and Mi Lu",
  title =        "Floating-point numbers in residue number systems",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "22",
  number =       "10",
  pages =        "127--140",
  month =        "????",
  year =         "1991",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 19:11:01 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/089812219190200N",
  abstract =     "Introduce a new type of the residue number system
                 (RNS), floating-point RNS, which can significantly
                 increase the range of the numbers represented by RNS.
                 The concept of the RNS floating-point arithmetics are
                 presented, and the approaches to perform these
                 arithmetic operations are proposed. The introduced
                 methods are simple, efficient and easy to implement.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Electr. Eng., Texas A and M University,
                 College Station, TX, USA",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  keywords =     "Floating-point RNS; Residue number system; RNS",
  pubcountry =   "UK",
  thesaurus =    "Digital arithmetic",
}

@InProceedings{Chiang:1991:GDA,
  author =       "J.-S. Chiang and M. Lu",
  title =        "A general division algorithm for residue number
                 systems",
  crossref =     "Kornerup:1991:PIS",
  pages =        "76--83",
  year =         "1991",
  DOI =          "https://doi.org/10.1109/ARITH.1991.145537",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Chiang.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10; residue arithmetic; residue number system",
  summary =      "A general algorithm for signed number division in
                 residue number systems (RNSs) is presented. A parity
                 checking technique is used to accomplish the sign and
                 overflow detection in this algorithm. Compared with
                 conventional methods of sign and \ldots{}",
}

@Article{Cmelik:1991:AMS,
  author =       "Robert F. Cmelik and Shing I. Kong and David R. Ditzel
                 and Edmund J. Kelly",
  title =        "An Analysis of {MIPS} and {SPARC} Instruction Set
                 Utilization on the {SPEC} Benchmarks",
  journal =      j-SIGPLAN,
  volume =       "26",
  number =       "4",
  pages =        "290--301 (or 290--302??)",
  month =        apr,
  year =         "1991",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The dynamic instruction counts of MIPS and SPARC are
                 compared using the SPEC benchmarks. MIPS typically
                 executes more user-level instructions than SPARC. This
                 difference can be accounted for by architectural
                 differences, compiler differences, and library
                 differences. The most significant differences are that
                 SPARC's double-precision floating point load/store is
                 an architectural advantage in the SPEC floating point
                 benchmarks while MIPS's compare-and-branch instruction
                 is an architectural advantage in the SPEC integer
                 benchmarks. After the differences in the two
                 architectures are isolated, it appears that although
                 MIPS and SPARC each have strengths and weaknesses in
                 their compilers and library routines, the combined
                 effect of compilers and library routines does not give
                 either MIPS or SPARC a clear advantage in these
                 areas.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sun Microsyst. Inc., Mountain View, CA, USA",
  classification = "C5220 (Computer architecture); C5470 (Performance
                 evaluation and testing); C6140B (Machine-oriented
                 languages)",
  confdate =     "8-11 April 1991",
  conflocation = "Santa Clara, CA, USA",
  confsponsor =  "IEEE; ACM",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "Architectural differences; Compare-and-branch
                 instruction; Compiler differences; Double-precision
                 floating point load/store; Dynamic instruction counts;
                 Instruction set utilization; Library differences; MIPS;
                 SPARC; SPEC floating point benchmarks; SPEC integer
                 benchmarks; User-level instructions",
  thesaurus =    "Instruction sets; Performance evaluation; Reduced
                 instruction set computing",
}

@InProceedings{Cody:1991:KAA,
  author =       "W. J. Cody",
  title =        "Keynote Address: Arithmetic Standards: The Long Road",
  crossref =     "Kornerup:1991:PIS",
  pages =        "ix--ix",
  year =         "1991",
  bibdate =      "Sat Nov 17 08:46:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_keynote.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}

@Article{Cody:1991:PEP,
  author =       "W. J. Cody",
  title =        "Performance Evaluation of Programs Related to the Real
                 Gamma Function",
  journal =      j-TOMS,
  volume =       "17",
  number =       "1",
  pages =        "46--54",
  month =        mar,
  year =         "1991",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20 (65Y20)",
  MRnumber =     "91m:65052",
  bibdate =      "Sun Sep 04 23:33:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://doi.acm.org/10.1145/103147.103153;
                 http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p46-cody/",
  abstract =     "Methods are presented for evaluating the performance
                 of programs for the functions $ \Gamma (x) $, $ \ln
                 \Gamma (x) $, and $ \psi (x) $. Accuracy estimates are
                 based on comparisons using the manipulation theorem.
                 Ideas for checking robustness are also given, and
                 details on specific implementations of test programs
                 are included.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "measurement; performance; reliability",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Certification and testing.",
}

@Article{Cody:1991:UTS,
  author =       "W. J. Cody and L. Stoltz",
  title =        "The Use of {Taylor} Series to Test Accuracy of
                 Function Programs",
  journal =      j-TOMS,
  volume =       "17",
  number =       "1",
  pages =        "55--63",
  month =        mar,
  year =         "1991",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20 (65Y20)",
  MRnumber =     "91m:65053",
  bibdate =      "Sun Sep 04 23:36:36 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://doi.acm.org/10.1145/103147.103154;
                 http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p55-cody/",
  abstract =     "This paper discusses the use of local Taylor series
                 expansions for determining the accuracy of computer
                 programs for special functions. The main example is
                 testing of programs for exponential integrals.
                 Additional applications include testing of programs for
                 certain Bessel functions, Dawson's integral, and error
                 functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; measurement; performance; verification",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms.",
}

@Article{Compan:1991:GPS,
  author =       "A. Compan and P. Debaud and V. Delorme and J. A.
                 Fran{\c{c}}ois and H. Mehrez and F. Pecheux",
  title =        "{GAF}: a portable standard-cell floating point adder
                 generator using the {CXgen} function library",
  journal =      j-MICROPROC-MICROPROG,
  volume =       "32",
  number =       "1",
  pages =        "637--644",
  month =        aug,
  year =         "1991",
  CODEN =        "MMICDT",
  ISSN =         "0165-6074 (print), 1878-7061 (electronic)",
  ISSN-L =       "0165-6074",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Microprocessing and Microprogramming",
  journal-URL =  "https://www.sciencedirect.com/journal/microprocessing-and-microprogramming/issues",
}

@Book{Counihan:1991:F,
  author =       "Martin Counihan",
  title =        "{Fortran 90}",
  publisher =    pub-PITMAN,
  address =      pub-PITMAN:adr,
  pages =        "309",
  year =         "1991",
  ISBN =         "0-273-03073-6",
  ISBN-13 =      "978-0-273-03073-7",
  LCCN =         "QA76.73.F25 C68 1991",
  bibdate =      "Sun May 02 07:48:16 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "See \cite{ANSI:ftn92}.",
  acknowledgement = ack-nhfb,
  keywords =     "Fortran 90 (computer program language); Programming
                 languages; {Fortran 90} (Computer program language)",
  libnote =      "Not yet in my library.",
  tableofcontents = "1: Introduction \\
                 1.1: Fortran 90 / 1 \\
                 1.2: Programs and Programming / 2 \\
                 2: What is Fortran 90? \\
                 2.1: Program Structure / 5 \\
                 2.2: Intrinsic Procedures / 6 \\
                 2.3: Statement Types / 7 \\
                 2.4: What Fortran 90 Isn't / 7 \\
                 2.5: New Features in Fortran 90 / 8 \\
                 Notes / 10 \\
                 3: Getting Started \\
                 3.1: The Character Set / 11 \\
                 3.2: A Simple Program / 14 \\
                 3.3: Arithmetic Operators / 18 \\
                 Exercises 3A / 19 \\
                 3.4: Names and Other Lexical Tokens / 20 \\
                 3.5: Fortran Source Form / 21 \\
                 Exercises 3B / 24 \\
                 Notes / 25 \\
                 4: Intrinsic Data Types \\
                 4.1: Integers / 26 \\
                 4.2: Real Numbers / 29 \\
                 Exercises A / 31 \\
                 4.3: Simple Form of the Type Declaration Statement / 32
                 \\
                 4.4: Kinds Real Numbers / 32 \\
                 4.5: Complex Numbers / 33 \\
                 4.6: Logical Data; Logical and Relational Operators /
                 35 \\
                 4.7: Characters and Strings / 38 \\
                 Exercises 4B / 40 \\
                 Notes / 42 \\
                 5: Some Intrinsic Procedures \\
                 5.1: An Intrinsic Subroutine / 43 \\
                 5.2: Mathematical Functions / 44 \\
                 5.3: Numeric Functions / 46 \\
                 Exercises 5A / 50 \\
                 Notes / 52 \\
                 6: More About Characters \\
                 6.1: Declaring Character Data / 53 \\
                 6.2: Character Constants / 54 \\
                 6.3: Character Operators / 55 \\
                 6.4: Intrinsic Character Functions / 56 \\
                 6.5: Substrings / 59 \\
                 Exercises / 61 \\
                 Notes / 62 \\
                 7: Arrays \\
                 7.1: Declaring Arrays / 63 \\
                 7.2: Using Arrays / 65 \\
                 7.3: Array Constructors / 67 \\
                 7.4: Array Sections / 68 \\
                 7.5: Array Sections, Character Strings and Substrings /
                 70 \\
                 7.6: Where / 72 \\
                 7.7: Arrays and Intrinsic Functions / 73 \\
                 Exercises 7B / 74 \\
                 8: Execution Control \\
                 8.1: The ``CASE'' Construct / 76 \\
                 8.2: The ``IF'' Construct / 80 \\
                 Exercises / 81 \\
                 8.3: The ``DO'' Construct / 82 \\
                 8.4: Stop / 88 \\
                 Exercises 8B / 88 \\
                 Notes / 89 \\
                 9: Functions and Subroutines (1) \\
                 9.1: Functions / 90 \\
                 Exercises 9A / 93 \\
                 9.2: Subroutines / 93 \\
                 9.3: Procedures and Arrays / 96 \\
                 Exercises 9B / 99 \\
                 Notes / 100 \\
                 10: More Intrinsic Procedures; Statement Labels \\
                 10.1: Intrinsic Subroutines / 102 \\
                 10.2: Functions for Use with Arrays / 104 \\
                 Exercises 10A / 110 \\
                 10.3: Numeric Inquiry Functions and Floating-Point
                 Manipulation Functions / 110 \\
                 10.4: Statement Labels and ``GO TO'' / 111 \\
                 Notes / 114 \\
                 11: Modules \\
                 11.1: Data Modules / 116 \\
                 Module Procedures / 120 \\
                 11.3: More About ``USE'' Statements / 124 \\
                 Exercises / 126 \\
                 Notes / 127 \\
                 12: Functions and Subroutines (2) \\
                 12.1: Recursive Procedures / 128 \\
                 Exercises 12A / 130 \\
                 12.2: Interface Blocks / 131 \\
                 12.3: Argument Keywords / 132 \\
                 12.4: More About Arguments: ``PRESENT'' / 133 \\
                 12.5: Functions / 134 \\
                 12.6: Operators / 135 \\
                 12.7: Generic Names / 138 \\
                 12.8: Parallel Processing / 141 \\
                 Exercises 12B / 142 \\
                 Notes / 143 \\
                 13: The Type Declaration Statement \\
                 13.1: General Form of the TDS / 144 \\
                 13.2: Character Length Selectors / 147 \\
                 13.3: Attribute Specifications / 149 \\
                 13.4: Array Specifications / 152 \\
                 13.5: The Entity Declaration List / 157 \\
                 13.6: Summary / 158 \\
                 Exercises 13A / 159 \\
                 Notes / 161 \\
                 14: Derived Types \\
                 14.1: Derived-Type Definition / 164 \\
                 14.2: Structure Constructors / 166 \\
                 14.3: Structure Components / 168 \\
                 Exercises 14A / 169 \\
                 14.4: Structures of Structures / 170 \\
                 Exercises 14B / 171 \\
                 14.5: Functions and Operators with Derived Types / 172
                 \\
                 14.6: Defined Assignment / 174 \\
                 Exercises 14C / 178 \\
                 Notes / 180 \\
                 15: Arrays and Pointers \\
                 15.1: Array Element Order, Array Constructors; RESHAPE
                 / 181 \\
                 15.2: Vector Subscripts / 184 \\
                 15.3: Allocatable Arrays / 187 \\
                 Exercises 15A / 190 \\
                 15.4: LBOUND, SHAPE and SIZE / 190 \\
                 Exercises 15B / 191 \\
                 15.5: Simple Pointers / 192 \\
                 15.6: Pointers as Structures and as Structure
                 Components / 197 \\
                 15.7: Pointers and Procedures / 204 \\
                 15.8: Array Pointers / 205 \\
                 Exercises 15C / 207 \\
                 Notes / 208 \\
                 16: Input and Output; Data Format Specifications \\
                 16.1: Data Transfer Statements / 209 \\
                 16.2: The Item List / 210 \\
                 16.3: List-Directed Input / 212 \\
                 16.4: List-Directed Output / 216 \\
                 16.5: Explicit Formats / 217 \\
                 Exercises 16A / 219 \\
                 16.6: Data Edit Descriptors and Character Edit
                 Descriptors / 219 \\
                 16.7: Control Edit Descriptors / 223 \\
                 Exercises 16B / 225 \\
                 16.8: Namelists / 226 \\
                 16.9: Unformatted / 228 \\
                 16.10: The TRANSFER Function / 229 \\
                 16.11: Summary / 231 \\
                 Notes / 232 \\
                 17: File Handling \\
                 17.1: Units, Files and Records / 233 \\
                 17.2: Opening and Closing Files / 235 \\
                 17.3: BACKSPACE, ENDFTLE and REWIND / 240 \\
                 17.4: Control Specifications for / 240 \\
                 17.5: The ``INQUIRE'' Statement / 242 \\
                 17.6: Internal Files / 246 \\
                 Exercises 17A / 248 \\
                 Notes / 249 \\
                 18: Bits \\
                 18.1: Inside Integers / 250 \\
                 18.2: Bit Logic / 251 \\
                 18.3: A Warning / 252 \\
                 Exercises 18A / 253 \\
                 19: Programming Conventions and Program Architecture:
                 Putting It All Together \\
                 19.1: Coding Conventions / 254 \\
                 19.2: Towards Fortran 90 / 255 \\
                 Fortran 90 Recommended Statements / 256 \\
                 Intrinsic Functions / 257 \\
                 19.3: Program Unit Structure / 258 \\
                 19.4: Program Structure / 261 \\
                 19.5: Final Remarks / 262 \\
                 Answers to Selected Exercises / 263 \\
                 Appendices \\
                 A: Fortran 90 Statements \\
                 B: Intrinsic Procedures / 286 \\
                 C: Intrinsic Procedures: Names / 292 \\
                 D: Argument Keywords in Intrinsic Procedures / 294 \\
                 E: Edit Descriptors / 297 \\
                 F: The ASCII Character Set / 301 \\
                 Index / 304",
}

@Article{Cox:1991:TSS,
  author =       "Christopher L. Cox and James A. Knisely",
  title =        "A tridiagonal system solver for distributed memory
                 parallel processors with vector nodes",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "13",
  number =       "3",
  pages =        "325--331",
  month =        nov,
  year =         "1991",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Clemson Univ",
  affiliationaddress = "Clemson, SC, USA",
  classification = "721; 722; 723; 921; C4140 (Linear algebra); C5220P
                 (Parallel architecture); C5230 (Digital arithmetic
                 methods); C5470 (Performance evaluation and testing);
                 C7310 (Mathematics)",
  corpsource =   "Department of Math. Sci., Clemson University, SC,
                 USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "algebraic routine; algorithm; computer; Computer
                 Programming languages--fortran; Computer
                 Programming--Algorithms; Computer Systems, Digital;
                 Cyclic reduction algorithms; Data Storage, Digital;
                 digital arithmetic; Distributed memories; distributed
                 memory parallel; divide and conquer strategy; Floating
                 Point Systems FPS T-20; FORTRAN; Intel iPSC/2-VX;
                 linear algebra; Mathematical Techniques--Matrix
                 Algebra; mathematics computing; odd-even cyclic
                 reduction; parallel architectures; Parallel Processing;
                 partitioning; performance evaluation; processors;
                 programs; redundancy; scaled speedup; tridiagonal
                 system solver; Tridiagonal systems; Vector nodes;
                 vector nodes; vector processors",
  treatment =    "A Application; P Practical",
}

@Article{Crenshaw:1991:SRS,
  author =       "J. W. Crenshaw",
  title =        "Square roots are simple?",
  journal =      j-EMBED-SYS-PROG,
  volume =       "4",
  number =       "11",
  pages =        "30--52",
  month =        nov,
  year =         "1991",
  CODEN =        "EYPRE4",
  ISSN =         "1040-3272",
  bibdate =      "Wed Sep 14 19:14:52 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Embedded Systems Programming",
}

@Article{Davida:1991:FPA,
  author =       "George I. Davida and Bruce Litow",
  title =        "Fast Parallel Arithmetic via Modular Representation",
  journal =      j-SIAM-J-COMPUT,
  volume =       "20",
  number =       "4",
  pages =        "756--765",
  month =        aug,
  year =         "1991",
  CODEN =        "SMJCAT",
  ISSN =         "0097-5397 (print), 1095-7111 (electronic)",
  ISSN-L =       "0097-5397",
  MRclass =      "68Q10",
  MRnumber =     "92c:68046",
  bibdate =      "Mon Nov 29 11:01:48 MST 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/20/4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Computing",
  journal-URL =  "http://epubs.siam.org/sicomp",
}

@MastersThesis{Davies:1991:FPS,
  author =       "Davies, T. C. (Tudor Craddock)",
  title =        "A floating point systolic array processing element
                 using serial communication",
  type =         "Thesis ({M.Eng.})",
  school =       "Royal Military College of Canada",
  address =      "Kingston, ON, Canada",
  year =         "1991",
  ISBN =         "0-315-60644-4",
  ISBN-13 =      "978-0-315-60644-9",
  LCCN =         "????",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "2 microfiches. University Microfilms order no.
                 UMI00285885",
  series =       "National Library of Canada = Bibliotheque nationale du
                 Canada; Canadian theses = Theses canadiennes",
  acknowledgement = ack-nhfb,
}

@Article{Davis:1991:CC,
  author =       "Warren Davis and Kan Yabumoto",
  title =        "A coprocessor for a coprocessor?",
  journal =      j-DDJ,
  volume =       "16",
  number =       "5",
  pages =        "16--28, 84--88",
  month =        may,
  year =         "1991",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Tue Sep 10 09:11:02 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 UnCover database",
  abstract =     "When fast graphics aren't fast enough, the TI 34020
                 graphics coprocessor employs its own coprocessor -- the
                 34082 FPU -- for even higher system performance.",
  acknowledgement = ack-nhfb,
  affiliation =  "Pixelab Inc., Lisle, IL, USA",
  classification = "C5130 (Microprocessor chips); C5540 (Terminals and
                 graphic displays)",
  fjournal =     "Dr. Dobb's Journal of Software Tools",
  keywords =     "Built-in graphics-related instructions; Floating point
                 coprocessor; General-purpose microprocessor; Graphics
                 System Processor; Programmable graphics coprocessor;
                 Texas Instruments; TMS34020; TMS34082; Video control
                 circuitry",
  thesaurus =    "Assembly language listings; C listings; Computer
                 graphic equipment; Microprocessor chips; Satellite
                 computers; Texas Instruments computers",
}

@PhdThesis{Deb:1991:BFF,
  author =       "Kalyanmoy Deb",
  title =        "Binary and floating-point function optimization using
                 messy genetic algorithms",
  type =         "Thesis ({Ph.D.})",
  school =       "Department of Engineering Mechanics, University of
                 Alabama",
  address =      "Tuscaloosa, AL, USA",
  pages =        "xvii + 166",
  year =         "1991",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithms.; Combinatorial optimization.",
}

@InProceedings{deLange:1991:DIF,
  author =       "Alfons A. J. de Lange and Ed F. Deprettere",
  title =        "Design and implementation of a floating-point
                 quasi-systolic general purpose {CORDIC} rotator for
                 high-rate parallel data and signal processing",
  crossref =     "Kornerup:1991:PIS",
  pages =        "272--281",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Lange.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}

@Article{Demmel:1991:OIA,
  author =       "James W. Demmel",
  title =        "On the odor of {IEEE} arithmetic",
  journal =      j-NA-DIGEST,
  volume =       "91",
  number =       "39",
  day =          "29",
  month =        sep,
  year =         "1991",
  bibdate =      "Thu Aug 23 06:19:41 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Rebuttal to \cite{Grcar:1991:IAS}.",
  URL =          "http://www.netlib.org/na-digest/91/v91n39",
  acknowledgement = ack-nhfb,
  fjournal =     "NA Digest",
}

@InProceedings{Dongarra:1991:GBP,
  author =       "J. J. Dongarra and A. Karp and K. Miura and H. D.
                 Simon",
  title =        "{Gordon Bell Prize} lectures (supercomputer
                 applications)",
  crossref =     "IEEE:1991:PSA",
  pages =        "328--337",
  year =         "1991",
  bibdate =      "Wed Apr 15 16:28:01 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C5440 (Multiprocessor systems and techniques)",
  corpsource =   "Department of Computer Science, Tennessee University,
                 Knoxville, TN, USA",
  keywords =     "128-node Intel iPSC/860; compiler speedup; Connections
                 Machine; electronic structure; floating point
                 processors; Fortran 77; Fortran 90; grid generation
                 program; parallel processing; partial differential
                 equation; price/performance award; scientific and
                 engineering problems; supercomputers",
  sponsororg =   "IEEE; ACM",
  treatment =    "G General Review; P Practical",
}

@Article{Dunham:1991:ABA,
  author =       "C. Dunham",
  title =        "Applications of Best Approximation",
  journal =      j-SIGNUM,
  volume =       "26",
  number =       "2",
  pages =        "2--10",
  month =        apr,
  year =         "1991",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Thu Sep 1 10:15:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}

@InProceedings{Duprat:1991:NRR,
  author =       "Jean Duprat and Yvan Herreros and Sylvanus Kla",
  title =        "New redundant representations of complex numbers and
                 vectors",
  crossref =     "Kornerup:1991:PIS",
  pages =        "2--9",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Duprat.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}

@Article{Duprat:1991:WND,
  author =       "J. Duprat and Jean-Michel Muller",
  title =        "Writing numbers differently for faster calculation",
  journal =      j-TECHNIQUE-SCI-INFORMATIQUES,
  volume =       "10",
  number =       "3",
  pages =        "211--224",
  month =        "????",
  year =         "1991",
  CODEN =        "TTSIDJ",
  ISSN =         "0752-4072, 0264-7419",
  ISSN-L =       "0752-4072",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Instead of Avizienis' or the carry save methods a
                 borrow save (BS) notation is proposed. Examples are
                 given of BS addition, subtraction, shifting and
                 multiplication with the necessary elementary cells
                 being proposed and circuits for testing zero and sign
                 being described. Floating point arithmetic is
                 explained, involving pseudo normalisation and
                 applications are covered including the Cordic
                 algorithm.",
  acknowledgement = ack-nhfb,
  affiliation =  "Ecole Normale Superieure de Lyon, France",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "Technique et science informatiques : TSI",
  keywords =     "Addition; Borrow save; Carry save methods; Cordic
                 algorithm; Floating point arithmetic; Multiplication;
                 Pseudo normalisation; Shifting; Subtraction; Zero",
  language =     "French",
  pubcountry =   "France",
  thesaurus =    "Digital arithmetic",
}

@Article{Ercegovac:1991:MPM,
  author =       "Milo{\v{s}} D. Ercegovac and Tomas Lang",
  title =        "Module to perform multiplication, division, and square
                 root in systolic arrays for matrix computations",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "11",
  number =       "3",
  pages =        "212--221",
  month =        mar,
  year =         "1991",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ of California Los Angeles",
  affiliationaddress = "Los Angeles, CA, USA",
  classification = "722; 723; 921; C4140 (Linear algebra); C5220
                 (Computer architecture); C5230 (Digital arithmetic
                 methods)",
  corpsource =   "Department of Computer Science, California University,
                 Los Angeles, CA, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "Applications; carry-save; complexity; Computer
                 Programming --- Algorithms; Computers; digital
                 arithmetic; division; matrix algebra; Matrix
                 Computations; matrix computations; module;
                 multiplication; Multiplication/Division/Square Root
                 Module; Normalization; On-The-Fly Conversion; radix-2
                 divider; result-digit selection; Rounding;
                 signed-digit; square root; Systolic Arrays; systolic
                 arrays",
  treatment =    "P Practical",
}

@Article{Even:1991:SMM,
  author =       "Shimon Even",
  title =        "Systolic Modular Multiplication",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "537",
  pages =        "619--??",
  year =         "1991",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:48:02 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t0537.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/0537/05370619.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/0537/05370619.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InProceedings{Ferguson:1991:AMA,
  author =       "Warren E. {Ferguson, Jr.} and Tom Brightman",
  title =        "Accurate and Monotone Approximations of Some
                 Transcendental Functions",
  crossref =     "Kornerup:1991:PIS",
  pages =        "237--244",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Ferguson.pdf",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  keywords =     "ARITH-10",
}

@Article{Ferguson:1991:SMC,
  author =       "Warren E. {Ferguson, Jr.}",
  title =        "Selecting math coprocessors",
  journal =      j-IEEE-SPECTRUM,
  volume =       "28",
  number =       "7",
  pages =        "38--41",
  month =        jul,
  year =         "1991",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/6.83469",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Thu Sep 01 16:17:34 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "floating-point arithmetic",
  remark =       "Contains performance-comparison tables for Cyrix,
                 Intel, Motorola, and Weitek floating-point coprocessor
                 chips.",
}

@InProceedings{Fleurkens:1991:HLD,
  author =       "H. Fleurkens and R. Tangelder",
  title =        "The high level design of the long accumulator chip",
  crossref =     "IEEE:1991:PFC",
  pages =        "299--301",
  year =         "1991",
  bibdate =      "Wed Dec 13 13:13:34 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The authors discuss an architecture and its high level
                 description of a long accumulator chip suited for the
                 exact calculation of the inner products of floating
                 point numbers. A highly parallel implementation is
                 developed using eight independent adder stations, which
                 add products to two circular long accumulators. A
                 dispatcher schedules each product to the best available
                 station. To validate this architecture and to calculate
                 its performance, a high level description is created.
                 This description is made with ESCHER+, an interactive
                 schematic entry tool with a built-in simulator. The
                 resulting description showed to be the basis for the
                 further implementation of the chip.",
  acknowledgement = ack-nhfb,
  affiliation =  "Eindhoven University of Technol., Netherlands",
  classification = "B1130B (Computer-aided circuit analysis and design);
                 B1265B (Logic circuits); C5120 (Logic and switching
                 circuits); C5210B (Computer-aided logic design); C5220P
                 (Parallel architecture); C5230 (Digital arithmetic
                 methods); C7410D (Electronic engineering)",
  keywords =     "Built-in simulator; ESCHER+; Floating point numbers;
                 High level description; High level design; Highly
                 parallel implementation; Inner products calculation;
                 Interactive schematic entry tool; Long accumulator
                 chip",
  thesaurus =    "Circuit CAD; Digital arithmetic; Integrated logic
                 circuits; Logic CAD; Parallel architectures",
}

@Article{Fossmeier:1991:ALH,
  author =       "R. F{\"o}{\ss}meier",
  title =        "{Zur Axiomatisierung logarithmischer und
                 halblogarithmischer Zahlensysteme}. ({German}) [{On}
                 the axiomatization of logarithmic and semi-logarithmic
                 number systems]",
  journal =      j-COMPUTING,
  volume =       "46",
  number =       "2",
  pages =        "175--182",
  month =        jun,
  year =         "1991",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65G99",
  MRnumber =     "92e:65064",
  bibdate =      "Tue Oct 12 16:33:42 MDT 1999",
  bibsource =    "Compendex database;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database; OCLC Contents1st database",
  abstract =     "In the history of numerical analysis there have been
                 various approaches to gain stricter control of
                 numerical computation by axiomatization of
                 approximative arithmetic systems. In the case of
                 floating-point-like systems, the limitations to this
                 approach originate essentially in the fact that
                 addition is not associative. By suitably weakening the
                 axiomatic system of the real numbers the author arrives
                 at a system which can be fulfilled by approximative
                 arithmetic structures. Comparisons show that structures
                 fulfilling this system cannot be arbitrarily distant
                 from reasonable approximative structures. This shows
                 that it is possible to describe approximative
                 structures by approximations of the laws of the
                 original structure.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. f{\"u}r Inf., Tech. University of Munchen,
                 Germany",
  classification = "723; 921; C4100 (Numerical analysis)",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Comput Vienna New York",
  keywords =     "Approximative arithmetic structures; Axiomatization;
                 computers, digital --- Computational Methods;
                 Floating-Point Arithmetic; Logarithmic; mathematical
                 techniques; Number systems; Number Systems; Numerical
                 analysis; Semi-logarithmic number systems",
  language =     "German",
  pubcountry =   "Austria",
  thesaurus =    "Number theory; Numerical analysis",
}

@Article{Fossmeier:1991:ALS,
  author =       "R. Fossmeier",
  title =        "On the axiomatization of logarithmic and
                 semi-logarithmic number systems",
  journal =      j-COMPUTING,
  volume =       "46",
  number =       "2",
  pages =        "175--182",
  month =        "????",
  year =         "1991",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In the history of numerical analysis there have been
                 various approaches to gain stricter control of
                 numerical computation by axiomatization of
                 approximative arithmetic systems. In the case of
                 floating-point-like systems, the limitations to this
                 approach originate essentially in the fact that
                 addition is not associative. By suitably weakening the
                 axiomatic system of the real numbers the author arrives
                 at a system which can be fulfilled by approximative
                 arithmetic structures. Comparisons show that structures
                 fulfilling this system cannot be arbitrarily distant
                 from reasonable approximative structures. This shows
                 that it is possible to describe approximative
                 structures by approximations of the laws of the
                 original structure.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Inf., Tech. University of Munchen, Germany",
  classification = "C4100 (Numerical analysis)",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "Approximative arithmetic structures; Axiomatization;
                 Logarithmic; Number systems; Numerical analysis;
                 Semi-logarithmic number systems",
  language =     "German",
  pubcountry =   "Austria",
  thesaurus =    "Number theory; Numerical analysis",
}

@Article{Foster:1991:PM,
  author =       "Kenneth R. Foster",
  title =        "Prepackaged math",
  journal =      j-IEEE-SPECTRUM,
  volume =       "28",
  number =       "11",
  pages =        "44--50",
  month =        nov,
  year =         "1991",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/6.99016",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Wed Jan 15 16:15:28 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/axiom.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/macsyma.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "Chemical analysis; Data engineering; Data
                 visualization; Differential equations; Graphics; Hard
                 disks; manipulation; mathematical problems; mathematics
                 computing; matrices; matrix algebra; Packaging;
                 Personal communication networks; software packages;
                 Software packages; Workstations",
}

@InProceedings{Frougny:1991:RNN,
  author =       "Christiane Frougny",
  title =        "Representation of numbers in nonclassical numeration
                 systems",
  crossref =     "Kornerup:1991:PIS",
  pages =        "17--21",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Frougny.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}

@Article{Gal:1991:AEM,
  author =       "Shmuel Gal and Boris Bachelis",
  title =        "An Accurate Elementary Mathematical Library for the
                 {IEEE} Floating Point Standard",
  journal =      j-TOMS,
  volume =       "17",
  number =       "1",
  pages =        "26--45",
  month =        mar,
  year =         "1991",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20 (65-04 65D15)",
  MRnumber =     "92a:65069",
  bibdate =      "Sun Sep 04 23:33:02 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://doi.acm.org/10.1145/103147.103151;
                 http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p26-gal/",
  abstract =     "The algorithms used by the IBM Israel Scientific
                 Center for the elementary mathematical library using
                 the IEEE standard for binary floating point arithmetic
                 are described. The algorithms are based on the
                 ``accurate tables method.'' This methodology achieves
                 high performance and produces very accurate results. It
                 overcomes one of the main problems encountered in
                 elementary mathematical functions computations:
                 achieving last bit accuracy. The results obtained are
                 correctly rounded for almost all argument
                 values.\par

                 Our main idea in the accurate tables method is to use
                 ``nonstandard tables,'' which are different from the
                 natural tables of equally spaced points in which the
                 rounding error prevents obtaining last bit accuracy. In
                 order to achieve a small error we use the following
                 idea: Perturb the original, equally spaced, points in
                 such a way that the table value (or tables values in
                 case we need several tables) will be very close to
                 numbers which can be exactly represented by the
                 computer (much closer than the usual double precision
                 representation). Thus we were able to control the error
                 introduced by the computer representation of real
                 numbers and extended the accuracy without actually
                 using extended precision arithmetic.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; correct rounding; floating-point
                 arithmetic; theory",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.2}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation.",
}

@InProceedings{Gamberger:1991:NAI,
  author =       "Dragan Gamberger",
  title =        "New approach to integer division in residue number
                 systems",
  crossref =     "Kornerup:1991:PIS",
  pages =        "84--91",
  year =         "1991",
  DOI =          "https://doi.org/10.1109/ARITH.1991.145538",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Gamberger.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10; residue arithmetic; residue number system",
  summary =      "A novel division algorithm that is especially
                 appropriate for residue number systems (RNSs) is
                 presented. It makes use of the fact that the
                 multiplicative inverse element of a divisor which is
                 relatively prime to system moduli can be easily
                 \ldots{}",
}

@Article{Gladshtein:1991:MDD,
  author =       "M. A. Gladshtein",
  title =        "A method of designing a decimal arithmetic processor",
  journal =      j-AUTO-CTL-COMP-SCI,
  volume =       "25",
  number =       "6",
  pages =        "51--56",
  month =        "????",
  year =         "1991",
  CODEN =        "ACCSCE",
  ISSN =         "0132-4160",
  ISSN-L =       "0146-4116",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The advantages and drawbacks of binary numeric coding
                 in digital computers are considered. This type of
                 coding has is shown to be ineffective in processing
                 large data arrays especially when represented in the
                 floating-point form. Also, the low efficiency of
                 conventionally employed decimal computational
                 procedures using the so-called corrections is noted. It
                 is proposed, in designing digital computers, to
                 renounce the principle of binary computations in favor
                 of decimal operations on the basis of stored addition
                 and multiplication tables using binary-decimal numeric
                 coding. A version of circuit design for a decimal
                 processor, algorithms and microprograms for addition
                 and multiplication operations are described. Advantages
                 inherent in the method proposed are analyzed. (10
                 Refs.)",
  acknowledgement = ack-nhfb,
  classification = "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5230 (Digital arithmetic
                 methods)",
  fjournal =     "Automatic Control and Computer Sciences",
  keywords =     "Addition tables; BCD code; Binary numeric coding;
                 Binary-decimal numeric coding; Circuit design; Decimal
                 arithmetic processor; decimal floating-point
                 arithmetic; Decimal operations; Digital computers;
                 Microprograms; Multiplication tables",
  pubcountry =   "Latvia",
  remark =       "English translation of: Avtomatika i Vychislitel'naya
                 Tekhnika",
  thesaurus =    "Digital arithmetic; Microprocessor chips",
}

@Article{Goldberg:1991:CWE,
  author =       "David Goldberg",
  title =        "Corrigendum: {``What Every Computer Scientist Should
                 Know About Floating-Point Arithmetic''}",
  journal =      j-COMP-SURV,
  volume =       "23",
  number =       "3",
  pages =        "413--413",
  month =        sep,
  year =         "1991",
  CODEN =        "CMSVAN",
  ISSN =         "0360-0300 (print), 1557-7341 (electronic)",
  ISSN-L =       "0360-0300",
  bibdate =      "Sun Sep 25 09:58:43 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compsurv.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See
                 \cite{Goldberg:1991:WEC,Dunham:1992:SFW,Wichmann:1992:SFW}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J204",
}

@Article{Goldberg:1991:WEC,
  author =       "David Goldberg",
  title =        "What Every Computer Scientist Should Know About
                 Floating-Point Arithmetic",
  journal =      j-COMP-SURV,
  volume =       "23",
  number =       "1",
  pages =        "5--48",
  month =        mar,
  year =         "1991",
  CODEN =        "CMSVAN",
  DOI =          "https://doi.org/10.1145/103162.103163",
  ISSN =         "0360-0300 (print), 1557-7341 (electronic)",
  ISSN-L =       "0360-0300",
  bibdate =      "Thu Jun 19 09:40:16 MDT 2008",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also
                 \cite{Goldberg:1991:CWE,Dunham:1992:SFW,Wichmann:1992:SFW}.",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/0360-0300/103163.html",
  abstract =     "Floating-point arithmetic is considered an esoteric
                 subject by many people. This is rather surprising,
                 because floating-point is ubiquitous in computer
                 systems: almost every language has a floating-point
                 datatype; computers from PCs to supercomputers have
                 floating-point accelerators; most compilers will be
                 called upon to compile floating-point algorithms from
                 time to time; and virtually every operating system must
                 respond to floating-point exceptions such as overflow.
                 This paper presents a tutorial on the aspects of
                 floating-point that have a direct impact on designers
                 of computer systems. It begins with background on
                 floating-point representation and rounding error,
                 continues with a discussion of the IEEE floating-point
                 standard, and concludes with examples of how computer
                 system builders can better support floating point.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Xerox Palo Alto Res. Center, CA, USA",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J204",
  keywords =     "algorithms; compilers; computer scientist; computer
                 systems; denormalized number; design; exception;
                 floating-point; floating-point accelerators;
                 floating-point algorithms; floating-point datatype;
                 floating-point exceptions; floating-point
                 representation; floating-point standard; gradual
                 underflow; guard digit; IEEE floating-point standard;
                 languages; NaN; operating system; overflow; PCs;
                 relative error; rounding error; rounding mode;
                 standardization; supercomputers; ulp; underflow",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf K.1}:
                 Computing Milieux, THE COMPUTER INDUSTRY, Standards.
                 {\bf C.0}: Computer Systems Organization, GENERAL,
                 Instruction set design. {\bf G.1.0}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Numerical
                 algorithms.",
  thesaurus =    "digital arithmetic; roundoff errors",
}

@TechReport{Golubev:1991:FPM,
  author =       "Yu. F. Golubev and I. A. Seregin and R. Z.
                 Kha{\u\i}rullin",
  title =        "The floating point method in problems of the
                 optimization of motion during the descent of a
                 spacecraft into the atmosphere. ({Russian})",
  type =         "{Inst. Prikl. Mat.} Preprint",
  number =       "50",
  institution =  "Akad. Nauk SSSR",
  pages =        "28",
  year =         "1991",
  MRclass =      "65K10 (49N55 70-08 70Q05)",
  MRnumber =     "166 839",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}

@Article{Gonnella:1991:ACF,
  author =       "J. Gonnella",
  title =        "The application of core functions to residue number
                 systems",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "39",
  number =       "1",
  pages =        "69--75",
  month =        jan,
  year =         "1991",
  CODEN =        "ITPRED",
  DOI =          "https://doi.org/10.1109/78.80766",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2655",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A theory of core functions is presented, and the
                 application of this theory to the difficult residue
                 number system (RNS) operations is described. Potential
                 applications for special-purpose core-based RNS
                 processors include adaptive array processing,
                 \ldots{}",
}

@Article{Gotze:1991:SRD,
  author =       "J. G{\"o}tze and U. Schwiegelshohn",
  title =        "A Square Root and Division Free {Givens} Rotation for
                 Solving Least Squares Problems on Systolic Arrays",
  journal =      j-SIAM-J-SCI-STAT-COMP,
  volume =       "12",
  number =       "4",
  pages =        "800--807",
  month =        jul,
  year =         "1991",
  CODEN =        "SIJCD4",
  ISSN =         "0196-5204",
  MRclass =      "65F20 (65F25)",
  MRnumber =     "92a:65125",
  bibdate =      "Sat Oct 24 13:20:45 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific and Statistical Computing",
  journal-URL =  "http://epubs.siam.org/loi/sijcd4",
}

@Article{Grcar:1991:IAS,
  author =       "Joe Grcar",
  title =        "{IEEE} Arithmetic Stinks",
  journal =      j-NA-DIGEST,
  volume =       "91",
  number =       "33",
  day =          "18",
  month =        aug,
  year =         "1991",
  bibdate =      "Thu Aug 23 06:22:13 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See rebuttal \cite{Demmel:1991:OIA}.",
  URL =          "http://www.netlib.org/na-digest/91/v91n33",
  acknowledgement = ack-nhfb,
  fjournal =     "NA Digest",
}

@Article{Griffin:1991:REA,
  author =       "C. Griffin and P. Rao and F. Taylor",
  title =        "Roundoff error analysis of the discrete {Wigner}
                 distribution using fixed-point arithmetic",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "39",
  number =       "9",
  pages =        "2096--2098",
  month =        sep,
  year =         "1991",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "The issue of roundoff noise effects in the
                 implementation of the discrete Wigner distribution
                 using fixed-point arithmetic is addressed. The
                 sign-magnitude number representation is assumed
                 throughout the analysis. The measure of roundoff noise
                 \ldots{}",
}

@Article{Gusev:1991:NCS,
  author =       "A. V. Gusev and I. V. Melezhnikov",
  title =        "Noise in a Constant-Current {SQUID} with a Floating
                 Operating Point",
  journal =      j-TELECOMM-RADIO-ENG,
  volume =       "46",
  number =       "8",
  pages =        "125--127",
  year =         "1991",
  CODEN =        "TCREAG",
  ISSN =         "0040-2508 (print), 1943-6009 (electronic)",
  ISSN-L =       "0040-2508",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Telecommunications and Radio Engineering",
}

@InProceedings{Guyot:1991:OAV,
  author =       "Alain Guyot",
  title =        "{OCAPI}: Architecture of a {VLSI} Coprocessor for the
                 {GCD} and the Extended {GCD} of Large Numbers",
  crossref =     "Kornerup:1991:PIS",
  pages =        "226--231",
  year =         "1991",
  bibdate =      "Sat Nov 17 08:46:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Guyot.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}

@Article{Hamza:1991:MBD,
  author =       "K. M. Hamza and M. A. H. Abdul-Karim",
  title =        "Microprocessor Based Direct Square Root Extractor",
  journal =      "Modelling",
  volume =       "34",
  number =       "1",
  pages =        "45--48",
  month =        "????",
  year =         "1991",
  bibdate =      "Thu Sep 1 10:15:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Heidtmann:1991:ASA,
  author =       "K. D. Heidtmann",
  title =        "Arithmetic spectrum applied to fault detection for
                 combinational networks",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "40",
  number =       "3",
  pages =        "320--324",
  month =        mar,
  year =         "1991",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.76409",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 12:52:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=76409",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@MastersThesis{Holmes:1991:FSD,
  author =       "Ian Holmes",
  title =        "A feasibility study into the design of a 64-bit
                 floating point processor",
  type =         "Thesis ({M.Sc. in Electronics})",
  school =       "University of Southampton, Department of Electronics
                 and Computer Science",
  address =      "Southampton, UK",
  year =         "1991",
  bibdate =      "Thu May 09 08:35:32 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Horiguchi:1991:HFN,
  author =       "Hiroshi Horiguchi and Tsutomu Tayama and Kazuaki
                 Kajitori",
  title =        "{Hamada} Floating-Point Numbers and Real Numbers",
  journal =      j-ADV-SOFT-SCI-TECH,
  volume =       "2",
  number =       "??",
  pages =        "123--??",
  year =         "1991",
  ISSN =         "1044-7997",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Advances in software science and technology",
}

@Article{Horiguchi:1991:PEP,
  author =       "Susumu Horiguchi and Takeo Nakada",
  title =        "Performance Evaluation of Parallel Fast {Fourier}
                 Transform on a Multiprocessor Workstation",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "12",
  number =       "2",
  pages =        "158--163",
  month =        jun,
  year =         "1991",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 17:13:17 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C4190 (Other numerical methods); C4240 (Programming
                 and algorithm theory); C5440 (Multiprocessor systems
                 and techniques)",
  corpsource =   "Department of Inf. Sci., Tohoku University, Sendai,
                 Japan",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "algorithms; cache protocols; fast Fourier transform;
                 fast Fourier transforms; FFT; floating-; multiprocess
                 operating system; multiprocessing systems;
                 multiprocessor workstation; multithread operating
                 system; operating systems; parallel; parallel FFT;
                 performance; performance evaluation; point
                 coprocessors",
  treatment =    "P Practical",
}

@Misc{Hough:1991:TBC,
  author =       "David G. Hough and Vern Paxson",
  title =        "Testbase: base conversion test program",
  howpublished = "World-Wide Web document",
  day =          "20",
  month =        jul,
  year =         "1991",
  bibdate =      "Wed May 26 07:22:52 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Paxson:1991:PTI}.",
  URL =          "http://www.netlib.org/fp/testbase",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point testing",
}

@InProceedings{Hsiao:1991:CHA,
  author =       "Shen-Fu Hsiao and Jean-Marc Delosme",
  title =        "The {CORDIC Householder} algorithm",
  crossref =     "Kornerup:1991:PIS",
  pages =        "256--263",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Hsiao.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}

@Article{Hu:1991:ERC,
  author =       "X. Hu and R. G. Harber and S. C. Bass",
  title =        "Expanding the Range of Convergence of the {CORDIC}
                 Algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "40",
  number =       "1",
  pages =        "13--21",
  month =        jan,
  year =         "1991",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.67316",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 08 00:50:12 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Hui:1991:DFD,
  author =       "S. Hui and D. P. Brown",
  booktitle =    "{IEEE} Pacific Rim Conference on Communications,
                 Computers and Signal Processing, 9--10 May 1991",
  title =        "Digital filter design with a combination of fixed
                 point and residue number systems",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "331--334",
  year =         "1991",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/PACRIM.1991.160746",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A new design method using a combination of fixed-point
                 and RNS (residue number system) arithmetics is
                 presented. It is proven that an IIR digital filter can
                 be efficiently implemented in a system that combines
                 both fixed-point and RNS arithmetics. \ldots{}",
}

@InProceedings{Hull:1991:SVP,
  author =       "T. E. Hull and M. S. Cohen and C. B. Hall",
  title =        "Specifications for a variable-precision arithmetic
                 coprocessor",
  crossref =     "Kornerup:1991:PIS",
  pages =        "127--131",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Hull.pdf",
  abstract =     "The authors have been developing a programming system
                 intended to be especially convenient for scientific
                 computing. Its main features are variable precision
                 (decimal) floating-point arithmetic and convenient
                 exception handling. The software implementation of the
                 system has evolved over a number of years, and a
                 partial hardware implementation of the arithmetic
                 itself was constructed and used during the early stages
                 of the project. Based on this experience, the authors
                 have developed a set of specifications for an
                 arithmetic coprocessor to support such a system. These
                 specifications are described. An outline of the
                 language features and how they can be used is also
                 provided, to help justify the particular choice of
                 coprocessor specifications. The authors also indicate
                 what other hardware features would be most helpful to
                 the systems programmer, especially for implementation
                 of the exception handling.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, Toronto University,
                 Ont., Canada",
  classification = "B1265B (Logic circuits); B1265F (Microprocessors and
                 microcomputers); B2570 (Semiconductor integrated
                 circuits); C5120 (Logic and switching circuits); C5130
                 (Microprocessor chips); C5230 (Digital arithmetic
                 methods)",
  keywords =     "ARITH-10; decimal floating-point arithmetic; Exception
                 handling; Floating-point arithmetic; Programming
                 system; Scientific computing; Variable-precision
                 arithmetic coprocessor",
  thesaurus =    "Digital arithmetic; Logic circuits; Microprocessor
                 chips; Satellite computers",
}

@Book{Ince:1991:SQR,
  author =       "D. (Darrel) Ince",
  title =        "Software quality and reliability tools and methods",
  publisher =    "Chapman and Hall",
  address =      "London, UK",
  pages =        "178",
  year =         "1991",
  ISBN =         "0-442-31314-4, 0-412-37810-8",
  ISBN-13 =      "978-0-442-31314-2, 978-0-412-37810-2",
  LCCN =         "????",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Unicom applied information technology reports; [6]",
  acknowledgement = ack-nhfb,
  keywords =     "Computer software --- Quality control.; Computer
                 software --- Reliability.; Software --- Quality
                 control",
  remark =       "Aspects of path testing and mutation testing / M. R.
                 Woodward --- Quality-- an integrated approach / A.
                 Smith --- Quality management and software engineering /
                 R. Hailstone --- The role of verification and
                 validation tools in the production of critical software
                 / J.T. Webb --- The real importance of software quality
                 and the role of quality systems / A. Voss --- Software
                 testing tools / E. Fergus \ldots{} [et al.] --- FPV-- a
                 floating point validation package / J. Du Croz ---
                 Building in quality through the use of software tools /
                 P.A.V. Hall --- Software requirements analysis, formal
                 methods and software prototyping / D. Ince ---
                 Increasing software quality by objectives and residual
                 fault prognosis / K. Moller --- Towards a software
                 quality control environment / M. Adam \ldots{} [et al.]
                 --- Expert system software quality problems / S. Ronchi
                 and M. Martignano --- Quality assurance management for
                 real-time software systems: the experience of the
                 Spanish Civil Aviation Administration / J.P. Buendia,
                 C. Bravo --- The PRX/A software reliability
                 investigation / A.E.J. van Delft.",
}

@InCollection{Iri:1991:HAD,
  author =       "M. Iri",
  editor =       "A. Griewank and G. F. Corliss",
  booktitle =    "Automatic Differentiation of Algorithms: Theory,
                 Implementation, and Application",
  title =        "History of automatic differentiation and rounding
                 error estimation",
  crossref =     "Griewank:1991:ADA",
  pages =        "3--16",
  year =         "1991",
  bibdate =      "Thu May 27 07:45:02 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Jain:1991:CSN,
  author =       "Suneel Jain",
  title =        "Circular scheduling: a new technique to perform
                 software pipelining",
  journal =      j-SIGPLAN,
  volume =       "26",
  number =       "6",
  pages =        "219--228",
  month =        jun,
  year =         "1991",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:16:07 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/proceedings/pldi/113445/index.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/pldi/113445/p219-jain/",
  abstract =     "With the advent of deeply pipelined RISC processors,
                 static instruction scheduling by the compiler has
                 become extremely important to obtain high processor
                 performance. This is especially true for floating point
                 code. The author suggests using a new algorithm called
                 circular scheduling to perform software pipelining.
                 Software pipelining has previously been investigated
                 mostly for VLIW architectures. The algorithm described
                 is shown to be quite effective for a scalar
                 architecture. Register renaming, an idea that
                 originates from dynamic instruction scheduling, is used
                 in conjunction with this algorithm to augment its
                 performance. The techniques described here have been
                 implemented as part of a commercial, production quality
                 optimizing compiler for a RISC architecture. The
                 resulting performance improvement has verified the
                 feasibility and practicality of the techniques.",
  acknowledgement = ack-nhfb,
  affiliation =  "MIPS Comput. Syst. Inc., Sunnyvale, CA, USA",
  classification = "C5220 (Computer architecture); C6110 (Systems
                 analysis and programming); C6150C (Compilers,
                 interpreters and other processors); C6150J (Operating
                 systems)",
  confdate =     "26-28 June 1991",
  conflocation = "Toronto, Ont., Canada",
  confsponsor =  "ACM",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "algorithms; Circular scheduling; Deeply pipelined RISC
                 processors; Dynamic instruction scheduling;
                 experimentation; performance; Production quality
                 optimizing compiler; RISC architecture; Scalar
                 architecture; Software pipelining; Static instruction
                 scheduling; VLIW architectures",
  subject =      "{\bf D.3.4} Software, PROGRAMMING LANGUAGES,
                 Processors, Compilers. {\bf D.3.4} Software,
                 PROGRAMMING LANGUAGES, Processors, Optimization.",
  thesaurus =    "Parallel programming; Pipeline processing; Program
                 compilers; Reduced instruction set computing;
                 Scheduling",
}

@InProceedings{Jain:1991:NRS,
  author =       "V. K. Jain and G. E. Perez and J. M. Wills",
  title =        "Novel reciprocal and square-root {VLSI} cell:
                 architecture and application to signal processing",
  crossref =     "IEEE:1991:VCA",
  volume =       "2",
  pages =        "1201--1204",
  year =         "1991",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  summary =      "A novel high-speed cell, capable of performing a
                 square-root or a reciprocal function in two clock
                 cycles, is presented. Its performance signifies an
                 estimated three-fold increase in speed over existing
                 approaches. Furthermore, since both functions
                 \ldots{}",
}

@TechReport{Kahan:1991:APL,
  author =       "William Kahan and J. W. Thomas",
  title =        "Augmenting a Programming Language with Complex
                 Arithmetic",
  number =       "NCEG/91-039, UCB/CSD 91/667",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "8",
  day =          "15",
  month =        nov,
  year =         "1991",
  bibdate =      "Mon Dec 26 21:13:51 GMT 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
}

@Article{Kahan:1991:ARL,
  author =       "W. Kahan",
  title =        "Analysis and Refutation of the {LCAS}",
  journal =      j-SIGNUM,
  volume =       "26",
  number =       "3",
  pages =        "2--15",
  month =        jul,
  year =         "1991",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Fri Jan 5 07:58:42 MST 1996",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/signum.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "LCAS (Language Compatible Arithmetic Standard)",
}

@InProceedings{Kantabutra:1991:DOC,
  author =       "Vitit Kantabutra",
  title =        "Designing optimum carry-skip adders",
  crossref =     "Kornerup:1991:PIS",
  pages =        "146--153",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Kantabutra.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}

@Article{Kim:1991:ERB,
  author =       "Jin Yul Kim and Kyu Ho Park and Hwang Soo Lee",
  title =        "Efficient residue-to-binary conversion technique with
                 rounding error compensation",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "38",
  number =       "3",
  pages =        "315--317",
  month =        mar,
  year =         "1991",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 11:25:03 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "An improved scaled-decoding technique (defined as
                 residue-to-binary conversion of which outputs are
                 scaled by a constant) for hardware implementations in
                 the residue number system (RNS) is presented. The
                 technique is based on the Chinese remainder \ldots{}",
}

@InProceedings{Kim:1991:NIC,
  author =       "S. W. Kim and T. Stouraitis",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, 11--14 June 1991",
  title =        "New implementations of converters for the residue and
                 quadratic residue number system",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2959--2962",
  year =         "1991",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1991.176166",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Full adder (FA)-based converters are proposed for
                 efficiently performing complex number calculations. The
                 basic idea is to use FA arrays to decompose 2 i terms
                 into 2 j terms, where j{$<$}i, by modulo arithmetic.
                 \ldots{}",
}

@Book{Klatte:1991:PSB,
  author =       "R. Klatte and U. Kulisch and M. Neaga and D. Ratz and
                 Ch. Ullrich",
  title =        "{PASCAL-XSC: Sprachbeschreibung mit Beispielen}",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 345",
  year =         "1991",
  ISBN =         "0-387-53714-7",
  ISBN-13 =      "978-0-387-53714-6",
  LCCN =         "QA76.73.P2 P42 1991",
  bibdate =      "Mon Dec 18 09:37:18 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "English translation is available as
                 \cite{Klatte:1991:PXP}.",
  acknowledgement = ack-nhfb,
}

@Book{Klatte:1991:PXP,
  author =       "R. Klatte and U. Kulisch and M. Neaga and D. Ratz and
                 Ch. Ullrich",
  title =        "{PASCAL-XSC}: {A PASCAL} Extension for Scientific
                 Computation",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 344",
  year =         "1991",
  ISBN =         "0-387-55137-9 (New York), 3-540-55137-9 (Berlin)",
  ISBN-13 =      "978-0-387-55137-1 (New York), 978-3-540-55137-9
                 (Berlin)",
  LCCN =         "QA76.73.P2 P4213 1992",
  bibdate =      "Thu Nov 8 14:50:35 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "English translation of \cite{Klatte:1991:PSB}.",
  price =        "DM64.00",
  acknowledgement = ack-nhfb,
  referred =     "[Corl91a].",
}

@InProceedings{Knofel:1991:FHU,
  author =       "Andreas Kn{\"o}fel",
  title =        "Fast hardware units for the computation of accurate
                 dot products",
  crossref =     "Kornerup:1991:PIS",
  pages =        "70--74",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Knofel.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}

@InProceedings{Knowles:1991:APD,
  author =       "S. Knowles",
  title =        "Arithmetic Processor Design for the {T9000}
                 Transputer",
  crossref =     "SPIE:1991:PSI",
  pages =        "230--243",
  year =         "1991",
  bibdate =      "Wed Sep 7 22:32:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Koc:1991:FAG,
  author =       "Cetin K. Koc and Sarath N. Arachchige",
  title =        "A fast algorithm for {Gaussian} elimination over
                 {GF(2)} and its implementation on the {GAPP}",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "13",
  number =       "1",
  pages =        "118--122",
  day =          "1",
  month =        sep,
  year =         "1991",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ of Houston",
  affiliationaddress = "Houston, TX, USA",
  classification = "722; 723; 921; C4140 (Linear algebra); C4240
                 (Programming and algorithm theory)",
  corpsource =   "Department of Electr. Eng., Houston University, TX,
                 USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "1s location; Algorithms; algorithms; arithmetic
                 parallel processor; binary matrix; binary search;
                 Binary search technique; bit operations; bit-array;
                 columns; computational complexity; Computer
                 Programming; Computer Systems, Digital--Parallel
                 Processing; Galois fields; GAPP; Gaussian elimination;
                 geometric; Geometric arithmetic parallel processors;
                 GF(2); Large binary matrices; Mathematical
                 Techniques--Matrix Algebra; matrix algebra; ones
                 location; parallel; Triangularization; triangularize;
                 vertical memory",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Koc:1991:IAM,
  author =       "{\c{C}}etin K. Ko{\c{c}}",
  title =        "An improved algorithm for mixed-radix conversion of
                 residue numbers",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "22",
  number =       "8",
  pages =        "63--71",
  month =        "????",
  year =         "1991",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 19:11:04 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/089812219190014U",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@MastersThesis{Kohprasert:1991:FAC,
  author =       "Teera Kohprasert",
  title =        "32-bit floating-point arithmetic coprocessor design
                 using {VHDL}",
  type =         "Thesis ({M.S.})",
  school =       "Florida Institute of Technology",
  address =      "Melbourne, FL, USA",
  pages =        "xiv + 456",
  year =         "1991",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic and logic units --- Design and
                 construction.; VHDL (Computer hardware description
                 language).",
}

@Article{Kostopoulos:1991:ACB,
  author =       "D. K. Kostopoulos",
  title =        "An Algorithm for the Computation of Binary
                 Logarithms",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "40",
  number =       "11",
  pages =        "1267--1270",
  month =        nov,
  year =         "1991",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.102831",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:16:09 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@TechReport{Kramer:1991:EFA,
  author =       "David Kramer and Isaac D. Scherson",
  title =        "The effect of {FPU} architecture on a dynamic
                 precision algorithm for the solution of differential
                 equations",
  type =         "Technical report",
  number =       "91-73",
  institution =  "Information and Computer Science, University of
                 California, Irvine",
  address =      "Irvine, CA, USA",
  pages =        "18",
  year =         "1991",
  LCCN =         "Z699 .C3 no. 91-73",
  bibdate =      "Fri Jan 5 11:51:46 MST 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kuhnel:1991:OPS,
  author =       "Lars K{\"u}hnel",
  title =        "Optimal purely systolic addition",
  crossref =     "Kornerup:1991:PIS",
  pages =        "172--179",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Kuhnel.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}

@Article{Kurokawa:1991:CGU,
  author =       "T. Kurokawa and T. Mizukoshi",
  title =        "Computer graphics using logarithmic number systems",
  journal =      "IEICE Transactions",
  volume =       "E74",
  number =       "2",
  pages =        "447--451",
  month =        feb,
  year =         "1991",
  ISSN =         "0917-1673",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Logarithmic arithmetic (LA) is a very fast
                 computational method for real numbers. Its precision is
                 better than a floating point arithmetic of equivalent
                 word length and range. This paper shows a method to use
                 LA in computer graphics-picture generation of almost
                 any kind. Various experiments are done-from curve
                 drawing to 3D image generation. The results are all
                 excellent for quality and speed.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Ind. Eng., Aichi Inst. of Technol.,
                 Toyota, Japan",
  classification = "C5230 (Digital arithmetic methods); C6130B (Graphics
                 techniques)",
  keywords =     "3D image generation; Computer graphics; Curve drawing;
                 Fast computational method for real numbers; Logarithmic
                 arithmetic; Logarithmic number systems; Picture
                 generation; Precision; Word length",
  pubcountry =   "Japan",
  thesaurus =    "Computer graphics; Digital arithmetic",
}

@Article{Lai:1991:HNS,
  author =       "F.-S. Lai and C.-F. E. Wu",
  title =        "A hybrid number system processor with geometric and
                 complex arithmetic capabilities",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "40",
  number =       "8",
  pages =        "952--962",
  month =        aug,
  year =         "1991",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.83639",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 12:52:23 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=83639",
  abstract =     "The architecture, design, and performance of a hybrid
                 number system processor are described. The processor
                 performs multiplication, division, square root, and
                 square in the logarithmic number system (LNS) domain.
                 However, the input, output, addition, and subtraction
                 are all executed in the 32-b IEEE standard
                 floating-point number system. With the LNS multiplier
                 and pipelined architecture, the processor is able to
                 perform the geometric and complex arithmetic very
                 effectively. The processor is also shown to compare
                 well to an existing 32-b floating-point DSP (digital
                 signal processor) chip. For the same level of CMOS
                 technology, the performance ratios between the hybrid
                 number system and the floating-point processor are
                 shown to be 6.4:1 and 8:1 for division and square root,
                 respectively; for the complex FFT (fast Fourier
                 transform) algorithm, the ratio is around 2:1. (27
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Thomas J. Watson Res. Center, Yorktown Heights,
                 NY, USA",
  ajournal =     "IEEE Trans. Comput.",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Complex arithmetic; Division; Floating-point number
                 system; Geometric; Hybrid number system processor;
                 Logarithmic number system; Multiplication; Square;
                 Square root",
  thesaurus =    "Digital arithmetic",
}

@Article{Lee:1991:FPPa,
  author =       "Roland L. Lee and Alex Y. Kwok and Fay{\'e} A.
                 Briggs",
  title =        "The Floating Point Performance of a superscalar
                 {SPARC} Processor",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "19",
  number =       "2",
  pages =        "28--37",
  month =        apr,
  year =         "1991",
  CODEN =        "CANED2",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Fri May 12 09:40:40 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Co-published in {\em Operating Systems Review}, {\bf
                 28}(3S).",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
}

@Article{Lee:1991:FPPb,
  author =       "Roland L. Lee and Alex Y. Kwok and Fay{\'e} A.
                 Briggs",
  title =        "The floating-point performance of a superscalar
                 {SPARC} processor",
  journal =      j-OPER-SYS-REV,
  volume =       "25",
  number =       "3S",
  pages =        "28--37",
  month =        apr,
  year =         "1991",
  CODEN =        "OSRED8",
  ISSN =         "0163-5980 (print), 1943-586X (electronic)",
  ISSN-L =       "0163-5980",
  bibdate =      "Sat Aug 26 15:24:15 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Operating Systems Review",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J597",
}

@Article{Lee:1991:FPPc,
  author =       "Roland L. Lee and Alex Y. Kwok and Fay{\'e} A.
                 Briggs",
  title =        "The Floating-Point Performance of a Superscalar
                 {SPARC} Processor",
  journal =      j-SIGPLAN,
  volume =       "26",
  number =       "4",
  pages =        "28--37",
  month =        apr,
  year =         "1991",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The floating point performance of superscalar SPARC
                 processors is evaluated based on empirical data from 12
                 benchmarks. This evaluation is done in the context of
                 two software instruction scheduling optimizations: loop
                 unrolling and software pipelining, and for three
                 machine models: 1-scalar, 2-scalar and 4-scalar. The
                 authors also consider the effect of the memory system
                 on the performance improvements. Superscalar hardware
                 alone exhibit little performance improvement without
                 software optimization. Of the two scheduling methods,
                 software pipelining more effectively takes advantage of
                 increased hardware parallelism, and achieves near
                 optimal speedup on the 4-scalar machine model. The
                 performance of loop unrolling is restricted by the
                 limited number of floating point registers in the SPARC
                 architecture. The best performance level is obtained by
                 applying both optimization techniques. A superscalar
                 SPARC processor can provide improved floating point
                 performance but with significant software and hardware
                 development costs.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sun Microsyst. Inc., Mountain View, CA, USA",
  classification = "C5220 (Computer architecture); C5470 (Performance
                 evaluation and testing)",
  confdate =     "8-11 April 1991",
  conflocation = "Santa Clara, CA, USA",
  confsponsor =  "IEEE; ACM",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "Benchmarks; Development costs; Floating point
                 performance; Floating point registers; Hardware
                 parallelism; Loop unrolling; Memory system; N-scalar
                 machine models; Optimal speedup; Software instruction
                 scheduling optimizations; Software pipelining; SPARC
                 architecture; Superscalar SPARC processor",
  thesaurus =    "Optimisation; Parallel architectures; Performance
                 evaluation; Pipeline processing; Scheduling",
}

@InProceedings{Lee:1991:SCF,
  author =       "Jeong-A. Lee and Tom{\'a}s Lang",
  title =        "{SVD} by constant-factor-redundant-{CORDIC}",
  crossref =     "Kornerup:1991:PIS",
  pages =        "264--271",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Lee.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}

@Article{Letcher:1991:GNC,
  author =       "John H. Letcher",
  title =        "Getting numeric coprocessors up to speed",
  journal =      j-DDJ,
  volume =       "16",
  number =       "5",
  pages =        "36, 38, 40, 42",
  month =        may,
  year =         "1991",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Tue Sep 10 09:11:02 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 UnCover database",
  abstract =     "Memory-mapped math coprocessors can boost performance
                 without sacrificing compatibility.",
  acknowledgement = ack-nhfb,
  affiliation =  "Tulsa University, OK, USA",
  classification = "C5130 (Microprocessor chips); C5230 (Digital
                 arithmetic methods)",
  fjournal =     "Dr. Dobb's Journal of Software Tools",
  keywords =     "80*86 Integer CPU; Floating point coprocessors;
                 Numeric coprocessors; Processing speeds",
  thesaurus =    "Digital arithmetic; Microprocessor chips; Satellite
                 computers",
}

@Article{Lo:1991:BHS,
  author =       "H.-Y. Lo and T. C. Yang",
  title =        "Balanced high-speed residue number {VLSI} multiplier
                 with error detection",
  journal =      "Circuits, Devices and Systems, IEE Proceedings G",
  volume =       "138",
  number =       "3",
  pages =        "421--423",
  month =        jun,
  year =         "1991",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/78.80821",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=6544",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A balanced residue number VLSI multiplier is proposed
                 which eliminates the extra delay for an unbalanced
                 residue multiplier. The number of adding stages used in
                 the VLSI multiplier is reduced from three to two. The
                 authors also describe how \ldots{}",
}

@Article{Lyashenko:1991:PAR,
  author =       "N. N. Lyashenko and M. S. Nikulin",
  title =        "Probability Analysis of Round-Off Errors in
                 Floating-Point Arithmetic",
  journal =      j-THEORY-PROBAB-APPL,
  volume =       "35",
  number =       "1",
  pages =        "66--74",
  month =        "????",
  year =         "1991",
  CODEN =        "TPRBAU",
  DOI =          "https://doi.org/10.1137/1135006",
  ISSN =         "0040-585X (print), 1095-7219 (electronic)",
  ISSN-L =       "0040-585X",
  bibdate =      "Tue Apr 1 10:40:31 MDT 2014",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/TVP/35/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/theoryprobabappl.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Theory of Probability and its Applications",
  journal-URL =  "http://epubs.siam.org/tvp",
  onlinedate =   "January 1991",
}

@InProceedings{Lynch:1991:RCA,
  author =       "Tom Lynch and Earl {Swartzlander, Jr.}",
  title =        "The redundant cell adder",
  crossref =     "Kornerup:1991:PIS",
  pages =        "165--170",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Lynch.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}

@InProceedings{Lyons:1991:FMF,
  author =       "Ken Lyons",
  title =        "A fast method for finding an integer square root",
  crossref =     "Koopman:1991:PST",
  pages =        "27--30",
  year =         "1991",
  bibdate =      "Tue May 4 05:57:50 MDT 1999",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/plan/259965/p27-lyons/",
  acknowledgement = ack-nhfb,
}

@InProceedings{MacKenzie:1991:FMS,
  author =       "Donald MacKenzie",
  title =        "Formal methods and the sociology of proof",
  crossref =     "Morris:1991:RWP",
  pages =        "115--124",
  year =         "1991",
  DOI =          "https://doi.org/10.1007/978-1-4471-3756-6_6",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The paper begins by asking whether a sociology of
                 mathematical knowledge is possible. Having answered in
                 the affirmative (drawing examples from the history of
                 mathematics), it goes on to discuss the development of
                 a similar analysis of the mathematical aspects of
                 computer science. A brief vignette is presented: the
                 processes of negotiation of the IEEE floating-point
                 arithmetic specifications. Then the discussion moves on
                 to the verification of software and hardware. If the
                 sociology of mathematics is correct, then formal proofs
                 can be seen as social, not just in the processes of
                 their acceptance, but also in their internal structure.
                 Placed in the context of pressure for formal
                 verification of safety-critical and security-critical
                 systems, this argument led the author and colleagues to
                 the prediction that litigation involving the nature of
                 mathematical proof was bound to occur. That prediction
                 has now been borne out.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Sociol., Edinburgh University, UK",
  classification = "C0230 (Economic, social and political aspects);
                 C4240 (Programming and algorithm theory); C6110B
                 (Software engineering techniques)",
  keywords =     "Computer science; Formal proofs; Formal verification;
                 IEEE floating-point arithmetic specifications;
                 Litigation; Mathematical aspects; Mathematical
                 knowledge; Negotiation; Safety-critical systems;
                 Security-critical systems; Sociology of proof;
                 Verification",
  thesaurus =    "Economic and sociologic effects; Formal verification;
                 Safety; Security of data; Software reliability; Theorem
                 proving",
}

@Article{MacKenzie:1991:IAL,
  author =       "Donald MacKenzie",
  title =        "The Influence of the {Los Alamos} and {Livermore
                 National Laboratories} on the Development of
                 Supercomputing",
  journal =      j-ANN-HIST-COMPUT,
  volume =       "13",
  number =       "2",
  pages =        "179--201",
  month =        apr # "\slash " # jun,
  year =         "1991",
  CODEN =        "AHCOE5",
  ISSN =         "0164-1239",
  bibdate =      "Fri Nov 1 15:29:15 MST 2002",
  bibsource =    "Compendex database;
                 ftp://ftp.ira.uka.de/pub/bibliography/Parallel/super.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC
                 Contents1st database",
  URL =          "http://dlib.computer.org/an/books/an1991/pdf/a2179.pdf;
                 http://www.computer.org/annals/an1991/a2179abs.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of the History of Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
  remark =       "The author has this remark about Metropolis on page
                 194: ``What are the architectural consequences of this
                 kind of influence? [of Los Alamos on computer design]
                 One apparent in Stretch is that machine's noisy mode
                 facility (Los Alamos interviews). The inspiration of
                 these was Los Alamos Nicholas Metropolis, who in the
                 1950s developed what he called significance arithmetic:
                 the attempt to determine the consequences, for the
                 reliability of results, of errors caused by the need to
                 represent numbers by words of finite length. In noisy
                 mode the effects of truncation were handled differently
                 from in normal operation so as to allow errors caused
                 by truncation to be detected.

                 By definition of ordinary normalized [floating-point]
                 operations, numbers are frequently extended on the
                 right by attaching zeros. During addition the $n$-digit
                 operand that is not preshifted is extended with n
                 zeros, so as to provide the extra positions to which
                 the preshifted operand can be added. Any operand or
                 result that is shifted left to be normalized requires a
                 corresponding number of zeros to be shifted in at the
                 right. Both sets of zeros tend to produce numbers
                 smaller in absolute value than they would have been if
                 more digits had been carried. In the noisy mode these
                 numbers are simply extended with 1s instead of zeros
                 (1s in a binary machine, 9s in a decimal machine). Now
                 all numbers tend to be too large in absolute value. The
                 true value, if there had been no significance loss,
                 should lie between these two extremes. Hence, two runs,
                 one made without and one made with the noisy mode,
                 should show differences in result that indicate which
                 digits may have been affected by significance loss
                 (Buchholz 1962, p. 102).''

                 See \cite{Buchholz:1962:PCS} for more information about
                 the Stretch noisy mode.",
}

@Book{MacKenzie:1991:NAC,
  author =       "Donald MacKenzie and Edinburgh Pict",
  title =        "Negotiating arithmetic, construction proof: the
                 sociology of mathematics and information technology",
  volume =       "38",
  publisher =    "Research Centre for Social Sciences, University of
                 Edinburgh",
  address =      "Edinburgh",
  pages =        "27",
  year =         "1991",
  ISBN =         "1-872287-42-5",
  ISBN-13 =      "978-1-872287-42-3",
  LCCN =         "????",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Edinburgh PICT working paper",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic; Computer security; Floating-point
                 arithmetic",
}

@Article{Marcus:1991:HSR,
  author =       "Marvin Marcus and Markus Sandy",
  title =        "{Hadamard} Square Roots",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "12",
  number =       "1",
  pages =        "49--69",
  month =        jan,
  year =         "1991",
  CODEN =        "SJMAEL",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "15A57 (15A18 15A48 15A52 47B15 60H25)",
  MRnumber =     "92a:15027",
  MRreviewer =   "Zdzis{\l}aw W. Trzaska",
  bibdate =      "Tue Jan 21 08:54:30 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@InProceedings{Markstein:1991:WFF,
  author =       "V. Markstein and P. Markstein and T. Nguyen and S.
                 Poole",
  title =        "Wide Format Floating-Point Math Libraries",
  crossref =     "IEEE:1991:PSA",
  pages =        "130--138",
  year =         "1991",
  DOI =          "https://doi.org/10.1145/125826.125903",
  bibdate =      "Wed Dec 13 18:34:51 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The authors present the performance and accuracy
                 evaluations of eleven transcendental functions found in
                 64- and 128-bit floating-point formats in math
                 libraries on the Cray Y-MP, the IBM 3090E/VF, the
                 Convex C-240, the Hewlett--Packard 9000/720, and the
                 IBM System/6000. Both architecture and algorithms are
                 shown to impact the results.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "ISQUARE, Inc., Austin, TX, USA",
  classification = "C5230 (Digital arithmetic methods); C5470
                 (Performance evaluation and testing); C7310
                 (Mathematics)",
  confdate =     "18-22 Nov. 1991",
  conflocation = "Albuquerque, NM, USA",
  confsponsor =  "IEEE; ACM",
  keywords =     "128 Bit; 64 Bit; Accuracy evaluations; Convex C-240;
                 Cray Y-MP; Floating-point formats; Hewlett--Packard
                 9000/720; IBM 3090E/VF; IBM System/6000; Math
                 libraries; Performance; Transcendental functions; Wide
                 format floating point math libraries",
  numericalindex = "Word length 6.4E+01 bit; Word length 1.28E+02 bit",
  thesaurus =    "Digital arithmetic; Mathematics computing; Parallel
                 processing; Performance evaluation",
}

@Article{McQuillan:1991:HPV,
  author =       "S. E. McQuillan and J. V. McCanny and R. F. Woods",
  title =        "High performance {VLSI} architecture for division and
                 square root",
  journal =      j-ELECT-LETTERS,
  volume =       "27",
  number =       "1",
  pages =        "19--21",
  day =          "3",
  month =        jan,
  year =         "1991",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  summary =      "A novel high performance bit parallel architecture to
                 perform square root and division is proposed. Relevant
                 VLSI design issues have been addressed. By employing
                 redundant arithmetic and a semisystolic schedule, the
                 throughput has been made \ldots{}",
}

@InProceedings{McQuillan:1991:VAM,
  author =       "S. E. McQuillan and J. V. McCanny",
  booktitle =    "1991 International Conference on Acoustics, Speech,
                 and Signal Processing: {ICASSP-91, 14--17} April 1991",
  title =        "A {VLSI} architecture for multiplication, division and
                 square root",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1205--1208",
  year =         "1991",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "A high-performance VLSI architecture to perform
                 combined multiply-accumulate, divide, and square root
                 operations is proposed. The circuit is highly regular,
                 requires only minimal control, and can be reconfigured
                 for every cycle. The execution time \ldots{}",
}

@PhdThesis{Mehrez:1991:AVP,
  author =       "Habib Mehrez",
  title =        "Des architectures {VLSI} pipelin{\'e}s pour les
                 algorithmes num{\'e}riques {\`a} flots de donn{\'e}es
                 en repr{\'e}sentations arithm{\'e}tiques virgule fixe
                 et virgule flottante. ({French}) [{Pipelined VLSI}
                 architectures for numerical algorithms for numerical
                 data in fixed- and floating-point arithmetic]",
  type =         "Th{\`e}se Doctoral",
  school =       "Sciences Appliqu{\'e}es, Universit{\'e} Paris 6",
  address =      "Paris, France",
  year =         "1991",
  bibdate =      "Thu May 09 10:10:32 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Sous la direction de Alain Greiner.",
  abstract =     "Dans cette th{\`e}se, on se propose d'exposer
                 certaines reflexions et contributions dans le
                 d{\'e}veloppement et la recherche en architectures VLSI
                 pour l'implantation des algorithmes de traitement
                 num{\'e}rique {\`a} flots des donn{\'e}es. On exposera
                 en particulier une m{\'e}thodologie g{\'e}n{\'e}rale
                 d'implantation concr{\'e}tis{\'e}e par des {\'e}tudes
                 et des r{\'e}alisations des architectures
                 sp{\'e}cifiques {\`a} la transform{\'e}e de Fourier
                 rapide (TFR ou FFT). Ces architectures concernent aussi
                 bien des traitements arithm{\'e}tiques en virgule fixe
                 qu'en virgule flottante et seront de type pipelin{\'e}s
                 serie systolique. Des propositions d'implantation des
                 op{\'e}rateurs arithm{\'e}tiques de base et des chemins
                 des donn{\'e}es seront developp{\'e}es ainsi que les
                 {\'e}valuations des performances et de leur
                 complexit{\'e} correspondantes. Il sera discut{\'e} des
                 facteurs de classification et d'interactions entre les
                 aspects fonctionnels et algorithmiques, les aspects
                 structurels et architecturaux et finalement les aspects
                 li{\'e}s aux implantations VLSI. Ces derniers aspects
                 concernent notamment les compromis et les choix
                 logiques, {\'e}lectriques et topologiques. La
                 m{\'e}thode de conception est bas{\'e}e sur
                 l'utilisation d'une biblioth{\`e}que de cellules
                 standards qui inclut la technique LSSD, de test et
                 testabilit{\'e}, au moment de la conception des
                 circuits VLSI.",
  acknowledgement = ack-nhfb,
  language =     "French",
}

@InProceedings{Mehta:1991:HSM,
  author =       "Mayur Mehta and Vijay Parmar and Earl {Swartzlander,
                 Jr.}",
  title =        "High-speed multiplier design using multi-input counter
                 and compressor circuits",
  crossref =     "Kornerup:1991:PIS",
  pages =        "43--50",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Mehta.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}

@InProceedings{Metafas:1991:FPP,
  author =       "D. E. Metafas and C. E. Goutis",
  booktitle =    "{1991 IEEE International Symposium on Circuits and
                 Systems (ISCAS)}",
  title =        "A floating point pipeline {CORDIC} processor with
                 extended operation set",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "3066--3069 (vol. 5)",
  year =         "1991",
  DOI =          "https://doi.org/10.1109/ISCAS.1991.176195",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Arithmetic; Computer architecture; Convergence;
                 Digital signal processing; Equations; Hardware;
                 Iterative algorithms; Iterative methods; Pipelines;
                 Signal processing algorithms",
}

@Manual{Microsoft:1991:MCC,
  author =       "{Microsoft Corporation}",
  title =        "{Microsoft C, C++}: version 7.0: programming
                 techniques for {MS-DOS} and {Windows} operating
                 systems",
  organization = "Microsoft Corp.",
  address =      "Redmond, WA, USA",
  pages =        "xix + 323",
  year =         "1991",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Microsoft C++.; Microsoft C.; MS - DOS (Computer
                 file); Windows (Computer programs)",
  remark =       "Improving program performance: optimizing your
                 programs; using precompiled header files; reducing
                 program size with p-code; managing memory in C;
                 managing memory in C++; using the inline assembler;
                 controlling floating-point math operations --- Special
                 environments: compiling with the QuickWin windows
                 library; communicating with graphics; creating charts
                 and graphs; programming with mixed languages; writing
                 portable C programs --- P-code instruction tables. [The
                 book] describes how to take advantage of the special
                 features of Microsoft C/C++. The topics covered by this
                 manual include language extensions, special-purpose
                 library functions, and the interaction between
                 programming strategies and compiler options. This
                 manual is not a reference for the tools included with
                 Microsoft C/C++. -Introd.",
}

@Article{Montuschi:1991:OAE,
  author =       "P. Montuschi and M. Mezzalama",
  title =        "Optimal Absolute Error Starting Values for
                 {Newton--Raphson} Calculation of Square Root",
  journal =      j-COMPUTING,
  volume =       "46",
  number =       "1",
  pages =        "67--86",
  year =         "1991",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65H05 (65G99)",
  MRnumber =     "92a:65161",
  bibdate =      "Tue Oct 12 16:33:42 MDT 1999",
  bibsource =    "Compendex database;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database; OCLC Contents1st database",
  acknowledgement = ack-nhfb,
  affiliation =  "Politecnico di Torino",
  affiliationaddress = "Torino, Italy",
  classification = "723; 921",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Comput Vienna New York",
  keywords =     "Absolute Error; Computer Programming --- Algorithms;
                 Mathematical Techniques; Newton--Raphson Method;
                 Optimization; Square Roots",
}

@InProceedings{Montuschi:1991:SRD,
  author =       "Paolo Montuschi and Luigi Ciminiera",
  title =        "Simple radix 2 division and square root with skipping
                 of some addition steps",
  crossref =     "Kornerup:1991:PIS",
  pages =        "202--209",
  year =         "1991",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Montuschi.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
  summary =      "The authors present a novel algorithm for shared radix
                 2 division and square root whose main characteristic is
                 the ability to avoid any addition when the digit 0 has
                 been selected. The solution presented uses a redundant
                 representation of the \ldots{}",
}

@Article{Mulder:1991:AMC,
  author =       "J. M. Mulder and N. T. Quach and M. J. Flynn",
  title =        "An area model for on-chip memories and its
                 application",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "26",
  number =       "2",
  pages =        "98--105",
  month =        feb,
  year =         "1991",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
}

@InProceedings{Muller:1991:EAF,
  author =       "Michael M{\"u}ller and Christine R{\"u}b and Wolfgang
                 R{\"u}lling",
  title =        "Exact accumulation of floating-point numbers",
  crossref =     "Kornerup:1991:PIS",
  pages =        "64--69",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Muller.pdf",
  abstract =     "The authors present a new idea for designing a chip
                 which computes the exact sum of arbitrarily many
                 floating-point numbers, i.e., it can accumulate the
                 floating-point numbers without cancellation. Such a
                 chip is needed to provide a fast implementation of
                 Kulisch arithmetic. This is a new theory of
                 floating-point arithmetic which makes it possible to
                 compute least significant bit accurate solutions to
                 even ill-conditioned numerical problems. The proposed
                 approach avoids the disadvantages of previously
                 suggested designs which are too large, too slow, or
                 consume too much power. The crucial point is a
                 technique for a fast carry resolution in a long
                 accumulator. It can also be implemented in software.",
  acknowledgement = ack-nhfb,
  affiliation =  "Max-Planck-Inst., Saarbrucken, Germany",
  classification = "B1265B (Logic circuits); C5120 (Logic and switching
                 circuits); C5230 (Digital arithmetic methods)",
  keywords =     "Accumulator; ARITH-10; Chip; Exact accumulation; Exact
                 sum; Fast carry resolution; Floating-point arithmetic;
                 Floating-point numbers; Ill-conditioned numerical
                 problems; Kulisch arithmetic; Least significant bit
                 accurate solutions",
  thesaurus =    "Adders; Digital arithmetic",
}

@InProceedings{Muller:1991:FSC,
  author =       "Jean-Michel Muller and Peter Kornerup and David W.
                 Matula",
  title =        "Foreword: {10th Symposium on Computer Arithmetic,
                 Grenoble, France, June 26--28, 1991}",
  crossref =     "Kornerup:1991:PIS",
  pages =        "v--v",
  year =         "1991",
  bibdate =      "Sat Nov 17 08:46:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_contents.pdf;
                 http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_foreword.pdf;
                 http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_preface.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}

@Article{Mundie:1991:OOR,
  author =       "David A. Mundie and David A. Fisher",
  title =        "Optimized Overload Resolution and Type Matching for
                 {Ada}",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "3",
  pages =        "83--90",
  month =        "Spring",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Sat Aug 9 09:05:41 MDT 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C6140D (High level languages); C5230 (Digital
                 arithmetic methods)",
  conflocation = "Redondo Beach, CA, USA; 30 April-2 May 1990",
  conftitle =    "1st International Symposium on Environments and Tools
                 for Ada",
  corpsource =   "Incremental Syst. Corp., Pittsburgh, PA, USA; Computer
                 Sci. Dept., University of Wisconsin, Madison, WI, USA",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "Ada; computational methods; digital arithmetic;
                 incremental environment; microprogramming interval
                 arithmetic; nodes; overload resolution; pruning
                 heuristics; recursive strategy; tree; type matching",
  sponsororg =   "IEEE",
  treatment =    "P Practical; A Application",
}

@PhdThesis{Mutrie:1991:TSS,
  author =       "Mark P. W. Mutrie",
  title =        "Towards a Symbolic System for Floating-Point Error
                 Analysis",
  school =       "University of Waterloo",
  year =         "1991",
  bibdate =      "Thu Nov 8 14:50:35 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@InProceedings{Myczkowski:1991:SMA,
  author =       "J. Myczkowski and G. Steele",
  title =        "Seismic modeling at {15 Gigaflops} on the {Connection
                 Machine}",
  crossref =     "IEEE:1991:PSA",
  pages =        "316--326",
  year =         "1991",
  bibdate =      "Wed Apr 15 16:28:01 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "A9130 (Seismology); C4170 (Differential equations);
                 C5440 (Multiprocessor systems and techniques); C7340
                 (Geophysics)",
  corpsource =   "Thinking Machines Corp., Cambridge, MA, USA",
  keywords =     "14 GFLOPS; acoustic wave equation; CM-2 supercomputer;
                 Connection Machine; difference equations; finite
                 difference algorithm; floating point unit; geophysics
                 computing; instruction sequence; interprocessor grid
                 communication; massively parallel machine; memory
                 interface; parallel processing; seismic modelling code;
                 seismology; sponge boundary conditions; stencil
                 compiler",
  sponsororg =   "IEEE; ACM",
  treatment =    "A Application; P Practical",
}

@Article{Nagal:1991:PEM,
  author =       "T. Nagal",
  title =        "Performance evaluation of mathematical functions",
  journal =      j-SUPERCOMPUTER,
  volume =       "8",
  number =       "8",
  pages =        "46--56",
  month =        nov,
  year =         "1991",
  CODEN =        "SPCOEL",
  ISSN =         "0168-7875",
  bibdate =      "Thu Sep 1 10:15:07 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Supercomputer",
}

@InProceedings{Nakano:1991:MBM,
  author =       "H. Nakano and M. Nakajima and Y. Nakahura and T.
                 Yoshida and Y. Goi and Y. Nakai and R. Segawa and T.
                 Kishida and H. Kadora",
  title =        "A 80 {MFLOPS} 64-bit Microprocessor for Parallel
                 Computer",
  crossref =     "IEEE:1991:PIC",
  pages =        "15.2/1--4",
  year =         "1991",
  bibdate =      "Wed Sep 7 22:32:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Book{Nelson:1991:SPM,
  editor =       "Greg Nelson",
  title =        "Systems Programming with {Modula-3}",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "ix + 267",
  year =         "1991",
  ISBN =         "0-13-590464-1",
  ISBN-13 =      "978-0-13-590464-0",
  LCCN =         "QA76.66 .S87 1991",
  bibdate =      "Mon Sep 12 08:08:01 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "A description of the Modula 3 programming language by
                 the committee that designed it, with an entertaining
                 appendix on how various design decisions were made.
                 Section 3.4 describes three floating-point interfaces
                 that provide parameters of the underlying
                 floating-point system, access primitives, and exception
                 handling.",
  acknowledgement = ack-nj,
}

@Article{Ochs:1991:NRU,
  author =       "T. Ochs",
  title =        "Numerics for the rest of us",
  journal =      j-COMP-LANG-MAG,
  volume =       "8",
  number =       "10",
  pages =        "113--127",
  month =        oct,
  year =         "1991",
  CODEN =        "COMLEF",
  ISSN =         "0749-2839",
  bibdate =      "Thu Sep 1 10:15:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computer Language Magazine",
}

@Article{Ochs:1991:NTR,
  author =       "T. Ochs",
  title =        "Numeric types, representations, and other fictions",
  journal =      j-COMP-LANG-MAG,
  volume =       "8",
  number =       "8",
  pages =        "93--101",
  month =        aug,
  year =         "1991",
  CODEN =        "COMLEF",
  ISSN =         "0749-2839",
  bibdate =      "Thu Sep 1 10:14:15 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computer Language Magazine",
}

@Article{Ochs:1991:RF,
  author =       "T. Ochs",
  title =        "A rotten foundation",
  journal =      j-COMP-LANG-MAG,
  volume =       "8",
  number =       "2",
  pages =        "103--107",
  month =        feb,
  year =         "1991",
  CODEN =        "COMLEF",
  ISSN =         "0749-2839",
  bibdate =      "Thu Sep 1 10:15:05 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computer Language Magazine",
}

@Article{Ochs:1991:SRF,
  author =       "T. Ochs",
  title =        "Son of rotten foundation: The sequel",
  journal =      j-COMP-LANG-MAG,
  volume =       "8",
  number =       "3",
  pages =        "85--91",
  month =        mar,
  year =         "1991",
  CODEN =        "COMLEF",
  ISSN =         "0749-2839",
  bibdate =      "Fri Dec 08 13:04:29 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computer Language Magazine",
}

@Article{OGrady:1991:HOA,
  author =       "E. Pearse O'Grady and Baek-Kyu K. Young",
  title =        "A Hardware-Oriented Algorithm for Floating-Point
                 Function Generation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "40",
  number =       "2",
  pages =        "237--241",
  month =        feb,
  year =         "1991",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.73596",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 12:52:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=73596",
  abstract =     "An algorithm is presented for performing accurate,
                 high-speed, floating-point function generation for
                 univariate functions defined at arbitrary breakpoints.
                 Rapid identification of the breakdown interval, which
                 includes the input argument, is the key operation in
                 the algorithm. A hardware implementation which makes
                 extensive use of read\slash write memories illustrates
                 the algorithm.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Okabe:1991:LDC,
  author =       "Y. Okabe and N. Takagi and S. Yaima",
  key =          "OTY91",
  title =        "Log-Depth Circuits for Elementary Functions Using
                 Residue Number System",
  journal =      j-ELECTRON-COMMUN-JPN,
  volume =       "74",
  number =       "8",
  pages =        "31--37",
  year =         "1991",
  CODEN =        "ECOJAL",
  ISSN =         "0424-8368",
  bibdate =      "Mon May 19 15:16:09 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Theory/arith.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Translated from Denshi Joho Tsushin Gakkai Ronbunshi,
                 vol.\ 21-DI, no.\ 9, September 1990, pp.\ 723-728",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics and communications in Japan",
}

@InProceedings{Orup:1991:HRH,
  author =       "Holger Orup and Peter Kornerup",
  title =        "{A} high-radix hardware algorithm for calculating the
                 exponential {$ M^E \bmod N $}",
  crossref =     "Kornerup:1991:PIS",
  pages =        "51--56",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Orup.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}

@Article{Ozawa:1991:FND,
  author =       "K. Ozawa",
  title =        "A Fast {$ O(n^2) $} Division Algorithm for
                 Multiple-Precision Floating-Point Numbers",
  journal =      j-INFO-PROC,
  volume =       "14",
  number =       "3",
  pages =        "354--356",
  month =        "????",
  year =         "1991",
  bibdate =      "Thu Sep 1 10:15:09 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Ozawa:1991:FOD,
  author =       "K. Ozawa",
  title =        "A Fast {$ O(n^2) $} Division Algorithm for
                 Multiple-Precision Floating-Point Numbers",
  journal =      j-J-INF-PROCESS,
  volume =       "14",
  number =       "3",
  pages =        "354--356",
  month =        "????",
  year =         "1991",
  CODEN =        "JIPRDE",
  ISSN =         "0387-6101",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A fast O(n/sup 2/) algorithm is derived for the
                 division of multiple-precision floating-point numbers,
                 where $n$ is the number of digits in each of the
                 numbers. This algorithm, which is a modification of the
                 conventional pencil-and-paper technique, is as fast as
                 the conventional $ O(n^2) $ multiplication and 2.67
                 times faster than the algorithm based on the Newton
                 method.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, Coll. of Gen. Educ.,
                 Tohoku University, Miyagi, Japan",
  classification = "C4240 (Programming and algorithm theory)",
  fjournal =     "Journal of Information Processing",
  keywords =     "Fast O(n/sup 2/) division algorithm;
                 Multiple-precision floating-point numbers; Newton
                 method",
  pubcountry =   "Japan",
  thesaurus =    "Algorithm theory; Digital arithmetic",
}

@InProceedings{Parikh:1991:RBE,
  author =       "Shrikant N. Parikh and David W. Matula",
  title =        "A redundant binary {Euclidean GCD} algorithm",
  crossref =     "Kornerup:1991:PIS",
  pages =        "220--225",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Parikh.pdf",
  abstract =     "An efficient implementation of the Euclidean GCD
                 (greatest common divisor) algorithm employing the
                 redundant binary number system is described. The time
                 complexity is O(n), utilizing O(n)4-2 signed 1-b adders
                 to determine the GCD of two n-b integers. The process
                 is similar to that used in SRT division. The efficiency
                 of the algorithm is competitive, to within a small
                 factor, with floating point division in terms of the
                 number of shift and add/subtract operations. The
                 novelty of the algorithm is based on properties derived
                 from the proposed scheme of normalization of signed bit
                 fractions. The implementation is well suited for
                 systolic hardware design.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM, Westlake, TX, USA",
  classification = "C5230 (Digital arithmetic methods)",
  keywords =     "ARITH-10; Euclidean GCD; Floating point division;
                 Greatest common divisor; Redundant binary number
                 system; Signed bit fractions; Systolic hardware design;
                 Time complexity",
  thesaurus =    "Computational complexity; Digital arithmetic",
}

@InProceedings{Paterson:1991:SMC,
  author =       "Michael S. Paterson and Uri Zwick",
  title =        "Shallow multiplication circuits",
  crossref =     "Kornerup:1991:PIS",
  pages =        "28--34",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Peterson.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}

@Misc{Paxson:1991:PTI,
  author =       "Vern Paxson and W. Kahan",
  title =        "A Program for Testing {IEEE} Binary--Decimal
                 Conversion",
  howpublished = "World-Wide Web document",
  month =        may,
  year =         "1991",
  bibdate =      "Wed Jan 29 17:59:29 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.ee.lbl.gov/testbase-report.ps.Z;
                 ftp://ftp.ee.lbl.gov/testbase.tar.Z",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic; floating-point
                 testing",
}

@InProceedings{Piestrak:1991:DRG,
  author =       "Stanis{\l}aw J. Piestrak",
  title =        "Design of Residue Generators and Multioperand Modular
                 Adders Using Carry-Save Adders",
  crossref =     "Kornerup:1991:PIS",
  pages =        "100--107",
  year =         "1991",
  bibdate =      "Sat Nov 17 08:46:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Piestrak.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}

@Article{Plauger:1991:AF,
  author =       "P. J. Plauger",
  title =        "Approximating functions",
  journal =      j-COMP-LANG-MAG,
  volume =       "8",
  number =       "6",
  pages =        "17--25",
  month =        jun,
  year =         "1991",
  CODEN =        "COMLEF",
  ISSN =         "0749-2839",
  bibdate =      "Thu Sep 1 10:15:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computer Language Magazine",
}

@Article{Plauger:1991:EP,
  author =       "P. J. Plauger",
  title =        "Economizing polynomials",
  journal =      j-COMP-LANG-MAG,
  volume =       "8",
  number =       "7",
  pages =        "21--27",
  month =        jul,
  year =         "1991",
  CODEN =        "COMLEF",
  ISSN =         "0749-2839",
  bibdate =      "Thu Sep 1 10:15:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computer Language Magazine",
}

@Article{Plauger:1991:FPA,
  author =       "P. J. Plauger",
  title =        "Floating-Point Arithmetic",
  journal =      j-EMBED-SYS-PROG,
  volume =       "4",
  number =       "8",
  pages =        "95--99",
  month =        aug,
  year =         "1991",
  CODEN =        "EYPRE4",
  ISSN =         "1040-3272",
  bibdate =      "Thu Sep 1 10:14:15 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Embedded Systems Programming",
}

@Article{Plauger:1991:FPP,
  author =       "P. J. Plauger",
  title =        "Floating-Point Primitives",
  journal =      j-JCLT,
  volume =       "3",
  number =       "2",
  pages =        "89--100",
  month =        sep,
  year =         "1991",
  ISSN =         "1042-5721",
  bibdate =      "Thu Nov 8 14:50:36 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "The Journal of {C} Language Translation",
}

@Article{Plauger:1991:HTF,
  author =       "P. J. Plauger",
  title =        "The Header {{\tt <float.h>}}",
  journal =      j-CUJ,
  volume =       "9",
  type =         "{Standard C}",
  number =       "1",
  pages =        "9--??",
  month =        jan,
  year =         "1991",
  ISSN =         "0898-9788",
  bibdate =      "Fri Aug 30 16:52:23 MDT 1996",
  bibsource =    "http://www.cuj.com/cbklist.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "C Users Journal",
}

@Article{Plauger:1991:WW,
  author =       "P. J. Plauger",
  title =        "Washing the watchers",
  journal =      j-COMP-LANG-MAG,
  volume =       "8",
  number =       "9",
  pages =        "23--32",
  month =        sep,
  year =         "1991",
  CODEN =        "COMLEF",
  ISSN =         "0749-2839",
  bibdate =      "Thu Sep 1 10:15:07 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computer Language Magazine",
}

@InProceedings{Priest:1991:AAP,
  author =       "Douglas M. Priest",
  title =        "Algorithms for Arbitrary Precision Floating Point
                 Arithmetic",
  crossref =     "Kornerup:1991:PIS",
  pages =        "132--143",
  year =         "1991",
  DOI =          "https://doi.org/10.1109/ARITH.1991.145549",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Priest.pdf",
  abstract =     "The author presents techniques for performing
                 computations of very high accuracy using only
                 straightforward floating-point arithmetic operations of
                 limited precision. The validity of these techniques is
                 proved under very general hypotheses satisfied by most
                 implementations of floating-point arithmetic. To
                 illustrate the applications of these techniques, an
                 algorithm is presented which computes the intersection
                 of a line and a line segment. The algorithm is
                 guaranteed to correctly decide whether an intersection
                 exists and, if so, to produce the coordinates of the
                 intersection point accurate to full precision. The
                 algorithm is usually quite efficient; only in a few
                 cases does guaranteed accuracy necessitate an expensive
                 computation.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Department of Math., California University, Berkeley,
                 CA, USA",
  classification = "C1160 (Combinatorial mathematics); C5230 (Digital
                 arithmetic methods)",
  keywords =     "accurate floating-point summation; ARITH-10;
                 coordinates; floating point arithmetic; intersection
                 point; line intersection; line segment",
  thesaurus =    "Digital arithmetic; Number theory",
}

@Article{Pugh:1991:TFV,
  author =       "Kenneth Pugh and Hugo Calleens",
  title =        "{{\tt float}}s Versus {{\tt double}}s",
  journal =      j-CUJ,
  volume =       "9",
  type =         "Questions and Answers",
  number =       "6",
  pages =        "117--??",
  month =        jun,
  year =         "1991",
  ISSN =         "0898-9788",
  bibdate =      "Fri Aug 30 16:52:23 MDT 1996",
  bibsource =    "http://www.cuj.com/cbklist.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "C Users Journal",
}

@TechReport{Quach:1991:DIS,
  author =       "N. Quach and M. Flynn",
  title =        "Design and implementation of the {SNAP} floating-point
                 adder",
  type =         "Technical Report",
  number =       "CSL-TR-91-501",
  institution =  "Computer Systems Laboratory, Stanford University",
  address =      "Stanford, CA, USA",
  month =        dec,
  year =         "1991",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}

@TechReport{Quach:1991:FIR,
  author =       "N. Quach and N. Takagi and M. J. Flynn",
  title =        "On Fast {IEEE} Rounding",
  type =         "Technical Report",
  number =       "CSL-TR-91-459",
  institution =  "Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "v + 27",
  month =        jan,
  year =         "1991",
  bibdate =      "Sun Dec 10 14:08:33 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://i.stanford.edu/pub/cstr/reports/csl/tr/91/459/CSL-TR-91-459.pdf",
  abstract =     "A systematic general rounding procedure is proposed.
                 This procedure consists of 2 steps: constructing a
                 rounding table and selecting a prediction scheme.
                 Optimization guidelines are given in each step to
                 minimize the hardware used. This procedure-based
                 rounding method has the additional advantage that
                 verification and generalization are trivial. Two
                 rounding hardware models are described. The first is
                 shown to be identical to that reported by Santoro, et
                 al. The second is more powerful, providing solutions
                 where the first fails. Applying this approach to the
                 IEEE rounding modes for high-speed conventional binary
                 multipliers reveals that round to infinity is more
                 difficult to implement than the round to nearest mode;
                 more adders are potentially needed. Round to zero
                 requires the least amount of hardware. A generalization
                 of this procedure to redundant binary multipliers
                 reveals two major advantages over conventional binary
                 multipliers. First, the computation of the sticky bit
                 consumes considerably less hardware. Second,
                 implementing round to positive and minus infinity modes
                 does not require the examination of the sticky bit,
                 removing a possible worst-case path. A generalization
                 of this approach to addition produces a similar
                 solution to that reported by Quach and Flynn. Although
                 generalizable to other kinds of rounding as well as
                 other arithmetic operations, we only treat the case of
                 IEEE rounding for addition and multiplication; IEEE
                 rounding because it is the current standard on
                 rounding, addition and multiplication because they are
                 the most frequently used arithmetic operations in a
                 typical scientific computation.",
  acknowledgement = ack-nhfb,
  keywords =     "high-speed floating-point adders; high-speed parallel
                 multipliers; IEEE rounding; redundant binary
                 multipliers; redundant binary representation",
}

@TechReport{Quach:1991:LOP,
  author =       "N. T. Quach and M. J. Flynn",
  title =        "Leading one prediction --- implementation,
                 generalization, and application",
  type =         "Technical Report",
  number =       "CSL-TR-91-463",
  institution =  "Computer Systems Laboratory, Stanford University",
  address =      "Stanford, CA, USA",
  month =        mar,
  year =         "1991",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}

@Article{Raja:1991:NDT,
  author =       "Paruvachi V. R. Raja",
  title =        "Novel Design Techniques for {RNS} Systolic {VLSI}
                 Arrays",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "507",
  pages =        "206--??",
  year =         "1991",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Mon May 13 08:51:55 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InProceedings{Rao:1991:ARN,
  author =       "B. D. Rao",
  booktitle =    "Acoustics, Speech, and Signal Processing, 1991.
                 {ICASSP-91., 1991} International Conference on. 14--17
                 April 1991",
  title =        "Analysis of roundoff noise in floating point digital
                 filters",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1893--1896",
  year =         "1991",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "A systematic approach for the analysis of roundoff
                 noise in floating point digital filters is presented.
                 The analysis is based on a high level model developed
                 to deal with the errors in the inner product operation.
                 The model consists of an efficient \ldots{}",
}

@Article{Rees:1991:RRA,
  author =       "Jonathan Rees and William Clinger and others",
  title =        "The revised$^4$ report on the algorithmic language
                 {Scheme}",
  journal =      "ACM SIGPLAN Lisp Pointers",
  volume =       "4",
  number =       "3",
  pages =        "1--55",
  month =        jul # "\slash " # sep,
  year =         "1991",
  bibdate =      "Wed Jan 29 16:50:56 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "From \cite{Steele:2004:RHP}: ``the result [of a
                 binary-to-decimal conversion] is expressed using the
                 minimum number of digits\ldots{}''",
}

@Article{Rump:1991:CAI,
  author =       "Siegfried M. Rump",
  title =        "A Class of Arbitrarily Ill-Conditioned Floating-Point
                 Matrices",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "12",
  number =       "4",
  pages =        "645--653",
  month =        oct,
  year =         "1991",
  CODEN =        "SJMAEL",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F35 (15A12 65G05)",
  MRnumber =     "92d:65076",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Scott:1991:MCS,
  author =       "T. J. Scott",
  title =        "Mathematics and computer science at odds over real
                 numbers",
  journal =      j-SIGCSE,
  volume =       "23",
  number =       "1",
  pages =        "130--139",
  month =        mar,
  year =         "1991",
  CODEN =        "SIGSD3",
  ISSN =         "0097-8418 (print), 2331-3927 (electronic)",
  bibdate =      "Tue Dec 12 09:20:21 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "22nd SIGCSE Technical Symposium on Computer Science
                 Education.",
  abstract =     "Discusses the `real numbers' data type as implemented
                 by `floating point' numbers. Floating point
                 implementations and a theorem that characterizes their
                 truncations are presented. A teachable floating point
                 system is presented, chosen so that most problems can
                 be worked out with paper and pencil. Then major
                 differences between floating point number systems and
                 the continuous real number system are presented.
                 Important floating point formats are next discussed.
                 Two examples derived from actual computing practice on
                 mainframes, minicomputers, and PCs are presented. The
                 paper concludes with a discussion of where floating
                 point arithmetic should be taught in standard courses
                 in the ACM curriculum.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, Western Illinois
                 University, Macomb, IL, USA",
  classification = "C0220 (Education and training); C5230 (Digital
                 arithmetic methods)",
  confdate =     "7-8 March 1991",
  conflocation = "San Antonio, TX, USA",
  confsponsor =  "ACM",
  fjournal =     "SIGCSE Bulletin (ACM Special Interest Group on
                 Computer Science Education)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J688",
  keywords =     "ACM curriculum; Computer science; Floating point
                 arithmetic; Floating point formats; Floating point
                 number systems; Real number data types; Standard
                 courses; Teaching; Truncations",
  thesaurus =    "Computer science education; Data structures; Digital
                 arithmetic; Educational courses; Number theory",
}

@TechReport{Seznec:1991:OCE,
  author =       "Andre Seznec and Karl Courtel",
  title =        "{OPAC}: a cost-effective floating-point coprocessor =
                 Le coprocessor num{\'e}rique {OPAC}",
  institution =  "Institut National de Recherche en Informatique et en
                 Automatique",
  address =      "Le Chesnay, France",
  pages =        "24",
  year =         "1991",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Rapports de recherche. Institut National de Recherche
                 en Informatique et en Automatique; 1461 Rapports de
                 recherche (Institut national de recherche en
                 informatique et en automatique (France)); 1461.",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Microprocessors.",
  remark =       "Abstracts in English and French. ``Mai 1991.''
                 Abstract: ``The effective performance of RISC
                 microprocessors on numerical applications remains on
                 the order of a few megaflops/s. In this paper, we show
                 that the static addressing of the registers in standard
                 RISC floating-point coprocessors is one of the main
                 bottleneck [sic] for performance. In the architecture
                 of the coprocessor OPAC, we propose an alternative
                 using only FIFO queues for storing intermediate results
                 and reusable operands. Performance close to
                 multiplication-accumulation every cycle is expected on
                 a large set of numerical applications at a reasonable
                 hardware cost.'' Supported in part by the CNRS PRC-AMN
                 Supported in part by the French Ministry of Defense.",
}

@TechReport{Seznec:1991:OFP,
  author =       "Andre Seznec and Karl Courtel",
  title =        "{OPAC}: a floating-point coprocessor dedicated to
                 compute-bound kernels = {OPAC}: un coprocesseur
                 flottant dedi{\'e} au calcul matriciel",
  type =         "Rapports de recherche",
  number =       "1555",
  institution =  "Institut National de Recherche en Informatique et en
                 Automatique",
  address =      "Le Chesnay, France",
  pages =        "27",
  year =         "1991",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Array processors.; Kernel functions.; Parallel
                 programming (Computer science)",
  remark =       "Abstracts in English and French. ``October 7, 1991.''
                 Abstract: ``In various application domains, programmers
                 are not specialists of parallel programming, but are
                 demanding for performance that cannot be reached
                 without using parallelism. Nevertheless, in many
                 applications, the main part of the computations may be
                 encapsulated in compute-bounds kernels with [sic]
                 exhibit high potential parallelism. Achieving high
                 performance on compute-bound primitives at a low
                 hardware cost has became [sic] an important challenge.
                 In this paper, we present the architecture of the OPAC
                 floating-point operator. OPAC has been designed in
                 order to be the basic cell in a multi-cell
                 floating-point coprocessor dedicated to the execution
                 of the most useful compute-bound kernels. The peak
                 performance of one floating-point multiply-add per
                 cycle per cell obtained on the OPAC prototype may be
                 approached in a microprocessor environment on a
                 multi-cell OPAC floating-point coprocessor on a large
                 set of numerical applications.'' Supported in part by
                 the French ministry of defense. Supported in part by
                 the CNRS (PRC-ANM and GCIS)",
}

@Article{Shaeffer:1991:HEP,
  author =       "D. L. Shaeffer and J. R. Kimbrough and S. M. Denton
                 and J. L. Kaschmitter and J. W. Wilburn and R. W. Davis
                 and N. J. Colella and D. B. Holtkamp",
  title =        "High energy proton {SEU} test results for the
                 commercially available {MIPS R3000} microprocessor and
                 {R3010} floating point unit",
  journal =      j-IEEE-TRANS-NUCL-SCI,
  volume =       "38",
  number =       "6",
  pages =        "1421--1428",
  month =        dec,
  year =         "1991",
  CODEN =        "IRNSAM",
  ISSN =         "0018-9499 (print), 1558-1578 (electronic)",
  ISSN-L =       "0018-9499",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Nuclear Science",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=23",
  keywords =     "floating-point testing",
  summary =      "Proton single event upset (SEU) cross sections and
                 proton total dose hardness of commercially available
                 MIPS R3000 microprocessors (CPU) and R3010 floating
                 point units (FPU) were obtained by exposing these parts
                 to 256 MeV protons from the linear accelerator
                 \ldots{}",
}

@Article{Shand:1991:HSL,
  author =       "M. Shand and P. Bertin and J. Vuillemin",
  title =        "Hardware speedups in long integer multiplication",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "19",
  number =       "1",
  pages =        "106--113",
  month =        mar,
  year =         "1991",
  CODEN =        "CANED2",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Fri May 12 09:40:33 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
}

@Book{Siewiorek:1991:AST,
  author =       "Daniel P. Siewiorek and Philip John {Koopman, Jr.}",
  title =        "The Architecture of Supercomputers\emdash Titan, {A}
                 Case Study",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xvii + 202",
  year =         "1991",
  ISBN =         "0-12-643060-8",
  ISBN-13 =      "978-0-12-643060-8",
  LCCN =         "QA76.5 S536 1991",
  bibdate =      "Sun Jan 23 17:54:38 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Skavantzos:1991:PRN,
  author =       "A. Skavantzos and F. J. Taylor",
  title =        "On the polynomial residue number system [digital
                 signal processing]",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "39",
  number =       "2",
  pages =        "376--382",
  month =        feb,
  year =         "1991",
  CODEN =        "ITPRED",
  DOI =          "https://doi.org/10.1109/78.80821",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2656",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The theory of the polynomial residue number system
                 (PRNS), a system in which totally parallel polynomial
                 multiplication can be achieved provided that the
                 arithmetic takes place in some carefully chosen ring,
                 is examined. Such a system is defined by \ldots{}",
}

@Article{Smith:1991:AFP,
  author =       "David M. Smith",
  title =        "{Algorithm 693}: {A FORTRAN} Package for
                 Floating-Point Multiple-Precision Arithmetic",
  journal =      j-TOMS,
  volume =       "17",
  number =       "2",
  pages =        "273--283",
  month =        jun,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/108556.108585",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Dec 13 18:36:25 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-2/p273-smith/",
  abstract =     "FM is a collection of FORTRAN-77 routines which
                 performs floating-point multiple-precision arithmetic
                 and elementary functions. Results are almost always
                 correctly rounded, and due to improved algorithms used
                 for elementary functions, reasonable efficiency is
                 obtained.",
  acknowledgement = ack-nhfb,
  affiliation =  "Loyola Marymount University, Los Angeles, CA, USA",
  classification = "C4130 (Interpolation and function approximation);
                 C5230 (Digital arithmetic methods); C7310
                 (Mathematics)",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Accuracy; correct rounding; Elementary functions;
                 floating-point arithmetic; Floating-point
                 multiple-precision arithmetic; FM; FORTRAN-77 routines;
                 Mathematical library; Portable software; Rounding off",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf D.3.2}:
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN 77.",
  thesaurus =    "Digital arithmetic; Function approximation;
                 Mathematics computing; Software packages; Subroutines",
}

@Article{Sorensen:1991:OEC,
  author =       "D. C. Sorensen and Ping Tak Peter Tang",
  title =        "On the Orthogonality of Eigenvectors Computed by
                 Divide and Conquer Techniques",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "28",
  number =       "6",
  pages =        "1752--1775",
  month =        dec,
  year =         "1991",
  CODEN =        "SJNAAM",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  MRclass =      "65F15 (65G05)",
  MRnumber =     "92h:65065",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database; Parallel/par.lin.alg.bib;
                 Theory/Matrix.bib",
  note =         "Pages 1759--1761 discuss implementation of useful
                 primitives for higher-precision arithmetic: DPAdd2(),
                 DPAdd3(), DPDiv().",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
  kwds =         "nla, eig, prll, symmetric matrix",
}

@PhdThesis{Sparmann:1991:SBT,
  author =       "U. Sparmann",
  title =        "Structure Based Test Methods for Arithmetic Circuits",
  type =         "{Ph.D.} thesis",
  school =       "Computer Science Department, University of Saarland",
  address =      "Saarbr{\"u}cken, Germany",
  year =         "1991",
  bibdate =      "Tue Mar 13 10:30:20 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "In German.",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point testing",
  remark =       "Cited in \cite{Mueller:2000:CAC}.",
}

@Article{Squire:1991:ANS,
  author =       "Jon S. Squire",
  title =        "{Ada} numerics standardization and testing",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  address =      "New York, NY, USA",
  pages =        "1--286",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "Ada (Computer program language); floating-point
                 testing",
  remark =       "A special edition from SIGAda \ldots{} presented by
                 SIGAda Numerics Working Group and Ada-Europe Numerics
                 Working Group and ISO- IEC/JTC1/SC22/WG9 Numerics
                 Rapporteur Group.",
  tableofcontents = "Introduction to the proposed standard for the
                 elementary functions in Ada / Kenneth W. Dritz\\
                 Proposed standard for a generic package of elementary
                 functions for Ada / edited by Kenneth W. Dritz\\
                 Rationale for the proposed standard for a generic
                 package of elementary functions for Ada; Proposed
                 standard for a generic package of primitive functions
                 for Ada; Rationale for the proposed standard for a
                 generic package of primitive functions for Ada /
                 Kenneth W. Dritz\\
                 Proposed standard for packages of real and complex type
                 declarations and basic operations for Ada (including
                 vector and matrix types) / edited by Graham S.
                 Hodgson\\
                 Rationale for the proposed standard for packages of
                 real and complex type declarations and basic operations
                 for Ada (including vector and matrix types) / Graham S.
                 Hodgson. Proposed standard for a generic package of
                 complex elementary functions / edited by Jon S. Squire
                 \\
                 Rationale for the proposed standard for a generic
                 package of complex elementary functions / Jon S. Squire
                 \\
                 A portable generic elementary function package in Ada
                 and an accurate test suite / Ping Tak Peter Tang \\
                 Towards validation of generic elementary functions and
                 other standard Ada numerics packages / Jon S. Squire\\
                 Floating point attributes in Ada / Dik T. Winter\\
                 An Ada math library for real-time avionics / Donald A.
                 Celarier and Donald W. Sando\\
                 Predefined floating point type names, uniformity
                 rapporteur group UI-48 / edited by Jon S. Squire.",
}

@InProceedings{Steidley:1991:FPA,
  author =       "C. W. Steidley",
  title =        "Floating point arithmetic basic exercises in
                 mathematical reasoning for computer science majors",
  crossref =     "ASEE:1991:CCW",
  pages =        "191--197 vol.1",
  year =         "1991",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The author gives examples demonstrating how an
                 unsuspecting user of floating point arithmetic on
                 computers may be misled by results. Specifically, there
                 are cases where the fundamental rules of arithmetic
                 break down. Thus, it is even more imperative that
                 fledgling computer scientists have some insight into
                 the machinations of floating point arithmetic on
                 computers.",
  acknowledgement = ack-nhfb,
  affiliation =  "Central Washington University, Ellensburg, WA, USA",
  classification = "C0220 (Education and training); C5230 (Digital
                 arithmetic methods)",
  keywords =     "Computer science majors; Computers; Floating point
                 arithmetic; Mathematical reasoning",
  thesaurus =    "Computer science education; Digital arithmetic",
}

@Article{Takagi:1991:RCM,
  author =       "N. Takagi and T. Asada and S. Yajima",
  title =        "Redundant {CORDIC} Methods with a Constant Scale
                 Factor for Sine and Cosine Computation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "C-40",
  number =       "9",
  pages =        "989--995",
  month =        sep,
  year =         "1991",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.83660",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:15:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Takagi:1991:RMM,
  author =       "Naofumi Takagi",
  title =        "{A} radix-$4$ modular multiplication hardware
                 algorithm efficient for iterative modular
                 multiplications",
  crossref =     "Kornerup:1991:PIS",
  pages =        "35--42",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Takagi.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}

@TechReport{Tang:1991:TLAa,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Lookup Algorithms for Elementary Functions and
                 Their Error Analysis",
  type =         "Technical Report",
  number =       "MCS-P194-1190",
  institution =  "Argonne National Laboratory",
  address =      "Argonne, IL, USA",
  pages =        "????",
  year =         "1991",
  bibdate =      "Thu Jan 30 16:25:10 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Tang:1991:TLAb,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Lookup Algorithms for Elementary Functions and
                 Their Error Analysis",
  crossref =     "Kornerup:1991:PIS",
  pages =        "232--236",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Tang.pdf",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  keywords =     "ARITH-10",
}

@InProceedings{Taylor:1991:TFA,
  author =       "V. E. Taylor and A. Ranade and D. G. Messerschmitt",
  title =        "Three-dimensional finite-element analyses:
                 implications for computer architectures",
  crossref =     "IEEE:1991:PSA",
  pages =        "786--795",
  year =         "1991",
  bibdate =      "Wed Apr 15 16:28:01 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C4140 (Linear algebra); C4185 (Finite element
                 analysis); C4240P (Parallel programming and algorithm
                 theory); C5220P (Parallel architecture); C6110P
                 (Parallel programming); C6120 (File organisation)",
  corpsource =   "Department of Electr. Eng. and Computer Science,
                 California University, Berkeley, CA, USA",
  keywords =     "columns; computer architectures; data path design;
                 data structure; data structures; finite element
                 analysis; floating-point units; matrix algebra; memory
                 bandwidth; parallel architectures; parallel
                 programming; programming theory; rows; sparse matrices;
                 sparsity pattern",
  sponsororg =   "IEEE; ACM",
  treatment =    "P Practical; T Theoretical or Mathematical",
}

@Article{teRiele:1991:NLB,
  author =       "H. J. J. {te Riele}",
  title =        "A new lower bound for the {de Bruijn-Newman}
                 constant",
  journal =      j-NUM-MATH,
  volume =       "58",
  number =       "6",
  pages =        "661--667",
  year =         "1991",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "30D10 (11M26 30D15 65E05)",
  MRnumber =     "92c:30030",
  MRreviewer =   "George L. Csordas",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290F (Interpolation and function approximation);
                 B0290R (Integral equations); C4130 (Interpolation and
                 function approximation); C4180 (Integral equations)",
  corpsource =   "Centre for Math. and Computer Science, Amsterdam,
                 Netherlands",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "complex zeros; de Bruijn-Newman constant;
                 high-precision floating-point computations; integral
                 equations; Jensen polynomial; lover bound; polynomials;
                 Riemann hypothesis; Sturm sequence",
  treatment =    "T Theoretical or Mathematical",
}

@Manual{TI:1991:TDH,
  title =        "{TMS34082} designer's handbook",
  organization = "{Texas Instruments Incorporated}",
  address =      "Dallas, TX, USA",
  edition =      "Revised",
  pages =        "various",
  year =         "1991",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer graphics --- Equipment and supplies.;
                 Floating-point arithmetic --- Computer simulation.;
                 Integrated circuits --- Very large scale integration
                 --- Handbooks,; manuals, etc.",
  remark =       "``Datapath VLSI products''--Cover. ``2564007-9721
                 revision A, May 1991''--T.p.",
}

@Manual{TI:1991:TFDa,
  title =        "{TMS320} floating-point {DSP} optimizing {C} compiler
                 user's guide",
  organization = "{Texas Instruments Incorporated}",
  address =      "Dallas, TX, USA",
  edition =      "Revised",
  pages =        "various",
  year =         "1991",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Compilers (Computer programs).; manuals, etc.; Signal
                 processing --- Digital techniques --- Equipment and;
                 supplies.; Texas Instruments TMS320 series
                 microprocessors --- Handbooks",
  remark =       "``Microprocessor development systems''--Cover.
                 ``2576391-9721 revision A, October 1991''--T.p.",
}

@Manual{TI:1991:TFDb,
  title =        "{TMS320} floating-point {DSP} assembly language tools
                 user's guide",
  organization = "{Texas Instruments Incorporated}",
  address =      "Dallas, TX, USA",
  edition =      "Revised",
  pages =        "various",
  year =         "1991",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Assembler language (Computer program language).;
                 Handbooks, manuals, etc.; Signal processing --- Digital
                 techniques --- Equipment and; supplies.; Texas
                 Instruments TMS320 series microprocessors ---
                 Programming --",
  remark =       "``Microprocessor development systems''--Cover.
                 ``2576328-9721 revision A, September 1991''--T.p.",
}

@Manual{TI:1991:TST,
  title =        "{TMS34082} software tool kit user's guide",
  organization = "Texas Instruments Incorporated",
  address =      "Dallas",
  edition =      "2547321-9721 revision.",
  pages =        "various",
  year =         "1991",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer storage devices.; TMS34082 Floating-Point
                 Processor.",
  remark =       "``Datapath VLSI products''--Cover. ``SSCA001''--P. [4]
                 of cover.",
}

@InProceedings{Tomabechi:1991:DMD,
  author =       "N. Tomabechi",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, 11--14 June 1991",
  title =        "Design method of defect-tolerant {WSI} systems based
                 on the residue number system",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "3082--3085",
  year =         "1991",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1991.176199",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A design method is proposed for defect-tolerant WSI
                 arithmetic systems based on the RNS (residue number
                 system). The yield analysis has shown that the features
                 of the RNS are very well suited for the defect recovery
                 of WSIs. In the RNS, addition and \ldots{}",
}

@TechReport{Tsang:1991:SDC,
  author =       "Annie Tsang and Manfred Olschanowsky",
  title =        "A Study of {DataBase 2} Customer Queries",
  type =         "Technical Report",
  number =       "TR 03.413",
  institution =  "IBM Santa Teresa Laboratory",
  address =      "San Jose, CA, USA",
  month =        apr,
  year =         "1991",
  bibdate =      "Mon Mar 06 08:07:19 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
  remark =       "This report surveys the numeric data types used in
                 commercial databases by 51 major organizations, and
                 finds that 98.6\% of the numeric data are decimal.",
}

@Article{Tsubokawa:1991:FEA,
  author =       "Hiroshi Tsubokawa and Hajime Kubota and Shigeo
                 Tsujii",
  title =        "Floating-Point Error Analysis for Recursive
                 Least-Square Algorithm Using {UD} Factorization",
  journal =      j-ELECT-COMM-JAPAN-3-FUND-ELECT-SCI,
  volume =       "74",
  number =       "6",
  pages =        "1--10",
  year =         "1991",
  CODEN =        "ECJSER",
  ISSN =         "1042-0967 (print), 1520-6440 (electronic)",
  ISSN-L =       "1042-0967",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics and communications in Japan. Part 3,
                 Fundamental electronic science",
}

@InProceedings{Tu:1991:ALA,
  author =       "Paul K.-G. Tu and Milo{\v{s}} D. Ercegovac",
  title =        "Application of on-line arithmetic algorithms to the
                 {SVD} computation: preliminary results",
  crossref =     "Kornerup:1991:PIS",
  pages =        "246--255",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Tu.pdf",
  abstract =     "A scheme for the singular value decomposition (SVD)
                 problem, based on online arithmetic, is discussed. The
                 design, using radix-2 floating-point online operations,
                 implemented in the LSI HCMOS gate-array technology, is
                 compared with a compatible conventional arithmetic
                 implementation. The preliminary results indicate that
                 the proposed online approach achieves a speedup of
                 2.4-3.2 with respect to the conventional solutions,
                 with 1.3-5.5 more gates and more than 6 times fewer
                 interconnections.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Corp., Austin, TX, USA",
  classification = "C5230 (Digital arithmetic methods)",
  keywords =     "ARITH-10; Floating-point online operations; Online;
                 Online arithmetic; Radix-2; Singular value
                 decomposition",
  thesaurus =    "Digital arithmetic",
}

@Article{Tu:1991:GAI,
  author =       "Paul K.-G. Tu and Milo{\v{s}} D. Ercegovac",
  title =        "Gate Array Implementation of On-Line Algorithms for
                 Floating-Point Operations",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "3",
  number =       "4",
  pages =        "307--318",
  month =        oct,
  year =         "1991",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1007/BF00936903",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present gate array designs of on-line arithmetic
                 units for radix-2 floating-point addition,
                 multiplication and division operations. Performance and
                 complexity characteristics of the implementations of
                 on-line arithmetic units are discussed and compared
                 with those of the compatible conventional
                 floating-point algorithms implemented in the same
                 technology.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
}

@InProceedings{Turner:1991:IAE,
  author =       "Peter R. Turner",
  title =        "Implementation and analysis of extended {SLI}
                 operations",
  crossref =     "Kornerup:1991:PIS",
  pages =        "118--126",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Turner.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}

@Article{Umemura:1991:FNL,
  author =       "K. Umemura",
  title =        "Floating-point number {LISP}",
  journal =      j-SPE,
  volume =       "21",
  number =       "10",
  pages =        "1015--1026",
  month =        oct,
  year =         "1991",
  CODEN =        "SPEXBL",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Tue Dec 12 09:26:54 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A floating-point-number-oriented LISP has been
                 developed. Though it performs type checking on every
                 numeric operation, it runs as fast as Fortran for
                 simple differential-equation problems. The author
                 describes the implementation, provides some
                 measurements of its efficiency and discusses the
                 feasibility of this type of implementation.",
  acknowledgement = ack-nhfb,
  affiliation =  "Software Labs., NTT Corp., Tokyo, Japan",
  classification = "C5230 (Digital arithmetic methods); C6130 (Data
                 handling techniques); C6140D (High level languages);
                 C7310 (Mathematics)",
  fjournal =     "Software---Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  keywords =     "Floating-point-number-oriented LISP; Numeric
                 operation; Simple differential-equation problems; Type
                 checking",
  pubcountry =   "UK",
  thesaurus =    "Digital arithmetic; LISP; Mathematics computing;
                 Symbol manipulation",
}

@Article{Umemura:1991:FPN,
  author =       "Kyoji Umemura",
  title =        "Floating-point Number {LISP}",
  journal =      j-SPE,
  volume =       "21",
  number =       "10",
  pages =        "1015--1026",
  month =        oct,
  year =         "1991",
  CODEN =        "SPEXBL",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A floating-point-number-oriented LISP has been
                 developed. Though it performs type checking on every
                 numeric operation, it runs as fast as Fortran for
                 simple differential-equation problems. The author
                 describes the implementation, provides some
                 measurements of its efficiency and discusses the
                 feasibility of this type of implementation.",
  acknowledgement = ack-nhfb,
  affiliation =  "Software Labs., NTT Corp., Tokyo, Japan",
  classification = "C5230 (Digital arithmetic methods); C6130 (Data
                 handling techniques); C6140D (High level languages);
                 C7310 (Mathematics)",
  fjournal =     "Software---Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  keywords =     "Floating-point-number-oriented LISP; Numeric
                 operation; Simple differential-equation problems; Type
                 checking",
  pubcountry =   "UK",
  thesaurus =    "Digital arithmetic; LISP; Mathematics computing;
                 Symbol manipulation",
}

@Article{Vassiliadis:1991:HWM,
  author =       "S. Vassiliadis and E. M. Schwarz and B. M. Sung",
  title =        "Hard-wired multipliers with encoded partial products",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "40",
  number =       "11",
  pages =        "1181--1197",
  month =        nov,
  year =         "1991",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.102823",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 12:52:24 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=102823",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@MastersThesis{Vishin:1991:FPP,
  author =       "Sanjay Vishin",
  title =        "A floating point primitive classifier for the ray
                 casting machine",
  type =         "Typescript. Thesis ({M.S.})",
  school =       "Duke University. Department of Computer Science",
  address =      "Durham, NC 27708, USA",
  pages =        "ix + 79",
  year =         "1991",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer graphics.; Floating-point arithmetic.;
                 Geometry, Analytic --- Solid --- Data processing.;
                 Image processing.",
}

@InProceedings{Vuillemin:1991:CTA,
  author =       "Jean E. Vuillemin",
  title =        "Constant time arbitrary length synchronous binary
                 counters",
  crossref =     "Kornerup:1991:PIS",
  pages =        "180--183",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Vuillemin.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}

@Article{Walter:1991:FMM,
  author =       "Colin D. Walter",
  title =        "Faster Modular Multiplication by Operand Scaling",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "576",
  pages =        "313--??",
  year =         "1991",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:48:11 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t0576.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/0576/05760313.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/0576/05760313.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Wigley:1991:FMR,
  author =       "N. W. Wigley and G. A. Jullien",
  title =        "Flexible modulus residue number system for complex
                 digital signal processing",
  journal =      j-ELECT-LETTERS,
  volume =       "27",
  number =       "16",
  pages =        "1436--1438",
  month =        aug,
  year =         "1991",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2666",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The quadratic residue number system (QRNS) is often
                 used for integer calculation on complex data streams. A
                 finite polynomial ring mapping technique is presented
                 that removes the $4k + 1$ prime divisor restriction of
                 the QRNS, albeit with an \ldots{}",
}

@InProceedings{Wigley:1991:SMR,
  author =       "N. Wigley and G. A. Jullien and D. Reaume and W. C.
                 Miller",
  title =        "Small moduli replications in the {MRRNS}",
  crossref =     "Kornerup:1991:PIS",
  pages =        "92--99",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Wigley.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}

@InProceedings{Williams:1991:NBC,
  author =       "Ted E. Williams and Mark A. Horowitz",
  title =        "{A} 160 ns 54 bit {CMOS} division implementation using
                 self-timing and symmetrically overlapped {SRT} stages",
  crossref =     "Kornerup:1991:PIS",
  pages =        "210--217",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Williams.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}

@Article{Williams:1991:ZOS,
  author =       "Ted E. Williams and Mark A. Horowitz",
  title =        "A zero-overhead self-timed 160-ns 54-b {CMOS}
                 divider",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "26",
  number =       "11",
  pages =        "1651--1661",
  month =        nov,
  year =         "1991",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
}

@Article{Winter:1991:FPA,
  author =       "Dik T. Winter",
  title =        "Floating point attributes in {Ada}",
  journal =      j-SIGADA-LETTERS,
  volume =       "11",
  number =       "7",
  pages =        "244--273",
  month =        "Fall",
  year =         "1991",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Sat Aug 9 09:05:43 MDT 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  abstract =     "The Ada programming language offers a number of
                 facilities to simplify the writing of portable
                 programs. One of these is the concept of attributes.
                 Many types and objects carry with them a set of
                 attributes that a program may interrogate to get
                 information about the actual implementation. The author
                 is concerned with the set of attributes belonging to
                 floating point types. One should hope that the floating
                 point attributes give correct results. In fact, they
                 are compile time constants. A little experimentation
                 shows that that is not true. Many systems deliver
                 incorrect attributes in a number of cases. Also, due to
                 the inappropriate definition of some of the attributes,
                 many attributes deliver results that are misleading.
                 The author considers the floating point attributes the
                 language gives and shows that indeed some definitions
                 are inappropriate. A program that verifies the validity
                 of the results given by a system is also presented. (3
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "Centrum voor Wiskunde en Inf., Amsterdam,
                 Netherlands",
  classcodes =   "C6140D (High level languages); C6110B (Software
                 engineering techniques); C6150G (Diagnostic, testing,
                 debugging and evaluating systems); C5230 (Digital
                 arithmetic methods)",
  classification = "C5230 (Digital arithmetic methods); C6110B (Software
                 engineering techniques); C6140D (High level languages);
                 C6150G (Diagnostic, testing, debugging and evaluating
                 systems)",
  corpsource =   "Centrum voor Wiskunde en Inf., Amsterdam,
                 Netherlands",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "Ada; Ada programming language; compile; Compile time
                 constants; digital arithmetic; Floating point
                 attributes; floating point attributes; Floating point
                 types; floating point types; Objects; objects;
                 portability; Portable programs; portable programs;
                 program verification; software; time constants; Types;
                 types; Validity; validity",
  thesaurus =    "Ada; Digital arithmetic; Program verification;
                 Software portability",
  treatment =    "P Practical",
}

@InProceedings{Wong:1991:FDU,
  author =       "Derek C. Wong and Michael J. Flynn",
  title =        "Fast division using accurate quotient approximations
                 to reduce the number of iterations",
  crossref =     "Kornerup:1991:PIS",
  pages =        "191--201",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Wong.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}

@Article{Yan:1991:RFA,
  author =       "Tak W. Yan",
  title =        "A Rational Function Arithmetic and Simplification
                 System in {Common Lisp}",
  journal =      j-SIGSAM,
  volume =       "25",
  number =       "4",
  pages =        "4--6",
  month =        oct,
  year =         "1991",
  CODEN =        "SIGSBZ",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Fri Feb 8 18:27:01 MST 2002",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C7310 (Mathematics); C6140D (High level languages)",
  corpsource =   "California University, Berkeley, CA, USA",
  fjournal =     "SIGSAM Bulletin",
  issue =        "98",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
  keywords =     "arithmetic simplification; Common Lisp;
                 exponentiation; freely-distributed computer algebra;
                 LISP; Lisp prefix form; mathematics computing;
                 multiplication; multivariate rational function;
                 rational addition; rational expressions; symbol
                 manipulation; system",
  treatment =    "P Practical",
}

@InProceedings{Yassine:1991:FAB,
  author =       "H. M. Yassine",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, 11--14 June 1991",
  title =        "Fast arithmetic based on residue number system
                 architectures",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2947--2950",
  year =         "1991",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1991.176163",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A new approach is described for transforming residue
                 numbers into equivalent decimal numbers. The approach
                 is based on the periodicity inherent in residue numbers
                 and uses matrix techniques to achieve high-speed
                 residue-to-decimal conversion. In \ldots{}",
}

@Article{Yassine:1991:IMR,
  author =       "H. M. Yassine and W. R. Moore",
  title =        "Improved mixed-radix conversion for residue number
                 system architectures",
  journal =      "Circuits, Devices and Systems, IEE Proceedings G",
  volume =       "138",
  number =       "1",
  pages =        "120--124",
  month =        feb,
  year =         "1991",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/78.80821",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2864",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Processor architectures, based on arithmetic cells
                 using residue number systems, are inherently parallel,
                 modular and fault isolating. The fundamental
                 characteristic of a residue number system is its being
                 an unweighted numbering system. The authors \ldots{}",
}

@InProceedings{Yokoo:1991:OUF,
  author =       "Hidetoshi Yokoo",
  title =        "Overflow\slash underflow-free floating-point number
                 representations with self-delimiting variable-length
                 exponent field",
  crossref =     "Kornerup:1991:PIS",
  pages =        "110--117",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Yokoo.pdf",
  abstract =     "A class of new floating-point representations of real
                 numbers, based on representations of the integers, is
                 described. In the class, every representation uses a
                 self-delimiting representation of the integers as a
                 variable length field, and neither overflow nor
                 underflow appears in practice. The adopted
                 representations of the integers are defined
                 systematically, so that representations of numbers
                 greater than one have both exponent-significant and
                 integer-fraction interpretations. Since representation
                 errors are characterized by the length function of an
                 underlying representation of the integers, systems
                 superior in precision can be easily selected from the
                 proposed class.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, Gunma University,
                 Japan",
  classification = "C1160 (Combinatorial mathematics); C5230 (Digital
                 arithmetic methods)",
  keywords =     "ARITH-10; Exponent-significant; Floating-point number
                 representations; Integer-fraction; Integers; Length
                 function; Real numbers; Representation errors;
                 Self-delimiting variable-length exponent field",
  thesaurus =    "Digital arithmetic; Number theory",
}

@Article{Yoshida:1991:PRT,
  author =       "N. Yoshida and E. Goto and S. Ichikawa",
  title =        "Pseudorandom Rounding for Truncated Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "40",
  number =       "9",
  pages =        "1065--1067",
  month =        sep,
  year =         "1991",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.83650",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 12:52:23 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=83650",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "An economical, unbiased, overflow-free rounding scheme
                 for multiplication of multiple-precision floating-point
                 numbers is proposed. The scheme, called pseudorandom
                 rounding, saves multiplications of lower bits and makes
                 use of statistical properties \ldots{}",
}

@TechReport{Yu:1991:FCF,
  author =       "Tsung Lun Yu and William B. Ribbens",
  title =        "A floating-point coprocessor for fault detection and
                 isolation in electronically controlled internal
                 combustion engines",
  number =       "{GLCTTR} 03-91/1",
  institution =  "Great Lakes Center for Truck Transportation Research",
  address =      "Ann Arbor, MI, USA",
  pages =        "68",
  month =        sep,
  year =         "1991",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Fault location (Engineering); Floating-point
                 arithmetic.; Internal combustion engines --- Defects.;
                 Microprocessors.; Motor vehicles --- Electronic
                 equipment.",
  remark =       "Performed in cooperation with the University
                 Transportation Centers Program by Vehicle Electronics
                 Laboratory, University of Michigan.",
}

@Article{Zelniker:1991:RCF,
  author =       "G. Zelniker and F. J. Taylor",
  title =        "A Reduced Complexity Finite Field {ALU}",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "38",
  number =       "12",
  pages =        "1571--1573",
  month =        dec,
  year =         "1991",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Jun 24 19:51:42 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "arithmetic logic unit (ALU)",
}

@Article{Zeng:1991:AFP,
  author =       "B. Zeng and Y. Neuvo",
  title =        "Analysis of floating point roundoff errors using dummy
                 multiplier coefficient sensitivities",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "38",
  number =       "6",
  pages =        "590--601",
  month =        jun,
  year =         "1991",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  summary =      "A simple method for analyzing roundoff errors in
                 floating-point digital filters is presented. The method
                 is based on the coefficient sensitivities of dummy
                 multipliers with gains of one and connects the roundoff
                 error analysis to coefficient sensitive \ldots{}",
}

@PhdThesis{Zeng:1991:ARR,
  author =       "Bing Zeng",
  title =        "Analysis and reduction of roundoff errors in
                 floating-point recursive digital filters",
  volume =       "72",
  type =         "Avhandling (doktorgrad)",
  school =       "Tampereen teknillinen korkeakoulu",
  address =      "Tampere, Finland",
  pages =        "45 + 80",
  year =         "1991",
  ISBN =         "951-721-697-1",
  ISBN-13 =      "978-951-721-697-5",
  bibdate =      "Thu May 09 08:15:51 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Julkaisuja",
  acknowledgement = ack-nhfb,
}

@InProceedings{Zhang:1991:ADN,
  author =       "D. Zhang and G. A. Jullien and W. C. Miller and Earl
                 {Swartzlander, Jr.}",
  title =        "Arithmetic for digital neural networks",
  crossref =     "Kornerup:1991:PIS",
  pages =        "58--63",
  year =         "1991",
  bibdate =      "Sat Nov 27 12:40:58 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith10/papers/ARITH10_Zhang.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-10",
}

@InProceedings{Zhang:1991:HSE,
  author =       "C. N. Zhang and H. D. Cheng",
  booktitle =    "Reliable Systems and Applications. 5th Annual European
                 Computer Conference. Proceedings. {CompEuro 91}.
                 Advanced Computer Technology, 13--16 May 1991",
  title =        "A high speed error correcting converter for residue
                 number processing",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "816--820",
  year =         "1991",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/CMPEUR.1991.257495",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A novel pipelined systolic design for residue error
                 correction using the Chinese remainder theorem (CRT) is
                 described. This design has a higher throughput compared
                 to previous methods and minimum time latency. The
                 design also has overflow detection \ldots{}",
}

@Article{Zhang:1991:HSS,
  author =       "C. N. Zhang and H. D. Cheng",
  title =        "High-speed single error correcting convertor for
                 residue number processing",
  journal =      j-IEE-PROC-COMPUT-DIGIT-TECH,
  volume =       "138",
  number =       "4",
  pages =        "177--182",
  month =        jul,
  year =         "1991",
  CODEN =        "ICDTEA",
  DOI =          "https://doi.org/10.1109/78.80821",
  ISSN =         "1350-2387 (print), 1359-7027 (electronic)",
  ISSN-L =       "1350-2387",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=2686",
  acknowledgement = ack-nhfb,
  fjournal =     "IEE Proceedings. Computers and Digital Techniques",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A pipelined systolic design for residue error
                 correction using the Chinese remainder theorem is
                 described which has a higher throughput compared with
                 previous methods and minimum time latency. In addition,
                 the design has the capability of overflow \ldots{}",
}

@Article{Ziv:1991:FEE,
  author =       "Abraham Ziv",
  title =        "Fast Evaluation of Elementary Mathematical Functions
                 with Correctly Rounded Last Bit",
  journal =      j-TOMS,
  volume =       "17",
  number =       "3",
  pages =        "410--423",
  month =        sep,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/114697.116813",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Sep 1 10:15:31 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p410-ziv/",
  acknowledgement = ack-nj,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; correct rounding; floating-point
                 arithmetic; standardization; theory",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf G.1.2}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Efficiency.",
}

@Article{Acha:1992:LOF,
  author =       "J. I. Acha and J. Calvo",
  title =        "Low-frequency oscillator for floating-point digital
                 signal processor chips",
  journal =      j-ELECT-LETTERS,
  volume =       "28",
  number =       "17",
  pages =        "1582--??",
  month =        aug,
  year =         "1992",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}

@Article{Anonymous:1992:FPa,
  author =       "Anonymous",
  title =        "Floating Point",
  journal =      j-COMPUT-AIDED-ENG,
  volume =       "11",
  number =       "8",
  pages =        "58--??",
  month =        aug,
  year =         "1992",
  CODEN =        "CCAEDJ",
  ISSN =         "0733-3536 (print), 2162-1365 (electronic)",
  ISSN-L =       "0733-3536",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "OpenGL: The NeWs of 3D Graphics?",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer-aided engineering: CAE",
}

@Article{Anonymous:1992:FPb,
  author =       "Anonymous",
  title =        "Floating Point",
  journal =      j-COMPUT-AIDED-ENG,
  volume =       "11",
  number =       "11",
  pages =        "62--??",
  month =        nov,
  year =         "1992",
  CODEN =        "CCAEDJ",
  ISSN =         "0733-3536 (print), 2162-1365 (electronic)",
  ISSN-L =       "0733-3536",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Software with a View.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer-aided engineering: CAE",
}

@Article{Anonymous:1992:FPc,
  author =       "Anonymous",
  title =        "Floating Point",
  journal =      j-COMPUT-AIDED-ENG,
  volume =       "11",
  number =       "10",
  pages =        "101--??",
  month =        oct,
  year =         "1992",
  CODEN =        "CCAEDJ",
  ISSN =         "0733-3536 (print), 2162-1365 (electronic)",
  ISSN-L =       "0733-3536",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A Helping Hand for FEA.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer-aided engineering: CAE",
}

@Manual{ANSI:ftn92,
  title =        "{American National Standard Programming Language
                 Fortran Extended X3.198--1992}",
  organization = pub-ANSI,
  address =      pub-ANSI:adr,
  year =         "1992",
  bibdate =      "Sat Feb 8 10:28:55 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  acknowledgement = ack-nhfb,
  xxnote =       "This US Standard is identical to the international
                 standard, ISO 1539:1991. See also
                 \cite{Adams:1992:FHC,Brainerd:1990:PGF,Counihan:1991:F,Metcalf:1990:FE}.",
}

@Article{Arazi:1992:BDC,
  author =       "B. Arazi and D. Naccache",
  title =        "Binary-to-Decimal Conversion Based on the Divisibility
                 of $ 2^8 - 1 $ by 5",
  journal =      j-ELECT-LETTERS,
  volume =       "28",
  number =       "3",
  pages =        "2151--2152",
  month =        nov,
  year =         "1992",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "decimal floating-point arithmetic",
}

@PhdThesis{Arjomand:1992:FPC,
  author =       "Ata'u'llah Arjomand",
  title =        "Fast Parallel Computation of the {Singular Value
                 Decomposition} of Real Matrices Using {CORDIC}
                 Arithmetic",
  type =         "{Ph.D.} thesis",
  school =       "Yale University",
  address =      "New Haven, CT, USA",
  pages =        "250",
  year =         "1992",
  ISBN-13 =      "979-82-08-71568-0",
  MRclass =      "99-05",
  MRnumber =     "2688864",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Thesis (Ph.D.)--Yale University",
  URL =          "https://www.proquest.com/dissertations-theses/fast-parallel-computation-singular-value/docview/304011601/se-2",
  acknowledgement = ack-nhfb,
  advisor =      "Jean-Marc Delosme",
  keywords =     "0405:Mathematics; 0544:Electrical engineering;
                 0984:Computer science; Applied sciences; Computer
                 science; Electrical engineering; Mathematics; Pure
                 sciences",
  ris-m1 =       "9314783",
  xxaddress =    "Ann Arbor, MI",
  xxpublisher =  "ProQuest LLC",
}

@Article{Arnold:1992:AFI,
  author =       "M. G. Arnold and T. A. Bailey and J. R. Cowles and M.
                 D. Winkel",
  title =        "Applying features of {IEEE 754} to sign\slash
                 logarithm arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "1040--1050",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156547",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156547",
  abstract =     "Various features found in standard floating point
                 arithmetic (IEEE 754) are examined in light of their
                 appropriateness for sign/logarithm arithmetic. The
                 emphasis is on a 32-b word size comparable to IEEE 754
                 single precision, although other word sizes are
                 possible. A multilayer sign/logarithm format is
                 considered. The lowest layer, similar to previous
                 implementations, would provide only normalized
                 representations but would not provide representations
                 for zero, denormalized values, infinities, and NaNs.
                 The highest layer would provide most of the features
                 found in IEEE 754, including zeros, denormalized
                 values, infinities, and NaNs. Novel algorithms for
                 implementing logarithmic denormalized arithmetic are
                 presented. Simulation results show that the error
                 characteristics of the proposed logarithmic
                 denormalized arithmetic algorithms are similar to those
                 of the denormalized floating point arithmetic in IEEE
                 754.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, Wyoming University,
                 Laramie, WY, USA",
  ajournal =     "IEEE Trans. Comput.",
  classification = "B0250 (Combinatorial mathematics); B1265B (Logic
                 circuits); C1160 (Combinatorial mathematics); C5230
                 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "32 Bit; Denormalized values; IEEE 754; Infinities;
                 Logarithmic denormalized arithmetic algorithms;
                 Multilayer sign/logarithm format; NaNs; Sign/logarithm
                 arithmetic; Standard floating point arithmetic; Zeros",
  numericalindex = "Word length 3.2E+01 bit",
  thesaurus =    "Digital arithmetic; Number theory; Standards",
}

@TechReport{Bailey:1992:ATF,
  author =       "David H. Bailey",
  title =        "Automatic Translation of {Fortran} Programs to
                 Multiprecision",
  type =         "{RNR} Technical Report",
  number =       "RNR-91-025",
  institution =  "NAS Applied Research Branch, NASA Ames Research
                 Center",
  address =      "Moffett Field, CA 94035",
  day =          "17",
  month =        apr,
  year =         "1992",
  bibdate =      "Mon Sep 12 23:55:57 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Bailey:1992:PHP,
  author =       "David H. Bailey",
  title =        "A Portable High Performance Multiprecision Package",
  type =         "{RNR} Technical Report",
  number =       "RNR-90-022",
  institution =  "NAS Applied Research Branch, NASA Ames Research
                 Center",
  address =      "Moffett Field, CA 94035",
  day =          "29",
  month =        may,
  year =         "1992",
  bibdate =      "Mon Sep 12 23:56:03 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Baker:1992:LCE,
  author =       "H. G. Baker",
  title =        "Less Complex Elementary Functions",
  journal =      j-SIGPLAN,
  volume =       "27",
  number =       "11",
  pages =        "15--16",
  month =        nov,
  year =         "1992",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Thu Sep 08 08:11:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}

@Article{Bakhrakh:1992:NIF,
  author =       "S. M. Bakhrakh and S. V. Velichko and N. E.
                 Pilipchatin and V. F. Spiridonov and E. G. Sukhov and
                 Yu. G. Fedorova and V. I. Kheifets",
  title =        "Numerical investigation of floating-point arithmetic
                 operations. ({Russian})",
  journal =      j-PROGRAMMIROVANIE,
  volume =       "6",
  pages =        "13--17",
  year =         "1992",
  CODEN =        "PROGD3",
  ISSN =         "0132-3474, 0361-7688",
  MRclass =      "65G05",
  MRnumber =     "1 227 941",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "English translation appears in
                 \cite{Bakhrakh:1993:NIF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Programmirovanie",
  language =     "Russian",
}

@TechReport{Bewick:1992:BMU,
  author =       "G. Bewick and M. J. Flynn",
  title =        "Binary multiplication using partially redundant
                 multiples",
  type =         "Technical Report",
  number =       "CSL-TR-92-528",
  institution =  "Computer Systems Laboratory, Stanford University",
  address =      "Stanford, CA, USA",
  month =        jun,
  year =         "1992",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}

@TechReport{Blair:1992:PMD,
  author =       "M. Blair and S. Obenski and P. Bridickas",
  title =        "{Patriot} missile defense: Software problem led to
                 system failure at {Dhahran, Saudi Arabia}",
  type =         "Report",
  number =       "GAO/IMTEC-92-26",
  institution =  "Information Management and Technology Division, United
                 States General Accounting Office",
  address =      "Washington, DC, USA",
  year =         "1992",
  bibdate =      "Sat Apr 01 07:34:33 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.gao.gov/assets/220/215614.pdf;
                 http://www.gao.gov/products/IMTEC-92-26",
  abstract =     "Pursuant to a congressional request, GAO reviewed the
                 facts associated with the failure of a Patriot missile
                 defense system in Dhahran, Saudi Arabia, during
                 Operation Desert Storm.\par

                 GAO found that: (1) the Patriot battery at Dhahran
                 failed to track and intercept a Scud missile due to a
                 software problem in the system's weapons control
                 computer; (2) the software problem caused an inaccurate
                 tracking calculation which became worse the longer the
                 system operated; (3) at the time of the incident, the
                 battery had operated continuously for over 100 hours
                 and the inaccuracy was serious enough to cause the
                 system to look in the wrong place for the incoming
                 Scud; (4) two weeks before the incident, Army officials
                 received Israeli data indicating some loss in accuracy
                 after the system had been running for 8 consecutive
                 hours; (5) the Army had never used the Patriot to
                 defend against tactical ballistic missiles or expected
                 the Patriot to operate continuously for long periods of
                 time; and (6) Army officials modified the software, but
                 the new software did not reach Dhahran until the day
                 after the incident. \ldots{} The precision of a
                 computer's calculations depends on the number of bits
                 in its registers. Since the Patriot's registers are
                 only 24 bits long, precision beyond 24 bits is not
                 possible unless the software is specifically written to
                 adjust for such hardware limitations. Computers built
                 today have registers that contain as many as 64 bits,
                 permitting calculations with far greater precision.
                 \ldots{} During the conflict the Patriot's software was
                 modified six times. Patriots had to be shut down for at
                 least 1 to 2 hours to install each software
                 modification.",
  acknowledgement = ack-nhfb,
  remark =       "From the report: ``Because of the way the Patriot
                 computer performs its calculations and the fact that
                 its registers are only 24 bits long, the conversion of
                 time from an integer to a real number cannot be any
                 more precise than 24 bits. This conversion results in a
                 loss of precision causing a less accurate time
                 calculation. The effect of this inaccuracy on the range
                 gate's calculation is directly proportional to the
                 target's velocity and the length of time the system has
                 been running. Consequently, performing the conversion
                 after the Patriot has been running continuously for
                 extended periods causes the range gate to shift away
                 from the center of the target, making it less likely
                 that the target, in this case a Scud, will be
                 successfully intercepted. \ldots{} On February 25,
                 Alpha Battery had been in operation for over 100
                 consecutive hours. Because the system had been on so
                 long, the resulting inaccuracy in the time calculation
                 caused the range gate to shift so much that the system
                 could not track the incoming Scud. Consequently, Alpha
                 Battery did not engage the Scud, which then struck an
                 Army barracks and killed 28 American soldiers.''",
  xxremark =     "Report of integer overflow in a timer that made the
                 guidance system erroneous; the ultimate solution proved
                 to be to reboot the guidance computer every few hours,
                 before the overflow.",
}

@Article{Bohlender:1992:PAF,
  author =       "G. Bohlender and D. Cordes and A. Kn{\"o}fel and U.
                 Kulisch and R. Lohner and W. V. Walter",
  title =        "Proposal for Accurate Floating-Point Vector
                 Arithmetic",
  journal =      j-MATH-SCI-ENG,
  volume =       "189",
  number =       "??",
  pages =        "87--104",
  year =         "1992",
  CODEN =        "MTSEAT",
  ISSN =         "0076-5392",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics in Science and Engineering",
}

@Article{Borwein:1992:MHP,
  author =       "Jonathan M. Borwein and Mark A. Limber",
  title =        "{Maple} as a High Precision Calculator",
  journal =      j-MAPLE-TECH-NEWS,
  volume =       "0",
  number =       "8",
  pages =        "39--44",
  month =        "Fall",
  year =         "1992",
  ISSN =         "1061-5733",
  ISSN-L =       "1061-5733",
  bibdate =      "Fri May 09 22:33:19 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-tech.bib",
  URL =          "http://www.can.nl/Systems_and_Packages/Per_Purpose/General/Maple/mtn/mtn8.html",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  fjournal =     "Maple technical newsletter",
  journal-URL =  "http://web.mit.edu/maple/www/plibrary/mtn.html",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}

@Article{Brosgol:1992:ADA,
  author =       "Benjamin M. Brosgol and Robert I. Eachus and David E.
                 Emery",
  title =        "An {Ada} Decimal Arithmetic Capability",
  journal =      "CrossTalk: The Journal of Defense Software
                 Engineering",
  volume =       "36",
  publisher =    "Software Technology Support Center",
  address =      "Hill AFB, Odgen, UT, USA",
  month =        sep,
  year =         "1992",
  bibdate =      "Fri Nov 28 16:01:38 2003",
  bibsource =    "http://www.stsc.hill.af.mil/crosstalk/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.iste.uni-stuttgart.de/ps/AdaBasis/pal_1195/ada/ajpo/work-grp/ev-team/ev-info/summary.txt",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
  pagecount =    "8 (approx)",
  xxCODEN =      "none",
  xxISSN =       "none",
}

@InProceedings{Brosgol:1992:DAA,
  author =       "Benjamin M. Brosgol and Robert I. Eachus and David E.
                 Emery",
  title =        "Decimal arithmetic in {Ada}",
  crossref =     "Katwijk:1992:AMT",
  pages =        "138--149",
  year =         "1992",
  DOI =          "https://doi.org/10.1007/3-540-55585-4_1",
  bibdate =      "Thu Aug 07 17:11:50 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@Article{Calvetti:1992:SRE,
  author =       "Daniela Calvetti",
  title =        "A Stochastic Roundoff Error Analysis for the
                 Convolution",
  journal =      j-MATH-COMPUT,
  volume =       "59",
  number =       "200",
  pages =        "569--582",
  month =        oct,
  year =         "1992",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65G05 (44A35 65T20)",
  MRnumber =     "93a:65061",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib;
                 JSTOR database; Theory/Matrix.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "C4190 (Other numerical methods); C4110 (Error analysis
                 in numerical methods)",
  corpsource =   "Dept. of Pure and Appl. Math., Stevens Inst. of
                 Technol., Hoboken, NJ, USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "accuracy; convolution; error analysis; fast Fourier
                 transforms; Radix-2 fast Fourier transforms; roundoff
                 errors; stochastic roundoff error analysis",
  kwds =         "nla, fft, convolution, rounding error, stochastic
                 analysis",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Clarkson:1992:SED,
  author =       "K. L. Clarkson",
  title =        "Safe and effective determinant evaluation",
  crossref =     "IEEE:1992:ASF",
  pages =        "387--395",
  year =         "1992",
  bibdate =      "Tue Nov 22 05:54:53 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}

@Article{Cosentino:1992:AMJ,
  author =       "R. J. Cosentino and J. J. Vaccaro",
  title =        "Adaptation of the {Mactaggart} and {Jack} Complex
                 Multiplication Algorithm for Floating-Point Operators",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "10",
  pages =        "1324--1326",
  month =        oct,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.166608",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=166608",
  abstract =     "With a suitable treatment of the exponents in the
                 input operands, a hardware implementation of the
                 Mactaggart and Jack fixed-point complex multiplication
                 algorithm can also calculate a floating-point product
                 with no loss in accuracy from the greater dynamic range
                 of the floating-point inputs. This floating-point
                 technique can be extended to any sum to two products
                 operation, such as encountered in matrix multiplication
                 and vector cross-products.",
  acknowledgement = ack-nhfb,
  affiliation =  "Mitre Corp., Bedford, MA, USA",
  ajournal =     "IEEE Trans. Comput.",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Floating-point operators; Hardware implementation;
                 Jack complex multiplication algorithm; Mactaggart
                 complex multiplication; Matrix multiplication; Vector
                 cross-products",
  summary =      "With a suitable treatment of the exponents in the
                 input operands, a hardware implementation of the
                 Mactaggart and Jack fixed-point complex multiplication
                 algorithm can also calculate a floating-point product
                 with no loss in accuracy from the greater \ldots{}",
  thesaurus =    "Digital arithmetic",
}

@Article{Dao-Trong:1992:SCI,
  author =       "S. Dao-Trong and K. Helwig",
  title =        "A single-chip {IBM System}\slash 390 floating-point
                 processor in {CMOS}",
  journal =      j-IBM-JRD,
  volume =       "36",
  number =       "4",
  pages =        "733--749",
  month =        jul,
  year =         "1992",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Wed Sep 7 22:32:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}

@Article{Dao-Trong:1992:SIS,
  author =       "S. Dao-Trong and K. Helwig",
  title =        "A single-chip {IBM} System\slash 390 floating-point
                 processor in {CMOS}",
  journal =      j-IBM-JRD,
  volume =       "36",
  number =       "4",
  pages =        "733--750",
  month =        jul,
  year =         "1992",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}

@Article{DaoTrong:1992:SIS,
  author =       "S. Dao-Trong and K. Helwig",
  title =        "A single-chip {IBM} system\slash 390 floating-point
                 processor in {CMOS}",
  journal =      j-IBM-JRD,
  volume =       "36",
  number =       "4",
  pages =        "733--749",
  month =        jul,
  year =         "1992",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A floating-point processor with the IBM System/390
                 architecture is implemented in one CMOS VLSI chip
                 containing over 70000 cells (equivalent inverters),
                 using a transistor channel length of 0.5 mu m. All
                 floating-point instructions are hard-wired, including
                 the binary integer multiplications. The chip is
                 implemented in a 1- mu m technology with three layers
                 of metal. All circuits are realized in standard cells
                 except for a floating-point register and a multiplier
                 array macro, which are custom designed to save chip
                 area. Instructions are performed in a five-stage
                 pipeline with a maximum operating frequency of 37 MHz.
                 The chip measures 12.7 mm*12.7 mm, and dissipates 2 W.
                 It is part of the chip set which forms the core of the
                 IBM Enterprise System/9000 Type 9221 entry-level
                 models.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Germany, Boeblingen, Germany",
  classification = "B1265F (Microprocessors and microcomputers); B2570D
                 (CMOS integrated circuits); C5130 (Microprocessor
                 chips); C5230 (Digital arithmetic methods)",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "37 MHz; Binary integer multiplications; Chip set;
                 CMOS; Equivalent inverters; Five-stage pipeline; IBM
                 Enterprise System/9000; Single-chip IBM system/390
                 floating-point processor; Transistor channel length",
  numericalindex = "Frequency 3.7E+07 Hz",
  thesaurus =    "CMOS integrated circuits; Digital arithmetic;
                 Equipment evaluation; IBM computers; Microprocessor
                 chips",
}

@MastersThesis{Daumas:1992:BIR,
  author =       "Marc Daumas",
  title =        "Basis for the implementation of a reliable dot
                 product",
  type =         "{Master}'s Thesis",
  school =       "Southern Methodist University",
  address =      "Dallas, Texas",
  year =         "1992",
  bibdate =      "Wed Nov 24 12:42:59 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Davarakis:1992:PPA,
  author =       "C. T. Davarakis and D. G. Maritsas",
  title =        "A Probabilistic Parallel Associative Search and Query
                 Set of Algorithms",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "14",
  number =       "1",
  pages =        "37--49",
  month =        jan,
  year =         "1992",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 19:06:31 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Computer Technology Inst",
  affiliationaddress = "Patras, Greece",
  classification = "723; 921; 922; C1230 (Artificial intelligence);
                 C4240P (Parallel programming and algorithm theory);
                 C5470 (Performance evaluation and testing); C7310
                 (Mathematics)",
  corpsource =   "Department of Comput. Eng., Comput. Technol. Inst.,
                 Patras, Greece",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "Algorithms; arithmetic applications; Associative
                 searching; Computer Programming; computing; Data
                 Storage, Digital--Associative; digital arithmetic;
                 extrema algorithm; extrema queries; generic associative
                 process; heuristic programming; heuristics; high
                 performance systems; Mathematical
                 Techniques--Heuristic; mathematics; multilayer
                 associative process; parallel algorithms; parallel
                 associative search; parallel threshold; performance
                 evaluation; Primitive algorithms; primitive algorithms;
                 probabilistic; Probability; query set of algorithms;
                 symbol manipulation; symbolic applications; threshold
                 searches; time performance",
  treatment =    "A Application; P Practical",
}

@InProceedings{Dawid:1992:BSC,
  author =       "H. Dawid and G. Fettweis",
  title =        "Bit-level systolic carry-save array division",
  crossref =     "IEEE:1992:GCG",
  pages =        "484--488 vol.1",
  year =         "1992",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A bit-level systolic carry-save division array that
                 allows bit-level pipelining, just as for carry-save
                 array multipliers, is presented. This architecture
                 leads to very fast, efficient and regular division
                 implementations as needed in digital signal processing
                 (DSP) applications such as speech processing or
                 cryptography. The architecture is very well suited for
                 integer division as well as for the division of
                 normalized fixed-point mantissas used in floating-point
                 number system implementations.",
  acknowledgement = ack-nhfb,
  affiliation =  "Aachen University of Technol., Germany",
  classification = "B1265B (Logic circuits); C5130 (Microprocessor
                 chips); C5230 (Digital arithmetic methods); C5260
                 (Digital signal processing)",
  keywords =     "Bit-level pipelining; Carry-save array multipliers;
                 Cryptography; Digital signal processing; DSP;
                 Floating-point number system; Integer division;
                 Normalized fixed-point mantissas; Speech processing;
                 Systolic carry-save array division",
  thesaurus =    "Digital arithmetic; Systolic arrays",
}

@InProceedings{Dawid:1992:VIC,
  author =       "H. Dawid and H. Meyr",
  booktitle =    "{[Proceedings] 1992 IEEE International Symposium on
                 Circuits and Systems}",
  title =        "{VLSI} implementation of the {CORDIC} algorithm using
                 redundant arithmetic",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1089--1092 (vol. 3)",
  year =         "1992",
  DOI =          "https://doi.org/10.1109/ISCAS.1992.230290",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Arithmetic; Circuits; Clocks; Computer architecture;
                 Delay; Force control; Frequency; Signal processing
                 algorithms; Throughput; Very large scale integration",
}

@Article{Dawson:1992:RLS,
  author =       "Jeffrey Dawson and Mary Payne and Craig Schaffert",
  title =        "The Role of {LIA-1} in Software Portability",
  journal =      j-SIGNUM,
  volume =       "27",
  number =       "4",
  pages =        "9--12",
  month =        oct,
  year =         "1992",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:22 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "LIA is now an International Standard, ISO/IEC
                 10967-1:1994; it is ``92 pages of small print, densely
                 mathematical, not counting 8 pages of front matter, and
                 it is not available electronically.'' Its adoption has
                 been rather controversial.",
  abstract =     "The second committee draft of language independent
                 arithmetic-Part 1: Integer and floating point
                 arithmetic is now available. This document was formerly
                 called the Language Compatible Arithmetic Standard
                 (LCAS) and is now referred to as LIA-1. This draft was
                 prepared by ISO/IEC JTC1/SC22/WG11, with assistance
                 from standards committees in several countries. The
                 authors explain the goals of the standard and methods
                 for achieving those goals. They present them to clear
                 up previous misunderstandings, misconceptions, and
                 misrepresentations of the purpose of the standard. (0
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "Digital Equipment Corp., Maynard, MA, USA",
  classification = "C0310F (Software development management); C6110B
                 (Software engineering techniques); C7310
                 (Mathematics)",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "Floating point arithmetic; Integer arithmetic; ISO/IEC
                 JTC1/SC22/WG11; Language independent arithmetic; LIA-1;
                 Software portability; Standard",
  thesaurus =    "Mathematics computing; Software portability;
                 Standards",
}

@Book{DEC:1992:AAH,
  author =       "Digital Equipment Corporation",
  title =        "{Alpha} Architecture Handbook",
  publisher =    pub-DP,
  address =      pub-DP:adr,
  year =         "1992",
  bibdate =      "Mon Jan 18 15:08:40 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Demmel:1992:LWN,
  author =       "James Demmel",
  title =        "{LAPACK} working note 49 draft: a specification for
                 floating point parallel prefix",
  type =         "Technical report",
  number =       "CS-92-167",
  institution =  "University of Tennessee, Computer Science Dept.",
  address =      "Knoxville, TN, USA",
  pages =        "8 + 1",
  month =        may,
  year =         "1992",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Parallel prefix is a useful operation for various
                 linear algebra operations, including solving bidiagonal
                 systems of equations and finding the eigenvalues of a
                 symmetric tridiagonal matrix. However, the simplest
                 implementations of parallel prefix for the operations
                 of scalar floating point add and scalar floating point
                 multiply are inadequate to solve these important
                 problems. This is because they are too susceptible to
                 over/underflow, and because they apparently cannot
                 solve the general two term recurrence needed to find
                 eigenvalues. In this note we propose a specification
                 for parallel prefix operations overcoming these
                 drawbacks.",
  acknowledgement = ack-nhfb,
  keywords =     "Linear algebraic groups.",
}

@TechReport{Demmel:1992:SFP,
  author =       "J. Demmel",
  title =        "A Specification for Floating Point Parallel Prefix",
  type =         "LAPACK Working Note",
  number =       "49",
  institution =  inst-UT-CS,
  address =      inst-UT-CS:adr,
  month =        may,
  year =         "1992",
  bibdate =      "Fri Apr 22 17:06:37 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "UT-CS-92-167, May 1992.",
  URL =          "http://www.netlib.org/lapack/lawns/lawn49.ps;
                 http://www.netlib.org/lapack/lawnspdf/lawn49.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Devine:1992:RTT,
  author =       "M. L. Devine",
  title =        "Real time trigonometric function evaluation",
  journal =      j-MICROPROC-MICROSYS,
  volume =       "16",
  number =       "8",
  pages =        "417--425",
  month =        aug,
  year =         "1992",
  CODEN =        "MIMID5",
  ISSN =         "0141-9331 (print), 1872-9436 (electronic)",
  ISSN-L =       "0141-9331",
  bibdate =      "Thu Sep 1 10:16:09 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Microprocessors and Microsystems",
}

@Article{Dimauro:1992:NMF,
  author =       "G. Dimauro and S. Impedovo and G. Pirlo",
  title =        "A new magnitude function for fast numbers comparison
                 in the residue number system",
  journal =      j-MICROPROC-MICROPROG,
  volume =       "35",
  number =       "1--2",
  pages =        "97--104",
  month =        sep,
  year =         "1992",
  CODEN =        "MMICDT",
  DOI =          "https://doi.org/10.1016/0165-6074(92)90300-V",
  ISSN =         "0165-6074 (print), 1878-7061 (electronic)",
  ISSN-L =       "0165-6074",
  bibdate =      "Thu Nov 18 09:52:10 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this paper a new magnitude function, called the
                 `diagonal function', has been defined from a Residue
                 Number System to the integers. The `diagonal function'
                 provides an efficient technique for fast magnitude
                 comparison of numbers in the residue representation.
                 The superiority of this technique with respect to the
                 approaches based on the Chinese Remainder Theorem and
                 on the Mixed Radix Transformation is shown.",
  acknowledgement = ack-nhfb,
  fjournal =     "Microprocessing and Microprogramming",
  journal-URL =  "https://www.sciencedirect.com/journal/microprocessing-and-microprogramming/issues",
}

@MastersThesis{Du:1992:CAB,
  author =       "Sihai Du",
  title =        "Cellular automata based floating-point adder and
                 multiplier with a single transition rule",
  type =         "Thesis ({M.S.C.E.})",
  school =       "Wright State University",
  address =      "Dayton, OH, USA",
  pages =        "ix + 68",
  year =         "1992",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Cellular automata --- Research.; Computer Simulation.;
                 Floating-point arithmetic --- Research.",
}

@Article{Dunham:1992:SFW,
  author =       "Charles B. Dunham",
  title =        "Surveyor's Forum: {``What Every Computer Scientist
                 Should Know About Floating-Point Arithmetic''}",
  journal =      j-COMP-SURV,
  volume =       "24",
  number =       "3",
  pages =        "319--319",
  month =        sep,
  year =         "1992",
  CODEN =        "CMSVAN",
  ISSN =         "0360-0300 (print), 1557-7341 (electronic)",
  ISSN-L =       "0360-0300",
  bibdate =      "Sun Sep 25 10:14:37 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compsurv.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See
                 \cite{Goldberg:1991:WEC,Goldberg:1991:CWE,Wichmann:1992:SFW}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J204",
}

@InProceedings{Duprat:1992:DOF,
  author =       "J. Duprat and M. Fiallos-Aguilar and Jean-Michel
                 Muller and H. J. Yeh",
  title =        "Delays of on-line floating point operators in
                 borrow-save representation",
  crossref =     "Quinton:1992:APV",
  pages =        "273--278",
  year =         "1992",
  bibdate =      "Wed Dec 13 13:13:34 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "On-line computation using redundant notations to
                 represent numbers is an interesting field of computer
                 arithmetic. In these systems, different operators can
                 operate together in a digit level pipelining mode. In
                 integer or fixed-point format, implementations of the
                 main operations have been proposed. This paper focuses
                 on a floating point format. The authors show that, more
                 so in addition than in multiplication, critical loss of
                 information due to the variation of the length of the
                 mantissas can be avoided by partial normalizations.
                 Furthermore, these normalizations do not break the
                 circulation of the digit though they do delay the
                 operations even more.",
  acknowledgement = ack-nhfb,
  affiliation =  "Ecole Normale Superieure de Lyon, France",
  classification = "C5230 (Digital arithmetic methods); C5440
                 (Multiprocessor systems and techniques)",
  keywords =     "Borrow-save representation; Computer arithmetic;
                 Delays; Digit level pipelining mode; Floating point
                 format; Mantissas; On-line floating point operators;
                 Partial normalizations; Redundant notations",
  thesaurus =    "Delays; Digital arithmetic; Pipeline processing",
}

@Article{Duprat:1992:SPF,
  author =       "J. Duprat and M. Fiallos Aguilar",
  title =        "On the Simulation of Pipelining of Fully Digit On-Line
                 Floating-Point Adder Networks on Massively Parallel
                 Computers",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "??",
  number =       "634",
  pages =        "707--712",
  year =         "1992",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Ercegovac:1992:FRC,
  author =       "M. D. Ercegovac and T. Lang",
  title =        "On-the-fly rounding [computing arithmetic]",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "12",
  pages =        "1497--1503",
  month =        dec,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.214659",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:21 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=214659",
  abstract =     "In implementations of operations based on
                 digit-recurrence algorithms such as division,
                 left-to-right multiplication and square root, the
                 result is obtained in digit-serial form, from most
                 significant digit to least significant. To reduce the
                 complexity of the result-digit selection and allow the
                 use of redundant addition, the result-digit has values
                 from a signed-digit set. As a consequence, the result
                 has to be converted to conventional representation,
                 which can be done on-the-fly as the digits are
                 produced, without the use of a carry-propagate adder.
                 The authors describe three ways to modify this
                 conversion process so that the result is rounded. The
                 resulting operation is fast because no carry-propagate
                 addition is needed. The schemes described apply also to
                 online arithmetic operations.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Fagin:1992:LIM,
  author =       "Barry S. Fagin",
  title =        "Large Integer Multiplication on Hypercubes",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "14",
  number =       "4",
  pages =        "426--430",
  month =        apr,
  year =         "1992",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Apr 12 17:13:17 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C4230M (Multiprocessor interconnection); C4240P
                 (Parallel programming and algorithm theory); C5230
                 (Digital arithmetic methods)",
  corpsource =   "Thayer Sch. of Eng., Dartmouth Coll., Hanover, NH,
                 USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "Connection Machine; digital arithmetic; Fermat Number
                 Transform; hypercube networks; hypercubes; integer
                 multiplication; parallel algorithms; polynomial
                 transforms; transforms",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Filanovsky:1992:SCA,
  author =       "I. M. Filanovsky and H. P. Baltes",
  title =        "Simple {CMOS} analog square-rooting and squaring
                 circuits",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-I-FUNDAM-THEORY-APPL,
  volume =       "39",
  number =       "4",
  pages =        "312--315",
  month =        apr,
  year =         "1992",
  CODEN =        "ITCAEX",
  ISSN =         "1057-7122 (print), 1558-1268 (electronic)",
  ISSN-L =       "1057-7122",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems I:
                 Fundamental Theory and Applications",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=81",
  summary =      "Two closely related CMOS circuits are described. In
                 the first circuit, the input signal is a current, and
                 the output is a voltage proportional to the square root
                 of input current. In the second circuit, the input is a
                 voltage, and the output is the \ldots{}",
}

@Article{Fujii:1992:FCL,
  author =       "H. Fujii and C. Hori and T. Takada and N. Hatanaka and
                 T. Demura and G. Ootomo",
  title =        "A Floating-Point Cell Library and a {100-MFLOPS} Image
                 Signal Processor",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "27",
  number =       "7",
  pages =        "1080--1088",
  month =        jul,
  year =         "1992",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
}

@Article{Fujii:1992:FPC,
  author =       "H. Fujii and C. Hori and T. Takada and N. Hatanaka and
                 T. Demura and G. Ootomo",
  title =        "A floating-point cell library and a {100-Mflops} image
                 signal processor",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "27",
  number =       "7",
  pages =        "1080--1088",
  month =        jul,
  year =         "1992",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "A novel floating-point cell library for image signal
                 processors that includes a floating-point arithmetic
                 logic unit (ALU), a floating-point multiplier (MPY), an
                 instruction RAM, and a data register file is
                 considered. It has been designed for high-speed
                 \ldots{}",
}

@Article{Gamberger:1992:IIM,
  author =       "D. Gamberger",
  title =        "Inversion of integer matrices in residue number
                 system",
  journal =      j-IEE-PROC-COMPUT-DIGIT-TECH,
  volume =       "139",
  number =       "5",
  pages =        "465--468",
  month =        sep,
  year =         "1992",
  CODEN =        "ICDTEA",
  DOI =          "https://doi.org/10.1109/78.157231",
  ISSN =         "1350-2387 (print), 1359-7027 (electronic)",
  ISSN-L =       "1350-2387",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4186",
  acknowledgement = ack-nhfb,
  fjournal =     "IEE Proceedings. Computers and Digital Techniques",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The presented algorithm makes use of the recently
                 introduced incompletely specified residue number
                 system. This system enables the operations necessary in
                 the inversion process to be done quickly, completely in
                 parallel for different moduli, even if \ldots{}",
}

@Article{Goldberg:1992:DFD,
  author =       "D. Goldberg",
  title =        "The design of floating-point data types",
  journal =      j-LOPLAS,
  volume =       "1",
  number =       "2",
  pages =        "138--151",
  month =        jun,
  year =         "1992",
  CODEN =        "ALPSE8",
  ISSN =         "1057-4514 (print), 1557-7384 (electronic)",
  ISSN-L =       "1057-4514",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The issues involved in designing the floating-point
                 part of a programming language are discussed. Looking
                 at the language specifications for most existing
                 languages might suggest that this design involves only
                 trivial issues, such as whether to have one or two
                 types of REALs or how to name the functions that
                 convert from INTEGER to REAL. It is shown that there
                 are more significant semantic issues involved. After
                 discussing the tradeoffs for the major design
                 decisions, they are illustrated by presenting the
                 design of the floating-point part of the Modula-3
                 language.",
  acknowledgement = ack-nhfb,
  affiliation =  "Xerox Palo Alto Res. Center, CA, USA",
  classification = "C6120 (File organisation)",
  fjournal =     "ACM Letters on Programming Languages and Systems",
  keywords =     "Design; Floating-point data types; Language
                 specifications; Modula-3 language; Programming
                 language; REALs",
  thesaurus =    "Data structures; Digital arithmetic",
}

@Article{Gray:1992:UMF,
  author =       "A. Gray and R. Knill",
  title =        "Using {Mathematica} to Find Closed Form Expressions
                 for Approximations to the Square Root of $x$",
  journal =      j-MATHEMATICA-EDUC,
  volume =       "1",
  number =       "4",
  pages =        "12--13",
  month =        "Summer",
  year =         "1992",
  ISSN =         "1065-2965",
  bibdate =      "Sat Apr 6 16:22:43 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-ble,
  fjournal =     "Mathematica in Education",
}

@InProceedings{Hartwig:1992:AFQ,
  author =       "F. Hartwig and A. Lacroix",
  title =        "Analysis of floating-point quantization errors using
                 stochastic models",
  crossref =     "Vandewalle:1992:SPV",
  pages =        "247--250 vol.1",
  year =         "1992",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Some results concerning the single quantizer with
                 limited exponent wordlength are presented. In addition
                 to roundoff, the authors present a generalization for
                 magnitude truncation. The method is also applied to
                 digital filters. The theoretical results are tested in
                 comparison with simulation results.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Angewandte Phys., J. W. Goethe-University,
                 Frankfurt am Main, Germany",
  classification = "B0240Z (Other and miscellaneous); B0290B (Error
                 analysis in numerical methods); B1265H (A/D and D/A
                 convertors); B6140 (Signal processing and detection);
                 C1140Z (Other and miscellaneous); C5230 (Digital
                 arithmetic methods); C5240 (Digital filters)",
  keywords =     "Digital filters; Digital signal processing devices;
                 Floating-point quantization errors; Limited exponent
                 wordlength; Magnitude truncation; Roundoff; Simulation
                 results; Stochastic models; Theoretical results",
  thesaurus =    "Analogue-digital conversion; Digital arithmetic;
                 Digital filters; Error analysis; Signal processing;
                 Stochastic processes",
}

@InProceedings{Hartwig:1992:MFA,
  author =       "F. Hartwig and A. Lacroix",
  title =        "Multi-operand floating-point addition utilizing
                 operand sorting",
  crossref =     "White:1992:IIS",
  pages =        "1800--1803 vol.4",
  year =         "1992",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In many signal processing applications repeated
                 additions have to be calculated with a considerable
                 number of operands. It is known that proper sorting of
                 operands has a positive influence on the precision of
                 the result of multioperand floating-point additions.
                 This is investigated for different operand statistics
                 and for proper sorting strategies. In addition to
                 successive addition techniques, adder trees are
                 included in the investigation. The densities of the
                 addition errors for different floating-point addition
                 methods are compared.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fuer Angewandte Phys., J. W. Goethe-University,
                 Frankfurt am Main, Germany",
  classification = "C1260 (Information theory); C5230 (Digital
                 arithmetic methods); C5260 (Digital signal processing);
                 C6130 (Data handling techniques)",
  keywords =     "Adder trees; Addition errors densities; Floating-point
                 addition; Floating-point addition methods; Multioperand
                 floating-point additions; Operand sorting; Operand
                 statistics; Repeated additions; Signal processing;
                 Sorting strategies; Successive addition techniques",
  thesaurus =    "Digital arithmetic; Signal processing; Sorting",
}

@Article{Hasan:1992:BSS,
  author =       "M. A. Hasan and V. K. Bhargava",
  title =        "Bit-serial systolic divider and multiplier for finite
                 fields {$ \mathrm {GF}(2^m) $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "972--980",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156540",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156540",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Hasan:1992:MCL,
  author =       "M. A. Hasan and M. Wang and V. K. Bhargava",
  title =        "Modular construction of low complexity parallel
                 multipliers for a class of finite fields {$ \mathrm
                 {GF}(2^m) $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "962--971",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156539",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156539",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Hegeman:1992:AF,
  author =       "Frederick W. Hegeman",
  title =        "Arithmetic In Factorial-Base",
  journal =      j-CUJ,
  volume =       "10",
  number =       "2",
  pages =        "73--??",
  month =        feb,
  year =         "1992",
  ISSN =         "0898-9788",
  bibdate =      "Fri Aug 30 16:52:23 MDT 1996",
  bibsource =    "http://www.cuj.com/cbklist.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "C Users Journal",
}

@Article{Hoehfeld:1992:LLN,
  author =       "M. Hoehfeld and S. E. Fahlman",
  title =        "Learning with limited numerical precision using the
                 cascade-correlation algorithm",
  journal =      j-IEEE-TRANS-NEURAL-NETW,
  volume =       "3",
  number =       "4",
  pages =        "602--611",
  month =        jul,
  year =         "1992",
  CODEN =        "ITNNEP",
  DOI =          "https://doi.org/10.1109/72.143374",
  ISSN =         "1045-9227 (print), 1941-0093 (electronic)",
  ISSN-L =       "1045-9227",
  bibdate =      "Fri Sep 22 17:49:00 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Neural Networks",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=72",
}

@InProceedings{Hoff:1992:FCH,
  author =       "J. R. Hoff and G. W. Foster",
  title =        "A full custom, high speed, floating point adder",
  crossref =     "Alley:1992:CRI",
  pages =        "450 vol.1",
  year =         "1992",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Summary form only. A high-speed pipelined floating
                 point adder for use by the Solenoidal Detector
                 Collaboration (SDC) at the Superconducting Super
                 Collider (SSC) is discussed. The adder uses a unique
                 floating point format. The chip is designed to be a
                 two-stage pipeline and to operate at a peak speed of at
                 least 63 MHz. Static rather than dynamic logic was
                 desired, to permit operation at lower speeds and to
                 ease system testing. The chip is implemented using
                 Orbit Semiconductor's 1.2 mu m n-well process.
                 Simulations indicate that the device will operate at 63
                 MHz. Initial testing performed at Fermilab, limited by
                 test equipment, indicates speeds of at least 63 MHz,
                 with some tests demonstrating speeds in excess of 150
                 MHz.",
  acknowledgement = ack-nhfb,
  affiliation =  "Fermilab, Batavia, IL, USA",
  classification = "A2980C (Computer systems); B1265B (Logic circuits);
                 B7430 (Counting circuits and electronics); C5120 (Logic
                 and switching circuits); C5230 (Digital arithmetic
                 methods); C7320 (Physics and Chemistry)",
  keywords =     "150 MHz; 63 MHz; Fermilab; Floating point adder; High
                 speed; Orbit Semiconductor; Pipelined; SDC; Simulation;
                 Static logic; System testing; Testing; Two-stage
                 pipeline",
  numericalindex = "Frequency 6.3E+07 Hz; Frequency 1.5E+08 Hz",
  thesaurus =    "Adders; Digital arithmetic; Nuclear electronics;
                 Physics computing; Pipeline processing",
}

@Article{Hohfeld:1992:PRN,
  author =       "Markus H{\"o}hfeld and Scott E. Fahlman",
  title =        "Probabilistic rounding in neural network learning with
                 limited precision",
  journal =      j-NEUROCOMPUTING,
  volume =       "4",
  number =       "6",
  pages =        "291--299",
  month =        dec,
  year =         "1992",
  CODEN =        "NRCGEO",
  DOI =          "https://doi.org/10.1016/0925-2312(92)90014-g",
  ISSN =         "0925-2312 (print), 1872-8286 (electronic)",
  ISSN-L =       "0925-2312",
  bibdate =      "Fri Sep 22 17:46:22 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Neurocomputing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/09252312",
}

@Article{Horiguchi:1992:FNR,
  author =       "Hiroshi Horiguchi and Tsutomu Tayama",
  title =        "Floating-Point Numbers and Real Numbers {II}",
  journal =      j-ADV-SOFT-SCI-TECH,
  volume =       "3",
  number =       "??",
  pages =        "151--156",
  year =         "1992",
  ISSN =         "1044-7997",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Advances in software science and technology",
}

@MastersThesis{Hoyt:1992:MFP,
  author =       "Brian S. Hoyt",
  title =        "The {Macintosh} floating point arithmetic
                 visualization system",
  type =         "Thesis ({M.S.--Electrical Engineering})",
  school =       "Bucknell University",
  address =      "Lewisburg, PA, USA",
  pages =        "ix + 88",
  year =         "1992",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Supervised by Richard J. Zaccone. Describes the
                 design, development, implementation, and use of MacFavs
                 (Macintosh Floating point arithmetic visualization
                 system). MacFavs uses simulation, visual displays, and
                 animations to allow students to see actual machine
                 representations of floating point numbers.",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Macintosh (Computer);
                 Numerical analysis --- Computer-assisted instruction.",
}

@Article{Hudak:1992:RPL,
  author =       "Paul Hudak and Simon Peyton Jones and Philip Wadler
                 and Brian Boutel and Jon Fairbairn and Joseph Fasel and
                 Mar{\'\i}a M. Guzm{\'a}n and Kevin Hammond and John
                 Hughes and Thomas Johnsson and Dick Kieburtz and
                 Rishiyur Nikhil and Will Partain and John Peterson",
  title =        "Report on the programming language {Haskell}: a
                 non-strict, purely functional language (Version 1.2)",
  journal =      j-SIGPLAN,
  volume =       "27",
  number =       "5",
  pages =        "Ri--Rx, R1--R163",
  month =        may,
  year =         "1992",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:16:21 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Haskell is a general purpose, purely functional
                 programming language incorporating many recent
                 innovations in programming language research, including
                 higher-order functions, non-strict semantics, static
                 polymorphic typing, user-defined algebraic datatypes,
                 pattern-matching, list comprehensions, a module system,
                 and a rich set of primitive datatypes, including lists,
                 arrays, arbitrary and fixed precision integers, and
                 floating-point numbers. Haskell is both the culmination
                 and solidification of many years of research on
                 functional languages-the design has been influenced by
                 languages as old as ISWIM and as new as Miranda. The
                 report defines the syntax for Haskell programs and an
                 informal abstract semantics for the meaning of such
                 programs.",
  acknowledgement = ack-nhfb,
  affiliation =  "Yale University, New Haven, CT, USA",
  classification = "C6140D (High level languages)",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "Abstract semantics; Arrays; Fixed precision integers;
                 Floating-point numbers; Functional programming
                 language; Haskell; Higher-order functions; List
                 comprehensions; Lists; Module system; Non-strict
                 semantics; Pattern-matching; Primitive datatypes;
                 Static polymorphic typing; Syntax; User-defined
                 algebraic datatypes",
  thesaurus =    "Functional programming; High level languages",
}

@Article{IFIF:1992:CVD,
  author =       "{IFIP Working Group 2.5 (Numerical Software)}",
  title =        "Comments on version 3.1 of draft {ISO\slash IEC
                 10967:1991 Language Compatible Arithmetic}",
  journal =      j-SIGNUM,
  volume =       "27",
  number =       "1",
  pages =        "2--3",
  month =        jan,
  year =         "1992",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:21 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}

@InProceedings{Jackson:1992:DTF,
  author =       "P. B. Jackson",
  title =        "Developing a toolkit for floating-point hardware in
                 the {Nuprl} proof development system",
  crossref =     "Prinetto:1992:CHD",
  pages =        "401--419",
  year =         "1992",
  bibdate =      "Wed Dec 13 13:13:34 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Describes current work in building a toolkit of
                 theorems, definitions and tactics in the Nuprl proof
                 development system for the verification of
                 floating-point hardware designs. The approach
                 emphasizes reasoning over a wide range of levels of
                 abstraction within a single system. For example the
                 specification of the IEEE's floating point standard
                 makes free use of rational arithmetic, as well as
                 talking explicitly about the input and output
                 bit-vectors of floating-point circuits.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, Cornell University,
                 Ithaca, NY, USA",
  classification = "C4210 (Formal logic); C5230 (Digital arithmetic
                 methods); C6110B (Software engineering techniques);
                 C6115 (Programming support)",
  keywords =     "Floating-point hardware; Nuprl proof development
                 system; Rational arithmetic; Reasoning; Toolkit;
                 Verification",
  thesaurus =    "Digital arithmetic; Formal specification; Software
                 tools; Theorem proving",
}

@Article{Jacobson:1992:ETF,
  author =       "David Jacobson",
  title =        "Engineer's Toolbox: Floating Point in {Mathematica}",
  journal =      j-MATHEMATICA-J,
  volume =       "2",
  number =       "3",
  pages =        "42--46",
  month =        "Summer",
  year =         "1992",
  CODEN =        "????",
  ISSN =         "1047-5974 (print), 1097-1610 (electronic)",
  ISSN-L =       "1047-5974",
  bibdate =      "Sat Nov 6 13:33:40 MDT 2010",
  bibsource =    "http://www.mathematica-journal.com/issue/v2i3/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mathematica-journal.com/issue/v2i3/tutorials/toolbox/index.html",
  abstract =     "Mathematica provides both traditional machine-level
                 floating point numbers and software-implemented
                 variable-precision floating-point numbers. There are
                 two different notions of precision: an estimate of the
                 maximum possible relative error, which is propagated
                 through arithmetic operations based on the precision of
                 the operands; and the number of digits used to
                 represent the significand (mantissa). Mathematica links
                 the first notion to the second, throwing away digits
                 that it cannot prove are significant. In iterative
                 calculations the precision can ratchet down a little
                 each iteration, until there is nothing left.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematica Journal",
  journal-URL =  "http://www.mathematica-journal.com/",
}

@Article{Jaffar:1992:AMC,
  author =       "Joxan Jaffar and Peter J. Stuckey and Spiro Michaylov
                 and Roland H. C. Yap",
  title =        "An abstract machine for {CLP$ (\mathcal {R}) $}",
  journal =      j-SIGPLAN,
  volume =       "27",
  number =       "7",
  pages =        "128--139",
  month =        jul,
  year =         "1992",
  CODEN =        "SINODQ",
  ISBN =         "0-89791-475-9",
  ISBN-13 =      "978-0-89791-475-8",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  LCCN =         "QA76.7.S53 1992",
  bibdate =      "Sun Dec 14 09:16:22 MST 2003",
  bibsource =    "Compendex database; http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/proceedings/pldi/143095/index.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/pldi/143095/p128-jaffar/",
  abstract =     "An abstract machine is described for the CLP$
                 (\mathcal {R}) $ programming language. It is intended
                 as a first step toward enabling CLP$ (\mathcal {R}) $
                 programs to be executed with efficiency approaching
                 that of conventional languages. The core Constraint
                 Logic Arithmetic Machine (CLAM) extends the Warren
                 Abstract Machine (WAM) for compiling Prolog with
                 facilities for handling real arithmetic constraints.
                 The full CLAM includes facilities for taking advantage
                 of information obtained from global program analysis.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM T. J. Watson Research Cent",
  affiliationaddress = "Yorktown Heights, NY, USA",
  annote =       "Published as part of the Proceedings of PLDI'92.",
  classification = "723.1",
  conference =   "Proceedings of the ACM SIGPLAN '92 Conference on
                 Programming Language Design and Implementation",
  conferenceyear = "1992",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  journalabr =   "SIGPLAN Not",
  keywords =     "Abstract machine; algorithms; Computer programming;
                 Computer programming languages; Constraint logic
                 arithmetic machine; design; Global program analysis;
                 languages; Program compilers; prolog (programming
                 language)",
  meetingaddress = "San Francisco, CA, USA",
  meetingdate =  "Jun 17--19 1992",
  meetingdate2 = "06/17--19/92",
  sponsor =      "ACM",
  subject =      "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Prolog. {\bf D.1.6} Software,
                 PROGRAMMING TECHNIQUES, Logic Programming. {\bf D.3.3}
                 Software, PROGRAMMING LANGUAGES, Language Constructs
                 and Features, Data types and structures. {\bf D.3.4}
                 Software, PROGRAMMING LANGUAGES, Processors,
                 Optimization.",
}

@InProceedings{Jain:1992:AEA,
  author =       "V. K. Jain and G. E. Perez and E. E. Swartzlander",
  title =        "Arithmetic Error Analysis of a New Reciprocal Cell",
  crossref =     "IEEE:1992:IIC",
  pages =        "106--109",
  year =         "1992",
  bibdate =      "Thu Sep 08 00:34:18 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@MastersThesis{James:1992:DRC,
  author =       "Shelton L. James",
  title =        "A distributed remote computational server",
  type =         "Thesis ({M.S.})",
  school =       "University of Missouri, Columbia",
  address =      "Columbia, MO, USA",
  pages =        "vi + 183",
  year =         "1992",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Distributed operating systems (Computers); Electronic
                 networks.; Floating-point systems.; OSI (Computer
                 network standard)",
}

@InProceedings{Johnstone:1992:RNA,
  author =       "P. Johnstone and F. E. Petry",
  title =        "Rational number approximation in higher radix floating
                 point systems",
  crossref =     "IEEE:1992:PIS",
  pages =        "501--504 vol.2",
  year =         "1992",
  bibdate =      "Wed Dec 13 13:13:34 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Recent research has shown that hybrid non-binary
                 floating point bases, particularly decimal-based
                 systems, can match or exceed the error performance of
                 more traditional binary systems. The authors address a
                 more general question of whether such bases offer any
                 further advantages in the domain of rational number
                 approximation. They consider the effect of the choice
                 of floating point base on rational number approximation
                 in systems which exhibit the typical characteristics of
                 floating point representations, normalized encodings,
                 limited exponent range, and storage allocated in a
                 fixed number of bits per datum. The frequency with
                 which terminating and representable results can be
                 expected is considered for binary, decimal, and other
                 potentially interesting bases (base 30 and base 210).",
  acknowledgement = ack-nhfb,
  affiliation =  "Telerate Syst. Inc., New Orleans, LA, USA",
  classification = "C5230 (Digital arithmetic methods)",
  keywords =     "Base 10; Base 2; Base 210; Base 30; Bits per datum;
                 decimal floating-point arithmetic; Error performance;
                 Floating point representations; Fractions; Higher radix
                 floating point systems; Limited exponent range;
                 Normalized encodings; Rational number approximation;
                 Storage allocated",
  thesaurus =    "Digital arithmetic",
}

@Article{Kahan:1992:ARL,
  author =       "W. Kahan",
  title =        "Analysis and Refutation of the {LCAS}",
  journal =      j-SIGPLAN,
  volume =       "27",
  number =       "1",
  pages =        "61--74",
  month =        jan,
  year =         "1992",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Thu Aug 18 02:37:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "LCAS (Language Compatible Arithmetic Standard)",
}

@Unpublished{Kahan:1992:FPE,
  author =       "W. Kahan",
  title =        "Floating-Point Exception-Handling",
  institution =  inst-BERKELEY-CS,
  address =      inst-BERKELEY-CS:adr,
  pages =        "2",
  day =          "31",
  month =        jul,
  year =         "1992",
  bibdate =      "Mon Apr 25 18:24:02 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Manuscript",
  acknowledgement = ack-nhfb,
}

@Article{Kahaner:1992:SJC,
  author =       "D. K. Kahaner and U. Wattenberg",
  title =        "{Supercomputing-Japan}: a competitive assessment",
  journal =      j-IEEE-SPECTRUM,
  volume =       "29",
  number =       "9",
  pages =        "42--47",
  month =        sep,
  year =         "1992",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/6.155708",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Thu Jan 16 07:37:23 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/super.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "5 to 8 GFLOPS; Arithmetic; Central Processing Unit;
                 Computer industry; Hardware; high-speed single
                 processor systems; Home computing; Information
                 technology; intuitive information processing; Japanese
                 supercomputers; Manufacturing industries; Ministry of
                 International Trade and Industry; National electric
                 code; parallel machines; Real-World Computing Program;
                 research initiatives; Supercomputers; Telephony; US
                 machines; vector processing functions",
}

@InProceedings{Kalliojarvi:1992:DRN,
  author =       "K. Kalliojarvi and Y. Neuvo",
  title =        "Distribution of roundoff noise in binary
                 floating-point addition",
  crossref =     "White:1992:IIS",
  volume =       "4",
  bookpages =    "3028",
  pages =        "1796--1799",
  year =         "1992",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A method for deriving the distribution of relative
                 round off error in addition of two binary
                 floating-point numbers is introduced. The distribution
                 is needed in the calculation of variance of the
                 relative roundoff error in floating-point addition. The
                 resulting distribution depends on the statistics of the
                 addends and the rounding strategy chosen. As an
                 example, the distribution is derived for the addition
                 of two uncorrelated numbers from Gaussian distribution.
                 The result was verified by simulation.",
  acknowledgement = ack-nhfb,
  affiliation =  "Signal Process. Lab., Tampere University of Technol.,
                 Finland",
  classification = "C1260 (Information theory); C5230 (Digital
                 arithmetic methods); C5260 (Digital signal
                 processing)",
  keywords =     "Addends; Binary floating-point addition; Calculation
                 of variance; Distribution of relative round off error;
                 Gaussian distribution; Relative roundoff error;
                 Rounding strategy; Roundoff noise; Simulation; Two
                 uncorrelated numbers",
  thesaurus =    "Digital arithmetic; Digital simulation; Roundoff
                 errors; Signal processing",
}

@Book{Kane:1992:MRA,
  author =       "Gerry Kane and Joe Heinrich",
  title =        "{MIPS RISC} Architecture",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  year =         "1992",
  ISBN =         "0-13-590472-2",
  ISBN-13 =      "978-0-13-590472-5",
  LCCN =         "QA76.8.M52 K37 1992",
  bibdate =      "Wed Dec 15 10:35:45 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/microchip.bib",
  acknowledgement = ack-nhfb,
  keywords =     "computer architecture; MIPS R2000 series
                 microprocessors; reduced instruction set computers",
  tableofcontents = "RISC Architecture: An Overview \\
                 MIPS Processor Architecture Overview \\
                 CPU Instruction Set Summary \\
                 Memory Management System \\
                 Caches \\
                 Exception Processing \\
                 FPU Overview \\
                 FPU Instruction Set Summary and Instruction Pipeline
                 \\
                 Floating Point Exceptions \\
                 Appendixes \\
                 Index",
}

@Book{Klatte:1992:PXP,
  author =       "Rudi Klatte and Ulrich Kulisch and Michael Neaga and
                 Dietmar Ratz and Christian Ullrich",
  title =        "{PASCAL-XSC}: language reference with examples",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 344",
  year =         "1992",
  DOI =          "https://doi.org/10.1007/978-3-642-77277-1",
  ISBN =         "3-540-55137-9 (Berlin), 0-387-55137-9 (New York)",
  ISBN-13 =      "978-3-540-55137-9 (Berlin), 978-0-387-55137-1 (New
                 York)",
  LCCN =         "QA76.73.P2 P4213 1992",
  bibdate =      "Thu Jan 21 17:16:51 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Translated by G. F. Corliss and others.",
  price =        "DM 64.00",
  abstract =     "The programming language PASCAL-XSC (PASCAL eXtension
                 for Scientific Computation) significantly simplifies
                 programming in the area of scientific and technical
                 computing. PASCAL-XSC provides a large number of
                 predefined data types with arithmetic operators and
                 predefined functions of highest accuracy for real and
                 complex numbers, for real and complex intervals, and
                 for the corresponding vectors and matrices. Thus
                 PASCAL-XSC makes the computer more powerful concerning
                 the arithmetic. Through an implementation in C,
                 compilers for PASCAL-XSC are available for a large
                 variety of computers such as personal computers,
                 workstations, mainframes, and supercomputers.
                 PASCAL-XSC provides a module concept, an operator
                 concept, functions and operators with general result
                 type, overloading of functions, procedures, and
                 operators, dynamic arrays, access to subarrays,
                 rounding control by the user, and accurate evaluation
                 of expressions. The language is particularly suited for
                 the development of numerical algorithms that deliver
                 highly accurate and automatically verified results. A
                 number of problem-solving routines with automatic
                 result verification have already been implemented.
                 PASCAL-XSC contains Standard PASCAL. It is immediately
                 usable by PASCAL programmers. PASCAL-XSC is easy to
                 learn and ideal for programming education. The book can
                 be used as a textbook for lectures on computer
                 programming. It contains a major chapter with sample
                 programs, exercises, and solutions. A complete set of
                 syntax diagrams, detailed tables, and indices complete
                 the book.",
  acknowledgement = ack-nhfb,
  language =     "English.",
  remark =       "Translation of: PASCAL-XSC.",
  subject =      "Pascal (Computer program language)",
  tableofcontents = "1 Introduction \\
                 1.1 Typography \\
                 1.2 Historical Remarks and Motivation \\
                 1.3 Advanced Computer Arithmetic \\
                 1.4 Connection with Programming Languages \\
                 1.5 Survey of PASCAL-XSC \\
                 2 Language Reference \\
                 2.1 Basic Symbols \\
                 2.2 Identifiers \\
                 2.3 Constants, Types, and Variables \\
                 2.4 Expressions \\
                 2.5 Statements \\
                 2.6 Program Structure \\
                 2.7 Subroutines \\
                 2.8 Modules \\
                 2.9 String Handling and Text Processing \\
                 2.10 How to Use Dynamic Arrays \\
                 3 The Arithmetic Modules \\
                 3.1 The Module C\_ARI \\
                 3.2 The Module I\_ARI \\
                 3.3 The Module CI\_ARI \\
                 3.4 The Module MV\_ARI \\
                 3.5 The Module MVC\_ARI \\
                 3.6 The Module MVI\_ARI \\
                 3.7 The Module MVCI\_ARI \\
                 3.8 The Hierarchy of the Arithmetic Modules \\
                 3.9 A Complete Sample Program \\
                 4 Problem-Solving Routines \\
                 5 Exercises with Solutions \\
                 5.1 Test of Representability \\
                 5.2 Summation of Exponential Series \\
                 5.3 Influence of Rounding Errors \\
                 5.4 Scalar Product \\
                 5.5 Boothroyd/Dekker Matrices \\
                 5.6 Complex Functions \\
                 5.7 Surface Area of a Parallelepiped \\
                 5.8 Parallelism and Intersection of Lines \\
                 5.9 Transposed Matrix, Symmetry \\
                 5.10 Rail Route Map \\
                 5.11 Inventory Lists \\
                 5.12 Complex Numbers and Polar Representation \\
                 5.13 Complex Division \\
                 5.14 Electric Circuit \\
                 5.15 Alternating Current Measuring Bridge \\
                 5.16 Optical Lens \\
                 5.17 Interval Evaluation of a Polynomial \\
                 5.18 Calculations for Interval Matrices \\
                 5.19 Differentiation Arithmetic \\
                 5.20 Newton's Method with Automatic Differentiation \\
                 5.21 Measurement of Time \\
                 5.22 Iterative Method \\
                 5.23 Trace of a Product Matrix \\
                 5.24 Calculator for Polynomials \\
                 5.25 Interval Newton Method \\
                 5.26 Runge-Kutta Method \\
                 5.27 Rational Arithmetic \\
                 5.28 Evaluation of Polynomials \\
                 A Syntax Diagrams \\
                 B Indices and Lists \\
                 B.1 Syntax Diagrams \\
                 B.2 Reserved Words \\
                 B.3 Predefined Identifiers \\
                 B.4 Operators \\
                 B.4.1 Basic Operators \\
                 B.4.2 Arithmetic Operators \\
                 B.4.3 Relational Operators for the Arithmetic Types \\
                 B.4.4 Assignment Operators \\
                 B.5 Predefined Functions \\
                 B.6 Transfer Functions \\
                 B.7 Predefined Procedures \\
                 B.8 \#-Expressions \\
                 B.8.1 Real and Complex \#-Expressions \\
                 B.8.2 Real and Complex Interval \#-Expressions \\
                 Bibliography \\
                 Index",
}

@Article{Koc:1992:AAS,
  author =       "{\c{C}}etin K. Ko{\c{c}} and Ching-Yu Hung",
  title =        "Adaptive $m$-ary segmentation and canonical recoding
                 algorithms for multiplication of large binary numbers",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "24",
  number =       "3",
  pages =        "3--12",
  month =        aug,
  year =         "1992",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 19:11:08 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/089812219290209Z",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Kola:1992:MQP,
  author =       "M. Kol{\'a}r and T. Sasaki",
  title =        "Multivariate quotient by power-series division",
  journal =      j-SIGSAM,
  volume =       "26",
  number =       "3",
  pages =        "17--20",
  month =        aug,
  year =         "1992",
  CODEN =        "SIGSBZ",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Fri Feb 8 18:27:02 MST 2002",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGSAM Bulletin",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}

@InProceedings{Kontro:1992:FAS,
  author =       "J. Kontro and K. Kalliojarvi and Y. Neuvo",
  title =        "Floating-point arithmetic in signal processing",
  crossref =     "White:1992:IIS",
  pages =        "1784--1791 vol.4",
  year =         "1992",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The use of floating-point arithmetic in digital signal
                 processing is considered. An introduction to
                 floating-point arithmetic based on the IEEE
                 floating-point standards is given. Finite wordlength
                 effects of these arithmetic systems are presented.
                 Floating-point hardware is discussed. The emphasis is
                 on audio applications. As an example, amplitude
                 distributions and signal-to-noise ratios of quantized
                 music are considered, and audio standards using
                 floating-point arithmetic are presented.",
  acknowledgement = ack-nhfb,
  affiliation =  "Signal Process. Lab., Tampere University of Technol.,
                 Finland",
  classification = "B1265F (Microprocessors and microcomputers); B6140
                 (Signal processing and detection); B6450 (Audio
                 equipment and systems); C1260 (Information theory);
                 C5130 (Microprocessor chips); C5230 (Digital arithmetic
                 methods); C5260 (Digital signal processing)",
  keywords =     "Amplitude distributions; Audio applications; Audio
                 standards; Digital signal processing; Finite wordlength
                 effects; Floating-point arithmetic; Hardware; IEEE
                 floating-point standards; Quantized music;
                 Signal-to-noise ratios",
  thesaurus =    "Audio equipment; Audio signals; Digital arithmetic;
                 Digital signal processing chips; Roundoff errors;
                 Signal processing",
}

@Article{Kontro:1992:USF,
  author =       "J. Kontro and K. Kalliojarvi and Y. Neuvo",
  title =        "Use of Short Floating-Point Formats in Audio
                 Applications",
  journal =      j-IEEE-TRANS-CONSUMER-ELECTRONICS,
  volume =       "38",
  number =       "3",
  pages =        "200--207",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCEDA",
  ISSN =         "0098-3063 (print), 1558-4127 (electronic)",
  ISSN-L =       "0098-3063",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Consumer Electronics",
  summary =      "Use of short floating-point formats that are shorter
                 than the IEEE floating-point standard (ANSI/IEEE S+A
                 754-1985), 24+8-b, in digital audio applications is
                 studied. The performance of these formats is analyzed
                 in different parts of the digital audio \ldots{}",
}

@Article{Krishna:1992:CTA,
  author =       "H. Krishna and K.-Y. Lin and J.-D. Sun",
  title =        "A coding theory approach to error control in redundant
                 residue number systems. {I}. Theory and single error
                 correction",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "39",
  number =       "1",
  pages =        "8--17",
  month =        jan,
  year =         "1992",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.204106",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5240",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems. 2, Analog
                 and Digital Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A coding theory approach to error control in redundant
                 residue number systems (RRNSs) is presented. The
                 concepts of Hamming weight, minimum distance, weight
                 distribution, and error detection and correction
                 capabilities in redundant residue number \ldots{}",
}

@Article{Krishnan:1992:CGF,
  author =       "R. Krishnan and G. A. Jullien and W. C. Miller",
  title =        "Computation of generalized {FIR} filter structure
                 using the modified quadratic residue number system",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "39",
  number =       "1",
  pages =        "58--62",
  month =        jan,
  year =         "1992",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.204110",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5240",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems. 2, Analog
                 and Digital Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The systematic approach for generating the generalized
                 number theoretic FIR filter structure based on the
                 complex number theoretic z-transform is presented. A
                 step-by-step computational method that can be used in
                 the implementation and \ldots{}",
}

@InProceedings{Kubosawa:1992:BFP,
  author =       "H. Kubosawa and A. Katsuno and H. Takahashi and T.
                 Sato and A. Suga and G. Goto",
  title =        "A 64-bit floating point processing unit for a {RISC}
                 microprocessor",
  crossref =     "Anonymous:1992:EAP",
  pages =        "270--273",
  year =         "1992",
  DOI =          "https://doi.org/10.1109/EUASIC.1992.228042",
  bibdate =      "Thu Mar 02 09:45:28 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/iel2/416/5911/00228042.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "25MHz SPARC S-25 microprocessor; CMOS; PGA; RISC",
}

@InProceedings{Kutuso:1992:EMO,
  author =       "K. N. Kutuso and H. M. Yassine",
  booktitle =    "Proceedings of the 35th Midwest Symposium on Circuits
                 and Systems, 1992",
  title =        "Effect of moduli ordering of mixed radix conversion
                 methods in residue number systems",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "678--680",
  year =         "1992",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1992.271232",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The effect of moduli ordering in different methods for
                 converting residue numbers to decimal numbers using the
                 mixed radix approach is investigated. The number of
                 operations involved in the conversion process of
                 residue numbers to their decimal \ldots{}",
}

@InProceedings{Lacroix:1992:DDM,
  author =       "A. Lacroix and F. Hartwig",
  title =        "Distribution densities of the mantissa and exponent of
                 floating point numbers",
  crossref =     "White:1992:IIS",
  pages =        "1792--1795 vol.4",
  year =         "1992",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "6 vol.",
  abstract =     "The relations between the probability densities of
                 real numbers and the corresponding mantissa and
                 exponent densities in the floating point number format
                 are investigated. Assumptions about continuity of the
                 probability density of real numbers lead to certain
                 restrictions in terms of the density of the mantissa. A
                 few real number densities of practical importance were
                 treated analytically and experimentally. During
                 arithmetic operations like addition and multiplication
                 which are essential for signal processing the operand
                 density is altered. The effect concerning the densities
                 of mantissa and exponent of the result is discussed.
                 The reciprocal density of the mantissas plays a central
                 role. Applications in roundoff-noise-analysis of signal
                 processing with finite wordlength are considered. (5
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fuer Angewandte Phys., J. W. Goethe-University,
                 Frankfurt am Main, Germany",
  classification = "B1270F (Digital filters); B6140 (Signal processing
                 and detection); C1260 (Information theory); C5230
                 (Digital arithmetic methods); C5240 (Digital filters);
                 C5260 (Digital signal processing)",
  keywords =     "Addition; Arithmetic operations; Exponent densities;
                 Finite wordlength; Floating point number format;
                 Floating point numbers; Mantissa densities;
                 Multiplication; Operand density; Probability densities;
                 Real numbers; Reciprocal density;
                 Roundoff-noise-analysis; Signal processing",
  thesaurus =    "Digital arithmetic; Digital filters; Roundoff errors;
                 Signal processing",
}

@Article{Lang:1992:HRS,
  author =       "T. Lang and P. Montuschi",
  title =        "Higher radix square root with prescaling",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "996--1009",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156542",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156542",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "A scheme for performing higher radix square root based
                 on prescaling of the radicand is presented to reduce
                 the complexity of the result-digit selection. The
                 scheme requires several steps, namely multiplication
                 for prescaling the radicand, square \ldots{}",
}

@Article{Lee:1992:ACR,
  author =       "J. H. M. Lee and M. H. {van Emden}",
  title =        "Adapting {$ {\rm CLP}(\sc {R}) $} to floating-point
                 arithmetic",
  journal =      "Fifth generation computer systems, vol 1",
  volume =       "2",
  publisher =    "Ohm",
  address =      "Tokyo, Japan",
  pages =        "996--1003",
  year =         "1992",
  MRclass =      "68N15 (68N17 68Q40)",
  MRnumber =     "93m:68027",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Lee:1992:FPP,
  author =       "K. Lee",
  title =        "On the Floating Point Performance of the i860
                 Microprocessor",
  journal =      j-INT-J-HIGH-SPEED-COMPUTING,
  volume =       "4",
  number =       "4",
  pages =        "251--268",
  month =        dec,
  year =         "1992",
  CODEN =        "IHSCEZ",
  ISSN =         "0129-0533",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of High Speed Computing",
  journal-URL =  "http://www.worldscientific.com/worldscinet/ijhsc",
}

@Book{Leighton:1992:IPA,
  author =       "Frank Thomson Leighton",
  title =        "Introduction to Parallel Algorithms and Architectures:
                 Arrays, Trees, Hypercubes",
  publisher =    pub-MORGAN-KAUFMANN,
  address =      pub-MORGAN-KAUFMANN:adr,
  pages =        "xviii + 831",
  year =         "1992",
  ISBN =         "1-55860-117-1",
  ISBN-13 =      "978-1-55860-117-8",
  LCCN =         "QA76.5 .L45 1992",
  bibdate =      "Mon Sep 16 16:21:01 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$54.95",
  acknowledgement = ack-nhfb,
}

@Article{Li:1992:CSC,
  author =       "Zhenyu Li and Victor Milenkovic",
  title =        "Constructing Strongly Convex Hulls Using Exact or
                 Rounded Arithmetic",
  journal =      j-ALGORITHMICA,
  volume =       "8",
  number =       "5--6",
  pages =        "345--364",
  year =         "1992",
  CODEN =        "ALGOEJ",
  ISSN =         "0178-4617 (print), 1432-0541 (electronic)",
  ISSN-L =       "0178-4617",
  MRclass =      "68U05 (52B55)",
  MRnumber =     "MR1195157 (93k:68104)",
  MRreviewer =   "Nikolaj M. Korneenko",
  bibdate =      "Mon Jan 22 05:31:33 MST 2001",
  bibsource =    "dblp-journals-algorithmica.bib;
                 http://dblp.uni-trier.de/db/journals/algorithmica/algorithmica8.html#LiM92;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/index-table-a.html#algorithmica;
                 MathSciNet database",
  note =         "1990 Computational Geometry Symposium (Berkeley, CA,
                 1990)",
  acknowledgement = ack-nhfb,
  fjournal =     "Algorithmica. An International Journal in Computer
                 Science",
  journal-URL =  "http://link.springer.com/journal/453",
  keywords =     "exact arithmetic; floating-point arithmetic; rounding
                 errors",
  oldlabel =     "LiM92",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/algorithmica/LiM92",
}

@TechReport{Lee:1992:RAC,
  author =       "Ren-Cang Lee",
  title =        "Reciproot Algorithm --- Correctly Rounded?",
  type =         "Technical Report",
  number =       "UCB/CSD-94-850",
  institution =  "Department of Mathematics, University of California,
                 Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "13",
  day =          "6",
  month =        sep,
  year =         "1992",
  bibdate =      "Fri Dec 12 15:15:46 2025",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://apps.dtic.mil/sti/citations/ADA636844;
                 https://apps.dtic.mil/sti/pdfs/ADA636844.pdf",
  abstract =     "This note attempts to give a detailed error analysis
                 of Reciproot Algorithm proposed by Kahan and Ng in
                 1986. It is shown that the algorithm yields correctly
                 rounded square root under all rounding modes.",
  acknowledgement = ack-nhfb,
  remark =       "Report also carries date of December 1994. See also
                 \cite{Hyland:20xx:FIS}.",
}

@Article{Lim:1992:SPM,
  author =       "Y. C. Lim",
  title =        "Single-precision multiplier with reduced circuit
                 complexity for signal processing applications",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "10",
  pages =        "1333--1336",
  month =        oct,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.166611",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=166611",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Liu:1992:QBS,
  author =       "K. J. R. Liu and E. Frantzeskakis",
  booktitle =    "Workshop on {VLSI} Signal Processing, V, 1992",
  title =        "Qrd-based Square Root Free and Division Free
                 Algorithms and Architectures",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "459--468",
  year =         "1992",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Not \ldots{}",
}

@Article{Lozier:1992:RPC,
  author =       "D. W. Lozier and P. R. Turner",
  title =        "Robust Parallel Computation in Floating-Point and
                 {SLI} Arithmetic. {Robuste Parallel-Verarbeitung in
                 Gleitkomma-und SLI-Arithmetik}",
  journal =      j-COMPUTING,
  volume =       "48",
  number =       "3-4",
  pages =        "239--258 (or 239--257??)",
  year =         "1992",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65Y05 (65-04 65G05)",
  MRnumber =     "93e:65161",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Article{Lozier:1992:RPV,
  author =       "D. W. Lozier and P. R. Turner",
  title =        "{Robuste Parallel-Verarbeitung in Gleitkomma- und
                 SLI-Arithmetik}. ({German}) [{Robust} Parallel
                 Computation in Floating-Point and {SLI} Arithmetic]",
  journal =      j-COMPUTING,
  volume =       "48",
  number =       "3--4",
  pages =        "239--257",
  month =        sep,
  year =         "1992",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65Y05 (65-04 65G05)",
  MRnumber =     "93e:65161",
  bibdate =      "Mon Oct 11 20:38:38 MDT 1999",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database; OCLC Contents1st database",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  language =     "German",
}

@Article{Lozier:1992:SLI,
  author =       "Daniel W. Lozier and P. R. Turner",
  title =        "Symmetric Level-Index Arithmetic in Simulation and
                 Modeling",
  journal =      j-J-RES-NATL-BUR-STAND,
  volume =       "97",
  number =       "4",
  pages =        "471--485",
  month =        jul,
  year =         "1992",
  CODEN =        "JRNBAG",
  DOI =          "https://doi.org/10.6028/jres.097.020",
  ISSN =         "0091-0635 (print), 2376-5305 (electronic)",
  ISSN-L =       "0091-0635",
  bibdate =      "Fri Jul 09 07:24:16 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://nvlpubs.nist.gov/nistpubs/jres/097/jresv97n4p471_A1b.pdf",
  abstract =     "This paper begins with a general introduction to the
                 symmetric level-index, SLI, system of number
                 representation and arithmetic. This system provides a
                 robust framework in which experimental computation can
                 be performed without the risk of failure due to
                 overflow/underflow or to poor scaling of the original
                 problem. There follows a brief summary of some existing
                 computational experience with this system to illustrate
                 its strengths in numerical, graphical and parallel
                 computational settings. An example of the use of SLI
                 arithmetic to overcome graphics failure in the modeling
                 of a turbulent combustion problem is presented. The
                 main thrust of this paper is to introduce the idea of
                 SLI-linear least squares data fitting. The use of
                 generalized logarithm and exponential functions is seen
                 to offer significant improvement over the more
                 conventional linear regression tools for fitting data
                 from a compound exponential decay such as the decay of
                 radioactive materials.",
  acknowledgement = ack-nhfb,
  journal-URL =  "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
  keywords =     "computer graphics; generalized logarithms and
                 exponentials; least-squares data-fitting; overflow,
                 underflow, and scaling; parallel computing; symmetric
                 level-index arithmetic.",
}

@Article{Lu:1992:NDA,
  author =       "M. Lu and J.-S. Chiang",
  title =        "A novel division algorithm for the residue number
                 system",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "1026--1032",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156545",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4052;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156545",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A novel general algorithm for signed number division
                 in the residue number system (RNS) is presented. The
                 parity checking technique used for sign and overflow
                 detection in this algorithm is more efficient and
                 practical than conventional methods. \ldots{}",
}

@InProceedings{Lynch:1992:FCA,
  author =       "Thomas W. Lynch and Earl E. {Swartzlander, Jr.}",
  title =        "A Formalization for Computer Arithmetic",
  crossref =     "Atanassova:1992:CAE",
  pages =        "137--145",
  year =         "1992",
  bibdate =      "Sat Sep 17 19:09:42 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "From the abstract: ``The formalism, when applied to
                 IEEE Std 754 shows that the non-trapping mode can
                 produce incorrect numeric and non-numeric results.''",
  acknowledgement = ack-nhfb,
}

@Misc{Lynch:1992:HSD,
  author =       "T. Lynch and S. McIntyre and K. Tseng and S. Shaw and
                 T. Hurson",
  title =        "High speed divider with square root capability",
  year =         "1992",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "U.S. Patent No. 5,128,891.",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}

@InProceedings{Madrid:1992:MBA,
  author =       "P. E. Madrid and B. Millar and E. E. Swartzlander",
  editor =       "Dwight Hill",
  booktitle =    "Proceedings of the {1992 IEEE International Conference
                 on Computer Design: VLSI in Computers \& Processors,
                 11--14 October 1992, Cambridge, MA, USA}",
  title =        "Modified {Booth} algorithm for high radix
                 multiplication",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  bookpages =    "xvii + 605",
  pages =        "118--212",
  year =         "1992",
  DOI =          "https://doi.org/10.1109/ICCD.1992.276194",
  ISBN =         "0-8186-3110-4 (paperback), 0-8186-3111-2 (microfiche),
                 0-8186-3112-0",
  ISBN-13 =      "978-0-8186-3110-8, 978-0-8186-3111-5,
                 978-0-8186-3112-2",
  ISSN =         "1063-6404",
  LCCN =         "TK7888.4 .I35 1992",
  bibdate =      "Thu Nov 13 10:39:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/document/276194/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Maguire:1992:MD,
  author =       "J. Maguire",
  title =        "{MC8810}: Datapath",
  crossref =     "Juj:1992:NCR",
  pages =        "193--197",
  year =         "1992",
  bibdate =      "Wed Sep 7 22:32:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@MastersThesis{Makhdumi:1992:CCS,
  author =       "Shazia Makhdumi",
  title =        "Comparison of current switch bipolar circuits for high
                 performance floating point arithmetic",
  type =         "Thesis ({M.S.})",
  school =       "Massachusetts Institute of Technology, Dept. of
                 Electrical Engineering and Computer Science",
  address =      "Cambridge, MA, USA",
  pages =        "107",
  year =         "1992",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{Mar:1992:DSP,
  editor =       "Amy Mar",
  title =        "Digital signal processing applications using the
                 {ADSP}-2100 family",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "????",
  year =         "1992",
  ISBN =         "0-13-219726-X (vol. 1), 0-13-178567-2 (vol. 2)",
  ISBN-13 =      "978-0-13-219726-7 (vol. 1), 978-0-13-178567-0 (vol.
                 2)",
  LCCN =         "TK5102.9 .D53 1992",
  bibdate =      "Sat Jan 15 05:58:58 MST 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  remark =       "Vol. 2: edited by Jere Babst. System requirements for
                 computer disks: IBM-compatible PC; DOS 3.0 or higher;
                 high-density disk drive.",
  subject =      "Signal processing; Digital techniques;
                 Microprocessors",
}

@Article{McQuillan:1992:VMH,
  author =       "S. E. McQuillan and J. V. McCanny",
  title =        "{VLSI} module for high-performance multiply, square
                 root and divide",
  journal =      j-IEE-PROC-COMPUT-DIGIT-TECH,
  volume =       "139",
  number =       "6",
  pages =        "505--510",
  month =        nov,
  year =         "1992",
  CODEN =        "ICDTEA",
  ISSN =         "1350-2387 (print), 1359-7027 (electronic)",
  ISSN-L =       "1350-2387",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEE Proceedings. Computers and Digital Techniques",
  summary =      "A high-performance VLSI architecture to perform
                 multiply-accumulate, division and square root
                 operations is proposed. The circuit is highly regular,
                 requires only minimal control and ean be pipelined
                 right down to the bit level. The system can also
                 \ldots{}",
}

@TechReport{MenissierMorain:1992:CNR,
  author =       "V. M{\'e}nissier-Morain",
  title =        "{CAML} numbers reference manual",
  number =       "141",
  institution =  "Inst. Nat. Recherche Inf. Autom.",
  address =      "Le Chesnay, France",
  pages =        "157",
  month =        jul,
  year =         "1992",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "An overview is given of the arithmetic of the
                 functional language CAML V3.1. This arithmetic includes
                 floating point numbers, arbitrary large integers and
                 rationals and a complete set of primitives. Its
                 implementation relies on the efficient BigNum package
                 (J.-C. Herve et al., 1989).",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods); C6110 (Systems
                 analysis and programming); C6140D (High level
                 languages); C7310 (Mathematics)",
  keywords =     "Arbitrary large integers; Arithmetic; BigNum package;
                 Floating point numbers; Functional language CAML;
                 Primitives; Rationals",
  pubcountry =   "France",
  thesaurus =    "Digital arithmetic; Functional programming; High level
                 languages; Mathematics computing",
}

@Book{Menninger:1992:NWN,
  author =       "Karl Menninger",
  title =        "Number Words and Number Symbols: a Cultural History of
                 Numbers",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xiii + 480",
  year =         "1992",
  ISBN =         "0-486-27096-3",
  ISBN-13 =      "978-0-486-27096-8",
  LCCN =         "QA141.2 .M4513 1992",
  bibdate =      "Fri Nov 28 18:29:23 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}

@Article{Meredith:1992:NPF,
  author =       "Roger W. Meredith",
  title =        "Numeric precision in {FORTRAN} computing",
  journal =      j-COMPUT-PHYS,
  volume =       "6",
  number =       "5",
  pages =        "506--512",
  month =        sep # "\slash " # oct,
  year =         "1992",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.168438",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Wed Apr 10 08:45:36 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.168438",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}

@Article{Mikami:1992:NDO,
  author =       "N. Mikami and M. Kobayashi and Y. Yokoyama",
  title =        "A New {DSP}-Oriented Algorithm for Calculation of the
                 Square Root Using a Nonlinear Digital Filter",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "40",
  number =       "7",
  pages =        "1663--1669",
  month =        jul,
  year =         "1992",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "A high-speed algorithm for calculating the square root
                 is proposed. This algorithm, which can be regarded as
                 calculation of the step response of a kind of nonlinear
                 IIR filter, requires no divisions. Therefore, it is
                 suitable for a VLSI digital \ldots{}",
}

@Article{Mitchell:1992:VFA,
  author =       "H. B. Mitchell",
  title =        "Very fast accurate square-root algorithm for use with
                 gradient edge operators",
  journal =      j-ELECT-LETTERS,
  volume =       "28",
  number =       "10",
  pages =        "922--923",
  day =          "7",
  month =        may,
  year =         "1992",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  summary =      "Commonly used gradient edge operators such as the
                 Sobel, Prewitt and Roberts operators all required a
                 square root operation; this is, however,
                 computationally intensive and, consequently, simple but
                 very inaccurate approximations are often used
                 \ldots{}",
}

@InProceedings{Montuschi:1992:DAC,
  author =       "P. Montuschi and L. Ciminiera and A. Giustina",
  title =        "A Division Architecture Combining {Newton--Raphson}
                 Approximations and Direct Methods Iterations",
  crossref =     "Singh:1992:CRT",
  pages =        "376--380",
  year =         "1992",
  bibdate =      "Wed Dec 13 18:19:38 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The authors consider the possibility of designing
                 architectures which combine in the best possible way
                 the convergence with the square advantages of the
                 Newton--Raphson method with the precision
                 characteristics of the digit-by-digit algorithms so as
                 to obtain units which satisfy the IEEE 754 floating
                 point standard requirements. This is a general method
                 which can be extended with simple and minor changes
                 also to square root. Attention is focused on a possible
                 implementation of this design methodology for division.
                 The evaluation shows that the proposed unit offers an
                 alternative architecture for division which provides
                 interesting performances.",
  acknowledgement = ack-nj,
  affiliation =  "Dipartimento di Autom. e Inf., Politecnico di Torino,
                 Italy",
  classification = "B0290F (Interpolation and function approximation);
                 B1265B (Logic circuits); C4130 (Interpolation and
                 function approximation); C5230 (Digital arithmetic
                 methods)",
  keywords =     "Convergence; Digit-by-digit algorithms; Direct methods
                 iterations; Division architecture; IEEE 754 floating
                 point standard; Newton--Raphson method; Square
                 advantages; Square root",
  thesaurus =    "Convergence of numerical methods; Digital arithmetic;
                 Dividing circuits; Iterative methods",
}

@Article{Montuschi:1992:DRD,
  author =       "P. Montuschi and L. Ciminiera",
  title =        "Design of a radix $4$ division unit with simple
                 selection table",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "12",
  pages =        "1606--1611",
  month =        dec,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.214670",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=214670",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Moore:1992:PRP,
  author =       "David L. Moore",
  title =        "Programming the 29050 ({RISC} programming)",
  journal =      j-DDJ,
  volume =       "17",
  number =       "1",
  pages =        "34, 36, 38, 40, 42",
  month =        jan,
  year =         "1992",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Tue Sep 10 10:06:23 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C5220 (Computer architecture); C6110 (Systems
                 analysis and programming); C6140B (Machine-oriented
                 languages)",
  fjournal =     "Dr. Dobb's Journal of Software Tools",
  keywords =     "29000 Family; AM29050; Assembly language programming;
                 Flat address space; Floating-point operations;
                 Registers; RISC processors",
  thesaurus =    "Assembly language; Microprogramming; Reduced
                 instruction set computing",
}

@Book{Morgan:1992:NM,
  author =       "Don Morgan",
  title =        "Numerical Methods: Real-time and Embedded Systems
                 Programming",
  publisher =    pub-MT,
  address =      pub-MT:adr,
  pages =        "496",
  year =         "1992",
  ISBN =         "1-55851-232-2 (book only), 1-55851-233-0 (disk only),
                 1-55851-234-9 (book and disk set)",
  ISBN-13 =      "978-1-55851-232-0 (book only), 978-1-55851-233-7 (disk
                 only), 978-1-55851-234-4 (book and disk set)",
  LCCN =         "QA76.6 .M669 1992",
  bibdate =      "Wed Sep 14 19:16:35 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$34.95",
  acknowledgement = ack-nj,
}

@Article{Mou:1992:OSA,
  author =       "Z.-J. Mou and F. Jutand",
  title =        "{`Overturned-stairs'} adder trees and multiplier
                 design",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "940--948",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156536",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156536",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Mutrie:1992:AFE,
  author =       "Mark P. W. Mutrie and Richard H. Bartels and Bruce W.
                 Char",
  title =        "An approach for floating-point error analysis using
                 computer algebra",
  crossref =     "Wang:1992:PII",
  pages =        "284--293",
  year =         "1992",
  bibdate =      "Thu Mar 12 08:39:32 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/issac.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/143242/p284-mutrie/",
  acknowledgement = ack-nhfb,
  keywords =     "algorithms",
  subject =      "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, General. {\bf I.1.2} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Algorithms, Algebraic algorithms. {\bf G.1.0}
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Computer arithmetic. {\bf I.1.3} Computing
                 Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION,
                 Languages and Systems, Maple. {\bf G.2.2} Mathematics
                 of Computing, DISCRETE MATHEMATICS, Graph Theory, Graph
                 algorithms.",
}

@PhdThesis{Mutrie:1992:TSS,
  author =       "Mark P. W. Mutrie",
  title =        "Towards a symbolic system for floating-point error
                 analysis",
  type =         "Thesis ({Ph.D.})",
  publisher =    "National Library of Canada = Bibliotheque nationale du
                 Canada",
  school =       "University of Waterloo",
  address =      "Waterloo, ON, Canada",
  year =         "1992",
  ISBN =         "0-315-72486-2",
  ISBN-13 =      "978-0-315-72486-0",
  LCCN =         "????",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "8 microfiches. University Microfilms order no.
                 UMI00359027",
  series =       "Canadian theses = Theses canadiennes",
  acknowledgement = ack-nhfb,
}

@Article{Nakano:1992:AHS,
  author =       "H. Nakano and M. Nakajima and Y. Nakakura and T.
                 Yoshida and Y. Goi and Y. Nakai and R. Segawa and T.
                 Kishida",
  title =        "An accurate, high speed implementation of division by
                 the quasi-unity divisor method",
  journal =      j-IFIP-TRANS-A,
  volume =       "A-12",
  pages =        "261--267",
  month =        "????",
  year =         "1992",
  CODEN =        "ITATEC",
  ISSN =         "0926-5473",
  bibdate =      "Thu Dec 14 15:33:50 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Algorithms, Software, Architecture. Information
                 Processing 92. IFIP 12th World Computer Congress.",
  abstract =     "A first-order convergent division algorithm is
                 generally thought to be accurate but slow. Using a
                 large look-up table and a multiplier improves speed.
                 Since a partial quotient is not negative and iterations
                 use only one formula, an iteration is carried out in
                 the form of a partial carry and a partial sum. This
                 paper describes a new developed division algorithm with
                 the above-mentioned characteristics. This algorithm is
                 compared to other similar algorithms. In a hardware
                 implementation, this algorithm is applied to the 53-bit
                 significand part of a floating-point double precision
                 divider. The execution time is division of 8 or 9
                 cycles.",
  acknowledgement = ack-nhfb,
  affiliation =  "Corporate R and D, Matsushita Electric Industrial Co.
                 Ltd., Osaka, Japan",
  classification = "C5230 (Digital arithmetic methods)",
  confdate =     "7-11 Sept. 1992",
  conflocation = "Madrid, Spain",
  confsponsor =  "IFIP",
  fjournal =     "IFIP Transactions. A. Computer Science and
                 Technology",
  keywords =     "53-Bit significand part; First-order convergent
                 division algorithm; Floating-point double precision
                 divider; Look-up table; Multiplier; Partial carry;
                 Partial sum; Quasi-unity divisor method",
  pubcountry =   "Netherlands",
  thesaurus =    "Digital arithmetic; Table lookup",
}

@Article{Nakano:1992:FPB,
  author =       "H. Nakano and M. Nakajima and Y. Nakakura and T.
                 Yoshida and Y. Goi and Y. Nakai and R. Segawa and T.
                 Kishida and H. Kadota",
  title =        "An 80-{FLOPS} (Peak) 64-b Microprocessor for Parallel
                 Computer",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "27",
  number =       "3",
  pages =        "365--372",
  month =        mar,
  year =         "1992",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Wed Sep 7 22:32:42 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "IEEE Journal of Solid-State Circuits",
}

@Article{Ng:1992:ARH,
  author =       "K. C. Ng",
  title =        "Argument Reduction for Huge Arguments: Good to the
                 Last Bit",
  journal =      "SunPro",
  volume =       "??",
  number =       "??",
  day =          "13",
  month =        jul,
  year =         "1992",
  bibdate =      "Thu Sep 1 10:16:08 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Work in progress.",
  URL =          "http://www.validlab.com/arg.pdf",
  acknowledgement = ack-nj,
  keywords =     "range reduction",
}

@InProceedings{Nishimura:1992:FPR,
  author =       "S. Nishimura",
  booktitle =    "Proceedings of the 35th Midwest Symposium on Circuits
                 and Systems, 1992",
  title =        "A fixed-point roundoff error analysis of adaptive
                 notch filters",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "373--376",
  year =         "1992",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Methods to analyze the convergence and steady-state
                 characteristics of an adaptive notch filter when the
                 effects of fixed-point arithmetic are taken into
                 account are presented. The adaptive detection of a
                 sinusoid with white Gaussian noise is \ldots{}",
}

@Article{Obaidat:1992:DMA,
  author =       "Mohammad S. Obaidat and Saleh A. Bleha",
  title =        "A Decimal Multiplication Algorithm for
                 Microcomputers",
  journal =      j-COMPUT-ELECTR-ENG,
  volume =       "18",
  number =       "5",
  pages =        "357--363",
  month =        sep,
  year =         "1992",
  CODEN =        "CPEEBQ",
  ISSN =         "0045-7906 (print), 1879-0755 (electronic)",
  ISSN-L =       "0045-7906",
  bibdate =      "Thu Sep 1 10:16:11 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computers and Electrical Engineering",
  keywords =     "decimal floating-point arithmetic",
}

@Article{Ochs:1992:SIR,
  author =       "T. Ochs",
  title =        "This sine is also right!",
  journal =      j-COMP-LANG-MAG,
  volume =       "9",
  number =       "1",
  pages =        "89--93",
  month =        jan,
  year =         "1992",
  CODEN =        "COMLEF",
  ISSN =         "0749-2839",
  bibdate =      "Thu Sep 01 10:44:04 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computer Language Magazine",
}

@Article{Okada:1992:AQE,
  author =       "Kazuho Okada and Yasuaki Kuroe",
  title =        "Analysis of Quantization Errors in Digital Control
                 Systems Using Floating-Point Arithmetic--Considering
                 Computational Order in Controller",
  journal =      j-ELECT-COMM-JAPAN-3-FUND-ELECT-SCI,
  volume =       "75",
  number =       "6",
  pages =        "1--??",
  month =        jun,
  year =         "1992",
  CODEN =        "ECJSER",
  ISSN =         "1042-0967 (print), 1520-6440 (electronic)",
  ISSN-L =       "1042-0967",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics and communications in Japan. Part 3,
                 Fundamental electronic science",
}

@Article{Orton:1992:NFT,
  author =       "G. A. Orton and L. E. Peppard and S. E. Tavares",
  title =        "New fault tolerant techniques for residue number
                 systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "11",
  pages =        "1453--1464",
  month =        nov,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.177315",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:21 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4475;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=177315",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Previously proposed error detection algorithms for the
                 residue number system require a complete recombination.
                 A weighted approximation via the Chinese remainder
                 theorem is shown to be sufficient to detect 100\% of
                 single errors. This makes real-time \ldots{}",
}

@InProceedings{Paliouras:1992:SDP,
  author =       "V. Paliouras and D. Soudris and T. Stouraitis",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems. {ISCAS '92}. Proceedings, 3--6 May 1992",
  title =        "Systematic derivation of the processing element of a
                 systolic array based on residue number system",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "815--818",
  year =         "1992",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1992.230097",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A systematic methodology for synthesizing optimal VLSI
                 residue number system architectures using full adders
                 (FAs) as the basic building block is introduced. The
                 design methodology derives array architectures starting
                 from the algorithmic level. \ldots{}",
}

@TechReport{Pan:1992:CWU,
  author =       "V. Y. Pan",
  title =        "Can we utilize the cancellation of the most
                 significant digits?",
  type =         "Report",
  number =       "TR 92 061",
  institution =  "The International Computer Science Institute",
  address =      "Berkeley, CA, USA",
  year =         "1992",
  bibdate =      "Mon Mar 06 17:00:31 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Park:1992:MED,
  author =       "Haesun Park",
  title =        "On Multiple Error Detection in Matrix
                 Triangularizations Using Checksum Methods",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "14",
  number =       "1",
  pages =        "90--97",
  month =        jan,
  year =         "1992",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  MRclass =      "65F05 (65F25)",
  MRnumber =     "92i:65060",
  bibdate =      "Mon Apr 14 08:15:42 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ of Minnesota",
  affiliationaddress = "Minneapolis, MN, USA",
  classification = "722; 723; 921; 922; C4110 (Error analysis in
                 numerical methods); C5220P (Parallel architecture);
                 C5230 (Digital arithmetic methods); C5470 (Performance
                 evaluation and testing)",
  corpsource =   "Department of Computer Science, Minnesota University,
                 Minneapolis, MN, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  journalabr =   "J Parallel Distrib Comput",
  keywords =     "Checksum methods; checksum methods; Codes,
                 Symbolic--Error Detection; Computer Systems,
                 Digital--Fault Tolerant Capability; correct rounding;
                 detection; digital arithmetic; error; error analysis;
                 error correction; errors; floating-point arithmetic;
                 floating-point error analysis; Gaussian elimination; LU
                 decomposition; Mathematical Techniques; matrix; Matrix
                 Algebra; Matrix triangularizations; multiple error
                 correction; multiple error detection; pairwise
                 pivoting; parallel architectures; performance
                 evaluation; QR decomposition; rounding; transient
                 errors; triangularizations",
  treatment =    "P Practical",
}

@Article{Parker:1992:OVN,
  author =       "A. Parker and J. O. Hamblen",
  title =        "Optimal value for the {Newton--Raphson} division
                 algorithm",
  journal =      j-INFO-PROC-LETT,
  volume =       "42",
  number =       "3",
  pages =        "141--144",
  day =          "25",
  month =        may,
  year =         "1992",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Wed Nov 11 07:31:13 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  keywords =     "fast division; floating-point arithmetic",
}

@Article{Pichat:1992:SFR,
  author =       "Mich{\`e}le Pichat",
  title =        "Sets of floating-point results associated with an
                 algebraic algorithm",
  journal =      "Computational and applied mathematics, I (Dublin,
                 1991)",
  pages =        "409--418",
  year =         "1992",
  MRclass =      "68M07 (65G05)",
  MRnumber =     "93m:68010",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{Plauger:1992:SCL,
  author =       "P. J. Plauger",
  title =        "The {Standard C} Library",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xiv + 498",
  year =         "1992",
  ISBN =         "0-13-838012-0",
  ISBN-13 =      "978-0-13-838012-0",
  LCCN =         "QA76.73.C15 P563 1991",
  bibdate =      "Wed Dec 15 10:40:47 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/ansistd.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/litprog.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  abstract =     "\booktitle{The Standard C Library} shows you how to
                 use all of the library functions mandated by the ANSI
                 and ISO Standards for the programming language C. To
                 help you understand how to use the library, this book
                 also shows you how to implement it. You see
                 approximately 9,000 lines of tested, working code that
                 is highly portable across diverse computer
                 architectures. \booktitle{The Standard C Library}
                 explains how the library was meant to be used and how
                 it can be used. It places particular emphasis on
                 features added to C as part of the C Standard. These
                 features include support for multiple locales (cultural
                 conventions) and very large character sets (such as
                 Kanji). The code presented in this book has been tested
                 with C compilers from Borland, Saber, Project Gnu, Sun,
                 UNIX, and VAX, ULTRIX. It has passed the widely used
                 Plum Hall Validation Suite tests for library functions.
                 It has also survived an assortment of public-domain
                 programs designed to stress C implementations and
                 illuminate their darker corners. The mathematical
                 functions are particularly well-engineered and tested.
                 Finally, \booktitle{The Standard C Library} shows you
                 many principles of library design in general. You learn
                 how to design and implement libraries that are highly
                 cohesive and reusable.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Preface / ix \\
                 Introduction / 1 \\
                 <assert.h> / 17 \\
                 <ctype.h> / 25 \\
                 <errno.h> / 47 \\
                 <float.h> / 57 \\
                 <limits.h> / 73 \\
                 <locale.h> / 81 \\
                 <math.h> / 127 \\
                 <setjmp.h> / 181 \\
                 <signal.h> / 193 \\
                 <stdarg.h> / 205 \\
                 <stddef.h> / 215 \\
                 <stdio.h> / 225 \\
                 <stdlib.h> / 333 \\
                 <string.h> / 387 \\
                 <time.h> / 415 \\
                 Interfaces / 445 \\
                 Names / 453 \\
                 Terms / 463 \\
                 Index / 475",
}

@TechReport{Posch:1992:MRR,
  author =       "K. C. Posch and R. Posch",
  title =        "Modulo reduction in residue number systems",
  institution =  "Inst., TU, Ges.",
  address =      "????",
  pages =        "16",
  year =         "1992",
  bibdate =      "Thu Nov 18 09:44:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "IIG-report-series",
  URL =          "http://books.google.com/books?id=YPLKHAAACAAJ",
  abstract =     "Residue number systems provide a good means for
                 extremely long integer arithmetic. Their carry-free
                 operations make parallel implementations feasible. Some
                 applications involving very long integers, such as
                 public key encryption, rely heavily on fast modulo
                 reductions. This paper shows a new combination of
                 residue number systems with efficient modulo reduction
                 methods. Two methods are compared, and the faster one
                 is scrutinized in detail. Both methods have the same
                 order of complexity, $ O(\log n) $, with $n$ denoting
                 the amount of registers involved.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Posch:1992:RNS,
  author =       "K. C. Posch and R. Posch",
  booktitle =    "Proceedings of the Fourth {IEEE} Symposium on Parallel
                 and Distributed Processing 1992",
  title =        "Residue number systems: a key to parallelism in public
                 key cryptography",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "432--435",
  year =         "1992",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/SPDP.1992.242713",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Public key cryptography and parallel algorithms are
                 considered. Special attention is paid to algorithms
                 using long integer modulo arithmetic. A modification of
                 the commonly known RSA algorithm is taken as a
                 candidate. So far all implementations have \ldots{}",
}

@Book{Press:1992:NRC,
  author =       "W. H. Press and B. P. Flannery and S. A. Teukolsky and
                 W. T. Vetterling",
  title =        "Numerical Recipes in {C}: The Art of Scientific
                 Computing",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  edition =      "Second",
  pages =        "xxvi + 994",
  year =         "1992",
  ISBN =         "0-521-43108-5, 0-521-43720-2",
  ISBN-13 =      "978-0-521-43108-8, 978-0-521-43720-2",
  LCCN =         "QA297 .N864 1992",
  bibdate =      "Thu Sep 01 22:12:07 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@PhdThesis{Priest:1992:PFP,
  author =       "Douglas M. Priest",
  title =        "On Properties of Floating Point Arithmetics: Numerical
                 Stability and the Cost of Accurate Computations",
  type =         "Thesis ({Ph.D.} in Mathematics)",
  school =       "Department of Computer Science, University of
                 California, Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "iv + 136",
  month =        dec,
  year =         "1992",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "UMI order number GAX93-30692.",
  URL =          "ftp://ftp.icsi.berkeley.edu/pub/theory/priest-thesis.ps.Z",
  abstract =     "Floating point arithmetics generally possess many
                 regularity properties in addition to those that are
                 typically used in roundoff error analyses; these
                 properties can be exploited to produce computations
                 that are more accurate and cost effective than many
                 programmers might think possible. Furthermore, many of
                 these properties are quite simple to state and to
                 comprehend, but few programmers seem to be aware of
                 them (or at least willing to rely on them).\par

                 This dissertation presents some of these properties and
                 explores their consequences for computability,
                 accuracy, cost, and portability. For example, we
                 consider several algorithms for summing a sequence of
                 numbers and show that under very general hypotheses, we
                 can compute a sum to full working precision at only
                 somewhat greater cost than a simple accumulation, which
                 can often produce a sum with no significant figures at
                 all. This example, as well as others we present, can be
                 generalized further by substituting still more complex
                 algorithms; consequently, examples such as these oblige
                 us to consider more carefully the tradeoffs between
                 cost and accuracy.\par

                 At one end of the accuracy spectrum we find one of the
                 least obvious consequences of the properties of
                 floating point arithmetic: the accuracy of a
                 computation consisting of rational arithmetic
                 operations and comparisons need not be limited by the
                 precision of the floating point arithmetic in which it
                 is carried out. Of course, the more accuracy desired,
                 the greater the cost of the computation, and the cost
                 of computing a very accurate result may be quite high;
                 we illustrate this possibility in the case of
                 polynomial evaluation. At the other end of the
                 spectrum, however, we give an example of a problem for
                 which simply computing a result to a modest guaranteed
                 accuracy costs far less than the contortions required
                 to accommodate inaccurate results. As a consequence of
                 examples such as these, we conclude that programmers
                 and theorists alike must be willing to adopt a more
                 sophisticated view of floating point arithmetic, even
                 if only to consider that more accurate and reliable
                 computations than those presently in common use might
                 be possible based on stronger hypotheses than are
                 customarily assumed.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation; Dept. of
                 Mathematics; Dissertations; floating-point arithmetic;
                 University of California, Berkeley",
}

@Article{Quach:1992:HSA,
  author =       "N. T. Quach and M. J. Flynn",
  title =        "High-speed addition in {CMOS}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "12",
  pages =        "1612--1615",
  month =        dec,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.214671",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@TechReport{Quach:1992:RFP,
  author =       "N. Quach and M. Flynn",
  title =        "A radix-64 floating-point divider",
  type =         "Technical Report",
  number =       "CSL-TR-92-529",
  institution =  "Computer Systems Laboratory, Stanford University",
  address =      "Stanford, CA, USA",
  month =        jun,
  year =         "1992",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}

@Article{Rao:1992:FPA,
  author =       "B. D. Rao",
  title =        "Floating point arithmetic and digital filters",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "40",
  number =       "1",
  pages =        "85--95",
  month =        jan,
  year =         "1992",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "The roundoff noise properties of floating point
                 digital filters are examined. To make the analysis
                 tractable, a high level model to deal with the errors
                 in the inner product operation is developed. This model
                 establishes a broad connection between \ldots{}",
}

@InProceedings{Rix:1992:CBF,
  author =       "B. Rix and D. Timmermann and H. Hahn and B. J.
                 Hosticka",
  booktitle =    "{1992 Proceedings of the IEEE Custom Integrated
                 Circuits Conference}",
  title =        "A {CORDIC}-based Floating-point Arithmetic Unit",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "30.3.1--30.3.4",
  year =         "1992",
  DOI =          "https://doi.org/10.1109/CICC.1992.591874",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; Floating-point arithmetic; Generators;
                 Microelectronics; Pipelines; Registers; Routing;
                 Throughput; Transistors; Vectors",
}

@InProceedings{Rix:1992:CFA,
  author =       "B. Rix and D. Timmermann and H. Hahn and B. J.
                 Hosticka",
  title =        "A {CORDIC}-based floating-point arithmetic unit",
  crossref =     "IEEE:1992:PIC",
  bookpages =    "766",
  pages =        "30.3/1--4",
  year =         "1992",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A floating-point arithmetic unit based on the CORDIC
                 algorithm is described. It computes a wide range of
                 arithmetic, trigonometric, and hyperbolic functions and
                 achieves a normalized peak performance of 220 MFLOPS.
                 The unit is implemented in 1.6- mu m double-metal CMOS
                 technology and packaged in a 280-pin PGA.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Electr. Eng., Duisburg University,
                 Germany",
  classification = "B1265F (Microprocessors and microcomputers); B2570D
                 (CMOS integrated circuits); C5135 (Digital signal
                 processing chips); C5230 (Digital arithmetic methods);
                 C5260 (Digital signal processing)",
  keywords =     "1.6 Micron; 220 MFLOPS; 280-Pin PGA; CORDIC algorithm;
                 Double-metal CMOS technology; DSP; Floating-point
                 arithmetic unit; Hyperbolic functions; Trigonometric
                 functions",
  numericalindex = "Computer speed 2.2E+08 FLOPS; Size 1.6E-06 m",
  thesaurus =    "CMOS integrated circuits; Digital arithmetic; Digital
                 signal processing chips",
}

@InProceedings{Sanz-Gonzalez:1992:OFP,
  author =       "J. L. Sanz-Gonzalez and F. Lopez-Ferreras",
  booktitle =    "Proceedings of the 3rd {AFRICON} Conference: {AFRICON
                 '92}",
  title =        "Optimal floating-point structures for low roundoff
                 noise digital filters",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "194--197",
  year =         "1992",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "A theoretical analysis of roundoff noise power in
                 floating-point realizations of digital filters is
                 presented. Formulas are given for single-length and
                 double-length accumulators. The minimal-noise
                 floating-point structure is found to be identical
                 \ldots{}",
}

@Article{Scherson:1992:BPA,
  author =       "I. D. Scherson and D. A. Kramer and B. D. Alleyne",
  title =        "Bit-parallel arithmetic in a massively-parallel
                 associative processor",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "10",
  pages =        "1201--1210",
  month =        oct,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.166599",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=166599",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Schwarz:1992:ASF,
  author =       "E. M. Schwarz and M. J. Flynn",
  title =        "Approximating the Sine Function With Combinational
                 Logic",
  crossref =     "Singh:1992:CRT",
  pages =        "386--390",
  year =         "1992",
  bibdate =      "Thu Sep 08 08:02:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Seznec:1992:CSH,
  author =       "Andr{\'e} Seznec and Karl Courtel",
  title =        "Controlling and sequencing a heavily pipelined
                 floating-point operator",
  journal =      j-SIGMICRO,
  volume =       "23",
  number =       "1--2",
  pages =        "111--114",
  month =        dec,
  year =         "1992",
  CODEN =        "SIGMDJ",
  DOI =          "https://doi.org/10.1145/144965.145008",
  ISSN =         "0163-5751, 1050-916X",
  ISSN-L =       "0163-5751",
  bibdate =      "Fri Apr 16 10:27:43 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigmicro.bib",
  URL =          "https://dl.acm.org/doi/10.1145/144965.145008",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMICRO Newsletter",
  journal-URL =  "https://dl.acm.org/loi/sigmicro",
}

@Article{Seznec:1992:OAF,
  author =       "Andr{\'e} Seznec and Karl Courtel",
  title =        "{OPAC} (abstract): a floating-point coprocessor
                 dedicated to compute-bound kernels",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "20",
  number =       "2",
  pages =        "427--427",
  month =        may,
  year =         "1992",
  CODEN =        "CANED2",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Fri May 12 09:40:43 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
}

@Article{Seznec:1992:OFC,
  author =       "A. Seznec and K. Courtel",
  title =        "{OPAC}: a Floating-Point Coprocessor Dedicated to
                 Compute-Bound Kernels",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "20",
  number =       "2",
  pages =        "427--427",
  month =        may,
  year =         "1992",
  CODEN =        "CANED2",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
}

@Article{Simar:1992:FPP,
  author =       "Ray {Simar, Jr.} and Peter Koeppen and Jerald Leach
                 and Steve Marshall and Dave Francis and Greg Mekras and
                 Jeffrey Rosenstrauch and Scott Anderson",
  title =        "Floating-Point Processors Join Forces in Parallel
                 Processing Architectures",
  journal =      j-IEEE-MICRO,
  volume =       "12",
  number =       "4",
  pages =        "60--69",
  month =        jul # "\slash " # aug,
  year =         "1992",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/40.149737",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Achieving cost-effective design performance goals with
                 parallel DSP building blocks supported by extensive
                 software",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  summary =      "The hardware architecture and software capabilities of
                 the TMS320C40 floating-point digital signal processor
                 are described. The C40 operates at 275 million
                 operations per second (MOPS) and transfers data at a
                 rate of 320 Mbytes/s with a 40-ns cycle time \ldots{}",
}

@Book{Sites:1992:AAR,
  author =       "Richard L. Sites and Richard Witek and others",
  title =        "Alpha Architecture Reference Manual",
  publisher =    pub-DP # " and " # pub-PH,
  address =      pub-DP:adr # " and " # pub-PH:adr,
  year =         "1992",
  ISBN =         "0-13-033663-7 (PH), 1-55558-098-X (DP: print)",
  ISBN-13 =      "978-0-13-033663-7 (PH), 978-1-55558-098-8 (DP:
                 print)",
  LCCN =         "QA76.9.A73 A46 1992",
  bibdate =      "Wed Jan 23 08:49:36 MST 2019",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/microchip.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "Foreword \\
                 Preface \\
                 Common Architecture \\
                 Introduction \\
                 Basic Architecture \\
                 Instruction Formats \\
                 Instruction Descriptions \\
                 System Architecture and Programming Implications \\
                 Common PALcode Architecture \\
                 Console Subsystem Overview \\
                 Input/Output \\
                 OpenVMS Alpha Software \\
                 Introduction to OpenVMS Alpha \\
                 OpenVMS PALcode Instruction Descriptions \\
                 OpenVMS Memory Management \\
                 OpenVMS Process Structure \\
                 OpenVMS Internal Processor Registers \\
                 OpenVMS Exceptions, Interrupts, and Machine Checks \\
                 DEC OSF/1 Alpha Software \\
                 Introduction to DEC OSF/1 Alpha \\
                 OSF/1 PALcode Instruction Descriptions \\
                 OSF/1 Memory Management \\
                 OSF/I Process Structure \\
                 OSF/1 Exceptions and Interrupts \\
                 Appendix A: Software Considerations \\
                 Appendix B: IEEE Floating-Point Conformance \\
                 Appendix C: Instruction Encodings \\
                 Index",
  xxauthor =     "{Alpha Architecture Committee}",
}

@Article{Skavantzos:1992:DCM,
  author =       "A. Skavantzos and T. Stouraitis",
  title =        "Decomposition of complex multipliers using polynomial
                 encoding",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "10",
  pages =        "1331--1333",
  month =        oct,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.166610",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  note =         "See comments \cite{Katti:1994:CDC}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=166610",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Skavantzos:1992:NMM,
  author =       "A. Skavantzos and P. B. Rao",
  title =        "New multipliers modulo {$ 2^N - 1 $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "957--961",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156538",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156538",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Skavantzos:1992:TII,
  author =       "A. Skavantzos and N. Mitash",
  booktitle =    "{IEEE} Southeastcon '92, Proceedings, 12--15 April
                 1992",
  title =        "Theory and implementation issues of the 2-dimensional
                 polynomial residue number system",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "226--233",
  year =         "1992",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/SECON.1992.202342",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The authors present 2D polynomial residue number
                 system techniques for parallel polynomial
                 multiplication in modular rings and discuss array
                 implementation issues of such 2D polynomial
                 multipliers. A specific example design is presented.
                 The \ldots{}",
}

@Article{Skeel:1992:REP,
  author =       "R. Skeel",
  title =        "Roundoff error and the {Patriot} missile",
  journal =      j-SIAM-NEWS,
  volume =       "25",
  number =       "4",
  pages =        "11--1",
  month =        jul,
  year =         "1992",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibdate =      "Sat Apr 28 19:10:25 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.siam.org/siamnews/general/patriot.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM News",
  journal-URL =  "https://sinews.siam.org/",
}

@Article{Smith:1992:FPR,
  author =       "L. Montgomery Smith and B. W. Bomar and R. D. Joseph
                 and G. C. J. Yang",
  title =        "Floating-Point Roundoff Noise Analysis of Second-Order
                 State-Space Digital Filter Structures",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "39",
  number =       "2",
  pages =        "90--98",
  month =        feb,
  year =         "1992",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.205812",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE transactions on circuits and systems. 2, Analog
                 and digital signal processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  summary =      "A parametric approach is used to determine the
                 roundoff noise in all real second-order floating-point
                 state-space realizations of a transfer function having
                 complex conjugate poles. The parametric roundoff noise
                 analysis is then verified by experiment \ldots{}",
}

@InProceedings{Soudris:1992:SDAa,
  author =       "D. Soudris and V. Paliouras and T. Stouraitis",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing. {ICASSP-92, 23--26} March 1992",
  title =        "Systematic development of architectures for
                 multidimensional {DSP} using the residue number
                 system",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "397--400",
  year =         "1992",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICASSP.1992.226192",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A systematic methodology for mapping multidimensional
                 algorithms onto array processor architectures based on
                 the quadratic residue number system is presented. A
                 class of algorithms with separable functions, which can
                 be reduced to the computation of \ldots{}",
}

@InProceedings{Soudris:1992:SDAb,
  author =       "D. Soudris and V. Paliouras and T. Stouraitis",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing. {ICASSP-92, 23--26} March 1992",
  title =        "Systematic development of architectures for
                 multidimensional {DSP} using the residue number
                 system",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "397--400",
  year =         "1992",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICASSP.1992.226192",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A systematic methodology for mapping multidimensional
                 algorithms onto array processor architectures based on
                 the quadratic residue number system is presented. A
                 class of algorithms with separable functions, which can
                 be reduced to the computation of \ldots{}",
}

@Book{SPARC:1992:SAM,
  author =       "{SPARC International, Inc.}",
  title =        "The {SPARC} Architecture Manual\emdash{}Version 8",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xxix + 316",
  year =         "1992",
  ISBN =         "0-13-825001-4",
  ISBN-13 =      "978-0-13-825001-0",
  LCCN =         "QA76.9.A73 S647 1992",
  bibdate =      "Thu Dec 16 09:12:32 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Sparmann:1992:DHQ,
  author =       "Uwe Sparmann",
  title =        "Derivation of high quality tests for large
                 heterogeneous circuits: floating-point operations",
  journal =      "Informatik",
  volume =       "1",
  pages =        "425--439",
  year =         "1992",
  MRclass =      "94C12 (93C05)",
  MRnumber =     "93j:94039",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Teubner-Texte Inform.",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point testing",
  reviewer =     "Adrian Ad{\u{a}}sc{\u{a}}li{\c{t}}ei",
}

@Article{Srinivas:1992:SFV,
  author =       "S. Srinivas and K. Dybvig",
  title =        "Superscalar Floating-Point Vector Computation in
                 Scheme",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "??",
  number =       "634",
  pages =        "811--812",
  year =         "1992",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Steidley:1992:FPA,
  author =       "C. W. Steidley",
  title =        "Floating point arithmetic basic exercises in
                 mathematical reasoning for computer science majors",
  journal =      j-COMP-EDU-J,
  volume =       "2",
  number =       "4",
  pages =        "1--6",
  month =        oct # "--" # dec,
  year =         "1992",
  CODEN =        "CEJOE7",
  ISSN =         "1069-3769",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Efficient mathematical (numerical) computing requires
                 floating point computation since fixed point arithmetic
                 limits the range of the numbers being manipulated.
                 Fixed point arithmetic also adds to the complexity of
                 operation by demanding a great deal of scaling among
                 numbers with different `implicit' radix (base) points.
                 Thus, floating point arithmetic has become a modern
                 computing necessity. In 1988, Central Washington
                 University introduced CPSC 321 Systems Programming into
                 the curriculum. The course was intended to give
                 students an opportunity to learn more about the
                 hardware, architecture, and organization of computing
                 machines by studying and writing systems software. Some
                 topics considered for the initial offering of the
                 course included: a simple assembler, a basic loader, or
                 a simple compiler. However, many of these topics are
                 covered in other courses and after discussions with
                 many colleagues in the Department of Mathematics
                 regarding the coverage of representation and use of
                 decimal arithmetic on computers, it was decided that
                 the fundamentals of some systems programs could be
                 covered by introducing the basic aspects of doing
                 mathematics on a computer from the systems point of
                 view.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, Southeastern Louisiana
                 University, Hammond, LA, USA",
  classification = "C0220 (Education and training); C5230 (Digital
                 arithmetic methods); C6110 (Systems analysis and
                 programming); C7310 (Mathematics)",
  fjournal =     "Computers in education journal",
  keywords =     "Computer science majors; Computing machines; Computing
                 necessity; CPSC 321 Systems Programming; Curriculum;
                 decimal floating-point arithmetic; Floating point
                 arithmetic; Floating point computation; Mathematical
                 reasoning; Students; Systems software",
  thesaurus =    "Computer science education; Digital arithmetic;
                 Educational courses; Mathematics computing; Systems
                 analysis; Teaching",
}

@Article{Stetter:1992:ICR,
  author =       "F. Stetter",
  title =        "Internal computer representation of integer numbers",
  journal =      j-INFORMATIK-SPEKTRUM,
  volume =       "15",
  number =       "6",
  pages =        "352--354",
  month =        dec,
  year =         "1992",
  CODEN =        "INSKDW",
  ISSN =         "0170-6012 (print), 1432-122X (electronic)",
  ISSN-L =       "0170-6012",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Compares floating point and integer representations
                 and presents a proposal for a unified integer
                 representation which allows for sign. Definitions are
                 given of two's complement and one's complement
                 representations and rules are proposed for integer
                 addition and subtraction, multiplication and division
                 with various translation algorithms.",
  acknowledgement = ack-nhfb,
  affiliation =  "Mannheim University, Germany",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "Informatik Spektrum",
  journal-URL =  "http://link.springer.com/journal/287",
  keywords =     "Division; Floating point; Integer addition; Integer
                 numbers; Integer representations; Multiplication;
                 Subtraction; Unified integer representation",
  language =     "German",
  pubcountry =   "Germany",
  thesaurus =    "Digital arithmetic",
}

@Article{Stouraitis:1992:ECR,
  author =       "T. Stouraitis",
  title =        "Efficient convertors for residue and quadratic-residue
                 number systems",
  journal =      "Circuits, Devices and Systems, IEE Proceedings G",
  volume =       "139",
  number =       "6",
  pages =        "626--634",
  month =        dec,
  year =         "1992",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/78.157231",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4741",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The quadratic-residue number system (QRNS) is known to
                 be efficient for complex-number calculations, since it
                 eliminates the need for cross-product terms and offers
                 high speed with small hardware complexity. However, the
                 conversion overhead between \ldots{}",
}

@Article{Sun:1992:CTA,
  author =       "J.-D. Sun and H. Krishna",
  title =        "A coding theory approach to error control in redundant
                 residue number systems. {II}. Multiple error detection
                 and correction",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "39",
  number =       "1",
  pages =        "18--34",
  month =        jan,
  year =         "1992",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.204107",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5240",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems. 2, Analog
                 and Digital Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  keywords =     "residue arithmetic; residue number system",
  summary =      "For pt.I see ibid., vol.39, no.1, p.8-17 (1992). The
                 coding theory approach to error control in redundant
                 residue number systems (RRNSs) is extended by deriving
                 computationally efficient algorithms for correcting
                 multiple errors, single-burst-error, \ldots{}",
}

@Article{Takagi:1992:MMH,
  author =       "N. Takagi and S. Yajima",
  title =        "Modular multiplication hardware algorithms with a
                 redundant representation and their application to {RSA}
                 cryptosystem",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "7",
  pages =        "887--891",
  month =        jul,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.256444",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:18 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=256444",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Takagi:1992:RMM,
  author =       "N. Takagi",
  title =        "A radix-$4$ modular multiplication hardware algorithm
                 for modular exponentiation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "949--956",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156537",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156537",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Tang:1992:TDI,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Driven Implementation of the {{\tt Expm1}}
                 Function in {IEEE} Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "18",
  number =       "2",
  pages =        "211--222",
  month =        jun,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/146847.146928",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D15",
  MRnumber =     "1 167 891",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See independent analysis and accuracy confirmation of
                 this algorithm in \cite{Kramer:1998:PWC}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p211-tang/",
  abstract =     "Algorithms and implementation details for the function
                 $ e^x - 1 $ in both single and double precision of IEEE
                 754 arithmetic are presented here. With a table of
                 moderate size, the implementations need only
                 working-precision arithmetic and are provably accurate
                 to within 0.58 ulp.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis. {\bf G.1.0}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis.",
}

@InProceedings{Teufel:1992:IFP,
  author =       "Thomas Teufel",
  title =        "Implementation of a floating-point arithmetic with an
                 accurate scalar product for digital signal processing",
  crossref =     "Atanassova:1992:CAE",
  pages =        "147--156",
  year =         "1992",
  bibdate =      "Sat Sep 17 19:12:26 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@MastersThesis{Thirumalaiswamy:1992:DSB,
  author =       "Vijayashree Thirumalaiswamy",
  title =        "Design and simulation of bit-serial floating point
                 arithmetic co-processor",
  type =         "Thesis ({M.S.})",
  school =       "University of Texas at El Paso",
  address =      "El Paso, TX, USA",
  pages =        "xii + 113",
  year =         "1992",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Array processors --- Design.; Floating-point
                 arithmetic.",
}

@Article{Timmermann:1992:LLT,
  author =       "D. Timmermann and H. Hahn and B. J. Hosticka",
  title =        "Low Latency Time {CORDIC} Algorithms",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "1010--1015",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156543",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 08 00:52:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Vowels:1992:D,
  author =       "R. A. Vowels",
  title =        "Division by 10",
  journal =      j-AUSTRALIAN-COMP-J,
  volume =       "24",
  number =       "3",
  pages =        "81--85",
  month =        aug,
  year =         "1992",
  CODEN =        "ACMJB2",
  ISSN =         "0004-8917",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Division of a binary integer and a binary
                 floating-point mantissa by 10 can be performed with
                 shifts and adds, yielding a significant improvement in
                 hardware execution time, and in software execution time
                 if no hardware divide instruction is available. Several
                 algorithms are given, appropriate to specific machine
                 word sizes, hardware and hardware instructions
                 available, and depending on whether a remainder is
                 required. The integer division algorithms presented
                 here contain a new strategy that produces the correct
                 quotient directly, without the need for the
                 supplementary correction required of
                 previously-published algorithms. The algorithms are
                 competitive in time with binary coded decimal (BCD)
                 divide by 10. Both the integer and floating-point
                 algorithms are an order of magnitude faster than
                 conventional division.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, R. Melbourne Inst. of
                 Technol. Ltd., Vic., Australia",
  classification = "C7310 (Mathematics)",
  fjournal =     "Australian Computer Journal",
  keywords =     "Binary integer; decimal floating-point arithmetic;
                 Floating-point algorithms; Hardware execution time;
                 Integer division algorithms; Software execution time",
  pubcountry =   "Australia",
  thesaurus =    "Digital arithmetic; Mathematics computing",
}

@MastersThesis{Wang:1992:RAF,
  author =       "Jie Wang",
  title =        "Response analysis for floating point implementations
                 of linear discrete systems",
  type =         "Thesis ({M.S.E.E.})",
  school =       "University of Notre Dame",
  address =      "Notre Dame, IN 46556, USA",
  pages =        "xi + 83",
  year =         "1992",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Weber-Wulff:1992:REC,
  author =       "Debora Weber-Wulff",
  title =        "Rounding error changes {Parliament} makeup",
  journal =      "The Risks Digest",
  volume =       "13",
  number =       "37",
  pages =        "8--8",
  year =         "1992",
  bibdate =      "Sat Apr 28 19:12:42 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://catless.ncl.ac.uk/Risks/13.37.html#subj4",
  acknowledgement = ack-nhfb,
}

@Article{Werter:1992:SLC,
  author =       "M. J. Werter",
  title =        "Suppression of limit cycles in the first-order
                 two-dimensional direct form digital filter with a
                 controlled rounding arithmetic",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "40",
  number =       "6",
  pages =        "1599--1601",
  month =        jun,
  year =         "1992",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sat Jul 16 11:25:03 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "The first-order two-dimensional direct-form digital
                 filter with magnitude truncation is known to be free
                 from limit cycles for a limited range of allowed filter
                 coefficients. In this correspondence, the quantization
                 technique of controlled rounding \ldots{}",
}

@Article{Wesner:1992:TS,
  author =       "J. Wesner",
  title =        "{Ein Tick schneller} \toenglish {A Tick Faster}
                 \endtoenglish",
  journal =      j-MC,
  volume =       "2",
  pages =        "80--86",
  year =         "1992",
  ISSN =         "0720-4442, 0941-777x, 0943-5409",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "MC: Die Mikrocomputer-Zeitschrift",
}

@Article{Wichmann:1992:NUF,
  author =       "Brian A. Wichmann",
  title =        "A Note on the Use of Floating Point in Critical
                 Systems",
  journal =      j-COMP-J,
  volume =       "35",
  number =       "1",
  pages =        "41--44",
  month =        feb,
  year =         "1992",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www3.oup.co.uk/computer_journal/Volume_35/Issue_01/Vol35_01.index.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/Volume_35/Issue_01/Vol35_01.body.html#AbstractWichmann",
  abstract =     "Floating point is a well tried technology which, it
                 might seem, can be used without reservation.
                 Unfortunately, there are dangers which arise from
                 faults in implementation and incorrect use. These are
                 often hard to locate. The paper addresses these
                 dangers.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "NPL, Teddington, UK",
  author-1-adr = "National Physical Laboratory, Teddington, Middlesex
                 TW11 OLW",
  classcodes =   "C5230 (Digital arithmetic methods)",
  classification = "C5230 (Digital arithmetic methods)",
  corpsource =   "NPL, Teddington, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "critical systems; digital arithmetic; faults; floating
                 point; Floating point; safety systems",
  pubcountry =   "UK",
  thesaurus =    "Digital arithmetic; Safety systems",
  treatment =    "P Practical",
}

@Article{Wichmann:1992:SFW,
  author =       "Brian A. Wichmann",
  title =        "{Surveyor's Forum}: ``{What} Every Computer Scientist
                 Should Know About Floating-Point Arithmetic''",
  journal =      j-COMP-SURV,
  volume =       "24",
  number =       "3",
  pages =        "319--319",
  month =        sep,
  year =         "1992",
  CODEN =        "CMSVAN",
  ISSN =         "0360-0300 (print), 1557-7341 (electronic)",
  ISSN-L =       "0360-0300",
  bibdate =      "Sun Sep 25 10:14:37 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See
                 \cite{Goldberg:1991:WEC,Goldberg:1991:CWE,Dunham:1992:SFW}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J204",
}

@Article{Wilkes:1992:E,
  author =       "Maurice V. Wilkes",
  title =        "{EDSAC 2}",
  journal =      j-IEEE-ANN-HIST-COMPUT,
  volume =       "14",
  number =       "4",
  pages =        "49--56",
  month =        oct # "--" # dec,
  year =         "1992",
  CODEN =        "IAHCEX",
  DOI =          "https://doi.org/10.1109/85.194055",
  ISSN =         "1058-6180 (print), 1934-1547 (electronic)",
  ISSN-L =       "1058-6180",
  bibdate =      "Thu Jul 12 06:22:54 MDT 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeeannhistcomput.bib",
  URL =          "http://dlib.computer.org/an/books/an1992/pdf/a4049.pdf;
                 http://www.computer.org/annals/an1992/a4049abs.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Annals of the History of Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85",
  remark =       "From page 54: ``When the machine was initialized for a
                 new program to be run, every bit in the memory was set
                 to a 1, rather than to a 0. Since, according to the
                 format used for floating numbers, no floating number
                 could consist entirely of 1's, any attempt to read a
                 floating-point number from part of the memory that had
                 not been written into caused the machine to stop. Many
                 a programmer must have been grateful to [David J.]
                 Wheeler for his foresight in making this happen.''",
}

@Article{Wilt:1992:ALP,
  author =       "Nicholas Wilt",
  title =        "Assembly language programming for the 80*87",
  journal =      j-DDJ,
  volume =       "17",
  number =       "3",
  pages =        "36, 38, 40, 42, 88",
  month =        mar,
  year =         "1992",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Tue Sep 10 10:06:23 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C5130 (Microprocessor chips); C5230 (Digital
                 arithmetic methods); C6110 (Systems analysis and
                 programming)",
  fjournal =     "Dr. Dobb's Journal of Software Tools",
  keywords =     "80*87 Coprocessor; Assembly language programming;
                 Floating point arithmetic; Numeric coprocessors;
                 Optimization",
  thesaurus =    "Assembly language listings; Digital arithmetic;
                 Microprocessor chips; Optimisation; Programming;
                 Satellite computers",
}

@Article{Wong:1992:DSR,
  author =       "W. F. Wong and E. Goto",
  title =        "Division and square-rooting using a split multiplier",
  journal =      j-ELECT-LETTERS,
  volume =       "28",
  number =       "18",
  pages =        "1758--1759",
  day =          "27",
  month =        aug,
  year =         "1992",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Wed Dec 13 13:13:34 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A modification is proposed to the traditional design
                 of a fast floating point multiplication circuit such
                 that instead of just performing $ A * B $ where $A$ and
                 $B$ are $m$ bits long, it is also capable of performing
                 $ C * x_0$ and $ D * x_1$ where $C$ and $D$ are still m
                 bits long but $ x_0$ and $ x_1$ are $ m / 2$ bits long
                 using about the same amount of hardware resources but
                 in two thirds of the time. Such a circuit is called a
                 split multiplier. The authors show how such a split
                 multiplier can be used to compute division and $ Y
                 \sqrt {X}$ accurately and quickly.",
  acknowledgement = ack-nhfb,
  affiliation =  "Goto Lab., Inst. of Phys. and Chem. Res., Saitama,
                 Japan",
  classification = "B1265B (Logic circuits); C5120 (Logic and switching
                 circuits); C5230 (Digital arithmetic methods)",
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "Division; Fast floating point multiplication circuit;
                 Split multiplier; Square-rooting",
  pubcountry =   "UK",
  thesaurus =    "Digital arithmetic; Dividing circuits; Logic circuits;
                 Multiplying circuits",
}

@Article{Wong:1992:FDU,
  author =       "D. Wong and M. Flynn",
  title =        "Fast Division Using Accurate Quotient Approximations
                 to Reduce the Number of Iterations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "981--995",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156541",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156541",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Woods:1992:HPD,
  author =       "R. F. Woods and S. E. McQuillan and J. Dowling and J.
                 V. McCanny",
  booktitle =    "Proceedings of Fifth Annual {IEEE} International
                 {ASIC} Conference and Exhibit, 1992",
  title =        "High performance {DSP} {ASIC} for multiply, divide and
                 square root",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "209--213",
  year =         "1992",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The design of a high-speed ASIC that combines the
                 operations of multiplication, division and square root
                 is described. The chip is based on a systolic array
                 architecture that uses a redundant number system and
                 allows multiplication, division, and \ldots{}",
}

@Article{Yeyios:1992:TSA,
  author =       "A. K. Yeyios",
  title =        "On two sequences of algorithms for approximating
                 square roots",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "40",
  number =       "1",
  pages =        "63--72",
  month =        jun,
  year =         "1992",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Thu Sep 1 10:15:56 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Yokoo:1992:OUF,
  author =       "H. Yokoo",
  title =        "Overflow\slash Underflow-Free Floating-Point Number
                 Representations with Self-Delimiting Variable-Length
                 Exponent Field",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "41",
  number =       "8",
  pages =        "1033--1039",
  month =        aug,
  year =         "1992",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.156546",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 10:49:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=156546",
  abstract =     "A class of new floating-point representations of real
                 numbers, based on representations of the integers, is
                 described. In the class, every representation uses a
                 self-delimiting representation of the integers as a
                 variable length field of the exponent, and neither
                 overflow nor underflow appears in practice. The adopted
                 representations of the integers are defined
                 systematically, so that representation's of numbers
                 greater than one have both exponent-significant and
                 integer-fraction interpretations. Since representation
                 errors are characterized by the length function of an
                 underlying representation of the integers, superior
                 systems in precision can be easily selected from the
                 proposed class.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, Gunma University,
                 Kiryu, Japan",
  ajournal =     "IEEE Trans. Comput.",
  classification = "B0250 (Combinatorial mathematics); B1265B (Logic
                 circuits); C1160 (Combinatorial mathematics); C5230
                 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Floating-point number representations; Integer
                 representation; Real numbers; Self-delimiting
                 variable-length exponent field",
  summary =      "A class of new floating-point representations of real
                 numbers, based on representations of the integers, is
                 described. In the class, every representation uses a
                 self-delimiting representation of the integers as a
                 variable length field of the exponent \ldots{}",
  thesaurus =    "Digital arithmetic; Number theory",
}

@Article{Zelniker:1992:RMC,
  author =       "G. S. Zelniker and F. J. Taylor",
  title =        "On the reduction in multiplicative complexity achieved
                 by the polynomial residue number system",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "40",
  number =       "9",
  pages =        "2318--2320",
  month =        sep,
  year =         "1992",
  CODEN =        "ITPRED",
  DOI =          "https://doi.org/10.1109/78.157231",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4075",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The polynomial residue number system is known to
                 reduce the complexity of polynomial multiplication from
                 O(N 2) to O(N). A new interpretation of this complexity
                 reduction is given in the context of \ldots{}",
}

@Article{Alam:1993:RTO,
  author =       "M. S. Alam and M. A. Karim",
  title =        "Real-Time Optical Arithmetic\slash Logical
                 Processing",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "17",
  number =       "3",
  pages =        "251--258",
  month =        mar,
  year =         "1993",
  CODEN =        "JPDCER",
  DOI =          "https://doi.org/10.1006/jpdc.1993.1024",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Thu Mar 9 09:18:51 MST 2000",
  bibsource =    "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.idealibrary.com/links/doi/10.1006/jpdc.1993.1024/production;
                 http://www.idealibrary.com/links/doi/10.1006/jpdc.1993.1024/production/pdf",
  acknowledgement = ack-nhfb,
  classification = "B4180 (Optical logic devices and optical computing
                 techniques); C5110D (Optical logic elements)C5120
                 (Logic and switching circuits); C5230 (Digital
                 arithmetic methods); C5270 (Optical computing
                 techniques)",
  corpsource =   "Department of Eng., Purdue University, Fort Wayne, IN,
                 USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "autocorrelation peaks; binary; coding scheme; digital
                 arithmetic; full adder; input joint image; joint
                 transform correlator; minterms; multiple outputs;
                 optical logic; real time logical processing; real-time
                 optical arithmetic; real-time systems",
  treatment =    "P Practical",
}

@Book{Albrecht:1993:VNT,
  editor =       "R. (Rudolf F.) Albrecht and G. (G{\"o}tz) Alefeld and
                 H. (Hans) J. Stetter",
  title =        "Validation numerics: theory and applications",
  volume =       "9",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "291",
  year =         "1993",
  ISBN =         "3-211-82451-0 (Wien), 0-387-82451-0 (New York)",
  ISBN-13 =      "978-3-211-82451-1 (Wien), 978-0-387-82451-2 (New
                 York)",
  LCCN =         "QA297 .V27 1993",
  bibdate =      "Thu Apr 02 09:18:32 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "This volume is dedicated to Professor Dr. Ulrich
                 Kulisch, \ldots{} on the occasion of his 60th
                 birthday.",
  series =       "Computing (Springer-Verlag). Supplementum",
  acknowledgement = ack-nhfb,
}

@MastersThesis{Alqeisi:1993:FPF,
  author =       "Yousuf Alqeisi",
  title =        "A 16-bit floating point fast {Fourier} transform
                 processor using {Xlinx}'s {FPGA's}",
  type =         "Thesis ({M.S.})",
  school =       "Department of Electrical Engineering, Southern
                 Illinois University at Carbondale",
  address =      "Carbondale, IL, USA",
  pages =        "v + 60",
  year =         "1993",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Anonymous:1993:FPa,
  author =       "Anonymous",
  title =        "Floating Point",
  journal =      j-COMPUT-AIDED-ENG,
  volume =       "12",
  number =       "1",
  pages =        "56--??",
  month =        jan,
  year =         "1993",
  CODEN =        "CCAEDJ",
  ISSN =         "0733-3536 (print), 2162-1365 (electronic)",
  ISSN-L =       "0733-3536",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Making a Case for Pencil Plotters.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer-aided engineering: CAE",
}

@Article{Anonymous:1993:FPb,
  author =       "Anonymous",
  title =        "Floating Point",
  journal =      j-COMPUT-AIDED-ENG,
  volume =       "12",
  number =       "5",
  pages =        "67--??",
  month =        may,
  year =         "1993",
  CODEN =        "CCAEDJ",
  ISSN =         "0733-3536 (print), 2162-1365 (electronic)",
  ISSN-L =       "0733-3536",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Component Technology.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer-aided engineering: CAE",
}

@Article{Anonymous:1993:FPc,
  author =       "Anonymous",
  title =        "Floating Point",
  journal =      j-COMPUT-AIDED-ENG,
  volume =       "12",
  number =       "9",
  pages =        "48--??",
  month =        sep,
  year =         "1993",
  CODEN =        "CCAEDJ",
  ISSN =         "0733-3536 (print), 2162-1365 (electronic)",
  ISSN-L =       "0733-3536",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "ProStep.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer-aided engineering: CAE",
}

@Article{Anonymous:1993:FPd,
  author =       "Anonymous",
  title =        "Floating Point",
  journal =      j-COMPUT-AIDED-ENG,
  volume =       "12",
  number =       "10",
  pages =        "98--??",
  month =        oct,
  year =         "1993",
  CODEN =        "CCAEDJ",
  ISSN =         "0733-3536 (print), 2162-1365 (electronic)",
  ISSN-L =       "0733-3536",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Open Modeling Still Going Strong.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer-aided engineering: CAE",
}

@Article{Anonymous:1993:FPe,
  author =       "Anonymous",
  title =        "Floating Point",
  journal =      j-COMPUT-AIDED-ENG,
  volume =       "12",
  number =       "11",
  pages =        "42--??",
  month =        nov,
  year =         "1993",
  CODEN =        "CCAEDJ",
  ISSN =         "0733-3536 (print), 2162-1365 (electronic)",
  ISSN-L =       "0733-3536",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Cost Benefits CAD/CAM.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer-aided engineering: CAE",
}

@Article{Anonymous:1993:FSB,
  author =       "Anonymous",
  title =        "The ``fastest system on the block'' label must be
                 qualified with new multiplatform, floating-point
                 benchmarks",
  journal =      j-PC-WEEK,
  volume =       "10",
  number =       "22",
  pages =        "85--??",
  month =        jun,
  year =         "1993",
  ISSN =         "0740-1604",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "PC Week",
}

@Book{Anonymous:1993:SRT,
  author =       "Anonymous",
  title =        "The Square Root of Two to 100,000 digits",
  volume =       "52",
  publisher =    pub-PROJECT-GUTENBERG,
  address =      pub-PROJECT-GUTENBERG:adr,
  year =         "1993",
  bibdate =      "Sun Jan 24 10:00:27 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-PROJECT-GUTENBERG,
  URL =          "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext93/2sqrt10.zip",
  acknowledgement = ack-nhfb # " and " # ack-st,
  subject =      "Mathematical constants.",
}

@Article{Asprey:1993:PFP,
  author =       "T. Asprey and G. Averill and E. DeLano and R. Mason
                 and B. Weiner and J. Yetter",
  title =        "Performance features of the {PA7100} microprocessor",
  journal =      j-IEEE-MICRO,
  volume =       "13",
  number =       "3",
  pages =        "22--35",
  month =        may # "\slash " # jun,
  year =         "1993",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/40.216746",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}

@Book{ASTM:1993:AES,
  author =       "{ASTM}",
  title =        "{ASTM E29-08}: Standard Practice for Using Significant
                 Digits in Test Data to Determine Conformance with
                 Specifications",
  publisher =    "ASTM International",
  address =      "West Conshohocken, PA, USA",
  year =         "1993",
  bibdate =      "Mon May 21 17:19:21 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Superseded by \cite{ASTM:2008:AES}.",
  URL =          "https://www.astm.org/DATABASE.CART/HISTORICAL/E29-08.htm",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite[ref. 32]{Carter:2013:ESF}.",
}

@Article{Bailey:1993:AMT,
  author =       "David H. Bailey",
  title =        "{Algorithm 719}: Multiprecision Translation and
                 Execution of {FORTRAN} Programs",
  journal =      j-TOMS,
  volume =       "19",
  number =       "3",
  pages =        "288--319",
  month =        sep,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/155743.155767",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Dec 13 18:37:31 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-3/p288-bailey/",
  abstract =     "This paper describes two Fortran utilities for
                 multiprecision computation. The first is a package of
                 Fortran subroutines that perform a variety of
                 arithmetic operations and transcendental functions on
                 floating point numbers of arbitrarily high precision.
                 This package is in some cases over 200 times faster
                 than that of certain other packages that have been
                 developed for this purpose.\par

                 The second utility is a translator program, which
                 facilitates the conversion of ordinary Fortran programs
                 to use this package. By means of source directives
                 (special comments) in the original Fortran program, the
                 user declares the precision level and specifies which
                 variables in each subprogram are to be treated as
                 multiprecision. The translator program reads this
                 source program and outputs a program with the
                 appropriate multiprecision subroutine calls.\par

                 This translator supports multiprecision integer, real,
                 and complex datatypes. The required array space for
                 multiprecision data types is automatically allocated.
                 In the evaluation of computational expressions, all of
                 the usual conventions for operator precedence and mixed
                 mode operations are upheld. Furthermore, most of the
                 Fortran-77 intrinsics, such as ABS, MOD, NINT, COS, EXP
                 are supported and produce true multiprecision values.",
  abstract-2 =   "The author describes two Fortran utilities for
                 multiprecision computation. The first is a package of
                 Fortran subroutines that perform a variety of
                 arithmetic operations and transcendental functions on
                 floating point numbers of arbitrarily high precision.
                 This package is in some cases over 200 times faster
                 than that of certain other packages that have been
                 developed for this purpose. The second utility is a
                 translator program, which facilitates the conversion of
                 ordinary Fortran programs to use this package. By means
                 of source directives (special comments) in the original
                 Fortran program, the user declares the precision level
                 and specifies which variables in each subprogram are to
                 be treated as multiprecision. The translator program
                 reads this source program and outputs a program with
                 the appropriate multiprecision subroutine calls. This
                 translator supports multiprecision integer, real, and
                 complex datatypes. The required array space for
                 multiprecision data types is automatically allocated.
                 In the evaluation of computational expressions, all of
                 the usual conventions for operator precedence and mixed
                 mode operations are upheld. Furthermore, most of the
                 Fortran-77 intrinsics, such as ABS, MOD, NINT, COS, EXP
                 are supported and produce true multiprecision values.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "NASA Ames Res. Center, Moffett Field, CA, USA",
  classification = "C5230 (Digital arithmetic methods); C6120 (File
                 organisation); C6140D (High level languages); C6150C
                 (Compilers, interpreters and other processors); C7310
                 (Mathematics)",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Algorithm 719; Arithmetic operations; Array space;
                 Complex data types; Computational expressions; Floating
                 point numbers; Fortran programs; Fortran subroutines;
                 Fortran utilities; Fortran-77 intrinsics; Mixed mode
                 operations; Multiprecision computation; Multiprecision
                 data types; Multiprecision subroutine calls;
                 Multiprecision translation; Operator precedence; Source
                 directives; Transcendental functions; Translator
                 program",
  subject =      "F.2.1 [Analysis of Algorithms and Problem Complexity]:
                 Numerical Algorithms and Problems; G.1.0 [Numerical
                 Analysis]: General; G.1.2 [Numerical Analysis];
                 Approximation",
  thesaurus =    "Data structures; Digital arithmetic; FORTRAN;
                 Mathematics computing; Program interpreters;
                 Subroutines",
}

@InProceedings{Bailey:1993:MPM,
  author =       "David H. Bailey and Robert Krasny and Richard Pelz",
  title =        "Multiple precision, multiple processor vortex sheet
                 roll-up computation",
  crossref =     "Sincovec:1993:PSS",
  pages =        "52--56",
  year =         "1993",
  bibdate =      "Thu Nov 25 10:04:31 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bajard:1993:BNH,
  author =       "J. C. Bajard and S. Kla and Jean-Michel Muller",
  title =        "{BKM}: a New Hardware Algorithm for Complex Elementary
                 Functions",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "146--153",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Bajard.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}

@Article{Baker:1993:SLR,
  author =       "Henry G. {Baker, Jr.}",
  title =        "Safe and leakproof resource management using {Ada83}
                 limited types",
  journal =      j-SIGADA-LETTERS,
  volume =       "13",
  number =       "5",
  pages =        "32--42",
  month =        sep # "\slash " # oct,
  year =         "1993",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Sat Aug 9 09:05:49 MDT 2003",
  bibsource =    "Compendex database; http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  abstract =     "Safe, leakproof and automatic resource managers are
                 essential to the implementation of every embedded
                 system, yet the standard examples of Ada83 resource
                 managers are either unsafe: they risk allocating the
                 same resource for two different purposes, leaky: they
                 risk permanently losing track of some resources, or
                 non-automatic: they require explicit deallocation,
                 which allows for a host of opportunities for
                 single-point system failures. Nevertheless, it is
                 possible to construct a safe, leakproof and automatic
                 resource manager --- at least for systems with only a
                 single task --- by a careful combination of certain
                 features of Ada83, and a careful avoidance of other
                 features. We illustrate our scheme with a safe,
                 leakproof and fully automatic dynamic-string package.
                 The same techniques also work for an arbitrary
                 precision arithmetic package [Fisher83] and for
                 managing the `roots' of a real-time garbage-collected
                 heap [Baker78] [Baker91SP] [Baker92Tread]. Suggestions
                 are offered to improve the use of limited private types
                 in Ada9X for automatic, safe and leakproof resource
                 management.",
  acknowledgement = ack-nhfb,
  affiliation =  "Nimble Computer Corp",
  affiliationaddress = "Encino, CA, USA",
  classcodes =   "C6150J (Operating systems); C6110B (Software
                 engineering techniques); C6120 (File organisation);
                 C6140D (High level languages)",
  classification = "722.1; 722.4; 723.1; 723.1.1; 723.2",
  conferenceyear = "1993",
  corpsource =   "Nimble Comput. Corp., Encino, CA, USA",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  journalabr =   "Ada Lett",
  keywords =     "Ada; Ada (programming language); Ada listings; Ada83
                 limited types; Ada83 resource; Ada9X; arbitrary
                 precision; Arbitrary precision arithmetic package;
                 arithmetic package; Automatic resource manager;
                 automatic resource managers; Computer operating
                 systems; Computer system recovery; Computer systems
                 programming; Data collection; data structures;
                 Deallocation; dynamic-string package; Embedded system;
                 embedded system; explicit deallocation; failures;
                 Information management; Interfaces (computer); Large
                 scale systems; leakproof resource management; limited
                 private types; management; managers; Program debugging;
                 Real time garbage collected heap; Real time systems;
                 real-time garbage-collected heap; real-time systems;
                 Resource allocation; resource allocation; Resource
                 management; Single point system failures; single-point
                 system; software reliability; storage; Storage
                 allocation (computer); Supervisory and executive
                 programs; System failure",
  treatment =    "P Practical; T Theoretical or Mathematical",
}

@Article{Bakhrakh:1993:NIF,
  author =       "S. M. Bakhrakh and S. V. Velichko and N. E.
                 Pilipchatin and V. F. Spiridonov and E. G. Sukhov and
                 Yu. G. Fedorova and V. I. Kheifets",
  title =        "Numerical investigation of floating-point arithmetic
                 operations",
  journal =      j-PROG-COMP-SOFT,
  volume =       "18",
  number =       "6",
  pages =        "255--258",
  year =         "1993",
  CODEN =        "PCSODA",
  ISSN =         "0361-7688 (print), 1608-3261 (electronic)",
  ISSN-L =       "0361-7688",
  bibdate =      "Wed Dec 13 18:18:07 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Original Russian language paper in
                 \cite{Bakhrakh:1992:NIF}.",
  abstract =     "This article analyzes the sources of accumulated
                 computational error in certain computers (of ES and PS
                 types) in floating-point mode. Results of numerical
                 experiments are given. These experiments demonstrate
                 the influence of rounding on accumulated error. (5
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. for Control Sci., Acad. of Sci., Russia",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "Programming and Computer Software; translation of
                 Programmirovaniye (Moscow, USSR) Plenum",
  journal-URL =  "http://link.springer.com/journal/11086",
  keywords =     "Accumulated error rounding; Computational error;
                 Digital arithmetic; ES computers; Floating-point
                 arithmetic; Numerical investigation; PS computers",
  pubcountry =   "Russia",
  remark =       "English translation of: Programmirovanie",
  thesaurus =    "Digital arithmetic",
}

@Article{Barrera:1993:IBS,
  author =       "Tony Barrera and Pelle Olsson",
  title =        "An Integer Based Square Root Algorithm",
  journal =      j-BIT,
  volume =       "33",
  number =       "2",
  pages =        "253--261",
  month =        jun,
  year =         "1993",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01989748",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "68M07",
  MRnumber =     "1 326 017",
  bibdate =      "Wed Dec 13 18:20:52 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mai.liu.se/BIT/contents/bit33.html;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=33&issue=2&spage=253",
  abstract =     "The authors propose a fast integer based method for
                 computing square roots of floating point numbers. This
                 implies high accuracy and robustness, since no
                 precision will be lost during the computation. Only
                 integer addition and shifts are necessary to obtain the
                 square root. Comparisons made with the modified Newton
                 method indicate that the suggested method is twice as
                 fast for computing floating point square roots. (5
                 Refs.)",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "AB Consonant, Uppsala, Sweden",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "Floating point numbers; floating-point arithmetic;
                 Integer based square root algorithm; Modified Newton
                 method; Robustness",
  pubcountry =   "Denmark",
  thesaurus =    "Digital arithmetic",
  xxpages =      "254--261",
}

@Article{Bauer:1993:LCB,
  author =       "P. H. Bauer and J. Wang",
  title =        "Limit cycle bounds for floating point implementations
                 of second-order recursive digital filters",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "40",
  number =       "8",
  pages =        "493--501",
  month =        aug,
  year =         "1993",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.242338",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems. 2, Analog
                 and Digital Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  summary =      "It is shown that floating point realizations of
                 linearly stable systems can exhibit four fundamental
                 types of free responses. Sufficient conditions for the
                 existence or nonexistence of some of these periodic
                 response types in a given system are presented
                 \ldots{}",
}

@Article{Beckmann:1993:FFTa,
  author =       "P. E. Beckmann and B. R. Musicus",
  title =        "Fast fault-tolerant digital convolution using a
                 polynomial residue number system",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "41",
  number =       "7",
  pages =        "2300--2313",
  month =        jul,
  year =         "1993",
  CODEN =        "ITPRED",
  DOI =          "https://doi.org/10.1109/78.224241",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5864",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A fault-tolerant convolution algorithm that is an
                 extension of residue-number-system fault-tolerance
                 schemes applied to polynomial rings is described. The
                 algorithm is suitable for implementation on
                 multiprocessor systems and is able to concurrently
                 \ldots{}",
}

@Article{Beckmann:1993:FFTb,
  author =       "P. E. Beckmann and B. R. Musicus",
  title =        "Fast fault-tolerant digital convolution using a
                 polynomial residue number system",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "41",
  number =       "7",
  pages =        "2300--2313",
  month =        jul,
  year =         "1993",
  CODEN =        "ITPRED",
  DOI =          "https://doi.org/10.1109/78.224241",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5864",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A fault-tolerant convolution algorithm that is an
                 extension of residue-number-system fault-tolerance
                 schemes applied to polynomial rings is described. The
                 algorithm is suitable for implementation on
                 multiprocessor systems and is able to concurrently
                 \ldots{}",
}

@InProceedings{Benouamer:1993:LEA,
  author =       "M. O. Benouamer and P. Jaillon and D. Michelucci and
                 J.-M. Moreau",
  title =        "A Lazy Exact Arithmetic",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "242--249",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Benouamer.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}

@InProceedings{Bickerstaff:1993:RAM,
  author =       "K'Andrea C. Bickerstaff and Michael J. Schulte and
                 Earl E. {Swartzlander, Jr.}",
  title =        "Reduced Area Multipliers",
  crossref =     "Wah:1993:ICA",
  pages =        "478--489",
  year =         "1993",
  bibdate =      "Sun Mar 04 10:43:38 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1993-03.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bizzan:1993:IMA,
  author =       "S. S. Bizzan and G. A. Jullien and N. M. Wigley and W.
                 C. Miller",
  title =        "Integer Mapping Architectures for the Polynomial Ring
                 Engine",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "44--51",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Bizzan.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}

@InCollection{Bohlender:1993:PAF,
  author =       "G. Bohlender and D. Cordes and A. Kn{\"o}fel and U.
                 Kulisch and R. Lohner and W. V. Walter",
  title =        "Proposal for accurate floating-point vector
                 arithmetic",
  crossref =     "Adams:1993:SCA",
  pages =        "87--102",
  year =         "1993",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Many computers provide accurate and reliable scalar
                 arithmetic for floating point numbers. An accurate
                 definition of the four elementary floating-point
                 operations +, -, *, / is given in the IEEE standards
                 for floating-point arithmetic and was well established
                 long before. An increasing number of computers
                 (especially PC's and workstations) feature IEEE
                 arithmetic. In many numerical algorithms, however,
                 compound operations such as the summation of a sequence
                 of numbers or the dot product of two vectors are highly
                 common. A simulation of these compound operations by
                 means of elementary floating-point operations leads to
                 accumulation of rounding errors and may suffer from
                 catastrophic cancellation of leading digits. Existing
                 standards for floating-point arithmetic do not improve
                 this situation. The goal of the proposal is to define
                 vector operations in a manner consistent with the
                 elementary scalar arithmetic operations. The rounding
                 modes and accuracy requirements as well as the data
                 formats of the operands and results of the vector
                 operations described in the proposal are chosen to be
                 fully consistent with the existing scalar
                 floating-point arithmetic.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Angewandte Math., Karlsruhe University,
                 Germany",
  classification = "C5230 (Digital arithmetic methods); C6130 (Data
                 handling techniques); C7310 (Mathematics)",
  keywords =     "Accuracy requirements; Catastrophic cancellation;
                 Compound operations; Data formats; Dot product;
                 Elementary floating-point operations; Elementary scalar
                 arithmetic operations; Floating point numbers; IEEE
                 arithmetic; IEEE standards; Leading digits; Numerical
                 algorithms; Operands; Rounding errors; Rounding modes;
                 Scalar floating-point arithmetic; Sequence; Standards;
                 Summation; Vector operations",
  thesaurus =    "Digital arithmetic; Mathematics computing; Roundoff
                 errors; Standards",
}

@InProceedings{Booth:1993:ECA,
  author =       "Andrew D. Booth",
  title =        "Early Computer Arithmetic",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "ix--ix",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_keynote.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
  remark =       "The author developed ``Booth's Algorithm'' for two's
                 complement multiplication, the APEXC computer at the
                 University of London (one of the world's first three
                 electronic digital computers), and the M3 series of
                 computers at the University of Saskatchewan (the first
                 all Canadian electronic computer).",
}

@InProceedings{Briggs:1993:XBM,
  author =       "W. S. Briggs and D. W. Matula",
  title =        "A $ 17 \times 69 $ Bit Multiply and Add Unit with
                 Redundant Binary Feedback and Single Cycle Latency",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "163--170",
  year =         "1993",
  bibdate =      "Thu Jun 20 10:16:11 2002",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Briggs.pdf",
  acknowledgement = ack-nj,
  keywords =     "ARITH-11",
}

@InProceedings{Callaway:1993:EPC,
  author =       "Thomas K. Callaway and Earl E. {Swartzlander, Jr.}",
  title =        "Estimating the Power Consumption of {CMOS} Adders",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "210--216",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Callaway.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}

@Article{Chang:1993:REP,
  author =       "Long-Wen Chang",
  title =        "Roundoff Error Problem of the Systolic Array for
                 {DFT}",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "41",
  number =       "1",
  pages =        "395",
  month =        jan,
  year =         "1993",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "Not \ldots{}",
}

@InProceedings{Choi:1993:FPR,
  author =       "H. Choi and W. P. Burleson and D. S. Phatak",
  booktitle =    "Proceedings of 1993 International Joint Conference on
                 Neural Networks. {IJCNN '93-Nagoya}",
  title =        "Fixed-point roundoff error analysis of large
                 feedforward neural networks",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1947--1950",
  year =         "1993",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Digital implementations of neural nets must consider
                 finite wordlength effects. For large sized nets, it is
                 particularly important to investigate the roundoff
                 errors in order to realize low-cost hardware
                 implementations while satisfying precision \ldots{}",
}

@Misc{Chu:1993:FPA,
  author =       "Tan V. Chu and Faraydon O. Karim and Christopher H.
                 Olson",
  title =        "Floating point arithmetic unit with size efficient
                 pipelined multiply-add architecture",
  howpublished = "US Patent 5,241,493",
  day =          "31",
  month =        aug,
  year =         "1993",
  bibdate =      "Thu Oct 17 10:40:01 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://patents.google.com/patent/US5241493A",
  abstract =     "An architecture and method relating to a floating
                 point operation which performs the mathematical
                 computation of A * B + C. The multiplication is
                 accomplished in two or more stages, each stage
                 involving corresponding sets of partial products and
                 concurrently accomplished incremental summations. A
                 pipelined architecture provides for the summation of
                 the least significant bits of an intermediate product
                 with operand C at a stage preceding entry into a full
                 adder. Thereby, a significant portion of the full adder
                 can be replaced by a simpler and smaller incrementer
                 circuit. Partitioning of the multiplication operation
                 into two or more partial product operations
                 proportionally reduces the size of the multiplier
                 required. Pipelining and concurrence execution of
                 multiplication and addition operation in the multiplier
                 provides in two cycles the results of the mathematical
                 operation A * B + C while using a full adder of
                 three-quarters normal size.",
  acknowledgement = ack-nhfb,
  remark =       "Patent filed 16 December 1991, granted to IBM on 31
                 August 1993, possibly expired 16 December 2011.",
}

@Article{Cody:1993:ACP,
  author =       "W. J. Cody",
  title =        "{Algorithm 714}: {CELEFUNT}: a Portable Test Package
                 for Complex Elementary Functions",
  journal =      j-TOMS,
  volume =       "19",
  number =       "1",
  pages =        "1--21",
  month =        mar,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/151271.151272",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 09:15:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p1-cody/",
  abstract =     "This paper discusses CELEFUNT, a package of Fortran
                 programs for testing complex elementary functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; measurement; performance",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms.",
}

@Article{Cody:1993:AFS,
  author =       "W. J. Cody and Jerome T. Coonen",
  title =        "{Algorithm 722}: Functions to Support the {IEEE}
                 Standard for Binary Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "19",
  number =       "4",
  pages =        "443--451",
  month =        dec,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/168173.168185",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p443-cody/",
  abstract =     "This paper describes C programs for the support
                 functions {\em copysign(x,y), logb(x), scalb(x,n),
                 nextafter(x,y), finite(x)}, and {\em isnan(x)}
                 recommended in the Appendix to the {\em IEEE Standard
                 for Binary Floating-Point Arithmetic.} In the case of
                 {\em logb}, the modified definition given in the later
                 {\em IEEE Standard for Radix-Independent Floating-Point
                 Arithmetic} is followed. These programs should run
                 without modification on most systems conforming to the
                 binary standard.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Argonne Nat. Lab., IL, USA",
  classification = "C5230 (Digital arithmetic methods); C6130 (Data
                 handling techniques); C7310 (Mathematics)",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "C programs; Copysign(x,y); Finite(x); IEEE Standard
                 for Binary Floating-point arithmetic; Isnan(x);
                 Logb(x); Nextafter(x,y); Numerical software;
                 Scalb(x,n)",
  subject =      "G.1.0 [Numerical Analysis]: General -- numerical
                 algorithms; G.4 [Numerical Analysis]: Mathematical
                 Software -- certification and testing",
  thesaurus =    "Data handling; Digital arithmetic; Mathematics
                 computing; Standards",
}

@Article{Cody:1993:ASE,
  author =       "W. J. Cody",
  title =        "{Algorithm 715}: {SPECFUN}\emdash {A} Portable
                 {FORTRAN} Package of Special Function Routines and Test
                 Drivers",
  journal =      j-TOMS,
  volume =       "19",
  number =       "1",
  pages =        "22--32",
  month =        mar,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/151271.151273",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:23:18 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See remark \cite{Price:1996:RA}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p22-cody/",
  abstract =     "SPECFUN is a package containing transportable FORTRAN
                 special function programs for real arguments and
                 accompanying test drivers. Components include Bessel
                 functions, exponential integrals, error functions and
                 related functions, and gamma functions and related
                 functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms.",
}

@Article{Cole:1993:SAA,
  author =       "T. J. Cole",
  title =        "Statistical Algorithms: {Algorithm AS 281}: Scaling
                 and Rounding Regression Coefficients to Integers",
  journal =      j-APPL-STAT,
  volume =       "42",
  number =       "1",
  pages =        "261--268",
  year =         "1993",
  CODEN =        "APSTAG",
  ISSN =         "0035-9254 (print), 1467-9876 (electronic)",
  ISSN-L =       "0035-9254",
  bibdate =      "Sat Apr 21 10:26:43 MDT 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 JSTOR database",
  URL =          "http://lib.stat.cmu.edu/apstat/281",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Statistics",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}

@InProceedings{Cortadella:1993:DSQ,
  author =       "Jordi Cortadella and Tom{\'a}s Lang",
  title =        "Division with Speculation of Quotient Digits",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "87--94",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Cortadella.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}

@InProceedings{Dadda:1993:MPC,
  author =       "Luigi Dadda and Vincenzo Piuri and Renato Stefanelli",
  title =        "Multi-Parallel Convolvers",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "70--77",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Dadda.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "29 April 1923--26 October 2012",
  keywords =     "ARITH-11",
}

@InProceedings{Daumas:1993:DFV,
  author =       "Marc Daumas and D. W. Matula",
  title =        "Design of a Fast Validated Dot Product Operation",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "62--69",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Daumas.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}

@MastersThesis{Delgado:1993:DSP,
  author =       "Maria Luisa Delgado",
  title =        "Design and simulation of a pipeline floating-point
                 adder",
  type =         "Thesis ({M.S.})",
  school =       "University of Texas at El Paso",
  address =      "El Paso, TX, USA",
  pages =        "x + 90",
  year =         "1993",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Parallel processing
                 (Electronic computers)",
}

@InProceedings{Demmel:1993:FNA,
  author =       "James W. Demmel and Xiaoye Li",
  title =        "Faster numerical algorithms via exception handling",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "234--241",
  year =         "1993",
  bibdate =      "Thu Jun 20 10:16:21 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Demmel.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}

@TechReport{Desaulniers:1993:BEA,
  author =       "H. Desaulniers and Stewart, N. F. (Neil Frederick)",
  title =        "Backward error analysis for floating-point operations
                 on rectilinear $r$-sets",
  type =         "Publication",
  number =       "816",
  institution =  "Universit{\'{e}} de Montr{\'{e}}al, Departement
                 d'informatique et de recherche operationnelle",
  address =      "Montr{\'{e}}al, Qu{\'{e}}bec, Canada",
  pages =        "64",
  year =         "1993",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer-aided design.",
  remark =       "``January 5, 1993.'' Supported in part by the Natural
                 Sciences and Engineering Research Council of Canada",
}

@Article{DiClaudio:1993:SRR,
  author =       "E. D. {Di Claudio} and G. Orlandi and F. Piazza",
  title =        "A systolic redundant residue arithmetic error
                 correction circuit",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "4",
  pages =        "427--432",
  month =        apr,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.214689",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:48 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=214689",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{DiLecce:1993:CES,
  author =       "V. Di Lecce and E. Di Sciascio",
  title =        "A comparative evaluation of solutions for inner
                 product",
  journal =      j-INT-J-MINI-MICROCOMPUTERS,
  volume =       "15",
  number =       "2",
  pages =        "71--77",
  month =        "????",
  year =         "1993",
  CODEN =        "IJMMDE",
  ISSN =         "0702-0481",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper proposes the design and performance
                 evaluation of a bit-serial processing element for inner
                 product computation in fine-grain architectures. Some
                 solutions proposed in the scientific literature for
                 inner product are presented and evaluated. The
                 processing element architecture and its operating mode
                 are described; a single floating-point inner product
                 computation can be accomplished in e*(n+1) clock cycles
                 (2*(n+1) in pipelined mode), supposing that mantissas
                 and exponents have the same length n. The VLSI
                 implementation of the processing element is discussed
                 with reference to both standard cell and full custom
                 design styles. A comparative evaluation with the
                 previously described solutions is proposed, relative to
                 some particularly significant parameters.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Electron. Eng., Politecnico di Bari,
                 Italy",
  classification = "B1265F (Microprocessors and microcomputers); C5135
                 (Digital signal processing chips); C5220 (Computer
                 architecture); C5230 (Digital arithmetic methods);
                 C5260 (Digital signal processing)",
  fjournal =     "International Journal of Mini and Microcomputers",
  keywords =     "Bit-serial processing element; Comparative evaluation;
                 DSP chips; Exponents; Fine-grain architectures; Full
                 custom design styles; Inner product; Mantissas;
                 Operating mode; Performance evaluation; VLSI
                 implementation",
  thesaurus =    "Digital arithmetic; Digital signal processing chips;
                 Performance evaluation",
}

@Article{Dimauro:1993:NTF,
  author =       "G. Dimauro and S. Impedovo and G. Pirlo",
  title =        "A new technique for fast number comparison in the
                 residue number system",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "5",
  pages =        "608--612",
  month =        may,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.223680",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:49 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=5840;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=223680",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A technique for number comparison in the residue
                 number system is presented, and its theoretical
                 validity is proved. The proposed solution is based on
                 using a diagonal function to obtain a magnitude order
                 of the numbers. In a first approach the \ldots{}",
}

@Article{Dittmer:1993:EUC,
  author =       "Ingo Dittmer",
  title =        "Error in {Unix} commands {\tt dc} and {\tt bc} for
                 multiple-precision-arithmetic",
  journal =      j-SIGNUM,
  volume =       "28",
  number =       "2",
  pages =        "8--11",
  month =        apr,
  year =         "1993",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:23 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}

@Book{Dowd:1993:HPC,
  author =       "Kevin Dowd",
  title =        "High Performance Computing",
  publisher =    pub-ORA,
  address =      pub-ORA:adr,
  pages =        "xxv + 371",
  year =         "1993",
  ISBN =         "1-56592-032-5",
  ISBN-13 =      "978-1-56592-032-3",
  LCCN =         "QA76.88 .D6 1993; QA76.9.A73 D68 1993",
  bibdate =      "Mon Jan 3 18:34:37 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/hpfortran.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/ora.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "US\$25.95",
  series =       "RISC architectures, optimization and benchmarks; A
                 Nutshell handbook",
  URL =          "http://www.oreilly.com/catalog/9781565920323",
  acknowledgement = ack-nhfb,
  subject =      "Computer architecture; Electronic digital computers;
                 Parallel processing (Electronic computers);
                 Supercomputers",
  tableofcontents = "Preface / xxi \\
                 Who Should Buy This Book? / xxii \\
                 What's in This Book / xxii \\
                 Conventions / xxiv \\
                 Acknowledgments / xxv \\
                 1 Modern Computer Architectures / 1 \\
                 1: What is High Performance Computing? / 3 \\
                 Why Worry About Performance? / 3 \\
                 Measuring Performance / 5 \\
                 The Next Step / 6 \\
                 2: RISC Computers / 9 \\
                 Why CISC? / 10 \\
                 Space and Time / 10 \\
                 Beliefs About Complex Instruction Sets / 11 \\
                 Memory Addressing Modes / 12 \\
                 Microcode / 14 \\
                 Making the Most of a Clock Tick / 17 \\
                 Pipelines / 18 \\
                 Instruction Pipelining / 19 \\
                 Why RISC? / 21 \\
                 Characterizing RISC / 22 \\
                 A Few More Words About Pipelining / 27 \\
                 Memory References / 27 \\
                 Floating Point Pipelines / 28 \\
                 Classes of Processors / 29 \\
                 Superscalar Processors / 30 \\
                 Superpipelined Processors / 32 \\
                 Long Instruction Word (LIW) / 34 \\
                 Other Advanced Features / 35 \\
                 Register Bypass / 36 \\
                 Register Renaming / 36 \\
                 Reducing Branch Penalties / 37 \\
                 Closing Notes / 40 \\
                 3: Memory / 43 \\
                 Memory Technology / 44 \\
                 Random Access Memory / 45 \\
                 Access Time / 47 \\
                 Caches / 48 \\
                 Direct Mapped Cache / 50 \\
                 Fully Associative Cache / 52 \\
                 Set Associative Cache / 52 \\
                 Uses of Cache / 54 \\
                 Virtual Memory / 54 \\
                 Page Tables / 55 \\
                 Translation Lookaside Buffer / 56 \\
                 Page Faults / 57 \\
                 Improving Bandwidth / 59 \\
                 Large Caches / 60 \\
                 Interleaved Memory Systems / 60 \\
                 Software Managed Caches / 64 \\
                 Memory Reference Reordering / 64 \\
                 Multiple References / 66 \\
                 Closing Notes / 67 \\
                 IL Porting and Tuning Software / 91 \\
                 4: What an Optimizing Compiler Does / 69 \\
                 Optimizing Compiler Tour / 70 \\
                 Intermediate Language Representation / 70 \\
                 Basic Blocks / 72 \\
                 Forming a DAG / 74 \\
                 Uses and Definitions / 76 \\
                 Loops / 78 \\
                 Object Code Generation / 80 \\
                 Classical Optimizations / 81 \\
                 Copy Propagation / 81 \\
                 Constant Folding / 82 \\
                 Dead Code Removal / 83 \\
                 Strength Reduction / 84 \\
                 Variable Renaming / 84 \\
                 Common Subexpression Elimination / 85 \\
                 Loop Invariant Code Motion / 86 \\
                 Induction Variable Simplification / 87 \\
                 Register Variable Detection / 88 \\
                 Closing Notes / 88 \\
                 5: Clarity / 93 \\
                 Under Construction / 94 \\
                 Comments / 94 \\
                 Clues in the Landscape / 95 \\
                 Variable Names / 96 \\
                 Variable Types / 98 \\
                 Named Constants / 99 \\
                 INCLUDE Statements / 100 \\
                 Use of COMMON / 101 \\
                 The Shape of Data / 102 \\
                 Closing Notes / 104 \\
                 6: Finding Porting Problems / 105 \\
                 Problems in Argument Lists / 106 \\
                 Aliasing / 106 \\
                 Argument Type Mismatch / 108 \\
                 Storage Issues / 110 \\
                 Equivalenced Storage / 111 \\
                 Memory Reference Alignment Restrictions / 112 \\
                 Closing Notes / 115 \\
                 7: Timing and Profiling / 119 \\
                 Timing / 120 \\
                 Timing a Whole Program / 120 \\
                 Timing a Portion of the Program / 124 \\
                 Using Timing Information / 126 \\
                 Subroutine Profiling / 127 \\
                 prof / 130 \\
                 gprof / 133 \\
                 gprofs Flat Profile / 138 \\
                 Accumulating the Results of Several gprof Runs / 139
                 \\
                 A Few Words About Accuracy / 140 \\
                 Basic Block Profilers / 140 \\
                 tcov / 141 \\
                 !prof / 142 \\
                 pixie / 143 \\
                 Closing Notes / 144 \\
                 8: Understanding Parallelism / 147 \\
                 A Few Important Concepts / 148 \\
                 Constants / 148 \\
                 Scalars / 150 \\
                 Vectors and Vector Processing / 150 \\
                 Dependencies / 153 \\
                 Data Dependencies / 154 \\
                 Control Dependencies / 159 \\
                 Ambiguous References / 161 \\
                 Closing Notes / 162 \\
                 9: Eliminating Clutter / 165 \\
                 Subroutine Calls / 166 \\
                 Macros / 168 \\
                 Procedure Inlining / 170 \\
                 Branches / 171 \\
                 Wordy Conditionals / 171 \\
                 Redundant Tests / 172 \\
                 Branches Within Loops / 173 \\
                 Loop Invariant Conditionals / 174 \\
                 Loop Index Dependent Conditionals / 175 \\
                 Independent Loop Conditionals / 176 \\
                 Dependent Loop Conditionals / 177 \\
                 Reductions / 178 \\
                 Conditionals That Transfer Control / 179 \\
                 A Few Words About Branch Probability / 180 \\
                 Other Clutter / 181 \\
                 Data Type Conversions / 181 \\
                 Doing Your Own Common Subexpression Elimination / 182
                 \\
                 Doing Your Own Code Motion / 183 \\
                 Handling Array Elements in Loops / 184 \\
                 Closing Notes / 185 \\
                 10: Loop Optimizations / 187 \\
                 Basic Loop Unrolling / 188 \\
                 Qualifying Candidates for Loop Unrolling / 189 \\
                 Loops with Low Trip Counts / 190 \\
                 Fat Loops / 191 \\
                 Loops Containing Procedure Calls / 191 \\
                 Loops with Branches in Them / 193 \\
                 Recursive Loops / 194 \\
                 Negatives of Loop Unrolling / 195 \\
                 Unrolling by the Wrong Factor / 196 \\
                 Register Thrashing / 196 \\
                 Instruction Cache Miss / 197 \\
                 Other Hardware Delays / 197 \\
                 Outer Loop Unrolling / 197 \\
                 Outer Loop Unrolling to Expose Computations / 199 \\
                 Associative Transformations / 200 \\
                 Reductions / 202 \\
                 Dot Products and daxpys / 204 \\
                 Matrix Multiplication / 206 \\
                 Loop Interchange / 208 \\
                 Loop Interchange to Move Computations to the Center /
                 208 \\
                 Operation Counting / 209 \\
                 Closing Notes / 211 \\
                 11: Memory Reference Optimizations / 213 \\
                 Memory Access Patterns / 214 \\
                 Loop Interchange to Ease Memory Access Patterns / 215
                 \\
                 Blocking to Ease Memory Access Patterns / 216 \\
                 Ambiguity in Memory References / 223 \\
                 Ambiguity in Vector Operations / 224 \\
                 Pointer Ambiguity in Numerical C Applications / 225 \\
                 Programs That Require More Memory Than You Have / 227
                 \\
                 Software-Managed, Out-of-Core Solutions / 227 \\
                 Virtual Memory / 228 \\
                 Instruction Cache Ordering / 231 \\
                 Closing Notes / 232 \\
                 12: Language Support for Performance / 235 \\
                 Subroutine Libraries / 235 \\
                 Vectorizing Preprocessors / 237 \\
                 Explicitly Parallel Languages / 243 \\
                 Fortran 90 / 244 \\
                 High Performance Fortran (HPF) / 250 \\
                 Explicitly Parallel Programming Environments / 251 \\
                 Closing Notes / 253 \\
                 1/L Evaluating Performance / 255 \\
                 13: Industry Benchmarks / 257 \\
                 What is a MIP? / 258 \\
                 VAX MIPS / 259 \\
                 Dhrystones / 259 \\
                 Floating Point Benchmarks / 261 \\
                 Linpack / 262 \\
                 Whetstone / 264 \\
                 The SPEC Benchmarks / 265 \\
                 Individual SPEC Benchmarks / 266 \\
                 030.matrix300 Was Deleted / 272 \\
                 Transaction Processing Benchmarks / 272 \\
                 TPC-A / 273 \\
                 TPC-B / 273 \\
                 TPC-C / 273 \\
                 Closing Notes / 273 \\
                 14: Running Your Own Benchmarks / 275 \\
                 Choosing What to Benchmark / 275 \\
                 Benchmark Run Time / 276 \\
                 Benchmark Memory Size / 277 \\
                 Kernels and Sanitized Benchmarks / 277 \\
                 Benchmarking Third Party Codes / 278 \\
                 Types of Benchmarks / 279 \\
                 Single Stream Benchmarks / 280 \\
                 Throughput Benchmarks / 282 \\
                 Interactive Benchmarks / 283 \\
                 Preparing the Code / 285 \\
                 Portability / 285 \\
                 Making a Benchmark Kit / 286 \\
                 Benchmarking Checklist / 287 \\
                 Closing Notes / 288 \\
                 IV. Parallel Computing / 291 \\
                 15: Large Scale Parallel Computing / 293 \\
                 Problem Decomposition / 294 \\
                 Data Decomposition / 295 \\
                 Control Decomposition / 299 \\
                 Distributing Work Fairly / 300 \\
                 Classes of Parallel Architectures / 302 \\
                 Single Instruction, Multiple Data / 303 \\
                 SIMD Architecture / 305 \\
                 Mechanics of Programming a SIMD Machine / 309 \\
                 Multiple Instruction, Multiple Data / 312 \\
                 Distributed Memory MIMD Architecture / 314 \\
                 Programming a Distributed Memory MIMD Machine / 315 \\
                 A Few Words About Data Layout Directives / 319 \\
                 Virtual Shared Memory / 320 \\
                 Closing Notes / 323 \\
                 16: Shared-Memory Multiprocessors / 325 \\
                 Symmetric Multiprocessing / 326 \\
                 Operating System Support for Multiprocessing / 327 \\
                 Multiprocessor Architecture / 329 \\
                 Shared Memory / 330 \\
                 Conservation of Bandwidth / 330 \\
                 Coherency / 332 \\
                 Data Placement / 334 \\
                 Multiprocessor Software Concepts / 334 \\
                 Fork and Join / 335 \\
                 Synchronization with Locks / 337 \\
                 Synchronization with Barriers / 340 \\
                 Automatic Parallelization / 341 \\
                 Loop Splitting / 341 \\
                 Subroutine Calls in Loops / 342 \\
                 Nested Loops / 342 \\
                 Manual Parallelism / 344 \\
                 Closing Notes / 345 \\
                 A: Processor Overview / 347 \\
                 B: How to Tell When Loops Can Be Interchanged / 351 \\
                 C: Obtaining Sample Programs and Problem Set Answers /
                 357 \\
                 FTP / 357 \\
                 FTPMAIL / 358 \\
                 BITFTP / 359 \\
                 UUCP / 359 \\
                 Figures \\
                 2: RISC Computers / 9 \\
                 2-1 Registers, a single common data path, and an adder
                 / 15 \\
                 2-2 A pipeline / 18 \\
                 2-3 Three instructions in flight through one pipeline /
                 20 \\
                 2-4 Variable length instructions make pipelining
                 difficult / 23 \\
                 2-5 Variable length CISC versus fixed length RISC
                 instructions / 23 \\
                 2-6 Processor encounters a branch / 26 \\
                 2-7 The Branch Delay Slot --- ZERO R3 executes either
                 way / 27 \\
                 2-8 Memory references scheduled early to account for
                 pipeline depth / 28 \\
                 2-9 Decomposing a serial stream / 30 \\
                 2-10 RS/ 6000 functional blocks / 31 \\
                 2-11 MIPS R4000 Instruction Pipeline / 33 \\
                 2-12 Intel i860 transition between modes / 35 \\
                 3: Memory / 43 \\
                 3-1 Row--Column memory address / 46 \\
                 3-2 Direct mapping of memory address to RAM / 46 \\
                 3-3 Cache lines can come from different parts of memory
                 / 49 \\
                 3-4 Many memory addresses map to same cache line / 51
                 \\
                 3-5 Two -way set associative cache / 53 \\
                 3-6 Virtual to physical address mapping / 55 \\
                 3-7 Simple memory system / 59 \\
                 3-8 Page mode cache refill / 60 \\
                 3-9 Multi-banked memory system / 62 \\
                 3-10 Cache refill from interleaved memory / 63 \\
                 4: What an Optimizing Compiler Does / 69 \\
                 4-1 Example 4-1 divided into basic blocks / 73 \\
                 4-2 Tuple mapped into a DAG / 74 \\
                 4-3 Basic Block B / 75 \\
                 4-4 DAG for Block B / 75 \\
                 4-5 Revised Basic Block B / 76 \\
                 4-6 Flow graph for data flow analysis / 77 \\
                 4-7 Flow graph with a loop in it / 79 \\
                 5: Clarity / 93 \\
                 5-1 Array C in two -dimensional memory / 103 \\
                 6: Finding Porting Problems / 105 \\
                 6-1 IEEE 754 floating point formats / 109 \\
                 6-2 IBM 370 floating point formats / 110 \\
                 6-3 Equivalence storage relationship on most computers
                 / 111 \\
                 6-4 Misaligned variables / 113 \\
                 7: Timing and Pro.filing / 119 \\
                 7-1 The built-in csh time function / 123 \\
                 7-2 Sharp profile --- dominated by routine 1 / 128 \\
                 7-3 Flat profile --- no routine predominates / 129 \\
                 7-4 Simple call graph / 134 \\
                 7-5 FORTRAN example / 135 \\
                 7-6 Quantization Errors in Profiling / 140 \\
                 8: Understanding Parallelism / 147 \\
                 8-1 Vector Computer / 152 \\
                 8-2 A little section of your program / 159 \\
                 8-3 Expensive operation moved so that it's rarely
                 executed / 160 \\
                 11: Memory Reference Optimizations / 213 \\
                 11-1 Arrays A and B / 217 \\
                 11-2 How array elements are stored / 218 \\
                 11-3 2x2 squares / 219 \\
                 11-4 Picture of unblocked versus blocked references /
                 220 \\
                 11-5 Optimization performance for various sized loops /
                 222 \\
                 11-6 Vector machine memory access / 223 \\
                 12: Language Support for Performance / 235 \\
                 12-1 Linda's Tuple Space Bulletin Board / 252 \\
                 14: Running Your Own Benchmarks / 275 \\
                 14-1 Kernel benchmark / 278 \\
                 14-2 Single stream benchmarks / 280 \\
                 14-3 Computing an overall benchmark score / 281 \\
                 14-4 Wrong way to run a throughput benchmark / 282 \\
                 14-5 Benchmark stone wall / 283 \\
                 14-6 Interactive use benchmark / 284 \\
                 _15:Large Scale Parallel Computing / 293 \\
                 15-1 Domain decomposition / 295 \\
                 15-2 Cells with X's have life / 296 \\
                 15-3 One iteration later / 297 \\
                 15-4 Two examples of division of cells between four
                 CPUs / 298 \\
                 15-5 Each processor with a piece of the domain / 300
                 \\
                 15-6 Duplicated data domain / 301 \\
                 15-7 Iterations mapped onto SIMD nodes / 304 \\
                 15-8 Mapping a route through a strictly Cartesian mesh
                 / 306 \\
                 15-9 Four nodes / 307 \\
                 15-10 A 3-cube and a 4-cube / 307 \\
                 15-11 Front-end and SIMD machine / 309 \\
                 15-12 KSR-1 ring of rings architecture / 322 \\
                 16: Shared-Memory Multiprocessors / 325 \\
                 16-1 A typical bus architecture / 329 \\
                 16-2 A $4 \times 4$ crossbar / 330 \\
                 16-3 High cache hit rate reduces main memory traffic /
                 331 \\
                 16-4 Multiple copies of variable A / 332 \\
                 16-5 Fork and join / 335 \\
                 16-6 Integration / 337 \\
                 16-7 Implementation of a spinlock / 339 \\
                 B: How to Tell When Loops Can Be Interchanged / 351 \\
                 B-1 $4 \times 4$ matrix / 352 \\
                 B-2 One iteration complete / 353 \\
                 B-3 All iterations completed / 354 \\
                 B-4 Movement of data in array A / 355 \\
                 Examples \\
                 4: What an Optimizing Compiler Does / 69 \\
                 4-1 Intermediate Language for a Single Loop / 72 \\
                 5: Clarity / 93 \\
                 5-1 Comments, asterisks, and pretty printing / 95 \\
                 5-2 Variable names count / 97 \\
                 5-3 Parameter statements \\
                 5-4 Declarations / 100 \\
                 5-5 Routine using both INCLUDE files / 100 \\
                 5-6 Changing the Shape of an Array / 100 \\
                 / 102 \\
                 6: Finding Porting Problems / 105 \\
                 6-1 Program for creating misaligned references \\
                 6-2 Misaligned reference in C / 114 \\
                 / 115 \\
                 7: Timing and Profiling / 119 \\
                 7-1 FORTRAN program using etime / 125 \\
                 7-2 etime implemented in C / 126 \\
                 7-3 loops.c --- a program for testing profilers / 131
                 \\
                 7-4 Profile of loops.c / 132 \\
                 7-5 A portion of gprof output / 135 \\
                 7-6 gprof flat profile / 138 \\
                 8: Understanding Parallelism / 147 \\
                 8-1 Vector Addition / 150 \\
                 9: Eliminating Clutter / 165 \\
                 9-1 Macro definition and use / 168 \\
                 10: Loop Optimizations / 187 \\
                 10-1 Loop containing a procedure call / 192 \\
                 10-2 Matrix multiply with daxpy inner loop / 206 \\
                 10-3 Matrix multiply with dot product inner loop / 206
                 \\
                 11: Memory Reference Optimizations / 213 \\
                 11-1 Two-dimensional vector sum / 216 \\
                 11-2 Outer and inner loop unrolled / 217 \\
                 B: How to Tell When Loops Can Be Interchanged / 351 \\
                 B-1 Each iteration is independent / 351 \\
                 B-2 Can we interchange these loops? / 352 \\
                 B-3 Legal alternate loop nests / 354 \\
                 B-4 More complicated references / 355 \\
                 B-5 More complicated references / 356 \\
                 Tables \\
                 6: Finding Porting Problems / 105 \\
                 6-1 Preferred Alignment Boundaries on Most Computers /
                 113 \\
                 15: Large Scale Parallel Computing / 293 \\
                 15-1 Worst Case Communication / 308 \\
                 A: Processor Overview / 347 \\
                 A-1 CPU Characteristics / 347 \\
                 A-2 Cache and Branch Architecture / 348 \\
                 A-2 Cache and Branch Architecture (continued) / 349",
}

@Article{Duncan:1993:CES,
  author =       "Roy Duncan and John Tunstall and Brian T. Smith and
                 Richard Brankin",
  title =        "Correspondence: Expert Systems for Re-ordering
                 Arithmetic Expressions?",
  journal =      j-FORTRAN-FORUM,
  volume =       "12",
  number =       "3",
  pages =        "12--14",
  month =        sep,
  year =         "1993",
  CODEN =        "????",
  ISSN =         "1061-7264 (print), 1931-1311 (electronic)",
  ISSN-L =       "1061-7264",
  bibdate =      "Tue Apr 23 14:50:51 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Fortran Forum",
  issue =        "35",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J286",
}

@Article{Duprat:1993:CAN,
  author =       "J. Duprat and J. Muller",
  title =        "The {CORDIC} Algorithm: New Results for Fast {VLSI}
                 Implementation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "2",
  pages =        "168--178",
  month =        feb,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.204786",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:15:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Eisig:1993:DBI,
  author =       "David Eisig and Josh Rotstain and Israel Koren",
  title =        "The Design of a 64-bit Integer Multiplier\slash
                 Divider Unit",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "171--178",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Eisig.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}

@Article{Eldridge:1993:HIM,
  author =       "S. E. Eldridge and C. D. Walter",
  title =        "Hardware implementation of {Montgomery}'s modular
                 multiplication algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "6",
  pages =        "693--699",
  month =        jun,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.277287",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:49 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=277287",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Ercegovac:1993:VHR,
  author =       "Milo{\v{s}} D. Ercegovac and Tom{\'a}s Lang and Paolo
                 Montuschi",
  title =        "Very high radix division with selection by rounding
                 and prescaling",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "112--119",
  year =         "1993",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Ercegovac.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
  summary =      "A division algorithm in which the quotient-digit
                 selection is performed by rounding the shifted residual
                 in carry-save form is presented. To allow the use of
                 this simple function, the divisor (and dividend) is
                 prescaled to a range close to one. The \ldots{}",
}

@InProceedings{Etiemble:1993:AMV,
  author =       "D. Etiemble and K. Navi",
  title =        "Algorithms and Multi-Valued Circuits for the
                 Multioperand Addition in the Binary Stored-Carry Number
                 System",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "194--201",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Etiemble.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}

@InProceedings{Fortune:1993:EEA,
  author =       "Steven Fortune and Christopher J. {Van Wyk}",
  editor =       "{ACM}",
  booktitle =    "{Proceedings of the 9th ACM Symposium on Computational
                 Geometry, May 19--21, 1993, San Diego, CA, USA}",
  title =        "Efficient Exact Arithmetic for Computational
                 Geometry",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  bookpages =    "vii + 406",
  pages =        "163--172",
  year =         "1993",
  DOI =          "https://doi.org/10.1145/160985.161015",
  ISBN =         "0-89791-582-8",
  ISBN-13 =      "978-0-89791-582-3",
  LCCN =         "QA448.D38 S96 1993",
  bibdate =      "Tue Nov 13 21:44:58 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Fowkes:1993:HEA,
  author =       "R. E. Fowkes",
  title =        "Hardware Efficient Algorithms for Trigonometric
                 Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "3",
  pages =        "235--239",
  month =        feb,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.204796",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 1 10:16:09 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  acknowledgement = ack-nj,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Fox:1993:HLS,
  author =       "J. R. Fox",
  title =        "A higher level of synthesis ({CAD})",
  journal =      j-IEEE-SPECTRUM,
  volume =       "30",
  number =       "3",
  pages =        "43--47",
  month =        mar,
  year =         "1993",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/6.211955",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Thu Jan 16 07:37:23 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum1990.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "abstraction; Arithmetic; CAD; Circuit synthesis;
                 Clocks; design automation; Design automation; Design
                 engineering; design synthesis systems; Fabrication;
                 Hardware; hardware description languages; Logic
                 circuits; Logic design; Microarchitecture; software
                 tools; specification languages; testability; top-down
                 design",
}

@MastersThesis{Geraminejad:1993:DIC,
  author =       "Mohsen Geraminejad",
  title =        "Design and implementation of a 16-bit {CMOS} floating
                 point multiplier",
  type =         "Research paper ({M.S.})",
  school =       "Department of Electrical Engineering, Southern
                 Illinois University at Carbondale",
  address =      "Carbondale, IL, USA",
  pages =        "vii + 54",
  year =         "1993",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gibbons:1993:FMW,
  author =       "Jeremy Gibbons",
  editor =       "John Hosking",
  booktitle =    "{Proceedings of the 13th New Zealand Computer Society
                 Conference: Applying the future today, Aotea Centre,
                 Auckland, 18--20 August 1993}",
  title =        "Formal Methods: {Why} Should {I} Care? {The}
                 development of the {T800} transputer floating-point
                 unit",
  publisher =    "New Zealand Computer Society",
  address =      "Wellington, NZ",
  pages =        "207--217",
  year =         "1993",
  ISBN =         "0-9597657-6-X; 0-9597657-5-1",
  ISBN-13 =      "978-0-9597657-6-2; 978-0-9597657-5-5",
  LCCN =         "????",
  bibdate =      "Tue Nov 13 21:37:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The term `formal methods' is a general term for
                 precise mathematically-based techniques used in the
                 development of computer systems, both hardware and
                 software. This paper discusses formal methods in
                 general, and in particular describes their successful
                 role in specifying, constructing and proving correct
                 the floating-point unit of the Inmos T800 transputer
                 chip.",
  acknowledgement = ack-nhfb,
  keywords =     "Inmos T800 transputer",
}

@TechReport{Goldberg:1993:DFP,
  author =       "David Goldberg",
  title =        "The design of floating-point data types",
  type =         "Technical report",
  number =       "CSL-93-3",
  institution =  "Xerox Corp., Palo Alto Research Center",
  address =      "Palo Alto, CA, USA",
  pages =        "19",
  year =         "1993",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Abstract data types (Computer science)",
  remark =       "``A version of this paper will appear in Letters on
                 Programming Languages and Systems.'' ``February 1993.''
                 Abstract: ``We discuss the issues involved in designing
                 the floating-point part of a programming language.
                 Looking at the language specifications for most
                 existing languages might suggest that this design
                 involves only trivial issues such as whether to have
                 one or two types of REALs or how to name the functions
                 that convert from INTEGER to REAL. We show that there
                 are more significant semantic issues involved. After
                 discussing the tradeoffs for the major design
                 decisions, we illustrate them by presenting the design
                 of the floating-point part of the Modula-3
                 language.''",
}

@TechReport{Gudeman:1993:RTI,
  author =       "David Gudeman",
  title =        "Representing Type Information in Dynamically Typed
                 Languages",
  type =         "Technical report",
  number =       "TR 93-27",
  institution =  "Department of Computer Science, The University of
                 Arizona",
  address =      "Tucson, AZ 85721, USA",
  pages =        "40",
  month =        oct,
  year =         "1993",
  bibdate =      "Wed Oct 13 08:12:36 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.cs.arizona.edu/reports/1993/TR93-27.ps;
                 http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.4394",
  abstract =     "This report is a discussion of various techniques for
                 representing type information in dynamically typed
                 languages, as implemented on general-purpose machines
                 (and costs are discussed in terms of modern RISC
                 machines). It is intended to make readily available a
                 large body of knowledge that currently has to be
                 absorbed piecemeal from the literature or re-invented
                 by each language implementer. This discussion covers
                 not only tagging schemes but other forms of
                 representation as well, although the discussion is
                 strictly limited to the representation of type
                 information. It should also be noted that this report
                 does not purport to contain a survey of the relevant
                 literature. Instead, this report gathers together a
                 body of folklore, organizes it into a logical
                 structure, makes some generalizations, and then
                 discusses the results in terms of modern hardware.",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; integer arithmetic; Lisp;
                 Prolog; typed objects",
  remark =       "Discusses implementation of fast arithmetic for typed
                 integer and floating-point data.",
}

@Misc{Gupta:1993:NPF,
  author =       "S. Gupta and R. Periman and T. Lynch and B. McMinn",
  title =        "Normalizing pipelined floating point processing
                 units",
  day =          "30",
  month =        nov,
  year =         "1993",
  bibdate =      "Fri Nov 28 15:27:34 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "U.S. Patent No. 5,267,186.",
  acknowledgement = ack-nhfb,
}

@InCollection{Hammer:1993:PXN,
  author =       "R. Hammer and M. Neaga and D. Ratz",
  title =        "{PASCAL-XSC}: New Concepts for Scientific Computation
                 and Numerical Data Processing",
  crossref =     "Adams:1993:SCA",
  pages =        "15--44",
  year =         "1993",
  bibdate =      "Wed Oct 13 22:38:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Hasan:1993:MMO,
  author =       "M. A. Hasan and M. Z. Wang and V. K. Bhargava",
  title =        "A modified {Massey--Omura} parallel multiplier for a
                 class of finite fields",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "10",
  pages =        "1278--1280",
  month =        oct,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.257715",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=257715",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Hatzinakos:1993:AFP,
  author =       "D. Hatzinakos",
  title =        "Analysis of floating point roundoff errors in the
                 estimation of higher-order statistics",
  journal =      "IEE proceedings. F, Radar and signal processing",
  volume =       "140",
  number =       "6",
  pages =        "371--379",
  month =        dec,
  year =         "1993",
  ISSN =         "0956-375X",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "A floating point roundoff error analysis in the
                 estimation of higher-order statistics, moments or
                 cumulants of real stationary processes from single data
                 records is provided. Closed form expressions or upper
                 bounds are derived for the mean and \ldots{}",
}

@Book{Heinrich:1993:MRM,
  author =       "Joe Heinrich",
  title =        "{MIPS R4000} Microprocessor User's Manual",
  publisher =    pub-PHPTR,
  address =      pub-PHPTR:adr,
  pages =        "xxvi + 438 + A182 + B62 + C6 + D4 + E4",
  year =         "1993",
  ISBN =         "0-13-105925-4",
  ISBN-13 =      "978-0-13-105925-2",
  LCCN =         "QA76.8.M523H45 1993",
  bibdate =      "Wed Aug 10 11:02:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\$34.00",
  acknowledgement = ack-nhfb,
  libnote =      "Not yet in my library.",
  tableofcontents = "Introduction \\
                 CPU Instruction Set Summary \\
                 The CPU Pipeline \\
                 Memory Management \\
                 CPU Exception Processing \\
                 Floating-Point Unit \\
                 Floating-Point Exceptions \\
                 R4000 Processor Signal Descriptions \\
                 Initialization Interface \\
                 Clock Interface \\
                 Cache Organization, Operation, and Coherency \\
                 System Interface \\
                 Secondary Cache Interface \\
                 JTAG Interface \\
                 R4000 Processor Interrupts \\
                 Error Checking and Correcting \\
                 CPU Instruction Set Details \\
                 FPU Instruction Set Details \\
                 Subblock Ordering \\
                 Output Buffer \ldots{} Di \ldots{} Dt Control Mechanism
                 \\
                 PLL Passive Components \\
                 R4000 Coprocessor 0 Hazards",
}

@InProceedings{Hekstra:1993:FPC,
  author =       "Gerben J. Hekstra and Ed F. A. Deprettere",
  title =        "Floating Point {Cordic}",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "130--137",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Hekstra.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}

@InProceedings{Hemkumar:1993:ECM,
  author =       "Nariankadu D. Hemkumar and Joseph R. Cavallaro",
  title =        "Efficient Complex Matrix Transformations with
                 {CORDIC}",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "122--129",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Hemkumar.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}

@Article{Hendtlass:1993:MNIa,
  author =       "T. Hendtlass",
  title =        "Math-who needs it?",
  journal =      j-FORTH-DIMENSIONS,
  volume =       "14",
  number =       "6",
  pages =        "27--38",
  month =        mar # "--" # apr,
  year =         "1993",
  CODEN =        "FODMD5",
  ISSN =         "0884-0822",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A thorough treatment of integer, double-precision,
                 fixed-point, and floating-point mathematics. A
                 mathematician's toolbox of code is presented, and
                 tables compare the benefits bestowed and the penalties
                 extracted by the routines.",
  acknowledgement = ack-nhfb,
  classification = "C6140D (High level languages); C7310 (Mathematics)",
  fjournal =     "Forth Dimensions",
  keywords =     "Code toolbox; Double precision arithmetic; Fixed-point
                 arithmetic; Floating-point mathematics; Integer",
  thesaurus =    "FORTH; FORTH listings; Mathematics computing",
}

@Article{Hendtlass:1993:MNIb,
  author =       "T. Hendtlass",
  title =        "Math---who needs it?",
  journal =      j-FORTH-DIMENSIONS,
  volume =       "15",
  number =       "1",
  pages =        "38--39",
  month =        may # "--" # jun,
  year =         "1993",
  CODEN =        "FODMD5",
  ISSN =         "0884-0822",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The continuation of the source code for a Forth
                 program is presented (see ibid., vol.14, no.6, 1993).
                 The software is a math professor's toolbox of integer,
                 double-precision, fixed-point and floating-point
                 routines.",
  acknowledgement = ack-nhfb,
  classification = "C6110 (Systems analysis and programming); C7310
                 (Mathematics)",
  fjournal =     "Forth Dimensions",
  keywords =     "Double-precision; Fixed-point; Floating-point
                 routines; Forth program; Math; Source code; Toolbox",
  thesaurus =    "Digital arithmetic; FORTH listings; Mathematics
                 computing; Programming",
}

@Article{Higginbotham:1993:ISR,
  author =       "T. F. Higginbotham",
  title =        "The integer square root of {N} via a binary search",
  journal =      j-SIGCSE,
  volume =       "25",
  number =       "4",
  pages =        "41--45",
  month =        dec,
  year =         "1993",
  CODEN =        "SIGSD3",
  DOI =          "https://doi.org/10.1145/164205.164229",
  ISSN =         "0097-8418 (print), 2331-3927 (electronic)",
  ISSN-L =       "0097-8418",
  bibdate =      "Sat Nov 17 18:57:24 MST 2012",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigcse1990.bib",
  abstract =     "An algorithm is presented which may be used to find
                 the integer square root of N. The method is intended
                 for use on a binary computer, where only addition,
                 subtraction, multiplication, or division by 2 is
                 required. The problem arose when the author was working
                 on factoring large numbers, where the machine, the
                 Honeywell DPS 8, had double precision integer addition
                 and subtraction, and the simulation of multiplication
                 was easy. The actual factoring of the large number was
                 to be Fermat's Method, requiring only addition and
                 subtraction, but the integer square root is required in
                 order to test for termination. The algorithm is
                 implemented in FORTRAN for ease of reading. Students
                 enjoy the unconventional approach to solving this
                 problem. It isn't long before some of them think of
                 other unusual solutions.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGCSE Bulletin (ACM Special Interest Group on
                 Computer Science Education)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J688",
}

@Article{Higham:1993:AFP,
  author =       "Nicholas J. Higham",
  title =        "The accuracy of floating point summation",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "14",
  number =       "4",
  pages =        "783--799",
  month =        jul,
  year =         "1993",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/0914050",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65G05 (65B10)",
  MRnumber =     "94a:65025",
  bibdate =      "Thu Aug 23 06:36:53 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://citeseer.nj.nec.com/higham93accuracy.html;
                 http://www.maths.man.ac.uk/~nareports/narep198.pdf;
                 http://www.maths.man.ac.uk/~nareports/narep198.ps.gz",
  abstract =     "The usual recursive summation technique is just one of
                 several ways of computing the sum of $n$ floating point
                 numbers. Five summation methods and their variations
                 are analyzed. The accuracy of the methods is compared
                 using rounding error analysis and numerical
                 experiments. Four of the methods are shown to be
                 special cases of a general class of methods, and an
                 error analysis is given for this class. No one method
                 is uniformly more accurate than the others, but some
                 guidelines are given on the choice of method in
                 particular cases.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Math., Manchester University, UK",
  classification = "C4110 (Error analysis in numerical methods); C5230
                 (Digital arithmetic methods)",
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  keywords =     "accurate floating-point summation; floating point
                 numbers; numerical experiments; recursive summation
                 technique; rounding error analysis",
  thesaurus =    "Digital arithmetic; Error analysis",
}

@MastersThesis{Holler:1993:IFP,
  author =       "Paul T. Holler",
  title =        "Integrating a floating point unit into the {AT\&T
                 Hobbit} microprocessor",
  type =         "Thesis ({M.S.})",
  school =       "Lehigh University",
  address =      "Bethlehem, PA, USA",
  pages =        "viii + 85",
  year =         "1993",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Microprocessors.",
}

@Article{Hopkins:1993:CEM,
  author =       "Tim Hopkins and John Slater",
  title =        "A Comment on the {Eispack} Machine Epsilon Routine",
  journal =      j-SIGNUM,
  volume =       "28",
  number =       "4",
  pages =        "2--6",
  month =        oct,
  year =         "1993",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/165639.165641",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:24 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The authors analyze the algorithm used to generate the
                 value for the machine epsilon in the Eispack suite of
                 routines and show that it can fail on a binary
                 floating-point system. The comments in the code
                 describing the conditions under which this method will
                 work are not restrictive enough and the authors provide
                 a replacement set of assumptions. They conclude by
                 suggesting how the algorithm may be modified to
                 overcome most of the shortcomings.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Comput. Lab., Kent University, Canterbury, UK",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "Binary floating-point system; Eispack machine epsilon
                 routine",
  thesaurus =    "Digital arithmetic",
}

@TechReport{Horning:1993:SUM,
  author =       "Jim Horning and Bill Kalsow and Paul McJones and Greg
                 Nelson",
  title =        "Some Useful {Modula-3} Interfaces",
  type =         "Memo",
  number =       "113",
  institution =  "Digital Equipment Corporation, Systems Research
                 Center",
  address =      "Palo Alto, CA, USA",
  month =        dec,
  year =         "1993",
  bibdate =      "Wed Jan 29 16:39:06 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "From \cite{Steele:2004:RHP}: ``The floating-point
                 reader has been implemented in \ldots{} to
                 Modula-3''.",
}

@Article{Hu:1993:EIS,
  author =       "X. Hu and S. C. Bass and R. G. Harber",
  title =        "An Efficient Implementation of Singular Value
                 Decomposition Rotation Transformations with {CORDIC}
                 Processors",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "17",
  number =       "4",
  pages =        "360--362",
  month =        apr,
  year =         "1993",
  CODEN =        "JPDCER",
  DOI =          "https://doi.org/10.1006/jpdc.1993.1034",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Thu Mar 9 09:18:52 MST 2000",
  bibsource =    "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.idealibrary.com/links/doi/10.1006/jpdc.1993.1034/production;
                 http://www.idealibrary.com/links/doi/10.1006/jpdc.1993.1034/production/pdf",
  acknowledgement = ack-nhfb,
  classification = "C4140 (Linear algebra); C5230 (Digital arithmetic
                 methods); C7310 (Mathematics)",
  corpsource =   "General Motors Res. Labs., Warren, MI, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "2*2 matrices; CORDIC processors; digital arithmetic;
                 mathematics computing; matrix algebra; singular value
                 decomposition rotation transformations",
  treatment =    "A Application; P Practical",
}

@InProceedings{Hu:1993:NES,
  author =       "Xiaobo Hu and Steven C. Bass",
  title =        "Neglected Error Source in the {CORDIC} Algorithm",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "766--769",
  year =         "1993",
  bibdate =      "Wed Nov 12 10:45:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{IBM:1993:IPA,
  author =       "{IBM Corporation}",
  title =        "The {IBM PowerPC} Architecture: a New Family of {RISC}
                 Processors",
  publisher =    pub-MORGAN-KAUFMANN,
  address =      pub-MORGAN-KAUFMANN:adr,
  year =         "1993",
  ISBN =         "1-55860-316-6",
  ISBN-13 =      "978-1-55860-316-5",
  LCCN =         "QA76.8.P67P68 1994",
  bibdate =      "Sat Oct 15 12:26:00 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$49.95",
  acknowledgement = ack-nhfb,
}

@Article{Ide:1993:CFP,
  author =       "N. Ide and H. Fukuhisa and Y. Kondo and T. Yoshida and
                 M. Nagamatsu and J. Mori and I. Yamazaki and K. Ueno",
  title =        "A {320-MFLOPS} {CMOS} Floating-Point Processing Unit
                 for Superscalar Processors",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "28",
  number =       "3",
  pages =        "352--361",
  month =        mar,
  year =         "1993",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
}

@Article{Ide:1993:MCF,
  author =       "Nobuhiro Ide and Hiroto Fukuhisa and Yoshihisa Kondo
                 and Takeshi Yoshida and Masato Nagamatsu and Junji Mori
                 and Itaru Yamazaki and Kiyoji Ueno",
  title =        "A 320-{MFLOPS CMOS} Floating-Point Processing Unit for
                 Superscalar Processors",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "28",
  number =       "3",
  pages =        "352--361",
  month =        mar,
  year =         "1993",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "A CMOS pipelined floating-point processing unit (FPU)
                 for superscalar processors is described. It is
                 fabricated using a 0.5 $\mu$m CMOS triple-metal-layer
                 technology on a 61 mm 2 die. The FPU has two execution
                 modes to meet precise scientific computations and
                 real-time applications. It can start two FPU operations
                 in each cycle, and this achieves a peak performance of
                 160 MFLOPS double or single precision with an 80 MHz
                 clock. Furthermore, the original computation mode, twin
                 single-precision computation, double the peak
                 performance and delivers 320 MFLOPS single precision.
                 Its full bypass reduces the latency of operations,
                 including load and store, and achieves an effective
                 throughput even in nonvectorizable computations. An
                 out-of-order completion is provided by using a new
                 exception prediction method and a pipeline stall
                 technique.",
}

@Article{Jahn:1993:LIF,
  author =       "K.-U. Jahn",
  title =        "Loop Invariants in Floating Point Algorithms.
                 {Schleifen-Invarianten in Gleitpunktalgorithmen}",
  journal =      j-COMPUTING,
  volume =       "50",
  number =       "3",
  pages =        "255--264",
  year =         "1993",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65G05 (65G10)",
  MRnumber =     "94f:65052",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "It is shown that by using directed roundings with
                 respect to enclosure sets for the exact values, the
                 loop conditions and loop invariants of numerical
                 algorithms can be generalized for computing in a
                 discrete screen. It is possible to verify the received
                 results. Thereby only inherent properties of the
                 algorithms are used, which moreover guarantee that the
                 loops terminate.",
  acknowledgement = ack-nhfb,
  classification = "C4240P (Parallel programming and algorithm theory);
                 C6150G (Diagnostic, testing, debugging and evaluating
                 systems)",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "Directed roundings; Enclosure sets; Floating point
                 algorithms; Loop conditions; Loop invariants",
  pubcountry =   "Austria",
  thesaurus =    "Program verification",
}

@Article{Jahn:1993:SIG,
  author =       "K.-U. Jahn",
  title =        "{Schleifen-Invarianten in Gleitpunktalgorithmen}.
                 ({German}) [{Loop} Invariants in Floating Point
                 Algorithms]",
  journal =      j-COMPUTING,
  volume =       "50",
  number =       "3",
  pages =        "255--264",
  month =        sep,
  year =         "1993",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65G05 (65G10)",
  MRnumber =     "94f:65052",
  bibdate =      "Mon Oct 11 20:38:38 MDT 1999",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database; OCLC Contents1st database",
  abstract =     "It is shown that by using directed roundings with
                 respect to enclosure sets for the exact values, the
                 loop conditions and loop invariants of numerical
                 algorithms can be generalized for computing in a
                 discrete screen. It is possible to verify the received
                 results. Thereby only inherent properties of the
                 algorithms are used, which moreover guarantee that the
                 loops terminate.",
  acknowledgement = ack-nhfb,
  classification = "C4240P (Parallel programming and algorithm theory);
                 C6150G (Diagnostic, testing, debugging and evaluating
                 systems)",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "Directed roundings; Enclosure sets; Floating point
                 algorithms; Loop conditions; Loop invariants",
  language =     "German",
  pubcountry =   "Austria",
  thesaurus =    "Program verification",
}

@InProceedings{Jebelean:1993:CSG,
  author =       "T. Jebelean",
  title =        "Comparing Several {GCD} Algorithms",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "180--185",
  month =        jun,
  year =         "1993",
  bibdate =      "Wed Nov 14 18:46:15 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Jebelean.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}

@InProceedings{Jenkins:1993:CSL,
  author =       "W. K. Jenkins and B. A. Schnaufer and A. J. Mansen",
  title =        "Combined System-Level Redundancy and Modular
                 Arithmetic for Fault Tolerant Digital Signal
                 Processing",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "28--35",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Jenkins.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}

@Article{Johnstone:1993:RNA,
  author =       "P. Johnstone and F. E. Petry",
  title =        "Rational number approximation in higher radix floating
                 point systems",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "25",
  number =       "6",
  pages =        "103--108",
  month =        mar,
  year =         "1993",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Mathematical researchers have long recognized that
                 some bases offer some representational advantages in
                 that they generate fewer nonterminate values when
                 representing arbitrary rational numbers. While such
                 results are true for abstract number systems, little
                 attention has been paid to machine based computation
                 and its finite resources. In the paper, such results
                 are considered in an environment more typical of
                 computer based models of number systems. Specifically,
                 the authors consider the effect of the choice of
                 floating point base on rational number approximation in
                 systems which exhibit the typical characteristics of
                 floating point representations-normalized encodings,
                 limited exponent range and storage allocated in a fixed
                 number of `bits' per datum. The frequency with which
                 terminate and representable results can be expected is
                 considered for binary, decimal, and other potentially
                 interesting bases.",
  acknowledgement = ack-nhfb,
  affiliation =  "New Orleans Tech. Dev. Group, Telerate Systems Inc.,
                 LA, USA",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  keywords =     "Computer based models; decimal floating-point
                 arithmetic; Floating point base; Floating point
                 systems; Number systems; Rational number
                 approximation",
  pubcountry =   "UK",
  thesaurus =    "Digital arithmetic",
}

@InProceedings{Ju:1993:WCB,
  author =       "Chwen-Jye Ju",
  title =        "What can block floating-point arithmetic do for {DSP}
                 applications",
  crossref =     "Anonymous:1993:IPF",
  bookpages =    "1675",
  pages =        "641--650 vol.1",
  year =         "1993",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Block floating-point arithmetic for filtering was
                 proposed by Oppenheim two decades ago. Although it has
                 the advantages of both integer and floating-point
                 arithmetic, it is scarcely used in DSP applications
                 because the required signal reference level adjustment
                 (scaling) usually offsets its advantages. To conquer
                 the scaling problem, the unified indexing concept has
                 been proposed by the author for the M-D FFT
                 implementation. This paper will extend the concept to
                 derive the general block-oriented block floating-point
                 DSP algorithms. Therefore, the block floating-point
                 processors such as the LH9124/LH9320 can provide
                 self-contained solutions for some classes of DSP
                 applications.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sharp Microelectron. Technol. Inc., Camas, WA, USA",
  classification = "B1265F (Microprocessors and microcomputers); B6140
                 (Signal processing and detection); C5135 (Digital
                 signal processing chips); C5230 (Digital arithmetic
                 methods); C5260 (Digital signal processing)",
  keywords =     "Block floating-point arithmetic; Block floating-point
                 processors; DSP applications; General block-oriented
                 block floating-point DSP algorithms; LH9124/LH9320; M-D
                 FFT implementation; Oppenheim; Scaling problem; Signal
                 reference level adjustment; Unified indexing concept",
  thesaurus =    "Array signal processing; Digital arithmetic; Digital
                 filters; Digital signal processing chips; Fast Fourier
                 transforms",
}

@TechReport{Juffa:1993:EYA,
  author =       "Norbert Juffa",
  title =        "Everything You Always Wanted to Know about Math
                 Coprocessors",
  type =         "Report",
  institution =  "????",
  address =      "????",
  month =        jan,
  year =         "1993",
  bibdate =      "Thu Nov 13 06:08:13 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://dougx.net/gaming/coproc.html",
  acknowledgement = ack-nhfb,
  remark-1 =     "From the report: ``Unlike Intel's coprocessors, which
                 use the CORDIC algorithm to compute the transcendental
                 functions, Cyrix uses polynomial and rational
                 approximations to the functions.''",
  remark-2 =     "From the report: ``The Cyrix 83D87 uses a fast array
                 multiplier, making its transcendental functions faster
                 than those of any other 387 compatible coprocessor. It
                 also uses 75 bit for the mantissa in intermediate
                 calculations (as opposed to 68 bits on other
                 coprocessors), making its transcendental functions more
                 accurate than those of any other coprocessor or FPU.''",
  remark-3 =     "From the report: ``The Weitek Abacus 3167 and 4167
                 coprocessors are 'mostly compatible' with IEEE-754.
                 \ldots{} One of the most notable omissions is the
                 missing support for denormal numbers; denormals are
                 always flushed to zero on Weitek chips.''",
  remark-4 =     "This is an interesting comparison, made a dozen years
                 after the Intel 8087 floating-point coprocessor
                 appeared on the market, of pin-compatible chips from
                 Intel and others. The 8087 uses CORDIC algorithms for
                 all of its elementary functions, and does the job in
                 about 64K transistors, with 67-bit significands. That
                 gives three additional bits over the 64 needed for the
                 IEEE 754 binary80 format, and they serve as the Guard,
                 Round, and Sticky bits needed to implement the four
                 required rounding modes. Measured worst-case errors in
                 the functions are below 3 units in the last place
                 (ulps).\par

                 The transcendental functions offered in hardware on the
                 8087 have restricted argument ranges, and thus require
                 a software interface to carry out range reduction of
                 general arguments before the chip instructions can be
                 used.\par

                 Juffa reports that the Cyrix FasMath CX-83D87
                 coprocessor instead uses rational polynomial
                 representations of the elementary functions, with
                 75-bit significands. Its accuracy is superior to all of
                 its competitors: Cyrix claimed that results are almost
                 always within 0.5 ulp of the infinitely precise exact
                 value, and thus, are almost always correctly
                 rounded.\par

                 Thanks to semiconductor density improvements, the Intel
                 486DX, introduced in 1989, put the coprocessor on the
                 same chip as the CPU, more than tripling floating-point
                 performance over the previous generation Intel 387DX.
                 By the mid 1990s, floating-point support was available
                 in all major commercial CPUs, but in some, such as the
                 DEC Alpha, it takes a major part of the chip
                 area.\par

                 Although not mentioned in this article, Motorola's
                 68881 and 68882 coprocessors offered similar
                 floating-point hardware instructions as the Intel 8087,
                 but later CPUs from ARM, DEC (Alpha), HP (HPPA), IBM
                 (POWER, PowerPC, s390x, and z-Series), Loongson, MIPS,
                 RISC-V, and Sun/Fujitsu SPARC. and also the Intel i860,
                 omit the elementary functions, requiring their
                 implementation in software.",
}

@TechReport{Karp:1993:HPD,
  author =       "A. H. Karp and P. Markstein",
  title =        "High precision division and square root",
  number =       "HPL-93-42",
  institution =  "Hewlett--Packard Lab.",
  address =      "Palo Alto, CA, USA",
  pages =        "20",
  month =        jun,
  year =         "1993",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The authors present division and square root
                 algorithms for calculations with more bits than are
                 handled by the floating point hardware. These
                 algorithms avoid the need to multiply two high
                 precision numbers, speeding up the last iteration by as
                 much as a factor of ten.",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods)",
  keywords =     "Division; Floating point hardware; Square root
                 algorithms",
  thesaurus =    "Digital arithmetic",
}

@InProceedings{Kim:1993:FABa,
  author =       "S. W. Kim and T. Stouraitis and A. Skavantzos",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, {ISCAS '93}, 3--6 May 1993",
  title =        "Full adder-based inner product step processors for
                 residue and quadratic residue number systems",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1821--1824",
  year =         "1993",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1993.394100",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A full adder-based arithmetic unit of a modulus $m$,
                 called an FA-based AU$_m$, is proposed. It performs
                 both addition and multiplication at the same time.
                 Since the proposed AU$_m$'s use full adders as their
                 basic units, they lead to modular and regular designs
                 which result in lower cost and easier implementation in
                 VLSI.",
}

@InProceedings{Kim:1993:FABb,
  author =       "Seon Wook Kim and T. Stouraitis and A. Skavantzos",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, {ISCAS '93}, 3--6 May 1993",
  title =        "Full adder-based inner product step processors for
                 residue and quadratic residue number systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1821--1824",
  year =         "1993",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/EDAC.1993.386412",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
}

@InProceedings{Kim:1993:FABc,
  author =       "S. W. Kim and T. Stouraitis and A. Skavantzos",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, {ISCAS '93}, 3--6 May 1993",
  title =        "Full adder-based inner product step processors for
                 residue and quadratic residue number systems",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1821--1824",
  year =         "1993",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1993.394100",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A full adder-based arithmetic unit of a modulus m,
                 called an FA-based AU m, is proposed. It performs both
                 addition and multiplication at the same time. Since the
                 proposed AU m's use full adders as their basic units,
                 they \ldots{}",
}

@InProceedings{Kim:1993:FABd,
  author =       "Seon Wook Kim and T. Stouraitis and A. Skavantzos",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, {ISCAS '93}, 3--6 May 1993",
  title =        "Full adder-based inner product step processors for
                 residue and quadratic residue number systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1821--1824",
  year =         "1993",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/EDAC.1993.386412",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
}

@InProceedings{Kirsch:1993:ABU,
  author =       "Bary J. Kirsch and Peter R. Turner",
  title =        "Adaptive Beamforming Using {RNS} Arithmetic",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "36--43",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Kirsch.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11; residue number system",
}

@Book{Klatte:1993:CXC,
  editor =       "Rudi Klatte and Ulrich Kulisch and Christian Lawo and
                 Michael Rauch and Andreas Wiethoff",
  title =        "{C-XSC}: a {C++} class library for extended scientific
                 computing",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xii + 269",
  year =         "1993",
  ISBN =         "3-540-56328-8 (Berlin), 0-387-56328-8 (New York)",
  ISBN-13 =      "978-3-540-56328-0 (Berlin), 978-0-387-56328-2 (New
                 York)",
  LCCN =         "QA76.73.C153 C9 1993",
  bibdate =      "Fri Jun 24 20:05:29 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "DM74.00",
  abstract =     "C-XSC is a tool for the development of numerical
                 algorithms delivering highly accurate and automatically
                 verified results. It provides a large number of
                 predefined numerical data types and operators. These
                 types are implemented as C++ classes. Thus, C-XSC
                 allows high-level programming of numerical applications
                 in C and C++. The most important features of C-XSC are:
                 real, complex, interval, and complex interval
                 arithmetic; dynamic vectors and matrices; subarrays of
                 vectors and matrices; dotprecision data types,
                 predefined arithmetic operators with maximum accuracy;
                 standard functions of high accuracy; multiple precision
                 arithmetic and standard functions; rounding control for
                 I/O data; error handling, and library of problem
                 solving routines with automatic result verification.
                 Thus, C-XSC makes the computer more powerful concerning
                 the arithmetic. C-XSC is immediately usable by C
                 programmers, easy to learn, user-extendable, and may
                 also be combined with other tools. The book can be used
                 as a textbook and as a reference manual. It consists of
                 an introduction to advanced computer arithmetic, a
                 chapter describing the programming languages C and C++,
                 the major chapter ``C-XSC Reference'', sample programs,
                 and indices.",
  acknowledgement = ack-nhfb,
  remark =       "This book is a translation of an unpublished German
                 manuscript.",
  subject =      "C++ (Computer program language); C-XSC; Mathematics;
                 Numerical analysis; Mathematics.; Numerical analysis.",
  tableofcontents = "1 Introduction \\
                 1.1 Typography \\
                 1.2 C-XSC: A Class Library in the Programming Language
                 C++ \\
                 1.3 C-XSC: A Programming Environment for Scientific
                 Computing with Result Verification \\
                 1.4 Survey of C-XSC \\
                 2 The Programming Languages C and C++ \\
                 2.1 A Short Introduction to C \\
                 2.2 Additional Features in C++ \\
                 3 C-XSC Reference \\
                 3.1 Constants, Data Types, and Variables \\
                 3.2 Expressions \\
                 3.3 Statements \\
                 3.4 Error Handling \\
                 3.5 Pitfalls for Programming with C XSC \\
                 A Syntax Diagrams \\
                 A.1 Data Types \\
                 A.2 Management of Vectors and Matrices \\
                 A.3 Definition of Variables \\
                 A.4 Expressions \\
                 A.5 Logical Expressions \\
                 A.6 Type Castings \\
                 A.7 Assignments \\
                 A.8 Arithmetic Standard Functions \\
                 A.9 Other Functions \\
                 A.10 Input and Output \\
                 A.11 Extension of a Syntax Diagram of C++ \\
                 B The Structure of the C-XSC Package \\
                 B.1 Header Files \\
                 B.2 Module Libraries \\
                 C Error List \\
                 D Sample Programs \\
                 D.1 Rounding Control of Arithmetic Operations \\
                 D.2 Rounding Control of Input and Output \\
                 D.3 Scalar Product \\
                 D.4 Transpose of a Matrix \\
                 D.5 Trace of a Product Matrix \\
                 D.6 Inverse of a Matrix \\
                 D.7 Multiple-Precision Arithmetic \\
                 D.8 Interval Newton Method \\
                 D.9 Runge-Kutta Method \\
                 D.10 Complex Polynomial Arithmetic \\
                 D.11 Automatic Differentiation \\
                 E Scientific Computation with Verified Results \\
                 E.1 Evaluation of Polynomials \\
                 E.2 Matrix Inversion \\
                 E.3 Linear Systems of Equations \\
                 E.4 Eigenvalues of Symmetric Matrices \\
                 E.5 Fast Fourier Transform \\
                 E.6 Zeros of a Nonlinear Equation \\
                 E.7 System of Nonlinear Equations \\
                 E.8 Ordinary Differential Equations",
}

@Book{Koren:1993:CAA,
  author =       "Israel Koren",
  title =        "Computer Arithmetic Algorithms",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xiii + 210",
  year =         "1993",
  ISBN =         "0-13-151952-2",
  ISBN-13 =      "978-0-13-151952-7",
  LCCN =         "76.9.C62 K67 1993",
  bibdate =      "Thu Sep 1 10:12:51 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@InProceedings{Kornerup:1993:HRM,
  author =       "Peter Kornerup",
  title =        "High-Radix Modular Multiplication for Cryptosystems",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "277--283",
  year =         "1993",
  bibdate =      "Wed Nov 14 18:46:45 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Kornerup.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}

@Book{Kortemeyer:1993:CPT,
  author =       "Gerd Kortemeyer and others",
  title =        "{Coprozessoren Programmierung mit Turbo Pascal und
                 C++: eine grundlegende Einf{\"u}hrung in die
                 mathematischen Coprozessoren ab 80387 und deren
                 Programmierung} \toenglish Coprocessor Programming with
                 {Turbo Pascal} and {C++}\relax \endtoenglish",
  publisher =    pub-IWT,
  address =      pub-IWT:adr,
  pages =        "391",
  year =         "1993",
  ISBN =         "3-88322-439-1",
  ISBN-13 =      "978-3-88322-439-8",
  LCCN =         "????",
  bibdate =      "Mon Sep 16 17:08:22 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Kota:1993:NAH,
  author =       "K. Kota and J. R. Cavallaro",
  title =        "Numerical Accuracy and Hardware Tradeoffs for {CORDIC}
                 Arithmetic for Special-Purpose Processors",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "7",
  pages =        "769--779",
  month =        jul,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.237718",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:50 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=237718",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Krandick:1993:EMF,
  author =       "Werner Krandick and Jeremy R. Johnson",
  title =        "Efficient multiprecision floating point multiplication
                 with optimal directional rounding",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "228--233",
  year =         "1993",
  bibdate =      "Thu Dec 14 11:25:18 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Krandick.pdf",
  abstract =     "An algorithm is described for multiplying
                 multiprecision floating-point numbers. The algorithm
                 can produce either the smallest floating-point number
                 greater than or equal to the true product, or the
                 greatest floating-point number smaller than or equal to
                 the true product. Software implementations of
                 multiprecision floating-point multiplication can reduce
                 the computation time by a factor of two if they do not
                 compute the low-order digits of the product of the two
                 mantissas. However, these algorithms do not necessarily
                 provide optimally rounded results. The algorithms
                 described here is guaranteed to produce optimally
                 rounded results and typically obtains the same
                 savings.",
  acknowledgement = ack-nhfb,
  affiliation =  "Res. Inst. for Symbolic Comput., Johannes Kepler
                 University, Linz, Austria",
  classification = "C5230 (Digital arithmetic methods)",
  confdate =     "29 June-2 July 1993",
  conflocation = "Windsor, Ont., Canada",
  confsponsor =  "IEEE Comput. Soc.; IEEE Tech. Committee on VLSI;
                 Natural Sci. and Eng. Res.; Council of Canada",
  keywords =     "ARITH-11; Floating-point numbers; Multiprecision
                 floating point multiplication; Optimal directional
                 rounding; Optimally rounded results",
  thesaurus =    "Floating point arithmetic",
}

@Article{Krishna:1993:TFA,
  author =       "H. Krishna and J.-D. Sun",
  title =        "On theory and fast algorithms for error correction in
                 residue number system product codes",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "7",
  pages =        "840--853",
  month =        jul,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.237724",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:50 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=6095;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=237724",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The authors develop a coding theory approach to error
                 control in residue number system product codes. Based
                 on this coding theory framework, computationally
                 efficient algorithms are derived for correcting single
                 errors, double errors, and multiple \ldots{}",
}

@Article{Lee:1993:DAE,
  author =       "Joong-Eon Lee and Oh-Young Kwon and Tack-Don Han",
  title =        "Design of an area efficient unit for floating-point
                 division and square root",
  journal =      j-J-KOREA-INFO-SCI-SOCIETY,
  volume =       "20",
  number =       "7",
  pages =        "1060--1071",
  month =        jul,
  year =         "1993",
  CODEN =        "HJKHDC",
  ISSN =         "0258-9125",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The authors propose an algorithm for a high
                 performance floating point division and square root
                 unit that uses a parallel multiplier. The basic
                 algorithm used in the design is the continued-product
                 normalization method. In this method, an arbitrary
                 number is constantly multiplied to the divisor and
                 dividend and dividend/divisor ends up with quotient/1
                 and the desired result attained. However this method
                 requires computation of x*(2-x) and x*(3-x)/2 and this
                 is quite an overhead. Therefore they propose a new
                 algorithm to compute (2-x) and (3-x)/2 by using the
                 modified Booth algorithm. When applied to the
                 continued-product normalization method, this algorithm
                 can maximize the inherent parallelism of the
                 continued-product normalization method, and reduce
                 computation time by effectively applying pipelining,
                 and also achieve area efficient design by eliminating
                 one register and one carry propagate adder needed for
                 computing (2-x) and (3-x)/2. When the designed unit is
                 used with the seed generator which has the accuracy of
                 2/sup -7/, division can be executed in eight cycles and
                 the square root operation in 13 cycles.",
  acknowledgement = ack-nhfb,
  classification = "B1265B (Logic circuits); C4240P (Parallel
                 programming and algorithm theory); C5120 (Logic and
                 switching circuits); C5230 (Digital arithmetic
                 methods)",
  fjournal =     "Journal of the Korea Information Science Society =
                 Chongbo Kwahakhoe nonmunji",
  keywords =     "Area efficient unit; Continued-product normalization
                 method; Floating-point division; Modified Booth
                 algorithm; Parallel multiplier; Pipelining; Seed
                 generator; Square root",
  language =     "Korean",
  pubcountry =   "South Korea",
  thesaurus =    "Adders; Digital arithmetic; Parallel algorithms",
}

@InProceedings{Lewis:1993:ALA,
  author =       "D. M. Lewis",
  title =        "An accurate {LNS} arithmetic unit using interleaved
                 memory function interpolator",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "2--9",
  year =         "1993",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Lewis.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
  summary =      "A logarithmic number system (LNS) arithmetic unit
                 using a new method for polynomial interpolation in
                 hardware is described. The use of an interleaved memory
                 reduces storage requirements by allowing each stored
                 function value to be used in \ldots{}",
}

@Misc{Lindsley:1993:DME,
  author =       "Brett L. Lindsley",
  title =        "Device and method for evaluating exponentials",
  howpublished = "United States Patent 5,177,702",
  day =          "5",
  month =        jan,
  year =         "1993",
  bibdate =      "Tue Jan 08 22:31:05 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.freepatentsonline.com/5177702.html",
  abstract =     "A method and apparatus are described for processing an
                 input value to provide an output exponential value of a
                 desired base raised to the power of the input value.
                 The method includes, and the apparatus included
                 hardware for implementing, the steps of adjusting the
                 input value relative to the input value, a
                 predetermined base of a first exponential value, and
                 the desired base of the output exponential value to
                 obtain a first scaled value, modifying the scaled value
                 to obtain an approximation value, determining the first
                 exponential value of the approximation value,
                 generating an adjusted error value relative to the
                 first scaled value, the approximation value, and a
                 logarithm of the predetermined base of the first
                 exponential value, determining a correction value for
                 the first exponential value and combining the first
                 exponential value with the correction value to obtain,
                 substantially, the output exponential value having the
                 desired base raised to the power of the input value.",
  acknowledgement = ack-nhfb,
}

@Article{Linzer:1993:IEF,
  author =       "E. N. Linzer and E. Feig",
  title =        "Implementation of Efficient {FFT} Algorithms on Fused
                 Multiply-Add Architectures",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "41",
  number =       "1",
  year =         "1993",
  CODEN =        "ITPRED",
  DOI =          "https://doi.org/10.1109/TSP.1993.193130",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sun Feb 20 10:11:17 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
}

@Article{Lo:1993:BCP,
  author =       "J.-C. Lo and S. Thanawastien and T. R. N. Rao",
  title =        "{Berger} check prediction for array multipliers and
                 array dividers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "7",
  pages =        "892--896",
  month =        jul,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.237731",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:50 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  note =         "See correction \cite{Lo:1996:CBC}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=237731",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Louie:1993:DRD,
  author =       "M. E. Louie and M. D. Ercegovac",
  title =        "On Digit-Recurrence Division Implementations for Field
                 Programmable Gate Arrays",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "202--209",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Louie.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}

@InProceedings{Louie:1993:DRS,
  author =       "M. E. Louie and M. D. Ercegovac",
  booktitle =    "Proceedings of the {IEEE} Workshop on {FPGAs} for
                 Custom Computing Machines, 5--7 April 1993",
  title =        "A digit-recurrence square root implementation for
                 field programmable gate arrays",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "178--183",
  year =         "1993",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Creating efficient arithmetic processors requires a
                 pairing of high speed arithmetic algorithms with
                 optimal mapping strategies for a given technology. The
                 authors propose bit reduction as key to an efficient
                 pairing process for lookup table based \ldots{}",
}

@InProceedings{Lozier:1993:UGF,
  author =       "D. W. Lozier",
  title =        "An underflow-induced graphics failure solved by {SLI}
                 arithmetic",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "10--17",
  year =         "1993",
  bibdate =      "Thu Dec 14 11:25:18 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Lozier.pdf",
  abstract =     "Floating-point underflow is often regarded as either
                 harmless or as an indication that the computational
                 algorithm is in need of scaling. A counterexample to
                 this view is given of a function for which contour
                 plotting is difficult due to floating-point underflow.
                 The function arose as an asymptotic solution to a model
                 problem in turbulent combustion in which two chemical
                 species (fuel and oxidizer) mix and react in a vortex
                 field. Scaling is not a viable option because of
                 extreme sensitivity to a small physical parameter.
                 Standard graphics software packages produce erroneous
                 contours without any indication of difficulty. This
                 example provides support for considering symmetric
                 level-index arithmetic, a new form of computer
                 arithmetic which is immune to underflow and overflow.",
  acknowledgement = ack-nhfb,
  affiliation =  "Nat. Inst. of Stand. and Technol., Gaithersburg, MD,
                 USA",
  classification = "C5230 (Digital arithmetic methods); C6130B (Graphics
                 techniques)",
  confdate =     "29 June-2 July 1993",
  conflocation = "Windsor, Ont., Canada",
  confsponsor =  "IEEE Comput. Soc.; IEEE Tech. Committee on VLSI;
                 Natural Sci. and Eng. Res.; Council of Canada",
  keywords =     "ARITH-11; Asymptotic solution; Computer arithmetic;
                 Contour plotting; Floating point underflow; Graphics
                 failure; Graphics software packages; Turbulent
                 combustion",
  thesaurus =    "Computer graphics; Floating point arithmetic",
}

@Article{MacKenzie:1993:NAC,
  author =       "Donald MacKenzie",
  title =        "Negotiating Arithmetic, Constructing Proof: The
                 Sociology of Mathematics and Information Technology",
  journal =      j-SOC-STUD-SCI,
  volume =       "23",
  number =       "1",
  pages =        "37--65",
  day =          "1",
  month =        feb,
  year =         "1993",
  CODEN =        "SSSCDH",
  DOI =          "https://doi.org/10.1177/030631293023001002",
  ISSN =         "0306-3127 (print), 1460-3659 (electronic)",
  ISSN-L =       "0306-3127",
  bibdate =      "Mon Dec 3 09:12:55 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/socstudsci.bib",
  note =         "Summary of the process of IEEE 754, several years
                 after its initial adoption.",
  URL =          "https://ieeemilestones.ethw.org/w/images/1/10/Negotiating_Arithmetic_MacKenzie.pdf;
                 https://journals.sagepub.com/doi/pdf/10.1177/030631293023001002",
  acknowledgement = ack-nhfb,
  fjournal =     "Social Studies of Science",
  journal-URL =  "http://sss.sagepub.com/content/by/year",
}

@Article{Mandelbaum:1993:SRS,
  author =       "D. M. Mandelbaum",
  title =        "Some results on a {SRT} type division scheme",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "1",
  pages =        "102--106",
  month =        jan,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.192218",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:46 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=192218",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@MastersThesis{Maryoung:1993:DBP,
  author =       "James Maryoung",
  title =        "Development of a binary phase shift keying modem
                 receiver with a floating point processor {TMS320C30}",
  type =         "Thesis ({M.S.})",
  school =       "California State University, Long Beach",
  address =      "Long Beach, CA, USA",
  pages =        "xi + 265",
  year =         "1993",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Signal processing --- Algorithms.; Signal processing
                 --- Digital techniques.",
}

@Article{Masotti:1993:FNE,
  author =       "G. Masotti",
  title =        "Floating-point numbers with error estimates",
  journal =      j-CAD,
  volume =       "25",
  number =       "9",
  pages =        "524--538",
  month =        sep,
  year =         "1993",
  CODEN =        "CAIDA5",
  ISSN =         "0010-4485 (print), 1879-2685 (electronic)",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Addresses the problem of precision in floating-point
                 computations. A method for estimating the errors which
                 affect intermediate and final results is presented, and
                 a synthesis of many software simulations is discussed.
                 The basic idea is to represent floating-point numbers
                 by means of a data-structure collecting value and
                 estimated error information. It has been found that,
                 under certain circumstances, the estimate of the
                 absolute error is accurate and has a compact
                 statistical distribution. It is also shown that, by
                 monitoring the estimated relative error during a
                 computation (an ad hoc definition of relative error is
                 used), the validity of results can be ensured. The
                 error estimates enable robust algorithms to be
                 implemented and ill-conditioned problems to be
                 detected. A hardware implementation of the method by
                 means of a special floating-point processor is
                 outlined. A dynamic extension of number precision,
                 under the control of error estimates, is also
                 advocated, in order to compute results within given
                 error bounds.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dept. di Elettr. Inf. e Sistem., Universita degli
                 Studi di Bologna, Bologna, Italy",
  classification = "C5230 (Digital arithmetic methods)",
  keywords =     "Compact statistical distribution; Computer arithmetic;
                 Data-structure collecting value; Dynamic extension;
                 Dynamic precision extension; Error bounds; Error
                 estimates; Final results; Floating-point numbers;
                 Floating-point processor; Hardware implementation;
                 Ill-conditioned problems; Intermediate results;
                 Numerical accuracy; Relative error; Robust algorithms;
                 Software simulations; Validity",
  pubcountry =   "UK",
  thesaurus =    "Digital arithmetic; Error statistics; Roundoff
                 errors",
}

@Article{Mazenc:1993:CFU,
  author =       "Christophe Mazenc and Xavier Merrheim and Jean-Michel
                 Muller",
  title =        "Computing functions $ \cos^{-1} $ and $ \sin^{-1} $
                 using {Cordic}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "1",
  pages =        "118--122",
  month =        jan,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.192222",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:47 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=192222",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@TechReport{McClellan:1993:AFP,
  author =       "Scott McClellan",
  title =        "Alternatives to floating point representation",
  type =         "Honors paper",
  number =       "4",
  institution =  "United States Naval Academy Honors Paper. Dept. of
                 Mathematics",
  pages =        "various",
  year =         "1993",
  bibdate =      "Sat May 04 17:18:52 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.",
  remark =       "Honors paper--United States Naval Academy, 1993.",
}

@Article{McKeeman:1993:AOC,
  author =       "W. M. McKeeman",
  title =        "Avoiding Overflow in Constant Expression Evaluation",
  journal =      j-JCLT,
  volume =       "5",
  number =       "1",
  pages =        "27--31",
  month =        sep,
  year =         "1993",
  ISSN =         "1042-5721",
  bibdate =      "Fri Nov 21 14:40:20 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Journal of {C} Language Translation",
  remark =       "Predicting overflow before it occurs",
}

@InProceedings{McQuillan:1993:NAV,
  author =       "S. E. McQuillan and J. V. McCanny and R. Hamill",
  title =        "New algorithms and {VLSI} architectures for {SRT}
                 division and square root",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "80--86",
  year =         "1993",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_McQuillan.pdf",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  keywords =     "ARITH-11",
  summary =      "Radix two algorithms for SRT division and
                 square-rooting are developed. For these schemes, the
                 result digits and the residuals are computed
                 concurrently and the computations in adjacent rows are
                 overlapped. Consequently, their performance should
                 \ldots{}",
}

@Article{Meier:1993:EMC,
  author =       "Willi Meier and Othmar Staffelbach",
  title =        "Efficient Multiplication on Certain Nonsupersingular
                 Elliptic Curves",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "740",
  pages =        "333--344",
  year =         "1993",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:48:51 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t0740.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/0740/07400333.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/0740/07400333.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
  keywords =     "CRYPTO; cryptology",
}

@InProceedings{Mellott:1993:GMG,
  author =       "Jonathon D. Mellott and Jeremy C. Smith and Fred J.
                 Taylor",
  title =        "The {Gauss} Machine: a {Galois}-Enhanced Quadratic
                 Residue Number System Systolic Array",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "156--162",
  year =         "1993",
  DOI =          "https://doi.org/10.1109/ARITH.1993.378097",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Mellott.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11; residue arithmetic; residue number system",
  summary =      "The Gauss machine is a SIMD systolic array
                 architecture that takes advantage of the
                 Galois-enhanced residue number system (GEQRNS) to form
                 reduced-complexity arithmetic elements. The Gauss
                 machine is targeted at front-end signal and image
                 processing applications. A discrete prototype that
                 achieves a peak rating of 320 million complex
                 arithmetic operations per second while operating at 10
                 MHz has been constructed. A VLSI implementation of the
                 Gauss machine's processor cell has been created. The
                 VLSI implementation is implemented in 2.0-$\mu$m CMOS
                 and achieves greater than 20-MHz performance, using
                 less than 2.0-mm$^2$ die area. It is shown that
                 techniques for defect tolerance in RNS systolic arrays
                 can result in substantial yield enhancement, thereby
                 making larger than conventional (ULSI) systems
                 possible",
}

@InProceedings{Merrheim:1993:FEP,
  author =       "Xavier Merrheim and Jean-Michel Muller and Hong-Jin
                 Yeh",
  title =        "Fast Evaluation of Polynomials and Inverses of
                 Polynomials",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "186--192",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Merrheim.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}

@MastersThesis{Mesfin:1993:IHP,
  author =       "Biniam Mesfin",
  title =        "Implementation of a high performance floating point
                 unit multiplier",
  type =         "Thesis ({M.A.Sc.})",
  school =       "University of Windsor",
  address =      "Windsor, ON, Canada",
  year =         "1993",
  ISBN =         "0-315-78864-X",
  ISBN-13 =      "978-0-315-78864-0",
  LCCN =         "????",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "National Library of Canada = Bibliotheque nationale du
                 Canada; Canadian theses = Theses canadiennes",
  acknowledgement = ack-nhfb,
  remark =       "3 microfiches. University Microfilms order no.
                 UMI00399117",
}

@Article{Metzger:1993:IFR,
  author =       "D. Metzger",
  title =        "Investigation of Finite Register Length Effects on
                 {Winograd} {FFT} Computation Using Floating Point
                 Math",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "41",
  number =       "1",
  pages =        "449",
  month =        jan,
  year =         "1993",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
}

@Manual{MicrosoftCorporation:1993:PGM,
  author =       "{Microsoft Corporation}",
  title =        "Programmer's guides: {Microsoft Visual C++}
                 development system for {Windows}: version 1.0",
  organization = "Microsoft Corp.",
  address =      "Redmond, WA, USA",
  pages =        "various",
  year =         "1993",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "C++ (Computer program language); Microsoft Visual
                 C++.",
  remark =       "C++ tutorial: introduction to C++: a first look at
                 C++; C++ enhancements to C; references; classes:
                 introduction to classes; classes and dynamic memory
                 allocation; more features of classes; inheritance and
                 polymorphism; operator overloading and conversion
                 functions; object-oriented design: fundamentals of
                 object-oriented design; design example, a windowing
                 class --- Class library user's guide for the Microsoft
                 Foundation Class Library: introducing the class
                 library; creating a new application with AppWizard;
                 creating the document, view; constructing the user
                 interface with App Studio; binding visual objects to
                 code using ClassWizard; adding a dialog box; enhancing
                 views, printing; adding context-sensitive help;
                 general-prupose classes; CObject class; collections;
                 files and serialization; diagnostics; exceptions;
                 programming with VBX controls; OLE support ---
                 Programming techniques: improving program performance:
                 using precompiled headers; managing memory for 16-bit C
                 programs; controlling floating-point math operations;
                 special environments: programming for Windows;
                 programming with mixed languages; writing portable C
                 programs. [Section one of the book], the C++ tutorial,
                 provides an introduction to the C++ language and
                 object-oriented programming. [It] assumes [the reader
                 is] familiar with C \ldots{} [Section two] contains a
                 tutorial for the Microsoft Foundation Class Library.
                 The class library is a set of C++ classes that
                 encapsulate the functionality of applications written
                 for the Microsoft Windows operating system \ldots{}
                 [Section three], programming techniques, describes how
                 to take advantage of the special features of Microsoft
                 Visual C++. The topics covered \ldots{} include
                 language extensions, special-purpose library functions,
                 and the interaction between programming strategies and
                 compiler options. [This section] is divided into two
                 parts. Part I, ``Improving Program Performance,'' helps
                 [the reader] write more efficient programs \ldots{}
                 Part 2, ``Special Environments,'' covers techniques
                 specific to certain programming situations. -Introds.",
}

@Article{Mikami:1993:RER,
  author =       "N. Mikami and M. Kobayashi and Y. Yokoyama",
  title =        "Roundoff-error reduction for evaluation of a function
                 by polynomial approximation with error feedback in
                 fixed-point arithmetic",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "41",
  number =       "5",
  pages =        "1953--1955",
  month =        may,
  year =         "1993",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "The relationship between Hornor's method for
                 polynomial evaluation and a first-order recursive
                 filter with error feedback (EFB) is described. It is
                 shown that EFB is a useful technique for reducing the
                 roundoff errors that occur in evaluating a \ldots{}",
}

@InProceedings{Montuschi:1993:CSM,
  author =       "Paolo Montuschi and Luigi Ciminiera",
  title =        "$ n \times n $ Carry-Save Multipliers without Final
                 Addition",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "54--61",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Montuschi.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}

@Article{Montuschi:1993:RIT,
  author =       "P. Montuschi and L. Ciminiera",
  title =        "Reducing iteration time when result digit is zero for
                 radix $2$ {SRT} division and square root with redundant
                 remainders",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "2",
  pages =        "239--246",
  month =        feb,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.204797",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:47 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  note =         "See remark \cite{Montuschi:1995:RRI}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=204797",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "A new architecture is presented for shared radix 2
                 division and square root whose main characteristic is
                 the ability to avoid any addition/subtraction, when the
                 digit 0 has been selected. The solution presented uses
                 a redundant representation of the \ldots{}",
}

@Article{Motteler:1993:APF,
  author =       "Frederick C. Motteler",
  title =        "Arbitrary Precision Floating-Point Arithmetic",
  journal =      j-DDJ,
  volume =       "18",
  number =       "9",
  pages =        "28, 30, 32, 34, 84, 86--87",
  month =        sep,
  year =         "1993",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Tue Sep 03 09:15:43 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 UnCover database",
  abstract =     "The C library presented was developed with IEEE-754
                 compatibility and portability as its primary goals. Its
                 first application was as part of a portable cross
                 compiler. It is a general-purpose library that supports
                 single, double, double-extended, and longer IEEE-754
                 like formats. The library has been ported to and tested
                 on a variety of systems including CP/M, PCs running
                 MS-DOS, PCs running Coherent, Sun 3s, Sparcstations
                 (Sun's C compiler), and the IBM RS/6000 under AIX. The
                 package is K and R, ANSI C, and C++ compatible. A
                 table-driven tester included with the library checks if
                 it has compiled properly. The tester also gives an idea
                 of what the package is capable of doing.",
  acknowledgement = ack-nhfb,
  affiliation =  "Zetron Inc., Redmond, WA, USA",
  classification = "C5230 (Digital arithmetic methods); C7310
                 (Mathematics)",
  fjournal =     "Dr. Dobb's Journal of Software Tools",
  keywords =     "C library; Coherent; CP/M; Double-extended;
                 Floating-point arithmetic; General-purpose library; IBM
                 RS/6000; IEEE-754 compatibility; IEEE-754 like formats;
                 MS-DOS; PCs; Portability; Portable cross compiler;
                 Sparcstations; Sun 3s; Table-driven tester",
  thesaurus =    "C listings; Digital arithmetic; Mathematics computing;
                 Software portability; Subroutines",
}

@Misc{Ng:1993:FV,
  author =       "K-C Ng",
  title =        "{FDLIBM} Version 5.3",
  howpublished = "Web site",
  year =         "1993",
  bibdate =      "Thu Oct 17 06:21:14 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.netlib.org/fdlibm/readme",
  acknowledgement = ack-nhfb,
  keywords =     "FDLIBM (Freely Distributable Math Library)",
}

@InProceedings{Nguyen:1993:LDR,
  author =       "Q. H. Nguyen and I. Kollar",
  booktitle =    "Instrumentation and Measurement Technology Conference,
                 1993. {IMTC/93}. Conference Record., {IEEE. 18--20} May
                 1993",
  title =        "Limited dynamic range of spectrum analysis due to
                 roundoff errors of the {FFT}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "47--50",
  year =         "1993",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Roundoff errors of the block-float fast Fourier
                 transform (FFT) are treated. Special emphasis is given
                 to the case when signals containing sine waves are
                 analyzed. In the detection and analysis of sine waves,
                 root-mean-square values and overall \ldots{}",
}

@Article{North:1993:FPA,
  author =       "R. C. North and J. R. Zeidler and W. H. Ku and T. R.
                 Albert",
  title =        "A floating-point arithmetic error analysis of direct
                 and indirect coefficient updating techniques for
                 adaptive lattice filters",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "41",
  number =       "5",
  pages =        "1809--1823",
  month =        may,
  year =         "1993",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "The ways in which finite precision arithmetic effects
                 can deleteriously manifest themselves in both the
                 stochastic gradient and the recursive least squares
                 adaptive lattice filters are discussed. closed form
                 expressions are derived for the steady-state \ldots{}",
}

@Article{Ozawa:1993:SAE,
  author =       "K. Ozawa and M. Miyazaki",
  title =        "A summation algorithm with error correction for
                 parallel computers",
  journal =      j-SYS-COMP-JAPAN,
  volume =       "24",
  number =       "7",
  pages =        "62--68",
  month =        "????",
  year =         "1993",
  CODEN =        "SCJAEP",
  ISSN =         "0882-1666 (print), 1520-684X (electronic)",
  ISSN-L =       "0882-1666",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Proposes an algorithm to accurately compute the sum of
                 floating-point numbers on parallel computers. This
                 algorithm is an extension of the well-known recursive
                 doubling technique which computes the sum of n
                 floating-point number in log/sub 2/n parallel steps.
                 The time complexity of the present algorithm also is
                 O(logn), and the space complexity is O(n). This
                 algorithm enables a highly accurate result to be
                 obtained with guarantee. The theoretical analysis and
                 the numerical experiments on a parallel computer show
                 that this algorithm is as accurate as Kahan's, which is
                 the fastest and an accurate serial algorithm for the
                 summation of the numbers, and also that the present
                 algorithm is faster than Kahan's provided that two or
                 more processors are available.",
  acknowledgement = ack-nhfb,
  affiliation =  "Coll. of Gen. Educ., Tohoku University, Sendai,
                 Japan",
  classification = "C4110 (Error analysis in numerical methods); C4240P
                 (Parallel programming and algorithm theory)",
  fjournal =     "Systems and computers in Japan",
  keywords =     "accurate floating-point summation; correct rounding;
                 error correction; floating-point numbers; guaranteed
                 accuracy; parallel computation; parallel computers;
                 recursive doubling; recursive doubling technique;
                 round-off error analysis; space complexity; summation;
                 summation algorithm; time complexity",
  thesaurus =    "computational complexity; error correction; parallel
                 algorithms",
}

@PhdThesis{Pan:1993:TFVa,
  author =       "Jing Pan",
  title =        "Toward a formal verification of a floating-point
                 coprocessor and its composition with a central
                 processing unit",
  type =         "Thesis ({Ph.D.})",
  school =       "Computer Science Department, University of California,
                 Davis",
  address =      "Davis, CA, USA",
  pages =        "221",
  year =         "1993",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Pan:1993:TFVb,
  author =       "Jing Pan and K. N. Levitt and M. Archer and S.
                 Kalvala",
  title =        "Towards a formal verification of a floating point
                 coprocessor and its composition with a central
                 processing unit",
  journal =      j-IFIP-TRANS-A,
  volume =       "A20",
  pages =        "427--447",
  month =        "????",
  year =         "1993",
  CODEN =        "ITATEC",
  ISSN =         "0926-5473",
  bibdate =      "Tue Dec 12 09:27:13 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Higher Order Logic Theorem Proving and its
                 Applications IFIP TC\slash WG10.2 International
                 Workshop - HOL '92.",
  abstract =     "The authors discuss verification (ultimately down to
                 the microcode level) of a microprocessor that consists
                 of a central processing unit that is the master of a
                 floating point coprocessor; the design is drawn from
                 the MC68881 floating point coprocessor slaved to the
                 MC68000, but greatly simplified. The coprocessor in
                 isolation is verified with respect to a specification
                 that captures the IEEE floating point standard. In the
                 authors system, CPU and floating point instructions are
                 allowed to execute concurrently, but the appearance to
                 the programmer of the composed system is that of a
                 sequentially executing instruction stream. The CPU and
                 floating point coprocessor communicate through the
                 four-phase handshaking protocol. The verification
                 involves reasoning about a form of behavioural
                 abstraction wherein concurrently executing instruction
                 steams are mapped to a sequential stream.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, California University,
                 Davis, CA, USA",
  classification = "C4210 (Formal logic); C5130 (Microprocessor chips);
                 C5230 (Digital arithmetic methods); C6110B (Software
                 engineering techniques)",
  confdate =     "21-24 Sept. 1992",
  conflocation = "Leuven, Belgium",
  fjournal =     "IFIP Transactions. A. Computer Science and
                 Technology",
  keywords =     "Behavioural abstraction; Central processing unit;
                 Concurrently executing instruction steams; Floating
                 point coprocessor; Formal verification; Four-phase
                 handshaking protocol; MC68000; MC68881; Microprocessor;
                 Reasoning; Sequentially executing instruction stream;
                 Specification",
  pubcountry =   "Netherlands",
  thesaurus =    "Digital arithmetic; Formal verification;
                 Microprocessor chips; Theorem proving",
}

@InProceedings{Panneerselvam:1993:MAF,
  author =       "G. Panneerselvam and B. Nowrouzian",
  title =        "Multiply-add fused {RISC} architectures for {DSP}
                 applications",
  crossref =     "IEEE:1993:PIP",
  volume =       "1",
  pages =        "108--111",
  year =         "1993",
  DOI =          "https://doi.org/10.1109/PACRIM.1993.407210",
  bibdate =      "Sun Feb 20 10:47:10 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The development of a fixed-point bit-parallel
                 multiply-add fused (MAF) architecture together with a
                 corresponding VLSI implementation is presented. The
                 proposed MAF implementation employs 1.2 CMOS
                 technology. This MAF implementation finds a variety of
                 practical applications in high-speed real-time digital
                 signal processing. The MAF implementation employs a
                 parallel modified Booth multiplier incorporating an
                 array of carry-save adders for the addition of the
                 intermediate partial products, and a hardware efficient
                 carry-skip adder for carry propagation. The performance
                 characteristics of the MAF implementation have been
                 successfully verified by an HSPICE simulation at speeds
                 of up to 100 MHz.",
  acknowledgement = ack-nhfb,
}

@Article{Parhami:1993:IAS,
  author =       "B. Parhami",
  title =        "On the implementation of arithmetic support functions
                 for generalized signed-digit number systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "3",
  pages =        "379--384",
  month =        mar,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.210182",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:48 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=210182",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Parker:1993:OHS,
  author =       "A. Parker",
  title =        "Optimization of high speed function generation using
                 table-lookup",
  journal =      j-TRANS-SOC-COMP-SIM,
  volume =       "10",
  number =       "2",
  pages =        "105--114",
  month =        jun,
  year =         "1993",
  CODEN =        "TSCSEV",
  ISSN =         "0740-6797",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A process is presented for the use of generic operator
                 optimization for the evaluation of unary floating point
                 functions using table lookup. The process involves the
                 identification of an underlying architecture and the
                 symbolic-numeric optimization of operators to minimize
                 a least-squares representation of total error. The
                 approach is illustrated for the case of floating point
                 division.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Electr. and Comput. Eng., Alabama
                 University, Huntsville, AL, USA",
  classification = "C1160 (Combinatorial mathematics); C4120 (Functional
                 analysis); C6130 (Data handling techniques)",
  fjournal =     "Transactions of the Society for Computer Simulation",
  keywords =     "Floating point division; High speed function
                 generation; Least-squares representation;
                 Symbolic-numeric optimization; Table lookup",
  thesaurus =    "Equivalence classes; Function evaluation; Symbol
                 manipulation; Table lookup",
}

@Book{Pichat:1993:IDC,
  author =       "Mich{\`e}le Pichat and Jean Vignes",
  title =        "Ing{\'e}nierie du contr{\^o}le de la pr{\'e}cision des
                 calculs sur ordinateur",
  publisher =    "Editions Technip",
  address =      "Paris, France",
  pages =        "xvii + 233",
  year =         "1993",
  ISBN =         "2-7108-0653-3",
  ISBN-13 =      "978-2-7108-0653-0",
  LCCN =         "TJ213 .P478 1993",
  bibdate =      "Wed Nov 24 12:28:18 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Collection Informatique",
  acknowledgement = ack-nhfb,
  subject =      "Automatic control; Microcomputers",
}

@Article{Plauger:1993:FCE,
  author =       "P. J. Plauger",
  title =        "Floating-Point {C} Extensions",
  journal =      j-CUJ,
  volume =       "11",
  type =         "{Standard C}",
  number =       "9",
  pages =        "10--??",
  month =        sep,
  year =         "1993",
  ISSN =         "0898-9788",
  bibdate =      "Fri Aug 30 16:52:23 MDT 1996",
  bibsource =    "http://www.cuj.com/cbklist.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "C Users Journal",
}

@Book{Plauger:1993:PPIc,
  author =       "P. J. Plauger",
  title =        "Programming on Purpose {III}: Essays on Software
                 Technology",
  volume =       "3",
  publisher =    pub-PHPTR,
  address =      pub-PHPTR:adr,
  pages =        "viii + 224",
  year =         "1993",
  ISBN =         "0-13-328113-2",
  ISBN-13 =      "978-0-13-328113-2",
  LCCN =         "QA76.76.D47 P53 1994",
  bibdate =      "Wed Jul 6 14:26:01 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\$19.95",
  acknowledgement = ack-nhfb,
  libnote =      "Not yet in my library.",
  remark =       "Originally published in the author's monthly column in
                 Computer language magazine, 1986-1992. Contents: Volume
                 I: Essays on software design -- volume II: Essays on
                 software people -- volume III: Essays on software
                 technology.",
  tableofcontents = "You Must Be Joking \\
                 Computer Arithmetic \\
                 Floating-Point Arithmetic \\
                 The Central Folly \\
                 Safe Math \\
                 Do-It-Yourself Math Functions \\
                 Locking the Barn Door \\
                 Half a Secret \\
                 It's (Almost) Alive \\
                 The (Almost) Right Stuff \\
                 Instant Lies \\
                 What Meets the Eye \\
                 Technicolor and Cinemascope \\
                 What Meets the Ear \\
                 Warm Fuzzies \\
                 Font Follies \\
                 Text Editors \\
                 Approximating Functions \\
                 Economizing Polynomials \\
                 Technical Writing \\
                 All I Want to Do Is \\
                 Programming for the Billions \\
                 All Sorts of Sorts \\
                 Transforming Strings \\
                 Books for Our Times \\
                 Through the Grapevine \\
                 List of Columns \\
                 Bibliography \\
                 Index",
}

@Article{Posch:1993:BKR,
  author =       "K. C. Posch and R. Posch",
  title =        "{Basiserweiterung mit einer Konvolutionssumme in
                 Restklassenzahlensystemen}. ({German}) [{Base}
                 Extension Using a Convolution Sum in Residue Number
                 Systems]",
  journal =      j-COMPUTING,
  volume =       "50",
  number =       "2",
  pages =        "93--104",
  year =         "1993",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "68M07 (11Y16)",
  MRnumber =     "94e:68024",
  bibdate =      "Mon Oct 11 20:38:38 MDT 1999",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database; OCLC Contents1st database",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  language =     "German",
}

@Article{Pugh:1993:FPC,
  author =       "Kenneth Pugh",
  title =        "Floating Point Constants",
  journal =      j-CUJ,
  volume =       "11",
  type =         "Questions and Answers",
  number =       "10",
  pages =        "130--??",
  month =        oct,
  year =         "1993",
  ISSN =         "0898-9788",
  bibdate =      "Fri Aug 30 16:52:23 MDT 1996",
  bibsource =    "http://www.cuj.com/cbklist.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "C Users Journal",
}

@Article{Reid:1993:LIA,
  author =       "John Reid",
  title =        "{Language Independent Arithmetic} ({LIA}) --- a {Draft
                 International Standard} ({DIS})",
  journal =      j-SIGNUM,
  volume =       "28",
  number =       "1",
  pages =        "2--7",
  month =        jan,
  year =         "1993",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:23 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "LIA is now an International Standard, ISO/IEC
                 10967-1:1994; it is ``92 pages of small print, densely
                 mathematical, not counting 8 pages of front matter, and
                 it is not available electronically.'' Its adoption has
                 been rather controversial.",
  abstract =     "The UK and US votes have been decided on the draft
                 international standard ISO/IEC CD 10967-1:1992:
                 language independent arithmetic-part 1: integer and
                 floating point arithmetic. The stated goals of the
                 draft are: to enhance the portability of numeric
                 programs across a wide range of numeric architectures.
                 To help programming languages express the semantics of
                 their numerical types. It defines integer and
                 (normalized and denormalized) floating point types. It
                 defines integer and (normalized and denormalized)
                 floating point types. It specifies the primitive
                 computational operations with source and destination
                 operands of the same type, comparison operations on two
                 operands of the same type, and conversions from any
                 arithmetic type to any other arithmetic type. The
                 values of parameters define the exact arithmetic
                 behaviour of any particular platform.",
  acknowledgement = ack-nhfb,
  affiliation =  "Rutherford Appleton Lab., Didcot, UK",
  classification = "C5230 (Digital arithmetic methods); C6140D (High
                 level languages)",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "International standard; Language independent
                 arithmetic; Numeric architectures; Numeric programs;
                 Portability; Programming languages",
  thesaurus =    "Digital arithmetic; High level languages; Standards",
}

@InProceedings{Richardson:1993:ETR,
  author =       "S. E. Richardson",
  title =        "Exploiting trivial and redundant computation",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "220--227",
  year =         "1993",
  bibdate =      "Thu Jun 20 10:16:15 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Richardson.pdf",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  keywords =     "ARITH-11",
}

@Article{Ris:1993:WFP,
  author =       "Fred Ris and Ed Barkmeyer and Craig Schaffert and
                 Peter Farkas",
  title =        "When Floating-Point Addition Isn't Commutative",
  journal =      j-SIGNUM,
  volume =       "28",
  number =       "1",
  pages =        "8--13",
  month =        jan,
  year =         "1993",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/156301.156303",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:23 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In the early 1980s, the IEEE floating-point standards
                 (754 for binary formats adopted in 1985 and 854 for
                 more general situations adopted in 1987) were
                 developed. There are now many more-or-less IEEE 754
                 conformant products on the market. A fully compliant
                 implementation must provide conforming representations
                 of floating-point values, perform arithmetic operations
                 as specified by the standard, provide four rounding
                 modes and five exception flags defined by the standard,
                 support infinities, NaNs, signed zeros, and unordered
                 comparisons, and provide access to all these features
                 from programming languages (as supported by the
                 compiler and runtime library). Not surprisingly, very
                 few implementations comply fully with the IEEE 754
                 standard in all respects. But one might imagine that if
                 there were such compliance one could expect bit-for-bit
                 identical results for a given algorithm executed on any
                 conforming implementation. The paper explains why this
                 is not always the case.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "IBM Federal Syst. Co., Boulder, CO, USA",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "Arithmetic operations; Conforming implementation;
                 Exception flags; Floating-point addition;
                 Floating-point values; IEEE 754; IEEE floating-point
                 standards; Rounding modes",
  thesaurus =    "Digital arithmetic; Standards",
}

@InProceedings{Samani:1993:SVP,
  author =       "D. M. Samani and J. Ellinger and E. J. Powers and E.
                 E. Swartzlander",
  title =        "Simulation of variable precision {IEEE} floating point
                 using {C}++ and its application in digital signal
                 processor design",
  crossref =     "IEEE:1993:PMS",
  pages =        "1509--1514 vol.2",
  year =         "1993",
  bibdate =      "Thu Dec 14 11:25:18 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We use a C++ class to transparently emulate
                 variable-precision floating point arithmetic using
                 standard arithmetic. This allows the determination of
                 an algorithm's susceptibility to errors produced by
                 finite-precision arithmetic and the determination of
                 the minimum precision necessary for stability. The
                 class, called Real, offers several advantages for many
                 applications, e.g., ALU design, signal processing,
                 systolic and lattice filter design, etc. Since it
                 supports the IEEE floating point standard, it produces
                 identical results on any compliant platform. An
                 algorithm can be adapted for simulation with minimal
                 effort and without interfering with normal operation.
                 We also consider how the acceptance of the IEEE
                 standard and the development of fast hardware for
                 microcomputers have changed common assumptions about
                 algorithm timing. Finally, we examine the potential use
                 of the new floating point DSP chips for adaptive
                 filtering. Historically, the computational requirements
                 of adaptive filters confined implementations to
                 specialized hardware or supercomputers. Today's DSP
                 chips offer a relatively inexpensive alternative. We
                 have implemented several adaptive filtering algorithms
                 that are based on Least Squares estimation criterion on
                 Motorola's DSP96002. Our experience indicates that the
                 DSP96K is a viable medium for such algorithms and one
                 can expect a ten-fold speed improvement over a i486
                 running at 50 MHz.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Electr. and Comput. Eng., Texas
                 University, Austin, TX, USA",
  classification = "B1265F (Microprocessors and microcomputers); B1270F
                 (Digital filters); B6140 (Signal processing and
                 detection); C5135 (Digital signal processing chips);
                 C5220P (Parallel architecture); C5230 (Digital
                 arithmetic methods); C5240 (Digital filters); C5260
                 (Digital signal processing); C6140D (High level
                 languages)",
  keywords =     "Adaptive filtering; Algorithm timing; ALU design; C++
                 language; Digital signal processor design; DSP chips;
                 Floating point arithmetic; IEEE standard; Lattice
                 filter; Least squares estimation criterion; Motorola
                 DSP96002; Real; Systolic filter; Variable precision
                 IEEE floating point",
  thesaurus =    "Adaptive filters; C language; Digital signal
                 processing chips; Floating point arithmetic; Lattice
                 filters; Least squares approximations; Systolic
                 arrays",
}

@InProceedings{Sarma:1993:MAR,
  author =       "D. D. Sarma and D. W. Matula",
  title =        "Measuring the Accuracy of {ROM} Reciprocal Tables",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "95--102",
  year =         "1993",
  bibdate =      "Wed Nov 14 18:47:17 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Sarma.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}

@Article{Scannell:1993:DMM,
  author =       "Robert K. Scannell and John K. Hagge",
  title =        "Development of a Multichip Module {DSP}",
  journal =      j-COMPUTER,
  volume =       "26",
  number =       "4",
  pages =        "13--21",
  month =        apr,
  year =         "1993",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Tue May 14 16:20:44 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A highly modular processor architecture based on
                 off-the-shelf components supports an MCM design
                 implementation that delivers 400 million floating-point
                 operations per second in a 75-gram package.",
  acknowledgement = ack-nhfb,
  affiliation =  "Rockwell Int., Anaheim, CA, USA",
  classification = "B0170J (Product packaging); B1265F (Microprocessors
                 and microcomputers); B2220J (Hybrid integrated
                 circuits); B2570 (Semiconductor integrated circuits);
                 C5135 (Digital signal processing chips)",
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
  keywords =     "Cost; Highly modular processor architecture;
                 Interconnect-substrate design; MCM package assembly;
                 Multichip module DSP; Signal processor packaging
                 design; Size; Weight",
  thesaurus =    "Digital signal processing chips; Multichip modules",
}

@Article{Schorn:1993:AAR,
  author =       "Peter Schorn",
  title =        "An Axiomatic Approach to Robust Geometric Programs",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "16",
  number =       "2",
  pages =        "155--166 (or 155--165??)",
  month =        aug,
  year =         "1993",
  CODEN =        "JSYCEH",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  MRclass =      "68U07",
  MRnumber =     "94k:68196",
  bibdate =      "Sat May 10 15:54:09 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "C4260 (Computational geometry); C1180 (Optimisation
                 techniques)",
  corpsource =   "Inst. fur Theor. Inf., Eidgenossische Tech.
                 Hochschule, Zurich, Switzerland",
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171",
  keywords =     "axiomatic approach; computational geometry; digital
                 arithmetic; floating point arithmetic; geometric;
                 imprecise primitives; non-trivial; plane sweep
                 algorithm; primitives; programming; robust geometric
                 programs",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Schulte:1993:ERC,
  author =       "M. Schulte and E. Swartzlander",
  title =        "Exact rounding of certain elementary functions",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "138--145",
  year =         "1993",
  bibdate =      "Thu Jun 20 10:16:17 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1993-01.pdf;
                 http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Schulte.pdf",
  abstract =     "An algorithm is described which produces exactly
                 rounded results for the functions of reciprocal, square
                 root, 2/sup x/, and log 2/sup x/. Hardware designs
                 based on this algorithm are presented for floating
                 point numbers with 16- and 24-b significands. These
                 designs use a polynomial approximation in which
                 coefficients are originally selected based on the
                 Chebyshev series approximation and are then adjusted to
                 ensure exactly rounded results for all inputs. To
                 reduce the number of terms in the approximation, the
                 input interval is divided into subintervals of equal
                 size and different coefficients are used for each
                 subinterval. For floating point numbers with 16-b
                 significands, the exactly rounded value of the function
                 can be computed in 51 ns on a 20-mm/sup 2/ chip. For
                 floating point numbers with 24-b significands, the
                 functions can be computed in 80 ns on a 98-mm/sup 2/
                 chip.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Electr. and Comput. Eng., Texas
                 University, Austin, TX, USA",
  classification = "C4120 (Functional analysis); C5230 (Digital
                 arithmetic methods)",
  confdate =     "29 June--2 July 1993",
  conflocation = "Windsor, Ont., Canada",
  confsponsor =  "IEEE Comput. Soc.; IEEE Tech. Committee on VLSI;
                 Natural Sci. and Eng. Res.; Council of Canada",
  keywords =     "ARITH-11; Elementary functions; Exact rounding;
                 Floating point numbers; Polynomial approximation;
                 Reciprocal; Rounded results; Square root",
  thesaurus =    "Floating point arithmetic; Function evaluation",
}

@InProceedings{Schulte:1993:PHD,
  author =       "M. J. Schulte and E. E. {Swartzlander, Jr.}",
  title =        "Parallel Hardware Designs for Correctly Rounded
                 Elementary Functions",
  crossref =     "Corliss:1993:AIC",
  pages =        "65--87 (or 65--88??)",
  year =         "1993",
  bibdate =      "Tue Oct 22 13:37:58 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Schulte:1993:TMC,
  author =       "M. J. Schulte and E. E. {Swartzlander, Jr.}",
  title =        "Truncated Multiplication with Correction Constant",
  crossref =     "Eggermont:1993:VSP",
  pages =        "388--396",
  year =         "1993",
  bibdate =      "Sun Mar 04 10:38:15 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1993-02.pdf",
  acknowledgement = ack-nhfb,
}

@TechReport{Schwarz:1993:HRAa,
  author =       "E. Schwarz",
  title =        "High-radix algorithms for high-order arithmetic
                 operations",
  type =         "Technical Report",
  number =       "CSL-TR-93-559",
  institution =  "Computer Systems Laboratory, Stanford University",
  address =      "Stanford, CA, USA",
  month =        jan,
  year =         "1993",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}

@PhdThesis{Schwarz:1993:HRAb,
  author =       "Eric Mark Schwarz",
  title =        "High-radix algorithms for high-order arithmetic
                 operations",
  type =         "Thesis ({Ph.D.})",
  school =       "Department of Electrical Engineering, Stanford
                 University",
  address =      "Stanford, CA, USA",
  pages =        "224",
  month =        apr,
  year =         "1993",
  bibdate =      "Mon Jan 07 22:38:06 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Many common algorithms for high-order arithmetic
                 operations require an initial approximation. The
                 Newton--Raphson algorithm starts with an approximation
                 and then quadratically converges on the solution. The
                 initial approximation determines the number of
                 iterations of the algorithm and is typically
                 implemented as a look-up table in the form of a ROM or
                 PLA. A novel method is suggested which describes
                 high-order arithmetic operations with a partial product
                 array. This method applies to the operations of
                 division, reciprocal, square root, natural logarithm,
                 exponential, and trigonometric functions. The partial
                 product array of Boolean elements which describes the
                 operation can be summed on an existing floating-point
                 multiplier. The hardware needed is only the logic gates
                 to create the Boolean elements in the array and a
                 multiplexor, and the latency is that of the multiplier.
                 Thus, by reusing a floating-point multiplier, a
                 high-precision approximation to a high-order arithmetic
                 operation can be implemented with a low marginal
                 cost.\par

                 This dissertation describes the implementation and
                 shows a method for deriving partial product arrays to
                 approximate arithmetic operations. Then the proposed
                 method is applied and evaluated for several operations.
                 The proposed method yields a minimum approximation of
                 twelve bits correct for the reciprocal operation and
                 sixteen bits for the square root operation. The
                 proposed method is shown to be as small as 0.05\% the
                 size (in gates) of an equivalent precision look-up
                 table and has up to four times the accuracy (in bits)
                 as an equivalent latency polynomial approximation.
                 Also, three new iterative algorithms to increase the
                 precision of the approximations and a theoretical
                 analysis of the partial product array representation
                 are detailed. Thus, high-radix algorithms of many
                 arithmetic operations are possible at low cost.",
  acknowledgement = ack-nhfb,
  keywords =     "division; elementary functions; exponential;
                 logarithm; PPA (partial product array); reciprocal
                 square root; square root",
  remark =       "AAT 9317816. ProQuest document ID 746798521.",
}

@InProceedings{Schwarz:1993:HSA,
  author =       "Eric M. Schwarz and Michael J. Flynn",
  title =        "Hardware starting approximation for the square root
                 operation",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "103--111",
  year =         "1993",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Schwarz.pdf",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  keywords =     "ARITH-11",
  summary =      "A method for obtaining high-precision approximations
                 of high-order arithmetic operations is presented. These
                 approximations provide an accurate starting
                 approximation for high-precision iterative algorithms,
                 which translates into few iterations and \ldots{}",
}

@Article{Schwarz:1993:PHR,
  author =       "E. M. Schwarz and M. J. Flynn",
  title =        "Parallel high-radix nonrestoring division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "10",
  pages =        "1234--1246",
  month =        oct,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.257709",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=257709",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@TechReport{Schwarz:1993:UFM,
  author =       "Eric Mark Schwarz and M. J. (Michael J.) Flynn",
  title =        "Using a floating-point multiplier's internals for
                 high-radix division and square root",
  type =         "Technical report",
  number =       "CSL-TR-93-554",
  institution =  "Computer Systems Laboratory, Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "iv + 45",
  year =         "1993",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic.",
  remark =       "``January 1993.'' Abstract: ``A method for obtaining
                 high-precision approximations of high-order arithmetic
                 operations at low-cost is presented in this study.
                 Specifically, high-precision approximations of the
                 reciprocal (12 bits worst case) and square root (16
                 bits) operations are obtained using the internal
                 hardware of a floating-point multiplier without the use
                 of look-up tables. The additional combinatorial logic
                 necessary is very small due to the reuse of existing
                 hardware. These low-cost high-precision approximations
                 are used by iterative algorithms to perform the
                 operations of division and square root. The method
                 presented also applies to several other high-order
                 arithmetic operations. Thus, high-radix algorithms for
                 high-order arithmetic operations such as division and
                 square root are possible at low-cost.''",
}

@InProceedings{Shanbhag:1993:REAa,
  author =       "N. R. Shanbhag and K. K. Parhi",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems: {ISCAS '93}, 3--6 May 1993",
  title =        "Roundoff error analysis of the pipelined {ADPCM}
                 coder",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "886--889",
  year =         "1993",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Not \ldots{}",
}

@InProceedings{Shanbhag:1993:REAb,
  author =       "N. R. Shanbhag and K. K. Parhi",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems: {ISCAS '93}, 3--6 May 1993",
  title =        "Roundoff error analysis of the pipelined {ADPCM}
                 coder",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "886--889",
  year =         "1993",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Roundoff error analysis of a pipelined adaptive
                 differential pulse code modulation (ADPCM) coder is
                 presented. The pipelined coder has been developed by
                 employing the relaxed look-ahead technique. It is shown
                 that the precision of the quantized \ldots{}",
}

@InProceedings{Shand:1993:FIR,
  author =       "M. Shand and J. Vuillemin",
  title =        "Fast Implementations of {RSA} Cryptography",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "252--259",
  year =         "1993",
  bibdate =      "Wed Nov 14 18:47:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Shand.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}

@Book{Shannon:1993:CES,
  author =       "Claude Elwood Shannon and N. J. A. (Neil James
                 Alexander) Sloane and A. D. (Aaron D.) Wyner",
  title =        "{Claude Elwood Shannon}: collected papers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xliv + 924",
  year =         "1993",
  ISBN =         "0-7803-0434-9",
  ISBN-13 =      "978-0-7803-0434-5",
  LCCN =         "TK5101 .S448 1993",
  bibdate =      "Sat Nov 20 09:04:51 MST 2010",
  bibsource =    "catalog.princeton.edu:7090/voyager;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Claude Elwood Shannon (1916--2001)",
  subject =      "telecommunication; information theory; computers",
}

@Article{Sharp:1993:PRN,
  author =       "W. E. Sharp and Carter Bays",
  title =        "A portable random number generator for
                 single-precision floating-point arithmetic",
  journal =      j-COMP-GEOSCI,
  volume =       "19",
  number =       "4",
  pages =        "593--??",
  month =        apr,
  year =         "1993",
  CODEN =        "CGEODT, CGOSDN",
  ISSN =         "0098-3004 (print), 1873-7803 (electronic)",
  ISSN-L =       "0098-3004",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Geosciences",
}

@InProceedings{Shirayanagi:1993:MCM,
  author =       "Kiyoshi Shirayanagi",
  title =        "An algorithm to compute floating point {Gr{\"o}bner}
                 bases",
  crossref =     "Lee:1993:MCM",
  pages =        "95--106",
  year =         "1993",
  MRclass =      "68Q40 (13P10 68Q25)",
  MRnumber =     "94j:68129",
  bibdate =      "Fri Dec 8 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Shute:1993:AAB,
  author =       "Malcolm J. Shute",
  title =        "{Abotec}: an automatic back-of-the-envelope
                 calculator",
  journal =      j-SIGPLAN,
  volume =       "28",
  number =       "8",
  pages =        "90--98",
  month =        aug,
  year =         "1993",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:16:40 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The trial-and-error method, iteratively applied, is
                 invariably involved in any kind of design work, with
                 much back-of-the-envelope calculation to guide the
                 process. In this, the `what-if' game is a very useful
                 tactic in the search for unexpected solutions in
                 complex design spaces, made all the more effective by
                 the availability of automated interpreters. These are
                 needed to perform the tedious re-calculation of the
                 model each time a change is made to a small part. In
                 the financial world, the interpreter generally takes
                 the form of the spread-sheet, of which Quattro is a
                 fine example; in mathematics it takes the form of
                 packages such as Mathematica. Neither of these is
                 ideally tailored for engineering design, and so Abotec
                 was developed when the author had need of such a tool.
                 There are four main characteristics which fit Abotec
                 for its purpose: it works with floating-point numbers
                 throughout; it uses a richer than normal set of
                 arithmetic operators and functions; it uses mnemonic
                 labelling throughout; and, most importantly it treats
                 all variables as having an upper and lower bound.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, Manchester University,
                 UK",
  classification = "C6140D (High level languages); C7310 (Mathematics);
                 C7400 (Engineering)",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "Abotec; Arithmetic operators; Automated interpreters;
                 Automatic back-of-the-envelope calculator;
                 Back-of-the-envelope calculation; Complex design
                 spaces; Design work; Engineering design; Floating-point
                 numbers; Mnemonic labelling; Re-calculation;
                 Trial-and-error method; Unexpected solutions; What-if",
  thesaurus =    "CAD; High level languages; Mathematics computing",
}

@Article{Smith:1993:PFC,
  author =       "Ross Smith and Gerald Sobelman and George Luk and
                 Koichi Suda and Jeff Bracken",
  title =        "A Programmable Floating-Point Cell for Systolic Signal
                 Processing",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "5",
  number =       "1",
  pages =        "75--84",
  month =        jan,
  year =         "1993",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1007/BF01880273",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The FPC controller and the AMD Am29325 32-bit
                 floating-point mathematics processor form a two-chip
                 cell designed for one- or two-dimensional systolic
                 arrays which can be used to implement a wide variety of
                 signal processing applications. The FPC controls the
                 Am29325, routes data to and from it, and routes data
                 and control to other cells in the array. Unique
                 architectural features include two interchangeable data
                 memories, an input port which can be used as either a
                 local or global port, and a 32-bit instruction word
                 that allows concurrent use of all cell resources.
                 Additional features include a program memory, two data
                 streams, and three control streams.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
}

@Article{Smith:1993:VFP,
  author =       "William Smith",
  title =        "Varying Floating-Point Precision",
  journal =      j-CUJ,
  volume =       "11",
  number =       "7",
  pages =        "87--??",
  month =        jul,
  year =         "1993",
  ISSN =         "0898-9788",
  bibdate =      "Fri Aug 30 16:52:23 MDT 1996",
  bibsource =    "http://www.cuj.com/cbklist.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "C Users Journal",
}

@Article{Smith:1993:WDF,
  author =       "William Smith",
  title =        "Windows, {DLLs}, and Floating Point Types",
  journal =      j-CUJ,
  volume =       "11",
  number =       "9",
  pages =        "21--??",
  month =        sep,
  year =         "1993",
  ISSN =         "0898-9788",
  bibdate =      "Fri Aug 30 16:52:23 MDT 1996",
  bibsource =    "http://www.cuj.com/cbklist.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "C Users Journal",
}

@InProceedings{Soulas:1993:AMC,
  author =       "T. Soulas and D. Villeger and V. G. Oklobdzija",
  title =        "An {ASIC} macro cell multiplier for complex numbers",
  crossref =     "IEEE:1993:PEC",
  pages =        "589--593",
  year =         "1993",
  bibdate =      "Thu Dec 14 11:25:18 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "An architecture for ASIC macro cell implementing a
                 complex number multiplier with applications in a
                 digital signal processing ASIC chip is described. The
                 complex numbers are packed into one 32-bit word. The
                 design is unique and combines shared Booth encoding for
                 the real and imaginary parts including only one
                 combined modified Wallace tree. The regular Wallace
                 tree and the tree of 4:2 adders for the complex
                 multiplier implementation are compared. The authors
                 took advantage of 4:2 adders in implementing the
                 combined bit compression tree for each part. This
                 design resulted in a more compact wiring structure and
                 balanced delays resulting in faster multiplier circuit.
                 The number of adders was also decreased.",
  acknowledgement = ack-nhfb,
  affiliation =  "Ecole Superieure d'Ingenieurs en Electrotech. et
                 Electron., Noisy le Grand, France",
  classification = "B1130B (Computer-aided circuit analysis and design);
                 B1265B (Logic circuits); B1265F (Microprocessors and
                 microcomputers); B2570D (CMOS integrated circuits);
                 C5120 (Logic and switching circuits); C5135 (Digital
                 signal processing chips); C5210B (Computer-aided logic
                 design); C5230 (Digital arithmetic methods); C7410D
                 (Electronic engineering computing)",
  confsponsor =  "IEEE; EDA Assoc.; AEIA, Spain; AFCET, France; AICA,
                 Italy; Bull SA, France; CEC ESPRIT Basic Research",
  keywords =     "32 Bit; ASIC macro cell multiplier; Balanced delays;
                 CMOS; Combined bit compression tree; Compact wiring
                 structure; Complex numbers; Digital signal processing
                 ASIC chip; Floating point number representation; Shared
                 Booth encoding; Wallace tree",
  numericalindex = "Word length 3.2E+01 bit",
  thesaurus =    "Application specific integrated circuits; Cellular
                 arrays; CMOS logic circuits; Digital signal processing
                 chips; Floating point arithmetic; Integrated circuit
                 design; Logic arrays; Logic CAD; Multiplying circuits",
}

@Article{Subramaniam:1993:PPP,
  author =       "Ramesh Subramaniam and Kiran Kundargi and J. Dahms",
  title =        "Programming The {Pentium} Processor",
  journal =      j-DDJ,
  volume =       "18",
  number =       "6",
  pages =        "34, 36, 38, 40--42",
  month =        jun,
  year =         "1993",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Tue Sep 03 09:15:41 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 UnCover database",
  abstract =     "Intel's recent entry into the 32-bit microprocessor
                 race ups the performance ante. Our authors discuss the
                 Pentium's superscalar, pipelined architecture, focusing
                 on floating-point code. John Dahms shares some of his
                 experiences in writing a Pentium-aware compiler.",
  acknowledgement = ack-nhfb,
  affiliation =  "Intel, Santa Clara, CA, USA",
  classification = "C5130 (Microprocessor chips); C5220 (Computer
                 architecture); C6110 (Systems analysis and
                 programming); C6150C (Compilers, interpreters and other
                 processors)",
  fjournal =     "Dr. Dobb's Journal of Software Tools",
  keywords =     "32 Bit; 32-Bit microprocessor; Floating-point code;
                 High performance architecture; Intel Pentium;
                 Pentium-aware compiler; Programming; Superscalar
                 pipelined architecture",
  thesaurus =    "Computer architecture; Microprocessor chips;
                 Microprogramming; Pipeline processing; Program
                 compilers",
}

@InProceedings{Swartzlander:1993:FSC,
  author =       "Earl Swartzlander and Mary Jane Irwin and Graham
                 Jullien",
  title =        "Foreword: {11th Symposium on Computer Arithmetic,
                 Windsor, Ontario, Canada, June 29--July 2, 1993}",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "v--v",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_contents.pdf;
                 http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_foreword.pdf;
                 http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_preface.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}

@InProceedings{Takagi:1993:MMA,
  author =       "N. Takagi",
  title =        "Modular Multiplication Algorithm with Triangle
                 Addition",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "272--276",
  year =         "1993",
  bibdate =      "Wed Nov 14 18:48:15 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Takagi.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}

@Article{Thompson:1993:CCQ,
  author =       "William J. Thompson",
  title =        "Cutting Corners: Quick Square Roots and Trig
                 Functions",
  journal =      j-COMPUT-PHYS,
  volume =       "7",
  number =       "1",
  pages =        "18--??",
  month =        jan,
  year =         "1993",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.4823136",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Wed Apr 10 08:45:39 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.4823136",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}

@Manual{TI:1993:ITC,
  title =        "Interfacing {TI} clocked {FIFOs} with {TI}
                 floating-point digital signal processors: first-in,
                 first-out technology",
  organization = "Texas Instruments Incorporated",
  address =      "S.l",
  pages =        "iv + 15",
  year =         "1993",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer input-output equipment.; Signal processing
                 --- Digital techniques --- Equipment and; supplies.",
  remark =       "``SCAA005'' --- back cover.",
}

@Misc{TI:1993:ITT,
  key =          "TI '1993",
  title =        "Inside technology today 32-bit floating point
                 multi-port {DSP} \slash{} produced by {Texas
                 Instruments}",
  howpublished = "VHS format. High-speed, multi-port DSPs can be used in
                 parallel processing applications to really enhance
                 computation time and power. A popular 6-port floating
                 point DSP and high speed design integration and
                 applications are described in this tape.",
  address =      "Dallas, TX, USA",
  year =         "1993",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "1 videocassette",
  acknowledgement = ack-nhfb,
  keywords =     "Computer --- Circuits.; Electronic calculating
                 machines circuits.",
  publication =  "Texas Instruments Inc.",
}

@Article{Timmermann:1993:GFR,
  author =       "D. Timmermann and B. Rix and B. Hosticka",
  title =        "{Gleitkommaprozessor f{\"u}r rechenintensive
                 Echtzeitanwendungen} \toenglish {Floating-point
                 Processor for Computationally Intensive Real-Time Use}
                 \endtoenglish",
  journal =      j-ELECTRONIK,
  volume =       "20",
  number =       "??",
  pages =        "142--146",
  month =        "????",
  year =         "1993",
  CODEN =        "EKRKAR",
  ISSN =         "0013-5658",
  bibdate =      "Fri Dec 08 13:05:00 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  fjournal =     "Elektronik",
}

@Article{Tiwari:1993:NCP,
  author =       "Neeraj Tiwari and A. K. Nigam",
  title =        "A note on constructive procedure for unbiased
                 controlled rounding",
  journal =      j-STAT-PROB-LETT,
  volume =       "18",
  number =       "5",
  pages =        "415--420",
  day =          "2",
  month =        dec,
  year =         "1993",
  CODEN =        "SPLTDC",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  bibdate =      "Sun Jun 1 11:14:48 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/statproblett1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/016771529390036I",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01677152",
}

@Article{Tsuji:1993:FNS,
  author =       "Kumiko Tsuji",
  title =        "Floating-point number solutions in a simple linear
                 equation with addition algorithm. Numerical calculation
                 methods with guaranteed accuracy and their applications
                 ({Japanese}) ({Kyoto}, 1992)",
  journal =      "S{\=u}rikaisekikenky{\=u}sho K{\=o}ky{\=u}roku",
  volume =       "831",
  pages =        "33--45",
  year =         "1993",
  MRclass =      "65G05",
  MRnumber =     "95a:65083",
  bibdate =      "Fri Dec 8 08:24:11 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Turner:1993:CSA,
  author =       "P. R. Turner",
  title =        "Complex {SLI} arithmetic: Representation, algorithms
                 and analysis",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "18--25",
  year =         "1993",
  bibdate =      "Thu Dec 14 11:25:18 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Turner.pdf",
  abstract =     "The extension of the SLI (symmetric level index)
                 system to complex numbers and arithmetic is discussed.
                 The natural form for representation of complex
                 quantities in SLI is in the modulus-argument form, and
                 this can be sensibly packed into a single 64-b word for
                 the equivalent of the 32-b real SLI representation. The
                 arithmetic algorithms prove to be very slightly more
                 complicated than for real SLI arithmetic. The
                 representation, the arithmetic algorithms, and the
                 control of errors within these algorithms are
                 described.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Math., US Naval Acad., Annapolis, MD,
                 USA",
  classification = "C5230 (Digital arithmetic methods)",
  keywords =     "ARITH-11; Arithmetic algorithms; Complex numbers;
                 Modulus-argument form; Representation; SLI; SLI
                 arithmetic; Symmetric level index",
  thesaurus =    "Floating point arithmetic",
}

@Article{Vassiliadis:1993:CHW,
  author =       "S. Vassiliadis and E. M. Schwarz",
  title =        "Correction to {``Hard-wired multipliers with encoded
                 partial products''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "1",
  pages =        "127--127",
  month =        jan,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.192224",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:47 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=192224",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Veselic:1993:FPH,
  author =       "Kre{\v{s}}imir Veseli{\'c} and Ivan Slapni{\v{c}}ar",
  title =        "Floating-Point Perturbations of {Hermitian} Matrices",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "195",
  number =       "??",
  pages =        "81--116",
  month =        dec,
  year =         "1993",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  MRclass =      "65F15 (15A18 15A57)",
  MRnumber =     "94m:65066",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Article{Vignes:1993:SAR,
  author =       "J. Vignes",
  title =        "A stochastic arithmetic for reliable scientific
                 computation",
  journal =      j-MATH-COMPUT-SIMUL,
  volume =       "35",
  number =       "3",
  pages =        "233--261",
  month =        sep,
  year =         "1993",
  CODEN =        "MCSIDR",
  DOI =          "https://doi.org/10.1016/0378-4754(93)90003-D",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  bibdate =      "Thu Mar 24 20:56:34 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://portal.acm.org/citation.cfm?id=165789.165792",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics and Computers in Simulation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784754",
}

@Article{vonNeumann:1993:FDR,
  author =       "John von Neumann",
  title =        "First Draft of a Report on the {EDVAC}",
  journal =      j-IEEE-ANN-HIST-COMPUT,
  volume =       "15",
  number =       "4",
  pages =        "28--75",
  month =        oct # "\slash " # dec,
  year =         "1993",
  CODEN =        "IAHCEX",
  ISSN =         "1058-6180 (print), 1934-1547 (electronic)",
  ISSN-L =       "1058-6180",
  bibdate =      "Thu Jul 12 06:22:55 MDT 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeeannhistcomput.bib",
  note =         "Edited and corrected by Michael D. Godfrey.",
  URL =          "http://dlib.computer.org/an/books/an1993/pdf/a4027.pdf;
                 http://www.computer.org/annals/an1993/a4027abs.htm",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Ann. Hist. Comput.",
  fjournal =     "IEEE Annals of the History of Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85",
  keywords =     "floating-point arithmetic; rounding",
  xxpages =      "27--??",
}

@Article{Vornberger:1993:BBM,
  author =       "Cal Vornberger",
  title =        "Beyond Bit Maps: Multiple floating objects deliver new
                 power and flexibility to bit-map image processing.
                 {Micrografx Picture Publisher} 4.0 and {Fractal Design
                 Painter X2} feature object layers and other useful
                 innovations",
  journal =      j-BYTE,
  volume =       "18",
  number =       "13",
  pages =        "165--166, 168",
  month =        dec,
  year =         "1993",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Thu Sep 12 16:34:03 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "D2010 (Business and professional); D2020 (Design and
                 graphics)",
  fjournal =     "BYTE Magazine",
  keywords =     "Bit maps; Ease of use; Fractal design painterX2;
                 Functionality; Micrografx; Object technology; Picture
                 Publisher 4.0",
  thesaurus =    "Business graphics; Desktop publishing",
}

@Article{Walter:1993:SMM,
  author =       "C. D. Walter",
  title =        "Systolic modular multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "3",
  pages =        "376--378",
  month =        mar,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.210181",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:48 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=210181",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Wang:1993:SAC,
  author =       "Chin-Liang Wang and Jung-Lung Lin",
  title =        "A systolic architecture for computing inverses and
                 divisions in finite fields {$ \mathrm {GF}(2^m) $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "42",
  number =       "9",
  pages =        "1141--1146",
  month =        sep,
  year =         "1993",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.241603",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:58:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=241603",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Wei:1993:CTA,
  author =       "D.-Y. D. Wei and J. H. Kim and T. R. N. Rao",
  title =        "Complete tests in algorithm-based fault-tolerant
                 matrix operation on processor arrays",
  crossref =     "Lombardi:1993:PII",
  pages =        "255--262",
  year =         "1993",
  bibdate =      "Thu Dec 14 11:25:18 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Recently, F. T. Assaad and S. Dutt (1992) proposed the
                 hybrid checksum test method for the floating-point
                 matrix-matrix multiplication in ABFT environment, by
                 which the error coverage can be greatly increased.
                 However, the thresholded test in their approach is
                 still not avoidable in the floating-point additions
                 involved in matrix multiplication and the number of
                 error detections decrease with the increase in the
                 dynamic range of data, which is not totally
                 satisfactory. The authors present an effective method,
                 called concurrent floating-point checksum (CFPC) test,
                 which provides very convincing error
                 detection/correction capabilities for the part of
                 floating-point addition with a minimum time latency and
                 hardware overhead.",
  acknowledgement = ack-nhfb,
  affiliation =  "Center for Adv. Comput. Studies, University of
                 Southwestern Louisiana, Lafayette, LA, USA",
  classification = "B0290H (Linear algebra); B1265 (Digital
                 electronics); B6120B (Codes); C4140 (Linear algebra);
                 C5210 (Logic design methods); C5230 (Digital arithmetic
                 methods); C6130 (Data handling techniques)",
  keywords =     "concurrent floating-point checksum; error correction;
                 error detections; fault-tolerant matrix; floating-point
                 additions; floating-point matrix-matrix multiplication;
                 floating-point testing; hardware overhead; hybrid
                 checksum test; minimum time latency; processor arrays;
                 thresholded test",
  thesaurus =    "Computational complexity; Error correction; Error
                 detection; Fault tolerant computing; Floating point
                 arithmetic; Logic arrays; Logic testing; Matrix
                 multiplication",
}

@Book{Weste:1993:PCV,
  author =       "Neil H. E. Weste and Kamran Eshraghian",
  title =        "Principles of {CMOS VLSI} Design: a Systems
                 Perspective",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Second",
  pages =        "xxii + 713",
  year =         "1993",
  ISBN =         "0-201-53376-6",
  ISBN-13 =      "978-0-201-53376-7",
  LCCN =         "TK7874 .W46 1993",
  bibdate =      "Mon Sep 16 16:32:31 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Williams:1993:BFM,
  author =       "Al Williams",
  title =        "Bit Floating-Point Math",
  journal =      j-DDJ,
  volume =       "18",
  number =       "6",
  pages =        "70--??",
  month =        jun,
  year =         "1993",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This approach to floating-point math uses 32-bit
                 instructions. Although Al uses the 80386 as an example,
                 these techniques can be applied to other 32-bit
                 processors as well.",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@Article{Williams:1993:FM,
  author =       "Al Williams",
  title =        "32-bit floating-point math",
  journal =      j-DDJ,
  volume =       "18",
  number =       "6",
  pages =        "70, 72, 74, 76, 80",
  month =        jun,
  year =         "1993",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Tue Sep 10 08:57:56 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 UnCover database",
  abstract =     "This approach to floating-point math uses 32-bit
                 instructions. Although Al uses the 80386 as an example,
                 these techniques can be applied to other 32-bit
                 processors as well.",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "Dr. Dobb's Journal of Software Tools",
  keywords =     "32 Bit; 32-Bit instructions; 32-Bit processors; 386
                 Instruction set; 80386; Floating-point mathematics",
  thesaurus =    "Digital arithmetic; Microprocessor chips",
}

@InProceedings{Wrzyszcz:1993:DDCa,
  author =       "A. Wrzyszcz and D. Caban and E. L. Dagless",
  booktitle =    "Proceedings. [4th] European Conference on Design
                 Automation, 1993, with the European Event in {ASIC}
                 Design",
  title =        "Design of a discrete cosine transform circuit using
                 the residue number system",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "584--588",
  year =         "1993",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/EDAC.1993.386412",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The design of an integrated circuit aimed at efficient
                 discrete cosine transform computation is presented.
                 High performance is obtained through the use of
                 pipelining and residue arithmetic. An approach to
                 high-speed modular multiplication employing \ldots{}",
}

@InProceedings{Wrzyszcz:1993:DDCb,
  author =       "A. Wrzyszcz and D. Caban and E. L. Dagless",
  booktitle =    "Proceedings. [4th] European Conference on Design
                 Automation, 1993, with the European Event in {ASIC}
                 Design",
  title =        "Design of a discrete cosine transform circuit using
                 the residue number system",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "584--588",
  year =         "1993",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/EDAC.1993.386412",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The design of an integrated circuit aimed at efficient
                 discrete cosine transform computation is presented.
                 High performance is obtained through the use of
                 pipelining and residue arithmetic. An approach to
                 high-speed modular multiplication employing \ldots{}",
}

@Article{Zeng:1993:CFA,
  author =       "Chuan-Qing Zeng and Kousuke Tsukamoto and Takeo
                 Miyata",
  title =        "Charge-balancing floating-point analogue-to-digital
                 converter using acyclic conversion",
  journal =      j-INT-J-ELECTRON,
  volume =       "74",
  number =       "5",
  pages =        "705--??",
  month =        may,
  year =         "1993",
  CODEN =        "IJELA2",
  ISSN =         "0020-7217 (print), 1362-3060 (electronic)",
  ISSN-L =       "0020-7217",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Electronics Theoretical \&
                 Experimental",
}

@Article{Zhang:1993:EAP,
  author =       "C. N. Zhang and B. Shirazi and D. Y. Y. Yun",
  title =        "An Efficient Algorithm and Parallel Implementations
                 for Binary and Residue Number Systems",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "15",
  number =       "4",
  pages =        "451--462",
  month =        apr,
  year =         "1993",
  CODEN =        "JSYCEH",
  DOI =          "https://doi.org/10.1006/jsco.1993.1030",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  MRclass =      "65G10 (65Y05)",
  MRnumber =     "94j:65066",
  MRreviewer =   "De Ren Wang",
  bibdate =      "Sat May 10 15:54:09 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Arithmetic units based on a Residue Number System
                 (RNS) are fast and simple, and therefore attractive for
                 use in digital signal processing and symbolic
                 computation applications. However, RNS suffers from
                 overheads of converting numbers to and from residue
                 system. We present a new simple and uniform computation
                 formula for both conversion from RNS to binary and vice
                 versa. Two levels of parallelism for VLSI hardware
                 design of the proposed algorithm are introduced.",
  acknowledgement = ack-nhfb,
  classcodes =   "C7310 (Mathematics); C7410D (Electronic engineering)",
  corpsource =   "Department of Computer Science, Regina University,
                 Sask., Canada",
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171",
  keywords =     "algorithm; binary number systems; circuit CAD;
                 computation; digital signal processing; parallel
                 implementations; parallelism; residue number systems;
                 symbol manipulation; symbolic; VLSI; VLSI hardware
                 design",
  treatment =    "A Application; P Practical",
}

@InProceedings{Zuras:1993:SML,
  author =       "D. Zuras",
  title =        "On Squaring and Multiplying Large Integers",
  crossref =     "Swartzlander:1993:SCA",
  pages =        "260--271",
  year =         "1993",
  bibdate =      "Sat Nov 17 09:46:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith11/papers/ARITH11_Zuras.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}

@Book{Zuse:1993:CML,
  author =       "Konrad Zuse",
  title =        "The Computer, My Life",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "245",
  year =         "1993",
  ISBN =         "3-540-56453-5 (Berlin), 0-387-56453-5 (New York)",
  ISBN-13 =      "978-3-540-56453-9 (Berlin), 978-0-387-56453-1 (New
                 York)",
  LCCN =         "TK7885.22.Z87 A3 1993",
  bibdate =      "Mon Nov 4 07:46:57 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "computer engineers --- Germany --- biography;
                 computers --- Germany --- history; Zuse, Konrad",
  tableofcontents = "1: Ancestors and parents --- Early childhood
                 memories --- School days --- Metropolis --- Abitur / 1
                 \\
                 2: Studies (not without detours and byways) and general
                 studies --- First inventions --- The \emph{Akademische
                 Verein Motiv} --- Student life between science and
                 politics / 15 \\
                 3: The early years of the computer and a digression on
                 its prehistory --- Colleagues remember --- From
                 mechanics to electromechanics --- Schreyer's electronic
                 computing machine --- First outside contacts ---
                 Thoughts on the future / 33 \\
                 4: Outbreak of the war and first callup --- Structural
                 engineer in aircraft construction --- The Z2 and Z3 ---
                 Second callup --- \emph{Zuse Ingenieurb{\"u}ro und
                 Apparatebau, Berlin} --- The first process computer /
                 55 \\
                 5: Origins of the Z4 --- News from the United States
                 --- Attempt at a PhD dissertation --- Computing machine
                 for logic operations --- Final months of the war in
                 Berlin --- The evacuation --- Z4 completed in
                 G{\"o}ttingen --- Final war days in the Allg{\"a}u / 75
                 \\
                 6: End of the war --- Refugees in Hinterstein --- The
                 \emph{Plankalk{\"u}l} --- The computing universe ---
                 Automation and self-reproducing systems --- A
                 logarithmic computing machine --- Computer development
                 in Germany and the United States --- Move to Hopferau
                 near F{\"u}ssen --- The mill of the Patent Office / 95
                 \\
                 7: The \emph{Zuse-Ingenieurb{\"u}ro, Hopferau bei
                 F{\"u}ssen} --- First business partners: IBM and
                 Remington Rand --- The first pipelining design ---
                 Founding of ZUSE KG in Neukirchen --- The Z4 in the ETH
                 in Z{\"u}rich --- The computer in Europe: taking stock
                 --- Lost opportunities --- The first German contract:
                 the Z5 / 113 \\
                 8: The partners leave --- Computing machine for land
                 use zoning --- Electronics gains acceptance --- First
                 funds from the \emph{Deutsche Forschungsgemeinschaft}
                 --- Losing one's way (and possibly a lost opportunity)
                 --- The array processor --- Custom work for geodesics
                 --- The Graphomat Z64 --- Growth and crisis of ZUSE KG
                 --- The end / 133 \\
                 9: Free for science (again) --- Honors --- A look to
                 the future / 157 \\
                 Appendices \\
                 1: From Forms to Program Control / 185 \\
                 2: Construction of Devices / 190 \\
                 3: On Computer Architecture / 210 \\
                 4: On the Plan Calculus / 211 \\
                 5: Lecture on the Occasion of the Award of the Honorary
                 Doctorate by the Technical University of Berlin
                 (Extract) / 222 \\
                 6: The Computer Did Not Fall From Heaven / 225 \\
                 Notes / 229 \\
                 References / 231 \\
                 Name Index / 235 \\
                 Subject Index / 239 \\
                 Computer Index / 245",
}

@Article{Agarwal:1994:EFP,
  author =       "R. C. Agarwal and F. G. Gustavson and M. Zubair",
  title =        "Exploiting functional parallelism of {POWER2} to
                 design high-performance numerical algorithms",
  journal =      j-IBM-JRD,
  volume =       "38",
  number =       "5",
  pages =        "563--576",
  month =        sep,
  year =         "1994",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Tue Mar 25 14:26:59 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.almaden.ibm.com/journal/rd38-5.html#eight",
  abstract =     "We describe the algorithms and architecture approach
                 to produce high-performance codes for numerically
                 intensive computations. In this approach, for a given
                 computation, we design algorithms so that they perform
                 optimally when run on a target machine --- in this
                 case, the new POWER2* machines from the RS\slash 6000
                 family of RISC processors. The algorithmic features
                 that we emphasize are functional parallelism,
                 cache/register blocking, algorithmic prefetching, loop
                 unrolling, and algorithmic restructuring. The
                 architectural features of the POWER2 machine that we
                 describe and that lead to high performance are multiple
                 functional units, high bandwidth between registers,
                 cache, and memory, a large number of fixed- and
                 floating-point registers, and a large cache and TLB
                 (translation lookaside buffer). The paper gives two
                 examples that illustrate how the algorithms and
                 architectural features interplay to produce
                 high-performance codes. They are BLAS (basic linear
                 algebra subroutines) and narrow-band matrix routines.
                 These routines are included in ESSL (Engineering and
                 Scientific Subroutine Library); an overview of ESSL is
                 also given in this paper.",
  acknowledgement = ack-nhfb,
  affiliation =  "Res. Div., IBM Thomas J. Watson Res. Center, Yorktown
                 Heights, NY, USA",
  classcodes =   "C7310 (Mathematics computing); C5430 (Microcomputers);
                 C6140B (Machine-oriented languages); C6110P (Parallel
                 programming)",
  classification = "C5430 (Microcomputers); C6110P (Parallel
                 programming); C6140B (Machine-oriented languages);
                 C7310 (Mathematics computing)",
  corpsource =   "Res. Div., IBM Thomas J. Watson Res. Center, Yorktown
                 Heights, NY, USA",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "algorithmic; Algorithmic prefetching; algorithmic
                 restructuring; Algorithmic restructuring; algorithms;
                 and Scientific Subroutine Library; basic linear
                 algebra; Basic linear algebra subroutines; BLAS;
                 cache/register blocking; Cache/register blocking;
                 computations; Engineering; Engineering and Scientific
                 Subroutine Library; ESSL; floating-point registers;
                 Floating-point registers; functional parallelism;
                 Functional parallelism; high-performance codes;
                 High-performance codes; high-performance numerical;
                 High-performance numerical algorithms; IBM computers;
                 loop unrolling; Loop unrolling; mathematics computing;
                 multiple functional units; Multiple functional units;
                 narrow-band matrix routines; Narrow-band matrix
                 routines; numerically intensive; Numerically intensive
                 computations; parallel algorithms; POWER2 workstations;
                 prefetching; processors; reduced instruction set
                 computing; RISC; RISC processors; RS/6000 family;
                 software libraries; subroutines; translation lookaside
                 buffer; Translation lookaside buffer; workstations",
  thesaurus =    "IBM computers; Mathematics computing; Parallel
                 algorithms; Reduced instruction set computing; Software
                 libraries; Workstations",
  treatment =    "P Practical",
}

@Article{Anonymous:1994:C,
  author =       "Anonymous",
  title =        "Corrigenda",
  journal =      j-TOMS,
  volume =       "20",
  number =       "4",
  pages =        "553--553",
  month =        dec,
  year =         "1994",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 14 16:17:03 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Hull:1994:ICE}",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  xxURL =        "Missing from ACM Digital Library",
}

@Article{Anonymous:1994:FPa,
  author =       "Anonymous",
  title =        "Floating Point",
  journal =      j-COMPUT-AIDED-ENG,
  volume =       "13",
  number =       "6",
  pages =        "65--??",
  month =        jun,
  year =         "1994",
  CODEN =        "CCAEDJ",
  ISSN =         "0733-3536 (print), 2162-1365 (electronic)",
  ISSN-L =       "0733-3536",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Interactive Analysis Presentations.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer-aided engineering: CAE",
}

@Article{Anonymous:1994:FPb,
  author =       "Anonymous",
  title =        "Floating Point",
  journal =      j-COMPUT-AIDED-ENG,
  volume =       "13",
  number =       "7",
  pages =        "85--??",
  month =        jul,
  year =         "1994",
  CODEN =        "CCAEDJ",
  ISSN =         "0733-3536 (print), 2162-1365 (electronic)",
  ISSN-L =       "0733-3536",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Misplaced Value of CE.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer-aided engineering: CAE",
}

@Article{Anonymous:1994:FPc,
  author =       "Anonymous",
  title =        "Floating Point",
  journal =      j-COMPUT-AIDED-ENG,
  volume =       "13",
  number =       "10",
  pages =        "122--??",
  month =        oct,
  year =         "1994",
  CODEN =        "CCAEDJ",
  ISSN =         "0733-3536 (print), 2162-1365 (electronic)",
  ISSN-L =       "0733-3536",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Integration's Relational Dimension.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer-aided engineering: CAE",
}

@Article{Anonymous:1994:SCSa,
  author =       "Anonymous",
  title =        "Single chip supercomputer: Vector processing is key to
                 high performance in floating point calculations",
  journal =      "New electronics",
  volume =       "27",
  number =       "4",
  pages =        "7--??",
  day =          "1",
  month =        apr,
  year =         "1994",
  ISSN =         "0047-9624",
  bibdate =      "Fri Aug 23 08:32:16 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 UnCover library database",
  acknowledgement = ack-nhfb,
}

@Article{Anonymous:1994:SPF,
  author =       "Anonymous",
  title =        "Signal Path: Floating-point tactics",
  journal =      j-ELECTRONIC-ENG-TIMES,
  volume =       "??",
  number =       "807",
  pages =        "78--??",
  month =        jul,
  year =         "1994",
  ISSN =         "0192-1541",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronic engineering times",
}

@Book{Anonymous:1994:SRT,
  author =       "Anonymous",
  title =        "The Square Root of Two to 5 million digits",
  volume =       "129",
  publisher =    pub-PROJECT-GUTENBERG,
  address =      pub-PROJECT-GUTENBERG:adr,
  year =         "1994",
  bibdate =      "Sun Jan 24 10:00:27 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-PROJECT-GUTENBERG,
  URL =          "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext94/2sqrt10a.zip",
  acknowledgement = ack-nhfb # " and " # ack-st,
  subject =      "Mathematical constants.",
  url-contents = "ZIP",
}

@Book{Apple:1994:IMP,
  author =       "{Apple Computers, Inc.}",
  title =        "Inside {Macintosh}: {PowerPC Numerics}",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "xx + 300",
  year =         "1994",
  ISBN =         "0-201-40728-0",
  ISBN-13 =      "978-0-201-40728-0",
  LCCN =         "QA76.8.M3 I5622 1994",
  bibdate =      "Wed Sep 07 21:08:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$28.95",
  acknowledgement = ack-nj,
}

@Article{Bajard:1994:BNH,
  author =       "J.-C. Bajard and S. Kla and Jean-Michel Muller",
  title =        "{BKM}: a New Hardware Algorithm for Complex Elementary
                 Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "8",
  pages =        "955--963",
  month =        aug,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.295857",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon May 20 06:16:49 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  remark =       "Selected revised and extended papers from ARITH'11
                 \cite{Swartzlander:1993:SCA}.",
}

@Article{Bajard:1994:SOL,
  author =       "J.-C. Bajard and J. Duprat and S. Kla and J.-M.
                 Muller",
  title =        "Some Operators for On-Line Radix-2 Computations",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "22",
  number =       "2",
  pages =        "336--345",
  month =        aug,
  year =         "1994",
  CODEN =        "JPDCER",
  DOI =          "https://doi.org/10.1006/jpdc.1994.1093",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Thu Mar 9 09:18:55 MST 2000",
  bibsource =    "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.idealibrary.com/links/doi/10.1006/jpdc.1994.1093/production;
                 http://www.idealibrary.com/links/doi/10.1006/jpdc.1994.1093/production/pdf",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods)",
  corpsource =   "Lab. LIP, Ecole Normale Superieure de Lyon, France",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "bit-level representation; Borrow-Save; delay; digital
                 arithmetic; online radix-2 computations; operators;
                 optimal online; radix-2 digits; representation",
  treatment =    "P Practical",
}

@Article{Barsi:1994:TOM,
  author =       "Ferruccio Barsi and M. Cristina Pinotti",
  title =        "Time optimal mixed radix conversion for residue number
                 applications",
  journal =      j-COMP-J,
  volume =       "37",
  number =       "10",
  pages =        "907--916",
  month =        "????",
  year =         "1994",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Wed Jul 21 09:54:19 MDT 1999",
  bibsource =    "http://www3.oup.co.uk/computer_journal/Volume_37/Issue_10/Vol37_10.index.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/Volume_37/Issue_10/Vol37_10.body.html#AbstractBarsi",
  acknowledgement = ack-nhfb,
  affiliation =  "Dipartimento di Matematica, Perugia University,
                 Italy",
  author-1-adr = "Dipartimento at Matematica, Universita di Perugia, Via
                 Vanvitelli, 061OO Perugia, Italy",
  author-2-adr = "Istituto di Elaborazione dell'Informazione del CNR,
                 Via S. Maria 46, 56100 Pisa, Italy",
  classcodes =   "B2570 (Semiconductor integrated circuits); C5230
                 (Digital arithmetic methods); C6130 (Data handling
                 techniques); C4240C (Computational complexity)",
  classification = "B2570 (Semiconductor integrated circuits); C4240C
                 (Computational complexity); C5230 (Digital arithmetic
                 methods); C6130 (Data handling techniques)",
  corpsource =   "Dipartimento di Matematica, Perugia University,
                 Italy",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "applications; asymptotic conversion time; Chinese
                 Remainder Theorem; computational complexity;
                 constructive VLSI design; Constructive VLSI design;
                 conventional logic; Conventional logic; logic
                 circuitry; Logic circuitry; lookup; lookup table
                 implementations; Lookup table implementations; mixed
                 radix; Mixed radix notation; notation; practical ECL
                 IC; Practical ECL IC; residue integer conversion;
                 Residue integer conversion; residue number; Residue
                 number applications; residue number systems;
                 residue-to-weighted system; Residue-to-weighted system
                 asymptotic conversion time; table; time optimal mixed
                 radix conversion; Time optimal mixed radix conversion;
                 VLSI",
  thesaurus =    "Computational complexity; Residue number systems;
                 Table lookup; VLSI",
  treatment =    "P Practical",
}

@Article{Bartolucci:1994:REC,
  author =       "M. Bartolucci and G. R. Sechi",
  title =        "Rounding error in the computation of opposite sign
                 floating point number parametric addition: a case
                 study",
  journal =      j-MICROPROC-MICROPROG,
  volume =       "40",
  number =       "10-12",
  pages =        "833--839",
  month =        dec,
  year =         "1994",
  CODEN =        "MMICDT",
  ISSN =         "0165-6074 (print), 1878-7061 (electronic)",
  ISSN-L =       "0165-6074",
  bibdate =      "Thu Dec 14 15:33:45 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "20th Annual Euromicro Conference. System Architecture
                 and Integration.",
  abstract =     "Presents a study about rounding errors arising in the
                 addition of opposite-sign floating-point operands. The
                 algebraic study of the adder functionalities provides
                 the possibility of modifying the hardware in order to
                 measure the rounding error effect in terms of error
                 size and incoming rate.",
  acknowledgement = ack-nhfb,
  affiliation =  "Istituto di Fisica Cosmica e Tecnologie Relative, CNR,
                 Milano, Italy",
  classification = "C1110 (Algebra); C5230 (Digital arithmetic
                 methods)",
  confdate =     "Sept. 1994",
  conflocation = "Liverpool, UK",
  fjournal =     "Microprocessing and Microprogramming",
  journal-URL =  "https://www.sciencedirect.com/journal/microprocessing-and-microprogramming/issues",
  keywords =     "Adder functionalities; Algebraic properties; Case
                 study; Computational units; Error size; Errors
                 detection; Errors elimination; Floating-point operands;
                 Hardware modification; High-speed floating point
                 operators; Incoming rate; Opposite-sign floating-point
                 number parametric addition; Real time applications;
                 Rounding error",
  pubcountry =   "Netherlands",
  thesaurus =    "Algebra; Error detection; Floating point arithmetic;
                 Roundoff errors",
}

@Article{Bauer:1994:MDS,
  author =       "F. L. Bauer",
  title =        "Multiplication and dual system",
  journal =      j-INFORMATIK-SPEKTRUM,
  volume =       "17",
  number =       "4",
  pages =        "245--250",
  month =        aug,
  year =         "1994",
  CODEN =        "INSKDW",
  ISSN =         "0170-6012 (print), 1432-122X (electronic)",
  ISSN-L =       "0170-6012",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A history of methods of multiplication is introduced
                 with a table showing the assignments of Greek and
                 Hebrew letters to the units, tens and hundreds up to
                 900, with no zero. The ancient Egyptian method using
                 decimal-to-binary conversion with addition of
                 successive even multiples of the multiplicand is
                 explained. Napier's (1617) method of `numeri locales'
                 is described with the aid of a multiplication table for
                 algebraic symbols each representing a different power
                 of 2. The application of these principles in electronic
                 computing circuits is discussed with reference to
                 Braun's (1963) full-adder correction circuit and
                 Wallace's (1964) cascaded half-adders. Progress from
                 the 8*8 field multiplier chips of 1971 to the
                 floating-point 1.2 mu m CMOS 56*56 RISC multiplier of
                 1989 is summarised.",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "Informatik Spektrum",
  journal-URL =  "http://link.springer.com/journal/287",
  keywords =     "Algebraic symbols; Cascaded half-adders; decimal
                 floating-point arithmetic; Decimal-to-binary
                 conversion; Egyptian method; Electronic computing
                 circuits; Floating-point; Full-adder correction
                 circuit; Multiplication; Multiplier chips; Numeri
                 locales; RISC",
  language =     "German",
  pubcountry =   "Germany",
  thesaurus =    "Digital arithmetic; History; Multiplying circuits",
}

@PhdThesis{Bewick:1994:FMA,
  author =       "Gary Bewick",
  title =        "Fast Multiplication: Algorithms and Implementations",
  type =         "{Ph.D.} thesis",
  school =       "Computer Systems Laboratory, Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "170",
  month =        feb,
  year =         "1994",
  bibdate =      "Mon Dec 24 09:59:22 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Also issued as report CSL-TR-94-617",
  acknowledgement = ack-nhfb,
}

@Article{BrinchHansen:1994:MLD,
  author =       "Per {Brinch Hansen}",
  title =        "Multiple-length Division Revisited: a Tour of the
                 Minefield",
  journal =      j-SPE,
  volume =       "24",
  number =       "6",
  pages =        "579--601",
  month =        jun,
  year =         "1994",
  CODEN =        "SPEXBL",
  DOI =          "https://doi.org/10.1002/spe.4380240605",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Fri Nov 28 17:07:54 2003",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/bibnet/authors/h/hansen-per-brinch.bib;
                 https://www.math.utah.edu/pub/tex/bib/cryptography1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/litprog.bib;
                 https://www.math.utah.edu/pub/tex/bib/spe.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "This paper derives an algorithm for division of long
                 integers, and implements it as a literate program,
                 although without identifier cross-references. See also
                 related work on division
                 \cite{BrinchHansen:1995:LDA,Regener:1984:MID} .",
  URL =          "http://brinch-hansen.net/papers/1994b.pdf",
  abstract =     "Long division of natural numbers plays a crucial role
                 in Cobol arithmetic, cryptography, and primality
                 testing. Only a handful of textbooks discuss the theory
                 and practice of long division, and none of them do it
                 satisfactorily. This tutorial attempts to fill this
                 surprising gap in the literature on computer
                 algorithms. We illustrate the subtleties of long
                 division by examples, define the problem concisely,
                 summarize the theory, and develop a complete Pascal
                 algorithm using a consistent terminology.",
  acknowledgement = ack-nj # " and " # ack-mfc # " and " # ack-nhfb,
  ajournal =     "Softw. Pract. Exp.",
  fjournal =     "Software --- Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  keywords =     "algorithms; multiple-length integer division",
  onlinedate =   "30 Oct 2006",
}

@InProceedings{Brosgol:1994:ISD,
  author =       "Benjamin M. Brosgol and Robert I. Eachus and David E.
                 Emery",
  title =        "Information Systems Development in {Ada}",
  crossref =     "ACM:1994:AAW",
  pages =        "2--16",
  year =         "1994",
  bibdate =      "Fri Nov 28 16:05:55 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this paper we survey how to use Ada (both Ada 83
                 and Ada 9X) for IS applications, with a focus on two
                 principal issues: Specification of the information
                 architecture of an IS application, and Programming
                 techniques relevant to financial and related
                 applications.\par

                 We cover both the language features and the
                 supplemental packages for IS development. Special
                 attention will be paid to the Ada Decimal-Associated
                 Reusabilia (`ADAR') components for Ada 83 and
                 transitioning to Ada 9X.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@MastersThesis{Bull:1994:SFF,
  author =       "Nathan Lee Bull",
  title =        "A study of frequency-sampling filters realized on
                 floating-point digital signal processors",
  type =         "Thesis ({M.S.})",
  school =       "University of Tennessee, Knoxville",
  address =      "Knoxville, TN, USA",
  pages =        "vii + 56",
  year =         "1994",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Digital filters (Mathematics)",
}

@Article{Carr:1994:IRM,
  author =       "S. Carr and K. Kennedy",
  title =        "Improving the Ratio of Memory Operations in
                 Floating-Point Operations in Loops",
  journal =      j-TOPLAS,
  volume =       "16",
  number =       "6",
  pages =        "1768--1810",
  month =        nov,
  year =         "1994",
  CODEN =        "ATPSDT",
  ISSN =         "0164-0925 (print), 1558-4593 (electronic)",
  ISSN-L =       "0164-0925",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Over the past decade, microprocessor design strategies
                 have focused on increasing the computational power on a
                 single chip. Because computations often require more
                 data from cache per floating-point operation than a
                 machine can deliver and because operations are
                 pipelined, idle computational cycles are common when
                 scientific applications are executed. To overcome these
                 bottlenecks, programmers have learned to use a coding
                 style that ensures a better balance between memory
                 references and floating-point operations. In our view,
                 this is a step in the wrong direction because it makes
                 programs more machine-specific. A programmer should not
                 be required to write a new program version for each new
                 machine; instead, the task of specializing a program to
                 a target machine should be left to the compiler. But is
                 our view practical? Can a sophisticated optimizing
                 compiler obviate the need for the myriad of programming
                 tricks that have found their way into practice to
                 improve the performance of the memory hierarchy? In
                 this paper we attempt to answer that question. To do
                 so, we develop and evaluate techniques that
                 automatically restructure program loops to achieve high
                 performance on specific target architectures. These
                 methods attempt to balance computation and memory
                 accesses and seek to eliminate or reduce pipeline
                 interlock. To do this, they estimate statically the
                 balance between memory operations and floating-point
                 operations for each loop in a particular program and
                 use these estimates to determine whether to apply
                 various loop transformations. Experiments with our
                 automatic techniques show that integer-factor speedups
                 are possible on kernels. Additionally, the estimate of
                 the balance between memory operations and computation,
                 and the application of the estimate are very
                 accurate-experiments reveal little difference between
                 the balance achieved by our automatic system and that
                 possible by hand optimization.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, Michigan Technol.
                 University, Houghton, MI, USA",
  classification = "C5230 (Digital arithmetic methods); C6120 (File
                 organisation); C6150C (Compilers, interpreters and
                 other processors)",
  fjournal =     "ACM Transactions on Programming Languages and
                 Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J783",
  keywords =     "Bottlenecks; Floating-point operations; Integer-factor
                 speedups; Memory operations; Memory references;
                 Microprocessor design strategies; Pipeline interlock;
                 Program loops; Sophisticated optimizing compiler",
  thesaurus =    "Floating point arithmetic; Optimising compilers;
                 Pipeline processing; Program control structures;
                 Storage management",
}

@MastersThesis{Chandramouli:1994:DSP,
  author =       "V. Chandramouli",
  title =        "Design of a self-timed, pipelined, floating point
                 multiplier in gallium arsenide",
  type =         "Thesis ({M.S.})",
  school =       "Department of Computer Science, University of Utah",
  address =      "Salt Lake City, UT, USA",
  pages =        "xiii + 121",
  year =         "1994",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer architecture.; Gallium arsenide
                 semiconductors.",
}

@InProceedings{Chen:1994:EDU,
  author =       "Sau-Gee Chen and Chieh-Chih Li",
  booktitle =    "Proceedings of {TENCON '94}. {IEEE} Region 10's Ninth
                 Annual International Conference. Theme: `Frontiers of
                 Computer Technology'",
  title =        "Efficient designs of unified $2$'s complement division
                 and square root algorithm and architecture",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "943--947",
  year =         "1994",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Efficient unified 2's complement division and square
                 root algorithm, and their architectures are proposed in
                 this work. The designs are high speed, small area and
                 high compatibility. The architectures provide bit level
                 pipelined operation, as well \ldots{}",
}

@Article{Chesneaux:1994:ERS,
  author =       "J.-M. Chesneaux",
  title =        "The equality relations in scientific computing",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "7",
  number =       "2-4",
  pages =        "129--143",
  month =        jul,
  year =         "1994",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The equality relation (more generally, the ordering
                 relations) in floating point arithmetic is the exact
                 translation of the mathematical equality relation.
                 Because of the propagation of round-off errors, the
                 floating point arithmetic is not the exact
                 representation of the theoretical arithmetic which is
                 continuous on the real numbers. This leads to some
                 incoherence when the equality concept is used in
                 floating point arithmetic. A well known example is the
                 detection of a zero element in the pivoting column and
                 equation when applying Gaussian elimination, which is
                 almost impossible in floating point arithmetic. The
                 author begins by showing the inadequacy of the equality
                 relation used in floating point arithmetic (the author
                 calls it floating point equality), and then introduces
                 two new concepts stochastic numbers and the equality
                 relation between such numbers which is called the
                 stochastic equality. It is shown how these concepts
                 allow recovery of the coherence between the arithmetic
                 operators and the ordering relations that was missing
                 in floating point computations.",
  acknowledgement = ack-nhfb,
  affiliation =  "Laboratoire MASI, Universit{\'e} Pierre et Marie
                 Curie, Paris, France",
  classification = "C5230 (Digital arithmetic methods); C7310
                 (Mathematics)",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "Arithmetic operators; Equality relations; Floating
                 point arithmetic; Floating point equality; Gaussian
                 elimination; Ordering relations; Pivoting column;
                 Round-off errors; Scientific computing; Stochastic
                 equality; Stochastic numbers; Zero element",
  pubcountry =   "Switzerland",
  thesaurus =    "Digital arithmetic; Mathematics computing; Roundoff
                 errors",
}

@InProceedings{Chren:1994:ALIa,
  author =       "W. A. {Chren, Jr.}",
  booktitle =    "Proceedings of the 37th Midwest Symposium on Circuits
                 and Systems, 1994",
  title =        "Area and latency improvements for direct digital
                 synthesis using the residue number system",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "269--273",
  year =         "1994",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1994.519237",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Two residue number system-based direct digital
                 synthesizers are presented. The High-Agility Direct
                 Synthesizer exhibits a frequency switching latency
                 which is reduced by as much as 50\% below that of
                 traditional, binary number system-based designs.
                 \ldots{}",
}

@InProceedings{Chren:1994:ALIb,
  author =       "W. A. {Chren, Jr.}",
  booktitle =    "Proceedings of the 37th Midwest Symposium on Circuits
                 and Systems, 1994. 3--5 August 1994, Lafayette, {LA},
                 {USA}",
  title =        "Area and latency improvements for direct digital
                 synthesis using the residue number system",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "269--273",
  year =         "1994",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1994.519237",
  ISBN =         "0-7803-2428-5",
  ISBN-13 =      "978-0-7803-2428-2",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Two residue number system-based direct digital
                 synthesizers are presented. The High-Agility Direct
                 Synthesizer exhibits a frequency switching latency
                 which is reduced by as much as 50\% below that of
                 traditional, binary number system-based designs. The
                 Reduced Area Direct Synthesizer has a chip area which
                 is reduced by more than 40\%. The area reduction is due
                 primarily to the decomposition of the sine ROM into
                 several small look-up tables, while the latency
                 reduction is due to the shortening of the carry paths
                 in the phase accumulator",
}

@InCollection{Clarke:1994:RAC,
  author =       "C. T. Clarke and G. R. Nudd",
  booktitle =    "Mathematics in signal processing {III}. Based on the
                 proceedings of the third {IMA} conference on signal
                 processing, University of Warwick, Coventry, {UK},
                 December 15-17, 1992",
  title =        "A redundant arithmetic {CORDIC} system with a unit
                 scale factor",
  publisher =    "Oxford: Clarendon Press",
  pages =        "63--71",
  year =         "1994",
  ISBN =         "0-19-853480-9",
  ISBN-13 =      "978-0-19-853480-8",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0852.65141",
  acknowledgement = ack-nhfb,
  keywords =     "65T40,65D20,33B10",
  ZBmath =       "922639",
}

@Article{Cortadella:1994:HRD,
  author =       "J. Cortadella and T. Lang",
  title =        "High-Radix Division and Square-Root with Speculation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "8",
  pages =        "919--931",
  month =        aug,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.295854",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:13:57 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib;
                 OCLC Proceedings database",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=295854",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  remark =       "Selected revised and extended papers from ARITH'11
                 \cite{Swartzlander:1993:SCA}.",
  summary =      "The speed of high-radix digit-recurrence dividers and
                 square-root units is mainly determined by the
                 complexity of the result-digit selection. We present a
                 scheme in which a simpler function speculates the
                 result digit, and, when this speculation is \ldots{}",
}

@TechReport{Dallaway:1994:DAC,
  author =       "Richard Z. Dallaway",
  title =        "Dynamics of Arithmetic: a Connectionist View of
                 Arithmetic Skills",
  type =         "Technical report",
  number =       "CSRP 306",
  institution =  "Univerity of Sussex",
  address =      "Brighton, UK",
  pages =        "159",
  month =        feb,
  year =         "1994",
  ISSN =         "1350-3162",
  bibdate =      "Fri Nov 28 16:36:28 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}

@Article{DasSarma:1994:MAR,
  author =       "D. DasSarma and D. W. Matula",
  title =        "Measuring the Accuracy of {ROM} Reciprocal Tables",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "8",
  pages =        "932--940",
  month =        aug,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.295855",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon May 20 06:16:49 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  remark =       "Selected revised and extended papers from ARITH'11
                 \cite{Swartzlander:1993:SCA}.",
}

@InProceedings{Daumas:1994:FAR,
  author =       "Marc Daumas and C. Mazenc and X. Merrheim and J. M.
                 Muller",
  title =        "Fast and accurate range reduction for computation of
                 the elementary functions",
  crossref =     "Ames:1994:IPI",
  pages =        "??--??",
  year =         "1994",
  bibdate =      "Sat Jun 25 08:57:47 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "range reduction",
}

@Article{Daumas:1994:RFP,
  author =       "Marc Daumas and David W. Matula",
  title =        "Rounding of floating point intervals",
  journal =      j-INTERVAL-COMP,
  volume =       "4",
  pages =        "28--45",
  year =         "1994",
  ISSN =         "0135-4868",
  MRclass =      "65G10 (65G05)",
  MRnumber =     "1 332 074",
  bibdate =      "Fri Dec 8 08:24:03 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Interval Computations = Interval'nye vychisleniia",
  xxnote =       "SCAN-93 (Vienna, 1993)",
}

@Article{De:1994:FPA,
  author =       "M. De and B. P. Sinha",
  title =        "Fast parallel algorithm for ternary multiplication
                 using multivalued {$ I^2 L $} technology",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "5",
  pages =        "603--607",
  month =        may,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.280807",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:13:55 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=280807",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{delaSerna:1994:TBF,
  author =       "A. E. de la Serna and M. A. Soderstrand",
  booktitle =    "Conference Record of the Twenty-Eighth Asilomar
                 Conference on Signals, Systems and Computers, 1994",
  title =        "Trade-off between {FPGA} resource utilization and
                 roundoff error in optimized {CSD} {FIR} digital
                 filters",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "187--191",
  year =         "1994",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "In this paper, we investigate the trade off between
                 filter order and bits of coefficient precision in
                 fixed-coefficient FIR digital filters utilizing
                 canonical signed digit (CSD) coefficient
                 representation. We demonstrate that the use of
                 optimized \ldots{}",
}

@Article{delRosario:1994:HIM,
  author =       "J. M. del Rosario and A. N. Choudhary",
  title =        "High-performance {I/O} for massively parallel
                 computers: problems and prospects",
  journal =      j-COMPUTER,
  volume =       "27",
  number =       "3",
  pages =        "59--68",
  month =        mar,
  year =         "1994",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Fri Sep 13 16:03:42 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Electr. and Comput. Eng., Syracuse
                 University, NY, USA",
  classification = "B6210L (Computer communications); C5440
                 (Multiprocessor systems and techniques); C5620
                 (Computer networks and techniques); C6110P (Parallel
                 programming); C6150N (Distributed systems)",
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
  keywords =     "Access patterns; Compilers; File systems;
                 Floating-point operations per second; Hardware
                 technology; High-performance I/O; High-performance
                 storage systems; High-speed networking; I/O
                 infrastructure; Language interfaces; Massive parallel
                 processing; Massively parallel computers; Networking
                 technology; Operating systems; Parallel I/O problem;
                 Powerful supercomputers; Resource-management
                 approaches; Runtime system; Teraflops barrier;
                 Visualization systems",
  thesaurus =    "Computer networks; Input-output programs; Network
                 operating systems; Parallel machines; Parallel
                 programming",
}

@TechReport{Demmel:1994:CPBa,
  author =       "James Demmel and Inderjit Dhillon and Huan Ren",
  title =        "On the correctness of parallel bisection in floating
                 point",
  type =         "Report",
  number =       "UCB/CSD 94/805",
  institution =  "Computer Science Division (EECS), University of
                 California",
  address =      "Berkeley, CA, USA",
  pages =        "38",
  month =        mar,
  year =         "1994",
  bibdate =      "Thu Aug 23 06:41:11 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Also known as LAPACK Working Note number 70.",
  URL =          "http://www.neglib.org/lapack/lawns/lawn70.ps",
  acknowledgement = ack-nhfb,
}

@TechReport{Demmel:1994:CPBb,
  author =       "James Demmel and Inderjit Dhillon and Huan Ren",
  title =        "On the Correctness of Parallel Bisection in Floating
                 Point",
  type =         "LAPACK Working Note",
  number =       "70",
  institution =  inst-UT-CS,
  address =      inst-UT-CS:adr,
  month =        mar,
  year =         "1994",
  bibdate =      "Fri Apr 22 17:06:37 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "UT-CS-94-228, March 1994.",
  URL =          "http://www.netlib.org/lapack/lawns/lawn70.ps;
                 http://www.netlib.org/lapack/lawnspdf/lawn70.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Demmel:1994:FNA,
  author =       "James W. Demmel and Xiaoye Li",
  title =        "Faster Numerical Algorithms via Exception Handling",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "8",
  pages =        "983--992",
  month =        aug,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.295860",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon May 20 06:16:49 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib;
                 OCLC Proceedings database",
  note =         "This is an expanded version of
                 \cite{Demmel:1993:FNA}.",
  URL =          "http://www.cs.berkeley.edu/~xiaoye/ieee.ps.gz",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  remark =       "Selected revised and extended papers from ARITH'11
                 \cite{Swartzlander:1993:SCA}.",
}

@InProceedings{Dimauro:1994:DFNa,
  author =       "G. Dimauro and S. Impedovo and G. Pirlo",
  booktitle =    "Proceedings of the 20th {EUROMICRO} Conference,
                 {EUROMICRO 94}. System Architecture and Integration",
  title =        "The `diagonal function' in non-redundant residue
                 number system",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "590--596",
  year =         "1994",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/EURMIC.1994.390354",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Although the `diagonal function' of a Residue Number
                 System has been recently introduced as a powerful tool
                 to perform non modular operations, its implementation
                 is generally realized using an additional modulus
                 external to the set of system moduli. \ldots{}",
}

@InProceedings{Dimauro:1994:DFNb,
  author =       "G. Dimauro and S. Impedovo and G. Pirlo",
  booktitle =    "{EUROMICRO 94}. System Architecture and Integration.
                 Proceedings of the 20th {EUROMICRO} Conference",
  title =        "The `diagonal function' in non-redundant residue
                 number system",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "590--596",
  year =         "1994",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/EURMIC.1994.390354",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Although the `diagonal function' of a Residue Number
                 System has been recently introduced as a powerful tool
                 to perform non modular operations, its implementation
                 is generally realized using an additional modulus
                 external to the set of system moduli. \ldots{}",
}

@Misc{Edelman:1994:W,
  author =       "Alan Edelman",
  title =        "When is $ x \star (1 / x) \neq 1 $ ?",
  howpublished = "Web document",
  day =          "7",
  month =        dec,
  year =         "1994",
  bibdate =      "Wed Aug 07 15:04:56 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://math.mit.edu/~edelman/homepage/papers/ieee.pdf",
  acknowledgement = ack-nhfb,
}

@Book{Ercegovac:1994:DSR,
  author =       "Milo{\v{s}} D. (Dragutin) Ercegovac and Tomas Lang",
  title =        "Division and Square Root: Digit-recurrence Algorithms
                 and Implementations",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "x + 230",
  year =         "1994",
  ISBN =         "0-7923-9438-0",
  ISBN-13 =      "978-0-7923-9438-9",
  LCCN =         "QA76.9.C62 E73 1994",
  bibdate =      "Fri Mar 27 09:46:24 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "Preface / 1 \\
                 1. General Comments / 5 \\
                 2. Division by Digit Recurrence / 5 \\
                 3. Theory of Digit-Recurrence Division / 19 \\
                 4. Division With Scaling and Prediction /65 \\
                 5. Higher Radix Division / 91 \\
                 6. On-The-Fly Conversion and Round / 121 \\
                 7. Square Root by Digit Recurrence / 135 \\
                 8. Implementations of Square Root / 153 \\
                 A: Restoring and Non-Restoring Division / 182 \\
                 B: Evaluation of Some Implementations / 182 \\
                 Bibliography / 207 \\
                 Index / 227",
}

@Article{Ercegovac:1994:VHR,
  author =       "M. D. Ercegovac and T. Lang and P. Montuschi",
  title =        "Very-High Radix Division with Prescaling and Selection
                 by Rounding",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "8",
  pages =        "909--918",
  month =        aug,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.295853",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:13:57 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib;
                 OCLC Proceedings database",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=295853",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  remark =       "Selected revised and extended papers from ARITH'11
                 \cite{Swartzlander:1993:SCA}.",
  summary =      "A division algorithm in which the quotient-digit
                 selection is performed by rounding the shifted residual
                 in carry-save form is presented. To allow the use of
                 this simple function, the divisor (and dividend) is
                 prescaled to a range close to one. The \ldots{}",
  xxtitle =      "Very high radix division with selection by rounding
                 and prescaling",
}

@Article{Fagin:1994:FPG,
  author =       "B. Fagin and C. Renard",
  title =        "Field Programmable Gate Arrays and Floating Point
                 Arithmetic",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "2",
  number =       "3",
  pages =        "365--367",
  month =        sep,
  year =         "1994",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/92.311646",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present empirical results describing the
                 implementation of an IEEE Standard 754 compliant
                 floating-point adder/multiplier using field
                 programmable gate arrays. The use of FPGA's permits
                 fast and accurate quantitative evaluation of a variety
                 of circuit design tradeoffs for addition and
                 multiplication. PPGA's also permit accurate assessments
                 of the area and time costs associated with various
                 features of the IEEE floating-point standard, including
                 rounding and gradual underflow. These costs are
                 analyzed, along with the effects of architectural
                 correlation, a phenomenon that occurs when the cost of
                 combining architectural features exceeds the sum of
                 separate implementation. We conclude with an assessment
                 of the strengths and weaknesses of using FPGA's for
                 floating-point arithmetic.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, US Air Force Acad.,
                 Colorado Springs, CO, USA",
  classification = "B1265B (Logic circuits); B2570 (Semiconductor
                 integrated circuits); C5120 (Logic and switching
                 circuits); C5230 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
  keywords =     "Addition; Architectural correlation; Area costs; Field
                 programmable gate arrays; Floating point arithmetic;
                 Floating-point adder; Floating-point multiplier; FPGA;
                 IEEE Standard 754 compliance; Multiplication; Time
                 costs",
  summary =      "We present empirical results describing the
                 implementation of an IEEE Standard 754 compliant
                 floating-point adder/multiplier using field
                 programmable gate arrays. The use of FPGA's permits
                 fast and accurate quantitative evaluation of a variety
                 of \ldots{}",
  thesaurus =    "Adders; Application specific integrated circuits;
                 Digital arithmetic; Logic arrays; Multiplying
                 circuits",
}

@Book{Farquhar:1994:MPH,
  author =       "Erin Farquhar and Philip Bruce",
  title =        "The {MIPS} Programmer's Handbook",
  publisher =    pub-MORGAN-KAUFMANN,
  address =      pub-MORGAN-KAUFMANN:adr,
  pages =        "viii + 408",
  year =         "1994",
  ISBN =         "1-55860-297-6",
  ISBN-13 =      "978-1-55860-297-7",
  LCCN =         "QA76.6 .F375 1994",
  bibdate =      "Fri May 13 18:21:14 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/microchip.bib",
  price =        "US\$36.95",
  abstract =     "A hands-on view of the highly successful MIPS family
                 of microprocessors, written for programmers developing
                 systems applications for the MIPS platform. The MIPS
                 Programmer's Handbook describes the MIPS architecture
                 from the perspective of assembly- and C-language
                 programmers, with special emphasis on issues related to
                 embedded applications. Engineers writing system-level
                 programs for MIPS-based embedded systems will find the
                 topic selection especially useful including the
                 sections on software conventions, initializing the
                 processor in a bare machine environment, and writing
                 exception handlers. For convenient use, the instruction
                 set reference is presented with only one page per
                 instruction. The authors focus on the instructions
                 available to assembly-language programmers, rather than
                 on the hardware-level instruction set documented in
                 data books released by vendors of the MIPS processor.
                 Provides enough detail for anyone doing serious
                 system-level programming. Also included are ten
                 complete program examples, with line-by-line
                 explanations.",
  acknowledgement = ack-nhfb,
  libnote =      "Not yet in my library.",
  tableofcontents = "1: Introduction \\
                 2: Software Conventions \\
                 3: Initialization \\
                 4: Exceptions \\
                 5: Instruction Set Reference \\
                 A: Overview of the MIPS1 Architecture \\
                 B: Instruction Summary \\
                 C: Prologue and Epilogue Templates \\
                 D: Include Files \\
                 E: Libraries \\
                 F: Vendors of MIPS Products",
}

@InProceedings{FiallosAguilar:1994:HPA,
  author =       "M. Fiallos-Aguilar",
  title =        "High precision arithmetic units for fine-grain
                 massively parallel computing",
  crossref =     "IEEE:1994:PFI",
  pages =        "403--407",
  year =         "1994",
  bibdate =      "Thu Dec 14 11:25:18 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this paper we deal with new high precision
                 arithmetic units (AUs). These AUs are specialized in
                 the computation of one arithmetic operation (division,
                 addition, etc.), but when hundreds of them are
                 interconnected by a reconfigurable network, a parallel
                 architecture that uses massive digit-level pipelining
                 between floating-point arithmetic units (allowing fast
                 computation of scientific jobs) becomes interesting. In
                 this paper we present several new AUs for the fast
                 computation of arithmetic expressions that will be used
                 on a high precision massively parallel computer. (6
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "Lab. LIP-IMAG, Ecole Normale Superieure de Lyon,
                 France",
  classification = "C5220P (Parallel architecture); C5230 (Digital
                 arithmetic methods)",
  keywords =     "Arithmetic units; Fine-grain; Floating-point
                 arithmetic units; High precision; Massively parallel
                 computing; Parallel architecture",
  thesaurus =    "Digital arithmetic; Parallel architectures; Pipeline
                 arithmetic",
}

@Article{Gander:1994:AFP,
  author =       "H. Gander and M. Vincze and J. P. Prenninger",
  title =        "Application of a Floating Point Digital Signal
                 Processor to the Control of a Laser Tracking System",
  journal =      j-IEEE-TRANS-CONTROL-SYST-TECHNOL,
  volume =       "2",
  number =       "4",
  pages =        "290--298",
  month =        dec,
  year =         "1994",
  CODEN =        "IETTE2",
  ISSN =         "1063-6536 (print), 1558-0865 (electronic)",
  ISSN-L =       "1063-6536",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Control Systems Technology",
  summary =      "Laser tracking systems represent the most promising
                 technique for dynamic position measurement of
                 industrial robots. The Institute of Flexible Automation
                 at the Vienna University of Technology a new tracking
                 algorithm has been developed. It is shown \ldots{}",
}

@InProceedings{Gerber:1994:DPH,
  author =       "S. Gerber and M. Goessel",
  title =        "Detection of permanent hardware faults of a floating
                 point adder by pseudoduplication",
  crossref =     "Echtle:1994:PFI",
  pages =        "327--335",
  year =         "1994",
  DOI =          "https://doi.org/10.1007/3-540-58426-9_139",
  bibdate =      "Thu Dec 14 11:25:18 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this paper the detection of hardware faults by
                 pseudoduplication for a special floating point adder is
                 investigated. For a special floating point adder all
                 single stuck-at-0/1 faults are injected. In a first
                 simulation experiment for random input patterns all the
                 faults are determined which can be detected by
                 pseudoduplication. In a second experiment for sequences
                 of random input vectors with different length the
                 probability to detect an arbitrary single fault is
                 determined.",
  acknowledgement = ack-nhfb,
  affiliation =  "Max-Planck-Society Fault-Tolerant Comput. Group,
                 Potsdam University, Germany",
  classification = "B1130B (Computer-aided circuit analysis and design);
                 B1265B (Logic circuits); C5120 (Logic and switching
                 circuits); C5210B (Computer-aided logic design); C7410D
                 (Electronic engineering computing)",
  keywords =     "Arbitrary single fault; Floating point adder;
                 Permanent hardware faults; Probability;
                 Pseudoduplication; Random input patterns; Stuck at
                 faults",
  thesaurus =    "Adders; Digital simulation; Fault location; Floating
                 point arithmetic; Logic CAD; Logic testing",
}

@Article{Granlund:1994:DII,
  author =       "Torbj{\"o}rn Granlund and Peter L. Montgomery",
  title =        "Division by invariant integers using multiplication",
  journal =      j-SIGPLAN,
  volume =       "29",
  number =       "6",
  pages =        "61--72",
  month =        jun,
  year =         "1994",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/178243.178249",
  ISBN =         "0-89791-598-4",
  ISBN-13 =      "978-0-89791-598-4",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:16:51 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/proceedings/pldi/178243/index.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.cwi.nl/pub/pmontgom/divcnst.psa4.gz;
                 ftp://ftp.cwi.nl/pub/pmontgom/divcnst.psl.gz;
                 http://www.acm.org:80/pubs/citations/proceedings/pldi/178243/p61-granlund/",
  abstract =     "Integer division remains expensive on today's
                 processors as the cost of integer multiplication
                 declines. We present code sequences for division by
                 arbitrary nonzero integer constants and run-time
                 invariants using integer multiplication. The algorithms
                 assume a two's complement architecture. Most also
                 require that the upper half of an integer product be
                 quickly accessible. We treat unsigned division, signed
                 division where the quotient rounds towards zero, signed
                 division where the quotient rounds towards $ - \infty
                 $, and division where the result is known a priori to
                 be exact. We give some implementation results using the
                 C compiler GCC.",
  acknowledgement = ack-nhfb,
  affiliation =  "Cygnus Support, Mountain View, CA, USA",
  annote =       "Published as part of the Proceedings of PLDI'94.",
  classification = "C5230 (Digital arithmetic methods); C6110 (Systems
                 analysis and programming); C6150C (Compilers,
                 interpreters and other processors)",
  confdate =     "20-24 June 1994",
  conflocation = "Orlando, FL, USA",
  confsponsor =  "ACM",
  conftitle =    "ACM SIGPLAN '94 Conference on Programming Language
                 Design and Implementation (PLDI)",
  corpsource =   "Cygnus Support, Mountain View, CA, USA",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "algorithms; Arbitrary nonzero integer constants;
                 arbitrary nonzero integer constants; C compiler; Code
                 sequences; code sequences; digital arithmetic; Floating
                 point arithmetic; floating point arithmetic; GCC;
                 Integer division; integer division; Integer
                 multiplication; integer multiplication; Invariant
                 integers; invariant integers; mathematics computing;
                 Multiplication; multiplication; performance; program;
                 program compilers; programming; reduced instruction set
                 computing; RISC processors; Run-time invariants;
                 run-time invariants; Signed division; signed division;
                 Two's complement architecture; two's complement
                 architecture; Unsigned division; unsigned division",
  sponsororg =   "ACM",
  subject =      "{\bf G.1.0} Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf F.2.1}
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems.
                 {\bf D.3.4} Software, PROGRAMMING LANGUAGES,
                 Processors, Compilers.",
  thesaurus =    "Digital arithmetic; Mathematics computing; Program
                 compilers; Programming; Reduced instruction set
                 computing",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Grosse:1994:IRS,
  author =       "Eric Grosse and John D. Hobby",
  title =        "Improved rounding for spline coefficients and knots",
  journal =      j-MATH-COMPUT,
  volume =       "63",
  number =       "207",
  pages =        "175--194",
  month =        jul,
  year =         "1994",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D07",
  MRnumber =     "94j:65019",
  bibdate =      "Tue Mar 25 15:38:13 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Comput. Sci. Res., AT\&T Bell Labs., Murray Hill, NJ,
                 USA",
  ajournal =     "Math. Comput.",
  classcodes =   "B0290F (Interpolation and function approximation);
                 B0290B (Error analysis in numerical methods); C4130
                 (Interpolation and function approximation); C4110
                 (Error analysis in numerical methods)",
  corpsource =   "Comput. Sci. Res., AT\&T Bell Labs., Murray Hill, NJ,
                 USA",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "affine model; algorithm; error; error analysis;
                 infinite-precision value; knot; knots; Lovasz basis
                 reduction; optimal full-precision free-; parameterized
                 spline; quadratic error model; rounding; roundoff
                 errors; spline coefficients; splines (mathematics)",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Hahn:1994:UDF,
  author =       "H. Hahn and D. Timmermann and B. J. Hosticka and B.
                 Rix",
  title =        "A unified and division-free {CORDIC} argument
                 reduction method with unlimited convergence domain
                 including inverse hyperbolic functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "11",
  pages =        "1339--1344",
  month =        nov,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.324568",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:13:58 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=324568",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Hartwig:1994:FPA,
  author =       "F. Hartwig and A. Lacroix",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems: {ISCAS '94}, 2 June 1994",
  title =        "Floating point addition errors and their effect on the
                 roundoff noise in digital signal processing",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "121--124",
  year =         "1994",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "An improved adder model is derived which takes into
                 account correlations between signal and error. For
                 different adder strategies is shown the influence of
                 the improved adder model on the estimated of the
                 resulting \ldots{}",
}

@MastersThesis{Hauser:1994:PEH,
  author =       "John R. Hauser",
  title =        "Programmed exception handling: research project",
  type =         "{Master of Science, Plan II}",
  school =       "Department of Computer Science, University of
                 California, Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "82",
  year =         "1994",
  LCCN =         "T7.49.1994 H286",
  bibdate =      "Mon Feb 18 12:39:53 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Hegland:1994:SSP,
  author =       "Markus Hegland",
  title =        "A self-sorting in-place fast {Fourier} transform
                 algorithm suitable for vector and parallel processing",
  journal =      j-NUM-MATH,
  volume =       "68",
  number =       "4",
  pages =        "507--547",
  year =         "1994",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65T20 (65Y05)",
  MRnumber =     "96e:65082",
  bibdate =      "Mon May 26 11:49:34 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "B0290Z (Other numerical methods); C4190 (Other
                 numerical methods); C5220P (Parallel architecture);
                 C5440 (Multiprocessing systems); C7310 (Mathematics
                 computing)",
  corpsource =   "Centre for Math. Anal. and its Applications,
                 Australian Nat. University, Canberra, ACT, Australia",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "data analysis; distributed memory computers; fast
                 Fourier transforms; floating point pipelines; Fujitsu
                 VP2200; index digit permutations; mathematics
                 computing; matrix recursions; parallel processing;
                 self-sorting in-place fast Fourier transform algorithm;
                 splitting formulas; uniformly long vector lengths;
                 vector processing; vector processor systems",
  treatment =    "A Application; P Practical; T Theoretical or
                 Mathematical",
}

@Article{Hemkumar:1994:RLC,
  author =       "N. D. Hemkumar and J. R. Cavallaro",
  title =        "Redundant and On-Line {CORDIC} for Unitary
                 Transformations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "8",
  pages =        "941--954",
  month =        aug,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.295856",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon May 20 06:16:49 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  remark =       "Selected revised and extended papers from ARITH'11
                 \cite{Swartzlander:1993:SCA}.",
}

@Article{Hester:1994:PPP,
  author =       "P. D. Hester and W. J. Filip",
  title =        "Preface: {Power2} and {PowerPC} Architecture and
                 Implementation",
  journal =      j-IBM-JRD,
  volume =       "38",
  number =       "5",
  pages =        "490--491",
  month =        sep,
  year =         "1994",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Mon Feb 12 08:14:00 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.almaden.ibm.com/journal/rd38-5.html#one",
  abstract =     "During the four years since the RISC System\slash
                 6000* (RS\slash 6000) announcement in February of 1990,
                 IBM* has strengthened its product line with
                 microprocessor enhancements, increased memory capacity,
                 improved graphics, greatly expanded I/O adapters, and
                 new AIX* and compiler releases. In 1991, IBM began
                 planning for future RS\slash 6000 systems that would
                 span the range from small, battery-operated products to
                 very large supercomputers and mainframes. As the first
                 step toward achieving this ``palmtop to teraFLOPS''
                 goal with a single architecture, IBM investigated
                 further optimizations for the original POWER
                 Architecture*. This effort led to the creation of the
                 PowerPC* alliance (IBM Corporation, Motorola*, Inc.,
                 and Apple* Computer Corporation) and the definition of
                 the PowerPC Architecture*. Today, the single-chip
                 PowerPC 601* processor is the basis of IBM's entry
                 systems. A more aggressively superscalar version of the
                 original POWER processor, the multichip POWER2*
                 processor, is exploited in our current IBM high-end
                 RISC systems. As technology continues to advance,
                 PowerPC implementations will provide the basis for
                 high-performance 64-bit super servers. This special
                 issue of the IBM Journal of Research and Development
                 focuses on the POWER2 and PowerPC portions of IBM's
                 wide-ranging announcement in the Fall of 1993. The new
                 POWER2 processor nearly doubles the performance of the
                 earlier high-end models. The PowerPC 601 processor was
                 introduced in the RISC System\slash 6000 Model 250, the
                 first system in the industry to use the PowerPC
                 Architecture created by the strategic
                 IBM/Motorola/Apple alliance. These workstations
                 achieved industry-leading performance and
                 price/performance on virtually every industry-standard
                 benchmark, including SPECint92*, SPECfp92*, Linpack,
                 TPP, TPC-A*, and TPC-C*. Compared to the 1990
                 offerings, SPEC performance nearly quadrupled,
                 transaction performance improved by a factor of almost
                 five, maximum memory capacity quadrupled, and the
                 maximum disk capacity grew by an order of magnitude.
                 The POWER2 design exploits both multichip technology
                 and a larger die size to execute up to six instructions
                 (eight operations) per clock cycle. Many of the
                 higher-performance POWER2-based systems provide peak
                 execution rates in excess of a half billion operations
                 per second. The paper by White and Dhawan provides an
                 overview of the POWER2 design. Shippy and Griffith
                 describe the dual fixed-point unit design, the data
                 cache unit, and the storage control unit. Hicks, Fry,
                 and Harvey describe the dual floating-point unit
                 design. Barreh et al. describe hardware strategies to
                 minimize compare-branch penalties in the instruction
                 cache unit. Welbon et al. describe a POWER2 hardware
                 performance- monitoring facility which provides
                 execution characteristics that can identify
                 opportunities for application performance improvement.
                 This facility can also be used to gather information
                 crucial to future design decisions. Two performance
                 papers conclude the POWER2 portion of this issue.
                 Franklin et al. analyze some of the key POWER2 hardware
                 contributions to performance on the commercial
                 workloads. Agarwal, Gustavson, and Zubair relate their
                 experiences with optimizing the high-performance
                 Engineering/Scientific Subroutine Library (ESSL) for
                 the POWER2 implementation. While POWER2 and PowerPC
                 implementations provide the opportunity for
                 high-performance systems, optimizing software is also
                 key in delivering end-user performance. Blainey
                 describes aspects of the TOBEY compiler, with special
                 emphasis on instruction scheduling for the RS\slash
                 6000 products. Heisch describes TDPR, a prototype
                 version of FDPR, a program restructuring tool which
                 improves application performance by placing frequently
                 executed code blocks so as to minimize instruction
                 cache misses and branch penalties. IBM and the PowerPC
                 alliance are currently developing a family of five
                 PowerPC designs. IBM and Motorola designers at the
                 Somerset Design Center in Austin will optimize
                 single-chip implementations of the PowerPC Architecture
                 for high-volume products. The high-end requirements of
                 the large server and workstation products will be
                 addressed with multichip PowerPC implementations from
                 IBM.\par

                 IBM entry-level workstation products introduced the
                 PowerPC 601 microprocessor, the first member of the
                 PowerPC family. The goal for the PowerPC 601 designers
                 was to quickly bring PowerPC to the market. Vaden et
                 al. describe the microarchitecture and performance
                 aspects of the PowerPC 601 processor. Brodnax et al.
                 discuss the PowerPC 601 circuitry and chip
                 implementation details. Future products are planned
                 that will incorporate the PowerPC 603*, PowerPC 604*,
                 and the 64-bit PowerPC 620* implementations as they
                 become available. In addition, the price and
                 price/performance of the PowerPC family enable
                 lower-cost ``RISC PCs'' to be built using PowerPC
                 microprocessors. These ``RISC PCs'' will be developed
                 by the IBM POWER Personal Systems Division.\par

                 The PowerPC and POWER2 systems signify a major
                 milestone in IBM's commitment to the ``palmtops to
                 teraFLOPS'' strategy. The PowerPC 601 chip extends the
                 entry products further into the high-volume market by
                 providing exceptional performance in a low-cost
                 single-chip microprocessor. The high-end POWER2
                 implementation extracts the maximum performance
                 achievable in today's technology, thrusting the IBM
                 RISC processors into the supercomputing and
                 large-server environments. IBM POWER Parallel Systems
                 extends the RS\slash 6000 processing capability by
                 providing IBM POWER Parallel SP2* systems with up to
                 512 POWER/POWER2 nodes. In addition to scalability,
                 four-way High Availability Cluster Multi-Processor
                 (HACMP) systems provide the reliability/availability
                 that one would expect from mainframe-class systems by
                 supporting a ``no single point of failure'' capability,
                 even when one processor is off line. This impressive
                 base of processing technology complements a commitment
                 to high-performance compilers and strong graphics
                 offerings.\par

                 This robust product line addresses the cost-driven
                 requirements of the entry workstation market, the
                 transaction and server requirements of the commercial
                 market, and the computation-intensive requirements of
                 the technical market. These hardware offerings result
                 from a team effort by many dedicated and talented
                 individuals from around the world. Their expertise and
                 skill in a wide range of disciplines were key to
                 achieving this significant step toward the goal of a
                 comprehensive architecture. We want to thank all those
                 involved in continuing the success of the RISC
                 System\slash 6000 line.",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}

@Article{Hicks:1994:PFU,
  author =       "T. N. Hicks and R. E. Fry and P. E. Harvey",
  title =        "{POWER2} floating-point unit: Architecture and
                 implementation",
  journal =      j-IBM-JRD,
  volume =       "38",
  number =       "5",
  pages =        "525--536",
  month =        sep,
  year =         "1994",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The POWER2 floating-point unit (FPU) extends the
                 concept of the innovative multiply-add fused (MAF) ALU
                 of the RISC System/6000 processor to provide a
                 floating-point unit that sets new standards, not only
                 for computation capability but for data throughput and
                 processor flexibility. The POWERS FPU achieves a
                 performance (MFLOPS) rate never accomplished before by
                 a personal workstation machine by: (1) integrating dual
                 generic MAF ALUs, (2) doubling the instruction
                 bandwidth and quadrupling the data bandwidth over that
                 of the POWER FPU, (3) adding support for additional
                 functions, and (4) using dynamic instruction scheduling
                 techniques to maximize instruction-level parallelism
                 not only among its own internal units but with the rest
                 of the CPU.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Corp., Austin, TX, USA",
  classification = "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5220P (Parallel architecture);
                 C5230 (Digital arithmetic methods)",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "Data bandwidth; Dynamic instruction scheduling;
                 Floating-point unit; Instruction bandwidth;
                 Instruction-level parallelism; Multiply add fused
                 arithmetic logic unit; POWER2; RISC System/6000
                 processor",
  thesaurus =    "Floating point arithmetic; Microprocessor chips;
                 Parallel architectures; Parallel processing; Reduced
                 instruction set computing",
}

@InProceedings{Hilker:1994:NMM,
  author =       "S. Hilker and N. Phan and D. Rainey",
  title =        "A 3.4 ns 0.8 mu m {BiCMOS} 53*53 b multiplier tree",
  crossref =     "Wuorinen:1994:IIS",
  pages =        "292--293",
  year =         "1994",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A 53*53 b multiplier tree with 3.4 ns latency, 10
                 mm/sup 2/ active area, and 5 W power dissipation at 200
                 MHz and 3.6 V supply is implemented in 0.8 mu m n-well
                 BiCMOS with 115 AA gate oxide, 0.45 mu m effective
                 channel length, and 4 levels of metal. This 3.4ns
                 low-latency multiplier is for a floating-point unit
                 (FPU) on a BiCMOS RISC processor capable of performing
                 IEEE double precision multiply-add operations in three
                 pipelined stages at 200MHz (15ns latency, 5ns
                 throughput, 400MFLOPs peak rate) using multiply-add
                 fused dataflow.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Corp., Rochester, MN, USA",
  classification = "B1265B (Logic circuits); B2570K (Mixed technology
                 integrated circuits); C5120 (Logic and switching
                 circuits); C5220P (Parallel architecture); C5230
                 (Digital arithmetic methods)",
  keywords =     "0.8 Micron; 200 MHz; 3.4 Ns; 3.6 V; 400 MFLOPS; 5 W;
                 Effective channel length; Floating-point unit; IEEE
                 double precision multiply-add operations; Latency;
                 Multiplier tree; Multiply-add fused dataflow; N-well
                 BiCMOS; Pipelined stages; Power dissipation; RISC
                 processor",
  numericalindex = "Time 3.4E-09 s; Size 8.0E-07 m; Power 5.0E+00 W;
                 Frequency 2.0E+08 Hz; Voltage 3.6E+00 V; Computer speed
                 4.0E+08 FLOPS",
  thesaurus =    "BiCMOS integrated circuits; Digital arithmetic;
                 Multiplying circuits; Parallel processing; Pipeline
                 processing; Reduced instruction set computing",
}

@Book{Hill:1994:GPL,
  author =       "Patricia Hill",
  title =        "The {G{\"o}del} Programming Language",
  publisher =    pub-MIT,
  address =      pub-MIT:adr,
  pages =        "xx + 348",
  year =         "1994",
  ISBN =         "0-262-08229-2",
  ISBN-13 =      "978-0-262-08229-7",
  LCCN =         "QA76.73.G17H55 1994",
  bibdate =      "Thu Sep 15 07:47:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Section 13.3 (pp. 206--218) defines floating-point
                 numbers and standard functions conforming to Version
                 4.0 (August 1992) of the Language Independent
                 Arithmetic Standard (LIAS) ISO\slash IEC CD
                 10967-1:1992 (JTC1/SC22/WG11 N318, ANSI X3T3 92-064).
                 It also conforms to the ANSI\slash IEEE Standard for
                 Binary Floating-Point Arithmetic 754-1985.",
  acknowledgement = ack-nhfb,
}

@TechReport{Hopkins:1994:CEM,
  author =       "Tim Hopkins and John Slater",
  title =        "A Comment on the {Eispack} Machine Epsilon Routine",
  type =         "Technical Report",
  number =       "18-94",
  institution =  "University of Kent, Computing Laboratory, University
                 of Kent",
  address =      "Canterbury, UK",
  year =         "1994",
  bibdate =      "Tue Apr 12 12:00:52 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.kent.ac.uk/pubs/1994/74/content.ps.gz",
  acknowledgement = ack-nhfb,
}

@Article{Horvath:1994:PPM,
  author =       "Tam{\'a}s Horv{\'a}th and Spyros S. Magliveras and
                 Tran van Trung",
  title =        "A Parallel Permutation Multiplier for a {PGM}
                 Crypto-Chip",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "839",
  pages =        "108--113",
  year =         "1994",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:49:18 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t0839.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/0839/08390108.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/0839/08390108.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
  keywords =     "CRYPTO; cryptology; IACR; IEEE",
}

@Article{Hsu:1994:CPF,
  author =       "Chau-Yun Hsu and Jui Chi Yao",
  title =        "Comparative performance of fast cosine transform with
                 fixed-point roundoff error analysis",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "42",
  number =       "5",
  pages =        "1256--1259",
  month =        may,
  year =         "1994",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "Suitable scaling schemes are chosen for the Lee's and
                 the Hou's (1984) fast DCT algorithms, and the relative
                 fixed-point roundoff error analyses are carried out,
                 respectively. The average output signal-to-noise ratio
                 are then calculated, and it is \ldots{}",
}

@Article{Hsu:1994:NFP,
  author =       "Chau-Yun Hsu",
  title =        "Novel fixed-point roundoff analysis of the
                 decimation-in-time {FHT}",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "42",
  number =       "1",
  pages =        "206--208",
  month =        jan,
  year =         "1994",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "A least upper bound for the increasing factor of the
                 magnitude of the decimation-in-time fast Hartley
                 transform (FHT) in fixed-point arithmetic is developed
                 and a new scaling model for the roundoff analysis in
                 the fixed-point arithmetic computation \ldots{}",
}

@Article{Hull:1994:ICE,
  author =       "T. E. Hull and Thomas F. Fairgrieve and Ping Tak Peter
                 Tang",
  title =        "Implementing Complex Elementary Functions Using
                 Exception Handling",
  journal =      j-TOMS,
  volume =       "20",
  number =       "2",
  pages =        "215--244",
  month =        jun,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/178365.178404",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 21 15:10:29 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See correction \cite{Anonymous:1994:C}, and improved
                 analysis, tightened bounds, and exhibition of worst
                 cases for complex square roots
                 \cite{Jeannerod:2017:REC}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-2/p215-hull/",
  abstract =     "Algorithms are developed for reliable and accurate
                 evaluations of the complex elementary functions
                 required in Fortran 77 and Fortran 90, namely cabs,
                 csqrt, cexp, clog, csin, and ccos. The algorithms are
                 presented in a pseudocode that has a convenient
                 exception-handling facility. A tight error bound is
                 derived for each algorithm. Corresponding Fortran
                 programs for an IEEE environment have also been
                 developed to illustrate the practicality of the
                 algorithms, and these programs have been tested very
                 carefully to help confirm the correctness of the
                 algorithms and their error bounds. The results are of
                 these tests are included in the paper, but the Fortran
                 programs are not; the programs are available from
                 Fairgrieve, (tff@cs.toronto.edu).",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; complex elementary functions; design;
                 implementation",
  subject =      "G.1.0 [Numerical Analysis]: General--error analysis;
                 numerical algorithms; G.1.2 [Numerical Analysis]:
                 Approximation--elementary function approximation; G.4
                 [Mathematics of Computing]: Mathematical
                 Software--algorithm analysis; reliability and
                 robustness; verification",
}

@Article{Hung:1994:ASD,
  author =       "C. Y. Hung and B. Parhami",
  title =        "An approximate sign detection method for residue
                 numbers and its application to {RNS} division",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "27",
  number =       "4",
  pages =        "23--35",
  month =        feb,
  year =         "1994",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 19:11:19 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122194900523",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Hung:1994:FRD,
  author =       "Ching Yu Hung and Behrooz Parhami",
  title =        "Fast {RNS} division algorithms for fixed divisors with
                 application to {RSA} encryption",
  journal =      j-INFO-PROC-LETT,
  volume =       "51",
  number =       "4",
  pages =        "163--169",
  day =          "24",
  month =        aug,
  year =         "1994",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  MRclass =      "94A60",
  MRnumber =     "1 294 308",
  bibdate =      "Fri Oct 25 18:39:09 2002",
  bibsource =    "Compendex database;
                 http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/infoproc.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ of California",
  affiliationaddress = "Santa Barbara, CA, USA",
  classification = "722.4; 723.1; 723.2; 921.6; C4240 (Programming and
                 algorithm theory)C6130S (Data security); C7310
                 (Mathematics)",
  corpsource =   "Department of Electr. and Comput. Eng., California
                 University, Santa Barbara, CA, USA",
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  journalabr =   "Inf Process Lett",
  keywords =     "Algorithms; Chinese remainder theorem; Chinese
                 remainder theorem decoding and table lookup;
                 Computational complexity; computational complexity;
                 Computational complexity; Computational methods;
                 Computer software; Cryptography; cryptography;
                 Cryptography; Decoding; Digital arithmetic; digital
                 arithmetic; Digital arithmetic; Division; divisor
                 reciprocal; Exponentiation; fast RNS division
                 algorithms; fixed divisors; Fixed divisors; Function
                 evaluation; mathematics computing; Modular
                 multiplication; multiplication; Numbering systems;
                 on-line speed; ordinary integer division; Parallel
                 processing systems; preprocessing; Residue number
                 system; Residue processors; RSA encryption; Sign
                 detection; Table lookup; Time complexity; time
                 complexity; Time complexity",
  treatment =    "A Application; T Theoretical or Mathematical",
}

@Book{IBM:1994:IRS,
  editor =       "Steve White and John Reysa",
  title =        "{IBM RISC} System\slash 6000 Technology: Volume {II}",
  publisher =    pub-IBM,
  address =      pub-IBM:adr,
  year =         "1994",
  bibdate =      "Fri Mar 18 10:25:19 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "A partial draft is available via anonymous ftp to
                 \path|ibminet.awdpa.ibm.com| in the PostScript file
                 \path|/pub/rs6kpapers/techbook.ps|.",
  acknowledgement = ack-nhfb,
}

@Book{IBM:1994:OA,
  author =       "{IBM Corporation}",
  title =        "The {PowerPC} Architecture: a Specification for a New
                 Family of {RISC} Processors",
  publisher =    pub-MORGAN-KAUFMANN,
  address =      pub-MORGAN-KAUFMANN:adr,
  edition =      "Second",
  pages =        "xxxi + 518",
  year =         "1994",
  ISBN =         "1-55860-316-6",
  ISBN-13 =      "978-1-55860-316-5",
  LCCN =         "QA76.8.P67 P68 1994",
  bibdate =      "Wed Jul 6 14:15:23 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$49.95",
  acknowledgement = ack-nhfb,
}

@Article{Ienne:1994:BSM,
  author =       "P. Ienne and M. A. Viredaz",
  title =        "Bit-serial multipliers and squarers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "12",
  pages =        "1445--1450",
  month =        dec,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.338107",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:13:59 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=338107",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Ignatowski:1994:CNA,
  author =       "R. Ignatowski and E. E. Swartzlander",
  title =        "Creating New Algorithms and Modifying Old Algorithms
                 to Use the Variable Precision Floating Point
                 Simulator",
  journal =      "Conference record",
  pages =        "152--??",
  year =         "1994",
  ISSN =         "1058-6393",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{Isaacson:1994:ANM,
  author =       "Eugene Isaacson and Herbert Bishop Keller",
  title =        "Analysis of numerical methods",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xv + 541",
  year =         "1994",
  ISBN =         "0-486-68029-0 (paperback)",
  ISBN-13 =      "978-0-486-68029-3 (paperback)",
  LCCN =         "QA297 .I8 1994",
  bibdate =      "Fri Aug 20 09:37:14 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/description/dover031/94007740.html",
  acknowledgement = ack-nhfb,
  remark =       "Originally published in \cite{Isaacson:1966:ANM}.
                 Contains new preface.",
  subject =      "Numerical analysis",
}

@Book{ISO:1994:IIIa,
  author =       "{ISO}",
  title =        "{ISO\slash IEC 10967-1 (1994-12)}: {Information}
                 technology --- {Language} independent arithmetic ---
                 {Part 1}: {Integer} and floating point arithmetic",
  publisher =    pub-ISO,
  address =      pub-ISO:adr,
  pages =        "viii + 92",
  day =          "15",
  month =        dec,
  year =         "1994",
  bibdate =      "Sun Mar 15 11:09:44 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "CHF 176, US\$136.00",
  URL =          "http://standards.iso.org/ittf/PubliclyAvailableStandards/c018939_ISO_IEC_10967-1_1994(E).zip;
                 http://www.iec.ch/cgi-bin/procgi.pl/www/iecwww.p?wwwlang=E&wwwprog=cat-det.p&wartnum=019729;
                 http://www.iso.ch/cate/d18939.html",
  acknowledgement = ack-nhfb,
}

@TechReport{Jackson:1994:PCE,
  author =       "K. R. Jackson and N. S. Nedialkov",
  title =        "Precision Control and Exception Handling in Scientific
                 Computing",
  type =         "Technical Report",
  institution =  "Department of Computer Science, University of
                 Toronto",
  address =      "Toronto, ON, Canada",
  pages =        "8",
  year =         "1994",
  bibdate =      "Tue May 22 15:45:43 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.toronto.edu/NA/reports.html#prec.except;
                 http://www.cs.toronto.edu/pub/reports/na/prec.except.ps.Z",
  abstract =     "This paper describes convenient language facilities
                 for precision control and exception handling. Nedialkov
                 has developed a variable-precision and exception
                 handling library, SciLib, implemented as a numerical
                 class library in C++. A new scalar data type, {\em
                 real}, is introduced, consisting of variable-precision
                 floating-point numbers. Arithmetic, relational, and
                 input and output operators of the language are
                 overloaded for reals, so that mathematical expressions
                 can be written without explicit function calls.
                 Precision of computations can be changed during program
                 execution. The exception handling mechanism treats only
                 numerical exceptions and does not distinguish between
                 different types of exceptions.\par

                 The proposed precision control and exception handling
                 facilities are illustrated by sample SciLib programs.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Jain:1994:SRR,
  author =       "V. K. Jain and Lei Lin",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing: {ICASSP-94, 19--22} April 1994",
  title =        "Square-root, reciprocal, sine\slash cosine, arctangent
                 cell for signal and image processing",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "II/521--II/524",
  year =         "1994",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper discusses an efficient interpolation method
                 for nonlinear function generation. Based on this, a 24
                 bit VLSI cell, capable of computing the (1) square
                 root, (2) reciprocal, (3) sine/cosine, and (4)
                 arctangent functions, is presented for \ldots{}",
}

@Article{Jaromczyk:1994:CCH,
  author =       "Jerzy W. Jaromczyk and G. W. Wasilkowski",
  title =        "Computing convex hull in a floating point arithmetic",
  journal =      j-COMP-GEOM,
  volume =       "4",
  number =       "5",
  pages =        "283--292",
  year =         "1994",
  ISSN =         "0925-7721 (print), 1879-081X (electronic)",
  ISSN-L =       "0925-7721",
  MRclass =      "68U05",
  MRnumber =     "95j:68159",
  bibdate =      "Fri Dec 8 08:24:07 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computational Geometry. Theory and Applications",
}

@Article{Johnstone:1994:DAN,
  author =       "Paul Johnstone and Frederick E. Petry",
  title =        "Design and analysis of non-binary radix floating point
                 representations",
  journal =      j-COMPUT-ELECTR-ENG,
  volume =       "20",
  number =       "1",
  pages =        "39--50",
  month =        jan,
  year =         "1994",
  CODEN =        "CPEEBQ",
  ISSN =         "0045-7906 (print), 1879-0755 (electronic)",
  ISSN-L =       "0045-7906",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The authors examine the feasibility of higher radix
                 floating point representations and in particular
                 decimal based representations. Traditional analyses of
                 such representations have assumed the format of a
                 floating point datum to be roughly identical to that of
                 traditional binary floating point encodings such as the
                 IEEE P754 task group standard representations. We relax
                 this restriction and propose a method of encoding
                 higher radix floating point data with range, precision
                 and storage requirements comparable to those exhibited
                 by traditional binary representations. Results from W.
                 M. McKeeman's (1967) maximum and average relative
                 representational error (MRRE and ARRE) analyses, R. P.
                 Brent's (1973) RMS error evaluation, D. W. Matula's
                 (1970) ratio of significance space and gap functions,
                 and W. S. Brown and P. L. Richman's (1969) exponent
                 range estimates are extended to accommodate the
                 proposed representation. A decimal alternative to
                 traditional binary representations is proposed and the
                 behavior of such a system is contrasted with that of a
                 comparable binary system.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dow Jones Telerate, New Orleans, LA, USA",
  classification = "B1265 (Digital electronics); C5230 (Digital
                 arithmetic methods)",
  fjournal =     "Computers and Electrical Engineering",
  keywords =     "ARRE; Average relative representational error; Decimal
                 alternative; Decimal based representations; decimal
                 floating-point arithmetic; Exponent range estimates;
                 Floating point datum; Gap functions; Higher radix
                 floating point representations; MRRE; Non-binary radix
                 floating point representations; RMS error evaluation;
                 Significance space ratio; Storage requirements",
  thesaurus =    "Digital arithmetic; Roundoff errors",
}

@Article{Kabuo:1994:ARS,
  author =       "H. Kabuo and T. Taniguchi and A. Miyoshi and H.
                 Yamashita and M. Urano and H. Edamatsu and S.
                 Kuninobu",
  title =        "Accurate Rounding Scheme for the {Newton--Raphson}
                 Method Using Redundant Binary Representation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "1",
  pages =        "43--51",
  month =        jan,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.250608",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:13:53 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=250608",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "Proposes a new algorithm of estimation and
                 compensation of the error effect for rounding in the
                 case of implementation of division and square root
                 using the Newton--Raphson method. The authors analyze
                 the error of the hardware system to confirm the
                 \ldots{}",
}

@Article{Kalliojarvi:1994:RCW,
  author =       "K. Kalliojarvi and J. Astola",
  title =        "Required coefficient word length in floating-point and
                 logarithmic digital filters",
  journal =      j-IEEE-SIGNAL-PROCESS-LETT,
  volume =       "1",
  number =       "3",
  pages =        "52--54",
  month =        mar,
  year =         "1994",
  CODEN =        "ISPLEM",
  ISSN =         "1070-9908 (print), 1558-2361 (electronic)",
  ISSN-L =       "1070-9908",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Signal Processing Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=97",
  summary =      "The effects of coefficient quantization to the
                 response of a digital filter are studied. Easy-to-use
                 expressions for the required coefficient word length,
                 with which the filter response deviations are within
                 specified bounds, are derived for filters \ldots{}",
}

@MastersThesis{Kambi:1994:EAD,
  author =       "Shivaprakash Jayadev Kambi",
  title =        "Error analysis of digital filters realized with
                 floating-point arithmetic",
  type =         "Thesis ({M.S.})",
  school =       "Mississippi State University. Department of Electrical
                 and Computer Engineering",
  address =      "Mississippi State, MS 39762, USA",
  pages =        "viii + 82",
  year =         "1994",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Digital filters (Mathematics); Electric filters,
                 Digital.; Floating-point arithmetic.; Mississippi State
                 University --- Thesis --- (1994)",
}

@InProceedings{Kanellakis:1994:FPR,
  author =       "A. Kanellakis and P. Agathoklis",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems: {ISCAS '94}, 2 June 1994",
  title =        "Floating-point roundoff noise analysis of {$2$-D}
                 state-space digital filters",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "601--604",
  year =         "1994",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "In this paper the analysis of roundoff noise in
                 floating point state-space realizations of $2$-D
                 digital filters is considered. The variance of the
                 roundoff noise at the output of a $2$-D digital filter
                 is derived. It is shown that this variance is
                 \ldots{}",
}

@Misc{Karp:1994:FPA,
  author =       "Alan H. Karp and Peter Markstein and Dennis
                 Brzezinski",
  title =        "Floating point arithmetic unit using modified
                 {Newton--Raphson} technique for division and square
                 root",
  howpublished = "US Patent 5,341,321",
  day =          "23",
  month =        aug,
  year =         "1994",
  bibdate =      "Thu Oct 17 10:20:52 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Patent filed 5 May 1993, granted to Hewlett-Packard
                 Company on 23 August 1994. Patent expired 5-May-2013.
                 See criticism in \cite{Zimmermann:2005:XXX}.",
  URL =          "http://patft.uspto.gov/netahtml/PTO/search-bool.html;
                 https://patents.google.com/patent/US5341321A",
  abstract =     "A floating point processing system which uses a
                 multiplier unit and an adder unit to perform floating
                 point division and square root operations using both a
                 conventional and a modified form of the Newton--Raphson
                 method. The modified form of the Newton--Raphson method
                 is used in place of the final iteration of the
                 conventional Newton--Raphson so as to compute high
                 precision approximated results with a substantial
                 improvement in speed. The invention computes
                 approximated results faster and simplifies hardware
                 requirements because no multiplications of numbers of
                 the precision of the result are required.",
  acknowledgement = ack-nhfb,
}

@Article{Katti:1994:CDC,
  author =       "R. Katti",
  title =        "Comments on {``Decomposition of Complex Multipliers
                 Using Polynomial Encoding''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "3",
  pages =        "381--383",
  month =        mar,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.272441",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:13:54 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  note =         "See \cite{Skavantzos:1992:DCM}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=272441",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Kawahito:1994:HSA,
  author =       "S. Kawahito and M. Ishida and T. Nakamura and M.
                 Kameyama and T. Higuchi",
  title =        "High-speed area-efficient multiplier design using
                 multiple-valued current-mode circuits",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "1",
  pages =        "34--42",
  month =        jan,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.250607",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:13:53 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  note =         "See comments \cite{Parhami:1996:CHS}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=250607",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Kim:1994:FPF,
  author =       "Seehyun Kim and Wonyong Sung",
  title =        "A Floating-Point to Fixed-Point Assembly Program
                 Translator for the {TMS} {320C25}",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "41",
  number =       "11",
  pages =        "730--739",
  month =        nov,
  year =         "1994",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.331543",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems. 2, Analog
                 and Digital Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  summary =      "A floating-point digital signal processor-like
                 programming environment is developed for the Texas
                 Instruments TMS 320C25, a fixed-point digital signal
                 professor. Programmers first develop an assembly
                 program using a hypothetical floating-point instrument
                 \ldots{}",
}

@Article{Kobbelt:1994:FDP,
  author =       "L. Kobbelt",
  title =        "A Fast Dot-Product Algorithm with Minimal Rounding
                 Errors",
  journal =      j-COMPUTING,
  volume =       "52",
  number =       "4",
  pages =        "355--369",
  year =         "1994",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "68Q20 (68Q25)",
  MRnumber =     "1 287 970",
  bibdate =      "Tue Oct 12 16:33:42 MDT 1999",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database; OCLC Contents1st database",
  abstract =     "Presents a new algorithm which computes dot-products
                 of arbitrary length with minimal rounding errors,
                 independent of the number of addends. The algorithm has
                 an O(n) time and O(1) memory complexity, and does not
                 need extensions of the arithmetic kernel, i.e., the
                 usual floating-point operations. A slight modification
                 yields an algorithm which computes the dot-product in
                 machine precision. Due to its simplicity, the algorithm
                 can easily be implemented in hardware.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. f{\"u}r Betriebs-und Dialogsyst., Karlsruhe
                 University, Germany",
  classification = "721.1; 722.4; 921.1; 921.6; C4140 (Linear algebra);
                 C4240 (Programming and algorithm theory); C5230
                 (Digital arithmetic methods)",
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Comput Vienna New York",
  keywords =     "Addends; Algorithms; Arbitrary length; Arithmetic
                 kernel; Computational complexity; Computer arithmetic;
                 Computer hardware; Digital arithmetic; Dot product
                 computation; Errors; Exact computer arithmetic; Fast
                 dot-product algorithm; Floating-point operations;
                 Hardware implementation; Machine precision; Matrix
                 algebra; Matrix multiplications; Memory complexity;
                 Minimal rounding errors; Numerical algorithms;
                 Numerical methods; Stability; Summation; Time
                 complexity",
  pubcountry =   "Austria",
  thesaurus =    "Computational complexity; Digital arithmetic; Matrix
                 algebra; Numerical analysis; Roundoff errors; Vectors",
}

@Article{Kornerup:1994:SLA,
  author =       "P. Kornerup",
  title =        "A Systolic, Linear-Array Multiplier for a Class of
                 Right-Shift Algorithms",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "8",
  pages =        "892--898",
  month =        aug,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.295851",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:13:57 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib;
                 OCLC Proceedings database",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=295851",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  remark =       "Selected revised and extended papers from ARITH'11
                 \cite{Swartzlander:1993:SCA}.",
}

@InProceedings{Krandick:1994:EMF,
  author =       "W. Krandick and J. R. Johnson",
  title =        "Efficient multiprecision floating point multiplication
                 with exact rounding",
  crossref =     "Calmet:1994:RWC",
  pages =        "207--??",
  year =         "1994",
  bibdate =      "Thu Dec 14 11:25:18 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "An algorithm is described for multiplying
                 multiprecision floating point numbers. The returned
                 result is equal to the floating point number obtained
                 by rounding the exact product. Software implementations
                 of multiprecision floating point multiplication can
                 reduce the computing time by a factor of two if they do
                 not compute the low order digits of the product of the
                 two mantissas. However, these algorithms do not
                 necessarily provide exactly rounded results. The
                 algorithm described in this paper is guaranteed to
                 produce exactly rounded results and typically obtains
                 the same savings. The method can be modified to take
                 advantage of Karatsuba's algorithm for fast integer
                 multiplication.",
  acknowledgement = ack-nhfb,
  affiliation =  "Res. Inst. for Symbolic Comput., Johannes Kepler
                 University, Linz, Austria",
  classification = "C5230 (Digital arithmetic methods); C7310
                 (Mathematics computing)",
  keywords =     "Exact rounding; Fast integer multiplication;
                 Karatsuba's algorithm; Multiprecision floating point
                 multiplication; Software implementations",
  thesaurus =    "Digital arithmetic; Mathematics computing",
}

@Article{Laakso:1994:BFP,
  author =       "T. I. Laakso and L. B. Jackson",
  title =        "Bounds for Floating-Point Roundoff Noise",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "41",
  number =       "6",
  pages =        "424--426",
  month =        jun,
  year =         "1994",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.300204",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems. 2, Analog
                 and Digital Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  summary =      "The dummy multiplier model and the conventional
                 estimates for roundoff noise variance in floating-point
                 implementations are compared. Common upper and lower
                 bounds for the noise estimates are derived and
                 experimental results are presented. Although \ldots{}",
}

@Article{Laakso:1994:ELC,
  author =       "T. Laakso and B. Zeng and I. Hartimo and Y. Neuvo",
  title =        "Elimination of limit cycles in floating-point
                 implementations of direct-form recursive digital
                 filters",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "41",
  number =       "4",
  pages =        "308--313",
  month =        apr,
  year =         "1994",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.285707",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems. 2, Analog
                 and Digital Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  summary =      "This paper focuses on the limit cycle analysis of
                 floating-point implementations of direct form recursive
                 digital filters. A sufficient criterion for the absence
                 of zero-input limit cycles is derived for a direct-form
                 implementation with a single \ldots{}",
}

@Article{Ledoux:1994:TOW,
  author =       "C. Ledoux and J. F. Grandin",
  title =        "Two original weight pruning methods based on
                 statistical tests and rounding techniques",
  journal =      "Vision, Image and Signal Processing, IEE
                 Proceedings-",
  volume =       "141",
  number =       "4",
  pages =        "230--237",
  month =        aug,
  year =         "1994",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:03 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The authors focus on the use of neural networks to
                 approximate continuous decision functions. In this
                 context, the parameters to be estimated are the
                 synaptic weights of the network. The number of such
                 parameters and the quantity of data \ldots{}",
}

@Article{Lewis:1994:IMF,
  author =       "D. M. Lewis",
  title =        "Interleaved Memory Function Interpolators with
                 Application to an Accurate {LNS} Arithmetic Unit",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "8",
  pages =        "974--982",
  month =        aug,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.295859",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:13:57 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib;
                 OCLC Proceedings database",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=295859",
  abstract =     "This paper describes a new method for polynomial
                 interpolation in hardware, with advantages demonstrated
                 by its application to an accurate logarithmic number
                 system (LNS) arithmetic unit. The use of an interleaved
                 memory reduces storage requirements by allowing each
                 stored function value to be used in interpolation
                 across several segments. This strategy can be shown to
                 always use fewer words of memory than an optimized
                 polynomial with stored polynomial coefficients.
                 Interleaved memory function interpolators are then
                 applied to the specific goal of an accurate logarithmic
                 number system arithmetic unit. Many accuracy
                 requirements for the LNS arithmetic unit are possible.
                 Although a round to nearest would be desirable, it
                 cannot be easily achieved. The goal suggested is to
                 insure that the worst case LNS relative error is
                 smaller than the worst case floating point (FP)
                 relative error. Using the interleaved memory
                 interpolator, the detailed design of an LNS arithmetic
                 unit is performed using a second order polynomial
                 interpolator including approximately 91K bits of ROM.
                 This arithmetic unit has better accuracy and less
                 complexity than previous LNS units.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Electr. and Comput. Eng., Toronto
                 University, Ont., Canada",
  ajournal =     "IEEE Trans. Comput.",
  classification = "C4110 (Error analysis in numerical methods); C4130
                 (Interpolation and function approximation); C5230
                 (Digital arithmetic methods); C5320G (Semiconductor
                 storage)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "32 Bit; 91 Kbit; Accuracy requirements; Accurate
                 logarithmic number system (LNS) arithmetic unit;
                 Floating point; Interleaved memory function
                 interpolators; Polynomial interpolation; ROM; Round to
                 nearest; Storage requirements",
  numericalindex = "Word length 3.2E+01 bit; Storage capacity 9.3E+04
                 bit",
  remark =       "Selected revised and extended papers from ARITH'11
                 \cite{Swartzlander:1993:SCA}.",
  summary =      "This paper describes a new method for polynomial
                 interpolation in hardware, with advantages demonstrated
                 by its application to an accurate logarithmic number
                 system (LNS) arithmetic unit. The use of an interleaved
                 memory reduces storage requirements \ldots{}",
  thesaurus =    "Approximation theory; Digital arithmetic; Error
                 analysis; Interpolation; Polynomials; Read-only
                 storage",
}

@Article{Lo:1994:RFP,
  author =       "Jien-Chung Lo",
  title =        "Reliable Floating-Point Arithmetic Algorithms for
                 Error-Coded Operands",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "4",
  pages =        "400--412",
  month =        apr,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.278479",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:13:55 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=278479",
  abstract =     "Reliable floating-point arithmetic is vital for
                 dependable computing systems. It is also important for
                 future high-density VLSI realizations that are
                 vulnerable to soft-errors. However, the direct checking
                 of floating-point arithmetic is still an open problem.
                 The author presents a set of reliable floating-point
                 arithmetic algorithms for low-cost residue encoded and
                 Berger encoded operands, respectively. Closed form
                 equations are derived for floating-point addition,
                 subtraction, multiplication, and division. Given the
                 standard IEEE floating-point numbers, the proposed
                 reliable floating-point multiplication algorithms for
                 low-cost residue encoded operands are extremely
                 low-cost: it requires less than 8\% of hardware
                 redundancy in all cases. For reliable floating-point
                 addition and subtraction, the author finds the hardware
                 redundancy ratios of applying low-cost residue code is
                 about the same as that of applying Berger code: less
                 than 40\% of hardware redundancy for single precision
                 numbers and about 16\% for double precision numbers.
                 For reliable floating-point division, Berger encoded
                 operands yields hardware cost-effectiveness: about 45\%
                 for single precision numbers and about 36\% for double
                 precision numbers.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Electr. Eng., Rhode Island University,
                 Kingston, RI, USA",
  ajournal =     "IEEE Trans. Comput.",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Berger check prediction; Berger encoded; Computer
                 arithmetic; Concurrent error detection; Error-coded
                 operands; Floating-point arithmetic; Hardware
                 redundancy; High-density VLSI; Low-cost residue codes;
                 Redundancy ratios; Reliable floating-point
                 multiplication; Residue encoded; Soft-errors; Standard
                 IEEE floating-point numbers",
  summary =      "Reliable floating-point arithmetic is vital for
                 dependable computing systems. It is also important for
                 future high-density VLSI realizations that are
                 vulnerable to soft-errors. However, the direct checking
                 of floating-point arithmetic is still an open
                 \ldots{}",
  thesaurus =    "Digital arithmetic; Error correction codes;
                 Redundancy",
}

@Book{May:1994:PAS,
  editor =       "Cathy May and Ed Silha and Rick Simpson and Hank
                 Warren",
  title =        "The {PowerPC} Architecture: a Specification for a New
                 Family of {RISC} Processors",
  publisher =    pub-MORGAN-KAUFMANN,
  address =      pub-MORGAN-KAUFMANN:adr,
  edition =      "Second",
  pages =        "xxxi + 518",
  year =         "1994",
  ISBN =         "1-55860-316-6",
  ISBN-13 =      "978-1-55860-316-5",
  LCCN =         "QA76.8.P67 P68 1994",
  bibdate =      "Sat Feb 24 10:55:16 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/microchip.bib",
  price =        "US\$49.95",
  acknowledgement = ack-nhfb,
  oldlabel =     "IBM:1994:PAS",
  tableofcontents = "Book III. PowerPC Operating Environment
                 Architecture \\
                 2. Branch Processor \\
                 3. Fixed-Point Processor \\
                 4. Storage Control \\
                 5. Interrupts \\
                 6. Timer Facilities \\
                 7. Synchronization Requirements for Special Registers
                 and for Lookaside Buffers \\
                 Appendix A. Optional Facilities and Instructions \\
                 Appendix B. Assembler Extended Mnemonics \\
                 Appendix C. Cross-Reference for Changed POWER Mnemonics
                 \\
                 Appendix D. New Instructions \\
                 Appendix E. Implementation-Specific SPRs \\
                 Appendix F. Interpretation of the DSISR as Set by an
                 Alignment Interrupt \\
                 Appendix G. PowerPC Operating Environment Instruction
                 Set",
}

@Article{McGrath:1994:OMC,
  author =       "Gary McGrath",
  title =        "Optimizing {MC68882} Code",
  journal =      j-DDJ,
  volume =       "19",
  number =       "6",
  pages =        "58, 60, 62, 64, 66, 98--99",
  month =        jun,
  year =         "1994",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Tue Sep 03 09:15:49 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 UnCover database",
  abstract =     "The MC68882 floating-point coprocessor adds 46
                 instructions to the MC68020/030 32-bit microprocessor,
                 substantially increasing the speed of floating-point
                 calculations. Gary examines these instructions and
                 finds certain combinations to be faster than others.",
  acknowledgement = ack-nhfb,
  affiliation =  "Stanford Linear Accel. Center, Stanford University,
                 CA, USA",
  classification = "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5220P (Parallel architecture);
                 C5230 (Digital arithmetic methods)",
  fjournal =     "Dr. Dobb's Journal of Software Tools",
  keywords =     "32 Bit; 80 Bit; 80-Bit extended precision; ANSI-IEEE
                 754-1985 binary floating-point arithmetic standard;
                 FPCP; MC68020 microprocessor; MC68030 microprocessor;
                 MC68882 floating-point coprocessor; Optimizing MC68882
                 code; Parallel operation; Pipeline architecture",
  thesaurus =    "Digital arithmetic; Microprocessor chips; Parallel
                 processing; Pipeline processing; Satellite computers",
}

@Article{Meek:1994:PLT,
  author =       "Brian L. Meek",
  title =        "Programming languages: towards greater commonality",
  journal =      j-SIGPLAN,
  volume =       "29",
  number =       "4",
  pages =        "49--57",
  month =        apr,
  year =         "1994",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:16:49 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C6110 (Systems analysis and programming); C6140
                 (Programming languages)",
  corpsource =   "Comput. Centre, King's Coll., London, UK",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "cross-language standardisation; JTC1; language
                 independent arithmetic; language independent calling;
                 language independent datatypes; language independent
                 procedure calling; language independent standards;
                 language standardisation; OSI; programming; programming
                 guidelines; programming languages; programming
                 languages commonality; programming languages
                 differences; remote procedure calling; remote procedure
                 calls; SC22; standardisation; standards; subcommittee;
                 working group",
  treatment =    "G General Review",
}

@InProceedings{Mehlhorn:1994:IGA,
  author =       "Kurt Mehlhorn and Stefan Naher",
  title =        "The Implementation of Geometric Algorithms",
  crossref =     "Pehrson:1994:IPP",
  volume =       "1",
  pages =        "223--231",
  year =         "1994",
  bibdate =      "Tue Nov 13 21:47:31 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Montgomery:1994:SRP,
  author =       "Peter L. Montgomery",
  title =        "Square roots of products of algebraic numbers",
  crossref =     "Gautschi:1994:MCH",
  pages =        "567--571",
  year =         "1994",
  bibdate =      "Thu Oct 25 14:53:00 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Montuschi:1994:DUN,
  author =       "P. Montuschi and L. Ciminiera and A. Giustina",
  title =        "Division unit with {Newton--Raphson} approximation and
                 digit-by-digit refinement of the quotient",
  journal =      j-IEE-PROC-COMPUT-DIGIT-TECH,
  volume =       "141",
  number =       "6",
  pages =        "317--324",
  month =        nov,
  year =         "1994",
  CODEN =        "ICDTEA",
  ISSN =         "1350-2387 (print), 1359-7027 (electronic)",
  ISSN-L =       "1350-2387",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The advantages of the convergence with the square of
                 the Newton--Raphson method are combined with the
                 precision characteristics of digit-by-digit algorithms
                 to obtain units for fast division that satisfy the IEEE
                 754 floating point standard requirements. A general
                 design methodology that leads to a class of alternative
                 architectures providing interesting performances for
                 division is presented, together with one example of
                 possible implementation. In particular, the proposed
                 implementation achieves a speedup varying from 20\% to
                 about 30\% in comparison with a previous architecture
                 by Fandrianto, with a relatively small additional
                 hardware cost if a multiplier is already available on
                 the arithmetic unit.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dipartimento di Autom. e Inf., Politecnico di Torino,
                 Italy",
  classification = "C4130 (Interpolation and function approximation);
                 C5120 (Logic and switching circuits); C5230 (Digital
                 arithmetic methods)",
  fjournal =     "IEE Proceedings. Computers and Digital Techniques",
  keywords =     "Convergence; Digit-by-digit refinement; Fast division;
                 Floating point standard; Newton--Raphson
                 approximation",
  pubcountry =   "UK",
  thesaurus =    "Dividing circuits; Floating point arithmetic;
                 Newton--Raphson method",
}

@Article{Montuschi:1994:RDO,
  author =       "P. Montuschi and L. Ciminiera",
  title =        "Radix-8 division with over-redundant digit set",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "7",
  number =       "3",
  pages =        "259--270",
  month =        may,
  year =         "1994",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1007/BF02409402",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present a radix-8 divider that uses an
                 over-redundant digit set for the quotient in order to
                 obtain simple digit selection rules. We show that the
                 proposed enlarged set of values for the quotient digit
                 does not lead to increases both in the complexity and
                 the delay of the adder required to update the
                 remainder, with respect to similar solutions, since the
                 values allowed for the quotient digit have been
                 selected carefully. The digit selection process is
                 subdivided into two concurrent steps, each one making
                 reference to a secondary digit set and the resulting
                 implementation can be cheaper and faster than other
                 units which do not use over-redundant digit sets. A
                 performance analysis estimates a speed improvement from
                 25\% to 35\% with respect to a radix-8 architecture by
                 Fandrianto (1987, 1989), and from 21\% to 30\% with
                 respect to a radix-4 architecture with prescaling,
                 presented by Ercegovac and Lang (1990). As required
                 from the IEEE 754 floating point standard, the proposed
                 algorithm features the correct remainder of the
                 division.",
  acknowledgement = ack-nhfb,
  affiliation =  "Dipartimento di Autom. e Inf., Politecnico di Torino,
                 Italy",
  classification = "B1265B (Logic circuits); C5120 (Logic and switching
                 circuits); C5230 (Digital arithmetic methods)",
  fjournal =     "Journal of VLSI Signal Processing",
  keywords =     "Algorithm; Delay; Digit selection rules; IEEE 754
                 floating point standard; Over-redundant digit set;
                 Performance analysis; Quotient; Radix-8 divider;
                 Radix-8 division; Remainder; Speed improvement",
  pubcountry =   "Netherlands",
  thesaurus =    "Digital arithmetic; Dividing circuits",
}

@Article{Montuschi:1994:RDS,
  author =       "P. Montuschi and L. Ciminiera",
  title =        "Over-redundant digit sets and the design of
                 digit-by-digit division units",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "3",
  pages =        "269--277",
  month =        mar,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.272428",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:13:54 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=272428",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Muller:1994:SCF,
  author =       "Jean-Michel Muller",
  title =        "Some characterizations of functions computable in
                 on-line arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "6",
  pages =        "752--755",
  month =        jun,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.286308",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:13:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=286308",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Murofushi:1994:RBR,
  author =       "Makoto Murofushi and Hideko Nagasaka",
  title =        "The relationship between the round-off errors and
                 {M{\o}ller}'s algorithm in the extrapolation method",
  journal =      j-ANN-NUM-MATH,
  volume =       "1",
  number =       "1--4",
  pages =        "451--458",
  year =         "1994",
  ISSN =         "1021-2655",
  ISSN-L =       "1021-2655",
  MRclass =      "65L05 (65L70)",
  MRnumber =     "1340673",
  MRreviewer =   "Haydar Ak{\c{c}}a",
  bibdate =      "Sat Feb 08 09:16:09 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Scientific computation and differential equations
                 (Auckland, 1993).",
  acknowledgement = ack-nhfb,
  ajournal =     "Ann. Numer. Math.",
  fjournal =     "Annals of Numerical Mathematics",
}

@InProceedings{Nakamura:1994:EPV,
  author =       "H. Nakamura and H. Imori and Y. Yamashita and K.
                 Nakazawa and T. Boku and H. Li and I. Nakata",
  title =        "Evaluation of pseudo vector processor based on
                 slide-windowed registers",
  crossref =     "Mudge:1994:PTS",
  pages =        "368--377",
  year =         "1994",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present a new scalar processor for high-speed
                 vector processing and its evaluation. The proposed
                 processor can hide long main memory access latency by
                 introducing slide-windowed floating-point registers
                 with data preloading feature and pipelined memory.
                 Owing to the slide-window structure, the proposed
                 processor can utilize more floating-point registers in
                 keeping upward compatibility with existing scalar
                 architecture. We have evaluated its performance on
                 Livermore Fortran Kernels. The evaluation results show
                 that the proposed processor drastically reduces the
                 penalty of main memory access compared with an ordinary
                 scalar processor. For example, the proposed processor
                 with 96 registers hides memory access latency of 70 CPU
                 cycles when the throughput of main memory is 8
                 byte/cycle. From these results, it is concluded that
                 the proposed architecture is very suitable for
                 high-speed vector processing.",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. of Inf. Sci. and Electron., Tsukuba University,
                 Ibaraki, Japan",
  classification = "C5220P (Parallel architecture); C5440
                 (Multiprocessor systems and techniques); C5470
                 (Performance evaluation and testing)",
  keywords =     "Data preloading feature; Floating-point registers;
                 High-speed vector processing; Livermore Fortran
                 Kernels; Performance; Pipelined memory; Pseudo vector
                 processor; Scalar processor; Slide-windowed registers",
  thesaurus =    "FORTRAN; Performance evaluation; Vector processor
                 systems",
}

@Article{Narayanaswami:1994:AE,
  author =       "Chandrasekhar Narayanaswami and William Luken",
  title =        "Approximating $ x^n $ efficiently",
  journal =      j-INFO-PROC-LETT,
  volume =       "50",
  number =       "4",
  pages =        "205--210",
  day =          "25",
  month =        may,
  year =         "1994",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  MRclass =      "65D20 (41-04 65B99)",
  MRnumber =     "95b:65031",
  bibdate =      "Wed Nov 11 12:16:26 MST 1998",
  bibsource =    "Compendex database;
                 http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Advanced Workstations and Systems Div",
  affiliationaddress = "Austin, TX, USA",
  classification = "721.1; 723.2; 723.5; 741.2; 921.1; 921.6; B0290F
                 (Interpolation and function approximation); C4130
                 (Interpolation and function approximation); C6130B
                 (Graphics techniques)",
  corpsource =   "IBM Adv. Workstations and Syst. Div., Austin, TX,
                 USA",
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  journalabr =   "Inf Process Lett",
  keywords =     "$x^n$ approximation; approximation theory;
                 Approximation theory; Color computer graphics;
                 Computational complexity; Computational methods;
                 computer graphics; elementary functions; floating-point
                 arithmetic; Function evaluation; graphics modeling;
                 Image quality; Light intensity computation; look-up
                 tables; performance requirements; Polynomial
                 evaluation; Polynomials; polynomials; power function;
                 scientific applications; Semiconducting silicon; Table
                 lookup",
  treatment =    "T Theoretical or Mathematical",
}

@MastersThesis{Nedialkov:1994:PCE,
  author =       "Nedialko (Ned) Stoyanov Nedialkov",
  title =        "Precision Control and Exception Handling in Scientific
                 Computing",
  type =         "{M.Sc.} Thesis",
  school =       "Department of Computer Science, University of
                 Toronto",
  address =      "Toronto, ON, Canada",
  pages =        "51",
  year =         "1994",
  bibdate =      "Tue May 22 15:44:16 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.toronto.edu/NA/reports.html#ned-94-msc;
                 http://www.cs.toronto.edu/pub/reports/na/ned-94-msc.ps.Z",
  acknowledgement = ack-nhfb,
}

@MastersThesis{Niescier:1994:DIC,
  author =       "Richard J. Niescier",
  title =        "Design of an {IEEE} compliant 32-bit floating point
                 multiplier\slash accumulator",
  type =         "Thesis ({M.S.})",
  school =       "Lehigh University",
  address =      "Bethlehem, PA, USA",
  pages =        "vii + 94",
  year =         "1994",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Floating-point arithmetic.; Microprocessors.",
}

@MastersThesis{Novak:1994:AFP,
  author =       "Joseph Herschel Novak",
  title =        "An asynchronous floating point unit",
  type =         "Thesis ({M.S.})",
  school =       "Department of Computer Science, University of Utah",
  address =      "Salt Lake City, UT, USA",
  pages =        "xi + 151",
  year =         "1994",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Asynchronous circuits.; Computers --- Circuits.;
                 Floating-point arithmetic.",
}

@TechReport{Oberman:1994:DIH,
  author =       "S. Oberman and N. Quach and M. Flynn",
  title =        "The design and implementation of a high-performance
                 floating-point divider",
  type =         "Technical Report",
  number =       "CSL-TR-94-599",
  institution =  "Computer Systems Laboratory, Stanford University",
  address =      "Stanford, CA, USA",
  month =        jan,
  year =         "1994",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}

@InProceedings{Oh:1994:IPDa,
  author =       "S. Oh and D. Garcia",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing. {ICASSP-94, 19--22} April 1994",
  title =        "Implementation of a parallel {DFE} using residue
                 number system",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "III/237--III/240",
  year =         "1994",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICASSP.1994.390024",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A parallel decision feedback equalizer (DFE)
                 implementation using residue number system (RNS) is
                 considered When the DFE implementation for a system
                 requires a wide input data width and high sampling
                 rates, RNS provides a speed advantage over \ldots{}",
}

@InProceedings{Oh:1994:IPDb,
  author =       "S. Oh and D. Garcia",
  booktitle =    "{IEEE} International Conference on Acoustics, Speech,
                 and Signal Processing. {ICASSP-94, 19--22} April 1994",
  title =        "Implementation of a parallel {DFE} using residue
                 number system",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "III/237--III/240",
  year =         "1994",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICASSP.1994.390024",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A parallel decision feedback equalizer (DFE)
                 implementation using residue number system (RNS) is
                 considered When the DFE implementation for a system
                 requires a wide input data width and high sampling
                 rates, RNS provides a speed advantage over \ldots{}",
}

@Article{Ohta:1994:INP,
  author =       "S. Ohta and E. Goto and Weng Fai Wong and N. Yoshida",
  title =        "Improvement and new proposal on fast evaluation of
                 elementary functions",
  journal =      j-TRANS-INFO-PROCESSING-SOC-JAPAN,
  volume =       "35",
  number =       "5",
  pages =        "926--933",
  month =        may,
  year =         "1994",
  CODEN =        "JSGRD5",
  ISSN =         "0387-5806",
  ISSN-L =       "0387-5806",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Wong, Gore, and Yoshida (ibid., vol. 34, no. 7, pp.
                 1570-1579, 1993) introduced fast methods for numerical
                 evaluation of elementary functions based on table
                 lookup. They are called ATA (add/table-lookup/add) and
                 ATA-M (add/table-lookup/add and multiply) methods for
                 single- and double-precision calculations respectively.
                 In this paper, an improvement to these methods that
                 shrinks the size of the table by a factor of about 3/16
                 is presented. Another method called the `split parallel
                 multiplication method', which is characterized by
                 simpler table lookup than ATA-M and by split and
                 parallel use of double-precision floating point
                 circuitry, is also introduced, These new methods fit on
                 to integrated circuits of a size comparable with
                 commercially available floating-point accelerators.
                 Methods for accelerating double-precision division,
                 generating uniform pseudo-random numbers in
                 double-precision, and accelerating the multiplication
                 of single-precision complex numbers using the same
                 circuitry are proposed.",
  acknowledgement = ack-nhfb,
  affiliation =  "RIKEN, Inst. of Phys. and Chem. Res., Saitama, Japan",
  classification = "C4120 (Functional analysis); C5230 (Digital
                 arithmetic methods); C6130 (Data handling techniques)",
  fjournal =     "Transactions of the Information Processing Society of
                 Japan",
  keywords =     "Add/table-lookup/add method;
                 Add/table-lookup/add/multiply method; ATA method; ATA-M
                 method; Double-precision calculations; Double-precision
                 division; Double-precision floating point circuitry;
                 Elementary functions evaluation; Floating-point
                 accelerators; Integrated circuits; Numerical
                 evaluation; Single-precision calculations;
                 Single-precision complex number multiplication; Split
                 parallel multiplication method; Table size; Uniform
                 pseudo-random number generation",
  language =     "Japanese",
  pubcountry =   "Japan",
  thesaurus =    "Digital arithmetic; Function evaluation; Random number
                 generation; Table lookup",
}

@Book{Omondi:1994:CAS,
  author =       "Amos R. Omondi",
  title =        "Computer Arithmetic Systems: Algorithms, Architecture,
                 and Implementation",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xvi + 520",
  year =         "1994",
  ISBN =         "0-13-334301-4",
  ISBN-13 =      "978-0-13-334301-4",
  LCCN =         "QA76.9.C62 O46 1994",
  bibdate =      "Sat Dec 09 11:57:03 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\$40.00",
  acknowledgement = ack-nhfb,
  tableofcontents = "Preface \\
                 Preliminary notes \\
                 Fixed-point number systems / 3 \\
                 Fixed-point addition and subtraction / 13 \\
                 Fixed-point multiplication / 119 \\
                 Fixed-point division / 192 \\
                 Floating-point number systems and arithmetic / 293 \\
                 Basic floating-point operations: implementation / 345
                 \\
                 Elementary functions / 371 \\
                 Unconventional number systems and arithmetic / 439 \\
                 Bibliography / 469 \\
                 Appendix A: Pipelining / 489 \\
                 Appendix B: Design of shifters / 505 \\
                 Index / 514",
}

@Article{Ooyama:1994:CSC,
  author =       "M. Ooyama and H. Hamada",
  title =        "A circuit to separate and to connect the exponent part
                 and the mantissa part for {URR} floating point
                 arithmetic and its application to a {URR} processor",
  journal =      j-TRANS-INFO-PROCESSING-SOC-JAPAN,
  volume =       "35",
  number =       "8",
  pages =        "1642--1651",
  month =        aug,
  year =         "1994",
  CODEN =        "JSGRD5",
  ISSN =         "0387-5806",
  ISSN-L =       "0387-5806",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "To overcome overflows and underflows in computation,
                 several new floating-point arithmetics have been
                 proposed. But in these new arithmetics, a boundary
                 between the exponent part and the mantissa part moves
                 according to the exponent value and data formats are
                 usually more complicated. So, fast separation and
                 connection of the exponent and the mantissa is a key
                 technology to achieve fast computation of these new
                 arithmetics. In this paper, a circuit scheme to
                 separate and connect the exponent and the mantissa for
                 URR floating-point arithmetic based on double
                 exponential cut is presented. To separate the exponent
                 from the mantissa, this circuit scheme firstly detects
                 the boundary and the position is encoded to a short
                 code. Then barrel shifters, logical operation circuits,
                 and bit pattern generators controlled by the code
                 separate the exponent and the mantissa from URR. To
                 form URR from the exponent and the mantissa, a number
                 of bits of the exponent is counted and encoded to a
                 short code. The boundary can be settled by this code,
                 and using the same circuits controlled by the code, the
                 exponent part and the mantissa part are generated and
                 combined into URR. To achieve fast execution, these
                 processes are executed by the combination logic
                 circuits in bit parallel manner and meet to pipelined
                 architectures. We applied this circuit scheme to an
                 experimental 64 bits URR processor and verified its
                 realization. Its performance was also evaluated. (11
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "Central Res. Lab., Hitachi Ltd., Tokyo, Japan",
  classification = "B1265B (Logic circuits); C5120 (Logic and switching
                 circuits); C5220P (Parallel architecture); C5230
                 (Digital arithmetic methods)",
  fjournal =     "Transactions of the Information Processing Society of
                 Japan",
  keywords =     "64 Bit; Barrel shifters; Bit parallel processing; Bit
                 pattern generators; Combination logic circuits; Double
                 exponential cut; Exponent part; Logical operation
                 circuits; Mantissa part; Pipelined architectures; URR
                 floating point arithmetic; URR processor",
  language =     "Japanese",
  numericalindex = "Word length 6.4E+01 bit",
  pubcountry =   "Japan",
  thesaurus =    "Combinatorial circuits; Digital arithmetic; Parallel
                 processing; Pipeline processing",
}

@InProceedings{Paliouras:1994:SDMa,
  author =       "V. Paliouras and T. Stouraitis",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, {ISCAS '94}, 2 June 1994",
  title =        "Systematic design of multi-modulus\slash
                 multi-function {Residue Number System} processors",
  volume =       "4",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "79--82",
  year =         "1994",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1994.409201",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A methodology for the design of novel Residue Number
                 System (RNS) processors is presented. It results in
                 ROM-less processors, which perform basic residue
                 arithmetic algorithms in more than one moduli channel,
                 either serially or concurrently. \ldots{}",
}

@InProceedings{Paliouras:1994:SDMb,
  author =       "V. Paliouras and T. Stouraitis",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, {ISCAS '94}, 2 June 1994",
  title =        "Systematic design of multi-modulus\slash
                 multi-function {Residue Number System} processors",
  volume =       "4",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "79--82",
  year =         "1994",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1994.409201",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A methodology for the design of novel Residue Number
                 System (RNS) processors is presented. It results in
                 ROM-less processors, which perform basic residue
                 arithmetic algorithms in more than one moduli channel,
                 either serially or concurrently. \ldots{}",
}

@InProceedings{Parhami:1994:OTLa,
  author =       "B. Parhami and C. Y. Hung",
  booktitle =    "Workshop on {VLSI} Signal Processing, {VII, 1994}",
  title =        "Optimal table lookup schemes for {VLSI} implementation
                 of input\slash output conversions and other residue
                 number operations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "470--481",
  year =         "1994",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/VLSISP.1994.574771",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Residue number representation has become a viable
                 alternative for fast, area-efficient VLSI realization
                 of high-performance signal processing hardware. Wider
                 applicability and improved cost/performance of
                 residue-based VLSI implementations of signal \ldots{}",
}

@InProceedings{Parhami:1994:OTLb,
  author =       "B. Parhami and C. Y. Hung",
  booktitle =    "Workshop on {VLSI} Signal Processing, {VII, 1994}",
  title =        "Optimal table lookup schemes for {VLSI} implementation
                 of input\slash output conversions and other residue
                 number operations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "470--481",
  year =         "1994",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/VLSISP.1994.574771",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Residue number representation has become a viable
                 alternative for fast, area-efficient VLSI realization
                 of high-performance signal processing hardware. Wider
                 applicability and improved cost/performance of
                 residue-based VLSI implementations of signal \ldots{}",
}

@InProceedings{Parker:1994:FTLa,
  author =       "M. G. Parker and M. Benaissa",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, {ISCAS '94}, 2 June 1994",
  title =        "Fault-tolerant linear convolution using residue number
                 systems",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "441--444",
  year =         "1994",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1994.408997",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper proposes a fault-tolerant linear
                 convolution architecture using Residue Number Systems
                 (RNS) and Polynomial Residue Number Systems (PRNS). The
                 RNS and PRNS are both given error-detection capability
                 by the addition of redundant residue \ldots{}",
}

@InProceedings{Parker:1994:FTLb,
  author =       "M. G. Parker and M. Benaissa",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, {ISCAS '94}, 2 June 1994",
  title =        "Fault-tolerant linear convolution using residue number
                 systems",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "441--444",
  year =         "1994",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1994.408997",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper proposes a fault-tolerant linear
                 convolution architecture using Residue Number Systems
                 (RNS) and Polynomial Residue Number Systems (PRNS). The
                 RNS and PRNS are both given error-detection capability
                 by the addition of redundant residue \ldots{}",
}

@MastersThesis{Patankar:1994:SHA,
  author =       "Rashmi Arun Patankar",
  title =        "Software and hardware approaches to data compression
                 of {IEEE} 64-bit floating point data",
  type =         "Thesis ({M.S.})",
  school =       "Iowa State University",
  address =      "Ames, IA, USA",
  pages =        "55",
  year =         "1994",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Phatak:1994:HSD,
  author =       "D. S. Phatak and I. Koren",
  title =        "Hybrid Signed-Digit Number Systems: a Unified
                 Framework for Redundant Number Representations With
                 Bounded Carry Propagation Chains",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "8",
  pages =        "880--891",
  month =        aug,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.295850",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon May 20 06:16:49 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  remark =       "Selected revised and extended papers from ARITH'11
                 \cite{Swartzlander:1993:SCA}.",
}

@Article{Popova:1994:EIA,
  author =       "Evgenija D. Popova",
  title =        "Extended interval arithmetic in {IEEE} floating-point
                 environment",
  journal =      j-INTERVAL-COMP,
  volume =       "4",
  pages =        "100--129",
  year =         "1994",
  ISSN =         "0135-4868",
  MRclass =      "65-04 (65G10)",
  MRnumber =     "1 332 078",
  bibdate =      "Fri Dec 8 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Interval Computations = Interval'nye vychisleniia",
  xxnote =       "SCAN-93 (Vienna, 1993)",
}

@Article{Prince:1994:TFM,
  author =       "Timothy Prince",
  title =        "{{\tt float}}-Precision Math Library",
  journal =      j-CUJ,
  volume =       "12",
  number =       "6",
  pages =        "45--??",
  month =        jun,
  year =         "1994",
  ISSN =         "0898-9788",
  bibdate =      "Fri Aug 30 16:52:23 MDT 1996",
  bibsource =    "http://www.cuj.com/cbklist.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "C Users Journal",
}

@Article{Pritchard:1994:RAR,
  author =       "A. J. Pritchard and S. J. Sangwine and R. E. N.
                 Horne",
  title =        "Rational arithmetic representation of colour image
                 pixels",
  journal =      j-ELECT-LETTERS,
  volume =       "30",
  number =       "18",
  pages =        "1474--1475",
  month =        sep,
  year =         "1994",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Fri Nov 30 07:42:41 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}

@InProceedings{Rajski:1994:DRP,
  author =       "J. Rajski and J. Tyszer",
  title =        "Design of random pattern testable floating point
                 adders",
  crossref =     "IEEE:1994:PTA",
  pages =        "227--232",
  year =         "1994",
  bibdate =      "Thu Dec 14 11:25:18 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The paper presents a floating point adder with
                 enhanced testability and test response compaction
                 capabilities. It is shown that the testability of the
                 conventional adders can be improved by changing the
                 functionality of some of their internal modules in the
                 testing mode. It is also demonstrated that the floating
                 point units can perform an efficient test response
                 compaction in a built-in self test environment. (7
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Electr. Eng., McGill University,
                 Montreal, Que., Canada",
  classification = "B0170E (Production facilities and engineering);
                 B1265B (Logic circuits); B7210B (Automatic test and
                 measurement systems); C5120 (Logic and switching
                 circuits); C5210 (Logic design methods); C5230 (Digital
                 arithmetic methods); C7410D (Electronic engineering
                 computing)",
  keywords =     "built-in self test environment; enhanced testability;
                 floating point accumulator; floating point units;
                 floating-point testing; functionality; internal
                 modules; random pattern testable floating point adders;
                 rotate shifter; simulation experiments; test response
                 compaction; testability",
  thesaurus =    "adders; built-in self test; design for testability;
                 digital simulation; floating point arithmetic; logic
                 design; modules; shift registers",
}

@MastersThesis{Robe:1994:SME,
  author =       "Edward D. Robe",
  title =        "{SIMULINK} modules that emulate digital controllers
                 realized with fixed-point or floating-point
                 arithmetic",
  type =         "Thesis ({M.S.})",
  school =       "Ohio University",
  address =      "Athens, OH, USA",
  pages =        "v + 130",
  month =        jun,
  year =         "1994",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Digital control systems.; Emulators (Computer
                 programs); Floating-point arithmetic.",
}

@TechReport{Rothberg:1994:ILD,
  author =       "Edward Rothberg and Robert Schreiber",
  title =        "Improved load distribution in parallel sparse
                 {Cholesky} factorization",
  institution =  "Research Institute for Advanced Computer Science, NASA
                 Ames Research Center; National Technical Information
                 Service, distributor",
  address =      "Moffett Field, CA, USA",
  pages =        "????",
  year =         "1994",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "[NASA contractor report]; NASA CR-196380 RIACS
                 technical report; 94.13 RIACS technical report; TR
                 94.13.",
  acknowledgement = ack-nhfb,
  govtdocnumber = "NAS 1.26:196380 0830-H-14 (MF)",
  keywords =     "Cholesky factorization.; Computer systems
                 performance.; Floating point arithmetic.; Heuristic
                 methods.; Parallel processing (Computers).",
  remark =       "Distributed to depository libraries in microfiche.
                 Shipping list no.: 94-0871-M. Microfiche. [Washington,
                 D.C.: National Aeronautics and Space Administration,
                 1994] 1 microfiche.",
}

@Article{Schaefer:1994:POU,
  author =       "Mark J. Schaefer",
  title =        "Precise optimization using range arithmetic",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "53",
  number =       "3",
  pages =        "341--351",
  day =          "30",
  month =        aug,
  year =         "1994",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:24:32 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042794900620",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@MastersThesis{Schaffer:1994:FPM,
  author =       "Jonathan T. Schaffer",
  title =        "A floating point multiplier for a superscalar
                 microprocessor",
  type =         "Thesis ({M.S.})",
  school =       "North Carolina State University",
  address =      "Raleigh, NC, USA",
  pages =        "viii + 104",
  year =         "1994",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Schorn:1994:DGC,
  author =       "Peter Schorn",
  title =        "Degeneracy in geometric computation and the
                 perturbation approach",
  journal =      j-COMP-J,
  volume =       "37",
  number =       "1",
  pages =        "35--42",
  month =        "????",
  year =         "1994",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Wed Jul 21 09:54:00 MDT 1999",
  bibsource =    "http://www3.oup.co.uk/computer_journal/Volume_37/Issue_01/Vol37_01.index.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/Volume_37/Issue_01/Vol37_01.body.html#AbstractSchorn",
  acknowledgement = ack-nhfb,
  affiliation =  "Inst. fur Theor. Inf., ETH, Zurich, Switzerland",
  author-1-adr = "Institut f{\"u}r Theoretische Informatik, ETH, CH-8092
                 Zurich, Switzerland",
  classcodes =   "C4260 (Computational geometry); C4240 (Programming and
                 algorithm theory)",
  classification = "C4240 (Programming and algorithm theory); C4260
                 (Computational geometry)",
  corpsource =   "Inst. fur Theor. Inf., ETH, Zurich, Switzerland",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "algorithm construction; Algorithm construction;
                 algorithm theory; algorithm-dependent;
                 Algorithm-dependent degeneracies; approach;
                 computational geometry; degeneracies; Euclidean
                 constructions; floating; Floating point arithmetic;
                 geometric computation; Geometric computation;
                 input-output; Input-output specifications; integer
                 arithmetic; Integer arithmetic; lexicographic;
                 Lexicographic ordering; ordering; perturbation;
                 Perturbation approach; point arithmetic;
                 problem-dependent degeneracies; Problem-dependent
                 degeneracies; provably correct results; Provably
                 correct results; specifications; theory; winding
                 number; Winding number",
  thesaurus =    "Algorithm theory; Computational geometry; Perturbation
                 theory",
  treatment =    "T Theoretical or Mathematical",
}

@MastersThesis{Schoss:1994:ISF,
  author =       "H. Schoss",
  title =        "{Intervall Standardfunktionen f{\"u}r das bin{\"a}re
                 IEEE Zahlenformat} \toenglish {Interval Standard
                 Functions for the Binary IEEE Number Format}
                 \endtoenglish",
  type =         "{Diplomarbeit}",
  school =       "Institut f{\"u}r angewandte Mathematik,
                 Universit{\"a}t Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "??",
  month =        mar,
  year =         "1994",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Article{Schulte:1994:HDE,
  author =       "M. J. Schulte and E. E. {Swartzlander, Jr.}",
  title =        "Hardware Designs for Exactly Rounded Elementary
                 Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "8",
  pages =        "964--973",
  month =        aug,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.295858",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon May 20 06:16:49 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib;
                 OCLC Proceedings database",
  abstract =     "This paper presents hardware designs that produce
                 exactly rounded results for the functions of
                 reciprocal, square-root, 2/sup x/, and log/sub 2/(x).
                 These designs use polynomial approximation in which the
                 terms in the approximation are generated in parallel,
                 and then summed by using a multi-operand adder. To
                 reduce the number of terms in the approximation, the
                 input interval is partitioned into subintervals of
                 equal size, and different coefficients are used for
                 each subinterval. The coefficients used in the
                 approximation are initially determined based on the
                 Chebyshev series approximation. They are then adjusted
                 to obtain exactly rounded results for all inputs.
                 Hardware designs are presented, and delay and area
                 comparisons are made based on the degree of the
                 approximating polynomial and the accuracy of the final
                 result. For single-precision floating point numbers, a
                 design that produces exactly rounded results for all
                 four functions has an estimated delay of 80 ns and a
                 total chip area of 98 mm/sup 2/ in a 1.0-micron CMOS
                 technology. Allowing the results to have a maximum
                 error of one unit in the last place reduces the
                 computational delay by 5\% to 30\% and the area
                 requirements by 33\% to 77\%.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Department of Electr. and Comput. Eng., Texas
                 University, Austin, TX, USA",
  ajournal =     "IEEE Trans. Comput.",
  classification = "B0290F (Interpolation and function approximation);
                 B1265B (Logic circuits); B2570D (CMOS integrated
                 circuits); C4130 (Interpolation and function
                 approximation); C5120 (Logic and switching circuits);
                 C5230 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "1 Micron; 1.0-Micron CMOS technology; Argument
                 reduction; Chebyshev series approximation; Chip area;
                 Computational delay; Computer arithmetic; Exact
                 rounding; Exactly rounded elementary functions;
                 Hardware designs; Multi-operand adder; Parallel
                 multiplier; Polynomial approximation; Reciprocal;
                 Single-precision floating point numbers;
                 Special-purpose hardware; Square-root",
  numericalindex = "Size 1.0E-06 m",
  remark =       "Selected revised and extended papers from ARITH'11
                 \cite{Swartzlander:1993:SCA}.",
  thesaurus =    "Approximation theory; Chebyshev approximation; CMOS
                 integrated circuits; Digital arithmetic; Multiplying
                 circuits; Polynomials; Summing circuits",
  xxtitle =      "Hardware Design for Exactly Rounded Elementary
                 Functions",
}

@Article{Schulte:1994:OIA,
  author =       "M. J. Schulte and J. Omar and E. E. {Swartzlander,
                 Jr.}",
  title =        "Optimal initial approximations for the
                 {Newton--Raphson} division algorithm",
  journal =      j-COMPUTING,
  volume =       "53",
  number =       "3--4",
  pages =        "233--242",
  month =        sep,
  year =         "1994",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65D99",
  MRnumber =     "1 308 764",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database; OCLC Contents1st database",
  note =         "International Symposium on Scientific Computing,
                 Computer Arithmetic and Validated Numerics (Vienna,
                 1993).",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@InProceedings{Schulte:1994:VIA,
  author =       "M. J. Schulte and E. E. {Swartzlander, Jr.}",
  title =        "A variable-precision interval arithmetic processor",
  crossref =     "Cappello:1994:PIC",
  pages =        "248--258",
  year =         "1994",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper presents a special-purpose processor which
                 implements variable-precision, interval arithmetic.
                 Variable-precision arithmetic allows the precision of
                 the computation to be specified, based on the problem
                 to be solved and the required accuracy of the
                 computation. Interval arithmetic produces two values
                 for each result, such that the true result is
                 guaranteed to be between the two values. The distance
                 between the two values gives an upper bound on the
                 error. Direct hardware support for variable-precision,
                 interval arithmetic greatly improves the accuracy of
                 the computation, and is much faster than existing
                 software methods for controlling numerical error. Area
                 and delay estimates indicate that the processor can be
                 implemented on a single chip with a cycle time which is
                 comparable to existing IEEE double-precision floating
                 point processors. For computationally intensive
                 problems, an application-specific array of
                 variable-precision, interval arithmetic processors can
                 execute in parallel to provide high-performance and
                 numerically reliable results.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Electr. and Comput. Eng., Texas
                 University, Austin, TX, USA",
  classification = "B0290B (Error analysis in numerical methods); B1265F
                 (Microprocessors and microcomputers); C4110 (Error
                 analysis in numerical methods); C5130 (Microprocessor
                 chips); C5220P (Parallel architecture); C5230 (Digital
                 arithmetic methods)",
  keywords =     "Application-specific array; Hardware support; IEEE
                 double-precision floating point processors; Numerical
                 error; Parallel arithmetic; Special-purpose processor;
                 Variable-precision interval arithmetic processor",
  thesaurus =    "Digital arithmetic; Error analysis; Microprocessor
                 chips; Parallel architectures",
}

@Article{Schwandt:1994:IAD,
  author =       "Hartmut Schwandt",
  title =        "An interval arithmetic domain decomposition method for
                 a class of elliptic {PDEs} on nonrectangular domains",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "50",
  number =       "1--3",
  pages =        "509--521",
  day =          "20",
  month =        may,
  year =         "1994",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:02:23 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042794903247",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@TechReport{Sharangpani:1994:SAF,
  author =       "H. P. Sharangpani and M. L. Barton",
  title =        "Statistical analysis of floating point flaw in the
                 {Pentium} processor",
  institution =  pub-INTEL,
  address =      pub-INTEL:adr,
  month =        nov,
  year =         "1994",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://home1.gte.net/deleyd/pentbug/white11.ps;
                 http://www.intel.com/procs/support/pentium/fdiv/white11.ps",
  abstract =     "A subtle flaw in the hardware divide unit of the
                 PentiumTM Processor was discovered by Intel.
                 Subsequently, a characterization of its impact to the
                 end-user application base was conducted. The flaw is
                 rare and data-dependent, and causes a reduction in
                 precision of the divide instruction and certain other
                 operations in certain cases.\par

                 The significance of the flaw depends upon (a) the rate
                 of use of specific FP instructions in the PentiumTM
                 CPU, (b) the data fed to them, (c) the way in which the
                 results of these instructions are propagated into
                 further computation in the application; and (d) the way
                 in which the final results of the application are
                 interpreted.\par

                 The thorough and detailed characterization of the flaw
                 and the subsequent investigations of its impact on
                 applications through elaborate surveys, analyses and
                 empirical observation lead us to the overall conclusion
                 that the flaw is of no concern to the vast majority of
                 users of Pentium processor based systems. A few users
                 of applications in the scientific/engineering and
                 financial engineering fields who require unusual
                 precision and invoke millions of divides per day may
                 need to employ either an updated Pentium processor
                 without the flaw or a software workaround.",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  keywords =     "Intel Pentium divide flaw; Thomas R. Nicely",
  remark =       "This Intel white paper was controversial, and its
                 minimization of the problem was refuted by others: see
                 \cite{Edelman:1997:MPD}.",
}

@Article{Shippy:1994:PFD,
  author =       "D. J. Shippy and T. W. Griffith",
  title =        "{POWER2} fixed-point, data cache, and storage control
                 units",
  journal =      j-IBM-JRD,
  volume =       "38",
  number =       "5",
  pages =        "503--524",
  month =        sep,
  year =         "1994",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Tue Mar 25 14:26:59 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.almaden.ibm.com/journal/rd38-5.html#three",
  abstract =     "The POWER2* fixed-point, data cache, and storage
                 control units provide a tightly integrated subunit for
                 a second-generation high-performance superscalar RISC
                 processor. These functional units provide dual
                 fixed-point execution units and a large multiported
                 data cache, as well as high-performance interfaces to
                 memory, I/O, and the other execution units in the
                 processor. These units provide the following features:
                 dual fixed-point execution units, improved
                 fixed-point/floating-point synchronization, new
                 floating-point load and store quadword instructions,
                 improved address translation, improved fixed-point
                 multiply/divide, large multiported D-cache, increased
                 bandwidth into and out of the caches through wider data
                 buses, an improved external interrupt mechanism, and an
                 improved I/O DMA mechanism to support
                 multiple-streaming Micro Channels.*",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Corp., Austin, TX, USA",
  classcodes =   "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5470 (Performance evaluation
                 and testing); C5610S (System buses); C5320G
                 (Semiconductor storage)",
  classification = "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5320G (Semiconductor storage);
                 C5470 (Performance evaluation and testing); C5610S
                 (System buses)",
  corpsource =   "IBM Corp., Austin, TX, USA",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "address translation; Address translation; cache; cache
                 storage; data buses; Data buses; data cache; Data
                 cache; dual fixed-point; Dual fixed-point execution
                 units; execution units; external interrupt; External
                 interrupt mechanism; floating-; Floating-point;
                 mechanism; memory interface; Memory interface;
                 microprocessor chips; multiple-streaming micro
                 channels; Multiple-streaming micro channels;
                 multiported data; Multiported data cache; performance
                 evaluation; point; POWER2; reduced instruction set
                 computing; storage control units; Storage control
                 units; storage management; superscalar RISC processor;
                 Superscalar RISC processor; synchronisation;
                 synchronization; Synchronization; system buses",
  thesaurus =    "Cache storage; Microprocessor chips; Performance
                 evaluation; Reduced instruction set computing; Storage
                 management; Synchronisation; System buses",
  treatment =    "P Practical",
}

@Article{Smith:1994:PAT,
  author =       "James E. Smith and Shlomo Weiss",
  title =        "{PowerPC 601} and {Alpha 21064}: a Tale of Two
                 {RISCs}",
  journal =      j-COMPUTER,
  volume =       "27",
  number =       "6",
  pages =        "46--58",
  month =        jun,
  year =         "1994",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Mon Feb 3 07:28:57 MST 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Both PowerPC and Alpha are RISC architectures, but
                 they have little in common beyond that. The design
                 philosophy of one emphasizes powerful instructions, the
                 other simplicity.",
  acknowledgement = ack-nhfb,
  affiliation =  "Cray Res. Inc., Chippewa Falls, WI, USA",
  affiliationaddress = "Chippewa Falls, WI, USA",
  classification = "721.3; 722.1; 722.4; 723.1; C5220P (Parallel
                 architecture); C5440 (Multiprocessor systems and
                 techniques); C6140B (Machine-oriented languages)",
  conferenceyear = "1994",
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
  journalabr =   "Computer",
  keywords =     "Access memory; Alpha 21064; Buffering; Cache memory;
                 Computer software; Data storage equipment; Digital
                 arithmetic; Digital Equipment Corporation; Floating
                 point instructions; High performance;
                 IBM/Motorola/Apple; Implementation philosophies;
                 Instruction sets; Load/store architecture;
                 Microprocessor chips; Out of order dispatch; Parallel
                 processing systems; Performance; Philosophical aspects;
                 Pipeline processing systems; Pipelined implementations;
                 PowerPC 601; Processing order; Program compilers;
                 Program debugging; Reduced instruction set computing;
                 RISC implementations; RISC microprocessors; Streamlined
                 implementation structure; Superscalar implementations;
                 User interfaces; Very fast clock; Virtual storage",
  publisherinfo = "IEEE Service Center",
  thesaurus =    "Instruction sets; Pipeline processing; Reduced
                 instruction set computing",
}

@Article{Smith:1994:SFT,
  author =       "William Smith",
  title =        "A Short Floating-Point Type in {C++}",
  journal =      j-CUJ,
  volume =       "12",
  number =       "1",
  pages =        "23--??",
  month =        jan,
  year =         "1994",
  ISSN =         "0898-9788",
  bibdate =      "Fri Aug 30 16:52:23 MDT 1996",
  bibsource =    "http://www.cuj.com/cbklist.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "C Users Journal",
}

@TechReport{Solhaug:1994:FDK,
  author =       "Fredrik Solhaug",
  title =        "Flyttalls {A/D}-konverter = Floating Point {A/D}
                 Converter",
  type =         "Hovedoppgave",
  institution =  "Institutt for teleteknikk, NTH",
  address =      "Trondheim, Norway",
  year =         "1994",
  bibdate =      "Thu May 09 08:14:17 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Srivastava:1994:ASB,
  author =       "A. Srivastava and A. Eustace",
  title =        "{ATOM}: a system for building customized program
                 analysis tools",
  journal =      j-SIGPLAN,
  volume =       "29",
  number =       "6",
  pages =        "196--205",
  month =        jun,
  year =         "1994",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "ACM SIGPLAN '94 Conference on Programming Language
                 Design and Implementation (PLDI).",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}

@Article{Stockman:1994:OMM,
  author =       "Harlan W. Stockman",
  title =        "Optimizing Matrix Math On The {Pentium}",
  journal =      j-DDJ,
  volume =       "19",
  number =       "5",
  pages =        "52, 54, 56, 60, 62, 66",
  month =        may,
  year =         "1994",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Tue Sep 03 09:15:49 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 UnCover database",
  abstract =     "The Pentium processor is more than just a fast 486.
                 Its pipeline and floating-point and integer operations
                 require that you pay more attention to the flow of data
                 on the off the FPU. Harlan presents and measures
                 methods for speeding up Pentium matrix-math
                 operations.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Geochem., Sandia Nat. Labs.,
                 Albuquerque, NM, USA",
  classification = "C1180 (Optimisation techniques); C4140 (Linear
                 algebra); C5130 (Microprocessor chips); C5230 (Digital
                 arithmetic methods); C7310 (Mathematics)",
  fjournal =     "Dr. Dobb's Journal of Software Tools",
  keywords =     "1 MByte; 100 MHz; 256 KByte; 33 MHz; 486DX; 60 MHz; 64
                 Bit; 64 KByte; 8 Bit; 8-Byte boundaries; Code
                 optimization; Data alignment; Floating-point unit;
                 Gateway 486/33C; Gateway P5-60; Global register
                 allocation; IRIX 4.0.5H; LINPACK routines; Loop
                 unrolling; Matrix multiplication; Matrix operations
                 optimization; MIPS R4000; Pentium microprocessor chip;
                 Pentium-optimized compilers; Performance gains; SGI
                 Elan; Simultaneous linear equations; Symantec C++ 6.0
                 for DOS; UNIX cc version 3.1; Write-through L2 cache",
  thesaurus =    "Assembly language listings; Digital arithmetic;
                 Mathematics computing; Matrix algebra; Microprocessor
                 chips; Optimisation",
}

@Article{Thompson:1994:PSN,
  author =       "Tom Thompson and Bob Ryan",
  title =        "{PowerPC} 620 Soars: The newest member of the
                 {PowerPC} family targets the workstation market with
                 fast throughput and speedy floating-point performance",
  journal =      j-BYTE,
  volume =       "19",
  number =       "11",
  pages =        "113--??",
  month =        nov,
  year =         "1994",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Tue Jan 2 10:01:41 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "BYTE Magazine",
}

@Article{Timmermann:1994:CFP,
  author =       "D. Timmermann and B. Rix and H. Hahn and B. J.
                 Hosticka",
  title =        "A {CMOS} Floating-Point Vector-Arithmetic Unit",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "29",
  number =       "5",
  pages =        "634--639",
  month =        may,
  year =         "1994",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "This work describes a floating-point arithmetic unit
                 based on the CORDIC algorithm. The unit computes a full
                 set of high level arithmetic and elementary functions:
                 multiplication, division, (co)sine, hyperbolic
                 (co)sine, square root, natural logarithm \ldots{}",
}

@Article{Timmermann:1994:CFV,
  author =       "D. Timmermann and B. Rix and H. Hahn and B. J.
                 Hosticka",
  title =        "A {CMOS} floating-point vector-arithmetic unit",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "29",
  number =       "5",
  pages =        "634--639",
  month =        may,
  year =         "1994",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This work describes a floating-point arithmetic unit
                 based on the CORDIC algorithm. The unit computes a full
                 set of high level arithmetic and elementary functions:
                 multiplication, division, (co)sine, hyperbolic
                 (co)sine, square root, natural logarithm, inverse
                 (hyperbolic) tangent, vector norm, and phase. The chip
                 has been integrated in 1.6 mu m double-metal n-well
                 CMOS technology and achieves a normalized peak
                 performance of 220 MFLOPS.",
  acknowledgement = ack-nhfb,
  affiliation =  "Fraunhofer Inst. of Microelectron. Circuits and Syst.,
                 Duisburg, Germany",
  classification = "B1265B (Logic circuits); B2570D (CMOS integrated
                 circuits); C5120 (Logic and switching circuits); C5220P
                 (Parallel architecture); C5230 (Digital arithmetic
                 methods)",
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "1.6 Micron; 220 MFLOPS; CORDIC algorithm; Cosine;
                 Division; Double-metal n-well CMOS technology;
                 Floating-point vector-arithmetic unit; Hyperbolic sine;
                 Inverse tangent; Multiplication; Natural logarithm;
                 Phase; Sine; Square root; Vector norm",
  numericalindex = "Size 1.6E-06 m; Computer speed 2.2E+08 FLOPS",
  thesaurus =    "CMOS integrated circuits; Digital arithmetic;
                 Integrated logic circuits; Parallel architectures;
                 Pipeline processing; Vector processor systems",
}

@Article{Turner:1994:SRM,
  author =       "Stephen M. Turner",
  title =        "Square roots mod $p$",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "101",
  number =       "5",
  pages =        "443--449",
  month =        may,
  year =         "1994",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "11A07",
  MRnumber =     "95c:11004",
  MRreviewer =   "David Lee Hilliker",
  bibdate =      "Wed Dec 3 17:17:33 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Article{Tydeman:1994:WCT,
  author =       "Fred Tydeman",
  title =        "What causes a Trap in {IEEE-754} Floating-Point?",
  journal =      j-SIGNUM,
  volume =       "29",
  number =       "1",
  pages =        "2--4",
  month =        jan,
  year =         "1994",
  CODEN =        "SNEWD6",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:24 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In the ANSI/IEEE Std 754-1985 (IEEE standard for
                 binary floating-point arithmetic), and the ANSI/IEEE
                 Std 854-1987 (IEEE standard for radix-independent
                 floating-point arithmetic), is signaling a trap an
                 `edge-triggered' or a `level-sensitive' event? The
                 authors discusses the question: Does it matter if an
                 exception is signaled by an arithmetic operation versus
                 a user setting a status flag?.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Corp., Austin, TX, USA",
  classification = "C5230 (Digital arithmetic methods)",
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
  keywords =     "ANSI/IEEE Std 754-1985; ANSI/IEEE Std 854-1987; Binary
                 floating-point arithmetic; Exception; IEEE standard;
                 Radix-independent floating-point arithmetic",
  thesaurus =    "Digital arithmetic; Standards",
}

@Article{Upton:1994:RAH,
  author =       "Michael Upton and Thomas Huff and Trevor Mudge and
                 Richard Brown",
  title =        "Resource allocation in a high clock rate
                 microprocessor",
  journal =      j-SIGPLAN,
  volume =       "29",
  number =       "11",
  pages =        "98--109",
  month =        nov,
  year =         "1994",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:16:57 MST 2003",
  bibsource =    "http://portal.acm.org/; http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/asplos/195473/p98-upton/",
  abstract =     "This paper discusses the design of a high clock rate
                 (300 MHz) processor. The architecture is described, and
                 the goals for the design are explained. The performance
                 of three processor models is evaluated using
                 trace-driven simulation. A cost model is used to
                 estimate the resources required to build processors
                 with varying sizes of on-chip memories, in both single
                 and dual issue models. Recommendations are then made to
                 increase the effectiveness of each of the models.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Electr. Eng. and Computer Science,
                 Michigan University, Ann Arbor, MI, USA",
  classification = "C5130 (Microprocessor chips); C5220 (Computer
                 architecture); C5230 (Digital arithmetic methods);
                 C6150J (Operating systems)",
  confdate =     "4-7 Oct. 1994",
  conflocation = "San Jose, CA, USA; 4--7 Oct. 1994",
  confsponsor =  "ACM; IEEE Comput. Soc",
  conftitle =    "Sixth International Conference on Architectural
                 Support for Programming Languages and Operating Systems
                 (ASPLOS-VI)",
  corpsource =   "Department of Electr. Eng. and Computer Science,
                 Michigan University, Ann Arbor, MI, USA",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "computer architecture; Cost model; cost model; design;
                 floating point arithmetic; Floating point latency;
                 floating point latency; High clock rate microprocessor;
                 high clock rate microprocessor; measurement;
                 microprocessor chips; Nonblocking cache; nonblocking
                 cache; On-chip memories; on-chip memories; performance;
                 performance evaluation; Pipelining; pipelining;
                 Prefetching; prefetching; Processor model performance;
                 processor model performance; Resource allocation;
                 resource allocation; theory; Trace-driven simulation;
                 trace-driven simulation; virtual machines",
  sponsororg =   "ACM; IEEE Comput. Soc",
  subject =      "{\bf C.1.2} Computer Systems Organization, PROCESSOR
                 ARCHITECTURES, Multiple Data Stream Architectures
                 (Multiprocessors), Pipeline processors**. {\bf D.4.2}
                 Software, OPERATING SYSTEMS, Storage Management,
                 Allocation/deallocation strategies. {\bf C.4} Computer
                 Systems Organization, PERFORMANCE OF SYSTEMS.",
  thesaurus =    "Computer architecture; Floating point arithmetic;
                 Microprocessor chips; Performance evaluation; Resource
                 allocation; Virtual machines",
  treatment =    "P Practical; T Theoretical or Mathematical",
}

@Book{vanSomeren:1994:ARC,
  author =       "Alex {van Someren} and Carol Atack",
  title =        "The {ARM RISC} Chip: a Programmer's Guide",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "xviii + 346",
  year =         "1994",
  ISBN =         "0-201-62410-9",
  ISBN-13 =      "978-0-201-62410-6",
  LCCN =         "QA76.5.V275 1994",
  bibdate =      "Wed Sep 14 22:16:36 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Vinnakota:1994:FCTa,
  author =       "B. Vinnakota and V. V. Bapeswara Rao",
  title =        "Fast conversion techniques for binary-residue number
                 systems",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-I-FUNDAM-THEORY-APPL,
  volume =       "41",
  number =       "12",
  pages =        "927--929",
  month =        dec,
  year =         "1994",
  CODEN =        "ITCAEX",
  DOI =          "https://doi.org/10.1109/81.340862",
  ISSN =         "????",
  ISSN-L =       "1057-7122",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=7979",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems I:
                 Fundamental Theory and Applications",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=81",
  keywords =     "residue arithmetic; residue number system",
  summary =      "An easy and efficient procedure for converting a
                 binary number into a residue number on moduli 2 n -1, 2
                 n, 2 n+1 is presented. The procedure presented reveals
                 an inversion technique. The paper also includes a
                 \ldots{}",
}

@Article{Vinnakota:1994:FCTb,
  author =       "B. Vinnakota and V. V. Bapeswara Rao",
  title =        "Fast conversion techniques for binary-residue number
                 systems",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-I-FUNDAM-THEORY-APPL,
  volume =       "41",
  number =       "12",
  pages =        "927--929",
  month =        dec,
  year =         "1994",
  CODEN =        "ITCAEX",
  DOI =          "https://doi.org/10.1109/81.340862",
  ISSN =         "????",
  ISSN-L =       "1057-7122",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=7979",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems I:
                 Fundamental Theory and Applications",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=81",
  keywords =     "residue arithmetic; residue number system",
  summary =      "An easy and efficient procedure for converting a
                 binary number into a residue number on moduli 2 n -1, 2
                 n, 2 n+1 is presented. The procedure presented reveals
                 an inversion technique. The paper also includes a
                 \ldots{}",
}

@Article{Vinnakota:1994:SBR,
  author =       "B. Vinnakota",
  title =        "Selection of bases for a residue number system",
  journal =      j-ELECT-LETTERS,
  volume =       "30",
  number =       "11",
  pages =        "836--837",
  day =          "26",
  month =        may,
  year =         "1994",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=7164",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A procedure is presented for selecting the bases in a
                 residue number system (RNS) for which the conversion
                 procedure from RNS to decimal is simple. The conversion
                 procedure is not based on the Chinese remainder
                 \ldots{}",
}

@Article{Vuillemin:1994:CN,
  author =       "Jean E. Vuillemin",
  title =        "On Circuits and Numbers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "8",
  pages =        "868--879",
  month =        aug,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.295849",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon May 20 06:16:49 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  remark =       "Selected revised and extended papers from ARITH'11
                 \cite{Swartzlander:1993:SCA}.",
}

@Article{Walker:1994:SMA,
  author =       "W. J. Walker",
  title =        "A summability method for the arithmetic {Fourier}
                 transform",
  journal =      j-BIT,
  volume =       "34",
  number =       "2",
  pages =        "304--309",
  month =        jun,
  year =         "1994",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01955877",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "42A99 (65T20)",
  MRnumber =     "97i:42010",
  bibdate =      "Wed Jan 4 18:52:23 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=34&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mai.liu.se/BIT/contents/bit34.html;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=34&issue=2&spage=304",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@TechReport{Walters:1994:CTR,
  author =       "H. R. Walters",
  title =        "A Complete Term Rewriting System for Decimal Integer
                 Arithmetic",
  type =         "Technical report",
  number =       "CS-9435",
  institution =  "Centrum voor Wiskunde en Informatica (CWI)",
  address =      "Amsterdam, The Netherlands",
  pages =        "9",
  month =        aug,
  year =         "1994",
  bibdate =      "Fri Nov 28 19:36:09 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present a term rewriting system for decimal
                 integers with addition and subtraction. We prove that
                 the system is confluent and terminating.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}

@Article{Wang:1994:MQF,
  author =       "Mu-Cheng Wang and Wayne G. Nation and James B.
                 Armstrong and Howard Jay Siegel and Shin Dug Kim and
                 Mark A. Nichols and Michael Gherrity",
  title =        "Multiple Quadratic Forms: a Case Study in the Design
                 of Data-Parallel Algorithms",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "21",
  number =       "1",
  pages =        "124--139",
  month =        apr,
  year =         "1994",
  CODEN =        "JPDCER",
  DOI =          "https://doi.org/10.1006/jpdc.1994.1046",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Thu Mar 9 09:18:54 MST 2000",
  bibsource =    "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.idealibrary.com/links/doi/10.1006/jpdc.1994.1046/production;
                 http://www.idealibrary.com/links/doi/10.1006/jpdc.1994.1046/production/pdf",
  acknowledgement = ack-nhfb,
  classification = "C4240P (Parallel programming and algorithm theory)",
  corpsource =   "Department of Computer Science, City University of New
                 York, NY, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "communication overhead; complex arithmetic operation
                 count; complexity; computational complexity;
                 data-parallel algorithms; MasPar; memory storage; MP-1;
                 multiple quadratic forms; nCUBE 2; parallel algorithms;
                 partitioning; PASM; real-time; systems",
  treatment =    "P Practical",
}

@Book{Weaver:1994:SAM,
  author =       "David L. Weaver and Tom Germond",
  title =        "The {SPARC} Architecture Manual: Version 9",
  publisher =    pub-PHPTR,
  address =      pub-PHPTR:adr,
  pages =        "xxii + 357",
  year =         "1994",
  ISBN =         "0-13-099227-5",
  ISBN-13 =      "978-0-13-099227-7",
  LCCN =         "QA76.9.A73S648 1992",
  bibdate =      "Fri Jul 22 08:37:56 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/microchip.bib",
  price =        "US\$33.00",
  URL =          "http://www.sparc.org/standards/SPARCV9.pdf",
  abstract =     "SPARC (Scalable Processor Architecture) is the
                 industry's only openly defined and evolved RISC
                 architecture. Version 9 is the new 64-bit incarnation
                 of SPARC --- the most significant change since SPARC's
                 introduction in 1987! Unlike other RISC (Reduced
                 Instruction Set Computer) designs, SPARC specifies not
                 a hardware implementation (``chip''), but an open,
                 standard architecture belonging to the community of
                 SPARC vendors and users. The SPARC specification is
                 defined by the SPARC Architecture Committee, a
                 technical arm of the computer-maker consortium, SPARC
                 International. Version 9 provides 64-bit data and
                 addressing, support for fault tolerance, fast context
                 switching, support for advanced compiler optimizations,
                 efficient design for Superscalar processors, and a
                 clean structure for modern operating systems. The V9
                 architecture supplements, rather than replaces, the
                 32-bit Version 8 architecture. The non-privileged
                 features of Version 9 are upward-compatible from
                 Version 8, so 32-bit application software can execute
                 natively, without modification, on Version 9 systems no
                 special ``compatibility mode'' is required. Publication
                 of the Version 9 architecture marks a three-year
                 development effort by SPARC International member
                 companies from a broad cross-section of disciplines.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Introduction \\
                 Overview \\
                 Definitions \\
                 Architectural Overview \\
                 Data Formats \\
                 Registers \\
                 Instructions \\
                 Traps \\
                 Memory Models \\
                 (Normative) Instruction Definitions \\
                 (Normative) IEEE 754-1985 Requirements for SPARC-V9 \\
                 (Normative) SPARC-V9 Implementation Dependencies \\
                 (Normative) Formal Specification of the Memory Models
                 \\
                 (Informative) Opcode Maps \\
                 (Informative) SPARC-V9 MMU Requirements \\
                 (Informative) Suggested Assembly Language Syntax \\
                 (Informative) Software Considerations \\
                 (Informative) Extending the SPARC-V9 Architecture \\
                 (Informative) Programming With the Memory Models \\
                 (Informative) Changes from SPARC-V8 to SPARC-V9 \\
                 Bibliography \\
                 Index",
}

@InProceedings{Wei:1994:REF,
  author =       "D.-Y. D. Wei and J. H. Kim and T. R. N. Rao",
  booktitle =    "Proceedings of the {IEEE} International Workshop on
                 Defect and Fault Tolerance in {VLSI} Systems, 1994",
  title =        "Roundoff error-free tests in algorithm-based fault
                 tolerant matrix operations on {$2$-D} processor
                 arrays",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "74--82",
  year =         "1994",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point testing",
  summary =      "Assaad and Dutt [1992] proposed the hybrid checksum
                 test method for the floating-point matrix-matrix
                 multiplication in ABFT environment, by which the error
                 coverage can be greatly increased. However, the
                 threshold test in their approach is still \ldots{}",
}

@Book{Weiss:1994:PPP,
  author =       "Shlomo Weiss and James E. Smith",
  title =        "{Power} and {PowerPC}: Principles, Architecture,
                 Implementation",
  publisher =    pub-MORGAN-KAUFMANN,
  address =      pub-MORGAN-KAUFMANN:adr,
  pages =        "xvi + 408",
  year =         "1994",
  ISBN =         "1-55860-279-8",
  ISBN-13 =      "978-1-55860-279-3",
  LCCN =         "QA76.8.P67 W45 1994",
  bibdate =      "Wed Aug 10 10:06:55 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/microchip.bib",
  price =        "US\$54.95",
  acknowledgement = ack-nhfb,
  tableofcontents = "Foreword by Michael Slater \\
                 Preface \\
                 Modern Computer Design Concepts / 1 \\
                 POWER Architecture / 31 \\
                 POWER Implementation: Pipelines / 71 \\
                 POWER1 Implementation / 97 \\
                 POWER1 Implementation: Cache Memories / 115 \\
                 POWER2: The Next Generation / 135 \\
                 PowerPC Architecture / 173 \\
                 PowerPC 601 Implementation / 223 \\
                 PowerPC: Support for Multiprocessing / 253 \\
                 System Organization / 271 \\
                 PowerPC 601 and Alpha 21064 / 305 \\
                 App. A. IEEE 754 Floating-Point Standard / 333 \\
                 App. B. POWER Instruction Formats / 341 \\
                 App. C. POWER Instruction Set Sorted by Mnemonic / 349
                 \\
                 App. D. PowerPC Instruction Formats / 355 \\
                 App. E. PowerPC Instruction Set Sorted by Mnemonic /
                 365 \\
                 App. F. Cross Reference for Changed POWER Mnemonics /
                 377 \\
                 Bibliography / 383 \\
                 Index / 391",
}

@Article{White:1994:PNG,
  author =       "S. W. White and S. Dhawan",
  title =        "{POWER2}: {Next} generation of the {RISC System\slash
                 6000} family",
  journal =      j-IBM-JRD,
  volume =       "38",
  number =       "5",
  pages =        "493--502",
  month =        sep,
  year =         "1994",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Tue Mar 25 14:26:59 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.almaden.ibm.com/journal/rd38-5.html#two",
  abstract =     "Since its announcement, the IBM RISC System\slash
                 6000* processor has characterized the aggressive
                 instruction-level parallelism approach to achieving
                 performance. Recent enhancements to the architecture
                 and implementation provide greater superscalar
                 capability. This paper describes the architectural
                 extensions which improve storage reference bandwidth,
                 allow hardware square-root computation, and speed
                 floating-point-to-integer conversion. The
                 implementation, which exploits these extensions and
                 doubles the number of functional units, is also
                 described. A comparison of performance results on a
                 variety of industry standard benchmarks demonstrates
                 that superscalar capabilities are an attractive
                 alternative to aggressive clock rates.",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM Corp., Austin, TX, USA",
  classcodes =   "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5220P (Parallel architecture);
                 C5470 (Performance evaluation and testing)",
  classification = "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5220P (Parallel architecture);
                 C5470 (Performance evaluation and testing)",
  corpsource =   "IBM Corp., Austin, TX, USA",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "bandwidth; evaluation; floating-point-to-;
                 Floating-point-to-integer conversion;
                 Floating-point-to-integer conversion, POWER2; IBM RISC
                 System/6000 processor; IBM RISC System\slash 6000
                 processor; instruction-level; Instruction-level
                 parallelism; integer conversion; microprocessor chips;
                 parallel architectures; parallelism; performance;
                 POWER2; reduced instruction set computing; Square-root
                 computation; square-root computation; storage
                 reference; Storage reference bandwidth; superscalar
                 capability; Superscalar capability",
  thesaurus =    "Microprocessor chips; Parallel architectures;
                 Performance evaluation; Reduced instruction set
                 computing",
  treatment =    "P Practical",
}

@Article{Wichmann:1994:CSP,
  author =       "B. A. Wichmann",
  title =        "Contribution of standard programming languages to
                 software quality",
  journal =      j-SEJ,
  volume =       "9",
  number =       "1",
  pages =        "3--12",
  month =        jan,
  year =         "1994",
  CODEN =        "SEJOED",
  ISSN =         "0268-6961",
  bibdate =      "Sun Mar 15 17:49:58 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Software Engineering Journal",
  remark =       "Brief mention of floating-point issues in software
                 validation.",
}

@Misc{Williams:1994:MAM,
  author =       "T. Williams",
  title =        "Method and apparatus for multiplying denormalized
                 binary floating point numbers without additional
                 delay",
  day =          "13",
  month =        sep,
  year =         "1994",
  bibdate =      "Fri Nov 28 15:24:41 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "U.S. Patent No. 5,347,481.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Wong:1994:FEE,
  author =       "W. F. Wong and E. Goto",
  title =        "Fast evaluation of the elementary functions in double
                 precision",
  crossref =     "Mudge:1994:PTS",
  pages =        "349--358",
  year =         "1994",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "One of the most spectacular development in computer
                 technology is the growth in memory density and speed.
                 It is with this development in mind that we intend to
                 tackle the old problem of computing the elementary
                 functions. Since the dawn of computing, the fast and
                 accurate computation of the elementary functions has
                 been a constant concern of numerical computing. It now
                 seems possible to use tables of sizes in the range of
                 megabits to aid in such computation. To this end, in
                 this paper, we propose a method called ATA-M (Add-Table
                 Lookup-Add with Multiplication) for evaluating
                 polynomials with the aid of tables. When applied to the
                 elementary functions, we obtained a set of algorithms
                 which computes the reciprocal, square root,
                 exponential, sine, cosine, logarithm, are tangent and
                 the hyperbolic functions in about 3 to 4 double
                 precision floating point multiplication time and
                 utilizing about 2 Mbyte of tables.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Inf. Syst. and Computer Science, Nat.
                 University of Singapore, Singapore",
  classification = "C4130 (Interpolation and function approximation);
                 C5230 (Digital arithmetic methods)",
  keywords =     "Add-Table Lookup-Add with Multiplication; ATA-M;
                 Double precision; Elementary functions; Floating point
                 multiplication time; Hyperbolic functions; Memory
                 density; Memory speed; Numerical computing;
                 Polynomials",
  thesaurus =    "Digital arithmetic; Polynomials; Table lookup",
}

@Article{Wong:1994:FHB,
  author =       "W. F. Wong and E. Goto",
  title =        "Fast Hardware-Based Algorithms for Elementary Function
                 Computations Using Rectangular Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "3",
  pages =        "278--294",
  month =        mar,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.272429",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 7 07:13:54 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=272429",
  abstract =     "As the name suggests, elementary functions play a
                 vital role in scientific computations. Yet due to their
                 inherent nature, they are a considerable computing task
                 by themselves. Not surprisingly, since the dawn of
                 computing, the goal of speeding up elementary function
                 computation has been pursued. This paper describes new
                 hardware based algorithms for the computation of the
                 common elementary functions, namely division,
                 logarithm, reciprocal square root, arc tangent, sine
                 and cosine. These algorithms exploit microscopic
                 parallelism using specialized hardware with heavy use
                 of truncation based on detailed accuracy analysis. The
                 contribution of this work lies in the fact that these
                 algorithms are very fast and yet are accurate. If we
                 let the time to perform an IEEE Standard 754 double
                 precision floating point multiplication be $
                 \tau_\times $, our algorithms to achieve roughly $ 3.68
                 \tau_\times $, $ 4.56 \tau_\times $, $ 5.25 \tau_\times
                 $, $ 3.69 \tau_\times $, $ 7.06 \tau_\times $, and $
                 6.5 \tau_\times $, for division, logarithm, square
                 root, exponential, are tangent and complex exponential
                 (sine and cosine) respectively. The trade-off is the
                 need for tables and some specialized hardware. The
                 total amount of tables required, however, is less than
                 128 Kbytes. We discuss the hardware, algorithmic and
                 accuracy aspects of these algorithms.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliation =  "Department of Inf. Syst. and Computer Science, Nat.
                 University of Singapore, Singapore",
  ajournal =     "IEEE Trans. Comput.",
  classification = "C4110 (Error analysis in numerical methods); C5230
                 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Arc tangent; Common elementary functions; Cosine;
                 Elementary function computations; Floating point
                 multiplication; Hardware-based algorithms; Microscopic
                 parallelism; Reciprocal square root; Rectangular
                 multipliers; Scientific computations; Sine",
  language =     "English",
  pubcountry =   "USA",
  thesaurus =    "Digital arithmetic; Error analysis",
}

@Article{Yang:1994:NIPa,
  author =       "Ming-Chwen Yang and Ja-Ling Wu",
  title =        "A new interpretation of ``polynomial residue number
                 system''",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "42",
  number =       "8",
  pages =        "2190--2191",
  month =        aug,
  year =         "1994",
  CODEN =        "ITPRED",
  DOI =          "https://doi.org/10.1109/78.301857",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=7453",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The authors show that the polynomial residue number
                 system can be interpreted in terms of the Chinese
                 remainder theorem for polynomials (CRTP) over a finite
                 ring which is useful for signal \ldots{}",
}

@Article{Yang:1994:NIPb,
  author =       "Ming-Chwen Yang and Ja-Ling Wu",
  title =        "A new interpretation of ``polynomial residue number
                 system''",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "42",
  number =       "8",
  pages =        "2190--2191",
  month =        aug,
  year =         "1994",
  CODEN =        "ITPRED",
  DOI =          "https://doi.org/10.1109/78.301857",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=7453",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The authors show that the polynomial residue number
                 system can be interpreted in terms of the Chinese
                 remainder theorem for polynomials (CRTP) over a finite
                 ring which is useful for signal \ldots{}",
}

@Article{Yuen:1994:PMC,
  author =       "C. K. Yuen and M. D. Feng",
  title =        "Parallel multiplication: a case study in parallel
                 programming",
  journal =      j-SIGPLAN,
  volume =       "29",
  number =       "3",
  pages =        "12--17",
  month =        mar,
  year =         "1994",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:16:48 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C6110P (Parallel programming); C7310 (Mathematics)",
  corpsource =   "Department of Inf. Syst. and Computer Science, Nat.
                 University of Singapore, Singapore",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "AND/OR parallel problems; bottom up design method;
                 mathematics computing; parallel multiplication;
                 parallel program; parallel programming; performance
                 evaluation; program structure design; speculative
                 processing; systems analysis; top down design method;
                 tuplespace",
  treatment =    "P Practical",
}

@InProceedings{Zhang:1994:EMR,
  author =       "Qihong Zhang and J. H. Kim",
  title =        "An efficient method to reduce roundoff error in matrix
                 multiplication with algorithm-based fault tolerance",
  crossref =     "Lea:1994:PSA",
  pages =        "32--39",
  year =         "1994",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Algorithm-Based Fault Tolerance (ABFT) schemes have
                 been proposed by a number of researchers recently.
                 Although all errors can be theoretically detected and
                 corrected by using these techniques, some practical
                 problems, especially the roundoff errors, degrade the
                 performance drastically. In this paper, we proposed a
                 new scheme called Extended Mantissa Checksum (EMC) test
                 in which the mantissa of the product of two input
                 matrices are divided into two sections and extended for
                 faulty detection and correction. Using this scheme, the
                 number of undetected errors and false alarms are
                 decreased largely and the error coverage is improved
                 significantly. In addition, the time latency is short
                 and the hardware overhead is small compared with other
                 schemes.",
  acknowledgement = ack-nhfb,
  affiliation =  "Center for Adv. Comput. Studies, Southwestern
                 Louisiana University, Lafayette, LA, USA",
  classification = "C1110 (Algebra); C4240P (Parallel programming and
                 algorithm theory); C5230 (Digital arithmetic methods)",
  keywords =     "Algorithm-based fault tolerance; correct rounding;
                 Error coverage; Extended mantissa checksum test; False
                 alarms; Fault correction; Fault detection; Floating
                 point test; Hardware overhead; Matrix multiplication;
                 Roundoff error; Time latency",
  thesaurus =    "Algorithm theory; Digital arithmetic; Error
                 correction; Error detection; Fault tolerant computing;
                 Matrix algebra; Roundoff errors",
}

@Article{Zhang:1994:TDN,
  author =       "M. Zhang and J. G. Delgado-Frias and S. Vassiliadis",
  title =        "Table driven {Newton} scheme for high precision
                 logarithm generation",
  journal =      j-IEE-PROC-COMPUT-DIGIT-TECH,
  volume =       "141",
  number =       "5",
  pages =        "281--292",
  month =        sep,
  year =         "1994",
  CODEN =        "ICDTEA",
  ISSN =         "1350-2387 (print), 1359-7027 (electronic)",
  ISSN-L =       "1350-2387",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Based on the Newton method, a table driven iterative
                 scheme is proposed to compute the logarithm function.
                 The proposed scheme provides high performance and high
                 precision and it is implementable with currently
                 available technologies. It is shown, assuming the
                 availability of a parallel multiplier and an adder and
                 the IEEE floating point format, that a computation
                 delay of 12 machine cycles can be obtained with
                 precision of 0.761*2/sup -53/ requiring 18432 bytes of
                 read only memory (ROM). Based on performance and
                 look-up table size estimations of other existing
                 schemes also using table driven approaches a speed-up
                 of over 1.5 for the proposed scheme can be obtained.",
  acknowledgement = ack-nhfb,
  affiliation =  "McCaw Cellular Commun. Inc., Kirkland, WA, USA",
  classification = "C5230 (Digital arithmetic methods); C6130 (Data
                 handling techniques)",
  fjournal =     "IEE Proceedings. Computers and Digital Techniques",
  keywords =     "12 Machine cycles; Adder; High precision logarithm
                 generation; IEEE floating point format; Iterative
                 scheme; Newton method; Parallel multiplier; Table
                 driven",
  pubcountry =   "UK",
  thesaurus =    "Digital arithmetic; Iterative methods; Table lookup",
}

@Article{Zuras:1994:MSM,
  author =       "D. Zuras",
  title =        "More On Squaring and Multiplying Large Integers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "43",
  number =       "8",
  pages =        "899--908",
  month =        aug,
  year =         "1994",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.295852",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon May 20 06:16:49 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  remark =       "Selected revised and extended papers from ARITH'11
                 \cite{Swartzlander:1993:SCA}.",
}

@Article{Zuse:1994:PPV,
  author =       "K. Zuse",
  title =        "Past and present view on computer architecture",
  journal =      j-IFIP-TRANS-A,
  volume =       "A-52",
  pages =        "248--250",
  month =        "????",
  year =         "1994",
  CODEN =        "ITATEC",
  ISSN =         "0926-5473",
  bibdate =      "Tue Dec 12 09:29:07 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Applications and Impacts. Information Processing '94
                 IFIP 13th World Computer Congress.",
  abstract =     "The author discusses his work in developing binary
                 instruction stream based computers. He chose the
                 half-logarithmic form, where he stored only the
                 exponent in a logarithmic notation, which is the same
                 as the floating point numbers, used in today's
                 computers. Following this principle, he developed new
                 machines. He started with a mechanical working
                 construction. This was a storage utility which was
                 concentrated and enabled the storage of a thousand
                 words. This storage device was completed in 1936. It
                 occurred to him that one could also build this machine
                 with electrical parts. First he built small computers,
                 the model Z2 and immediately after this the model Z3,
                 which was based entirely on relays. Both machines
                 worked satisfactory. Then he discovered Boolean
                 algebra. He could now design a computer on paper. He
                 continued to develop machines and founded a company in
                 Germany where a number of machines such as the Z11 were
                 built.",
  acknowledgement = ack-nhfb,
  classification = "C0200 (General computer topics); C5220 (Computer
                 architecture); C5420 (Mainframes and minicomputers)",
  confdate =     "28 Aug.-2 Sept. 1994",
  conflocation = "Hamburg, Germany",
  fjournal =     "IFIP Transactions. A. Computer Science and
                 Technology",
  keywords =     "Binary instruction stream based computers; Boolean
                 algebra; Computer architecture; Exponent; Floating
                 point numbers; Half-logarithmic form; Storage device;
                 Z11; Z2; Z3; ZUSE KG",
  pubcountry =   "Netherlands",
  thesaurus =    "Computer architecture; Digital computers; History",
}

@InProceedings{Aagaard:1995:FVP,
  author =       "M. Aagaard and C. Seger",
  title =        "The formal verification of a pipelined
                 double-precision {IEEE} floating-point multiplier",
  crossref =     "IEEE:1995:IAI",
  pages =        "7--10",
  year =         "1995",
  bibdate =      "Sat Jun 02 07:46:35 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Abdallah:1995:SASa,
  author =       "M. Abdallah and A. Skavantzos",
  booktitle =    "Proceedings of the Twenty-Seventh Southeastern
                 Symposium on System Theory, 12--14 March 1995",
  title =        "A systematic approach for selecting practical moduli
                 sets for residue number systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "445--449",
  year =         "1995",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/SSST.1995.390542",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The residue number system (RNS) is a useful tool for
                 digital signal processing (DSP) since it can support
                 parallel, carry free, high speed arithmetic. An RNS is
                 defined by a set of relatively prime integers called
                 the moduli set. The most important \ldots{}",
}

@InProceedings{Abdallah:1995:SASb,
  author =       "M. Abdallah and A. Skavantzos",
  booktitle =    "Proceedings of the Twenty-Seventh Southeastern
                 Symposium on System Theory, 12--14 March 1995",
  title =        "A systematic approach for selecting practical moduli
                 sets for residue number systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "445--449",
  year =         "1995",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/SSST.1995.390542",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The residue number system (RNS) is a useful tool for
                 digital signal processing (DSP) since it can support
                 parallel, carry free, high speed arithmetic. An RNS is
                 defined by a set of relatively prime integers called
                 the moduli set. The most important \ldots{}",
}

@Article{Al-Mouhamed:1995:ELF,
  author =       "Mayez Al-Mouhamed and Lubomir Bic",
  title =        "Effects of Loop Fusion and Statement Migration on the
                 Speedup of Vector Multiprocessors",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "31",
  number =       "1",
  pages =        "56--64",
  day =          "15",
  month =        nov,
  year =         "1995",
  CODEN =        "JPDCER",
  DOI =          "https://doi.org/10.1006/jpdc.1995.1144",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Thu Mar 9 09:18:58 MST 2000",
  bibsource =    "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.idealibrary.com/links/doi/10.1006/jpdc.1995.1144/production;
                 http://www.idealibrary.com/links/doi/10.1006/jpdc.1995.1144/production/pdf",
  acknowledgement = ack-nhfb,
  classification = "C5220P (Parallel architecture); C6150C (Compilers,
                 interpreters and other processors); C6150N (Distributed
                 systems software)",
  corpsource =   "Department of Comput. Eng., King Fahd University of
                 Pet. and Miner., Dhahran, Saudi Arabia",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "arithmetic pipelines; C240; cache reuse; commercial
                 optimizing compiler; load and store operations; loop
                 fusion; optimising compilers; optimization; parallel
                 architectures; parallel-vector loops; processor;
                 resource allocation; scheduled; scheduling; statement
                 migration; vector multiprocessors; vector processor
                 systems",
  treatment =    "P Practical",
}

@TechReport{Altwaijry:1995:PAT,
  author =       "H. Altwaijry and M. Flynn",
  title =        "Performance\slash area tradeoffs in {Booth}
                 multipliers",
  type =         "Technical Report",
  number =       "CSL-TR-95-684",
  institution =  "Computer Systems Laboratory, Stanford University",
  address =      "Stanford, CA, USA",
  month =        nov,
  year =         "1995",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}

@Article{Anonymous:1995:FEF,
  author =       "Anonymous",
  title =        "Fraction eliminate floating-point multiply",
  journal =      j-EDN,
  volume =       "40",
  number =       "24",
  pages =        "88--??",
  year =         "1995",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "EDN",
}

@Article{Anonymous:1995:INM,
  author =       "Anonymous",
  title =        "{IBM}'s new {Model 3CT RS\slash 6000} workstation
                 provides the industry's best floating-point price\slash
                 performance numbers in the {US}\$35,000 to {US}\$50,000
                 price range",
  journal =      j-OPEN-SYSTEMS-TODAY,
  volume =       "??",
  number =       "169",
  pages =        "32--??",
  month =        feb,
  year =         "1995",
  ISSN =         "1061-0839",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Open Systems Today",
}

@Article{Anonymous:1995:MVW,
  author =       "Anonymous",
  title =        "Micro View --- What lessons can chip makers and their
                 customers take from the {Pentium} floating-point divide
                 flaw and the resultant tidal wave of publicity?",
  journal =      j-IEEE-MICRO,
  volume =       "15",
  number =       "2",
  pages =        "88--??",
  month =        mar # "\slash " # apr,
  year =         "1995",
  CODEN =        "IEMIDZ",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}

@Article{Anonymous:1995:PCH,
  author =       "Anonymous",
  title =        "Program converts hex to floating point",
  journal =      j-EDN,
  volume =       "40",
  number =       "15",
  pages =        "76--??",
  year =         "1995",
  CODEN =        "EDNSBH",
  ISSN =         "0012-7515, 0364-6637",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "EDN",
}

@InProceedings{Antelo:1995:RCR,
  author =       "Elisardo Antelo and Javier D. Bruguera and Julio
                 Villalba and Emilio L. Zapata",
  title =        "Redundant {CORDIC} Rotator Based on Parallel
                 Prediction",
  crossref =     "Knowles:1995:PSC",
  pages =        "172--179",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC
                 Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Antelo.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}

@Article{Bailey:1995:FBM,
  author =       "David H. Bailey",
  title =        "A {Fortran-90} Based Multiprecision System",
  journal =      j-TOMS,
  volume =       "21",
  number =       "4",
  pages =        "379--387",
  month =        dec,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/212066.212075",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Apr 29 15:15:44 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also extension to complex arithmetic
                 \cite{Smith:1998:AMP}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p379-bailey/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "arithmetic; Fortran 90; multiprecision",
  subject =      "D.3.2 [Programming Languages]: Language
                 Classifications -- Fortran 90; D.3.4 [Programming
                 Languages]: Processors; G.1.0 [Numerical Analysis]:
                 General; G.1.2 [Numerical Analysis]: Approximation",
}

@InProceedings{Bannon:1995:IAA,
  author =       "P. Bannon and J. Keller",
  title =        "Internal architecture of {Alpha 21164}
                 microprocessor",
  crossref =     "IEEE:1995:DPC",
  pages =        "79--87",
  month =        mar,
  year =         "1995",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}

@Article{Baron:1995:FPP,
  author =       "P. Baron and A. Joudon and F. Lugiez and M. Rouger",
  title =        "Floating Point Processor for Photomultiplier Tube
                 Signals",
  journal =      j-IEEE-TRANS-NUCL-SCI,
  volume =       "42",
  number =       "4",
  pages =        "750--752",
  month =        aug,
  year =         "1995",
  CODEN =        "IRNSAM",
  ISSN =         "0018-9499 (print), 1558-1578 (electronic)",
  ISSN-L =       "0018-9499",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Nuclear Science",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=23",
  summary =      "A fast digital readout system has been designed for
                 synchronous processing of the current signals delivered
                 by a 64-channel multichannel photomultiplier tube
                 (MCPMT) associated with fast scintillators. This mixed
                 analog digital full custom chip uses \ldots{}",
}

@Article{Bauer:1995:AEB,
  author =       "P. H. Bauer",
  title =        "Absolute Error Bounds for Block Floating-Point
                 Direct-Form Digital Filters",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "43",
  number =       "8",
  pages =        "1994--1996",
  month =        aug,
  year =         "1995",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "Provides an asymptotic response analysis of digital
                 filters, which are implemented in block floating-point
                 format. Using absolute bounds on the quantization
                 error, conditions for the existence of certain response
                 types and the corresponding bounds on \ldots{}",
}

@Article{Bauer:1995:ARE,
  author =       "P. H. Bauer",
  title =        "Absolute Response Error Bounds for Floating Point
                 Digital Filters in State Space Representation",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "42",
  number =       "9",
  pages =        "610--613",
  month =        sep,
  year =         "1995",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.466642",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems. 2, Analog
                 and Digital Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  summary =      "A deterministic study of the zero input asymptotic
                 behavior of second order state space digital filters
                 with floating point arithmetic is carried out. Using a
                 consecutive bound reduction method, asymptotic bounds
                 on the state response are derived. It \ldots{}",
}

@InProceedings{Baumhof:1995:NVV,
  author =       "Christoph Baumhof",
  title =        "A New {VLSI} Vector Arithmetic Coprocessor for the
                 {PC}",
  crossref =     "Knowles:1995:PSC",
  pages =        "210--215",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Baumhof.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}

@Article{Beaty:1995:EAS,
  author =       "Steven J. Beaty and Gearold R. Johnson",
  title =        "Effect of adding a scalar {D-cache} to the {Cray-4}
                 vector processor",
  journal =      j-IEEE-INT-CONF-ALG-ARCH-PAR-PROC,
  volume =       "1",
  pages =        "227--230",
  year =         "1995",
  bibdate =      "Mon Aug 26 10:51:12 MDT 1996",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog number 95TH0682-5.",
  abstract =     "In the past, vector supercomputers achieved high
                 performance with long arithmetic pipelines coupled with
                 fast scalar processors. Processor speed has increased
                 at a rate greater than memory speed. Indeed, current
                 vector processors have cycle times far faster than the
                 memories they are connected to. When compilers can
                 predict memory access patterns, they vectorize
                 computations and thereby hide the processor\slash
                 memory disparity. When memory access patterns are not
                 known until run-time, caches can pay large dividends.
                 This paper studies the effects of adding a scalar data
                 cache to a modern vector processor and shows some
                 encouraging results.",
  acknowledgement = ack-nhfb,
  affiliation =  "Cray Computer Corp",
  affiliationaddress = "Colorado Springs, CO, USA",
  classification = "722.1; 722.4; 723.1; 723.2",
  conference =   "Proceedings of the IEEE 1st International Conference
                 on Algorithms and Architectures for Parallel
                 Processing. Part 1 (of 2)",
  fjournal =     "IEEE International Conference on Algorithms and
                 Architectures for Parallel Processing",
  journalabr =   "IEEE Int Conf Algorithms Archit Parall Process",
  keywords =     "Buffer storage; Cray memory hierarchy; Cray-4 vector
                 processor; Data processing; Hierarchical systems;
                 Program processors; Scalar D-cache; Supercomputers;
                 Systems analysis",
  meetingaddress = "Brisbane, Aust",
  meetingdate =  "Apr 19--21 1995",
  meetingdate2 = "04/19--21/95",
  sponsor =      "IEEE",
}

@InProceedings{Bederr:1995:AAE,
  author =       "H. Bederr and M. Nicolaidis and A. Guyot",
  title =        "Analytic Approach for Error Masking Elimination in
                 On-Line Multipliers",
  crossref =     "Knowles:1995:PSC",
  pages =        "30--37",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Bederr.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}

@Article{Bickerstaff:1995:PRA,
  author =       "K'Andrea C. Bickerstaff and Michael J. Schulte and
                 Earl E. {Swartzlander, Jr.}",
  title =        "Parallel reduced area multipliers",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "9",
  number =       "3",
  pages =        "181--191",
  month =        apr,
  year =         "1995",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1007/BF02407084",
  ISSN =         "0922-5773 (print), 1573-109X (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Mon Mar 05 08:29:38 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://springerlink.metapress.com/content/761m0225754r4440/fulltext.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
}

@Article{Bierman:1995:FAI,
  author =       "Keith Bierman",
  title =        "{Fortran} access to {IEEE 754} exceptions",
  journal =      j-FORTRAN-FORUM,
  volume =       "14",
  number =       "3",
  pages =        "15--18",
  month =        sep,
  year =         "1995",
  CODEN =        "????",
  ISSN =         "1061-7264 (print), 1931-1311 (electronic)",
  ISSN-L =       "1061-7264",
  bibdate =      "Wed Feb 6 18:50:05 MST 2002",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Fortran Forum",
  issue =        "43",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J286",
}

@Article{Boley:1995:FPF,
  author =       "D. Boley and G. H. Golub and S. Makar and N. Saxena
                 and E. J. McCluskey",
  title =        "Floating Point Fault Tolerance with Backward Error
                 Assertions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "2",
  pages =        "302--311",
  month =        feb,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.364541",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:01:26 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=364541",
  abstract =     "The paper introduces an assertion scheme based on the
                 backward error analysis for error detection in
                 algorithms that solve dense systems of linear
                 equations, Ax=b. Unlike previous methods, this backward
                 error assertion model is specifically designed to
                 operate in an environment of floating point arithmetic
                 subject to round-off errors, and it can be easily
                 instrumented in a Watchdog processor environment. The
                 complexity of verifying assertions is O(n/sup 2/),
                 compared to the O(n/sup 3/) complexity of algorithms
                 solving Ax=b. Unlike other proposed error detection
                 methods, this assertion model does not require any
                 encoding of the matrix A. Experimental results under
                 various error models are presented to validate the
                 effectiveness of this assertion scheme.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, Minnesota University,
                 Minneapolis, MN, USA",
  ajournal =     "IEEE Trans. Comput.",
  classification = "C4140 (Linear algebra); C4240C (Computational
                 complexity); C5230 (Digital arithmetic methods); C5470
                 (Performance evaluation and testing)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Assertion scheme; Backward error analysis; Backward
                 error assertions; Complexity; Dense systems; Error
                 detection; Error models; Floating point arithmetic;
                 Floating point fault tolerance; Linear equations;
                 Round-off errors; Watchdog processor environment",
  summary =      "The paper introduces an assertion scheme based on the
                 backward error analysis for error detection in
                 algorithms that solve dense systems of linear
                 equations, Ax=b. Unlike previous methods, this backward
                 error assertion model is specifically designed
                 \ldots{}",
  thesaurus =    "Computational complexity; Error analysis; Error
                 detection; Fault tolerant computing; Floating point
                 arithmetic; Linear algebra",
}

@Article{Bomar:1995:RNA,
  author =       "B. W. Bomar and L. M. Smith and R. D. Joseph",
  title =        "Roundoff Noise Analysis of State-Space Digital Filters
                 Implemented on Floating-Point Digital Signal
                 Processors",
  journal =      "Proceedings - IEEE International Symposium on Circuits
                 and Systems",
  volume =       "??",
  number =       "3",
  pages =        "III-2023",
  year =         "1995",
  ISSN =         "0271-4310",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Booker:1995:FER,
  author =       "Alan Booker",
  title =        "Floating-Point Emulation and Representation",
  journal =      j-EMBED-SYS-PROG,
  volume =       "8",
  number =       "9",
  pages =        "111--??",
  year =         "1995",
  CODEN =        "EYPRE4",
  ISSN =         "1040-3272",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Embedded Systems Programming",
}

@Article{BrinchHansen:1995:LDA,
  author =       "Per {Brinch Hansen}",
  title =        "The Long Division Algorithm of {Linger}, {Mills} and
                 {Witt}",
  journal =      j-SPE,
  volume =       "25",
  number =       "1",
  pages =        "109--109",
  month =        jan,
  year =         "1995",
  CODEN =        "SPEXBL",
  DOI =          "https://doi.org/10.1002/spe.4380250107",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Sat May 31 13:36:16 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/hansen-per-brinch.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/litprog.bib;
                 https://www.math.utah.edu/pub/tex/bib/spe.bib",
  note =         "See \cite{Linger:1979:SPT,BrinchHansen:1994:MLD}.",
  abstract =     "The long division algorithm of Linger, Mills and Witt
                 \cite{Linger:1979:SPT} is discussed and found to be
                 significantly slower than a recent algorithm developed
                 by the author.",
  acknowledgement = ack-nhfb,
  ajournal =     "Softw. Pract. Exp.",
  fjournal =     "Software --- Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  onlinedate =   "30 Oct 2006",
}

@Article{Burgess:1995:COT,
  author =       "N. Burgess and T. Williams",
  title =        "Choices of operand truncation in the {SRT} division
                 algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "7",
  pages =        "933--937",
  month =        jul,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.392852",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:01:28 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=392852",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Burnikel:1995:EGC,
  author =       "Christoph Burnikel and Jochen Konemann and Kurt
                 Mehlhorn and Stefan Naher and Stefan Schirra and
                 Christian Uhrig",
  title =        "Exact Geometric Computation in {LEDA}",
  crossref =     "ACM:1995:PEA",
  pages =        "C18--C19",
  year =         "1995",
  bibdate =      "Tue Nov 13 21:49:22 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Carreno:1995:IIF,
  author =       "Victor A. Carreno",
  title =        "Interpretation of {IEEE-854} floating-point standard
                 and definition in the {HOL} system",
  type =         "{NASA} technical memorandum",
  number =       "110189",
  institution =  pub-NASA,
  address =      pub-NASA:adr,
  pages =        "????",
  year =         "1995",
  bibdate =      "Thu Oct 24 14:19:35 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Shipping list no. 96-0366-M.",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; formalism; standards",
}

@InProceedings{Carreno:1995:SIF,
  author =       "Victor A. Carre{\~n}o and Paul S. Miner",
  title =        "Specification of the {IEEE-854} Floating-Point
                 Standard in {HOL} and {PVS}",
  crossref =     "Anonymous:1995:HEI",
  year =         "1995",
  bibdate =      "Wed Nov 24 09:09:34 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://shemesh.larc.nasa.gov/fm/ftp/larc/vac/hug95.ps",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  pagecount =    "16",
}

@InProceedings{Chang:1995:REA,
  author =       "P. S. Chang and A. N. {Willson, Jr.}",
  booktitle =    "Conference Record of the Twenty-Ninth Asilomar
                 Conference on Signals, Systems and Computers, 1995",
  title =        "A roundoff error analysis of the normalized {LMS}
                 algorithm",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1337--1341",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper describes an analysis of the normalized LMS
                 algorithm under finite word-length effects. It is shown
                 that, using the averaging principle, it is possible to
                 derive a good approximation for the total MSE in
                 steady-state. Implementation \ldots{}",
}

@InProceedings{Chen:1995:UCA,
  author =       "San-Gee Chen and Chieh-Chih Li",
  booktitle =    "{IEEE} Signal Processing Society Workshop on {VLSI}
                 Signal Processing, {VIII, 1995}",
  title =        "A unified cellular array for multiplication, division
                 and square root",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "533--541",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "A unified fast, small-area processor capable of
                 executing multiplication, division and square-root
                 operations, all starting from MSD is proposed. Unlike
                 the existing designs which require both addition and
                 subtraction operations, and complicated \ldots{}",
}

@Article{Cheng:1995:PBS,
  author =       "Fuhua Cheng and G. W. Wasilkowski and Jiaye Wang and
                 Caiming Zhang and Wenping Wang",
  title =        "Parallel {B}-Spline Surface Interpolation on a
                 Mesh-Connected Processor Array",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "24",
  number =       "2",
  pages =        "224--229",
  day =          "1",
  month =        feb,
  year =         "1995",
  CODEN =        "JPDCER",
  DOI =          "https://doi.org/10.1006/jpdc.1995.1022",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Thu Mar 9 09:18:56 MST 2000",
  bibsource =    "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.idealibrary.com/links/doi/10.1006/jpdc.1995.1022/production;
                 http://www.idealibrary.com/links/doi/10.1006/jpdc.1995.1022/production/pdf",
  acknowledgement = ack-nhfb,
  classification = "B0290F (Interpolation and function approximation);
                 C4130 (Interpolation and function approximation);
                 C4240C (Computational complexity); C4240P (Parallel
                 programming and algorithm theory)",
  corpsource =   "Department of Computer Science, Kentucky University,
                 Lexington, KY, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "algorithms; B-spline surface interpolation; bicubic
                 B-spline surface; Chebyshev approximation; Chebyshev
                 method; computational complexity; constant; control;
                 data points; finite precision; floating-point
                 arithmetic; interconnection networks; interpolation;
                 iterative methods; mesh-connected processor array;
                 multiprocessor; numerical stability; optimal; parallel;
                 parallel implementation; points; splines (mathematics);
                 time",
  treatment =    "T Theoretical or Mathematical",
}

@PhdThesis{Chesneaux:1995:LSL,
  author =       "Jean-Marie Chesneaux",
  title =        "L'arithm{\'e}tique stochastique et le logiciel
                 {CADNA}. ({French}) [{Stochastic} arithmetic and
                 {CADNA} software]",
  type =         "Habilitation {\`a} diriger des recherches",
  school =       "Universit{\'e} Pierre et Marie Curie",
  address =      "Paris, France",
  pages =        "????",
  year =         "1995",
  bibdate =      "Mon Mar 19 14:07:57 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Coe:1995:CAP,
  author =       "Tim Coe and Terje Mathisen and Cleve Moler and Vaughan
                 Pratt",
  title =        "Computational Aspects of the {Pentium} Affair",
  journal =      j-IEEE-COMPUT-SCI-ENG,
  volume =       "2",
  number =       "1",
  pages =        "18--30",
  month =        "Spring",
  year =         "1995",
  CODEN =        "ISCEE4",
  ISSN =         "1070-9924 (print), 1558-190X (electronic)",
  ISSN-L =       "1070-9924",
  bibdate =      "Sat Jan 9 08:57:23 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.computer.org/cse/cs1998/c1018abs.htm",
  abstract =     "The Pentium affair has been widely publicized. It
                 started with an obscure defect in the floating-point
                 unit of Intel Corporation's flagship Pentium
                 microprocessor. This is the story of how the Pentium
                 floating-point division problem was discovered, and
                 what you need to know about the maths and computer
                 engineering involved before deciding whether to replace
                 the chip, install the workaround provided here, or do
                 nothing. The paper also discusses broader issues of
                 computational correctness.",
  acknowledgement = ack-nhfb,
  affiliation =  "Vitesse Semicond. Corp., Camarillo, CA, USA",
  classcodes =   "C5130 (Microprocessor chips); C5230 (Digital
                 arithmetic methods)",
  classification = "C5130 (Microprocessor chips); C5230 (Digital
                 arithmetic methods)",
  corpsource =   "Vitesse Semicond. Corp., Camarillo, CA, USA",
  fjournal =     "IEEE Computational Science \& Engineering",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=99",
  keywords =     "computational aspects; computational correctness;
                 computer engineering; division problem; floating point
                 arithmetic; Floating-point division problem;
                 floating-point unit; Intel Corporation; microprocessor
                 chips; Pentium affair; Pentium microprocessor",
  thesaurus =    "Floating point arithmetic; Microprocessor chips",
  treatment =    "P Practical; T Theoretical or Mathematical",
}

@Article{Coe:1995:IPF,
  author =       "Tim Coe",
  title =        "Inside the {Pentium FDIV} Bug",
  journal =      j-DDJ,
  volume =       "20",
  number =       "4",
  pages =        "129--??",
  month =        apr,
  year =         "1995",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/documents/s=992/ddj9504l/;
                 http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
  keywords =     "Intel Pentium divide flaw; Thomas R. Nicely",
}

@InProceedings{Coe:1995:ITS,
  author =       "Tim Coe and Ping Tak Peter Tang",
  title =        "It Takes Six Ones to Reach a Flaw",
  crossref =     "Knowles:1995:PSC",
  pages =        "140--148",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  note =         "Also available as Chinese University of Hong Kong
                 technical report 95-5 (61), 1995.",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Coe.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12; Pentium divide flaw",
}

@Article{Crenshaw:1995:PTFa,
  author =       "Jack W. Crenshaw",
  title =        "Programmer's Toolbox: Floating-Point Math",
  journal =      j-EMBED-SYS-PROG,
  volume =       "8",
  number =       "11",
  pages =        "25--??",
  year =         "1995",
  CODEN =        "EYPRE4",
  ISSN =         "1040-3272",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Embedded Systems Programming",
}

@Article{Crenshaw:1995:PTFb,
  author =       "Jack W. Crenshaw",
  title =        "Programmer's Toolbox: Floating-Point Math, Part 2",
  journal =      j-EMBED-SYS-PROG,
  volume =       "8",
  number =       "12",
  pages =        "29--??",
  year =         "1995",
  CODEN =        "EYPRE4",
  ISSN =         "1040-3272",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Embedded Systems Programming",
}

@InProceedings{Cui:1995:GIFa,
  author =       "S. Cui and N. Burgess and M. Liebelt and K.
                 Eshraghian",
  title =        "A 32-bit {GaAs IEEE} floating point multiplier using
                 {Trailing-1}'s rounding algorithm",
  crossref =     "Jain:1995:PET",
  pages =        "246--252",
  year =         "1995",
  bibdate =      "Thu Dec 14 11:25:18 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Jain.pdf",
  abstract =     "The paper presents a GaAs 32-bit IEEE floating point
                 multiplier. A modified carry save array is used in
                 conjunction with Booth's algorithm to reduce the
                 partial product addition and interconnection. A special
                 rounding technique called Trailing-1's Predictor is
                 used to speed up the final addition and rounding. This
                 chip uses a new layout methodology for easy design
                 structure and improved GaAs technology layout density.
                 The combination of the fast arithmetic architecture and
                 compact layout style achieves 4ns multiplication time
                 with 3.5 W power dissipation at 75 degrees C. The area
                 is 2.43 mm by 3.77 mm (excluding pads) and uses 28000
                 transistors to give a density of 3056
                 transistors/mm/sup 2/ for 0.8 mu m GaAs technology. (11
                 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Electr. and Electron. Eng., Adelaide
                 University, SA, Australia",
  classification = "B1265B (Logic circuits); C5120 (Logic and switching
                 circuits); C5130 (Microprocessor chips); C5230 (Digital
                 arithmetic methods)",
  keywords =     "3.5 W; 32 Bit; 32 Bit GaAs IEEE floating point
                 multiplier; 75 DegC; Booth algorithm; Compact layout
                 style; Easy design structure; Fast arithmetic
                 architecture; GaAs technology; Improved GaAs technology
                 layout density; Layout methodology; Modified carry save
                 array; Multiplication time; Partial product addition;
                 Power dissipation; Special rounding technique;
                 Trailing-1s rounding algorithm; Transistors",
  numericalindex = "Word length 3.2E+01 bit; Power 3.5E+00 W;
                 Temperature 3.48E+02 K",
  thesaurus =    "Floating point arithmetic; Gallium arsenide;
                 Microprocessor chips; Multiplying circuits; Roundoff
                 errors; Societies",
}

@InProceedings{Cui:1995:GIFb,
  author =       "S. Cui and N. Burgess and M. Liebelt and K.
                 Eshraghian",
  title =        "A {GaAs} {IEEE} Floating Point Standard Single
                 Precision Multiplier",
  crossref =     "Knowles:1995:PSC",
  pages =        "91--97",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Cui.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}

@Article{Das:1995:IFC,
  author =       "D. Das and K. Mukhopadhyaya and B. P. Sinha",
  title =        "Implementation of four common functions on an {LNS}
                 co-processor",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "1",
  pages =        "155--161",
  month =        jan,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.367997",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "We propose a scheme for evaluating four commonly used
                 functions namely, (1) inverse trigonometric functions,
                 (2) trigonometric functions, (3) the exponential
                 function, and (4) the logarithmic function with the
                 help of a logarithmic number system (\ldots{})",
}

@Article{Daumas:1995:MRR,
  author =       "Marc Daumas and Christophe Mazenc and Xavier Merrheim
                 and Jean-Michel Muller",
  title =        "Modular range reduction: a new algorithm for fast and
                 accurate computation of the elementary functions",
  journal =      j-J-UCS,
  volume =       "1",
  number =       "3",
  pages =        "162--175",
  day =          "28",
  month =        mar,
  year =         "1995",
  CODEN =        "????",
  ISSN =         "0948-6968",
  ISSN-L =       "0948-6968",
  MRclass =      "68M07 (65D20 68Q20)",
  MRnumber =     "97b:68012",
  bibdate =      "Wed May 28 19:32:35 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.iicm.edu/jucs_1_3/modular_range_reduction",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
  keywords =     "range reduction",
}

@Article{Demmel:1995:CSB,
  author =       "James W. Demmel and Inderjit Dhillon and Huan Ren",
  title =        "On the correctness of some bisection-like parallel
                 eigenvalue algorithms in floating point arithmetic",
  journal =      j-ELECTRON-TRANS-NUMER-ANAL,
  volume =       "3",
  pages =        "116--149",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "1068-9613 (print), 1097-4067 (electronic)",
  ISSN-L =       "1068-9613",
  bibdate =      "Mon Sep 6 12:28:29 MDT 2010",
  bibsource =    "http://etna.mcs.kent.edu/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://etna.mcs.kent.edu/vol.3.1995/pp116-149.dir/pp116-149.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronic Transactions on Numerical Analysis",
  journal-URL =  "http://etna.mcs.kent.edu/",
}

@Article{DiClaudio:1995:FCR,
  author =       "E. D. {Di Claudio} and F. Piazza and G. Orlandi",
  title =        "Fast combinatorial {RNS} processors for {DSP}
                 applications",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "5",
  pages =        "624--633",
  month =        may,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.381948",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:01:27 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=381948",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Doman:1995:SAP,
  author =       "B. G. S. Doman and C. J. Pursglove and W. M. Coen",
  title =        "A Set of {Ada} Packages for High Precision
                 Calculations",
  journal =      j-TOMS,
  volume =       "21",
  number =       "4",
  pages =        "416--431",
  month =        dec,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/212066.212087",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 14 09:57:55 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p416-doman/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "accuracy; Ada; arithmetic elementary-function
                 evaluation; floating-point; multiple-precision portable
                 software",
  subject =      "G.1.0 [Numerical Analysis]: General -- computer
                 arithmetic; G.1.2 [Numerical Analysis]: Approximation
                 -- elementary function approximation; G.4 [Mathematics
                 of Computing]: Mathematical Software -- algorithm
                 analysis; efficiency; portability",
}

@Article{Doran:1995:SCD,
  author =       "R. W. Doran",
  title =        "Special Cases of Division",
  journal =      j-J-UCS,
  volume =       "1",
  number =       "3",
  pages =        "176--194",
  day =          "28",
  month =        mar,
  year =         "1995",
  CODEN =        "????",
  ISSN =         "0948-6968",
  ISSN-L =       "0948-6968",
  MRclass =      "68M07 (68Q20)",
  MRnumber =     "97b:68013",
  bibdate =      "Wed May 28 19:32:35 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.iicm.edu/jucs_1_3/special_cases_of_division",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
}

@InProceedings{Ercegovac:1995:SDC,
  author =       "Milo{\v{s}} D. Ercegovac and Tom{\'a}s Lang",
  title =        "Sign Detection and Comparison Networks with a Small
                 Number of Transitions",
  crossref =     "Knowles:1995:PSC",
  pages =        "59--66",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Ercegovac.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}

@Article{Espelid:1995:FPS,
  author =       "T. O. Espelid",
  title =        "On Floating-Point Summation",
  journal =      j-SIAM-REVIEW,
  volume =       "37",
  number =       "4",
  pages =        "603--607",
  month =        dec,
  year =         "1995",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1037130",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "65Gxx (65Bxx)",
  MRnumber =     "1 368 391",
  bibdate =      "Sat Mar 29 09:55:35 MDT 2014",
  bibsource =    "Compendex database;
                 http://epubs.siam.org/toc/siread/37/4;
                 http://www.siam.org/journals/sirev/sirev374.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "http://epubs.siam.org/27303.htm",
  abstract =     "In this paper we focus on some general error analysis
                 results in floating-point summation. We emphasize
                 analysis that is useful from both a scientific and a
                 teaching point of view.",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ of Bergen",
  affiliationaddress = "Bergen, Norway",
  classification = "721.1; 921.4; 921.6; C4110 (Error analysis in
                 numerical methods); C5230 (Digital arithmetic
                 methods)",
  corpsource =   "Department of Inf., Bergen University, Norway",
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  journalabr =   "SIAM Rev",
  keywords =     "accurate floating-point summation; algorithm sum;
                 algorithms; binary summation tree; digital arithmetic;
                 error analysis; floating-point arithmetic;
                 floating-point summation; number theory; numerical
                 analysis; ordering; root of the tree; rounding errors;
                 roundoff errors; set theory; trees (mathematics)",
  onlinedate =   "December 1995",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Fateman:1995:FFP,
  author =       "Richard J. Fateman and Kevin A. Broughan and Diane K.
                 Willcock and Duane Rettig",
  title =        "Fast Floating Point Processing in {Common Lisp}",
  journal =      j-TOMS,
  volume =       "21",
  number =       "1",
  pages =        "26--62",
  month =        mar,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/200979.200989",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:20:50 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See remark \cite{Reid:1996:RFF}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-1/p26-fateman/",
  acknowledgement = ack-nhfb # " and " # ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "C programming language; Common Lisp; compiler
                 optimization; floating-point arithmetic; Fortran; Lisp;
                 numerical algorithms; symbolic computation",
  subject =      "D.3.4 [Programming Languages]: Processors ---
                 compilers; interpreters; optimization; G.4 [Mathematics
                 of Computing]: Mathematical Software --- efficiency;
                 portability",
}

@InProceedings{Ferguson:1995:ECS,
  author =       "Warren E. {Ferguson, Jr.}",
  title =        "Exact Computation of a Sum or Difference with
                 Applications to Argument Reduction",
  crossref =     "Knowles:1995:PSC",
  pages =        "216--221",
  year =         "1995",
  DOI =          "https://doi.org/10.1109/ARITH.1995.465355",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Ferguson.pdf",
  abstract =     "Results are presented that identify when the computed
                 value of a sum or difference is exact. The accuracy of
                 an argument reduction algorithm is analyzed using these
                 results. This analysis demonstrates that catastrophic
                 cancellation does not occur in this algorithm's
                 computation of the reduced argument.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation; ARITH-12; range
                 reduction",
}

@Article{Figueroa:1995:WDR,
  author =       "Samuel A. Figueroa",
  title =        "When is Double Rounding Innocuous?",
  journal =      j-SIGNUM,
  volume =       "30",
  number =       "3",
  pages =        "21--26",
  month =        jul,
  year =         "1995",
  CODEN =        "SNEWD6",
  DOI =          "https://doi.org/10.1145/221332.221334",
  ISSN =         "0163-5778 (print), 1558-0237 (electronic)",
  ISSN-L =       "0163-5778",
  bibdate =      "Tue Apr 12 07:50:26 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.nyu.edu/csweb/Research/Theses/figueroa_sam.pdf",
  abstract =     "Double rounding is the phenomenon that occurs when the
                 result of an operation is rounded to fit some
                 intermediate destination, and then again when delivered
                 to its final destination. This can be a common
                 occurrence when using some floating-point arithmetic
                 engines which lack single precision registers: results
                 of operations are typically rounded to fit in a
                 register, whose width may be double precision or wider,
                 before being stored in some memory location possibly in
                 a format narrower than that of the registers. Examples
                 of such floating-point arithmetic engines include
                 Intel's x87 series and IBM's POWER architecture.
                 (Implementations of the latter are found in some IBM
                 workstations.)",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGNUM Newsletter",
  journal-URL =  "https://dl.acm.org/loi/signum",
}

@TechReport{Flynn:1995:ADA,
  author =       "Michael J. Flynn and Stuart F. Oberman",
  title =        "An analysis of division algorithms and
                 implementations",
  type =         "Report",
  number =       "CSL-TR-95-675",
  institution =  "Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "58",
  month =        jul,
  year =         "1995",
  bibdate =      "Wed Dec 13 08:55:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://searchworks.stanford.edu/view/4639530",
  abstract =     "Floating-point division is generally regarded as a low
                 frequency, high latency operation in typical
                 floating-point applications. However, the increasing
                 emphasis on high performance graphics and the
                 industry-wide usage of performance benchmarks forces
                 processor designers to pay close attention to all
                 aspects of floating-point computation. Many algorithms
                 are suitable for implementing division in hardware.
                 This paper presents four major classes of algorithms in
                 a unified framework, namely digit recurrence,
                 functional iteration, very high radix, and variable
                 latency. Digit recurrence algorithms, the most common
                 of which is SRT, use subtraction as the fundamental
                 operator, and they converge to a quotient linearly.
                 Division by functional iteration converges to a
                 quotient quadratically using multiplication. Very high
                 radix division algorithms are similar to digit
                 recurrence algorithms, but they incorporate
                 multiplication to reduce the latency. Variable latency
                 division algorithms reduce the average latency to form
                 the quotient. These algorithms are explained and
                 compared in this work. It is found that for low-cost
                 implementations where chip area must be minimized,
                 digit recurrence algorithms are suitable. An
                 implementation of division by functional iteration can
                 provide the lowest latency for typical multiplier
                 latencies. Variable latency algorithms show promise for
                 simultaneously minimizing average latency while also
                 minimizing area.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Flynn:1995:SPT,
  author =       "M. J. Flynn and K. Nowka and G. Bewick and E. Schwarz
                 and N. Quach",
  title =        "The {SNAP} Project: Towards Sub-Nanosecond
                 Arithmetic",
  crossref =     "Knowles:1995:PSC",
  pages =        "75--83",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "ftp://arith.stanford.edu/tr/snap_arith12.ps.Z;
                 http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Flynn.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}

@InProceedings{Freeman:1995:CAD,
  author =       "S. Freeman and M. O'Donnell",
  booktitle =    "{1995 International Conference on Acoustics, Speech,
                 and Signal Processing}",
  title =        "A complex arithmetic digital signal processor using
                 {CORDIC} rotators",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "3191--3194 (vol. 5)",
  year =         "1995",
  DOI =          "https://doi.org/10.1109/ICASSP.1995.479563",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; Clocks; Digital arithmetic; Digital signal
                 processors; Process design; Random access memory; Read
                 only memory; Registers; Signal design; Signal
                 processing",
}

@Article{Fried:1995:PON,
  author =       "Stephen S. Fried",
  title =        "{Pentium} Optimizations and Numeric Performance",
  journal =      j-DDJ,
  volume =       "20",
  number =       "1",
  pages =        "18--20, 22, 26--29",
  month =        jan,
  year =         "1995",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Thu Sep 05 07:21:01 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 UnCover database",
  abstract =     "The Pentium is the first member of the Intel x86
                 family that requires RISC-style instruction scheduling
                 to achieve its full potential. Steve analyzes what this
                 means in terms of Pentium floating-point performance
                 and how you can get full throughput from a Pentium.",
  acknowledgement = ack-nhfb,
  affiliation =  "Microway, Kingston, MA, USA",
  classification = "C5130 (Microprocessor chips); C5230 (Digital
                 arithmetic methods); C5470 (Performance evaluation and
                 testing); C6150C (Compilers, interpreters and other
                 processors)",
  fjournal =     "Dr. Dobb's Journal of Software Tools",
  keywords =     "Compilers; Floating-point performance; Full
                 throughput; Intel x86 family; Numeric performance;
                 Optimizations; Pentium; RISC-style instruction
                 scheduling; Tools",
  thesaurus =    "Floating point arithmetic; Microprocessor chips;
                 Optimisation; Performance evaluation; Program
                 compilers; Reduced instruction set computing",
}

@PhdThesis{Gluss:1995:DIA,
  author =       "Robert Joseph Gluss",
  title =        "Design and implementation of an asynchronous radix-$4$
                 pre-scaling floating-point divider",
  type =         "Thesis ({M.S.})",
  school =       "Department of Electrical and Computer Engineering,
                 University of California, Davis",
  address =      "Davis, CA, USA",
  year =         "1995",
  LCCN =         "LD781.D5j 1995 G587",
  bibdate =      "Thu Oct 24 14:19:35 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "dissertations, academic -- University of California,
                 Davis -- Electrical and Computer Engineering",
}

@InProceedings{Greenley:1995:UNG,
  author =       "D. Greenley and J. Bauman and D. Chang and Dennis Chen
                 and R. Eltejaein and P. Ferolito and P. Fu and Robert
                 B. Garner and D. Greenhill and H. Grewal and Kalon
                 Holdbrook and B. Kim and Leslie Kohn and H. Kwan and M.
                 Levitt and Guillermo Maturana and D. Mrazek and
                 Chitresh Narasimhaiah and Kevin Normoyle and N. Parveen
                 and P. Patel and A. Prabhu and Marc Tremblay and
                 Michelle Wong and L. Yang and Krishna Yarlagadda and
                 Robert K. Yu and Robert Yung and Gregory B. Zyner",
  title =        "{UltraSPARC}: the next generation superscalar 64-bit
                 {SPARC}",
  crossref =     "IEEE:1995:DPC",
  pages =        "442--451",
  month =        mar,
  year =         "1995",
  DOI =          "https://doi.org/10.1109/CMPCON.1995.512421",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "UltraSPARC is the first microprocessor from Sun
                 Microsystems' SPARC Technology Business to implement
                 the new 64-bit SPARC V9 architecture. ULtraSPARC is
                 equipped with unique multimedia capabilities and is
                 capable of 4-way superscalar instruction dispatch, with
                 an emphasis on maximal system efficiency and throughput
                 in the execution of complex, memory-intensive
                 applications. UltraSPARC maintains a strict binary
                 compatibility with the thousands of existing 32-bit
                 applications developed for other SPARC processors. This
                 paper describes the feature set and operation of
                 UltraSPARC.",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}

@Article{Halfhill:1995:TBP,
  author =       "Tom R. Halfhill",
  title =        "The Truth Behind the {Pentium} Bug: How often do the
                 five empty cells in the {Pentium}'s {FPU} lookup table
                 spell miscalculation?",
  journal =      j-BYTE,
  volume =       "20",
  number =       "3",
  pages =        "163--??",
  month =        mar,
  year =         "1995",
  CODEN =        "BYTEDJ",
  ISSN =         "0360-5280 (print), 1082-7838 (electronic)",
  ISSN-L =       "0360-5280",
  bibdate =      "Tue Jan 2 10:01:41 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "BYTE Magazine",
}

@InProceedings{Hamano:1995:DCA,
  author =       "Takafumi Hamano and Naofumi Takagi and Shuzo Yajima
                 and Franco P. Preparata",
  title =        "{$ O(n) $}-Depth Circuit Algorithm for Modular
                 Exponentiation",
  crossref =     "Knowles:1995:PSC",
  pages =        "188--192",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Hamano.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}

@Article{Harrison:1995:FPV,
  author =       "J. Harrison",
  title =        "Floating Point Verification in {HOL}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "??",
  number =       "971",
  pages =        "186--??",
  year =         "1995",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InProceedings{Hassler:1995:FET,
  author =       "Hannes Hassler and Naofumi Takagi",
  title =        "Function Evaluation by Table Look-up and Addition",
  crossref =     "Knowles:1995:PSC",
  pages =        "10--16",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Hassler.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}

@TechReport{Hauser:1995:HFE,
  author =       "John R. Hauser",
  title =        "Handling floating-point exceptions in numeric
                 programs",
  type =         "Report",
  number =       "UCB/CSD 95-870",
  institution =  "Computer Science Division (EECS), University of
                 California",
  address =      "Berkeley, CA, USA",
  pages =        "31",
  month =        mar,
  year =         "1995",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@MastersThesis{Helsley:1995:SZL,
  author =       "Harold David Helsley",
  title =        "A study of zero-input limit cycles in floating-point
                 digital signal processors",
  type =         "Thesis ({M.S.})",
  school =       "University of Tennessee, Knoxville",
  address =      "Knoxville, TN, USA",
  pages =        "vii + 65",
  year =         "1995",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Limit cycles.; Signal processing --- Digital
                 techniques.",
}

@InProceedings{Hiasat:1995:HSDa,
  author =       "A. A. Hiasat and H. S. Abdel-Aty-Zohdy",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, {ISCAS '95}, 3 May 1995",
  title =        "A high-speed division algorithm for residue number
                 system",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1996--1999",
  year =         "1995",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1995.523813",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A new algorithm for one of the longstanding problems
                 in residue number system, namely division, is
                 presented. The algorithm is very simple. It approaches
                 the paper-and-pencil division procedure where the
                 quotient is selected to guarantee a non- \ldots{}",
}

@InProceedings{Hiasat:1995:HSDb,
  author =       "A. A. Hiasat and H. S. Abdel-Aty-Zohdy",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems, {ISCAS '95}, 3 May 1995",
  title =        "A high-speed division algorithm for residue number
                 system",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1996--1999",
  year =         "1995",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1995.523813",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A new algorithm for one of the longstanding problems
                 in residue number system, namely division, is
                 presented. The algorithm is very simple. It approaches
                 the paper-and-pencil division procedure where the
                 quotient is selected to guarantee a non- \ldots{}",
}

@Article{Hitz:1995:IDR,
  author =       "Markus A. Hitz and Erich Kaltofen",
  title =        "Integer division in residue number systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "8",
  pages =        "983--989",
  month =        aug,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.403714",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:01:29 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=9076;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=403714",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue arithmetic; residue number system",
  summary =      "This contribution to the ongoing discussion of
                 division algorithm for residue number systems (RNS) is
                 based on Newton iteration for computing the reciprocal.
                 An extended RNS with twice the number of moduli
                 provides the range required for \ldots{}",
}

@InProceedings{Ho:1995:CFF,
  author =       "H. Ho and V. Szwarc and L. Desormeaux",
  booktitle =    "Proceedings of the Eighth Annual {IEEE} International
                 {ASIC} Conference and Exhibit, 1995",
  title =        "A comparison of {FIR} filter implementations based on
                 two's complement and residue number arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "35--38",
  year =         "1995",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ASIC.1995.580676",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Two FIR filter designs based on residue number
                 arithmetic (RNA) are presented and compared with a
                 conventional design based on two's complement
                 arithmetic (TCA). For the RNA based designs the
                 arithmetic operations are implemented by means of small
                 \ldots{}",
}

@MastersThesis{Ho:1995:FPI,
  author =       "Lei Ho",
  title =        "Floating point implementation for {Motorola HC6811C}:
                 {GNU C} cross-compiler",
  type =         "{Master}'s Thesis",
  school =       "Department of Electrical Engineering, Ryerson
                 Polytechnic University",
  address =      "Toronto, Ontario, Canada",
  year =         "1995",
  bibdate =      "Mon Apr 18 06:29:41 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  xxnote =       "Check thesis type?? Ryerson library catalog does not
                 specify.",
}

@Article{Hobson:1995:EMR,
  author =       "R. F. Hobson and M. W. Fraser",
  title =        "An efficient maximum-redundancy radix-$8$ {SRT}
                 division and square-root method",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "30",
  number =       "1",
  pages =        "29--38",
  month =        jan,
  year =         "1995",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A new approach to integrating hardware multiplication,
                 division, and square-root is presented. We use a fully
                 integrated control path which simultaneously reduces
                 part of the redundant partial-remainder and performs a
                 truncated multiplication of the next quotient or
                 square-root digit by the divisor or square-root value.
                 A separate (parallel) full precision iterative
                 multiplier is used for partial remainder production.
                 Strategic details of a radix-8 implementation are
                 discussed. It is shown that a maximally redundant digit
                 set is a viable choice for high performance in this
                 case.",
  acknowledgement = ack-nhfb,
  affiliation =  "Sch. of Computer Science, Simon Fraser University,
                 Burnaby, BC, Canada",
  classification = "B1265B (Logic circuits); B2570D (CMOS integrated
                 circuits); C5230 (Digital arithmetic methods)",
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "1.2 Mum; CMOS adder cell; CMOS divider; Division; IEEE
                 floating point algorithm; Integrated control path;
                 Maximally redundant digit set; Maximum-redundancy
                 radix-8 SRT algorithm; Multiplication; Parallel
                 iterative multiplier; Partial remainder production;
                 Redundant partial-remainder; Square-root method; Table
                 lookup",
  numericalindex = "Size 1.2E-06 m",
  summary =      "A new approach to integrating hardware multiplication,
                 division, and square-root is presented. We use a fully
                 integrated control path which simultaneously reduces
                 part of the redundant partial-remainder and performs a
                 truncated multiplication of the \ldots{}",
  thesaurus =    "Adders; CMOS digital integrated circuits; Digital
                 arithmetic; Dividing circuits; Floating point
                 arithmetic; Multiplying circuits",
}

@InProceedings{Houelle:1995:AFL,
  author =       "A. Houelle and H. Mehrez and N. Vaucher and L.
                 Montalvo and A. Guyot",
  title =        "Application of Fast Layout Synthesis Environment to
                 Dividers Evaluation",
  crossref =     "Knowles:1995:PSC",
  pages =        "67--74",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Houelle.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}

@TechReport{Hough:1995:EPD,
  author =       "David Hough",
  title =        "Effects of {Pentium} Division Flaw and its Software
                 Workaround",
  type =         "Report",
  institution =  "Sun Microsystems",
  address =      "Mountain View, CA 94043, USA",
  pages =        "22",
  day =          "28",
  month =        feb,
  year =         "1995",
  bibdate =      "Mon Dec 16 11:29:48 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.validlab.com/reports/pentium/",
  abstract =     "The infamous Intel Pentium floating-point division
                 flaw is seldom visible in the results of realistic
                 technical applications, nor does it perceptibly affect
                 performance. But some programs skillfully designed to
                 look for arithmetic flaws can find it. In contrast, the
                 expected harmless differences between 486 and Pentium
                 elementary transcendental functions, due to the
                 improved approximations in the latter, are often
                 evident in ordinary applications.\par

                 Intel and Cygnus published a recommended compiler
                 workaround that reduces the effect of the Pentium
                 division flaw to at most one unit per division, in the
                 least significant bit of extended precision. Intel has
                 also modified its math library product libm.a to avoid
                 the division flaw. The compiler and libm workarounds do
                 not affect results of CPU chips other than flawed
                 Pentium chips.\par

                 The two modifications to the compiler and libm avoid
                 any severe effects of the Pentium flaw, but sometimes
                 cause harmlessly different results in realistic
                 technical applications. The modifications degrade
                 performance of flawed CPUs by a median of 1\%, and
                 SPECfp92 ratios by about 9\%.",
  acknowledgement = ack-nhfb,
  keywords =     "Pentium divide flaw",
}

@TechReport{Hough:1995:UVP,
  author =       "David Hough",
  title =        "{UCBTEST} vs. {Pentium}",
  type =         "Report",
  institution =  "Sun Microsystems",
  address =      "Mountain View, CA 94043, USA",
  pages =        "3",
  day =          "5",
  month =        mar,
  year =         "1995",
  bibdate =      "Mon Dec 16 11:40:24 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.validlab.com/reports/testing.pdf",
  abstract =     "University of California research into systematic
                 verification of computer arithmetic has been put into a
                 form in which anybody could in principle test any
                 computer arithmetic.\par

                 So it's exceedingly unlikely that another
                 microprocessor will come to market with bugs that
                 UCBTEST software might detect, or with uninitialized
                 entries in a divider's PLA. But to avoid the situation
                 of generals always fighting the last war, what can be
                 done to detect, or better prevent, the next arithmetic
                 flaw",
  acknowledgement = ack-nhfb,
  keywords =     "Pentium divide flaw",
}

@InProceedings{Hunt:1995:APF,
  author =       "D. Hunt",
  title =        "Advanced performance features of the 64-bit
                 {PA-8000}",
  crossref =     "IEEE:1995:DPC",
  pages =        "123--128",
  month =        mar,
  year =         "1995",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}

@TechReport{Ito:1995:EIAa,
  author =       "Masayuki Ito and Naofumi Takagi and Shuzo Yajima",
  title =        "Efficient Initial Approximation Methods for Division
                 and Square Using a Multiply-Add Unit",
  type =         "SIG Notes",
  number =       "95-HPC-55-10",
  institution =  "IPSJ",
  address =      "????",
  pages =        "73--80",
  month =        mar,
  year =         "1995",
  bibdate =      "Wed Dec 13 10:53:57 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "I cannot find this online, so institution and address
                 are uncertain. Is this a journal article or technical
                 report?",
}

@InProceedings{Ito:1995:EIAb,
  author =       "Masayuki Ito and Naofumi Takagi and Shuzo Yajima",
  title =        "Efficient Initial Approximation and Fast Converging
                 Methods for Division and Square Root",
  crossref =     "Knowles:1995:PSC",
  pages =        "2--9",
  month =        jul,
  year =         "1995",
  DOI =          "https://doi.org/10.1109/arith.1995.465383",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Ito.pdf",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  keywords =     "ARITH-12",
  summary =      "Efficient initial approximations and fast converging
                 algorithms are important to achieve the desired
                 precision faster at lower hardware cost in
                 multiplicative division and square root. In this paper,
                 a new initial approximation method for division,
                 \ldots{}",
}

@InProceedings{Jain:1995:HSD,
  author =       "V. K. Jain and L. Lin",
  title =        "High-Speed Double Precision Computation of Nonlinear
                 Functions",
  crossref =     "Knowles:1995:PSC",
  pages =        "107--114",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}

@Article{Jang:1995:OSA,
  author =       "Ju-Wook Jang and Viktor K. Prasanna",
  title =        "An Optimal Sorting Algorithm on Reconfigurable Mesh",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "25",
  number =       "1",
  pages =        "31--41",
  day =          "15",
  month =        feb,
  year =         "1995",
  CODEN =        "JPDCER",
  DOI =          "https://doi.org/10.1006/jpdc.1995.1027",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Thu Mar 9 09:18:56 MST 2000",
  bibsource =    "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.idealibrary.com/links/doi/10.1006/jpdc.1995.1027/production;
                 http://www.idealibrary.com/links/doi/10.1006/jpdc.1995.1027/production/pdf",
  acknowledgement = ack-nhfb,
  classification = "C4240P (Parallel programming and algorithm theory);
                 C5220P (Parallel architecture); C6130 (Data handling
                 techniques)",
  corpsource =   "University of Southern California, Los Angeles, CA,
                 USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "architectures; arithmetic; bit model; computational
                 complexity; constant time; constant time algorithm;
                 lower bound; optimal sorting algorithm; parallel;
                 parallel algorithms; problems; reconfigurable
                 architecture; reconfigurable architectures;
                 reconfigurable mesh; sorting; VLSI",
  treatment =    "T Theoretical or Mathematical",
}

@Unpublished{Kahan:1995:TSD,
  author =       "W. Kahan",
  title =        "A Test for {SRT} Division",
  year =         "1995",
  bibdate =      "Mon Apr 25 05:50:41 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Lecture notes",
  URL =          "http://www.cs.berkeley.edu/~wkahan/srtest",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point testing",
}

@Misc{Kahan:1995:USP,
  author =       "{Students of Prof.W.Kahan}",
  title =        "{UCBTEST}: a suite of programs for testing certain
                 difficult cases of {IEEE 754} floating-point
                 arithmetic",
  howpublished = "World-Wide Web document",
  day =          "12",
  month =        mar,
  year =         "1995",
  bibdate =      "Wed May 26 07:29:55 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.netlib.org/fp/ucbtest.tgz",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point testing",
  remark =       "From the source code, students and authors credited
                 are (in alphabetical order) M. Alemi, D. Feenberg,
                 Warren Ferguson David G. Hough, David Gay, W. J. Cody,
                 R. Karpkinski, Z. A. Liu, S. Ma, Stephen Moshier, M.
                 Mueller, K. C. Ng, D. Priest, T. Quarles, T. Sumner, G.
                 Taylor, B. Toy, W. Waite, and B. Wichmann.",
}

@Article{Kaliski:1995:MIA,
  author =       "Burton S. {Kaliski, Jr.}",
  title =        "The {Montgomery} inverse and its applications",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "8",
  pages =        "1064--1065",
  month =        aug,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.403725",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:01:29 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=403725",
  abstract =     "The Montgomery inverse of $b$ modulo $a$ is $ b^{-1}
                 2^n \bmod a $, where $n$ is the number of bits in $a$.
                 The right-shifting binary algorithm for modular
                 inversion is shown naturally to compute the new inverse
                 in fewer operations than the ordinary modular inverse.
                 The new inverse facilitates recent work by Ko{\c{c}} on
                 modular exponentiation and has other applications in
                 cryptography",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@PhdThesis{Kalliojarvi:1995:FWL,
  author =       "Kari Kallioj{\"a}rvi",
  title =        "Finite word length effects in floating-point and
                 block-floating-point digital signal processing
                 systems",
  volume =       "159",
  type =         "Avhandling (doktorgrad)",
  school =       "Tampereen teknillinen korkeakoulu",
  address =      "Tampere, Finland",
  pages =        "vii + 71 + 68",
  year =         "1995",
  ISBN =         "951-722-330-7",
  ISBN-13 =      "978-951-722-330-0",
  bibdate =      "Thu May 09 08:21:36 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Julkaisuja",
  acknowledgement = ack-nhfb,
}

@Article{Ke:1995:SFQ,
  author =       "Qing Ke and M. J. Feldman",
  title =        "Single Flux Quantum Circuits Using the Residue Number
                 System",
  journal =      j-IEEE-TRANS-APPL-SUPERCOND,
  volume =       "5",
  number =       "2",
  pages =        "2988--2991",
  month =        jun,
  year =         "1995",
  CODEN =        "ITASE9",
  DOI =          "https://doi.org/10.1109/77.403220",
  ISSN =         "1051-8223 (print), 1558-2515 (electronic)",
  ISSN-L =       "1051-8223",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=9069",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Applied Superconductivity",
  keywords =     "residue arithmetic; residue number system (RNS)",
  summary =      "We have designed and developed superconducting single
                 flux quantum (SFQ) digital signal processing circuits
                 using the residue number system (RNS). RNS arithmetic
                 is a complete alternative to binary arithmetic for
                 performing digital computations, \ldots{}",
}

@InProceedings{Kistermann:1995:RWS,
  author =       "Friedrich Wilhelm Kistermann",
  title =        "{Die Rechentechnik um 1600 und Wilhelm Schickards
                 Rechenmaschine}. ({German}) [{The} calculating
                 technique of 1600 and {Wilhelm Schickard}'s
                 calculator]",
  crossref =     "Seck:1995:GWS",
  pages =        "241--272",
  year =         "1995",
  bibdate =      "Sat Jul 27 12:43:03 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/scicontext.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@InProceedings{Knowles:1995:FSC,
  author =       "Simon Knowles and William H. McAllister",
  title =        "Foreword: {12th Symposium on Computer Arithmetic,
                 Assembly Rooms, Bath, England, July 19--21, 1995}",
  crossref =     "Knowles:1995:PSC",
  pages =        "ix--x",
  year =         "1995",
  bibdate =      "Sat Nov 17 12:02:52 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_contents.pdf;
                 http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_foreword.pdf;
                 http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_preface.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}

@Article{Koko:1995:FP,
  author =       "Boma Koko",
  title =        "Floating Point",
  journal =      j-COMPUT-AIDED-ENG,
  volume =       "14",
  number =       "10",
  pages =        "132--??",
  year =         "1995",
  CODEN =        "CCAEDJ",
  ISSN =         "0733-3536 (print), 2162-1365 (electronic)",
  ISSN-L =       "0733-3536",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer-aided engineering: CAE",
}

@Article{Kubota:1995:DRE,
  author =       "K. Kubota",
  title =        "On distribution of rounding errors generated in
                 additions and subtractions of floating-point numbers",
  journal =      "Transactions of the Japan Society for Industrial and
                 Applied Mathematics",
  volume =       "5",
  number =       "1",
  pages =        "37--46",
  month =        "????",
  year =         "1995",
  ISSN =         "0917-2246",
  bibdate =      "Thu Dec 14 11:25:18 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Analyzing the behaviour of rounding errors generated
                 in additions and subtractions of floating-point numbers
                 and regarding them as random variables, we propose a
                 slightly strange model for their distribution. The
                 model gives distributions which approximate the
                 observed generated relative errors more precisely than
                 the uniform distribution which is usually adopted in
                 probabilistic analysis of rounding errors.",
  acknowledgement = ack-nhfb,
  affiliation =  "Fac. of Sci. and Eng., Chuo University, Tokyo, Japan",
  classification = "C1140 (Probability and statistics); C4110 (Error
                 analysis in numerical methods); C5230 (Digital
                 arithmetic methods)",
  keywords =     "Additions; Distribution; Floating-point numbers;
                 Probabilistic analysis; Random variables; Relative
                 errors; Rounding errors; Subtractions; Uniform
                 distribution",
  language =     "Japanese",
  pubcountry =   "Japan",
  thesaurus =    "Error analysis; Floating point arithmetic;
                 Probability; Random processes",
}

@InProceedings{Kwan:1995:CII,
  author =       "Hercule Kwan and Robert Leonard {Nelson, Jr.} and Earl
                 E. {Swartzlander, Jr.}",
  title =        "Cascaded Implementation of an Iterative
                 Inverse-Square-Root Algorithm, with Overflow
                 Lookahead",
  crossref =     "Knowles:1995:PSC",
  pages =        "115--122",
  year =         "1995",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Kwan.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
  summary =      "We present an unconventional method of computing the
                 inverse of the square root. It implements the
                 equivalent of two iterations of a well-known
                 multiplicative method to obtain 24-bit mantissa
                 accuracy. We implement each ``iteration'' as a
                 \ldots{}",
}

@InProceedings{Lang:1995:VHR,
  author =       "Tom{\'a}s Lang and Paolo Montuschi",
  title =        "Very-High Radix Combined Division and Square Root with
                 Prescaling and Selection by Rounding",
  crossref =     "Knowles:1995:PSC",
  pages =        "124--131",
  year =         "1995",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Lang.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
  summary =      "An algorithm for square root with prescaling is
                 developed and combined with a similar scheme for
                 division. An implementation is described, evaluated and
                 compared with other combined div/sqrt \ldots{}",
}

@InProceedings{Leeser:1995:VSR,
  author =       "M. Leeser and J. O'Leary",
  booktitle =    "Proceedings of the {IEEE} International Conference on
                 Computer Design: {VLSI} in Computers and Processors,
                 {ICCD '95}",
  title =        "Verification of a subtractive radix-$2$ square root
                 algorithm and implementation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "526--531",
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Many modern microprocessors implement floating point
                 square root hardware using subtractive algorithms. Such
                 processors include the HP PA7200, the MIPS R4400, and
                 the Intel Pentium. The Intel Pentium division bug
                 highlights the importance of \ldots{}",
}

@InProceedings{Lehmann:1995:SLE,
  author =       "N. Joachim Lehmann",
  title =        "{Schickard und Leibniz als Erfinder von
                 rechenmaschinen}. ({German}) [{Schickard} and
                 {Leibniz}, the inventors of calculators]",
  crossref =     "Seck:1995:GWS",
  pages =        "273--286",
  year =         "1995",
  bibdate =      "Sat Jul 27 12:46:37 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/scicontext.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Liu:1995:SRV,
  author =       "S.-I. Liu",
  title =        "Square-rooting and vector summation circuits using
                 current conveyors",
  journal =      "IEE Proceedings on Circuits, Devices and Systems [see
                 also IEE Proceedings G- Circuits, Devices and
                 Systems]",
  volume =       "142",
  number =       "4",
  pages =        "223--226",
  month =        aug,
  year =         "1995",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
  summary =      "New analogue squaring, square-rooting and vector
                 summation circuits using current conveyors (CCIIs) are
                 presented. They consist of MOS transistors biased in
                 the triode region, a buffered unity-gain inverting
                 amplifier, resistors and CCIIs. A general \ldots{}",
}

@Article{Louie:1995:VPS,
  author =       "Marianne E. Louie and Milo{\v{s}} D. Ercegovac",
  title =        "A Variable-Precision Square Root Implementation for
                 Field Programmable Gate Arrays",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "9",
  number =       "3",
  pages =        "315--336",
  month =        sep,
  year =         "1995",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1007/BF01212874",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Wed Jul 6 11:13:09 MDT 2005",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0920-8542&volume=9&issue=3;
                 http://www.wkap.nl/issuetoc.htm/0920-8542+9+3+1995;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0920-8542&volume=9&issue=3&spage=315;
                 http://www.wkap.nl/oasis.htm/95692",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, California University,
                 Los Angeles, CA, USA",
  classification = "C5120 (Logic and switching circuits); C5230 (Digital
                 arithmetic methods)",
  corpsource =   "Department of Computer Science, California University,
                 Los Angeles, CA, USA",
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
  keywords =     "digital arithmetic; field programmable gate arrays;
                 square root; square root implementation;
                 variable-precision; Xilinx XC4010",
  treatment =    "P Practical",
}

@TechReport{Lozier:1995:EBL,
  author =       "Daniel W. Lozier and P. R. Turner",
  title =        "Error-Bounding in Level-Index Computer Arithmetic",
  type =         "Internal Report",
  number =       "NISTIR-5724",
  institution =  "National Bureau of Standards",
  address =      "Gaithersburg, MD, USA",
  year =         "1995",
  bibdate =      "Tue Nov 05 15:20:28 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.nist.gov/publications/error-bounding-level-index-computer-arithmetic",
  acknowledgement = ack-nhfb,
}

@Article{Lynch:1995:HRL,
  author =       "Thomas Lynch and Michael J. Schulte",
  title =        "A High Radix On-line Arithmetic for Credible and
                 Accurate Computing",
  journal =      j-J-UCS,
  volume =       "1",
  number =       "7",
  pages =        "439--453",
  day =          "28",
  month =        jul,
  year =         "1995",
  CODEN =        "????",
  ISSN =         "0948-6968",
  ISSN-L =       "0948-6968",
  MRclass =      "68M07",
  MRnumber =     "1 403 706",
  bibdate =      "Wed May 28 19:32:35 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.jucs.org/a_high_radix_online_arithmetic",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
}

@InProceedings{Lynch:1995:KTF,
  author =       "Tom Lynch and Ahmed Ahmed and Mike Schulte and Tom
                 Callaway and Robert Tisdale",
  title =        "The {K5} Transcendental Functions",
  crossref =     "Knowles:1995:PSC",
  pages =        "163--171",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1995-04.pdf;
                 http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Lynch.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}

@InProceedings{Lyu:1995:RBB,
  author =       "Chung Nan Lyu and David W. Matula",
  title =        "Redundant Binary {Booth} Recoding",
  crossref =     "Knowles:1995:PSC",
  pages =        "50--58",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Chung.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}

@Article{Mandelbaum:1995:DUL,
  author =       "D. M. Mandelbaum",
  title =        "Division using a logarithmic-exponential transform to
                 form a short reciprocal",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "11",
  pages =        "1326--1330",
  month =        nov,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.475129",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:01:30 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=475129",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Martel:1995:DSO,
  author =       "Charles Martel and Vojin Oklobdzija and R. Ravi and
                 Paul F. Stelling",
  title =        "Design Strategies for Optimal Multiplier Circuits",
  crossref =     "Knowles:1995:PSC",
  pages =        "42--49",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Martel.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}

@InProceedings{Matsubara:1995:NBS,
  author =       "Gensoh Matsubara and Nobuhiro Ide and Haruyuki Tago
                 and Seigo Suzuki and Nobuyuki Goto",
  title =        "30-ns 55-b Shared Radix $2$ Division and Square Root
                 Using a Self-Timed Circuit",
  crossref =     "Knowles:1995:PSC",
  pages =        "98--105",
  year =         "1995",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Matsubara.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
  summary =      "A shared radix 2 division and square root
                 implementation using a self-timed circuit is presented.
                 The same execution time for division and square root is
                 achieved by using an on-the-fly digit decoding and a
                 root multiple generation technique. Most \ldots{}",
}

@Article{Meissner:1995:EAD,
  author =       "Loren P. Meissner",
  title =        "From the {Editor}: Allocatable Dummy Argument Arrays;
                 How Should {Fortran Standards} Describe Arithmetic?
                 {Are} External Procedures Obsolete?; {When} are Local
                 Variables Initialized in {F77} and {F90}?",
  journal =      j-FORTRAN-FORUM,
  volume =       "14",
  number =       "3",
  pages =        "1--3",
  month =        sep,
  year =         "1995",
  CODEN =        "????",
  ISSN =         "1061-7264 (print), 1931-1311 (electronic)",
  ISSN-L =       "1061-7264",
  bibdate =      "Thu Feb 07 06:54:12 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Fortran Forum",
  issue =        "43",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J286",
}

@Article{Metafas:1995:FAC,
  author =       "D. E. Metafas and C. E. Goutis",
  title =        "A Floating-Point Advanced {CORDIC} Processor",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "10",
  number =       "1",
  pages =        "53--65",
  month =        jun,
  year =         "1995",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1007/BF02407026",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this paper, a novel architecture of a
                 floating-point digital signal processor is presented.
                 It introduces a single hardware structure with a full
                 set of elementary arithmetic functions which includes
                 sin, cos, tan, arctanh, circular rotation and
                 vectoring, sinh, cosh, tanh, arctanh, hyperbolic
                 rotation and vectoring, square root, logarithm,
                 exponential as well as addition, multiplication and
                 division. The architecture of the processor is based on
                 the COordinate Rotation DIgital Computer (CORDIC) and
                 the Convergence Computing Method (CCM) algorithms for
                 computing arithmetic functions and it is fully parallel
                 and pipelined. Its advanced functionality is achieved
                 without significant increase in hardware, in comparison
                 to ordinary CORDIC processor, and makes it an ideal
                 processing element in high speed multiprocessor
                 applications, e.g. real time Digital Signal Processing
                 (DSP) and computer graphics.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
}

@InProceedings{Michelucci:1995:ARD,
  author =       "D. Michelucci",
  title =        "An $ \epsilon $ Arithmetic for Removing Degeneracies",
  crossref =     "Knowles:1995:PSC",
  pages =        "230--238",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Michelucci.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}

@TechReport{Miner:1995:DIF,
  author =       "Paul S. Miner",
  title =        "Defining the {IEEE-854} floating-point standard in
                 {PVS}",
  number =       "110167",
  institution =  "National Aeronautics and Space Administration, Langley
                 Research Center; National Technical Information
                 Service, distributor",
  address =      "Hampton, VA, USA",
  pages =        "????",
  year =         "1995",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "NASA technical memorandum",
  acknowledgement = ack-nhfb,
  alttitle =     "Defining the IEEE 854 floating point standard in PVS
                 Defining the IEEE eight hundred fifty-four floating
                 point standard in PVS",
  govtdocnumber = "NAS 1.15:110167 0830-D (MF)",
  keywords =     "Floating point arithmetic.; Formalism.; Prototypes.;
                 Proving.",
  remark =       "Distributed to depository libraries in microfiche.
                 Shipping list no.: 96-0033-M. Microfiche. [Washington,
                 D.C.: National Aeronautics and Space Administration,
                 1995] 1 microfiche.",
}

@TechReport{Moler:1995:CCT,
  author =       "Cleve B. Moler",
  title =        "{Cleve}'s Corner: a Tale of Two Numbers: {With} the
                 {Pentium}, there is a very small chance of making a
                 very large error",
  type =         "Technical note",
  institution =  inst-MATHWORKS,
  address =      inst-MATHWORKS:adr,
  month =        "Winter",
  year =         "1995",
  bibdate =      "Thu Oct 24 07:16:21 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mathworks.com/company/newsletter/pdf/win95cleve.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Matlab; Pentium FDIV divide flaw",
}

@Article{Moler:1995:TTN,
  author =       "Cleve B. Moler",
  title =        "A tale of two numbers",
  journal =      j-SIAM-NEWS,
  volume =       "28",
  number =       "1",
  pages =        "16--16",
  day =          "1",
  month =        jan,
  year =         "1995",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibdate =      "Wed Nov 13 07:16:43 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Discusses the Intel Pentium chip divide flaw.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM News",
  journal-URL =  "https://sinews.siam.org/",
}

@Article{Montuschi:1995:RRI,
  author =       "P. Montuschi and L. Ciminiera",
  title =        "A remark on {``Reducing iteration time when result
                 digit is zero for radix-$2$ SRT division and square
                 root with redundant remainders''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "1",
  pages =        "144--146",
  month =        jan,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.368000",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:01:25 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  note =         "See \cite{Montuschi:1993:RIT}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=368000",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "In a previous paper by P. Montuschi and L. Ciminiera
                 (ibid., vol. 42, no.2 p239-246, Feb 1993), an
                 architecture for shared radix 2 division and square
                 root has been presented whose main characteristic is
                 the ability to avoid any addition/subtraction,
                 \ldots{}",
}

@InProceedings{Muller:1995:SLN,
  author =       "Jean-Michel Muller and Arnaud Tisserand and Alexandre
                 Scherbyna",
  title =        "Semi-Logarithmic Number Systems",
  crossref =     "Knowles:1995:PSC",
  pages =        "201--207",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Muller.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}

@Article{Nielsen:1995:MFD,
  author =       "Asger Munk Nielsen and Peter Kornerup",
  title =        "{MSB}-First Digit Serial Arithmetic",
  journal =      j-J-UCS,
  volume =       "1",
  number =       "7",
  pages =        "527--547",
  day =          "28",
  month =        jul,
  year =         "1995",
  CODEN =        "????",
  ISSN =         "0948-6968",
  ISSN-L =       "0948-6968",
  MRclass =      "68Mxx",
  MRnumber =     "1 403 711",
  bibdate =      "Wed May 28 19:32:35 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.jucs.org/jucs_1_7/msb_first_digit_serial",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
}

@PhdThesis{Nowka:1995:HPC,
  author =       "Kevin Nowka",
  title =        "High Performance {CMOS} {VLSI} System Design Using
                 Wave Pipelining",
  type =         "Thesis ({Ph.D.})",
  school =       "Department of Electrical Engineering, Stanford
                 University",
  address =      "Stanford, CA, USA",
  pages =        "????",
  month =        sep,
  year =         "1995",
  bibdate =      "Mon Dec 24 11:03:54 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Oberman:1995:DRC,
  author =       "S. F. Oberman and M. J. Flynn",
  title =        "On division and reciprocal caches",
  type =         "Technical Report",
  number =       "CSL-TR-95-666",
  institution =  "Computer Systems Laboratory, Stanford University",
  address =      "Stanford, CA, USA",
  month =        apr,
  year =         "1995",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}

@Article{OGara:1995:SET,
  author =       "Linda O'Gara and Jeanne Adams and Walt Brainerd and
                 Vic Kelson and Craig Dedo and Keith Bierman and Jerry
                 Wagener and Richard Maine and Leonard J. Moss and James
                 H. Billen and Robert Corbett and Dick Hendrickson and
                 Jamie Shiers and David Levine and David L. Epstein and
                 John Reid and Lawrie Schonfelder and Kurt W. Hirchert
                 and Jens Helmers and William Behrman and A. C. Marshall
                 and William B. Clodius",
  title =        "Some Email threads: Is {Fortran 90} Succeeding?;
                 {Fortran} Market Acceptance; {Fortran--C}
                 Interoperability; {Fortran} Preprocessors or
                 Conditional Compilation: Is Standardization Needed?;
                 Floating Point Subsets of Enable; Pointers to
                 Procedures, or Procedure Names as Variables; Standard
                 Linear Algebra and Advanced Math Functions Modules; Re:
                 Allocatable arrays in structures; Restricted Module
                 Visibility",
  journal =      j-FORTRAN-FORUM,
  volume =       "14",
  number =       "1",
  pages =        "11--28",
  month =        mar,
  year =         "1995",
  CODEN =        "????",
  ISSN =         "1061-7264 (print), 1931-1311 (electronic)",
  ISSN-L =       "1061-7264",
  bibdate =      "Thu Feb 07 06:54:12 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Fortran Forum",
  issue =        "41",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J286",
}

@InProceedings{Ohi:1995:RCN,
  author =       "Y. Ohi and T. Aoki and T. Higuchi",
  title =        "Redundant Complex Number Systems",
  crossref =     "IEEE:1995:ISM",
  pages =        "14--??",
  year =         "1995",
  DOI =          "https://doi.org/10.1109/ISMVL.1995.513504",
  bibdate =      "Sat Aug 22 08:43:14 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper presents redundant complex number systems
                 (RCNSs)-new complex number representations for
                 high-speed arithmetic circuits. RCNS is a positional
                 number system that has a complex radix $ r_j $ and a
                 digit set $ \{ - \alpha, \ldots {}, 0, \ldots {},
                 \alpha \} $, where $ r \geq 2 $ and $ [(r^2 - 1) / 2] <
                 \alpha \leq r^2 - 1 $. The use of complex radix $ r_j $
                 allows additions and multiplications of complex numbers
                 to be done without treating real part and imaginary
                 part separately. Also the redundancy in the number
                 representation enables carry-free addition as well as
                 binary-tree multiple-operand addition. This paper
                 discusses the basic arithmetic algorithms of RCNSs and
                 their implementations.",
  acknowledgement = ack-nhfb,
}

@Article{Ohkubo:1995:CBM,
  author =       "N. Ohkubo and M. Suzuki and T. Shinbo and T. Yamanaka
                 and A. Shimizu and K. Sasaki and Y. Nakagome",
  title =        "A 4.4ns {CMOS} $ 54 \times 54 $-b multiplier using
                 pass-transistor multiplexor",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "SC-30",
  number =       "3",
  pages =        "251--257",
  month =        mar,
  year =         "1995",
  CODEN =        "IJSCBC",
  DOI =          "https://doi.org/10.1109/4.364439",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Mon Dec 24 10:23:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  xxpages =      "294--305",
}

@Article{OLeary:1995:NRI,
  author =       "J. O'Leary and M. Leeser and J. Hickey and M.
                 Aagaard",
  title =        "Non-Restoring Integer Square Root: a Case Study in
                 Design by Principled Optimization",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "901",
  pages =        "52--??",
  year =         "1995",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat May 11 13:45:32 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InProceedings{Orup:1995:SQD,
  author =       "Holger Orup",
  title =        "Simplifying Quotient Determination in High-Radix
                 Modular Multiplication",
  crossref =     "Knowles:1995:PSC",
  pages =        "193--200",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Orup.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}

@InProceedings{Owens:1995:RNC,
  author =       "Robert M. Owens and Raminder S. Bajwa and Mary Jane
                 Irwin",
  title =        "Reducing the Number of Counters Needed for Integer
                 Multiplication",
  crossref =     "Knowles:1995:PSC",
  pages =        "38--41",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Owens.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}

@Article{Parker:1995:MUP,
  author =       "M. G. Parker and M. Benaissa",
  title =        "{$ \mathrm {GF}(p^m) $} multiplication using
                 polynomial residue number systems",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "42",
  number =       "11",
  pages =        "718--721",
  month =        nov,
  year =         "1995",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.475249",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=10018",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems. 2, Analog
                 and Digital Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  keywords =     "residue arithmetic; residue number system",
  summary =      "$\mathrm{GF}(p^m)$ multiplication is computed in two
                 stages. First, the polynomial product is computed
                 modulus: a highly factorizable degree S polynomial,
                 $M(x)$, with $S \geq 2m - 1$. This enables the product
                 to be computed using a polynomial residue number
                 system. \ldots{}",
}

@Article{Popova:1995:FCI,
  author =       "E. Popova",
  title =        "On a Formally Correct Implementation of {IEEE}
                 Computer Arithmetic",
  journal =      j-J-UCS,
  volume =       "1",
  number =       "7",
  pages =        "560--??",
  day =          "28",
  month =        jul,
  year =         "1995",
  CODEN =        "????",
  ISSN =         "0948-6968",
  ISSN-L =       "0948-6968",
  bibdate =      "Wed May 28 19:32:35 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.iicm.edu/jucs_1_7/on_a_formally_correct",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
}

@Article{Posch:1995:MRRa,
  author =       "Karl C. Posch and Reinhard Posch",
  title =        "Modulo Reduction in Residue Number Systems",
  journal =      j-IEEE-TRANS-PAR-DIST-SYS,
  volume =       "6",
  number =       "5",
  pages =        "449--454",
  month =        may,
  year =         "1995",
  CODEN =        "ITDSEO",
  DOI =          "https://doi.org/10.1109/71.382314",
  ISSN =         "1045-9219 (print), 1558-2183 (electronic)",
  ISSN-L =       "1045-9219",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=8666",
  acknowledgement = ack-nhfb,
  classification = "721.1; 722.4; 723.1; 723.2; 921.6; C4240C
                 (Computational complexity); C4240P (Parallel
                 programming and algorithm theory); C5230 (Digital
                 arithmetic methods); C6110P (Parallel programming)",
  corpsource =   "Inst. for Appl. Inf. Process., Graz University of
                 Technol., Austria",
  fjournal =     "IEEE Transactions on Parallel and Distributed
                 Systems",
  journal-URL =  "http://www.computer.org/tpds/archives.htm",
  journalabr =   "IEEE Trans Parallel Distrib Syst",
  keywords =     "Approximation theory; Carry free operations;
                 complexity; computational complexity; Computational
                 complexity; Computer arithmetic; Computer hardware;
                 Cryptography; cryptography; Digital arithmetic;
                 Distributed computer systems; distributed systems;
                 extremely long; integer arithmetic; Iterative methods;
                 Long integer arithmetic; Modulo reduction; modulo
                 reduction; number systems; Number theory; Parallel
                 algorithms; parallel algorithms; parallel
                 implementations; Parallel processing systems; residue
                 arithmetic; Residue number systems; residue number
                 systems",
  summary =      "Residue number systems provide a good means for
                 extremely long integer arithmetic. Their carry-free
                 operations make parallel implementations feasible. Some
                 applications involving very long integers, such as
                 public key encryption, rely heavily on \ldots{}",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Posch:1995:MRRb,
  author =       "K. C. Posch and R. Posch",
  title =        "Modulo reduction in residue number systems",
  journal =      j-IEEE-TRANS-PAR-DIST-SYS,
  volume =       "6",
  number =       "5",
  pages =        "449--454",
  month =        may,
  year =         "1995",
  CODEN =        "ITDSEO",
  DOI =          "https://doi.org/10.1109/71.382314",
  ISSN =         "1045-9219 (print), 1558-2183 (electronic)",
  ISSN-L =       "1045-9219",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=8666",
  acknowledgement = ack-nhfb,
  affiliation =  "Graz Univ of Technology",
  affiliationaddress = "Graz, Austria",
  classification = "721.1; 722.4; 723.1; 723.2; 921.6; C4240C
                 (Computational complexity); C4240P (Parallel
                 programming and algorithm theory); C5230 (Digital
                 arithmetic methods); C6110P (Parallel programming)",
  corpsource =   "Inst. for Appl. Inf. Process., Graz University of
                 Technol., Austria",
  fjournal =     "IEEE Transactions on Parallel and Distributed
                 Systems",
  journal-URL =  "http://www.computer.org/tpds/archives.htm",
  journalabr =   "IEEE Trans Parallel Distrib Syst",
  keywords =     "Approximation theory; Carry free operations;
                 complexity; computational complexity; Computational
                 complexity; Computer arithmetic; Computer hardware;
                 Cryptography; cryptography; Digital arithmetic;
                 Distributed computer systems; distributed systems;
                 extremely long; integer arithmetic; Iterative methods;
                 Long integer arithmetic; Modulo reduction; modulo
                 reduction; number systems; Number theory; Parallel
                 algorithms; parallel algorithms; parallel
                 implementations; Parallel processing systems; residue;
                 Residue number systems; residue number systems",
  summary =      "Residue number systems provide a good means for
                 extremely long integer arithmetic. Their carry-free
                 operations make parallel implementations feasible. Some
                 applications involving very long integers, such as
                 public key encryption, rely heavily on \ldots{}",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Prabhu:1995:MRD,
  author =       "J. A. Prabhu and G. B. Zyner",
  title =        "{167 MHz} Radix-$8$ Divide and Square Root Using
                 Overlapped Radix-$2$ Stages",
  crossref =     "Knowles:1995:PSC",
  pages =        "155--162",
  year =         "1995",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
  summary =      "UltraSPARC's IEEE-754 compliant floating point divide
                 and square root implementation is presented. Three
                 overlapping stages of SRT radix-$2$ quotient selection
                 logic enable an effective radix-$8$ calculation at 167
                 MHz while only a single radix-$2$ \ldots{}",
}

@InProceedings{Prabhu:1995:MRF,
  author =       "J. Arjun Prabhu and Gregory B. Zyner",
  title =        "167 {MHz} Radix-8 floating point divide and square
                 root using overlapped radix-2 stages",
  crossref =     "Knowles:1995:PSC",
  month =        jul,
  year =         "1995",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Prabhu.pdf",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  keywords =     "ARITH-12; UltraSPARC",
}

@Article{Pratt:1995:APB,
  author =       "V. Pratt",
  title =        "Anatomy of the {Pentium} Bug",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "915",
  pages =        "97--107",
  year =         "1995",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat May 11 13:45:32 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://boole.stanford.edu/pub/FDIV/anapent.ps.gz",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
  keywords =     "Intel Pentium divide flaw; Thomas R. Nicely",
}

@Article{Price:1995:PFF,
  author =       "Dick Price",
  title =        "{Pentium FDIV} Flaw --- Lessons Learned",
  journal =      j-IEEE-MICRO,
  volume =       "15",
  number =       "2",
  pages =        "88, 86--87",
  month =        mar # "\slash " # apr,
  year =         "1995",
  CODEN =        "IEMIDZ",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Dec 14 06:08:58 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Science Citation Index database (1980--2000)",
  URL =          "https://ieeexplore.ieee.org/iel1/40/8521/00372360.pdf",
  abstract =     "As the tidal wave of publicity surrounding the Pentium
                 floating-point divide bug subsides, questions about the
                 controversy's lasting impact linger. Intel's
                 competitors may rejoice at the industry giant's
                 technical and public relations missteps, but they too
                 must worry about damage done to customer confidence,
                 shuddering at the prospect of taking a similar public
                 pratfall. And consumers, justified or not, have new
                 reliability worries with every new product release.
                 Intel recently adopted a `no questions asked'
                 replacement policy for defective Pentium chips,
                 reversing its earlier stance. As part of a new
                 commitment to openness, Intel has posted a variety of
                 documents on its World Wide Web home page
                 (http://www.intel.com) describing the flaw, analysing
                 its severity, and providing replacement procedures.
                 Industry observers have pointed to the benefits that
                 will come from Intel's woes: more openness by
                 manufacturers, better understanding among consumers of
                 the problems facing chip makers, and greater emphasis
                 on testing. For chip makers and computer users alike,
                 it remains then to calculate the lessons learned.",
  acknowledgement = ack-nhfb,
  classcodes =   "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5470 (Performance evaluation
                 and testing); C5230 (Digital arithmetic methods)",
  classification = "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5230 (Digital arithmetic
                 methods); C5470 (Performance evaluation and testing)",
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  keywords =     "Chip makers; chip makers; circuit testing; computer
                 testing; Defective Pentium chips; defective Pentium
                 chips; floating point arithmetic; integrated; Intel;
                 Intel Pentium divide flaw; Pentium floating-point
                 divide bug; reliability; Reliability; replacement
                 procedures; Replacement procedures; Thomas R. Nicely",
  thesaurus =    "Computer testing; Floating point arithmetic;
                 Integrated circuit testing",
  treatment =    "G General Review",
}

@Article{Rogers:1995:UMP,
  author =       "John Rogers",
  title =        "Using the Multiple Precision Library",
  journal =      j-DDJ,
  volume =       "20",
  number =       "1",
  pages =        "36, 38, 40, 42, 86, 88--89",
  month =        jan,
  year =         "1995",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 UnCover database",
  abstract =     "Although most implementations of C boast 32-bit
                 integer arithmetic, many applications are beginning to
                 require higher precision. However, even the IEEE
                 double-precision floating-point format only gives 15
                 digits of precision. What is needed is a way to deal
                 with multiple-precision integers, independent of the
                 machine's word size. The multiple precision (MP)
                 integer library available with UNIX V7, UNIX SVR4,
                 4.3BSD, and other versions of UNIX provide infinite
                 precision signed integer operations for C programs. I
                 have also ported the GMP library to Windows NT. In this
                 article, I describe how to use the scantily documented
                 MP routines, along with providing sample code,
                 portability information, some MP helpers, and a few
                 other hints.",
  acknowledgement = ack-nhfb,
  classification = "C6110B (Software engineering techniques); C6140D
                 (High level languages)",
  fjournal =     "Dr. Dobb's Journal of Software Tools",
  keywords =     "4.3BSD; C; C programs; GMP library; IEEE
                 double-precision floating-point format; Infinite
                 precision signed integer operations; Integer
                 arithmetic; MP routines; Multiple precision library;
                 Multiple-precision integers; Portability; UNIX; UNIX
                 SVR4; UNIX V7; Windows NT; Word size",
  thesaurus =    "C language; Software libraries; Software portability;
                 Subroutines; Unix",
}

@Article{Rubenking:1995:UNI,
  author =       "Neil J. Rubenking",
  title =        "User-to-User --- The natural imperfection of
                 floating-point calculations; customizing the {Windows}
                 95 boot process; providing a way for the user to exit",
  journal =      j-PC-MAGAZINE,
  volume =       "14",
  number =       "20",
  pages =        "293--??",
  year =         "1995",
  CODEN =        "PCMGEP",
  ISSN =         "0888-8507 (print), 1078-8085 (electronic)",
  ISSN-L =       "0888-8507",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "PC Magazine",
}

@Article{Sammut:1995:AUD,
  author =       "K. M. Sammut and S. R. Jones",
  title =        "Arithmetic unit design for neural accelerators: cost
                 performance issues",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "10",
  pages =        "1256--1260",
  month =        oct,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.467702",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:01:30 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=467702",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Sangwine:1995:CIT,
  author =       "S. J. Sangwine and D. A. Riach",
  booktitle =    "{Fifth International Conference on Image Processing
                 and its Applications: 4-6 July 1995: venue, Heriot-Watt
                 University, Edinburgh, UK}",
  title =        "Colour image thresholding at pixel rate using rational
                 arithmetic hardware",
  publisher =    pub-IEE,
  address =      pub-IEE:adr,
  pages =        "828--832",
  year =         "1995",
  ISBN =         "0-85296-642-3",
  ISBN-13 =      "978-0-85296-642-6",
  LCCN =         "A1632 .I553 1995",
  bibdate =      "Fri Nov 30 07:37:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Thresholding of images is a common precursor to many
                 object recognition or image analysis methods. Colours
                 images contain more information than monochrome images
                 of the same spatial resolution and in many applications
                 of colour image processing there will be a need for
                 thresholding. The paper presents a hardware
                 implementation and development of a technique published
                 by Pritchard et al. (1994). A brief review is given of
                 the rational arithmetic representation; the authors
                 then discuss the definition of colour purity, present a
                 description of the thresholding algorithm as
                 implemented in hardware and finally, give a block-level
                 description of the hardware implementation and some
                 results obtained",
  acknowledgement = ack-nhfb,
}

@Article{Sanyal:1995:CAS,
  author =       "S. Sanyal",
  title =        "Computer Arithmetic Systems",
  journal =      j-COMP-J,
  volume =       "38",
  number =       "1",
  pages =        "79--79",
  month =        "????",
  year =         "1995",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/38.1.79",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:48:43 MST 2012",
  bibsource =    "http://comjnl.oxfordjournals.org/content/38/1.toc;
                 https://www.math.utah.edu/pub/tex/bib/compj1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/38/1/79.full.pdf+html",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@InProceedings{Sarma:1995:FBR,
  author =       "Debjit Das Sarma and David W. Matula",
  title =        "Faithful Bipartite {ROM} Reciprocal Tables",
  crossref =     "Knowles:1995:PSC",
  pages =        "17--29",
  month =        jul,
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Sarma.pdf",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  keywords =     "ARITH-12",
  xxnote =       "Check: page 29 is missing from PDF file; is it
                 blank?",
  xxpages =      "17--28??",
}

@InProceedings{Schulte:1995:DAV,
  author =       "M. J. Schulte and E. E. {Swartzlander, Jr.}",
  title =        "Design and applications for variable-precision,
                 interval arithmetic coprocessors",
  crossref =     "Kearfott:1996:AICa",
  pages =        "166--172",
  year =         "1995",
  bibdate =      "Tue Apr 07 16:25:50 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb # " and " # ack-jf,
}

@InProceedings{Schulte:1995:HDA,
  author =       "Michael J. Schulte and Eearl E. {Swartzlander, Jr.}",
  title =        "Hardware Design and Arithmetic Algorithms for a
                 Variable-Precision, Interval Arithmetic Coprocessor",
  crossref =     "Knowles:1995:PSC",
  pages =        "222--229",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1995-03.pdf;
                 http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Schulte.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}

@InProceedings{Schulte:1995:PSI,
  author =       "Michael J. Schulte and Eearl E. {Swartzlander, Jr.}",
  title =        "A Processor for Staggered Interval Arithmetic",
  crossref =     "Cappello:1995:ICA",
  pages =        "104--112",
  year =         "1995",
  bibdate =      "Mon Oct 20 07:16:07 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1995-02.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Schwarz:1995:RQC,
  author =       "E. M. Schwarz",
  title =        "Rounding for quadratically converging algorithms for
                 division and square root",
  crossref =     "Singh:1995:CRT",
  volume =       "1",
  pages =        "600--603",
  month =        oct,
  year =         "1995",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  summary =      "Exactly rounded results are necessary for many
                 architectures such as IEEE 754 standard. For division
                 and square root, rounding is easy to perform if a
                 remainder is available. But for quadratically
                 converging algorithms, the remainder is not \ldots{}",
}

@InProceedings{Shirazi:1995:QAF,
  author =       "N. Shirazi and A. Walters and P. Athanas",
  title =        "Quantitative analysis of floating point arithmetic on
                 {FPGA} based custom computing machines",
  crossref =     "Athanas:1995:PIS",
  pages =        "155--162",
  year =         "1995",
  DOI =          "https://doi.org/10.1109/FPGA.1995.477421",
  bibdate =      "Sat Oct 9 13:02:18 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Many algorithms rely on floating point arithmetic for
                 the dynamic range of representations and require
                 millions of calculations per second. Such
                 computationally intensive algorithms are candidates for
                 acceleration using custom computing machines (CCMs)
                 being tailored for the application. Unfortunately,
                 floating point operators require excessive area (or
                 time) for conventional implementations. Instead, custom
                 formats, derived for individual applications, are
                 feasible on CCMs, and can be implemented on a fraction
                 of a single FPGA. Using higher-level languages, like
                 VHDL, facilitates the development of custom operators
                 without significantly impacting operator performance or
                 area. Properties, including area consumption and speed
                 of working arithmetic operator units used in real-time
                 applications, are discussed",
  acknowledgement = ack-nhfb,
}

@TechReport{Sigvartsen:1995:TBF,
  author =       "Roy L. Sigvartsen and Roar Skogstr{\o}m",
  title =        "A test bench for floating point arithmetic",
  type =         "{FFI} rapport",
  number =       "95/04099",
  institution =  "Forsvarets forskningsinstitut",
  address =      "Kjeller, Norway",
  pages =        "54",
  year =         "1995",
  bibdate =      "Thu May 09 08:08:19 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point testing",
}

@Book{Sites:1995:AAA,
  author =       "Richard L. Sites and Richard L. Witek",
  title =        "{Alpha AXP} Architecture Reference Manual",
  publisher =    pub-DP,
  address =      pub-DP:adr,
  edition =      "Second",
  pages =        "various",
  year =         "1995",
  ISBN =         "1-55558-145-5",
  ISBN-13 =      "978-1-55558-145-9",
  LCCN =         "QA76.9.A73A46 1995",
  bibdate =      "Thu Aug 07 13:41:17 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/microchip.bib",
  price =        "US\$52.95",
  acknowledgement = ack-nhfb,
  tableofcontents = "Foreword \\
                 Preface to the First Edition \\
                 Preface to the Second Edition \\
                 Part 1: Common Architecture (I) \\
                 1. Introduction (I) \\
                 1.1 The Alpha AXP Approach to RISC Architecture \\
                 1.2 Data Format Overview \\
                 1.3 Instruction Format Overview \\
                 1.4 Instruction Overview \\
                 1.5 Instruction Set Characteristics \\
                 1.6 Terminology and Conventions \\
                 2. Basic Architecture (I) \\
                 2.1 Addressing \\
                 2.2 Data Types \\
                 2.3 Big-endian Addressing Support \\
                 3. Instruction Formats (I) \\
                 3.1 Alpha AXP Registers \\
                 3.2 Notation \\
                 3.3 Instruction Formats \\
                 4. Instruction Descriptions (I) \\
                 4.1 Instruction Set Overview \\
                 4.2 Memory Integer Load/Store Instructions \\
                 4.3 Control Instructions \\
                 4.4 Integer Arithmetic Instructions \\
                 4.5 Logical and Shift Instructions \\
                 4.6 Byte-Manipulation Instructions \\
                 4.7 Floating-Point Instructions \\
                 4.8 Memory Format Floating-Point Instructions \\
                 4.9 Branch Format Floating-Point Instructions \\
                 4.10 Floating-Point Operate Format Instructions \\
                 4.11 Miscellaneous Instructions \\
                 4.12 VAX Compatibility Instructions \\
                 5. System Architecture and Programming Implications \\
                 5.1 Introduction \\
                 5.2 Physical Address Space Characteristics \\
                 5.3 Translation Buffers and Virtual Caches \\
                 5.4 Caches and Write Buffers \\
                 5.5 Data Sharing \\
                 5.6 Read/Write Ordering \\
                 5.7 Arithmetic Traps \\
                 6. Common PALcode Architecture (I) \\
                 6.1 PALcode \\
                 6.2 PALcode Instructions and Functions \\
                 6.3 PALcode Environment \\
                 6.4 Special Functions Required for PALcode \\
                 6.5 PALcode Effects on System Code \\
                 6.6 PALcode Replacement \\
                 6.7 Required PALcode Instructions \\
                 7. Console Subsystem Overview (I) \\
                 8. Input/Output Overview (I) \\
                 Specific Operating System PALcode Architecture (II) \\
                 Part 2: OpenVMS AXP Software (II-A) \\
                 1. Introduction to OpenVMS AXP (II-A) \\
                 1.1 Register Usage \\
                 2. OpenVMS AXP PALcode Instruction Descriptions (II-A)
                 \\
                 2.1 Unprivileged General OpenVMS AXP PALcode
                 Instructions \\
                 2.2 OpenVMS AXP Queue Data Types \\
                 2.3 Unprivileged OpenVMS AXP Queue PALcode Instructions
                 \\
                 2.4 Unprivileged VAX Compatibility PALcode Instructions
                 \\
                 2.5 Unprivileged PALcode Thread Instructions \\
                 2.6 Privileged PALcode Instructions \\
                 3. OpenVMS AXP Memory Management (II-A) \\
                 3.1 Introduction \\
                 3.2 Virtual Address Space \\
                 3.3 Physical Address Space \\
                 3.4 Memory Management Control \\
                 3.5 Page Table Entries \\
                 3.6 Memory Protection \\
                 3.7 Address Translation \\
                 3.8 Translation Buffer \\
                 3.9 Address Space Numbers \\
                 3.10 Memory Management Faults \\
                 4. OpenVMS AXP Process Structure (II-A) \\
                 4.1 Process Definition \\
                 4.2 Hardware Privileged Process Context \\
                 4.3 Asynchronous System Traps (AST) \\
                 4.4 Process Context Switching \\
                 5. OpenVMS AXP Internal Processor Registers (II-A) \\
                 5.1 Internal Processor Registers \\
                 5.2 Stack Pointer Internal Processor Registers \\
                 5.3 IPR Summary",
}

@Article{Siu:1995:TMP,
  author =       "Kai-Yeung Y. Siu and V. Roychowdhury and T. Kailath",
  title =        "Toward Massively Parallel Design of Multipliers",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "24",
  number =       "1",
  pages =        "86--93",
  month =        jan,
  year =         "1995",
  CODEN =        "JPDCER",
  DOI =          "https://doi.org/10.1006/jpdc.1995.1008",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Thu Mar 9 09:18:56 MST 2000",
  bibsource =    "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.idealibrary.com/links/doi/10.1006/jpdc.1995.1008/production;
                 http://www.idealibrary.com/links/doi/10.1006/jpdc.1995.1008/production/pdf",
  acknowledgement = ack-nhfb,
  classification = "C4210 (Formal logic); C4240C (Computational
                 complexity); C5110 (Logic elements); C5120 (Logic and
                 switching circuits); C5220P (Parallel architecture);
                 C5230 (Digital arithmetic methods)",
  corpsource =   "Department of Electr. and Comput. Eng., California
                 University, Irvine, CA, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "AND-OR circuits; arithmetic computation; asymptotic
                 time complexity; circuits; computation delays;
                 computational complexity; digital arithmetic; fan-in
                 threshold circuits; gates; hardware; logic; massively
                 parallel design; massively parallel high-speed
                 multipliers; multiplication; multipliers; multiplying;
                 parallel processing; parity; polynomial; speed;
                 symmetric functions; threshold; threshold elements;
                 unbounded fan-in/fan-out; VLSI technology",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Sleijpen:1995:MCP,
  author =       "G{\`e}rard L. G. Sleijpen and Henk A. van der Vorst",
  title =        "Maintaining convergence properties of {BiCGstab}
                 methods in finite precision arithmetic",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "10",
  number =       "3--4",
  pages =        "203--223",
  month =        oct,
  year =         "1995",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "65F10 (65Y20)",
  MRnumber =     "MR1355732 (96g:65037)",
  bibdate =      "Sat Dec 31 06:28:14 2005",
  bibsource =    "http://www.math.psu.edu/dna/contents/na.html;
                 https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  classification = "B0290F (Interpolation and function approximation);
                 B0290H (Linear algebra); C4130 (Interpolation and
                 function approximation); C4140 (Linear algebra); C4240C
                 (Computational complexity)",
  corpsource =   "Math. Inst., Utrecht University, Netherlands",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "Bi-CG coefficient accuracy; Bi-CG iteration
                 coefficients; Bi-CG process; BiCGstab methods;
                 computational complexity; conjugate gradient methods;
                 convergence of numerical methods; convergence property
                 maintenance; convergence speed; finite precision
                 arithmetic; hybrid methods; matrix algebra; rounding
                 errors; roundoff errors",
  pubcountry =   "Switzerland",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Smith:1995:CFA,
  author =       "Roger Alan Smith",
  title =        "A Continued-Fraction Analysis of Trigonometric
                 Argument Reduction",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "11",
  pages =        "1348--1351",
  month =        nov,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.475133",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Dec 08 10:21:28 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  abstract =     "The calculation of a trigonometric function of a large
                 argument x is effectively carried out by finding the
                 integer $N$ and $ 0 \leq \alpha < 1 $ such that $ x =
                 (N + \alpha) \pi / 4 $. This reduction modulo $ \pi / 4
                 $ makes it possible to calculate a trigonometric
                 function of a reduced argument, either $ \alpha \pi / 4
                 $ or $ (1 - \alpha) \pi / 4 $, which lies in the
                 interval $ (0, \pi / 4) $. Payne and Hanek [1]
                 described an efficient algorithm for computing $ \alpha
                 $ to a predetermined level of accuracy. They noted that
                 if $x$ differs only slightly from an integral multiple
                 $ \pi / 2 $, the reduction must be carried out quite
                 accurately to avoid loss of significance in the reduced
                 argument. We present a simple method using continued
                 fractions for determining, for all numbers $x$ for
                 which the greatest number of insignificant leading bits
                 occur. Applications are made IEEE single-precision and
                 double-precision formats and two extended- precision
                 formats.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "argument reduction; computer arithmetic; continued
                 fractions; nonlinear optimization; Payne/Hanek radian
                 reduction; range reduction; trigonometric functions",
}

@Article{Smith:1995:FTC,
  author =       "J. C. Smith and F. J. Taylor",
  title =        "A fault-tolerant {CEQRNS} processing element for
                 linear systolic array {DSP} applications",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "9",
  pages =        "1121--1130",
  month =        sep,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.464390",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:01:29 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=464390",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Soderquist:1995:APC,
  author =       "Peter Soderquist and Miriam Leeser",
  title =        "An Area\slash Performance Comparison of Subtractive
                 and Multiplicative Divide\slash Square Root
                 Implementations",
  crossref =     "Knowles:1995:PSC",
  pages =        "132--139",
  month =        jul,
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Soderquist.pdf",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  keywords =     "ARITH-12",
}

@PhdThesis{Song:1995:RCT,
  author =       "Gi-Yong Song",
  title =        "Robust checksum test in algorithm-based fault
                 tolerance on {2-D} processor arrays",
  type =         "Thesis ({Ph.D.})",
  school =       "University of Southwestern Louisiana",
  address =      "Lafayette, LA, USA",
  pages =        "95",
  year =         "1995",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "error-correcting codes (information theory);
                 fault-tolerant computing; floating-point arithmetic;
                 floating-point testing",
}

@Article{Srinivas:1995:FRD,
  author =       "H. R. Srinivas and K. K. Parhi",
  title =        "A fast radix-4 division algorithm and its
                 architecture",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "6",
  pages =        "826--831",
  month =        jun,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.391179",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:01:28 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=391179",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@PhdThesis{Suarez:1995:CAA,
  author =       "Elisardo Antelo Su{\'a}rez",
  title =        "Algoritmos y arquitecturas {CORDIC} con aritm{\'e}tica
                 redundante para procesamiento de alta velocidad
                 ({Spanish}) [{CORDIC} algorithms and architectures with
                 redundant arithmetic for high-speed processing]",
  type =         "Tesis doctorales",
  school =       "Universidade de Santiago de Compostela",
  address =      "Santiago de Compostela, Spain",
  pages =        "ix + 210",
  year =         "1995",
  ISBN =         "84-8121-348-9",
  ISBN-13 =      "978-84-8121-348-5",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://login.ezproxy.lib.utah.edu/login?url=https://www.proquest.com/dissertations-theses/cordic-algorithms-architectures-with-redundant/docview/304224973/se-2",
  acknowledgement = ack-nhfb,
  keywords =     "0544:Electrical engineering; Applied sciences;
                 Electrical engineering",
  language =     "Spanish",
  ris-m1 =       "C519384",
}

@Article{Tatsaki:1995:ICB,
  author =       "A. Tatsaki and T. Stouraitis and C. Goutis",
  title =        "Image coder based on residue number system for
                 progressive transmission",
  journal =      j-ELECT-LETTERS,
  volume =       "31",
  number =       "6",
  pages =        "442--443",
  month =        mar,
  year =         "1995",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1109/12.403714",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=8573",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A computationally efficient algorithm for image
                 compression and progressive transmission is presented.
                 A prime-factor discrete cosine transform (DCT) is
                 applied, where the coefficients are computed in three
                 groups and are residue represented by a \ldots{}",
}

@Article{Thimbleby:1995:NCW,
  author =       "Harold Thimbleby",
  title =        "A New Calculator and Why it is Necessary",
  journal =      j-COMP-J,
  volume =       "38",
  number =       "6",
  pages =        "418--433",
  month =        "????",
  year =         "1995",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/38.6.418",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:48:45 MST 2012",
  bibsource =    "http://comjnl.oxfordjournals.org/content/38/6.toc;
                 http://www3.oup.co.uk/computer_journal/Volume_38/Issue_06/Vol38_06.index.html;
                 https://www.math.utah.edu/pub/tex/bib/compj1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/38/6/418.full.pdf+html;
                 http://www3.oup.co.uk/computer_journal/Volume_38/Issue_06/Vol38_06.body.html#AbstractThimbleby",
  acknowledgement = ack-nhfb,
  classcodes =   "C5430 (Microcomputers); C6180 (User interfaces)",
  corpsource =   "Department of Computer Science, Middlesex University,
                 London, UK",
  email-1 =      "haro1d@mdx.ac.UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "conventional calculators; declarative design;
                 declarative system; design issues; electronic
                 calculators; interactive system; user interfaces",
  treatment =    "P Practical",
}

@Article{Thomas:1995:IFC,
  author =       "Jim Thomas and Jerome T. Coonen",
  title =        "An Introduction to Floating-Point {C} Extensions",
  journal =      j-CCCUJ,
  volume =       "13",
  number =       "1",
  pages =        "49--??",
  month =        jan,
  year =         "1995",
  CODEN =        "CCUJEX",
  ISSN =         "1075-2838",
  bibdate =      "Fri Aug 30 16:52:23 MDT 1996",
  bibsource =    "http://www.cuj.com/cbklist.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "C/C++ Users Journal",
}

@InProceedings{Tsuji:1995:ASF,
  author =       "K. Tsuji",
  title =        "An Algorithm for Sum of Floating-Point Numbers without
                 Round-Off Error",
  crossref =     "Bainov:1995:PTI",
  pages =        "181--190",
  year =         "1995",
  bibdate =      "Sat Jun 02 08:14:13 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}

@TechReport{Turner:1995:PSI,
  author =       "P. R. Turner Daniel W. Lozier",
  title =        "Parallel and Serial Implementations of {SLI}
                 Arithmetic",
  type =         "Internal report",
  number =       "NISTIT-5660",
  institution =  "National Institute of Standards and Technology",
  address =      "Gaithersburg, MD, USA",
  day =          "1",
  month =        jun,
  year =         "1995",
  bibdate =      "Tue Nov 05 15:29:02 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Misc{Ueda:1995:DMA,
  author =       "T. Ueda",
  title =        "Decimal Multiplying Assembly and Multiply Module",
  howpublished = "U.S. Patent number 5,379,245.",
  month =        jan,
  year =         "1995",
  bibdate =      "Fri Jun 24 20:43:45 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@InProceedings{VanDrunen:1995:ARA,
  author =       "R. VanDrunen and L. Spaanenburg and P. Lucassen and J.
                 A. G. Nijhuis",
  title =        "Arithmetic for Relative Accuracy",
  crossref =     "Knowles:1995:PSC",
  pages =        "208--209, 239--250",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_vanDrunen.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}

@Article{Vinnakota:1995:IMS,
  author =       "B. Vinnakota",
  title =        "Implementing multiplication with split read-only
                 memory",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "11",
  pages =        "1352--1356",
  month =        nov,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.475134",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:01:30 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=475134",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Wang:1995:NDT,
  author =       "Zhongde Wang and G. A. Jullien and W. C. Miller",
  title =        "A new design technique for column compression
                 multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "8",
  pages =        "962--970",
  month =        aug,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.403712",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:01:29 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=403712",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Wei:1995:CNM,
  author =       "Belle W. Y. Wei and He Du and Honglu Chen",
  title =        "A Complex-Number Multiplier Using Radix-$4$ Digits",
  crossref =     "Knowles:1995:PSC",
  pages =        "84--90",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Wei.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}

@Article{Williams:1995:SBA,
  author =       "T. Williams and N. Patkar and G. Shen",
  title =        "{SPARC64}: a 64-b 64-active-instruction
                 out-of-order-execution {MCM} processor",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "30",
  number =       "11",
  pages =        "1215--1226",
  month =        nov,
  year =         "1995",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
}

@Article{Wong:1995:FEE,
  author =       "W. F. Wong and E. Goto",
  title =        "Fast evaluation of the elementary functions in single
                 precision",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "44",
  number =       "3",
  pages =        "453--457",
  month =        mar,
  year =         "1995",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.372037",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Dec 14 11:25:18 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  abstract =     "In this paper we introduce a new method for the fast
                 evaluation of the elementary functions in single
                 precision based on the evaluation of truncated Taylor
                 series using a difference method. We assume the
                 availability of large and fast (at least for read
                 purposes) memory. We call this method the ATA
                 (Add-Table lookup-Add) method. As the name implies, the
                 hardware required for the method are adders (both two/
                 and multi/operand adders) and fast tables. For IEEE
                 single precision numbers our initial estimates indicate
                 that we can calculate the basic elementary functions,
                 namely reciprocal, square root, logarithm, exponential,
                 trigonometric and inverse trigonometric functions,
                 within the latency of two to four floating point
                 multiplies.",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Inf. Syst. and Computer Science, Nat.
                 University of Singapore, Singapore",
  ajournal =     "IEEE Trans. Comput.",
  classification = "C4110 (Error analysis in numerical methods); C5230
                 (Digital arithmetic methods)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Adders; Difference method; Elementary functions; Fast
                 evaluation; Floating point multiplies; Inverse
                 trigonometric functions; Logarithm functions;
                 Reciprocal; Single precision; Square root; Truncated
                 Taylor series",
  thesaurus =    "Error analysis; Floating point arithmetic",
}

@Article{Wu:1995:SRM,
  author =       "Youfeng Wu",
  title =        "Strength Reduction of Multiplications by Integer
                 Constants",
  journal =      j-SIGPLAN,
  volume =       "30",
  number =       "2",
  pages =        "42--48",
  month =        feb,
  year =         "1995",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:17:00 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}

@Article{Ypma:1995:HDN,
  author =       "Tjalling J. Ypma",
  title =        "Historical Development of the {Newton--Raphson}
                 Method",
  journal =      j-SIAM-REVIEW,
  volume =       "37",
  number =       "4",
  pages =        "531--551",
  month =        dec,
  year =         "1995",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1037125",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "01A05 (65-03)",
  MRnumber =     "97b:01003",
  MRreviewer =   "M. Z. Nashed",
  bibdate =      "Sat Mar 29 09:55:35 MDT 2014",
  bibsource =    "Compendex database;
                 http://epubs.siam.org/toc/siread/37/4;
                 http://www.siam.org/journals/sirev/sirev374.htm;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "http://epubs.siam.org/23425.htm;
                 http://link.aip.org/link/?SIR/37/531/1",
  abstract =     "This expository paper traces the development of the
                 Newton--Raphson method for solving nonlinear algebraic
                 equations through the extant notes, letters, and
                 publications of Isaac Newton, Joseph Raphson, and
                 Thomas Simpson. It is shown how Newton's formulation
                 differed from the iterative process of Raphson, and
                 that Simpson was the first to give a general
                 formulation, in terms of fluxional calculus, applicable
                 to nonpolynomial equations. Simpson's extension of the
                 method to systems of equations is exhibited.",
  acknowledgement = ack-nhfb,
  affiliation =  "Western Washington Univ",
  affiliationaddress = "Bellingham, WA, USA",
  classification = "921.1; 921.2; 921.6",
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  journalabr =   "SIAM Rev",
  keywords =     "Algebra; Algorithms; Approximation theory;
                 Differentiation (calculus); Finite difference method;
                 Fluxional calculus; Isaac Newton; Iterative methods;
                 Joseph Raphson; Linearization; Newton--Raphson method;
                 Nonlinear algebraic equations; Nonlinear equations;
                 Nonpolynomial equation; Polynomials; Secant method;
                 Thomas Simpson",
  onlinedate =   "December 1995",
}

@InProceedings{Yu:1995:MRF,
  author =       "Robert K. Yu and Gregory B. Zyner",
  title =        "{167 MHz} Radix-$4$ Floating Point Multiplier",
  crossref =     "Knowles:1995:PSC",
  pages =        "149--154",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Yu.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12; UltraSPARC",
}

@Article{Zaytoun:1995:SFR,
  author =       "M. M. Zaytoun and T. J. Owens",
  title =        "State feedback robust to rounding errors",
  journal =      j-ELECT-LETTERS,
  volume =       "31",
  number =       "13",
  pages =        "1108--1109",
  day =          "22",
  month =        jun,
  year =         "1995",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Jul 16 11:25:03 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  summary =      "An algorithm for delivering a state feedback
                 controller that assigns desired distinct closed-loop
                 eigenvalues to the closed-loop system and is robust to
                 rounding errors in the elements of the controller is
                 \ldots{}",
}

@InProceedings{Zhou:1995:HSD,
  author =       "Feng Zhou and Peter Kornerup",
  title =        "High Speed {DCT}\slash {IDCT} Using a Pipelined
                 {CORDIC} Algorithm",
  crossref =     "Knowles:1995:PSC",
  pages =        "180--187",
  year =         "1995",
  bibdate =      "Mon May 20 06:05:24 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC
                 Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith12/papers/ARITH12_Feng.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}

@InProceedings{Ahrendt:1996:FHC,
  author =       "Timm Ahrendt",
  title =        "Fast High-Precision Computations of Complex Square
                 Roots",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "142--149",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p142-ahrendt/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; measurement;
                 SIGNUM; SIGSAM; symbolic computation",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.1.0} Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
                 F.1.1} Theory of Computation, COMPUTATION BY ABSTRACT
                 DEVICES, Models of Computation, Bounded-action devices.
                 {\bf G.1.5} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Roots of Nonlinear Equations, Iterative
                 methods. {\bf G.1.2} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation.",
  xxtitle =      "Fast high-precision computation of complex square
                 roots",
}

@TechReport{Al-Twaijry:1996:OPR,
  author =       "H. Al-Twaijry and M. J. Flynn",
  title =        "Optimum placement and routing of multiplier partial
                 product trees",
  type =         "Technical report",
  number =       "CSL-TR-96-706",
  institution =  "Computer Systems Laboratory, Stanford University",
  address =      "Stanford, CA, USA",
  month =        sep,
  year =         "1996",
  bibdate =      "Mon Dec 24 10:13:01 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Alefeld:1996:EII,
  author =       "G. E. Alefeld and F. A. Potra and W. Voelker",
  title =        "Effective Improvements of the
                 Internal-{Newton}-Method",
  crossref =     "Alefeld:1996:SCV",
  pages =        "133--139",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@InProceedings{Andraos:1996:FPU,
  author =       "S. Andraos",
  booktitle =    "{IEEE 39th} Midwest symposium on Circuits and Systems,
                 1996",
  title =        "Fixed point unsigned fractional representation in
                 residue number system",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "555--558",
  year =         "1996",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1996.594239",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Representing fractions is one of the fundamental
                 problems in the Residue Number System (RNS) which is
                 considered an integer number system with no fractional
                 representation. This is one of its main drawbacks and
                 one of the main obstacles in its \ldots{}",
}

@MastersThesis{Angarai:1996:NRS,
  author =       "Vijayanand Jaganaathan Angarai",
  title =        "Number representation schemes for energy efficient
                 computer arithmetic",
  type =         "Thesis ({M.S.})",
  school =       "University of Texas at Dallas",
  address =      "Dallas, TX, USA",
  pages =        "ix + 57",
  year =         "1996",
  bibdate =      "Mon Mar 05 14:32:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Anonymous:1996:DC,
  author =       "Anonymous",
  editor =       "Barry Cipra and Paul Zorn",
  booktitle =    "What's Happening in the Mathematical Sciences",
  title =        "Divide and Conquer",
  volume =       "3",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  bookpages =    "vi + 111",
  pages =        "39--47",
  year =         "1996",
  ISBN =         "0-8218-0355-7 (paperback)",
  ISBN-13 =      "978-0-8218-0355-4 (paperback)",
  LCCN =         "QA3 .C57 1996",
  bibdate =      "Thu Dec 08 16:31:52 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ams.org/samplings/math-history/divide.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Pentium divide flaw",
}

@Article{Anonymous:1996:FPF,
  author =       "Anonymous",
  title =        "Floating Point --- Finding Electronic\slash Mechanical
                 Parts",
  journal =      j-COMPUT-AIDED-ENG,
  volume =       "15",
  number =       "1",
  pages =        "76--??",
  year =         "1996",
  CODEN =        "CCAEDJ",
  ISSN =         "0733-3536 (print), 2162-1365 (electronic)",
  ISSN-L =       "0733-3536",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer-aided engineering: CAE",
}

@Article{Anonymous:1996:IBT,
  author =       "Anonymous",
  title =        "Inquiry Board Traces {Ariane 5} Failure to Overflow
                 Error",
  journal =      j-SIAM-NEWS,
  volume =       "29",
  number =       "8",
  pages =        "1, 12, 13",
  month =        oct,
  year =         "1996",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibdate =      "Sat Apr 28 18:48:53 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.siam.org/siamnews/general/ariane.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM News",
  journal-URL =  "https://sinews.siam.org/",
}

@Book{Anonymous:1996:SROa,
  author =       "Anonymous",
  title =        "The Square Root of 3 to one million digits",
  volume =       "628",
  publisher =    pub-PROJECT-GUTENBERG,
  address =      pub-PROJECT-GUTENBERG:adr,
  year =         "1996",
  bibdate =      "Sun Jan 24 10:00:27 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-PROJECT-GUTENBERG,
  URL =          "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/3sqrt10.zip",
  acknowledgement = ack-nhfb # " and " # ack-st,
  subject =      "Mathematical constants.",
}

@Book{Anonymous:1996:SROb,
  author =       "Anonymous",
  title =        "The Square Root of 5 to one million digits",
  volume =       "629",
  publisher =    pub-PROJECT-GUTENBERG,
  address =      pub-PROJECT-GUTENBERG:adr,
  year =         "1996",
  bibdate =      "Sun Jan 24 10:00:27 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-PROJECT-GUTENBERG,
  URL =          "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/5sqrt10.zip",
  acknowledgement = ack-nhfb # " and " # ack-st,
  subject =      "Mathematical constants.",
}

@Book{Anonymous:1996:SROc,
  author =       "Anonymous",
  title =        "The Square Root of 6 to one million digits",
  volume =       "630",
  publisher =    pub-PROJECT-GUTENBERG,
  address =      pub-PROJECT-GUTENBERG:adr,
  year =         "1996",
  bibdate =      "Sun Jan 24 10:00:27 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-PROJECT-GUTENBERG,
  URL =          "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/6sqrt10.zip",
  acknowledgement = ack-nhfb # " and " # ack-st,
  subject =      "Mathematical constants.",
}

@Book{Anonymous:1996:SROd,
  author =       "Anonymous",
  title =        "The Square Root of 7 to one million digits",
  volume =       "631",
  publisher =    pub-PROJECT-GUTENBERG,
  address =      pub-PROJECT-GUTENBERG:adr,
  year =         "1996",
  bibdate =      "Sun Jan 24 10:00:27 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-PROJECT-GUTENBERG,
  URL =          "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/7sqrt10.zip",
  acknowledgement = ack-nhfb # " and " # ack-st,
  subject =      "Mathematical constants.",
}

@Book{Anonymous:1996:SROe,
  author =       "Anonymous",
  title =        "The Square Root of 8 to one million digits",
  volume =       "632",
  publisher =    pub-PROJECT-GUTENBERG,
  address =      pub-PROJECT-GUTENBERG:adr,
  year =         "1996",
  bibdate =      "Sun Jan 24 10:00:27 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-PROJECT-GUTENBERG,
  URL =          "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/8sqrt10.zip",
  acknowledgement = ack-nhfb # " and " # ack-st,
  subject =      "Mathematical constants.",
}

@Book{Anonymous:1996:SROf,
  author =       "Anonymous",
  title =        "The Square Root of 10 to one million digits",
  volume =       "635",
  publisher =    pub-PROJECT-GUTENBERG,
  address =      pub-PROJECT-GUTENBERG:adr,
  year =         "1996",
  bibdate =      "Sun Jan 24 10:00:27 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-PROJECT-GUTENBERG,
  URL =          "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/etext96/10srt10.zip",
  acknowledgement = ack-nhfb # " and " # ack-st,
  subject =      "Mathematical constants.",
}

@InBook{Antelo:1996:HRC,
  author =       "E. Antelo and J. D. Bruguera and T. Lang and J.
                 Villalba and E. L. Zapata",
  booktitle =    "Euro-Par 96 Parallel Processing",
  title =        "High radix {CORDIC} rotation based on selection by
                 rounding",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "155--164",
  year =         "1996",
  DOI =          "https://doi.org/10.1007/bfb0024698",
  ISBN =         "3-540-70636-4",
  ISBN-13 =      "978-3-540-70636-6",
  ISSN =         "1611-3349",
  bibdate =      "Tue Oct 28 07:04:09 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Anuta:1996:BLA,
  author =       "M. A. Anuta and Daniel W. Lozier and N. Schabanel and
                 P. R. Turner",
  title =        "Basic Linear Algebra Operations in {SLI} Arithmetic",
  crossref =     "Bouge:1996:EPP",
  pages =        "193--202",
  year =         "1996",
  DOI =          "https://doi.org/10.1007/BFb0024702",
  bibdate =      "Fri Jul 09 07:17:24 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir5811.ps.Z;
                 https://www.nist.gov/publications/basic-linear-algebra-operations-sli-arithmetic",
  acknowledgement = ack-nhfb,
}

@Article{Anuta:1996:MMC,
  author =       "M. A. Anuta and Daniel W. Lozier and P. R. Turner",
  title =        "The {MasPar MP-1} as a Computer Arithmetic
                 Laboratory",
  journal =      j-J-RES-NATL-BUR-STAND,
  volume =       "101",
  number =       "2",
  pages =        "165--174",
  month =        mar # "\slash " # apr,
  year =         "1996",
  CODEN =        "JRNBAG",
  DOI =          "https://doi.org/10.6028/jres.101.018",
  ISSN =         "0091-0635 (print), 2376-5305 (electronic)",
  ISSN-L =       "0091-0635",
  bibdate =      "Fri Jul 09 07:18:42 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4907584/",
  abstract =     "This paper is a blueprint for the use of a massively
                 parallel SIMD computer architecture for the simulation
                 of various forms of computer arithmetic. The particular
                 system used is a DEC/MasPar MP-1 with 4096 processors
                 in a square array. This architecture has many
                 advantages for such simulations due largely to the
                 simplicity of the individual processors. Arithmetic
                 operations can be spread across the processor array to
                 simulate a hardware chip. Alternatively they may be
                 performed on individual processors to allow simulation
                 of a massively parallel implementation of the
                 arithmetic. Compromises between these extremes permit
                 speed-area tradeoffs to be examined. The paper includes
                 a description of the architecture and its features. It
                 then summarizes some of the arithmetic systems which
                 have been, or are to be, implemented. The
                 implementation of the level-index and symmetric
                 level-index, LI and SLI, systems is described in some
                 detail. An extensive bibliography is included.",
  acknowledgement = ack-nhfb,
  journal-URL =  "https://www.nist.gov/nist-research-library/journal-research-nist/past-papers",
  keywords =     "computer arithmetic, fixed-point and floating-point
                 arithmetic, logarithmic and level-index arithmetic,
                 residue number system arithmetic, serial and parallel
                 simulation of computer arithmetic",
}

@Article{Arioli:1996:REA,
  author =       "M. Arioli and C. Fassino",
  title =        "Roundoff error analysis of algorithms based on
                 {Krylov} subspace methods",
  journal =      j-BIT-NUM-MATH,
  volume =       "36",
  number =       "2",
  pages =        "189--205",
  month =        jun,
  year =         "1996",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01731978",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65F10 (15A23 65G05)",
  MRnumber =     "98e:65018",
  MRreviewer =   "Jean-Marie Chesneaux",
  bibdate =      "Wed Jan 4 18:52:24 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mai.liu.se/BIT/contents/bit36.html;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=2&spage=189",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point arithmetic; rounding errors",
}

@InProceedings{Bajard:1996:NED,
  author =       "J.-C. Bajard and L.-S. Didier and Jean-Michel Muller",
  booktitle =    "Proceedings of International Conference on Application
                 Specific Systems, Architectures and Processors, 1996.
                 {ASAP 96}",
  title =        "A new {Euclidean} division algorithm for residue
                 number systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "45--54",
  year =         "1996",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ASAP.1996.542800",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "We propose in this paper a new algorithm and
                 architecture for performing divisions in residue number
                 systems. Our algorithm is suitable for residue number
                 systems with large moduli, with the aim of manipulating
                 very large integers on a parallel \ldots{}",
}

@Article{Barber:1996:QAC,
  author =       "C. Bradford Barber and David P. Dobkin and Hannu
                 Huhdanpaa",
  title =        "The {Quickhull Algorithm} for Convex Hulls",
  journal =      j-TOMS,
  volume =       "22",
  number =       "4",
  pages =        "469--483",
  month =        dec,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/235815.235821",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Nov 8 14:50:36 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p469-barber/",
  abstract =     "The convex hull of a set of points is the smallest
                 convex set that contains the points. This article
                 presents a practical convex hull algorithm that
                 combines the two-dimensional Quickhull Algorithm with
                 the general-dimensional Beneath-Beyond Algorithm. It is
                 similar to the randomized, incremental algorithms for
                 convex hull and Delaunay triangulation. We provide
                 empirical evidence that the algorithm runs faster when
                 the input contains nonextreme points and that it uses
                 less memory. Computational geometry algorithms have
                 traditionally assumed that input sets are well behaved.
                 When an algorithm is implemented with floating-point
                 arithmetic, this assumption can lead to serious errors.
                 We briefly describe a solution to this problem when
                 computing the convex hull in two, three, or four
                 dimensions. The output is a set of ``thick'' facets
                 that contain all possible exact convex hulls of the
                 input. A variation is effective in five or more
                 dimensions.",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, reliability",
  subject =      "{\bf I.3.5}: Computing Methodologies, COMPUTER
                 GRAPHICS, Computational Geometry and Object Modeling,
                 Geometric algorithms, languages and systems.",
}

@InProceedings{Berlejung:1996:PSM,
  author =       "H. M. E. Berlejung",
  title =        "Processing Software Metrics in an Integrated
                 Development Environment for {Pascal-XSC}",
  crossref =     "Alefeld:1996:SCV",
  pages =        "79--83",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@InProceedings{Berner:1996:PMV,
  author =       "S. Berner",
  title =        "A Parallel Method for Verified Global Optimization",
  crossref =     "Alefeld:1996:SCV",
  pages =        "200--206",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@Article{Blum:1996:RPD,
  author =       "Manuel Blum and H. Wasserman",
  title =        "Reflections on the {Pentium} Division Bug",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "4",
  pages =        "385--393",
  month =        apr,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.494097",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:10 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://http.cs.berkeley.edu/~blum/pentium.ps;
                 http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=494097",
  abstract =     "We review the field of {\em result-checking\/} and
                 suggest that it be extended to a methodology for
                 enforcing hardware\slash software reliability. We
                 thereby formulate a vision for ``self-monitoring''
                 hardware\slash software whose reliability is augmented
                 through embedded suites of run-time correctness
                 checkers. In particular, we suggest that embedded
                 checkers and correctors may be employed to safeguard
                 against arithmetic errors such as that which has
                 bedeviled the Intel Pentium Microprocessor. We specify
                 checkers and correctors suitable for monitoring the
                 multiplication and division functionalities of an
                 arbitrary arithmetic processor and seamlessly
                 correcting erroneous output which may occur for any
                 reason during the lifetime of the chip.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Built-in testing; concurrent error detection; fault
                 tolerance; Pentium; reliability; result-checking;
                 verification",
}

@Article{Bockenfeld:1996:TNT,
  author =       "Don Bockenfeld",
  title =        "{TSQRT}: a New Trick for an Old Dog",
  journal =      j-CCCUJ,
  volume =       "14",
  number =       "3",
  pages =        "39--41",
  month =        mar,
  year =         "1996",
  CODEN =        "CCUJEX",
  ISSN =         "1075-2838",
  bibdate =      "Sat Feb 10 08:57:37 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Implements a small table-driven square root function
                 in C, using exclusively integer operations.",
  acknowledgement = ack-nhfb,
  fjournal =     "C/C++ Users Journal",
}

@Article{Burger:1996:PFP,
  author =       "Robert G. Burger and R. Kent Dybvig",
  title =        "Printing Floating-Point Numbers Quickly and
                 Accurately",
  journal =      j-SIGPLAN,
  volume =       "31",
  number =       "5",
  pages =        "108--116",
  month =        may,
  year =         "1996",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/231379.231397",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Mon Feb 03 07:07:43 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/proceedings/pldi/231379/index.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "This paper offers a significantly faster algorithm
                 than that of \cite{Steele:1990:HPF}, together with a
                 correctness proof and an implementation in Scheme. See
                 also
                 \cite{Clinger:1990:HRF,Abbott:1999:ASS,Steele:2004:RHP,Clinger:2004:RHR}.",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/pldi/231379/p108-burger/",
  acknowledgement = ack-nhfb,
  affiliation =  "Department of Computer Science, Indiana University,
                 Bloomington, IN, USA",
  annote =       "Published as part of the Proceedings of PLDI'96.",
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "algorithms; design; theory",
  subject =      "{\bf I.3.3} Computing Methodologies, COMPUTER
                 GRAPHICS, Picture/Image Generation, Display algorithms.
                 {\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems. {\bf I.1.2} Computing Methodologies,
                 SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms.",
}

@TechReport{Burnikel:1996:HPF,
  author =       "Christoph Burnikel and Jochen K{\"o}nemann",
  title =        "High precision floating point numbers in {LEDA}",
  type =         "Report",
  number =       "MPI I 96 1 002",
  institution =  "Max-Planck-Institut f{\"u}r Informatik",
  address =      "Saarbr{\"u}cken, Germany",
  pages =        "7",
  year =         "1996",
  bibdate =      "Thu May 09 09:03:32 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Candev:1996:AIA,
  author =       "M. Candev",
  title =        "On the Application of an Interval Algorithm for Set
                 Inversion",
  crossref =     "Alefeld:1996:SCV",
  pages =        "140--146",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@Article{Cappuccino:1996:DDH,
  author =       "G. Cappuccino and P. Corsonello and G. Cocorullo",
  title =        "Design and demonstration of high throughput square
                 rooting circuit",
  journal =      j-ELECT-LETTERS,
  volume =       "32",
  number =       "5",
  pages =        "434",
  month =        "????",
  year =         "1996",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  summary =      "Not \ldots{}",
}

@Article{Chaitin-Chatelin:1996:FPA,
  author =       "F. Chaitin-Chatelin",
  title =        "Is Finite Precision Arithmetic Useful For Physics?",
  journal =      j-J-UCS,
  volume =       "2",
  number =       "5",
  pages =        "380--??",
  day =          "28",
  month =        may,
  year =         "1996",
  CODEN =        "????",
  ISSN =         "0948-6968",
  ISSN-L =       "0948-6968",
  bibdate =      "Wed May 28 19:32:35 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.jucs.org/is_finite_precision_arithmetic_useful_for_physics",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
}

@Book{Chaitin-Chatelin:1996:LFP,
  author =       "Fran{\c{c}}oise Chaitin-Chatelin and Val{\'e}rie
                 Frayss{\'e}",
  title =        "Lectures on Finite Precision Computations",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xv + 235",
  year =         "1996",
  ISBN =         "0-89871-358-7",
  ISBN-13 =      "978-0-89871-358-9",
  LCCN =         "QA297 .C417 1996",
  bibdate =      "Wed Nov 16 14:38:30 MST 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Software, environments, tools",
  acknowledgement = ack-nhfb,
  keywords =     "Matlab",
  subject =      "numerical calculations; data processing; error
                 analysis (mathematics); toolbox PRECISE",
  tableofcontents = "1. General Presentation \\
                 2. Computability in Finite Precision \\
                 3. Measures of Stability for Regular Problems \\
                 4. Computation in the Neighbourhood of a Singularity
                 \\
                 5. Arithmetic Quality of Reliable Algorithms \\
                 6. Numerical Stability in Finite Precision \\
                 7. Software Tools for Round-Off Error Analysis in
                 Algorithms \\
                 8. The Toolbox PRECISE for Computer Experimentation \\
                 9. Experiments with PRECISE \\
                 10. Robustness to Nonnormality \\
                 11. Qualitative Computing \\
                 12. More Numerical Illustrations with PRECISE \\
                 Annex: The Toolbox PRECISE for MATLAB.",
}

@Article{Chen:1996:VAC,
  author =       "Y.-A. Chen and E. Clarke and P.-H. Ho and Y. Hoskote
                 and T. Kam and M. Khaira and J. O. Leary and X. Zhao",
  title =        "Verification of All Circuits in a Floating-Point Unit
                 Using Word-Level Model Checking",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1166",
  pages =        "19--33",
  year =         "1996",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Jun 02 07:43:02 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InProceedings{Chesneaux:1996:CSS,
  author =       "J.-M. Chesneaux and B. Troff",
  title =        "Computational Stability Study Using the {CADNA}
                 Software Applied to the {Navier--Stokes} Solver
                 {PEGASE}",
  crossref =     "Alefeld:1996:SCV",
  pages =        "84--90",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chren:1996:DPP,
  author =       "W. A. {Chren, Jr.} and C. H. Brogdon and D.
                 Andrevska",
  booktitle =    "{IEEE 39th} Midwest symposium on Circuits and Systems,
                 1996",
  title =        "Delay-power product simulation results for one-hot
                 residue number system arithmetic circuits",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "544--547",
  year =         "1996",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1996.594237",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "We present Spice simulations which verify previous
                 analytical estimates of the delay-power product of
                 One-Hot Residue adders and multipliers. These
                 simulations show greater than a 50\% reduction in the
                 product below binary adders and an order of \ldots{}",
}

@InProceedings{Chren:1996:DSD,
  author =       "W. A. {Chren, Jr.}",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems. {ISCAS '96}, Connecting the World, 12--15 May
                 1996",
  title =        "Delta-sigma demodulator with large oversampling ratio
                 using the one-hot residue number system",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "473--476",
  year =         "1996",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1996.541749",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A residue number system-based delta-sigma demodulator
                 is presented which demonstrates a significant
                 improvement in oversampling ratio in comparison with
                 equivalent binary designs. The second order design
                 employs a two-stage cascade architecture with
                 \ldots{}",
}

@InProceedings{Chren:1996:RDU,
  author =       "W. A. {Chren, Jr.} and C. H. Brogdon",
  booktitle =    "{IEEE 39th} Midwest symposium on Circuits and Systems,
                 1996",
  title =        "{RSA} decryption using the one-hot residue number
                 system",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "551--554",
  year =         "1996",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1996.594238",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The design of an RSA decryption circuit which uses the
                 One-Hot Residue Number System is presented. Large
                 modulus adders and multipliers are described which
                 reduce the area of previous (barrel shifter-based)
                 designs while preserving their low power \ldots{}",
}

@Article{Ciminiera:1996:CSM,
  author =       "L. Ciminiera and P. Montuschi",
  title =        "Carry-save multiplication schemes without final
                 addition",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "9",
  pages =        "1050--1055",
  month =        sep,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.537128",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:13 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=537128",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Clarke:1996:VSD,
  author =       "E. M. Clarke and S. M. German and X. Zhao",
  title =        "Verifying the {SRT} division algorithm using theorem
                 proving techniques",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1102",
  pages =        "111--??",
  year =         "1996",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Fri Sep 6 19:46:15 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InProceedings{Clarke:1996:WLS,
  author =       "E. M. Clarke and M. Khaira and X. Zhao",
  title =        "Word-level symbolic model checking: avoiding the
                 {Pentium FDIV} error",
  crossref =     "IEEE:1996:DAC",
  pages =        "645--648",
  year =         "1996",
  bibdate =      "Sat Jun 02 07:44:08 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/dac/240518/p645-clarke/p645-clarke.pdf;
                 http://www.acm.org/pubs/citations/proceedings/dac/240518/p645-clarke/;
                 http://www.acm.org/pubs/contents/proceedings/dac/240518/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Corliss:1996:VPE,
  author =       "G. F. Corliss and R. Rihm",
  title =        "Validating an {A} Priori Enclosure Using High-Order
                 {Taylor} Series",
  crossref =     "Alefeld:1996:SCV",
  pages =        "228--238",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@Article{Crenshaw:1996:PTF,
  author =       "Jack W. Crenshaw",
  title =        "Programmer's Toolbox: Floating-Point Math, Part 3",
  journal =      j-EMBED-SYS-PROG,
  volume =       "9",
  number =       "1",
  pages =        "19--??",
  year =         "1996",
  CODEN =        "EYPRE4",
  ISSN =         "1040-3272",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Embedded Systems Programming",
}

@TechReport{Darcy:1996:FMF,
  author =       "Joseph D. Darcy and David Gay",
  title =        "{FLECKmarks}: Measuring Floating Point Performance
                 using a {FulL IEEE Compliant Arithmetic BenchmarK}",
  type =         "Technical report",
  institution =  "Department of Computer Science, University of
                 California, Berkeley",
  address =      "Berkeley, CA, USA",
  month =        dec,
  year =         "1996",
  bibdate =      "Mon Feb 18 12:25:24 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~darcy/Research/fleckmrk.pdf",
  acknowledgement = ack-nhfb,
  remark =       "From the first author's home Web page: ``Errata: The
                 `subnormal' timings for x86 processors are incorrect;
                 they do not perform operations on subnormals at full
                 speed. However, what values are subnormals on the x86
                 are different than on other processors due to that
                 architecture's unusual floating-point register design.
                 On the x86, when a 64-bit double value is loaded into a
                 register, it has the 15 bit exponent of the 80-bit
                 double extended format instead of the 11 bit exponent
                 of the double format. Confusingly, this occurs even if
                 the processor's precision control is set to round to
                 double precision. The test programs in this project
                 used computations that would be subnormal in a pure
                 double format, not in double with extended exponent
                 range (non-zero subnormals in double with extended
                 exponent range would round to zero in pure double).
                 Operations on subnormals in double precision with
                 extended exponent range should take about 100 cycles on
                 the Pentium Pro and subsequent Intel x86
                 chips.\par

                 Thanks to David Scott of Intel for pointing out this
                 error.",
}

@InProceedings{Dimitrov:1996:NCD,
  author =       "V. Dimitrov and Saeid Sadeghi-Emamchaie and G. A.
                 Jullien and W. C. Miller",
  title =        "Near Canonic Double-Based Number System ({DBNS}) with
                 Applications in Digital Signal Processing",
  crossref =     "Luk:1996:PSC",
  pages =        "14--25",
  year =         "1996",
  DOI =          "https://doi.org/10.1117/12.255433",
  bibdate =      "Sat May 14 17:15:05 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://spie.org/x648.html?product_id=235316;
                 http://www.gbv.de/dms/bowker/toc/9780819422347",
  acknowledgement = ack-nhfb,
  keywords =     "Double-Based Number System (DBNS)",
}

@InProceedings{Dimitrov:1996:RNS,
  author =       "V. S. Dimitrov and G. A. Jullien and W. C. Miller",
  booktitle =    "{IEEE 39th} Midwest symposium on Circuits and Systems,
                 1996",
  title =        "A residue number system implementation of real
                 orthogonal transforms via approximation over a direct
                 product of quadratic number rings",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "533--536",
  year =         "1996",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1996.594227",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Recent work has focused on doing residue computations
                 that are quantization within a dense ring of integers
                 in the real domain. The aims of the paper are to
                 provide and efficient algorithm for approximation of
                 the real input signal with arbitrarily \ldots{}",
}

@InProceedings{Dimitrova:1996:NAS,
  author =       "N. S. Dimitrova",
  title =        "On a Numerical Approach for Solving a Class of
                 Nonlinear Systems",
  crossref =     "Alefeld:1996:SCV",
  pages =        "147--153",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@InProceedings{Djebbari:1996:GAS,
  author =       "A. Djebbari and S. A. Elahmar and M. F. Belbachir and
                 J. M. Rouvaen",
  booktitle =    "3rd International Conference on Signal Processing,
                 1996",
  title =        "Global asymptotic stability of normal digital filters
                 with rounding and two's complement truncation
                 quantization",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "154--157",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Normal form digital filters are investigated for limit
                 cycles due to both two's complement truncation and
                 rounding quantization. Conditions for existence are
                 derived. A method, based on an exhaustive search and
                 applicable to above types of \ldots{}",
}

@InProceedings{Dobner:1996:AAD,
  author =       "H.-J. Dobner and W. Klein",
  title =        "Application of Automatic Differentiation Techniques to
                 Circuit Simulation",
  crossref =     "Alefeld:1996:SCV",
  pages =        "329--333",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@InProceedings{Dobronets:1996:PEE,
  author =       "B. S. Dobronets",
  title =        "A Posteriori Error Estimation for Partial Differential
                 Equations",
  crossref =     "Alefeld:1996:SCV",
  pages =        "239--244",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@InProceedings{El-Guibaly:1996:HSC,
  author =       "Fayez El-Guibaly and A. Sabaa",
  title =        "High-speed {CORDIC} algorithm",
  crossref =     "Luk:1996:PSC",
  pages =        "512--512",
  year =         "1996",
  DOI =          "https://doi.org/10.1117/12.255460",
  bibdate =      "Tue Jun 14 18:26:06 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Farag:1996:LPR,
  author =       "Emad N. Farag and M. Anwarul Hasan and Mohamed I.
                 Elmasry",
  title =        "Low-power radix 2 division algorithm with minimum
                 add\slash sub operations",
  crossref =     "Luk:1996:PSC",
  pages =        "39--511",
  year =         "1996",
  DOI =          "https://doi.org/10.1117/12.255450",
  bibdate =      "Tue Jun 14 18:26:06 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Feldstein:1996:OUM,
  author =       "Alan Feldstein and Peter R. Turner",
  title =        "Overflow and underflow in multiplication and
                 division",
  journal =      j-APPL-NUM-MATH,
  volume =       "21",
  number =       "3",
  pages =        "221--239",
  day =          "20",
  month =        aug,
  year =         "1996",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  MRclass =      "65Y99",
  MRnumber =     "97f:65086; 1 416 857",
  bibdate =      "Wed Jul 28 14:36:31 MDT 1999",
  bibsource =    "Compendex database;
                 http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1996&volume=21&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_sub/browse/browse.cgi?year=1996&volume=21&issue=3&aid=692",
  acknowledgement = ack-nhfb,
  affiliation =  "Arizona State Univ",
  affiliationaddress = "AZ, USA",
  classification = "721.1; 723.2; 921; 921.2; 921.6",
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274",
  journalabr =   "Appl Numer Math",
  keywords =     "Differential equations; Digital arithmetic; Division;
                 Floating point exponents; Floating point fractions;
                 Logarithmic distribution; Mathematical models;
                 Multiplication; Natural sciences computing; Overflow;
                 Underflow",
}

@Article{Fenn:1996:MDD,
  author =       "S. T. J. Fenn and M. Benaissa and D. Taylor",
  title =        "{$ \mathrm {GF}(2^m) $} multiplication and division
                 over the dual basis",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "3",
  pages =        "319--327",
  month =        mar,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.485570",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485570",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Flynn:1996:SPT,
  author =       "Michael J. Flynn and Stuart Oberman and Steve Fu and
                 Hesham Al-Twaijry and Kevin Nowka and Gary Bewick and
                 Eric Schwarz and Nhon Quach",
  booktitle =    "{NSF\slash MIPS} Conference on Experimental Research
                 on Computer Systems, June 1996",
  title =        "The {SNAP} Project: Towards Sub-Nanosecond
                 Arithmetic",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "1996",
  bibdate =      "Mon Jul 18 17:18:49 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://arith.stanford.edu/tr/snap_nsf.ps.Z",
  acknowledgement = ack-nhfb,
  pagecount =    "12",
}

@Article{Fortune:1996:SAY,
  author =       "Steven Fortune and Christopher J. {Van Wyk}",
  title =        "Static analysis yields efficient exact integer
                 arithmetic for computational geometry",
  journal =      j-TOG,
  volume =       "15",
  number =       "3",
  pages =        "223--248",
  month =        jul,
  year =         "1996",
  CODEN =        "ATGRDF",
  ISSN =         "0730-0301 (print), 1557-7368 (electronic)",
  ISSN-L =       "0730-0301",
  bibdate =      "Sat Aug 31 16:39:46 MDT 1996",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/0730-0301/230533.html",
  abstract =     "Geometric algorithms as usually described assuming
                 that arithmetic operations are performed exactly on
                 real numbers. A program implemented using a naive
                 substitution of floating-point arithmetic for real
                 arithmetic can fail, since geometric primitives depend
                 upon sign-evaluation and may not be reliable if
                 evaluated approximately. Geometric primitives are
                 reliable if evaluated exactly with integer arithmetic,
                 but this degrades performance since software
                 extended-precision arithmetic is required.\par

                 We describe static-analysis techniques that reduce the
                 performance cost of exact integer arithmetic used to
                 implement geometric algorithms. We have used the
                 techniques for a number of examples, including
                 line-segment intersection in two dimensions, Delaunay
                 triangulations, and a tree-dimensional boundary-based
                 polyhedral modeler. In general, the techniques are
                 appropriate for algorithms that use primitives of
                 relatively low algebraic total degree, e.g., those
                 involving flat objects (points, lines, planes) in two
                 or three dimensions. The techniques have been package
                 in a preprocessor for reasonably convenient use.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Graphics",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J778",
  keywords =     "algorithms; experimentation",
  subject =      "{\bf I.3.5}: Computing Methodologies, COMPUTER
                 GRAPHICS, Computational Geometry and Object Modeling,
                 Geometric algorithms, languages, and systems. {\bf
                 D.3.4}: Software, PROGRAMMING LANGUAGES, Processors,
                 Preprocessors. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Reliability and robustness.",
}

@Article{Ganesan:1996:CSM,
  author =       "Ravikanth Ganesan and Kannan Govindarajan and Min-You
                 Wu",
  title =        "Comparing {SIMD} and {MIMD} Programming Modes",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "35",
  number =       "1",
  pages =        "91--96",
  day =          "25",
  month =        may,
  year =         "1996",
  CODEN =        "JPDCER",
  DOI =          "https://doi.org/10.1006/jpdc.1996.0071",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Thu Mar 9 09:19:00 MST 2000",
  bibsource =    "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.idealibrary.com/links/doi/10.1006/jpdc.1996.0071/production;
                 http://www.idealibrary.com/links/doi/10.1006/jpdc.1996.0071/production/pdf",
  acknowledgement = ack-nhfb,
  classification = "C5220P (Parallel architecture); C6110P (Parallel
                 programming)",
  corpsource =   "Department of Computer Science, State University of
                 New York, Buffalo, NY, USA",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "application benchmarks; arithmetic operations; CM;
                 CM-5; communication; Connection Machine; Fortran;
                 message-passing Fortran; MIMD; parallel architectures;
                 parallel programming; performance evaluation;
                 programming modes; SIMD; software; synthetic
                 benchmarks; time",
  treatment =    "P Practical",
}

@InProceedings{Garg:1996:FTP,
  author =       "H. K. Garg and F. V. C. Mendis",
  booktitle =    "Conference Record of the Thirtieth Asilomar Conference
                 on Signals, Systems and Computers, 1996",
  title =        "On fault-tolerant polynomial residue number systems",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "206--209",
  year =         "1996",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ACSSC.1996.600858",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Fault-tolerant convolution techniques have been
                 described for polynomials defined over the fields of
                 complex and real numbers. Fault-tolerant convolution
                 schemes are derived for polynomials defined over finite
                 integer rings. A new algorithm for \ldots{}",
}

@InProceedings{Gibb:1996:FFI,
  author =       "S. Gibb and P. J. W. Graumann and Laurence E. Turner",
  title =        "{FIR} filter implementation using bit-serial
                 arithmetic and partial summation trees",
  crossref =     "Luk:1996:PSC",
  pages =        "63--74",
  year =         "1996",
  DOI =          "https://doi.org/10.1117/12.255462",
  bibdate =      "Tue Jun 14 18:26:06 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Goldberg:1996:CA,
  author =       "David Goldberg",
  title =        "Computer Arithmetic",
  crossref =     "Hennessy:1996:CAQ",
  chapter =      "A",
  pages =        "A-1--A-77",
  year =         "1996",
  bibdate =      "Mon May 20 10:05:22 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Goldstine:1996:ENI,
  author =       "H. H. Goldstine and A. Goldstine",
  title =        "The {Electronic Numerical Integrator and Computer}
                 ({ENIAC})",
  journal =      j-IEEE-ANN-HIST-COMPUT,
  volume =       "18",
  number =       "1",
  pages =        "10--16",
  month =        "Spring",
  year =         "1996",
  CODEN =        "IAHCEX",
  DOI =          "https://doi.org/10.1109/85.476557",
  ISSN =         "1058-6180 (print), 1934-1547 (electronic)",
  ISSN-L =       "1058-6180",
  bibdate =      "Fri Nov 28 16:50:50 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Reprint of 1946 technical report and
                 \cite{Goldstine:1946:ENI}.",
  URL =          "https://ieeexplore.ieee.org/iel4/85/10202/00476557.pdf",
  abstract =     "It is our purpose in the succeeding pages to give a
                 brief description of the ENIAC and an indication of the
                 kinds of problems for which it can be used. This
                 general purpose electronic computing machine was
                 recently made public by the Army Ordnance Department
                 for which it was developed by the Moore School of
                 Electrical Engineering. The machine was developed
                 primarily for the purpose of calculating firing tables
                 for the armed forces. Its design is, however,
                 sufficiently general to permit the solution of a large
                 class of numerical problems which could hardly be
                 attempted by more conventional computing tools.\par

                 In order easily to obtain sufficient accuracy for
                 scientific computations, the ENIAC was designed as a
                 digital device. The equipment normally handles signed
                 10-digit numbers expressed in the decimal system. It
                 is, however, so constructed that operations with as
                 many as 20 digits are possible.\par

                 The machine is automatically sequenced in the sense
                 that all instructions needed to carry out a computation
                 are given to it before the computation commences. It
                 will be seen below how these instructions are given to
                 the machine.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "IEEE Annals of the History of Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85",
  keywords =     "decimal floating-point arithmetic",
}

@InProceedings{Gudenberg:1996:HSI,
  author =       "J. W. Von Gudenberg",
  title =        "Hardware Support for Interval Arithmetic",
  crossref =     "Alefeld:1996:SCV",
  pages =        "32--37",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@Book{Guedj:1996:EN,
  author =       "Denis Guedj",
  title =        "{L}'empire des nombres",
  publisher =    "Gallimard",
  address =      "Paris, France",
  pages =        "176",
  year =         "1996",
  ISBN =         "2-07-053373-5",
  ISBN-13 =      "978-2-07-053373-2",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 06:57:01 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Gupta:1996:AAG,
  author =       "S. Gupta and J. Rajski and J. Tyszer",
  title =        "Arithmetic additive generators of pseudo-exhaustive
                 test patterns",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "8",
  pages =        "939--949",
  month =        aug,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.536236",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:13 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=536236",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Guyot:1996:STD,
  author =       "A. Guyot and M. Renaudin and B. El Hassan and V.
                 Levering",
  booktitle =    "Proceedings of the Ninth International Conference on
                 {VLSI} Design, 1996",
  title =        "Self timed division and square-root extraction",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "376--381",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper describes a self-timed integrated circuit
                 for division and square-root extraction. First it
                 concentrates on the development and the proof of a new
                 mathematical algorithm. Then the design methodology and
                 the architecture of a self-timed \ldots{}",
}

@Article{Haller:1996:AFP,
  author =       "G. M. Haller and D. R. Freytag",
  title =        "Analog floating-point {BiCMOS} sampling chip and
                 architecture of the {BaBar CsI} calorimeter front-end
                 electronics system at the {SLAC} {B}-factory",
  journal =      j-IEEE-TRANS-NUCL-SCI,
  volume =       "43",
  number =       "3",
  pages =        "1610--1614",
  month =        jun,
  year =         "1996",
  CODEN =        "IRNSAM",
  ISSN =         "0018-9499 (print), 1558-1578 (electronic)",
  ISSN-L =       "0018-9499",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Nuclear Science",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=23",
  summary =      "The design and implementation of an analog
                 floating-point sampling integrated circuit for the
                 BaBar detector at the SLAC B-Factory is described. The
                 CARE (Custom Auto-Range Encoding) circuit is part of an
                 18-bit dynamic range sampling system with a \ldots{}",
}

@Book{Hamacher:1996:CO,
  author =       "V. Carl Hamacher and Zvonko G. Vranesic and Safwat G.
                 Zaky",
  title =        "Computer organization",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  edition =      "Fourth",
  pages =        "xix + 555",
  year =         "1996",
  ISBN =         "0-07-025883-X",
  ISBN-13 =      "978-0-07-025883-9",
  LCCN =         "QA76.9.C643 H36 1996",
  bibdate =      "Sat May 18 14:24:11 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "McGraw-Hill series in computer organization and
                 architecture",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hartwig:1996:RNA,
  author =       "F. Hartwig and A. Lacroix",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems: {ISCAS '96}, `Connecting the World', 12--15
                 May 1996",
  title =        "Roundoff noise analysis on the basis of an improved
                 floating point error model",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "133--136",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Until now floating point roundoff analysis utilized
                 the assumption of statistical decorrelation between
                 roundoff error and internal signals subject to a signal
                 flow graph. A quantization within a signal flow graph
                 has been treated like a single \ldots{}",
}

@Article{Hauser:1996:HFE,
  author =       "John R. Hauser",
  title =        "Handling floating-point exceptions in numeric
                 programs",
  journal =      j-TOPLAS,
  volume =       "18",
  number =       "2",
  pages =        "139--174",
  month =        mar,
  year =         "1996",
  CODEN =        "ATPSDT",
  DOI =          "https://doi.org/10.1145/227699.227701",
  ISSN =         "0164-0925 (print), 1558-4593 (electronic)",
  ISSN-L =       "0164-0925",
  bibdate =      "Tue Aug 13 11:46:35 MDT 1996",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/toc/Abstracts/0164-0925/227701.html",
  abstract =     "There are a number of schemes for handling arithmetic
                 exceptions that can be used to improve the speed (or
                 alternatively the reliability) of numeric code.
                 Overflow and underflow are the most troublesome
                 exceptions, and depending on the context in which the
                 exception can occur, they may be addressed either: (1)
                 through a ``brute force'' reevaluation with extended
                 range, (2) by reevaluating using a technique known as
                 {\em scaling}, (3) by substituting an infinity or zero,
                 or (4) in the case of underflow, with gradual
                 underflow. In the first two of these cases, the
                 offending computation is simply reevaluated using a
                 safer but slower method. The latter two cases are
                 cheaper, more automated schemes that ideally are built
                 in as options within the computer system. Other
                 arithmetic exceptions can be handled with similar
                 methods. These and some other techniques are examined
                 with an eye toward determining the support programming
                 languages and computer systems ought to provide for
                 floating-point exception handling. It is argued that
                 the cheapest short-term solution would be to give full
                 support to most of the {\em required\/} (as opposed to
                 recommended) special features of the IEC/IEEE Standard
                 for Binary Floating-Point Arithmetic. An essential part
                 of this support would include standardized access from
                 high-level languages to the exception flags defined by
                 the standard. Some possibilities outside the IEEE
                 Standard are also considered, and a few thought on
                 possible better-structured support within programming
                 languages are discussed.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Programming Languages and
                 Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J783",
  keywords =     "accurate floating-point summation; algorithms; design;
                 languages; performance; standardization",
  subject =      "{\bf D.3.3}: Software, PROGRAMMING LANGUAGES, Language
                 Constructs and Features, Control structures. {\bf
                 D.3.0}: Software, PROGRAMMING LANGUAGES, General,
                 Standards. {\bf G.1.0}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Computer arithmetic. {\bf
                 G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Numerical algorithms.",
}

@Book{Heck:1996:IM,
  author =       "Andr{\'e} Heck",
  title =        "Introduction to {Maple}",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "xx + 699",
  year =         "1996",
  DOI =          "https://doi.org/10.1007/978-1-4684-0484-5",
  ISBN =         "0-387-94535-0 (hardcover), 1-4684-0484-9,
                 1-4684-0486-5",
  ISBN-13 =      "978-0-387-94535-4 (hardcover), 978-1-4684-0484-5,
                 978-1-4684-0486-9",
  LCCN =         "QA155.7.E4H43 1993",
  MRclass =      "65-01, 65B10, 65D18, 65Dxx, 65Fxx, 65Lxx, 68-01,
                 68N15, 68W30, 68NXX",
  MRnumber =     "MR1405611 (97c:68076)",
  bibdate =      "Tue Jun 06 17:57:02 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\$39.00",
  abstract =     "The first edition of this book has been very well
                 received by the community. The new version 4 of Maple V
                 contains so many new mathematical features and
                 improvements in the user interface that Waterloo Maple
                 Inc. markets it as ``the Power Edition.'' These two
                 facts have made it necessary to write a second edition
                 within a short period of the first. I corrected
                 typographical errors, rephrased text, updated and
                 improved many examples, and added much new material.
                 Hardly any chapter has been left untouched.
                 Substantially changed or added sections and chapters
                 address the assume facility, I/O, approximation theory,
                 integration, composite data types, simplification,
                 graphics, differential equations, and matrix algebra.
                 Tables summarize features, command options, etc., and
                 constitute a quick reference. The enlarged index of the
                 book has been carefully compiled to make locating
                 search items quick and easy. Many new examples have
                 been included showing how to use Maple as a problem
                 solver, how to assist the system during computations,
                 and how to extend its built-in facilities. About the
                 Maple Version Used: The second edition of this book is
                 fully revised and updated to Maple V Release 4. More
                 precisely, the second edition of this book was produced
                 with Maple V Release 4, beta 3 on a SUN SPARCstation
                 20, Model 71. There should be hardly any difference
                 between this beta version and the final release; only
                 minor differences in the user interface are not
                 excluded.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Preface to the Second Edition / v \\
                 Preface to the First Edition / ix \\
                 List of Tables / xix \\
                 1 Introduction to Computer Algebra / 1 \\
                 1.1 What is Computer Algebra? / 1 \\
                 1.2 Computer Algebra Systems / 2 \\
                 1.3 Some Properties of Computer Algebra Systems / 5 \\
                 1.4 Advantages of Computer Algebra / 11 \\
                 1.5 Limitations of Computer Algebra / 24 \\
                 1.6 Design of Maple / 30 \\
                 2 The First Steps: Calculus on Numbers / 35 \\
                 2.1 Getting Started / 35 \\
                 2.2 Getting Help / 38 \\
                 2.3 Integers and Rational Numbers / 44 \\
                 2.4 Irrational Numbers and Floating-Point Numbers / 48
                 \\
                 2.5 Algebraic Numbers / 54 \\
                 2.6 Complex Numbers / 59 \\
                 2.7 Exercises / 63 \\
                 3 Variables and Names / 65 \\
                 3.1 Assignment and Unassignment / 65 \\
                 3.2 Evaluation / 73 \\
                 3.3 Names of Variables / 77 \\
                 3.4 Basic Data Types / 82 \\
                 3.5 Attributes / 86 \\
                 3.6 Properties / 87 \\
                 3.7 Exercises / 92 \\
                 4 Getting Around with Maple / 95 \\
                 4.1 Maple Input and Output / 95 \\
                 4.2 The Maple Library / 101 \\
                 4.3 Reading and Writing Files / 105 \\
                 4.4 Importing and Exporting Numerical Data / 110 \\
                 4.5 Low-Level I/O / 113 \\
                 4.6 Code Generation / 123 \\
                 4.7 Changing Maple to Your Own Taste / 129 \\
                 4.8 Exercises / 133 \\
                 5 Polynomials and Rational Functions / 135 \\
                 5.1 Univariate Polynomials / 135 \\
                 5.2 Multivariate Polynomials / 140 \\
                 5.3 Rational Functions / 142 \\
                 5.4 Conversions / 144 \\
                 5.5 Exercises / 147 \\
                 6 Internal Data Representation and Substitution / 149
                 \\
                 6.1 Internal Representation of Polynomials / 149 \\
                 6.2 Generalized Rational Expressions / 155 \\
                 6.3 Substitution / 158 \\
                 6.4 Exercises / 170 \\
                 7 Manipulation of Polynomials and Rational Expressions
                 / 173 \\
                 7.1 Expansion / 173 \\
                 7.2 Factorization / 176 \\
                 7.3 Canonical Form and Normal Form / 179 \\
                 7.4 Normalization / 181 \\
                 7.5 Collection / 183 \\
                 7.6 Sorting / 186 \\
                 7.7 Exercises / 186 \\
                 8 Functions / 189 \\
                 8.1 Mathematical Functions / 189 \\
                 8.2 Arrow Operators / 193 \\
                 8.3 Piecewise Defined Functions / 195 \\
                 8.4 Maple Procedures / 202 \\
                 8.5 Recursive Procedure Definitions / 204 \\
                 8.6 unapply / 209 \\
                 8.7 Operations on Functions / 210 \\
                 8.8 Anonymous Functions / 211 \\
                 8.9 Exercises / 212 \\
                 9 Differentiation / 213 \\
                 9.1 Symbolic Differentiation / 213 \\
                 9.2 Automatic Differentiation / 221 \\
                 9.3 Exercises / 224 \\
                 10 Integration and Summation / 227 \\
                 10.1 Indefinite Integration / 227 \\
                 10.2 Definite Integration / 236 \\
                 10.3 Numerical Integration / 241 \\
                 10.4 Integral Transforms / 242 \\
                 10.5 Assisting Maple's Integrator / 252 \\
                 10.6 Summation / 256 \\
                 10.7 Exercises / 261 \\
                 11 Series, Approximation, and Limits / 267 \\
                 11.1 Truncated Series / 267 \\
                 11.2 Approximation of Functions / 278 \\
                 11.3 Power Series / 285 \\
                 11.4 Limits / 288 \\
                 11.5 Exercises / 291 \\
                 12 Composite Data Types / 293 \\
                 12.1 Sequence / 293 \\
                 12.2 Set / 296 \\
                 12.3 List / 298 \\
                 12.4 Array / 304 \\
                 12.5 Table / 310 \\
                 12.6 Last Name Evaluation / 314 \\
                 12.7 Function Call / 317 \\
                 12.8 Conversion Between Composite Data Types / 319 \\
                 12.9 Exercises / 322 \\
                 13 The Assume Facility / 325 \\
                 13.1 The Need for an Assume Facility / 325 \\
                 13.2 Basics of assume / 329 \\
                 13.3 An Algebra of Properties / 332 \\
                 13.4 Implementation of assume / 335 \\
                 13.5 Exercises / 340 \\
                 13.6 Hierarchy of Properties / 340 \\
                 14 Simplification / 343 \\
                 14.1 Automatic Simplification / 344 \\
                 14.2 expand / 346 \\
                 14.3 combine / 353 \\
                 14.4 simplify / 358 \\
                 14.5 convert / 364 \\
                 14.6 Trigonometrie Simplification / 367 \\
                 14.7 Simplification w.r.t. Side Relations / 370 \\
                 14.8 Control Over Simplification / 374 \\
                 14.9 Defining Your Own Simplification Routines / 378
                 \\
                 14.10 Exercises / 383 \\
                 14.11 Simplification Chart / 385 \\
                 15 Graphics / 387 \\
                 15.1 Some Basic Two-Dimensional Plots / 389 \\
                 15.2 Options of plot / 393 \\
                 15.3 The Structure of Two-Dimensional Graphics / 406
                 \\
                 15.4 The plottools Package / 412 \\
                 15.5 Special Two-Dimensional Plots / 416 \\
                 15.6 Two-Dimensional Geometry / 429 \\
                 15.7 Plot Aliasing / 432 \\
                 15.8 A Common Mistake / 433 \\
                 15.9 Some Basic Three-Dimensional Plots / 434 \\
                 15.10 Options of plot3d / 436 \\
                 15.11 The Structure of Three-Dimensional Graphics / 444
                 \\
                 15.12 Special Three-Dimensional Plots / 449 \\
                 15.13 Data Plotting / 457 \\
                 15.14 Animation / 467 \\
                 15.15 List of Plot Options / 469 \\
                 15.16 Exercises / 475 \\
                 16 Solving Equations / 479 \\
                 16.1 Equations in One Unknown / 479 \\
                 16.2 Abbreviations in solve / 480 \\
                 16.3 Some Difficulties / 481 \\
                 16.4 Systems of Equations / 488 \\
                 16.5 The Gr{\"o}bner Basis Method / 499 \\
                 16.6 Inequalities / 505 \\
                 16.7 Numerical Solvers / 507 \\
                 16.8 Other Solvers in Maple / 509 \\
                 16.9 Exercises / 515 \\
                 17 Differential Equations / 519 \\
                 17.1 First Glance at ODEs / 519 \\
                 17.2 Analytic Solutions / 520 \\
                 17.3 Taylor Series Method / 532 \\
                 17.4 Power Series Method / 534 \\
                 17.5 Numerical Solutions / 536 \\
                 17.6 DEtools / 548 \\
                 17.7 Perturbation Methods / 555 \\
                 17.8 Partial Differential Equations / 567 \\
                 17.9 Lie Point Symmetries of PDEs / 569 \\
                 17.10 Exercises / 572 \\
                 18 Linear Algebra: The linaig Package / 575 \\
                 18.1 Loading the linaig Package / 575 \\
                 18.2 Creating New Vectors and Matrices / 576 \\
                 18.3 Vector and Matrix Arithmetic / 580 \\
                 18.4 Basic Matrix Functions / 584 \\
                 18.5 Structural Operations / 589 \\
                 18.6 Vector Operations / 592 \\
                 18.7 Standard Forms of Matrices / 592 \\
                 18.8 Exercises / 597 \\
                 19 Linear Algebra: Applications / 601 \\
                 19.1 Kinematics of the Stanford Manipulator / 601 \\
                 19.2 A Three-Compartment Model of Cadmium Transfer /
                 606 \\
                 19.3 Molecular-Orbital H{\"u}ckel Theory / 618 \\
                 19.4 Vector Analysis / 623 \\
                 19.5 Moore--Penrose Inverse / 631 \\
                 19.6 Exercises / 633 \\
                 References / 635 \\
                 Index / 651",
}

@Article{Hecker:1996:LGF,
  author =       "Chris Hecker",
  title =        "Let's get to the (floating) point",
  journal =      "Game Developer",
  volume =       "2",
  number =       "??",
  pages =        "19--24",
  month =        feb # "\slash " # mar,
  year =         "1996",
  ISSN =         "1073-922X",
  bibdate =      "Fri Jan 06 07:46:23 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "accurate floating-point summation; splitting of
                 floating-point numbers into high and low parts",
  URL =          "http://chrishecker.com/images/f/fb/Gdmfp.pdf;
                 https://www.gamasutra.com/php-bin/store.php?item_id=220&category=22&book=",
  acknowledgement = ack-nhfb,
}

@InProceedings{Heikes:1996:DFP,
  author =       "Craig Heikes and Glenn Colon-Bonet",
  title =        "A Dual Floating Point Coprocessor with an {FMAC}
                 Architecture",
  crossref =     "Wuorinen:1996:DTP",
  pages =        "354--355",
  year =         "1996",
  bibdate =      "Fri Jun 24 10:49:14 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Heindl:1996:MVC,
  author =       "G. Heindl",
  title =        "A Method for Verified Computing of Inner and Outer
                 Approximations of the Interval Hull of a Tolerance
                 Polyhedron",
  crossref =     "Alefeld:1996:SCV",
  pages =        "207--213",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@Article{Heinrich:1996:AAF,
  author =       "Peter Heinrich",
  title =        "Algorithm Alley: a Fast Integer Square Root",
  journal =      j-DDJ,
  volume =       "21",
  number =       "4",
  pages =        "113--114, 130",
  month =        apr,
  year =         "1996",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@InProceedings{Herzberger:1996:OCC,
  author =       "J. Herzberger",
  title =        "On the {$R$}-Order of Convergence of a Class of
                 Simultaneous Methods for the Inclusions of Polynomial
                 Roots",
  crossref =     "Alefeld:1996:SCV",
  pages =        "154--159",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@TechReport{Hickey:1996:FSP,
  author =       "Timothy J. Hickey and Qun Ju",
  title =        "Fast, Sound, and Precise Narrowing of the Exponential
                 Function",
  type =         "Technical report",
  institution =  "Computer Science Department, Brandeis University",
  address =      "Waltham, MA, USA 02254",
  month =        mar,
  year =         "1996",
  bibdate =      "Sat Nov 05 15:42:23 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.brandeis.edu/~tim/Papers/eiianuia.ps.gz",
  acknowledgement = ack-nhfb,
}

@Book{Higham:1996:ASN,
  author =       "Nicholas J. Higham",
  title =        "Accuracy and Stability of Numerical Algorithms",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xxviii + 688",
  year =         "1996",
  ISBN =         "0-89871-355-2 (paperback)",
  ISBN-13 =      "978-0-89871-355-8 (paperback)",
  LCCN =         "QA297.H53 1996",
  MRclass =      "65Fxx, 15-04, 65-02, 65G50",
  bibdate =      "Tue Jan 30 11:01:35 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/texbook2.bib",
  price =        "US\$39.00",
  URL =          "http://www.ma.man.ac.uk/~higham/asna.html",
  acknowledgement = ack-njh # " and " # ack-nhfb,
  remark =       "Typeset with \LaTeX2e.",
  tableofcontents = "Principles of Finite Precision Computation \\
                 Relative Error and Significant Digits \\
                 Sources of Errors \\
                 Precision Versus Accuracy \\
                 Backward and Forward Errors \\
                 Conditioning \\
                 Cancellation \\
                 Solving a Quadratic Equation \\
                 Computing the Sample Variance \\
                 Solving Linear Equations \\
                 Accumulation of Rounding Errors \\
                 Instability Without Cancellation \\
                 Increasing the Precision \\
                 Cancellation of Rounding Errors \\
                 Rounding Errors Can Be Beneficial \\
                 Stability of an Algorithm Depends on the Problem \\
                 Rounding Errors Are Not Random \\
                 Designing Stable Algorithms \\
                 Misconceptions \\
                 Rounding Errors in Numerical Analysis \\
                 Floating Point Arithmetic \\
                 Floating Point Number System \\
                 Model of Arithmetic \\
                 IEEE Arithmetic \\
                 Aberrant Arithmetics \\
                 Exact Subtraction \\
                 Fused Multiply-Add Operation \\
                 Choice of Base and Distribution of Numbers \\
                 Statistical Distribution of Rounding Errors \\
                 Alternative Number Systems \\
                 Elementary Functions \\
                 Accuracy Tests \\
                 Inner and Outer Products \\
                 The Purpose of Rounding Error Analysis \\
                 Running Error Analysis \\
                 Notation for Error Analysis \\
                 Matrix Multiplication \\
                 Complex Arithmetic \\
                 Miscellany \\
                 Error Analysis Demystified \\
                 Other Approaches \\
                 Summation \\
                 Summation Methods \\
                 Error Analysis \\
                 Compensated Summation \\
                 Other Summation Methods \\
                 Statistical Estimates of Accuracy \\
                 Choice of Method \\
                 Polynomials \\
                 Horner's Method \\
                 Evaluating Derivatives \\
                 The Newton Form and Polynomial Interpolation \\
                 Matrix Polynomials \\
                 Norms \\
                 Vector Norms",
}

@Article{Hong:1996:NMM,
  author =       "Seong-Min Hong and Sang-Yeop Oh and Hyunsoo Yoon",
  title =        "New Modular Multiplication Algorithms for Fast Modular
                 Exponentiation",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1070",
  pages =        "166--??",
  year =         "1996",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Mon Feb 4 12:02:22 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1070.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1070/10700166.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1070/10700166.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InProceedings{Hyvoenen:1996:SCE,
  author =       "E. Hyvoenen and S. De Pascale",
  title =        "Shared Computations for Efficient Interval Functions
                 Evaluation",
  crossref =     "Alefeld:1996:SCV",
  pages =        "38--44",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@Article{Inacio:1996:DDF,
  author =       "Christopher Inacio and Denise Ombres",
  title =        "The {DSP} decision: fixed point or floating?",
  journal =      j-IEEE-SPECTRUM,
  volume =       "33",
  number =       "9",
  pages =        "72--74",
  month =        sep,
  year =         "1996",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/6.535397",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Thu Sep 01 16:15:25 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
}

@Article{ISO:1996:TRF,
  author =       "{ISO\slash IEC JTC1\slash SC22\slash WG5 --- N1231}",
  title =        "Technical report for floating-point exception
                 handling",
  journal =      j-FORTRAN-FORUM,
  volume =       "15",
  number =       "3",
  pages =        "1--28",
  month =        dec,
  year =         "1996",
  CODEN =        "????",
  ISSN =         "1061-7264 (print), 1931-1311 (electronic)",
  ISSN-L =       "1061-7264",
  bibdate =      "Wed Feb 6 18:50:06 MST 2002",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "7th October 1996.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Fortran Forum",
  issue =        "47",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J286",
}

@Article{Ito:1996:SRI,
  author =       "Masayuki Ito and Naofumi Takagi and Shuzo Yajima",
  title =        "Square rooting by iterative multiply-additions",
  journal =      j-INFO-PROC-LETT,
  volume =       "60",
  number =       "5",
  pages =        "267--269",
  day =          "8",
  month =        dec,
  year =         "1996",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  MRclass =      "68M07",
  MRnumber =     "97i:68014",
  bibdate =      "Wed Nov 11 12:16:26 MST 1998",
  bibsource =    "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C4130 (Interpolation and function approximation);
                 C5230 (Digital arithmetic methods)",
  corpsource =   "Department of Inf. Sci., Kyoto University, Japan",
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  keywords =     "computer arithmetic; convergence of numerical methods;
                 digital arithmetic; iterative methods; iterative
                 multiply-additions; linear converging ratio;
                 multiplicative methods; Newton--Raphson method;
                 read-only storage; ROM sizes; square root algorithm",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Jayasuriya:1996:MAU,
  author =       "Kumara Jayasuriya",
  title =        "Multiprecision arithmetic using fast {Hartley}
                 transforms",
  journal =      j-APPL-MATH-COMP,
  volume =       "75",
  number =       "2--3",
  pages =        "239--251",
  day =          "15",
  month =        mar,
  year =         "1996",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/0096-3003(96)90067-3",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Nov 20 21:02:36 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0096300396900673",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Jessani:1996:FPU,
  author =       "R. M. Jessani and C. H. Olson",
  title =        "The floating point unit of the {PowerPC 603e}
                 microprocessor",
  journal =      j-IBM-JRD,
  volume =       "40",
  number =       "5",
  pages =        "559--566",
  month =        sep,
  year =         "1996",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Tue Mar 25 14:26:59 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.almaden.ibm.com/journal/rd40-5.html#four",
  abstract =     "The IBM PowerPC 603e* floating-point unit (FPU) is an
                 on-chip functional unit to support IEEE 754 standard
                 single- and double-precision binary floating-point
                 arithmetic operations. The design objectives are to be
                 a low-cost, low-power, high-performance engine in a
                 single-chip superscalar microprocessor. Using less than
                 15 mm$^2$ of the available silicon area on the chip
                 (the size of the PowerPC 603e microprocessor is 98
                 mm$^2$) and operating at the peak clock frequency of
                 100 MHz, an average single-pumping multiply-add-fuse
                 instruction has one-cycle throughput and four-cycle
                 latency. An average double-pumping multiply-add-fuse
                 instruction has two-cycle throughput and five-cycle
                 latency. The estimated performance at 100 MHz is 105
                 against the SPECfp92** benchmark.",
  acknowledgement = ack-nhfb,
  classcodes =   "B1265F (Microprocessors and microcomputers); C5130
                 (Microprocessor chips); C5230 (Digital arithmetic
                 methods)",
  corpsource =   "Somerset Design Center, Motorola Inc., Austin, TX,
                 USA",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "add-fuse instruction; design objectives; digital
                 arithmetic; double-pumping multiply-add-fuse; floating
                 point unit; functional unit; IEEE 754 standard;
                 instruction; microprocessor chips; on-chip; peak clock
                 frequency; PowerPC 603e microprocessor; silicon area;
                 single-pumping multiply-",
  treatment =    "A Application; P Practical",
  xxlibnote =    "Issue missing from UofUtah Marriott Library",
}

@InProceedings{Jullien:1996:VDS,
  author =       "Graham A. Jullien",
  title =        "{VLSI} Digital Signal Processing: Some Arithmetic
                 Issues",
  crossref =     "Luk:1996:PSC",
  pages =        "1--13",
  year =         "1996",
  DOI =          "https://doi.org/10.1117/12.255423",
  bibdate =      "Tue Jun 14 18:18:32 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.atips.ca/research/documents/ca/aa/1996_keynote.pdf",
  acknowledgement = ack-nhfb,
  remark =       "Keynote address: VLSI Arithmetic and DSP
                 Implementations.",
}

@Misc{Kahan:1996:BEC,
  author =       "W. Kahan",
  title =        "The baleful effect of computer benchmarks upon applied
                 mathematics, physics, and chemistry",
  howpublished = "World-Wide Web document.",
  year =         "1996",
  bibdate =      "Sat Apr 28 18:52:17 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/baleful.ps",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1996:LNS,
  author =       "W. Kahan",
  title =        "Lecture notes on the status of {IEEE Standard 754} for
                 binary floating-point arithmetic",
  howpublished = "World-Wide Web document.",
  year =         "1996",
  bibdate =      "Sat Apr 28 18:52:17 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/ieee754.ps",
  acknowledgement = ack-nhfb,
}

@Unpublished{Kahan:1996:WCY,
  author =       "W. Kahan",
  key =          "Kah96a",
  title =        "What can you learn about floating-point arithmetic in
                 one hour?",
  institution =  inst-BERKELEY-EECS,
  address =      inst-BERKELEY-EECS:adr,
  pages =        "23",
  year =         "1996",
  bibdate =      "Mon Apr 25 17:58:22 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Postscript version accessible electronically at
                 \path=http://http.cs.berkeley.edu/~wkahan/ieee754status=.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/cs267fp.ps",
  acknowledgement = ack-nhfb,
}

@Article{Kalantari:1996:HOI,
  author =       "B. Kalantari and I. Kalantari",
  title =        "High order iterative methods for approximating square
                 roots",
  journal =      j-BIT-NUM-MATH,
  volume =       "36",
  number =       "2",
  pages =        "395--399",
  month =        jun,
  year =         "1996",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01731991",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65D15 (65H99)",
  MRnumber =     "97k:65039",
  bibdate =      "Wed Jan 4 18:52:24 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mai.liu.se/BIT/contents/bit36.html;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=2&spage=395",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Kalliojarvi:1996:REB,
  author =       "K. Kalliojarvi and J. Astola",
  title =        "Roundoff errors in block-floating-point systems",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "44",
  number =       "4",
  pages =        "783--790",
  month =        apr,
  year =         "1996",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "Block-floating-point representation is a special case
                 of floating-point representation, where several numbers
                 have a joint exponent term. In this paper, roundoff
                 errors in signal processing systems utilizing
                 block-floating-point representation are \ldots{}",
}

@Book{Kane:1996:PRA,
  author =       "Gerry Kane",
  title =        "{PA-RISC 2.0} Architecture",
  publisher =    pub-PHPTR,
  address =      pub-PHPTR:adr,
  pages =        "various",
  year =         "1996",
  ISBN =         "0-13-182734-0",
  ISBN-13 =      "978-0-13-182734-9",
  LCCN =         "QA76.8.H48K36 1996",
  bibdate =      "Tue Jan 09 12:34:37 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\$34.40",
  URL =          "http://devresource.hp.com/devresource/Docs/Refs/PA2_0/index.html;
                 http://devresource.hp.com/devresource/Docs/Refs/PA2_0/updates/index.html",
  abstract =     "This is the authoritative definition of
                 Hewlett-Packard's 2.0 PA-RISC architecture, one of the
                 most mature and efficient RISC (Reduced Instruction Set
                 Computer) processor architectures in the industry.
                 PA-RISC is the foundation for machines proving
                 especially well-suited for such markets as high
                 performance graphics, mission critical transaction
                 processing, and emerging multimedia applications such
                 as interactive video services.",
  acknowledgement = ack-nhfb,
  keywords =     "Hewlett--Packard computers; PA-RISC microprocessors",
  tableofcontents = "1: Overview \\
                 2: Processing Resources \\
                 3: Addressing and Access Control \\
                 4: Control Flow \\
                 5: Interruptions \\
                 6: Instruction Set Overview \\
                 7: Instruction Descriptions \\
                 8: Floating-point Coprocessor \\
                 9: Floating-Point Instruction Set \\
                 10: Floating-Point Exceptions \\
                 11: Performance Monitor Coprocessor \\
                 B: Instruction Formats \\
                 C: Operation Codes \\
                 D: Conditions \\
                 E: Instruction Notation Control Structures \\
                 F: TLB and Cache Control \\
                 G: Memory Ordering Model \\
                 H: Address Formation Details \\
                 I: Programming Notes \\
                 PA-RISC 2 Instruction Completers and Pseudo-Ops",
}

@Article{Katti:1996:NRA,
  author =       "Rajendra S. Katti",
  title =        "A new residue arithmetic error correction scheme",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "1",
  pages =        "13--19",
  month =        jan,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.481482",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "68M07",
  MRnumber =     "MR1372160 (96j:68011)",
  bibdate =      "Wed Jul 6 19:47:08 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=481482",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Kearfott:1996:OPI,
  author =       "R. B. Kearfott and X. Shi",
  title =        "Optimal Preconditioners for Interval {Gauss--Seidel}
                 Methods",
  crossref =     "Alefeld:1996:SCV",
  pages =        "173--178",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kearfott:1996:TNS,
  author =       "R. B. Kearfott",
  title =        "Treating Non-Smooth Functions as Smooth Functions in
                 Global Optimization and Nonlinear Systems Solvers",
  crossref =     "Alefeld:1996:SCV",
  pages =        "160--172",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@InProceedings{Koeber:1996:IIF,
  author =       "M. Koeber",
  title =        "Inclusion of the Inverse of a Functions in $n$
                 Variables",
  crossref =     "Alefeld:1996:SCV",
  pages =        "179--185",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kowaleski:1996:DEP,
  author =       "J. A. Kowaleski and G. M. Wolrich and T. C. Fischer
                 and R. J. Dupcak and P. L. Kroesen and T. Pham and A.
                 Olesin",
  title =        "A dual execution pipelined floating-point {CMOS}
                 processor",
  crossref =     "Wuorinen:1996:DTP",
  pages =        "358--359",
  year =         "1996",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
}

@InProceedings{Kraemer:1996:CNI,
  author =       "W. Kraemer and S. Wedner",
  title =        "Computing Narrow Inclusions for {Cauchy} Principal
                 Value Integrals",
  crossref =     "Alefeld:1996:SCV",
  pages =        "45--51",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kreinovich:1996:CCI,
  author =       "V. Kreinovich and A. Lakeyev and J. Rohn",
  title =        "Computational Complexity of Interval Algebraic
                 Problems: Some Are Feasible and Some Are
                 Computationally Intractable --- a Survey",
  crossref =     "Alefeld:1996:SCV",
  pages =        "293--306",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@Article{Ley:1996:PDU,
  author =       "Eduardo Ley",
  title =        "On the Peculiar Distribution of the {U.S.} Stock
                 Indexes' Digits",
  journal =      j-AMER-STAT,
  volume =       "50",
  number =       "4",
  pages =        "311--313",
  month =        nov,
  year =         "1996",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Mon Nov 14 15:09:04 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.jstor.org/stable/2684926",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@InProceedings{Li:1996:NNR,
  author =       "Yamin Li and Wanming Chu",
  booktitle =    "Proceedings of the {IEEE} International Conference on
                 Computer Design: {VLSI} in Computers and Processors:
                 {ICCD '96}",
  title =        "A new non-restoring square root algorithm and its
                 {VLSI} implementations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "538--544",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "We present a new non-restoring square root algorithm
                 that is very efficient to implement. The new algorithm
                 presented here has the following features unlike other
                 square root algorithms. First, the focus of the
                 ``non-restoring'' is on the {\&} \ldots{}",
}

@TechReport{Lions:1996:AFF,
  author =       "Jacques-Louis Lions and Mauro Balduccini and Yvan
                 Choquer and Remy Hergott and Bernard Humbert and Eric
                 Lefort",
  title =        "{Ariane 5 Flight 501} failure, report by the {Inquiry
                 Board}",
  type =         "Technical Report",
  institution =  "European Space Agency",
  address =      "Paris, France",
  year =         "1996",
  bibdate =      "Sat Apr 01 07:39:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "From the foreword: ``On 4 June 1996, the maiden flight
                 of the Ariane 5 launcher ended in a failure. Only about
                 40 seconds after initiation of the flight sequence, at
                 an altitude of about 3700 m, the launcher veered off
                 its flight path, broke up and exploded. Engineers from
                 the Ariane 5 project teams of CNES and Industry
                 immediately started to investigate the failure.'' From
                 the report: ``The internal SRI software exception was
                 caused during execution of a data conversion from
                 64-bit floating point to 16-bit signed integer value.
                 The floating point number which was converted had a
                 value greater than what could be represented by a
                 16-bit signed integer. This resulted in an Operand
                 Error. The data conversion instructions (in Ada code)
                 were not protected from causing an Operand Error,
                 although other conversions of comparable variables in
                 the same place in the code were protected.''",
  URL =          "http://sunnyday.mit.edu/accidents/Ariane5accidentreport.html",
  acknowledgement = ack-nhfb,
  remark =       "Report of an arithmetic error that put an expensive
                 space missile off course, requiring its destruction in
                 the air. Presumably-reliable code in Ada adapted from
                 an earlier missile generated had not been updated for
                 the new design.",
}

@Article{Lo:1996:CBC,
  author =       "Jien-Chung Lo and S. Thanawastien and T. R. N. Rao",
  title =        "Correction to {``Berger Check Prediction for Array
                 Multipliers and Array Dividers''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "3",
  pages =        "383--383",
  month =        mar,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1996.485579",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:10 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  note =         "See \cite{Lo:1993:BCP}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485579",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Louca:1996:IIS,
  author =       "L. Louca and T. A. Cook and W. H. Johnson",
  title =        "Implementation of {IEEE} single precision floating
                 point addition and multiplication on {FPGAs}",
  crossref =     "Pocek:1996:ISF",
  pages =        "107--116",
  year =         "1996",
  DOI =          "https://doi.org/10.1109/FPGA.1996.564761",
  bibdate =      "Sat Oct 9 12:52:57 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Floating point operations are hard to implement on
                 FPGAs because of the complexity of their algorithms. On
                 the other hand, many scientific problems require
                 floating point arithmetic with high levels of accuracy
                 in their calculations. Therefore, we have explored FPGA
                 implementations of addition and multiplication for IEEE
                 single precision floating-point numbers. Customizations
                 were performed where this was possible in order to save
                 chip area, or get the most out of our prototype board.
                 The implementations tradeoff area and speed for
                 accuracy. The adder is a bit-parallel adder, and the
                 multiplier is a digit-serial multiplier. Prototypes
                 have been implemented on Altera FLEX8000s, and peak
                 rates of 7 MFlops for 32-bit addition and 2.3 MFlops
                 for 32-bit multiplication have been obtained.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lozier:1996:EBL,
  author =       "Daniel W. Lozier and P. R. Turner",
  title =        "Error-Bounding in Level-Index Computer Arithmetic",
  crossref =     "Alefeld:1996:NME",
  pages =        "138--145",
  year =         "1996",
  bibdate =      "Fri Jul 09 07:20:57 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://math.nist.gov/acmd/Staff/DLozier/publications/oldenburg95.ps.Z",
  acknowledgement = ack-nhfb,
}

@InProceedings{Luther:1996:CAG,
  author =       "W. Luther and W. Otten",
  title =        "The Complex Arithmetic-Geometric Mean and
                 Multiple-Precision Matrix Functions",
  crossref =     "Alefeld:1996:SCV",
  pages =        "52--58",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@Article{MacDonald:1996:NSS,
  author =       "D. A. MacDonald",
  title =        "A note on the summation of slowly convergent
                 alternating series",
  journal =      j-BIT-NUM-MATH,
  volume =       "36",
  number =       "4",
  pages =        "766--774",
  month =        dec,
  year =         "1996",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01733790",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "40A25 (65B10 65B15)",
  MRnumber =     "98c:40001",
  MRreviewer =   "Vanna Zanelli",
  bibdate =      "Wed Jan 4 18:52:24 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mai.liu.se/BIT/contents/bit36.html;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=4&spage=766",
  abstract =     "The kth term of the infinite series $ \sum
                 \nolimits_{k = 0}^\infty {( - 1)^k [\ln (k + 2)]^{ -
                 0.1} } $ is larger than $ 0.5 $ whenever $ k < k_0 $,
                 where $ k_0 + 1 = e^{1024} $. To sum this series
                 correct to order $ 10^{-1} $ using direct summation
                 seems an impossible task, notwithstanding the power of
                 modern computers. This note will present an alternative
                 approach to those classical methods (the Euler
                 transformation is one) which can accurately sum such
                 series. The theory to be presented has the added
                 advantage of providing accurate bounds for the error in
                 the approximate result. The method used will be
                 Euler--Maclaurin summation, revitalised by computer
                 algebra.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "accurate floating-point summation; Euler--Maclaurin
                 formula; slowly convergent alternating series;
                 summation",
}

@Article{Macpherson:1996:RAP,
  author =       "George W. Macpherson",
  title =        "A reusable {Ada} package for scientific dimensional
                 integrity",
  journal =      j-SIGADA-LETTERS,
  volume =       "16",
  number =       "3",
  pages =        "56--69",
  month =        may # "\slash " # jun,
  year =         "1996",
  CODEN =        "AALEE5",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Sat Aug 9 09:05:57 MDT 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  acknowledgement = ack-nhfb,
  classcodes =   "A0650M (Computing devices and techniques); A0620F
                 (Measurement units); C7320 (Physics and chemistry
                 computing); C6130 (Data handling techniques); C5230
                 (Digital arithmetic methods)",
  corpsource =   "CACI Inc.-Federal, Colorado Springs, CO, USA",
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
  keywords =     "Ada; Ada programming language; arithmetic operations;
                 ASSIGN function; checking; computational reliability;
                 data integrity; declaration; digital arithmetic;
                 entries; exponents; floating point numeric value;
                 fundamental physical units; generic package;
                 information hiding; integer; length; limited private;
                 mass; multiplication operation; numeric; operator;
                 overloading; PHYSICAL QUANTITY type; physics computing;
                 relational operations; reusability; reusable Ada
                 package; scientific dimensional integrity; software;
                 software modifiability; software packages; software
                 reliability; software reusability; strong typing;
                 symbol creation; time; types; units; units
                 (measurement); values; variables",
  treatment =    "P Practical",
}

@Article{Maeder:1996:MPLa,
  author =       "Roman E. Maeder",
  title =        "The {Mathematica} Programmer: Long Integers: Basic
                 Arithmetic and Data Types",
  journal =      j-MATHEMATICA-J,
  volume =       "6",
  number =       "2",
  pages =        "32--40",
  month =        "Spring",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "1047-5974 (print), 1097-1610 (electronic)",
  ISSN-L =       "1047-5974",
  bibdate =      "Sat Nov 6 13:34:10 MDT 2010",
  bibsource =    "http://www.mathematica-journal.com/issue/v6i2/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mathematica-journal.com/issue/v6i2/columns/maeder/index.html;
                 http://www.mathematica-journal.com/issue/v6i2/columns/maeder/maeder62.pdf",
  abstract =     "Long-integer arithmetic is a fundamental part of
                 symbolic computation. This article introduces the
                 fundamentals of long-integer calculations by
                 implementing a prototype system in Mathematica. Our
                 code is strictly procedural and could be translated
                 into C or assembler easily. The tools needed are arrays
                 that behave like arrays in procedural languages, as
                 well as tools for software testing and debugging.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematica Journal",
  journal-URL =  "http://www.mathematica-journal.com/",
}

@Article{Maeder:1996:MPLb,
  author =       "Roman E. Maeder",
  title =        "The {Mathematica} Programmer: Long Integers: Efficient
                 Algorithms",
  journal =      j-MATHEMATICA-J,
  volume =       "6",
  number =       "3",
  pages =        "37--43",
  month =        "Summer",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "1047-5974 (print), 1097-1610 (electronic)",
  ISSN-L =       "1047-5974",
  bibdate =      "Sat Nov 6 13:34:12 MDT 2010",
  bibsource =    "http://www.mathematica-journal.com/issue/v6i3/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mathematica-journal.com/issue/v6i3/columns/maeder/contents/63maeder.pdf;
                 http://www.mathematica-journal.com/issue/v6i3/columns/maeder/index.html",
  abstract =     "This is the second part of an article on long-integer
                 arithmetic. It discusses the data type for long
                 integers and investigates a few asymptotically
                 efficient algorithms for multiplication and division.
                 We will not discuss all our code in detail, but point
                 out a few important ideas.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematica Journal",
  journal-URL =  "http://www.mathematica-journal.com/",
}

@Article{Makino:1996:MBF,
  author =       "H. Makino and H. Suzuki and H. Morinaka and Y. Nakase
                 and K. Mashiko and T. Sumi",
  title =        "A {286 MHz} 64-b floating point multiplier with
                 enhanced {CG} operation",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "31",
  number =       "4",
  pages =        "504--513",
  month =        apr,
  year =         "1996",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "This paper presents a high speed 64-b floating point
                 (FP) multiplier that has a useful function for computer
                 graphics (CG). The critical path delay is minimized by
                 using high speed logic gates and limiting the stage
                 number of series transmission gate \ldots{}",
}

@MastersThesis{Manickavasagam:1996:ATI,
  author =       "SenthilKumar Manickavasagam",
  title =        "``$ a + b $'' arithmetic: theory and implementation",
  type =         "Thesis ({M.S.})",
  school =       "Electrical Engineering and Computer Science, Ohio
                 University",
  address =      "Athens, OH, USA",
  pages =        "xi + 152",
  year =         "1996",
  bibdate =      "Mon Mar 05 14:33:56 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Manning:1996:FS,
  author =       "Evan Manning",
  title =        "Floating-point Summation",
  journal =      j-CCCUJ,
  volume =       "14",
  number =       "9",
  pages =        "51--??",
  month =        sep,
  year =         "1996",
  CODEN =        "CCUJEX",
  ISSN =         "1075-2838",
  bibdate =      "Wed Nov 6 07:30:58 MST 1996",
  bibsource =    "http://www.cuj.com/cbklist.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "C/C++ Users Journal",
  keywords =     "accurate floating-point summation",
}

@InProceedings{Markov:1996:FIA,
  author =       "S. M. Markov",
  title =        "On the Foundations of Interval Arithmetic",
  crossref =     "Alefeld:1996:SCV",
  pages =        "307--313",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mayer:1996:SEI,
  author =       "G. Mayer",
  title =        "Success in Epsilon-Inflation",
  crossref =     "Alefeld:1996:SCV",
  pages =        "98--104",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@Article{Mikov:1996:LSA,
  author =       "Alexander I. Mikov",
  title =        "Large-scale addition of machine real numbers:
                 {Accuracy} estimates",
  journal =      j-THEOR-COMP-SCI,
  volume =       "162",
  number =       "1",
  pages =        "151--170",
  day =          "05",
  month =        aug,
  year =         "1996",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Mon Jul 19 22:20:05 MDT 1999",
  bibsource =    "http://www.elsevier.com/cgi-bin/cas/tree/store/tcs/cas_free/browse/browse.cgi?year=1996&volume=162&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tcs1995.bib",
  URL =          "http://www.elsevier.com/cgi-bin/cas/tree/store/tcs/cas_sub/browse/browse.cgi?year=1996&volume=162&issue=1&aid=2194",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods)",
  corpsource =   "Department of Computer Science, Perm State University,
                 Russia",
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975/",
  keywords =     "accuracy estimates; digital arithmetic; floating-point
                 arithmetic; large-scale addition; machine real numbers;
                 positive independent random variables; random
                 variables; real distribution interval; roundoff error",
  pubcountry =   "Netherlands",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Miner:1996:VIC,
  author =       "Paul S. Miner and James F. {Leathrum, Jr.}",
  title =        "Verification of {IEEE} Compliant Subtractive Division
                 Algorithms",
  crossref =     "Srivas:1996:FMC",
  pages =        "64--78",
  year =         "1996",
  bibdate =      "Wed Nov 24 12:01:07 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ece.odu.edu/~leathrum/Formal_Methods/computer_arithmetic/fmcad.ps",
  acknowledgement = ack-nhfb,
  remark =       "fmcad.ps actually contains two separate versions of
                 this article, and must be split manually before
                 printing.",
}

@TechReport{Moler:1996:CCF,
  author =       "Cleve B. Moler",
  title =        "{Cleve}'s Corner: {Floating} points: {IEEE Standard}
                 unifies arithmetic model",
  type =         "Technical note",
  institution =  inst-MATHWORKS,
  address =      inst-MATHWORKS:adr,
  pages =        "3",
  month =        "Fall",
  year =         "1996",
  bibdate =      "Thu Oct 24 07:16:21 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mathworks.com/company/newsletter/pdf/Fall96Cleve.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Matlab",
}

@InProceedings{Mraz:1996:ELB,
  author =       "F. Mraz",
  title =        "The Exact Lower Bound of Optimal Values in Interval
                 {LP}",
  crossref =     "Alefeld:1996:SCV",
  pages =        "214--220",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mrozek:1996:IPC,
  author =       "M. Mrozek",
  title =        "Inheritable Properties and Computer Assisted Proofs in
                 Dynamics",
  crossref =     "Alefeld:1996:SCV",
  pages =        "245--257",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@Article{Muller:1996:CES,
  author =       "Michael M{\"u}ller and Christine R{\"u}b and Wolfgang
                 R{\"u}lling",
  title =        "A circuit for exact summation of floating-point
                 numbers",
  journal =      j-INFO-PROC-LETT,
  volume =       "57",
  number =       "3",
  pages =        "159--163",
  day =          "12",
  month =        feb,
  year =         "1996",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Sat Nov 7 17:55:43 MST 1998",
  bibsource =    "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  keywords =     "accurate floating-point summation",
}

@InProceedings{Muller:1996:TER,
  author =       "Jean-Michel Muller and A. Tisserand",
  title =        "Towards Exact Rounding of the Elementary Functions",
  crossref =     "Alefeld:1996:SCV",
  pages =        "59--71",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@InProceedings{Nakao:1996:GEB,
  author =       "M. T. Nakao and N. Yamamoto and Y. Watanabe",
  title =        "Guaranteed Error Bounds for Finite Element Solutions
                 of the {Stokes} Problem",
  crossref =     "Alefeld:1996:SCV",
  pages =        "258--264",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@InProceedings{Nonnenmacher:1996:LCS,
  author =       "A. Nonnenmacher and D. A. Mlynski",
  title =        "Liquid Crystal Simulation Using Automatic
                 Differentiation and Interval Arithmetic",
  crossref =     "Alefeld:1996:SCV",
  pages =        "334--340",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@PhdThesis{Oberman:1996:DIH,
  author =       "Stuart Franklin Oberman",
  title =        "Design Issues in High Performance Floating Point
                 Arithmetic Units",
  type =         "Thesis ({Ph.D.})",
  school =       "Department of Electrical Engineering, Stanford
                 University",
  address =      "Stanford, CA, USA",
  pages =        "xiv + 151",
  month =        nov,
  year =         "1996",
  bibdate =      "Fri Mar 27 10:14:18 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://umunhum.stanford.edu/tr/oberman.nov96.thesis.ps.Z;
                 https://www.proquest.com/pqdtglobal/docview/304386888",
  acknowledgement = ack-nhfb,
}

@TechReport{Oberman:1996:FIR,
  author =       "Stuart F. Oberman and Michael J. Flynn",
  title =        "Fast {IEEE} Rounding for Division by Functional
                 Iteration",
  type =         "Technical Report",
  number =       "CSL-TR-96-700",
  institution =  "Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "v + 16",
  month =        jul,
  year =         "1996",
  bibdate =      "Sun Dec 10 13:50:59 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://i.stanford.edu/pub/cstr/reports/csl/tr/96/700/CSL-TR-96-700.pdf",
  abstract =     "A class of high performance division algorithms is
                 functional iteration. Division by functional iteration
                 uses multiplication as the fundamental operator. The
                 main advantage of division by functional iteration is
                 quadratic convergence to the quotient. However, unlike
                 non-restoring division algorithms such as SRT division,
                 functional iteration does not directly provide a final
                 remainder. This makes fast and exact rounding
                 difficult. This paper clarifies the methodology for
                 correct IEEE compliant rounding for
                 quadratically-converging division algorithms. It
                 proposes an extension to previously reported techniques
                 of using extended precision in the computation to
                 reduce the frequency of back multiplications required
                 to obtain the final remainder. Further, a technique
                 applicable to all IEEE rounding modes is presented
                 which replaces the final subtraction for remainder
                 computation with very simple combinational logic.",
  acknowledgement = ack-nhfb,
  keywords =     "division, Goldschmidt's algorithm, IEEE rounding,
                 Newton--Raphson, variable latency",
}

@InProceedings{Oberman:1996:IDO,
  author =       "Stuart F. Oberman and Michael J. Flynn",
  title =        "Implementing Division and Other Floating-Point
                 Operations: a System Perspective",
  crossref =     "Alefeld:1996:SCV",
  pages =        "18--24",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "ftp://arith.stanford.edu/tr/scan_system.ps.Z",
  acknowledgement = ack-nhfb,
  summary =      "Modern computer applications have increased in their
                 computation complexity in recent years. The
                 industry-wide usage of performance benchmarks, such as
                 SPECmarks forces processor designers to pay particular
                 attention to floating-point (FP) computation.
                 Furthermore, special purpose applications, such as high
                 performance graphics rendering systems, have placed
                 further demands on processors. The development of high
                 speed FP hardware is a requirement to meet these
                 increasing computation demands.",
}

@Article{Oberman:1996:RDL,
  author =       "S. F. Oberman and M. J. Flynn",
  title =        "Reducing division latency with reciprocal caches",
  journal =      j-RELIABLE-COMPUTING,
  volume =       "2",
  number =       "2",
  pages =        "147--153",
  month =        apr,
  year =         "1996",
  CODEN =        "RCOMF8",
  ISSN =         "1385-3139 (print), 1573-1340 (electronic)",
  ISSN-L =       "1385-3139",
  bibdate =      "Thu Apr 2 08:38:35 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://arith.stanford.edu/tr/scan_recip.ps.Z",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  fjournal =     "Reliable Computing = Nadezhnye vychisleniia",
  journal-URL =  "http://link.springer.com/journal/11155",
}

@Article{Oberman:1996:VLP,
  author =       "S. F. Oberman and M. J. Flynn",
  title =        "A Variable Latency Pipelined Floating-Point Adder",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1124",
  pages =        "183--192",
  year =         "1996",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Fri Mar 27 10:07:13 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://arith.stanford.edu/tr/fpadd_euro.ps.Z",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Oklobdzija:1996:MSO,
  author =       "V. G. Oklobdzija and D. Villeger and S. S. Liu",
  title =        "A method for speed optimized partial product reduction
                 and generation of fast parallel multipliers using an
                 algorithmic approach",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "3",
  pages =        "294--306",
  month =        mar,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.485568",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485568",
  acknowledgement = ack-sfo # " and " # ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Paar:1996:NAP,
  author =       "C. Paar",
  title =        "A new architecture for a parallel finite field
                 multiplier with low complexity based on composite
                 fields",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "7",
  pages =        "856--861",
  month =        jul,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.508323",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:12 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=508323",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Parhami:1996:CHS,
  author =       "B. Parhami and S. Kawahito and M. Ishida and T.
                 Nakamura and M. Kameyama and T. Higuchi",
  title =        "Comments on {``High-speed area-efficient multiplier
                 design using multiple-valued current-mode circuits''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "5",
  pages =        "637--639",
  month =        may,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.509918",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:11 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  note =         "See \cite{Kawahito:1994:HSA}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=509918",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Park:1996:OHW,
  author =       "Edwards Park",
  title =        "The Object at Hand: What a difference the {Difference
                 Engine} made: from {Charles Babbage}'s calculator
                 emerged today's computer",
  journal =      j-SMITHSONIAN,
  volume =       "26",
  number =       "11",
  pages =        "20--??",
  day =          "01",
  month =        feb,
  year =         "1996",
  CODEN =        "SMSNA5",
  ISSN =         "0037-7333 (print), 1930-5508 (electronic)",
  ISSN-L =       "0037-7333",
  bibdate =      "Fri Jun 21 14:38:22 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
                 https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Smithsonian",
}

@Article{Park:1996:PAG,
  author =       "Taegeun Park",
  title =        "A Parallel Algorithm for Global Routing Using an
                 Associative Processor",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "38",
  number =       "1",
  pages =        "51--62",
  day =          "10",
  month =        oct,
  year =         "1996",
  CODEN =        "JPDCER",
  DOI =          "https://doi.org/10.1006/jpdc.1996.0128",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Thu Mar 9 09:19:01 MST 2000",
  bibsource =    "http://www.idealibrary.com/servlet/useragent?func=showAllIssues&curIssueID=jpdc;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.idealibrary.com/links/doi/10.1006/jpdc.1996.0128/production;
                 http://www.idealibrary.com/links/doi/10.1006/jpdc.1996.0128/production/pdf",
  acknowledgement = ack-nhfb,
  classification = "C1180 (Optimisation techniques); C4240C
                 (Computational complexity); C4240P (Parallel
                 programming and algorithm theory); C5230 (Digital
                 arithmetic methods); C5340 (Associative storage)",
  corpsource =   "Design Lab., Hyundai Electron. Ind., Kyoungki, South
                 Korea",
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
  keywords =     "addressable storage; array; associative processing;
                 associative processor; benchmark problems;
                 computational complexity; content-; content-addressable
                 memory; control section; digital arithmetic; global
                 routing; layout process; matching; minimisation;
                 minimum-; multiple data device; O(d) complexity;
                 parallel algorithm; parallel algorithms; parallel
                 arithmetic; problem; processing elements; randomly
                 generated data; row logic; rudimentary logic;
                 search-oriented applications; selective; single
                 instruction; weight path",
  treatment =    "A Application; P Practical",
}

@InProceedings{Petunin:1996:UMI,
  author =       "D. Petunin and A. Semenov",
  title =        "The Use of Multi-Intervals in the {UniCalc} Solver",
  crossref =     "Alefeld:1996:SCV",
  pages =        "91--97",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@InProceedings{Plum:1996:ETP,
  author =       "M. Plum",
  title =        "Enclosure for Two-Point Boundary Value Problems Near
                 Bifurcation Points",
  crossref =     "Alefeld:1996:SCV",
  pages =        "265--279",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@Article{Popova:1996:IOI,
  author =       "E. D. Popova",
  title =        "Interval operations involving {NaNs}",
  journal =      j-RELIABLE-COMPUTING,
  volume =       "2",
  number =       "2",
  pages =        "161--166",
  month =        jun,
  year =         "1996",
  CODEN =        "RCOMF8",
  ISSN =         "1385-3139 (print), 1573-1340 (electronic)",
  ISSN-L =       "1385-3139",
  bibdate =      "Sat Feb 4 17:45:55 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-vk,
  fjournal =     "Reliable Computing = Nadezhnye vychisleniia",
  journal-URL =  "http://link.springer.com/journal/11155",
}

@Article{Posch:1996:DRN,
  author =       "K. C. Posch and R. Posch",
  title =        "Division in residue number systems involving length
                 indicators",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "66",
  number =       "1--2",
  pages =        "411--419",
  day =          "31",
  month =        jan,
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:27:48 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042795001646",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Price:1996:RA,
  author =       "David T. Price",
  title =        "Remark on {Algorithm 715}",
  journal =      j-TOMS,
  volume =       "22",
  number =       "2",
  pages =        "258--258",
  month =        jun,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/229473.236186",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Feb 8 10:28:55 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Cody:1993:ASE}",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-2/p258-price/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@InProceedings{Rao:1996:NHS,
  author =       "Vishwas M. Rao and Behrouz Nowrouzian",
  title =        "Novel high-speed bit-parallel multiply accumulate
                 arithmetic architecture",
  crossref =     "Luk:1996:PSC",
  pages =        "26--38",
  year =         "1996",
  DOI =          "https://doi.org/10.1117/12.255442",
  bibdate =      "Tue Jun 14 18:26:06 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Rao:1996:RTS,
  author =       "V. M. Rao and B. Nowrouzian",
  booktitle =    "Canadian Conference on Electrical and Computer
                 Engineering. 26--29 May 1996",
  title =        "Rounding techniques for signed binary arithmetic",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "294--297",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper is concerned with the derivation of the
                 relationship that exists between the number truncation
                 in two's complement (TC) arithmetic and the
                 corresponding truncation in signed-binary (SB)
                 arithmetic. The resulting relationship is subsequently
                 exploited and applied to the development of a pair of
                 novel techniques for SB rounding. These techniques are
                 then translated into algorithm suitable for two-level
                 logic implementation. Finally, the resulting algorithms
                 are applied to the design and implementation of a
                 high-speed SB-kernel based TC multiply-accumulate
                 arithmetic architecture.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Ratz:1996:BRS,
  author =       "D. Ratz",
  title =        "On Branching Rules in Second-Order Branch-and-Bound
                 Methods for Global Optimization",
  crossref =     "Alefeld:1996:SCV",
  pages =        "221--227",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@Article{Reid:1996:RFF,
  author =       "J. K. Reid",
  title =        "Remark on ``{Fast Floating-Point Processing in Common
                 Lisp}''",
  journal =      j-TOMS,
  volume =       "22",
  number =       "4",
  pages =        "496--497",
  month =        dec,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/235815.235824",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 9 10:21:08 1999",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Fateman:1995:FFP}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p496-reid/",
  abstract =     "We explain why we feel that the comparison between
                 Common Lisp and Fortran in a recent article by Fateman
                 et al. in this journal is not entirely fair.",
  acknowledgement = ack-nhfb # " and " # ack-rfb,
  affiliation =  "Rutherford Appleton Lab",
  classification = "721.1; 723.1.1; 902.2; 921.6",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  journalabr =   "ACM Trans Math Software",
  keywords =     "Common Lisp language; Control structures; Digital
                 arithmetic; Floating point computation; fortran
                 (programming language); Lisp (programming language);
                 Standards",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, General,
                 Standards. {\bf D.3.3}: Software, PROGRAMMING
                 LANGUAGES, Language Constructs and Features, Modules,
                 packages.",
}

@InProceedings{Rump:1996:DBR,
  author =       "Siegfried M. Rump",
  title =        "The Distance Between Regularity and Strong
                 Regularity",
  crossref =     "Alefeld:1996:SCV",
  pages =        "105--117",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sarma:1996:HRT,
  author =       "D. Das Sarma and D. W. Matula",
  title =        "Hardware Reciprocal Table Compression\slash
                 Decompression Techniques",
  crossref =     "Alefeld:1996:SCV",
  pages =        "11--17",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@TechReport{Saunders:1996:TGF,
  author =       "Kevin Saunders",
  title =        "Third generation floating point {DSP} design",
  type =         "Report",
  number =       "800 XY/N-1",
  institution =  "University of Bristol. Department of Aerospace
                 Engineering",
  address =      "Bristol, UK",
  year =         "1996",
  bibdate =      "Thu May 09 08:52:59 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Schatzman:1996:ADF,
  author =       "James C. Schatzman",
  title =        "Accuracy of the discrete {Fourier} transform and the
                 fast {Fourier} transform",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "17",
  number =       "5",
  pages =        "1150--1166",
  month =        sep,
  year =         "1996",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/S1064827593247023",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65T20 (42A65 42C10 68Q25)",
  MRnumber =     "97e:65155",
  bibdate =      "Fri Dec 4 14:47:53 MST 1998",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/17/5;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/24702",
  acknowledgement = ack-nhfb,
  ajournal =     "SIAM J. Sci. Comput.",
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  remark =       "This article analyzes errors in computing
                 one-dimensional Fourier transforms, the fast way (FFT)
                 and the slow way. The author identifies two main causes
                 of accuracy loss in the computed transforms: (1)
                 inaccurate sine and cosine functions, and (2) failure
                 to use accurate summation methods, such as Kahan's
                 compensated summation.",
}

@InProceedings{Schulte:1996:HDI,
  author =       "M. J. Schulte and K. C. Bickerstaff and E. E.
                 {Swartzlander, Jr.}",
  editor =       "????",
  booktitle =    "Proceedings of the {II} Workshop on Computer
                 Arithmetic, Interval and Symbolic Computation, Recife,
                 Brazil, August, 1996",
  title =        "Hardware Designs for Interval Multiplication",
  publisher =    "????",
  address =      "????",
  pages =        "85--87",
  year =         "1996",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sun Mar 04 10:51:30 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Schulte:1996:PAS,
  author =       "M. J. Schulte and E. E. Swartzlander",
  title =        "A Processor for Accurate, Self-Validating Computing",
  crossref =     "Alefeld:1996:SCV",
  pages =        "25--31",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@InProceedings{Schwandt:1996:GCI,
  author =       "H. Schwandt",
  title =        "Globally Convergent Iterative Domain Decomposition
                 Methods for the Parallel Solution of a Class of
                 Nonlinear Systems of Equations",
  crossref =     "Alefeld:1996:SCV",
  pages =        "280--286",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@Article{Schwarz:1996:HSA,
  author =       "Eric M. Schwarz and Michael J. Flynn",
  title =        "Hardware Starting Approximation Method and Its
                 Application to the Square Root Operation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "12",
  pages =        "1356--1369",
  month =        dec,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.545966",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:15 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=545966",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "Quadratically converging algorithms for high-order
                 arithmetic operations typically are accelerated by a
                 starting approximation. The higher the precision of the
                 starting approximation, the less number of iterations
                 required for convergence. \ldots{}",
}

@Article{Sezgin:1996:SIR,
  author =       "F. Sezgin",
  title =        "Some improvements for a random number generator with
                 single-precision floating-point arithmetic",
  journal =      j-COMP-GEOSCI,
  volume =       "22",
  number =       "4",
  pages =        "453--455",
  month =        may,
  year =         "1996",
  CODEN =        "CGEODT, CGOSDN",
  ISSN =         "0098-3004 (print), 1873-7803 (electronic)",
  ISSN-L =       "0098-3004",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Ingenta database",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Geosciences",
  pagecount =    "3",
}

@InProceedings{Shary:1996:NAA,
  author =       "S. P. Shary",
  title =        "A New Approach to the Analysis of Static Systems Under
                 Internal Uncertainty",
  crossref =     "Alefeld:1996:SCV",
  pages =        "118--132",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@TechReport{Shewchuk:1996:APF,
  author =       "Jonathan Richard Shewchuk",
  title =        "Adaptive precision floating-point arithmetic and fast
                 robust geometric predicates",
  type =         "Report",
  number =       "CMU-CS-96-140",
  institution =  "Department of Computer Science, Carnegie-Mellon
                 University",
  address =      "Pittsburgh, PA, USA",
  pages =        "53",
  year =         "1996",
  bibdate =      "Fri Jan 06 11:59:17 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Exact computer arithmetic has a variety of uses
                 including, but not limited to, the robust
                 implementation of geometric algorithms. This report has
                 three purposes. The first is to offer fast
                 software-level algorithms for exact addition and
                 multiplication of arbitrary precision floating-point
                 values. The second is to propose a technique for
                 adaptive-precision arithmetic that can often speed
                 these algorithms when one wishes to perform
                 multiprecision calculations that do not always require
                 exact arithmetic, but must satisfy some error bound.
                 The third is to provide a practical demonstration of
                 these techniques, in the form of implementations of
                 several common geometric calculations whose required
                 degree of accuracy depends on their inputs. These
                 robust geometric predicates are adaptive; their running
                 time depends on the degree of uncertainty of the
                 result, and is usually small.\par

                 These algorithms work on computers whose floating-point
                 arithmetic uses radix two and exact rounding, including
                 machines complying with the IEEE 754 standard. The
                 inputs to the predicates may be arbitrary single or
                 double precision floating-point numbers. C code is
                 publicly available for the 2D and 3D orientation and
                 incircle tests, and robust Delaunay triangulation using
                 these tests. Timings of the implementations demonstrate
                 their effectiveness.",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; multiple-precision
                 arithmetic",
}

@InProceedings{Shewchuk:1996:RAF,
  author =       "Jonathan Richard Shewchuk",
  booktitle =    "{Proceedings of the 12th Annual ACM Symposium on
                 Computational Geometry}",
  title =        "Robust Adaptive Floating-Point Geometric Predicates",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "141--150",
  year =         "1996",
  DOI =          "https://doi.org/10.1145/237218.237337",
  bibdate =      "Sat May 1 15:33:15 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.cmu.edu/afs/cs/project/quake/public/papers/robust-predicates.ps",
  acknowledgement = ack-nhfb,
}

@Article{Shewchuk:1996:TEQ,
  author =       "J. R. Shewchuk",
  editor =       "Ming C. Lin and Dinesh Manocha",
  booktitle =    "Applied Computational Geometry: Towards Geometric
                 Engineering",
  title =        "{Triangle}: Engineering a {$2$D} Quality Mesh
                 Generator and {Delaunay} Triangulator",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1148",
  pages =        "203--222",
  year =         "1996",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/BFb0014497",
  ISBN =         "3-540-61785-X (softcover), 3-540-70680-1 (e-book)",
  ISBN-13 =      "978-3-540-61785-3 (softcover), 978-3-540-70680-9
                 (e-book)",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Dec 21 09:47:26 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs1996b.bib",
  URL =          "https://link.springer.com/chapter/10.1007/BFb0014497",
  acknowledgement = ack-nhfb,
  book-URL =     "https://link.springer.com/book/10.1007/BFb0014474",
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
  keywords =     "Delaunay triangulation; exact arithmetic; refinement
                 algorithm; refinement stage; roundoff error",
  remark =       "First ACM Workshop on Applied Computational
                 Geometry.",
}

@Article{Shirayanagi:1996:FPG,
  author =       "Kiyoshi Shirayanagi",
  title =        "Floating point {Gr{\"o}bner} bases",
  journal =      j-MATH-COMPUT-SIMUL,
  volume =       "42",
  number =       "4--6",
  pages =        "509--528",
  month =        nov,
  year =         "1996",
  CODEN =        "MCSIDR",
  DOI =          "https://doi.org/10.1016/S0378-4754(96)00027-4",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  bibdate =      "Mon Aug 18 12:50:38 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomputsimul1990.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/S0378475496000274",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput. Simul.",
  fjournal =     "Mathematics and Computers in Simulation",
  journal-URL =  "https://www.sciencedirect.com/science/journal/03784754",
}

@InProceedings{Shokin:1996:IPI,
  author =       "Y. I. Shokin",
  title =        "On Interval Problems, Interval Algorithms and Their
                 Computational Complexity",
  crossref =     "Alefeld:1996:SCV",
  pages =        "314--328",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@Article{Sinclair:1996:ORS,
  author =       "R. Sinclair",
  title =        "Optimization of reciprocals and square roots on the
                 {i860} microprocessor",
  journal =      j-INT-J-HIGH-SPEED-COMPUTING,
  volume =       "8",
  number =       "1",
  pages =        "57--64",
  year =         "1996",
  CODEN =        "IHSCEZ",
  ISSN =         "0129-0533",
  bibdate =      "Mon Feb 25 11:19:22 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Article1st database",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of High Speed Computing",
  journal-URL =  "http://www.worldscientific.com/worldscinet/ijhsc",
}

@Article{Singer:1996:EAP,
  author =       "Benjamin Singer and George Saon",
  title =        "An efficient algorithm for parallel integer
                 multiplication",
  journal =      j-J-NETW-COMPUT-APPL,
  volume =       "19",
  number =       "4",
  pages =        "415--418",
  month =        oct,
  year =         "1996",
  CODEN =        "JNCAF3",
  ISSN =         "1084-8045 (print), 1095-8592 (electronic)",
  ISSN-L =       "1084-8045",
  bibdate =      "Wed Jan 28 15:41:22 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jnetwcomputappl.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1084804596900296",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Netw. Comput. Appl.",
  fjournal =     "Journal of Network and Computer Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/10848045",
}

@Article{Soderquist:1996:AFT,
  author =       "Peter Soderquist and Miriam Leeser",
  title =        "Area and Performance Tradeoffs in Floating-Point
                 Divide and Square-Root Implementations",
  journal =      j-COMP-SURV,
  volume =       "28",
  number =       "3",
  pages =        "518--564",
  month =        sep,
  year =         "1996",
  CODEN =        "CMSVAN",
  ISSN =         "0360-0300 (print), 1557-7341 (electronic)",
  ISSN-L =       "0360-0300",
  bibdate =      "Wed Nov 13 06:52:01 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J204",
}

@Article{Soderquist:1996:APT,
  author =       "Peter Soderquist and Miriam Leeser",
  title =        "Area and Performance Tradeoffs in Floating-Point
                 Divide and Square-Root Implementations",
  journal =      j-COMP-SURV,
  volume =       "28",
  number =       "3",
  pages =        "518--564",
  month =        sep,
  year =         "1996",
  CODEN =        "CMSVAN",
  DOI =          "https://doi.org/10.1145/243439.243481",
  ISSN =         "0360-0300 (print), 1557-7341 (electronic)",
  ISSN-L =       "0360-0300",
  bibdate =      "Thu Jun 19 09:54:32 MDT 2008",
  bibsource =    "http://www.acm.org/pubs/contents/journals/surveys/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/surveys/1996-28-3/p518-soderquist/",
  abstract =     "Floating-point divide and square-root operations are
                 essential to many scientific and engineering
                 applications, and are required in all computer systems
                 that support the IEEE floating-point standard. Yet many
                 current microprocessors provide only weak support for
                 these operations. The latency and throughput of
                 division are typically far inferior to those of
                 floating-point addition and multiplication, and
                 square-root performance is often even lower. This
                 article argues the case for high-performance division
                 and square root. It also explains the algorithms and
                 implementations of the primary techniques, subtractive
                 and multiplicative methods, employed in microprocessor
                 floating-point units with their associated
                 area/performance tradeoffs. Case studies of
                 representative floating-point unit configurations are
                 presented, supported by simulation results using a
                 carefully selected benchmark, Givens rotation, to show
                 the dynamic performance impact of the various
                 implementation alternatives. The topology of the
                 implementation is found to be an important performance
                 factor. Multiplicative algorithms, such as the
                 Newton--Raphson method and Goldschmidt's algorithm, can
                 achieve low latencies. However, these implementations
                 serialize multiply, divide, and square root operations
                 through a single pipeline, which can lead to low
                 throughput. While this hardware sharing yields low size
                 requirements for baseline implementations,
                 lower-latency versions require many times more area.
                 For these reasons, multiplicative implementations are
                 best suited to cases where subtractive methods are
                 precluded by area constraints, and modest performance
                 on divide and square root operations is tolerable.
                 Subtractive algorithms, exemplified by radix-4 SRT and
                 radix-16 SRT, can be made to execute in parallel with
                 other floating-point operations.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J204",
  keywords =     "area and performance tradeoffs; arithmetic and logic
                 structures; computer arithmetic.; computer system
                 implementation; design studies. {\bf c.5.3}: computer
                 systems organization; design styles; division;
                 floating-point; FPU; general; microcomputers;
                 microprocessors. {\bf g.1.0}: mathematics of computing;
                 numerical analysis; parallel. {\bf c.4}: computer
                 systems organization; performance of systems; square
                 root; SRT; {\bf b.2.1}: hardware",
  subject =      "{\bf B.2.1}: Hardware, ARITHMETIC AND LOGIC
                 STRUCTURES, Design Styles, Parallel. {\bf C.4}:
                 Computer Systems Organization, PERFORMANCE OF SYSTEMS,
                 Design studies. {\bf C.5.3}: Computer Systems
                 Organization, COMPUTER SYSTEM IMPLEMENTATION,
                 Microcomputers, Microprocessors. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Computer arithmetic.",
}

@InCollection{Steele:1996:EL,
  author =       "Guy L. {Steele Jr.} and Richard P. Gabriel",
  title =        "The evolution of {Lisp}",
  crossref =     "Bergin:1996:HPL",
  pages =        "233--330",
  year =         "1996",
  bibdate =      "Wed Jan 29 17:01:12 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
  remark =       "From \cite{Steele:2004:RHP}: ``In early 1971, he
                 [White] began to analyze the machine-language algorithm
                 used in the implementation of MacLisp (described in
                 this report) to convert PDP-10 floating-point numbers
                 into decimal notation.''",
}

@Book{Stewart:1996:ANA,
  author =       "G. W. (Gilbert W.) Stewart",
  title =        "Afternotes on numerical analysis: a series of lectures
                 on elementary numerical analysis presented at the
                 {University of Maryland at College Park} and recorded
                 after the fact",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "x + 200",
  year =         "1996",
  DOI =          "https://doi.org/10.1137/1.9781611971491",
  ISBN =         "0-89871-362-5 (paperback)",
  ISBN-13 =      "978-0-89871-362-6 (paperback)",
  LCCN =         "QA297 .S785 1996",
  MRclass =      "65-01",
  MRnumber =     "1372060",
  bibdate =      "Tue May 27 08:35:41 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana1990.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0726/95047768-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0726/95047768-t.html",
  acknowledgement = ack-nhfb,
  keywords =     "numerical analysis",
  subject =      "Numerical analysis",
  tableofcontents = "Part I. Nonlinear Equations \\
                 \\
                 Lecture 1. By the Dawn's Early Light \\
                 Interval Bisection \\
                 Relative Error \\
                 \\
                 Lecture 2. Newton's Method \\
                 Reciprocals and Square Roots \\
                 Local Convergence Analysis \\
                 Slow Death \\
                 \\
                 Lecture 3. A Quasi-Newton Method \\
                 Rates of Convergence \\
                 Iterating for a Fixed Point \\
                 Multiple Zeros \\
                 Ending with a Proposition \\
                 \\
                 Lecture 4. The Secant Method \\
                 Convergence \\
                 Rate of Convergence \\
                 Multipoint Methods \\
                 Muller's Method \\
                 The Linear-Fractional Method \\
                 \\
                 Lecture 5. A Hybrid Method \\
                 Errors, Accuracy, and Condition Numbers \\
                 \\
                 Part II. Computer Arithmetic: \\
                 \\
                 Lecture 6. Floating-Point Numbers \\
                 Overflow and Underflow \\
                 Rounding Error \\
                 Floating-point Arithmetic \\
                 \\
                 Lecture 7. Computing Sums \\
                 Backward Error Analysis \\
                 Perturbation Analysis \\
                 Cheap and Chippy Chopping \\
                 \\
                 Lecture 8. Cancellation \\
                 The Quadratic Equation \\
                 That Fatal Bit of Rounding Error \\
                 Envoi \\
                 \\
                 Part III. Linear Equations \\
                 \\
                 Lecture 9. Matrices, Vectors, and Scalars \\
                 Operations with Matrices \\
                 Rank-One Matrices \\
                 Partitioned Matrices \\
                 \\
                 Lecture 10. Theory of Linear Systems \\
                 Computational Generalities \\
                 Triangular Systems \\
                 Operation Counts \\
                 \\
                 Lecture 11. Memory Considerations \\
                 Row Oriented Algorithms \\
                 A Column Oriented Algorithm \\
                 General Observations on Row and Column Orientation \\
                 Basic Linear Algebra Subprograms \\
                 \\
                 Lecture 12. Positive Definite Matrices \\
                 The Cholesky Decomposition \\
                 Economics \\
                 \\
                 Lecture 13. Inner-Product Form of the Cholesky
                 Algorithm \\
                 Gaussian Elimination \\
                 \\
                 Lecture 14. Pivoting \\
                 BLAS \\
                 Upper Hessenberg and Tridiagonal Systems \\
                 \\
                 Lecture 15. Vector Norms \\
                 Matrix Norms \\
                 Relative Error \\
                 Sensitivity of Linear Systems \\
                 \\
                 Lecture 16. The Condition of Linear Systems \\
                 Artificial Ill Conditioning \\
                 Rounding Error and Gaussian Elimination \\
                 Comments on the Analysis \\
                 \\
                 Lecture 17. The Wonderful Residual: A Project \\
                 Introduction \\
                 More on Norms \\
                 The Wonderful Residual \\
                 Matrices with Known Condition \\
                 Invert and Multiply \\
                 Cramer's Rule \\
                 Submission \\
                 \\
                 Part IV. Polynomial Interpolation \\
                 \\
                 Lecture 18. Quadratic Interpolation \\
                 Shifting \\
                 Polynomial Interpolation \\
                 Lagrange Polynomials and Existence \\
                 Uniqueness \\
                 \\
                 Lecture 19. Synthetic Division \\
                 The Newton Form of the Interpolant \\
                 Evaluation \\
                 Existence \\
                 Divided Differences \\
                 \\
                 Lecture 20. Error in Interpolation \\
                 Error Bounds \\
                 Convergence \\
                 Chebyshev Points \\
                 \\
                 Part V. Numerical Integration and Differentiation \\
                 \\
                 Lecture 21. Numerical Integration \\
                 Change of Intervals \\
                 The Trapezoidal Rule \\
                 The Composite Trapezoidal Rule \\
                 Newton-Cotes Formulas \\
                 Undetermined Coefficients and Simpson's Rule \\
                 \\
                 Lecture 22. The Composite Simpson's Rule \\
                 Errors in Simpson's Rule \\
                 Weighting Functions \\
                 Gaussian Quadrature \\
                 \\
                 Lecture 23. The Setting \\
                 Orthogonal Polynomials \\
                 Existence \\
                 Zeros of Orthogonal Polynomials \\
                 Gaussian Quadrature \\
                 Error and Convergence \\
                 Examples \\
                 \\
                 Lecture 24. Numerical Differentiation and Integration
                 \\
                 Formulas From Power Series \\
                 Limitations \\
                 Bibliography",
}

@Article{Suzuki:1996:LZA,
  author =       "H. Suzuki and H. Morinaka and H. Makino and Y. Nakase
                 and K. Mashiko and T. Sumi",
  title =        "Leading-zero anticipatory logic for high-speed
                 floating point addition",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "31",
  number =       "8",
  pages =        "1157--1164",
  month =        aug,
  year =         "1996",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See comments \cite{Oklobdzija:1997:CLZ}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "This paper describes a new leading-zero anticipatory
                 (LZA) logic for high-speed floating-point addition
                 (FADD). This logic carries out the pre-decoding for
                 normalization concurrently with addition for the
                 significand. It also performs the shift operation
                 \ldots{}",
}

@MastersThesis{Tan:1996:MPF,
  author =       "Kien Beng Tan",
  title =        "A micro-power, floating point analog-to-digital
                 converter",
  type =         "Thesis ({M.S.})",
  school =       "Department of Electrical Engineering, University of
                 California, Los Angeles",
  address =      "Los Angeles, CA, USA",
  pages =        "????",
  year =         "1996",
  bibdate =      "Thu Oct 24 14:19:35 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "dissertations, academic -- UCLA -- Electrical
                 Engineering",
}

@InProceedings{Tatsaki:1996:AIC,
  author =       "A. Tatsaki",
  booktitle =    "Proceedings of the Third {IEEE} International
                 Conference on Electronics, Circuits, and Systems, 1996.
                 {ICECS 96}",
  title =        "An adaptive image coder based on residue number
                 system",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "700--703",
  year =         "1996",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICECS.1996.584458",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "An efficient coder for adaptive lossy compression of
                 still images is presented. It is based on a
                 computational efficient extraction of the details of
                 image blocks. The Discrete Cosine Transform and an
                 efficient Lattice Vector Quantizer based on the
                 \ldots{}",
}

@MastersThesis{Trott:1996:AWL,
  author =       "Aaron Gregory Trott",
  title =        "The application of wavelets to lossless compression
                 and progressive transmission of floating point data in
                 three-dimensional curvilinear grids",
  type =         "{M.S.E.E.} thesis",
  school =       "Mississippi State University",
  address =      "Mississippi State, MS 39762, USA",
  pages =        "103",
  year =         "1996",
  bibdate =      "Fri Feb 1 09:20:32 MST 2013",
  bibsource =    "http://search.proquest.com/;
                 https://www.math.utah.edu/pub/tex/bib/datacompression.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://search.proquest.com/docview/304273691",
  acknowledgement = ack-nhfb,
  advisor =      "Robert J. Moorhead",
  classification = "0538: Aerospace materials; 0544: Electrical
                 engineering",
  dissertation-thesis-number = "1379238",
  subject =      "Electrical engineering; Aerospace materials",
}

@Misc{Urano:1996:MAN,
  author =       "M. Urano and T. Taniguchi",
  title =        "Method and apparatus for normalization of a floating
                 point binary number",
  day =          "30",
  month =        apr,
  year =         "1996",
  bibdate =      "Fri Nov 28 15:31:26 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "U.S. Patent No. 5,513,362.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}

@Article{Vassilladis:1996:ARA,
  author =       "S. Vassilladis and S. Contofana and K. Bertels",
  title =        "$2$-$1$ addition and related arithmetic operations
                 with threshold logic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "9",
  pages =        "1062--1067",
  month =        sep,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.537130",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:13 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=537130",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Venners:1996:FPA,
  author =       "Bill Venners",
  title =        "Under the Hood: Floating-point arithmetic",
  journal =      j-JAVAWORLD,
  volume =       "1",
  number =       "9",
  month =        nov,
  year =         "1996",
  CODEN =        "????",
  ISSN =         "1091-8906",
  bibdate =      "Thu Aug 13 08:48:26 MDT 1998",
  bibsource =    "http://www.javaworld.com/javaworld/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.javaworld.com/javaworld/jw-10-1996/jw-10-hood.htm",
  acknowledgement = ack-nhfb,
}

@Article{vonMatt:1996:RES,
  author =       "Urs {von Matt} and G. W. Stewart",
  title =        "Rounding errors in solving block {Hessenberg}
                 systems",
  journal =      j-MATH-COMPUT,
  volume =       "65",
  number =       "213",
  pages =        "115--135",
  month =        jan,
  year =         "1996",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65F05 (65G05)",
  MRnumber =     "96e:65019",
  MRreviewer =   "Alfonso Laratta",
  bibdate =      "Fri Jul 16 10:38:30 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1996-65-213;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-96-00667-9&u=/mcom/1996-65-213/",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  classcodes =   "C4140 (Linear algebra); C1110 (Algebra); C4240
                 (Programming and algorithm theory)",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "algebra; algorithm; algorithm theory; block diagonally
                 dominant; block Hessenberg; block Hessenberg system;
                 divide and conquer methods; divide-and-conquer; linear;
                 linear system solution; linear systems; M-matrices;
                 matrices; matrix algebra; rounding error analysis;
                 rounding errors; solution; stable solution",
  treatment =    "T Theoretical or Mathematical",
}

@InProceedings{Vrahatis:1996:GBM,
  author =       "M. N. Vrahatis",
  title =        "A Generalized Bisection Method for Large and Imprecise
                 Problems",
  crossref =     "Alefeld:1996:SCV",
  pages =        "186--192",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@InProceedings{Werner:1996:CIW,
  author =       "K. Werner",
  title =        "Calculations of the Inverse {Weierstrass} Functions in
                 an Arbitrary Machine Arithmetic",
  crossref =     "Alefeld:1996:SCV",
  pages =        "72--78",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@InProceedings{Wiethoff:1996:PAE,
  author =       "A. Wiethoff",
  title =        "A Parallel Algorithm for Enclosing All Zeros of a
                 Nonlinear System of Equations",
  crossref =     "Alefeld:1996:SCV",
  pages =        "193--199",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@Article{Williams:1996:TMF,
  author =       "K. B. Williams",
  title =        "Testing Math Functions: {When} requirements are tight,
                 we must carefully examine all potential sources of
                 error. {Make} sure your math library isn't the weak
                 link in the chain",
  journal =      j-CCCUJ,
  volume =       "14",
  number =       "12",
  pages =        "49--54, 58--65",
  month =        dec,
  year =         "1996",
  CODEN =        "CCUJEX",
  ISSN =         "1075-2838",
  bibdate =      "Mon Apr 10 06:32:36 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Describes a package that extends the
                 Cody-Waite-Plauger work on the ELEFUNT package for the
                 testing of the elementary functions, including the
                 inverse hyperbolic functions, cube root, and Bessel
                 functions of the first and second kinds. The C++
                 package implements 192-bit extended precision versions
                 of all of the functions, so that accurate results are
                 available for comparison with the normal
                 double-precision results.",
  acknowledgement = ack-nhfb,
  fjournal =     "C/C++ Users Journal",
}

@InCollection{Zachary:1996:ESD,
  author =       "Joseph L. Zachary",
  title =        "{Eratosthenes}: Significant Digits and Interval
                 Arithmetic",
  crossref =     "Zachary:1996:ISP",
  pages =        "29--43",
  year =         "1996",
  DOI =          "https://doi.org/10.1007/978-1-4612-2366-5_3",
  bibdate =      "Sat Feb 16 15:23:11 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Zachary:1996:SHA,
  author =       "Joseph L. Zachary",
  title =        "Stairway to Heaven: Accumulation of Roundoff Error",
  crossref =     "Zachary:1996:ISP",
  pages =        "45--61",
  year =         "1996",
  DOI =          "https://doi.org/10.1007/978-1-4612-2366-5_4",
  bibdate =      "Sat Feb 16 15:30:56 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Zgliczynski:1996:RVC,
  author =       "P. Zgliczynski",
  title =        "Rigorous Verification of Chaos in the {Roessler}
                 Equations",
  crossref =     "Alefeld:1996:SCV",
  pages =        "287--292",
  year =         "1996",
  bibdate =      "Mon May 20 06:32:10 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
}

@PhdThesis{Al-Twaijry:1997:APO,
  author =       "Hesham Abdulaziz Al-Twaijry",
  title =        "Area And Performance Optimized {CMOS} Multipliers",
  type =         "{Ph.D.} thesis",
  school =       "Department of Electrical Engineering, Stanford
                 University",
  address =      "Stanford, CA, USA",
  pages =        "????",
  month =        aug,
  year =         "1997",
  bibdate =      "Mon Dec 24 10:02:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Allaart:1997:ISC,
  author =       "Pieter C. Allaart",
  title =        "An Invariant-Sum Characterization of {Benford's Law}",
  journal =      j-J-APPL-PROBAB,
  volume =       "34",
  number =       "1",
  pages =        "288--291",
  month =        mar,
  year =         "1997",
  CODEN =        "JPRBAM",
  DOI =          "https://doi.org/10.2307/3215195",
  ISSN =         "0021-9002 (print), 1475-6072 (electronic)",
  ISSN-L =       "0021-9002",
  bibdate =      "Fri Mar 30 11:25:14 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://links.jstor.org/sici?sici=0021-9002%28199703%2934%3A1%3C288%3AAICOBL%3E2.0.CO%3B2-S&size=LARGE",
  abstract =     "The accountant Nigrini remarked that in tables of data
                 distributed according to Benford's law, the sum of all
                 elements with first digit $ d (d = 1, 2, \cdots, 9) $
                 is approximately constant. In this note, a mathematical
                 formulation of Nigrini's observation is given and it is
                 shown that Benford's law is the unique probability
                 distribution such that the expected sum of all elements
                 with first digits $ d_1, \cdots, d_k $ is constant for
                 every fixed $k$.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Probability",
  journal-URL =  "http://www.jstor.org/journals/00219002.html;
                 http://projecteuclid.org/euclid.jap/",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@TechReport{Althaus:1997:MNF,
  author =       "Ernst Althaus and Kurt Mehlhorn",
  title =        "Maximum network flow with floating point arithmetic",
  type =         "Forschungsbericht",
  number =       "MPI-I-97-1-022",
  institution =  "Max-Planck-Institut f{\"u}r Informatik",
  address =      "Saarbr{\"u}cken, Germany",
  pages =        "5",
  year =         "1997",
  ISSN =         "0946-011X",
  bibdate =      "Thu May 09 08:55:36 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Anonymous:1997:BRPk,
  author =       "Anonymous",
  title =        "Book Review: {{\booktitle{Primes of the form $ x^2 + n
                 y^2 $: Fermat, class field theory, and complex
                 multiplication}}: David A. Cox. John Wiley \& Sons, New
                 York. (1989). 351 pages. \$49.95, \pounds 29.95}",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "34",
  number =       "10",
  pages =        "141--141",
  month =        nov,
  year =         "1997",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:48:40 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122197902650",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Anonymous:1997:SIS,
  author =       "Anonymous",
  title =        "{SCAN-97} International Symposium on Scientific
                 Computing Computer Arithmetic and Validated Numerics",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "81",
  number =       "2",
  pages =        "N13--N14",
  day =          "8",
  month =        jul,
  year =         "1997",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:36:02 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042797900741",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Aoki:1997:RCR,
  author =       "Takafumi Aoki and Hiroaki Amada and Tatsuo Higuchi",
  title =        "Real\slash Complex Reconfigurable Arithmetic Using
                 Redundant Complex Number Systems",
  crossref =     "Lang:1997:ISC",
  pages =        "200--207",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Aoki.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@InProceedings{Arnold:1997:ACT,
  author =       "Mark G. Arnold and Thomas A. Bailey and John R. Cowles
                 and Mark D. Winkel",
  title =        "Arithmetic Co-Transformations in the Real and Complex
                 Logarithmic Number Systems",
  crossref =     "Lang:1997:ISC",
  pages =        "190--199",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Arnold.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@Article{Atkinson-Barr:1997:LEP,
  author =       "Martin Atkinson-Barr",
  title =        "Letter to the {Editor}: {Pentium II} Math Bug",
  journal =      j-DDJ,
  volume =       "22",
  number =       "10",
  pages =        "10--10",
  month =        oct,
  year =         "1997",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Thu Nov 8 14:50:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Identifies himself as the ``Mr. X'' cited in
                 \cite{Collins:1997:IPI}, and provides more the
                 background on the discovery of the Pentium FIST
                 (floating-point to integer store) instruction.",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@Article{Avnaim:1997:ESD,
  author =       "Francis Avnaim and Jean-Daniel Boissonnat and Olivier
                 Devillers and Franco P. Preparata and Mariette Yvinec",
  title =        "Evaluating Signs of Determinants Using
                 Single-Precision Arithmetic",
  journal =      j-ALGORITHMICA,
  volume =       "17",
  number =       "2",
  pages =        "111--132",
  month =        feb,
  year =         "1997",
  CODEN =        "ALGOEJ",
  ISSN =         "0178-4617 (print), 1432-0541 (electronic)",
  ISSN-L =       "0178-4617",
  MRclass =      "65Y25 (65F99 68U05)",
  MRnumber =     "MR1425729 (97k:65311)",
  MRreviewer =   "Luiz Henrique de Figueiredo",
  bibdate =      "Fri Jan 6 11:38:07 MST 2006",
  bibsource =    "dblp-journals-algorithmica.bib;
                 http://dblp.uni-trier.de/db/journals/algorithmica/algorithmica17.html#AvnaimBDPY97;
                 http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0178-4617&volume=17&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/index-table-a.html#algorithmica;
                 MathSciNet database",
  URL =          "http://www.springerlink.com/link.asp?id=nlr883hde9w2av31;
                 http://www.springerlink.com/openurl.asp?genre=article&eissn=1432-0541&volume=17&issue=2&spage=111;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=0178-4617&volume=17&issue=2&spage=111",
  abstract =     "We propose a method to evaluate signs of $ 2 \times 2
                 $ and $ 3 \times 3 $ determinants with $b$-bit integer
                 entries using only $b$ and $ (b + 1) $-bit arithmetic
                 respectively. This algorithm has numerous applications
                 in geometric computation and provides a general and
                 practical approach to robustness. The algorithm has
                 been implemented and experimental results show that it
                 slows down the computing time by only a small factor
                 with respect to floating-point calculation.",
  acknowledgement = ack-nhfb,
  fjournal =     "Algorithmica. An International Journal in Computer
                 Science",
  journal-URL =  "http://link.springer.com/journal/453",
  keywords =     "exact arithmetic; floating-point arithmetic",
  oldlabel =     "AvnaimBDPY97",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/algorithmica/AvnaimBDPY97",
}

@InProceedings{Bajard:1997:RMM,
  author =       "Jean-Claude Bajard and Laurent-St{\'e}phane Didier and
                 Peter Kornerup",
  title =        "An {RNS Montgomery} Modular Multiplication Algorithm",
  crossref =     "Lang:1997:ISC",
  pages =        "234--239",
  year =         "1997",
  bibdate =      "Wed Nov 14 18:54:27 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "A revised version published in IEEE Transactions on
                 Computers, Vol.46(7), July 1998",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Bajard.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@Article{Baker:1997:LEP,
  author =       "Louis Baker",
  title =        "Letter to the {Editor}: {Pentium II} Math Bug",
  journal =      j-DDJ,
  volume =       "22",
  number =       "10",
  pages =        "10--10",
  month =        oct,
  year =         "1997",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Thu Nov 8 14:50:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Comments on the Ariane 5 missile failure mentioned in
                 \cite{Collins:1997:IPI}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@InProceedings{Beaumont-Smith:1997:GBA,
  author =       "Andrew Beaumont-Smith and Neil Burgess",
  title =        "A {GaAs} 32-Bit Adder",
  crossref =     "Lang:1997:ISC",
  pages =        "10--17",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Beaumont_Smith.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@Article{Blackford:1997:PEN,
  author =       "L. S. Blackford and A. Cleary and A. Petitet and R. C.
                 Whaley and J. Demmel and I. Dhillon and H. Ren and K.
                 Stanley and J. Dongarra and S. Hammarling",
  title =        "Practical Experience in the Numerical Dangers of
                 Heterogeneous Computing",
  journal =      j-TOMS,
  volume =       "23",
  number =       "2",
  pages =        "133--147",
  month =        jun,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/264029.264030",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Nov 8 14:50:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-2/p133-blackford/",
  abstract =     "Special challenges exist in writing reliable numerical
                 library software for heterogeneous computing
                 environments. Although a lot of software for
                 distributed-memory parallel computers has been written,
                 porting this software to a network of workstations
                 requires careful consideration. The symptoms of
                 heterogeneous computing failures can range from
                 erroneous results without warning to deadlock. Some of
                 the problems are straightforward to solve, but for
                 others the solutions are not so obvious, or incur an
                 unacceptable overhead. Making software robust on
                 heterogeneous systems often requires additional
                 communication. We describe and illustrate the problems
                 encountered during the development of ScaLAPACK and the
                 NAG Numerical PVM Library. Where possible, we suggest
                 ways to avoid potential pitfalls, or if that is not
                 possible, we recommend that the software not be used on
                 heterogeneous networks.",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "distributed-memory systems, floating-point arithmetic,
                 heterogeneous processor networks, message passing,
                 numerical software, reliability",
  subject =      "{\bf D.1.3} Software, PROGRAMMING TECHNIQUES,
                 Concurrent Programming, Distributed programming. {\bf
                 G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Computer arithmetic. {\bf G.1.0} Mathematics
                 of Computing, NUMERICAL ANALYSIS, General, Parallel
                 algorithms.",
}

@Article{Blinn:1997:JBC,
  author =       "James F. Blinn",
  title =        "{Jim Blinn}'s Corner: Floating-Point Tricks",
  journal =      j-IEEE-CGA,
  volume =       "17",
  number =       "4",
  pages =        "80--84",
  month =        jul # "\slash " # aug,
  year =         "1997",
  CODEN =        "ICGADZ",
  DOI =          "https://doi.org/10.1109/38.595279",
  ISSN =         "0272-1716 (print), 1558-1756 (electronic)",
  ISSN-L =       "0272-1716",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Discusses use of IEEE 754 single-precision
                 floating-point bit patterns as integers for
                 implementations of fast, but low-accuracy, functions
                 useful in computer graphics.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Computer Graphics and Applications",
  journal-URL =  "http://www.computer.org/portal/web/csdl/magazines/cga",
  summary =      "The author discusses IEEE floating point
                 representation that stores numbers in what amounts to
                 scientific notation. He considers the sign bit, the
                 logarithm function, function approximations, errors and
                 refinements \ldots{}",
}

@Article{Bomar:1997:RNA,
  author =       "B. W. Bomar and L. M. Smith and R. D. Joseph",
  title =        "Roundoff noise analysis of state-space digital filters
                 implemented on floating-point digital signal
                 processors",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "44",
  number =       "11",
  pages =        "952--955",
  month =        nov,
  year =         "1997",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.644048",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems. 2, Analog
                 and Digital Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  summary =      "An expression is obtained for the output
                 floating-point roundoff noise variance of a general
                 Nth-order state-space digital filter with zero-mean
                 white noise input signal. This expression is then
                 simplified for the case there the filter is implemented
                 \ldots{}",
}

@Article{Bshouty:1997:TBA,
  author =       "Nader H. Bshouty and Yishay Mansour and Baruch
                 Schieber and Prasoon Tiwari",
  title =        "A tight bound for approximating the square root",
  journal =      j-INFO-PROC-LETT,
  volume =       "63",
  number =       "4",
  pages =        "211--213",
  day =          "10",
  month =        sep,
  year =         "1997",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  MRclass =      "68Q25 (65B15 68Q40)",
  MRnumber =     "1 477 306",
  bibdate =      "Sat Nov 7 17:55:54 MST 1998",
  bibsource =    "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}

@InProceedings{Burgess:1997:SUR,
  author =       "Neil Burgess",
  title =        "Scaled and unscaled residue number system to binary
                 conversion techniques using the core function",
  crossref =     "Lang:1997:ISC",
  pages =        "250--257",
  year =         "1997",
  DOI =          "https://doi.org/10.1109/ARITH.1997.614902",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Burgess.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13; residue arithmetic; residue number system",
  summary =      "The paper presents related techniques for converting a
                 residue number system (RNS) number to binary, with and
                 without scaling, that use the core function. The
                 techniques remove the difficulties associated with
                 conversion procedures based on the \ldots{}",
}

@InProceedings{Callaway:1997:PDC,
  author =       "Thomas K. Callaway and Earl E. {Swartzlander, Jr.}",
  title =        "Power-Delay Characteristics of {CMOS} Multipliers",
  crossref =     "Lang:1997:ISC",
  pages =        "26--33",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Callaway.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@InProceedings{Cao:1997:HPH,
  author =       "Jun Cao and Belle W. Y. Wei",
  title =        "High-Performance Hardware for Function Generation",
  crossref =     "Lang:1997:ISC",
  pages =        "184--189",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Cao.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@InProceedings{Cena:1997:QCA,
  author =       "Gianluca Cena and Paolo Montuschi and Luigi Ciminiera
                 and Andrea Sanna",
  title =        "A {Q}-Coder Algorithm with Carry Free Addition",
  crossref =     "Lang:1997:ISC",
  pages =        "282",
  year =         "1997",
  bibdate =      "Sat Nov 17 12:22:42 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Cena.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@TechReport{Chen:1997:PEG,
  author =       "Yirng-An Chen and Randal E. Bryant",
  title =        "{PBHD}: an efficient graph representation for floating
                 point circuit verification",
  type =         "Report",
  number =       "CMU-CS-97-134",
  institution =  "Department of Computer Science, Carnegie-Mellon
                 University",
  address =      "Pittsburgh, PA, USA",
  year =         "1997",
  bibdate =      "Thu May 09 08:39:56 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Collins:1997:IPI,
  author =       "Robert C. Collins",
  title =        "Inside the {Pentium II} Math Bug",
  journal =      j-DDJ,
  volume =       "22",
  number =       "8",
  pages =        "52, 55--57",
  month =        aug,
  year =         "1997",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Sat Mar 07 08:27:48 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See letters
                 \cite{Atkinson-Barr:1997:LEP,Baker:1997:LEP}.",
  abstract =     "Two days before Intel's biggest processor announcement
                 in years, a math bug in the Pentium Pro and Pentium II
                 came to light. Robert takes you inside the Dan-0411
                 flag erratum,' and tells how the story unfolded.",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@Article{Compagner:1997:RER,
  author =       "A. Compagner and A. S. Berdnikov and S. B. Turtia and
                 A. Larionov",
  title =        "Rounding errors in random number generators",
  journal =      j-COMP-PHYS-COMM,
  volume =       "106",
  number =       "3",
  pages =        "207--218",
  month =        nov,
  year =         "1997",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(97)00070-2",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Thu Dec 29 21:19:40 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465597000702",
  abstract =     "The deviations of the cumulative distribution function
                 from the uniform one for the pseudorandom floating
                 point values produced by integer arithmetics are
                 discussed. It is shown that the conversion from fixed
                 point values into floating point values introduces
                 specific artefacts even when the integer arithmetics
                 guarantees ideal uniformity. Two type of defects are
                 considered: the appearance of the value 1.0 among
                 pseudorandom values, and the sharp jumps of uniformity
                 at the level of discreteness which corresponds to the
                 computer representation of the floating point values.
                 The non-uniformity at small level of discreteness can
                 be neglected in most cases, but the appearance of the
                 parasitic value 1.0 where nobody expects it can be very
                 dangerous if special precautions are not taken by the
                 user. Both defects are demonstrated using the random
                 number generator from the system library of the
                 Microsoft Power Station Fortran 1.0.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Cuyt:1997:FPV,
  author =       "A. Cuyt",
  title =        "Floating-point versus Symbolic Computations in the
                 {QD}-algorithm",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "24",
  number =       "6",
  pages =        "695--703",
  month =        dec,
  year =         "1997",
  CODEN =        "JSYCEH",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Ingenta database",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171",
  pagecount =    "9",
}

@TechReport{Daumas:1997:RPC,
  author =       "Marc Daumas and D. W. Matula",
  title =        "Recoders for partial compression and rounding",
  type =         "Technical Report",
  number =       "97-01",
  institution =  "Laboratoire de l'Informatique du Parall{\`e}lisme",
  address =      "Lyon, France",
  year =         "1997",
  bibdate =      "Thu Nov 13 10:48:03 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Daumas:1997:VRD,
  author =       "Marc Daumas and D. W. Matula",
  title =        "Validated roundings of dot products by sticky
                 accumulation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "5",
  pages =        "623--629",
  month =        may,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.589241",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:23 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=589241",
  abstract =     "The dot product operation is very prevalent in
                 scientific computation and has therefore been
                 incorporated as a primitive operation in some
                 languages. The implementation of the dot product
                 operation by a sequence of IEEE standard
                 multiplications and additions does not prevent a
                 substantial accumulation of the round-off errors or
                 warn the user about a catastrophic cancellation. We
                 present the design of a double precision dot product
                 operation employing sticky accumulation, where the
                 final rounded result is validated by raising a new
                 exception flag if the result incurred catastrophic
                 cancellation. Sticky accumulation can be implemented in
                 a pipeline or parallel environment to sustain double
                 precision with an extended control of the error. Our
                 design allows that, in the absence of catastrophic
                 cancellation, one ulp accuracy is guaranteed",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "floating-point arithmetic",
}

@InProceedings{Dimitrov:1997:AME,
  author =       "V. S. Dimitrov and G. A. Jullien and W. C. Miller",
  title =        "Algorithms for Multi-Exponentiation Based on Complex
                 Arithmetic",
  crossref =     "Lang:1997:ISC",
  pages =        "208--217",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Dimitrov_algorithms.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@InProceedings{Dimitrov:1997:ERN,
  author =       "V. Dimitrov and G. A. Jullien and W. C. Miller",
  booktitle =    "Proceedings of the 40th Midwest Symposium on Circuits
                 and Systems, 1997",
  title =        "{Eisenstein} residue number system with applications
                 to {DSP}",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "675--678",
  year =         "1997",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1997.662165",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A new approach for processing complex numbers has been
                 proposed, Basically, it is aimed at the implementation
                 of radix-3 FFTs, but it can be used in any situation
                 where the requirement to process Eisenstein integers
                 arises, The comparison between \ldots{}",
}

@InProceedings{Dimitrov:1997:TAD,
  author =       "V. S. Dimitrov and G. A. Jullien and W. C. Miller",
  title =        "Theory and Applications for a Double-Base Number
                 System",
  crossref =     "Lang:1997:ISC",
  pages =        "44--53",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Dimitrov_theory.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@Article{Doring:1997:DAL,
  author =       "Andreas D{\"o}ring and Wolfgang J. Paul",
  title =        "Decimal adjustment of long numbers in constant time",
  journal =      j-INFO-PROC-LETT,
  volume =       "62",
  number =       "3",
  pages =        "161--163",
  day =          "4",
  month =        jun,
  year =         "1997",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  MRclass =      "68M07 (68M20)",
  MRnumber =     "1 453 700",
  bibdate =      "Sat Nov 7 17:55:52 MST 1998",
  bibsource =    "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  keywords =     "decimal floating-point arithmetic",
}

@Article{Drmac:1997:IJR,
  author =       "Zlatko Drma{\v{c}}",
  title =        "Implementation of {Jacobi} Rotations for Accurate
                 Singular Value Computation in Floating Point
                 Arithmetic",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "18",
  number =       "4",
  pages =        "1200--1222",
  month =        jul,
  year =         "1997",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/S1064827594265095",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65F15 (65G10)",
  MRnumber =     "98e:65027; 1 453 565",
  MRreviewer =   "Ljiljana Petkovi{\'c}",
  bibdate =      "Fri Dec 4 14:47:53 MST 1998",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/18/4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/26509",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}

@InProceedings{Drolshagen:1997:PES,
  author =       "A. Drolshagen and H. Henkelmann and W. Anheier",
  booktitle =    "{IEEE} International Conference on
                 Application-Specific Systems, Architectures and
                 Processors, Proceedings, 14--16 July 1997",
  title =        "Processor elements for the standard cell
                 implementation of residue number systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "116--123",
  year =         "1997",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ASAP.1997.606818",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "In this article processor elements for the effective
                 implementation of standard cell circuits based on
                 residue number systems (RNS) are presented. Two new
                 processors are proposed helping to reduce the hardware
                 requirements of the implementations. \ldots{}",
}

@Manual{EC:1997:IER,
  author =       "{European Commission}",
  title =        "The Introduction of the Euro and the Rounding of
                 Currency Amounts",
  organization = "European Commission Directorate General II Economic
                 and Financial Affairs",
  address =      "Brussels, Belgium",
  pages =        "29",
  year =         "1997",
  bibdate =      "Fri Nov 28 11:18:05 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Edelman:1997:MPD,
  author =       "Alan Edelman",
  title =        "The Mathematics of the {Pentium} Division Bug",
  journal =      j-SIAM-REVIEW,
  volume =       "39",
  number =       "1",
  pages =        "54--67",
  month =        mar,
  year =         "1997",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/S0036144595293959",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "68M07",
  MRnumber =     "1 439 485",
  bibdate =      "Sat Mar 29 09:55:47 MDT 2014",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/39/1;
                 http://epubs.siam.org/toc/siread/39/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/29395;
                 http://www-math.mit.edu/~edelman/homepage/papers/pentiumbug.pdf;
                 http://www.siam.org/journals/sirev/sirev391.htm",
  abstract =     "Despite all of the publicity surrounding the Pentium
                 bug of 1994, the mathematical details of the bug are
                 poorly understood. We discuss these details and supply
                 a new proof of the Coe--Tang result that the at-risk
                 divisors have six consecutive ones in positions 5
                 through 10. Also, we prove that the worst-case absolute
                 error for arguments in $ [1, 2) $ is on the order of
                 1e-5.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  keywords =     "Intel Pentium divide flaw; Thomas R. Nicely",
  onlinedate =   "January 1997",
}

@InProceedings{Even:1997:DIC,
  author =       "Guy Even and Wolfgang Paul",
  title =        "On the Design of {IEEE} Compliant Floating Point
                 Units",
  crossref =     "Lang:1997:ISC",
  pages =        "54--63",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Even.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
  remark =       "Cited in \cite{Mueller:2000:CAC}.",
}

@Article{Fitzpatrick:1997:EBE,
  author =       "P. Fitzpatrick",
  title =        "Extending backward error assertions to tolerance of
                 large errors in floating point computations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "4",
  pages =        "505--510",
  month =        apr,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.588072",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=588072",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "The use of backward error assertions combined with
                 iterative refinement has been suggested for the
                 correction of small fault induced errors in the
                 floating point solution of linear systems. We extend
                 this to the correction of large errors, typically
                 \ldots{}",
}

@InProceedings{Frougny:1997:FAS,
  author =       "Christiane Frougny",
  title =        "On-the-Fly Algorithms and Sequential Machines",
  crossref =     "Lang:1997:ISC",
  pages =        "260--265",
  year =         "1997",
  bibdate =      "Wed Nov 14 18:57:13 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Frougny.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@Article{Garber:1997:NBB,
  author =       "Lee Garber",
  title =        "News Briefs: Binary Version Could Bring {VRML} into
                 the Mainstream. {FCC} Jumps Into {Internet} Fray.
                 {Java} and Floating-Point Math. {Intel} to Design
                 {NDRAM}. Battle over Net Telephony. Vendors Seek Fast
                 Modems. {US} Permits Export of Strong Encryption.
                 {E}-commerce Nears \$1 Billion. Chasing the Blue Light.
                 Personal {E}-mail Use Will Soar",
  journal =      j-COMPUTER,
  volume =       "30",
  number =       "4",
  pages =        "25--27",
  month =        apr,
  year =         "1997",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Tue May 06 16:51:53 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}

@InProceedings{Garjanov:1997:CRE,
  author =       "A. E. Garjanov",
  booktitle =    "Proceedings of the 1st International Conference on
                 Control of Oscillations and Chaos, 1997",
  title =        "Controlled round-off error oscillations for initial
                 value problem numerical solution",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "333--334",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "A new methodology of a computer simulation is desired
                 for the accumulated round-off error elimination to be
                 possible. It is well known that the propagation of
                 round-off error in the numerical integration of
                 differential equations may be crucial \ldots{}",
}

@Article{Giachetti:1997:PRF,
  author =       "Ronald E. Giachetti and Robert E. Young",
  title =        "A Parametric Representation of Fuzzy Numbers and Their
                 Arithmetic Operators",
  journal =      j-FUZZY-SETS-SYSTEMS,
  volume =       "92",
  number =       "2",
  pages =        "??--??",
  day =          "1",
  month =        sep,
  year =         "1997",
  CODEN =        "FSSYD8",
  ISSN =         "0165-0114 (print), 1872-6801 (electronic)",
  ISSN-L =       "0165-0114",
  bibdate =      "Tue Nov 05 15:22:41 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.nist.gov/publications/parametric-representation-fuzzy-numbers-and-their-arithmetic-operators",
  abstract =     "Direct implementation of extended arithmetic operators
                 on fuzzy numbers is computationally complex.
                 Implementation of the extension principle is equivalent
                 to solving a nonlinear programming problem. To overcome
                 this difficulty many applications limit the membership
                 functions to certain shapes, usually either triangular
                 fuzzy numbers (TFN) or trapezoidal fuzzy numbers
                 (TrFN). Then calculation of the extended operators can
                 be performed on the parameters defining the fuzzy
                 numbers, thus making the calculations trivial.
                 Unfortunately the TFN shape is not closed under
                 multiplication and division. The result of these
                 operators is a polynomial membership function and the
                 triangular shape only approximates the actual
                 result.The linear approximation can be quite poor and
                 may lead to incorrect results when used in engineering
                 applications. We analyze this problem and propose six
                 parameters which define parameterized fuzzy numbers
                 (PFN), of which TFNs are a special case. We provide the
                 methods for performing fuzzy arithmetic and show that
                 the PFN representation is closed under the arithmetic
                 operations. The new representation in conjunction with
                 the arithmetic operators obeys many of the same
                 arithmetic properties as TFNs. The new method has
                 better accuracy and similar computational speed to
                 using TFNs and appears to have benefits when used in
                 engineering applications.",
  acknowledgement = ack-nhfb,
  fjournal =     "Fuzzy Sets and Systems",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01650114",
  keywords =     "arithmetic approximations; Fuzzy arithmetic;
                 membership functions; triangular fuzzy numbers",
}

@Misc{Gosling:1997:ENC,
  author =       "James A. Gosling",
  title =        "The Evolution of Numerical Computing in {Java}",
  howpublished = "World Wide Web document.",
  year =         "1997",
  bibdate =      "Mon May 06 17:11:19 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://java.sun.com/people/jag/FP.html",
  acknowledgement = ack-nhfb,
}

@InProceedings{Grosse:1997:RI,
  author =       "Eric Grosse",
  title =        "Real {Inferno}",
  crossref =     "Boisvert:1997:QNS",
  pages =        "270--279",
  year =         "1997",
  bibdate =      "Tue Jul 21 11:18:48 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/grosse-eric.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://cm.bell-labs.com/inferno/real.ps",
  acknowledgement = ack-nhfb,
  remark =       "From \cite{Steele:2004:RHP}: ``the language Limbo
                 adopted accurate base conversion as one of its
                 improvements over C (p. 271 of this article)''.",
}

@Book{Guedj:1997:NUL,
  author =       "Denis Guedj",
  title =        "Numbers: The Universal Language",
  publisher =    "Harry N. Abrams, Inc.",
  address =      "New York, NY, USA",
  pages =        "175",
  year =         "1997",
  ISBN =         "0-8109-2845-0",
  ISBN-13 =      "978-0-8109-2845-9",
  LCCN =         "QA141.G8413 1997",
  bibdate =      "Fri Nov 28 17:05:12 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Translated from the French edition
                 \cite{Guedj:1996:EN} by Lory Frankel.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}

@Article{Hagihara:1997:FPD,
  author =       "Y. Hagihara and S. Inui and F. Okamoto and M. Nishida
                 and T. Nakamura and H. Yamada",
  title =        "Floating-point datapaths with online built-in self
                 speed test",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "32",
  number =       "3",
  pages =        "444--449",
  month =        mar,
  year =         "1997",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "This paper describes floating-point (FP) datapaths
                 developed for graphics and simulation applications. The
                 datapaths are fabricated using 0.35 $\mu$m CMOS
                 technology and embedded in a 125 MHz, 291 MFLOPS vector
                 pipelined processor for use in supercomputers
                 \ldots{}",
}

@InProceedings{Haller:1997:HIS,
  author =       "B. Haller and M. Streiff and U. Fleisch and R.
                 Zimmermann",
  booktitle =    "{1997 IEEE International Conference on Acoustics,
                 Speech, and Signal Processing}",
  title =        "Hardware implementation of a systolic antenna array
                 signal processor based on {CORDIC} arithmetic",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "4141--4144 (vol. 5)",
  year =         "1997",
  DOI =          "https://doi.org/10.1109/ICASSP.1997.604858",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Adaptive arrays; Antenna arrays; Application specific
                 integrated circuits; Hardware; Minimization; Radar
                 antennas; Real time systems; Signal processing
                 algorithms; Sonar; Systolic arrays",
}

@Book{Hanson:1997:CII,
  author =       "David R. Hanson",
  title =        "{C} Interfaces and Implementations: Techniques for
                 Creating Reusable Software",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "xvii + 519",
  year =         "1997",
  ISBN =         "0-201-49841-3",
  ISBN-13 =      "978-0-201-49841-7",
  LCCN =         "QA76.73.C15H37 1997",
  bibdate =      "Fri Feb 27 16:08:11 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/litprog.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  series =       "Addison-Wesley Professional Computing Series",
  URL =          "http://www.cs.princeton.edu/software/cii/",
  acknowledgement = ack-nhfb,
  subject =      "C (Computer program language); Computer software;
                 Reusability; Literate Programming",
  tableofcontents = "1. Introduction \\
                 2. Interfaces and Implementations \\
                 3. Atoms \\
                 4. Exceptions and Assertions \\
                 5. Memory Management \\
                 6. More Memory Management \\
                 7. Lists \\
                 8. Tables \\
                 9. Sets \\
                 10. Dynamic Arrays \\
                 11. Sequences \\
                 12. Rings \\
                 13. Bit Vectors \\
                 14. Formatting \\
                 15. Low-Level Strings \\
                 16. High-Level Strings \\
                 17. Extended-Precision Arithmetic \\
                 18. Arbitrary-Precision Arithmetic \\
                 19. Multiple-Precision Arithmetic \\
                 20. Threads",
}

@TechReport{Hanson:1997:ECR,
  author =       "Kenton L. Hanson",
  title =        "Economical Correctly Rounded Binary Decimal
                 Conversion",
  type =         "Report",
  number =       "??",
  institution =  "????",
  address =      "????",
  day =          "19",
  month =        dec,
  year =         "1997",
  bibdate =      "Sat May 07 09:46:31 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Cited in \cite[p. 134, reference 4]{Hack:2004:IPR},
                 and reported there to be now inaccessible. Further
                 queries in May 2022 to four search engines fail to find
                 this document, or its institution and address.",
  acknowledgement = ack-nhfb,
}

@Misc{Hanson:1997:MAD,
  author =       "Kenton L. Hanson",
  title =        "Method and apparatus for determining a precision of an
                 intermediate arithmetic for converting values between a
                 first numeric format and a second numeric format",
  howpublished = "US Patent 5652862",
  day =          "29",
  month =        jul,
  year =         "1997",
  bibdate =      "Thu Oct 14 14:54:45 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentgenius.com/patent/5652862.html",
  abstract =     "A method and apparatus for efficient allocation of
                 temporary storage for performing accurate and correct
                 numeric base conversions on a computer system is
                 provided. Numeric base conversions are common because
                 computers operate in binary whereas the values that are
                 input into computers are based on a decimal system. A
                 common source of error occurs when converted values are
                 rounded. The intermediate arithmetic used to perform
                 the conversion requires greater precision than the
                 target floating point format. It is known that to
                 always insure correctly rounded results, an extremely
                 high precision intermediate arithmetic may be used.
                 However, in many case this is a waste of system memory.
                 To efficiently allocate system memory to this task, the
                 most difficult rounding case is determined. The
                 precision needed to correctly round the most difficult
                 case is then derived. This information is then stored
                 and subsequently used to allocate an efficient amount
                 of storage whenever a numeric base conversion is to
                 take place.",
  acknowledgement = ack-nhfb,
  remark =       "Patent held by Apple Computer, Inc., Cupertino, CA,
                 USA.",
}

@InProceedings{Harris:1997:SDA,
  author =       "David L. Harris and Stuart F. Oberman and Mark A.
                 Horowitz",
  title =        "{SRT} Division Architectures and Implementations",
  crossref =     "Lang:1997:ISC",
  pages =        "18--25",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "ftp://arith.stanford.edu/tr/srtcircuits.ps.Z;
                 http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Harris.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@TechReport{Harrison:1997:FPV,
  author =       "John Robert Harrison",
  title =        "Floating point verification in {HOL Light}: the
                 exponential function",
  type =         "Technical Report",
  number =       "428",
  institution =  "University of Cambridge Computer Laboratory",
  address =      "Cambridge, UK",
  pages =        "ii + 110",
  month =        jun,
  year =         "1997",
  LCCN =         "QA76.9.A96 H367 1997",
  bibdate =      "Thu Oct 24 14:30:40 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cl.cam.ac.uk/users/jrh/papers/tang.ps.gz",
  acknowledgement = ack-nhfb,
  keywords =     "automatic theorem proving; floating-point arithmetic;
                 proof theory",
}

@InProceedings{Harrison:1997:VAP,
  author =       "John Harrison",
  editor =       "Elsa L. Gunter and Amy Felty",
  booktitle =    "Theorem Proving in Higher Order Logics: {10th
                 International Conference, TPHOLs'97, Murray Hill, NJ,
                 USA, August 19--22, 1997, Proceedings}",
  title =        "Verifying the accuracy of polynomial approximations in
                 {HOL}",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "137--152",
  year =         "1997",
  DOI =          "https://doi.org/10.1007/BFb0028391",
  ISBN =         "3-540-63379-0 (print), 3-540-69526-5 (electronic)",
  ISBN-13 =      "978-3-540-63379-2 (print), 978-3-540-69526-4
                 (electronic)",
  LCCN =         "QA76.9.A96 I577 1997",
  bibdate =      "Tue May 07 16:45:16 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/BFb0028381",
}

@Article{Hasan:1997:DA,
  author =       "M. A. Hasan",
  title =        "Division-and-accumulation over {$ \mathrm {GF}(2^m)
                 $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "6",
  pages =        "705--708",
  month =        jun,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.600829",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:23 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=600829",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Hekstra:1997:FRL,
  author =       "Gerber J. Hekstra and Ed F. A. Deprettere",
  title =        "Fast Rotations: Low-Cost Arithmetic Methods for
                 Orthonormal Rotation",
  crossref =     "Lang:1997:ISC",
  pages =        "116--125",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Hekstra.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@InProceedings{Hiasat:1997:DIR,
  author =       "Ahmad A. Hiasat and Hoda S. Abdel-Aty-Zohdy",
  title =        "Design and Implementation of an {RNS} Division
                 Algorithm",
  crossref =     "Lang:1997:ISC",
  pages =        "240--249",
  year =         "1997",
  bibdate =      "Wed Nov 14 18:57:54 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Hiasat.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13; residue number system",
}

@MastersThesis{Hix:1997:CTV,
  author =       "Robert W. Hix",
  title =        "A comparison of two {VHDL} design environments for
                 {FPGA}-based computer arithmetic",
  type =         "Thesis ({M.S.})",
  school =       "Tennessee Technological University",
  address =      "Cookeville, TN, USA",
  pages =        "x + 301",
  year =         "1997",
  bibdate =      "Mon Mar 05 14:38:08 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Holmes:1997:CAP,
  author =       "W. Neville Holmes",
  title =        "Composite Arithmetic: Proposal for a New Standard",
  journal =      j-COMPUTER,
  volume =       "30",
  number =       "3",
  pages =        "65--73",
  month =        mar,
  year =         "1997",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Fri May 9 17:30:55 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.comp.utas.edu.au/pub/nholmes/ca/dsdf.ps;
                 ftp://ftp.comp.utas.edu.au/pub/nholmes/ca/dsrf.ps;
                 ftp://ftp.comp.utas.edu.au/pub/nholmes/ca/dssf.ps",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods)",
  corpsource =   "Department of Comput., Tasmania University,
                 Launceston, Tas., Australia",
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
  keywords =     "composite arithmetic; digital arithmetic; exact
                 numbers; extended arithmetic; floating point
                 arithmetic; formatting scheme; general computation;
                 general-purpose arithmetic standard; inexact numbers;
                 number display; number format; number storage;
                 reliability; stability; standards",
  treatment =    "P Practical",
}

@Article{Irmay:1997:RBZ,
  author =       "Shragga Irmay",
  title =        "The relationship between {Zipf}'s law and the
                 distribution of first digits",
  journal =      j-J-APPL-STAT,
  volume =       "24",
  number =       "4",
  pages =        "383--393",
  day =          "1",
  month =        aug,
  year =         "1997",
  CODEN =        "????",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  MRclass =      "62E15",
  MRnumber =     "98h:62015",
  bibdate =      "Sat Apr 13 11:27:31 MDT 2002",
  bibsource =    "http://www.catchword.co.uk/titles/carfax/02664763/;
                 http://www.tandf.co.uk/journals/routledge/02664763.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.catchword.co.uk/cgi-bin/cgi?ini=carfax&body=linker&reqidx=/catchword/carfax/13600532/v24n4/s2/p383",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
  keywords =     "Benford's Law; Zipf's Law",
  xxpages =      "383--394",
}

@Article{Ito:1997:EIA,
  author =       "M. Ito and N. Takagi and S. Yajima",
  title =        "Efficient initial approximation for multiplicative
                 division and square root by a multiplication with
                 operand modification",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "4",
  pages =        "495--498",
  month =        apr,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.588066",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=588066",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "An efficient initial approximation method for
                 multiplicative division and square root is proposed. It
                 is a modification of the piecewise linear
                 approximation. The multiplication and the addition
                 required for the linear approximation are replaced by
                 \ldots{}",
}

@Misc{Kahan:1997:JNL,
  author =       "W. Kahan",
  title =        "The {John von Neumann} lecture at the {SIAM} 45th
                 annual meeting",
  howpublished = "World-Wide Web document.",
  year =         "1997",
  bibdate =      "Sat Apr 28 18:52:17 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/SIAMjvnl.ps",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:1997:LNS,
  author =       "W. Kahan",
  title =        "Lecture Notes on the Status of {IEEE Standard 754 for
                 Binary Floating-Point Arithmetic}",
  howpublished = "World-Wide Web document",
  pages =        "30",
  day =          "1",
  month =        oct,
  year =         "1997",
  bibdate =      "Mon Apr 25 17:54:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/IEEE754.PDF",
  acknowledgement = ack-nhfb,
}

@TechReport{Kahan:1997:RDI,
  author =       "W. Kahan and Melody Y. Ivory",
  title =        "Roundoff Degrades an Idealized Cantilever",
  type =         "Technical report",
  institution =  "Department of Mathematics and Department of Electrical
                 Engineering and Computer Science, University of
                 California, Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "11",
  day =          "3",
  month =        jul,
  year =         "1997",
  bibdate =      "Fri May 03 12:15:09 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Cantilever.pdf;
                 http://www.cs.berkeley.edu/~wkahan/Cantilever.ps",
  acknowledgement = ack-nhfb,
}

@Article{Kako:1997:PEF,
  author =       "Fujio Kako and Tateaki Sasaki",
  title =        "Proposal of {``Effective} Floating-Point Number'' for
                 Approximate Algebraic Computation",
  journal =      j-SIGSAM,
  volume =       "31",
  number =       "3",
  pages =        "31--31",
  month =        sep,
  year =         "1997",
  CODEN =        "SIGSBZ",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Wed Dec 17 07:49:58 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Poster abstract only. Discusses fuzzy and interval
                 floating-point arithmetic.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGSAM Bulletin",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}

@Article{Kapur:1997:MVA,
  author =       "Deepak Kapur and M. Subramaniam",
  title =        "Mechanizing Verification of Arithmetic Circuits: {SRT}
                 Division",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1346",
  pages =        "103--??",
  year =         "1997",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:51:29 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1346.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1346/13460103.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1346/13460103.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Karp:1997:HPD,
  author =       "Alan H. Karp and Peter Markstein",
  title =        "High-Precision Division and Square Root",
  journal =      j-TOMS,
  volume =       "23",
  number =       "4",
  pages =        "561--589",
  month =        dec,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/279232.279237",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Nov 8 14:50:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/articles/journals/toms/forthcoming/a0-karp/a0-karp.ps;
                 http://www.acm.org/pubs/citations/journals/toms/1997-23-4/p561-karp/",
  abstract =     "We present division and square root algorithms for
                 calculation with more bits than are handled by the
                 floating-point hardware. These algorithms avoid the
                 need to multiply two high-precision numbers, speeding
                 up the last iteration by as much as a factor of 10. We
                 also show how to produce the floating-point number
                 closest to the exact result with relatively few
                 additional operations.",
  accepted =     "June 1997",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, performance, division, quad precision,
                 square root.",
  subject =      "G.1.0 [Numerical Analysis]: General -- computer
                 arithmetic. G.4 [Mathematics of Computing]:
                 Mathematical Software.",
}

@Book{Khinchin:1997:CF,
  author =       "Aleksandr Iakovlevich Khinchin",
  title =        "Continued fractions",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xi + 95",
  year =         "1997",
  ISBN =         "0-486-69630-8 (paperback)",
  ISBN-13 =      "978-0-486-69630-0 (paperback)",
  LCCN =         "QA295 .K513 1997",
  bibdate =      "Fri Nov 30 06:55:53 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/description/dover032/97008056.html;
                 http://www.loc.gov/catdir/toc/dover031/97008056.html",
  acknowledgement = ack-nhfb,
  author-dates = "1894--1959",
  remark =       "Translated from the Russian by Scripta Technica, Inc.
                 Originally published: Chicago : University of Chicago
                 Press, 1964. Edited by Herbert Eagle.",
}

@InProceedings{King:1997:DDT,
  author =       "E. J. King and E. E. {Swartzlander, Jr.}",
  title =        "Data-Dependent Truncation Scheme for Parallel
                 Multipliers",
  crossref =     "Fargues:1997:CRT",
  pages =        "1178--1182",
  year =         "1997",
  bibdate =      "Fri Jun 24 20:50:14 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Kinoshita:1997:RAE,
  author =       "Eisuke Kinoshita and Ki-Ja Lee",
  title =        "A Residue Arithmetic Extension for Reliable Scientific
                 Computation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "2",
  pages =        "129--138",
  month =        feb,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.565587",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "65G10 (65Y99)",
  MRnumber =     "MR1434396 (97j:65080)",
  bibdate =      "Wed Jul 6 10:06:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=565587",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Koc:1997:FSE,
  author =       "{\c{C}}. K. Ko{\c{c}} and T. Acar",
  title =        "Fast Software Exponentiation in {$ \mathrm {GF}(2^k)
                 $}",
  crossref =     "Lang:1997:ISC",
  pages =        "225--231",
  year =         "1997",
  bibdate =      "Sat Nov 17 12:22:42 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Koc.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@InProceedings{Kramer:1997:PWC,
  author =       "Walter Kr{\"a}mer",
  title =        "A Priori Worst-Case Error Bounds for Floating-Point
                 Computations",
  crossref =     "Lang:1997:ISC",
  pages =        "64--73",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Kramer.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "1952--2014",
  keywords =     "ARITH-13",
}

@Article{Kravchenko:1997:AEP,
  author =       "Yu. P. Kravchenko and M. A. Liberman",
  title =        "On the Application of Extended Precision Arithmetic to
                 Quantum Mechanical Calculations",
  journal =      j-IJQC,
  volume =       "62",
  number =       "6",
  pages =        "593--601",
  month =        "????",
  year =         "1997",
  CODEN =        "IJQCB2",
  DOI =          "https://doi.org/10.1002/(SICI)1097-461X(1997)62:6<593::AID-QUA3>3.0.CO;2-R",
  ISSN =         "0020-7608 (print), 1097-461X (electronic)",
  ISSN-L =       "0020-7608",
  bibdate =      "Tue Oct 4 06:59:08 MDT 2011",
  bibsource =    "Compendex database;
                 http://www3.interscience.wiley.com/journalfinder.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijqc1990.bib",
  URL =          "http://www3.interscience.wiley.com/cgi-bin/abstract?ID=42544;
                 http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=42544&PLACEBO=IE.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Quantum Chem.",
  fjournal =     "International Journal of Quantum Chemistry",
  journal-URL =  "http://www.interscience.wiley.com/jpages/0020-7608/",
  journalabr =   "Int J Quant Chem",
  onlinedate =   "6 Dec 1998",
}

@InProceedings{Lang:1997:CVA,
  author =       "Tom{\'a}s Lang and Elisardo Antelo",
  title =        "{CORDIC} Vectoring with Arbitrary Target Value",
  crossref =     "Lang:1997:ISC",
  pages =        "108--115",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC
                 Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Lang.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@InProceedings{Lang:1997:FIS,
  author =       "Tom{\'a}s Lang and Jean-Michel Muller and Naofumi
                 Takagi",
  title =        "Foreword: {13th IEEE Symposium on Computer Arithmetic,
                 July 6--9, 1997, Asilomar, California, USA}",
  crossref =     "Lang:1997:ISC",
  pages =        "viii--viii",
  year =         "1997",
  bibdate =      "Sat Nov 17 12:22:42 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_contents.pdf;
                 http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_foreword.pdf;
                 http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_preface.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@InProceedings{Lee:1997:SSA,
  author =       "Choong Ho Lee and M. Kawamata and T. Higuchi",
  booktitle =    "Proceedings of 1997 {IEEE} International Symposium on
                 Circuits and Systems: {ISCAS '97}, 9--12 June 1997",
  title =        "State-space approach to roundoff error analysis of
                 fractal image coding",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1341--1344",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Roundoff error due to iterative computation with
                 finite wordlength degrades the quality of decoded
                 images in fractal image coding that employs a
                 deterministic iterated function system. This paper
                 presents a state-space approach to roundoff error
                 \ldots{}",
}

@InProceedings{Lee:1997:VDA,
  author =       "Inseop Lee and W. K. Jenkins",
  booktitle =    "Proceedings of the 40th Midwest Symposium on Circuits
                 and Systems, 1997",
  title =        "{VLSI} design for an adaptive equalizer using a
                 residue number system architecture for magnetic
                 channels",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "782--785",
  year =         "1997",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.1997.662191",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper presents the design of an experimental ASIC
                 for an all-digital adaptive equalizer for magnetic
                 channels. The equalizer design, which is based on an
                 RNS chip architecture, is presented at a system level,
                 with particular attention to \ldots{}",
}

@InProceedings{Lefevre:1997:TCR,
  author =       "Vincent Lef{\`e}vre and Jean-Michel Muller and Arnaud
                 Tisserand",
  title =        "Towards Correctly Rounded Transcendentals",
  crossref =     "Lang:1997:ISC",
  pages =        "132--139",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Lefevre.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13; correct rounding; floating-point
                 arithmetic",
  summary =      "The Table Maker's Dilemma is the problem of always
                 getting exactly rounded results when computing the
                 elementary functions. After a brief presentation of
                 this problem, we present new developments that helped
                 us to solve this problem for the double \ldots{}",
}

@InProceedings{LeLann:1997:AAF,
  author =       "G{\'e}rard {Le Lann}",
  booktitle =    "{Proceedings of the International Conference and
                 Workshop on Engineering of Computer-Based Systems}",
  title =        "An Analysis of the {Ariane 5 Flight 501} Failure --- A
                 System Engineering Perspective",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "339--346",
  year =         "1997",
  DOI =          "https://doi.org/10.1109/ECBS.1997.581900",
  bibdate =      "Sat Apr 01 08:29:32 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "From the article: ``The SRI S/W exception was raised
                 during a conversion from a 64-bit floating point number
                 F to a 16-bit signed integer number. F had a value
                 greater than what can be represented by a 16-bit signed
                 integer, which caused an Operand Error (data conversion
                 --- in Ada code --- was not protected, for the reason
                 that a maximum workload target of 80\% had been set for
                 the SRI computer). \ldots{} The value of BH was much
                 higher than expected because the early part of the
                 trajectory of Ariane 5 differs from that of Ariane 4,
                 which results in considerably higher horizontal
                 velocity values.''",
  URL =          "https://ieeexplore.ieee.org/document/581900/",
  acknowledgement = ack-nhfb,
  remark =       "Report of an arithmetic error that put an expensive
                 space missile off course, requiring its destruction in
                 the air. Presumably-reliable code in Ada adapted from
                 an earlier missile generated had not been updated for
                 the new design.",
}

@InProceedings{Li:1997:ISP,
  author =       "Yamin Li and Wanming Chu",
  booktitle =    "Proceedings of the 5th Annual {IEEE} Symposium on
                 {FPGAs} for Custom Computing Machines, 16--18 April
                 1997",
  title =        "Implementation of single precision floating point
                 square root on {FPGAs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "226--232",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The square root operation is hard to implement on
                 FPGAs because of the complexity of the algorithms. In
                 this paper, we present a non-restoring square root
                 algorithm and two very simple single precision floating
                 point square root implementations \ldots{}",
}

@InProceedings{Li:1997:PAI,
  author =       "Yamin Li and Wanming Chu",
  booktitle =    "Proceedings of the 1997 {IEEE} International
                 Conference on Computer Design: {VLSI} in Computers and
                 Processors: {ICCD '97}",
  title =        "Parallel-array implementations of a non-restoring
                 square root algorithm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "690--695",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "In this paper we present a parallel-array
                 implementation of a new non-restoring square root
                 algorithm (PASQRT). The carry-save adder (CSA) is used
                 in the parallel array. The PASQRT has several features
                 unlike other implementations. First, it does \ldots{}",
}

@Article{Lin:1997:DOA,
  author =       "Ming-Bo Lin and A. Y. Oruc",
  title =        "The design of an optoelectronic arithmetic processor
                 based on permutation networks",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "2",
  pages =        "142--153",
  month =        feb,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.565589",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=565589",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@PhdThesis{Lin:1997:HSN,
  author =       "Lei Lin",
  title =        "High-speed nonlinear computer arithmetic: algorithms,
                 {VLSI} design, and accuracy prediction",
  type =         "Thesis ({Ph.D.})",
  school =       "University of South Florida",
  address =      "Tampa, FL, USA",
  pages =        "xv + 204",
  year =         "1997",
  bibdate =      "Mon Mar 05 14:36:45 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Lu:1997:SMK,
  author =       "Chung-Chin Lu",
  title =        "A search of minimal key functions for normal basis
                 multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "5",
  pages =        "588--592",
  month =        may,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.589230",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=589230",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Lutz:1997:HAF,
  author =       "David R. Lutz and D. N. Jayasimha",
  title =        "The Half-Adder Form and Early Branch Condition
                 Resolution",
  crossref =     "Lang:1997:ISC",
  pages =        "266--273",
  year =         "1997",
  bibdate =      "Sat Nov 17 12:22:42 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Lutz.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@InProceedings{Matsubara:1997:LPZ,
  author =       "G. Matsubara and N. Ide",
  booktitle =    "Proceedings of the Third International Symposium on
                 Advanced Research in Asynchronous Circuits and Systems,
                 7--10 April 1997",
  title =        "A low power zero-overhead self-timed division and
                 square root unit combining a single-rail static circuit
                 with a dual-rail dynamic circuit",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "198--209",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "An asynchronous pipeline scheme that combines a low
                 power static circuit with a high-speed dual-rail
                 dynamic circuit is proposed. The scheme utilizes a
                 dual-rail circuit only in the critical path of an SRT
                 division and square root calculation unit. \ldots{}",
}

@InProceedings{Matula:1997:PPF,
  author =       "David W. Matula and Asger Munk Nielsen",
  title =        "Pipelined Packet-Forwarding Floating Point: {I}.
                 Foundations and a Rounder",
  crossref =     "Lang:1997:ISC",
  pages =        "140--147",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Matula.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
  summary =      "The paper presents the foundations for a packet
                 forwarding floating point format and the design of a
                 rounder ensuring compatibility between packet
                 forwarding format and the standard binary IEEE 754
                 floating point format. The packet forwarding format
                 \ldots{}",
}

@Article{McClain:1997:EC,
  author =       "Dylan Loeb McClain",
  title =        "The Evolution of the Calculator",
  journal =      j-NY-TIMES,
  volume =       "??",
  number =       "??",
  pages =        "D3--D3",
  day =          "1",
  month =        sep,
  year =         "1997",
  CODEN =        "NYTIAO",
  ISSN =         "0362-4331 (print), 1542-667X, 1553-8095",
  ISSN-L =       "0362-4331",
  bibdate =      "Sat Aug 17 16:58:52 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
                 https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://search.proquest.com/docview/109786292",
  acknowledgement = ack-nhfb,
  fjournal =     "New York Times",
  journal-URL =  "http://www.nytimes.com/",
  keywords =     "Charles Babbage: Difference Engine",
}

@Article{Michelucci:1997:LA,
  author =       "D. Michelucci and J.-M. Moreau",
  title =        "Lazy arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "9",
  pages =        "961--975",
  month =        sep,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.620478",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:24 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=620478",
  abstract =     "Finite-precision leads to many problems in geometric
                 methods from CAD or Computational Geometry. Until now,
                 using exact rational arithmetic was a simple, yet much
                 too slow, solution to be of any practical use in
                 real-scale applications. A recent optimization-the lazy
                 rational arithmetic-seems promising: It defers exact
                 computations until they become either unnecessary (in
                 most cases) or unavoidable; in such a context, only
                 indispensable computations are performed exactly, that
                 is, those without which any given decision cannot be
                 reached safely using only floating-point arithmetic.
                 This paper takes stock of the lazy arithmetic paradigm:
                 principles, functionalities and limits, speed, possible
                 variants and extensions, difficulties, problems solved
                 or left unresolved",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@MastersThesis{Mizukami:1997:AFP,
  author =       "Etsuko Mizukami",
  title =        "The Accuracy of Floating Point Summations for
                 {CG}-Like Methods",
  type =         "{Master's Thesis}",
  school =       "Department of Computer Science, Indiana
                 University-Bloomington",
  address =      "Bloomington, IN, USA",
  pages =        "v + 55",
  year =         "1997",
  bibdate =      "Tue Nov 22 07:27:31 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Also issued as Technical report 486.",
  URL =          "ftp://ftp.cs.indiana.edu/pub/techreports/TR486.pdf;
                 ftp://ftp.cs.indiana.edu/pub/techreports/TR486.ps;
                 ftp://ftp.cs.indiana.edu/pub/techreports/TR486.ps.Z;
                 http://www.cs.indiana.edu/cgi-bin/techreports/TRNNN.cgi?trnum=TR486",
  abstract =     "It is well known that different ordering of summations
                 in floating point arithmetic can give different sums
                 due to rounding error. This dissertation reviews
                 classic analytic error bounds. A new accurate algorithm
                 is explained thoroughly along with its analytic error
                 bound. These summation algorithms were implemented as
                 dotproducts in an iterative solver to determine which
                 summation ordering is more accurate in practice.
                 Another issue is the relationship between dotproduct
                 accuracy and the convergence of iterative solvers.
                 Analysis and experiments indicate there are two primary
                 sources of errors, and show which summation methods are
                 better for reducing these errors. Results also indicate
                 little correlation between dotproduct accuracy and
                 numbers of iterations required by a solver, within a
                 wide range of accuracies.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}

@Article{MRaihi:1997:XFO,
  author =       "David M'Ra{\"\i}hi and David Naccache and Jacques
                 Stern and Serge Vaudenay",
  title =        "{XMX}: a Firmware-Oriented Block Cipher Based on
                 Modular Multiplications",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1267",
  pages =        "166--??",
  year =         "1997",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:51:07 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1267.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1267/12670166.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1267/12670166.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Mukherjee:1997:DTM,
  author =       "N. Mukherjee and J. Rajski and J. Tyszer",
  title =        "Design of testable multipliers for fixed-width data
                 paths",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "7",
  pages =        "795--810",
  month =        jul,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.599900",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:23 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=599900",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Book{Muller:1997:EFA,
  author =       "Jean-Michel Muller",
  title =        "Elementary Functions: Algorithms and Implementation",
  publisher =    pub-BIRKHAUSER,
  address =      pub-BIRKHAUSER:adr,
  pages =        "xv + 204",
  year =         "1997",
  ISBN =         "0-8176-3990-X",
  ISBN-13 =      "978-0-8176-3990-7",
  LCCN =         "QA331.M866 1997",
  bibdate =      "Fri Jul 25 12:00:55 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\$59.95",
  URL =          "http://www.birkhauser.com/cgi-win/ISBN/0-8176-3990-X;
                 http://www.ens-lyon.fr/~jmmuller/book_functions.html",
  abstract =     "The elementary functions (sine, cosine, tan,
                 exponentials, and logarithms) are the most commonly
                 used mathematical functions in science and engineering.
                 Computing these functions quickly and accurately is a
                 major goal in computer arithmetic. This new book gives
                 the concepts and background necessary to understand and
                 build algorithms for computing these functions,
                 presenting and structuring the algorithms
                 (hardware-oriented as well as software-oriented), and
                 discusses issues related to the accurate floating-point
                 implementation. The purpose is not to give ``cookbook
                 recipes'' that allow one to implement some given
                 function, but to provide the reader with the knowledge
                 that is necessary to build, or adapt, algorithms to
                 their specific computing environment. The book provides
                 an up-to-date presentation of the information needed to
                 understand and accurately use mathematical functions
                 and algorithms in computational work and design.
                 Graduates, professionals and researchers in scientific
                 computing, software engineering and computer
                 engineering will find the book a useful reference and
                 resource.",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "1: Introduction \\
                 2: Computer arithmetic \\
                 I: Algorithms based on polynomial approximation and/or
                 table lookup \\
                 3: Polynomial approximations \\
                 4: Table-based methods \\
                 II: Shift-and-Add algorithms \\
                 5: Shift-and-Add algorithms 6: The CORDIC algorithm \\
                 7: Other shift-and-add algorithms \\
                 III: Range reduction, final rounding and exceptions \\
                 8: Range reduction \\
                 9: Final rounding \\
                 10: Miscellaneous",
  tableofcontents = "1 Introduction / 1 \\
                 2 Computer Arithmetic / 9 \\
                 2.1 Floating-Point Arithmetic / 9 \\
                 2.1.1 Floating-point formats / 9 \\
                 2.1.2 Rounding modes / 10 \\
                 2.1.3 Subnormal numbers and exceptions / 12 \\
                 2.1.4 ULPs / 13 \\
                 2.1.5 Testing your computational environment / 13 \\
                 2.2 Redundant Number Systems / 13 \\
                 2.2.1 Signed-digit number systems / 14 \\
                 2.2.2 Radix-2 redundant number systems / 15 \\
                 I Algorithms Based on Polynomial Approximation and/or
                 Table Lookup / 19 \\
                 3 Polynomial Approximations / 21 \\
                 3.1 Least Squares Polynomial Approximations / 22 \\
                 3.1.1 Legendre polynomials / 23 \\
                 3.1.2 Chebyshev polynomials / 23 \\
                 3.1.3 Jacobi polynomials / 23 \\
                 3.2 Least Maximum Approximations / 24 \\
                 3.3 Speed of Convergence / 31 \\
                 3.4 Rational Approximations / 34 \\
                 3.5 Actual Computation / 38 \\
                 3.6 Example: the Cyrix FasMath Processor / 41 \\
                 3.7 Algorithms and Architectures / 43 \\
                 3.7.1 The E-Method / 45 \\
                 3.7.2 Estrin's Method / 47 \\
                 3.8 Miscellaneous / 47 \\
                 4 Table-Based Methods / 51 \\
                 4.1 Introduction / 51 \\
                 4.2 Table-Driven Algorithms / 53 \\
                 4.2.1 Tang's algorithm for $\exp(x)$ in IEEE
                 floating-point arithmetic / 55 \\
                 4.2.2 $\ln(x)$ on $[1,2]$ / 57 \\
                 4.2.3 $\sin(x)$ on $[0,\pi/4]$ / 58 \\
                 4.3 Gal's Accurate Tables Method / 58 \\
                 4.4 Methods Requiring Specialized Hardware / 62 \\
                 4.4.1 Wong and Goto, logarithm / 62 \\
                 4.4.2 Wong and Goto, exponential / 65 \\
                 II Shift-and-Add Algorithms / 69 \\
                 5 Shift-and-Add algorithms / 71 \\
                 5.1 The Restoring and Nonrestoring Algorithms / 73 \\
                 5.2 Simple Algorithms for Exponentials and Logarithms /
                 77 \\
                 5.2.1 The restoring algorithm for exponentials / 77 \\
                 5.2.2 The restoring algorithm for logarithms / 79 \\
                 5.3 Faster Algorithms / 81 \\
                 5.3.1 Faster computation of exponentials / 81 \\
                 5.3.2 Faster computation of logarithms / 87 \\
                 5.4 Baker's Predictive Algorithm / 90 \\
                 5.5 Bibliographic notes / 98 \\
                 6 The CORDIC Algorithm / 101 \\
                 6.1 Introduction / 101 \\
                 6.2 The Conventional Iteration / 101 \\
                 6.3 Scale Factor Compensation / 107 \\
                 6.4 CORDIC With Redundant Number Systems / 109 \\
                 6.4.1 Signed-digit implementation / 111 \\
                 6.4.2 Carry-save implementation / 111 \\
                 6.4.3 The variable scale factor problem / 112 \\
                 6.5 The Double Rotation Method / 112 \\
                 6.6 Branching CORDIC / 115 \\
                 6.7 Differential CORDIC / 118 \\
                 6.8 Computation of $\cos^{-1}$ and $\sin^{-1}$ / 122
                 \\
                 6.9 Variations on CORDIC / 124 \\
                 7 Other Shift-and-Add Algorithms / 127 \\
                 7.1 High-Radix Algorithms / 127 \\
                 7.1.1 Ercegovac's radix-16 algorithms / 127 \\
                 7.2 The BKM Algorithm / 131 \\
                 7.2.1 The BKM iteration / 133 \\
                 7.2.2 Computation of the exponential function (E-mode)
                 / 133 \\
                 7.2.3 Computation of the logarithm function (L-mode) /
                 137 \\
                 7.2.4 Application to the computation of elementary
                 functions / 138 \\
                 III Range Reduction, Final Rounding and Exceptions /
                 141 \\
                 8 Range Reduction / 143 \\
                 8.1 Introduction / 143 \\
                 8.2 Cody and Waite's Method for Range Reduction / 148
                 \\
                 8.3 Worst Cases for Range Reduction / 149 \\
                 8.3.1 A few basic notions on continued fractions / 149
                 \\
                 8.3.2 Finding worst cases using continued fractions /
                 151 \\
                 8.4 The Payne and Hanek Algorithm / 154 \\
                 8.5 The Modular Algorithm / 158 \\
                 8.5.1 Fixed-point reduction / 158 \\
                 8.5.2 Floating-point reduction / 161 \\
                 8.5.3 Architectures for Modular Reduction / 161 \\
                 9 Final Rounding / 163 \\
                 9.1 Introduction / 163 \\
                 9.2 Monotonicity / 164 \\
                 9.3 Exact Rounding: Presentation of the Problem / 165
                 \\
                 9.4 Some Experiments / 168 \\
                 9.5 A ``Probabilistic'' Approach / 168 \\
                 9.6 Upper Bounds on $m$ / 171 \\
                 9.6.1 Frequency of failures / 173 \\
                 9.6.2 Computing with one million bits / 173 \\
                 10 Miscellaneous / 175 \\
                 10.1 Exceptions / 175 \\
                 10.1.1 NaNs / 176 \\
                 10.1.2 Exact results / 177 \\
                 10.2 Notes on $x^y$ / 178 \\
                 10.3 Multiple Precision / 180",
}

@InProceedings{Nielsen:1997:PPF,
  author =       "Asger Munk Nielsen and David Matula and C. Lyu and Guy
                 Even",
  title =        "Pipelined Packet-Forwarding Floating Point: {II}. An
                 Adder",
  crossref =     "Lang:1997:ISC",
  pages =        "148--155",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Nielsen_Matula.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@InProceedings{Nielsen:1997:RRR,
  author =       "Asger Munk Nielsen and Peter Kornerup",
  title =        "On Radix Representation of Rings",
  crossref =     "Lang:1997:ISC",
  pages =        "34--43",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Nielsen.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@Article{Oberman:1997:DAI,
  author =       "S. F. Oberman and M. J. Flynn",
  title =        "Division Algorithms and Implementations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "8",
  pages =        "833--854",
  month =        aug,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.609274",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:24 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "ftp://arith.stanford.edu/tr/divalgo_TOC.pdf;
                 http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=609274",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Oberman:1997:DID,
  author =       "S. F. Oberman and M. J. Flynn",
  title =        "Design Issues in Division and Other Floating-Point
                 Operations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "2",
  pages =        "154--161",
  month =        feb,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.565590",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "ftp://arith.stanford.edu/tr/desissues_TOC.pdf;
                 http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=565590",
  abstract =     "Floating-point division is generally regarded as a low
                 frequency, high latency operation in typical
                 floating-point applications. However, in the worst
                 case, a high latency hardware floating-point divider
                 can contribute an additional 0.50 CPI to a system
                 executing SPECfp92 applications. This paper presents
                 the system performance impact of floating-point
                 division latency for varying instruction issue rates.
                 It also examines the performance implications of shared
                 multiplication hardware, shared square root, on-the-fly
                 rounding and conversion, and fused functional units.
                 Using a system level study as a basis, it is shown how
                 typical floating-point applications can guide the
                 designer in making implementation decisions and
                 trade-offs.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "Floating-point division is generally regarded as a low
                 frequency, high latency operation in typical
                 floating-point applications. However, in the worst
                 case, a high latency hardware floating-point divider
                 can contribute an additional 0.50 CPI to a \ldots{}",
}

@InProceedings{Oberman:1997:SPD,
  author =       "Stuart F. Oberman and Hesham Al-Twaijry and Michael J.
                 Flynn",
  title =        "The {SNAP} Project: Design of Floating Point
                 Arithmetic Units",
  crossref =     "Lang:1997:ISC",
  pages =        "156--165",
  year =         "1997",
  DOI =          "https://doi.org/10.1109/ARITH.1997.614891",
  bibdate =      "Mon May 27 09:39:18 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "ftp://arith.stanford.edu/tr/snap13.ps.Z;
                 http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Oberman.pdf",
  abstract =     "In recent years computer applications have increased
                 in their computational complexity. The industry wide
                 usage of performance benchmarks, such as SPECmarks, and
                 the popularity of 3D graphics applications forces
                 processor designers to pay particular attention to
                 implementation of the floating point unit, or FPU. The
                 paper presents results of the Stanford subnanosecond
                 arithmetic processor (SNAP) research effort in the
                 design of hardware for floating point addition,
                 multiplication and division. We show that one cycle FP
                 addition is achievable 32\% of the time using a
                 variable latency algorithm. For multiplication, a
                 binary tree is often inferior to a Wallace tree
                 designed using an algorithmic layout approach for
                 contemporary feature sizes (0.3 $ \mu $ m). Further, in
                 most cases two bit Booth encoding of the multiplier is
                 preferable to non Booth encoding for partial product
                 generation. It appears that for division, optimum area
                 performance is achieved using functional iteration, and
                 we present two techniques to further reduce average
                 division latency.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
  remark =       "Pages 166--167 left blank.",
}

@Article{Oklobdzija:1997:CLZ,
  author =       "V. Oklobdzija and H. Suzuki and H. Morinaka and H.
                 Makino and Y. Nakase and K. Mashiko and T. Sumi",
  title =        "Comments on {``Leading-zero anticipatory logic for
                 high-speed floating point addition''} [with reply]",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "32",
  number =       "2",
  pages =        "292--292",
  month =        feb,
  year =         "1997",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Suzuki:1996:LZA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "For original article see H. Suzuki, H. Morinaka, H.
                 Makino, Y. Nakase, K. Mashiko and T. Sumi, ibid.,
                 vol.31, pp.1157-69 (Aug. 1996). I have read with a
                 great interest the article by H. Suzuki et al. I am
                 familiar with their work, and I found their \ldots{}",
}

@Article{Paar:1997:FAA,
  author =       "Christof Paar and Pedro Soria-Rodriguez",
  title =        "Fast Arithmetic Architectures for Public-Key
                 Algorithms over {Galois} Fields {{\em GF\/}$ ((2^n)^m)
                 $}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1233",
  pages =        "363--??",
  year =         "1997",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Mon Feb 4 12:02:26 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1233.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1233/12330363.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1233/12330363.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Pan:1997:SPE,
  author =       "Victor Y. Pan",
  title =        "Solving a Polynomial Equation: Some History and Recent
                 Progress",
  journal =      j-SIAM-REVIEW,
  volume =       "39",
  number =       "2",
  pages =        "187--220",
  month =        jun,
  year =         "1997",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/S0036144595288554",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "65Hxx (01A99 65-03)",
  MRnumber =     "1 453 318",
  bibdate =      "Sat Mar 29 09:55:49 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/39/2;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/28855",
  acknowledgement = ack-nhfb,
  ajournal =     "SIAM Rev.",
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "January 1997",
}

@Article{Parker:1997:MAU,
  author =       "M. G. Parker and M. Benaissa",
  title =        "Modular arithmetic using low order redundant bases",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "5",
  pages =        "611--616",
  month =        may,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.589237",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=589237",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@TechReport{Parker:1997:MCAa,
  author =       "Douglass Stott Parker",
  title =        "{Monte Carlo} arithmetic: exploiting randomness in
                 floating-point arithmetic",
  number =       "CSD 970002",
  institution =  "Department of Computer Science, University of
                 California, Los Angeles",
  address =      "Los Angeles, CA, USA",
  pages =        "86",
  year =         "1997",
  LCCN =         "QA75.5 .R46 no.970002 1997",
  bibdate =      "Thu Oct 24 14:31:00 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.ucla.edu/~stott/mca/CSD-970002.ps.gz",
  acknowledgement = ack-nhfb,
}

@TechReport{Parker:1997:MCAb,
  author =       "Douglass Stott Parker and Paul R. Eggert and Brad
                 Pierce",
  title =        "{Monte Carlo} arithmetic: a framework for the
                 statistical analysis of roundoff error",
  type =         "Technical report",
  number =       "CSD-970014",
  institution =  "Computer Science Department, University of California,
                 Los Angeles",
  address =      "Los Angeles, CA 90095-1596, USA",
  pages =        "23",
  day =          "30",
  month =        mar,
  year =         "1997",
  bibdate =      "Sun Jun 17 18:24:01 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://fmdb.cs.ucla.edu/treports/970014.pdf;
                 https://pdfs.semanticscholar.org/b728/afdb230aa1869f79bdc21ff7a6252d3be9ab.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ANSI\slash IEEE floating-point standards;
                 floating-point arithmetic; floating-point rounding;
                 Monte Carlo methods; random rounding; roundoff error;
                 significance arithmetic",
}

@PhdThesis{Pierce:1997:ARF,
  author =       "Brad Pierce",
  title =        "Applications of randomization to floating-point
                 arithmetic and to linear systems solution",
  type =         "Thesis ({Ph.D.})",
  school =       "Department of Computer Science, University of
                 California, Los Angeles",
  address =      "Los Angeles, CA, USA",
  year =         "1997",
  bibdate =      "Thu Oct 24 14:19:35 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "dissertations, academic -- UCLA -- Computer Science",
}

@InProceedings{Priest:1997:FTD,
  author =       "Douglas M. Priest",
  title =        "Fast Table-Driven Algorithms for Interval Elementary
                 Functions",
  crossref =     "Lang:1997:ISC",
  pages =        "168--174",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Priest.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@Article{Rederlechner:1997:NCP,
  author =       "B. Rederlechner and J. Keller",
  title =        "A Note on Correctness Proofs for Overflow Detection
                 Logic in Adders for $d$-th Complement Numbers",
  journal =      j-J-UCS,
  volume =       "3",
  number =       "10",
  pages =        "1121--1125",
  day =          "28",
  month =        oct,
  year =         "1997",
  CODEN =        "????",
  ISSN =         "0948-6968",
  ISSN-L =       "0948-6968",
  bibdate =      "Wed Mar 4 15:32:49 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://medoc.springer.de:8000/jucs/jucs_3_10/a_note_on_correctness",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
}

@Misc{Reppy:1997:EAH,
  author =       "John H. Reppy and others",
  title =        "The {Standard ML} Basis Library",
  howpublished = "World-Wide Web document",
  month =        oct,
  year =         "1997",
  bibdate =      "Wed Jan 29 16:52:50 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "To be published in/as \cite{Gansner:2003:SMB}.",
  URL =          "http://cm.bell-labs.com/cm/cs/what/smlnj/doc/basis/pages/real.html",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
  remark =       "From \cite{Steele:2004:RHP}: ``toDecimal should
                 produce only as many digits as are necessary for
                 fromDecimal to convert back to the same number, i.e.,
                 for any Normal or SubNormal real value r, we have:
                 fromDecimal (toDecimal r) = r \ldots{} Algorithms for
                 accurately and efficiently converting between binary
                 and decimal real representations are readily available,
                 e.g., see the technical report \cite{Gay:1990:CRB}.''",
}

@InProceedings{Rice:1997:MDB,
  author =       "Eric Rice and Richard Hughey",
  title =        "Multiprecision Division on an 8-Bit Processor",
  crossref =     "Lang:1997:ISC",
  pages =        "74--81",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Rice.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@InProceedings{Sanz-Gonzalez:1997:TBR,
  author =       "J. L. Sanz-Gonzalez",
  booktitle =    "Acoustics, Speech, and Signal Processing, 1997.
                 {ICASSP-97., 1997} {IEEE} International Conference on.
                 21--24 April 1997",
  title =        "Tradeoff between roundoff and overflow errors in
                 digital filter realizations",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2189--2192",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper is concerned with a linked analysis of
                 overflow and roundoff errors in fixed-point digital
                 filter realizations. Upper bounds for the overflow
                 error power are obtained, having considered the
                 saturation quantizer characteristics. Also, \ldots{}",
}

@InProceedings{Sarma:1997:FIR,
  author =       "Debjit Das Sarma and David W. Matula",
  title =        "Faithful Interpolation in Reciprocal Tables",
  crossref =     "Lang:1997:ISC",
  pages =        "82--91",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Sarma.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@InProceedings{Schulte:1997:AFA,
  author =       "M. J. Schulte and James E. Stine",
  title =        "Accurate Function Approximations by Symmetric Table
                 Lookup and Addition",
  crossref =     "Thiele:1997:IIC",
  pages =        "144--153",
  year =         "1997",
  bibdate =      "Sun Mar 04 10:55:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1997-02.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Schulte:1997:HSR,
  author =       "M. J. Schulte and J. E. Stine and K. E. Wires",
  title =        "High-Speed Reciprocal Approximations",
  crossref =     "Fargues:1997:CRT",
  pages =        "1183--1187",
  year =         "1997",
  bibdate =      "Sun Mar 04 10:53:45 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1997-03.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Schulte:1997:SBT,
  author =       "Michael J. Schulte and James E. Stine",
  title =        "Symmetric Bipartite Tables for Accurate Function
                 Approximation",
  crossref =     "Lang:1997:ISC",
  pages =        "175--183",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1997-01.pdf;
                 http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Schulte.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@Article{Schwarz:1997:CFP,
  author =       "E. M. Schwarz and L. Sigal and T. J. McPherson",
  title =        "{CMOS} floating-point unit for the {S/390 Parallel
                 Enterprise Server G4}",
  journal =      j-IBM-JRD,
  volume =       "41",
  number =       "4/5",
  pages =        "475--488",
  month =        "????",
  year =         "1997",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Mon Feb 12 08:10:59 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.almaden.ibm.com/journal/rd/414/schwarz.html",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}

@InProceedings{Schwarz:1997:RCM,
  author =       "Eric M. Schwarz and Robert M. {Averill III} and Leon
                 J. Sigal",
  title =        "A Radix-8 {CMOS S/390} Multiplier",
  crossref =     "Lang:1997:ISC",
  pages =        "2--9",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Schwarz.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@Article{Shewchuk:1997:APF,
  author =       "Jonathan Richard Shewchuk",
  title =        "Adaptive precision floating-point arithmetic and fast
                 robust geometric predicates",
  journal =      j-DISCRETE-COMPUT-GEOM,
  volume =       "18",
  number =       "3",
  pages =        "305--363",
  year =         "1997",
  CODEN =        "DCGEER",
  DOI =          "https://doi.org/10.1007/PL00009321",
  ISSN =         "0179-5376 (print), 1432-0444 (electronic)",
  ISSN-L =       "0179-5376",
  bibdate =      "Sat Apr 28 19:08:39 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.cmu.edu/~quake/robust.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Discrete and Computational Geometry",
  journal-URL =  "http://link.springer.com/journal/454",
  keywords =     "accurate floating-point summation",
}

@Article{Soderquist:1997:DSR,
  author =       "Peter Soderquist and Miriam Leeser",
  title =        "Division and Square Root: Choosing the Right
                 Implementation: Exploring the major design choices for
                 microprocessor implementations of floating-point
                 division and square root",
  journal =      j-IEEE-MICRO,
  volume =       "17",
  number =       "4",
  pages =        "56--66",
  month =        jul # "\slash " # aug,
  year =         "1997",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/40.612224",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Dec 14 06:08:58 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Science Citation Index database (1980--2000)",
  URL =          "http://pascal.computer.org/mi/books/mi1997/pdf/m4056.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}

@Article{Solinas:1997:IAA,
  author =       "Jerome A. Solinas",
  title =        "An Improved Algorithm for Arithmetic on a Family of
                 Elliptic Curves",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1294",
  pages =        "357--??",
  year =         "1997",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:51:15 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1294.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1294/12940357.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1294/12940357.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Srinivas:1997:RDR,
  author =       "H. R. Srinivas and K. K. Parhi and L. A. Montalvo",
  title =        "Radix $2$ division with over-redundant quotient
                 selection",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "1",
  pages =        "85--92",
  month =        jan,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.559806",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=559806",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Stan:1997:SUC,
  author =       "Mircea R. Stan",
  title =        "Synchronous Up\slash Down Counter with Clock Period
                 Independent of Counter Size",
  crossref =     "Lang:1997:ISC",
  pages =        "274--281",
  year =         "1997",
  bibdate =      "Sat Nov 17 12:22:42 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Stan.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@Article{Stankovic:1997:ASM,
  author =       "M. Stankovi{\'c} and J. Madi{\'c} and P.
                 Stanimirovi{\'c}",
  title =        "Addition, subtraction and multiplication of sequences
                 of fractions by means of residue arithmetic and
                 mathematical spectra",
  journal =      "Math. Balkanica (N.S.)",
  volume =       "11",
  number =       "1--2",
  pages =        "11--23",
  year =         "1997",
  ISSN =         "0205-3217",
  MRclass =      "11Y55 (11A67 68R99)",
  MRnumber =     "MR1606580 (98m:11141)",
  MRreviewer =   "Marc Del{\'e}glise",
  bibdate =      "Thu Nov 8 14:50:38 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematica Balkanica. New Series",
}

@InProceedings{Stelling:1997:IMA,
  author =       "Paul F. Stelling and Voji. G. Oklobdzija",
  title =        "Implementing Multiply-Accumulate Operation In
                 Multiplication Time",
  crossref =     "Lang:1997:ISC",
  pages =        "99--107",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Stelling.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@Article{Strzebonski:1997:CFC,
  author =       "Adam Wojciech Strzebo{\'n}ski",
  title =        "Computing in the Field of Complex Algebraic Numbers",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "24",
  number =       "6",
  pages =        "647--656",
  month =        dec,
  year =         "1997",
  CODEN =        "JSYCEH",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  MRclass =      "68Q40",
  MRnumber =     "98h:68125",
  bibdate =      "Tue Nov 10 06:53:22 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171/",
}

@InProceedings{Szabo:1997:REAa,
  author =       "T. Szabo and G. Horvath",
  booktitle =    "Acoustics, Speech, and Signal Processing, 1997.
                 {ICASSP-97., 1997} {IEEE} International Conference on.
                 21--24 April 1997",
  title =        "A roundoff error analysis of the {Oja}'s subspace
                 rule",
  volume =       "4",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "3297--3300",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper deals with the effects of finite precision
                 data representation and arithmetic in principal
                 component analysis (PCA) networks. PCA or Karhunen
                 Loeve transform (KLT) is a statistical method that
                 determines an optimal linear transformation \ldots{}",
}

@InProceedings{Szabo:1997:REAb,
  author =       "T. Szabo and G. Horvath",
  booktitle =    "Instrumentation and Measurement Technology Conference,
                 1997. {IMTC/97}. Proceedings. 'Sensing, Processing,
                 Networking'., {IEEE. 19--21} May 1997",
  title =        "Roundoff error analysis of the {PCA} networks",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "263--268",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper deals with some of the effects of finite
                 precision data representation and arithmetics in
                 principal component analysis (PCA) neural networks. The
                 PCA networks are single layer linear neural networks
                 that use some versions of Oja's \ldots{}",
}

@Misc{Taborn:1997:DSM,
  author =       "M. P. Taborn and S. M. Burchfiel and D. T. Matheny",
  title =        "Denormalization system and method of operation",
  day =          "8",
  month =        jul,
  year =         "1997",
  bibdate =      "Fri Nov 28 15:28:39 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "U.S. Patent No. 5,646,875.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Takagi:1997:GPO,
  author =       "Naofumi Takagi",
  title =        "Generating a Power of an Operand by a Table Look-Up
                 and a Multiplication",
  crossref =     "Lang:1997:ISC",
  pages =        "126--131",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Takagi.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@Manual{TI:1997:TUG,
  title =        "{TMS320C3x} User's Guide",
  organization = "Texas Instruments",
  address =      "Post Office box 655303, Dallas, TX 75265, USA",
  year =         "1997",
  bibdate =      "Wed Nov 24 09:20:17 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www-s.ti.com/sc/psheets/spru031e/spru031e.pdf;
                 http://www-s.ti.com/sc/psheets/spru031f/spru031f.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "digital signal processor (DSP)",
  remark =       "No longer accessible at the first URL. A 2004 edition
                 is at the second URL.",
}

@InProceedings{Tomabechi:1997:WOD,
  author =       "N. Tomabechi",
  booktitle =    "Proceedings of 1997 {IEEE} International Symposium on
                 Circuits and Systems, {ISCAS '97}, 9--12 June 1997",
  title =        "{WSI} oriented design for noise-tolerant systems based
                 on the residue number system",
  volume =       "4",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2733--2736",
  year =         "1997",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1997.612890",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper presents a design method for noise-tolerant
                 WSI systems in which the features of the residue number
                 system and multiple clock pulses are effectively
                 combined. The analysis shows that the reliability of
                 the presented system is greatly \ldots{}",
}

@Article{Tsai:1997:FPR,
  author =       "Chimin Tsai",
  title =        "Floating-point roundoff noises of first- and
                 second-order sections in parallel form digital
                 filters",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "44",
  number =       "9",
  pages =        "774--779",
  month =        sep,
  year =         "1997",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.625021",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems. 2, Analog
                 and Digital Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  summary =      "Assuming wide-sense stationary white noise input, we
                 investigated the floating-point roundoff noises of
                 first- and second order digital subfilters. For
                 first-order subfilters, the roundoff noise of parallel
                 form 3P realization is invariably smaller \ldots{}",
}

@InProceedings{Turner:1997:FFR,
  author =       "Peter R. Turner",
  title =        "Fraction-Free {RNS} Algorithms for Solving Linear
                 Systems",
  crossref =     "Lang:1997:ISC",
  pages =        "218--224",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Turner.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@Book{Ueberhuber:1997:NCM,
  author =       "Christoph W. Ueberhuber",
  title =        "Numerical Computation: Methods, Software, and
                 Analysis",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xvi + 474 (vol. 1), xvi + 495 (vol. 2)",
  year =         "1997",
  DOI =          "https://doi.org/10.1007/978-3-642-59118-1",
  ISBN =         "3-540-62058-3 (vol. 1: softcover), 3-540-62057-5 (vol.
                 2: softcover), 3-642-59118-3 (e-book)",
  ISBN-13 =      "978-3-540-62058-7 (vol. 1: softcover),
                 978-3-540-62057-0 (vol. 2: softcover),
                 978-3-642-59118-1 (e-book)",
  LCCN =         "QA297 .U2413 1997",
  bibdate =      "Thu Oct 28 15:17:48 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana1990.bib",
  price =        "US\$44.95 (vol. 1), US\$49.95 (vol. 2)",
  abstract =     "This book is the first part of a modern, two-volume
                 introduction to numerical computation, which strongly
                 emphasizes software aspects. It can serve as a textbook
                 for courses on numerical analysis, particularly for
                 engineers. The book can also be used as a reference
                 book and it includes an extensive bibliography. The
                 author is a well-known specialist in numerical analysis
                 who was involved in the creation of the software
                 package QUADPACK.",
  acknowledgement = ack-nhfb,
  tableofcontents = "1 Scientific Modeling \\
                 1.1 Reality Versus Model \\
                 1.2 The Model Subject and the Model \\
                 1.3 The Model Subject and Reality \\
                 1.4 Model Building \\
                 2 Fundamental Principles of Numerical Methods \\
                 2.1 From Application Problems to their Numerical
                 Solution \\
                 2.2 Numerical Problems \\
                 2.3 Types of Errors in Numerics \\
                 2.4 The Condition of Mathematical Problems \\
                 2.5 The Condition of Application Problems \\
                 2.6 The Mathematical Elements of Condition Estimation
                 \\
                 2.7 Validation of Numerical Computations \\
                 3 Computers for Numerical Data Processing \\
                 3.1 Processors \\
                 3.2 Memory \\
                 3.3 Performance Quantification \\
                 3.4 Analytical Performance Assessment \\
                 3.5 Empirical Performance Assessment \\
                 4 Numerical Data and Numerical Operations \\
                 4.1 Mathematical Data \\
                 4.2 Numerical Data on Computers \\
                 4.3 Operations on Numerical Data \\
                 4.4 Number Systems on Computers \\
                 4.5 Structure of Floating-Point Systems \\
                 4.6 Standardization of Floating-Point Number Systems
                 \\
                 4.7 Arithmetics for Floating-Point Systems \\
                 4.8 Inquiry Functions and Manipulation of Numbers in
                 Fortran 90 \\
                 4.9 Operations with Algebraic Data \\
                 4.10 Operations with Arrays \\
                 4.11 Operations with Analytic Data \\
                 5 Numerical Algorithms \\
                 5.1 The Intuitive Notion of an Algorithm \\
                 5.2 Properties of Algorithms \\
                 5.3 Existence of Algorithms \\
                 5.4 Practical Solvability of Problems \\
                 5.5 Complexity of Algorithms \\
                 5.6 Representation of Algorithms \\
                 5.7 Influence of Rounding Errors on Numerical
                 Algorithms \\
                 5.8 Case Study: Floating-Point Summation \\
                 6 Numerical Programs \\
                 6.1 The Quality of Numerical Programs \\
                 6.2 Reasons for Poor Efficiency \\
                 6.3 The Measurement of Performance Indices \\
                 6.4 Performance Optimization \\
                 6.5 Architecture Independent Optimizations \\
                 6.6 Loop Optimizations \\
                 6.7 Blocked Memory Access \\
                 6.8 Case Study: Multiplication of Matrices \\
                 7 Available Numerical Software \\
                 7.1 The Cost of Software \\
                 7.2 Sources of Numerical Software \\
                 7.3 Software and the Internet \\
                 7.4 Interactive Multifunctional Systems \\
                 7.5 Problem Solving Environments \\
                 7.6 Case Study: Software for Elliptic PDEs \\
                 8 Using Approximation in Mathematical Model Building
                 \\
                 8.1 Analytic Models \\
                 8.2 Information and Data \\
                 8.3 Discrete Approximation \\
                 8.4 Function Approximation \\
                 8.5 Choosing a Model Function \\
                 8.6 Choice of the Distance Function \\
                 8.7 Transformation of the Problem \\
                 9 Interpolation \\
                 9.1 Interpolation Problems \\
                 9.2 Mathematical Foundations \\
                 9.3 Univariate Polynomial Interpolation \\
                 9.4 Univariate, Piecewise, Polynomial Interpolation \\
                 9.5 Polynomial Splines \\
                 9.6 B-Splines \\
                 9.7 Cubic Spline Interpolation \\
                 9.8 Splines Without Undesirable Oscillations \\
                 9.9 Multivariate Interpolation \\
                 9.10 Multivariate Polynomial Interpolation \\
                 9.11 Multivariate (Sub-) Spline Interpolation \\
                 9.12 Related Problems and Methods \\
                 Glossary of Notation \\
                 Author Index",
}

@Article{Verschaeren:1997:NPF,
  author =       "Dennis Verschaeren and Annie Cuyt and Brigitte
                 Verdonk",
  title =        "On the Need for Predictable Floating-Point Arithmetic
                 in the Programming Languages {Fortran 90} and {C\slash
                 C++}",
  journal =      j-SIGPLAN,
  volume =       "32",
  number =       "3",
  pages =        "57--64",
  month =        mar,
  year =         "1997",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:17:30 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}

@InProceedings{Walter:1997:EUD,
  author =       "Colin D. Walter",
  title =        "Exponentiation using Division Chains",
  crossref =     "Lang:1997:ISC",
  pages =        "92--98",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith13/papers/ARITH13_Walter.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
}

@Article{Walter:1997:STT,
  author =       "C. D. Walter",
  title =        "Space\slash time trade-offs for higher radix modular
                 multiplication using repeated addition",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "2",
  pages =        "139--141",
  month =        feb,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.565588",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=565588",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Wang:1997:MSM,
  author =       "Shaoyun Wang and V. Piuri and E. E. Swartzlander",
  booktitle =    "{1997 IEEE International Symposium on Circuits and
                 Systems (ISCAS)}",
  title =        "Merged scaling multiplication {CORDIC} algorithm",
  volume =       "4",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2581--2584 (vol. 4)",
  year =         "1997",
  DOI =          "https://doi.org/10.1109/ISCAS.1997.612852",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Application software; Arithmetic; Clocks; Complexity
                 theory; Computer applications; Control system
                 synthesis; Iterative algorithms; Signal processing
                 algorithms; Throughput; Very large scale integration",
}

@Article{Wilkes:1997:AE,
  author =       "M. V. Wilkes",
  title =        "Arithmetic on the {EDSAC}",
  journal =      j-IEEE-ANN-HIST-COMPUT,
  volume =       "19",
  number =       "1",
  pages =        "13--15",
  month =        jan # "\slash " # mar,
  year =         "1997",
  CODEN =        "IAHCEX",
  DOI =          "https://doi.org/10.1109/85.560726",
  ISSN =         "1058-6180 (print), 1934-1547 (electronic)",
  ISSN-L =       "1058-6180",
  bibdate =      "Thu Jul 12 08:14:44 MDT 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeeannhistcomput.bib",
  URL =          "https://ieeexplore.ieee.org/iel4/85/12228/00560726.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Ann. Hist. Comput.",
  fjournal =     "IEEE Annals of the History of Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85",
}

@Article{Williams:1997:IPC,
  author =       "C. Williams",
  title =        "{Intel}'s {Pentium} chip crisis: an ethical analysis",
  journal =      j-IEEE-TRANS-PROF-COMMUN,
  volume =       "40",
  number =       "1",
  pages =        "13--19",
  month =        mar,
  year =         "1997",
  CODEN =        "IEPCBU",
  DOI =          "https://doi.org/10.1109/47.557513",
  ISSN =         "0361-1434 (print), 1558-1500 (electronic)",
  ISSN-L =       "0361-1434",
  bibdate =      "Sat Dec 18 11:57:01 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransprofcommun.bib",
  abstract =     "In October 1994 a mathematics professor informed the
                 Intel Corporation that its Pentium chip had a flaw
                 which caused mathematical errors. Intel's response to
                 the professor and its customers created a backlash of
                 anger and a public relations crisis. By analyzing
                 Intel's actions using the work of two relevant ethical
                 philosophies, the article shows that some of the
                 company's errors in public relations were also ethical
                 errors. However, it also points out that Intel has made
                 improvements which will help it avoid future problems
                 and which could set an ethical precedent for the
                 semiconductor industry.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Professional Communication",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=47",
  keywords =     "Pentium divide flaw; Thomas Nicely",
}

@Article{Woehr:1997:CWK,
  author =       "Jack Woehr",
  title =        "A Conversation with {William Kahan}: How important is
                 numerical accuracy?",
  journal =      j-DDJ,
  volume =       "22",
  number =       "11",
  pages =        "18--20, 22, 24, 26, 30, 32",
  month =        nov,
  year =         "1997",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Fri Nov 28 17:28:03 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Kahan, the father of the IEEE 754 floating-point
                 standard, talks about floating-point arithmetic issues,
                 and numerical deficiencies in Java.",
  abstract =     "Noted mathematician and computer scientist William
                 Kahan has played a central role in everything from the
                 design of the 8087 math coprocessor to defining the
                 ANSI\slash IEEE Standard for binary floating-point
                 arithmetic. He takes time out of his schedule to talk
                 with us about the current state of numeric computing.",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@Article{Xue:1997:DPK,
  author =       "Jinyun Xue and Ruth Davis",
  title =        "A Derivation and Proof of {Knuth}'s Binary to Decimal
                 Conversion Program",
  journal =      j-SOFTW-CONCEPTS-TOOLS,
  volume =       "18",
  number =       "4",
  pages =        "149--156",
  year =         "1997",
  CODEN =        "SCOTE5",
  ISSN =         "0945-8115 (print), 1432-2188 (electronic)",
  ISSN-L =       "0945-8115",
  bibdate =      "Sat Jan 6 12:49:28 2024",
  bibsource =    "dblp computer science bibliography; https://dblp.org;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/structprogram.bib",
  acknowledgement = ack-nhfb,
  biburl =       "https://dblp.org/rec/journals/stp/XueD97.bib",
  dblp-id =      "DBLP:journals/stp/XueD97",
  fjournal =     "Software---Concepts and Tools",
  journal-URL =  "https://link.springer.com/journal/378",
  timestamp =    "Thu Feb 26 09:17:35 2026",
}

@InProceedings{Zeng:1997:REA,
  author =       "Bing Zeng",
  booktitle =    "Proceedings of 1997 {IEEE} International Symposium on
                 Circuits and Systems: {ISCAS '97}, 9--12 June 1997",
  title =        "Roundoff error analysis of floating-point paraunitary
                 filter banks realized in lattice structure",
  volume =       "4",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2405--2408",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Floating-point roundoff noise characteristics of
                 two-channel paraunitary filter banks realized in
                 lattice structure are studied in detail in this paper.
                 Under the assumption that all quantization errors are
                 independent WSS white noise with zero-mean, \ldots{}",
}

@Article{Aberbour:1998:PMF,
  author =       "M. Aberbour and A. Houelle and H. Mehrez and N.
                 Vaucher and A. Guyot",
  title =        "On portable macrocell {FPU} generators for division
                 and square root operators complying to the full
                 {IEEE-754} standard",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "6",
  number =       "1",
  pages =        "114--121",
  month =        mar,
  year =         "1998",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/92.661253",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
  summary =      "In this paper, we investigate the design of macrocell
                 generators of division and square root floating-point
                 operators. The number representation used in our
                 operators is the IEEE-754-1985 standard for binary
                 floating-point numbers. The design and \ldots{}",
}

@Book{Aberth:1998:PNM,
  author =       "Oliver Aberth",
  title =        "Precise numerical methods using {C++}",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xiv + 238",
  year =         "1998",
  ISBN =         "0-12-041750-2",
  ISBN-13 =      "978-0-12-041750-6",
  LCCN =         "QA76.73.C153 A32 1998",
  bibdate =      "Wed Nov 3 09:30:14 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Contents: I. Introduction -- II. Various Arithmetics
                 -- III. Solvable Problems and Nonsolvable Problems --
                 IV. Computing Derivatives and Integrals -- V. Finding
                 Zeros of Real Functions -- VI. Finding Zeros of
                 Polynomials and Other Analytic Functions -- VII.
                 Problems of Linear Algebra -- VIII. Optimization
                 Problems -- IX. Numerical Solution of Ordinary
                 Differential Equations -- X. The C++ System for Precise
                 Computation.",
  price =        "US\$59.95",
  acknowledgement = ack-nhfb,
  keywords =     "C (computer program language); numerical analysis --
                 data processing",
}

@Article{Al-Twaijry:1998:SPB,
  author =       "H. A. Al-Twaijry and S. F. Oberman and S. T. Fu and M.
                 J. Flynn",
  title =        "The {SNAP} Project: Building Validated Floating
                 Point",
  journal =      j-J-UCS,
  volume =       "4",
  number =       "2",
  pages =        "99--109",
  day =          "28",
  month =        feb,
  year =         "1998",
  CODEN =        "????",
  ISSN =         "0948-6968",
  ISSN-L =       "0948-6968",
  bibdate =      "Wed Mar 4 15:32:49 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://medoc.springer.de:8000/jucs/jucs_4_2/the_snap_project_building;
                 http://www.jucs.org/jucs_4_2/the_snap_project_building/Al_twaijry_H_A.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
}

@Article{Al-Twaijry:1998:TSE,
  author =       "H. A. Al-Twaijry and M. J. Flynn",
  title =        "Technology scaling effects on multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "11",
  pages =        "1201--1215",
  month =        nov,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.736430",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=736430",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Althaus:1998:MNF,
  author =       "Ernst Althaus and Kurt Mehlhorn",
  title =        "Maximum network flow with floating point arithmetic",
  journal =      j-INFO-PROC-LETT,
  volume =       "66",
  number =       "3",
  pages =        "109--113",
  day =          "15",
  month =        may,
  year =         "1998",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Sat Nov 7 17:55:59 MST 1998",
  bibsource =    "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/
                 2/; https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}

@Article{Anonymous:1998:ANO,
  author =       "Anonymous",
  title =        "Announcements: New Official {Fortran} Technical
                 Reports; Working Group 5 Documents; {OpenGL} {Fortran
                 95} Bindings; {MPI} Module Provides Enhanced {Fortran}
                 Support; Variable Precision Arithmetic; {Fortran}
                 Information Sites; New {Fortran} Compiler Versions from
                 {Lahey} and {Fujitsu}; Downloadable Advanced {Fortran}
                 Textbook; {Fortran} Engineering Textbook",
  journal =      j-FORTRAN-FORUM,
  volume =       "17",
  number =       "3",
  pages =        "1--2",
  month =        dec,
  year =         "1998",
  CODEN =        "????",
  ISSN =         "1061-7264 (print), 1931-1311 (electronic)",
  ISSN-L =       "1061-7264",
  bibdate =      "Thu Feb 07 13:34:54 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Fortran Forum",
  issue =        "53",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J286",
}

@Article{Anonymous:1998:PIS,
  author =       "Anonymous",
  title =        "Papers from the {13th IEEE Symposium on Computer
                 Arithmetic}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "7",
  pages =        "721--721",
  month =        jul,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.1998.709371",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:55 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709371",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Antelo:1998:CVH,
  author =       "E. Antelo and T. Lang and J. D. Bruguera",
  title =        "Computation of $ \sqrt {(x / d)} $ in a very high
                 radix combined division\slash square-root unit with
                 scaling and selection by rounding",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "2",
  pages =        "152--161",
  month =        feb,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.663761",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:53 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=663761",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "A very-high radix digit-recurrence algorithm for the
                 operation {\surd}(x/d) is developed, with residual
                 scaling and digit selection by rounding. This is an
                 extension of the division and square-root algorithms
                 presented previously, and for which a \ldots{}",
}

@Book{Appel:1998:MCI,
  author =       "Andrew W. Appel",
  title =        "Modern Compiler Implementation in {ML}",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "x + 538",
  year =         "1998",
  DOI =          "https://doi.org/10.1017/CBO9780511811449",
  ISBN =         "0-521-58274-1, 0-521-60764-7 (paperback)",
  ISBN-13 =      "978-0-521-58274-2, 978-0-521-60764-3 (paperback)",
  LCCN =         "QA76.76.C65 A675 1998",
  bibdate =      "Sat Apr 1 07:46:22 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://proquest.safaribooksonline.com/9781107263826;
                 http://www.loc.gov/catdir/description/cam028/97031091.html;
                 http://www.loc.gov/catdir/toc/cam023/97031091.html",
  abstract =     "This new, expanded textbook describes all phases of a
                 modern compiler: lexical analysis, parsing, abstract
                 syntax, semantic actions, intermediate representations,
                 instruction selection via tree matching, dataflow
                 analysis, graph-coloring register allocation, and
                 runtime systems. It includes good coverage of current
                 techniques in code generation and register allocation,
                 as well as functional and object-oriented languages,
                 that are missing from most books. In addition, more
                 advanced chapters are now included so that it can be
                 used as the basis for two-semester or graduate course.
                 The most accepted and successful techniques are
                 described in a concise way, rather than as an
                 exhaustive catalog of every possible variant. Detailed
                 descriptions of the interfaces between modules of a
                 compiler are illustrated with actual C header files.
                 The first part of the book, Fundamentals of
                 Compilation, is suitable for a one-semester first
                 course in compiler design. The second part, Advanced
                 Topics, which includes the advanced chapters, covers
                 the compilation of object-oriented and functional
                 languages, garbage collection, loop optimizations, SSA
                 form, loop scheduling, and optimization for
                 cache-memory hierarchies.",
  acknowledgement = ack-nhfb,
  author-dates = "1960--",
  subject =      "ML (Computer program language); Compilers (Computer
                 programs); Compilers (Computer programs); ML (Computer
                 program language); Compiler",
  tableofcontents = "Part I. Fundamentals of Compilation: \\
                 1. Introduction \\
                 2. Lexical analysis \\
                 3. Parsing \\
                 4. Abstract syntax \\
                 5. Semantic analysis \\
                 6. Activation records \\
                 7. Translation to intermediate code \\
                 8. Basic blocks and traces \\
                 9. Instruction selection \\
                 10. Liveness analysis \\
                 11. Register allocation \\
                 12. Putting it all together \\
                 Part II. Advanced Topics: \\
                 13. Garbage collection \\
                 14. Object-oriented languages \\
                 15. Functional programming languages \\
                 16. Polymorphic types \\
                 17. Dataflow analysis \\
                 18. Loop optimizations \\
                 19. Static single-assignment form \\
                 20. Pipelining and scheduling \\
                 21. The memory hierarchy",
}

@Article{Arnold:1998:ACT,
  author =       "M. G. Arnold and T. A. Bailey and J. R. Cowles and M.
                 D. Winkel",
  title =        "Arithmetic co-transformations in the real and complex
                 logarithmic number systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "7",
  pages =        "777--786",
  month =        jul,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.709377",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:55 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709377",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Bailey:1998:OEF,
  author =       "Daniel V. Bailey and Christof Paar",
  title =        "Optimal Extension Fields for Fast Arithmetic in
                 Public-Key Algorithms",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1462",
  pages =        "472--??",
  year =         "1998",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:52:43 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1462.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1462/14620472.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1462/14620472.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Bajard:1998:NED,
  author =       "Jean-Claude Bajard and Laurent-St{\'e}phane Didier and
                 Jean-Michel Muller",
  title =        "A New {Euclidean} Division Algorithm for Residue
                 Number Systems",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "19",
  number =       "2",
  pages =        "167--178",
  month =        jul,
  year =         "1998",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1023/A:1008065819322",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Ingenta database",
  abstract =     "We propose a new algorithm and architecture for
                 performing divisions in residue number systems (RNS).
                 Our algorithm is suitable for RNS with large moduli,
                 with the aim of manipulating very large integers on a
                 parallel computer or a special-purpose architecture.
                 The two basic features of our algorithm are the use of
                 a high-radix division method, and the use of a
                 floating-point arithmetic that should run in parallel
                 with the modular arithmetic.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
  keywords =     "residue number systems (RNS)",
  pagecount =    "12",
}

@Article{Bajard:1998:RMM,
  author =       "J.-C. Bajard and L.-S. Didier and P. Kornerup",
  title =        "An {RNS} {Montgomery} modular multiplication
                 algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "7",
  pages =        "766--776",
  month =        jul,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.709376",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:55 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709376",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Bhardwaj:1998:RRN,
  author =       "M. Bhardwaj and B. Ljusanin",
  booktitle =    "Conference Record of the Thirty-Second Asilomar
                 Conference on Signals, Systems {\&} Computers, 1998",
  title =        "The {Renaissance} --- a residue number system based
                 vector co-processor for {DSP} dominated embedded
                 {ASICs}",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "202--207",
  year =         "1998",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ACSSC.1998.750854",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper reports our ongoing investigation of a new
                 paradigm to realize high performance DSP architectures
                 suitable for embedded ASICs. The reasons for the
                 significant gap between achievable MAC bandwidth and
                 that delivered by current embedded DSP \ldots{}",
}

@Misc{Bjorksten:1998:FFP,
  author =       "A. A. Bjorksten and J. D. G. Mikan and M. S.
                 Schmookler",
  title =        "Fast floating point results alignment apparatus",
  day =          "9",
  month =        jun,
  year =         "1998",
  bibdate =      "Fri Nov 28 15:36:39 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "U.S. Patent No. 5,764,549.",
  acknowledgement = ack-nhfb,
}

@Misc{Briggs:1998:DFP,
  author =       "Keith Briggs",
  title =        "Doubledouble floating point arithmetic",
  howpublished = "World-Wide Web document.",
  institution =  "Department of Plant Sciences, University of
                 Cambridge",
  address =      "Downing Street, Cambridge CB2 3EA, UK",
  year =         "1998",
  bibdate =      "Wed Nov 24 08:26:24 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://web.archive.org/web/20000520034826/http://www-epidem.plantsci.cam.ac.uk/~kbriggs/doubledouble.html;
                 http://web.archive.org/web/20000815202251/http://www-epidem.plantsci.cam.ac.uk/~kbriggs/doubledouble.html;
                 http://web.archive.org/web/20001207115000/http://www-epidem.plantsci.cam.ac.uk/~kbriggs/doubledouble.html;
                 http://web.archive.org/web/20010204072400/http://web.archive.org/web/20010204072400/http://www-epidem.plantsci.cam.ac.uk/~kbriggs/doubledouble.tgz;
                 http://web.archive.org/web/20010204072400/http://www-epidem.plantsci.cam.ac.uk/~kbriggs/doubledouble.html;
                 http://www-epidem.plantsci.cam.ac.uk/~kbriggs/doubledouble.html",
  acknowledgement = ack-nhfb,
  remark =       "Author no longer at Cambridge, and Web page gone;
                 however, www.archive.org has saved it (see the second
                 URL)",
}

@InProceedings{Bronnimann:1998:IAY,
  author =       "Herv{\'e} Br{\"o}nnimann and Christoph Burnikel and
                 Sylvain Pion",
  booktitle =    "Proc. 14th Annu. {ACM} Sympos. Comput. Geom. (1998)",
  title =        "Interval arithmetic yields efficient dynamic filters
                 for computational geometry",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "165--174",
  year =         "1998",
  bibdate =      "Fri Jan 6 11:53:51 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "citeseer.csail.mit.edu/onnimann98interval.html",
  abstract =     "We discuss floating-point filters as a means of
                 restricting the precision needed for arithmetic
                 operations while still computing the exact result. We
                 show that interval techniques can be used to speed up
                 the exact evaluation of geometric predicates and
                 describe an efficient implementation of interval
                 arithmetic that is strongly influenced by the rounding
                 modes of the widely used IEEE 754 standard. Using this
                 approach we engineer an efficient floating-point filter
                 for the computation of the sign of a determinant that
                 works for arbitrary dimensions. We validate our
                 approach experimentally, comparing it with other
                 static, dynamic and semi-static filters.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chang:1998:HPD,
  author =       "Yun-Nan Chang and Keshab K. Parhi",
  title =        "High-Performance Digit-Serial Complex-Number
                 Multiplier-Accumulator",
  crossref =     "IEEE:1998:IIC",
  pages =        "211--??",
  year =         "1998",
  DOI =          "https://doi.org/10.1109/ICCD.1998.727050",
  bibdate =      "Sat Aug 22 08:31:58 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper presents a fast highly regular digit-serial
                 complex-number multiplier-accumulator (CMAC)
                 architecture which is well suited for VLSI
                 implementations. This paper makes two contributions.
                 First, several complex-number representation schemes
                 are discussed. It is shown that the real-imaginary
                 alternate (RIA) scheme is the best among all
                 representation schemes and the prior designs of CMACs
                 based on the radix-(2j) Redundant Complex Number System
                 (RCNS) are not efficient with respect to hardware
                 complexity and processing speed. Second, digit-serial
                 CMAC architectures which can be pipelined at fine-grain
                 level to increase the throughput rate are designed
                 based on carry-save configuration.",
  acknowledgement = ack-nhfb,
  keywords =     "complex-number; digit-serial multiplier; redundant
                 arithmetic",
}

@Misc{Chatterjee:1998:MMP,
  author =       "Siddhardtha Chatterjee",
  title =        "{MPFUN++}: a multiple precision floating point
                 computation package in {C++}",
  howpublished = "World Wide Web document.",
  year =         "1998",
  bibdate =      "Thu Nov 25 10:08:42 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.unc.edu/Research/HARPOON/mpfun++/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chen:1998:PCL,
  author =       "Chichyang Chen and Chih-Huan Yang",
  booktitle =    "Proceedings International Conference on Computer
                 Design: {VLSI} in Computers and Processors: {ICCD
                 '98}",
  title =        "Pipelined computation of {LNS} addition\slash
                 subtraction with very small lookup tables",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "292--297",
  year =         "1998",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Logarithmic number system (LNS) has the advantages of
                 regular data flow high speed, and high precision.
                 However, the development of LNS arithmetic is hindered
                 by the large size of the lookup tables used in LNS
                 addition/subtraction, since the size is \ldots{}",
}

@TechReport{Chen:1998:VFP,
  author =       "Yirng-An Chen and Randal E. Bryant",
  title =        "Verification of floating-point adders",
  type =         "Report",
  number =       "CMU-CS-98-121",
  institution =  "Department of Computer Science, Carnegie-Mellon
                 University",
  address =      "Pittsburgh, PA, USA",
  year =         "1998",
  bibdate =      "Thu May 09 08:44:02 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Cheon:1998:TEA,
  author =       "Jung Hee Cheon and S. M. Park and S. W. Park and D.
                 Kim",
  title =        "Two efficient algorithms for arithmetic of elliptic
                 curves using {Frobenius} map",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1431",
  pages =        "195--??",
  year =         "1998",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Thu Oct 31 17:36:21 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Chren:1998:OHR,
  author =       "W. A. Chren",
  title =        "One-Hot Residue Coding for Low Delay Power Product
                 {CMOS} Design",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "45",
  number =       "3",
  pages =        "303--313",
  month =        mar,
  year =         "1998",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Jun 24 18:14:56 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
}

@Article{Citron:1998:AMM,
  author =       "Daniel Citron and Dror Feitelson and Larry Rudolph",
  title =        "Accelerating Multi-Media processing by Implementing
                 Memoing in Multiplication and Division Units",
  journal =      j-SIGPLAN,
  volume =       "33",
  number =       "11",
  pages =        "252--261",
  month =        nov,
  year =         "1998",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sat May 1 15:51:26 MDT 1999",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/asplos/291069/p252-citron/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "design; measurement; performance; theory",
  remark =       "This paper shows how memoing of multiply and divide
                 units in a 32-entry four-way set associative memo cache
                 can produces cache hit ratios of 0.11 for
                 floating-point multiply, and 0.16 for floating-point
                 divide on the Perfect benchmarks. For SPEC95, the
                 corresponding results are 0.20 and 0.17. For a
                 multimedia benchmark, the figures are 0.39 and 0.47,
                 and for integer multiply 0.59. Current architectures
                 require 2 to 5 cycles for pipelined floating-point
                 multiply (one result per clock, in the best case), but
                 22 to 40 cycles for floating-point division (not
                 pipelined). Such a cache would require about 1KB of
                 on-chip memory, which is currently feasible, since
                 several architectures offer on-chip caches of up to
                 64KB, and could offer significant speedups for
                 division.",
  subject =      "{\bf H.5.1} Information Systems, INFORMATION
                 INTERFACES AND PRESENTATION, Multimedia Information
                 Systems. {\bf H.5.2} Information Systems, INFORMATION
                 INTERFACES AND PRESENTATION, User Interfaces. {\bf
                 B.3.2} Hardware, MEMORY STRUCTURES, Design Styles,
                 Cache memories.",
}

@Article{Collins:1998:PFB,
  author =       "Robert R. Collins",
  title =        "The {Pentium F00F} Bug",
  journal =      j-DDJ,
  volume =       "23",
  number =       "5",
  pages =        "62, 64--66",
  month =        may,
  year =         "1998",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Sat Jun 05 14:14:22 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/dr-dobbs.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ddj.com/ftp/1998/1998_05/f00fbug.txt;
                 http://www.ddj.com/ftp/1998/1998_05/f00fbug.zip",
  abstract =     "When x86 processors encounter an invalid instruction
                 and the processor is supposed to generate an invalid
                 opcode exception. If this mechanism fails and however
                 and the program can bring the system down -- and that's
                 what happens with the F00F bug. Additional resources
                 include F00FBUG.TXT (listings) and f00fbug.zip (source
                 code).",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}

@Article{Cornea-Hasegan:1998:PIC,
  author =       "Marius Cornea-Hasegan",
  title =        "Proving the {IEEE} Correctness of Iterative
                 Floating-Point Square Root, Divide, and Remainder
                 Algorithms",
  journal =      j-INTEL-TECH-J,
  volume =       "Q2",
  pages =        "11",
  year =         "1998",
  bibdate =      "Fri Jun 01 06:02:08 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://developer.intel.com/technology/itj/q21998/articles/art_3.htm;
                 http://developer.intel.com/technology/itj/q21998/pdf/ieee.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Crenshaw:1998:ISR,
  author =       "Jack W. Crenshaw",
  title =        "Integer Square Roots",
  journal =      j-EMBED-SYS-PROG,
  volume =       "11",
  number =       "2",
  pages =        "15--32",
  month =        feb,
  year =         "1998",
  CODEN =        "EYPRE4",
  ISSN =         "1040-3272",
  bibdate =      "Fri Nov 28 16:31:58 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.embedded.com/98/9802fe2.htm",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "Embedded Systems Programming",
}

@TechReport{Darcy:1998:APE,
  author =       "Joseph D. Darcy and William Kahan",
  title =        "Analysis of {{\em Proposal for Extension to Java
                 Floating Point Semantics, Revision 1}}",
  institution =  "{Java Grande Numerics Working Group}",
  pages =        "18",
  day =          "7",
  month =        aug,
  year =         "1998",
  bibdate =      "Mon May 06 09:08:27 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sonic.net/~jddarcy/Research/jgrande.pdf",
  acknowledgement = ack-nhfb,
}

@MastersThesis{Darcy:1998:BAI,
  author =       "Joseph D. Darcy",
  title =        "{Borneo 1.0}: adding {IEEE 754} floating point support
                 to {Java}",
  type =         "{Master of Science, Plan II}",
  school =       "University of California, Berkeley, Dept. of
                 Electrical Engineering and Computer Sciences",
  address =      "Berkeley, CA, USA",
  pages =        "131",
  year =         "1998",
  LCCN =         "T7.49.1998 D27",
  bibdate =      "Mon May 06 09:01:22 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sonic.net/~jddarcy/Borneo/borneo.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Darcy:1998:EJF,
  author =       "Joseph D. Darcy",
  title =        "Evolving {Java}'s Floating Point Support: The Good,
                 The Bad, and the Ugly",
  crossref =     "MacKay:1998:PCT",
  pages =        "??--??",
  year =         "1998",
  bibdate =      "Mon May 06 09:11:13 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "31 slides.",
  URL =          "http://www.sonic.net/~jddarcy/Research/cascon.pdf",
  acknowledgement = ack-nhfb,
}

@TechReport{Darcy:1998:WRI,
  author =       "Joseph D. Darcy",
  title =        "Writing robust {IEEE} recommended functions in ``100
                 Pure {Java\TM}''",
  type =         "Report",
  number =       "UCB/CSD-98-1009",
  institution =  "University of California, Berkeley. Computer Science
                 Division",
  address =      "Berkeley, CA, USA",
  month =        aug,
  year =         "1998",
  bibdate =      "Mon May 06 09:03:35 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://sunsite.berkeley.edu/Dienst/UI/2.0/Describe/ncstrl.ucb/CSD-98-1009",
  acknowledgement = ack-nhfb,
}

@InProceedings{Daumas:1998:ELM,
  author =       "Marc Daumas",
  editor =       "????",
  booktitle =    "Architecture and Arithmetic Support for Multimedia,
                 Dagstuhl, Germany",
  title =        "Expansions: lightweight multiple precision
                 arithmetic",
  publisher =    "????",
  address =      "????",
  pages =        "14--??",
  year =         "1998",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Wed Nov 24 07:59:30 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Dimitrov:1998:AME,
  author =       "V. S. Dimitrov and G. A. Jullien and W. C. Miller",
  title =        "An algorithm for modular exponentiation",
  journal =      j-INFO-PROC-LETT,
  volume =       "66",
  number =       "3",
  pages =        "155--159",
  day =          "15",
  month =        may,
  year =         "1998",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Sat Nov 7 17:55:59 MST 1998",
  bibsource =    "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}

@Article{Dimitrov:1998:FRR,
  author =       "V. S. Dimitrov and G. A. Jullien and W. C. Miller",
  title =        "A fast and robust {RNS} algorithm for evaluating signs
                 of determinants",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "35",
  number =       "8",
  pages =        "9--14",
  month =        apr,
  year =         "1998",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:48:48 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122198000418",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Dimitrov:1998:RNS,
  author =       "V. S. Dimitrov and G. A. Jullien and W. C. Miller",
  title =        "A residue number system implementation of real
                 orthogonal transforms",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "46",
  number =       "3",
  pages =        "563--570",
  month =        mar,
  year =         "1998",
  CODEN =        "ITPRED",
  DOI =          "https://doi.org/10.1109/78.661325",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=14431",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Previous work has focused on performing residue
                 computations that are quantized within a dense ring of
                 integers in the real domain. The aims of this paper are
                 to provide an efficient algorithm for the approximation
                 of real input signals, with \ldots{}",
}

@Article{Drolet:1998:NRE,
  author =       "G. Drolet",
  title =        "A new representation of elements of finite fields {$
                 \mathrm {GF}(2^m) $} yielding small complexity
                 arithmetic circuits",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "9",
  pages =        "938--946",
  month =        sep,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.713313",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=713313",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Drolshagen:1998:RNA,
  author =       "A. Drolshagen and C. C. Sekhar and W. Anheier",
  booktitle =    "Eleventh International Conference on {VLSI} Design,
                 1998. Proceedings",
  title =        "A residue number arithmetic based circuit for
                 pipelined computation of autocorrelation coefficients
                 of speech signal",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "122--127",
  year =         "1998",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICVD.1998.646589",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper presents a new design for module
                 multipliers suitable for moduli that are not
                 necessarily prime. The design avoids the need for
                 building special purpose look-up tables. An RNS
                 arithmetic based autocorrelator circuit that uses a
                 large \ldots{}",
}

@InProceedings{Dunay:1998:DFP,
  author =       "Rezso Dunay and Istvan Kollar and Bernard Widrow",
  title =        "Dithering for Floating-Point Number Representation",
  crossref =     "Holub:1998:ILW",
  pages =        "0--1--9--12",
  year =         "1998",
  bibdate =      "Thu Sep 11 07:08:34 2003",
  bibsource =    "http://measure.feld.cvut.cz/dithering98/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://citeseer.nj.nec.com/cache/papers/cs/1878/ftp:zSzzSzftp.mit.bme.huzSzpubzSzstaffzSzkollarzSzpaperszSzditherws.ps.gz/dunay98dithering.ps.gz;
                 http://citeseer.nj.nec.com/dunay98dithering.html",
  abstract =     "Dithering is widely used for decreasing the bias in
                 fixed-point quantization and rounding. Since
                 floating-point digital signal processors (DSP's) and
                 floating-point arithmetic are becoming widely used, it
                 is timely to investigate the necessity and
                 possibilities of dithering for floating-point numbers.
                 The paper introduces a simple model of dithers for
                 floating-point, and discusses its practical use.",
  acknowledgement = ack-nhfb,
  keywords =     "digital signal processor; Dither; DSP; floating-point;
                 quantization; roundoff",
}

@TechReport{ECDG:1998:IER,
  author =       "{European Commission Directorate General II}",
  title =        "The Introduction of the Euro and the Rounding of
                 Currency Amounts",
  type =         "{II/28/99-EN Euro Papers}",
  number =       "22",
  institution =  "European Commission",
  pages =        "32",
  month =        mar,
  year =         "1998",
  bibdate =      "Wed Nov 24 12:56:20 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "DGII/C-4-SP(99) European Commission.",
  acknowledgement = ack-nhfb,
}

@Article{Emiris:1998:MAL,
  author =       "Ioannis Z. Emiris and Victor Y. Pan and Yanqiang Yu",
  title =        "Modular arithmetic for linear algebra computations in
                 the real field",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "26",
  number =       "1",
  pages =        "71--87",
  month =        jul,
  year =         "1998",
  CODEN =        "JSYCEH",
  DOI =          "https://doi.org/10.1006/jsco.1998.0201",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  MRclass =      "15-XX (68Q40)",
  MRnumber =     "1 633 585",
  bibdate =      "Tue Nov 10 06:41:20 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171/",
  keywords =     "accurate floating-point summation; floating-point
                 arithmetic",
}

@InProceedings{Ercegovac:1998:BSO,
  author =       "M. Ercegovac and D. Kirovski and G. Mustafa and M.
                 Potkonjak",
  booktitle =    "Proceedings of the 1998 {IEEE} International
                 Conference on Acoustics, Speech, and Signal Processing,
                 1998: {ICASSP '98}, 12--15 May 1998",
  title =        "Behavioral synthesis optimization using multiple
                 precision arithmetic",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "3113--3116",
  year =         "1998",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:53:44 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Modern image and video processing applications are
                 characterized by a unique combination of arithmetic and
                 computational features: fixed point arithmetic, a
                 variety of short data types, high degree of
                 instruction-level parallelism, strict timing \ldots{}",
}

@InProceedings{Fiore:1998:LR,
  author =       "P. D. Fiore",
  booktitle =    "{IEEE} Workshop on Signal Processing Systems, 1988:
                 {SIPS 98}",
  title =        "Lazy rounding",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "449--458",
  year =         "1998",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Intermediate results in digital signal processing
                 (DSP) hardware frequently must be truncated or rounded
                 to maintain reasonable wordlengths. Noise and bias are
                 introduced into the signal due to these operations. For
                 the addition operation, we \ldots{}",
}

@InProceedings{Garcia:1998:PHC,
  author =       "A. Garcia and U. Meyer-Baese and F. Taylor",
  booktitle =    "Proceedings of the 1998 {IEEE} International
                 Conference on Acoustics, Speech, and Signal Processing,
                 {ICASSP 98}, 12--15 May 1998",
  title =        "Pipelined Hogenauer {CIC} filters using
                 field-programmable logic and residue number system",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "3085--3088",
  year =         "1998",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICASSP.1998.678178",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Field-programmable logic (FPL) is on the verge of
                 revolutionizing digital signal processing (DSP) in the
                 manner that programmable DSP microprocessors did nearly
                 two decades ago. While FPL densities and performance
                 have steadily improved to the point \ldots{}",
}

@Article{Gordon:1998:CLF,
  author =       "Robert Gordon",
  title =        "A Calculated Look at Fixed-Point Arithmetic",
  journal =      j-EMBED-SYS-PROG,
  volume =       "11",
  number =       "4",
  pages =        "72--78",
  month =        apr,
  year =         "1998",
  CODEN =        "EYPRE4",
  ISSN =         "1040-3272",
  bibdate =      "Fri Nov 28 16:54:07 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "Embedded Systems Programming",
}

@PhdThesis{Grisoni-Busca:1998:LPF,
  author =       "Louisa Grisoni-Busca",
  title =        "Low power floating point {A/D} converters for audio
                 signals",
  type =         "Dissertation",
  school =       "Univ. Neuch{\^a}tel",
  address =      "Neuch{\^a}tel, Switzerland",
  pages =        "xii + 136",
  year =         "1998",
  bibdate =      "Thu May 09 09:08:18 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Misc{Grushin:1998:CMA,
  author =       "A. I. Grushin and E. S. Vlasenko",
  title =        "Computer methods and apparatus for eliminating leading
                 non-significant digits in floating point computations",
  day =          "24",
  month =        may,
  year =         "1998",
  bibdate =      "Fri Nov 28 15:34:04 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "U.S. Patent No. 5,732,007.",
  acknowledgement = ack-nhfb,
}

@Article{Guo:1998:SAI,
  author =       "Jyh-Huei Guo and Chin-Liang Wang",
  title =        "Systolic array implementation of {Euclid}'s algorithm
                 for inversion and division in {$ \mathrm {GF}(2^m) $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "10",
  pages =        "1161--1167",
  month =        oct,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.729800",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=729800",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Hars:1998:FCC,
  author =       "L. Hars",
  title =        "Fast Calculation of Common Mathematical Functions with
                 Floating-Point {DSPs}",
  crossref =     "Anonymous:1998:PNI",
  pages =        "521--525",
  year =         "1998",
  bibdate =      "Sat Jun 02 08:32:02 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Heckmann:1998:ABI,
  author =       "Reinhold Heckmann",
  title =        "The Appearance of Big Integers in Exact Real
                 Arithmetic Based on Linear Fractional Transformations",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1378",
  pages =        "172--??",
  year =         "1998",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:51:46 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1378.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1378/13780172.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1378/13780172.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Hill:1998:FDP,
  author =       "Theodore P. Hill",
  title =        "The First Digit Phenomenon",
  journal =      j-AM-SCI,
  volume =       "86",
  number =       "4",
  pages =        "358--363",
  month =        jul # "\slash " # aug,
  year =         "1998",
  CODEN =        "AMSCAC",
  DOI =          "https://doi.org/10.1511/1998.4.358",
  ISSN =         "0003-0996 (print), 1545-2786 (electronic)",
  ISSN-L =       "0003-0996",
  bibdate =      "Sat Dec 10 11:54:49 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://people.math.gatech.edu/~hill/publications/PAPER%20PDFS/TheFirstDigitPhenomenonAmericanScientist1996.pdf;
                 http://www.math.gatech.edu/~hill/publications/cv.dir/1st-dig.pdf",
  abstract =     "A century ago, Simon Newcomb observed an unexpected
                 pattern in the first digits of logarithm tables: The
                 digit $1$ is significantly more likely to occur than
                 $2$, $2$ than $3$, and so on. More than a half-century
                 later, Frank Benford rediscovered the first-digit
                 phenomenon and found that it applied to many tables of
                 numerical data, including the stock market, census
                 statistics and accounting figures. New mathematical
                 insights establish the empirical law developed by
                 Newcomb and Benford as part of modern probability
                 theory, and recent applications include testing of
                 mathematical models, design of computers and detection
                 of fraud in accounting.",
  acknowledgement = ack-nhfb,
  fjournal =     "American Scientist",
  journal-URL =  "http://www.americanscientist.org/issues/past.aspx",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@InProceedings{Huertgen:1998:TFP,
  author =       "F. Huertgen and H. Meyr and M. Willems",
  title =        "Transformation of Floating-Point into Fixed-Point
                 Algorithms by Interpolation Applying a Statistical
                 Approach",
  crossref =     "Anonymous:1998:PNI",
  pages =        "630--634",
  year =         "1998",
  bibdate =      "Sat Jun 02 08:29:37 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hussein:1998:LPA,
  author =       "A. E. Hussein and M. A. Hasan and M. I. Elmasry",
  booktitle =    "{IEEE} Canadian Conference on Electrical and Computer
                 Engineering, 24--28 May 1998",
  title =        "A low power algorithm for division in residue number
                 system ({RNS})",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "205--208",
  year =         "1998",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/CCECE.1998.682718",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A new algorithm for computing division in residue
                 number system (RNS) is presented. The algorithm imposes
                 no restrictions on the dividend and the divisor (except
                 zero divisor), and requires no initial quotient
                 estimation. It eliminates the need for \ldots{}",
}

@InCollection{IBM:1998:DAI,
  author =       "{IBM}",
  booktitle =    "{ESA\slash 390} Principles of Operation",
  title =        "Decimal Arithmetic Instructions",
  chapter =      "8",
  publisher =    pub-IBM,
  address =      pub-IBM:adr,
  year =         "1998",
  bibdate =      "Fri Nov 28 17:57:22 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The decimal instructions of this chapter perform
                 arithmetic and editing operations on decimal data.
                 Additional operations on decimal data are provided by
                 several of the instructions in Chapter 7, ``General
                 Instructions''. Decimal operands always reside in
                 storage, and all decimal instructions use the SS
                 instruction format. Decimal operands occupy storage
                 fields that can start on any byte boundary.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@Book{IEC:1998:IITa,
  author =       "{IEC}",
  title =        "{ISO\slash IEC\slash TR2 15580 (1998-12)}: Information
                 technology --- Programming languages --- {Fortran} ---
                 Floating-point exception handling",
  publisher =    pub-IEC,
  address =      pub-IEC:adr,
  pages =        "27",
  year =         "1998",
  bibdate =      "Mon Apr 24 06:32:09 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$56.00",
  URL =          "http://www.iec.ch/cgi-bin/procgi.pl/www/iecwww.p?wwwlang=E&wwwprog=cat-det.p&wartnum=023454",
  acknowledgement = ack-nhfb,
}

@Book{ISO:1998:IITc,
  author =       "{International Organization for Standardization}",
  title =        "{ISO\slash IEC TR 15580:1998}: {Information}
                 technology --- {Programming} languages --- {Fortran}
                 --- {Floating-point} exception handling",
  publisher =    pub-ISO,
  address =      pub-ISO:adr,
  pages =        "27",
  year =         "1998",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Tue Dec 12 06:45:58 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Available in English only.",
  price =        "CHF 104; US\$72.00",
  URL =          "http://webstore.ansi.org/ansidocstore/product.asp?sku=ISO%2FIEC+TR+15580%3A1998;
                 http://www.iso.ch/cate/d28230.html",
  acknowledgement = ack-nhfb,
  pricecode =    "N",
}

@Article{Jessani:1998:CSD,
  author =       "R. M. Jessani and M. Putrino",
  title =        "Comparison of Single- and Dual-Pass Multiply-Add Fused
                 Floating-Point Units",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "9",
  pages =        "927--937",
  month =        sep,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.713312",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=713312",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "alignment shifter; Booth encoding; floating-point
                 unit; multiply array; multiply-add fused; sign
                 encoding",
  summary =      "Low power, low cost, and high performance factors
                 dictate the design of many microprocessors targeted to
                 the low power computing market. The floating point unit
                 occupies a significant percentage of the silicon area
                 in a microprocessor due its wide data bandwidth (for
                 double-precision computations) and the area occupied by
                 the multiply array. For microprocessors designed for
                 portable products, the design-size of the
                 floating-point unit plays an important role in the low
                 cost factor driven by reduced chip area. Some
                 microprocessors have multiply-add fused floating-point
                 units with a reduced multiply array, requiring two
                 passes through the array for operations involving
                 double-precision multiplies. This paper discusses the
                 design complexities around the dual-pass multiply array
                 and its effect on area and performance. Floating-point
                 unit areas and their associated multiply array areas
                 are compared for a single- and dual-pass implementation
                 in a given technology (PowerPC 604e and PowerPC 603e
                 microprocessors, respectively).",
}

@TechReport{Kahan:1998:HJFa,
  author =       "W. Kahan and Joseph D. Darcy",
  title =        "How {Java}'s Floating-Point Hurts Everyone
                 Everywhere",
  type =         "Technical Report",
  institution =  "Department of Mathematics and Department of Electrical
                 Engineering and Computer Science, University of
                 California, Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "80",
  day =          "18",
  month =        jun,
  year =         "1998",
  bibdate =      "Sat Sep 12 18:53:11 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/JAVAhurt.pdf;
                 http://www.cs.berkeley.edu/~wkahan/JAVAhurt.ps",
  acknowledgement = ack-nhfb,
  remark =       "The authors deliver a biting criticism of Java for its
                 failure to use the 80-bit temporary real format on
                 Intel x86 architectures, failure to use multiply-add
                 instructions when available, and failure to compute
                 float subexpressions in double precision.",
}

@InProceedings{Kahan:1998:HJFb,
  author =       "William Kahan",
  title =        "How {Java}'s Floating-Point Hurts Everyone
                 Everywhere",
  crossref =     "ACM:1998:AWJ",
  pages =        "??--??",
  year =         "1998",
  bibdate =      "Sat Dec 01 07:55:27 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.ucsb.edu/conferences/java98/papers/javahurt.pdf",
  acknowledgement = ack-nhfb,
}

@TechReport{Kahan:1998:IPE,
  author =       "W. Kahan",
  title =        "The Improbability of Probabilistic Error Analyses for
                 Numerical Computations",
  institution =  "Department of Mathematics and Department of Electrical
                 Engineering and Computer Science, University of
                 California, Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "34",
  day =          "10",
  month =        jun,
  year =         "1998",
  bibdate =      "Fri May 03 12:30:29 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/improber.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Kelsey:1998:RRA,
  author =       "Richard Kelsey and William Clinger and Jonathan Rees",
  title =        "Revised$^5$ Report on the Algorithmic Language
                 {Scheme}",
  journal =      j-SIGPLAN,
  volume =       "33",
  number =       "9",
  pages =        "26--76",
  month =        sep,
  year =         "1998",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Tue Sep 15 17:01:28 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "With H. Abelson, N. I. {Adams, IV}, D. H. Bartley, G.
                 Brooks, R. K. Dybvig, D. P. Friedman, R. Halstead, C.
                 Hanson, C. T. Haynes, E. Kohlbecker, D. Oxley, K. M.
                 Pitman, G. J. Rozas, G. L. {Steele Jr.}, G. J. Sussman,
                 and M. Wand.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "decimal floating-point arithmetic",
  remark =       "From \cite{Steele:2004:RHP}: ``the result [of a
                 binary-to-decimal conversion] is expressed using the
                 minimum number of digits\ldots{}''",
}

@Article{Kiranon:1998:SRV,
  author =       "W. Kiranon and N. Kumprasert",
  title =        "Square-rooting and vector summation circuits using
                 current conveyors",
  journal =      "Circuits, Devices and Systems, IEE Proceedings [see
                 also IEE Proceedings G- Circuits, Devices and
                 Systems]",
  volume =       "145",
  number =       "2",
  pages =        "139",
  month =        apr,
  year =         "1998",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
  summary =      "Recently, Lui [1995] presented a square-rooting
                 circuit using CCII, MOS transistors and a buffered
                 unity-gain inverting amplifier. It is interesting since
                 it finds various applications as described in his
                 paper. However, an error occurred in the \ldots{}",
}

@Book{Knuth:1998:SA,
  author =       "Donald E. Knuth",
  title =        "Seminumerical Algorithms",
  volume =       "2",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Third",
  pages =        "xiii + 762",
  year =         "1998",
  ISBN =         "0-201-89684-2",
  ISBN-13 =      "978-0-201-89684-8",
  LCCN =         "QA76.6 .K64 1997",
  bibdate =      "Fri Jul 11 15:41:22 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/css.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/texbook2.bib",
  note =         "See section 4.2.4V, The Fraction Parts, pages
                 254--262, for a discussion of Benford's Law.",
  price =        "US\$52.75",
  series =       "The Art of Computer Programming",
  acknowledgement = ack-nhfb,
  remark =       "Knuth comments on page 255: ``The fact that the
                 leading digits tend to be small makes the most obvious
                 techniques of ``average error'' estimation for floating
                 point calculations invalid. The relative error due to
                 rounding is usually a little more than expected.",
  tableofcontents = "3: Random Numbers / 1 \\
                 3.1. Introduction / 1 \\
                 3.2. Generating Uniform Random Numbers / 10 \\
                 3.2.1. The Linear Congruential Method / 10 \\
                 3.2 1.1. Choice of modulus / 12 \\
                 3.2.1.2 Choice of multiplier / 16 \\
                 3.2.1.3. Potency / 23 \\
                 3.2.2. Other Methods / 26 \\
                 3.3. Statistical Tests / 41 \\
                 3.3.1. General Test Procedures for Studying Random Data
                 / 41 \\
                 3.3.2. Empirical Tests / 61 \\
                 *3.3.3. Theoretical Tests / 80 \\
                 3.3.4. The Spectral Test / 93 \\
                 3.4. Other Types of Random Quantities / 119 \\
                 3.4 1. Numerical Distributions / 119 \\
                 3.4.2. Random Sampling and Shuffling / 142 \\
                 *3.5. What Is a Random Sequence? / 149 \\
                 3.6. Summary / 184 \\
                 4: Arithmetic / 194 \\
                 4.1. Positional Number Systems / 195 \\
                 4.2. Floating Point Arithmetic / 214 \\
                 4.2.1. Single-Precision Calculations / 214 \\
                 4.2 2. Accuracy of Floating Point Arithmetic / 229 \\
                 *4.2.3. Double-Precision Calculations / 246 \\
                 4.2.4. Distribution of Floating Point Numbers / 253 \\
                 4.3 Multiple Precision Arithmetic / 265 \\
                 4.3.1. The Classical Algorithms / 265 \\
                 *4.3.2. Modular Arithmetic / 284 \\
                 *4.3.3. How Fast Can We Multiply? / 294 \\
                 4.4. Radix Conversion / 319 \\
                 4.5. Rational Arithmetic / 330 \\
                 4.5.1. Fractions / 330 \\
                 4.5.2. The Greatest Common Divisor / 333 \\
                 *4.5.3. Analysis of Euclid's Algorithm / 356 \\
                 4.5.4. Factoring into Primes / 379 \\
                 4.6. Polynomial Arithmetic / 418 \\
                 4.6.1. Division of Polynomials / 420 \\
                 *4.6.2. Factorization of Polynomials / 439 \\
                 4.6.3. Evaluation of Powers / 461 \\
                 4.6.4. Evaluation of Polynomials / 485 \\
                 *4.7. Manipulation of Power Series / 525 \\
                 Answers to Exercises / 538 \\
                 Appendix A: Tables of Numerical Quantities / 726 \\
                 1. Fundamental Constants (decimal) / 726 \\
                 2; Fundamental Constants ( octal) / 727 \\
                 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci
                 Numbers / 728 \\
                 Appendix B: Index to Notations / 730 \\
                 Index and Glossary / 735",
}

@Article{Koc:1998:LCB,
  author =       "C. K. Koc and B. Sunar",
  title =        "Low-complexity bit-parallel canonical and normal basis
                 multipliers for a class of finite fields",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "3",
  pages =        "353--356",
  month =        mar,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.660172",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:54 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=660172",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Kramer:1998:PWC,
  author =       "W. Kramer",
  title =        "A priori worst case error bounds for floating-point
                 computations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "7",
  pages =        "750--756",
  month =        jul,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.709374",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:55 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  note =         "See \cite{Tang:1992:TDI}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709374",
  abstract =     "A new technique for the a priori calculation of
                 rigorous error bounds for floating-point computations
                 is introduced. The theorems given in the paper combined
                 with interval arithmetic lead to the implementation of
                 reliable software routines, which enable the user to
                 compute the desired error bounds automatically by a
                 suitable computer program. As a prominent example, a
                 table-lookup algorithm for calculating the function $
                 {\rm exp}(x) - 1 $ that has been published by P. T. P.
                 Tang (1992) is analyzed using these new tools. The
                 result shows the high quality of the new approach",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Kuhlmann:1998:FLP,
  author =       "M. Kuhlmann and K. K. Parhi",
  booktitle =    "Proceedings of the 1998 International Conference on
                 Computer Design: {VLSI} in Computers and Processors.
                 {ICCD '98}",
  title =        "Fast low-power shared division and square-root
                 architecture",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "128--135",
  year =         "1998",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper addresses a fast low-power implementation
                 of a shared division and square-root architecture. Two
                 approaches are considered in this paper; these include
                 the SRT (Sweeney, Robertson and Tocher) approach which
                 does not require prescaling and \ldots{}",
}

@InProceedings{Kwak:1998:ILI,
  author =       "Jae-Hyuek Kwak and E. E. Swartzlander",
  booktitle =    "{Conference Record of Thirty-Second Asilomar
                 Conference on Signals, Systems and Computers (Cat. No.
                 98CH36284)}",
  title =        "An implementation of level-index arithmetic based on
                 the low latency {CORDIC} system",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "208--212 (vol. 1)",
  year =         "1998",
  DOI =          "https://doi.org/10.1109/ACSSC.1998.750855",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Calculators; Computer architecture; Concurrent
                 computing; Costs; Delay; Digital arithmetic; Equations;
                 Hardware; Parallel processing; Timing",
}

@Article{Labrosse:1998:FPA,
  author =       "Jean J. Labrosse",
  title =        "Fixed-Point Arithmetic for Embedded Systems",
  journal =      j-CCCUJ,
  volume =       "16",
  number =       "2",
  pages =        "??--??",
  month =        feb,
  year =         "1998",
  CODEN =        "CCUJEX",
  ISSN =         "1075-2838",
  bibdate =      "Tue May 14 18:09:14 MDT 2002",
  bibsource =    "http://www.cuj.com/articles/1998/9802/9802toc.htm?topic=articles;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Fixed-point arithmetic is fast: you just have to worry
                 more about overflow and significance loss.",
  acknowledgement = ack-nhfb,
  fjournal =     "C/C++ Users Journal",
}

@Article{Langer:1998:CFP,
  author =       "Steven H. Langer and Paul F. Dubois",
  title =        "A comparison of the floating-point performance of
                 current computers",
  journal =      j-COMPUT-PHYS,
  volume =       "12",
  number =       "4",
  pages =        "338--??",
  month =        jul,
  year =         "1998",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.168693",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Wed Apr 10 08:46:15 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.168693",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}

@Article{Langlois:1998:RBR,
  author =       "Ph. Langlois and F. Nativel",
  title =        "Reduction and bounding of the rounding error in
                 floating-point arithmetic",
  journal =      j-C-R-ACAD-SCI-PARIS-SER-I-MATH,
  volume =       "327",
  number =       "??",
  pages =        "781--786",
  year =         "1998",
  CODEN =        "CASMEI",
  ISSN =         "0249-6291",
  bibdate =      "Thu May 27 07:37:54 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Comptes Rendus des S{\'e}ances de l'Acad{\'e}mie des
                 Sciences. S{\'e}rie I. Math{\'e}matique",
  journal-URL =  "http://www.sciencedirect.com/science/journal/1631073X",
}

@InProceedings{Lee:1998:DRN,
  author =       "I. Lee and W. K. Jenkins",
  booktitle =    "Proceedings of the 8th Great Lakes Symposium on {VLSI,
                 1998}",
  title =        "The design of residue number system arithmetic units
                 for a {VLSI} adaptive equalizer",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "179--184",
  year =         "1998",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/GLSV.1998.665222",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper presents the design details of an
                 experimental ASIC for an all-digital adaptive
                 equalizer. In this design, the LMS algorithm is chosen
                 because of its simplicity. The adaptive equalizer
                 design, which is based on an RNS architecture,
                 \ldots{}",
}

@Article{Lefevre:1998:TCR,
  author =       "Vincent Lef{\`e}vre and Jean-Michel Muller and Arnaud
                 Tisserand",
  title =        "Toward correctly rounded transcendentals",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "11",
  pages =        "1235--1243",
  month =        nov,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.736435",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "The Table Maker's Dilemma is the problem of always
                 getting correctly rounded results when computing the
                 elementary functions. After a brief presentation of
                 this problem, we present new developments that have
                 helped us to solve this problem for the
                 double-precision exponential function in a small
                 domain. These new results show that this problem can be
                 solved, at least for the double-precision format, for
                 the most usual functions.",
}

@InProceedings{Ligon:1998:REP,
  author =       "W. B. {Ligon III} and S. McMillan and G. Monn and K.
                 Schoonover and F. Stivers and K. D. Underwood",
  title =        "A re-evaluation of the practicality of floating-point
                 operations on {FPGAs}",
  crossref =     "Pocek:1998:PIS",
  pages =        "206--215",
  year =         "1998",
  DOI =          "https://doi.org/10.1109/FPGA.1998.707898",
  bibdate =      "Sat Oct 9 12:51:26 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The use of reconfigurable hardware to perform high
                 precision operations such as IEEE floating point
                 operations has been limited in the past by FPGA
                 resources. We discuss the implementation of IEEE single
                 precision floating-point multiplication and addition.
                 Then, we assess the practical implications of using
                 these operations in the Xilinx 4000 series FPGAs
                 considering densities available now and scheduled for
                 the near future. For each operation, we present space
                 requirements and performance information. This is
                 followed by a discussion of an algorithm, matrix
                 multiplication, based on these operations, which
                 achieves performance comparable to conventional
                 microprocessors. Algorithm implementation options and
                 their performance implications are discussed and
                 corresponding measured results are given",
  acknowledgement = ack-nhfb,
}

@InProceedings{Looye:1998:MMF,
  author =       "A. Looye and G. Hekstra and E. Deprettere",
  booktitle =    "{1998 IEEE Workshop on Signal Processing Systems. SIPS
                 98. Design and Implementation (Cat. No. 98TH8374)}",
  title =        "Multiport memory and floating-point {CORDIC} pipeline
                 in {Jacobium} processing elements",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "406--416",
  year =         "1998",
  DOI =          "https://doi.org/10.1109/SIPS.1998.715803",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Data analysis; Jacobian matrices; Jacobium dataflow
                 processor; Pipelines; Process design; Symmetric
                 matrices",
}

@Misc{LPT:1998:SC,
  author =       "{Log Point Technologies}",
  title =        "Soft {CoProcessor}",
  howpublished = "World-Wide Web document.",
  month =        jun,
  year =         "1998",
  bibdate =      "Tue Jun 16 13:12:58 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "This product provides software emulation of a
                 logarithmic floating-point representation. Programming
                 support is provided by a drop-in module for the GNU C
                 compiler, {\tt gcc}, and user-callable library support
                 is available for several commercial compilers.",
  URL =          "http://www.logpoint.com/;
                 http://www.logpoint.com/prelimi.htm",
  acknowledgement = ack-nhfb,
}

@Article{Ma:1998:SAM,
  author =       "Yutai Ma",
  title =        "A simplified architecture for modulo $ (2^n + 1) $
                 multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "3",
  pages =        "333--337",
  month =        mar,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.660169",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:54 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=660169",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{McCullough:1998:ARS,
  author =       "B. D. McCullough",
  title =        "Assessing the Reliability of Statistical Software:
                 {Part I}",
  journal =      j-AMER-STAT,
  volume =       "52",
  number =       "4",
  pages =        "358--366",
  month =        nov,
  year =         "1998",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Fri Jan 27 14:51:25 MST 2012",
  bibsource =    "http://www.jstor.org/journals/00031305.html;
                 http://www.jstor.org/stable/i326502;
                 https://www.math.utah.edu/pub/tex/bib/amstat1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.jstor.org/stable/2685442",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@Article{Mohan:1998:EFC,
  author =       "P. V. Ananda Mohan",
  title =        "Evaluation of fast conversion techniques for
                 binary-residue number systems",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-I-FUNDAM-THEORY-APPL,
  volume =       "45",
  number =       "10",
  pages =        "1107--1109",
  month =        oct,
  year =         "1998",
  CODEN =        "ITCAEX",
  DOI =          "https://doi.org/10.1109/81.728866",
  ISSN =         "????",
  ISSN-L =       "1057-7122",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=15711",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems I:
                 Fundamental Theory and Applications",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=81",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Vinnakota and Rao's RNS-to-binary converter proposed
                 recently (see ibid., vol. CAS-41, p. 927-9, 1994) for
                 the moduli set {2 n -1, 2 n and 2 n +1} is shown to be
                 a simple modification of the well-known Mixed Radix
                 \ldots{}",
}

@Article{Montalvo:1998:NST,
  author =       "L. A. Montalvo and K. K. Parhi and A. Guyot",
  title =        "New {Svoboda--Tung} division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "9",
  pages =        "1014--1020",
  month =        sep,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.713319",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=713319",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Moore:1998:CMC,
  author =       "G. E. Moore",
  title =        "Cramming More Components Onto Integrated Circuits",
  journal =      j-PROC-IEEE,
  volume =       "86",
  number =       "1",
  pages =        "82--85",
  month =        jan,
  year =         "1998",
  CODEN =        "IEEPAD",
  DOI =          "https://doi.org/10.1109/jproc.1998.658762",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Fri Nov 14 07:42:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/intel-ia-64.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
  remark =       "Reprint of \cite{Moore:1965:CMC}, with layout changes,
                 and addition of roman numbering on section headings.",
}

@Article{Moore:1998:MCP,
  author =       "J. S. Moore and T. W. Lynch and M. Kaufmann",
  title =        "A mechanically checked proof of the {AMD5 K 86{\TM}}
                 floating-point division program",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "9",
  pages =        "913--926",
  month =        sep,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.713311",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=713311",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "We report on the successful application of a
                 mechanical theorem prover to the problem of verifying
                 the division microcode program used on the AMD5$_K$ 86
                 microprocessor. The division algorithm is an iterative
                 shift and subtract type. It was \ldots{}",
}

@InProceedings{Murabayashi:1998:WBP,
  author =       "F. Murabayashi and T. Yamauchi and R. Yamagata and T.
                 Shimizu",
  title =        "A {400MHz} 160-Word $ \times $ 64-Bit 14-Port
                 Floating-point Register File Macrocell for a
                 Superscalar {RISC} Processor",
  crossref =     "Huijsing:1998:EPE",
  pages =        "440--443",
  year =         "1998",
  bibdate =      "Sat Jun 02 08:21:00 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Misc{Naffziger:1998:MAB,
  author =       "S. D. Naffziger and R. G. Beraha",
  title =        "Method and apparatus for bounding alignment shifts to
                 enable at speed denormalized result generation in an
                 {FMAC}",
  day =          "26",
  month =        may,
  year =         "1998",
  bibdate =      "Fri Nov 28 15:35:29 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "U.S. Patent No. 5,757,687.",
  acknowledgement = ack-nhfb,
}

@Article{Nguyen:1998:MLS,
  author =       "Phong Nguyen",
  title =        "A {Montgomery}-Like Square Root for the Number Field
                 Sieve",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1423",
  pages =        "151--??",
  year =         "1998",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:52:18 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1423.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1423/14230151.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1423/14230151.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InProceedings{Oberman:1998:ATK,
  author =       "Stuart Oberman and Fred Weber and Norbert Juffa and
                 Greg Favor",
  title =        "{AMD 3DNow!} Technology and the {K6-2}
                 Microprocessor",
  crossref =     "IEEE:1998:HCC",
  pages =        "245--254",
  year =         "1998",
  bibdate =      "Mon Jan 08 17:02:55 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Oberman:1998:MCS,
  author =       "S. F. Oberman and M. J. Flynn",
  title =        "Minimizing the Complexity of {SRT} Tables",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "6",
  number =       "1",
  pages =        "141--149",
  month =        "????",
  year =         "1998",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/92.661256",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Fri Mar 27 09:56:17 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
}

@Article{Oberman:1998:RML,
  author =       "S. F. Oberman and M. J. Flynn",
  title =        "Reducing the mean latency of floating-point addition",
  journal =      j-THEOR-COMP-SCI,
  volume =       "196",
  number =       "1-2",
  pages =        "201--214",
  day =          "6",
  month =        apr,
  year =         "1998",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed May 27 07:21:35 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C5230 (Digital arithmetic methods)",
  corpsource =   "Comput. Syst. Lab., Stanford University, CA, USA",
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
  keywords =     "adders; floating point arithmetic; floating-point
                 adder; floating-point addition; maximum throughput;
                 mean addition latency; mean latency; microprocessors;
                 shift-add-shift-round data flow; single-cycle
                 throughput",
  pubcountry =   "Netherlands",
  treatment =    "P Practical",
}

@Article{Paar:1998:EMA,
  author =       "C. Paar and P. Fleischmann and P. Roeise",
  title =        "Efficient multiplier architectures for {Galois} fields
                 {$ \mathrm {GF}(2^{4n}) $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "2",
  pages =        "162--170",
  month =        feb,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.663762",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:53 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=663762",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Paul:1998:CBR,
  author =       "Wolfgang J. Paul and Peter-Michael Seidel",
  title =        "On the complexity of {Booth} recoding",
  crossref =     "Chesneaux:1998:PCR",
  pages =        "199--218",
  year =         "1998",
  bibdate =      "Tue Mar 13 10:23:30 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Mueller:2000:CAC}.",
}

@Article{Paulus:1998:CRI,
  author =       "Sachar Paulus and Andreas Stein",
  title =        "Comparing Real and Imaginary Arithmetics for Divisor
                 Class Groups of Hyperelliptic Curves",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1423",
  pages =        "576--??",
  year =         "1998",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:52:18 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1423.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1423/14230576.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1423/14230576.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@TechReport{Pena:1998:CDI,
  author =       "J. Pena",
  title =        "Computing the Distance to Infeasibility: Theoretical
                 and Practical Issues",
  type =         "Technical Report",
  institution =  "Center for Applied Mathematics, Cornell University",
  address =      "Ithaca, NY, USA",
  year =         "1998",
  bibdate =      "Tue Nov 22 06:34:32 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}

@InProceedings{Peuto:1998:ITM,
  author =       "Bernard L. Peuto and Leonard J. Shustek",
  title =        "An Instruction Timing Model of {CPU} Performance",
  crossref =     "Sohi:1998:YIS",
  pages =        "152--163",
  year =         "1998",
  bibdate =      "Fri Nov 28 18:36:16 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A model of high-performance computers is derived from
                 instruction timing formulas, with compensation for
                 pipeline and cache memory effects. The model is used to
                 predict the performance of the IBM 370/168 and the
                 Amdahl 470 V/6 on specific programs, and the results
                 are verified by comparison with actual performance.
                 Data collected about program behavior is combined with
                 the performance analysis to highlight some of the
                 problems with high-performance implementations of such
                 architectures.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}

@Book{Rajski:1998:ABS,
  author =       "Janusz Rajski and Jerzy Tyszer",
  title =        "Arithmetic built-in self-test for embedded systems",
  publisher =    pub-PHPTR,
  address =      pub-PHPTR:adr,
  pages =        "xii + 268",
  year =         "1998",
  ISBN =         "0-13-756438-4",
  ISBN-13 =      "978-0-13-756438-5",
  LCCN =         "TK7895.E42 R35 1998",
  bibdate =      "Mon Dec 24 09:18:51 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  keywords =     "BIST (Built-In Self Test); DFT (Design for
                 Testability); floating-point testing",
  subject =      "Embedded computer systems; Testing; Computer
                 firmware",
  tableofcontents = "1. Built-In Self-Test. Introduction. Design for
                 Testability. Generation of Test Vectors. Compaction of
                 Test Responses. BIST Schemes for Random Logic. BIST for
                 Memory Arrays\\
                 2. Generation of Test Vectors. Additive Generators of
                 Exhaustive Patterns. Other Generation Schemes.
                 Two-Dimensional Generators\\
                 3. Test-Response Compaction. Binary Adders. 1's
                 Complement Adders. Rotate-Carry Adders. Cascaded
                 Compaction Scheme\\
                 4. Fault Diagnosis. Analytical Model. Experimental
                 Validation. The Quality of Diagnostic Resolution. Fault
                 Diagnosis in Scan-Based Designs\\
                 5. BIST of Data-Path Kernel. Testing of ALU. Testing of
                 the MAC Unit. Testing of the Microcontroller\\
                 6. Fault Grading. Fault Simulation Framework.
                 Functional Fault Simulation. Experimental Results\\
                 7. High-Level Synthesis. Implementation-Dependent Fault
                 Grading. Synthesis Steps. Simulation Results\\
                 8. ABIST at Work. Testing of Random Logic. Memory
                 Testing. Digital Integrators. Leaking Integrators\\
                 9. Epilog\\
                 A. Tables of Generators\\
                 B. Assembly Language\\
                 Bibliography\\
                 Index",
}

@Article{Rivolo:1998:CDR,
  author =       "M. T. Rivolo and A. Simi",
  title =        "Il Calcolo delle Radici Quadrate e Cubiche in {Italia}
                 da {Fibonacci} a {Bombelli}. ({Italian}) [{The}
                 calculation of square and cube roots in {Italy} from
                 {Fibonacci} to {Bombelli}]",
  journal =      j-ARCH-HIST-EXACT-SCI,
  volume =       "52",
  number =       "2",
  pages =        "161--193",
  month =        feb,
  year =         "1998",
  CODEN =        "AHESAN",
  DOI =          "https://doi.org/10.1007/s004070050015",
  ISSN =         "0003-9519 (print), 1432-0657 (electronic)",
  ISSN-L =       "0003-9519",
  MRclass =      "01A35 (01A40)",
  MRnumber =     "1610136 (99d:01015)",
  MRreviewer =   "Massimo Galuzzi",
  bibdate =      "Fri Feb 4 21:50:33 MST 2011",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=52&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=52&issue=2&spage=161",
  acknowledgement = ack-nhfb,
  fjournal =     "Archive for History of Exact Sciences",
  journal-URL =  "http://link.springer.com/journal/407",
  language =     "Italian",
  MRtitle =      "The computation of square and cube roots in {Italy}
                 from {Fibonacci} to {Bombelli}",
}

@Misc{Russinoff:1998:MCPa,
  author =       "D. M. Russinoff",
  title =        "A mechanically-checked proof of {IEEE} compliance of a
                 register-transfer-level specification of the {AMD K7}
                 floating-point division and square root instructions",
  howpublished = "World-Wide Web document.",
  year =         "1998",
  bibdate =      "Fri Nov 29 09:41:27 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See journal article \cite{Russinoff:1998:MCPb}.",
  URL =          "http://www.onr.com/user/russ/david/k7-div-sqrt.html",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Mueller:2000:CAC}.",
}

@Article{Russinoff:1998:MCPb,
  author =       "David M. Russinoff",
  title =        "A mechanically checked proof of {IEEE} compliance of
                 the floating point multiplication, division and square
                 root algorithms of the {AMD-K7{\TM}} processor",
  journal =      j-LMS-J-COMPUT-MATH,
  volume =       "1",
  pages =        "148--200",
  year =         "1998",
  CODEN =        "????",
  ISSN =         "1461-1570",
  MRclass =      "68M07 (65Y99 68T15)",
  MRnumber =     "99m:68015",
  MRreviewer =   "J. Michel Muller",
  bibdate =      "Wed Nov 24 09:19:02 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Appendices A and B available to subscribers
                 electronically
                 (http://www.lms.ac.uk/jcm/1/lms98001/appendix-a/ and
                 http://www.lms.ac.uk/jcm/1/lms98001/appendix-b/)",
  URL =          "http://www.lms.ac.uk/jcm/1/lms1998-001/;
                 http://www.onr.com/user/russ/david/k7-div-sqrt.ps",
  acknowledgement = ack-nhfb,
  fjournal =     "LMS Journal of Computation and Mathematics",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=JCM",
}

@InProceedings{Sasaki:1998:ACE,
  author =       "Tateaki Sasaki and Satoshi Yamaguchi",
  title =        "An analysis of cancellation error in multivariate
                 {Hensel} construction with floating-point number
                 arithmetic",
  crossref =     "Gloor:1998:IPI",
  pages =        "1--8",
  year =         "1998",
  bibdate =      "Wed Sep 16 17:16:31 1998",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/issac/281508/index.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/issac/281508/p1-sasaki/",
  acknowledgement = ack-nhfb,
}

@Article{Sasaki:1998:CEM,
  author =       "Tateaki Sasaki and Tomoyuki Sato",
  title =        "Cancellation Errors in Multivariate Resultant
                 Computation with Floating-point Numbers",
  journal =      j-SIGSAM,
  volume =       "32",
  number =       "4",
  pages =        "13--20",
  month =        dec,
  year =         "1998",
  CODEN =        "SIGSBZ",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Wed Apr 14 15:21:10 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGSAM Bulletin",
  issue =        "126",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}

@Article{Sastry:1998:EIF,
  author =       "S. Subramanya Sastry and Subbarao Palacharla and James
                 E. Smith",
  title =        "Exploiting Idle Floating-Point Resources for Integer
                 Execution",
  journal =      j-SIGPLAN,
  volume =       "33",
  number =       "5",
  pages =        "118--129",
  month =        may,
  year =         "1998",
  CODEN =        "SINODQ",
  ISBN =         "0-89791-987-4",
  ISBN-13 =      "978-0-89791-987-6",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:17:47 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/proceedings/pldi/277650/index.html;
                 http://www.cs.virginia.edu/pldi98/program.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/pldi/277650/p118-sastry/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "algorithms; performance",
  remark =       "Published as part of the Proceedings of PLDI'98.",
  subject =      "{\bf D.3.4} Software, PROGRAMMING LANGUAGES,
                 Processors, Compilers. {\bf D.3.4} Software,
                 PROGRAMMING LANGUAGES, Processors, Optimization. {\bf
                 G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Computer arithmetic.",
}

@InProceedings{Seidel:1998:HHL,
  author =       "Peter-Michael Seidel",
  title =        "How to half [sic] the latency of {IEEE} compliant
                 floating-point multiplication",
  crossref =     "IEEE:1998:IOM",
  pages =        "329--332",
  year =         "1998",
  bibdate =      "Fri Jun 24 20:55:14 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Seidel:1998:HSR,
  author =       "P.-M. (Peter-Michael) Seidel",
  booktitle =    "Proceedings of the 3rd Conference on Real Numbers and
                 Computers ({RNC3}), Paris, April 1998",
  title =        "High-Speed Redundant Reciprocal Approximation",
  publisher =    "????",
  address =      "????",
  pages =        "219--229",
  year =         "1998",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Jun 25 07:46:25 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Misc{Severance:1998:IOM,
  author =       "C. Severance",
  title =        "An interview with the old man of floating-point:
                 Reminiscences elicited from {William Kahan}",
  howpublished = "World-Wide Web document.",
  year =         "1998",
  bibdate =      "Sat Apr 28 19:05:42 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "A shortened version appears in
                 \cite{Severance:1998:SII}.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/754story.html",
  acknowledgement = ack-nhfb,
}

@Article{Severance:1998:SII,
  author =       "Charles Severance",
  title =        "Standards: {IEEE 754}: An Interview with {William
                 Kahan}",
  journal =      j-COMPUTER,
  volume =       "31",
  number =       "3",
  pages =        "114--115",
  month =        mar,
  year =         "1998",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Wed Mar 4 10:07:59 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://pdf.computer.org/co/books/co1998/pdf/r3114.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}

@InProceedings{Simons:1998:IFP,
  author =       "N. R. S. Simons and G. E. Bridges and B. Ghosh and M.
                 Cuhaci",
  booktitle =    "1998. {IEEE} Antennas and Propagation Society
                 International Symposium. 21--26 June 1998",
  title =        "Investigation of floating-point round-off errors
                 within time-domain electromagnetic field computations",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "260--263",
  year =         "1998",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "We present an investigation of floating-point
                 round-off errors within time-domain electromagnetic
                 field computations. Our eventual goal is to determine
                 the minimal computational requirements for the
                 successful implementation of algorithms for \ldots{}",
}

@InProceedings{Skavantzos:1998:ERW,
  author =       "A. Skavantzos",
  booktitle =    "Proceedings of the 8th Great Lakes Symposium on {VLSI,
                 1998}",
  title =        "An efficient residue to weighted converter for a new
                 residue number system",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "185--191",
  year =         "1998",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/GLSV.1998.665223",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The Residue Number System (RNS) is an integer system
                 appropriate far implementing fast digital signal
                 processors since it can support parallel, carry-free,
                 high-speed arithmetic. In this paper a new RNS system
                 and an efficient implementation of its \ldots{}",
}

@Misc{Slabodkin:1998:SGL,
  author =       "G. Slabodkin",
  title =        "Software glitches leave {Navy Smart Ship} dead in the
                 water",
  howpublished = "Web site",
  day =          "31",
  month =        jul,
  year =         "1998",
  bibdate =      "Mon Aug 26 11:13:26 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.rose-hulman.edu/class/cs/csse442/current/hw/homework6-story.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Aegis missile cruiser USS Yorktown",
}

@Article{Smith:1998:AMP,
  author =       "David M. Smith",
  title =        "{Algorithm 786}: Multiple-Precision Complex Arithmetic
                 and Functions",
  journal =      j-TOMS,
  volume =       "24",
  number =       "4",
  pages =        "359--367",
  month =        dec,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/293686.293687",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:09:51 1999",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/1998-24/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also
                 \cite{Bailey:1995:FBM,Brent:1978:AMF,Brent:1979:RMF,Brent:1980:AIB}.",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-4/p359-smith/",
  abstract =     "The article describes a collection of Fortran routines
                 for multiple-precision complex arithmetic and
                 elementary functions. The package provides good
                 exception handling, flexible input and output, trace
                 features, and results that are almost always correctly
                 rounded. For best efficiency on different machines, the
                 user can change the arithmetic type used to represent
                 the multiple-precision numbers.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; correct rounding; floating-point
                 arithmetic; performance; reliability",
  subject =      "{\bf G.1.0} Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.2}
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation. {\bf
                 G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm design and analysis. {\bf G.4} Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4}
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Portability**.",
}

@Article{Stelling:1998:OCP,
  author =       "P. F. Stelling and C. U. Martel and V. G. Oklobdzija
                 and R. Ravi",
  title =        "Optimal circuits for parallel multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "3",
  pages =        "273--285",
  month =        mar,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.660163",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:54 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=660163",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Stine:1998:CIFa,
  author =       "J. E. Stine and M. J. Schulte",
  title =        "A Combined Interval and Floating Point Divider",
  crossref =     "Matthews:1998:CRT",
  pages =        "218--222",
  year =         "1998",
  bibdate =      "Sun Mar 04 10:59:12 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1998-02.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Stine:1998:CIFb,
  author =       "J. E. Stine and M. J. Schulte",
  title =        "A Combined Interval and Floating Point Multiplier",
  crossref =     "IEEE:1998:PGL",
  pages =        "208--213",
  year =         "1998",
  bibdate =      "Sun Mar 04 10:59:12 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1998-01.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Takagi:1998:PTL,
  author =       "N. Takagi",
  title =        "Powering by a table look-up and a multiplication with
                 operand modification",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "11",
  pages =        "1216--1222",
  month =        nov,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.736432",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=736432",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Takashi:1998:FPN,
  author =       "Y. Takashi",
  title =        "Floating Point Number Format with Number System with
                 Base of 1000",
  journal =      j-IBM-TDB,
  volume =       "01-98",
  pages =        "609--610",
  month =        jan,
  year =         "1998",
  CODEN =        "IBMTAA",
  ISSN =         "0018-8689",
  bibdate =      "Fri Nov 28 19:29:01 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Disclosed is a use number system with a base of 1000
                 instead of 2 at the mantissa part of a floating point
                 number. The unit is 10 bit. Each 10 bit keeps the value
                 between 0 and 1000. This format is superior to Binary
                 Coded Decimal (BCD) because it can keep more decimal
                 numbers in the same size. This format is superior to
                 binary because 1000 is 100 times of 10, and it makes no
                 difference when converted to/from human's decimal
                 format.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "IBM Technical Disclosure Bulletin",
}

@Article{Thorup:1998:FIS,
  author =       "M. Thorup",
  title =        "Floats, Integers, and Single Source Shortest Paths",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1373",
  pages =        "14--??",
  year =         "1998",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Apr 28 08:51:33 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Ulman:1998:HPF,
  author =       "Zenon D. Ulman and Maciej Czyzak",
  title =        "Highly parallel, fast scaling of numbers in
                 nonredundant residue arithmetic",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "46",
  number =       "2",
  pages =        "487--496",
  year =         "1998",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  MRclass =      "94A12 (11A67 65Y10 68W35)",
  MRnumber =     "MR1664521 (2000c:94006)",
  MRreviewer =   "Behrooz Parhami",
  bibdate =      "Thu Nov 8 14:50:38 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
}

@Article{Upton:1998:RH,
  author =       "Graham Upton",
  title =        "Rounding halves",
  journal =      j-J-APPL-STAT,
  volume =       "25",
  number =       "6",
  pages =        "811--816",
  day =          "1",
  month =        dec,
  year =         "1998",
  CODEN =        "????",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  bibdate =      "Sat Apr 13 11:27:32 MDT 2002",
  bibsource =    "http://www.carfax.co.uk/jas-con.htm;
                 http://www.catchword.co.uk/titles/carfax/02664763/;
                 http://www.tandf.co.uk/journals/routledge/02664763.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.catchword.co.uk/cgi-bin/cgi?ini=carfax&body=linker&reqidx=/catchword/carfax/13600532/v25n6/s9/p811",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
}

@Article{Vogt:1998:FPP,
  author =       "Christopher J. Vogt",
  title =        "Floating Point Performance of {Common Lisp}",
  journal =      j-SIGPLAN,
  volume =       "33",
  number =       "9",
  pages =        "103--107",
  month =        sep,
  year =         "1998",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:17:51 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}

@Article{Walter:1998:EUD,
  author =       "C. D. Walter",
  title =        "Exponentiation using division chains",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "7",
  pages =        "757--765",
  month =        jul,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.709375",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:55 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709375",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Walters:1998:SFF,
  author =       "A. Walters and P. Athanas",
  title =        "A scaleable {FIR} filter using 32-bit floating-point
                 complex arithmetic on a configurable computing
                 machine",
  crossref =     "Pocek:1998:PIS",
  pages =        "333--334",
  year =         "1998",
  DOI =          "https://doi.org/10.1109/FPGA.1998.707941",
  bibdate =      "Sat Oct 09 15:44:51 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper presents an approach for implementing a
                 scalable high-performance digital filter using the
                 WILDFORCE configurable computing platform. Although not
                 designed specifically for signal processing,
                 configurable computing platforms offer more flexibility
                 for algorithms than application-specific hardware,
                 which is often needed for instances when factors such
                 as environment or product volume dictate alterations in
                 computing. The added flexibility enables users to
                 construct deep pipelines to exploit properties of
                 specific computations. In this paper, wide 32-bit
                 floating-point arithmetic operators have been
                 implemented which provide compatibility with hosts
                 machines. The filter achieves 160 MFLOPs on a single
                 WILDFORCE configurable computing platform.",
  acknowledgement = ack-nhfb,
}

@PhdThesis{Wang:1998:CAP,
  author =       "Shaoyun Wang",
  title =        "A {CORDIC} arithmetic processor",
  type =         "{Ph.D.} thesis",
  school =       "The University of Texas at Austin",
  address =      "Austin, TX, USA",
  pages =        "136",
  year =         "1998",
  ISBN =         "0-591-91832-3",
  ISBN-13 =      "978-0-591-91832-8",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://login.ezproxy.lib.utah.edu/login?url=https://www.proquest.com/dissertations-theses/cordic-arithmetic-processor/docview/304459653/se-2",
  acknowledgement = ack-nhfb,
  advisor =      "Swartzlander, Earl E., Jr.",
  keywords =     "0544:Electrical engineering; 0984:Computer science;
                 Applied sciences; Arithmetic processor; Computer
                 science; Coordinate rotation; Cordic; Electrical
                 engineering; Plane rotation",
  ris-m1 =       "9838156",
}

@InProceedings{Wei:1998:RAC,
  author =       "Shugang Wei and Kensuke Shimizu",
  title =        "Residue Arithmetic Circuits Based on Signed-Digit
                 Multi-Valued Arithmetic Circuits",
  crossref =     "Sasao:1998:ISM",
  pages =        "276--281",
  year =         "1998",
  DOI =          "https://doi.org/10.1109/ISMVL.1998.679470",
  MRclass =      "68M07",
  MRnumber =     "MR1676993",
  bibdate =      "Fri Jun 24 19:50:29 2005",
  bibsource =    "http://www.informatik.uni-trier.de/~ley/db/conf/ismvl/ismvl1998.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://csdl.computer.org/dl/proceedings/ismvl/1998/8371/00/83710276.pdf",
  abstract =     "Multiple-valued residue arithmetic circuits using
                 integers $ 4^p $ and $ 4^p \pm 1 $ as moduli of residue
                 number system (RNS) are presented. Conventional residue
                 arithmetic circuits have been designed using binary
                 number arithmetic system, but the carry propagation
                 arises which limits the speed of arithmetic operations
                 in residue modules. In this paper, a radix-4
                 signed-digit(SD) number system is introduced, and the
                 compact SD adder based on the multiple-valued
                 current-mode circuits is applied for the implementation
                 of high-speed and compact residue arithmetic circuits.
                 The modulo $m$ addition, $ m = 4^p $ or $ m = 4^p \pm 1
                 $, can be performed by an SD adder or an
                 end-around-carry SD adder with the multiple-valued
                 circuits and the addition time is independent of the
                 word length of operands. Modulo $m$ multiplier can be
                 compactly constructed using a binary modulo $m$ SD
                 adder tree based on the multiple-valued addition
                 circuits, and the modulo m multiplication can be
                 performed in a time proportional to $ \log_2 p $.",
  acknowledgement = ack-nhfb,
}

@Article{Weiss:1998:FPM,
  author =       "S. Weiss and A. Goldstein",
  title =        "Floating point micropipeline performance",
  journal =      j-J-SYST-ARCH,
  volume =       "45",
  number =       "1",
  pages =        "15--29",
  month =        oct,
  year =         "1998",
  CODEN =        "JSARFB",
  ISSN =         "1383-7621 (print), 1873-6165 (electronic)",
  ISSN-L =       "1383-7621",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Ingenta database",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Systems Architecture",
  pagecount =    "15",
}

@Article{Wu:1998:LCB,
  author =       "Huapeng Wu and M. A. Hasan",
  title =        "Low complexity bit-parallel multipliers for a class of
                 finite fields",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "8",
  pages =        "883--887",
  month =        aug,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.707588",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:55 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=707588",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Wu:1998:NLC,
  author =       "H. Wu and M. A. Hasan and I. F. Blake",
  title =        "New low-complexity bit-parallel finite field
                 multipliers using weakly dual bases",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "11",
  pages =        "1223--1234",
  month =        nov,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.736433",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=736433",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Abbott:1999:ASS,
  author =       "P. H. Abbott and D. G. Brush and C. W. {Clark III} and
                 C. J. Crone and J. R. Ehrman and G. W. Ewart and C. A.
                 Goodrich and M. Hack and J. S. Kapernick and B. J.
                 Minchau and W. C. Shepard and R. M. {Smith, Sr.} and R.
                 Tallman and S. Walkowiak and A. Watanabe and W. R.
                 White",
  title =        "Architecture and software support in {IBM S/390
                 Parallel Enterprise Servers} for {IEEE} Floating-Point
                 arithmetic",
  journal =      j-IBM-JRD,
  volume =       "43",
  number =       "5/6",
  pages =        "723--760",
  month =        sep # "\slash " # nov,
  year =         "1999",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.435.0723",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Mon Feb 03 07:08:45 2003",
  bibsource =    "http://www.research.ibm.com/journal/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
  note =         "Besides important history of the development of the
                 S/360 floating-point architecture, this paper has a
                 good description of IBM's algorithm for exact
                 decimal-to-binary conversion, complementing earlier
                 ones
                 \cite{Steele:1990:HPF,Clinger:1990:HRF,Knuth:1990:SPW,Burger:1996:PFP,Steele:2004:RHP}.",
  URL =          "http://www.research.ibm.com/journal/rd/435/abbott.html",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "decimal floating-point arithmetic",
}

@InProceedings{Agarwal:1999:SAM,
  author =       "Rames C. Agarwal and Fred G. Gustavson and Martin S.
                 Schmookler",
  title =        "Series Approximation Methods for Divide and Square
                 Root in the {Power3\TM{}} Processor",
  crossref =     "Koren:1999:ISC",
  pages =        "116--123",
  year =         "1999",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-144.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-144.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Agarwal.pdf",
  abstract =     "The Power3 processor is a 64-bit implementation of the
                 PowerPC\TM{} architecture and is the successor to the
                 Power2\TM{} processor for workstations and servers
                 which require high performance floating point
                 capability. The previous processors used
                 Newton--Raphson algorithms for their implementations of
                 divide and square root. The Power3 processor has a
                 longer pipeline latency, which would substantially
                 increase the latency for these instructions. Instead,
                 new algorithms based on power series approximations
                 were developed which provide significantly better
                 performance than the Newton- Raphson algorithm for this
                 processor. This paper describes the algorithms, and
                 then shows how both the series based algorithms and the
                 Newton--Raphson algorithms are affected by pipeline
                 length. For the Power3, the power series algorithms
                 reduce the divide latency by over 20\% and the square
                 root latency by 35\%.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic",
}

@Article{Ait-Ameur:1999:RRE,
  author =       "Y. Ait-Ameur",
  title =        "Refinement of rational end-points real numbers by
                 means of floating-point numbers",
  journal =      j-SCI-COMPUT-PROGRAM,
  volume =       "33",
  number =       "2",
  pages =        "133--162",
  month =        feb,
  year =         "1999",
  CODEN =        "SCPGD4",
  ISSN =         "0167-6423 (print), 1872-7964 (electronic)",
  ISSN-L =       "0167-6423",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Ingenta database",
  acknowledgement = ack-nhfb,
  fjournal =     "Science of Computer Programming",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01676423",
  pagecount =    "30",
}

@Article{Allender:1999:BDA,
  author =       "Eric Allender and Andris Ambainis and David A. Mix
                 Barrington and Samir Datta and Huong L{\^e}Thanh",
  title =        "Bounded Depth Arithmetic Circuits: Counting and
                 Closure",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1644",
  pages =        "149--??",
  year =         "1999",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:54:23 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1644.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1644/16440149.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1644/16440149.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Anderson:1999:DAF,
  author =       "I. J. Anderson",
  title =        "A Distillation Algorithm for Floating-Point
                 Summation",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "20",
  number =       "5",
  pages =        "1797--1806",
  month =        sep,
  year =         "1999",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/S1064827596314200",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Sat Jul 17 19:14:38 MDT 1999",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/20/5;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/31420",
  abstract =     "The addition of two or more floating-point numbers is
                 fundamental to numerical computations. This paper
                 describes an efficient ``distillation'' style algorithm
                 which produces a precise sum by exploiting the natural
                 accuracy of compensated cancellation. The algorithm is
                 applicable to all sets of data but is particularly
                 appropriate for ill-conditioned data, where standard
                 methods fail due to the accumulation of rounding error
                 and its subsequent exposure by cancellation. The method
                 uses only standard floating-point arithmetic and does
                 not rely on the radix used by the arithmetic model, the
                 architecture of specific machines, or the use of
                 accumulators.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  keywords =     "accurate floating-point summation",
}

@Misc{Anonymous:1999:SLH,
  author =       "Anonymous",
  title =        "Standard libraries for the {Haskell 98} programming
                 language",
  howpublished = "World-Wide Web document",
  month =        feb,
  year =         "1999",
  bibdate =      "Wed Jan 29 16:42:05 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.haskell.org/definition/haskell98-library.pdf",
  acknowledgement = ack-nhfb,
  remark =       "From \cite{Steele:2004:RHP}: ``a comment that appears
                 in the code for the function floatToDigits in the
                 Haskell 98 library [p. 14 of this article] says that
                 the code is based on Burger and Dybvig's work
                 \cite{Burger:1996:PFP}.",
}

@InProceedings{Antelo:1999:VHR,
  author =       "E. Antelo and T. Lang and J. D. Bruguera",
  booktitle =    "{Proceedings 14th IEEE Symposium on Computer
                 Arithmetic (Cat. No. 99CB36336)}",
  title =        "Very-high radix {CORDIC} vectoring with scalings and
                 selection by rounding",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "204--213",
  year =         "1999",
  DOI =          "https://doi.org/10.1109/ARITH.1999.762846",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Contracts; Costs; Polynomials",
}

@InProceedings{Antelo:1999:VRC,
  author =       "Elisardo Antelo and Tom{\'a}s Lang and Javier D.
                 Bruguera",
  title =        "Very-High Radix {CORDIC} Vectoring with Scalings and
                 Selection by Rounding",
  crossref =     "Koren:1999:ISC",
  pages =        "204--213",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-154.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-154.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Antelo.pdf",
  abstract =     "A very-high radix algorithm and implementation for
                 circular CORDIC in vectoring mode is presented. As for
                 division, to simplify the selection function, the
                 operands are pre-scaled. However, in the CORDIC
                 algorithm the coordinate x varies during the execution
                 so several scalings might be needed; we show that two
                 scalings are sufficient. Moreover, the compensation of
                 the variable scale factor is done by computing the
                 logarithm of the scale factor and performing the
                 compensation by an exponential. Estimations of the
                 delay for 32-bit precision show a speed up of about two
                 with respect to the radix-4 case with redundant
                 addition. This speed up is obtained at the cost of an
                 increase in the hardware complexity, which is moderate
                 for the pipelined implementation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic",
  summary =      "A very-high radix algorithm and implementation for
                 circular CORDIC in vectoring mode is presented. As for
                 division, to simplify the selection function, the
                 operands are pre-scaled. However in the CORDIC
                 algorithm the coordinate x varies during the \ldots{}",
}

@InProceedings{Aoki:1999:RCA,
  author =       "Takafumi Aoki and Ken-ichi Hoshi and Tatsuo Higuchi",
  title =        "Redundant Complex Arithmetic and Its Application to
                 Complex Multiplier Design",
  crossref =     "IEEE:1999:PII",
  pages =        "200--207",
  year =         "1999",
  DOI =          "https://doi.org/10.1109/ISMVL.1999.779717",
  bibdate =      "Sat Aug 22 08:46:40 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper presents a class of complex number
                 representations called Redundant Complex Number Systems
                 (RCNSs), which are useful for designing VLSI signal
                 processors with complex arithmetic capability. A
                 redundant complex: number system is defined as an
                 imaginary-radix number system having a redundant
                 integer digit set. This makes possible the construction
                 of high-speed complex arithmetic circuits: examples
                 include a complex-number parallel adder with no carry
                 propagation chain, and a complex-number multiplier
                 using fast binary-tree addition structure. This paper
                 also presents the experimental fabrication of the
                 RCNS-based complex multiplier in 0.5 $ \mu $ m CMOS
                 technology",
  acknowledgement = ack-nhfb,
}

@Article{Bach:1999:NTS,
  author =       "E. Bach and K. Huber",
  title =        "Note on taking square-roots modulo {$N$}",
  journal =      j-IEEE-TRANS-INF-THEORY,
  volume =       "45",
  number =       "2",
  pages =        "807--809",
  month =        mar,
  year =         "1999",
  CODEN =        "IETTAW",
  DOI =          "https://doi.org/10.1109/18.749034",
  ISSN =         "0018-9448 (print), 1557-9654 (electronic)",
  ISSN-L =       "0018-9448",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Information Theory",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
  summary =      "In this article it is shown how Gauss' (1981) famous
                 cyclotomic sum formula can be used for extracting
                 square-roots modulo \ldots{}",
}

@InProceedings{Batten:1999:IBO,
  author =       "D. Batten and S. Jinturkar and J. Glossner and M.
                 Schulte and R. Peri and P. D'arcy",
  editor =       "????",
  booktitle =    "Proceedings of the International Conference on Signal
                 Processing Applications and Technologies, Orlando,
                 Florida, November, 1999",
  title =        "Interactions Between Optimizations and a New Type of
                 {DSP} Intrinsic Function",
  publisher =    "????",
  address =      "????",
  year =         "1999",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sun Mar 04 11:05:23 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Shortened version in \cite{Batten:1999:IFB}.",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1999-09.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Batten:1999:IFB,
  author =       "D. Batten and P. D'arcy",
  title =        "Intrinsic Functions Boost Compilers",
  journal =      "Electrical Engineering Times",
  volume =       "1085",
  pages =        "104--104",
  month =        nov,
  year =         "1999",
  bibdate =      "Sun Mar 04 11:06:22 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Beaumont-Smith:1999:RLI,
  author =       "A. Beaumont-Smith and N. Burgess and S. Lefrere and C.
                 C. Lim",
  title =        "Reduced Latency {IEEE} Floating-Point Standard Adder
                 Architectures",
  crossref =     "Koren:1999:ISC",
  pages =        "35--43",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-163.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-163.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Beaumont_Smith.pdf",
  abstract =     "The design and implementation of a double precision
                 floating-point IEEE-754 standard adder is described
                 which uses ``flagged prefix addition'' to merge
                 rounding with the significand addition. The
                 floating-point adder is implemented in $ 0.5 \mu $ m
                 CMOS, measures $ 1.8 $ mm$^2$, has a 3-cycle latency
                 and implements all rounding modes. A modified version
                 of this floating-point adder can perform accumulation
                 in 2-cycles with a small amount of extra hardware for
                 use in a parallel processor node. This is achieved by
                 feeding back the previous un-normalised but correctly
                 rounded result together with the normalisation
                 distance. A 2-cycle latency floating-point adder
                 architecture with potentially the same cycle time that
                 also employs flagged prefix addition is described. It
                 also incorporates a fast prediction scheme for the true
                 subtraction of significands with an exponent difference
                 of 1, with one less adder.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic; correct rounding;
                 floating-point arithmetic",
}

@Misc{Benschop:1999:MML,
  author =       "Nico Fritz Benschop",
  title =        "Multiplier for the multiplication of at least two
                 figures in an original format",
  howpublished = "US Patent number 5,923,888.",
  day =          "13",
  month =        jul,
  year =         "1999",
  bibdate =      "Fri Jun 24 15:16:03 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://patents.google.com/patent/US5923888A",
  abstract =     "The invention relates to a multiplier for the
                 multiplication of at least two figures in an original
                 format. Each of said figures is fed to a first
                 converter for conversion of each of said figures in the
                 product of a first binary number representing a power
                 of 2, and a second binary number representing a signed
                 power of 3, the exponents of the powers of 2 of the
                 concerning figures being fed to a first adder and the
                 exponents of the powers of 3 of the concerning figures
                 being fed to a second adder, whereby the combined
                 respective outputs of the first adder and the second
                 adder represent the multiplied value of said figures,
                 and the resulting powers of 2 and 3 as available at the
                 outputs of the first and second adder being fed to a
                 second converter for conversion of the multiplied value
                 into the original format.",
  acknowledgement = ack-nhfb,
  remark =       "Patent filed 15 December 1997, granted 13 July 1999,
                 expected expiration on 15 December 2017.",
}

@InProceedings{Bhardwaj:1999:RCM,
  author =       "M. Bhardwaj and T. Srikanthan and C. T. Clarke",
  title =        "A Reverse Converter for the $4$-Moduli Superset $ \{
                 2^n - 1 $, $ 2^n $, $ 2^n + 1 $, $ 2^(n + 1) + 1 \} $",
  crossref =     "Koren:1999:ISC",
  pages =        "168--175",
  year =         "1999",
  DOI =          "https://doi.org/10.1109/ARITH.1999.762842",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-137.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-137.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Bhardwaj.pdf",
  abstract =     "The authors propose an extension to the popular $ \{
                 2^n - 1, 2^n, 2^n + 1 \} $ moduli set by adding a
                 fourth modulus $ 2^{n + 1} + 1 $. This extension leads
                 to higher parallelism while keeping the forward
                 conversion and modular arithmetic units simple. The
                 main challenge of efficient reverse conversion is met
                 by three techniques described for the first time.
                 Firstly, we reverse convert linear combinations of
                 moduli hence reducing the number of non-zero bits in
                 the Booth encoded multiplicands from $n$ to merely 2.
                 Secondly, it is shown that division by 3, if introduced
                 at the right stage, can be implemented very efficiently
                 and can, in turn, reduce the cost of the converter. To
                 implement VLSI efficient modulo reduction, we propose
                 two techniques-multiple split tables (MST) and a
                 modified division algorithm (MDA). It is shown that the
                 MST can reduce exponential ROM requirements to
                 quadratic ROM requirements while the MDA can reduce
                 these further to linear requirements. As a result of
                 these innovations, the proposed reverse converter uses
                 simple shift and add operations and needs a lookup with
                 only 6 entries. The delay of the converter is
                 approximately $ 10 n + 13 $ full adder delays and the
                 area cost is quadratic in $n$.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic",
}

@InProceedings{Bhardwaj:1999:VCA,
  author =       "M. Bhardwaj and T. Srikanthan and C. T. Clarke",
  title =        "{VLSI} Costs of Arithmetic Parallelism: a Residue
                 Reverse Conversion Perspective",
  crossref =     "Koren:1999:ISC",
  pages =        "176--185",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-138.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-138.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Bhardwaj_VLSI.pdf",
  abstract =     "This paper reports how VLSI cost metrics (area, delay,
                 power) of residue reverse converters scale with the
                 cardinality and dynamic range of moduli sets. The study
                 uses CMAC reverse converters, reported previously by
                 the authors to be the most efficient known to date in
                 terms of area and delay. In all, 134 reverse converters
                 with dynamic ranges from 32 to 120 bits and set
                 cardinalities ranging from 4 to 20 are actually
                 constructed and analyzed. It is seen that area, delay
                 and power costs are cardinality insensitive once the
                 cardinality exceeds a threshold (usually between five
                 to eight). For cardinalities beyond this threshold,
                 conversion costs are essentially dynamic range
                 dependent. This insensitivity is explained in detail by
                 noting the counterbalancing effects of the various
                 sub-units of a CMAC reverse converter. Since practical
                 implementations of RNS usually employ cardinalities
                 beyond the abovementioned thresholds, the significance
                 of this study is its conclusion that increasing the set
                 cardinality in most implementations will have a
                 marginal, if any, effect on VLSI reverse conversion
                 costs.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic",
}

@InProceedings{Blum:1999:MME,
  author =       "Thomas Blum and Christoph Paar",
  title =        "{Montgomery} Modular Exponentiation on Reconfigurable
                 Hardware",
  crossref =     "Koren:1999:ISC",
  pages =        "70--77",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-133.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-133.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Blum.pdf",
  abstract =     "It is widely recognized that security issues will play
                 a crucial role in the majority of future computer and
                 communication systems. Central tools for achieving
                 system security are cryptographic algorithms. For
                 performance as well as for physical security reasons,
                 it is often advantageous to realize cryptographic
                 algorithms in hardware. In order to overcome the
                 well-known drawback of reduced flexibility that is
                 associated with traditional ASIC solutions, this
                 contribution proposes arithmetic architectures which
                 are optimized for modern field programmable gate arrays
                 (FPGAs). The proposed architectures perform modular
                 exponentiation with very long integers. This operation
                 is at the heart of many practical public-key algorithms
                 such as RSA and discrete logarithm schemes. We combine
                 the Montgomery modular multiplication algorithm with a
                 new systolic array design, which is capable of
                 processing a variable number of bits per array cell.
                 The designs are flexible, allowing any choice of
                 operand and modulus.\par

                 Unlike previous approaches, we systematically implement
                 and compare several variants of our new architecture
                 for different bit lengths. We provide absolute area and
                 timing measures for each architecture. The results
                 allow conclusions about the feasibility and time-space
                 trade-offs of our architecture for implementation on
                 Xilinx XC4000 series FPGAs. As a major practical result
                 we show that it is possible to implement modular
                 exponentiation at secure bit lengths on a single
                 commercially available FPGA.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic",
}

@TechReport{Boldo:1999:CRE,
  author =       "Sylvie Boldo",
  title =        "Calcul rapide et exact de fonctions
                 {\'e}l{\'e}mentaires en pr{\'e}cision arbitraire par la
                 moyenne arithm{\'e}tico-g{\'e}om{\'e}trique. ({French})
                 [Rapid and exact computation of elementary functions in
                 arbitrary precision by the arithmetic-geometric mean]",
  type =         "Report",
  institution =  "INRIA, Projet Spaces, LORIA, Campus Scientifique",
  address =      "B.P. 239, 54506 Vandoeuvre-l{\`e}s-Nancy Cedex,
                 France",
  pages =        "29",
  year =         "1999",
  bibdate =      "Tue Nov 23 11:00:03 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Under the direction of Paul Zimmermann.",
  URL =          "http://perso.ens-lyon.fr/sylvie.boldo/doc/mpfr.ps",
  acknowledgement = ack-nhfb,
  language =     "French",
}

@InProceedings{Brent:1999:CAP,
  author =       "Richard P. Brent",
  title =        "Computer Arithmetic --- a Programmer's Perspective",
  crossref =     "Koren:1999:ISC",
  pages =        "2--2",
  year =         "1999",
  bibdate =      "Wed Jan 20 09:38:39 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/brentr.pdf;
                 http://euler.ecs.umass.edu/paper/final/brentr.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Brent.pdf",
  abstract =     "Advances in computer hardware often have little impact
                 until they become accessible to programmers using
                 high-level languages. For example, the IEEE
                 floating-point arithmetic standard provides various
                 rounding modes and exceptions, but it is difficult or
                 impossible to take advantage of these from most
                 high-level languages, so the full capabilities of
                 IEEE-compatible hardware are seldom used. When they are
                 used by writing in machine or assembly language, there
                 is a high cost in program development and testing time,
                 lack of portability, and difficulty of software
                 maintenance.\par

                 In this talk we discuss several areas in which computer
                 hardware, especially arithmetic hardware, can or should
                 significantly influence programming language design.
                 These include: vector units, floating-point exception
                 handling, floating-point rounding modes, high/extended
                 precision registers/arithmetic, and use of unusual
                 number systems. Relevant application areas include
                 interval arithmetic, high-precision integer arithmetic
                 for computer algebra and cryptography, and testing of
                 hardware by comparison with software simulations.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14",
  remark =       "Abstract only: no text of the paper available.",
}

@Article{Bronnimann:1999:SDR,
  author =       "Herve Bronnimann and Ioannis Z. Emiris and Victor Y.
                 Pan and Sylvain Pion",
  title =        "Sign determination in residue number systems",
  journal =      j-THEOR-COMP-SCI,
  volume =       "210",
  number =       "1",
  pages =        "173--197",
  day =          "06",
  month =        jan,
  year =         "1999",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Mon Jul 19 22:22:18 MDT 1999",
  bibsource =    "http://www.elsevier.com/cgi-bin/cas/tree/store/tcs/cas_free/browse/browse.cgi?year=1999&volume=210&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.elsevier.com/cas/tree/store/tcs/sub/1999/210/1/2931.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}

@InProceedings{Bui:1999:DSI,
  author =       "H. Bui and S. Tahar",
  booktitle =    "1999 {IEEE} Canadian Conference on Electrical and
                 Computer Engineering, 9--12 May 1999",
  title =        "Design and synthesis of an {IEEE-754} exponential
                 function",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "450--455",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 17:14:11 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "We have designed a floating-point exponential function
                 using the table-driven method. The algorithm was first
                 implemented using sequential VHDL and later translated
                 to Concurrent Verilog. The main part of the work
                 consisted of creating modules that \ldots{}",
}

@InProceedings{Burgess:1999:EIR,
  author =       "N. Burgess and S. Knowles",
  booktitle =    "Conference Record of the Thirty-Third Asilomar
                 Conference on Signals, Systems, and Computers, 1999",
  title =        "Efficient implementation of rounding units",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1489--1493",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:05 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper shows how IEEE 754 floating-point standard
                 compliant rounding may be merged with carry-propagate
                 addition in high-performance FPU designs. The paper
                 considers addition/subtraction, multiplication and
                 divide/square root operations and \ldots{}",
}

@InProceedings{Burgess:1999:FIS,
  author =       "Neil Burgess and Luigi Ciminiera",
  title =        "{Fifteenth IEEE Symposium on Computer Arithmetic}:
                 Foreword",
  crossref =     "Koren:1999:ISC",
  pages =        "ix--ix",
  year =         "1999",
  bibdate =      "Sat Nov 17 21:53:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_contents.pdf;
                 http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_foreword.pdf;
                 http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_preface.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14",
}

@Article{Cappuccino:1999:HSS,
  author =       "G. Cappuccino and G. Cocorullo and P. Corsonello and
                 S. Perri",
  title =        "High speed self-timed pipelined datapath for square
                 rooting",
  journal =      "Circuits, Devices and Systems, IEE Proceedings [see
                 also IEE Proceedings G- Circuits, Devices and
                 Systems]",
  volume =       "146",
  number =       "1",
  pages =        "16--22",
  month =        feb,
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The authors describe a new high-performance self-timed
                 circuit for asynchronous square rooting. The new
                 architecture is based on a modified nonrestoring
                 algorithm. An asynchronous pipelined cellular array
                 without auxiliary system for the \ldots{}",
}

@Article{Chren:1999:DSM,
  author =       "W. A. {Chren, Jr.}",
  title =        "Delta-sigma modulator with large {OSR} using the
                 one-hot residue number system",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "46",
  number =       "8",
  pages =        "1002--1008",
  month =        aug,
  year =         "1999",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.782041",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=16972",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems. 2, Analog
                 and Digital Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A digital delta-sigma modulator using the one-hot
                 residue number system (OHRNS) is presented. It exhibits
                 a large oversampling ratio (OSR) in comparison with
                 equivalent binary designs. Its second-order
                 architecture employs a two-stage cascade \ldots{}",
}

@Article{Christensen:1999:BFP,
  author =       "E. L. Christensen",
  title =        "Block floating point for radar data",
  journal =      j-IEEE-TRANS-AEROSP-ELECTRON-SYST,
  volume =       "35",
  number =       "1",
  pages =        "308--318",
  month =        jan,
  year =         "1999",
  CODEN =        "IEARAX",
  ISSN =         "0018-9251 (print), 1557-9603 (electronic)",
  ISSN-L =       "0018-9251",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Aerospace and Electronic
                 Systems",
  summary =      "Integer, floating point, and block floating point
                 (BFP) data formats are analyzed and compared in order
                 to establish the mathematical tools for selection of an
                 optimal format which fulfils the demands of high
                 resolution radar (SAR) data to large \ldots{}",
}

@Article{Chung:1999:RAC,
  author =       "Sei-Jong Chung",
  title =        "Recursive algorithm with {C++} program for
                 floating-point arithmetic",
  journal =      j-SIGCSE,
  volume =       "31",
  number =       "2",
  pages =        "28--30",
  month =        jun,
  year =         "1999",
  CODEN =        "SIGSD3",
  DOI =          "https://doi.org/10.1145/571535.571562",
  ISSN =         "0097-8418 (print), 2331-3927 (electronic)",
  ISSN-L =       "0097-8418",
  bibdate =      "Sat Nov 17 16:56:38 MST 2012",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigcse1990.bib",
  abstract =     "Floating point Arithmetic is a topic included in
                 virtually all textbooks for Computer Systems (CS 3:
                 ACM's Curriculum Recommendation) or for Computer
                 Organization (CS 4: ACM's Curriculum Recommendation).
                 This paper presents a mathematical optimization model
                 for the topic. The problem of converting real (float)
                 numbers into binary equivalents is first modeled as a
                 Zero-One Integer Programming problem. Then, a Recursive
                 Algorithm is formulated for Floating-Point Formats.
                 Computer programs are written in both C and C++ for a
                 32-bit floating-point format, using the recursive
                 algorithm. [The computer programs are available at the
                 email \ldots{}.]",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGCSE Bulletin (ACM Special Interest Group on
                 Computer Science Education)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J688",
}

@Article{Cilio:1999:FPF,
  author =       "A. Cilio and H. Corporaal",
  title =        "Floating Point to Fixed Point Conversion of {C} Code",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1575",
  pages =        "229--243",
  year =         "1999",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 14 06:09:05 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs1999a.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
  keywords =     "CC; compiler construction; ETAPS; software",
}

@Article{Clarke:1999:VSD,
  author =       "Edmund M. Clarke and Steven M. German and Xudong
                 Zhao",
  title =        "Verifying the {SRT} Division Algorithm Using Theorem
                 Proving Techniques",
  journal =      j-FORM-METHODS-SYST-DES,
  volume =       "14",
  number =       "1",
  pages =        "7--44",
  month =        jan,
  year =         "1999",
  CODEN =        "FMSDE6",
  ISSN =         "0925-9856 (print), 1572-8102 (electronic)",
  ISSN-L =       "0925-9856",
  bibdate =      "Sat Jun 02 09:21:29 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Special issue on arithmetic circuits.",
  URL =          "http://www.wkap.nl/jrnltoc.htm/0925-9856;
                 http://www.wkap.nl/oasis.htm/194806",
  acknowledgement = ack-nhfb,
  fjournal =     "Formal Methods in System Design",
  journal-URL =  "https://dl.acm.org/loi/fmsd",
}

@Article{Clouser:1999:MSF,
  author =       "J. Clouser and M. Matson and R. Badeau and R. Dupcak
                 and S. Samudrala and R. Allmon and N. Fairbanks",
  title =        "A {600-MHz} superscalar floating-point processor",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "34",
  number =       "7",
  pages =        "1026--1029",
  month =        jul,
  year =         "1999",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "The floating-point unit of a 600-MHz, out-of order,
                 superscalar RISC Alpha microprocessor is described. The
                 unit achieves 59 SpecFP95 and can transfer register
                 data at up to 9.6 GB/s. It has two independent
                 pipelines for multiply and add/subtract \ldots{}",
}

@InProceedings{Coleman:1999:BLA,
  author =       "J. N. Coleman and E. I. Chester",
  title =        "A $ 32 $-Bit Logarithmic Arithmetic Unit and Its
                 Performance Compared to Floating-Point",
  crossref =     "Koren:1999:ISC",
  pages =        "142--151",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-160.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-160.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Coleman.pdf",
  abstract =     "As an alternative to floating-point, several papers
                 have proposed the use of a logarithmic number system,
                 in which a real number is represented as a fixed-point
                 logarithm. Multiplication and division therefore
                 proceed in minimal time with no rounding error.
                 However, the system can only offer an overall advantage
                 if addition and subtraction can be performed with speed
                 and accuracy at least equal to that of floating-point,
                 but these operations require the interpolation of a
                 non-linear function which has hitherto been either
                 time-consuming or inaccurate. We present a procedure by
                 which additions and subtractions can be performed
                 rapidly and accurately, and show that these operations
                 are thereby competitive with their floating-point
                 equivalents. We then show that the average performance
                 of the logarithmic system exceeds floating-point, in
                 terms of both speed and accuracy.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic",
}

@Article{Collavizza:1999:CPC,
  author =       "H. Collavizza and F. Delobel and M. Rueher",
  title =        "Comparing Partial Consistencies",
  journal =      j-RELIABLE-COMPUTING,
  volume =       "5",
  number =       "3",
  pages =        "213--228",
  year =         "1999",
  CODEN =        "RCOMF8",
  ISSN =         "1385-3139 (print), 1573-1340 (electronic)",
  ISSN-L =       "1385-3139",
  bibdate =      "Mon May 20 06:37:48 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  fjournal =     "Reliable Computing = Nadezhnye vychisleniia",
  journal-URL =  "http://link.springer.com/journal/11155",
  remark =       "Papers from Scientific computing, computer arithmetic
                 and validated numerics (SCAN '98), September 1998,
                 Budapest, Hungary.",
}

@TechReport{Connors:1999:SOF,
  author =       "Daniel A. Connors and Yoji Yamada and Wen-mei W. Hwu",
  title =        "A Software-Oriented Floating-Point Format for
                 Enhancing Automotive Control Systems",
  type =         "Report",
  institution =  "Department of Electrical and Computer Engineering, The
                 Coordinated Science Laboratory, University of
                 Illinois",
  address =      "Urbana, IL 61801, USA",
  day =          "11",
  month =        aug,
  year =         "1999",
  bibdate =      "Thu Jun 09 18:01:33 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Updated version of paper presented at the {\em
                 Workshop on Compiler and Architecture Support for
                 Embedded Computing Systems (CASES98), December,
                 1998}.",
  URL =          "http://rogue.colorado.edu/draco/papers/case-98-float.pd",
  acknowledgement = ack-nhfb,
  remark =       "Describes an embedded system with 32-bit floating
                 point with a 24-bit significand, 5-bit signed exponent
                 in excess-15 base-8 representation, with a single zero,
                 no hidden bit, no NaN, no Infinity, and no
                 subnormals.",
}

@Article{Constales:1999:PSS,
  author =       "Denis Constales",
  title =        "Problems and Solutions: Solutions: 10568. Subtracting
                 Square Roots Repeatedly",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "106",
  number =       "2",
  pages =        "167--167",
  month =        feb,
  year =         "1999",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Wed Dec 29 06:14:39 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
  xxnote =       "See problem \cite{Knuth:1997:xxx}",
}

@Article{Conway:1999:FCM,
  author =       "R. Conway and J. Nelson",
  title =        "Fast converter for 3 moduli {RNS} using new property
                 of {CRT}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "48",
  number =       "8",
  pages =        "852--860",
  month =        aug,
  year =         "1999",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.795127",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:46:58 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=795127",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Cornea-Hasegan:1999:CPO,
  author =       "Marius A. Cornea-Hasegan and Roger A. Golliver and
                 Peter Markstein",
  title =        "Correctness proofs outline for {Newton--Raphson} based
                 floating-point divide and square root algorithms",
  crossref =     "Koren:1999:ISC",
  pages =        "96--105",
  year =         "1999",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-121.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-121.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Cornea_Hasegan.pdf",
  abstract =     "This paper describes a study of a class of algorithms
                 for the floating-point divide and square root
                 operations, based on the Newton--Raphson iterative
                 method. The two main goals were:\par

                 (1) Proving the IEEE correctness of these iterative
                 floating-point algorithms, i.e. compliance with the
                 IEEE-754 standard for binary floating-point operations
                 [1]. The focus was on software driven iterative
                 algorithms, instead of the hardware based
                 implementations that dominated until now.\par

                 (2) Identifying the special cases of operands that
                 require software assistance due to possible overflow,
                 underflow, or loss of precision of intermediate
                 results.\par

                 This study was initiated in an attempt to prove the
                 IEEE correctness for a class of divide and square root
                 algorithms based on the Newton--Raphson iterative
                 methods. As more insight into the inner workings of
                 these algorithms was gained, it became obvious that a
                 formal study and proof were necessary in order to
                 achieve the desired objectives. The result is a
                 complete and rigorous proof of IEEE correctness for
                 floating-point divide and square root algorithms based
                 on the Newton--Raphson iterative method. Even more, the
                 method used in proving the IEEE correctness of the
                 square root algorithm is applicable in principle to any
                 iterative algorithm, not only based on the
                 Newton--Raphson method. Conditions requiring Software
                 Assistance (SWA) were also determined, and were used to
                 identify cases when alternate algorithms are needed to
                 generate correct results. Overall, this is one
                 important step toward flawless implementation of these
                 floating-point operations based on software
                 implementations.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic",
  summary =      "This paper describes a study of a class of algorithms
                 for the floating-point divide and square root
                 operations, based on the Newton--Raphson iterative
                 method. The two main goals were. (1) Proving the IEEE
                 correctness of these iterative floating-point
                 \ldots{}",
}

@Article{Cornea-Hasegan:1999:IFP,
  author =       "Marius Cornea-Hasegan and Bob Norin",
  title =        "{IA-64} Floating-Point Operations and the {IEEE}
                 Standard for Binary Floating-Point Arithmetic",
  journal =      j-INTEL-TECH-J,
  volume =       "Q4",
  pages =        "16",
  day =          "22",
  month =        nov,
  year =         "1999",
  ISSN =         "1535-766X",
  bibdate =      "Fri Jun 01 06:02:08 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/intel-tech-j.bib",
  URL =          "http://developer.intel.com/technology/itj/q41999/articles/art_6.htm;
                 http://developer.intel.com/technology/itj/q41999/pdf/ia64fpbf.pdf;
                 http://gec.di.uminho.pt/discip/minf/ac0203/icca03/ia64fpbf1.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Corsonello:1999:HPS,
  author =       "P. Corsonello and S. Perri",
  title =        "High performance square rooting circuit using hybrid
                 radix-$2$ adders",
  journal =      j-ELECT-LETTERS,
  volume =       "35",
  number =       "3",
  pages =        "185--186",
  day =          "4",
  month =        feb,
  year =         "1999",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  summary =      "A new high performance bit parallel architecture for
                 computing square roots is proposed. The architecture
                 implements a non-restoring algorithm and is structured
                 as a pipelined cellular array. To improve the
                 performance, hybrid radix-$2$ adders are \ldots{}",
}

@TechReport{Crandall:1999:VIM,
  author =       "Richard E. Crandall and Jason Klivington",
  title =        "Vector implementation of multiprecision arithmetic",
  type =         "Report",
  institution =  "Advanced Computation Group, Apple Computer",
  address =      "Cupertino, CA, USA",
  pages =        "11",
  day =          "25",
  month =        oct,
  year =         "1999",
  bibdate =      "Tue Mar 19 09:06:09 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://images.apple.com/acg/pdf/G4multiprecision.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Cucker:1999:CED,
  author =       "Felipe Cucker and Steve Smale",
  title =        "Complexity estimates depending on condition and
                 round-off error",
  journal =      j-J-ACM,
  volume =       "46",
  number =       "1",
  pages =        "113--184",
  month =        jan,
  year =         "1999",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Tue May 25 18:51:21 MDT 1999",
  bibsource =    "http://www.acm.org/pubs/contents/journals/jacm/1999-46/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org:80/pubs/citations/journals/jacm/1999-46-1/p113-cucker/",
  abstract =     "This paper has two agendas. One is to develop the
                 foundations of round-off in computation. The other is
                 to describe an algorithm for deciding feasibility for
                 polynomial systems of equations and inequalities
                 together with its complexity analysis and its round-off
                 properties. Each role reinforces the other.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  keywords =     "algorithms; theory",
  subject =      "{\bf F.2.1} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems. {\bf G.1.5} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Roots of Nonlinear Equations.",
}

@TechReport{Cuyt:1999:UR,
  author =       "Annie Cuyt and Peter Kuterna and Brigitte Verdonk and
                 Dennis Verschaeren",
  title =        "Underflow revisited",
  type =         "Technical report",
  institution =  "University of Antwerp (UIA)",
  address =      "Antwerp, Belgium",
  year =         "1999",
  bibdate =      "Mon Feb 25 12:26:10 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://wins.uia.ac.be/pub/preprints/99/underflow.ps",
  acknowledgement = ack-nhfb,
}

@InProceedings{Darcy:1999:JEF,
  author =       "J. D. Darcy",
  editor =       "Robert F. Enenkel",
  booktitle =    "{CASCON 1998} Workshop Report, Numerical Computing:
                 Compiler and Library Support",
  title =        "{Java}'s evolving floating-point support: The good,
                 the bad, and the ugly",
  publisher =    "IBM Center for Advanced Studies",
  address =      "Toronto, ON, Canada",
  pages =        "2--10",
  year =         "1999",
  bibdate =      "Sun May 28 18:36:17 2006",
  bibsource =    "https://www-927.ibm.com/ibm/cas/publications/TR-74.165/TR-74.165.shtml;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Technical report TR-74.165-n.",
  URL =          "https://www-927.ibm.com/ibm/cas/publications/TR-74.165/n/numcomp6.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Daumas:1999:DFP,
  author =       "Marc Daumas and C. Finot",
  title =        "Division of Floating Point Expansions with an
                 Application to the Computation of a Determinant",
  journal =      j-J-UCS,
  volume =       "5",
  number =       "6",
  pages =        "323--??",
  day =          "28",
  month =        jun,
  year =         "1999",
  CODEN =        "????",
  ISSN =         "0948-6968",
  ISSN-L =       "0948-6968",
  bibdate =      "Thu Oct 12 14:21:59 MDT 2000",
  bibsource =    "http://www.jucs.org/jucs;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.jucs.org/jucs_5_6/division_of_floating_point",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
}

@InProceedings{Daumas:1999:MFP,
  author =       "Marc Daumas",
  title =        "Multiplications of Floating Point Expansions",
  crossref =     "Koren:1999:ISC",
  pages =        "250--257",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-102.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-102.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Daumas.pdf",
  abstract =     "In modern computers, the floating point unit is the
                 part of the processor delivering the highest computing
                 power and getting most attention from the design team.
                 Performance of any multiple precision application will
                 be dramatically enhanced by adequate use of floating
                 point expansions. We present in this work three
                 multiplication algorithms faster and more integrated
                 than the stepwise algorithm proposed earlier. We have
                 tested these new algorithms on an application that
                 computes the determinant of a matrix. In the absence of
                 overflow or underflow, the process is error free and
                 possibly more efficient than its integer based
                 counterpart.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic",
}

@Article{Denise:1999:URG,
  author =       "A. Denise and P. Zimmermann",
  title =        "Uniform random generation of decomposable structures
                 using floating-point arithmetic",
  journal =      j-THEOR-COMP-SCI,
  volume =       "218",
  number =       "2",
  pages =        "233--248",
  day =          "26",
  month =        may,
  year =         "1999",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Ingenta database",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
  pagecount =    "16",
}

@Article{Dimitrov:1999:TAD,
  author =       "V. S. Dimitrov and G. A. Jullien and W. C. Miller",
  title =        "Theory and Applications for a Double-Base Number
                 System",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "48",
  number =       "10",
  pages =        "1098--1106",
  year =         "1999",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.805158",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Nov 14 18:56:28 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Dimitrova:1999:VCF,
  author =       "N. S. Dimitrova and S. M. Markov",
  title =        "Verified Computation of Fast Decreasing Polynomials",
  journal =      j-RELIABLE-COMPUTING,
  volume =       "5",
  number =       "3",
  pages =        "229--240",
  year =         "1999",
  CODEN =        "RCOMF8",
  ISSN =         "1385-3139 (print), 1573-1340 (electronic)",
  ISSN-L =       "1385-3139",
  bibdate =      "Mon May 20 06:37:48 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  fjournal =     "Reliable Computing = Nadezhnye vychisleniia",
  journal-URL =  "http://link.springer.com/journal/11155",
  remark =       "Papers from Scientific computing, computer arithmetic
                 and validated numerics (SCAN '98), September 1998,
                 Budapest, Hungary.",
}

@Misc{Dyke-Lewis:1999:MAP,
  author =       "M. D. V. Dyke-Lewis and W. Meeker",
  title =        "Method and Apparatus for performing fast floating
                 point operations",
  day =          "12",
  month =        oct,
  year =         "1999",
  bibdate =      "Fri Nov 28 15:17:46 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "U.S. Patent No. 5,966,085.",
  acknowledgement = ack-nhfb,
}

@Article{Dyllong:1999:ADC,
  author =       "E. Dyllong and W. Luther and W. Otten",
  title =        "An Accurate Distance-Calculation Algorithm for Convex
                 Polyhedra",
  journal =      j-RELIABLE-COMPUTING,
  volume =       "5",
  number =       "3",
  pages =        "241--253",
  year =         "1999",
  CODEN =        "RCOMF8",
  ISSN =         "1385-3139 (print), 1573-1340 (electronic)",
  ISSN-L =       "1385-3139",
  bibdate =      "Mon May 20 06:37:48 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  fjournal =     "Reliable Computing = Nadezhnye vychisleniia",
  journal-URL =  "http://link.springer.com/journal/11155",
  remark =       "Papers from Scientific computing, computer arithmetic
                 and validated numerics (SCAN '98), September 1998,
                 Budapest, Hungary.",
}

@Manual{ECDG:1999:IER,
  author =       "{European Commission Directorate General II}",
  title =        "The Introduction of the Euro and the Rounding of
                 Currency Amounts",
  organization = "European Commission Directorate General II Economic
                 and Financial Affairs",
  address =      "Brussels, Belgium",
  pages =        "32",
  month =        feb,
  year =         "1999",
  bibdate =      "Fri Nov 28 11:18:05 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "II/28/99-EN Euro Papers No. 22. Earlier edition dated
                 March 1998.",
  acknowledgement = ack-nhfb,
}

@Article{Edalat:1999:NIE,
  author =       "A. Edalat and M. Krznaric",
  title =        "Numerical Integration with Exact Real Arithmetic",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1644",
  pages =        "90--??",
  year =         "1999",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Mon Sep 13 16:57:02 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs1999b.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@TechReport{Ercegovac:1999:IGD,
  author =       "Milo{\v{s}} D. Ercegovac and Laurent Imbert and David
                 W. Matula and Jean-Michel Muller and Guoheng Wei",
  title =        "Improving {Goldschmidt} Division, Square Root, and
                 Square Root Reciprocal",
  type =         "Research Report",
  number =       "99-41",
  institution =  "Laboratoire de l'Informatique du Parall{\'e}lisme",
  address =      "Lyon, France",
  pages =        "ii + 17",
  month =        sep,
  year =         "1999",
  bibdate =      "Mon Dec 11 07:53:15 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://inria.hal.science/inria-00072909/file/RR1999-41.pdf",
  abstract =     "The aim of this paper is to accelerate division,
                 square root and square root reciprocal computations,
                 when Goldschmidt method is used on a pipelined
                 multiplier. This is done by replacing the last
                 iteration by the addition of a correcting term that can
                 be looked up during the early iterations. We describe
                 several variants of the Goldschmidt algorithm assuming
                 4-cycle pipelined multiplier and discuss obtained
                 number of cycles and error achieved. Extensions to
                 other than 4-cycle multipliers are given",
  acknowledgement = ack-nhfb,
  keywords =     "Computer Arithmetic; Convergence division; Division;
                 Goldschmidt iteration; Square root; Square root
                 reciprocal",
}

@InProceedings{Ercegovac:1999:LPB,
  author =       "M. Ercegovac and D. Kirovski and M. Potkonjak",
  booktitle =    "Proceedings of the 36th Design Automation Conference,
                 21--25 June 1999",
  title =        "Low-power behavioral synthesis optimization using
                 multiple precision arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "568--573",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:53:44 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Many modern multimedia applications such as image and
                 video processing are characterized by a unique
                 combination of arithmetic and computational features:
                 fixed-point arithmetic, a variety of short data types,
                 high degree of instruction-level \ldots{}",
}

@InProceedings{Even:1999:CTR,
  author =       "Guy Even and Peter-Michael Seidel",
  title =        "A Comparison of Three Rounding Algorithms for {IEEE}
                 Floating-Point Multiplication",
  crossref =     "Koren:1999:ISC",
  pages =        "225--232",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-100.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-100.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Even.pdf",
  abstract =     "A new IEEE compliant floating-point rounding algorithm
                 for computing the rounded product from a carry-save
                 representation of the product is presented. The new
                 rounding algorithm is compared with the rounding
                 algorithms of Yu and Zyner [23] and of Quach et al.
                 [18]. For each rounding algorithm, a logical
                 description and a block diagram is given and the
                 latency is analyzed.\par

                 We conclude that the new rounding algorithm is the
                 fastest rounding algorithm, provided that an injection
                 (which depends only on the rounding mode and the sign)
                 can be added in during the reduction of the partial
                 products into a carry-save encoded digit string. In
                 double precision the latency of the new rounding
                 algorithm is 12 logic levels compared to 14 logic
                 levels in the algorithm of Quach et al., and 16 logic
                 levels in the algorithm of Yu and Zyner.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic",
}

@InProceedings{Eweda:1999:REA,
  author =       "E. Eweda and W. M. Younis and S. H. El-Ramly",
  booktitle =    "Proceedings of the Sixteenth National Radio Science
                 Conference 1999: {NRSC '99}",
  title =        "Roundoff error analysis of the tracking performance of
                 the block {LMS} algorithm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "C30/1--C30/9",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The paper is concerned with analyzing the roundoff
                 error effect on the tracking performance of the block
                 least mean square (BLMS) algorithm when used in the
                 adaptive identification of a time-varying plant.
                 Rounding quantization is assumed. \ldots{}",
}

@Article{Farid:1999:RCA,
  author =       "T. Farid and D. Zerbino",
  title =        "Realization of Complex Arithmetic on Cellular
                 Automata",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1662",
  pages =        "479--??",
  year =         "1999",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Mon Sep 13 16:57:02 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs1999b.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Fateman:1999:SEN,
  author =       "Richard J. Fateman",
  title =        "Symbolic execution and {NaNs}: diagnostic tools for
                 tracking scientific computation",
  journal =      j-SIGSAM,
  volume =       "33",
  number =       "3",
  pages =        "25--26",
  month =        sep,
  year =         "1999",
  CODEN =        "SIGSBZ",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Fri Feb 8 18:27:06 MST 2002",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGSAM Bulletin",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}

@InProceedings{Fernandez:1999:NID,
  author =       "P. G. Fernandez and A. Garcia and J. Ramirez and L.
                 Parrilla and A. Lloris",
  booktitle =    "Conference Record of the Thirty-Third Asilomar
                 Conference on Signals, Systems, and Computers, 1999",
  title =        "A new implementation of the discrete cosine transform
                 in the residue number system",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1302--1306",
  year =         "1999",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ACSSC.1999.831917",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A field-programmable logic (FPL) implementation of a
                 discrete cosine transform (DCT) based on the residue
                 number system (RNS) is presented. Compared with a
                 binary distributed arithmetic implementation, the
                 presented architecture provides \ldots{}",
}

@Article{Fiore:1999:PMU,
  author =       "P. D. Fiore",
  title =        "Parallel multiplication using fast sorting networks",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "48",
  number =       "6",
  pages =        "640--645",
  month =        jun,
  year =         "1999",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.773800",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:46:58 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=773800",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Flynn:1999:FDA,
  author =       "Patrick Hung and Hossam Fahmy and Oskar Mencer and
                 Michael J. Flynn",
  editor =       "{IEEE}",
  booktitle =    "Asilomar Conference on Signals, Systems, and
                 Computers, California, Nov. 1999",
  title =        "Fast Division Algorithm with a Small Lookup Table",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "??--??",
  year =         "1999",
  bibdate =      "Mon Jul 18 17:26:03 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://arith.stanford.edu/tr/asil99div.ps.gz",
  abstract =     "This paper presents a new division algorithm, which
                 requires two multiplication operations and a single
                 lookup in a small table. The division algorithm takes
                 two steps. The table lookup and the first
                 multiplication are processed concurrently in the first
                 step, and the second multiplication is executed in the
                 next step. This divider uses a single multiplier and a
                 lookup table with $ 2^m(2 m + 1) $ bits to produce $ 2
                 m $-bit results that are guaranteed correct to one ulp.
                 By using a multiplier and a KB lookup table, the basic
                 algorithm generates a 24-bit result in two cycles.",
  acknowledgement = ack-nhfb,
  pagecount =    "4",
}

@InProceedings{Freking:1999:MMM,
  author =       "W. L. Freking and K. K. Parhi",
  booktitle =    "Conference Record of the Thirty-Third Asilomar
                 Conference on Signals, Systems, and Computers, 1999",
  title =        "{Montgomery} modular multiplication and exponentiation
                 in the residue number system",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1312--1316",
  year =         "1999",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ACSSC.1999.831919",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Modular exponentiation and its constituent operation,
                 modular multiplication, are fundamental to numerous
                 public-key cryptography schemes including RSA.
                 Efficient hardware implementations via ASIC or
                 coprocessor approaches are essential to high-
                 \ldots{}",
}

@Article{Frommer:1999:VEB,
  author =       "A. Frommer and A. Weinberg",
  title =        "Verified Error Bounds for Linear Systems Through the
                 {Lanczos} Process",
  journal =      j-RELIABLE-COMPUTING,
  volume =       "5",
  number =       "3",
  pages =        "255--267",
  year =         "1999",
  CODEN =        "RCOMF8",
  ISSN =         "1385-3139 (print), 1573-1340 (electronic)",
  ISSN-L =       "1385-3139",
  bibdate =      "Mon May 20 06:37:48 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  fjournal =     "Reliable Computing = Nadezhnye vychisleniia",
  journal-URL =  "http://link.springer.com/journal/11155",
  remark =       "Papers from Scientific computing, computer arithmetic
                 and validated numerics (SCAN '98), September 1998,
                 Budapest, Hungary.",
}

@Article{Garcia:1999:LSS,
  author =       "A. Garcia and A. Lloris",
  title =        "A look-up scheme for scaling in the {RNS}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "48",
  number =       "7",
  pages =        "748--751",
  month =        jul,
  year =         "1999",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.780883",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:46:58 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=780883",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Gay:1999:SAF,
  author =       "David M. Gay and Eric Grosse",
  title =        "Self-adapting {Fortran 77} Machine Constants: Comment
                 on {Algorithm 528}",
  journal =      j-TOMS,
  volume =       "25",
  number =       "1",
  pages =        "123--126",
  month =        mar,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/305658.305711",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 20 12:38:08 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Fox:1978:AFP}.",
  URL =          "http://cm.bell-labs.com/who/ehg/mach/d1mach.ps;
                 http://www.acm.org/pubs/citations/journals/toms/cgi-bin/TOMSbibget?Gay:1999:SAF;
                 http://www.acm.org/pubs/citations/journals/toms/cgi-bin/TOMScitation?Fox:1978:AFP;
                 http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p123-gay/",
  abstract =     "This note discusses user dissatisfaction with the need
                 to uncomment data statements in Algorithm 528, comments
                 on alternative approaches tried by the community, and
                 proposes a solution that is both automatic and safe.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; d1mach; languages; machine environment
                 parameters",
  subject =      "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN 77. {\bf G.1.0} Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Computer
                 arithmetic.",
}

@Article{German:1999:ISI,
  author =       "Steven M. German",
  title =        "Introduction to the Special Issue on Verification of
                 Arithmetic Hardware",
  journal =      j-FORM-METHODS-SYST-DES,
  volume =       "14",
  number =       "1",
  pages =        "5--6",
  month =        jan,
  year =         "1999",
  CODEN =        "FMSDE6",
  ISSN =         "0925-9856 (print), 1572-8102 (electronic)",
  ISSN-L =       "0925-9856",
  bibdate =      "Sat Jun 02 09:20:18 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.wkap.nl/jrnltoc.htm/0925-9856;
                 http://www.wkap.nl/oasis.htm/194805",
  acknowledgement = ack-nhfb,
  fjournal =     "Formal Methods in System Design",
  journal-URL =  "https://dl.acm.org/loi/fmsd",
}

@InProceedings{Gerwig:1999:FPU,
  author =       "Guenter Gerwig and Michael Kroener",
  title =        "Floating-Point Unit in Standard Cell Design with $ 116
                 $ bit Wide Dataflow",
  crossref =     "Koren:1999:ISC",
  pages =        "266--273",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-132.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-132.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Gerwig.pdf",
  abstract =     "The floating-point unit of a S/390 CMOS microprocessor
                 is described. It contains a 116 bit fraction dataflow
                 for addition and subtraction and a 64 bit-wide
                 multiplier. Besides the register array, there are no
                 other dataflow macros used; it is fully designed with
                 standard cell books and is placed flat with a timing
                 driven placement algorithm. This design method allows
                 more `irregular' structures than usually found in
                 custom designs.\par

                 An overview of the floating-point unit is given and
                 some interesting design items are shown: a 120 bit-wide
                 true-complement adder with precounting of leading zero
                 digits, a signed multiplier with bit-optimized Wallace
                 tree, intensive forwarding in source equal target cases
                 and the checking method.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic",
}

@Article{Gizopoulos:1999:EBS,
  author =       "D. Gizopoulos and A. Paschalis and Y. Zorian",
  title =        "An effective built-in self-test scheme for parallel
                 multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "48",
  number =       "9",
  pages =        "936--950",
  month =        sep,
  year =         "1999",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.795222",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:46:59 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=795222",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Misc{Gorshtein:1999:MAM,
  author =       "V. Y. Gorshtein and V. T. Khlobystov",
  title =        "Multiplication apparatus and methods which generate a
                 shift amount by which the product of the significands
                 is shifted for normalization or denormalization",
  day =          "5",
  month =        oct,
  year =         "1999",
  bibdate =      "Fri Nov 28 15:32:30 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "U.S. Patent No. 5,963,461.",
  acknowledgement = ack-nhfb,
}

@Article{Gueron:1999:FFP,
  author =       "Shay Gueron",
  title =        "Flying in a floating (point) world",
  journal =      "International Journal of Computers for Mathematical
                 Learning",
  volume =       "4",
  number =       "2--3",
  pages =        "225--234",
  month =        may,
  year =         "1999",
  DOI =          "https://doi.org/10.1023/A:1009818429410",
  ISSN =         "1382-3892 (print), 1573-1766 (electronic)",
  ISSN-L =       "1382-3892",
  bibdate =      "Wed Jul 01 15:36:52 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/content/j071k8608t578153/",
  acknowledgement = ack-nhfb,
  journal-URL =  "https://link.springer.com/journal/10758",
}

@InProceedings{Gustavson:1999:FMA,
  author =       "Fred G. Gustavson and Jos{\'e} E. Moreira and Robert
                 F. Enenk",
  editor =       "????",
  booktitle =    "{CASCON '99}: Proceedings of the 1999 Conference of
                 the Centre for Advanced Studies on Collaborative
                 Research. November 8--11, 1999, Mississauga, Ontario,
                 Canada",
  title =        "The fused multiply-add instruction leads to algorithms
                 for extended-precision floating point: applications to
                 {Java} and high-performance computing",
  publisher =    pub-IBM,
  address =      pub-IBM:adr,
  pages =        "4",
  year =         "1999",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Fri Nov 26 15:40:34 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Dedicated to Cleve Moler on his 60th birthday.",
  acknowledgement = ack-nhfb,
}

@Misc{Handlogten:1999:MAP,
  author =       "G. H. Handlogten",
  title =        "Method and apparatus to perform pipelined
                 denormalization of floating-point results",
  day =          "24",
  month =        aug,
  year =         "1999",
  bibdate =      "Fri Nov 28 15:37:38 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "U.S. Patent No. 5,943,249.",
  acknowledgement = ack-nhfb,
}

@Article{Harrison:1999:CTF,
  author =       "John Harrison and Ted Kubaska and Shane Story and Ping
                 Tak Peter Tang",
  title =        "The Computation of Transcendental Functions on the
                 {IA-64} Architecture",
  journal =      j-INTEL-TECH-J,
  volume =       "Q4",
  pages =        "7",
  day =          "22",
  month =        nov,
  year =         "1999",
  bibdate =      "Fri Jun 01 06:02:08 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://developer.intel.com/technology/itj/q41999/articles/art_5.htm;
                 http://developer.intel.com/technology/itj/q41999/pdf/transendental.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Harrison:1999:MCT,
  author =       "John Harrison",
  editor =       "Yves Bertot and Gilles Dowek and Andr{\'e} Hirschowitz
                 and Christine Paulin and Laurent Th{\'e}ry",
  booktitle =    "Theorem Proving in Higher Order Logics: 12th
                 International Conference, {TPHOLs'99}",
  title =        "A Machine-Checked Theory of Floating Point
                 Arithmetic",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1690",
  pages =        "113--130",
  year =         "1999",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/3-540-48256-3_9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Jun 5 10:53:14 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cl.cam.ac.uk/users/jrh/papers/fparith.html;
                 http://www.cl.cam.ac.uk/~jrh13/papers/fparith.pdf",
  acknowledgement = ack-jh,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Hayashi:1999:SRR,
  author =       "Takao Hayashi",
  title =        "A set of rules for the root-extraction prescribed by
                 the sixteenth-century {Indian} mathematicians,
                 {N{\=\i}laka{\d{n}}{\d{t}}ha Somastuvan} and
                 {{\'S}a{\.n}kara V{\=a}riyar}",
  journal =      j-HIST-SCI-2,
  volume =       "9",
  number =       "2",
  pages =        "135--153",
  month =        nov,
  year =         "1999",
  CODEN =        "HISCDU",
  ISSN =         "0285-4821",
  ISSN-L =       "0285-4821",
  MRclass =      "01A32",
  MRnumber =     "1762168",
  MRreviewer =   "A. I. Volodarski{\u\i}",
  bibdate =      "Sat Oct 6 17:22:25 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/histscijpn.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Historia Scientiarum. Second Series. International
                 Journal of the History of Science Society of Japan",
  journal-URL =  "http://hssj.info/",
}

@Article{Heindl:1999:RIH,
  author =       "G. Heindl",
  title =        "A Representation of the Interval Hull of a Tolerance
                 Polyhedron Describing Inclusions of Function Values and
                 Slopes",
  journal =      j-RELIABLE-COMPUTING,
  volume =       "5",
  number =       "3",
  pages =        "269--278",
  year =         "1999",
  CODEN =        "RCOMF8",
  ISSN =         "1385-3139 (print), 1573-1340 (electronic)",
  ISSN-L =       "1385-3139",
  bibdate =      "Mon May 20 06:37:48 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  fjournal =     "Reliable Computing = Nadezhnye vychisleniia",
  journal-URL =  "http://link.springer.com/journal/11155",
  remark =       "Papers from Scientific computing, computer arithmetic
                 and validated numerics (SCAN '98), September 1998,
                 Budapest, Hungary.",
}

@Article{Hiasat:1999:SCV,
  author =       "Ahmad A. Hiasat and Hoda Abdel-Aty-Zohdy",
  title =        "Semi-Custom {VLSI} Design and Implementation of a New
                 Efficient {RNS} Division Algorithm",
  journal =      j-COMP-J,
  volume =       "42",
  number =       "3",
  pages =        "232--240",
  month =        "????",
  year =         "1999",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Thu Sep 2 06:09:59 MDT 1999",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_42/Issue_03/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_42/Issue_03/420232.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_42/Issue_03/pdf/420232.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@MastersThesis{Hirn:1999:GBI,
  author =       "Ulrich Hirn",
  title =        "{Groebner} bases implementation using modular and
                 floating point arithmetic",
  type =         "{Dipl.-Arb.}",
  school =       "Technische Universit{\"a}t Graz",
  address =      "Graz, Austria",
  pages =        "87",
  year =         "1999",
  bibdate =      "Thu May 09 09:37:46 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hormigo:1999:ISC,
  author =       "J. Hormigo and J. Villalba and E. L. Zapata",
  title =        "Interval Sine and Cosine Functions Computation Based
                 on Variable Precision {CORDIC} Algorithm",
  crossref =     "Koren:1999:ISC",
  pages =        "186--193",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-128.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-128.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Hormigo.pdf",
  abstract =     "In this paper we design a CORDIC architecture for
                 variable-precision, and a new algorithm is proposed to
                 perform the interval sine and cosine functions. This
                 system allows us to specify the precision to perform
                 the sine and cosine functions, and control the accuracy
                 of the result, in such a way that recomputation of
                 inaccurate results can be carried out with higher
                 precision. An important reduction in the number of
                 iterations is obtained by taking advantage of the
                 differential angle, and the number of cycles per
                 iteration is reduced by avoiding the additions of the
                 leading all zero words. As a consequence, the
                 computation time of the interval function evaluation
                 obtained is close to that of a point function
                 evaluation. The problem of the large table of angles
                 and the scale factor compensation involved in a high
                 precision CORDIC has been solved efficiently.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic",
}

@InProceedings{Hung:1999:FDA,
  author =       "P. Hung and H. Fahmy and O. Mencer and M. J. Flynn",
  title =        "Fast division algorithm with a small lookup table",
  crossref =     "Matthews:1999:CRT",
  volume =       "2",
  pages =        "1465--1468",
  year =         "1999",
  DOI =          "https://doi.org/10.1109/ACSSC.1999.831992",
  bibdate =      "Sat Oct 9 12:45:46 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper presents a new division algorithm, which
                 requires two multiplication operations and a single
                 lookup in a small table. The division algorithm takes
                 two steps. The table lookup and the first
                 multiplication are processed concurrently in the first
                 step, and the second multiplication is executed in the
                 next step. This divider uses a single multiplier and a
                 lookup table with $ 2 m (2 m + 1) $ bits to produce $2$
                 $m$-bit results that are guaranteed correct to one ulp.
                 By using a multiplier and a 12.5 KB lookup table, the
                 basic algorithm generates a 24-bit result in two
                 cycles",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hyogo:1999:LVF,
  author =       "A. Hyogo and Y. Fukutomi and K. Sekine",
  booktitle =    "Proceedings of the 1999 {IEEE} International Symposium
                 on Circuits and Systems: {ISCAS '99}, 2 June 1999",
  title =        "Low voltage four-quadrant analog multiplier using
                 square-root circuit based on {CMOS} pair",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "274--277",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "We proposed a square-root circuit based on CMOS pairs.
                 In this paper, we propose a low voltage four-quadrant
                 analog multiplier using the square-root circuit. Also
                 we confirmed this operation by PSpice \ldots{}",
}

@InProceedings{Ide:1999:GFP,
  author =       "N. Ide and M. Hirano and Y. Endo and S. Yoshioka and
                 H. Murakami and A. Kunimatsu and T. Sato and T. Kamei
                 and T. Okada and M. Suzuoki",
  title =        "{2.44 GFLOPS 300MHz} floating-point vector processing
                 unit for high performance {$3$D} graphics computing",
  crossref =     "Hosticka:1999:EPE",
  pages =        "106--109",
  year =         "1999",
  bibdate =      "Sat Jun 02 08:23:03 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Iordache:1999:ARS,
  author =       "Cristina Iordache and David W. Matula",
  title =        "Analysis of Reciprocal and Square Root Reciprocal
                 Instructions in the {AMD K6-2} Implementation of
                 {3DNow!}",
  journal =      j-ELECT-NOTES-THEOR-COMP-SCI,
  volume =       "24",
  pages =        "34--62",
  month =        apr,
  year =         "1999",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/S1571-0661(05)80621-8",
  ISSN =         "1571-0661",
  ISSN-L =       "1571-0661",
  bibdate =      "Fri Jun 24 20:23:13 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Reciprocal and root reciprocal functions at ``half''
                 and IEEE single precision formats are specified in the
                 AMD 3DNow! instruction set. Implementations in the
                 recently released AMD K6-2 microprocessor are analyzed
                 herein by exhaustive computation and timing loops to
                 ascertain the accuracy and monotonicity properties of
                 the output and throughput\slash latency cycle counts.
                 Periodicities in stepwise function output were observed
                 and employed to construct an underlying bipartite table
                 that can serve as the core of the respective reciprocal
                 function outputs. The recommended RISC instruction
                 macros generated single precision reciprocals and root
                 reciprocals accurate to a unit in the last place.
                 However, the root reciprocal functions failed to
                 satisfy the desirable monotonicity property typically
                 implemented as an industry standard for elementary
                 functions on x86 floating point units. Reasons for the
                 failure are provided and an adjusted table is shown to
                 satisfy the monotonicity standard. Results are
                 summarized in Table 1 and described in the body of this
                 report.",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronic Notes in Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/15710661",
}

@InProceedings{Iordache:1999:IPR,
  author =       "Cristina Iordache and David W. Matula",
  title =        "On Infinitely Precise Rounding for Division, Square
                 Root, Reciprocal and Square Root Reciprocal",
  crossref =     "Koren:1999:ISC",
  pages =        "233--240",
  year =         "1999",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-164.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-164.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Iordache.pdf",
  abstract =     "Quotients, reciprocals, square roots and square root
                 reciprocals all have the property that infinitely
                 precise p-bit rounded results for p-bit input operands
                 can be obtained from approximate results of bounded
                 accuracy. We investigate lower bounds on the number of
                 bits of an approximation accurate to a unit in the last
                 place sufficient to guarantee that correct round and
                 sticky bits can be determined. Known lower bounds for
                 quotients and square roots are given and/or sharpened,
                 and a new lower bound for root reciprocals is proved.
                 Specifically for reciprocals, quotients and square
                 roots, tight bounds of order $ 2 p + O(1) $ are
                 presented. For infinitely precise rounding of the root
                 reciprocal a lower bound can be found at $ 3 p + O(1)
                 $, but exhaustive testing for small sizes of the
                 operand suggests that in practice $ (2 + \epsilon)p $
                 for small $ \epsilon $ is usually sufficient.
                 Algorithms can be designed for obtaining the round and
                 sticky bits based on the bit pattern of an
                 approximation computed to the required accuracy. We
                 show that some improvement of the known lower bound for
                 reciprocals and division is achievable at the cost of
                 somewhat more complex hardware for rounding. Tests for
                 the exactness of the quotient and square root are also
                 provided.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic; correct rounding;
                 floating-point arithmetic",
  summary =      "Quotients, reciprocals, square roots and square root
                 reciprocals all have the property that infinitely
                 precise p-bit rounded results for p-bit input operands
                 can be obtained from approximate results of bounded
                 accuracy. We investigate lower bounds \ldots{}",
}

@Article{Jamieson:1999:NRF,
  author =       "M. J. Jamieson",
  title =        "Notes: On rational function approximations to square
                 roots",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "106",
  number =       "1",
  pages =        "50--52",
  month =        jan,
  year =         "1999",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "11Yxx",
  MRnumber =     "1 674 202",
  bibdate =      "Tue Jun 22 10:29:34 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Article{Jamieson:1999:RFA,
  author =       "M. J. Jamieson",
  title =        "On rational function approximations to square roots",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "106",
  number =       "1",
  pages =        "50--52",
  year =         "1999",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "11Yxx",
  MRnumber =     "1 674 202",
  bibdate =      "Tue Jun 22 10:29:34 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@InProceedings{Jeong:1999:CPT,
  author =       "Cheol-Ho Jeong and Woo-Chan Park and Tack-Don Dan and
                 Shin-Dug Kim",
  title =        "Cost\slash performance Trade-off in Floating-point
                 Unit Design for {$3$D} Geometry Processor",
  crossref =     "IEEE:1999:AAF",
  pages =        "104--107",
  year =         "1999",
  DOI =          "https://doi.org/10.1109/APASIC.1999.824039",
  bibdate =      "Fri Jun 24 12:18:17 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Misc{Jones:1999:BAT,
  author =       "Douglas W. Jones",
  title =        "{BCD} Arithmetic, a tutorial",
  howpublished = "Web tutorial.",
  year =         "1999",
  bibdate =      "Tue Jan 22 07:13:24 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://homepage.cs.uiowa.edu/~jones/bcd/bcd.html",
  acknowledgement = ack-nhfb,
}

@Misc{Jones:1999:BDC,
  author =       "Douglas W. Jones",
  title =        "Binary to Decimal Conversion in Limited Precision",
  howpublished = "Web tutorial.",
  year =         "1999",
  bibdate =      "Tue Jan 22 07:13:24 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://homepage.cs.uiowa.edu/~jones/bcd/decimal.html",
  acknowledgement = ack-nhfb,
}

@Misc{Jones:1999:MDT,
  author =       "Douglas W. Jones",
  title =        "Modulus without Division, a tutorial",
  howpublished = "Web tutorial.",
  year =         "1999",
  bibdate =      "Tue Jan 22 07:13:24 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://homepage.cs.uiowa.edu/~jones/bcd/mod.shtml",
  acknowledgement = ack-nhfb,
}

@Misc{Jones:1999:RMT,
  author =       "Douglas W. Jones",
  title =        "Reciprocal Multiplication, a tutorial",
  howpublished = "Web tutorial.",
  year =         "1999",
  bibdate =      "Tue Jan 22 07:13:24 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://homepage.cs.uiowa.edu/~jones/bcd/divide.html",
  acknowledgement = ack-nhfb,
}

@InProceedings{Jullien:1999:HDP,
  author =       "G. A. Jullien and V. S. Dimitrov and B. Li and W. C.
                 Miller and A. Lee and M. Ahmadi",
  editor =       "{IEEE}",
  booktitle =    "{Proceedings of the 1999 IEEE International Symposium
                 on Circuits and Systems: ISCAS '99, May 30--June 2
                 1999, Orlando, Florida}",
  title =        "A Hybrid {DBNS} Processor for {DSP} Computation",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  bookpages =    "liv + 565",
  pages =        "5--8",
  year =         "1999",
  DOI =          "https://doi.org/10.1109/ISCAS.1999.777792",
  ISBN =         "0-7803-5471-0 (softbound), 0-7803-5472-9 (casebound),
                 0-7803-5473-7 (microfiche)",
  ISBN-13 =      "978-0-7803-5471-5 (softbound), 978-0-7803-5472-2
                 (casebound), 978-0-7803-5473-9 (microfiche)",
  LCCN =         "TK7801 .I22 1999",
  bibdate =      "Sat May 14 17:21:37 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog number 99CH36349.",
  acknowledgement = ack-nhfb,
  keywords =     "Double-Based Number System (DBNS)",
}

@Misc{Kahan:1999:SRD,
  author =       "W. Kahan",
  title =        "Square Root Without Division",
  howpublished = "World-Wide Web document",
  pages =        "3",
  day =          "23",
  month =        feb,
  year =         "1999",
  bibdate =      "Mon Apr 25 18:01:49 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/reciprt.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Kaplan:1999:JVA,
  author =       "Bonnie Kaplan",
  title =        "{John V. Atanasoff} (1903--1995) interview: {August
                 10, 1972}",
  journal =      "Computer Oral History Collection, Smithsonian
                 Institution Press",
  year =         "1999",
  bibdate =      "Fri Aug 08 08:33:46 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Article No. 17.",
  abstract =     "The conversation begins with Atanasoff's method of
                 adding and counting---an idea he conceived of while in
                 a honky-tonk bar in Illinois in 1937. This concept of
                 addition was to be performed by logic and not by
                 successive inching of a dial. Atanasoff further remarks
                 that his interest in electronic computation began by
                 thinking along the Eccles-Jordan lines. The
                 Eccles-Jordan circuit was used for part of the
                 operation and intended to do successive impulses.
                 Further comments about the Eccles-Jordan circuitry are
                 made. The use of vacuum tubes in Atanasoff's machine
                 was prompted be economy. Vacuum tube circuits were fast
                 enough to solve the sums of all digits and thus
                 economize on time and material. The use of base two for
                 arithmetic was employed because it was simpler. The use
                 of dual triodes (6F8G and then ultimately the 6C8G) in
                 the circuitry was also based on economy--original cost
                 and space. The difference between these two tubes is
                 discussed. Comments on the machines ability to do
                 subtraction using [Comptu's?] complements. Atanasoff
                 decided to use the complements in the memory in order
                 to subtract. This use of complements was not original
                 to Atanasoff. Atanasoff explains his use of lower base
                 numbers opposed to larger. The simplest way of storing
                 numbers up to 25 is by coding them into numbers
                 probably with a base of two. Numbers associated with
                 the base of two were associated with a simpler logical
                 system. While Atanasoff experimented with larger base
                 numbers, he found them to unsatisfactory. Atanasoff
                 discussed his decision to use base two with George
                 Gross and William Mercer who did the calculations which
                 were needed for the base ten- base two conversion
                 table. While doing the conversions on the machine, the
                 addition was automatically carried out in the computing
                 machine. Atanasoff explains the concept of a floating
                 grid. This type of grid implied that it did not have a
                 bias resistor to the ground, it was not connected.
                 Normal grids in vacuum tubes are connected to the
                 ground. Another of Atanasoff's addition to the machine
                 was the use of a dielectric sheet to record the base
                 two numbers. The dielectric had difficulty working
                 since Atanasoff could never find a satisfactory paper
                 on which to record the readings. Atanasoff discusses
                 his desire to have worked for IBM despite the rebuffs
                 he had received over the years. He notes that he wanted
                 to be more in the mainstream of the development of
                 computers with funding, and the possibilities of
                 research. IBM seemed to provide the best possible
                 future for computing. This transcript concludes with
                 several miscellaneous questions based on the court
                 transcripts from the litigation Honeywell vs.
                 Sperry-Rand. Individuals mentioned include: Ernest
                 Anderson, Clifford Berry, George Gross, James Elder,
                 Norman Fulmer, and Hazeltine.",
  acknowledgement = ack-nhfb,
}

@Book{Kaplan:1999:NNH,
  author =       "Robert Kaplan",
  title =        "The Nothing That Is: a Natural History of Zero",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "xii + 225",
  year =         "1999",
  ISBN =         "0-19-512842-7",
  ISBN-13 =      "978-0-19-512842-0",
  LCCN =         "QA141 .K36 1999",
  bibdate =      "Mon Dec 06 16:15:22 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$22.00",
  acknowledgement = ack-nhfb,
}

@InProceedings{Karamcheti:1999:CLR,
  author =       "V. Karamcheti and C. Li and I. Pechtchanski and C.
                 Yap",
  title =        "A core library for robust numerical and geometric
                 libraries",
  crossref =     "ACM:1999:PFA",
  pages =        "351--359",
  year =         "1999",
  bibdate =      "Sat Apr 28 18:58:05 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.nyu.edu/exact",
  acknowledgement = ack-nhfb,
}

@Article{Kern:1999:FVH,
  author =       "Christoph Kern and Mark R. Greenstreet",
  title =        "Formal verification in hardware design: a survey",
  journal =      j-TODAES,
  volume =       "4",
  number =       "2",
  pages =        "123--193",
  month =        apr,
  year =         "1999",
  CODEN =        "ATASFO",
  ISSN =         "1084-4309 (print), 1557-7309 (electronic)",
  ISSN-L =       "1084-4309",
  bibdate =      "Fri Jul 27 10:05:33 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/articles/journals/todaes/1999-4-2/p123-kern/p123-kern.pdf;
                 http://www.acm.org/pubs/citations/journals/todaes/1999-4-2/p123-kern/",
  abstract =     "In recent years, formal methods have emerged as an
                 alternative approach to ensuring the quality and
                 correctness of hardware designs, overcoming some of the
                 limitations of traditional validation techniques such
                 as simulation and testing.\par

                 There are two main aspects to the application of formal
                 methods in a design process: the formal framework used
                 to specify desired properties of a design and the
                 verification techniques and tools used to reason about
                 the relationship between a specification and a
                 corresponding implementation. We survey a variety of
                 frameworks and techniques proposed in the literature
                 and applied to actual designs. The specification
                 frameworks we describe include temporal logics,
                 predicate logic, abstraction and refinement, as well as
                 containment between -regular languages. The
                 verification techniques presented include model
                 checking, automata-theoretic techniques, automated
                 theorem proving, and approaches that integrate the
                 above methods.\par

                 In order to provide insight into the scope and
                 limitations of currently available techniques, we
                 present a selection of case studies where formal
                 methods were applied to industrial-scale designs, such
                 as microprocessors, floating-point hardware, protocols,
                 memory subsystems, and communications hardware.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Design Automation of Electronic
                 Systems (TODAES)",
  generalterms = "Design; Verification",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J776",
  keywords =     "case studies; formal methods; formal verification;
                 hardware verification; language containment; model
                 checking; survey; theorem proving",
  subject =      "General Literature --- Introductory and Survey (A.1);
                 Hardware --- Integrated Circuits --- Design Aids
                 (B.7.2): {\bf Verification}",
}

@InProceedings{Knowles:1999:FA,
  author =       "Simon Knowles",
  title =        "A Family of Adders",
  crossref =     "Koren:1999:ISC",
  pages =        "30--34",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-168.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-168.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Knowles.pdf",
  abstract =     "Binary carry-propagating addition can be efficiently
                 expressed as a prefix computation. Several examples of
                 adders based on such a formulation have been published,
                 and efficient implementations are numerous. Chief among
                 the known constructions are those of Kogge \& Stone and
                 Ladner \& Fischer. In this work we show that these are
                 end cases of a large family of addition structures, all
                 of which share the attractive property of minimum
                 logical depth. The intermediate structures allow
                 trade-offs between the amount of internal wiring and
                 the fanout of intermediate nodes, and can thus usually
                 achieve a more attractive combination of speed and
                 area/power cost than either of the known end-cases.
                 Rules for the construction of such adders are given, as
                 are examples of realistic 32b designs implemented in an
                 industrial 0u25 CMOS process.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic",
}

@InProceedings{Koren:1999:FIS,
  author =       "Israel Koren and Peter Kornerup",
  title =        "{Fourteenth IEEE Symposium on Computer Arithmetic}:
                 Foreword",
  crossref =     "Koren:1999:ISC",
  pages =        "viii--viii",
  year =         "1999",
  bibdate =      "Sat Nov 17 21:53:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_contents.pdf;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_foreword.pdf;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_preface.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14",
}

@Misc{Koren:1999:ITS,
  author =       "Israel Koren and Peter Kornerup",
  title =        "{IEEE TC} Special Issue on Computer Arithmetic ---
                 {May} 2000",
  howpublished = "World-Wide Web document.",
  year =         "1999",
  bibdate =      "Wed Jan 20 10:00:59 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ecs.umass.edu/ece/koren/sp-issue/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kornerup:1999:NSC,
  author =       "Peter Kornerup",
  title =        "Necessary and Sufficient Conditions for Parallel,
                 Constant Time Conversion and Addition",
  crossref =     "Koren:1999:ISC",
  pages =        "152--157",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-103.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Kornerup.pdf",
  abstract =     "This note presents necessary and sufficient conditions
                 for parallel and constant time conversions from one
                 digit-set into another, and thus also for constant time
                 addition. In the integer domain it is generally
                 believed that such conversion and addition is possible
                 if the target digit-set is redundant and complete. This
                 is also the case when the digit-set is a contiguous set
                 of integers. However, when this is not the case then
                 such conversion and addition in the integer domain is
                 not possible in general, and when more general rings
                 are considered, the same problem may be present.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic",
}

@Article{Krick:1999:AN,
  author =       "T. Krick and L. M. Pardo and M. Sombra",
  title =        "Arithmetic {Nullstellens{\"a}tze}",
  journal =      j-SIGSAM,
  volume =       "33",
  number =       "3",
  pages =        "17--17",
  month =        sep,
  year =         "1999",
  CODEN =        "SIGSBZ",
  ISSN =         "0163-5824 (print), 1557-9492 (electronic)",
  ISSN-L =       "0163-5824",
  bibdate =      "Fri Feb 8 18:27:06 MST 2002",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGSAM Bulletin",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}

@Article{Lang:1999:VHR,
  author =       "T. Lang and P. Montuschi",
  title =        "Very high radix square root with prescaling and
                 rounding and a combined division\slash square root
                 unit",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "48",
  number =       "8",
  pages =        "827--841",
  month =        aug,
  year =         "1999",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.795124",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:46:58 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=795124",
  abstract =     "An algorithm for square root with prescaling and
                 selection by rounding is developed and combined with a
                 similar scheme for division. Since division is usually
                 more frequent than square root, the main concern of the
                 combined implementation is to maintain the low
                 execution time of division, while accepting a somewhat
                 larger execution time for square root. The algorithm is
                 presented in detail, including the mathematical
                 development of bounds for the first square-root digit
                 and for the scaling factor. The proposed implementation
                 is described, evaluated and compared with other
                 combined div/sqrt units. The comparisons show that the
                 proposed scheme potentially produces a significant
                 speed-up for division, whereas, for square root, the
                 speed-up is small",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "An algorithm for square root with prescaling and
                 selection by rounding is developed and combined with a
                 similar scheme for division. Since division is usually
                 more frequent than square root, the main concern of the
                 combined implementation is to \ldots{}",
}

@Article{Langlois:1999:WAL,
  author =       "Ph. Langlois and F. Nativel",
  title =        "When automatic linear correction of rounding errors is
                 exact",
  journal =      j-C-R-ACAD-SCI-PARIS-SER-I-MATH,
  volume =       "328",
  number =       "??",
  pages =        "543--548",
  year =         "1999",
  CODEN =        "CASMEI",
  ISSN =         "0249-6291",
  bibdate =      "Thu May 27 07:37:54 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See erratum, p. 829, in same volume.",
  acknowledgement = ack-nhfb,
  fjournal =     "Comptes Rendus des S{\'e}ances de l'Acad{\'e}mie des
                 Sciences. S{\'e}rie I. Math{\'e}matique",
  journal-URL =  "http://www.sciencedirect.com/science/journal/1631073X",
}

@Article{Lee:1999:EFS,
  author =       "Sung-Woo Lee and Hyun-Sung Kim and Jung-Joon Kim and
                 Tae-Geun Kim and Kee-Young Yoo",
  title =        "Efficient Fixed-Size Systolic Arrays for the Modular
                 Multiplication",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1627",
  pages =        "442--??",
  year =         "1999",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:54:14 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1627.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1627/16270442.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1627/16270442.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Lee:1999:NAD,
  author =       "Chang-Hyi Lee and Jong-In Lim",
  title =        "A New Aspect of Dual Basis for Efficient Field
                 Arithmetic",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1560",
  pages =        "12--28",
  year =         "1999",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:53:42 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1560.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1560/15600012.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1560/15600012.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
  keywords =     "PKC; public key cryptography",
}

@InProceedings{Lee:1999:STS,
  author =       "Young-Sang Lee and Jun-Woo Kang and Lee-Sup Kim and
                 Seung-Ho Hwang",
  booktitle =    "6th International Conference on {VLSI} and {CAD}:
                 {ICVC '99}",
  title =        "Self-timed shared division and square-root
                 implementation using full redundant signed digit
                 numbers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "541--544",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "A radix-$2$ square root implementation for self-timed
                 dividers using redundant signed-digit (RSD) adders is
                 presented. In this method, two self-timed RSD adder
                 stages are used for each result bit selection. A very
                 efficient and simple result bit \ldots{}",
}

@InCollection{Lefevre:1999:ACL,
  author =       "V. Lef{\`e}vre",
  title =        "An Algorithm That Computes a Lower Bound on the
                 Distance Between a Segment and {$ \mathbb {Z}^2 $}",
  crossref =     "Csendes:1999:DRC",
  pages =        "203--212",
  year =         "1999",
  bibdate =      "Fri Jun 24 12:41:23 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lewis:1999:CLN,
  author =       "David Lewis",
  title =        "Complex Logarithmic Number System Arithmetic Using
                 High-Radix Redundant {CORDIC} Algorithms",
  crossref =     "Koren:1999:ISC",
  pages =        "194--203",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-135.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-135.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Lewis.pdf",
  abstract =     "This paper describes the application of high radix
                 redundant CORDIC algorithms to complex logarithmic
                 number system arithmetic. It shows that a CLNS addition
                 can be performed with approximately the same hardware
                 as a high-radix CORDIC operation. A design example
                 comparable to single precision floating point has been
                 designed and simulated.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic",
}

@Misc{Liao:1999:SDR,
  author =       "Yuyun Liao and Tom M. Hameenanttila and David B.
                 Roberts",
  howpublished = "US Patent 6,611,856B1",
  day =          "23",
  month =        dec,
  year =         "1999",
  bibdate =      "Thu Oct 17 12:11:10 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://patents.google.com/patent/US6611856B1",
  abstract =     "A multiply-accumulate unit, or MAC, may achieve high
                 throughput. The MAC need not use redundant hardware,
                 such as multiple Wallace trees, or pipelining logic,
                 yet may perform Wallace tree and carry look-ahead adder
                 functions simultaneously for different operations.",
  acknowledgement = ack-nhfb,
  remark =       "Patent filed 23 December 1999, priority claimed from
                 British patent GB0407413A of 4 December 2000, granted
                 26 August 2003 to Intel Corporation, expected
                 expiration 23 December 2019.",
}

@InProceedings{Liew:1999:SDR,
  author =       "T. H. Liew and L.-L. Yang and L. Hanzo",
  booktitle =    "{VTC 1999} --- Fall. {IEEE} {VTS 50th} Vehicular
                 Technology Conference",
  title =        "Soft-decision redundant residue number system based
                 error correction coding",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2546--2550",
  year =         "1999",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/VETECF.1999.800245",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Soft-decision-based redundant residue number system
                 (RRNS)-assisted error control coding is proposed and
                 its performance is evaluated. An RRNS(n,k) code is a
                 maximum-minimum distance block code, exhibiting
                 identical distance properties to Reed- \ldots{}",
}

@InProceedings{Lopez:1999:IPF,
  author =       "D. Lopez and J. Llosa and E. Ayguade and M. Valero",
  title =        "Impact on performance of fused multiply-add units in
                 aggressive {VLIW} architectures",
  crossref =     "Shiratori:1999:PIC",
  pages =        "22--29",
  year =         "1999",
  DOI =          "https://doi.org/10.1109/ICPP.1999.797384",
  bibdate =      "Sun Feb 20 09:51:00 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Loops are the main time consuming part of programs
                 based on floating point computations. The performance
                 of the loops is limited either by recurrences in the
                 computation or by the resources offered by the
                 architecture. Several general-purpose superscalar
                 microprocessors have been implemented with multiply-add
                 fused floating-point units, that reduces the latency of
                 the combined operation and the number of resources
                 used. This paper analyses the influence of these two
                 factors in the instruction-level parallelism
                 exploitable from loops executed on a broad set of
                 future aggressive processor configurations. The
                 estimation of implementation costs (area and cycle
                 time) enables a fair comparison of these configurations
                 in terms of final performance and implementation
                 feasibility. The paper performs technological
                 projection for the next years in order to foresee the
                 possible implementable alternatives. From this study we
                 conclude that multiply-add fused units may have a deep
                 impact in raising the performance of future processor
                 architectures with a reasonable increase in cost.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lue:1999:ADE,
  author =       "Jeng-Jong J. Lue and Dhananjay S. Phatak",
  title =        "Area $ \times $ Delay ({$ A \cdot T $}) Efficient
                 Multipliers Based on an Intermediate Hybrid
                 Signed-Digit ({HSD-1}) Representation",
  crossref =     "Koren:1999:ISC",
  pages =        "216--224",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-159.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-159.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Lue.pdf",
  abstract =     "Intermediate Signed Digit (SD) representation can
                 facilitate fast and compact VLSI implementations of
                 partial product accumulation trees. It achieves a
                 reduction ratio of 2:1 at every level and also leads to
                 more regular layouts. Its disadvantage is that the
                 number of bit lines that need to routed can be high.
                 This can lead to a significant area overhead especially
                 at smaller feature sizes where the wire/interconnect
                 area and delay can be dominant.\par

                 A Hybrid Signed Digit (HSD) representation lets some of
                 the digits be unsigned bits, thereby reducing the
                 number of bit lines. By arbitrarily varying the
                 positions of and distances between consecutive signed
                 digits, this representation can trade off latency for
                 area and offers a continuum of choices between the
                 two's complement representation on the one hand and
                 fully Signed Digit (FSD or simply SD) representation on
                 the other.\par

                 In this paper, we illustrate an $ A \cdot T $ (area $
                 \times $ delay) efficient multiplier based on the HSD?1
                 representation which is one of the many possible HSD
                 formats, wherein every alternate digit is signed and
                 the rest are unsigned (ordinary) bits. It is seen that
                 multipliers based on HSD?1 format require more
                 transistors than those based on FSD format. However,
                 they require fewer bit lines to be routed, which
                 substantially reduces the interconnect area; thereby
                 leading to a reduction in the total VLSI area and a
                 lower $ A \cdot T $ product. The design reaffirms that
                 the interconnect area can be significant especially at
                 small feature sizes.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic",
}

@InProceedings{Mahesh:1999:IAE,
  author =       "M. N. Mahesh and S. Gupta and M. Mehendale",
  booktitle =    "Twelfth International Conference on {VLSI} Design,
                 1999. Proceedings",
  title =        "Improving area efficiency of residue number system
                 based implementation of {DSP} algorithms",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "340--345",
  year =         "1999",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICVD.1999.745179",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Residue Number System based applications involve
                 modulo-arithmetic which is typically implemented using
                 look-up-tables (LUTs) for a small value of modulus. In
                 this paper we present a data coding technique to
                 minimize the area of these LUTs when \ldots{}",
}

@Article{McCullough:1999:ARS,
  author =       "B. D. McCullough",
  title =        "Assessing the Reliability of Statistical Software:
                 {Part II}",
  journal =      j-AMER-STAT,
  volume =       "53",
  number =       "2",
  pages =        "149--159",
  month =        may,
  year =         "1999",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Fri Jan 27 14:51:25 MST 2012",
  bibsource =    "http://www.amstat.org/publications/tas/toc_99.html;
                 http://www.jstor.org/journals/00031305.html;
                 http://www.jstor.org/stable/i326504;
                 https://www.math.utah.edu/pub/tex/bib/amstat1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.amstat.org/publications/tas/mccull.pdf;
                 http://www.jstor.org/stable/2685736",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@Article{McCullough:1999:NRE,
  author =       "B. D. McCullough and H. D. Vinod",
  title =        "The Numerical Reliability of Econometric Software",
  journal =      j-J-ECON-LIT,
  volume =       "37",
  number =       "2",
  pages =        "633--665",
  month =        jun,
  year =         "1999",
  CODEN =        "JECLB3",
  DOI =          "https://doi.org/10.1257/jel.37.2.633",
  ISSN =         "0022-0515 (print), 1547-1101 (electronic)",
  ISSN-L =       "0022-0515",
  bibdate =      "Thu Oct 17 05:56:48 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://www.jstor.org/stable/2565215;
                 https://www.aeaweb.org/articles?id=10.1257/jel.37.2.633",
  abstract =     "Numerous examples show that some econometric software
                 packages contain serious flaws, and that users cannot
                 safely assume that their software is accurate. A brief
                 survey of the fundamentals of computer arithmetic
                 discusses the sources of numerical error and emphasizes
                 that computer arithmetic is not at all like
                 pencil-and-paper arithmetic. Both users and developers
                 of econometrics software should first pay attention to
                 accuracy, and only later consider user-friendliness.
                 Details are provided for assessing the accuracy of
                 basic estimation routines, statistical distributions,
                 and random number generators. More accuracy benchmarks
                 are needed, especially for specialized econometric
                 procedures.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Economic Literature",
  journal-URL =  "https://www.aeaweb.org/journals/jel/issues",
  remark =       "This paper discusses the effect of both floating-point
                 arithmetic and random-number generators on econometric
                 computations.",
}

@InProceedings{McInerney:1999:HMC,
  author =       "S. McInerney and R. B. Reilly",
  booktitle =    "{1999 IEEE International Conference on Acoustics,
                 Speech, and Signal Processing. Proceedings. ICASSP99
                 (Cat. No. 99CH36258)}",
  title =        "Hybrid multiplier\slash {CORDIC} unit for online
                 handwriting recognition",
  volume =       "4",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1909--1912 (vol. 4)",
  year =         "1999",
  DOI =          "https://doi.org/10.1109/ICASSP.1999.758297",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Acceleration; Arithmetic; Character recognition;
                 Digital signal processing; Euclidean distance; Feature
                 extraction; Handwriting recognition; Hardware;
                 Iterative algorithms; Personal digital assistants",
}

@InProceedings{Montuschi:1999:BVH,
  author =       "Paolo Montuschi and Tom{\'a}s Lang",
  title =        "Boosting Very High Radix Division with Prescaling and
                 Selection by Rounding",
  crossref =     "Koren:1999:ISC",
  pages =        "52--59",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-150.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-150.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Montuschi.pdf",
  abstract =     "An extension of the very-high radix division with
                 prescaling and selection by rounding is presented. This
                 extension consists in increasing the effective radix of
                 the implementation by obtaining a few additional bits
                 of the quotient per iteration, without increasing the
                 complexity of the unit to obtain the prescaling factor
                 nor the delay of an iteration. As a consequence, for
                 some values of the effective radix, it permits an
                 implementation with a smaller area and the same
                 execution time than the original scheme. Estimations
                 are given for 54-bit and 114-bit quotients.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic",
}

@Article{Muller:1999:FRT,
  author =       "Jean-Michel Muller",
  title =        "A Few Results on Table-Based Methods",
  journal =      j-RELIABLE-COMPUTING,
  volume =       "5",
  number =       "3",
  pages =        "279--288",
  year =         "1999",
  CODEN =        "RCOMF8",
  ISSN =         "1385-3139 (print), 1573-1340 (electronic)",
  ISSN-L =       "1385-3139",
  bibdate =      "Mon May 20 06:37:48 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  fjournal =     "Reliable Computing = Nadezhnye vychisleniia",
  journal-URL =  "http://link.springer.com/journal/11155",
  remark =       "Papers from Scientific computing, computer arithmetic
                 and validated numerics (SCAN '98), September 1998,
                 Budapest, Hungary.",
}

@Article{Muroi:1999:ESR,
  author =       "Kazuo Muroi",
  title =        "Extraction of square roots in {Babylonian}
                 mathematics",
  journal =      j-HIST-SCI-2,
  volume =       "9",
  number =       "2",
  pages =        "127--133",
  month =        nov,
  year =         "1999",
  CODEN =        "HISCDU",
  ISSN =         "0285-4821",
  ISSN-L =       "0285-4821",
  MRclass =      "01A17",
  MRnumber =     "1762167",
  MRreviewer =   "Bruno Poizat",
  bibdate =      "Sat Oct 6 17:22:25 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/histscijpn.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Historia Scientiarum. Second Series. International
                 Journal of the History of Science Society of Japan",
  journal-URL =  "http://hssj.info/",
}

@InProceedings{Nannarelli:1999:LPDa,
  author =       "Alberto Nannarelli and Tomas Lang",
  title =        "Low-Power Division: Comparison among Implementations
                 of Radix $4$, $8$ and $ 16 $",
  crossref =     "Koren:1999:ISC",
  pages =        "60--69",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-158.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-158.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Nannarelli.pdf",
  abstract =     "Although division is less frequent than addition and
                 multiplication, because of its longer latency it
                 dissipates a substantial part of the energy in
                 floating-point units. In this paper we explore the
                 relation between the radix and the energy dissipated.
                 Previous work has been done on radix-4 and radix-8
                 division. Here we extend this study to a radix-16
                 scheme with two overlapped radix-4 stages and compare
                 the latency, area, and energy of the three
                 implementations.\par

                 Results show that by applying the low-power techniques
                 the energy dissipation is reduced from 30\% to 40\%,
                 with respect to the standard implementation. An
                 additional 20\% reduction can be obtained using a dual
                 voltage. Moreover, the energy dissipated to complete
                 the division is roughly the same for the three radices.
                 However, the power dissipation, proportional to the
                 average current, increases with the radix. If reducing
                 the energy is the priority, for the same latency
                 radix-16 with dual voltage produces the smallest energy
                 dissipation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic",
}

@Article{Nannarelli:1999:LPDb,
  author =       "A. Nannarelli and T. Lang",
  title =        "Low-Power Divider",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "48",
  number =       "1",
  pages =        "2--14",
  month =        jan,
  year =         "1999",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.743407",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:46:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=743407",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Nannarelli:1999:LPR,
  author =       "Alberto Nannarelli and Tomas Lang",
  booktitle =    "({ICCD '99}) International Conference on Computer
                 Design",
  title =        "Low-power radix-$4$ combined division and square
                 root",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "236--242",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Because of the similarities in the algorithm it is
                 quite common to implement division and square root in
                 the same unit. The purpose of this work is to implement
                 a low-power combined radix-$4$ division and square root
                 floating-point double precision \ldots{}",
}

@Article{Nedialkov:1999:IHO,
  author =       "N. S. Nedialkov and K. R. Jackson",
  title =        "An Interval Hermite-Obreschkoff Method for Computing
                 Rigorous Bounds on the Solution of an Initial Value
                 Problem for an Ordinary Differential Equation",
  journal =      j-RELIABLE-COMPUTING,
  volume =       "5",
  number =       "3",
  pages =        "289--310",
  year =         "1999",
  CODEN =        "RCOMF8",
  ISSN =         "1385-3139 (print), 1573-1340 (electronic)",
  ISSN-L =       "1385-3139",
  bibdate =      "Mon May 20 06:37:48 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  fjournal =     "Reliable Computing = Nadezhnye vychisleniia",
  journal-URL =  "http://link.springer.com/journal/11155",
  remark =       "Papers from Scientific computing, computer arithmetic
                 and validated numerics (SCAN '98), September 1998,
                 Budapest, Hungary.",
}

@InProceedings{Northrop:1999:GM,
  author =       "G. Northrop and R. Averill and K. Barkley and S. Carey
                 and Y. Chan and Y. H. Chan and M. Check and D. Hoffman
                 and W. Huott and B. Krumm and C. Krygowski and J.
                 Liptay and M. Mayo and T. McNamara and T. McPherson and
                 E. Schwarz and L. Sigal and T. Slegel and C. Webb and
                 D. Webber and P. Williams",
  title =        "{600MHz G5 S/390} Microprocessor",
  crossref =     "Wuorinen:1999:IIS",
  pages =        "??--??",
  year =         "1999",
  bibdate =      "Mon Jan 08 08:40:27 2001",
  bibsource =    "http://www.sscs.org/digests/1999/DATA/05_2.pdf;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  pagecount =    "9",
}

@InProceedings{Oberman:1999:FPD,
  author =       "Stuart F. Oberman",
  title =        "Floating point division and square root algorithms and
                 implementation in the {AMD-K7{\TM}} microprocessor",
  crossref =     "Koren:1999:ISC",
  pages =        "106--115",
  year =         "1999",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-139.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-139.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Oberman.pdf",
  abstract =     "This paper presents the AMD-K7 IEEE 754 and x87
                 compliant floating point division and square root
                 algorithms and implementation. The AMD-K7 processor
                 employs an iterative implementation of a series
                 expansion to converge quadratically to the quotient and
                 square root. Highly accurate initial approximations and
                 a high performance shared floating point multiplier
                 assist in achieving low division and square root
                 latencies at high operating frequencies. A novel
                 time-sharing technique allows independent floating
                 point multiplication operations to proceed while
                 division or square root computation is in progress.
                 Exact IEEE 754 rounding for all rounding modes and
                 target precisions has been verified by conventional
                 directed and random testing procedures, along with the
                 formulation of a mechanically-checked formal proof
                 using the ACL2 theorem prover.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic",
  summary =      "This paper presents the AMD-K7 IEEE 754 and $\times$87
                 compliant floating point division and square root
                 algorithms and implementation. The AMD-K7 processor
                 employs an iterative implementation of a series
                 expansion to converge quadratically to the \ldots{}",
}

@Article{OLeary:1999:FVI,
  author =       "John O'Leary and Xudong Zhao and Rob Gerth and
                 Carl-Johan H. Seger",
  title =        "Formally Verifying {IEEE} Compliance of Floating-Point
                 Hardware",
  journal =      j-INTEL-TECH-J,
  volume =       "Q1",
  pages =        "10",
  day =          "17",
  month =        feb,
  year =         "1999",
  bibdate =      "Fri Jun 01 06:02:08 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://developer.intel.com/technology/itj/q11999/articles/art_5.htm;
                 http://developer.intel.com/technology/itj/q11999/pdf/floating_point.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Paar:1999:FAP,
  author =       "C. Paar and P. Fleischmann and P. Soria-Rodriguez",
  title =        "Fast arithmetic for public-key algorithms in {Galois}
                 fields with composite exponents",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "48",
  number =       "10",
  pages =        "1025--1034",
  month =        oct,
  year =         "1999",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.805153",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 08:46:59 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=805153",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Paliouras:1999:MAR,
  author =       "V. Paliouras and T. Stouraitis",
  title =        "Multifunction Architectures for {RNS} Processors",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST,
  volume =       "46",
  number =       "8",
  pages =        "1041--1054",
  month =        aug,
  year =         "1999",
  CODEN =        "ICSYBT",
  ISSN =         "0098-4094 (print), 1558-1276 (electronic)",
  ISSN-L =       "0098-4094",
  bibdate =      "Fri Jun 24 18:26:56 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems",
  keywords =     "Residue Number System (RNS)",
}

@InProceedings{Paliouras:1999:NHR,
  author =       "V. Paliouras and T. Stouraitis",
  booktitle =    "{ISCAS '99}. Proceedings of the 1999 {IEEE}
                 International Symposium on Circuits and Systems, 2 June
                 1999",
  title =        "Novel high-radix residue number system multipliers and
                 adders",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "451--454",
  year =         "1999",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1999.777911",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Radix-r modulo r n multipliers and adders are
                 introduced in this paper. The proposed architectures
                 are shown to require several times less area than
                 previously reported architectures, for particular
                 moduli of operation. The proposed \ldots{}",
}

@InProceedings{Parhami:1999:ALT,
  author =       "B. Parhami",
  booktitle =    "Conference Record of the Thirty-Third Asilomar
                 Conference on Signals, Systems, and Computers, 1999",
  title =        "Analysis of the lookup table size for square-rooting",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1327--1330",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Convergence methods are widely used for division,
                 reciprocation, and square-rooting. With such methods,
                 it is common to use an initial table lookup step for
                 obtaining an approximate result that leads to faster
                 convergence. In the case of division \ldots{}",
}

@Article{Park:1999:FPM,
  author =       "W.-C. Park and T.-D. Han and S.-D. Kim and S.-B.
                 Yang",
  title =        "A floating point multiplier performing {IEEE} rounding
                 and addition in parallel",
  journal =      j-J-SYST-ARCH,
  volume =       "45",
  number =       "14",
  pages =        "1195--1207",
  month =        jul,
  year =         "1999",
  CODEN =        "JSARFB",
  ISSN =         "1383-7621 (print), 1873-6165 (electronic)",
  ISSN-L =       "1383-7621",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Ingenta database",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Systems Architecture",
  pagecount =    "13",
}

@Misc{Parker:1999:SPA,
  author =       "D. Stott Parker",
  title =        "A semi-portable {ANSI} {C} implementation of {Monte
                 Carlo} floating-point arithmetic",
  howpublished = "World-Wide Web document.",
  year =         "1999",
  bibdate =      "Mon Aug 25 15:08:02 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.ucla.edu/~stott/mca/MCAdemo.c",
  acknowledgement = ack-nhfb,
}

@InProceedings{Parks:1999:NTT,
  author =       "Michael Parks",
  title =        "Number-Theoretic Test Generation for Directed
                 Rounding",
  crossref =     "Koren:1999:ISC",
  pages =        "241--249",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-131.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-131.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Parks.pdf",
  abstract =     "We present methods to generate systematically the
                 hardest test cases for multiplication, division, and
                 square root subject to directed rounding, essentially
                 extending previous work on number-theoretic
                 floating-point testing to rounding modes other than
                 to-nearest. The algorithms focus upon the rounding
                 boundaries of the modes truncate, to-minus-infinity,
                 and to-infinity, and programs based on them require
                 little beyond exact arithmetic in the working precision
                 to create billions of edge cases. We will show that the
                 amount of work required to calculate trial
                 multiplicands pays off in the form of free extra tests
                 due to an interconnection among the operations
                 considered herein. Although these tests do not replace
                 proofs of correctness, they can be used to gain a high
                 degree of confidence that the accuracy requirements as
                 mandated by IEEE Standard 754 have been satisfied.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic; correct rounding;
                 floating-point arithmetic; floating-point testing",
  summary =      "We present methods to generate systematically the
                 hardest test cases for multiplication, division, and
                 square root subject to directed rounding, essentially
                 extending previous work on number-theoretic floating
                 point testing to rounding modes other \ldots{}",
}

@InProceedings{Phatak:1999:IVE,
  author =       "Dhananjay S. Phatak and I. Koren",
  title =        "Intermediate Variable Encodings that Enable
                 Multiplexor-Based Implementations of Two Operand
                 Addition",
  crossref =     "Koren:1999:ISC",
  pages =        "22--29",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-149.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-149.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Phatak.pdf",
  abstract =     "In two operand addition, bit-wise intermediate
                 variables such as the ``propagate'' and ``generate''
                 terms are defined \slash evaluated first. Basic carry
                 propagation recursion is then expressed in terms of
                 these variables and is ``unrolled'' to obtain a tree
                 structure for fast execution. In CMOS VLSI technology,
                 multiplexors are fast and efficient to implement.
                 Hence, we investigate in this paper all possible
                 two-bit encodings for the intermediate variables and
                 identify the ones that enable multiplexor-based
                 implementations. Some of these encodings enable further
                 simplification of the multiplexor-based realizations.
                 Our analysis also shows that adopting an intermediate
                 signed-digit representation simply amounts to selecting
                 one of the possible encodings. Thus, there is no
                 inherent advantage to the use of intermediate
                 signed-digit representations in a two operand addition.
                 Finally, we extend our analysis to the generalized
                 look-ahead-recursions proposed by Doran.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic",
}

@Article{Ralev:1999:RBF,
  author =       "K. R. Ralev and P. H. Bauer",
  title =        "Realization of block floating-point digital filters
                 and application to block implementations",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "47",
  number =       "4",
  pages =        "1076--1086",
  month =        apr,
  year =         "1999",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "Realization issues of block floating-point (BFP)
                 filters such as complexity, roundoff noise, and absence
                 of limit cycles are analyzed. Several new results are
                 established. Under certain conditions, BFP filters
                 perform better than fixed-point filters \ldots{}",
}

@Article{Ruess:1999:MVS,
  author =       "Harald Ruess and Natarajan Shankar and Mandayam K.
                 Srivas",
  title =        "Modular Verification of {SRT} Division",
  journal =      j-FORM-METHODS-SYST-DES,
  volume =       "14",
  number =       "1",
  pages =        "45--73",
  month =        jan,
  year =         "1999",
  CODEN =        "FMSDE6",
  ISSN =         "0925-9856 (print), 1572-8102 (electronic)",
  ISSN-L =       "0925-9856",
  bibdate =      "Sat Jun 02 09:22:39 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Special issue on arithmetic circuits.",
  URL =          "http://www.wkap.nl/jrnltoc.htm/0925-9856;
                 http://www.wkap.nl/oasis.htm/194807",
  acknowledgement = ack-nhfb,
  fjournal =     "Formal Methods in System Design",
  journal-URL =  "https://dl.acm.org/loi/fmsd",
}

@Article{Rugina:1999:APD,
  author =       "Radu Rugina and Martin Rinard",
  title =        "Automatic parallelization of divide and conquer
                 algorithms",
  journal =      j-SIGPLAN,
  volume =       "34",
  number =       "8",
  pages =        "72--83",
  month =        aug,
  year =         "1999",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:18:06 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/proceedings/ppopp/301104/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/proceedings/ppopp/301104/p72-rugina/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}

@InProceedings{Rump:1999:IIL,
  author =       "Siegfried M. Rump",
  title =        "{INTLAB--INTerval LABoratory}",
  crossref =     "Csendes:1999:DRC",
  pages =        "77--104",
  year =         "1999",
  bibdate =      "Tue Nov 22 06:39:33 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation; interval
                 arithmetic",
}

@Article{Russinoff:1999:MCP,
  author =       "David M. Russinoff",
  title =        "A mechanically checked proof of correctness of the
                 {AMD K5} floating point square root microcode",
  journal =      j-FORM-METHODS-SYST-DES,
  volume =       "14",
  number =       "1",
  pages =        "75--125",
  month =        jan,
  year =         "1999",
  CODEN =        "FMSDE6",
  DOI =          "https://doi.org/10.1023/A:1008669628911",
  ISSN =         "0925-9856 (print), 1572-8102 (electronic)",
  ISSN-L =       "0925-9856",
  bibdate =      "Sat Jun 02 07:51:51 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Special issue on arithmetic circuits.",
  URL =          "http://www.wkap.nl/jrnltoc.htm/0925-9856;
                 http://www.wkap.nl/oasis.htm/194808;
                 https://dl.acm.org/doi/abs/10.1023/A:1008669628911",
  abstract =     "We present a rigorous mathematical proof of the
                 correctness of the floating point square root
                 instruction of the AMD K5 microprocessor. The
                 instruction is represented as a program in a formal
                 language that was designed for this purpose, based on
                 the K5 microcode and the architecture of its FPU. We
                 prove a statement of its correctness that corresponds
                 directly with the IEEE Standard. We also derive an
                 equivalent formulation, expressed in terms of rational
                 arithmetic, which has been encoded as a formula in the
                 ACL2 logic and mechanically verified with the ACL2
                 prover. Finally, we describe a microcode modification
                 that was implemented as a result of this analysis in
                 order to ensure the correctness of the instruction.",
  acknowledgement = ack-nhfb,
  fjournal =     "Formal Methods in System Design",
  journal-URL =  "https://dl.acm.org/loi/fmsd",
}

@InProceedings{Saed:1999:ASA,
  author =       "Aryan Saed and Majid Ahmadi and Graham A. Jullien",
  title =        "Arithmetic with Signed Analog Digits",
  crossref =     "Koren:1999:ISC",
  pages =        "134--141",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-140.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-140.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Saed.pdf",
  abstract =     "This paper presents mathematical foundations of the
                 Overlap Resolution Number System (ORNS) which is based
                 on signed Continuous Valued Digits (CVD's). ORNS is a
                 redundant Number System employing residue arithmetic.
                 In contrast to the implementation of arithmetic by
                 binary or multiple-valued logic circuits, arithmetic
                 operations in this novel number system are performed by
                 analog digit manipulation circuitry. The redundancy in
                 an ensemble of Continuous Valued Digits that comprises
                 a number provides tolerance to implementation
                 imprecisions. Processing with these analog digits is
                 performed by carry-free arithmetic structures with
                 systematic circuit level redundancy.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic",
}

@InProceedings{SanGregory:1999:FLP,
  author =       "Samuel L. SanGregory and Charles Brothers and David
                 Gallagher and Raymond Siferd",
  editor =       "{IEEE}",
  booktitle =    "{Proceedings of 1999 Midwest Symposium on Circuits and
                 Systems: August 8--12, 1999, Corbett Center, New Mexico
                 State University, Las Cruces, New Mexico}",
  title =        "A Fast, Low-Power Logarithm Approximation with {CMOS
                 VLSI} Implementation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  bookpages =    "xl + 1150 (two volumes)",
  pages =        "388--391",
  year =         "1999",
  DOI =          "https://doi.org/10.1109/MWSCAS.1999.867287",
  ISBN =         "0-7803-5491-5 (softbound), 0-7803-5492-3 (casebound),
                 0-7803-5493-1 (microfiche)",
  ISBN-13 =      "978-0-7803-5491-3 (softbound), 978-0-7803-5492-0
                 (casebound), 978-0-7803-5493-7 (microfiche)",
  LCCN =         "TK3226 .M531 42nd 1999",
  bibdate =      "Wed Dec 20 07:16:14 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://digitalcommons.cedarville.edu/engineering_and_computer_science_presentations/13",
  abstract =     "A new technique and CMOS VLSI implementation for
                 computing approximate logarithms (base 2 and 10) for
                 binary integers is presented. The approximation is
                 performed using only combinational logic and requires
                 no multiplications. Additionally, as implemented, a ROM
                 of only $ N \times \log_2 (N) $ bits is used to convert
                 $N$ bit integers. The maximum error of the
                 approximation is 1.5\% when the input value is 3, and
                 decays exponentially to less than 0.5\% for input
                 values greater than 25.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Scherer:1999:OTW,
  author =       "Alisa Scherer and Michael Golden and Norbert Juffa and
                 Stephan Meier and Stuart Oberman and Hamid Partovi and
                 Fred Weber",
  title =        "An Out-of-Order Three-Way Superscalar Multimedia
                 Floating-Point Unit",
  crossref =     "Wuorinen:1999:IIS",
  pages =        "??--??",
  year =         "1999",
  bibdate =      "Mon Jan 08 08:35:15 2001",
  bibsource =    "http://www.sscs.org/digests/1999/DATA/05_5.pdf;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "AMD-K7 floating-point unit",
  pagecount =    "10",
  remark =       "The AMD-K7 floating-point unit is implemented as an
                 out-of-order coprocessor responsible for executing all
                 x86 FPU, MMX, and AMD 3DNow! instructions.",
}

@InProceedings{Schmookler:1999:LPH,
  author =       "Martin S. Schmookler and Michael Putrino and Charles
                 Roth and Mukesh Sharma and Anh Mather and Jon Tyler and
                 Huy Van Nguyen and Mydung N. Pham and Jeff Lent",
  title =        "A Low-Power, High-Speed Implementation of a
                 {PowerPC[TM]} Microprocessor Vector Extension",
  crossref =     "Koren:1999:ISC",
  pages =        "12--21",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-145.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-145.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Schmookler.pdf",
  abstract =     "The AltiVec{\TM} technology is an extension to the
                 PowerPC architecture{\TM} which provides new
                 computational and storage operations for handling
                 vectors of various data lengths and data types. The
                 first implementation using this technology is a low
                 cost, low power processor based on the acclaimed
                 PowerPC 750{\TM} microprocessor. This paper describes
                 the microarchitecture and design of the vector
                 arithmetic unit of this implementation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic",
}

@Article{Schulte:1999:AEF,
  author =       "M. Schulte and J. Stine",
  title =        "Approximating Elementary Functions with Symmetric
                 Bipartite Tables",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "48",
  number =       "8",
  pages =        "842--847",
  year =         "1999",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.795125",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jun 24 20:20:58 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1999-10.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Schulte:1999:CSI,
  author =       "M. J. Schulte and A. Akkas and V. Zelov and J. C.
                 Burley",
  booktitle =    "Proceedings of {16th IEEE Instrumentation and
                 Measurement Technology Conference, Venice, Italy, May,
                 1999}",
  title =        "Compiler Support for Interval Arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1189--1193",
  year =         "1999",
  bibdate =      "Fri Jun 11 05:44:37 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://home.ku.edu.tr/~ahakkas/publications/comp-supp.pdf;
                 http://mesa.ece.wisc.edu/publications/cp_1999-04.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Schulte:1999:ESO,
  author =       "M. J. Schulte and K. E. Wires",
  title =        "Efficient Second Order Approximations for Reciprocals
                 and Square Roots",
  crossref =     "Luk:1999:PSA",
  volume =       "3807",
  pages =        "10--18",
  year =         "1999",
  bibdate =      "Sun Mar 04 11:10:48 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1999-05.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Schulte:1999:HSI,
  author =       "Michael J. Schulte and Kent E. Wires",
  title =        "High-Speed Inverse Square Roots",
  crossref =     "Koren:1999:ISC",
  pages =        "124--131",
  year =         "1999",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-109.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-109.ps;
                 http://mesa.ece.wisc.edu/publications/cp_1999-03.pdf;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Schulte.pdf",
  abstract =     "Inverse square roots are used in several digital
                 signal processing, multimedia, and scientific computing
                 applications. This paper presents a high-speed method
                 for computing inverse square roots. This method uses a
                 table lookup, operand modification, and multiplication
                 to obtain an initial approximation to the inverse
                 square root. This is followed by a modified
                 Newton--Raphson iteration, consisting of one square,
                 one multiply-complement, and one multiply-add
                 operation. The initial approximation and
                 Newton--Raphson iteration employ specialized hardware
                 to reduce the delay, area, and power dissipation.
                 Application of this method is illustrated through the
                 design of an inverse square root unit for operands in
                 the IEEE single precision format. An implementation of
                 this unit with a 4-layer metal, 2.5 Volt, 0.25 micron
                 CMOS standard cell library has a cycle time of 6.7 ns,
                 an area of 0.41 mm$^2$, a latency of five cycles, and a
                 throughput of one result per cycle.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic",
  summary =      "Inverse square roots are used in several digital
                 signal processing, multimedia, and scientific computing
                 applications. This paper presents a high-speed method
                 for computing inverse square roots. This method uses a
                 table lookup, operand modification, \ldots{}",
}

@InProceedings{Schulte:1999:IEG,
  author =       "M. J. Schulte and V. A. Zelov and A. Akkas and J. C.
                 Burley",
  title =        "The interval-enhanced {GNU Fortran} compiler",
  crossref =     "Csendes:1999:DRC",
  pages =        "311--322",
  year =         "1999",
  bibdate =      "Wed Jan 29 16:56:25 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1999-12.pdf",
  acknowledgement = ack-nhfb,
  remark =       "From \cite{Steele:2004:RHP}: ``A recent extension of
                 the GNU Fortran compiler makes use of accurate
                 conversion techniques.''",
}

@InProceedings{Schulte:1999:RPD,
  author =       "M. J. Schulte and J. G. Jansen and J. E. Stine",
  title =        "Reduced Power Dissipation Through Truncated
                 Multiplication",
  crossref =     "Piuri:1999:IAV",
  pages =        "61--69",
  year =         "1999",
  bibdate =      "Sun Mar 04 11:16:43 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1999-01.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Schwarz:1999:GFPa,
  author =       "Eric M. Schwarz and Ronald M. Smith and Christopher A.
                 Krygowski",
  title =        "The {S/390 G5} Floating Point Unit Supporting Hex and
                 Binary Architectures",
  crossref =     "Koren:1999:ISC",
  pages =        "258--265",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://computer.org/proceedings/arith/0116/0116toc.htm;
                 http://euler.ecs.umass.edu/paper/final/paper-112.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-112.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Schwarz.pdf",
  abstract =     "The first high performance floating point unit to
                 support both IBM 360 hexadecimal based floating point
                 architecture and the IEEE 754 Standard binary floating
                 point architecture is described. The S/390 G5 floating
                 point unit supports the new S/390 architecture which
                 includes hexadecimal based short, long, and extended
                 precision formats and IEEE 754 standard single, double,
                 and quad formats. This floating point unit is part of
                 the microprocessor chip on the S/390 G5 mainframe
                 computer introduced in 1998 and generally available at
                 500 MHz speeds. The S/390 G5 represents the current
                 state of the art in CISC processor design. This paper
                 describes the S/390 architecture enhancements, the
                 internal format of the FPU, and the modifications to
                 the FPU dataflow.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic",
}

@Article{Schwarz:1999:GFPb,
  author =       "E. M. Schwarz and C. A. Krygowski",
  title =        "The {S/390 G5} floating-point unit",
  journal =      j-IBM-JRD,
  volume =       "43",
  number =       "5/6",
  pages =        "707--721",
  month =        sep # "\slash " # nov,
  year =         "1999",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.435.0707",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Wed Apr 19 18:58:23 MDT 2000",
  bibsource =    "http://www.research.ibm.com/journal/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
  URL =          "http://www.research.ibm.com/journal/rd/435/schwarz.html",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
}

@Misc{Schwarz:1999:MSE,
  author =       "E. M. Schwarz and B. Giamei and C. Krygowski and M.
                 Check and J. Liptay",
  title =        "Method and system for executing denormalized numbers",
  day =          "11",
  month =        may,
  year =         "1999",
  bibdate =      "Fri Nov 28 15:29:52 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "U.S. Patent No. 5,903,479.",
  acknowledgement = ack-nhfb,
}

@Article{Seidel:1999:HSR,
  author =       "Peter-Michael Seidel",
  title =        "High-Speed Redundant Reciprocal Approximation",
  journal =      j-INTEGRATION-VLSI-J,
  volume =       "28",
  number =       "1",
  pages =        "1--12",
  month =        sep,
  year =         "1999",
  CODEN =        "IVJODL",
  DOI =          "https://doi.org/10.1016/S0167-9260(99)00008-5",
  ISSN =         "0167-9260 (print), 1872-7522 (electronic)",
  ISSN-L =       "0167-9260",
  bibdate =      "Fri Jun 24 20:25:43 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper presents a fast implementation for
                 reciprocal approximation, that can compute a redundant
                 reciprocal of a normalized number with a precision of $
                 2^-28 $ in roughly 16--17 logic levels. Moreover, a
                 less accurate, but much cheaper implementation is
                 proposed. The redundant representation of the
                 reciprocal can directly be fed into a common Booth
                 multiplier. This allows to implement IEEE
                 floating-point division with correct rounding in all
                 rounding modes with a latency of 7 clock cycles in
                 double precision and 4 clock cycles in single
                 precision. We also consider fast redundant compressions
                 from carry-save representations to redundant
                 Booth-digit representations.",
  acknowledgement = ack-nhfb,
  fjournal =     "Integration, the VLSI journal",
  journal-URL =  "https://www.sciencedirect.com/journal/integration/issues",
  keywords =     "Booth recoding; correct rounding; floating-point
                 arithmetic; Multiplicative division; Reciprocal
                 approximation; Redundant compression",
}

@Article{Shary:1999:OEG,
  author =       "S. P. Shary",
  title =        "Outer Estimation of Generalized Solution Sets to
                 Interval Linear Systems",
  journal =      j-RELIABLE-COMPUTING,
  volume =       "5",
  number =       "3",
  pages =        "323--335",
  year =         "1999",
  CODEN =        "RCOMF8",
  ISSN =         "1385-3139 (print), 1573-1340 (electronic)",
  ISSN-L =       "1385-3139",
  bibdate =      "Mon May 20 06:37:48 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  fjournal =     "Reliable Computing = Nadezhnye vychisleniia",
  journal-URL =  "http://link.springer.com/journal/11155",
  remark =       "Papers from Scientific computing, computer arithmetic
                 and validated numerics (SCAN '98), September 1998,
                 Budapest, Hungary.",
}

@InProceedings{Skavantzos:1999:GMR,
  author =       "A. Skavantzos and T. Stouraitis",
  booktitle =    "{ISCAS '99}. Proceedings of the 1999 {IEEE}
                 International Symposium on Circuits and Systems, 2 June
                 1999",
  title =        "Grouped-moduli residue number systems for fast signal
                 processing",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "478--483",
  year =         "1999",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.1999.778887",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "In this paper a new class of multi-moduli residue
                 number systems (RNS) and their efficient
                 RNS-to-weighted converters are presented. The new RNS
                 systems are based on sets consisting of two groups of
                 moduli with the moduli-product within one group
                 \ldots{}",
}

@Article{Skavantzos:1999:IIT,
  author =       "A. Skavantzos and M. Abdallah",
  title =        "Implementation issues of the two-level residue number
                 system with pairs of conjugate moduli",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "47",
  number =       "3",
  pages =        "826--838",
  month =        mar,
  year =         "1999",
  CODEN =        "ITPRED",
  DOI =          "https://doi.org/10.1109/78.747787",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=16138",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  keywords =     "residue arithmetic; residue number system",
  summary =      "One of the most important considerations when
                 designing residue number systems (RNSs) is the choice
                 of the moduli set; this is due to the fact that the
                 dynamic range of the system, its speed, as well as its
                 hardware complexity, depend on both the \ldots{}",
}

@InProceedings{Skavantzos:1999:NER,
  author =       "A. Skavantzos and Y. Wang",
  booktitle =    "Conference Record of the Thirty-Third Asilomar
                 Conference on Signals, Systems, and Computers, 1999",
  title =        "New efficient {RNS}-to-weighted decoders for
                 conjugate-pair-moduli residue number systems",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1345--1350",
  year =         "1999",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ACSSC.1999.831926",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "New efficient residue-to-weighted converters for
                 multi-moduli residue number systems (RNS) based on sets
                 {2 n1 -1, 2 n1 +1, 2 n2 -1, 2 n2 +1, {\ldots}, 2 nL -1,
                 2 nL +1} are presented. The \ldots{}",
}

@Article{Skeel:1999:SIF,
  author =       "R. D. Skeel",
  title =        "Symplectic integration with floating-point arithmetic
                 and other approximations",
  journal =      j-APPL-NUM-MATH,
  volume =       "29",
  number =       "1",
  pages =        "3--18",
  month =        jan,
  year =         "1999",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Ingenta database",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274",
  pagecount =    "16",
}

@Article{Stine:1999:STA,
  author =       "J. E. Stine and M. J. Schulte",
  title =        "The Symmetric Table Addition Method for Accurate
                 Function Approximation",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "21",
  number =       "2",
  pages =        "167--177",
  month =        jun,
  year =         "1999",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1023/A:1008004523235",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Sun Mar 04 11:02:59 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1999-11.pdf",
  abstract =     "This paper presents a high-speed method for computing
                 elementary functions using parallel table lookups and
                 multi-operand addition. Increasing the number of tables
                 and inputs to the multi-operand adder significantly
                 reduces the amount of memory required. Symmetry and
                 leading zeros in the table coefficients are used to
                 reduce the amount of memory even further. This method
                 has a closed-form solution for the table entries and
                 can be applied to any differentiable function. For
                 24-bit operands, it requires two to three orders of
                 magn",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
}

@InProceedings{Story:1999:NAI,
  author =       "Shane Story and Ping Tak Peter Tang",
  title =        "New Algorithms for Improved Transcendental Functions
                 on {IA-64}",
  crossref =     "Koren:1999:ISC",
  pages =        "4--11",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-118.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-118.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Story.pdf",
  abstract =     "The IA-64 architecture provides new opportunities and
                 challenges for implementing an improved set of
                 transcendental functions. Using several novel
                 polynomial-based table-driven techniques, we are able
                 to provide new algorithms for the transcendental
                 functions. Major improvements include an accuracy level
                 of about 0.6 ulps (units in the last place) and forward
                 trigonometric functions that have a period of $ 2 \pi
                 $. The accuracy enhancements are achieved at improved
                 speed, yet without an increase in the table size. In
                 this paper, we highlight the key IA-64 architectural
                 features that influenced our designs and explain the
                 main ideas used in our new algorithms.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic",
}

@Article{Strzebonski:1999:RPD,
  author =       "A. Strzebonski",
  title =        "A Real Polynomial Decision Algorithm Using
                 Arbitrary-Precision Floating Point Arithmetic",
  journal =      j-RELIABLE-COMPUTING,
  volume =       "5",
  number =       "3",
  pages =        "337--346",
  year =         "1999",
  CODEN =        "RCOMF8",
  ISSN =         "1385-3139 (print), 1573-1340 (electronic)",
  ISSN-L =       "1385-3139",
  bibdate =      "Mon May 20 06:37:48 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  fjournal =     "Reliable Computing = Nadezhnye vychisleniia",
  journal-URL =  "http://link.springer.com/journal/11155",
  remark =       "Papers from Scientific computing, computer arithmetic
                 and validated numerics (SCAN '98), September 1998,
                 Budapest, Hungary.",
}

@Article{Sunar:1999:MMA,
  author =       "B. Sunar and {\c{C}}. K. Ko{\c{c}}",
  title =        "{Mastrovito} multiplier for all trinomials",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "48",
  number =       "5",
  pages =        "522--527",
  month =        may,
  year =         "1999",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.769434",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jun 24 21:18:53 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Book{Sutherland:1999:LEDk,
  author =       "Ivan Sutherland and Bob Sproull and David Harris",
  title =        "Logical Effort: Designing Fast {CMOS} Circuits",
  publisher =    pub-MORGAN-KAUFMANN,
  address =      pub-MORGAN-KAUFMANN:adr,
  pages =        "xv + 239",
  year =         "1999",
  ISBN =         "1-55860-557-6",
  ISBN-13 =      "978-1-55860-557-2",
  LCCN =         "TK7871.99.M44 S88 1999",
  bibdate =      "Thu Sep 21 17:07:13 MDT 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  subject =      "circuiti elettronici CMOS; circuiti integrati CMOS;
                 circuiti logici; CMOS (Circuit int{\'e}gr{\'e});
                 CMOS-Schaltung; Complementary; Conception et
                 construction; Delay faults (Semiconductors); Design and
                 construction; Dispositifs logiques; Logic design; Logic
                 devices; Logischer Entwurf; Metal oxide semiconductors,
                 Complementary; Metal oxide semiconductors; MOS
                 compl{\'e}mentaires; Pannes temporelles
                 (Semi-conducteurs); Progettazione Schaltungsentwurf;
                 Semiconductores; Structure logique; Transistores MOS
                 complementarios",
  tableofcontents = "1. The Method of Logical Effort \\
                 2. Design Examples \\
                 3. Deriving the Method of Logical Effort \\
                 4. Calculating the Logical Effort of Gates \\
                 5. Calibrating the Model \\
                 6. Asymmetric Logic Gates \\
                 7. Unequal Rising and Falling Delays \\
                 8. Circuit Families \\
                 9. Forks of Amplifiers \\
                 10. Branches and Interconnect \\
                 11. Wide Structures \\
                 12. Conclusions \\
                 App. A. Cast of Characters \\
                 App. B. Reference Process Parameters \\
                 App. C. Solutions to Selected Exercises",
}

@Article{Suzuoki:1999:MBC,
  author =       "M. Suzuoki and K. Kutaragi and T. Hiroi and H. Magoshi
                 and S. Okamoto and M. Oka and A. Ohba and Y. Yamamoto
                 and M. Furuhashi and M. Tanaka and T. Yutaka and T.
                 Okada and M. Nagamatsu and Y. Urakawa and M. Funyu and
                 A. Kunimatsu and H. Goto and K. Hashimoto and N. Ide
                 and H. Murakami and Y. Ohtaguro and A. Aono",
  title =        "A microprocessor with a 128-bit {CPU}, ten
                 floating-point {MAC}'s, four floating-point dividers,
                 and an {MPEG-2} decoder",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "34",
  number =       "11",
  pages =        "1608--1618",
  month =        nov,
  year =         "1999",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "A 250-MHz microprocessor intended for home computer
                 entertainment consists of a CPU core with 128-b
                 multimedia extensions, two single-instruction,
                 multiple-data (SIMD) very long instruction word (VLIW)
                 vector processors containing ten floating-point
                 \ldots{}",
}

@InProceedings{Swartzlander:1999:TMA,
  author =       "E. E. {Swartzlander, Jr.}",
  booktitle =    "Conference Record of the Thirty-Third Asilomar
                 Conference on Signals, Systems, and Computers, 1999",
  title =        "Truncated multiplication with approximate rounding",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1480--1483",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:05 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "In many signal processing applications it is desirable
                 to maintain constant word size through the basic
                 arithmetic operations of add, subtract, multiply and
                 divide. Of these operations, multiply is the biggest
                 concern as multiplying two n-bit data \ldots{}",
}

@InProceedings{Takagi:1999:DRA,
  author =       "Naofumi Takagi and Seiji Kuwahara",
  title =        "Digit-Recurrence Algorithm for Computing {Euclidean}
                 Norm of a {$3$-D} Vector",
  crossref =     "Koren:1999:ISC",
  pages =        "86--95",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-142.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-142.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Takagi.pdf",
  abstract =     "A digit-recurrence algorithm for computing the
                 Euclidean norm of a 3-dimensional vector is proposed.
                 Starting from the vector component with the highest
                 order of magnitude as the initial value of partial
                 result, correcting-digits produced by the recurrence
                 are added to it step by step. Partial products of the
                 squares of the other two components are added to the
                 residual, step by step. The addition\slash subtractions
                 in the recurrence are performed without carry\slash
                 borrow propagation by the use of a redundant
                 representation of the residual. An extension of the
                 on-the-fly conversion algorithm is used for updating
                 the partial result. Different specific versions of the
                 algorithm are possible, depending on the radix, the
                 redundancy factor of the correcting-digit set, the type
                 of representation of the residual, and the
                 correcting-digit selection function.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic",
}

@InProceedings{Tanskanen:1999:REF,
  author =       "J. M. A. Tanskanen and V. S. Dimitrov",
  booktitle =    "Conference Record of the Thirty-Third Asilomar
                 Conference on Signals, Systems, and Computers, 1999",
  title =        "Round-off error free fixed-point design of polynomial
                 {FIR} predictors",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1317--1321",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:05 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "We present a novel method for designing polynomial FIR
                 predictors for fixed-point environments. Our method
                 yields filters that perform exact prediction of
                 polynomial signals even with short coefficient word
                 lengths. Under ordinary coefficient \ldots{}",
}

@InProceedings{Tenca:1999:DHR,
  author =       "Alexandre F. Tenca and Milo{\v{s}} D. Ercegovac",
  title =        "On the Design of High-Radix On-Line Division for Long
                 Precision",
  crossref =     "Koren:1999:ISC",
  pages =        "44--51",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-143.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-143.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Tenca.pdf",
  abstract =     "We present a design of a high-radix on-line division
                 suitable for long precision computations. The proposed
                 scheme uses a quotient-digit selection function based
                 on the residual rounding and scaling of the operands.
                 The bounds on the number of cycles and the cycle time
                 for radix $ 2^k $ and $n$-bit precision are obtained in
                 terms of full-adder delays. The speedup with respect to
                 radix 2 is greater than 3.3 for $ k \geq 6 $ and $ n
                 \geq 64 $. The cost increases as a function of the
                 radix. For the case $ r = 64 $ and $ n = 64 $, the
                 increase in area with respect to $ r = 2 $ is about 6.6
                 times plus a $ 512 \times 10 $-bit table. The proposed
                 scheme has been designed and verified using VHDL and a
                 $ 1.2 \mu $ m CMOS standard gate technology from MOSIS
                 library.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic",
}

@InProceedings{Thompson:1999:BPF,
  author =       "D. U. Thompson and B. A. Wooley",
  title =        "A 15-bit Pipelined Floating-Point {A/D} Converter",
  crossref =     "Hosticka:1999:EPE",
  pages =        "170--173",
  year =         "1999",
  bibdate =      "Sat Jun 02 08:23:03 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Tisseur:1999:NMF,
  author =       "F. Tisseur",
  title =        "{Newton}'s method in floating point arithmetic and
                 iterative refinement of generalized eigenvalue
                 problems",
  type =         "Numerical analysis report",
  number =       "346-XY/N-1",
  institution =  "Manchester Centre for Computational Mathematics",
  address =      "Manchester, UK",
  month =        aug,
  year =         "1999",
  bibdate =      "Thu May 09 08:58:00 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Tropp:1999:HAI,
  author =       "Henry S. Tropp",
  title =        "{Howard Aiken} interview: {February 26--27, 1973}",
  journal =      "Computer Oral History Collection, Smithsonian
                 Institution Press",
  year =         "1999",
  bibdate =      "Thu Aug 07 19:21:30 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Article No. 1.",
  abstract =     "Howard Hathaway Aiken was born in 1900. He earned an
                 undergraduate degree in electrical engineering from the
                 University of Wisconsin in 1923, a Masters in Physics
                 from Harvard in 1937, and his Ph.d in Physics from
                 Harvard in 1939. He was the designer and developer of
                 the first large-scale operating relay calculator in the
                 United States. Aiken begins with a discussion of
                 problems associated with mechanical computation while
                 writing his thesis. He comments on Leslie John Comrie
                 and his contributions to computational techniques and
                 discusses his proposal for the MARK I and IBM's
                 agreement and involvement in 1939, to build the
                 machine. Aiken comments on his choice to design MARK I
                 as an electronic device. He was motivated by money
                 because digital counters made with vacuum tubes would
                 have involved thousands of parts which would have been
                 expensive. Aiken comments on early discussions with IBM
                 about what kind of machine would eventually be built
                 and their funding of the machine. He recalls learning
                 that IBM could not divide and how he invented the
                 technique of dividing by computing by reciprocals in
                 response to this problem. Because of what Aiken
                 introduced, the divider became a standard technique in
                 IBM's technical machine design thereafter. The MARK I
                 machine never did any computations for IBM, but rather
                 split its computing time between a project for the Navy
                 and for Harvard. Ultimately, Aiken's MARK machines were
                 used by several other government agencies. He comments
                 on his tenure on the National Academy of Sciences
                 Commission and he discusses the other individuals on
                 the committee---John von Neumann, George Stibitz, and
                 John Curtiss---to name a few. Curtiss promoted the idea
                 of starting an association for people interested in
                 computing machines, which Aiken was opposed to. Curtiss
                 ultimately founded the Association for Computing
                 Machinery which Aiken never joined. The conferences
                 Aiken held at Harvard University beginning in 1946 were
                 solely his doing. He selected the participants and
                 topics to be discussed. These conferences/lectures
                 were, according to Aiken, essential to getting the
                 field of computing ahead at that time. He comments at
                 length on his work outside of the United States,
                 specifically in Europe, and the individuals with whom
                 he worked. Because of Aiken's work at Harvard with
                 MARK, he had a steady stream of foreign researchers who
                 came to work with his machine. He discusses at length
                 the chronology of his four large scale calculators:
                 MARK I, II, III and IV. MARK II was built for the Naval
                 Proving Ground at Dahlgren and implemented in 1950.
                 Aiken would then proceed to design MARK III almost at
                 the same time, 1948 to 1950, and later MARK IV from
                 1950 to 1952. There was an overlap in the construction
                 and conceptual periods for all the MARK machines. After
                 all of Aiken's MARK machines were built, he felt his
                 effort with computers was completed too and that
                 competing with the industry would not be wise.\par

                 The second portion of this interview was conducted on
                 February 27, 1973, and begins with a discussion of
                 Aiken's method of division using the Newton-Raffson
                 rule. Comments include subsequent machines, problems
                 and users, historical digressions, elaboration on
                 specific computing techniques, documentation regarding
                 miscellaneous people and events, and some biographical
                 background information. Those mentioned frequently
                 include: Leon Chaffee, Leslie John Comrie, Donald
                 Menzel, Ted Brown, Harlow Shapley, J. G. Phillips, E.
                 B. Huntington, Ted Kimball, George Stibitz, Dick Bloch,
                 Norbert Wiener, and Grace Murray Hopper.",
  acknowledgement = ack-nhfb,
}

@Article{Tropp:1999:NRI,
  author =       "Henry S. Tropp and Jean Sammett",
  title =        "{Nat Rochester} interview: {July 24, 1973}",
  journal =      "Computer Oral History Collection, Smithsonian
                 Institution Press",
  year =         "1999",
  bibdate =      "Thu Aug 07 18:47:37 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Article No. 75.",
  abstract =     "Rochester studied electrical engineering at the
                 Massachusetts Institute of Technology (MIT) and was
                 working in acoustics at the outset of World War II.
                 During the war, he worked on radar at the MIT Radiation
                 Laboratory and at Sylvania, building equipment for the
                 Radiation Laboratory. After the war, he worked on the
                 arithmetic unit for Whirlwind and on cryptanalysis
                 equipment for the national Security Agency (NSA). In
                 1948, feeling that computers would be a ``major
                 thing,'' he went to IBM where he urged their
                 development. His work on a study of the significance of
                 magnetic tape lead to the IBM 700 series. He discusses
                 assembly programming, the switches from card to tape
                 and from decimal to binary systems, the seesawing of
                 the relative reliability of software and hardware, and
                 the advantages and disadvantages of system
                 compatibility. Special mention is made of: the 1946
                 summer school program at the University of
                 Pennsylvania; the 1947 Aberdeen meeting; and the
                 meeting called by Tom Watson, Jr., at which the
                 decision was made to go ahead with the 700 series, thus
                 making a commitment to computers. Jean Sammett sat in
                 on the interview. Among those often mentioned are John
                 von Neumann, Ralph Palmer, Werner Buchholz, Cuthbert
                 Hurd, and Steve Dunwell.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Tsuji:1999:REO,
  author =       "K. Tsuji",
  title =        "Round-off error of optimal control problems in
                 floating-point number systems",
  crossref =     "Begehr:1999:PSI",
  pages =        "929--944",
  year =         "1999",
  bibdate =      "Sat Jun 02 08:12:11 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Walter:1999:MTI,
  author =       "Colin D. Walter",
  title =        "Moduli for Testing Implementations of the {RSA}
                 Cryptosystem",
  crossref =     "Koren:1999:ISC",
  pages =        "78--85",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-130.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-130.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Walter.pdf",
  abstract =     "Comprehensive testing of any implementation of the RSA
                 cryptosystem requires the use of a number of moduli
                 with specific properties. It is shown how to generate a
                 sufficient variety of these to enable testing which
                 will justify high confidence in the correctness of both
                 the design and the operation of hardware
                 implementations. The tests avoid the necessity of
                 another implementation for comparison. Many of these
                 moduli are also suitable for testing software
                 implementations. Furthermore, the methods apply equally
                 well to other similar modular arithmetic based
                 cryptosystems which use exponentiation, such as
                 Diffie-Helman key exchange.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic; correctness;
                 cryptography; implementation validation benchmark.; RSA
                 modulus; testing; verification",
}

@Article{Watanabe:1999:NVM,
  author =       "Y. Watanabe and N. Yamamoto and M. T. Nakao",
  title =        "A Numerical Verification Method of Solutions for the
                 {Navier--Stokes} Equations",
  journal =      j-RELIABLE-COMPUTING,
  volume =       "5",
  number =       "3",
  pages =        "347--357",
  year =         "1999",
  CODEN =        "RCOMF8",
  ISSN =         "1385-3139 (print), 1573-1340 (electronic)",
  ISSN-L =       "1385-3139",
  bibdate =      "Mon May 20 06:37:48 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  fjournal =     "Reliable Computing = Nadezhnye vychisleniia",
  journal-URL =  "http://link.springer.com/journal/11155",
  remark =       "Papers from Scientific computing, computer arithmetic
                 and validated numerics (SCAN '98), September 1998,
                 Budapest, Hungary.",
}

@InProceedings{Wires:1999:CUT,
  author =       "K. E. Wires and M. J. Schulte and L. P. Marquette and
                 P. I. Balzola",
  title =        "Combined Unsigned and Two's Complement Squarers",
  crossref =     "Matthews:1999:CRT",
  pages =        "1215--1219",
  year =         "1999",
  bibdate =      "Sun Mar 04 11:08:58 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1999-06.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Wong:1999:OFP,
  author =       "W. F. Wong",
  title =        "Optimizing floating point operations in {Scheme}",
  journal =      j-COMP-LANGS,
  volume =       "25",
  number =       "2",
  pages =        "89--112",
  month =        jul,
  year =         "1999",
  CODEN =        "COLADA",
  ISSN =         "0096-0551 (print), 1873-6742 (electronic)",
  ISSN-L =       "0096-0551",
  bibdate =      "Thu Oct 12 10:20:10 MDT 2000",
  bibsource =    "http://www.elsevier.com/locate/complang;
                 https://www.math.utah.edu/pub/tex/bib/complngs.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.elsevier.nl/gej-ng/10/15/18/28/27/26/abstract.html;
                 http://www.elsevier.nl/gej-ng/10/15/18/28/27/26/article.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Languages",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00960551",
}

@InProceedings{Yadav:1999:PSF,
  author =       "N. Yadav and M. J. Schulte and J. Glossner",
  title =        "Parallel Saturating Fractional Arithmetic Units",
  crossref =     "Mazumder:1999:NGL",
  pages =        "214--217",
  year =         "1999",
  bibdate =      "Sun Mar 04 11:15:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1999-02.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Yang:1999:CIS,
  author =       "D. X. D. Yang and A. E. Gamal and B. Fowler and H.
                 Tian",
  title =        "A 640$ \times $512 {CMOS} image sensor with ultrawide
                 dynamic range floating-point pixel-level {ADC}",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "34",
  number =       "12",
  pages =        "1821--1834",
  month =        dec,
  year =         "1999",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "Analysis results demonstrate that multiple sampling
                 can achieve consistently higher signal-to-noise ratio
                 at equal or higher dynamic range than using other image
                 sensor dynamic range enhancement schemes such as well
                 capacity adjusting. Implementing \ldots{}",
}

@Article{Yang:1999:RNSa,
  author =       "Lie-Liang Yang and L. Hanzo",
  title =        "Residue number system arithmetic assisted {$M$}-ary
                 modulation",
  journal =      j-IEEE-COMMUN-LET,
  volume =       "3",
  number =       "2",
  pages =        "28--30",
  month =        feb,
  year =         "1999",
  CODEN =        "ICLEF6",
  DOI =          "https://doi.org/10.1109/4234.749352",
  ISSN =         "????",
  ISSN-L =       "1089-7798",
  bibdate =      "Fri Nov 9 11:38:58 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=16186",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Communications Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4234",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A residue number system based M-ary modem is proposed
                 and its performance is evaluated over Gaussian
                 channels. When one or two redundant moduli are
                 employed, a signal-to-noise ratio gain of 1.2-2 dB was
                 achieved for a 16-ary, 32-ary and 37-ary modem,
                 \ldots{}",
}

@InProceedings{Yang:1999:RNSb,
  author =       "Lie-Liang Yang and L. Hanzo",
  booktitle =    "{IEEE 49th} Vehicular Technology Conference, 16--20
                 May 1999",
  title =        "Residue number system based multiple code {DS-CDMA}
                 systems",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1450--1454",
  year =         "1999",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/VETEC.1999.780587",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A novel multi-code direct-sequence code division
                 multiple-access (DS-CDMA) system based on the so-called
                 residue number system (RNS) or the redundant residue
                 number system (RRNS) is proposed. Concatenated codes
                 employing RNS product codes (RNS-PC) \ldots{}",
}

@InProceedings{Yang:1999:RST,
  author =       "Lie-Liang Yang and L. Hanzo",
  booktitle =    "{IEEE 49th} Vehicular Technology Conference. 16--20
                 May 1999",
  title =        "Ratio statistic test assisted residue number system
                 based parallel communication schemes",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "894--898",
  year =         "1999",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/VETEC.1999.780477",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A residue number system (RNS) based parallel
                 communication system is proposed and its performance is
                 evaluated using non-coherent demodulation. Diversity
                 reception techniques with equal gain combining (EGC) or
                 selection combining (SC) are considered \ldots{}",
}

@Misc{Yap:1999:REI,
  author =       "C. Yap and K. Ouchi",
  title =        "{Real/Expr}: Implementation of Exact Computation",
  howpublished = "Web site",
  day =          "22",
  month =        jan,
  year =         "1999",
  bibdate =      "Tue Oct 22 06:22:39 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://cs.nyu.edu/exact/realexpr/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Yuan:1999:FPA,
  author =       "J. Yuan and J. Piper",
  title =        "Floating-Point Analog-To-Digital Converter",
  crossref =     "IEEE:1999:IPI",
  pages =        "1385--1388",
  year =         "1999",
  bibdate =      "Sat Jun 02 08:19:08 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Zimmermann:1999:EVI,
  author =       "Reto Zimmermann",
  title =        "Efficient {VLSI} Implementation of Modulo $ (2^n \pm
                 1) $ Addition and Multiplication",
  crossref =     "Koren:1999:ISC",
  pages =        "158--167",
  year =         "1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-127.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-127.ps;
                 http://www.acsel-lab.com/arithmetic/arith14/papers/ARITH14_Zimmermann.pdf",
  abstract =     "New VLSI circuit architectures for addition and
                 multiplication modulo $ (2 n - 1) $ and $ (2 n + 1) $
                 are proposed that allow the implementation of highly
                 efficient combinational and pipelined circuits for
                 modular arithmetic. It is shown that the
                 parallel-prefix adder architecture is well suited to
                 realize fast end-around-carry adders used for modulo
                 addition. Existing modulo multiplier architectures are
                 improved for higher speed and regularity. These allow
                 the use of common multiplier speedup techniques like
                 Wallace tree addition and Booth recoding, resulting in
                 the fastest known modulo multipliers. Finally, a
                 high-performance modulo multiplier-adder for the IDEA
                 block cipher is presented. The resulting circuits are
                 compared qualitatively and quantitatively, i.e., in a
                 standard cell technology, with existing solutions and
                 ordinary integer adders and multipliers.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14; computer arithmetic",
}

@TechReport{Zimmermann:1999:KSR,
  author =       "Paul Zimmermann",
  title =        "{Karatsuba} Square Root",
  type =         "Research Report",
  number =       "3805",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  pages =        "8",
  year =         "1999",
  bibdate =      "Sun Sep 10 08:56:48 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-3805.pdf;
                 ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-3805.ps.gz;
                 http://www.inria.fr/rrrt/rr-3805.html",
  abstract =     "We exhibit an algorithm to compute the square-root
                 with remainder of a $n$-word number in $ 3 / 2 $ word
                 operations, where $ K(n) $ is the number of words
                 operations to multiply two $n$-word numbers using
                 Karatsuba's algorithm. If the remainder is not needed,
                 the cost can be reduced to $ K(n) $ on average. This
                 algorithm can be used for floating-point or polynomial
                 computations too; although not optimal asymptotically,
                 its simplicity gives a wide range of use, from about 50
                 to 1,000,000 digits, as shown by computer
                 experiments.",
  acknowledgement = ack-nhfb,
}

@Article{Ziv:1999:SUR,
  author =       "Abraham Ziv",
  title =        "Sharp {ULP} rounding error bound for the hypotenuse
                 function",
  journal =      j-MATH-COMPUT,
  volume =       "68",
  number =       "227",
  pages =        "1143--1148",
  month =        jul,
  year =         "1999",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Fri Jul 16 10:39:05 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1999-68-227;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-99-01103-5&u=/mcom/1999-68-227/",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Periodical{FPS:19xx:R,
  author =       "{Floating Point Systems, Inc.Users Group Meeting}",
  key =          "FPS",
  title =        "Record",
  publisher =    "Floating Point Systems",
  address =      "Portland, OR, USA",
  pages =        "various",
  year =         "19xx",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  alttitle =     "Record (Floating Point Systems, Inc. Users Group.
                 Meeting) ARRAY (Organization). Conference.
                 Proceedings",
  keywords =     "Array processors --- Congresses; Parallel processing
                 (Electronic computers) --- Congresses",
}

@Manual{Intel:19xx:IAP,
  author =       "{Intel}",
  title =        "{Intel 8231A} Arithmetic Processing Unit",
  organization = "Intel Corp",
  address =      "San Jose, CA, USA",
  year =         "19xx",
  bibdate =      "Thu Oct 14 15:14:43 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "From the datasheet (p. 3-5): ``The mantissa is
                 expressed as a 24-bit (fractional) value; the exponent
                 is expressed as a two's complement 7-bit value having
                 the range $ - 64 $ to $ + 63 $. The most significant
                 bit is the sign of the mantissa ($0$ = positive, $1$ =
                 negative), for a total of 32 bits. The binary point is
                 assumed to be [to] the left of the most significant
                 mantissa bit (bit 23). All floating-point data values
                 must be normalized. Bit 23 must be equal to 1, except
                 for the value zero, which is represented by all zeros.
                 The range of values that can be represented in this
                 format is $ \pm (2.7 \time 10^{-10} \ldots {} 9.2
                 \times 10^{18}) $ and zero.''",
  URL =          "http://www.datasheetarchive.com/pdf-datasheets/Datasheets-14/DSA-276911.html",
  acknowledgement = ack-nhfb,
  remark =       "Undated processor datasheet.",
}

@Article{Anonymous:2000:BRCd,
  author =       "Anonymous",
  title =        "Book Review: {{\booktitle{Computer arithmetic:
                 Algorithms and hardware designs}}: By Behrooz Parhami.
                 Oxford University Press, New York. (2000). 490 pages.
                 \$85.00}",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "39",
  number =       "3--4",
  pages =        "264--264",
  month =        feb,
  year =         "2000",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:49:06 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122100900518",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Anonymous:2000:BRCg,
  author =       "Anonymous",
  title =        "Book Review: {{\booktitle{Computer arithmetic:
                 Algorithms and hardware designs}}: By Behrooz Parhami.
                 Oxford University Press, New York. (2000). 490 pages.
                 \$85.00}",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "39",
  number =       "7--8",
  pages =        "266--266",
  month =        apr,
  year =         "2000",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:49:08 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122100902955",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Antelo:2000:VHRa,
  author =       "Elisardo Antelo and Tom{\'a}s Lang and Javier D.
                 Bruguera",
  title =        "Very-High Radix {CORDIC} Rotation Based on Selection
                 by Rounding",
  journal =      j-J-VLSI-SIGNAL-PROC-SSIVT,
  volume =       "25",
  number =       "2",
  pages =        "141--153",
  month =        jun,
  year =         "2000",
  DOI =          "https://doi.org/10.1023/a:1008119006403",
  ISSN =         "1387-5485 (print), 1573-0506 (electronic)",
  ISSN-L =       "1387-5485",
  bibdate =      "Tue Oct 28 07:04:09 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0963.68238",
  acknowledgement = ack-nhfb,
  ajournal =     "J. VLSI Signal Process. Syst. Signal, Image Video
                 Tech.",
  fjournal =     "Journal of VLSI Signal Processing Systems for Signal,
                 Image, and Video Technology",
  journal-URL =  "https://link.springer.com/journal/11265",
  keywords =     "68W35",
  ZBmath =       "1507619",
}

@Article{Antelo:2000:VHRb,
  author =       "E. Antelo and T. Lang and J. D. Bruguera",
  title =        "Very-High Radix Circular {CORDIC}: Vectoring and
                 Unified Rotation\slash Vectoring",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "7",
  pages =        "727--739",
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.863043",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon May 20 06:47:55 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-14",
  remark =       "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
}

@Misc{Arnold:2000:EAS,
  author =       "D. Arnold",
  title =        "The Explosion of the {Ariane 5}. {Some} disasters
                 attributable to bad numerical computing",
  howpublished = "Web site.",
  day =          "23",
  month =        aug,
  year =         "2000",
  bibdate =      "Mon Aug 26 11:10:55 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www-users.math.umn.edu/~arnold/disasters/ariane.html",
  acknowledgement = ack-nhfb,
}

@PhdThesis{Baidas:2000:HLF,
  author =       "Zaher A. Baidas",
  title =        "High-level floating-point synthesis",
  type =         "Thesis ({Ph.D.})",
  school =       "University of Southampton, Department of Electronics
                 and Computer Science",
  address =      "Southampton, UK",
  pages =        "327",
  year =         "2000",
  bibdate =      "Thu May 09 08:47:14 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Batten:2000:NAD,
  author =       "D. Batten and S. Jinturkar and J. Glossner and M.
                 Schulte and P. D'arcy",
  title =        "A New Approach to {DSP} Intrinsic Functions",
  crossref =     "Sprague:2000:PAH",
  pages =        "2892--2901",
  year =         "2000",
  bibdate =      "Sun Mar 04 11:18:38 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2000-01.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Becker:2000:JSE,
  author =       "Pete Becker",
  title =        "The Journeyman's Shop: Error in Floating-Point
                 Calculations",
  journal =      j-CCCUJ,
  volume =       "18",
  number =       "7",
  pages =        "73--??",
  month =        jul,
  year =         "2000",
  CODEN =        "CCUJEX",
  ISSN =         "1075-2838",
  bibdate =      "Tue May 14 18:09:27 MDT 2002",
  bibsource =    "http://www.cuj.com/articles/2000/0007/0007toc.htm?topic=articles;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "And you thought error, accuracy, precision, and
                 significance were pretty synonymous.",
  acknowledgement = ack-nhfb,
  fjournal =     "C/C++ Users Journal",
}

@Article{Becker:2000:JSF,
  author =       "Pete Becker",
  title =        "The Journeyman's Shop: Floating-Point Basics",
  journal =      j-CCCUJ,
  volume =       "18",
  number =       "6",
  pages =        "??--??",
  month =        jun,
  year =         "2000",
  CODEN =        "CCUJEX",
  ISSN =         "1075-2838",
  bibdate =      "Tue May 14 18:09:26 MDT 2002",
  bibsource =    "http://www.cuj.com/articles/2000/0006/0006toc.htm?topic=articles;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "You can't overcome a fear of floating-point arithmetic
                 --- or complacency about it --- until you understand
                 what's going on.",
  acknowledgement = ack-nhfb,
  fjournal =     "C/C++ Users Journal",
}

@Article{Becker:2000:JST,
  author =       "Pete Becker",
  title =        "The Journeyman's Shop: Trap Handlers, Sticky Bits, and
                 Floating-Point Comparisons",
  journal =      j-CCCUJ,
  volume =       "18",
  number =       "12",
  pages =        "54--??",
  month =        dec,
  year =         "2000",
  CODEN =        "CCUJEX",
  ISSN =         "1075-2838",
  bibdate =      "Tue May 14 18:09:29 MDT 2002",
  bibsource =    "http://www.cuj.com/articles/2000/0012/0012toc.htm?topic=articles;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Pete wraps up his series on practical floating-point
                 math.",
  acknowledgement = ack-nhfb,
  fjournal =     "C/C++ Users Journal",
}

@Article{Becker:2000:JSWb,
  author =       "Pete Becker",
  title =        "The Journeyman's Shop: When Bad Things Happen to Good
                 Numbers",
  journal =      j-CCCUJ,
  volume =       "18",
  number =       "10",
  pages =        "54--??",
  month =        oct,
  year =         "2000",
  CODEN =        "CCUJEX",
  ISSN =         "1075-2838",
  bibdate =      "Tue May 14 18:09:28 MDT 2002",
  bibsource =    "http://www.cuj.com/articles/2000/0010/0010toc.htm?topic=articles;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "It takes a lot of preparation to write really robust
                 floating-point code.",
  acknowledgement = ack-nhfb,
  fjournal =     "C/C++ Users Journal",
}

@Article{Bekooij:2000:NAF,
  author =       "M. Bekooij and J. Huisken and K. Nowak",
  title =        "Numerical Accuracy of {Fast Fourier Transforms} with
                 {CORDIC} Arithmetic",
  journal =      j-J-VLSI-SIGNAL-PROC-SSIVT,
  volume =       "25",
  number =       "2",
  pages =        "187--193",
  month =        jun,
  year =         "2000",
  DOI =          "https://doi.org/10.1023/a:1008179225059",
  ISSN =         "1387-5485 (print), 1573-0506 (electronic)",
  ISSN-L =       "1387-5485",
  bibdate =      "Tue Oct 28 07:04:09 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "0963.68241",
  acknowledgement = ack-nhfb,
  ajournal =     "J. VLSI Signal Process. Syst. Signal, Image Video
                 Tech.",
  fjournal =     "Journal of VLSI Signal Processing Systems for Signal,
                 Image, and Video Technology",
  journal-URL =  "https://link.springer.com/journal/11265",
  keywords =     "68W35",
  ZBmath =       "1507623",
}

@Article{Bertossi:2000:RNS,
  author =       "A. A. Bertossi and A. Mei",
  title =        "A residue number system on reconfigurable mesh with
                 applications to prefix sums and approximate string
                 matching",
  journal =      j-IEEE-TRANS-PAR-DIST-SYS,
  volume =       "11",
  number =       "11",
  pages =        "1186--1199",
  month =        nov,
  year =         "2000",
  CODEN =        "ITDSEO",
  DOI =          "https://doi.org/10.1109/71.888638",
  ISSN =         "1045-9219 (print), 1558-2183 (electronic)",
  ISSN-L =       "1045-9219",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=19224",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Parallel Distrib. Syst.",
  fjournal =     "IEEE Transactions on Parallel and Distributed
                 Systems",
  journal-URL =  "http://www.computer.org/tpds/archives.htm",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Several new number representations based on a residue
                 number system are presented which use the smallest
                 prime numbers as moduli and are suited for parallel
                 computations on a reconfigurable mesh architecture. The
                 bit model of linear reconfigurable \ldots{}",
}

@TechReport{Boldo:2000:QDP,
  author =       "Sylvie Boldo",
  title =        "Quad double precision specification and proofs about
                 the addition",
  type =         "Traineeship report -- {MIM2}",
  institution =  "University of California, Berkeley, and {\'E}cole
                 Normale Sup{\'e}rieure de Lyon",
  address =      "Berkeley, CA, USA and 69364 Lyon Cedex 07, France",
  pages =        "51",
  month =        jun # "\slash " # aug,
  year =         "2000",
  bibdate =      "Tue Nov 23 10:59:46 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Under the direction of Jonathan Shewchuk.",
  URL =          "http://perso.ens-lyon.fr/sylvie.boldo/doc/qd.ps",
  acknowledgement = ack-nhfb,
}

@Article{Brooks:2000:VBC,
  author =       "David Brooks and Margaret Martonosi",
  title =        "Value-based clock gating and operation packing:
                 dynamic strategies for improving processor power and
                 performance",
  journal =      j-TOCS,
  volume =       "18",
  number =       "2",
  pages =        "89--126",
  month =        may,
  year =         "2000",
  CODEN =        "ACSYEC",
  ISSN =         "0734-2071 (print), 1557-7333 (electronic)",
  ISSN-L =       "0734-2071",
  bibdate =      "Tue Sep 26 07:54:31 MDT 2000",
  bibsource =    "http://www.acm.org/pubs/contents/journals/tocs/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/tocs/2000-18-2/p89-brooks/",
  abstract =     "The large address space needs of many current
                 applications have pushed processor designs toward
                 64-bit word widths. Although full 64-bit addresses and
                 operations are indeed sometimes needed, arithmetic
                 operations on much smaller quantities are still more
                 common. In fact, another instruction set trend has been
                 the introduction of instructions geared toward subword
                 operations on 16-bit quantities. For examples, most
                 major processors now include instruction set support
                 for multimedia operations allowing parallel execution
                 of several subword operations in the same ALU. This
                 article presents our observations demonstrating that
                 operations on ``narrow-width'' quantities are common
                 not only in multimedia codes, but also in more general
                 workloads. In fact, across the SPECint95 benchmarks,
                 over half the integer operation executions require 16
                 bits or less. Based on this data, we propose two
                 hardware mechanisms that dynamically recognize and
                 capitalize on these narrow-width operations. The first,
                 power-oriented optimization reduces processor power
                 consumption by using operand-value-based clock gating
                 to turn off portions of arithmetic units that will be
                 unused by narrow-width operations. This optimization
                 results in a 45\%--60\% reduction in the integer unit's
                 power consumption for the SPECint95 and MediaBench
                 benchmark suites. Applying this optimization to
                 SPECfp95 benchmarks results in slightly smaller power
                 reductions, but still seems warranted. These reductions
                 in integer unit power consumption equate to a 5\%--10\%
                 full-chip power savings. Our second,
                 performance-oriented optimization improves processor
                 performance by packing together narrow-width operations
                 so that they share a single arithmetic unit.
                 Conceptually similar to a dynamic form of MMX, this
                 optimization offers speedups of 4.3\%--6.2\% for
                 SPECint95 and 8.0\%--10.4\% for
                 MediaBench.\par

                 Overall, these optimizations highlight an increasing
                 opportunity for value-based optimizations to improve
                 both power and performance in current
                 microprocessors.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Computer Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J774",
  subject =      "Hardware --- Arithmetic and Logic Structures (B.2);
                 Computer Systems Organization --- Processor
                 Architectures --- Single Data Stream Architectures
                 (C.1.1): {\bf RISC/CISC, VLIW architectures}",
}

@InProceedings{Cardarilli:2000:RPD,
  author =       "G. C. Cardarilli and A. Nannarelli and M. Re",
  booktitle =    "Proceedings of the 43rd {IEEE} Midwest Symposium on
                 Circuits and Systems, 2000",
  title =        "Reducing power dissipation in {FIR} filters using the
                 residue number system",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "320--323",
  year =         "2000",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.2000.951651",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The aim of this work is to reduce the power dissipated
                 in high order finite impulse response (FIR) filters,
                 while maintaining the delay unchanged. We compare in
                 terms of performance, area, and power dissipation the
                 implementation of a traditional \ldots{}",
}

@Article{Chen:2000:PCV,
  author =       "Chichyang Chen and Rui-Lin Chen and Chih-Huan Yang",
  title =        "Pipelined Computation of Very Large Word-Length {LNS}
                 Addition\slash Subtraction with Polynomial Hardware
                 Cost",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "7",
  pages =        "716--726",
  month =        jul,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.863041",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-14",
  remark =       "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
  summary =      "A novel pipelined method is proposed to compute the
                 addition/subtraction in very large word-length
                 logarithmic number system (LNS) arithmetic.
                 Digit-parallel additive-normalization and digit on-line
                 multiplicative-normalization methods are adopted
                 \ldots{}",
}

@Article{Cheng:2000:STC,
  author =       "F.-C. Cheng and S. H. Unger and M. Theobald",
  title =        "Self-Timed Carry-Lookahead Adders",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "7",
  pages =        "659--672",
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.863035",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon May 20 06:47:55 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-14",
  remark =       "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
}

@TechReport{Cheng:2000:TID,
  author =       "Y.-T. Cheng",
  title =        "{TMS320C60000} integer division",
  type =         "Application Report",
  number =       "SPRA707",
  institution =  "Texas Instruments",
  address =      "Post Office box 655303, Dallas, TX 75265, USA",
  month =        oct,
  year =         "2000",
  bibdate =      "Fri Sep 22 16:24:20 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.ti.com/lit/an/spra707/spra707.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Cherri:2000:PCC,
  author =       "A. K. Cherri and M. S. Alam",
  title =        "Parallel computation of complex elementary functions
                 using quaternary signed-digit arithmetic",
  journal =      "Optics and Laser Technology",
  volume =       "32",
  number =       "6",
  pages =        "391--399",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "0030-3992",
  bibdate =      "Sat Dec 7 09:21:28 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Ingenta database",
  acknowledgement = ack-nhfb,
  pagecount =    "9",
}

@InProceedings{Chu:2000:CPT,
  author =       "Wanming Chu and Yamin Li",
  booktitle =    "{ACAC 2000}: 5th Australasian Computer Architecture
                 Conference",
  title =        "Cost\slash performance tradeoff of $n$-select square
                 root implementations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "9--16",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Hardware square-root units require large numbers of
                 gates even for iterative implementations. In this paper
                 we present four low-cost high-performance
                 fully-pipelined n-select implementations (nS-Root)
                 based on a non-restoring-remainder square root
                 \ldots{}",
}

@Article{Coleman:2000:AEL,
  author =       "J. N. Coleman and E. I. Chester and C. I. Softley and
                 J. Kadlec",
  title =        "Arithmetic on the {European Logarithmic
                 Microprocessor}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "7",
  pages =        "702--715",
  month =        jul,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.863040",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:35:24 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
                 OCLC Proceedings database",
  note =         "See corrections \cite{Coleman:2000:CAE}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=863040",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-14",
  remark =       "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
}

@Article{Coleman:2000:CAE,
  author =       "J. N. Coleman and E. I. Chester and C. I. Softley and
                 J. Kadlec",
  title =        "Corrections to {``Arithmetic on the European
                 Logarithmic Microprocessor''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "10",
  pages =        "1152--1152",
  month =        oct,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2000.888057",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:35:26 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  note =         "See \cite{Coleman:2000:AEL}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=888057",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Collins:2000:MFP,
  author =       "George E. Collins and Werner Krandick",
  title =        "Multiprecision floating point addition",
  crossref =     "Traverso:2000:IAU",
  pages =        "71--77",
  year =         "2000",
  bibdate =      "Tue Apr 17 09:15:54 MDT 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/issac/345542/p71-collins/p71-collins.pdf;
                 http://www.acm.org/pubs/citations/proceedings/issac/345542/p71-collins/",
  acknowledgement = ack-nhfb,
  keywords =     "FSUM; interval arithmetic; LEDA; MPADD; MPFUN;
                 polynomial root finding",
}

@InProceedings{Constantinides:2000:MPR,
  author =       "G. A. Constantinides and P. Y. K. Cheung and W. Luk",
  booktitle =    "{IEEE} Symposium on Field-Programmable Custom
                 Computing Machines, 17--19 April 2000",
  title =        "Multiple precision for resource minimization",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "307--308",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:53:44 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Presents the Synoptix high-level synthesis and
                 precision optimization system for FPGAs. Given abstract
                 specifications in the form of infinite-precision signal
                 flow graphs and a set of error constraints, Synoptix
                 creates hardware descriptions of \ldots{}",
}

@InProceedings{Cornea:2000:IDR,
  author =       "M. Cornea and C. Iordache and J. Harrison and P.
                 Markstein",
  editor =       "????",
  booktitle =    "{Fourth conference on Real numbers and Computers,
                 Schlo{\ss} Dagstuhl, April 2000}",
  title =        "Integer divide and remainder operations in the {IA-64}
                 architecture",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2000",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Fri Sep 22 16:50:51 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.imada.sdu.dk/kornerup/RNC4/papers/p17.ps",
  acknowledgement = ack-nhfb,
  remark =       "I cannot yet find this online.",
}

@Article{Corsonello:2000:PCB,
  author =       "P. Corsonello and S. Perri and G. Cocorullo",
  title =        "Performance comparison between static and dynamic
                 {CMOS} logic implementations of a pipelined
                 square-rooting circuit",
  journal =      "Circuits, Devices and Systems, IEE Proceedings [see
                 also IEE Proceedings G- Circuits, Devices and
                 Systems]",
  volume =       "147",
  number =       "6",
  pages =        "347--355",
  month =        dec,
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Pipelined cellular array implementations of arithmetic
                 circuits are usually adopted to obtain high throughput
                 at reasonable cost. The circuit design style used to
                 implement the array greatly influences both performance
                 and cost. The designer has to \ldots{}",
}

@InProceedings{Costello:2000:BSLa,
  author =       "J. Costello and D. Al-Khalili",
  booktitle =    "{ICECS 2000. 7th IEEE International Conference on
                 Electronics, Circuits and Systems (Cat. No. 00EX445)}",
  title =        "Behavioural synthesis of low power floating point
                 {CORDIC} processors",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "506--509 (vol. 1)",
  year =         "2000",
  DOI =          "https://doi.org/10.1109/ICECS.2000.911589",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Application software; Digital arithmetic; Digital
                 signal processing; Educational institutions; Embedded
                 system; Equations; Hardware design languages; Military
                 computing; Signal processing algorithms;
                 System-on-a-chip",
}

@MastersThesis{Costello:2000:BSLb,
  author =       "Joseph Patrick Costello",
  title =        "Behavioural synthesis of low-power floating point
                 {CORDIC} processors",
  type =         "{M.Eng.} thesis",
  school =       "Royal Military College of Canada",
  address =      "Kingston, ON, Canada",
  pages =        "183",
  year =         "2000",
  ISBN =         "0-612-65854-6",
  ISBN-13 =      "978-0-612-65854-7",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://login.ezproxy.lib.utah.edu/login?url=https://www.proquest.com/dissertations-theses/behavioural-synthesis-low-power-floating-point/docview/304678593/se-2",
  acknowledgement = ack-nhfb,
  advisor =      "Dhamin Al-Khalili",
  keywords =     "0544:Electrical engineering; Applied sciences;
                 Electrical engineering",
  ris-m1 =       "MQ65854",
}

@InProceedings{DAmora:2000:RPD,
  author =       "A. D'Amora and A. Nannarelli and M. Re and G. C.
                 Cardarilli",
  booktitle =    "Conference Record of the Thirty-Fourth Asilomar
                 Conference on Signals, Systems and Computers, 2000",
  title =        "Reducing power dissipation in complex digital filters
                 by using the quadratic residue number system",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "879--883",
  year =         "2000",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ACSSC.2000.910639",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper compares in terms of performance, area and
                 power dissipation, a complex FIR filter realized in the
                 traditional two's complement system with a Quadratic
                 Residue Number System (QRNS) based one. The resulting
                 implementations, designed to \ldots{}",
}

@InProceedings{Daumas:2000:EIT,
  author =       "Marc Daumas and Claire Moreau-Finot",
  editor =       "????",
  booktitle =    "Real Numbers and Computers, Dagstuhl, Germany, 2000",
  title =        "Exponential: implementation trade-offs for hundred bit
                 precision",
  publisher =    "????",
  address =      "????",
  pages =        "61--74",
  year =         "2000",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Wed Nov 24 12:44:20 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Delves:2000:MUI,
  author =       "L. M. Delves",
  title =        "Making Use of {IEEE} Arithmetic Facilities",
  journal =      j-FORTRAN-FORUM,
  volume =       "19",
  number =       "3",
  pages =        "9--12",
  month =        dec,
  year =         "2000",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/570899.570902",
  ISSN =         "1061-7264 (print), 1931-1311 (electronic)",
  ISSN-L =       "1061-7264",
  bibdate =      "Wed Jun 18 16:26:21 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Fortran Forum",
  issue =        "59",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J286",
}

@Article{Drmac:2000:AQS,
  author =       "Zlatko Drma{\v{c}} and Elizabeth R. Jessup",
  title =        "On accurate quotient singular value computation in
                 floating-point arithmetic",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "22",
  number =       "3",
  pages =        "853--873",
  year =         "2000",
  CODEN =        "SJMAEL",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F15 (65G20)",
  MRnumber =     "MR1799528 (2001j:65062)",
  MRreviewer =   "Fabio Di Benedetto",
  bibdate =      "Thu Nov 8 19:32:13 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Ercegovac:2000:IGD,
  author =       "Milo{\v{s}} D. Ercegovac and Laurent Imbert and David
                 W. Matula and Jean-Michel Muller and Guoheng Wei",
  title =        "Improving {Goldschmidt} Division, Square Root, and
                 Square Root Reciprocal",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "7",
  pages =        "759--763",
  month =        jul,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.863046",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:35:25 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
                 OCLC Proceedings database",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=863046",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-14; correct rounding; floating-point
                 arithmetic",
  remark =       "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
  remark-2 =     "From the first column: ``These methods do not directly
                 produce the remainder and correct rounding (as required
                 by the IEEE-754 standard [8]) requires extra quotient
                 digits. According to [7], roughly twice as many digits
                 of intermediate result are needed as in the final
                 result unless the iterations are performed using a
                 fused multiply-accumulate operator [1].''",
  summary =      "The aim of this paper is to accelerate division,
                 square root, and square root reciprocal computations
                 when the Goldschmidt method is used on a pipelined
                 multiplier. This is done by replacing the last
                 iteration by the addition of a correcting term that can
                 be looked up during the early iterations. We describe
                 several variants of the Goldschmidt algorithm, assuming
                 4-cycle pipelined multiplier, and discuss obtained
                 number of cycles and error achieved. Extensions to
                 other than 4-cycle multipliers are given. If we call
                 $G_m$ the Goldschmidt algorithm with $m$ iterations,
                 our variants allow us to reach an accuracy that is
                 between that of $G_3$ and that of $G_4$, with a number
                 of cycles equal to that of $G_3$.",
}

@Article{Ercegovac:2000:RSR,
  author =       "Milo{\v{s}} D. Ercegovac and Tom{\'a}s Lang and
                 Jean-Michel Muller and Arnaud Tisserand",
  title =        "Reciprocation, Square Root, Inverse Square Root, and
                 Some Elementary Functions Using Small Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "7",
  pages =        "628--637",
  month =        jul,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.863031",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "68M07 (65B15)",
  MRnumber =     "MR1783602 (2001e:68016)",
  bibdate =      "Tue Jul 5 10:35:24 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
                 OCLC Proceedings database",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=863031",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-14",
  remark =       "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
  summary =      "This paper deals with the computation of reciprocals,
                 square roots, inverse square roots, and some elementary
                 functions using small tables, small multipliers, and,
                 for some functions, a final ``large'' (almost
                 full-length) multiplication. \ldots{}",
}

@InProceedings{Eskritt:2000:DDF,
  author =       "J. Eskritt and R. Muscedere and G. A. Jullien and V.
                 S. Dimitrov and W. C. Miller",
  editor =       "Magdy A. Bayoumi and Eby G. Friedman",
  booktitle =    "{SiPS 2000: 2000 IEEE Workshop on Signal Processing
                 Systems: design and implementation: 11--13 October
                 2000: Lafayette, Louisiana}",
  title =        "A 2-Digit {DBNS} Filter Architecture",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  bookpages =    "xv + 836",
  pages =        "447--456",
  year =         "2000",
  DOI =          "https://doi.org/10.1109/SIPS.2000.886743",
  ISBN =         "0-7803-6488-0",
  ISBN-13 =      "978-0-7803-6488-2",
  LCCN =         "TK7874 .S58 2000",
  bibdate =      "Sat May 14 17:26:55 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Double-Based Number System (DBNS)",
}

@Article{Even:2000:CTR,
  author =       "Guy Even and Peter-Michael Seidel",
  title =        "A Comparison of Three Rounding Algorithms for {IEEE}
                 Floating-Point Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "7",
  pages =        "638--650",
  month =        jul,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.863033",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:35:24 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
                 OCLC Proceedings database",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=863033",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-14",
  remark =       "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
  summary =      "A new IEEE compliant floating-point rounding algorithm
                 for computing the rounded product from a carry-save
                 representation of the product is presented. The new
                 rounding algorithm is compared with the rounding
                 algorithms of Yu and Zyner (1995) and of \ldots{}",
}

@Article{Even:2000:DIC,
  author =       "Guy Even and Wolfgang J. Paul",
  title =        "On the design of {IEEE} compliant floating point
                 units",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "5",
  pages =        "398--413",
  month =        may,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.859536",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  MRclass =      "68M07",
  MRnumber =     "MR1764655",
  bibdate =      "Tue Jul 5 10:35:24 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=859536",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "Engineering design methodology recommends designing a
                 system as follows: Start with an unambiguous
                 specification, partition the system into blocks,
                 specify the functionality of each block, design each
                 block separately, and glue the blocks together.
                 \ldots{}",
}

@Article{Even:2000:DPI,
  author =       "Guy Even and Sylva M. Mueller and Peter-Michael
                 Seidel",
  title =        "A dual precision {IEEE} floating-point multiplier",
  journal =      j-INTEGRATION-VLSI-J,
  volume =       "29",
  number =       "2",
  pages =        "167--180",
  month =        sep,
  year =         "2000",
  CODEN =        "IVJODL",
  DOI =          "https://doi.org/10.1016/S0167-9260(00)00006-7",
  ISSN =         "0167-9260 (print), 1872-7522 (electronic)",
  ISSN-L =       "0167-9260",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Ingenta database",
  URL =          "https://www.sciencedirect.com/science/article/pii/S0167926000000067",
  acknowledgement = ack-nhfb,
  fjournal =     "Integration, the VLSI journal",
  journal-URL =  "https://www.sciencedirect.com/journal/integration/issues",
  pagecount =    "14",
}

@InProceedings{Ferguson:2000:IRM,
  author =       "M. I. Ferguson and M. D. Ercegovac",
  booktitle =    "Conference Record of the Thirty-Fourth Asilomar
                 Conference on Signals, Systems and Computers, 2000",
  title =        "The {IEEE} rounding for multiplier with redundant
                 operands",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1334--1338",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:05 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "We present a design for a multiplier with redundant
                 operands which conforms to the IEEE-754 floating-point
                 standard. The design consists of a multiplier core and
                 a rounding unit which conforms to the rounding modes
                 specified by the IEEE standard and \ldots{}",
}

@InProceedings{Fernandez:2000:FRB,
  author =       "Pedro G. Fern{\'a}ndez and Anton{\'\i}o Garc{\'\i}a
                 and Javier Ram{\'\i}rez and Luis Parrilla and
                 Anton{\'\i}o Lloris",
  title =        "Fast {RNS}-based {DCT} Computation with Fewer
                 Multiplication Stages",
  crossref =     "Anonymous:2000:DPX",
  pages =        "276--281",
  year =         "2000",
  bibdate =      "Fri Jun 24 18:22:06 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ditec.ugr.es/~grios/papers/dcis00_dct.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Discrete Cosine Transform (DCT); Residue Number System
                 (RNS)",
}

@Article{Fey:2000:DPA,
  author =       "Dietmar Fey and Marko Degenkolb",
  title =        "Digit Pipelined Arithmetic for {$3$-D} Massively
                 Parallel Optoelectronic Circuits",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "16",
  number =       "3",
  pages =        "177--196",
  month =        jul,
  year =         "2000",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1023/A:1008160925753",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Wed Jul 6 12:13:14 MDT 2005",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0920-8542&volume=16&issue=3;
                 http://www.wkap.nl/issuetoc.htm/0920-8542+16+3+2000;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0920-8542&volume=16&issue=3&spage=177;
                 http://www.wkap.nl/oasis.htm/262637",
  acknowledgement = ack-nhfb,
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
}

@PhdThesis{FigueroadelCid:2000:RFF,
  author =       "Samuel {Figueroa del Cid}",
  title =        "A Rigorous Framework for Fully Supporting the {IEEE
                 Standard} for Floating-Point Arithmetic in High-Level
                 Programming Languages",
  type =         "{Ph.D.} Thesis",
  school =       "Department of Computer Science, New York University",
  address =      "New York, NY, USA",
  pages =        "345",
  month =        jan,
  year =         "2000",
  ISBN =         "0-599-59894-8",
  ISBN-13 =      "978-0-599-59894-2",
  bibdate =      "Fri Oct 25 17:16:24 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.nyu.edu/csweb/Research/theses.html;
                 http://www.cs.nyu.edu/csweb/Research/Theses/figueroa_sam.html;
                 http://www.cs.nyu.edu/csweb/Research/Theses/figueroa_sam.pdf;
                 http://www.cs.nyu.edu/csweb/Research/Theses/figueroa_sam.ps.gz;
                 http://wwwlib.umi.com/dissertations/fullcit/9956669;
                 http://wwwlib.umi.com/dissertations/preview/9956669",
  abstract =     "Processors conforming to the IEEE Standard for
                 Floating-Point Arithmetic have been commonplace for
                 some years, and now several programming languages seem
                 to support or conform to this standard, from hereon
                 referred to as ``the IEEE Standard.'' For example, The
                 Java Language Specification by Gosling, Joy, and
                 Steele, which defines the Java language, frequently
                 mentions the IEEE Standard. Indeed, Java, as do other
                 languages, supports some of the features of the IEEE
                 Standard, including a couple floating-point data
                 formats, and even requires (in section 4.2.4
                 ``Floating-Point Operations'' of the aforementioned
                 book) that ``operators on floating-point numbers behave
                 exactly as specified by IEEE 754.'' Arguing that the
                 support current languages offer is not enough, this
                 thesis establishes clear criteria for what it means to
                 fully support the IEEE Standard in a programming
                 language. Each aspect of the IEEE Standard is examined
                 in detail from the point of view of how various
                 arithmetic engines implement that aspect of the IEEE
                 Standard, how different languages (and implementations
                 thereof) support it, and what the range of options are
                 in supporting that aspect. Practical recommendations
                 are then offered (particularly, but not exclusively,
                 for Ada and Java), taking, for example, programmer
                 convenience and impact on performance into
                 consideration. A detailed model specification following
                 these recommendations is provided for the Ada language.
                 In addition, a variety of issues related to the
                 floating-point aspects of programming languages are
                 discussed, so as to serve as a more complete guide to
                 language designers. One such issue is floating-point
                 expression evaluation schemes, and, more specifically,
                 whether bit-for-bit identical results are actually
                 achievable on a variety of platforms that conform to
                 the IEEE Standard, as the Java language promises.
                 Closely tied to this issue is that of double rounding,
                 which occurs when a (possibly intermediate) result is
                 rounded more than once before subsequent use or before
                 being delivered to its final destination. So this
                 thesis discusses when double rounding makes a
                 difference, how it can be avoided, and what the
                 performance impact is in avoiding it.",
  acknowledgement = ack-nhfb,
  keywords =     "double rounding",
  tableofcontents = "List of Tables / vii \\
                 1 Introduction / 1 \\
                 1.1 The IEEE Standard for Floating-Point Arithmetic / 1
                 \\
                 1.2 What does it mean to support the IEEE Standard? / 2
                 \\
                 1.3 Considerations in deciding how to support the IEEE
                 Standard in high-level languages / 2 \\
                 1.4 Prior Related Work / 3 \\
                 2 What Does It Mean to Support the IEEE Standard? / 5
                 \\
                 3 Supporting Data Formats in High-Level Languages / 9
                 \\
                 3.1 IEEE Standard requirements in regards to data
                 formats / 9 \\
                 3.2 Hardware facilities supporting data formats / 10
                 \\
                 3.3 Making data formats available in high-level
                 languages / 11 \\
                 3.4 Associating floating-point literals with data
                 formats / 13 \\
                 3.5 Other issues related to numeric literals / 13 \\
                 3.6 Issues related to mixed-language programming / 14
                 \\
                 3.7 What support exists in high-level languages / 15
                 \\
                 3.7.1 Traditional language designs / 15 \\
                 3.7.2 Implementations of traditional languages / 16 \\
                 3.7.3 Extensions to traditional languages / 16 \\
                 3.7.4 New language designs / 17 \\
                 3.8 What support should exist in high-level languages /
                 17 \\
                 4 Supporting Rounding Modes in High-Level Languages /
                 21 \\
                 4.1 IEEE Standard requirements in regards to rounding
                 modes / 21 \\
                 4.2 Hardware facilities for accessing rounding modes /
                 22 \\
                 4.2.1 Processors with dynamic rounding modes / 22 \\
                 4.2.2 Processors with static rounding modes / 24 \\
                 4.3 Making rounding modes available in high-level
                 languages / 25 \\
                 4.4 Handling static evaluation and numeric literals /
                 27 \\
                 4.5 Issues related to mixed-language programming / 29
                 \\
                 4.6 What support exists in high-level languages / 30
                 \\
                 4.6.1 Existing language designs / 30 \\
                 4.6.2 Compilers for existing languages / 30 \\
                 4.6.3 Extensions to existing languages / 30 \\
                 4.6.4 New language designs / 31 \\
                 4.7 Why having more than one rounding mode available is
                 useful / 32 \\
                 4.8 What support should exist in high-level languages /
                 33 \\
                 5 Supporting Precision Modes in High-Level Languages /
                 35 \\
                 5.1 IEEE Standard requirements in regards to precision
                 modes / 35 \\
                 5.2 Hardware facilities for accessing precision modes /
                 36 \\
                 5.2.1 Processors with dynamic precision modes / 36 \\
                 5.2.2 Processors with static precision modes / 36 \\
                 5.2.3 Processors without precision modes / 38 \\
                 5.3 Different ways of making precision modes available
                 in a high-level language / 39 \\
                 5.4 Handling static evaluation and numeric literals /
                 39 \\
                 5.5 Issues related to mixed-language programming / 39
                 \\
                 5.6 What support exists in high-level languages / 39
                 \\
                 5.6.1 Compilers for existing languages / 39 \\
                 5.6.2 Extensions to existing languages / 39 \\
                 5.6.3 Experimental language designs / 40 \\
                 5.7 Why it is useful to be able to change the precision
                 mode / 41 \\
                 5.8 Why compiler support is required in order to avoid
                 double rounding / 42 \\
                 5.9 What support should exist in high-level languages /
                 43 \\
                 6 Double Rounding / 47 \\
                 6.1 Why double rounding can be undesirable / 48 \\
                 6.2 When is double rounding innocuous? / 50 \\
                 6.2.1 Addition / 51 \\
                 6.2.2 Subtraction / 52 \\
                 6.2.3 Multiplication / 53 \\
                 6.2.4 Division / 54 \\
                 6.2.5 Square root / 55 \\
                 6.2.6 Additional comments / 57 \\
                 6.3 On avoiding double rounding / 58 \\
                 6.4 Practical ways of avoiding double rounding / 60 \\
                 7 Supporting the Standard Operations in High-Level
                 Languages / 63 \\
                 7.1 IEEE Standard requirements in regards to operations
                 / 63 \\
                 7.2 How different architectures implement these
                 operations / 66 \\
                 7.2.1 CISC architectures / 66 \\
                 7.2.2 RISC architectures / 68 \\
                 7.2.3 How different architectures implement comparison
                 / 69 \\
                 7.3 Making the standard operations available in
                 high-level languages / 70 \\
                 7.4 Handling static evaluation / 72 \\
                 7.5 What support exists in high-level languages / 72
                 \\
                 7.5.1 Existing language designs / 72 \\
                 7.5.2 Compilers for existing languages / 74 \\
                 7.5.3 Extensions to existing languages / 74 \\
                 7.5.4 New language designs / 75 \\
                 7.6 What support should exist in high-level languages /
                 76 \\
                 8 Supporting Exceptional Situations in High-Level
                 Languages / 79 \\
                 8.1 IEEE Standard requirements in regards to special
                 computational situations / 79 \\
                 8.2 Different architectures' support for exceptional
                 situations / 81 \\
                 8.2.1 CISC architectures / 81 \\
                 8.2.2 RISC architectures / 84 \\
                 8.2.3 How different architectures distinguish between
                 signaling and quiet NaNs / 87 \\
                 8.2.4 How different architectures detect underflow / 88
                 \\
                 8.3 Handling special computational situations in
                 high-level languages / 89 \\
                 8.3.1 Ways of representing special values / 89 \\
                 8.3.2 Handling static evaluation and numeric literals /
                 90 \\
                 8.3.3 Supporting arithmetic involving special
                 computational situations / 91 \\
                 8.3.4 Ways of allowing access to status flags / 92 \\
                 8.3.5 Ways of managing the status flags / 93 \\
                 8.3.6 Facilities for exception handling / 95 \\
                 8.4 Issues related to mixed-language programming / 96
                 \\
                 8.5 What support exists in high-level languages / 97
                 \\
                 8.5.1 Existing language designs / 97 \\
                 8.5.2 Compilers for existing languages / 98 \\
                 8.5.3 Extensions to existing languages / 98 \\
                 8.5.4 New language designs / 99 \\
                 8.6 What support should exist in high-level languages /
                 100 \\
                 9 Floating-Point Expression Evaluation Schemes / 105
                 \\
                 9.1 Predictable expression evaluation schemes / 106 \\
                 9.2 Advantages and disadvantages of various evaluation
                 schemes / 106 \\
                 9.3 Bit-for-bit identical results and the IEEE Standard
                 / 108 \\
                 9.3.1 Optional and implementation defined features of
                 the IEEE Standard / 108 \\
                 9.3.2 Are bit-for-bit identical results achievable in
                 Java? / 110 \\
                 10 Supporting the IEEE Standard in Ada and Java / 113
                 \\
                 10.1 Ada / 114 \\
                 10.1.1 Data formats / 114 \\
                 10.1.2 Rounding and rounding precision modes / 114 \\
                 10.1.3 Operations / 114 \\
                 10.1.4 Exceptional situations / 115 \\
                 10.1.5 Expression evaluation / 117 \\
                 10.1.6 Pragmas related to floating-point arithmetic /
                 117 \\
                 10.2 Java / 118 \\
                 10.2.1 Data formats / 118 \\
                 10.2.2 Rounding and (rounding) precision modes / 119
                 \\
                 10.2.3 Operations / 120 \\
                 10.2.4 Exceptional situations / 120 \\
                 11 Conclusion / 123 \\
                 11.1 How well current languages support the IEEE
                 Standard / 123 \\
                 11.2 Related unfinished work and open issues / 126 \\
                 A Supporting the IEEE Standard in Ada / 127 \\
                 A.1 The Package Standard FP Arithmetic / 127 \\
                 A.1.1 Data Formats / 130 \\
                 A.1.2 Operations of Floating-Point Types / 131 \\
                 A.1.3 Rounding Modes / 132 \\
                 A.1.4 Status Flags / 132 \\
                 A.1.5 Trap Handlers / 132 \\
                 A.2 Floating-Point Operations / 132 \\
                 A.2.1 The Package Generic FP Operations / 132 \\
                 A.2.2 Required Functions and Predicates / 136 \\
                 A.2.3 Recommended Functions and Predicate / 138 \\
                 A.3 Model of Floating-Point Arithmetic / 138 \\
                 A.3.1 Floating-Point Evaluation Format / 139 \\
                 A.3.2 Exception Handling / 139 \\
                 A.4 Pragmas Related to Floating-Point Arithmetic / 144
                 \\
                 A.4.1 Pragmas Related to the Accuracy of Results / 144
                 \\
                 A.4.2 Pragmas Related to Rounding Modes / 146 \\
                 A.4.3 Other Pragmas / 148 \\
                 Bibliography / 151",
}

@InProceedings{Freking:2000:MMR,
  author =       "W. L. Freking and K. K. Parhi",
  booktitle =    "Conference Record of the Thirty-Fourth Asilomar
                 Conference on Signals, Systems and Computers, 2000",
  title =        "Modular multiplication in the residue number system
                 with application to massively-parallel public-key
                 cryptography systems",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1339--1343",
  year =         "2000",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ACSSC.2000.911210",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Modular multiplication is a fundamental operation in
                 many public-key cryptography systems including RSA.
                 Residue number system (RNS) implementation of modular
                 multiplication has been of recent interest due to
                 inherent RNS properties of \ldots{}",
}

@PhdThesis{Fu:2000:CPO,
  author =       "Steve Fu",
  title =        "Cost Performance Optimizations of Microprocessors",
  type =         "{Ph.D.} Thesis",
  school =       "Department of Electrical Engineering, Stanford
                 University",
  address =      "Stanford, CA, USA",
  pages =        "????",
  year =         "2000",
  bibdate =      "Mon Dec 24 11:02:14 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Gallagher:2000:FTN,
  author =       "W. L. Gallagher and E. E. {Swartzlander, Jr.}",
  title =        "Fault-tolerant {Newton--Raphson} and {Goldschmidt}
                 dividers using time shared {TMR}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "6",
  pages =        "588--595",
  month =        jun,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.862218",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:35:24 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=862218",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@TechReport{Gay:2000:SAC,
  author =       "David M. Gay",
  title =        "Symbolic-Algebraic Computations in a Modeling Language
                 for Mathematical Programming",
  type =         "Technical Report",
  number =       "00-3-02",
  institution =  "Computing Sciences Research Center, Bell
                 Laboratories",
  address =      "Murray Hill, NJ, USA",
  month =        jul,
  year =         "2000",
  bibdate =      "Wed Jan 29 16:34:27 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "correct rounding; decimal floating-point arithmetic",
  remark =       "From \cite{Steele:2004:RHP}: ``AMPL and its solver
                 interface library use correctly rounded binary-decimal
                 conversions, which is now possible on all machines
                 where AMPL has run other than old Cray machines.''",
}

@InProceedings{Goldovsky:2000:DIL,
  author =       "A. Goldovsky and B. Patel and M. Schulte and R.
                 Kolagotla and H. Srinivas and G. Burns",
  title =        "Design and Implementation of a $ 16 $ by $ 16 $ Low
                 Power Two's Complement Multiplier",
  crossref =     "IEEE:2000:IGP",
  pages =        "345--348",
  year =         "2000",
  bibdate =      "Sun Mar 04 11:22:03 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2000-03.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Groza:2000:FPA,
  author =       "V. Groza",
  title =        "Floating-Point Analog-to-Digital Converters with
                 Predictive Auto-Ranging",
  crossref =     "IEEE:2000:IPI",
  pages =        "759--762",
  year =         "2000",
  bibdate =      "Sat Jun 02 08:27:44 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Misc{Hanrot:2000:ML,
  author =       "Guillaume Hanrot and Vincent Lef{\`e}vre and Patrick
                 P{\'e}lissier and Paul Zimmermann and Sylvie Boldo and
                 David Daney and Mathieu Dutour and Emmanuel Jeandel and
                 Laurent Fousse and Fabrice Rouillier and Kevin Ryde",
  title =        "The {MPFR} Library",
  howpublished = "World-Wide Web software project archive.",
  year =         "2000",
  bibdate =      "Fri Jun 24 14:53:37 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mpfr.org/",
  abstract =     "The MPFR library is a C library for multiple-precision
                 floating-point computations with exact rounding (also
                 called correct rounding). It is based on the GMP
                 multiple-precision library.\par

                 The main goal of MPFR is to provide a library for
                 multiple-precision floating-point computation which is
                 both efficient and has a well-defined semantics. It
                 copies the good ideas from the ANSI/IEEE-754 standard
                 for double-precision floating-point arithmetic (53-bit
                 mantissa).",
  acknowledgement = ack-nhfb,
}

@TechReport{Hanrot:2000:SDS,
  author =       "Guillaume Hanrot and Michel Quercia and Paul
                 Zimmermann",
  title =        "Speeding up the division and square root of power
                 series",
  type =         "Research Report",
  number =       "3973",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  pages =        "23",
  day =          "17",
  month =        jul,
  year =         "2000",
  ISSN =         "0249-6399",
  bibdate =      "Sun Sep 10 08:52:54 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-3973.ps.gz",
  abstract =     "We present new algorithms for the inverse, quotient,
                 or square root of power series. The key trick is a new
                 algorithm RecursiveMiddleProduct or RMP computing the
                 $n$ middle coefficients of a $ 2 n \times n $ product
                 in essentially the same number of operations $ K(n) $
                 than a full $ n \times n $ product with Karatsuba's
                 method. This improves previous work of Mulders, Karp
                 and Markstein, Burnikel and Ziegler. These results
                 apply both to series, polynomials, and multiple
                 precision floating-point numbers.",
  acknowledgement = ack-nhfb,
  keywords =     "division; Karatsuba's algorithm; Newton method; square
                 root",
}

@Article{Harrison:2000:FPV,
  author =       "John Harrison",
  title =        "Floating Point Verification in {HOL Light}: The
                 Exponential Function",
  journal =      j-FORM-METHODS-SYST-DES,
  volume =       "16",
  number =       "3",
  pages =        "271--305",
  year =         "2000",
  CODEN =        "FMSDE6",
  ISSN =         "0925-9856 (print), 1572-8102 (electronic)",
  ISSN-L =       "0925-9856",
  bibdate =      "Thu May 09 09:43:30 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Since they often embody compact but mathematically
                 sophisticated algorithms, operations for computing the
                 common transcendental functions in floating point
                 arithmetic seem good targets for formal verification
                 using a mechanical theorem prover. We discuss some of
                 the general issues that arise in verifications of this
                 class, and then present a machine-checked verification
                 of an algorithm for computing the exponential function
                 in IEEE-754 standard binary floating point arithmetic.
                 We confirm (indeed strengthen) the main result of a
                 previousl published error analysis, though we uncover a
                 minor error in the hand proof and are forced to
                 confront several subtle issues that might easily be
                 overlooked informally. The development described here
                 includes, apart from the proof itself, a formalization
                 of IEEE arithmetic, a mathematical semantics for the
                 programming language in which the algorithm is
                 expressed, and the body of pure mathematics needed. All
                 this is developed logically from first principles using
                 the HOL Light prover, which guarantees strict adherence
                 to simple rules of inference while allowing the user to
                 perform proofs using higher-level derived rules.",
  acknowledgement = ack-nhfb,
  fjournal =     "Formal Methods in System Design",
  journal-URL =  "https://dl.acm.org/loi/fmsd",
}

@Article{Harrison:2000:FVF,
  author =       "John Harrison",
  title =        "Formal Verification of Floating Point Trigonometric
                 Functions",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1954",
  pages =        "217--233",
  year =         "2000",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:08:55 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1954.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1954/19540217.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1954/19540217.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InProceedings{Harrison:2000:FVI,
  author =       "John Harrison",
  editor =       "Mark Aagaard and John Harrison",
  booktitle =    "Theorem Proving in Higher Order Logics: {13th
                 International Conference, TPHOLs 2000 Portland, OR,
                 USA, August 14-18, 2000 Proceedings}",
  title =        "Formal Verification of {IA-64} Division Algorithms",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "xi + 533",
  pages =        "233--251",
  year =         "2000",
  CODEN =        "1869",
  DOI =          "https://doi.org/10.1007/3-540-44659-1_15",
  ISBN =         "3-540-44659-1 (e-book), 3-540-67863-8 (paper)",
  ISBN-13 =      "978-3-540-44659-0 (e-book), 978-3-540-67863-2
                 (paper)",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  LCCN =         "QA76.9.A96 T655 2000",
  bibdate =      "Fri Sep 22 16:31:35 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/3-540-44659-1",
}

@TechReport{Harrison:2000:HOM,
  author =       "John Harrison and Ted Kubaska and Bob Norin and Shane
                 Story and Ping Tak Peter Tang",
  title =        "Highly Optimized Mathematical Functions for the
                 {IA-64} Architectures",
  type =         "Technical report",
  number =       "245410-002",
  institution =  "Intel Corporation",
  address =      "San Jose, CA, USA",
  month =        apr,
  year =         "2000",
  bibdate =      "Sat Jun 02 11:04:28 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://download.intel.com/design/IA-64/Downloads/libm.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hasan:2000:FPI,
  author =       "M. A. Hasan and A. A. Hasan and S. Rahman",
  booktitle =    "Proceedings of the 39th {IEEE} Conference on Decision
                 and Control",
  title =        "Fixed point iterations for computing square roots and
                 the matrix sign function of complex matrices",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "4253--4258",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The purpose of this work has been the development of
                 new set of rational iterations for computing square
                 roots and the matrix sign function of complex matrices.
                 Given any positive integer r{\&}ges;2, we presented a
                 systematic way of deriving rth order \ldots{}",
}

@Article{Hasan:2000:LTB,
  author =       "M. A. Hasan",
  title =        "Look-Up Table-Based Large Finite Field Multiplication
                 in Memory Constrained Cryptosystems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "7",
  pages =        "749--758",
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.863045",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon May 20 06:47:55 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-14",
  remark =       "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
}

@InProceedings{Hassibi:2000:ESR,
  author =       "B. Hassibi",
  booktitle =    "Proceedings. 2000 {IEEE} International Conference on
                 Acoustics, Speech, and Signal Processing: {ICASSP '00},
                 5--9 June 2000",
  title =        "An efficient square-root algorithm for {BLAST}",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "II737--II740",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Bell Labs Layered Space-Time (BLAST) is a scheme for
                 transmitting information over a rich-scattering
                 wireless environment using multiple receive and
                 transmit antennas. The main computational bottleneck in
                 the BLAST algorithm is a ``nulling and \ldots{}",
}

@InProceedings{Hassibi:2000:FSR,
  author =       "B. Hassibi",
  booktitle =    "Conference Record of the Thirty-Fourth Asilomar
                 Conference on Signals, Systems and Computers, 2000",
  title =        "A fast square-root implementation for {BLAST}",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1255--1259",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Bell Labs Layered Space-Time (BLAST) is a scheme for
                 transmitting information over a rich-scattering
                 wireless environment using multiple receive and
                 transmit antennas. The main computational bottleneck in
                 the BLAST algorithm is a ``nulling and \ldots{}",
}

@InProceedings{He:2000:UAA,
  author =       "Yun He and Chris H. Q. Ding",
  title =        "Using accurate arithmetics to improve numerical
                 reproducibility and stability in parallel
                 applications",
  crossref =     "Reynders:2000:IPI",
  pages =        "225--234",
  year =         "2000",
  DOI =          "https://doi.org/10.1145/335231.335253",
  bibdate =      "Sat Feb 8 18:35:50 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/pvm.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/335231.335253",
  abstract =     "Numerical reproducibility and stability of large scale
                 scientific simulations, especially climate modeling, on
                 distributed memory parallel computers are becoming
                 critical issues. In particular, global summation of
                 distributed arrays is most susceptible to rounding
                 errors, and their propagation and accumulation cause
                 uncertainty in final simulation results. We analyzed
                 several accurate summation methods and found that two
                 methods are particularly effective to improve (ensure)
                 reproducibility and stability: Kahan's self-compensated
                 summation and Bailey's double-double precision
                 summation. We provide an MPI operator MPLSUMDD to work
                 with MPI collective operations to ensure a scalable
                 implementation on large number of processors. The final
                 methods are particularly simple to adopt in practical
                 codes.",
  acknowledgement = ack-nhfb,
}

@Article{Hiasat:2000:NES,
  author =       "A. A. Hiasat",
  title =        "New efficient structure for a modular multiplier for
                 {RNS}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "2",
  pages =        "170--174",
  month =        feb,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.833113",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:35:23 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=833113",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@TechReport{Hida:2000:QDA,
  author =       "Yozo Hida and Xiaoye S. Li and David H. Bailey",
  title =        "Quad-Double Arithmetic: Algorithms, Implementation,
                 and Application",
  type =         "Technical report",
  number =       "LBNL-46996",
  institution =  "Lawrence Berkeley National Laboratory",
  address =      "1 Cycloton Rd, Berkeley, CA 94720",
  pages =        "28",
  day =          "30",
  month =        oct,
  year =         "2000",
  bibdate =      "Wed Nov 24 08:18:07 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~yozo/papers/LBNL-46996.ps.gz",
  acknowledgement = ack-nhfb,
}

@Article{Higuchi:2000:FAA,
  author =       "Akira Higuchi and Naofumi Takagi",
  title =        "A fast addition algorithm for elliptic curve
                 arithmetic in {$ {\rm GF}(2 n) $} using projective
                 coordinates",
  journal =      j-INFO-PROC-LETT,
  volume =       "76",
  number =       "3",
  pages =        "101--103",
  day =          "15",
  month =        dec,
  year =         "2000",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Wed Apr 18 07:11:20 MDT 2001",
  bibsource =    "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.elsevier.nl/gej-ng/10/23/20/67/27/25/abstract.html;
                 http://www.elsevier.nl/gej-ng/10/23/20/67/27/25/article.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}

@InProceedings{Hormigo:2000:HAVa,
  author =       "J. Hormigo and J. Villalba and M. Schulte",
  editor =       "????",
  booktitle =    "Proceedings of the 4th Conference on Real Numbers and
                 Computers, Dagstuhl, Germany, April, 2000",
  title =        "A Hardware Algorithm for Variable-Precision Division",
  publisher =    "????",
  address =      "????",
  pages =        "104--112",
  year =         "2000",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sun Mar 04 11:20:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2000-02.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hormigo:2000:HAVb,
  author =       "J. Hormigo and J. Villalba and M. Schulte",
  title =        "A Hardware Algorithm for Variable-Precision
                 Logarithm",
  crossref =     "Swartzlander:2000:IIC",
  pages =        "215--224",
  year =         "2000",
  bibdate =      "Sun Mar 04 11:20:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2000-04.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Ide:2000:GMF,
  author =       "Nobuhiro Ide and Masashi Hirano and Yukio Endo and
                 Shin ichi Yoshioka and Hiroaki Murakami and Atsushi
                 Kunimatsu and Toshinori Sato and Takayuki Kamei and
                 Toyoshi Okada and Masakazu Suzuoki",
  title =        "{2.44 GFLOPS 300-MHz} Floating-Point Vector-Processing
                 Unit for High-Performance {$3$-D} Graphics Computing",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "35",
  number =       "7",
  pages =        "1025--1033",
  month =        jul,
  year =         "2000",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.hwswworld.com/downloads/a7/1025ide.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "A vector unit for high-performance three-dimensional
                 graphics computing has been developed. We implement
                 four floating-point multiply-accumulate units, which
                 execute multiply-add operations with one throughput;
                 one floating-point divide/square root \ldots{}",
}

@Book{Ifrah:2000:UHN,
  author =       "Georges Ifrah",
  title =        "The Universal History of Numbers from Prehistory to
                 the Invention of the Computer",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xxii + 633",
  year =         "2000",
  ISBN =         "0-471-37568-3",
  ISBN-13 =      "978-0-471-37568-5",
  LCCN =         "QA141.I3713 2000",
  bibdate =      "Mon Dec 06 16:02:33 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Translated from the French edition, {\em Histoire
                 universelle des chiffres}, by David Bellos, E. F.
                 Harding, Sophie Wood, and Ian Monk.",
  price =        "US\$39.95",
  acknowledgement = ack-nhfb,
}

@InProceedings{Imajo:2000:CSB,
  author =       "Tetsuji Imajo and Tatsuki Miyake and Shinobu Sato and
                 Toshiyuki Ito and Daisuke Yokotsuka and Yoshihide
                 Tsujihata and Shunsuke Uemura",
  title =        "{COBOL Script}: a Business-Oriented Scripting
                 Language",
  crossref =     "IEEE:2000:EPI",
  pages =        "231--??",
  year =         "2000",
  bibdate =      "Thu Aug 07 17:50:59 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper describes COBOL Script, a Web-oriented
                 script language developed by Hitachi. COBOL Script
                 includes the following features: (1) The language
                 specifications, which consist of functions required for
                 Web computing, are a subset of COBOL85, the most
                 frequently used programming language in business
                 information systems. (2) COBOL Script supports decimal
                 arithmetic functions that have the same precision as in
                 standard COBOL85 on mainframe computers. (3) Efficient
                 implementation was based on analysis of the pros and
                 cons of the COBOL processing system. Using COBOL
                 Script, users can: (1) Process applications requiring
                 high precision, such as account-related applications,
                 over the Web. (2) Use a test debugger and a Coverage
                 Function with COBOL Script for large-scale development
                 projects. (3) Use Japanese in programs. (4) Achieve
                 good run-time performance.",
  acknowledgement = ack-nhfb,
  keywords =     "account-related applications; business information
                 systems; business-oriented scripting language; COBOL;
                 COBOL processing system; COBOL Script; COBOL85; decimal
                 arithmetic functions; decimal floating-point
                 arithmetic; language specifications; large-scale
                 development projects; test debugger; Web computing;
                 Web-oriented script language",
}

@Misc{Intel:2000:DSR,
  author =       "{Intel}",
  title =        "Divide, Square Root, and Remainder Algorithms for the
                 {Itanium} Architecture",
  howpublished = "Intel Software Development Products",
  month =        jul,
  year =         "2000",
  bibdate =      "Fri Sep 22 17:06:23 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://studylib.net/doc/7921762/divide--square-root-and-remainder-algorithms-for-the-ia-64",
  acknowledgement = ack-nhfb,
}

@Manual{Intel:2000:IPF,
  title =        "{Itanium} Processor Floating-point Software Assistance
                 and Floating-point Exception Handling",
  number =       "245415-001",
  organization = pub-INTEL,
  address =      pub-INTEL:adr,
  month =        jan,
  year =         "2000",
  bibdate =      "Tue Nov 18 16:18:52 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://cache-www.intel.com/cd/00/00/21/92/219290_fpswa_software.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{ISO:2000:FSI,
  author =       "{ISO/IEC JTC1/SC22/WG5}",
  title =        "Information technology --- Programming languages ---
                 {Fortran} -- Floating-point exception handing (draft)",
  howpublished = "World-Wide Web document.",
  edition =      "Second",
  day =          "19",
  month =        jan,
  year =         "2000",
  bibdate =      "Thu May 09 10:24:52 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.nag.co.uk/sc22wg5/N1351-N1400/N1378.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Joye:2000:OLR,
  author =       "M. Joye and S.-M. Yen",
  title =        "Optimal Left-to-Right Binary Signed-Digit Recoding",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "7",
  pages =        "740--748",
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.863044",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon May 20 06:47:55 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-14",
  remark =       "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
}

@Misc{Kahan:2000:MAA,
  author =       "W. Kahan",
  title =        "Miscalculating Area and Angles of a Needle-like
                 Triangle",
  howpublished = "World-Wide Web lecture notes for introductory
                 numerical analysis classes.",
  day =          "24",
  month =        mar,
  year =         "2000",
  bibdate =      "Fri Jul 15 12:30:24 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Triangle.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic",
}

@TechReport{Kahan:2000:MVM,
  author =       "W. Kahan",
  title =        "Marketing versus Mathematics and other Ruminations on
                 the design of floating-point arithmetic",
  howpublished = "World-Wide Web document.",
  institution =  "Mathematics Department and Electrical Engineering and
                 Computer Science Department, University of California,
                 Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "48",
  day =          "27",
  month =        aug,
  year =         "2000",
  bibdate =      "Fri May 03 12:19:56 2002",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MktgMath.pdf;
                 http://www.cs.nyu.edu/cs/faculty/overton/book/docs/KahanTalk.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2000:RDFa,
  author =       "W. Kahan",
  title =        "Ruminations on the Design of Floating-Point
                 Arithmetic",
  howpublished = "World-Wide Web document",
  pages =        "29",
  day =          "25",
  month =        apr,
  year =         "2000",
  bibdate =      "Sat Mar 03 18:19:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://cs.nyu.edu/cs/faculty/overton/book/docs/KahanTalk.pdf",
  acknowledgement = ack-nhfb,
}

@TechReport{Kahan:2000:RDFb,
  author =       "W. Kahan",
  title =        "Marketing versus Mathematics and other Ruminations on
                 the design of floating-point arithmetic",
  howpublished = "World-Wide Web document.",
  institution =  "Mathematics Department and Electrical Engineering and
                 Computer Science Department, University of California,
                 Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "48",
  day =          "27",
  month =        aug,
  year =         "2000",
  bibdate =      "Fri May 03 12:19:56 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/MktgMath.pdf;
                 http://www.cs.nyu.edu/cs/faculty/overton/book/docs/KahanTalk.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Kalampoukas:2000:HSP,
  author =       "L. Kalampoukas and D. Nikolos and C. Efstathiou and H.
                 T. Vergos and J. Kalamatianos",
  title =        "High-Speed Parallel-Prefix Modulo $ 2^{n - 1} $
                 Adders",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "7",
  pages =        "673--680",
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.863036",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon May 20 06:47:55 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-14",
  remark =       "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
}

@Article{Kao:2000:LTA,
  author =       "Ming-Yang Kao and Jie Wang",
  title =        "Linear-Time Approximation Algorithms for Computing
                 Numerical Summation with Provably Small Errors",
  journal =      j-SIAM-J-COMPUT,
  volume =       "29",
  number =       "5",
  pages =        "1568--1576",
  month =        oct,
  year =         "2000",
  CODEN =        "SMJCAT",
  DOI =          "https://doi.org/10.1137/S0097539798341594",
  ISSN =         "0097-5397 (print), 1095-7111 (electronic)",
  ISSN-L =       "0097-5397",
  bibdate =      "Fri Oct 27 06:28:34 MDT 2000",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/29/5;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/34159",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Computing",
  journal-URL =  "http://epubs.siam.org/sicomp",
}

@Article{Kapur:2000:UIP,
  author =       "Deepak Kapur and Mahadevan Subramaniam",
  title =        "Using an induction prover for verifying arithmetic
                 circuits",
  journal =      j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER,
  volume =       "3",
  number =       "1",
  pages =        "32--65",
  month =        sep,
  year =         "2000",
  CODEN =        "????",
  ISSN =         "1433-2779 (print), 1433-2787 (electronic)",
  ISSN-L =       "1433-2779",
  bibdate =      "Tue Nov 23 15:01:40 MST 2004",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=1433-2779;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal on Software Tools for Technology
                 Transfer: STTT",
  journal-URL =  "http://link.springer.com/journal/10009",
}

@Article{Kawamura:2000:CRA,
  author =       "Shinichi Kawamura and Masanobu Koike and Fumihiko Sano
                 and Atsushi Shimbo",
  title =        "{Cox-Rower} Architecture for Fast Parallel
                 {Montgomery} Multiplication",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1807",
  pages =        "523--??",
  year =         "2000",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Fri Feb 1 09:16:29 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1807.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1807/18070523.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1807/18070523.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Keller:2000:ARR,
  author =       "T. Keller and T. H. Liew and Lajos Hanzo",
  title =        "Adaptive redundant residue number system coded
                 multicarrier modulation",
  journal =      j-IEEE-J-SEL-AREAS-COMMUN,
  volume =       "18",
  number =       "11",
  pages =        "2292--2301",
  month =        nov,
  year =         "2000",
  CODEN =        "ISACEM",
  DOI =          "https://doi.org/10.1109/49.895034",
  ISSN =         "0733-8716 (print), 1558-0008 (electronic)",
  ISSN-L =       "0733-8716",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=19376",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal on Selected Areas in Communications",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The novel class of nonbinary maximum minimum distance
                 redundant residue number system (RRNS) codes is invoked
                 in the context of adaptively RRNS coded,
                 symbol-by-symbol adaptive multicarrier modulation, in
                 order to combat the effects of frequency- \ldots{}",
}

@Article{Kim:2000:PSA,
  author =       "Hyun-Sung Kim and Sung-Woo Lee and Kee-Young Yoo",
  title =        "Partitioned systolic architecture for modular
                 multiplication in {GF} (2 { m })",
  journal =      j-INFO-PROC-LETT,
  volume =       "76",
  number =       "3",
  pages =        "135--139",
  day =          "15",
  month =        dec,
  year =         "2000",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Wed Apr 18 07:11:20 MDT 2001",
  bibsource =    "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.elsevier.nl/gej-ng/10/23/20/67/27/30/abstract.html;
                 http://www.elsevier.nl/gej-ng/10/23/20/67/27/30/article.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}

@Article{Kobayashi:2000:HBF,
  author =       "Shiro Kobayashi and Gerhard P. Fettweis",
  title =        "A Hierarchical Block-Floating-Point Arithmetic",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "24",
  number =       "1",
  pages =        "19--30",
  month =        feb,
  year =         "2000",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1023/A:1008110410087",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Ingenta database",
  abstract =     "In order to give an answer to a question of the
                 arithmetic in future DSP architectures for mobile
                 communication applications, the signal processing
                 quality of different arithmetic representations has
                 been studied. Based on the result, a new approach for
                 implementing block-floating-point arithmetic is
                 proposed. This approach intends to preserve the
                 least-significant-bits (LSBs) to improve signal
                 processing quality. The preservation of LSBs is
                 automatically and perfectly done by hardware. Several
                 simulation results show that the proposed
                 block-floating-point implementation provides improved
                 SNRs over conventional block-floating-point
                 implementations. For the same number of bits in the
                 memory for each representation, the SNRs better than
                 floating-point are also observed. For multiple datapath
                 DSPs, this implementation also requires significantly
                 less hardware complexity than floating-point.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
  pagecount =    "12",
}

@Article{Koren:2000:GEI,
  author =       "Israel Koren and Peter Kornerup",
  title =        "{Guest Editors}' Introduction: Special Issue on
                 Computer Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "7",
  pages =        "625--627",
  month =        jul,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2000.863030",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:35:24 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=863030",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-14",
  remark =       "From the article: ``The papers included in this
                 special issue were selected from 56 manuscripts
                 submitted in response to the call for papers.
                 Submissions were also solicited from the authors of
                 papers presented at the 14th Symposium on Computer
                 Arithmetic (ARITH-14), held in Adelaide, Australia, on
                 April 14--16 1999. This symposium was the most recent
                 in a series of biannual events whose proceedings have
                 provided a wealth of much cited and often seminal
                 papers. As a result of the review process, 14 papers
                 were selected to be included in this special issue.
                 Four of these papers are extensions of papers presented
                 at ARITH-14, some are further descendents of such
                 papers and the rest have originated from the open call
                 for papers.''",
}

@TechReport{Krishnan:2000:PEM,
  author =       "S. Krishnan and M. Foskey and T. Culver and J. Keyser
                 and D. Manocha",
  title =        "{Precise}: Efficient multiprecision evaluation of
                 algebraic roots and predicates for reliable geometric
                 computations",
  type =         "Technical Report",
  number =       "TR00 008",
  institution =  "Department of Computer Science, University of North
                 Carolina",
  address =      "Chapel Hill, NC, USA",
  year =         "2000",
  bibdate =      "Mon Oct 21 18:00:02 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://citeseer.nj.nec.com/krishnan00precise.html",
  acknowledgement = ack-nhfb,
}

@Article{Kum:2000:ACO,
  author =       "Ki-Il Kum and Jiyang Kang and Wonyong Sung",
  title =        "{AUTOSCALER} for {C}: an optimizing floating-point to
                 integer {C} program converter for fixed-point digital
                 signal processors",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "47",
  number =       "9",
  pages =        "840--848",
  month =        sep,
  year =         "2000",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.868453",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems. 2, Analog
                 and Digital Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  summary =      "A translator which converts C-based floating-point
                 digital signal processing programs to optimized integer
                 C versions is developed for convenient programming and
                 efficient use of fixed-point digital signal processors
                 (DSPs). It not only converts data \ldots{}",
}

@Article{Lee:2000:LSM,
  author =       "Keon-Jik Lee and Kee-Young Yoo",
  title =        "Linear systolic multiplier\slash squarer for fast
                 exponentiation",
  journal =      j-INFO-PROC-LETT,
  volume =       "76",
  number =       "3",
  pages =        "105--111",
  day =          "15",
  month =        dec,
  year =         "2000",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Wed Apr 18 07:11:20 MDT 2001",
  bibsource =    "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.elsevier.nl/gej-ng/10/23/20/67/27/26/abstract.html;
                 http://www.elsevier.nl/gej-ng/10/23/20/67/27/26/article.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}

@Article{Leemis:2000:SDS,
  author =       "Lawrence M. Leemis and Bruce W. Schmeiser and Diane L.
                 Evans",
  title =        "Survival Distributions Satisfying {Benford}'s Law",
  journal =      j-AMER-STAT,
  volume =       "54",
  number =       "4",
  pages =        "236--??",
  month =        nov,
  year =         "2000",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Fri Jul 20 11:18:01 MDT 2001",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.amstat.org/publications/tas/Leemis.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@InProceedings{Lefevre:2000:CRF,
  author =       "V. D. Lefevre and Jean-Michel Muller",
  booktitle =    "Conference Record of the Thirty-Fourth Asilomar
                 Conference on Signals, Systems and Computers, 2000",
  title =        "Correctly rounded functions for better arithmetic",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "875--878",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:05 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The IEEE 754 standard for floating-point arithmetic
                 requires that the four arithmetic operations and the
                 square root should be correctly rounded. This has
                 improved the accuracy, reliability and portability of
                 numerical software. Unfortunately, such \ldots{}",
}

@PhdThesis{Lefevre:2000:MAP,
  author =       "Vincent Lef{\`e}vre",
  title =        "Moyens arithm{\'e}tiques pour un calcul fiable.
                 ({French}) [{Arithmetic} means for reliable
                 calculation]",
  type =         "{Ph.D.} dissertation",
  school =       "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "Lyon, France",
  pages =        "148",
  year =         "2000",
  bibdate =      "Fri Sep 22 16:11:21 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.theses.fr/2000ENSL0142",
  acknowledgement = ack-nhfb,
  advisor =      "Jean-Michel Muller",
}

@InProceedings{Liew:2000:IDR,
  author =       "T. H. Liew and L.-L. Yang and L. Hanzo",
  booktitle =    "{VTC 2000-Spring} Tokyo, {IEEE 51st} Vehicular
                 Technology Conference Proceedings, 15--18 May 2000",
  title =        "Iterative decoding of redundant residue number system
                 codes",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "576--580",
  year =         "2000",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/VETECS.2000.851523",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Turbo decoded redundant residue number system (RRNS)
                 codes are proposed and their performance is evaluated.
                 An RRNS (n,k) code is a maximum-minimum distance block
                 code, exhibiting identical distance properties to
                 Reed--Solomon (RS) codes. Hence their \ldots{}",
}

@Article{Lin:2000:NBP,
  author =       "Rong Lin and James L. Schwing",
  title =        "A Non-binary Parallel Arithmetic Architecture",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1800",
  pages =        "149--??",
  year =         "2000",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/3-540-45591-4_19",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Fri Feb 1 09:16:18 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1800.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1800/18000149.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1800/18000149.pdf",
  abstract =     "In this paper we present a novel parallel arithmetic
                 architecture using an efficient non-binary logic
                 scheme. We show that by using parallel broadcasting (or
                 domino propagating) state signals, on short
                 reconfigurable buses equipped with a type of switches,
                 called GP (generate-propagate) shift switches, several
                 arithmetic operations can be carried out efficiently.
                 We extend a recently proposed shift switching mechanism
                 by letting the switch array automatically generate a
                 semaphore to indicate the end of each domino process.
                 This reduces the complexity of the architecture and
                 improves the performance significantly.",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Lopez:2000:HSS,
  author =       "Julio L{\'o}pez and Ricardo Dahab",
  title =        "High-Speed Software Multiplication in $ \mathbb
                 {f}_{2^m} $",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1977",
  pages =        "203--??",
  year =         "2000",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:08:57 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1977.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1977/19770203.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1977/19770203.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Luo:2000:API,
  author =       "Z. Luo and M. Martonosi",
  title =        "Accelerating pipelined integer and floating-point
                 accumulations in configurable hardware with delayed
                 addition techniques",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "3",
  pages =        "208--218",
  month =        mar,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.841125",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:35:23 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=841125",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "The speed of arithmetic calculations in configurable
                 hardware is limited by carry propagation, even with the
                 dedicated hardware found in recent FPGAs. This paper
                 proposes and evaluates an approach called delayed
                 addition that reduces the carry-propagation \ldots{}",
}

@TechReport{Maclaren:2000:IEH,
  author =       "Nick Maclaren",
  title =        "{IEEE 754} Error Handling and Programming Languages",
  type =         "Report",
  institution =  "Cambridge University",
  address =      "Cambridge, UK",
  pages =        "15",
  month =        mar,
  year =         "2000",
  bibdate =      "Wed Nov 10 08:10:24 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://grouper.ieee.org/groups/1788/email/pdfmPSi1DgZZf.pdf",
  abstract =     "IEEE 754-1985 introduced order to a particularly
                 chaotic area and, in general, it has been very
                 successful, though experts disagree about which of its
                 properties are merits. Hindsight shows several areas
                 where some unfortunate decisions were taken, but few of
                 the problems were predicted at the time.",
  acknowledgement = ack-nhfb,
  keywords =     "exception handling; IEEE 754 arithmetic; Infinity;
                 quiet NaN; signaling NaN; signed zero; traps",
  remark =       "The author reviews the good and bad points of IEEE 754
                 arithmetic. He is particularly critical of the
                 inconsistencies in hardware and programming languages
                 in the handling of quiet and signaling NaN, real and
                 complex Infinity, signed zero, and failure of NaNs to
                 propagate in certain C99 functions. He has a clear
                 discussion of five distinct uses of NaN, and how they
                 ought to behave differently in numerical operations and
                 function calls. He also laments the unreliability of
                 {\tt errno}, exception handling, and traps,
                 particularly across platforms and code libraries.",
}

@InProceedings{Madhukumar:2000:DPR,
  author =       "A. S. Madhukumar and F. Chin",
  booktitle =    "Conference Record of the Thirty-Fourth Asilomar
                 Conference on Signals, Systems and Computers, 2000",
  title =        "Design and performance of residue number system based
                 multicarrier {CDMA} in frequency-selective {Rayleigh}
                 fading channels",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "884--888",
  year =         "2000",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ACSSC.2000.910640",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper is concerned with a new method to enhance
                 the bandwidth efficiency of an MC-CDMA system by using
                 a residue number based representation for information
                 symbols. The residues are mapped into a set of
                 orthogonal sequences and are transmitted \ldots{}",
}

@InProceedings{Madhukumar:2000:PRN,
  author =       "A. S. Madhukumar and F. Chin",
  booktitle =    "{IEEE} {VTS-Fall} {VTC 2000}. 52nd Vehicular
                 Technology Conference, 2000",
  title =        "Performance of a residue number system based
                 {DS--CDMA} system over bursty communication channels",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2433--2440",
  year =         "2000",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/VETECF.2000.883300",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper is concerned with the performance of a
                 residue number system (RNS) based direct-sequence CDMA
                 system over bursty communication channels. Concatenated
                 codes employing redundant RNS as inner codes and
                 convolution codes as outer codes are \ldots{}",
}

@InProceedings{Madhukumar:2000:RNS,
  author =       "A. S. Madhukumar and F. Chin and A. B. Premkumar",
  booktitle =    "Proceedings of the 43rd {IEEE} Midwest Symposium on
                 Circuits and Systems 2000",
  title =        "Residue number system based multicarrier {CDMA} for
                 broadband mobile communication systems",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "536--539",
  year =         "2000",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.2000.952812",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper is concerned with a new method to enhance
                 the bandwidth efficiency of an MC-CDMA system by using
                 a residue number based representation for information
                 symbols. The residues are mapped into a set of
                 orthogonal sequences and are transmitted \ldots{}",
}

@InProceedings{Mahesh:2000:LPR,
  author =       "M. N. Mahesh and M. Mehendale",
  booktitle =    "Thirteenth International Conference on {VLSI} Design,
                 2000",
  title =        "Low power realization of residue number system based
                 {FIR} filters",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "30--33",
  year =         "2000",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICVD.2000.812580",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "In this paper, we present algorithmic and
                 architectural transforms for low power realization of
                 Residue Number System (RNS) based FIR filters. These
                 transforms have been systematically derived so as to
                 achieve power reduction by voltage scaling, \ldots{}",
}

@Book{Markstein:2000:IEF,
  author =       "Peter Markstein",
  title =        "{IA-64} and Elementary Functions: Speed and
                 Precision",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xix + 298",
  year =         "2000",
  ISBN =         "0-13-018348-2",
  ISBN-13 =      "978-0-13-018348-4",
  LCCN =         "QA76.9.A73 M365 2000",
  bibdate =      "Fri Jan 5 08:00:52 MST 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/intel-ia-64.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/microchip.bib;
                 University of California MELVYL catalog.",
  series =       "Hewlett--Packard professional books",
  URL =          "http://www.markstein.org/",
  acknowledgement = ack-nhfb,
  keywords =     "correct rounding; floating-point arithmetic; IA-64
                 (computer architecture)",
  remark =       "Besides recipes for accurate computation of elementary
                 functions, this book also contains algorithms for the
                 correctly-rounded computation of floating-point
                 division and square-root, and of integer division,
                 starting from low-precision reciprocal approximations.
                 There is also a wealth of information on the tradeoffs
                 between integer and floating-point instruction use in a
                 pipelined parallel architecture.",
  tableofcontents = "IA-64 Architecture \\
                 New Architecture Objectives \\
                 VLIW \\
                 Memory Enhancements \\
                 Software Pipelining \\
                 Floating Point Enhancements \\
                 Summary \\
                 IA-64 Instructions And Registers \\
                 Instructions \\
                 Register Sets \\
                 Accessing Memory \\
                 Assembly Language \\
                 Problems \\
                 Increasing Instruction Level Parallelism \\
                 Branching \\
                 Speculation \\
                 Problems \\
                 Floating Point Architecture \\
                 Floating Point Status Register \\
                 Precision \\
                 Fused Multiply-Add \\
                 Division and Square Root Assists \\
                 Floating Comparisons \\
                 Communication between Floating Point and General
                 Purpose Registers \\
                 Fixed Point Multiplication \\
                 SIMD Arithmetic \\
                 Problems \\
                 Programming For IA-64 \\
                 Compiler Options \\
                 Pragmas \\
                 Floating Point Data Types \\
                 In-Line Assembly \\
                 The fenv.h Header \\
                 Extended Examples \\
                 Quad Precision \\
                 Problems \\
                 Computation of Elementary Functions \\
                 Mathematical Preliminaries \\
                 Floating Point \\
                 Approximation and Error Analysis \\
                 The Exclusion Theorem \\
                 Ulps \\
                 Problems \\
                 Approximation Of Functions \\
                 Taylor Series \\
                 Lagrangian Interpolation \\
                 Chebychev Approximation \\
                 Remez Approximation \\
                 Practical Considerations \\
                 Function Evaluation \\
                 Table Construction \\
                 Problems \\
                 Division \\
                 Approximations for the Reciprocal \\
                 Computing the Quotient \\
                 Division Using Only Final Precision Results \\
                 Fast Variants of Division \\
                 Remainder \\
                 Integer Division \\
                 An Implementation of Division \\
                 Problems \\
                 Square Root \\
                 Approximations \\
                 Rounding the Square Root \\
                 Computing the Square Root \\
                 Calculating the Reciprocal Square Root \\
                 An Implementation of Square Root \\
                 Problems \\
                 Exponential Functions \\
                 Definitions and Formulas \\
                 Argument Reduction \\
                 Error Containment \\
                 Computing the Exponential \\
                 The Function expm \\
                 Problems \\
                 Logarithmic Functions \\
                 General Relations \\
                 Argument Reductions \\
                 Error Analysis \\
                 The Function log1p \\
                 Computing the Logarithm \\
                 Problems \\
                 The Power Function \\
                 Definition \\
                 Single Precision \\
                 Double Precision \\
                 Double-Extended Precision \\
                 Quad Precision \\
                 Computing the Power Function \\
                 Problems \\
                 Trigonometric Functions \\
                 Formulas and Identities \\
                 Argument Reduction \\
                 Error Analysis \\
                 Computing the Trigonometric Functions \\
                 Problems \\
                 Inverse Sine And Cosine \\
                 Definitions and Formulas \\
                 Argument Reduction \\
                 Error Analysis \\
                 Computing the arcsin \\
                 Problems \\
                 Inverse Tangent Functions \\
                 Definitions and Formulas \\
                 Argument Reduction \\
                 Error Analysis \\
                 Computing the arctan \\
                 Problems \\
                 Hyperbolic Functions \\
                 Definitions and Formulas \\
                 Argument Reduction \\
                 Error Analysis \\
                 Computing the Hyperbolic Functions \\
                 Problems \\
                 Inverse Hyperbolic Functions \\
                 Definitions and Formulas. arcsinh. arccosh. arctanh \\
                 Problems \\
                 Odds And Ends \\
                 Correctly Rounded Functions \\
                 Monotonicity \\
                 Alternative Algorithms \\
                 Testing \\
                 New Architectural Directions \\
                 Problems \\
                 In-Line Assembly \\
                 Solutions To Problems \\
                 Bibliography \\
                 Subject Index",
}

@Article{Maryska:2000:SCR,
  author =       "J. Maryska and M. Rozlozn{\'\i}k and M. Tuma",
  title =        "{Schur} complement reduction in the mixed-hybrid
                 approximation of {Darcy}'s law: rounding error
                 analysis",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "117",
  number =       "2",
  pages =        "159--173",
  day =          "15",
  month =        may,
  year =         "2000",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:43:35 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042799003441",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{McKenzie:2000:ACP,
  author =       "Pierre McKenzie and Heribert Vollmer and Klaus W.
                 Wagner",
  title =        "Arithmetic Circuits and Polynomial Replacement
                 Systems",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1974",
  pages =        "164--??",
  year =         "2000",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Fri Feb 1 09:17:23 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1974.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1974/19740164.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1974/19740164.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@PhdThesis{Mencer:2000:RAU,
  author =       "Oskar Mencer",
  title =        "Rational Arithmetic Units in Computer Systems",
  type =         "{Ph.D.} Thesis",
  school =       "Department of Electrical Engineering, Stanford
                 University",
  address =      "Stanford, CA, USA",
  pages =        "????",
  month =        jan,
  year =         "2000",
  bibdate =      "Mon Dec 24 11:05:19 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Moreira:2000:FMJ,
  author =       "Jos{\'e} E. Moreira and Samuel P. Midkiff and Manish
                 Gupta",
  title =        "From flop to megaflops: {Java} for technical
                 computing",
  journal =      j-TOPLAS,
  volume =       "22",
  number =       "2",
  pages =        "265--295",
  month =        mar,
  year =         "2000",
  CODEN =        "ATPSDT",
  ISSN =         "0164-0925 (print), 1558-4593 (electronic)",
  ISSN-L =       "0164-0925",
  bibdate =      "Tue Sep 26 10:12:58 MDT 2000",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toplas/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toplas/2000-22-2/p265-moreira/",
  abstract =     "Although there has been some experimentation with Java
                 as a language for numerically intensive computing,
                 there is a perception by many that the language is
                 unsuited for such work because of performance
                 deficiencies. In this article we show how optimizing
                 array bounds checks and null pointer checks creates
                 loop nests on which aggressive optimizations can be
                 used. Applying these optimizations by hand to a simple
                 matrix-multiply test case leads to Java-compliant
                 programs whose performance is in excess of 500 Mflops
                 on a four-processor 332MHz RS/6000 model F50 computer.
                 We also report in this article the effect that various
                 optimizations have on the performance of six
                 floating-point-intensive benchmarks. Through these
                 optimizations we have been able to achieve with Java at
                 least 80\% of the peak Fortran performance on the same
                 benchmarks. Since all of these optimizations can be
                 automated, we conclude that Java will soon be a serious
                 contender for numerically intensive computing.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Programming Languages and
                 Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J783",
  keywords =     "arrays; compilers; Java",
  subject =      "Software --- Programming Languages --- Processors
                 (D.3.4): {\bf Compilers}; Software --- Programming
                 Languages --- Processors (D.3.4): {\bf Run-time
                 environments}; Software --- Programming Techniques ---
                 Concurrent Programming (D.1.3): {\bf Parallel
                 programming}; Software --- Programming Languages ---
                 Language Classifications (D.3.2): {\bf Java}",
}

@Book{Mueller:2000:CAC,
  author =       "Silvia M. Mueller and Wolfgang J. Paul",
  title =        "Computer Architecture: Complexity and Correctness",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xiii + 553",
  year =         "2000",
  ISBN =         "3-540-67481-0",
  ISBN-13 =      "978-3-540-67481-8",
  LCCN =         "QA76.9.A73 M845 2000",
  bibdate =      "Mon Mar 05 18:45:52 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  URL =          "http://www-wjp.cs.uni-sb.de/info/papers/#books",
  abstract =     "\booktitle{Computer Architecture: Complexity and
                 Correctness} develops, at the gate level, the complete
                 design of a pipelined RISC processor with delayed
                 branch, forwarding, hardware interlock, precise
                 maskable nested interrupts, caches, and a fully
                 IEEE-compliant floating point unit. In contrast to
                 other design approaches applied in practice and unlike
                 other textbooks available, the designs presented here
                 are modular, clean and complete up to the construction
                 of entire complex machines. The authors systematically
                 basing their approach on rigorous mathematical
                 formalisms allows for rigorous correctness proofs,
                 accurate hardware cost determination, and performance
                 evaluation as well as, generally speaking, for coverage
                 of a broad variety of relevant issues within a
                 reasonable number of pages. The book is written as a
                 text for classes on computer architecture and related
                 topics and will serve as source of reference for
                 professionals in hardware design. Numerous
                 illustrations, examples, exercises, and a subject index
                 support the reader in accessing the material
                 presented.",
  acknowledgement = ack-nhfb,
  keywords =     "correct rounding; DLX; floating-point arithmetic; IEEE
                 754; RISC",
  libnote =      "Not yet in my library.",
  remark =       "This book is about the design of the DLX (MIPS
                 derivative) processor, at the circuit level. As such,
                 it lacks the broad view of Hennessy \& Patterson's
                 books, but by considering actual gate implementation
                 costs, it is able to provide precise details of
                 implementation tradeoffs, in particular, on cache size
                 and design, and on why memory on chip is expensive (in
                 number of gates) [although the recent work by David
                 Patterson's group at UC/Berkeley on the Vector IRAM
                 processor is putting about 16MB RAM on chip, to make a
                 system-on-a-chip suitable for embedded devices, like
                 the 0.5B cell phones that will be manufactured in
                 2001].\par

                 The book includes mathematical correctness proofs of
                 all circuits, and automated verification of these
                 proofs is in progress.\par

                 From p. 10: ``\ldots{} All C programs associated with
                 the designs in this book are accessible at the our web
                 site.'' [see the URL field in this entry].\par

                 Chapter 7 ``IEEE Floating Point Standard and Theory of
                 Rounding'' has a good survey of the IEEE 754 Standard,
                 and its implications at the hardware level.\par

                 Chapter 8 ``Floating Point Algorithms and Data Paths'',
                 and Chapter 9 ``Pipelined DLX Machine with
                 Floating-Point Core'', examine the hardware
                 implementation of IEEE 754 arithmetic.\par

                 Chapter 9 makes very brief mention of the design issues
                 for fast interval arithmetic.",
  tableofcontents = "1: Introduction \\
                 2: Basics \\
                 2.1: Hardware Model \\
                 2.2: Number Representations and Basic Circuits \\
                 2.3: Basic Circuits \\
                 2.4: Arithmetic Circuits \\
                 2.5: Multipliers \\
                 2.6: Control Automata \\
                 3: A Sequential DLX Design \\
                 3.1: Instruction Set Architecture \\
                 3.2: High Level Data Paths \\
                 3.3: Environments \\
                 3.4: Sequential Control \\
                 3.5: Hardware Cost and Cycle Time \\
                 4: Basic Pipelining \\
                 4.1: Delayed Branch and Delayed PC \\
                 4.2: Prepared Sequential Machines \\
                 4.3: Pipelining as a Transformation \\
                 4.4: Result Forwarding \\
                 4.5: Hardware Interlock \\
                 4.6: Cost Performance Analysis \\
                 5: Interrupt Handling \\
                 5.1: Attempting a Rigorous Treatment of Interrupts \\
                 5.2: Extended Instruction Set Architecture",
}

@Article{Mulders:2000:SMD,
  author =       "Thom Mulders",
  title =        "On short multiplications and divisions",
  journal =      j-APPL-ALGEBRA-ENG-COMMUN-COMPUT,
  volume =       "11",
  number =       "1",
  pages =        "69--88",
  month =        aug,
  year =         "2000",
  CODEN =        "AAECEW",
  DOI =          "https://doi.org/10.1007/s002000000037",
  ISSN =         "0938-1279 (print), 1432-0622 (electronic)",
  ISSN-L =       "0938-1279",
  MRclass =      "68W30",
  MRnumber =     "MR1817699 (2001m:68187)",
  bibdate =      "Thu Nov 8 14:50:38 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See note \cite{Hanrot:2002:LNM}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Applicable Algebra in Engineering, Communication and
                 Computing",
}

@InProceedings{Muller:2000:SAP,
  author =       "J-M. Muller",
  editor =       "Peter Kornerup",
  booktitle =    "Proceedings of the {Fourth Conference on Real Numbers
                 and Computers, Schlo{\ss} Dagstuhl, April 2000}",
  title =        "Some algebraic properties of floating-point
                 arithmetic",
  publisher =    "????",
  address =      "????",
  pages =        "31--38",
  year =         "2000",
  bibdate =      "Sat Nov 15 07:04:16 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Nielsen:2000:ICF,
  author =       "Asger Munk Nielsen and David W. Matula and Chung Nan
                 Lyu and Guy Even",
  title =        "An {IEEE} compliant floating-point adder that conforms
                 with the pipeline packet-forwarding paradigm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "1",
  pages =        "33--47",
  month =        jan,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.822562",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:35:23 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=822562",
  abstract =     "This paper presents a floating-point addition
                 algorithm and adder pipeline design employing a packet
                 forwarding pipeline paradigm. The packet forwarding
                 format and the proposed algorithms constitute a new
                 paradigm for handling data hazards in deeply pipelined
                 floating-point pipelines. The addition and rounding
                 algorithms employ a four stage execution phase pipeline
                 with each stage suitable for implementation in a short
                 clock period, assuming about 15 logic levels per cycle.
                 The first two cycles are related to addition proper and
                 are the focus of this paper. The last two cycles
                 perform the rounding and have been covered in a paper
                 by D. W. Matula and A. M. Nielsen (1997). The addition
                 algorithm accepts one operand in a standard binary
                 floating-point formal at the start of cycle one. The
                 second operand is represented in the packet forwarding
                 floating-point format: namely, it is divided into four
                 parts: the sign bit, the exponent string, the principal
                 part of the significant, and the carry-round packet.
                 The first three parts of the second operand are input
                 at the start of cycle one and the carry-round packet is
                 input at the start of cycle two. The result is output
                 in two formats that both represent the rounded result
                 as required by the IEEE 754 standard. The result is
                 output in the packet forwarding floating-point format
                 at the end of cycles two and three to allow forwarding
                 with an effective latency of two cycles. The result is
                 also format at the end of cycle four for retirement to
                 a register. The packet forwarding result is thus
                 available with an effective two cycle latency for
                 forwarding to the start of the adder pipeline or to a
                 cooperating multiplier pipeline accepting a packet
                 forwarding operand. The effective latency of the
                 proposed design is two cycles for successive dependent
                 operations while perceiving IEEE 754 binary
                 floating-point compatibility.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "This paper presents a floating-point addition
                 algorithm and adder pipeline design employing a packet
                 forwarding pipeline paradigm. The packet forwarding
                 format and the proposed algorithms constitute a new
                 paradigm for handling data hazards in deeply \ldots{}",
}

@Article{Oh:2000:ENB,
  author =       "Sangho Oh and Chang Han Kim and Jongin Lim and Dong
                 Hyeon Cheon",
  title =        "Efficient normal basis multipliers in composite
                 fields",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "10",
  pages =        "1133--1138",
  month =        oct,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.888054",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:35:26 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=888054",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Paliouras:2000:FPP,
  author =       "Vassilis Paliouras and Konstantina Karagianni and
                 Thanos Stouraitis",
  title =        "A floating-point processor for fast and accurate
                 sine\slash cosine evaluation",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "47",
  number =       "5",
  pages =        "441--451",
  month =        may,
  year =         "2000",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.842112",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems. 2, Analog
                 and Digital Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  keywords =     "0.7 micron; Approximation algorithms; CMOS digital
                 integrated circuits; CMOS process technology;
                 computational complexity; Computer architecture;
                 coprocessors; digital signal processing chips; DSP
                 chip; error analysis; fast cosine evaluation; fast sine
                 evaluation; Fixed-point arithmetic; fixed-point
                 arithmetic; floating point arithmetic; floating-point
                 arithmetic; floating-point processor; Hardware;
                 Interleaved codes; interpolation; Interpolation;
                 mathematics computing; memory architecture; Memory
                 architecture; memory interleaving scheme; memory size
                 reduction; Partitioning algorithms; performance
                 evaluation; Polynomials; polynomials; roundoff error
                 bounds; roundoff errors; second order polynomial
                 interpolation; second-order Horner polynomial;
                 trigonometric functions; Very large scale integration;
                 VLSI; VLSI architecture",
  summary =      "A VLSI architecture for fast and accurate
                 floating-point sine/cosine evaluation is presented,
                 combining floating-point and simple fixed-point
                 arithmetic. The algorithm implemented by the
                 architecture is based on second order polynomial
                 interpolation \ldots{}",
}

@InProceedings{Paliouras:2000:HRR,
  author =       "V. Paliouras and T. Stouraitis",
  booktitle =    "The 7th {IEEE} International Conference on
                 Electronics, Circuits and Systems, 2000. {ICECS 2000}",
  title =        "High-radix residue number system forward and inverse
                 converters",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "858--861",
  year =         "2000",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICECS.2000.913011",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Novel radix-r modulo-r n forward and inverse
                 converters for residue number system (RNS)-based
                 processors are introduced in this paper. The proposed
                 circuits convert conventional radix-2 data to
                 high-radix residues and vice-versa with low \ldots{}",
}

@Article{Paliouras:2000:NHR,
  author =       "V. Paliouras and T. Stouraitis",
  title =        "Novel high-radix residue number system architectures",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "47",
  number =       "10",
  pages =        "1059--1073",
  month =        oct,
  year =         "2000",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/82.877147",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=18987",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems. 2, Analog
                 and Digital Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Novel radix-r modulo-r n arithmetic units for residue
                 number system (RNS)-based architectures are introduced
                 in this paper. The proposed circuits are shown to
                 require several times less area than previously
                 reported architectures for \ldots{}",
}

@MastersThesis{Papakonstantinou:2000:IUF,
  author =       "Alexandros Papakonstantinou",
  title =        "Implementations of units for floating point
                 arithmetic",
  type =         "Thesis ({M.Sc.})",
  school =       "Department of Electrical and Electronic Engineering,
                 Imperial College, London",
  address =      "London, UK",
  year =         "2000",
  bibdate =      "Thu May 09 08:42:09 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{Parhami:2000:CAA,
  author =       "Behrooz Parhami",
  title =        "Computer Arithmetic: Algorithms and Hardware Designs",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "xx + 490",
  year =         "2000",
  ISBN =         "0-19-512583-5 (hardcover), 3-540-04907-X (print),
                 3-540-36246-0 (e-book)",
  ISBN-13 =      "978-0-19-512583-2 (hardcover), 978-3-540-04907-4
                 (print), 978-3-540-36246-3 (e-book)",
  LCCN =         "QA76.9.C62P37 1999",
  bibdate =      "Sat Jun 17 12:26:40 2000",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\$85.00",
  abstract =     "The field of digital computer architecture has grown
                 explosively in the past two decades. Through a steady
                 stream of experimental research, tool-building efforts,
                 and theoretical studies, the design of an
                 instruction-set architecture has been transformed into
                 one of the most quantitative branches of computer
                 technology. However, this explosive growth has led to
                 unprecedented hardware complexity and almost
                 intolerable development costs. The challenge faxing
                 current and future computer designers is to institute
                 simplicity where we now have complexity; to use
                 fundamental theories being developed in this area to
                 gain performance and ease-of-use benefits from simpler
                 circuits; to understand the interplay between
                 technological capabilities/limitations and sound
                 architectural decisions. Computer arithmetic plays a
                 key role in the computer designers' quest for
                 user-friendliness, compactness, simplicity, high
                 performance, low cost, and low power. Parhami's
                 Computer Architecture emphasizes both the underlying
                 theory and actual hardware designs. and links computer
                 arithmetic to other subfields of computing. It is the
                 first computer arithmetic book to cover all topics
                 important for a balanced and complete view of the
                 field. IT will be accompanied by an instructor's
                 manual, with problem solutions and enlarged versions of
                 the figures/charts, suitable for reproduction as
                 transparencies. This is a textbook for senior/graduate
                 level courses in departments of computer science and
                 electrical and computer engineering. The course is
                 commonly called Computer Arithmetic. Students wishing
                 to enroll will usually have taken courses in computer
                 organization and advanced digital design before
                 enrolling. Computer Arithmetic is a sub-field of
                 digital computer organization. It deals with the
                 hardware realization of arithmetic functions to support
                 various computer architectures, as well as arithmetic
                 algorithms for firmware or software implementations. A
                 major thrust of digital computer arithmetic is the
                 design of hardware algorithms and circuits to enhance
                 the speed of numeric operations. Thus much of what is
                 presented in this book complements the architectural
                 and algorithmic speedup techniques studied in the
                 context of high performance computer architecture and
                 parallel processing.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Part I: Number Representation \\
                 1: Numbers and Arithmetic \\
                 2: Representing Signed Numbers \\
                 3: Redundant Number Systems \\
                 4: Residue Number Systems \\
                 Part II: Addition/Subtraction \\
                 5: Basic Addition and Counting \\
                 6: Carry-Lookahead Adders \\
                 7: Variations in Fast Adders \\
                 8: Multioperand Addition \\
                 Part III: Multiplication \\
                 9: Basic Multiplication Schemes \\
                 10: High-Radix Multipliers \\
                 11: Tree and Array Multipliers \\
                 12: Variations in Multipliers \\
                 Part IV: Division \\
                 13: Basic Division Schemes \\
                 14: High-Radix Dividers \\
                 15: Variations in Dividers \\
                 16: Division by Convergence \\
                 Part V: Real Arithmetic \\
                 17: Floating-Point Representations \\
                 18: Floating-Point Operations \\
                 19: Errors and Error Control",
}

@InProceedings{Parhami:2000:PER,
  author =       "B. Parhami",
  booktitle =    "Conference Record of the Thirty-Fourth Asilomar
                 Conference on Signals, Systems and Computers, 2000",
  title =        "On producing exactly rounded results in digit-serial
                 on-line arithmetic",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "889--893",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:05 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The input and output of an on-line computation
                 involving redundant numbers must generally be
                 compatible with standard nonredundant formats. When
                 rounding of a result is required in the last
                 computation step, the process can be combined with
                 on-the- \ldots{}",
}

@InProceedings{Park:2000:ESR,
  author =       "Woo-Chan Park and Tack-Don Han and Shin-Dug Kim",
  booktitle =    "Proceedings of the Second {IEEE} Asia Pacific
                 Conference on {ASICs 2000}: {AP-ASIC 2000}",
  title =        "Efficient simultaneous rounding method removing
                 sticky-bit from critical path for floating point
                 addition",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "223--226",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:05 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Processing flow of the conventional floating point
                 addition/subtraction operation consists of several
                 steps, i.e., alignment, addition/subtraction,
                 normalization, and rounding stages in this order. A
                 floating adder/subtractor performing addition/
                 \ldots{}",
}

@TechReport{Parker:2000:MCAa,
  author =       "D. Stott Parker and Brad Pierce and Paul R. Eggert",
  title =        "{Monte Carlo} arithmetic: a framework for the
                 statistical analysis of roundoff error",
  number =       "CSD 970014",
  institution =  "Department of Computer Science, University of
                 California, Los Angeles",
  address =      "Los Angeles, CA, USA",
  pages =        "18",
  month =        mar,
  year =         "2000",
  LCCN =         "QA75.5 .R46 no.970002 1997",
  bibdate =      "Mon Aug 25 15:03:13 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.ucla.edu/~stott/mca/CSD-970014.ps.gz",
  acknowledgement = ack-nhfb,
}

@Article{Parker:2000:MCAb,
  author =       "D. Stott Parker and Brad Pierce and Paul R. Eggert",
  title =        "{Monte Carlo} Arithmetic: How to Gamble with Floating
                 Point and Win",
  journal =      j-COMPUT-SCI-ENG,
  volume =       "2",
  number =       "4",
  pages =        "58--68",
  month =        jul # "\slash " # aug,
  year =         "2000",
  CODEN =        "CSENFA",
  ISSN =         "1521-9615 (print), 1558-366X (electronic)",
  ISSN-L =       "1521-9615",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://dlib.computer.org/cs/books/cs2000/pdf/c4058.pdf;
                 http://www.computer.org/cse/cs1999/c4058abs.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing in Science and Engineering",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
  summary =      "How sensitive to rounding errors are the results
                 generated from a particular code running on a
                 particular machine applied to a particular input? Monte
                 Carlo arithmetic illustrates the potential for tools to
                 support new kinds of a posteriori round-off analysis.",
}

@Article{Parks:2000:NTT,
  author =       "M. Parks",
  title =        "Number-Theoretic Test Generation for Directed
                 Rounding",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "7",
  pages =        "651--658",
  month =        jul,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.863034",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:35:24 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
                 OCLC Proceedings database",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=863034",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-14; floating-point testing",
  remark =       "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
  summary =      "We present methods to systematically generate the
                 hardest test cases for multiplication, division, and
                 square root subject to directed rounding, essentially
                 extending previous work on number-theoretic
                 floating-point testing to rounding modes other than
                 to-nearest. The algorithms focus upon the rounding
                 boundaries of the modes truncate, to-minus-infinity,
                 and to-infinity, and programs based on them require
                 little beyond exact arithmetic in the working precision
                 to create billions of edge cases. We will show that the
                 amount of work required to calculate trial
                 multiplicands pays off in the form of free extra tests
                 due to an interconnection among the operations
                 considered herein. Although these tests do not replace
                 proofs of correctness, they can be used to gain a high
                 degree of confidence that the accuracy requirements as
                 mandated by IEEE Standard 754 have been satisfied.",
}

@Article{Philippsen:2000:CNJ,
  author =       "Michael Philippsen and Edwin G{\"u}nthner",
  title =        "Complex numbers for {Java}",
  journal =      j-CPE,
  volume =       "12",
  number =       "6",
  pages =        "477--491",
  month =        may,
  year =         "2000",
  CODEN =        "CPEXEI",
  DOI =          "https://doi.org/10.1002/1096-9128(200005)12:6<477::AID-CPE486>3.0.CO;2-W",
  ISSN =         "1040-3108 (print), 1096-9128 (electronic)",
  ISSN-L =       "1040-3108",
  bibdate =      "Sun Oct 29 16:57:06 MST 2000",
  bibsource =    "http://www.interscience.wiley.com/jpages/1040-3108;
                 http://www3.interscience.wiley.com/journalfinder.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.interscience.wiley.com/cgi-bin/abstract/72515730/START;
                 http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=72515730&PLACEBO=IE.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Concurrency, practice and experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-0634/issues",
}

@Article{Pillai:2000:LPA,
  author =       "R. V. Pillai and D. Al-Khalili and A. J. Al-Khalili",
  title =        "Low Power Architecture for Floating-Point {MAC}
                 Fusion",
  journal =      j-IEE-PROC-COMPUT-DIGIT-TECH,
  volume =       "147",
  pages =        "288--296",
  year =         "2000",
  CODEN =        "ICDTEA",
  ISSN =         "1350-2387 (print), 1359-7027 (electronic)",
  ISSN-L =       "1350-2387",
  bibdate =      "Fri Jun 24 10:52:39 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEE Proceedings. Computers and Digital Techniques",
}

@InProceedings{Ploog:2000:MPB,
  author =       "H. Ploog and D. Timmermann",
  booktitle =    "Proceedings of the 2000 International Conference on
                 Computer Design",
  title =        "On multiple precision based {Montgomery}
                 multiplication without precomputation of {$ N'_0 = -
                 N_0^{-1} \bmod W $}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "589--590",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:53:44 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "An efficient implementation of modular exponentiation,
                 i.e., the main building block of many public key
                 cryptographic devices, is achieved by algorithmic
                 optimization of the Montgomery modular multiplication
                 algorithm based on multiple precision \ldots{}",
}

@Book{Poitras:2000:EHF,
  author =       "Geoffrey Poitras",
  title =        "The Early History of Financial Economics, 1478--1776:
                 from Commercial Arithmetic to Life Annuities and Joint
                 Stocks",
  publisher =    "Edward Elgar",
  address =      "Cheltenham, UK",
  pages =        "x + 522",
  year =         "2000",
  ISBN =         "1-84064-455-9",
  ISBN-13 =      "978-1-84064-455-5",
  LCCN =         "HG101 .P65 2000",
  bibdate =      "Sat Aug 12 14:42:20 MDT 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Geoffrey Poitras provides an exhaustive account of the
                 early development of the subject and, in so doing,
                 provides a sound basis for the study of modern
                 financial economics.",
  acknowledgement = ack-nhfb,
  author-dates = "1954--",
  subject =      "Finance; History; Economics; Business mathematics;
                 Life annuities; Stocks; Finances; Histoire;
                 {\'E}conomie politique; Math{\'e}matiques
                 financi{\`e}res; Rentes viag{\`e}res; Actions (Titres
                 de soci{\'e}t{\'e}); Business mathematics; Economics;
                 Finance; Life annuities; Stocks; Finanzierungstheorie;
                 Finanzwirtschaft; Finanzwissenschaft; Kredittheorie;
                 Financi{\"e}n.",
  tableofcontents = "1: Introduction \\
                 2: History of Commerce and Finance \\
                 3: The Scholastic Analysis of Usury and Other Subjects
                 \\
                 4: The Evolution of Commercial Arithmetic \\
                 5: Simple Interest and Compound Interest \\
                 6: The Valuation of Life Annuities \\
                 7: Foreign Exchange and the Bill Market \\
                 8: The Analysis of Joint Stocks \\
                 9: Development of Derivative Securities \\
                 10: Manias, Manipulations and Institutional Failures
                 \\
                 11: English Debates over Interest Rates and Public
                 Credit \\
                 12: Maritime Insurance, Life Insurance and Other
                 Subjects \\
                 13: Some Speculative Conclusions",
}

@InProceedings{Premkumar:2000:CLB,
  author =       "A. B. Premkumar and M. Bhardwaj",
  booktitle =    "The 2000 {IEEE} International Symposium on Circuits
                 and Systems, Proceedings, {ISCAS 2000} Geneva, 28--31
                 May 2000",
  title =        "Combinatorial logic based forward converters in
                 residue number systems",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "317--320",
  year =         "2000",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.2000.857428",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The Residue Number System (RNS) offers unlimited
                 opportunities for high performance arithmetic provided
                 efficient forward and reverse converters could be
                 constructed for the moduli set at hand. All forward
                 conversion proposals to date, require some \ldots{}",
}

@InProceedings{Ramirez:2000:NAC,
  author =       "J. Ramirez and A. Garcia and P. G. Fernandez and L.
                 Parrilla and A. Lloris",
  booktitle =    "Proceedings, {ISCAS 2000} Geneva, The 2000 {IEEE}
                 International Symposium on Circuits and Systems, 28--31
                 May 2000",
  title =        "A new architecture to compute the discrete cosine
                 transform using the quadratic residue number system",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "321--324",
  year =         "2000",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.2000.857429",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A new methodology to compute the N-point DCT (Discrete
                 Cosine Transform) in the QRNS (Quadratic Residue Number
                 System) is presented, with a significant improvement in
                 complexity and speed compared to the corresponding
                 binary version. This reduction \ldots{}",
}

@Article{Reyhani-Masoleh:2000:ENB,
  author =       "A. Reyhani-Masoleh and M. A. Hasan",
  title =        "On Efficient Normal Basis Multiplication",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1977",
  pages =        "213--??",
  year =         "2000",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:08:57 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1977.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1977/19770213.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1977/19770213.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Russinoff:2000:CSF,
  author =       "David M. Russinoff",
  title =        "A Case Study in Formal Verification of
                 Register-Transfer Logic with {ACL2}: The Floating Point
                 Adder of the {AMD Athlon} Processor",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1954",
  pages =        "3--36",
  year =         "2000",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Thu Sep 12 09:02:10 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1954.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1954/19540003.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1954/19540003.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Savas:2000:MMI,
  author =       "E. Savas and {\c{C}}. K. Ko{\c{c}}",
  title =        "The {Montgomery} Modular Inverse---Revisited",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "7",
  pages =        "763--766",
  month =        jul,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.863048",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:35:25 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
                 OCLC Proceedings database",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=863048",
  abstract =     "We modify an algorithm given by Kaliski to compute the
                 Montgomery inverse of an integer modulo a prime number.
                 We also give a new definition of the Montgomery
                 inverse, and introduce efficient algorithms for
                 computing the classical modular inverse, the
                 Kaliski-Montgomery inverse, and the new Montgomery
                 inverse. The proposed algorithms are suitable for
                 software implementations on general-purpose
                 microprocessors",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-14",
  remark =       "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
}

@InProceedings{Schulte:2000:CUT,
  author =       "M. Schulte and M. Gok and P. Balzola and R. Brocato",
  title =        "Combined Unsigned and Two's Complement Saturating
                 Multipliers",
  crossref =     "Luk:2000:PSA",
  pages =        "185--196",
  year =         "2000",
  bibdate =      "Sun Mar 04 11:31:05 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2000-05.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Schulte:2000:FVP,
  author =       "M. J. Schulte and E. E. {Swartzlander, Jr.}",
  title =        "A Family of Variable-Precision, Interval Arithmetic
                 Processors",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "5",
  pages =        "387--398",
  month =        may,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.859535",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:35:24 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2000-09.pdf;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=859535",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Schulte:2000:IMO,
  author =       "M. J. Schulte and P. I. Balzola and A. Akkas and R. W.
                 Brocato",
  title =        "Integer Multiplication with Overflow Detection or
                 Saturation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "7",
  pages =        "681--691",
  month =        jul,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.863038",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:35:24 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
                 OCLC Proceedings database",
  URL =          "http://home.ku.edu.tr/~ahakkas/publications/overflow.pdf;
                 http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=863038;
                 http://mesa.ece.wisc.edu/publications/cp_2000-08.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-14",
  remark =       "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
}

@InProceedings{Schulte:2000:PSM,
  author =       "M. J. Schulte and P. I. Balzola and J. Ruan and J.
                 Glossner",
  title =        "Parallel Saturating Multioperand Adders",
  crossref =     "ACM:2000:PIC",
  pages =        "172--179",
  year =         "2000",
  DOI =          "https://doi.org/10.1145/354880.354904",
  bibdate =      "Sun Mar 04 11:32:39 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2000-06.pdf",
  acknowledgement = ack-nhfb,
}

@PhdThesis{Seidel:2000:DIC,
  author =       "Peter-Michael Seidel",
  title =        "On the Design of {IEEE} Compliant Floating-point Units
                 and their Quantitative Analysis",
  type =         "{Ph.D.} thesis",
  school =       "Computer Science Department, University of Saarland",
  address =      "Saarbr{\"u}cken, Germany",
  pages =        "xii + 188",
  year =         "2000",
  bibdate =      "Tue Mar 13 10:27:30 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Mueller:2000:CAC}.",
}

@Book{Seife:2000:ZBD,
  author =       "Charles Seife",
  title =        "Zero: The Biography of a Dangerous Idea",
  publisher =    pub-VIKING,
  address =      pub-VIKING:adr,
  pages =        "vi + 248",
  year =         "2000",
  ISBN =         "0-670-88457-X, 0-14-029647-6 (paperback)",
  ISBN-13 =      "978-0-670-88457-5, 978-0-14-029647-1 (paperback)",
  LCCN =         "QA141 .S45 2000",
  bibdate =      "Fri Nov 28 19:15:01 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}

@Article{Shin:2000:HSC,
  author =       "Kyung-Wook Shin and Heung-Woo Jeon",
  title =        "High-speed complex-number multiplications based on
                 redundant binary representation of partial products",
  journal =      j-INT-J-ELECTRON,
  volume =       "87",
  number =       "6",
  pages =        "683--702",
  month =        jun,
  year =         "2000",
  CODEN =        "IJELA2",
  DOI =          "https://doi.org/10.1080/002072100131887",
  ISSN =         "1362-3060",
  ISSN-L =       "0020-7217",
  bibdate =      "Tue Nov 11 14:51:59 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Electronics Theoretical \&
                 Experimental",
}

@Article{Sleijpen:2000:DER,
  author =       "Gerard L. G. Sleijpen and Henk A. van der Vorst and
                 Jan Modersitzki",
  title =        "Differences in the Effects of Rounding Errors in
                 {Krylov} Solvers for Symmetric Indefinite Linear
                 Systems",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "22",
  number =       "3",
  pages =        "726--751 (electronic)",
  year =         "2000",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/S0895479897323087",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F10 (65N12)",
  MRnumber =     "MR1785632 (2001j:65058)",
  MRreviewer =   "Larisa V. Maslovskaya",
  bibdate =      "Sat Dec 31 06:28:14 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib;
                 MathSciNet database",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/32308;
                 http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/22/3",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Swider:2000:FPR,
  author =       "Zbigniew {\'S}wider",
  title =        "Floating-point roundoff errors of second-order
                 state-space digital filters",
  journal =      "Systems Sci.",
  volume =       "26",
  number =       "1",
  pages =        "67--81",
  year =         "2000",
  CODEN =        "SYSCDP",
  ISSN =         "0137-1223",
  MRclass =      "93E11 (65G20)",
  MRnumber =     "MR1787396",
  bibdate =      "Thu Nov 8 19:32:19 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Wroc\l aw University of Technology. Systems Science",
  keywords =     "rounding errors",
}

@InProceedings{Takahashi:2000:IMP,
  author =       "D. Takahashi",
  booktitle =    "Proceedings of the 2000 International Workshops on
                 Parallel Processing",
  title =        "Implementation of multiple-precision parallel division
                 and square root on distributed-memory parallel
                 computers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "229--235",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "We present efficient parallel algorithms for
                 multiple-precision division and square root operation
                 of more than several million decimal digits on
                 distributed-memory parallel computers. It is well known
                 that multiple-precision division and square \ldots{}",
}

@Article{Talahmeh:2000:ADR,
  author =       "S. Talahmeh and P. Siy",
  title =        "Arithmetic division in {RNS} using {Galois Field
                 GF($p$) }",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "39",
  number =       "5--6",
  pages =        "227--238",
  month =        mar,
  year =         "2000",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/S0898-1221(00)00056-0",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Thu Nov 18 09:47:08 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper develops an enhanced algorithm for the
                 arithmetic division problem in the Residue Number
                 System. The proposed algorithm is based on Galois Field
                 Theory GF($p$). Mapping the arithmetic division problem
                 over the Galois Field GF($p$) eliminates many of the
                 limitations of existing algorithms. The advantage of
                 the proposed algorithm is that it has no restriction on
                 the dividend and the divisor, no mixed radix
                 conversion, no quotient estimation before division, no
                 reciprocal estimation of the divisor, and no based
                 extension operation.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@InProceedings{Tchoumatchenko:2000:FBS,
  author =       "V. Tchoumatchenko and T. Vassileva and P. Gurov",
  booktitle =    "Proceedings of the 22nd {EUROMICRO} Conference
                 {EUROMICRO 96}. 'Beyond 2000: Hardware and Software
                 Design Strategies'",
  title =        "A {FPGA} based square-root coprocessor",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "520--525",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "We present an FPGA implementation of a non-restoring
                 integer square-root algorithm, that uses estimates for
                 result-digit selection and radix-$2$ redundant addition
                 in recurrence. On-the-fly conversion of the
                 result-digit and signed-digit adder/ \ldots{}",
}

@Article{Thimbleby:2000:CNB,
  author =       "Harold Thimbleby",
  title =        "Calculators are needlessly bad",
  journal =      "International Journal of Human-Computer Studies",
  volume =       "52",
  number =       "6",
  pages =        "1031--1069",
  month =        jun,
  year =         "2000",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1006/ijhc.1999.0341",
  ISSN =         "????",
  bibdate =      "Mon Jan 14 21:51:22 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
                 https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1071581999903415",
  acknowledgement = ack-nhfb,
  keywords =     "Charles Babbage",
}

@InProceedings{Tommiska:2000:AEI,
  author =       "M. T. Tommiska",
  booktitle =    "Proceedings of the 2000 Third {IEEE} International
                 Caracas Conference on Devices, Circuits and Systems,
                 15--17 March 2000",
  title =        "Area-efficient implementation of a fast square root
                 algorithm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "S18/1--S18/4",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "An area-efficient implementation of a fast-converging
                 square-root algorithm is presented. The design of
                 special arithmetic operations differs in many ways from
                 the traditional tasks that digital designers are used
                 to, and the role of \ldots{}",
}

@Article{Tong:2000:RPO,
  author =       "J. Y. F. Tong and D. Nagle and R. A. Rutenbar",
  title =        "Reducing power by optimizing the necessary
                 precision\slash range of floating-point arithmetic",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "8",
  number =       "3",
  pages =        "273--286",
  month =        jun,
  year =         "2000",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/92.845894",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
  summary =      "Low-power systems often find the power cost of
                 floating-point (FP) hardware prohibitively expensive.
                 This paper explores ways of reducing FP power
                 consumption by minimizing the bitwidth representation
                 of FP data. Analysis of several FP programs that
                 \ldots{}",
}

@InProceedings{Tsuji:2000:REO,
  author =       "Kumiko Tsuji",
  booktitle =    "Proceedings of the Second {ISAAC} Congress, Vol. 2
                 (Fukuoka, 1999)",
  title =        "Round-off error of optimal control problems in
                 floating-point number systems",
  volume =       "8",
  publisher =    "Kluwer Acad. Publ.",
  address =      "Dordrecht",
  pages =        "929--944",
  year =         "2000",
  MRclass =      "49M30 (65G50)",
  MRnumber =     "MR1940881",
  bibdate =      "Thu Nov 8 19:32:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Int. Soc. Anal. Appl. Comput.",
  acknowledgement = ack-nhfb,
  keywords =     "rounding errors",
}

@Article{vanderKolk:2000:FPV,
  author =       "K. J. van der Kolk and J. A. Lee and E. F. A.
                 Deprettere",
  title =        "A Floating Point Vectoring Algorithm Based on Fast
                 Rotations",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "25",
  number =       "2",
  pages =        "125--139",
  month =        jun,
  year =         "2000",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1023/A:1008166822333",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Thu May 09 09:46:25 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The idea of approximate rotations has been introduced
                 by J. G{\"o}tze and G. Hekstra. G. Hekstra and E.
                 Deprettere extended the concept to orthogonal fast
                 rotations and formalized the concept by providing a
                 fast rotation theory. In this theory, the emphasis has
                 been on fast rotation, whereas fast rotation-based
                 vectorization has only been considered in an
                 approximating sense in examples published by J.
                 G{\"o}tze and G. Hekstra. The formalization of fast
                 rotation-based vectorization is the subject of this
                 paper. The few known approximate fast vectorization
                 algorithms are special cases of the generic fast
                 rotation-based vectorization algorithm proposed in this
                 paper.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
}

@Article{Wang:2000:NSA,
  author =       "Chin-Liang Wang and Jyh-Huei Guo",
  title =        "New systolic arrays for {$ C + A B^2 $}, inversion,
                 and division in {$ \mathrm {GF}(2^m) $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "10",
  pages =        "1120--1125",
  month =        oct,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.888047",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:35:26 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=888047",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Wires:2000:VCT,
  author =       "K. E. Wires and M. J. Schulte and J. E. Stine",
  title =        "Variable-Correction Truncated Floating Point
                 Multipliers",
  crossref =     "Matthews:2000:CRT",
  pages =        "1344--1348",
  year =         "2000",
  bibdate =      "Sun Mar 04 11:34:32 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2000-07.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Yang:2000:EPG,
  author =       "Chia-Lin Yang and B. Sano and A. R. Lebeck",
  title =        "Exploiting parallelism in geometry processing with
                 general purpose processors and floating-point {SIMD}
                 instructions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "9",
  pages =        "934--946",
  month =        sep,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.869324",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:35:25 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=869324",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "Three-dimensional (3D) graphics applications have
                 become very important workloads running on today's
                 computer systems. A cost-effective graphics solution is
                 to perform geometry processing of 3D graphics on the
                 host CPU and have specialized hardware \ldots{}",
}

@Article{Yeh:2000:HSB,
  author =       "Wen-Chang Yeh and Chein-Wei Jen",
  title =        "High-Speed {Booth} Encoded Parallel Multiplier
                 Design",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "49",
  number =       "7",
  pages =        "692--701",
  month =        jul,
  year =         "2000",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.863039",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:35:24 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
                 OCLC Proceedings database",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=863039",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-14",
  remark =       "Selected papers from ARITH'14 \cite{Koren:1999:ISC}.",
}

@TechReport{Zimmermann:2000:PGF,
  author =       "Paul Zimmermann",
  title =        "A proof of {GMP} fast division and square root
                 implementations",
  type =         "Technical report",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  pages =        "14",
  month =        sep,
  year =         "2000",
  bibdate =      "Sun Sep 10 08:48:46 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.loria.fr/~zimmerma/papers/proof-div-sqrt.ps.gz",
  abstract =     "This short note gives a detailed correctness proof of
                 fast (i.e., subquadratic) versions of the GNU MP {\tt
                 mpn\_bz\_divrem\_n} and {\tt mpn\_sqrtrem} functions,
                 together with complete GMP code. The {\tt
                 mpn\_bz\_divrem\_n} function divides (with remainder) a
                 number of $ 2 n $ limbs by a divisor of $n$ limbs in $
                 2 K(n) $, where $ K(n) $ is the time spent in a $ (n
                 \times n) $ multiplication, using the
                 Moenck--Borodin--Jebelean--Burnikel--Ziegler algorithm.
                 The {\tt mpn\_sqrtrem} computes the square root and the
                 remainder of a number of $ 2 n $ limbs (square root and
                 remainder have about $n$ limbs each) in time $ 3 K(n) /
                 2 $; it uses Karatsuba Square Root.",
  acknowledgement = ack-nhfb,
}

@Article{Akishita:2001:FSS,
  author =       "Toru Akishita",
  title =        "Fast Simultaneous Scalar Multiplication on Elliptic
                 Curve with {Montgomery} Form",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2259",
  pages =        "255--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:07:44 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2259.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2259/22590255.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2259/22590255.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@PhdThesis{Akkas:2001:ISE,
  author =       "Ahmet Akkas",
  title =        "Instruction set enhancements for reliable
                 computations",
  type =         "{Ph.D.} Thesis",
  school =       "Lehigh University",
  address =      "Bethlehem, PA, USA",
  pages =        "159",
  year =         "2001",
  ISBN =         "0-493-49369-7",
  ISBN-13 =      "978-0-493-49369-5",
  bibdate =      "Fri Oct 25 17:09:55 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://wwwlib.umi.com/dissertations/fullcit/3036247;
                 http://wwwlib.umi.com/dissertations/preview/3036247",
  abstract =     "Although there have been significant advances in VLSI
                 technology and numerical computing, floating-point
                 computations still suffer from undetected errors due to
                 rounding and catastrophic cancellation. Fast computers
                 let programmers write numerically intensive programs,
                 but computed results can be far from the true results
                 due to the accumulation of errors in arithmetic
                 operations. Therefore, accurate and reliable
                 computations have become more important. Interval
                 arithmetic is one technique for accurate and reliable
                 computing. With interval arithmetic, each data value is
                 represented by two floating-point numbers which
                 correspond to the endpoints of an interval, such that
                 the true result is guaranteed to lie on this interval.
                 Since interval arithmetic represents ranges of numbers,
                 it also provides the ability to solve problems that
                 cannot be efficiently solved using floating-point
                 arithmetic. Although interval arithmetic provides an
                 efficient method for monitoring and controlling errors
                 in floating-point computations, it is not yet used
                 widely because it is not sufficiently fast. This
                 dissertation investigates instruction set enhancements
                 for interval arithmetic. Existing interval arithmetic
                 programs are examined to determine bottlenecks in
                 interval computations. Then, a variety of instruction
                 set enhancements are pro posed to overcome these
                 bottlenecks. The efficiency of the proposed
                 enhancements are evaluated using an interval-enhanced
                 compiler and a superscalar processor simulator.
                 Hardware modifications to support these enhancements
                 are evaluated, and a novel design for a combined
                 Interval and Floating-point Comparator is presented.
                 This dissertation also investigates instruction set
                 enhancements for extended precision arithmetic. In
                 particular, instruction set support for quadruple
                 precision arithmetic is examined. Hardware
                 modifications needed to support quadruple precision
                 arithmetic on superscalar processor is evaluated to
                 determine which extensions can be most efficiently
                 incorporated into superscalar processor designs.
                 Furthermore, a technique for performing parallel double
                 precision multiplication using quadruple precision
                 hardware is proposed.",
  acknowledgement = ack-nhfb,
}

@Book{Alefeld:2001:SAM,
  editor =       "G{\"o}tz Alefeld and Ji{\v{r}}i Rohn and Siegfried
                 Rump and Tetsuro Yamamoto",
  title =        "Symbolic algebraic methods and verification methods",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "ix + 266",
  year =         "2001",
  ISBN =         "3-211-83593-8",
  ISBN-13 =      "978-3-211-83593-7",
  LCCN =         "QA76.9.M35 S92 2001",
  bibdate =      "Thu May 09 07:34:15 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$69.95",
  series =       "Springer mathematics",
  URL =          "http://www.springer-ny.com/detail.tpl?cart=10209516271260963&isbn=3211835938",
  acknowledgement = ack-nhfb,
  contents =     "\begin{itemize}

                 \item Introduction (G. Alefeld, J. Rohn, S. Rump, T.
                 Yamamoto).

                 \item Topological Concepts for Hierarchies of
                 Variables, Types and Controls (R. Albrecht).

                 \item Modifications of the Oettli-Prager Theorem with
                 Application to the Eigenvalue Problem (G. Alefeld, V.
                 Kreinovich, G. Mayer).

                 \item Symbolic-Numeric Algorithms for Polynomials: Some
                 Recent Results (R. Corless).

                 \item Symbolic-Numeric QD-Algorithms with Applications
                 in Function Theory and Linear Algebra (A. Cuyt).

                 \item On the Isoefficiency of the Parallel Descartes
                 Method (Th. Decker, W. Krandick).

                 \item Matrix Methods for Solving Algebraic Systems (I.
                 Z. Emiris).

                 \item A Feasibility Result for Interval Gaussian
                 Elimination Relying on Graph Structure (A.
                 Frommer).

                 \item Solution of Systems of Polynomial Equations by
                 Using Bernstein Expansion (J. Garloff, A. P.
                 Smith).

                 \item Symbolic-Algebraic Computations in Modeling
                 Language for Mathematical Programming (D. M.
                 Gay).

                 \item Translation of Taylor Series into LFT Expansions
                 (R. Heckmann).

                 \item Quasi Convex-Concave Extensions (Chr.
                 Jansson).

                 \item Rewriting, Induction and Decision Procedures: A
                 Case Study of Presburger Arithmetic (D. Kapur).

                 \item Derivative-Based Subdivision in Multi-dimensional
                 Verified Gaussian Quadrature (B. Lang).

                 \item On the Shape of the Fixed Points of
                 $\overline{A}f\overline{U}(\overline{A}x\overline{U}) =
                 \overline{A}A\overline{U}\overline{A}x\overline{U} +
                 \overline{A}b\overline{U}$ (G. Mayer, I. Warnke).

                 \item Exact Computation with leda real --- Theory and
                 Geometric Applications (K. Mehlhorn, St.
                 Schirra).

                 \item Numerical Verification Method for Solutions of
                 Nonlinear Hyperbolic Equations (T. Minamoto).

                 \item Geometric Series Bounds for the Local Errors of
                 Taylor Methods for Linear $n$-th-Order ODEs (M.
                 Neher).

                 \item Save Numerical Error Bounds for Solutions of
                 Nonlinear Elliptic Boundary Value Problems (M.
                 Plum).

                 \item Fast Verification Algorithms in MATLAB (S.
                 Rump).

                 \item The Linear Complementarity Problem with Interval
                 Data (U. Sch{\"a}fer).

                 \item Some Numerical Methods for Nonlinear Least
                 Squares Problems (St. Shakhno).

                 \item A New Insight of the Shortley--Weller
                 Approximation for Dirichlet Problems (T.
                 Yamamoto).

                 \item How Orthogonality is Lost in Krylov Methods
                 (\ldots{})

                 \end{itemize}",
  keywords =     "Computer arithmetic; Floating-point arithmetic;
                 Numerical calculations--Verification",
  remark =       "From the publisher: ``The usual `implementation' of
                 real numbers as floating point numbers on existing
                 computers has the well-known disadvantage that most of
                 the real numbers are not exactly representable in
                 floating point. Also the four basic arithmetic
                 operations can usually not be performed exactly. During
                 the last years research in different areas has been
                 intensified in order to overcome these problems. ({\em
                 LEDA-Library}, by K. Mehlhorn et al., {\em Exact
                 arithmetic with real numbers}, by A. Edalat et al.,
                 Symbolic algebraic methods, verification methods). The
                 latest development is the combination of
                 symbolic-algebraic methods and verification methods to
                 so-called hybrid methods. This book contains a
                 collection of worked out talks on these subjects given
                 during a Dagstuhl seminar at the Forschungszentrum fuer
                 Informatik, Schlo{\ss} Dagstuhl, Germany, presenting
                 the state of the art.''",
}

@InProceedings{Ammar:2001:SIC,
  author =       "A. Ammar and A. Al Kabbany and M. Youssef and A.
                 Amam",
  booktitle =    "{NRSC 2001}, Proceedings of the Eighteenth National
                 Radio Science Conference, 27--29 March 2001",
  title =        "A secure image coding scheme using residue number
                 system",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "399--405",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/NRSC.2001.929397",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A secure image coding scheme using the residue number
                 system (RNS) is presented and tested. The proposed
                 scheme can be also used as the base for a full security
                 multiple access image communication system. Using RNS
                 with multiple look-up tables for \ldots{}",
}

@Article{Aoki:2001:ECA,
  author =       "Kazumaro Aoki and Fumitaka Hoshino and Tetsutaro
                 Kobayashi and Hiroaki Oguro",
  title =        "Elliptic Curve Arithmetic Using {SIMD}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2200",
  pages =        "235--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:06:44 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2200.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2200/22000235.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2200/22000235.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Armando:2001:PEM,
  author =       "A. Armando and S. Ranise",
  title =        "A Practical Extension Mechanism for Decision
                 Procedures: the Case Study of Universal {Presburger}
                 Arithmetic",
  journal =      j-J-UCS,
  volume =       "7",
  number =       "2",
  pages =        "124--??",
  day =          "28",
  month =        feb,
  year =         "2001",
  CODEN =        "????",
  ISSN =         "0948-6968",
  ISSN-L =       "0948-6968",
  bibdate =      "Wed Feb 20 07:23:08 MST 2002",
  bibsource =    "http://www.jucs.org/jucs;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.jucs.org/jucs_7_2/a_practical_extension_mechanism",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
}

@InProceedings{Arnold:2001:ACL,
  author =       "M. Arnold and T. Bailey and J. Cowles and C. Walter",
  booktitle =    "2001 {IEEE} Workshop on Signal Processing Systems",
  title =        "Analysis of complex {LNS} {FFTs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "58--69",
  year =         "2001",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The complex-logarithmic number system (CLNS), which
                 represents each complex point in log/polar coordinates,
                 may be practical to implement the fast Fourier
                 transform (FFT). The roots of unity needed by the FFT
                 have exact representations in CLNS and \ldots{}",
}

@InProceedings{Arnold:2001:DFL,
  author =       "M. G. Arnold",
  booktitle =    "Proceedings of the Euromicro Symposium on Digital
                 Systems, Design, 2001",
  title =        "Design of a faithful {LNS} interpolator",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "336--345",
  year =         "2001",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "A design is given for a quadratic interpolator needed
                 by the logarithmic number system (LNS). Unlike previous
                 LNS designs that have attempted to produce results
                 consistently better than a floating-paint
                 representation of the same word size (32 bits),
                 \ldots{}",
}

@InProceedings{Arnold:2001:PLA,
  author =       "M. G. Arnold",
  booktitle =    "Proceedings of the {IEEE} Computer Society Workshop on
                 {VLSI, 19--20} April 2001",
  title =        "A pipelined {LNS} {ALU}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "155--161",
  year =         "2001",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "A new ALU design is proposed that is more economical
                 than a conventional Logarithmic Number System (LNS) ALU
                 for pipelined multiply-accumulate applications (such as
                 FIR filters). A novel interpolator that accepts both
                 positive and negative arguments \ldots{}",
}

@InProceedings{Arnold:2001:SMQ,
  author =       "M. G. Arnold and M. D. Winkel",
  title =        "A Single-Multiplier Quadratic Interpolator for {LNS}
                 Arithmetic",
  crossref =     "IEEE:2001:PII",
  pages =        "178--183",
  year =         "2001",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "logarithmic number system (LNS)",
  summary =      "Linear interpolation requires a single multiplication
                 but is significantly less accurate than quadratic
                 interpolation. The latter requires two multiplications.
                 Two novel quadratic interpolation schemes are shown
                 that approximate the functions \ldots{}",
}

@InProceedings{Arnold:2001:UFR,
  author =       "Mark G. Arnold and Colin Walter",
  title =        "Unrestricted Faithful Rounding is Good Enough for Some
                 {LNS} Applications",
  crossref =     "Burgess:2001:ISC",
  pages =        "237--246",
  year =         "2001",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Arnold.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
  summary =      "We propose to relax the restricted form of faithful
                 rounding used in prior 32 bit logarithmic number system
                 (LNS) implementations. Unrestricted faithful rounding
                 yields three- to six-fold savings in VLSI ROM size (or
                 four- to six-fold savings in \ldots{}).",
}

@Article{Atlamazoglou:2001:ALP,
  author =       "P. E. Atlamazoglou and H. T. Anastassiu and D. I.
                 Kaklamani",
  title =        "Application of literate-programming principles for the
                 description of a {FORTRAN 90} extension to quaternion
                 arithmetic",
  journal =      j-IEEE-APM,
  volume =       "43",
  number =       "4",
  pages =        "104--114",
  month =        aug,
  year =         "2001",
  CODEN =        "IAPMEZ",
  DOI =          "https://doi.org/10.1109/74.951564",
  ISSN =         "1045-9243 (print), 1558-4143 (electronic)",
  ISSN-L =       "1045-9243",
  bibdate =      "Mon Jul 5 14:39:37 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In an effort to effectively annotate and document a
                 FORTRAN 90 module that extends the language's
                 mathematical capabilities to the performance of
                 quaternion operations, the literate-programming
                 paradigm is adopted. The basic principles of this
                 paradigm are discussed through a short introduction to
                 the features of a specific literate-programming system
                 known as FWEB. This system is then employed for the
                 efficient presentation of the FORTRAN 90 quaternion
                 arithmetic module",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Antennas and Propagation Magazine",
}

@Article{Baidas:2001:FPB,
  author =       "Z. Baidas and A. D. Brown and A. C. Williams",
  title =        "Floating-point behavioral synthesis",
  journal =      j-IEEE-TRANS-CAD-ICS,
  volume =       "20",
  number =       "7",
  pages =        "828--839",
  month =        jul,
  year =         "2001",
  CODEN =        "ITCSDI",
  ISSN =         "0278-0070 (print), 1937-4151 (electronic)",
  ISSN-L =       "0278-0070",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computer-Aided Design of
                 Integrated Circuits and Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=43",
  summary =      "Traditionally, the data processed by a synthesized
                 digital design is fixed (occasionally variable) width
                 integer, and the functional units available are
                 concomitantly simple ladders, subtractors, multipliers,
                 multiplexers, and so on. The aims of \ldots{}",
}

@InProceedings{Bajard:2001:MMB,
  author =       "Jean-Claude Bajard and Laurent-Stephane Didier and
                 Peter Kornerup",
  title =        "Modular Multiplication and Base Extensions in Residue
                 Number Systems",
  crossref =     "Burgess:2001:ISC",
  pages =        "59--65",
  year =         "2001",
  DOI =          "https://doi.org/10.1109/ARITH.2001.930104",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Bajard.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15; residue arithmetic; residue number system",
  summary =      "We present a new RNS modular multiplication for very
                 large operands. The algorithm is based on Montgomery's
                 (1985) method adapted to residue arithmetic. By
                 choosing the moduli of the RNS system reasonably large,
                 an effect corresponding to a \ldots{}",
}

@InProceedings{Balzola:2001:DAP,
  author =       "P. I. Balzola and M. J. Schulte and J. Ruan and J.
                 Glossner and E. Hokenek",
  title =        "Design Alternatives for Parallel Saturating
                 Multioperand Adders",
  crossref =     "IEEE:2001:PII",
  pages =        "172--177",
  year =         "2001",
  bibdate =      "Sun Mar 04 11:43:43 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2001-06.pdf",
  acknowledgement = ack-nhfb,
}

@InCollection{Barraud:2001:SAR,
  author =       "Alain Barraud and Suzanne Lesecq and Nicolai
                 Christov",
  booktitle =    "Numerical analysis and its applications (Rousse,
                 2000)",
  title =        "From sensitivity analysis to random floating point
                 arithmetics---application to {Sylvester} equations",
  volume =       "1988",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "35--41",
  year =         "2001",
  MRclass =      "65F35 (93B40)",
  MRnumber =     "MR1938402",
  bibdate =      "Thu Nov 8 19:16:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Lecture Notes in Computer Science",
  acknowledgement = ack-nhfb,
}

@Article{Bashagha:2001:NRS,
  author =       "A. E. Bashagha",
  title =        "Novel radix-$2$ $k$ square root module",
  journal =      "Circuits, Devices and Systems, IEE Proceedings [see
                 also IEE Proceedings G- Circuits, Devices and
                 Systems]",
  volume =       "148",
  number =       "4",
  pages =        "190--196",
  month =        aug,
  year =         "2001",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The conventional two's complement radix-$2$ k square
                 root algorithm requires a set of 2 k full precision
                 comparisons to generate all the 2 k possible values of
                 the partial remainder. The correct remainder is the
                 minimum \ldots{}",
}

@InProceedings{Beaumont-Smith:2001:PPA,
  author =       "Andrew Beaumont-Smith and Cheng-Chew Lim",
  title =        "Parallel Prefix Adder Design",
  crossref =     "Burgess:2001:ISC",
  pages =        "218--228",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Beaumont_Smith.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}

@Misc{Beebe:2001:IFP,
  author =       "Nelson H. F. Beebe",
  title =        "{IEEE 754} floating-point test software",
  howpublished = "World-Wide Web document.",
  pages =        "17",
  day =          "1",
  month =        dec,
  year =         "2001",
  bibdate =      "Sat Dec 01 16:34:39 2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.math.utah.edu/~beebe/software/ieee/",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point testing",
}

@Article{Berg:2001:FVV,
  author =       "Christoph Berg and Christian Jacobi",
  title =        "Formal Verification of the {VAMP} Floating Point
                 Unit",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2144",
  pages =        "325--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:05:47 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2144.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2144/21440325.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2144/21440325.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InProceedings{Bickerstaff:2001:ACC,
  author =       "K'Andrea C. Bickerstaff and Earl E. {Swartzlander,
                 Jr.} and Michael J. Schulte",
  title =        "Analysis of Column Compression Multipliers",
  crossref =     "Burgess:2001:ISC",
  pages =        "33--39",
  year =         "2001",
  bibdate =      "Fri May 3 13:52:01 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2001-02.pdf;
                 http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Bickerstaff.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}

@Article{Blanck:2001:ERA,
  author =       "Jens Blanck",
  title =        "Exact Real Arithmetic Systems: Results of
                 Competition",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2064",
  pages =        "389--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:04:19 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2064.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2064/20640389.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2064/20640389.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Blum:2001:HRM,
  author =       "T. Blum and C. Paar",
  title =        "High-radix {Montgomery} modular exponentiation on
                 reconfigurable hardware",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "50",
  number =       "7",
  pages =        "759--764",
  month =        jul,
  year =         "2001",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.936241",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:36:33 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=936241",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@MastersThesis{Boldo:2001:FAP,
  author =       "Sylvie Boldo",
  title =        "Formalisation, am{\'e}lioration et preuves
                 d'algorithmes en arithm{\'e}tique flottante. ({French})
                 [Formalization, improvement, and proofs of algorithms
                 in floating-point arithmetic]",
  type =         "{Master}'s thesis",
  school =       "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "69364 Lyon Cedex 07, France",
  pages =        "ix + 42",
  day =          "27",
  month =        jun,
  year =         "2001",
  bibdate =      "Tue Nov 23 09:48:04 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Also issued as Report DEA No. 2001-03.",
  URL =          "ftp://ftp.ens-lyon.fr/pub/LIP/Rapports/DEA/DEA2001/DEA2001-03.ps.Z",
  acknowledgement = ack-nhfb,
  language =     "French",
}

@InProceedings{Boldo:2001:MVT,
  author =       "Sylvie Boldo and Marc Daumas",
  title =        "A mechanically validated technique for extending the
                 available precision",
  crossref =     "Matthews:2001:CRT",
  pages =        "1299--1303",
  year =         "2001",
  bibdate =      "Tue Nov 23 10:22:31 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://perso.ens-lyon.fr/marc.daumas/SoftArith/BolDau01b.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Boldo:2001:PIA,
  author =       "Sylvie Boldo and Marc Daumas",
  editor =       "????",
  booktitle =    "{ASTI '2001\slash} {SYMPA 7}: 7{\`e}me Symposium en
                 Architectures Nouvelles de Machines, La Villette,
                 Paris, 24--27 avril, 2001",
  title =        "Performances d'implantations de l'addition en
                 pr{\'e}cision quad-double sur diff{\'e}rentes machines.
                 ({French}) [Performance of implantations of quad-double
                 precision on different machines]",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2001",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Tue Nov 23 10:28:39 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.laria.u-picardie.fr/~cerin/paris2001.html",
  acknowledgement = ack-nhfb,
  language =     "French",
}

@Article{Breyer:2001:NGE,
  author =       "Laird Breyer and Gareth O. Roberts and Jeffrey S.
                 Rosenthal",
  title =        "A note on geometric ergodicity and floating-point
                 roundoff error",
  journal =      j-STAT-PROB-LETT,
  volume =       "53",
  number =       "2",
  pages =        "123--127",
  day =          "1",
  month =        jun,
  year =         "2001",
  CODEN =        "SPLTDC",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  MRclass =      "60J10 (65C40)",
  MRnumber =     "MR1843871 (2002f:60138)",
  MRreviewer =   "Denis Talay",
  bibdate =      "Fri Nov 8 05:39:32 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Ingenta database",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01677152",
  pagecount =    "5",
}

@Misc{Briggs:2001:XER,
  author =       "Keith Briggs and Yannis Smaragdakis",
  title =        "{XR} --- Exact Real Arithmetic",
  howpublished = "World-Wide Web document and software package.",
  day =          "01",
  month =        mar,
  year =         "2001",
  bibdate =      "Sat Apr 28 10:07:59 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "From the overview: ``This is an implementation of
                 exact (or constructive) real arithmetic, as an
                 alternative to multiple-precision floating-point
                 (MPFP). An important distinction is that in MPFP one
                 sets the precision before starting a computation, and
                 then one cannot be sure of the final result. Interval
                 arithmetic is an improvement on this, but still not an
                 ideal solution because if the final interval is larger
                 than desired, there is no simple way to restart the
                 computation at higher precision. By contrast, in XR no
                 precision level is set in advance, and no computation
                 takes place until a final request takes place for some
                 output. Despite this, programming with XR is no
                 different from MPFP, except for the declaration of
                 critical variables as type `XR'.\par

                 The main aim is to produce a usably efficient
                 implementation, which can be easily interfaced with
                 existing C++ code. This contrasts with previous
                 implementations in functional languages (Haskell,
                 Miranda etc.), which, although theoretically important,
                 seem to be rather too slow for real use.\par

                 This code is designed as an add-on to Victor Shoup's
                 arbitrary-precision arithmetic package NTL, and
                 implements a new type XR, to complement NTL's ZZ and RR
                 integer and real types.",
  URL =          "http://www.btexact.com/people/briggsk2/XR.html",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bruguera:2001:URC,
  author =       "Javier D. Bruguera and Tom{\'a}s Lang",
  title =        "Using the Reverse-Carry Approach for Double-Datapath
                 Floating-Point Addition",
  crossref =     "Burgess:2001:ISC",
  pages =        "203--210",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Bruguera.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}

@Article{Bryant:2001:VAC,
  author =       "Randal E. Bryant and Yirng-An Chen",
  title =        "Verification of arithmetic circuits using binary
                 moment diagrams",
  journal =      j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER,
  volume =       "3",
  number =       "2",
  pages =        "137--155",
  month =        may,
  year =         "2001",
  CODEN =        "????",
  ISSN =         "1433-2779 (print), 1433-2787 (electronic)",
  ISSN-L =       "1433-2779",
  bibdate =      "Tue Nov 23 15:01:40 MST 2004",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=1433-2779;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal on Software Tools for Technology
                 Transfer: STTT",
  journal-URL =  "http://link.springer.com/journal/10009",
}

@InProceedings{Burgess:2001:DIR,
  author =       "N. Burgess and C. Hinds",
  booktitle =    "Conference Record of the Thirty-Fifth Asilomar
                 Conference on Signals, Systems and Computers, 2001",
  title =        "Design issues in radix-$4$ {SRT} square root {\&}
                 divide unit",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1646--1650",
  year =         "2001",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper introduces a number of design issues not
                 covered in the open literature that arose during the
                 design of a radix-$4$ SRT divide/square root unit for a
                 vector processing chip. These include compression of
                 the partial remainder's m.s.b.'s, \ldots{}",
}

@InProceedings{Busaba:2001:IZD,
  author =       "Fadi Y. Busaba and Christopher A. Krygowski and Wen H.
                 Li and Eric M. Schwarz and Steven R. Carlough",
  title =        "The {IBM z900} Decimal Arithmetic Unit",
  crossref =     "Matthews:2001:CRT",
  volume =       "2",
  pages =        "1335--1339",
  year =         "2001",
  DOI =          "https://doi.org/10.1109/ACSSC.2001.987708",
  bibdate =      "Fri Nov 28 16:15:49 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "As the cost for adding functions to a processor
                 continues to decline, processor designs are including
                 many additional features. An example of this trend is
                 the appearance of graphics engines and compression
                 engines on midrange and even low end microprocessors.
                 One area that has the potential to capture chip real
                 estate is the decimal arithmetic engine because of its
                 importance in financial and business applications.
                 Studies show that 55\% of the numeric data stored on
                 commercial databases are in decimal format. Although
                 decimal arithmetic is supported in many software
                 languages it is not yet available on many
                 microprocessors. This paper details the decimal
                 arithmetic engine in the recently announced z900
                 microprocessor.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@InProceedings{Cao:2001:HPA,
  author =       "Jun Cao and Belle W. Y. Wei and Jie Cheng",
  title =        "High-Performance Architectures for Elementary Function
                 Generation",
  crossref =     "Burgess:2001:ISC",
  pages =        "136--144",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Cao.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}

@InProceedings{Chen:2001:ADF,
  author =       "Chichyang Chen and Liang-An Chen and Jih-Ren Cheng",
  title =        "Architectural Design of a Fast Floating-Point
                 Multiplication-Add Fused Unit Using Signed-Digit
                 Addition",
  crossref =     "IEEE:2001:PES",
  pages =        "346--353",
  year =         "2001",
  DOI =          "https://doi.org/10.1109/DSD.2001.952324",
  bibdate =      "Fri Jun 24 10:45:22 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Signed digit (SD) addition is applied to the design of
                 a new floating-point (FLP) multiplication-add fused
                 (MAF) unit. This adoption, together with the proposed
                 two-step normalization method, can reduce the
                 three-word-length addition that is required in the
                 conventional FLP MAF unit to two-word-length addition.
                 Furthermore, the sign reversion of the intermediate
                 mantissa that requires three-word-length carry
                 propagation in the conventional MAF unit is replaced by
                 only single-word sign detection. These two improvements
                 can enhance the speed and cost of the MAF unit
                 significantly. With the use of the SD addition, the
                 circuit of the unit can be designed in a more regular
                 and simple manner, which is a property that is desired
                 in VLSI design. The proposed FLP MAF unit has been
                 designed and simulated by using Verilog hardware
                 description language. The functions of the deigned unit
                 are verified to be correct.",
  acknowledgement = ack-nhfb,
}

@Article{Coppersmith:2001:FSS,
  author =       "Don Coppersmith",
  title =        "Finding Small Solutions to Small Degree Polynomials",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2146",
  pages =        "20--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:05:49 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2146.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2146/21460020.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2146/21460020.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@TechReport{Cowlishaw:2001:DAJ,
  author =       "Mike Cowlishaw",
  title =        "Decimal Arithmetic for {\tt java.math}: {JSR 13}
                 Public Review Draft",
  type =         "Technical Report",
  number =       "Version 1.33",
  institution =  "IBM UK Laboratories",
  address =      "Hursley, UK",
  pages =        "iii + 60",
  day =          "16",
  month =        jul,
  year =         "2001",
  bibdate =      "Fri May 20 14:37:16 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www2.hursley.ibm.com/jsr13/jsr13spec.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
  remark =       "Describes a proposal for arbitrary-precision decimal
                 floating-point arithmetic in Java.",
}

@InProceedings{Cowlishaw:2001:DFP,
  author =       "Michael F. Cowlishaw and Eric M. Schwarz and Ronald M.
                 Smith and Charles F. Webb",
  title =        "A Decimal Floating-Point Specification",
  crossref =     "Burgess:2001:ISC",
  pages =        "147--154",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Cowlishaw.pdf;
                 http://www2.hursley.ibm.com/decimal/arith15-foils.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15; decimal floating-point arithmetic",
}

@Misc{Cuyt:2001:ARI,
  author =       "A. Cuyt and P. Kuterna and B. Verdonk and J.
                 Vervloet",
  title =        "{Arithmos}: a reliable integrated computational
                 environment",
  howpublished = "World Wide Web document.",
  year =         "2001",
  bibdate =      "Wed Nov 24 07:50:59 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://win-www.uia.ac.be/u/cant/arithmos/index.html",
  acknowledgement = ack-nhfb,
}

@Article{Cuyt:2001:REC,
  author =       "Annie Cuyt and Brigitte Verdonk and S. Becuwe and
                 Peter Kuterna",
  title =        "A Remarkable Example of Catastrophic Cancellation
                 Unraveled",
  journal =      j-COMPUTING,
  volume =       "66",
  number =       "3",
  pages =        "309--320",
  year =         "2001",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65-04 65G10 65Y99",
  bibdate =      "Thu Jul 12 05:20:09 MDT 2001",
  bibsource =    "http://link.springer-ny.com/link/service/journals/00607/tocs/t1066003.htm;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/journals/00607/bibs/1066003/10660309.htm;
                 http://link.springer-ny.com/link/service/journals/00607/papers/1066003/10660309.pdf",
  abstract =     "In this paper we reinvestigate a well-known expression
                 first published in [7], which is often used to
                 illustrate catastrophic cancellation as well as the
                 fact that identical output in different precisions does
                 not imply reliability. The purpose of revisiting this
                 expression is twofold. First, we show in Section 2 that
                 the effect of the cancellation is very different on
                 different IEEE 754 compliant platforms, and we unravel
                 the underlying (hardware) reasons which are unknown to
                 many numerical analysts. Besides illustrating
                 cancellation, this expression also counters the common
                 misbelief among many numerical analysts that a same
                 program will deliver identical results on all IEEE
                 conforming systems. Second, in Section 3 we use,
                 illustrate and comment upon the cross-platform
                 didactical tool Arithmetic Explorer developed at the
                 University of Antwerp, by means of which we performed
                 the bit level analysis of the expression evaluation
                 under investigation on the different machines. We
                 believe that this tool, which is freely available from
                 the authors, can be of use to all of us teaching a
                 first numerical analysis course.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Misc{Darcy:2001:BLH,
  author =       "Joseph D. Darcy",
  title =        "{Borneo} Language Homepage",
  howpublished = "World Wide Web site.",
  year =         "2001",
  bibdate =      "Mon May 06 09:06:04 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.jddarcy.org/Borneo",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; IEEE 754; Java",
}

@Misc{Darcy:2001:DLS,
  author =       "Joseph D. Darcy",
  title =        "Designing Language Support for {IEEE 754}",
  howpublished = "IEEE 754 Revision Committee meeting, October 18,
                 2001.",
  year =         "2001",
  bibdate =      "Mon May 06 09:16:52 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "50 slides.",
  URL =          "http://grouper.ieee.org/groups/754/meeting-materials/2001-10-18-langdesign.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Darcy:2001:WEU,
  author =       "Joseph D. Darcy",
  title =        "What Everybody Using the {Java\TM} Programming
                 Language Should Know About Floating-Point Arithmetic",
  crossref =     "Anonymous:2001:JJ",
  pages =        "??--??",
  year =         "2001",
  bibdate =      "Mon May 06 09:14:05 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "51 slides.",
  URL =          "http://java.sun.com/people/darcy/JavaOne/2001/1789darcy.pdf",
  acknowledgement = ack-nhfb,
}

@TechReport{Daumas:2001:CVP,
  author =       "Marc Daumas and Claire Moreau-Finot and Laurent
                 Thery",
  title =        "Computer validated proofs of a toolset for adaptable
                 arithmetic",
  type =         "Research report",
  number =       "4095",
  institution =  "Institut National de Recherche en Informatique et en
                 Automatique",
  address =      "Le Chesnay, France",
  year =         "2001",
  bibdate =      "Wed Nov 24 10:50:24 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Daumas:2001:GLF,
  author =       "Marc Daumas and Laurence Rideau and Laurent
                 Th{\'e}ry",
  title =        "A Generic Library for Floating-Point Numbers and Its
                 Application to Exact Computing",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2152",
  pages =        "169--184",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  MRclass =      "68T15 (65G50)",
  MRnumber =     "MR1907603",
  bibdate =      "Sat Feb 2 13:05:56 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2152.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2152/21520169.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2152/21520169.pdf;
                 https://hal.archives-ouvertes.fr/hal-00157285",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InProceedings{deDinechin:2001:SIM,
  author =       "Florent de Dinechin and Arnaud Tisserand",
  title =        "Some Improvements on Multipartite Table Methods",
  crossref =     "Burgess:2001:ISC",
  pages =        "128--135",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Dinechin.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}

@TechReport{Defour:2001:CREa,
  author =       "David Defour and Florent de Dinechin and Jean-Michel
                 Muller",
  title =        "Correctly rounded exponential function in double
                 precision arithmetic",
  type =         "Rapport de recherche",
  number =       "RR-4231",
  institution =  "INRIA Rhone-Alpes",
  address =      "ZIRST, 655 Avenue de l'Europe, Montbonnot, 38334 Saint
                 Ismier cedex, France",
  month =        jul,
  year =         "2001",
  bibdate =      "Sat Jun 25 11:10:46 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4231.pdf;
                 ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-4231.ps.gz;
                 http://www.inria.fr/rrrt/rr-4231.html",
  abstract =     "We present an algorithm for implementing correctly
                 rounded exponentials in double-precision floating point
                 arithmetic. This algorithm is based on floating-point
                 operations in the widespread IEEE-754 standard, and is
                 therefore more efficient than those using
                 multiprecision arithmetic, while being fully portable.
                 It requires a table of reasonable size and IEEE-754
                 double precision multiplications and additions. In a
                 preliminary implementation, the overhead due to correct
                 rounding is a 2.3 times slowdown when compared to the
                 standard library function.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Defour:2001:CREb,
  author =       "David Defour and Florida de Dinechin and Jean-Michel
                 Muller",
  title =        "Correctly rounded exponential function in double
                 precision arithmetic",
  crossref =     "Luk:2001:ASP",
  pages =        "156--167",
  year =         "2001",
  bibdate =      "Fri Jun 24 14:43:41 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://bookstore.spie.org/index.cfm?fuseaction=DetailPaper&ProductId=448644&coden=PSISDG",
  abstract =     "We present an algorithm for implementing correctly
                 rounded exponentials in double-precision floating point
                 arithmetic. This algorithm is based on floating-point
                 operations in the widespread EEE-754 standard, and is
                 therefore more efficient than those using
                 multiprecision arithmetic, while being fully portable.
                 It requires a table of reasonable size and IEEE-754
                 double precision multiplications and additions. In a
                 preliminary implementation, the overhead due to correct
                 rounding is a 6 times slowdown when compared to the
                 standard library function.",
  acknowledgement = ack-nhfb,
}

@TechReport{Defour:2001:NRRa,
  author =       "David Defour and Peter Kornerup and Jean-Michel Muller
                 and Nathalie Revol",
  title =        "A new range reduction algorithm",
  type =         "Research Report",
  number =       "{LIP RR 2001-33, INRIA RR-4267}",
  institution =  "LIP, {\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "Lyon, France",
  pages =        "13",
  year =         "2001",
  bibdate =      "Sat Jun 25 08:52:06 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.ens-lyon.fr/pub/LIP/Rapports/RR/RR2001/RR2001-33.ps.Z;
                 ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4267.pdf;
                 ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-4267.ps.gz;
                 http://www.inria.fr/rrrt/rr-4267.html",
  abstract =     "Range reduction is a key point for getting accurate
                 elementary function routines. We introduce a new
                 algorithm that is fast for input arguments belonging to
                 the most common domains, yet accurate over the full
                 double precision range.",
  acknowledgement = ack-nhfb,
  keywords =     "range reduction",
}

@InProceedings{Defour:2001:NRRb,
  author =       "David Defour and Peter Kornerup and Jean-Michel Muller
                 and Nathalie Revol",
  title =        "A new range reduction algorithm",
  crossref =     "Matthews:2001:CRT",
  pages =        "??--??",
  year =         "2001",
  bibdate =      "Fri Jun 24 12:12:10 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.imada.sdu.dk/~kornerup/papers/RR2.pdf",
  abstract =     "Range reduction is a key point for getting accurate
                 elementary function routines. We introduce a new
                 algorithm that is fast for input arguments belonging to
                 the most common domains, yet accurate over the full
                 double precision range.",
  acknowledgement = ack-nhfb,
  keywords =     "range reduction",
  pagecount =    "11",
}

@InProceedings{DelRe:2001:IDF,
  author =       "A. {Del Re} and A. Nannarelli and M. Re",
  booktitle =    "Conference Record of the Thirty-Fifth Asilomar
                 Conference on Signals, Systems and Computers, 2001",
  title =        "Implementation of digital filters in carry-save
                 residue number system",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1309--1313",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ACSSC.2001.987702",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "In this work, we present the implementation of a
                 finite impulse response (FIR) filter in the residue
                 number system (RNS), in which we use a carry-save
                 scheme in the binary representation of the residues to
                 speed-up modular additions. We compare the \ldots{}",
}

@Unpublished{Demmel:2001:CAF,
  author =       "J. Demmel and Ben Diament and W. Kahan and Plamen Koev
                 and Ming Gu and Stan Eisenstat and Ivan Slapni{\v{c}}ar
                 and Kresimir Veseli{\'c} and Zlatko Drma{\v{c}}",
  title =        "The Complexity of Accurate Floating Point Computation
                 and Symbolic Computing, or, Can we do Numerical Linear
                 Algebra In Polynomial Time?",
  pages =        "31",
  year =         "2001",
  bibdate =      "Mon Apr 25 06:47:21 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Lecture slides",
  URL =          "http://www.cs.berkeley.edu/~demmel/ISSAC2001_2.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Dhong:2001:ACR,
  author =       "Sang Hoo Dhong and Harm Peter Hofstee and Christian
                 Jacobi and Silvia Melitta Mueller and Hwa-Joon Oh",
  title =        "Apparatus for controlling rounding modes in single
                 instruction multiple data ({SIMD}) floating-point
                 units",
  howpublished = "US Patent 7447725",
  day =          "04",
  month =        dec,
  year =         "2001",
  bibdate =      "Tue Dec 23 15:06:47 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/7444367/fulltext.html",
  abstract =     "An apparatus for controlling rounding modes in a
                 single instruction multiple data (SIMD) floating-point
                 unit is disclosed. The SIMD floating-point unit
                 includes a floating-point status-and-control register
                 (FPSCR) having a first rounding mode bit field and a
                 second rounding mode bit field. The SIMD floating-point
                 unit also includes means for generating a first slice
                 and a second slice. During a floating-point operation,
                 the SIMD floating-point unit concurrently performs a
                 first rounding operation on the first slice and a
                 second rounding operation on the second slice according
                 to a bit in the first rounding mode bit field and a bit
                 in the second rounding mode bit field within the FPSCR,
                 respectively.",
  acknowledgement = ack-nhfb,
}

@Misc{Dickinson:2001:IRB,
  author =       "Patrick Dickinson",
  title =        "Instant Replay: Building a Game Engine with
                 Reproducible Behavior",
  howpublished = "Web site",
  day =          "13",
  month =        jul,
  year =         "2001",
  bibdate =      "Mon Dec 04 07:04:15 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.gamedeveloper.com/design/instant-replay-building-a-game-engine-with-reproducible-behavior#close-modal",
  acknowledgement = ack-nhfb,
  remark =       "Comments on problems of rerunning games on different
                 platforms where floating-point issues produce differing
                 outcomes, See also \cite{Fiedler:2010:GGF}.",
}

@InProceedings{Dimitrov:2001:UMD,
  author =       "V. S. Dimitrov and J. Eskritt and L. Imbert and G. A.
                 Jullien and W. C. Miller",
  title =        "The Use of the Multi-Dimensional Logarithmic Number
                 System in {DSP} Applications",
  crossref =     "Burgess:2001:ISC",
  pages =        "247--256",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Dimitrov.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}

@Article{Drmac:2001:AQS,
  author =       "Zlatko Drmac and Elizabeth R. Jessup",
  title =        "On Accurate Quotient Singular Value Computation in
                 Floating-Point Arithmetic",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "22",
  number =       "3",
  pages =        "853--873",
  month =        jul,
  year =         "2001",
  CODEN =        "SJMAEL",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Wed Oct 23 08:36:30 MDT 2002",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/22/3;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/31054",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@InProceedings{Fernandez:2001:IOD,
  author =       "P. G. Fernandez and J. Ramirez and A. Garcia and L.
                 Parrilla and A. Lloris",
  booktitle =    "The 8th {IEEE} International Conference on
                 Electronics, Circuits and Systems, {ICECS 2001}",
  title =        "Implementation of the one dimensional discrete cosine
                 transform using the residue number system",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "433--436",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICECS.2001.957772",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper shows the implementation of the one
                 dimensional discrete cosine transform (1D-DCT) based on
                 the residue number system (RNS). The 1D-DCT has been
                 derived by,the application of a previously developed
                 scaled fast cosine transform (FCT) \ldots{}",
}

@PhdThesis{Finot-Moreau:2001:PAU,
  author =       "Claire Finot-Moreau",
  title =        "Preuves et algorithmes utilisant l'arithm{\'e}tique
                 flottante normalis{\'e}e {IEEE}",
  type =         "{Ph.D.} thesis",
  school =       "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "Lyon, France",
  month =        jul,
  year =         "2001",
  bibdate =      "Sat Apr 01 08:46:03 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{Flynn:2001:ACA,
  author =       "Michael J. Flynn and Stuart F. Oberman",
  title =        "Advanced computer arithmetic design",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xv + 325",
  year =         "2001",
  ISBN =         "0-471-41209-0",
  ISBN-13 =      "978-0-471-41209-0",
  LCCN =         "TK7895.A65 F59 2001",
  bibdate =      "Tue May 07 05:20:32 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "From the preface: ``The book is not written as a
                 textbook, but rather, it is written with computer
                 designers and researchers in mind. Therefore its focus
                 is on {\em design}, not on other aspects of computer
                 arithmetic, such as number systems, representation, or
                 precision.'' Chapter 12, Rational Arithmetic, treats
                 the application of continued fractions to the
                 computation of elementary functions.",
  tableofcontents = "Preface \\
                 Acknowledgments \\
                 Notation \\
                 1. Integer Addition \\
                 2. Floating-Point Addition \\
                 3. Multiplication with Partially Redundant Multiples
                 \\
                 4. Multiplier Topologies \\
                 5. Technology Scaling Effects on Multipliers \\
                 6. Design Issues in Division \\
                 7. Minimizing the Complexity of SRT Tables \\
                 8. Very High-Radix Division \\
                 9. Using a Multiplier for Function Approximation \\
                 10. FUPA [Floating-point unit-cost performance analysis
                 metric] \\
                 11. High-Speed Clocking Using Wave Pipelining \\
                 12. Rational Arithmetic \\
                 Bibliography \\
                 Index",
}

@Article{Galan-Simon:2001:MLD,
  author =       "F. Javier Gal{\'a}n-Sim{\'o}n and Edgar
                 Mart{\'\i}nez-Moro and Juan G. Tena-Ayuso",
  title =        "Majority-Logic-Decodable Cyclic Arithmetic-Modular
                 {AN}-Codes in $1$, $2$, and {$L$} Steps",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2260",
  pages =        "128--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:07:45 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2260.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2260/22600128.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2260/22600128.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Gallant:2001:FPM,
  author =       "Robert P. Gallant and Robert J. Lambert and Scott A.
                 Vanstone",
  title =        "Faster Point Multiplication on Elliptic Curves with
                 Efficient Endomorphisms",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2139",
  pages =        "190--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:05:41 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2139.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2139/21390190.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2139/21390190.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Gelbukh:2001:ZHL,
  author =       "Alexander Gelbukh and Grigori Sidorov",
  title =        "{Zipf} and {Heaps Laws}' Coefficients Depend on
                 Language",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2004",
  pages =        "332--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:03:22 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2004.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2004/20040332.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2004/20040332.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Gil:2001:SAT,
  author =       "Joseph (Yossi) Gil",
  title =        "Subtyping arithmetical types",
  journal =      j-SIGPLAN,
  volume =       "36",
  number =       "3",
  pages =        "276--289",
  month =        mar,
  year =         "2001",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sun Dec 14 09:18:23 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/proceedings/series/popl/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org/pubs/articles/proceedings/plan/360204/p276-gil/p276-gil.pdf;
                 http://www.acm.org/pubs/citations/proceedings/plan/360204/p276-gil/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}

@InProceedings{Gok:2001:EIM,
  author =       "M. Gok and M. J. Schulte and P. I. Balzola",
  title =        "Efficient Integer Multiplication Overflow Detection
                 Circuits",
  crossref =     "Matthews:2001:CRT",
  pages =        "1661--1665",
  year =         "2001",
  bibdate =      "Sun Mar 04 11:45:08 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2001-07.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Goubault:2001:SAP,
  author =       "Eric Goubault",
  title =        "Static Analyses of the Precision of Floating-Point
                 Operations",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2126",
  pages =        "234--259",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  MRnumber =     "MR2051233",
  bibdate =      "Sat Feb 2 13:05:28 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2126.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2126/21260234.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2126/21260234.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Gowland:2001:SEA,
  author =       "Paul Gowland and David Lester",
  title =        "A Survey of Exact Arithmetic Implementations",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2064",
  pages =        "30--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:04:19 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2064.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2064/20640030.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2064/20640030.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Grossschadl:2001:BSU,
  author =       "J. Gro{\ss}sch{\"a}dl",
  title =        "A Bit-Serial Unified Multiplier Architecture for
                 Finite Fields {GF$ (p) $} and {GF$ (2^m) $}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2162",
  pages =        "202--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:06:06 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2162.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620202.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2162/21620202.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Groza:2001:HRF,
  author =       "V. Z. Groza",
  title =        "High-resolution floating-point {ADC}",
  journal =      j-IEEE-TRANS-INSTRUM-MEAS,
  volume =       "50",
  number =       "6",
  pages =        "1822--1829",
  month =        dec,
  year =         "2001",
  CODEN =        "IEIMAO",
  ISSN =         "0018-9456 (print), 1557-9662 (electronic)",
  ISSN-L =       "0018-9456",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Instrumentation and Measurement",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=19",
  summary =      "Floating-point analog-to-digital converters (FP-ADC)
                 are used for acquiring signals within a high dynamic
                 range. The quantization range of FP-ADCs is several
                 orders of magnitude higher than that of a fixed-point
                 analog-to-digital converter (ADC). \ldots{}",
}

@Article{Gunther:2001:SAK,
  author =       "Christian G{\"u}nther and Tanja Lange and Andreas
                 Stein",
  title =        "Speeding up the Arithmetic on {Koblitz} Curves of
                 Genus Two",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2012",
  pages =        "106--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:03:30 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2012.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2012/20120106.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2012/20120106.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InProceedings{Hasan:2001:ECM,
  author =       "M. A. Hasan",
  title =        "Efficient Computation of Multiplicative Inverses for
                 Cryptographic Applications",
  crossref =     "Burgess:2001:ISC",
  pages =        "66--72",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Hasan.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}

@Article{Hayes:2001:TB,
  author =       "Brian Hayes",
  title =        "Third Base",
  journal =      j-AM-SCI,
  volume =       "89",
  number =       "6",
  pages =        "490--495",
  month =        nov # "\slash " # dec,
  year =         "2001",
  CODEN =        "AMSCAC",
  ISSN =         "0003-0996 (print), 1545-2786 (electronic)",
  ISSN-L =       "0003-0996",
  bibdate =      "Tue Nov 08 08:06:17 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.americanscientist.org/content/AMSCI/AMSCI/ArticleAltFormat/20035214317_146.pdf",
  abstract =     "People count by tens and machines count by twos that
                 pretty much sums up the way we do arithmetic on this
                 planet. But there are countless other ways to count.
                 Here I want to offer three cheers for base 3, the
                 ternary system. The numerals in this sequence beginning
                 0, 1, 2, 10, 11, 12, 20, 21, 22, 100, 101 are not as
                 widely known or widely used as their decimal and binary
                 cousins, but they have charms all their own. They are
                 the Goldilocks choice among numbering systems: When
                 base 2 is too small and base 10 is too big, base 3 is
                 just right.",
  acknowledgement = ack-nhfb,
  fjournal =     "American Scientist",
  journal-URL =  "http://www.americanscientist.org/issues/past.aspx",
  keywords =     "ternary arithmetic",
}

@Article{He:2001:UAA,
  author =       "Yun He and Chris H. Q. Ding",
  title =        "Using Accurate Arithmetics to Improve Numerical
                 Reproducibility and Stability in Parallel
                 Applications",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "18",
  number =       "3",
  pages =        "259--277",
  month =        mar,
  year =         "2001",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1023/A:1008153532043",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Wed Jul 6 12:13:17 MDT 2005",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0920-8542&volume=18&issue=3;
                 http://www.wkap.nl/issuetoc.htm/0920-8542+18+3+2001;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0920-8542&volume=18&issue=3&spage=259;
                 http://www.wkap.nl/oasis.htm/323815",
  acknowledgement = ack-nhfb,
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
}

@Article{Hesse:2001:DUT,
  author =       "William Hesse",
  title =        "Division Is in Uniform {TC$^0$}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2076",
  pages =        "104--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Fri Feb 1 09:17:25 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2076.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2076/20760104.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2076/20760104.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InProceedings{Hida:2001:AQD,
  author =       "Yozo Hida and Xiaoye S. Li and David H. Bailey",
  title =        "Algorithms for Quad-Double Precision Floating Point
                 Arithmetic",
  crossref =     "Burgess:2001:ISC",
  pages =        "155--162",
  year =         "2001",
  DOI =          "https://doi.org/10.1109/ARITH.2001.930115",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Hida.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}

@TechReport{Hlavacs:2001:IAN,
  author =       "H. Hlavacs and C. W. Ueberhuber",
  title =        "Improving the Accuracy of Numerical Integration",
  type =         "Technical report",
  number =       "TR 2001-06",
  institution =  "Aurora: Advanced Models, Applications and Software
                 Systems for High Performance Computing",
  address =      "European Centre for Parallel Computing at Vienna
                 Nordbergstra{\ss}e 15/C/3, A-1090 Vienna, Austria",
  pages =        "i + 14",
  year =         "2001",
  bibdate =      "Tue Nov 22 06:22:21 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.vcpc.univie.ac.at/projects/aurora/reports/auroratr2001-06.ps.gz;
                 http://citeseer.ist.psu.edu/hlavacs01improving.html",
  abstract =     "In this report, a method for reducing the effect of
                 round-off errors occurring in one-dimensional
                 integration is presented. The new method, applicable to
                 uneven integrand functions, is based on an extended
                 version of Kahan--Babuska summation.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}

@Book{Hsu:2001:CAS,
  author =       "John Y. Hsu",
  title =        "Computer Architecture: Software Aspects, Coding,
                 Hardware",
  publisher =    pub-CRC,
  address =      pub-CRC:adr,
  pages =        "427",
  year =         "2001",
  ISBN =         "0-8493-1026-1, 1-351-83604-8, 1-4200-4110-X (e-book)",
  ISBN-13 =      "978-0-8493-1026-3, 978-1-351-83604-3,
                 978-1-4200-4110-1 (e-book)",
  LCCN =         "A76.9.A73 H758 2001",
  bibdate =      "Fri Jan 19 15:47:59 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/java2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/microchip.bib;
                 https://www.math.utah.edu/pub/tex/bib/virtual-machines.bib;
                 https://www.math.utah.edu/pub/tex/bib/visual-instruction-set.bib",
  price =        "US\$89.95, UK\pounds 59.99",
  abstract =     "With the new developments in computer architecture,
                 fairly recent publications can quickly become outdated.
                 Computer Architecture: Software Aspects, Coding, and
                 Hardware takes a modern approach. This comprehensive,
                 practical text provides that critical understanding of
                 a central processor by clearly detailing fundamentals,
                 and cutting edge design features. With its balanced
                 software/hardware perspective and its description of
                 Pentium processors, the book allows readers to acquire
                 practical PC software experience. The text presents a
                 foundation-level set of ideas, design concepts, and
                 applications that fully meet the requirements of
                 computer organization and architecture courses. The
                 book features a ``bottom up'' computer design approach,
                 based upon the author's thirty years experience in both
                 academe and industry. By combining computer engineering
                 with electrical engineering, the author describes how
                 logic circuits are designed in a CPU. The extensive
                 coverage of a microprogrammed CPU and new processor
                 design features gives the insight of current computer
                 development. Computer Architecture: Software Aspects,
                 Coding, and Hardware presents a comprehensive review of
                 the subject, from beginner to advanced levels. Topics
                 include: * Two's complement numbers * Integer overflow
                 * Exponent overflow and underflow * Looping *
                 Addressing modes * Indexing * Subroutine linking * I/O
                 structures * Memory mapped I/O * Cycle stealing *
                 Interrupts * Multitasking * Microprogrammed CPU *
                 Multiplication tree * Instruction queue * Multimedia
                 instructions * Instruction cache * Virtual memory *
                 Data cache * Alpha chip * Interprocessor communications
                 * Branch prediction * Speculative loading * Register
                 stack * JAVA virtual machine * Stack machine
                 principles.",
  acknowledgement = ack-nhfb,
  keywords =     "Compaq/DEC Alpha; floating-point arithmetic; Intel
                 x86; Java Virtual Machine; multimedia instructions;
                 Pentium",
  libnote =      "Not yet in my library.",
  tableofcontents = "Number Systems \\
                 Basic Computer Principles \\
                 Assembly Language Principles \\
                 Computer Architecture--General Features \\
                 Microprogrammed CPU Design \\
                 Superscalar Machine Principles \\
                 Vector and Multiple-Processor Machines \\
                 Processor Design Case Studies \\
                 Stack Machine Principles",
}

@Article{Hur:2001:GRO,
  author =       "Namhyun Hur and James H. Davenport",
  title =        "A Generic Root Operation for Exact Real Arithmetic",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2064",
  pages =        "82--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:04:19 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2064.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2064/20640082.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2064/20640082.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Book{ISO:2001:IIIc,
  author =       "{ISO}",
  title =        "{ISO\slash IEC 10967-2}: {Information} technology ---
                 {Language} independent arithmetic --- {Part} 2:
                 {Elementary} numerical functions",
  publisher =    pub-ISO,
  address =      pub-ISO:adr,
  pages =        "x + 177",
  day =          "15",
  month =        aug,
  year =         "2001",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sun Mar 15 11:09:44 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://standards.iso.org/ittf/PubliclyAvailableStandards/c024427_ISO_IEC_10967-2_2001(E).zip;
                 http://www.iso.ch/cate/d24427.html",
  acknowledgement = ack-nhfb,
}

@InProceedings{Jacobi:2001:FVT,
  author =       "Christian Jacobi",
  title =        "Formal verification of a theory of {IEEE} rounding",
  crossref =     "Boulton:2001:TPH",
  pages =        "239--254",
  year =         "2001",
  bibdate =      "Wed Nov 24 11:55:24 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.informatics.ed.ac.uk/publications/online/0046/b239.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Jamil:2001:CBN,
  author =       "T. Jamil",
  title =        "The complex binary number system",
  journal =      j-IEEE-POT,
  volume =       "20",
  number =       "5",
  pages =        "39--41",
  month =        dec,
  year =         "2001",
  CODEN =        "IEPTDF",
  DOI =          "https://doi.org/10.1109/45.983342",
  ISSN =         "0278-6648 (print), 1558-1772 (electronic)",
  ISSN-L =       "0278-6648",
  bibdate =      "Sat Dec 04 10:43:52 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Conversion algorithms and arithmetic procedures for a
                 $ ( - 1 + j) $-base binary number allow a given complex
                 number to be represented as one unit. This should
                 simplify the operations involving complex numbers in
                 today's microprocessors. With the division process
                 secure, we can implement the usual algorithms for
                 calculating functions and processes such as logarithms,
                 exponentials and trigonometric functions Currently,
                 work is underway to write Java applets for the
                 algorithms. We are planning to design an arithmetic
                 unit based on the new binary system which will then be
                 implemented using field programmable gate arrays",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Potentials",
}

@InProceedings{Jeong:2001:OIO,
  author =       "Cheol-Ho Jeong and Woo-Chan Park and Tack-Don Han and
                 Sang-Woo Kim and Moon-Key Lee",
  title =        "In-Order Issue Out-of-Order Execution Floating-Point
                 Coprocessor for {CalmRISC32}",
  crossref =     "Burgess:2001:ISC",
  pages =        "195--202",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Jeong.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}

@TechReport{Kahan:2001:NSF,
  author =       "W. Kahan",
  title =        "Names for Standardized Floating-Point Formats",
  institution =  "Mathematics Department and Electrical Engineering and
                 Computer Science Department, University of California,
                 Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "4",
  day =          "17",
  month =        may,
  year =         "2001",
  bibdate =      "Fri May 03 12:23:25 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/Names.pdf",
  acknowledgement = ack-nhfb,
}

@Unpublished{Kahan:2001:PDA,
  author =       "William Kahan",
  title =        "Pseudo-Division Algorithms for Floating-Point
                 Logarithms and Exponentials",
  pages =        "8",
  day =          "20",
  month =        may,
  year =         "2001",
  bibdate =      "Sat Aug 23 06:17:04 2025",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeemilestones.ethw.org/w/images/3/30/Wk_pseudo_division_log_exp_may01.pdf",
  abstract =     "Among the CORDIC-like algorithms for computing
                 elementary transcendental functions like log and exp,
                 certain pseudo-division algorithms are peculiarly well
                 suited to implementation in microcode or in conjunction
                 with software-implemented floating-point arithmetic.
                 These algorithms need tables of comparatively modest
                 size; they are almost as fast as the fastest
                 digit-by-digit algorithms known; and they can achieve
                 accuracy to within a unit or two in the last sig. bit
                 carried. Algorithms like these are used by the Intel
                 8087 family of numeric coprocessors. This document is
                 for people who wish to imitate or surpass them.",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2001:SFP,
  author =       "W. Kahan",
  title =        "{SRTEST}: a {Fortran} program to test any {SRT}
                 divider's logic for quotient-digit selection",
  howpublished = "World-Wide Web document",
  day =          "6",
  month =        aug,
  year =         "2001",
  bibdate =      "Mon Apr 25 17:47:53 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/srtest/",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point testing",
}

@TechReport{Kahan:2001:WVT,
  author =       "W. Kahan",
  title =        "What has the Volume of a Tetrahedron to do with
                 Computer Programming Languages?",
  institution =  "Department of Mathematics and Department of Electrical
                 Engineering and Computer Science, University of
                 California, Berkeley",
  address =      "Berkeley, CA, USA",
  day =          "20",
  month =        apr,
  year =         "2001",
  bibdate =      "Fri May 03 13:36:17 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/VtetLang.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Kaivola:2001:PEL,
  author =       "Roope Kaivola and Katherine Kohatsu",
  title =        "Proof Engineering in the Large: Formal Verification of
                 {Pentium\reg4} Floating-Point Divider",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2144",
  pages =        "196--211",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:05:47 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2144.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2144/21440196.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2144/21440196.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Kao:2001:MRE,
  author =       "Ming-Yang Kao and Jie Wang",
  title =        "Minimizing roundoff errors of prefix sums via dynamic
                 construction of {Huffman} trees",
  journal =      j-THEOR-COMP-SCI,
  volume =       "262",
  number =       "1--2",
  pages =        "101--115",
  day =          "6",
  month =        jul,
  year =         "2001",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Jul 25 18:49:25 MDT 2001",
  bibsource =    "http://www.elsevier.com/locate/issn/03043975;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.elsevier.nl/gej-ng/10/41/16/204/21/26/abstract.html;
                 http://www.elsevier.nl/gej-ng/10/41/16/204/21/26/article.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
  keywords =     "accurate floating-point summation",
}

@Article{Khachatrian:2001:FMI,
  author =       "Gurgen H. Khachatrian and Melsik K. Kuregian and Karen
                 R. Ispiryan and James L. Massey",
  title =        "Fast Multiplication of Integers for Public-Key
                 Applications",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2259",
  pages =        "245--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:07:44 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2259.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2259/22590245.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2259/22590245.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Kim:2001:AEE,
  author =       "Hyun-Sung Kim and Kee-Young Yoo",
  title =        "Area Efficient Exponentiation Using Modular
                 Multiplier\slash Squarer in {GF$ (2^m) $}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2108",
  pages =        "262--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:05:08 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2108.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2108/21080262.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2108/21080262.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{King:2001:IIE,
  author =       "Brian King",
  title =        "An Improved Implementation of Elliptic Curves over
                 {GF} (2) when Using Projective Point Arithmetic",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2259",
  pages =        "134--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:07:44 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2259.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2259/22590134.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2259/22590134.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Kistermann:2001:CHU,
  author =       "Friedrich W. Kistermann",
  title =        "Calculators: How to Use the {Schickard} Calculator",
  journal =      j-IEEE-ANN-HIST-COMPUT,
  volume =       "23",
  number =       "1",
  pages =        "80--85",
  month =        jan # "\slash " # mar,
  year =         "2001",
  CODEN =        "IAHCEX",
  DOI =          "https://doi.org/10.1109/85.929917",
  ISSN =         "1058-6180 (print), 1934-1547 (electronic)",
  ISSN-L =       "1058-6180",
  bibdate =      "Thu Jul 12 06:23:02 MDT 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeeannhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/scicontext.bib",
  URL =          "http://dlib.computer.org/an/books/an2001/pdf/a1080.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Ann. Hist. Comput.",
  fjournal =     "IEEE Annals of the History of Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85",
}

@InProceedings{Knowles:2001:FA,
  author =       "Simon Knowles",
  title =        "A Family of Adders",
  crossref =     "Burgess:2001:ISC",
  pages =        "277--284",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Knowles.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}

@InProceedings{Koc-Sahan:2001:STA,
  author =       "N. Koc-Sahan and J. Schlessman and M. J. Schulte",
  title =        "Symmetric Table Addition Methods for Neural Network
                 Approximations",
  crossref =     "Luk:2001:ASP",
  pages =        "126--133",
  year =         "2001",
  bibdate =      "Sun Mar 04 11:40:20 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2001-03.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Kosaraju:2001:MAM,
  author =       "S. Rao Kosaraju",
  title =        "Mesh Algorithms for Multiplication and Division",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2228",
  pages =        "17--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:07:14 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2228.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2228/22280017.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2228/22280017.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Koy:2001:SLRb,
  author =       "Henrik Koy and Claus Peter Schnorr",
  title =        "Segment {LLL}-Reduction with Floating Point
                 Orthogonalization",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2146",
  pages =        "81--96",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  MRclass =      "11H55 (11Y16)",
  MRnumber =     "MR1903889 (2003f:11096)",
  bibdate =      "Sat Feb 2 13:05:49 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2146.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2146/21460081.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2146/21460081.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Kramer:2001:AFE,
  author =       "Walter Kr{\"a}mer and Armin Bantle",
  title =        "Automatic forward error analysis for floating point
                 algorithms",
  journal =      j-RELIABLE-COMPUTING,
  volume =       "7",
  number =       "4",
  pages =        "321--340",
  year =         "2001",
  CODEN =        "RCOMF8",
  ISSN =         "1385-3139 (print), 1573-1340 (electronic)",
  ISSN-L =       "1385-3139",
  MRclass =      "65G40 (65G50)",
  MRnumber =     "MR1843023 (2002d:65046)",
  bibdate =      "Thu Nov 8 19:16:14 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1952--2014 (WK)",
  fjournal =     "Reliable Computing. An International Journal Devoted
                 to Reliable Mathematical Computations Based on Finite
                 Representations and Guaranteed Accuracy",
  journal-URL =  "http://link.springer.com/journal/11155",
}

@Article{Kreinovich:2001:INB,
  author =       "Vladik Kreinovich",
  title =        "{Itanium}'s New Basic Operation of Fused Multiply-Add:
                 Theoretical Explanation and Theoretical Challenge",
  journal =      j-SIGACT,
  volume =       "32",
  number =       "1",
  pages =        "115--117",
  year =         "2001",
  CODEN =        "SIGNDM",
  ISSN =         "0163-5700 (print), 1943-5827 (electronic)",
  ISSN-L =       "0163-5700",
  bibdate =      "Sat Dec 06 15:20:39 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.utep.edu/vladik/2000/tr00-42.pdf;
                 http://www.cs.utep.edu/vladik/2000/tr00-42.ps.gz",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGACT News",
  issue =        "118",
  journal-URL =  "http://dl.acm.org/citation.cfm?id=J697",
}

@InProceedings{Krishnan:2001:PEM,
  author =       "Shankar Krishnan and Mark Foskey and Tim Culver and
                 John Keyser and Dinesh Manocha",
  title =        "{PRECISE}: efficient multiprecision evaluation of
                 algebraic roots and predicates for reliable geometric
                 computation",
  crossref =     "ACM:2001:PSA",
  pages =        "274--283",
  year =         "2001",
  DOI =          "https://doi.org/10.1145/378583.378693",
  bibdate =      "Fri Jan 06 07:53:04 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Many geometric problems like generalized Voronoi
                 diagrams, medial axis computations and boundary
                 evaluation involve computation and manipulation of
                 non-linear algebraic primitives like curves and
                 surfaces. The algorithms designed for these problems
                 make decisions based on signs of geometric predicates
                 or on the roots of polynomials characterizing the
                 problem. The reliability of the algorithm depends on
                 the accurate evaluation of these signs and roots. In
                 this paper, we present a {\em naive precision-driven
                 computational model\/} to perform these computations
                 reliably and demonstrate its effectiveness on a certain
                 class of problems like sign of determinants with
                 rational entries, boundary evaluation and curve
                 arrangements. We also present a novel algorithm to
                 compute all the roots of a univariate polynomial to any
                 desired accuracy. The computational model along with
                 the underlying number representation, precision-driven
                 arithmetic and all the algorithms are implemented as
                 part of a stand-alone software library, PRECISE.",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; interval arithmetic;
                 multiple-precision arithmetic; PRECISE",
}

@InProceedings{Lang:2001:BRZ,
  author =       "Tom{\'a}s Lang and Jean-Michel Muller",
  title =        "Bounds on Runs of Zeros and Ones for Algebraic
                 Functions",
  crossref =     "Burgess:2001:ISC",
  pages =        "13--22",
  year =         "2001",
  bibdate =      "Fri May 3 13:52:01 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Lang.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}

@InProceedings{Lang:2001:CRR,
  author =       "Tom{\'a}s Lang and Elisardo Antelo",
  title =        "Correctly Rounded Reciprocal Square-Root by Digit
                 Recurrence and Radix-$4$ Implementation",
  crossref =     "Burgess:2001:ISC",
  pages =        "83--93",
  year =         "2001",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Lang_Antelo.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15; correct rounding; floating-point
                 arithmetic",
  summary =      "We present a reciprocal square-root algorithm by digit
                 recurrence and selection by a staircase function, and
                 the radix-$4$ implementation. As similar algorithms for
                 division and square-root, the results are obtained
                 correctly rounded in a \ldots{}",
}

@Article{Langlois:2001:ALC,
  author =       "Philippe Langlois",
  title =        "Automatic Linear Correction of Rounding Errors",
  journal =      j-BIT-NUM-MATH,
  volume =       "41",
  number =       "3",
  pages =        "515--539",
  month =        jun,
  year =         "2001",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1023/A:1021919329342",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 15:06:04 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=41&issue=3;
                 http://www.mai.liu.se/BIT/contents/bit41.html;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=41&issue=3&spage=515",
  abstract =     "A new automatic method to correct the first-order
                 effect of floating point rounding errors on the result
                 of a numerical algorithm is presented. A correcting
                 term and a confidence threshold are computed using
                 algorithmic differentiation, computation of elementary
                 rounding error and running error analysis. Algorithms
                 for which the accuracy of the result is not affected by
                 higher order terms are identified. The correction is
                 applied to the final result or to sensitive
                 intermediate results to improve the accuracy of the
                 computed result and\slash or the stability of the
                 algorithm.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "automatic error analysis; correct rounding;
                 floating-point arithmetic; rounding errors",
}

@InProceedings{Laurent:2001:UFV,
  author =       "O. Laurent and P. Michel and V. Wiels",
  title =        "Using formal verification techniques to reduce
                 simulation and test effort",
  crossref =     "Oliveira:2001:FFM",
  pages =        "465--477",
  year =         "2001",
  DOI =          "https://doi.org/10.1007/3-540-45251-6_27",
  bibdate =      "Wed Nov 24 11:58:06 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer.de/link/service/series/0558/papers/2021/20210465.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lee:2001:BPS,
  author =       "Chiou-Yng Lee and Erl-Huei Lu and Jau-Yien Lee",
  title =        "Bit-Parallel Systolic Modular Multipliers for a Class
                 of {$ \mathrm {GF}(2^m) $}",
  crossref =     "Burgess:2001:ISC",
  pages =        "51--58",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Chiou_Yng.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}

@InProceedings{Lee:2001:CAP,
  author =       "Ruby B. Lee",
  title =        "Computer Arithmetic --- a Processor Architect's
                 Perspective",
  crossref =     "Burgess:2001:ISC",
  pages =        "3--4",
  year =         "2001",
  bibdate =      "Fri May 3 13:52:01 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Lee.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}

@Article{Lee:2001:DLS,
  author =       "Won-Ho Lee and Keon-Jik Lee and Kee-Young Yoo",
  title =        "Design of a linear systolic array for computing
                 modular multiplication and squaring in {$ {\bf GF}(2^m)
                 $}",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "42",
  number =       "1--2",
  pages =        "231--240",
  month =        jul,
  year =         "2001",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:49:16 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S089812210100147X",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@InProceedings{Lefevre:2001:WCC,
  author =       "Vincent Lef{\`e}vre and Jean-Michel Muller",
  title =        "Worst Cases for Correct Rounding of the Elementary
                 Functions in Double Precision",
  crossref =     "Burgess:2001:ISC",
  pages =        "111--118",
  year =         "2001",
  DOI =          "https://doi.org/10.1109/ARITH.2001.930110",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Lefevre.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15; correct rounding; floating-point
                 arithmetic",
  summary =      "We give the results of a four-year search for the
                 worst cases for correct rounding of the major
                 elementary functions in double precision. These results
                 allow the design of reasonably fast routines that will
                 compute these functions with correct \ldots{}",
}

@Article{Lemieux:2001:FPM,
  author =       "Joe Lemieux",
  title =        "Fixed-Point Math in {C}",
  journal =      j-EMBED-SYS-PROG,
  volume =       "14",
  number =       "1",
  pages =        "??--??",
  month =        apr,
  year =         "2001",
  CODEN =        "EYPRE4",
  ISSN =         "1040-3272",
  bibdate =      "Fri Nov 28 18:24:03 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.embedded.com/story/OEG20010311S0022",
  abstract =     "Floating-point arithmetic can be expensive if you're
                 using an integer-only processor. But floating-point
                 values can be manipulated as integers, as a less
                 expensive alternative.",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "Embedded Systems Programming",
}

@Article{Leone:2001:NLC,
  author =       "M. Leone",
  title =        "A New Low Complexity Parallel Multiplier for a Class
                 of Finite Fields",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2162",
  pages =        "160--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:06:06 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2162.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620160.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2162/21620160.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InProceedings{Lester:2001:ECF,
  author =       "David Lester",
  title =        "Effective Continued Fractions",
  crossref =     "Burgess:2001:ISC",
  pages =        "163--172",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Lester.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}

@TechReport{Li:2001:LLF,
  author =       "Ren-Cang Li and Peter Markstein and Jon P. Okada and
                 James W. Thomas",
  title =        "The {\tt libm} library and floating-point arithmetic
                 for {HP-UX} on {Itanium}",
  type =         "Technical report",
  institution =  "Hewlett--Packard Company",
  address =      "Palo Alto, CA, USA",
  pages =        "??",
  month =        apr,
  year =         "2001",
  bibdate =      "Fri Jun 24 20:12:09 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://h21007.www2.hp.com/dspp/ddl/ddl_Download_File_TRX/1,1249,942,00.pdf;
                 http://h21007.www2.hp.com/dspp/tech/tech_TechDocumentDetailPage_IDX/1,1701,981,00.html",
  acknowledgement = ack-nhfb,
}

@Article{Li:2001:PMM,
  author =       "Keqin Li and V. Y. Pan",
  title =        "Parallel matrix multiplication on a linear array with
                 a reconfigurable pipelined bus system",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "50",
  number =       "5",
  pages =        "519--525",
  month =        may,
  year =         "2001",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.926164",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:03:10 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=926164",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Lippert:2001:HSM,
  author =       "Th. Lippert and N. Petkov and P. Palazzari and K.
                 Schilling",
  title =        "Hyper-systolic matrix multiplication",
  journal =      j-PARALLEL-COMPUTING,
  volume =       "27",
  number =       "6",
  pages =        "737--759",
  month =        may,
  year =         "2001",
  CODEN =        "PACOEJ",
  ISSN =         "0167-8191 (print), 1872-7336 (electronic)",
  ISSN-L =       "0167-8191",
  bibdate =      "Wed Jul 18 06:31:15 MDT 2001",
  bibsource =    "http://www.elsevier.com/locate/issn/01678191;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.elsevier.nl/gej-ng/10/35/21/47/30/23/abstract.html;
                 http://www.elsevier.nl/gej-ng/10/35/21/47/30/23/article.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Parallel Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01678191",
}

@InProceedings{Madhukumar:2001:EMH,
  author =       "A. S. Madhukumar and F. Chin",
  booktitle =    "12th {IEEE} International Symposium on Personal,
                 Indoor and Mobile Radio Communications, 2001",
  title =        "An efficient method for high-rate data transmission
                 using residue number system based {DS--CDMA}",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "C-1--C-5",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/PIMRC.2001.965450",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper presents an advanced architecture for a
                 residue number system (RNS) based CDMA system for
                 high-rate data transmission by combining RNS
                 representation, PSK/QAM modulation and orthogonal
                 modulation. The proposed system uses a lesser
                 \ldots{}",
}

@InProceedings{Madhukumar:2001:IBE,
  author =       "A. S. Madhukumar and F. Chin",
  booktitle =    "{VTC 2001} Fall. {IEEE} {VTS 54th} Vehicular
                 Technology Conference",
  title =        "Improving bandwidth efficiency for a residue number
                 system based {DS--CDMA} system",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "247--251",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/VTC.2001.956595",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper presents a new method to improve bandwidth
                 efficiency of RNS based CDMA system by combining RNS
                 representation, PSK/QAM modulation and orthogonal
                 modulation. Using the proposed method significantly
                 reduces the computational complexity of \ldots{}",
}

@InProceedings{Madhukumar:2001:IIR,
  author =       "A. S. Madhukumar and F. Chin",
  booktitle =    "{VTC 2001} Fall. {IEEE} {VTS 54th} Vehicular
                 Technology Conference",
  title =        "Incorporating incremental redundancy and link
                 adaptation in communication systems using residue
                 number systems",
  volume =       "4",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2272--2276",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/VTC.2001.957150",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper explores the use of redundant residue
                 number systems to incorporate incremental redundancy in
                 a communication system. By exploiting this property
                 further, one can design an appropriate coding scheme
                 for transmission at the currently \ldots{}",
}

@InProceedings{Matula:2001:ITL,
  author =       "David W. Matula",
  title =        "Improved Table Lookup Algorithms for Postscaled
                 Division",
  crossref =     "Burgess:2001:ISC",
  pages =        "101--110",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Matula.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}

@InProceedings{McFearin:2001:GAH,
  author =       "Lee D. McFearin and David W. Matula",
  title =        "Generation and Analysis of Hard to Round Cases for
                 Binary Floating Point Division",
  crossref =     "Burgess:2001:ISC",
  pages =        "119--127",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_McFearin.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
  summary =      "We investigate two sets of hard to round p$\times$p
                 bit fractions arising from division of a normalized p
                 bit floating point dividend by a normalized p bit
                 floating point divisor. These sets are characterized by
                 the p$\times$p bit fraction's quotient \ldots{}",
}

@Article{Michel:2001:SCF,
  author =       "Claude Michel and Michel Rueher and Yahia Lebbah",
  title =        "Solving Constraints over Floating-Point Numbers",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2239",
  pages =        "524--538",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  MRclass =      "90C08 (65G30 68T20)",
  MRnumber =     "MR1904621",
  bibdate =      "Sat Feb 2 13:07:24 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2239.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2239/22390524.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2239/22390524.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@PhdThesis{Mobley:2001:ICW,
  author =       "Byron Paul Mobley",
  title =        "The ingenuity of common workmen: and the invention of
                 the computer",
  type =         "{Ph.D.} thesis",
  school =       "Department of History, Iowa State University",
  address =      "Ames, IA, USA",
  pages =        "301",
  year =         "2001",
  ISBN =         "0-493-46949-4",
  ISBN-13 =      "978-0-493-46949-2",
  bibdate =      "Thu Nov 18 11:31:13 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Since World War II, state support for scientific
                 research has been assumed crucial to technological and
                 economic progress. Governments accordingly spent
                 tremendous sums to that end. Nothing epitomizes the
                 alleged fruits of that involvement better than the
                 electronic digital computer. The first such computer
                 has been widely reputed to be the ENIAC, financed by
                 the U.S. Army for the war but finished afterwards.
                 Vastly improved computers followed, initially paid for
                 in good share by the Federal Government of the United
                 States, but with the private sector then dominating,
                 both in development and use, and computers are of major
                 significance. Despite the supposed success of
                 public-supported science, evidence is that computers
                 would have evolved much the same without it but at less
                 expense. Indeed, the foundations of modern computer
                 theory and technology were articulated before World War
                 II, both as a tool of applied mathematics and for
                 information processing, and the computer was itself on
                 the cusp of reality. Contrary to popular understanding,
                 the ENIAC actually represented a movement backwards and
                 a dead end.\par

                 Rather, modern computation derived more directly, for
                 example, from the prewar work of John Vincent Atanasoff
                 and Clifford Berry, a physics professor and graduate
                 student, respectively, at Iowa State College (now
                 University) in Ames, Iowa. They built the Atanasoff
                 Berry Computer (ABC), which, although special purpose
                 and inexpensive, heralded the efficient and elegant
                 design of modern computers. Moreover, while no one
                 foresaw commercialization of computers based on the
                 ungainly and costly ENIAC, the commercial possibilities
                 of the ABC were immediately evident, although
                 unrealized due to war. Evidence indicates, furthermore,
                 that the private sector was willing and able to develop
                 computers beyond the ABC and could have done so more
                 effectively than government, to the most sophisticated
                 machines. A full and inclusive history of computers
                 suggests that Adam Smith, the eighteenth century
                 Scottish philosopher, had it right. He believed that
                 minimal and aloof government best served society, and
                 that the inherent genius of citizens was itself enough
                 to ensure the general prosperity.",
  acknowledgement = ack-nhfb,
  keywords =     "ABC (Atanasoff-Berry Computer); ENIAC (Electronic
                 Numerical Integrator and Computer)",
}

@Article{Moller:2001:SEC,
  author =       "Bodo M{\"o}ller",
  title =        "Securing Elliptic Curve Point Multiplication against
                 Side-Channel Attacks",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2200",
  pages =        "324--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:06:44 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2200.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2200/22000324.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2200/22000324.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Montuschi:2001:BVH,
  author =       "P. Montuschi and T. Lang",
  title =        "Boosting very-high radix division with prescaling and
                 selection by rounding",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "50",
  number =       "1",
  pages =        "13--27",
  month =        jan,
  year =         "2001",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.902750",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:03:08 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=902750",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "An extension of the very-high radix division with
                 prescaling and selection by rounding is presented. This
                 extension consists of increasing the effective radix of
                 the implementation by obtaining a few additional bits
                 of the quotient per iteration, \ldots{}",
}

@Article{Morioka:2001:TEV,
  author =       "Sumio Morioka and Yasunao Katayama and Toshiyuki
                 Yamane",
  title =        "Towards Efficient Verification of Arithmetic
                 Algorithms over {Galois} Fields {$ G F(2^m) $}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2102",
  pages =        "465--477",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:05:02 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2102.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2102/21020465.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2102/21020465.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{MRaihi:2001:ACR,
  author =       "David M'Ra{\"\i}hi and David Naccache and Michael
                 Tunstall",
  title =        "Asymmetric Currency Rounding",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1962",
  pages =        "192--201",
  year =         "2001",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/3-540-45472-1",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:02:55 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1962.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1962/19620192.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1962/19620192.pdf",
  abstract =     "The euro was introduced on the first of January 1999
                 as a common currency in fourteen European nations. EC
                 regulations are fundamentally different from usual
                 banking practices for they forbid fees when converting
                 national currencies to euros (fees would otherwise
                 deter users from adopting the euro); this creates a
                 unique fraud context where money can be made by taking
                 advantage of the EC's official rounding rules. This
                 paper proposes a public-key-based protection against
                 such attacks. In our scheme, the parties conducting a
                 transaction can not predict whether the rounding will
                 cause loss or gain while the expected statistical
                 difference between an amount and its euro-equivalent
                 decreases exponentially as the number of transactions
                 increases.",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Muller:2001:IEA,
  author =       "Norbert Th. M{\"u}ller",
  title =        "The {iRRAM}: Exact Arithmetic in {C++}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2064",
  pages =        "222--252",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:04:19 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2064.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2064/20640222.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2064/20640222.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InProceedings{Naini:2001:GHS,
  author =       "Ajay Naini and Atul Dhablania and Warren James and
                 Debjit Das Sarma",
  title =        "{1-GHz HAL SPARC64\reg{}} Dual Floating Point Unit
                 with {RAS} Features",
  crossref =     "Burgess:2001:ISC",
  pages =        "173--183",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Naini.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}

@Article{Nakamura:2001:AAA,
  author =       "Yoshimasa Nakamura",
  title =        "Algorithms associated with arithmetic, geometric and
                 harmonic means and integrable systems",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "131",
  number =       "1--2",
  pages =        "161--174",
  day =          "1",
  month =        jun,
  year =         "2001",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(00)00316-2",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "65P40 (37N30 39A10)",
  MRnumber =     "1835710",
  bibdate =      "Sat Feb 25 12:45:18 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700003162",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Nannarelli:2001:TBR,
  author =       "A. Nannarelli and M. Re and G. C. Cardarilli",
  booktitle =    "{ISCAS 2001}, The 2001 {IEEE} International Symposium
                 on Circuits and Systems, 6--9 May 2001",
  title =        "Tradeoffs between residue number system and
                 traditional {FIR} filters",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "305--308",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.2001.921068",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "In this work, a study on the implementation of FIR
                 filters in the Residue Number System (RNS) is carried
                 out. For different configurations, RNS filters are
                 compared with filters realized in the traditional two's
                 complement system (TCS) in terms of \ldots{}",
}

@Article{Ning:2001:ESI,
  author =       "Peng Ning and Yiqun Lisa Yin",
  title =        "Efficient Software Implementation for Finite Field
                 Multiplication in Normal Basis",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2229",
  pages =        "177--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:07:15 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2229.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2229/22290177.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2229/22290177.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Nozaki:2001:IRA,
  author =       "H. Nozaki and M. Motoyama and A. Shimbo and S.
                 Kawamura",
  title =        "Implementation of {RSA} Algorithm Based on {RNS
                 Montgomery} Multiplication",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2162",
  pages =        "364--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:06:06 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2162.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620364.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2162/21620364.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Oishi:2001:FEM,
  author =       "Shin'ichi Oishi",
  title =        "Fast enclosure of matrix eigenvalues and singular
                 values via rounding mode controlled computation",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "324",
  number =       "1--3",
  pages =        "133--146",
  day =          "15",
  month =        feb,
  year =         "2001",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Mon Mar 19 19:03:24 MST 2001",
  bibsource =    "http://www.elsevier.com/locate/laa;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.elsevier.nl/gej-ng/10/30/19/144/24/32/abstract.html;
                 http://www.elsevier.nl/gej-ng/10/30/19/144/24/32/article.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Article{Okeya:2001:EEC,
  author =       "K. Okeya and K. Sakurai",
  title =        "Efficient Elliptic Curve Cryptosystems from a Scalar
                 Multiplication Algorithm with Recovery of the
                 $y$-Coordinate on a {Montgomery}-Form Elliptic Curve",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2162",
  pages =        "126--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:06:06 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2162.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620126.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2162/21620126.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Book{Overton:2001:NCI,
  author =       "Michael L. Overton",
  title =        "Numerical Computing with {IEEE} Floating Point
                 Arithmetic, Including One Theorem, One Rule of Thumb,
                 and One Hundred and One Exercises",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xiv + 104",
  year =         "2001",
  ISBN =         "0-89871-482-6 (hardcover), 0-89871-571-7 (paperback),
                 0-89871-807-4 (ebook)",
  ISBN-13 =      "978-0-89871-482-1 (hardcover), 978-0-89871-571-2
                 (print), 978-0-89871-807-2 (e-book)",
  LCCN =         "QA76.9.M35 O94 2001",
  MRclass =      "65-02 (65G30 68M07 68N99)",
  MRnumber =     "MR1828597 (2003b:65002)",
  MRreviewer =   "Jesse L. Barlow",
  bibdate =      "Fri Apr 27 16:50:46 2001",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana2000.bib",
  price =        "US\$40.00",
  URL =          "http://www.cs.nyu.edu/cs/faculty/overton/book/;
                 http://www.siam.org/catalog/mcc07/ot76.htm",
  abstract =     "Are you familiar with the IEEE floating point
                 arithmetic standard? Would you like to understand it
                 better? This book gives a broad overview of numerical
                 computing, in a historical context, with a special
                 focus on the IEEE standard for binary floating point
                 arithmetic. Key ideas are developed step by step,
                 taking the reader from floating point representation,
                 correctly rounded arithmetic, and the IEEE philosophy
                 on exceptions, to an understanding of the crucial
                 concepts of conditioning and stability, explained in a
                 simple yet rigorous context. It gives technical details
                 that are not readily available elsewhere and includes
                 challenging exercises that go beyond the topics covered
                 in the text. Numerical Computing with IEEE Floating
                 Point Arithmetic provides an easily accessible yet
                 detailed discussion of IEEE Std 754-1985, arguably the
                 most important standard in the computer industry. The
                 result of an unprecedented cooperation between academic
                 computer scientists and the cutting edge of industry,
                 it is supported by virtually every modern computer.
                 Other topics include the floating point architecture of
                 the Intel microprocessors and a discussion of
                 programming language support for the standard.",
  acknowledgement = ack-nhfb,
  tableofcontents = "1: Introduction \\
                 2: The real numbers \\
                 3: Computer representation of numbers \\
                 4: IEEE floating point representation \\
                 5: Rounding \\
                 6: Correctly rounded floating point operations \\
                 7: Exceptions \\
                 8: The Intel microprocessors \\
                 9: Programming languages \\
                 10: Floating point in C \\
                 11: Cancellation \\
                 12: Conditioning of problems \\
                 13: Stability of algorithms \\
                 14: Conclusion",
}

@InProceedings{Paliouras:2001:LPP,
  author =       "V. Paliouras and T. Stouraitis",
  title =        "Low-Power Properties of the Logarithmic Number
                 System",
  crossref =     "Burgess:2001:ISC",
  pages =        "229--236",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Paliouras.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}

@Article{Park:2001:ADI,
  author =       "Young-Ho Park and Sangtae Jeong and Chang Han Kim and
                 Jongin Lim",
  title =        "An Alternate Decomposition of an Integer for Faster
                 Point Multiplication on Certain Elliptic Curves",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2274",
  pages =        "323--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:09:07 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2274.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2274/22740323.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2274/22740323.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Park:2001:IMM,
  author =       "Young-Ho Park and Sangho Oh and Sangjin Lee and Jongin
                 Lim and Maenghee Sung",
  title =        "An Improved Method of Multiplication on Certain
                 Elliptic Curves",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2274",
  pages =        "310--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:09:07 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2274.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2274/22740310.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2274/22740310.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InProceedings{Phillips:2001:MMM,
  author =       "B. Phillips",
  booktitle =    "Conference Record of the Thirty-Fifth Asilomar
                 Conference on Signals, Systems and Computers, 2001",
  title =        "Modular multiplication in the {Montgomery} residue
                 number system",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1637--1640",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ACSSC.2001.987762",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper considers the evaluation of long wordlength
                 modular products. An algorithm is described in which
                 long wordlength (e.g. 1024-bit) integers are
                 represented by short-wordlength (e.g. 32-bit)
                 Montgomery (1985) residues. Long integer modular
                 \ldots{}",
}

@Article{Phillips:2001:MRN,
  author =       "B. J. Phillips",
  title =        "{Montgomery} residue number systems",
  journal =      j-ELECT-LETTERS,
  volume =       "37",
  number =       "21",
  pages =        "1286--1287",
  day =          "11",
  month =        oct,
  year =         "2001",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:20010852",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=20889",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The Montgomery residue number system (MRNS) for long
                 word-length arithmetic is introduced. MRNS, a
                 modification of the residue number system (RNS),
                 represents a long integer as a set of smaller
                 Montgomery residues. Long integer addition, subtraction
                 \ldots{}",
}

@InProceedings{Phillips:2001:OSL,
  author =       "Braden Phillips",
  title =        "Optimised Squaring of Long Integers Using Precomputed
                 Partial Products",
  crossref =     "Burgess:2001:ISC",
  pages =        "73--82",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Phillips.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}

@Article{Pietronero:2001:EUD,
  author =       "L. Pietronero and E. Tosatti and V. Tosatti and A.
                 Vespignani",
  title =        "Explaining the uneven distribution of numbers in
                 nature: the laws of {Benford} and {Zipf}",
  journal =      j-PHYSICA-A,
  volume =       "293",
  number =       "??",
  pages =        "297--304",
  month =        "????",
  year =         "2001",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/S0378-4371(00)00633-6",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Thu Feb 15 16:36:18 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The distribution of first digits in numbers series
                 obtained from very different origins shows a marked
                 asymmetry in favor of small digits that goes under the
                 name of Benford's law. We analyze in detail this
                 property for different data sets and give a general
                 explanation for the origin of the Benford's law in
                 terms of multiplicative processes. We show that this
                 law can be also generalized to series of numbers
                 generated from more complex systems like the catalogs
                 of seismic activity. Finally, we derive a relation
                 between the generalized Benford's law and the popular
                 Zipf's law which characterize the rank order statistics
                 and has been extensively applied to many problems
                 ranging from city population to linguistics.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Pillai:2001:LPA,
  author =       "R. V. K. Pillai and D. Al-Khalili and A. J. Al-Khalili
                 and S. Y. A. Shah",
  title =        "A Low Power Approach to Floating Point Adder Design
                 for {DSP} Applications",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "27",
  number =       "3",
  pages =        "195--213",
  month =        mar,
  year =         "2001",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1023/A:1008140025773",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Thu May 09 09:49:01 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The demand for high performance, low power floating
                 point adder cores has been on the rise during the
                 recent years particularly for DSP applications. In this
                 paper, we present a new architecture for a low power,
                 IEEE compatible, floating point adder, that is fast and
                 has low latency. The functional partitioning of the
                 adder into three distinct, clock gated data paths
                 allows activity reduction. The switching activity
                 function of the proposed adder is represented as a
                 three state FSM. During any given operation cycle, only
                 one of the data paths is active, during which time, the
                 logic assertion status of the circuit nodes of the
                 other data paths are held at their previous states.
                 Critical path delay and latency are reduced by
                 incorporating speculative rounding and pseudo leading
                 zero anticipatory logic as well as data path
                 simplifications. In contrast to conventional high speed
                 floating point adders that use leading zero
                 anticipatory logic, the proposed scheme offers a worst
                 case power reduction of 50\%.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
}

@InProceedings{Pineiro:2001:FPC,
  author =       "J. A. Pi{\~n}eiro and J. D. Bruguera and J.-M.
                 Muller",
  title =        "Faithful Powering Computation Using Table Look-Up and
                 a Fused Accumulation Tree",
  crossref =     "Burgess:2001:ISC",
  pages =        "40--50",
  year =         "2001",
  bibdate =      "Fri May 3 13:52:01 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Pineiro.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
  xxnote =       "Check pages: one reference has 40--47??",
}

@InProceedings{Rajagopal:2001:LAD,
  author =       "Sridhar Rajagopal and Joseph R. Cavallaro",
  title =        "On-Line Arithmetic for Detection in Digital
                 Communication Receivers",
  crossref =     "Burgess:2001:ISC",
  pages =        "257--265",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Rajagopal.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}

@Book{Ralston:2001:FCN,
  author =       "Anthony Ralston and Philip Rabinowitz",
  title =        "A first course in numerical analysis",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  edition =      "Second",
  pages =        "xviii + 556 + 50",
  year =         "2001",
  ISBN =         "0-486-41454-X (paperback)",
  ISBN-13 =      "978-0-486-41454-6 (paperback)",
  LCCN =         "QA297 .R3 2001",
  bibdate =      "Fri Aug 20 10:13:32 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/description/dover032/00064343.html;
                 http://www.loc.gov/catdir/toc/dover031/00064343.html",
  acknowledgement = ack-nhfb,
  remark =       "This Dover edition, first published in 2001, is an
                 unabridged, slightly corrected republication of the
                 second edition of the work originally published in
                 \cite{Ralston:1965:FC} and issued in a revised second
                 edition in \cite{Ralston:1978:FCN}.",
  subject =      "Numerical analysis",
}

@InProceedings{Rejeb:2001:IDR,
  author =       "B. Rejeb and H. Henkelmann and W. Anheier",
  booktitle =    "The 8th {IEEE} International Conference on
                 Electronics, Circuits and Systems, {ICECS 2001}",
  title =        "Integer division in residue number system",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "259--262",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICECS.2001.957729",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Division, sign detection and number comparison are the
                 more difficult operations in residue number systems
                 (RNS). These shortcomings limited most RNS
                 implementations to additions, subtractions and
                 multiplications. In this paper, a high level \ldots{}",
}

@Article{Reyhani-Masoleh:2001:FNB,
  author =       "Arash Reyhani-Masoleh and M. Anwar Hasan",
  title =        "Fast Normal Basis Multiplication Using General Purpose
                 Processors",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2259",
  pages =        "230--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:07:44 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2259.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2259/22590230.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2259/22590230.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Rinfret:2001:BSI,
  author =       "Denis Rinfret and Patrick O'Neil and Elizabeth
                 O'Neil",
  title =        "Bit-sliced index arithmetic",
  journal =      j-SIGMOD,
  volume =       "30",
  number =       "2",
  pages =        "47--57",
  month =        jun,
  year =         "2001",
  CODEN =        "SRECD8",
  ISSN =         "0163-5808 (print), 1943-5835 (electronic)",
  ISSN-L =       "0163-5808",
  bibdate =      "Mon Jan 12 08:46:06 MST 2004",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMOD Record",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J689",
}

@Article{Ring:2001:MPA,
  author =       "Michael C. Ring",
  title =        "{MAPM}, {A} Portable Arbitrary Precision Math Library
                 in {C}",
  journal =      j-CCCUJ,
  volume =       "19",
  number =       "11",
  pages =        "??--??",
  month =        nov,
  year =         "2001",
  CODEN =        "CCUJEX",
  ISSN =         "1075-2838",
  bibdate =      "Tue May 14 18:09:34 MDT 2002",
  bibsource =    "http://www.cuj.com/articles/2001/0111/0111toc.htm?topic=articles;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Frustrated by the finiteness of fixed-size arithmetic?
                 This math library gives you the precision you need.",
  acknowledgement = ack-nhfb,
  fjournal =     "C/C++ Users Journal",
}

@Article{Rudra:2001:ERE,
  author =       "A. Rudra and P. K. Dubey and C. S. Jutla and V. Kumar
                 and J. R. Rao and P. Rohatgi",
  title =        "Efficient {Rijndael} Encryption Implementation with
                 Composite Field Arithmetic",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2162",
  pages =        "171--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:06:06 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2162.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620171.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2162/21620171.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Rugina:2001:RUD,
  author =       "Radu Rugina and Martin Rinard",
  title =        "Recursion Unrolling for Divide and Conquer Programs",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2017",
  pages =        "34--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:03:35 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2017.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2017/20170034.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2017/20170034.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Rump:2001:RPS,
  author =       "Siegfried M. Rump",
  title =        "Rigorous and Portable Standard Functions",
  journal =      j-BIT-NUM-MATH,
  volume =       "41",
  number =       "3",
  pages =        "540--562",
  month =        jun,
  year =         "2001",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1023/A:1021971313412",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 15:06:04 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=41&issue=3;
                 http://www.mai.liu.se/BIT/contents/bit41.html;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=41&issue=3&spage=540",
  abstract =     "Today's floating point implementations of elementary
                 transcendental functions are usually very accurate.
                 However, with few exceptions, the actual accuracy is
                 not known. In the present paper we describe a rigorous,
                 accurate, fast and portable implementation of the
                 elementary standard functions based on some existing
                 approximate standard functions. The scheme is outlined
                 for IEEE 754, but not difficult to adapt to other
                 floating point formats. A Matlab implementation is
                 available on the net. Accuracy of the proposed
                 algorithms can be rigorously estimated. As an example
                 we prove that the relative accuracy of the exponential
                 function is better than 2.07 eps in a slightly reduced
                 argument range (eps denoting the relative rounding
                 error unit). Otherwise, extensive computational tests
                 suggest for all elementary functions and all suitable
                 arguments an accuracy better than about 3 eps.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "elementary functions; floating-point arithmetic",
}

@Article{Sakai:2001:PMS,
  author =       "Yasuyuki Sakai and Kouichi Sakurai",
  title =        "On the Power of Multidoubling in Speeding Up Elliptic
                 Scalar Multiplication",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2259",
  pages =        "268--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:07:44 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2259.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2259/22590268.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2259/22590268.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Savas:2001:SUM,
  author =       "Erkay Savas and Alexandre F. Tenca and {\c{C}}etin K.
                 Ko{\c{c}}",
  title =        "A Scalable and Unified Multiplier Architecture for
                 Finite Fields {GF}$ (p) $ and {GF}$ (2 m) $",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1965",
  pages =        "277--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:02:57 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1965.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1965/19650277.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1965/19650277.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InProceedings{Schmookler:2001:LZA,
  author =       "Martin S. Schmookler and Kevin J. Nowka",
  title =        "Leading Zero Anticipation and Detection --- a
                 Comparison of Methods",
  crossref =     "Burgess:2001:ISC",
  pages =        "7--12",
  year =         "2001",
  DOI =          "https://doi.org/10.1109/ARITH.2001.930098",
  bibdate =      "Fri May 3 13:52:01 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Schmookler.pdf",
  abstract =     "Design of the leading zero anticipator (LZA) or
                 detector (LZD) is pivotal to the normalization of
                 results for addition and fused multiplication-addition
                 in high-performance floating point processors. This
                 paper formalizes the analysis and describes some
                 alternative organizations and implementations from the
                 known art. It shows how choices made in the design are
                 often dependent on the overall design of the addition
                 unit, on how subtraction is handled when the exponents
                 are the same, and on how it detects and corrects for
                 the possible one-bit error of the LZA.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}

@Article{Schonfelder:2001:VPA,
  author =       "J. L. Schonfelder",
  title =        "Variable Precision Arithmetic: a {Fortran 95} Module",
  journal =      j-FORTRAN-FORUM,
  volume =       "20",
  number =       "3",
  pages =        "2--11",
  month =        dec,
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/570822.570823",
  ISSN =         "1061-7264 (print), 1931-1311 (electronic)",
  ISSN-L =       "1061-7264",
  bibdate =      "Wed Jun 18 16:26:45 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper describes the design and development of a
                 software package supporting variable precision
                 arithmetic as a semantic extension to the core FORTRAN
                 language. The working precision of the arithmetic
                 supported by this package can be dynamically and
                 arbitrarily variable. The facility exploits the
                 data-abstraction capabilities of Fortran 95 and allows
                 the operations to be used elementally with array
                 operands as well as with scalars. The number system is
                 defined in such a way as to be closed under all of the
                 basic operations of normal arithmetic; no
                 program-terminating numerical exceptions can occur.
                 Precision loss situations like underflow and overflow
                 are handled by defining special value representations
                 that preserve as much of the numeric information as is
                 practical and the operation semantics are defined so
                 that these exceptional values propagate as appropriate
                 to reflect this loss of information. The number system
                 uses an essentially conventional variable precision
                 floating-point representation. Where operations can be
                 performed exactly within the currently-set working
                 precision limit, the excess trailing zero digits are
                 not stored, nor do they take part in future operations.
                 This is both economical in storage and improves
                 efficiency. By judiciously managing the working
                 precision, arithmetic operations that are potentially
                 exact can be performed exactly.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Fortran Forum",
  issue =        "62",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J286",
}

@InProceedings{Seidel:2001:BMR,
  author =       "Peter-Michael Seidel and Lee D. McFearin and David W.
                 Matula",
  title =        "Binary Multiplication Radix-$ 32 $ and Radix-$ 256 $",
  crossref =     "Burgess:2001:ISC",
  pages =        "23--32",
  year =         "2001",
  bibdate =      "Fri May 3 13:52:01 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Seidel.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}

@InProceedings{Seidel:2001:DFI,
  author =       "Peter-Michael Seidel and Guy Even",
  title =        "On the Design of Fast {IEEE} Floating-Point Adders",
  crossref =     "Burgess:2001:ISC",
  pages =        "184--194",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Seidel_Even.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}

@InProceedings{Seidel:2001:EAB,
  author =       "Peter-Michael Seidel",
  title =        "Exact arithmetic based on floating-point numbers",
  crossref =     "Kraemer:2001:SCV",
  pages =        "123--??",
  year =         "2001",
  bibdate =      "Wed Nov 24 10:53:43 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Smith:2001:AFS,
  author =       "David M. Smith",
  title =        "{Algorithm 814}: {Fortran 90} software for
                 floating-point multiple precision arithmetic, gamma and
                 related functions",
  journal =      j-TOMS,
  volume =       "27",
  number =       "4",
  pages =        "377--387",
  month =        dec,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/504210.504211",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Mar 13 08:49:29 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A collection of Fortran 90 routines for evaluating the
                 Gamma function and related functions using the FM
                 multiple-precision arithmetic package.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Misc{Steele:2001:SMFa,
  author =       "Guy L. {Steele Jr.}",
  title =        "System and method for floating-point computation",
  howpublished = "US Patent 6327604",
  day =          "04",
  month =        dec,
  year =         "2001",
  bibdate =      "Tue Dec 23 15:06:47 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/6327604/fulltext.html",
  abstract =     "A system is disclosed for performing floating point
                 computation in connection with numbers in a base
                 floating point representation (such as the
                 representation defined in IEEE Std. 754) that defines a
                 plurality of formats, including a normalized format and
                 a de-normalized format, using a common floating point
                 representation that defines a unitary normalized
                 format. The system includes a base to common
                 representation converter, a processor and a common to
                 base representation converter. The base to common
                 representation converter converts numbers from the base
                 floating point representation to the common floating
                 point representation, so that all numbers involved in a
                 computation will be expressed in the unitary normalized
                 format. The processor is configured to perform a
                 mathematical operation of at least one predetermined
                 type in connection with the converted numbers generated
                 by the base to common representation converter to
                 generate a floating point result in the common
                 representation. The common to base representation
                 converter converts numbers from the common floating
                 point representation selectively to either the
                 normalized or de-normalized format of the base
                 representation.",
  acknowledgement = ack-nhfb,
}

@Misc{Steele:2001:SMFb,
  author =       "Guy L. {Steele Jr.}",
  title =        "System and method for floating-point computation",
  howpublished = "US Patent 6289365",
  day =          "11",
  month =        sep,
  year =         "2001",
  bibdate =      "Tue Dec 23 15:06:47 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/6289365/fulltext.html",
  abstract =     "A system is disclosed for performing floating point
                 computation in connection with numbers in a base
                 floating point representation (such as the
                 representation defined in IEEE Std. 754) that defines a
                 plurality of formats, including a normalized format and
                 a de-normalized format, using a common floating point
                 representation that defines a unitary normalized
                 format. The system includes a base to common
                 representation converter, a processor and a common to
                 base representation converter. The base to common
                 representation converter converts numbers from the base
                 floating point representation to the common floating
                 point representation, so that all numbers involved in a
                 computation will be expressed in the unitary normalized
                 format. The processor is configured to perform a
                 mathematical operation of at least one predetermined
                 type in connection with the converted numbers generated
                 by the base to common representation converter to
                 generate a floating point result in the common
                 representation. The common to base representation
                 converter converts numbers from the common floating
                 point representation selectively to either the
                 normalized or denormalized format of the base
                 representation.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Stine:2001:CIH,
  author =       "J. E. Stine and M. J. Schulte",
  title =        "A Case for Interval Hardware on Superscalar
                 Processors",
  crossref =     "Kraemer:2001:SCV",
  pages =        "53--68",
  year =         "2001",
  bibdate =      "Tue Nov 25 12:33:34 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "interval arithmetic",
}

@PhdThesis{Stine:2001:DIA,
  author =       "James Edward {Stine, Jr.}",
  title =        "Design issues for accurate and reliable arithmetic",
  type =         "{Ph.D.} Thesis",
  school =       "Lehigh University",
  address =      "Bethlehem, PA, USA",
  year =         "2001",
  bibdate =      "Fri Oct 25 17:18:13 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://wwwlib.umi.com/dissertations/fullcit/9995540;
                 http://wwwlib.umi.com/dissertations/preview/9995540",
  abstract =     "The use of floating-point data types in high-level
                 languages is prevalent in many of today's scientific
                 applications. However, the approximation of real
                 numbers by finite precision floating-point numbers can
                 produce inaccurate results due to round off error and
                 catastrophic cancellation. Interval arithmetic provides
                 a method for monitoring errors in numerical
                 computations, and can provide solutions to problems
                 that cannot be efficiently solved with traditional
                 floating point arithmetic. Although several software
                 tools for interval arithmetic have been developed,
                 these tools have severe performance limitations due to
                 a lack of hardware support for interval arithmetic.
                 This dissertation investigates the design, development,
                 and evaluation of hardware and instruction set support
                 for interval arithmetic. In contrast to previous
                 research, which employed dedicated functional units and
                 coprocessors for interval arithmetic, this research
                 focuses on the integration of interval arithmetic
                 support with traditional IEEE floating point hardware.
                 Novel algorithms and hardware designs for interval
                 arithmetic are developed, and methods for adding
                 interval arithmetic instructions to the instruction set
                 architectures of conventional processors are presented.
                 To evaluate the cost and performance of this approach,
                 hardware designs with support for interval arithmetic
                 have been realized using VHDL and synthesized with the
                 Leonardo/Spectrum tool set from Exemplar. These designs
                 are compared to conventional floating point units in
                 terms of area and delay. Simulations of interval
                 benchmarks both with and without interval hardware
                 support are performed using an interval-enhanced
                 version of the SimpleScalar tool suite and GNU's gcc
                 compiler. The results of these simulations indicate
                 that the proposed hardware support for interval
                 arithmetic improves the execution time of interval
                 operations by a factor 6.3 to 14.9.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Stoffel:2001:VIM,
  author =       "Dominik Stoffel and Wolfgang Kunz",
  title =        "Verification of integer multipliers on the arithmetic
                 bit level",
  crossref =     "IEEE:2001:IPI",
  pages =        "183--189",
  year =         "2001",
  bibdate =      "Fri Aug 08 08:59:39 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "One of the most severe short-comings of currently
                 available equivalence checkers is their inability to
                 verify integer multipliers. In this paper, we present a
                 bit level reverse-engineering technique that can be
                 integrated into standard equivalence checking flows. We
                 propose a Boolean mapping algorithm that extracts a
                 network of half adders from the gate netlist of an
                 addition circuit. Once the arithmetic bit level
                 representation of the circuit is obtained, equivalence
                 checking can be performed using simple arithmetic
                 operations. Experimental results show the promise of
                 our approach.",
  acknowledgement = ack-nhfb,
}

@Article{Sun:2001:NSM,
  author =       "Fangyu Sun and Peter Kosmol",
  title =        "A new simultaneous method of fourth order for finding
                 complex zeros in circular interval arithmetic",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "130",
  number =       "1--2",
  pages =        "293--307",
  day =          "1",
  month =        may,
  year =         "2001",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:45:18 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042799003751",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Sunar:2001:EON,
  author =       "B. Sunar and C. K. Koc",
  title =        "An efficient optimal normal basis type {II}
                 multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "50",
  number =       "1",
  pages =        "83--87",
  month =        jan,
  year =         "2001",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.902754",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:03:08 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=902754",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Takagi:2001:HAC,
  author =       "Naofumi Takagi",
  title =        "A Hardware Algorithm for Computing Reciprocal Square
                 Root",
  crossref =     "Burgess:2001:ISC",
  pages =        "94--100",
  year =         "2001",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Takagi.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
  summary =      "A hardware algorithm for computing the reciprocal
                 square root which appears frequently in multimedia and
                 graphics applications is proposed. The reciprocal
                 square root is computed by iteration of
                 carry-propagation-free additions, shifts, and
                 \ldots{}",
}

@Article{Tasche:2001:WAC,
  author =       "Manfred Tasche and Hansmartin Zeuner",
  title =        "Worst and average case roundoff error analysis for
                 {FFT}",
  journal =      j-BIT-NUM-MATH,
  volume =       "41",
  number =       "3",
  pages =        "563--581",
  month =        jun,
  year =         "2001",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1023/A:1021923430250",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 15:06:04 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=41&issue=3;
                 http://www.mai.liu.se/BIT/contents/bit41.html;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=41&issue=3&spage=563",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "Fast Fourier Transform (FFT); floating-point
                 arithmetic; rounding errors",
}

@InProceedings{Tenca:2001:DRL,
  author =       "Alexandre F. Tenca and Syed Ubaid Hussaini",
  title =        "A Design of Radix-$2$ On-Line Division Using {LSA}
                 Organization",
  crossref =     "Burgess:2001:ISC",
  pages =        "266--276",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Tenca.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}

@Article{Tenca:2001:HRD,
  author =       "A. F. Tenca and G. Todorov and {\c{C}}.K. Ko{\c{c}}",
  title =        "High-Radix Design of a Scalable Modular Multiplier",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2162",
  pages =        "185--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:06:06 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2162.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2162/21620185.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2162/21620185.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Thompson:2001:BPC,
  author =       "D. U. Thompson and B. A. Wooley",
  title =        "A 15-b pipelined {CMOS} floating-point {A/D}
                 converter",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "36",
  number =       "2",
  pages =        "299--303",
  month =        feb,
  year =         "2001",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "A floating-point approach can be used to extend the
                 dynamic range of analog-to-digital (A/D) converters in
                 applications where large signals need not be encoded
                 with a precision greater than that required for small
                 signals. Owing to the nonuniform nature \ldots{}",
}

@Manual{TI:2001:TTPa,
  title =        "{TI-89\slash TI-92 Plus Sierra C} Assembler Reference
                 Manual, Beta Version .02",
  organization = "Texas Instruments",
  address =      "Post Office box 655303, Dallas, TX 75265, USA",
  pages =        "322",
  year =         "2001",
  bibdate =      "Thu Nov 25 09:44:52 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Manual{TI:2001:TTPb,
  title =        "{TI-89\slash TI-92 Plus} Developers Guide, Beta
                 Version .02",
  organization = "Texas Instruments",
  address =      "Post Office box 655303, Dallas, TX 75265, USA",
  pages =        "1356",
  year =         "2001",
  bibdate =      "Thu Nov 25 09:44:52 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Tisseur:2001:NMF,
  author =       "Fran{\c{c}}oise Tisseur",
  title =        "{Newton}'s Method in Floating Point Arithmetic and
                 Iterative Refinement of Generalized Eigenvalue
                 Problems",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "22",
  number =       "4",
  pages =        "1038--1057",
  month =        "????",
  year =         "2001",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/S0895479899359837",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "65F15 (65F35)",
  MRnumber =     "MR1824056 (2002b:65061)",
  MRreviewer =   "Raffaella Pavani",
  bibdate =      "Tue Feb 11 14:17:49 MST 2014",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/22/4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
  onlinedate =   "January 2001",
}

@Article{Trichina:2001:SAM,
  author =       "Elena Trichina and Alex Tiountchik",
  title =        "Scalable Algorithm for {Montgomery} Multiplication and
                 Its Implementation on the Coarse-Grain Reconfigurable
                 Chip",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2020",
  pages =        "235--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:03:38 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2020.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2020/20200235.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2020/20200235.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Um:2001:OAC,
  author =       "Junhyung Um and Taewhan Kim",
  title =        "An optimal allocation of carry-save-adders in
                 arithmetic circuits",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "50",
  number =       "3",
  pages =        "215--233",
  month =        mar,
  year =         "2001",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.910813",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:03:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=910813",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Verdonk:2001:PRIa,
  author =       "Brigitte Verdonk and Annie Cuyt and Dennis
                 Verschaeren",
  title =        "A precision- and range-independent tool for testing
                 floating-point arithmetic {I}: {Basic} operations,
                 square root, and remainder",
  journal =      j-TOMS,
  volume =       "27",
  number =       "1",
  pages =        "92--118",
  month =        mar,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/382043.382404",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.win.ua.ac.be/~cant/ieeecc754.html",
  abstract =     "This paper introduces a precision- and
                 range-independent tool for testing the compliance of
                 hardware or software implementations of
                 (multiprecision) floating-point arithmetic with the
                 principles of the IEEE standards 754 and 854. The tool
                 consists of a driver program, offering many options to
                 test only specific aspects of the IEEE standards, and a
                 large set of test vectors, encoded in a
                 precision-independent syntax to allow the testing of
                 basic and extended hardware formats as well as
                 multiprecision floating-point implementations. The
                 suite of test vectors stems on one hand from the
                 integration and fully precision- and range-independent
                 generalization of existing hardware test sets, and on
                 the other hand from the systematic testing of exact
                 rounding for all combinations of round and sticky bits
                 that can occur. The former constitutes only 50\% of the
                 resulting test set. In the latter we especially focus
                 on hard-to-round cases. In addition, the test suite
                 implicitly tests properties of floating-point
                 operations, following the idea of Paranoia, and it
                 reports which of the three IEEE-compliant underflow
                 mechanisms is used by the floating-point implementation
                 under consideration. We also check whether that
                 underflow mechanism is used consistently. The tool is
                 backward compatible with the UCBTEST package and with
                 Coonen's test syntax.",
  accepted =     "23 February 2001",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "arithmetic; floating-point testing; IEEE
                 floating-point standard; multiprecision; validation;
                 Verification",
  subject =      "Primary Classification: G. Mathematics of Computing
                 G.1 NUMERICAL ANALYSIS G.1.0 General Subjects: Computer
                 arithmetic\\
                 Additional Classification: D. Software D.3 PROGRAMMING
                 LANGUAGES D.3.0 General Subjects: Standards",
}

@Article{Verdonk:2001:PRIb,
  author =       "Brigitte Verdonk and Annie Cuyt and Dennis
                 Verschaeren",
  title =        "A precision- and range-independent tool for testing
                 floating-point arithmetic {II}: conversions",
  journal =      j-TOMS,
  volume =       "27",
  number =       "1",
  pages =        "119--140",
  month =        mar,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/382043.382405",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.win.ua.ac.be/~cant/ieeecc754.html",
  abstract =     "The IEEE 754 and 854 standards for floating-point
                 arithmetic are essentially a specification of a
                 programming environment, encompassing aspects from
                 computer hardware, operating systems and compilers to
                 programming languages (see especially section 8). Part
                 I and II of this paper together describe a tool to test
                 floating-point implementations of arbitrary precision
                 and exponent range (hardware as well as software) for
                 compliance with the principles outlined in the IEEE
                 standards. The tool consists of a driver program,
                 together with a very large set of test vectors encoded
                 in a precision independent syntax.\par

                 In Part I we have covered the testing of the basic
                 operations +, -, $ \times $, /, the square root and
                 remainder functions. In Part II we describe the
                 extension of the test tool to deal with conversions
                 between floating-point formats, conversions between
                 floating-point and integer formats, the rounding of
                 floating-point numbers to integral values and last but
                 not least binary-decimal conversions. Conversions can
                 now be tested from a floating-point format of arbitrary
                 precision and exponent range to another arbitrary
                 smaller (larger) floating-point format as well as to
                 and from fixed hardware integer formats. Conversions
                 between the bases 2 and 10 can be tested for a number
                 of precisions ranging from single (24 bits), double (53
                 bits), long double or extended (64 bits) to quadruple
                 (113 bits) precision and a proper multiprecision (240
                 bits) format.\par

                 We conclude Part II with some applications of our test
                 tool and report on the results of testing various
                 floating-point implementations, meaning various
                 language-compiler-hardware combinations as well as
                 multiprecision libraries.",
  accepted =     "23 February 2001",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "decimal floating-point arithmetic; floating-point
                 testing",
}

@InProceedings{Vergos:2001:HSP,
  author =       "H. T. Vergos and C. Efstathiou and D. Nikolos",
  title =        "High Speed Parallel-Prefix Modulo $ 2^{n + 1} $ Adders
                 for Diminished-One Operands",
  crossref =     "Burgess:2001:ISC",
  pages =        "211--217",
  year =         "2001",
  bibdate =      "Fri May 3 13:58:18 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 OCLC Proceedings database",
  URL =          "http://www.acsel-lab.com/arithmetic/arith15/papers/ARITH15_Vergos.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
}

@Article{Visavakul:2001:DSS,
  author =       "Chakkapas Visavakul and Peter Y. K. Cheung and Wayne
                 Luk",
  title =        "A Digit-Serial Structure for Reconfigurable
                 Multipliers",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2147",
  pages =        "565--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:05:49 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2147.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2147/21470565.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2147/21470565.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Walter:2001:DIH,
  author =       "Colin D. Walter",
  title =        "Data Integrity in Hardware for Modular Arithmetic",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1965",
  pages =        "204--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:02:57 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1965.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1965/19650204.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1965/19650204.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Walter:2001:PBM,
  author =       "Colin D. Walter",
  title =        "Precise Bounds for {Montgomery} Modular Multiplication
                 and Some Potentially Insecure {RSA} Moduli",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2271",
  pages =        "30--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:09:06 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2271.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2271/22710030.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2271/22710030.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InProceedings{Walters:2001:CUT,
  author =       "E. G. Walters and J. Schlessman and M. J. Schulte",
  title =        "Combined Unsigned and Two's Complement Hybrid
                 Squarers",
  crossref =     "Matthews:2001:CRT",
  pages =        "861--866",
  year =         "2001",
  bibdate =      "Sun Mar 04 11:46:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2001-08.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Wang:2001:LPF,
  author =       "Wei Wang and M. N. S. Swamy and M. O. Ahmad",
  booktitle =    "{MWSCAS 2001}, Proceedings of the 44th {IEEE 2001}
                 Midwest Symposium on Circuits and Systems",
  title =        "Low power {FIR} filter {FPGA} implementation based on
                 distributed arithmetic and residue number system",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "102--105",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.2001.986125",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "In this paper, several low power techniques are
                 proposed for the FPGA implementation of a distributed
                 arithmetic and residue number system-based FIR filter.
                 Two algorithms are proposed to reduce the size of the
                 residue-to-binary converter, which is \ldots{}",
}

@InProceedings{Wires:2001:FRR,
  author =       "K. E. Wires and M. J. Schulte and D. McCarley",
  title =        "{FPGA} Resource Reduction Through Truncated
                 Multiplication",
  crossref =     "Brebner:2001:FLA",
  pages =        "574--583",
  year =         "2001",
  DOI =          "https://doi.org/10.1007/3-540-44687-7_59",
  bibdate =      "Sun Mar 04 11:42:02 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2001-04.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Wirthlin:2001:ECC,
  author =       "Michael J. Wirthlin and Brian McMurtrey",
  title =        "Efficient Constant Coefficient Multiplication Using
                 Advanced {FPGA} Architectures",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2147",
  pages =        "555--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:05:49 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2147.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2147/21470555.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2147/21470555.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Wright:2001:EFP,
  author =       "Stephen J. Wright",
  title =        "Effects of Finite-Precision Arithmetic on
                 Interior-Point Methods for Nonlinear Programming",
  journal =      j-SIAM-J-OPT,
  volume =       "12",
  number =       "1",
  pages =        "36--78",
  month =        may # "\slash " # oct,
  year =         "2001",
  CODEN =        "SJOPE8",
  DOI =          "https://doi.org/10.1137/S1052623498347438",
  ISSN =         "1052-6234 (print), 1095-7189 (electronic)",
  ISSN-L =       "1052-6234",
  MRclass =      "90C51 (90C30 90C33)",
  MRnumber =     "MR1870586 (2002j:90107)",
  MRreviewer =   "Levent Tun{\c{c}}el",
  bibdate =      "Sat Oct 4 12:16:05 MDT 2003",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIOPT/12/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/34743",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Optimization",
  journal-URL =  "http://epubs.siam.org/siopt",
}

@Article{Wu:2001:MMSa,
  author =       "Huapeng Wu",
  title =        "{Montgomery} Multiplier and Squarer in {GF$ (2^m) $}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1965",
  pages =        "264--276",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:02:57 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1965.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1965/19650264.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1965/19650264.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Yamauchi:2001:AOO,
  author =       "Tsukasa Yamauchi and Shogo Nakaya and Takeshi Inuo and
                 Nobuki Kajihara",
  title =        "Arithmetic Operation Oriented Reconfigurable Chip:
                 {RHW}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2147",
  pages =        "618--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:05:49 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2147.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2147/21470618.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2147/21470618.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InProceedings{Yang:2001:LCB,
  author =       "Yi Yang and Chunyan Wang and M. Omair Ahmad and M. N.
                 S. Swamy",
  booktitle =    "{Proceedings of the Sixth International Symposium on
                 Signal Processing and its Applications (Cat. No.
                 01EX467)}",
  title =        "An on-line {CORDIC} based 2-D {IDCT} implementation
                 using distributed arithmetic",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "296--299",
  year =         "2001",
  DOI =          "https://doi.org/10.1109/ISSPA.2001.949836",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Arithmetic; CMOS technology; Computational modeling;
                 Computer architecture; Discrete cosine transforms;
                 Hardware; Read only memory; Throughput; Two dimensional
                 displays; Very large scale integration",
}

@InProceedings{Yang:2001:MDD,
  author =       "Lie-Liang Yang and L. Hanzo",
  booktitle =    "{ICC 2001}. {IEEE} International Conference on
                 Communications. 11--14 June 2001",
  title =        "Minimum-distance decoding of redundant residue number
                 system codes",
  volume =       "10",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2975--2979",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICC.2001.937218",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "In this contribution the conventional error-detection
                 and error-correction algorithms used for RRNS codes are
                 improved and unified in the context of a so-called
                 projection-based `minimum-distance decoding' algorithm,
                 which can efficiently detect or \ldots{}",
}

@InProceedings{Yang:2001:RRN,
  author =       "Lie-Liang Yang and L. Hanzo",
  booktitle =    "{VTC 2001} Fall. {IEEE} {VTS 54th} Vehicular
                 Technology Conference",
  title =        "Redundant residue number system based error correction
                 codes",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1472--1476",
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/VTC.2001.956442",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "In this paper residue number system (RNS) arithmetic
                 and redundant residue number system (RRNS) based codes
                 as well as their properties are reviewed. We propose a
                 number of applications for RRNS codes and demonstrate
                 how RRNS codes can be employed \ldots{}",
}

@Article{Yeh:2001:RAO,
  author =       "Thomas Y. Yeh and Hong Wang",
  title =        "Redundant Arithmetic Optimizations (Research Note)",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1900",
  pages =        "984--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:02:44 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1900.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1900/19000984.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1900/19000984.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Yu:2001:DID,
  author =       "Sungwook Yu and E. E. {Swartzlander, Jr.}",
  title =        "{DCT} implementation with distributed arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "50",
  number =       "9",
  pages =        "985--991",
  month =        sep,
  year =         "2001",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.954513",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 10:03:12 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=954513",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Zhang:2001:FSM,
  author =       "Fangguo Zhang and Futai Zhang and Yumin Wang",
  title =        "Fast Scalar Multiplication on the {Jacobian} of a
                 Family of Hyperelliptic Curves",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2229",
  pages =        "74--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:07:15 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2229.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2229/22290074.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2229/22290074.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Zhang:2001:NCP,
  author =       "Hong Zhang",
  title =        "Numerical condition of polynomials in different
                 forms",
  journal =      j-ELECTRON-TRANS-NUMER-ANAL,
  volume =       "12",
  pages =        "66--87",
  year =         "2001",
  CODEN =        "????",
  ISSN =         "1068-9613 (print), 1097-4067 (electronic)",
  ISSN-L =       "1068-9613",
  bibdate =      "Mon Sep 6 12:28:29 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/etna.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://etna.mcs.kent.edu/vol.12.2001/pp66-87.dir/pp66-87.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronic Transactions on Numerical Analysis",
  journal-URL =  "http://etna.mcs.kent.edu/",
}

@InProceedings{Zheng:2001:ARE,
  author =       "Liang Zheng and Shen Xu-Bang and Peng Zuo-Hui",
  title =        "The application of redundant encoding in iterative
                 implementation of division and square root",
  crossref =     "Tang:2001:ICA",
  pages =        "603--606",
  year =         "2001",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The purpose of this paper is to discuss the speed
                 improvement in division and square root computation
                 with small area penalty. The digit recurrence SRT
                 algorithm and functional iteration Newton--Raphson
                 algorithm are generally used in modern \ldots{}",
}

@Article{Zielke:2001:GLL,
  author =       "G. Zielke and V. Drygalla",
  title =        "{Genaue L{\"o}sung Linearer Gleichungssysteme}.
                 ({German}) [Exact solution of linear sets of
                 equations]",
  journal =      j-GAMM-MIT,
  volume =       "26",
  number =       "??",
  pages =        "7--107",
  year =         "2001",
  CODEN =        "????",
  ISSN =         "0936-7195",
  bibdate =      "Tue Nov 22 06:49:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mitteilungen der Gesellschaft f{\"u}r Angewandte
                 Mathematik und Mechanik",
  keywords =     "accurate floating-point summation",
  language =     "German",
}

@TechReport{Zimmermann:2001:AAC,
  author =       "Paul Zimmermann",
  title =        "De l'algorithmique {\`a} l'arithm{\'e}tique via le
                 calcul formel. ({French}) [{From} algorithmics to
                 arithmetic via symbolic calculation]",
  type =         "Technical report",
  institution =  "D{\'e}partement de formation doctorale en
                 informatique. {\'E}cole doctorale IAEM Lorraine, UFR
                 STMIA",
  address =      "B{\^a}timent A, Technop{\^o}le de Nancy-Brabois, 615
                 rue du jardin botanique, F-54602 Villers-l{\`e}s-Nancy
                 Cedex, France",
  pages =        "43",
  month =        nov,
  year =         "2001",
  bibdate =      "Sun Sep 10 08:37:41 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.loria.fr/~zimmerma/papers/hdr.ps.gz",
  abstract =     "This document presents my research contributions from
                 1988 to 2001, performed first at INRIA Rocquencourt
                 within the Algo project (1988 to 1992), then at INRIA
                 Lorraine and LORIA within the projects Eur{\'e}ca
                 (1993-1997), PolKA (1998-2000), and Spaces (2001).
                 Three main periods can be roughly distinguished: from
                 1988 to 1992 where my research focused on analysis of
                 algorithms and random generation, from 1993 to 1997
                 where I worked on computer algebra and related
                 algorithms, finally from 1998 to 2001 where I was
                 interested in arbitrary precision floating-point
                 arithmetic with well-defined semantics.",
  acknowledgement = ack-nhfb,
  language =     "French",
  remark =       "Habilitation {\`a} diriger des recherches",
}

@TechReport{Zimmermann:2001:APA,
  author =       "Paul Zimmermann",
  title =        "Arithm{\'e}tique en pr{\'e}cision arbitraire.
                 ({French}) [Arbitrary-precision arithmetic]",
  type =         "Research Report",
  number =       "4272",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  pages =        "25",
  day =          "29",
  month =        sep,
  year =         "2001",
  ISSN =         "0249-6399",
  bibdate =      "Sun Sep 10 08:43:26 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.loria.fr/~zimmerma/papers/RR4272.ps.gz",
  abstract =     "This paper surveys the available algorithms for
                 integer or floating-point arbitrary precision
                 calculations. After a brief discussion about possible
                 memory representations, known algorithms for
                 multiplication, division, square root, greatest common
                 divisor, input and output, are presented, together with
                 their complexity and usage. For each operation, we
                 present the naive algorithm, the asymptotically optimal
                 one, and also intermediate ``divide and conquer''
                 algorithms, which often are very useful. For
                 floating-points computations, some general-purpose
                 methods are presented for algebraic, elementary,
                 hypergeometric and special functions.",
  acknowledgement = ack-nhfb,
  language =     "French",
}

@Misc{Ziv:2001:APM,
  author =       "Abraham Ziv and Moshe Olshansky and Ealan Henis and
                 Anna Reitman",
  title =        "Accurate Portable Mathematical Library ({IBM
                 APMathLib})",
  howpublished = "World-Wide Web document",
  publisher =    pub-IBM,
  address =      pub-IBM:adr,
  day =          "20",
  month =        dec,
  year =         "2001",
  bibdate =      "Wed Nov 24 08:06:54 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://www-126.ibm.com/pub/mathlib/mathlib12.20.2001.tar.gz;
                 http://oss.software.ibm.com/mathlib/",
  acknowledgement = ack-nhfb,
}

@Article{Agarwal:2002:FPN,
  author =       "R. C. Agarwal and R. F. Enenkel and F. G. Gustavson
                 and A. Kothari and M. Zubair",
  title =        "Fast pseudorandom-number generators with modulus $ 2^k
                 $ or $ 2^{k - 1} $ using fused multiply--add",
  journal =      j-IBM-JRD,
  volume =       "46",
  number =       "1",
  pages =        "97--116",
  month =        jan,
  year =         "2002",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.461.0097",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Mon Mar 18 17:27:08 MST 2002",
  bibsource =    "http://www.research.ibm.com/journal/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.research.ibm.com/journal/rd/461/agarwal.html;
                 http://www.research.ibm.com/journal/rd/461/agarwal.pdf",
  abstract =     "Many numerically intensive computations done in a
                 scientific computing environment require uniformly
                 distributed pseudorandom numbers in the range $ (0, 1)
                 $ and $ ( - 1, 1) $. For multiplicative congruential
                 generators with modulus $ 2^k $, $ k \leq 52 $, and
                 period $ 2^k - 2 $, we show that the cost per random
                 number for these two distributions is 3 and 3.125
                 multiply-adds on RS/6000 processors. Our code, on the
                 IBM POWER2 Model 590, produces more than 40 million
                 uniformly distributed pseudorandom numbers per second
                 for both ranges $ (0, 1) $ and $ ( - 1, 1) $.
                 Additionally, our code sustains the 40 million per
                 second rate for data out of cache. The Numerical
                 Aerodynamic Simulation (NAS) parallel benchmarks use a
                 linear congruential generator with modulus 246. Our
                 result is about 50 times faster than the generic
                 implementation given in the benchmarks. The
                 extra-accuracy fused multiply-add instruction of
                 RS/6000 machines combined with a few algorithmic
                 innovations gives rise to the 50-fold increase. If IEEE
                 64-bit arithmetic is used with our Fortran code on
                 POWER and PowerPC architectures, the results we obtain
                 are bit-wise identical to the generic algorithms. The
                 paper gives several illustrations of a general
                 technique called the Algorithm and Architecture
                 approach. We demonstrate herein that
                 programmer-controlled unrolling of loops is equivalent
                 to ``customized vectorization of RISC-type code.''
                 Customized vectorization is more powerful than ordinary
                 vectorization, and it is only possible on RISC-type
                 machines. We illustrate its use to show that RS/6000
                 processors can compute the distribution $ ( - 1, 1) $
                 at the rate of 3.125 multiply-adds. We also specify a
                 linear congruential generator that is related to the
                 multiplicative congruential generator referred to
                 above. It has a full period of 2k, where 2k is the
                 modulus. The cost per random number [in the range $ (0,
                 1) $ ] for this generator is four multiply-adds on
                 RS/6000 processors. Our code, on the IBM POWER2 Model
                 590, for this generator produces more than 30 million
                 uniformly distributed pseudorandom numbers per second
                 for the range $ (0, 1) $. We show that this generator
                 is ``embarrassingly parallel,'' or EP. Using the
                 Algorithm and Architecture approach, we describe a new
                 concept called ``generalized unrolling.'' Finally, we
                 present a multiplicative congruential generator for
                 which the modulus is not a power of $2$. Such a
                 generator, as well as one with modulus $ 2^k $, is
                 selectable as the generator used in the RANDOM_NUMBER
                 intrinsic function of IBM XL Fortran and XL High
                 Performance Fortran. All of the generators reported
                 here are EP. Using an IBM SP2 machine with 250 wide
                 nodes, it is possible to compute more than ten billion
                 uniform random numbers in a second.",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  ordernumber =  "G322-0230",
}

@Article{Akbarpour:2002:FCS,
  author =       "Behzad Akbarpour and Abdelkader Dekdouk and
                 Sofi{\`e}ne Tahar",
  title =        "Formalization of Cadence {SPW} Fixed-Point Arithmetic
                 in {HOL}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2335",
  pages =        "185--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:09:38 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2335.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2335/23350185.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2335/23350185.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InProceedings{Akkas:2002:CIF,
  author =       "A. Akkas",
  booktitle =    "{IEEE 13th} International Conference on
                 Application-specific Systems, Architectures, and
                 Processors, San Jose, {USA}, July, 2002",
  title =        "A Combined Interval and Floating-point
                 Comparator\slash Selector",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "208--217",
  year =         "2002",
  bibdate =      "Fri Jun 11 05:39:44 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://home.ku.edu.tr/~ahakkas/publications/comparator.pdf",
  acknowledgement = ack-nhfb,
}

@PhdThesis{Akkas:2002:ISE,
  author =       "Ahmet Akkas",
  title =        "Instruction Set Enhancements for Reliable
                 Computations",
  type =         "{Ph.D.} Thesis",
  school =       "Lehigh University",
  address =      "Bethlehem, PA, USA",
  pages =        "159",
  year =         "2002",
  bibdate =      "Tue Nov 25 12:43:51 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3036247",
  abstract =     "Although there have been significant advances in VLSI
                 technology and numerical computing, floating-point
                 computations still suffer from undetected errors due to
                 rounding and catastrophic cancellation. Fast computers
                 let programmers write numerically intensive programs,
                 but computed results can be far from the true results
                 due to the accumulation of errors in arithmetic
                 operations. Therefore, accurate and reliable
                 computations have become more important.\par

                 Interval arithmetic is one technique for accurate and
                 reliable computing. With interval arithmetic, each data
                 value is represented by two floating-point numbers
                 which correspond to the endpoints of an interval, such
                 that the true result is guaranteed to lie on this
                 interval. Since interval arithmetic represents ranges
                 of numbers, it also provides the ability to solve
                 problems that cannot be efficiently solved using
                 floating-point arithmetic. Although interval arithmetic
                 provides an efficient method for monitoring and
                 controlling errors in floating-point computations, it
                 is not yet used widely because it is not sufficiently
                 fast.\par

                 This dissertation investigates instruction set
                 enhancements for interval arithmetic. Existing interval
                 arithmetic programs are examined to determine
                 bottlenecks in interval computations. Then, a variety
                 of instruction set enhancements are proposed to
                 overcome these bottlenecks. The efficiency of the
                 proposed enhancements are evaluated using an
                 interval-enhanced compiler and a superscalar processor
                 simulator. Hardware modifications to support these
                 enhancements are evaluated, and a novel design for a
                 combined Interval and Floating-point Comparator is
                 presented.\par

                 This dissertation also investigates instruction set
                 enhancements for extended precision arithmetic. In
                 particular, instruction set support for quadruple
                 precision arithmetic is examined. Hardware
                 modifications needed to support quadruple precision
                 arithmetic on superscalar processor is evaluated to
                 determine which extensions can be most efficiently
                 incorporated into superscalar processor designs.
                 Furthermore, a technique for performing parallel double
                 precision multiplication using quadruple precision
                 hardware is proposed.",
  acknowledgement = ack-nhfb,
  advisor =      "Michael J. Schulte",
  remark =       "Dissertation Abstracts International, Volume: 62-12,
                 Section: B, page: 5799.",
}

@Article{Alvarez:2002:IRF,
  author =       "C. Alvarez and J. Corbal and E. Salami and M. Valero",
  title =        "Initial Results on Fuzzy Floating Point Computation
                 for Multimedia Processors",
  journal =      j-IEEE-COMPUT-ARCHIT-LETT,
  volume =       "1",
  number =       "1",
  pages =        "1--1",
  month =        jan,
  year =         "2002",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/L-CA.2002.6",
  ISSN =         "1556-6056 (print), 1556-6064 (electronic)",
  ISSN-L =       "1556-6056",
  bibdate =      "Fri Jun 21 05:49:19 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeecomputarchitlett.bib",
  abstract =     "During the recent years the market of mid low end
                 portable systems such as PDAs or mobile digital phones
                 have experimented a revolution in both selling volume
                 and features as handheld devices incorporate Multimedia
                 applications. This fact brings to an increase in the
                 computational demands of the devices while still having
                 the limitation of power and energy consumption.
                 Instruction memoization is a promising technique to
                 help alleviate the problem of power consumption of
                 expensive functional units such as the floating point
                 one. Unfortunately this technique could be energy
                 inefficient for low end systems due to the additional
                 power consumption of the relatively big tables
                 required. In this paper we present a novel way of
                 understanding multimedia floating point operations
                 based on the fuzzy computation paradigm losses in the
                 computation precision may exchange performance for
                 negligible errors in the output. Exploiting the
                 implicit characteristics of media FP computation we
                 propose a new technique called fuzzy memoization. Fuzzy
                 memoization expands the capabilities of classic
                 memoization by attaching entries with similar inputs to
                 the same output. We present a case of study for a SH
                 like processor and report good performance and power
                 delay improvements with feasible hardware
                 requirements",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Computer Architecture Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=10208",
  keywords =     "Delay; Energy consumption; Fuzzy systems; Handheld
                 computers; Joining processes; Mobile computing;
                 Multimedia systems; Performance loss; Personal digital
                 assistants; Portable computers",
}

@Article{Anonymous:2002:AIVf,
  author =       "Anonymous",
  title =        "Author index volume 279 (2002)",
  journal =      j-THEOR-COMP-SCI,
  volume =       "279",
  number =       "1-2",
  pages =        "97",
  month =        may,
  year =         "2002",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Nov 20 18:08:56 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}

@TechReport{Anonymous:2002:OFP,
  author =       "Anonymous",
  title =        "{OpenVMS} floating-point arithmetic on the {Itanium}
                 architecture",
  institution =  inst-HP,
  address =      inst-HP:adr,
  month =        sep,
  year =         "2002",
  bibdate =      "Tue Nov 18 15:23:17 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://sysdoc.doors.ch/HP/openvms_ipf_floating_point_wp.pdf",
  acknowledgement = ack-nhfb,
}

@Manual{ARM:2002:VVF,
  title =        "{VFP9-S} Vector Floating-point Coprocessor (r0p2)
                 Technical Reference Manual",
  organization = "ARM Limited",
  address =      "Sunnyvale, CA, USA",
  pages =        "xvi + 156",
  year =         "2002",
  bibdate =      "Fri May 27 17:59:08 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.arm.com/pdfs/VFP-S_Vector_Floating_Point_Tech_Manual.pdf",
  acknowledgement = ack-nhfb,
  remark =       "From the manual, p. 1-7: ``The FMAC family of
                 instructions (FMAC, FNMAC, FMSC, and FNMSC) perform a
                 chained multiply and accumulate operation. The product
                 is computed, rounded according to the specified
                 rounding mode and destination precision, and checked
                 for exceptions before the accumulate operation is
                 performed. The accumulate operation is also rounded
                 according to the specified rounding mode and
                 destination precision, and checked for exceptions. The
                 final result is identical to the equivalent sequence of
                 operations executed in sequence.''\par

                 From p. 1-12: ``For instance, the VFP9-S coprocessor
                 does not process subnormal input values directly. To
                 provide correct handling of subnormal inputs according
                 to the IEEE 754 standard, a trap is made to support
                 code to process the operation. Using the support code
                 for processing this operation can require hundreds of
                 cycles.''\par

                 From p. 2-2: ``The VFP9-S register file contains
                 thirty-two 32-bit registers organized in four banks.
                 Each register can store either a single-precision
                 floating-point number or an integer.''\par

                 From p. 3-5: ``Any SNaN passed as input to an operation
                 causes an Invalid Operation exception, which is passed
                 to a user trap handler, if present. If a user trap
                 handler is not present, then a default QNaN is
                 created.''\par

                 From p. 3-7: ``In Flush-to-Zero mode, results that are
                 tiny before rounding, as described in the IEEE 754
                 standard, are flushed to a positive zero, and the UFC
                 flag, FPSCR[3], is set. Support code is not involved.
                 \ldots{} When the VFP9-S coprocessor is not in
                 Flush-to-Zero mode, any operation with a risk of
                 producing a tiny result, as described in the IEEE 754
                 standard, bounces to support code. If the operation
                 does not produce a tiny result, it returns the computed
                 result, and the UFC flag, FPSCR[3], is not set. The IXC
                 flag, FPSCR[4], is set if the operation is inexact. If
                 the operation produces a tiny result, the result is a
                 subnormal or zero value, and the UFC flag, FPSCR[3], is
                 set.",
}

@InProceedings{Arnold:2002:AOS,
  author =       "M. G. Arnold",
  booktitle =    "2002 {IEEE} Workshop on Multimedia Signal Processing",
  title =        "Avoiding oddification to simplify {MPEG}-1 decoding
                 with {LNS}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "125--129",
  year =         "2002",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Low-precision logarithmic number system (LNS)
                 arithmetic can reduce the power consumption for MPEG
                 decoding compared to conventional fixed-point
                 techniques. Although this introduces small numeric
                 errors, which violate the IEEE-1180 standard for the
                 \ldots{}",
}

@InProceedings{Arnold:2002:ICL,
  author =       "M. G. Arnold",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems: {ISCAS 2002}, 26--29 May 2002",
  title =        "Improved cotransformation for {LNS} subtraction",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "II-752--II-755",
  year =         "2002",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Two co-transformations have been proposed previously
                 to avoid interpolation difficulties for logarithmic
                 subtraction: Arnold's and Coleman's. We show these two
                 are closely related, but that Arnold's is considerably
                 more accurate in the worst case. \ldots{}",
}

@PhdThesis{Arnold:2002:LNS,
  author =       "Mark Gordon Arnold",
  title =        "Logarithmic Number Systems for {MPEG} and Multimedia
                 Applications",
  type =         "{Ph.D.} thesis",
  school =       "University of Manchester",
  address =      "Manchester, UK",
  pages =        "xiv + 358",
  month =        apr,
  year =         "2002",
  bibdate =      "Fri Dec 01 07:16:52 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.proquest.com/pqdtglobal/docview/2780144113",
  acknowledgement = ack-nhfb,
  advisor =      "Colin Donald Walter",
}

@InProceedings{Arnold:2002:RPC,
  author =       "Mark G. Arnold",
  title =        "Reduced Power Consumption for {MPEG} Decoding with
                 {LNS}",
  crossref =     "Schulte:2002:PII",
  pages =        "65--75",
  year =         "2002",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "LNS (logarithmic number system)",
  summary =      "By reducing the accuracy of the logarithmic number
                 system (LNS) it is possible to achieve lower power
                 consumption for multimedia applications, such as MPEG,
                 without significantly lowering the visual quality of
                 the output. An LNS wordsize of 8 to 10 \ldots{}",
}

@TechReport{Bailey:2002:AAP,
  author =       "David H. Bailey and Yozo Hida and Xiaoye S. Li and
                 Brandon Thompson",
  title =        "{ARPREC}: An arbitrary precision computation package",
  type =         "Technical Report",
  number =       "LBNL-53651",
  institution =  "Lawrence Berkeley National Laboratory",
  address =      "Berkeley, CA, USA",
  month =        sep,
  year =         "2002",
  DOI =          "https://doi.org/10.2172/817634",
  bibdate =      "Fri Jan 31 15:28:44 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://pubarchive.lbl.gov/islandora/object/ir:121949",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bailey:2002:HPC,
  author =       "David H. Bailey and David Broadhurst and Yozo Hida and
                 Xiaoye S. Li and Brandon Thompson",
  title =        "High Performance Computing Meets Experimental
                 Mathematics",
  crossref =     "IEEE:2002:STI",
  pages =        "??--??",
  year =         "2002",
  bibdate =      "Wed Nov 26 07:34:20 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sc-2002.org/paperpdfs/pap.pap124.pdf",
  abstract =     "In this paper we describe some novel applications of
                 high performance computing in a discipline now known as
                 experimental mathematics. The paper reviews some recent
                 published work, and then presents some new results that
                 have not yet appeared in the literature. A key
                 technique involved in this research is the PSLQ integer
                 relation algorithm (recently named one of ten
                 algorithms of the century by Computing in Science and
                 Engineering). This algorithm permits one to recognize a
                 numeric constant in terms of the formula that it
                 satisfies. We present a variant of PSLQ that is
                 well-suited for parallel computation, and give several
                 examples of new mathematical results that we have found
                 using it. Two of these computations were performed on
                 highly parallel computers, since they are not feasible
                 on conventional systems. We also describe a new
                 software package for performing arbitrary precision
                 arithmetic, which is required in this research.",
  acknowledgement = ack-nhfb,
}

@Article{Barrio:2002:REB,
  author =       "Roberto Barrio",
  title =        "Rounding error bounds for the {Clenshaw} and
                 {Forsythe} algorithms for the evaluation of orthogonal
                 polynomial series",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "138",
  number =       "2",
  pages =        "185--204",
  day =          "15",
  month =        jan,
  year =         "2002",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:45:23 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037704270100382X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Belanovic:2002:LPF,
  author =       "Pavle Belanovic and Miriam Leeser",
  title =        "A Library of Parameterized Floating-Point Modules and
                 Their Use",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2438",
  pages =        "657--666",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:10:28 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2438.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2438/24380657.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2438/24380657.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Bertot:2002:PGS,
  author =       "Yves Bertot and Nicolas Magaud and Paul Zimmermann",
  title =        "A Proof of {GMP} Square Root",
  journal =      j-J-AUTOM-REASON,
  volume =       "29",
  number =       "3--4",
  pages =        "225--252",
  month =        sep,
  year =         "2002",
  CODEN =        "JAREEW",
  DOI =          "https://doi.org/10.1023/A:1021987403425",
  ISSN =         "0168-7433 (print), 1573-0670 (electronic)",
  ISSN-L =       "0168-7433",
  bibdate =      "Sat Feb 08 08:59:09 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/gnu.bib;
                 https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
  URL =          "https://link.springer.com/article/10.1023/A:1021987403425",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Autom. Reason.",
  fjournal =     "Journal of Automated Reasoning",
  journal-URL =  "http://link.springer.com/journal/10817",
  keywords =     "GNU Multiple Precision library",
}

@Article{Beuchat:2002:SMB,
  author =       "Jean-Luc Beuchat and Arnaud Tisserand",
  title =        "Small Multiplier-Based Multiplication and Division
                 Operators for Virtex-{II} Devices",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2438",
  pages =        "513--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:10:28 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2438.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2438/24380513.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2438/24380513.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Blackford:2002:USB,
  author =       "L. Susan Blackford and James Demmel and Jack Dongarra
                 and Iain Duff and Sven Hammarling and Greg Henry and
                 Michael Heroux and Linda Kaufman and Andrew Lumsdaine
                 and Antoine Petitet and Roldan Pozo and Karin Remington
                 and R. Clint Whaley",
  title =        "An updated set of {Basic Linear Algebra Subprograms
                 (BLAS)}",
  journal =      j-TOMS,
  volume =       "28",
  number =       "2",
  pages =        "135--151",
  month =        jun,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/567806.567807",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 11:16:50 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This paper expands the specification of a set of
                 kernel routines for linear algebra, historically called
                 the Basic Linear Algebra Subprograms and commonly known
                 as the BLAS.\par

                 Numerical linear algebra, particularly the solution of
                 linear systems of equations, linear least squares
                 problems, eigenvalue problems and singular value
                 problems, is fundamental to most calculations in
                 scientific computing, and is often the computationally
                 intense part of such calculations. Designers of
                 computer programs involving linear algebraic operations
                 have frequently chosen to implement certain low level
                 operations, such as the dot product or the matrix
                 vector product, as separate subprograms. This may be
                 observed both in many published codes and in codes
                 written for specific applications at many computer
                 installations.\par

                 A major aim of the standards defined in this paper is
                 to enable linear algebra libraries (both public domain
                 and commercial) to interoperate efficiently, reliably
                 and easily.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@InProceedings{Boldo:2002:FRF,
  author =       "Sylvie Boldo and Marc Daumas",
  booktitle =    "10th {IMACS-GAMM} International Symposium on
                 Scientific Computing, Computer Arithmetic and Validated
                 Numerics, {SCAN-2002}, September 24--27, Paris,
                 France",
  title =        "Faithful rounding without fused multiply and
                 accumulate",
  publisher =    "????",
  address =      "????",
  bookpages =    "????",
  pages =        "??--??",
  year =         "2002",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Tue Nov 23 10:31:01 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://scan2002.lip6.fr/abstracts/boldo.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Boldo:2002:IAO,
  author =       "Sylvie Boldo",
  title =        "Introduction {\`a} l'arithm{\`e}tique des ordinateurs.
                 ({French}) [Introduction to computer arithmetic]",
  howpublished = "World-Wide Web document",
  publisher =    "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "69364 Lyon Cedex 07, France",
  year =         "2002",
  bibdate =      "Tue Nov 23 10:51:50 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Presented in 2002 at the ``Forum des jeunes
                 math{\`e}maticiennes et des jeunes
                 informaticiennes''.",
  URL =          "http://perso.ens-lyon.fr/sylvie.boldo/doc/FetM.ps",
  acknowledgement = ack-nhfb,
  language =     "French",
}

@TechReport{Boldo:2002:NSC,
  author =       "Sylvie Boldo and Marc Daumas",
  title =        "Necessary and sufficient conditions for exact floating
                 point operations",
  type =         "Research Report",
  number =       "2002-44",
  institution =  "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "69364 Lyon Cedex 07, France",
  month =        nov,
  year =         "2002",
  bibdate =      "Tue Nov 23 10:54:25 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4644.pdf",
  acknowledgement = ack-nhfb,
}

@TechReport{Boldo:2002:PSVa,
  author =       "Sylvie Boldo and Marc Daumas",
  title =        "Properties of the Subtraction Valid for any Floating
                 Point System",
  type =         "Research Report",
  number =       "2002-23",
  institution =  "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "69364 Lyon Cedex 07, France",
  month =        jun,
  year =         "2002",
  bibdate =      "Tue Nov 23 11:08:31 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.ens-lyon.fr/pub/LIP/Rapports/RR/RR2002/RR2002-23.ps.gz;
                 ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4473.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Boldo:2002:PSVb,
  author =       "Sylvie Boldo and Marc Daumas",
  editor =       "Rance Cleaveland and Hubert Garavel",
  booktitle =    "7th International {ERCIM} Workshop on Formal Methods
                 for Industrial Critical Systems ({FMICS 02}):
                 University of M{\'a}laga, Spain July 12--13, 2002",
  title =        "Properties of the Subtraction Valid for any Floating
                 Point System",
  publisher =    "Universidad de M{\'a}laga, Spain",
  address =      "M{\'a}laga, Spain",
  bookpages =    "v + 217",
  pages =        "137--149",
  year =         "2002",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Tue Nov 23 10:14:59 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Available as Technical Report ITI-2002-5, Dpto. de
                 Lenguajes y Ciencias de la Computaci{\'o}n, Universidad
                 de M{\'a}laga, Spain",
  URL =          "http://www.inrialpes.fr/vasy/fmics/workshop-7/proceedings.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cardarilli:2002:RNS,
  author =       "G. C. Cardarilli and A. Del Re and A. Nannarelli and
                 M. Re",
  booktitle =    "{ISCAS 2002}, {IEEE} International Symposium on
                 Circuits and Systems, 26--29 May 2002",
  title =        "Residue number system reconfigurable datapath",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "II-756--II-759",
  year =         "2002",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.2002.1011463",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "In this paper we describe a possible approach to
                 implement a reconfigurable datapath for digital signal
                 processing. The datapath should be programmable in
                 terms of dynamic range, type and sequence of
                 operations. We chose to implement it in the \ldots{}",
}

@Article{Chesneaux:2002:FRN,
  author =       "Jean-Marie Chesneaux and Christiane Frougny and
                 Jean-Michel Muller",
  title =        "Foreword: Real Numbers",
  journal =      j-THEOR-COMP-SCI,
  volume =       "279",
  number =       "1-2",
  pages =        "1--2",
  month =        may,
  year =         "2002",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Nov 20 18:08:56 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}

@Article{Chiricescu:2002:MM,
  author =       "Silviu Chiricescu and Michael Schuette and Robin
                 Glinton and Herman Schmit",
  title =        "Morphable Multipliers",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2438",
  pages =        "647--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:10:28 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2438.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2438/24380647.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2438/24380647.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InProceedings{Chotin:2002:FPU,
  author =       "R. Chotin and H. Mehrez",
  booktitle =    "9th International Conference on Electronics, Circuits
                 and Systems, 2002",
  title =        "A floating-point unit using stochastic arithmetic
                 compliant with the {IEEE-754} standard",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "603--606",
  year =         "2002",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 17:14:11 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "In this paper, we present CESTAC, a method to control
                 round-off errors in floating-point scientific
                 computation, based on stochastic arithmetic. The real
                 time use of this method suffers from a bottleneck of
                 software calculations. This paper gives a \ldots{}",
}

@Article{Col:2002:ALC,
  author =       "Marie-Andr{\'e}e Jacob-Da Col",
  title =        "About local configurations in arithmetic planes",
  journal =      j-THEOR-COMP-SCI,
  volume =       "283",
  number =       "1",
  pages =        "183--201",
  month =        jun,
  year =         "2002",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Nov 20 18:08:57 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}

@InProceedings{Conway:2002:NOH,
  author =       "Richard Conway and Thomas Conway and John Nelson",
  title =        "New One-Hot {RNS} Structures for High-Speed Signal
                 Processing",
  crossref =     "Luk:2002:PSA",
  pages =        "381--392",
  year =         "2002",
  bibdate =      "Fri Jun 24 18:17:01 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://bookstore.spie.org/index.cfm?fuseaction=DetailPaper&ProductId=452053",
  abstract =     "New efficient structures using the one-hot residue
                 number system (OHRNS) are presented. Normally the RNS
                 uses a binary representation for the residues, though
                 recently there has been renewed interest in the OHRNS,
                 which uses a simple, but novel representation for the
                 residues. The basic component of the OHRNS is the
                 barrel shifter, making the OHRNS suitable for very high
                 speed applications. The first of the new structures
                 presented reduces the power dissipation in OHRNS adder
                 trees. A modification to the normal barrel shifter is
                 proposed, which reduces the power dissipated by as much
                 as 30\%. This improvement is obtained through the use
                 of the modified barrel shifter and the appropriate
                 connection of active-low and active-high stages. This
                 overall power reduction offers the possibility of using
                 the OHRNS in place of a typical full adder based tree
                 in high speed DSP applications. A new storage register
                 for one-hot representations is detailed, which
                 overcomes the problem of having to use a large number
                 of registers. A new architecture is presented for fast
                 OHRNS sign detection. Sign detection is complex and
                 slow to perform in the RNS. A mixed radix conversion
                 (MRC) is typically used for sign detection in the
                 OHRNS. The new sign detection architecture is based on
                 a new property of the Chinese Remainder Theorem (CRT)
                 and is significantly faster than the MRC approach for
                 large moduli sets. Simulation results using SPICE are
                 detailed for the new structures.",
  acknowledgement = ack-nhfb,
  keywords =     "One-Hot Residue Number System (OHRNS); Residue Number
                 System (RNS)",
}

@Article{Conway:2002:SRI,
  author =       "T. Conway",
  title =        "Static register implementation for one hot residue
                 number systems",
  journal =      j-ELECT-LETTERS,
  volume =       "38",
  number =       "2",
  pages =        "63--64",
  day =          "17",
  month =        jan,
  year =         "2002",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:20020050",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=21138",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A method of implementing static registers for one-hot
                 residue number systems is described. The method
                 overcomes the high power dissipation problems
                 associated with conventional flip-flops and clock
                 distribution. The proposed design relies on the low
                 \ldots{}",
}

@Book{Cornea:2002:SCI,
  author =       "Marius Cornea and John Harrison and Ping Tak Peter
                 Tang",
  title =        "Scientific computing on {Itanium}-based systems",
  publisher =    pub-INTEL,
  address =      pub-INTEL:adr,
  pages =        "xvii + 406",
  year =         "2002",
  ISBN =         "0-9712887-7-1",
  ISBN-13 =      "978-0-9712887-7-5",
  LCCN =         "QA76.8.I83 C67 2002",
  bibdate =      "Sat Dec 06 15:02:26 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\$69.95",
  URL =          "http://www.intel.com/intelpress/sum_scientific.htm",
  abstract =     "Written for professionals who need to write, port, or
                 maintain reliable, accurate, and efficient numerical
                 software for the Itanium architecture, Scientific
                 Computing on Itanium-based Systems shows you how to
                 construct key numerical infrastructure and application
                 programs.\par

                 This book describes the crucial techniques required for
                 stability and reliability in developing numerical
                 kernels and applications. Through numerous tested
                 examples, the authors explain how you can get the most
                 from the 64-bit architecture. This combination of
                 explanation with example helps you to make difficult
                 computations more easily and to increase the
                 performance of your numerical software.\par

                 This book provides examples to solve problems
                 encountered in scientific and engineering computations,
                 such as:\par

                 * Polynomial evaluation\\
                 * Complex arithmetic\\
                 * Quad-precision arithmetic\\
                 * Software pipelining, to include register rotation and
                 modulo-scheduled loop support\\
                 * SIMD instructions\\
                 * Interval arithmetic\\
                 * Fast-Fourier Transformation (FFT) algorithms\\
                 * Numerical linear algebra and basic linear algebra
                 subprograms(BLAS)\\
                 * Vector Math Library (VML)\\
                 * Cryptography",
  acknowledgement = ack-nhfb,
}

@Article{Cowlishaw:2002:DPD,
  author =       "Michael F. Cowlishaw",
  title =        "Densely Packed Decimal Encoding",
  journal =      j-IEE-PROC-COMPUT-DIGIT-TECH,
  volume =       "149",
  number =       "3",
  pages =        "102--104",
  year =         "2002",
  CODEN =        "ICDTEA",
  DOI =          "https://doi.org/10.1049/ip-cdt:20020407",
  ISSN =         "1350-2387 (print), 1359-7027 (electronic)",
  ISSN-L =       "1350-2387",
  bibdate =      "Fri Jun 07 11:08:45 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEE Proceedings. Computers and Digital Techniques",
  keywords =     "decimal floating-point arithmetic",
}

@Misc{Cowlishaw:2002:TB,
  author =       "M. F. Cowlishaw",
  title =        "The `telco' benchmark",
  howpublished = "World-Wide Web document.",
  institution =  "IBM Hursley Laboratory",
  address =      "Hursley, UK",
  pages =        "3",
  year =         "2002",
  bibdate =      "Fri Nov 28 11:14:02 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www2.hursley.ibm.com/decimal/telco.html",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@TechReport{Crandall:2002:OPF,
  author =       "R. E. Crandall and J. Papadopoulos",
  title =        "Octuple-precision floating point on {Apple G4}",
  type =         "Report",
  institution =  "Advanced Computation Group, Apple Computer",
  address =      "Cupertino, CA, USA",
  pages =        "8",
  day =          "8",
  month =        may,
  year =         "2002",
  bibdate =      "Tue Mar 19 09:06:09 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://images.apple.com/acg/pdf/oct3a.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Daumas:2002:ASN,
  author =       "Marc Daumas and Philippe Langlois",
  title =        "Additive symmetries: the non-negative case",
  journal =      j-THEOR-COMP-SCI,
  volume =       "291",
  number =       "2",
  pages =        "143--157",
  month =        nov,
  year =         "2002",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Nov 20 18:15:29 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tcs2000.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Theor. Comput. Sci.",
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
  remark =       "Proceedings of the Fourth conference on Real numbers
                 and Computers, Schlo{\ss} Dagstuhl, April 2000.",
}

@InProceedings{deDinechin:2002:MTJ,
  author =       "Florent de Dinechin and J{\'e}r{\'e}mie Detrey",
  title =        "Multipartite Tables in {JBits} for the Evaluation of
                 Functions on {FPGA}'s",
  crossref =     "IEEE:2002:IRA",
  pages =        "154--160",
  year =         "2002",
  bibdate =      "Fri Jun 24 20:27:42 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ens-lyon.fr/LIP/Arenaire/News/JBits/",
  abstract =     "This paper presents the implementation, on Virtex
                 FPGAs, of a core generator for arbitrary numeric
                 functions in fixed-point format. The cores use the
                 state-of-theart multipartite table method, which allows
                 input and output precisions in the range of 8 to 24
                 bits on current Virtex chips. The implementation uses
                 the JBits API to embed elaborate optimisation
                 techniques in the description of the hardware.",
  acknowledgement = ack-nhfb,
}

@TechReport{Defour:2002:SCSa,
  author =       "David Defour and Florent de Dinechin",
  title =        "Software Carry-Save for Fast Multiple-Precision
                 Algorithms",
  type =         "Research Report",
  number =       "2002-08",
  institution =  "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "69364 Lyon Cedex 07, France",
  pages =        "12",
  month =        feb,
  year =         "2002",
  bibdate =      "Wed Nov 24 07:47:53 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.ens-lyon.fr/pub/LIP/Rapports/RR/RR2002/RR2002-08.ps.gz;
                 http://www.ens-lyon.fr/LIP/Arenaire/Ware/SCSLib/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Defour:2002:SCSb,
  author =       "David Defour and Florent de Dinechin",
  title =        "Software Carry-Save for Fast Multiple-Precision
                 Algorithms",
  crossref =     "Cohen:2002:MSP",
  pages =        "29--39",
  year =         "2002",
  bibdate =      "Fri Jun 24 19:59:47 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  xxbooktitle =  "35th International Congress of Mathematical Software,
                 Beijing, China, 2002",
  xxnote =       "Check: 1st or 35th congress??",
}

@InProceedings{Demmel:2002:AEA,
  author =       "J. Demmel and P. Koev",
  title =        "Accurate and Efficient Algorithms for Floating Point
                 Computation",
  crossref =     "Li:2002:PIC",
  pages =        "16",
  year =         "2002",
  bibdate =      "Mon Apr 25 07:13:09 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://math.mit.edu/~plamen/files/ICIAM_main.pdf",
  acknowledgement = ack-nhfb,
}

@TechReport{Demmel:2002:AFP,
  author =       "James Demmel and Yozo Hida",
  title =        "Accurate floating-point summation",
  type =         "Report",
  institution =  "Computer Science Division and Mathematics Department,
                 University of California, Berkeley",
  address =      "Berkeley, CA, USA",
  day =          "8",
  month =        may,
  year =         "2002",
  bibdate =      "Wed May 08 15:15:07 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~demmel/AccurateSummation.pdf;
                 http://www.cs.berkeley.edu/~demmel/AccurateSummation.ps",
  abstract =     "We present and analyze several simple algorithms for
                 accurately summing $n$ floating point numbers $ S =
                 \sum_{i = 1}^n s_i $ independent of how much
                 cancellation occurs in the sum. Let $f$ be the number
                 of significant bits in the $ s_i $. We assume a
                 register is available with $ F > f $ significant bits.
                 Then assuming that (1) $ n \leq \floor {2^{F - f} / (1
                 - 2^{-f})} + 1 $, (2) rounding is to nearest, (3) no
                 overflow occurs, and (4) all underflow is gradual,then
                 simply summing the $ s_i $ in decreasing order of
                 magnitude yields $S$ rounded to within just over 1.5
                 units in its last place. If $ S = 0 $, then it is
                 computed exactly. If we increase $n$ slightly to $
                 \floor {2^{F - f} / (1 - 2^{-f})} + 3 $ then all
                 accuracy can be lost. This result extends work of
                 Priest and others who considered double precision only
                 $ (F \geq 2 f) $. We apply this result to the floating
                 point formats in the (proposed revision of the) IEEE
                 floating point standard. For example, a dot product of
                 IEEE single precision vectors $ \sum_{i = 1}^n x_i \dot
                 {}y_i $ computed using double precision and sorting is
                 guaranteed correct to nearly $ 1.5 $ ulps as long as $
                 n \leq 33 $. If double extended is used $n$ can be as
                 large as $ 65537 $. We also show how sorting may be
                 avoided while retaining accuracy.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}

@InCollection{Demmel:2002:CAF,
  author =       "J. Demmel and Plamen Koev and Ben Diament",
  title =        "The Complexity of Accurate Floating Point
                 Computation",
  crossref =     "Li:2002:PIC",
  volume =       "III (1--3)",
  year =         "2002",
  MRclass =      "65G30 (65Y20)",
  MRnumber =     "MR1957571 (2004b:65060)",
  bibdate =      "Mon Apr 25 06:44:54 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~demmel/ICM_final.pdf;
                 http://www.fernuni-hagen.de/MATHPHYS/veselic/abstracts/abs_demmel.html",
  abstract =     "We consider the complexity of accurately evaluating
                 floating point expressions, by which we mean getting
                 some guaranteed relative accuracy, and identify a class
                 of expressions where this can be done in polynomial
                 time in the size of the expression and data. We also
                 have a simple expression not in this class for which we
                 have strong evidence that it cannot be evaluated
                 accurately in polynomial time. We extend these results
                 to the accurate computations of certain matrix
                 computations including inverses, LU decompositions, and
                 the SVD.\par

                 If time permits, we will also present a recent result
                 where we show that the complexity of approximate
                 condition estimation is as large as ``verifying''
                 matrix multiplication. Together with the
                 widely-believed conjecture that verifying that A*B=0
                 cannot be done more cheaply than by multiplying A*B,
                 this implies that all fast condition estimators in
                 widespread use have counterexamples, i.e. matrices for
                 which their estimates are arbitrarily wrong.",
  acknowledgement = ack-nhfb,
  pagecount =    "10",
  remark =       "Also presented at the Householder Symposium on
                 Numerical Linear Algebra June 17--21, 2002 Peebles
                 Hotel Hydro, Scotland, and the IV International
                 Workshop on Accurate Solution of Eigenvalue Problems
                 Split, Croatia, June 24--27, 2002.",
}

@TechReport{Devillers:2002:FPE,
  author =       "Olivier Devillers and Philippe Guigue",
  title =        "Finite Precision Elementary Geometric Constructions",
  type =         "Technical report",
  number =       "RR 4559",
  institution =  "Unit{\'e} de recherche INRIA Sophia Antipolis",
  address =      "2004, route des Lucioles, BP 93, 06902 Sophia
                 Antipolis C{\'e}dex, France",
  pages =        "17",
  month =        sep,
  year =         "2002",
  bibdate =      "Tue Nov 13 21:54:25 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www-sop.inria.fr/rapports/sophia/RR-4559.html",
  abstract =     "In this paper we propose a new approach for the robust
                 computation of the nearest integer lattice points of
                 some specific geometric constructions (intersection of
                 two planar segments, circumcenter of a planar triangle
                 and of a spatial tetrahedron). Given that the data and
                 the final results of the geometric constructions are
                 stored using single precision floating point
                 representation (typically fixed size integers), the
                 proposed algorithms first perform the geometric
                 construction in IEEE double precision floating point
                 arithmetic, the rounding error is estimated, and only
                 if the error estimation indicates that the result of
                 the floating point computation may be wrong, the
                 computation is repeated with exact arithmetic. The
                 basic advantage is that exact computations are in most
                 cases avoided, thus reducing both the storage and the
                 required computation time.",
  acknowledgement = ack-nhfb,
  keywords =     "computational geometry; Floating point filter;
                 robustness, floating point arithmetic",
}

@InProceedings{Dido:2002:FFP,
  author =       "J. Dido and N. Geraudie and L. Loiseau and O. Payeur
                 and Y. Savaria and D. Poirier",
  title =        "A flexible floating-point format for optimizing
                 data-paths and operators in {FPGA} based {DSPs}",
  crossref =     "Trimberger:2002:FTA",
  pages =        "50--55",
  year =         "2002",
  DOI =          "https://doi.org/10.1145/503048.503056",
  bibdate =      "Sat Oct 9 12:34:43 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Video signal processing requires complex algorithms
                 performing many basic operations on a video stream. To
                 perform these calculations in real-time in a FPGA, we
                 must use innovative structures to meet speed
                 requirements while managing complexity. As part of a
                 project aiming at the development of a video noise
                 reducer, we developed an optimized processing stream
                 that required some floating-point calculations. This
                 paper presents the rationale for developing a
                 floating-point unit, justifies the data representation
                 used, its implementation in a Xilinx VirtexE FPGA and
                 reports the performance we obtained. A divider using
                 this representation is also presented, with its
                 implementation and performances in the same FPGA.",
  acknowledgement = ack-nhfb,
}

@Article{Elia:2002:ISC,
  author =       "M. Elia and M. Leone",
  title =        "On the inherent space complexity of fast parallel
                 multipliers for {$ \mathrm {GF}(2^m) $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "51",
  number =       "3",
  pages =        "346--351",
  month =        mar,
  year =         "2002",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.990131",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 09:41:49 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=990131",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Erle:2002:PSD,
  author =       "Mark A. Erle and Michael J. Schulte and J. G.
                 Linebarger",
  title =        "Potential Speedup with Decimal Floating-Point
                 Hardware",
  crossref =     "Matthews:2002:PTS",
  pages =        "1073--1077",
  year =         "2002",
  bibdate =      "Thu Mar 24 13:47:20 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2002-05.pdf",
  abstract =     "This paper addresses the potential speedup achieved by
                 using decimal floating-point hardware, instead of
                 software routines, on a high-performance superscalar
                 architecture. Software routines were written to perform
                 decimal addition, subtraction, multiplication, and
                 division. Cycle counts were then measured for each
                 instruction using the Simplescalar simulator. After
                 this, new hardware algorithms were developed, existing
                 hardware algorithms were analyzed, and cycle counts
                 were estimated for the same set of instructions using
                 specialized decimal floating-point hardware. This data
                 was then used to show the potential speedup obtained
                 for programs with different instruction mixes and a
                 recently developed benchmark.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@Article{Etiemble:2002:CAH,
  author =       "Daniel Etiemble",
  title =        "Computer arithmetic and hardware: ``off the shelf''
                 microprocessors versus ``custom hardware''",
  journal =      j-THEOR-COMP-SCI,
  volume =       "279",
  number =       "1--2",
  pages =        "3--27",
  month =        may,
  year =         "2002",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Nov 20 18:08:56 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper discusses the relationship between computer
                 arithmetic and hardware implementation. First, we
                 examine the impact of computer arithmetic on the
                 overall performance of today's microprocessors. By
                 comparing their evolution over the last 10 years, we
                 show that the performance of arithmetic operators is
                 far less critical than the performance of the memory
                 hierarchy or the branch predictors. We then discuss the
                 potential for improvement in arithmetic performance,
                 both for pipelined and non-pipelined operations. We
                 then examine the possible impact of new technologies,
                 such as MMX technology or asynchronous control of
                 microprocessors, on computer arithmetic. Finally, we
                 show that programmable logic devices now permit a
                 cost-effective implementation of specific arithmetic
                 number representations, such as serial arithmetic or
                 logarithmic representations.",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}

@Article{Gaffar:2002:ACF,
  author =       "Altaf Abdul Gaffar and Wayne Luk and Peter Y. K.
                 Cheung and Nabeel Shirazi and James Hwang",
  title =        "Automating Customisation of Floating-Point Designs",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2438",
  pages =        "523--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:10:28 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2438.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2438/24380523.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2438/24380523.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Galbraith:2002:ASC,
  author =       "S. D. Galbraith and S. M. Paulus and N. P. Smart",
  title =        "Arithmetic on superelliptic curves",
  journal =      j-MATH-COMPUT,
  volume =       "71",
  number =       "237",
  pages =        "393--405",
  month =        jan,
  year =         "2002",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Thu Jan 31 06:16:28 MST 2002",
  bibsource =    "http://www.ams.org/mcom/2002-71-237;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ams.org/journal-getitem?pii=S0025-5718-00-01297-7;
                 http://www.ams.org/mcom/2002-71-237/S0025-5718-00-01297-7/S0025-5718-00-01297-7.dvi;
                 http://www.ams.org/mcom/2002-71-237/S0025-5718-00-01297-7/S0025-5718-00-01297-7.pdf;
                 http://www.ams.org/mcom/2002-71-237/S0025-5718-00-01297-7/S0025-5718-00-01297-7.ps;
                 http://www.ams.org/mcom/2002-71-237/S0025-5718-00-01297-7/S0025-5718-00-01297-7.tex",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@InProceedings{Garcia:2002:CBB,
  author =       "E. Garcia and M. J. Schulte",
  title =        "A Combined 16-Bit Binary and Dual {Galois} Field
                 Multiplier",
  crossref =     "IEEE:2002:IWS",
  pages =        "63--68",
  year =         "2002",
  bibdate =      "Sun Mar 04 17:49:09 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2002-04.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Geiselmann:2002:NRE,
  author =       "W. Geiselmann and J. Muller-Quade and R. Steinwandt",
  title =        "On {``A new representation of elements of finite
                 fields $ \mathrm {GF}(2^m) $ yielding small complexity
                 arithmetic circuits''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "51",
  number =       "12",
  pages =        "1460--1461",
  month =        dec,
  year =         "2002",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2002.1146713",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 09:42:01 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1146713",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Glossner:2002:JED,
  author =       "C. John Glossner and Michael Schulte and Stamatis
                 Vassiliadis",
  title =        "A {Java}-Enabled {DSP}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2268",
  pages =        "307--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:09:05 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2268.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2268/22680307.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2268/22680307.pdf;
                 http://mesa.ece.wisc.edu/publications/cp_2002-01.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InCollection{Goldberg:2002:CA,
  author =       "David Goldberg",
  title =        "Computer Arithmetic",
  crossref =     "Hennessy:2002:CAQ",
  chapter =      "H",
  pages =        "H-1--H-74",
  year =         "2002",
  bibdate =      "Fri May 31 16:10:43 2002",
  bibsource =    "http://www.mkp.com/CA3;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "The complete Appendix H is not in the printed book; it
                 is available only at the book's Web site:
                 \path=http://www.mkp.com/CA3=.",
  URL =          "http://books.elsevier.com/companions/1558605967/appendices/1558605967-appendix-h.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Gonzalez:2002:NME,
  author =       "Daniel Gonz{\'a}lez and Antonio Garc{\'\i}a and Graham
                 A. Jullien and Javier Ram{\'\i}rez and Luis Parrilla
                 and Antonio Lloris",
  title =        "A New Methodology for Efficient Synchronization of
                 {RNS}-Based {VLSI} Systems",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2451",
  pages =        "188--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:10:32 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2451.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2451/24510188.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2451/24510188.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Gottwald:2002:NBL,
  author =       "G. A. Gottwald and M. Nicol",
  title =        "On the nature of {Benford's Law}",
  journal =      j-PHYSICA-A,
  volume =       "303",
  number =       "??",
  pages =        "387--396",
  month =        "????",
  year =         "2002",
  CODEN =        "PHYADX",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Thu Feb 15 16:32:55 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Goubault:2002:APF,
  author =       "Eric Goubault and Matthieu Martel and Sylvie Putot",
  title =        "Asserting the Precision of Floating-Point
                 Computations: a Simple Abstract Interpreter",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2305",
  pages =        "209--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:09:22 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2305.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2305/23050209.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2305/23050209.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Guo:2002:RIB,
  author =       "Linfeng Guo and Yan Meng",
  title =        "Round-up of integer bit allocation",
  journal =      j-ELECT-LETTERS,
  volume =       "38",
  number =       "10",
  pages =        "466--467",
  day =          "9",
  month =        may,
  year =         "2002",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Jul 16 11:25:05 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  summary =      "A non-iterative algorithm is presented for the
                 round-up procedure of integer bit allocation. The
                 round-up algorithm will give the optimum result without
                 the disadvantages of the traditional iterative
                 \ldots{}",
}

@Book{Hamacher:2002:CO,
  author =       "V. Carl Hamacher and Zvonko G. Vranesic and Safwat G.
                 Zaky",
  title =        "Computer organization",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  edition =      "Fifth",
  pages =        "xx + 805",
  year =         "2002",
  ISBN =         "0-07-232086-9",
  ISBN-13 =      "978-0-07-232086-2",
  LCCN =         "QA76.9.C643 .H36 2002",
  bibdate =      "Sat May 18 14:24:11 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "McGraw-Hill series in computer organization and
                 architecture",
  acknowledgement = ack-nhfb,
}

@Article{Hanrot:2002:DRF,
  author =       "G. Hanrot and J. Rivat and G. Tenenbaum and P.
                 Zimmermann",
  title =        "Density results on floating-point invertible numbers",
  journal =      j-THEOR-COMP-SCI,
  volume =       "291",
  number =       "2",
  pages =        "135--141",
  month =        nov,
  year =         "2002",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Nov 20 18:15:29 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tcs2000.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Theor. Comput. Sci.",
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975/",
  remark =       "Proceedings of the Fourth conference on Real numbers
                 and Computers, Schlo{\ss} Dagstuhl, April 2000.",
}

@TechReport{Hanrot:2002:LNM,
  author =       "G. Hanrot and P. Zimmermann",
  title =        "A long note on {Mulders}' short product",
  type =         "Technical Report",
  number =       "RR-4654",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  pages =        "12",
  month =        nov,
  year =         "2002",
  bibdate =      "Sun Sep 10 08:17:26 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Mulders:2000:SMD}",
  abstract =     "The short product of two power series is the
                 meaningful part of the product of these objects, i.e.,
                 $ \sum_{i + j < n} a_i b_j x^{i + j} $. In [2], Mulders
                 gives an algorithm to compute a short product faster
                 than the full product in the case of Karatsuba's
                 multiplication [1]. This algorithm work by selecting a
                 cutoff point $k$ and performing a full $ k \times k $
                 product and two $ (n - k) \times (n - k) $ short
                 products recursively. Mulders also gives an
                 heuristically optimal cutoff point $ \beta n $. In this
                 paper, we determine the optimal cutoff point in
                 Mulders' algorithm. We also give a slightly more
                 general description of Mulders' method.",
  acknowledgement = ack-nhfb,
}

@Article{Heckmann:2002:CLF,
  author =       "Reinhold Heckmann",
  title =        "Contractivity of linear fractional transformations",
  journal =      j-THEOR-COMP-SCI,
  volume =       "279",
  number =       "1-2",
  pages =        "65--82",
  month =        may,
  year =         "2002",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Nov 20 18:08:56 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}

@Article{Helms:2002:IPM,
  author =       "D. Helms and E. Schmidt and A. Schulz and A.
                 Stammermann and W. Nebel",
  title =        "An Improved Power Macro-Model for Arithmetic Datapath
                 Components",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2451",
  pages =        "16--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:10:32 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2451.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2451/24510016.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2451/24510016.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Hertling:2002:LBR,
  author =       "Peter Hertling",
  title =        "A lower bound for range enclosure in interval
                 arithmetic",
  journal =      j-THEOR-COMP-SCI,
  volume =       "279",
  number =       "1-2",
  pages =        "83--95",
  month =        may,
  year =         "2002",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Nov 20 18:08:56 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}

@Article{Hiasat:2002:HSR,
  author =       "A. A. Hiasat",
  title =        "High-speed and reduced-area modular adder structures
                 for {RNS}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "51",
  number =       "1",
  pages =        "84--89",
  month =        jan,
  year =         "2002",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.980018",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 09:41:46 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=980018",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Book{Higham:2002:ASN,
  author =       "Nicholas J. Higham",
  title =        "Accuracy and Stability of Numerical Algorithms",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  edition =      "Second",
  pages =        "xxx + 680",
  year =         "2002",
  DOI =          "https://doi.org/10.1137/1.9780898718027",
  ISBN =         "0-89871-521-0 (hardcover), 0-89871-802-3 (e-book)",
  ISBN-13 =      "978-0-89871-521-7 (hardcover), 978-0-89871-802-7
                 (e-book)",
  LCCN =         "QA297 .H53 2002",
  MRclass =      "65G50 (65-02)",
  MRnumber =     "MR1927606 (2003g:65064)",
  bibdate =      "Wed Oct 30 14:20:02 2002",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  abstract =     "\booktitle{Accuracy and Stability of Numerical
                 Algorithms} gives a thorough, up-to-date treatment of
                 the behavior of numerical algorithms in finite
                 precision arithmetic. It combines algorithmic
                 derivations, perturbation theory, and rounding error
                 analysis, all enlivened by historical perspective and
                 informative quotations. This second edition expands and
                 updates the coverage of the first edition (1996) and
                 includes numerous improvements to the original
                 material. Two new chapters treat symmetric indefinite
                 systems and skew-symmetric systems, and nonlinear
                 systems and Newton's method. Twelve new sections
                 include coverage of additional error bounds for
                 Gaussian elimination, rank revealing $ L U $
                 factorizations, weighted and constrained least squares
                 problems, and the fused multiply-add operation found on
                 some modern computer architectures.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
  tableofcontents = "List of Figures \\
                 List of Tables \\
                 Preface to Second Edition \\
                 Preface to First Edition \\
                 About the Dedication \\
                 1: Principles of Finite Precision Computation \\
                 2: Floating Point Arithmetic \\
                 3: Basics \\
                 4: Summation \\
                 5: Polynomials \\
                 6: Norms \\
                 7: Perturbation Theory for Linear Systems \\
                 8: Triangular Systems \\
                 9: $ L U $ Factorization and Linear Equations \\
                 10: Cholesky Factorization \\
                 11: Symmetric Indefinite and Skew-Symmetric Systems \\
                 12: Iterative Refinement \\
                 13: Block LU Factorization \\
                 14: Matrix Inversion \\
                 15: Condition Number Estimation \\
                 16: The Sylvester Equation \\
                 17: Stationary Iterative Methods \\
                 18: Matrix Powers \\
                 19: QR Factorization \\
                 20: The Least Squares Problem \\
                 21: Underdetermined Systems \\
                 22: Vandermonde Systems \\
                 23: Fast Matrix Multiplication \\
                 24: The Fast Fourier Transform and Applications \\
                 25: Nonlinear Systems and Newton's Method \\
                 26: Automatic Error Analysis \\
                 27: Software Issues in Floating Point Arithmetic \\
                 28: A Gallery of Test Matrices \\
                 Appendix A: Solutions to Problems \\
                 Appendix B: Acquiring Software \\
                 Appendix C: Program Libraries \\
                 Appendix D: The Matrix Computation Toolbox \\
                 Bibliography \\
                 Name Index \\
                 Subject Index",
}

@Article{Hitchcock:2002:NEC,
  author =       "Yvonne Hitchcock and Paul Montague",
  title =        "A New Elliptic Curve Scalar Multiplication Algorithm
                 to Resist Simple Power Analysis",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2384",
  pages =        "214--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:10:02 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2384.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2384/23840214.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2384/23840214.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Hoenninger:2002:FPD,
  author =       "J. C. {Hoenninger III} and L. E. Crooks and M.
                 Arakawa",
  title =        "A floating-point digital receiver for {MRI}",
  journal =      j-IEEE-TRANS-BIOMED-ENG,
  volume =       "49",
  number =       "7",
  pages =        "689--693",
  month =        jul,
  year =         "2002",
  CODEN =        "IEBEAX",
  ISSN =         "0018-9294 (print), 1558-2531 (electronic)",
  ISSN-L =       "0018-9294",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Biomedical Engineering",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=10",
  summary =      "A magnetic resonance imaging (MRI) system requires the
                 highest possible signal fidelity and stability for
                 clinical applications. Quadrature analog receivers have
                 problems with channel matching, dc offset and
                 analog-to-digital linearity. Fixed-point \ldots{}",
}

@InProceedings{Honda:2002:DFT,
  author =       "M. Honda and H. Harada and M. Fujise",
  booktitle =    "{VTC} Spring 2002, {IEEE 55th} Vehicular Technology
                 Conference, 6--9 May 2002",
  title =        "Design of fault-tolerant digital filters based on
                 redundant residue number arithmetic for over-the-air
                 reconfiguration in software radio communication
                 systems",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "280--284",
  year =         "2002",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/VTC.2002.1002710",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Over-the-air reconfiguration is a key characteristic
                 of software defined radio communication systems. It
                 offers great advantages in terms of cost-effective
                 software deployment to a large number of user
                 terminals. It also enables manufacturers and \ldots{}",
}

@Article{Hug:2002:DBP,
  author =       "Hubert Hug and Rainer Schuler",
  title =        "{DNA}-based Parallel Computation of Simple
                 Arithmetic",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2340",
  pages =        "321--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:09:41 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2340.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2340/23400321.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2340/23400321.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Misc{Ide:2002:GTE,
  author =       "Nobuhiro Ide and Atsushi Kunimatsu and Maki Ueno",
  title =        "Graphic translate engine, floating point arithmetic
                 unit and floating point multiply-add calculation unit",
  howpublished = "US Patent 6,388,672",
  day =          "14",
  month =        may,
  year =         "2002",
  bibdate =      "Thu Oct 17 11:19:42 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://patents.google.com/patent/US6388672B1",
  abstract =     "An internal memory section is divided into plural
                 memory blocks. During a period of time, a relevant
                 memory block of the internal memory section is
                 connected to an external memory unit, while another
                 memory block thereof is connected to a data holding
                 section. During a succeeding period of time, the
                 relevant memory block is connected to the data holding
                 section, while the other memory block is connected to
                 the external memory unit. Data exchange between the
                 data holding section and the external memory unit via
                 the internal memory section is performed while the
                 alternative connection is repeated.",
  acknowledgement = ack-nhfb,
  remark =       "Patent filed 31 January 1997, granted to Toshiba
                 Corporation on 14 May 2002, possibly expired on 31
                 January 2019.",
}

@InProceedings{Iso:2002:NCI,
  author =       "Yuusuke Iso and Hiroshi Fujiwara",
  title =        "Numerical Computations for Ill-conditioned Problems by
                 Multiple-Precision Systems",
  crossref =     "Babuska:2002:MMN",
  volume =       "19",
  pages =        "185--194",
  year =         "2002",
  DOI =          "https://doi.org/10.1007/978-3-642-56288-4_13",
  bibdate =      "Sat Dec 22 08:36:17 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncse.bib",
  URL =          "http://link.springer.com/content/pdf/10.1007/978-3-642-56288-4_13",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-642-56288-4",
  book-URL =     "http://www.springerlink.com/content/978-3-642-56288-4",
}

@PhdThesis{Jacobi:2002:FVF,
  author =       "Christian Jacobi",
  title =        "Formal verification of a fully {IEEE} compliant
                 floating point unit",
  type =         "{Ph.D.} thesis",
  school =       "Universit{\"a}t Saarbr{\"u}cken Fakult{\"a}t 6 ---
                 Naturwissenschaftlich-Technische Fakult{\"a}t I.
                 Fachrichtung 6.2 --- Informatik",
  address =      "Saarbr{\"u}cken, Germany",
  year =         "2002",
  bibdate =      "Tue May 07 16:38:40 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this thesis we describe the formal verification of
                 a fully IEEE compliant floating point unit (FPU). The
                 hardware is verified on the gate-level against a
                 formalization of the IEEE standard. The verification is
                 performed using the theorem proving system PVS. The FPU
                 supports both single and double precision floating
                 point numbers, normal and denormal numbers, all four
                 IEEE rounding modes, and exceptions as required by the
                 standard. Beside the verification of the combinatorial
                 correctness of the FPUs we pipeline the FPUs to allow
                 the integration into an out-of-order processor. We
                 formally define the correctness criterion the pipelines
                 must obey in order to work properly within the
                 processor. We then describe a new methodology based on
                 combining model checking and theorem proving for the
                 verification of the pipelines",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2002:FPC,
  author =       "W. Kahan",
  title =        "{Fclass}: a Proposed Classification of Standard
                 Floating-Point Operands",
  howpublished = "World-Wide Web document",
  pages =        "6",
  day =          "23",
  month =        mar,
  year =         "2002",
  bibdate =      "Mon Apr 25 17:53:00 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ieee754status/Fclass.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Kim:2002:BSA,
  author =       "Hyun-Sung Kim and Kee-Young Yoo",
  title =        "Bit-Serial {AOP} Arithmetic Architectures over {GF$
                 (2^m) $}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2437",
  pages =        "303--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Nov 30 20:57:24 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2437.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer.de/link/service/series/0558/bibs/2437/24370303.htm;
                 http://link.springer.de/link/service/series/0558/papers/2437/24370303.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Kim:2002:IDS,
  author =       "Nam-Yeun Kim and Dae-Ghon Kho and Kee-Young Yoo",
  title =        "Inversion\slash Division Systolic Architecture for
                 Public-Key Cryptosystems in {GF($ 2^m $) }",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2433",
  pages =        "289--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Thu Sep 12 08:41:42 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2433.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2433/24330289.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2433/24330289.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Book{Koren:2002:CAA,
  author =       "Israel Koren",
  title =        "Computer Arithmetic Algorithms",
  publisher =    pub-A-K-PETERS,
  address =      pub-A-K-PETERS:adr,
  edition =      "Second",
  pages =        "xv + 281",
  year =         "2002",
  ISBN =         "1-56881-160-8 (hardcover), 1-4398-6371-7 (e-book)",
  ISBN-13 =      "978-1-56881-160-4 (hardcover), 978-1-4398-6371-8
                 (e-book)",
  LCCN =         "QA76.9.C62 K67",
  bibdate =      "Sat May 04 10:29:22 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  abstract =     "Concentrating on the underlying principles, this book
                 explains the algorithms used in arithmetic operations
                 on digital computers. It identifies the similarities
                 between the different algorithms and provides guidance
                 for selecting the appropriate algorithms for a given
                 technology. Chapters cover conventional number systems,
                 unconventional fixed-radix number systems, sequential
                 algorithms for multiplication and division, binary
                 floating-point numbers, fast addition, high-speed
                 multiplication, fast division, division through
                 multiplication, the evaluations of elementary
                 functions, logarithmic number systems, and the residue
                 number system.",
  acknowledgement = ack-nhfb,
  tableofcontents = "1: Conventional Number Systems \\
                 2: Unconventional Fixed-Radix Number Systems \\
                 3: Sequential Algorithms for Multiplication and
                 Division \\
                 4: Binary Floating-Point Numbers \\
                 5: Fast Addition \\
                 6: High-Speed Multiplication \\
                 7: Fast Division \\
                 8: Division Through Multiplication \\
                 9: Evaluation of Elementary Functions \\
                 10: Logarithmic Number Systems \\
                 11: The Residue Number System",
}

@Article{Kornerup:2002:PRN,
  author =       "Peter Kornerup and Jean-Claude Bajard and Christiane
                 Frougny and Jean-Michel Muller",
  title =        "Preface: Real Numbers and Computers",
  journal =      j-THEOR-COMP-SCI,
  volume =       "291",
  number =       "2",
  pages =        "133--134",
  month =        nov,
  year =         "2002",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Nov 20 18:15:29 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tcs2000.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Theor. Comput. Sci.",
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975/",
  remark =       "Proceedings of the Fourth conference on Real numbers
                 and Computers, Schlo{\ss} Dagstuhl, April 2000.",
}

@Article{Koutroumpezis:2002:ADR,
  author =       "G. Koutroumpezis and K. Tatas and D. Soudris and S.
                 Blionas and K. Masselos and A. Thanailakis",
  title =        "Architecture Design of a Reconfigurable Multiplier for
                 Flexible Coarse-Grain Implementations",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2438",
  pages =        "1027--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:10:28 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2438.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2438/24381027.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2438/24381027.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Misc{Krygowski:2002:FPM,
  author =       "C. A. Krygowski and E. M. Schwarz",
  title =        "Floating-point multiplier for de-normalized inputs",
  day =          "5",
  month =        sep,
  year =         "2002",
  bibdate =      "Fri Nov 28 15:26:12 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "U.S. Patent Application No. 2002/0124037 A1.",
  acknowledgement = ack-nhfb,
}

@Article{Ku:2002:NPA,
  author =       "Kyo-Min Ku and Kyeoung-Ju Ha and Hyun-Sung Kim and
                 Kee-Young Yoo",
  title =        "New Parallel Architecture for Modular Multiplication
                 and Squaring Based on Cellular Automata",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2367",
  pages =        "359--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:09:54 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2367.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2367/23670359.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2367/23670359.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Book{Kulisch:2002:AAD,
  author =       "U. Kulisch",
  title =        "Advanced Arithmetic for the Digital Computer: Design
                 of Arithmetic Units",
  publisher =    pub-SPRINGER-WIEN,
  address =      pub-SPRINGER-WIEN:adr,
  pages =        "xii + 141",
  year =         "2002",
  ISBN =         "3-211-83870-8",
  ISBN-13 =      "978-3-211-83870-9",
  LCCN =         "QA76.9.C62 K85 2002",
  bibdate =      "Mon Feb 03 07:48:36 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "EUR 25.00",
  URL =          "http://www.springer.at/main/book.jsp?bookID=3-211-83870-8&categoryID=10",
  acknowledgement = ack-nhfb,
  keywords =     "accuracy; computer algebra; floating-point arithmetic;
                 interval arithmetic; scalar product; speed of
                 computation; vector operations",
}

@InProceedings{Kulisch:2002:RNZ,
  author =       "Ulrich Kulisch",
  editor =       "Peter Kornerup and Jean-Claude Bajard and Christiane
                 Frougny and Jean-Michel Muller",
  booktitle =    "4th Real Numbers and Computers Conference, Dagstuhl,
                 Germany, 2000",
  title =        "Rounding near zero",
  volume =       "291(2)",
  publisher =    pub-ELSEVIER,
  address =      pub-ELSEVIER:adr,
  pages =        "23--29",
  day =          "5",
  month =        jan,
  year =         "2002",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Nov 24 09:14:41 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       j-THEOR-COMP-SCI,
  acknowledgement = ack-nhfb,
  remark =       "This reference is incorrect: there is no paper by
                 Kulisch in this journal issue. Where was it
                 published??",
}

@Article{Kwon:2002:EBS,
  author =       "Soonhak Kwon and Heuisu Ryu",
  title =        "Efficient Bit Serial Multiplication Using Optimal
                 Normal Bases of Type {II} in {{\em GF\/}}$ (2^m) $",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2433",
  pages =        "300--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Thu Sep 12 08:47:11 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2433.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2433/24330300.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2433/24330300.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InProceedings{Lang:2002:FPF,
  author =       "T. Lang and J. Bruguera",
  title =        "Floating-point fused multiply-add with reduced
                 latency",
  crossref =     "IEEE:2002:IIC",
  pages =        "145--150",
  year =         "2002",
  DOI =          "https://doi.org/10.1109/ICCD.2002.1106762",
  bibdate =      "Fri Jun 24 14:33:25 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://csdl.computer.org/dl/proceedings/iccd/2002/1700/00/17000145.pdf",
  abstract =     "We propose an architecture for the computation of the
                 floating-point multiply-add-fused (MAF) operation $ A +
                 (B \times C) $. This architecture is based on the
                 combined addition and rounding (using a dual adder) and
                 on the anticipation of the normalization step before
                 the addition. Because the normalization is performed
                 before the addition, it is not possible to overlap the
                 leading-zero-anticipator with the adder. Consequently,
                 to avoid the increase in delay we modify the design of
                 the LZA so that the leading bits of its output are
                 produced first and can be used to begin the
                 normalization. Moreover, parts of the addition are also
                 anticipated. We have estimated the delay of the
                 resulting architecture for double-precision format,
                 considering the load introduced by long connections,
                 and estimate a reduction of about 15\% to 20\% with
                 respect to traditional implementations of the
                 floating-point MAF unit.",
  acknowledgement = ack-nhfb,
}

@Article{Lee:2002:DSS,
  author =       "Keon-Jik Lee and Kee-Won Kim and Kee-Young Yoo",
  title =        "Digit-serial-in-serial-out systolic multiplier for
                 {Montgomery} algorithm",
  journal =      j-INFO-PROC-LETT,
  volume =       "82",
  number =       "2",
  pages =        "65--71",
  day =          "30",
  month =        apr,
  year =         "2002",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Mon Jan 26 06:35:43 MST 2004",
  bibsource =    "http://www.sciencedirect.com/science/journal/00200190;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.elsevier.com/gej-ng/10/23/20/86/33/27/abstract.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}

@InProceedings{Lee:2002:PFP,
  author =       "B. Lee and N. Burgess",
  title =        "Parameterisable floating-point operations on {FPGA}",
  crossref =     "Matthews:2002:PTS",
  volume =       "2",
  pages =        "1064--1068",
  year =         "2002",
  DOI =          "https://doi.org/10.1109/ACSSC.2002.1196947",
  bibdate =      "Sat Oct 9 12:47:53 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The paper presents a group of IEEE 754-style
                 floating-point units targeted at Xilinx VirtexII FPGA.
                 Special features of the technology are taken advantage
                 of to produce optimised components. Pipelined designs
                 are given that show the latency of 100 MHz
                 single-precision components. Non-pipelined reference
                 designs are included for future comparison purposes.",
  acknowledgement = ack-nhfb,
}

@TechReport{Leeser:2002:LPH,
  author =       "Miriam Leeser",
  title =        "A Library of Parameterized Hardware Modules for
                 Floating Point Arithmetic and Its Use",
  type =         "Technical report",
  institution =  "Department of Electrical and Computer Engineering,
                 Northeastern University",
  address =      "Boston, MA, USA",
  pages =        "28",
  year =         "2002",
  bibdate =      "Mon May 22 11:20:03 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Presented at High Performance Embedded Computing
                 (HPEC) Workshop (6th) held in Lexington, MA on 24--26
                 September 2002.",
  acknowledgement = ack-nhfb,
}

@Article{Leong:2002:IMM,
  author =       "P. C. Leong and E. C. Tan and P. C. Tan",
  title =        "An iterative modular multiplication algorithm",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "44",
  number =       "1--2",
  pages =        "175--180",
  month =        jul,
  year =         "2002",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:49:23 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122102001384",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Lester:2002:CAF,
  author =       "David Lester and Scott Chambers and Heoi Lee Lu",
  title =        "A constructive algorithm for finding the exact roots
                 of polynomials with computable real coefficients",
  journal =      j-THEOR-COMP-SCI,
  volume =       "279",
  number =       "1-2",
  pages =        "51--64",
  month =        may,
  year =         "2002",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Nov 20 18:08:56 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}

@Article{Lester:2002:UPV,
  author =       "David Lester and Paul Gowland",
  title =        "Using {PVS} to validate the algorithms of an exact
                 arithmetic",
  journal =      j-THEOR-COMP-SCI,
  volume =       "291",
  number =       "2",
  pages =        "203--218",
  month =        nov,
  year =         "2002",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Nov 20 18:15:29 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tcs2000.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Theor. Comput. Sci.",
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975/",
  remark =       "Proceedings of the Fourth conference on Real numbers
                 and Computers, Schlo{\ss} Dagstuhl, April 2000.",
}

@Article{Li:2002:DIT,
  author =       "Xiaoye S. Li and James W. Demmel and David H. Bailey
                 and Greg Henry and Yozo Hida and Jimmy Iskandar and
                 William Kahan and Suh Y. Kang and Anil Kapur and
                 Michael C. Martin and Brandon J. Thompson and Teresa
                 Tung and Daniel J. Yoo",
  title =        "Design, implementation and testing of extended and
                 mixed precision {BLAS}",
  journal =      j-TOMS,
  volume =       "28",
  number =       "2",
  pages =        "152--205",
  month =        jun,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/567806.567808",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 11:16:50 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://crd.lbl.gov/~xiaoye/XBLAS/",
  abstract =     "This paper describes the design rationale, a C
                 implementation, and conformance testing of a subset of
                 the new Standard for the BLAS (Basic Linear Algebra
                 Subroutines): Extended and Mixed Precision BLAS.
                 Permitting higher internal precision and mixed
                 input\slash output types and precisions allows us to
                 implement some algorithms that are simpler, more
                 accurate, and sometimes faster than possible without
                 these features. The new BLAS are challenging to
                 implement and test because there are many more
                 subroutines than in the existing Standard, and because
                 we must be able to assess whether a higher precision is
                 used for internal computations than is used for either
                 input or output variables. We have therefore developed
                 an automated process of generating and systematically
                 testing these routines. Our methodology is applicable
                 to languages besides C. In particular, our algorithms
                 used in the testing code will be valuable to all other
                 BLAS implementors. Our extra precision routines achieve
                 excellent performance---close to half of the machine
                 peak Megaflop rate even for the Level 2 BLAS, when the
                 data access is stride one.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "accurate floating-point summation",
}

@TechReport{Li:2002:LLF,
  author =       "Ren-Cang Li and Peter Markstein and Jon P. Okada and
                 James W. Thomas",
  title =        "The {\tt libm} library and floating-point arithmetic
                 for {HP-UX} on {Itanium-2}",
  type =         "Technical report",
  institution =  inst-HP,
  address =      inst-HP:adr,
  pages =        "??",
  year =         "2002",
  bibdate =      "Tue Nov 18 15:06:56 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "????",
  acknowledgement = ack-nhfb,
}

@PhdThesis{Liddicoat:2002:HPA,
  author =       "Albert Austin Liddicoat",
  title =        "High-performance arithmetic for division and the
                 elementary functions",
  type =         "{Ph.D.} Thesis",
  school =       "Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "141",
  year =         "2002",
  ISBN =         "0-493-53347-8",
  ISBN-13 =      "978-0-493-53347-6",
  bibdate =      "Fri Oct 25 17:06:55 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://wwwlib.umi.com/dissertations/fullcit/3040035;
                 http://wwwlib.umi.com/dissertations/preview/3040035",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lienhart:2002:UFP,
  author =       "G. Lienhart and A. Kugel and R. Manner",
  title =        "Using floating-point arithmetic on {FPGAs} to
                 accelerate scientific {$N$}-body simulations",
  crossref =     "Pocek:2002:FAI",
  pages =        "182--191",
  year =         "2002",
  DOI =          "https://doi.org/10.1109/FPGA.2002.1106673",
  bibdate =      "Sat Oct 9 12:49:37 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper investigates the usage of floating-point
                 arithmetic on FPGAs for N-Body simulation in natural
                 science. The common aspect of these applications is the
                 simple computing structure where forces between a
                 particle and its surrounding particles are summed up.
                 The role of reduced precision arithmetic is discussed,
                 and our implementation of a floating-point arithmetic
                 library with parameterized operators is presented. On
                 the base of this library, implementation strategies of
                 complex arithmetic units are discussed. Finally the
                 realization of a fully pipelined pressure force
                 calculation unit consisting of 60 floating-point
                 operators with a resulting performance of 3.9 Gflops on
                 an off the shelf FPGA is presented.",
  acknowledgement = ack-nhfb,
}

@Article{Loh:2002:RER,
  author =       "Eugene Loh and G. William Walster",
  title =        "{Rump}'s Example Revisited",
  journal =      j-RELIABLE-COMPUTING,
  volume =       "8",
  number =       "3",
  pages =        "245--248",
  month =        jun,
  year =         "2002",
  CODEN =        "RCOMF8",
  DOI =          "https://doi.org/10.1023/A:1015569431383",
  ISSN =         "1385-3139 (print), 1573-1340 (electronic)",
  ISSN-L =       "1385-3139",
  bibdate =      "Sat Jan 5 10:21:56 2013",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1385-3139&volume=8&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/reliablecomputing.bib",
  URL =          "http://link.springer.com/article/10.1023/A%3A1015569431383/;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=8&issue=3&spage=245;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=8&issue=3&spage=245-248",
  acknowledgement = ack-nhfb # "\slash " # ack-rbk # "\slash " # ack-vk,
  fjournal =     "Reliable Computing = Nadezhnye vychisleniia",
  journal-URL =  "http://link.springer.com/journal/11155",
}

@InProceedings{Lund:2002:MUC,
  author =       "T. Lund and M. Aguirre and A. Torralba",
  booktitle =    "{IEEE 2002 28th Annual Conference of the Industrial
                 Electronics Society. IECON 02}",
  title =        "Making use of {CORDICs} and distributed arithmetic to
                 produce a field-programmable fuzzy logic controller in
                 an {FPGA}",
  volume =       "4",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "3205--3208",
  year =         "2002",
  DOI =          "https://doi.org/10.1109/IECON.2002.1182911",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Arithmetic; Circuits; Digital signal processing;
                 Distributed computing; Field programmable gate arrays;
                 Fuzzy control; Fuzzy logic; Hardware; Iterative
                 algorithms; Signal processing algorithms",
}

@Article{Lutz:2002:BGB,
  author =       "Michael J. Lutz",
  title =        "Bookshelf: Getting the Bugs Out [{Debugging: The 9
                 Indispensable Rules for Finding Even the Most Elusive
                 Software and Hardware Problems}]; Saving Time With
                 Arithmetic and Logic [{Hacker's Delight}]; Probability
                 and Computing [{Probability and Statistics with
                 Reliability, Queuing and Computer Science Applications,
                 2nd edition}]; Graphics Toolbox [{Guide to Graphics
                 Software Tools}]",
  journal =      j-COMPUTER,
  volume =       "35",
  number =       "12",
  pages =        "117--117",
  month =        dec,
  year =         "2002",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Fri Dec 12 19:53:37 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://csdl.computer.org/dl/mags/co/2002/12/rz117.htm;
                 http://csdl.computer.org/dl/mags/co/2002/12/rz117.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}

@Article{Madhukumar:2002:RNS,
  author =       "A. S. Madhukumar and F. Chin",
  title =        "Residue number system-based multicarrier {CDMA} system
                 for high-speed broadband wireless access",
  journal =      j-IEEE-TRANS-BROADCAST,
  volume =       "48",
  number =       "1",
  pages =        "46--52",
  month =        mar,
  year =         "2002",
  CODEN =        "IETBAC",
  DOI =          "https://doi.org/10.1109/11.992855",
  ISSN =         "????",
  ISSN-L =       "0018-9316",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=21407",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Broadcasting",
  keywords =     "residue arithmetic; residue number system",
  summary =      "This correspondence is concerned with a new method to
                 enhance the bandwidth efficiency of a multicarrier CDMA
                 system by using a residue number based representation
                 for information symbols. The residues are mapped into a
                 set of orthogonal sequences \ldots{}",
}

@Article{Matousek:2002:LNS,
  author =       "Rudolf Matousek and Milan Tich{\'y} and Zdenek Pohl
                 and Jir{\'\i} Kadlec and Chris Softley and Nick
                 Coleman",
  title =        "Logarithmic Number System and Floating-Point
                 Arithmetics on {FPGA}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2438",
  pages =        "175--188",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:10:28 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2438.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2438/24380627.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2438/24380627.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
  xxpages =      "627--??",
}

@Article{Matula:2002:BFM,
  author =       "David W. Matula and Lee D. McFearin",
  title =        "A $ p \times p $ bit fraction model of binary floating
                 point division and extremal rounding cases",
  journal =      j-THEOR-COMP-SCI,
  volume =       "291",
  number =       "2",
  pages =        "159--182",
  month =        nov,
  year =         "2002",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Nov 20 18:15:29 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tcs2000.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Theor. Comput. Sci.",
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975/",
  remark =       "Proceedings of the Fourth conference on Real numbers
                 and Computers, Schlo{\ss} Dagstuhl, April 2000.",
}

@Article{Matula:2002:PTP,
  author =       "David W. Matula and Lee D. McFearin",
  title =        "A $ p \times p $ bit fraction model of binary floating
                 point division and extremal rounding cases",
  journal =      j-THEOR-COMP-SCI,
  volume =       "291",
  number =       "2",
  pages =        "159--182",
  month =        nov,
  year =         "2002",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Nov 20 18:15:29 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}

@Article{McCluskey:2002:MLF,
  author =       "Glen McCluskey",
  title =        "Math library functions in {C9X}",
  journal =      j-LOGIN,
  volume =       "27",
  number =       "2",
  pages =        "9--13",
  month =        apr,
  year =         "2002",
  CODEN =        "LOGNEM",
  ISSN =         "1044-6397 (print), 2169-9364 (electronic)",
  bibdate =      "Sat May 04 10:26:38 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     ";login: the USENIX Association newsletter",
}

@PhdThesis{McIlhenny:2002:CNL,
  author =       "Robert Dean McIlhenny",
  title =        "Complex Number On-line Arithmetic for Reconfigurable
                 Hardware: Algorithms, Implementations, and
                 Application",
  type =         "{Ph.D.} dissertation",
  school =       "Computer Science Department, University of California,
                 Los Angeles",
  address =      "Los Angeles, CA, USA",
  pages =        "xiv + 182",
  year =         "2002",
  ISBN =         "0-493-82665-3",
  ISBN-13 =      "978-0-493-82665-3",
  bibdate =      "Sat Dec 04 09:27:33 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Complex number arithmetic plays an important role in
                 various signal processing tasks, such as correlations,
                 convolutions, and digital filtering. There is a need in
                 such applications to exploit parallelism in
                 implementing sequences of arithmetic expressions, as
                 well as to reduce the bandwidth of the data path.
                 Reconfigurable architectures are emerging as a viable
                 technology for mapping numeric-intensive computations
                 onto hardware. In order to provide efficient
                 implementations that can accommodate changes with a
                 minimal amount of redesign, the methodology for
                 deriving algorithms and corresponding implementations
                 must be flexible toward change.\par

                 In this dissertation, we present an efficient
                 representation which treats the real and imaginary
                 components as a unified number. We propose algorithms
                 for various complex number on-line floating-point
                 arithmetic operations. The algorithms are translated
                 into actual implementations mapped onto reconfigurable
                 hardware. The implementations are applied toward
                 computing the complex singular value decomposition of a
                 matrix, with a significant reduction in cost compared
                 to networks of real number on-line and parallel
                 arithmetic approaches.",
  acknowledgement = ack-nhfb,
  advisor =      "Milo{\v{s}} Ercegovac",
}

@Article{Messine:2002:EAA,
  author =       "F. Messine",
  title =        "Extentions [sic] of Affine Arithmetic: Application to
                 Unconstrained Global Optimization",
  journal =      j-J-UCS,
  volume =       "8",
  number =       "11",
  pages =        "992--??",
  day =          "28",
  month =        nov,
  year =         "2002",
  CODEN =        "????",
  ISSN =         "0948-6968",
  ISSN-L =       "0948-6968",
  bibdate =      "Tue Dec 16 10:06:03 MST 2003",
  bibsource =    "http://www.jucs.org/jucs;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.jucs.org/jucs_8_11/extentions_of_affine_arithmetic",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
  keywords =     "interval arithmetic",
}

@InProceedings{Molina:2002:BLA,
  author =       "M. C. Molina and J. M. Mendias and R. Hermida",
  booktitle =    "Proceedings of the Euromicro Symposium on Digital
                 System Design",
  title =        "Bit-level allocation of multiple-precision
                 specifications",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "385--392",
  year =         "2002",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:53:44 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper proposes an allocation algorithm able to
                 perform the combined resource selection and operation
                 binding of multiple-precision specifications that
                 maximizes the bit-level reuse of hardware resources.
                 Additionally, it presents an analytic \ldots{}",
}

@InProceedings{Molina:2002:HLS,
  author =       "M. C. Molina and J. M. Mendias and R. Hermida",
  booktitle =    "Proceedings of the 39th Design Automation Conference,
                 10--14 June 2002",
  title =        "High-level synthesis of multiple-precision circuits
                 independent of data-objects length",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "612--615",
  year =         "2002",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:53:44 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper presents an heuristic method to perform the
                 high-level synthesis of multiple-precision
                 specifications. The scheduling is based on the balance
                 of the number of bits calculated per cycle, and the
                 allocation on the bit-level reuse of the \ldots{}",
}

@InProceedings{Molina:2002:MPC,
  author =       "M. C. Molina and J. M. Mendias and R. Hermida",
  booktitle =    "Proceedings of the Design, Automation and Test in
                 Europe Conference and Exhibition, 4--8 March 2002",
  title =        "Multiple-precision circuits allocation independent of
                 data-objects length",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "909--913",
  year =         "2002",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:53:44 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper presents an heuristic method to solve the
                 combined resource selection and binding problems for
                 the high-level synthesis of multiple-precision
                 specifications. Traditionally, the number of functional
                 (and storage) units in a datapath is \ldots{}",
}

@Article{Moller:2002:PEC,
  author =       "Bodo M{\"o}ller",
  title =        "Parallelizable Elliptic Curve Point Multiplication
                 Method with Resistance against Side-Channel Attacks",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2433",
  pages =        "402--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:10:26 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2433.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2433/24330402.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2433/24330402.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Motegi:2002:EGG,
  author =       "Makoto Motegi and Naofumi Homma and Takafumi Aoki and
                 Tatsuo Higuchi",
  title =        "Evolutionary Graph Generation System and Its
                 Application to Bit-Serial Arithmetic Circuit
                 Synthesis",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2439",
  pages =        "831--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Nov 30 20:57:24 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2439.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer.de/link/service/series/0558/bibs/2439/24390831.htm;
                 http://link.springer.de/link/service/series/0558/papers/2439/24390831.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Okeya:2002:FSM,
  author =       "Katsuyuki Okeya and Kunihiko Miyazaki and Kouichi
                 Sakurai",
  title =        "A Fast Scalar Multiplication Method with Randomized
                 Projective Coordinates on a {Montgomery}-Form Elliptic
                 Curve Secure against Side Channel Attacks",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2288",
  pages =        "428--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:09:14 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2288.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2288/22880428.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2288/22880428.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Book{Overton:2002:CNC,
  author =       "Michael L. Overton",
  title =        "{C}{\'o}mputo num{\'e}rico con aritm{\'e}tica de punto
                 flotante {IEEE}",
  volume =       "19",
  publisher =    "Sociedad Matem{\'a}tica Mexicana",
  address =      "M{\'e}xico",
  pages =        "xii + 123",
  year =         "2002",
  ISBN =         "970-32-0086-9",
  ISBN-13 =      "978-970-32-0086-3",
  MRclass =      "65-02 (65Bxx 65G30)",
  MRnumber =     "MR1925397 (2003g:65003)",
  bibdate =      "Thu Nov 8 19:16:14 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Con un teorema, una regla emp{\'\i}rica y ciento un
                 ejercicios. [Including one theorem, one rule of thumb
                 and one hundred and one exercises], Translated from the
                 2001 English original by Alejandro Casares Maldonado",
  series =       "Aportaciones Matem{\'a}ticas: Textos [Mathematical
                 Contributions: Texts]",
  acknowledgement = ack-nhfb,
}

@InProceedings{Paliouras:2002:LPC,
  author =       "V. Paliouras and A. Skavantzos and T. Stouraitis",
  booktitle =    "{ISCAS 2002}, {IEEE} International Symposium on
                 Circuits and Systems, 26--29 May 2002",
  title =        "Low power convolvers using the {Polynomial Residue
                 Number System}",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "II-748--II-751",
  year =         "2002",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.2002.1011461",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A novel approach for the reduction of the power
                 dissipated in a signal processing application is
                 introduced in this paper. By exploiting the properties
                 of the Polynomial Residue Number System (PRNS) and of
                 the arithmetic modulo (2/sup n/+1), the \ldots{}",
}

@InProceedings{Paliouras:2002:OLO,
  author =       "V. Paliouras",
  booktitle =    "{IEEE} International Symposium on Circuits and
                 Systems: {ISCAS 2002}, 26--29 May 2002",
  title =        "Optimization of {LNS} operations for embedded signal
                 processing applications",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "II-744--II-747",
  year =         "2002",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper introduces an optimization technique for
                 the design of logarithmic arithmetic-based embedded
                 signal processors. The fundamental concept of the
                 proposed technique is the determination of the optimal
                 values of the logarithmic base b, which \ldots{}",
}

@Article{Park:2002:SPM,
  author =       "Young-Ho Park and Sangtae Jeong and Jongin Lim",
  title =        "Speeding Up Point Multiplication on Hyperelliptic
                 Curves with Efficiently-Computable Endomorphisms",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2332",
  pages =        "197--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:09:37 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2332.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2332/23320197.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2332/23320197.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Paul:2002:BB,
  author =       "Wolfgang J. Paul and Peter-Michael Seidel",
  title =        "To {Booth} or not to {Booth}?",
  journal =      j-INTEGRATION-VLSI-J,
  volume =       "32",
  number =       "1--2",
  pages =        "5--40",
  month =        nov,
  year =         "2002",
  CODEN =        "IVJODL",
  DOI =          "https://doi.org/10.1016/S0167-9260(02)00040-8",
  ISSN =         "0167-9260 (print), 1872-7522 (electronic)",
  ISSN-L =       "0167-9260",
  URL =          "https://www.sciencedirect.com/science/article/pii/S0167926002000408",
  bibdate =      "Mon Dec 24 10:05:36 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Booth Recoding is a commonly used technique to recode
                 one of the operands in binary multiplication. In this
                 way the implementation of a multipliers' adder tree can
                 be improved in both cost and delay. The improvement due
                 to Booth Recoding is said to be due to improvements in
                 the layout of the adder tree especially regarding the
                 lengths of wire connections and thus cannot be analyzed
                 with a simple gate model. Although conventional VLSI
                 models consider wires in layouts, they usually neglect
                 wires when modeling the delay. To make the layout
                 improvements due to Booth recoding tractable in a
                 technology-independent way, we introduce a VLSI model
                 that also considers wire delays and constant factors.
                 Based on this model we consider the layouts of binary
                 multipliers in a parametric analysis providing answers
                 to the question whether to use Booth Recoding or not.
                 We formalize and prove the folklore theorems that Booth
                 recoding improves the cost and cycle time of standard'
                 multipliers by certain constant factors. We also
                 analyze the number of full adders in certain 4/2
                 trees.",
  acknowledgement = ack-nhfb,
  fjournal =     "Integration, the VLSI journal",
  journal-URL =  "https://www.sciencedirect.com/journal/integration/issues",
}

@InProceedings{Pillmeier:2002:DAB,
  author =       "M. R. Pillmeier and M. J. Schulte",
  title =        "Design Alternatives for Barrel Shifters and Rotators",
  crossref =     "Luk:2002:PSA",
  pages =        "436--447",
  year =         "2002",
  bibdate =      "Sun Mar 04 17:45:23 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2002-02.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Pineiro:2002:HRL,
  author =       "J.-A. Pineiro and M. D. Ercegovac and J. D. Bruguera",
  booktitle =    "Application-Specific Systems, Architectures and
                 Processors, 2002. Proceedings. The {IEEE} International
                 Conference on. 17--19 July 2002",
  title =        "High-radix logarithm with selection by rounding",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "101--110",
  year =         "2002",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:05 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "A high-radix digit-recurrence algorithm or the
                 computation of the logarithm is presented in this
                 paper. Selection by rounding is used in iterations
                 j/spl ges/2, and selection by table in the first
                 iteration is combined with a restricted digit-set
                 \ldots{}",
}

@Article{Pineiro:2002:HSD,
  author =       "J. A. Pi{\~n}eiro and J. D. Bruguera",
  title =        "High-Speed Double Precision Computation of Reciprocal,
                 Division, Square Root, and Inverse Square Root",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "51",
  number =       "12",
  pages =        "1377--1388",
  month =        dec,
  year =         "2002",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2002.1146704",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1146704",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "A new method for the high-speed computation of
                 double-precision floating-point reciprocal, division,
                 square root, and inverse square root operations is
                 presented in this paper. This method employs a
                 second-degree minimax polynomial approximation to
                 \ldots{}",
}

@Article{Puchta:2002:RNN,
  author =       "Jan-Christoph Puchta",
  title =        "Representation of Numbers with Negative Digits and
                 Multiplication of Small Integers",
  journal =      j-FIB-QUART,
  volume =       "40",
  number =       "1",
  pages =        "66--67",
  month =        feb,
  year =         "2002",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:03:31 MDT 2011",
  bibsource =    "http://www.fq.math.ca/40-1.html;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.fq.math.ca/Scanned/40-1/puchta1.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Ramasubramanian:2002:ACL,
  author =       "Narasimhan Ramasubramanian and Ram Subramanian and
                 Santosh Pande",
  title =        "Automatic Compilation of Loops to Exploit Operator
                 Parallelism on Configurable Arithmetic Logic Units",
  journal =      j-IEEE-TRANS-PAR-DIST-SYS,
  volume =       "13",
  number =       "1",
  pages =        "45--66",
  month =        jan,
  year =         "2002",
  CODEN =        "ITDSEO",
  ISSN =         "1045-9219 (print), 1558-2183 (electronic)",
  ISSN-L =       "1045-9219",
  bibdate =      "Sat Feb 23 09:26:04 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://dlib.computer.org/td/books/td2002/pdf/l0045.pdf;
                 http://www.computer.org/tpds/td2001/l0045abs.htm",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Parallel Distrib. Syst.",
  fjournal =     "IEEE Transactions on Parallel and Distributed
                 Systems",
  journal-URL =  "http://www.computer.org/tpds/archives.htm",
}

@Article{Ramirez:2002:FRF,
  author =       "J. Ram{\'\i}rez and A. Garc{\'\i}a and U. Meyer-Baese
                 and A. Lloris",
  title =        "Fast {RNS} {FPL}-based Communications Receiver Design
                 and Implementation",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2438",
  pages =        "472--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:10:28 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2438.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2438/24380472.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2438/24380472.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Reid-Green:2002:TEA,
  author =       "Keith S. Reid-Green",
  title =        "Three early algorithms: [{Bresenham}'s line-drawing
                 algorithm; a square-root algorithm; {Machin}'s
                 algorithm: computation of $ \pi $ ]",
  journal =      j-IEEE-ANN-HIST-COMPUT,
  volume =       "24",
  number =       "4",
  pages =        "10--13",
  month =        oct,
  year =         "2002",
  CODEN =        "IAHCEX",
  DOI =          "https://doi.org/10.1109/MAHC.2002.1114866",
  ISSN =         "1058-6180 (print), 1934-1547 (electronic)",
  ISSN-L =       "1058-6180",
  bibdate =      "Sat Nov 29 16:19:45 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeeannhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  URL =          "http://csdl.computer.org/dl/mags/an/2002/04/a4010.htm;
                 http://csdl.computer.org/dl/mags/an/2002/04/a4010.pdf;
                 http://csdl.computer.org/dl/mags/an/2002/04/a4010abs.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Annals of the History of Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85",
}

@TechReport{Revol:2002:MAPa,
  author =       "N. Revol and F. Rouillier",
  title =        "Motivations for an Arbitrary Precision Interval
                 Arithmetic and the {MPFI Library}",
  type =         "Report",
  institution =  "Laboratoire ANO, University of Lille and
                 CNRS/ENSL/INRIA Project Arenaire LIP, {\'E}cole Normale
                 Sup{\'e}rieure de Lyon, France, Project Spaces,
                 LORIA/INRIA/LIP 6, France",
  pages =        "6",
  day =          "17",
  month =        apr,
  year =         "2002",
  bibdate =      "Fri Mar 10 16:23:31 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://pauillac.inria.fr/cdrom/www/mpfi/ValidC02.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "interval arithmetic; multiple precision",
}

@InProceedings{Revol:2002:MAPb,
  author =       "Nathalie Revol and Fabrice Rouillier",
  editor =       "R. Baker Kearfott",
  booktitle =    "{SIAM} Workshop on Validated Computing 2002, Toronto,
                 Canada, May 23--25, 2002: extended abstracts",
  title =        "Motivations for an Arbitrary Precision Interval
                 Arithmetic and the {MPFI Library}",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  bookpages =    "187",
  pages =        "??--??",
  year =         "2002",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "QA76.76.R44 W67 2002",
  bibdate =      "Fri Jan 28 15:34:54 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "MPFI is a library implementing interval arithmetic
                 with arbitrary accuracy. It can be freely downloaded
                 (including source code and documentation). It is
                 written in C and is based on the MPFR library for
                 arbitrary precision floating-point arithmetic, which is
                 in turn built upon the GMP library. MPFR has been
                 chosen because it provides outward rounding, even for
                 the elementary functions, which is mandatory to
                 implement interval arithmetic. An important issue in
                 interval computation is ``computing in the large'',
                 i.e., getting tight enclosures for the range of a
                 function over a large interval. However, this issue has
                 no well established answer, and one common way to
                 circumvent the problem consists in bisecting the input
                 interval again and again, until the evaluation of the
                 function upon each sub-part is tight enough. For some
                 problems, such as roots approximations or optimization
                 of a ``very flat'' function, splitting beyond the
                 limits of usual (single or double) floating-point
                 capacities reveals necessary in order to reach the
                 required accuracy on the function evaluation.",
  acknowledgement = ack-nhfb,
}

@Article{Reyhani-Masoleh:2002:NCM,
  author =       "A. Reyhani-Masoleh and M. A. Hasan",
  title =        "A new construction of {Massey--Omura} parallel
                 multiplier over {$ \mathrm {GF}(2^m) $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "51",
  number =       "5",
  pages =        "511--520",
  month =        may,
  year =         "2002",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2002.1004590",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 09:41:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1004590",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Roesler:2002:NOH,
  author =       "Eric Roesler and Brent Nelson",
  title =        "Novel Optimizations for Hardware Floating-Point Units
                 in a Modern {FPGA} Architecture",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2438",
  pages =        "637--646",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:10:28 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2438.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2438/24380637.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2438/24380637.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Saed:2002:NSC,
  author =       "A. Saed and M. Ahmadi and G. A. Jullien",
  title =        "A number system with continuous valued digits and
                 modulo arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "51",
  number =       "11",
  pages =        "1294--1305",
  month =        nov,
  year =         "2002",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2002.1047754",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 09:42:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1047754",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Sahin:2002:FFP,
  author =       "Ibrahim Sahin and Clay S. Gloster and Christopher
                 Doss",
  title =        "Feasibility of floating-point arithmetic in
                 reconfigurable computing systems",
  crossref =     "Vladimirova:2002:TMA",
  pages =        "??--??",
  year =         "2002",
  bibdate =      "Sat Oct 9 12:59:55 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://klabs.org/richcontent/MAPLDCon00/Abstracts/sahin_a.txt",
  abstract =     "Reconfigurable Computing (RC) has emerged as a viable
                 computing solution for computationally intensive
                 applications. Applications mapped to RC systems include
                 image processing algorithms, pattern recognition in
                 high energy physics and genetic optimization
                 algorithms. Due to the hardware complexity of the
                 floating point modules and limited resources available
                 in prior RC systems, applications that required
                 floating point operations were either, not mapped to RC
                 systems, or converted to fixed point before developing
                 the RC implementation. Recent advances in Field
                 Programmable Gate Array (FPGA) technology offer the
                 user more hardware resources on a single FPGA device
                 and thus the greater potential to develop complex RC
                 systems. In this paper, the feasibility of mapping
                 applications containing floating point operations to RC
                 systems is presented. Three floating point modules:
                 vector addition, subtraction, and multiplication were
                 modeled using VHDL and mapped to a Xilinx XC4044XL FPGA
                 device. These modules are highly pipelined and
                 optimized for both speed and area. Our results verify
                 that floating point applications are feasible and that
                 significant speedup can be obtained when mapping these
                 applications to RC systems.",
  acknowledgement = ack-nhfb,
}

@Article{Sakai:2002:AES,
  author =       "Yasuyuki Sakai and Kouichi Sakurai",
  title =        "Algorithms for Efficient Simultaneous Elliptic Scalar
                 Multiplication with Reduced Joint {Hamming} Weight
                 Representation of Scalars",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2433",
  pages =        "484--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:10:26 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2433.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2433/24330484.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2433/24330484.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InProceedings{Sawada:2002:FVD,
  author =       "J. Sawada",
  title =        "Formal verification of divide and square root
                 algorithms using series calculation",
  crossref =     "Borrione:2002:TIW",
  pages =        "31--49",
  year =         "2002",
  bibdate =      "Fri Jun 24 15:14:00 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Sawada:2002:MVS,
  author =       "Jun Sawada and Ruben Gamboa",
  title =        "Mechanical Verification of a Square Root Algorithm
                 Using {Taylor}'s Theorem",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2517",
  pages =        "274--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Nov 30 20:58:00 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2517.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer.de/link/service/series/0558/bibs/2517/25170274.htm;
                 http://link.springer.de/link/service/series/0558/papers/2517/25170274.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Schwarz:2002:MIE,
  author =       "E. M. Schwarz and M. A. Check and C.-L. K. Shum and T.
                 Koehler and S. B. Swaney and J. D. MacDougall and C. A.
                 Krygowski",
  title =        "The microarchitecture of the {IBM eServer z900}
                 processor",
  journal =      j-IBM-JRD,
  volume =       "46",
  number =       "4/5",
  pages =        "381--395",
  month =        "????",
  year =         "2002",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Fri Nov 22 17:58:43 MST 2002",
  bibsource =    "http://www.research.ibm.com/journal/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.research.ibm.com/journal/rd/464/schwarz.html;
                 http://www.research.ibm.com/journal/rd/464/schwarz.pdf",
  abstract =     "The recent IBM ESA/390 CMOS line of processors, from
                 1997 to 1999, consisted of the G4, G5, and G6
                 processors. The architecture they implemented lacked
                 64-bit addressability and had only a limited set of
                 64-bit arithmetic instructions. The processors also
                 lacked data and instruction bandwidth, since they
                 utilized a unified cache. The branch performance was
                 good, but there were delays due to conflicts in
                 searching and writing the branch target buffer. Also,
                 the hardware data compression and decimal arithmetic
                 performance, though good, was in demand by database and
                 COBOL programmers. Most of the performance concerns
                 regarding prior processors were due to area
                 constraints. Recent technology advances have increased
                 the circuit density by 50 percent over that of the G6
                 processor. This has allowed the design of several
                 performance-critical areas to be revisited. The end
                 result of these efforts is the IBM eServer z900
                 processor, which is the first high-end processor based
                 on the new 64-bit z/Architecture{\TM}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "decimal floating-point arithmetic",
  ordernumber =  "G322-0232",
}

@Article{Serebrenik:2002:TLP,
  author =       "Alexander Serebrenik and Danny De Schreye",
  title =        "On Termination of Logic Programs with Floating Point
                 Computations",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2477",
  pages =        "151--164",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  MRnumber =     "MR2049473",
  bibdate =      "Tue Sep 10 19:11:24 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2477.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2477/24770151.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2477/24770151.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@MastersThesis{Shi:2002:SMF,
  author =       "Changchun Shi",
  title =        "Statistical method for floating-point to fixed-point
                 conversion",
  type =         "{Master of Science, Plan II}",
  school =       "Department of Electrical Engineering and Computer
                 Sciences, University of California, Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "x + 131",
  year =         "2002",
  LCCN =         "T7.49.2002 S55",
  bibdate =      "Thu Oct 24 14:20:51 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Soudris:2002:FAB,
  author =       "D. Soudris and M. Dasygenis and K. Mitroglou and K.
                 Tatas and A. Thanailakis",
  booktitle =    "9th International Conference on Electronics, Circuits
                 and Systems, 2002",
  title =        "A full adder based methodology for scaling operation
                 in residue number system",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "891--894",
  year =         "2002",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICECS.2002.1046391",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "A systematic methodology for designing
                 full-adder-based architectures in residue number system
                 for scaling operation and its software tool
                 development, are introduced. Starting from the
                 mathematical description of scaling operation in RNS,
                 we end up \ldots{}",
}

@Article{Spiteri:2002:PPA,
  author =       "Pierre Spiteri and Jean-Claude Miellou and Didier El
                 Baz",
  title =        "Perturbation of parallel asynchronous linear
                 iterations by floating point errors",
  journal =      j-ELECTRON-TRANS-NUMER-ANAL,
  volume =       "13",
  pages =        "38--55",
  year =         "2002",
  CODEN =        "????",
  ISSN =         "1068-9613 (print), 1097-4067 (electronic)",
  ISSN-L =       "1068-9613",
  MRclass =      "65F10 (65G50 65Y05)",
  MRnumber =     "MR1924261 (2003h:65042)",
  bibdate =      "Thu Nov 8 19:16:14 2007",
  bibsource =    "http://etna.mcs.kent.edu/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://etna.mcs.kent.edu/vol.13.2002/pp38-55.dir/pp38-55.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronic Transactions on Numerical Analysis",
  journal-URL =  "http://etna.mcs.kent.edu/",
}

@Article{Stakhov:2002:BTP,
  author =       "Alexey Stakhov",
  title =        "{Brousentsov}'s Ternary Principle, {Bergman}'s Number
                 System and Ternary Mirror-symmetrical Arithmetic",
  journal =      j-COMP-J,
  volume =       "45",
  number =       "2",
  pages =        "221--236",
  month =        "????",
  year =         "2002",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Thu Apr 4 07:33:05 MST 2002",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_45/Issue_02/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_45/Issue_02/450221.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_45/Issue_02/pdf/450221.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Misc{Steele:2002:SMF,
  author =       "Guy L. {Steele Jr.}",
  title =        "System and method for floating-point computation",
  howpublished = "US Patent 6356927",
  day =          "12",
  month =        mar,
  year =         "2002",
  bibdate =      "Tue Dec 23 15:06:47 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/6356927/fulltext.html",
  abstract =     "A system is disclosed for performing floating point
                 computation in connection with numbers in a base
                 floating point representation (such as the
                 representation defined in IEEE Std. 754) that defines a
                 plurality of formats, including a normalized format and
                 a de-normalized format, using a common floating point
                 representation that defines a unitary normalized
                 format. The system includes a base to common
                 representation converter, a processor and a common to
                 base representation converter. The base to common
                 representation converter converts numbers from the base
                 floating point representation to the common floating
                 point representation, so that all numbers involved in a
                 computation will be expressed in the unitary normalized
                 format. The processor is configured to perform a
                 mathematical operation of at least one predetermined
                 type in connection with the converted numbers generated
                 by the base to common representation converter to
                 generate a floating point result in the common
                 representation. The common to base representation
                 converter converts numbers from the common floating
                 point representation selectively to either the
                 normalized or de-normalized format of the base
                 representation.",
  acknowledgement = ack-nhfb,
}

@TechReport{Stehle:2002:WCL,
  author =       "Damien Stehl{\'e} and Vincent Lef{\`e}vre and Paul
                 Zimmermann",
  title =        "Worst Cases and Lattice Reduction",
  type =         "Research Report",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  pages =        "10",
  day =          "15",
  month =        oct,
  year =         "2002",
  bibdate =      "Sun Sep 10 08:24:59 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.loria.fr/~zimmerma/papers/wclr.ps.gz",
  abstract =     "We propose a new algorithm to find worst cases for
                 correct rounding of an analytic function. We first
                 reduce this problem to the {\em real small value
                 problem} --- i.e., for polynomials with real
                 coefficients. Then we show that this second problem can
                 be solved efficiently, by extending Coppersmith's work
                 on the {\em integer small value problem} --- for
                 polynomials with integer coefficients --- using lattice
                 reduction [4, 5, 6].\par

                 For floating-point numbers with a mantissa less than
                 $N$, and a polynomial approximation of degree $d$, our
                 algorithm finds all worst cases at distance $ < N^{-d^2
                 / (2d + 1)} $ from a machine number in time $ O(N^{(d +
                 1) / (2d + 1) + \epsilon }) $. For $ d = 2 $, this
                 improves on the $ O(N^{2 / 3 + \epsilon }) $ complexity
                 from Lef{\`e}vre's algorithm [12, 13] to $ O(N^{3 / 5 +
                 \epsilon }) $. We exhibit some new worst cases found
                 using our algorithm, for double-extended and quadruple
                 precision. For larger $d$, our algorithm can be used to
                 check that there exist no worst cases at distance $ <
                 N^{-k} $ in time $ O(N^{1 / 2 + O(1 / k)}) $.",
  acknowledgement = ack-nhfb,
  keywords =     "Coppersmith's theorem; correct rounding; Exact
                 rounding; floating-point arithmetic; IEEE-754; lattice
                 reduction; table maker's dilemma; worst case",
}

@Article{Stoianov:2002:AAB,
  author =       "Ivilin Stoianov and Marco Zorzi and Suzanna Becker and
                 Carlo Umilta",
  title =        "Associative Arithmetic with {Boltzmann} Machines: The
                 Role of Number Representations",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2415",
  pages =        "277--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:10:20 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2415.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2415/24150277.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2415/24150277.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Manual{Sun:2002:BJP,
  author =       "{Sun Microsystems}",
  title =        "{BigDecimal (Java 2 Platform SE v1.4.0)}",
  organization = "Sun Microsystems",
  address =      "Mountain View, CA, USA",
  pages =        "17",
  year =         "2002",
  bibdate =      "Fri Nov 28 11:16:16 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://java.sun/com/products",
  abstract =     "Immutable, arbitrary-precision signed decimal numbers.
                 A BigDecimal consists of an arbitrary precision integer
                 unscaled value and a non-negative 32-bit integer scale,
                 which represents the number of digits to the right of
                 the decimal point. The number represented by the
                 BigDecimal is $ (\mbox {unscaledValue} / 10^{\mbox
                 {scale}}) $. BigDecimal provides operations for basic
                 arithmetic, scale manipulation, comparison, hashing,
                 and format conversion.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@Manual{TI:2002:TFL,
  title =        "{TMS320C67x FastRTS} Library Programmer's Reference
                 ({SPRU100A})",
  organization = "Texas Instruments",
  address =      "Dallas, TX, USA",
  month =        oct,
  year =         "2002",
  bibdate =      "Sat Jan 15 06:11:57 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "The FastRTS library is a collection of 26 optimized
                 floating-point math functions for the TMS320C67x
                 device. This source code library includes C-callable
                 (ANSI-C-language compatible) optimized versions of the
                 floating-point math functions included in previous
                 run-time-support libraries.",
  URL =          "http://focus.ti.com/lit/ug/spru100a/spru100a.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Tornaria:2002:SRM,
  author =       "Gonzalo Tornar{\'\i}a",
  title =        "Square Roots Modulo $p$",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2286",
  pages =        "430--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:09:12 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2286.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2286/22860430.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2286/22860430.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Turner:2002:RPS,
  author =       "Peter R. Turner",
  title =        "Residue polynomial systems",
  journal =      j-THEOR-COMP-SCI,
  volume =       "279",
  number =       "1-2",
  pages =        "29--49",
  month =        may,
  year =         "2002",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Nov 20 18:08:56 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}

@Article{vanEmden:2002:NDI,
  author =       "M. H. van Emden",
  title =        "New Developments in Interval Arithmetic and Their
                 Implications for Floating-Point Standardization",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--12",
  day =          "16",
  month =        oct,
  year =         "2002",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/cs/0210015",
  abstract =     "We consider the prospect of a processor that can
                 perform interval arithmetic at the same speed as
                 conventional floating-point arithmetic. This makes it
                 possible for all arithmetic to be performed with the
                 superior security of interval methods without any
                 penalty in speed. In such a situation the IEEE
                 floating-point standard needs to be compared with a
                 version of floating-point arithmetic that is ideal for
                 the purpose of interval arithmetic. Such a comparison
                 requires a succinct and complete exposition of interval
                 arithmetic according to its recent developments. We
                 present such an exposition in this paper. We conclude
                 that the directed roundings toward the infinities and
                 the definition of division by the signed zeros are
                 valuable features of the standard. Because the
                 operations of interval arithmetic are always defined,
                 exceptions do not arise. As a result neither Nans nor
                 exceptions are needed. Of the status flags, only the
                 inexact flag may be useful. Denormalized numbers seem
                 to have no use for interval arithmetic; in the use of
                 interval constraints, they are a handicap.",
  acknowledgement = ack-nhfb,
  subject =      "Numerical Analysis (cs.NA)",
}

@InProceedings{Walters:2002:DTU,
  author =       "E. G. Walters and M. J. Schulte",
  title =        "Design Tradeoffs Using Truncated Multipliers in {FIR}
                 Filter Implementations",
  crossref =     "Luk:2002:PSA",
  pages =        "357--368",
  year =         "2002",
  bibdate =      "Sun Mar 04 17:47:29 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2002-03.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Winkler:2002:SVU,
  author =       "J{\"u}rgen F. H. Winkler",
  title =        "A safe variant of the unsafe integer arithmetic of
                 {Java$^{TM}$}",
  journal =      j-SPE,
  volume =       "32",
  number =       "7",
  pages =        "669--701",
  month =        jun,
  year =         "2002",
  CODEN =        "SPEXBL",
  DOI =          "https://doi.org/10.1002/spe.454",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Wed Oct 16 18:25:58 MDT 2002",
  bibsource =    "http://www.interscience.wiley.com/jpages/0038-0644;
                 http://www3.interscience.wiley.com/journalfinder.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.interscience.wiley.com/cgi-bin/abstract/94515736/START;
                 http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=94515736&PLACEBO=IE.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Software---Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  keywords =     "arithmetics in programming languages; divide-by-zero;
                 floating-point arithmetic; IEEE 754; Java; overflow;
                 program structure; range limitation; rounding; safe
                 arithmetic operations; underflow; zero-divide",
}

@Article{Wu:2002:BPF,
  author =       "Huapeng Wu",
  title =        "Bit-parallel finite field multiplier and squarer using
                 polynomial basis",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "51",
  number =       "7",
  pages =        "750--758",
  month =        jul,
  year =         "2002",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2002.1017695",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 09:41:54 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1017695",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Wu:2002:FFM,
  author =       "Huapeng Wu and M. A. Hasan and I. F. Blake and Shuhong
                 Gao",
  title =        "Finite field multiplier using redundant
                 representation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "51",
  number =       "11",
  pages =        "1306--1316",
  month =        nov,
  year =         "2002",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2002.1047755",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 09:42:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1047755",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Wu:2002:MMS,
  author =       "Huapeng Wu",
  title =        "{Montgomery} multiplier and squarer for a class of
                 finite fields",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "51",
  number =       "5",
  pages =        "521--529",
  month =        may,
  year =         "2002",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2002.1004591",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 09:41:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1004591",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@MastersThesis{Yang:2002:DAB,
  author =       "Yi Yang",
  title =        "A distributed arithmetic-based {CORDIC} algorithm and
                 its use in the {FPGA} implementation of the {2-D
                 IDCT}",
  type =         "{M.A.Sc.} thesis",
  school =       "Concordia University",
  address =      "Montreal, QC, Canada",
  pages =        "90",
  year =         "2002",
  ISBN =         "0-612-68448-2",
  ISBN-13 =      "978-0-612-68448-5",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://login.ezproxy.lib.utah.edu/login?url=https://www.proquest.com/dissertations-theses/distributed-arithmetic-based-cordic-algorithm-use/docview/305477205/se-2",
  acknowledgement = ack-nhfb,
  advisor =      "M. O. Ahmad and C. Wang",
  keywords =     "0544:Electrical engineering; Applied sciences;
                 Electrical engineering",
  ris-m1 =       "MQ68448",
}

@Article{Yang:2002:RNSa,
  author =       "Lie-Liang Yang and L. Hanzo",
  title =        "A residue number system based parallel communication
                 scheme using orthogonal signaling. {II}. {Multipath}
                 fading channels",
  journal =      j-IEEE-TRANS-VEH-TECHNOL,
  volume =       "51",
  number =       "6",
  pages =        "1547--1559",
  month =        nov,
  year =         "2002",
  CODEN =        "ITUTAB",
  DOI =          "https://doi.org/10.1109/TVT.2002.804849",
  ISSN =         "0018-9545 (print), 1939-9359 (electronic)",
  ISSN-L =       "0018-9545",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26382",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Vehicular Technology",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=25",
  keywords =     "residue arithmetic; residue number system",
  summary =      "For pt.I see ibid., vol.51, no.6, p.1534-46 (2002). A
                 novel signaling scheme is presented, where a set of
                 orthogonal signals is transmitted in parallel. The
                 signals are selected according to the so-called residue
                 number system (RNS). Hence the \ldots{}",
}

@Article{Yang:2002:RNSb,
  author =       "Lie-Liang Yang and L. Hanzo",
  title =        "A residue number system based parallel communication
                 scheme using orthogonal signaling. {I}. {System}
                 outline",
  journal =      j-IEEE-TRANS-VEH-TECHNOL,
  volume =       "51",
  number =       "6",
  pages =        "1534--1546",
  month =        nov,
  year =         "2002",
  CODEN =        "ITUTAB",
  DOI =          "https://doi.org/10.1109/TVT.2002.804850",
  ISSN =         "0018-9545 (print), 1939-9359 (electronic)",
  ISSN-L =       "0018-9545",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=26382",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Vehicular Technology",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=25",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A novel signaling scheme is presented, where a set of
                 orthogonal signals is transmitted in parallel. The
                 signals are selected according to the so-called residue
                 number system (RNS). Hence the system is essentially a
                 multiple code parallel \ldots{}",
}

@Article{Yang:2002:RNSc,
  author =       "Lie-Liang Yang and L. Hanzo",
  title =        "Residue number system assisted fast frequency-hopped
                 synchronous ultra-wideband spread-spectrum
                 multiple-access: a design alternative to impulse
                 radio",
  journal =      j-IEEE-J-SEL-AREAS-COMMUN,
  volume =       "20",
  number =       "9",
  pages =        "1652--1663",
  month =        dec,
  year =         "2002",
  CODEN =        "ISACEM",
  DOI =          "https://doi.org/10.1109/JSAC.2002.805059",
  ISSN =         "0733-8716 (print), 1558-0008 (electronic)",
  ISSN-L =       "0733-8716",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=24076",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal on Selected Areas in Communications",
  keywords =     "residue arithmetic; residue number system",
  summary =      "Ultra-wideband (UWB) systems having a bandwidth on the
                 order of gigahertz have received wide attention both in
                 the US and in Europe. The family of UWB systems may
                 communicate either, by generating ultra-wideband
                 signals or with the aid of \ldots{}",
}

@Article{Yen:2002:RSR,
  author =       "Sung-Ming Yen and Seungjoo Kim and Seongan Lim and
                 Sangjae Moon",
  title =        "{RSA} Speedup with Residue Number System Immune
                 against Hardware Fault Cryptanalysis",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2288",
  pages =        "397--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:09:14 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2288.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2288/22880397.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2288/22880397.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Ziv:2002:SGM,
  author =       "Abraham Ziv and Laurent Fournier",
  title =        "Solving the generalized mask constraint for test
                 generation of binary floating point add operation",
  journal =      j-THEOR-COMP-SCI,
  volume =       "291",
  number =       "2",
  pages =        "183--201",
  month =        nov,
  year =         "2002",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Nov 20 18:15:29 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tcs2000.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Theor. Comput. Sci.",
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975/",
  keywords =     "floating-point testing",
  remark =       "Proceedings of the Fourth conference on Real numbers
                 and Computers, Schlo{\ss} Dagstuhl, April 2000.",
}

@Article{Abed:2003:VIL,
  author =       "K. H. Abed and R. E. Siferd",
  title =        "{VLSI} implementation of a low-power antilogarithmic
                 converter",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "52",
  number =       "9",
  pages =        "1221--1228",
  month =        sep,
  year =         "2003",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2003.1228517",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 08:52:55 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1228517",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Agou:2003:SPR,
  author =       "Simon Joseph Agou and Marc Del{\'e}glise and
                 Jean-Louis Nicolas",
  title =        "Short Polynomial Representations for Square Roots
                 Modulo $p$",
  journal =      j-DESIGNS-CODES-CRYPTOGR,
  volume =       "28",
  number =       "1",
  pages =        "33--44",
  month =        jan,
  year =         "2003",
  CODEN =        "DCCREC",
  ISSN =         "0925-1022 (print), 1573-7586 (electronic)",
  ISSN-L =       "0925-1022",
  bibdate =      "Thu Dec 11 06:27:20 MST 2003",
  bibsource =    "http://www.wkap.nl/jrnltoc.htm/0925-1022;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ipsapp007.kluweronline.com/content/getfile/4630/45/2/abstract.htm;
                 http://ipsapp007.kluweronline.com/content/getfile/4630/45/2/fulltext.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Designs, codes, and cryptography",
  journal-URL =  "http://link.springer.com/journal/10623",
}

@InProceedings{Aharoni:2003:FTG,
  author =       "Merav Aharoni and Sigal Asaf and Laurent Fournier and
                 Anatoly Koifman and Raviv Nagel",
  booktitle =    "{Proceedings of the Eighth IEEE International
                 High-Level Design Validation and Test Workshop, 12--14
                 November, 2003 (HLDVT03)}",
  title =        "{FPgen} --- a Test Generation Framework for Datapath
                 Floating-Point Verification",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  bookpages =    "viii + 178",
  pages =        "17--22",
  month =        nov,
  year =         "2003",
  DOI =          "https://doi.org/10.1109/HLDVT.2003.1252469",
  ISBN =         "0-7803-8236-6",
  ISBN-13 =      "978-0-7803-8236-7",
  LCCN =         "QA76.76.V47 I35 2003; TK7895.M5 I34 2003",
  bibdate =      "Tue Jun 22 06:49:59 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.haifa.ibm.com/projects/verification/fpgen;
                 https://ieeexplore.ieee.org/servlet/opac?punumber=8873;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1252469;
                 https://www.research.ibm.com/haifa/projects/verification/fpgen/ieeets.html",
  abstract =     "FPgen is a new test generation framework targeted
                 toward the verification of the floating point (FP)
                 datapath, through the generation of test cases. This
                 framework provides the capacity to define virtually any
                 architectural FP coverage model, consisting of
                 verification tasks. The tool supplies strong constraint
                 solving capabilities, allowing the generation of random
                 tests that target these tasks. We present an overview
                 of FPgen's functionality, describe the results of its
                 use for the verification of several FP units, and
                 compare its efficiency with existing test generators.",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point testing",
}

@InProceedings{Akkas:2003:QPD,
  author =       "A. Akkas and M. J. Schulte",
  booktitle =    "Proceedings of the 2003 Euromicro Symposium on Digital
                 System Design, Antalya, Turkey, September 2003",
  title =        "A Quadruple Precision and Dual Double Precision
                 Floating-Point Multiplier",
  publisher =    "????",
  address =      "????",
  pages =        "76--81",
  year =         "2003",
  bibdate =      "Fri Jun 11 05:37:57 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://home.ku.edu.tr/~ahakkas/publications/quadruple_multiplier.pdf;
                 http://mesa.ece.wisc.edu/publications/cp_2003-07.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Al-Radadi:2003:RSD,
  author =       "E. Al-Radadi and P. Siy",
  title =        "{RNS}: sign detector based on {Chinese Remainder
                 Theorem II} ({CRT II})",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "46",
  number =       "10--11",
  pages =        "1559--1570",
  month =        nov # "\slash " # dec,
  year =         "2003",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:49:30 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S089812210390191X",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Altman:2003:RAN,
  author =       "Micah Altman and Michael P. McDonald",
  title =        "Replication with Attention to Numerical Accuracy",
  journal =      j-POLIT-ANAL,
  volume =       "11",
  number =       "3",
  pages =        "302--307",
  month =        "Summer",
  year =         "2003",
  DOI =          "https://doi.org/10.1093/pan/mpg016",
  ISSN =         "1047-1987 (print), 1476-4989 (electronic)",
  ISSN-L =       "1047-1987",
  bibdate =      "Sat Feb 8 10:28:55 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Political Analysis",
  journal-URL =  "https://www.cambridge.org/core/journals/political-analysis/all-issues",
  remark =       "The authors attempt to replicate numerically two
                 papers in the \booktitle{American Journal of Political
                 Science}, and find that the results in those papers are
                 dependent on the statistical package used. Their
                 abstract concludes: ``In the course of our
                 replications, we uncover other pitfalls that may
                 prevent accurate replication, and make recommendations
                 to ensure the ability for future researchers to
                 replicate results.''",
}

@InProceedings{Ammar:2003:NDH,
  author =       "A. Ammar and A. S. S. El-Kabbany and M. I. Youssef and
                 A. Emam",
  booktitle =    "{NRSC 2003}, Proceedings of the Twentieth National
                 Radio Science Conference, 18--20 March 2003",
  title =        "A novel data hiding technique using residue number
                 system",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "C15--1--12",
  year =         "2003",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/NRSC.2003.1217348",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Data hiding technique is a very attractive field. The
                 field of data hiding in imagery is relatively very
                 young and is growing at an exponential rate. This field
                 is highly multidisciplinary field that combines image
                 and signal processing with \ldots{}",
}

@InProceedings{Anonymous:2003:AI,
  author =       "Anonymous",
  title =        "Author index",
  crossref =     "Bajard:2003:ISC",
  pages =        "281--281",
  year =         "2003",
  bibdate =      "Fri Nov 28 11:06:15 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@TechReport{Anonymous:2003:FFP,
  author =       "Anonymous",
  title =        "Fast Floating-Point Arithmetic Emulation on the
                 {Blackfin} Processor Platform",
  type =         "Engineer To Engineer Note",
  number =       "EE-185",
  institution =  "Analog Devices",
  address =      "????",
  day =          "26",
  month =        may,
  year =         "2003",
  bibdate =      "Fri May 20 12:26:05 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.analog.com/UploadedFiles/Application_Notes/47485184002118EE185.pdf",
  acknowledgement = ack-nhfb,
  remark =       "Describes a software implementation of IEEE 754 32-bit
                 and 64-bit arithmetic for the Blackfin fixed-point
                 embedded processor.",
}

@Misc{Anonymous:2003:RHP,
  author =       "Anonymous",
  title =        "Recently heard {Pentium} jokes",
  howpublished = "World Wide Web document",
  day =          "20",
  month =        oct,
  year =         "2003",
  bibdate =      "Fri Jul 29 16:01:53 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://web.archive.org/web/20031020012234/http://www-pcd.stanford.edu/cousins/pentium.html;
                 http://www-pcd.stanford.edu/cousins/pentium.html",
  acknowledgement = ack-nhfb,
  keywords =     "Intel Pentium divide flaw; Thomas R. Nicely",
}

@Article{Arciniega:2003:REN,
  author =       "Armando Arciniega and Edward Allen",
  title =        "Rounding Error in Numerical Solution of Stochastic
                 Differential Equations",
  journal =      j-STOCH-ANAL-APPL,
  volume =       "21",
  number =       "2",
  pages =        "281--300",
  month =        jan,
  year =         "2003",
  CODEN =        "SAAPDA",
  DOI =          "https://doi.org/10.1081/sap-120019286",
  ISSN =         "0736-2994 (print), 1532-9356 (electronic)",
  ISSN-L =       "0736-2994",
  bibdate =      "Fri Apr 11 08:23:41 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.researchgate.net/publication/266011553_Rounding_Error_in_Numerical_Solution_of_Stochastic_Differential_Equations",
  abstract =     "The present investigation is concerned with estimating
                 the rounding error in numerical solution of stochastic
                 differential equations. A statistical rounding error
                 analysis of Euler's method for stochastic differential
                 equations is performed. In particular, numerical
                 evaluation of the quantities $ E|X(t_n) - Y^n|^2 $ and
                 $ E[F(Y^n) - F(X(t_n))] $ is investigated, where $
                 X(t_n) $ is the exact solution at the $n$ th time step
                 and $ Y^n$ is the approximate solution that includes
                 computer rounding error. It is shown that rounding
                 error is inversely proportional to the square root of
                 the step size. An extrapolation technique provides
                 second-order accuracy, and is one way to increase
                 accuracy while avoiding rounding error. Several
                 computational results are given.",
  acknowledgement = ack-nhfb,
  fjournal =     "Stochastic Analysis and Applications",
}

@Article{Arnold:2003:FFT,
  author =       "M. Arnold and T. Bailey and J. Cowles and C. Walter",
  title =        "{Fast Fourier Transforms} Using the Complex
                 Logarithmic Number System",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "33",
  number =       "3",
  pages =        "325--335",
  month =        mar,
  year =         "2003",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1023/A:1022236132192",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Sat Aug 22 09:28:10 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The complex-logarithmic number system (CLNS), which
                 represents each complex point in log/polar coordinates,
                 may be practical to implement the Fast Fourier
                 Transform (FFT). The roots of unity needed by the FFT
                 have exact representations in CLNS and do not require a
                 ROM.\par

                 We present an error analysis and simulation results for
                 a radix-two FFT that compares a rectangular fixed-point
                 representation of complex numbers to CLNS. We observe
                 that CLNS saves 9--12 bits in word-size for 256--1024
                 point FFTs compared to the fixed-point number system
                 while producing comparable accuracy.\par

                 The consequence of the word-size advantage is that the
                 number of full adders required for CLNS is
                 significantly smaller than for an equivalent
                 fixed-point implementation. The major cost of CLNS is
                 the memory, which unlike conventional LNS, is addressed
                 by both real and imaginary parts. Table-reduction
                 techniques can mitigate this. The simplicity of the
                 CLNS approach requires significantly fewer full adders,
                 which pays for some or all of the extra memory. In
                 applications needing the magnitude of the complex
                 parts, such as a power spectrum, the CLNS approach can
                 actually require less memory than the conventional
                 approach.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
}

@InProceedings{Arnold:2003:ILN,
  author =       "Mark G. Arnold and Jesus Garcia and Michael J.
                 Schulte",
  title =        "The interval logarithmic number system",
  crossref =     "Bajard:2003:ISC",
  pages =        "253--261",
  year =         "2003",
  bibdate =      "Wed Nov 26 12:04:40 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2003-01.pdf;
                 http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Arnold.pdf",
  abstract =     "This paper introduces the Interval Logarithmic Number
                 System (ILNS), in which the Logarithmic Number System
                 (LNS) is used as the underlying number system for
                 interval arithmetic. The basic operations in ILNS are
                 introduced and an efficient method for performing ILNS
                 addition and subtraction is presented. The paper
                 compares ILNS to Interval Floating Point (IFP) for a
                 few sample applications. For applications like the
                 N-body problem, which have a large percentage of
                 multiplies, divides and square roots, ILNS provides
                 much narrower intervals than IFP. In other
                 applications, like the Fast Fourier Transform, where
                 addition and subtraction dominate, ILNS and IFP produce
                 intervals having similar widths. Based on our analysis,
                 ILNS is an attractive alternative to IFP for
                 application that can tolerate low to moderate
                 precisions.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@InProceedings{Bajard:2003:EMG,
  author =       "J.-C. Bajard and L. Imbert and C. N{\`e}gre and T.
                 Plantard",
  title =        "Efficient multiplication in {$ \mathrm {GF}(p_k) $}
                 for Elliptic Curve Cryptography",
  crossref =     "Bajard:2003:ISC",
  pages =        "181--187",
  year =         "2003",
  bibdate =      "Wed Nov 26 12:04:35 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Bajard.pdf",
  abstract =     "We present a new multiplication algorithm for the
                 implementation of elliptic curve cryptography (ECC)
                 over the finite extension fields $ \mathrm {GF}(p_k) $
                 where $p$ is a prime number greater than $ 2 k $. In
                 the context of ECC we can assume that $p$ is a 7-to-10
                 bit number, and easily find values for $k$ which
                 satisfy: $ p > 2 k $, and for security reasons $ l o
                 g_2 (p) \times k \approx 160 $. All the computations
                 are performed within an alternate polynomial
                 representation of the field elements which is directly
                 obtained from the inputs. No conversion step is needed.
                 We describe our algorithm in terms of matrix operations
                 and point out some properties of the matrices that can
                 be used to improve the design. The proposed algorithm
                 is highly parallelizable and seems well adapted to
                 hardware implementation of elliptic curve
                 cryptosystems.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@InProceedings{Bajard:2003:FII,
  author =       "Jean-Claude Bajard and Michael Schulte",
  title =        "Foreword: {16th IEEE International Symposium on
                 Computer Arithmetic}",
  crossref =     "Bajard:2003:ISC",
  pages =        "viii--viii",
  year =         "2003",
  bibdate =      "Sat Nov 17 21:53:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_contents.pdf;
                 http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_foreword.pdf;
                 http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_preface.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@Article{Barrio:2003:NEL,
  author =       "Roberto Barrio and B. Melendo and S. Serrano",
  title =        "On the numerical evaluation of linear recurrences",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "150",
  number =       "1",
  pages =        "71--86",
  day =          "1",
  month =        jan,
  year =         "2003",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:32 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042702005654",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Barrio:2003:URE,
  author =       "Roberto Barrio",
  title =        "A unified rounding error bound for polynomial
                 evaluation",
  journal =      j-ADV-COMPUT-MATH,
  volume =       "19",
  number =       "4",
  pages =        "385--399",
  month =        nov,
  year =         "2003",
  CODEN =        "ACMHEX",
  DOI =          "https://doi.org/10.1023/A:1024203520270",
  ISSN =         "1019-7168 (print), 1572-9044 (electronic)",
  ISSN-L =       "1019-7168",
  MRclass =      "65G50",
  MRnumber =     "1989623",
  bibdate =      "Sat Feb 3 18:22:17 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 https://www.math.utah.edu/pub/tex/bib/advcomputmath.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer.com/article/10.1023/A:1024203520270",
  acknowledgement = ack-nhfb,
  fjournal =     "Advances in Computational Mathematics",
  journal-URL =  "http://link.springer.com/journal/10444",
  keywords =     "Bernstein polynomial; Clenshaw--Forsythe algorithm;
                 de-Casteljau algorithm; Horner's algorithm; polynomial
                 evaluation; recurrence relations; rounding errors;
                 Szeg{\H{o}} polynomial",
}

@Article{Bertoni:2003:EAA,
  author =       "Guido Bertoni and Jorge Guajardo and Sandeep Kumar and
                 Gerardo Orlando and Christof Paar and Thomas
                 Wollinger",
  title =        "Efficient $ {GF}(p^m) $ Arithmetic Architectures for
                 Cryptographic Applications",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2612",
  pages =        "158--175",
  year =         "2003",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Apr 4 18:46:22 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
  keywords =     "cryptology; Topics in Cryptology CT-RSA 2003",
}

@InProceedings{Boldo:2003:FPC,
  author =       "Sylvie Boldo and Marc Daumas and Laurent Th{\'e}ry",
  editor =       "Th{\'e}r{\`e}se Hardin and Renaud Rioboo",
  booktitle =    "{CALCULEMUS-2003: 11th} Symposium on the Integration
                 of Symbolic Computation and Mechanized Reasoning:
                 September 10--12, 2003, Roma, Italy",
  title =        "Formal proofs and computations in finite precision
                 arithmetic",
  publisher =    "????",
  address =      "????",
  bookpages =    "vii + 141",
  pages =        "101--111",
  year =         "2003",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Tue Nov 23 10:09:27 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ftp.lip6.fr/lip6/reports/2003/lip6.2003.010.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Boldo:2003:RCT,
  author =       "Sylvie Boldo and Marc Daumas",
  title =        "Representable correcting terms for possibly
                 underflowing floating point operations",
  crossref =     "Bajard:2003:ISC",
  pages =        "79--86",
  year =         "2003",
  bibdate =      "Wed Nov 26 11:59:51 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://csdl.computer.org/comp/proceedings/arith/2003/1894/00/1894toc.htm;
                 http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Boldo.pdf;
                 http://www.dec.usc.es/arith16/papers/paper-156.pdf",
  abstract =     "Studying floating point arithmetic, authors have shown
                 that the implemented operations (addition, subtraction,
                 multiplication, division and square root) can compute a
                 result and an exact correcting term using the same
                 format as the inputs. Following a path initiated in
                 1965, many authors supposed that neither underflow nor
                 overflow occurred in the process. Overflow is not
                 critical as this kind of exception creates persisting
                 nonnumeric quantities. Underflow may be fatal to the
                 process as it returns wrong numeric values with little
                 warning. Our new conditions guarantee that the
                 correcting term is exact when the result is a number.
                 We have validated our proofs against Coq automatic
                 proof checker. Our development has raised many
                 questions, some of them were expected while other ones
                 were surprising.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation; ARITH-16",
}

@TechReport{Boldo:2003:STQ,
  author =       "Sylvie Boldo and Marc Daumas",
  title =        "A simple test qualifying the accuracy of {Horner}'s
                 rule for polynomials",
  type =         "Research Report",
  number =       "2003-01",
  institution =  "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "69364 Lyon Cedex 07, France",
  pages =        "41",
  month =        jan,
  year =         "2003",
  bibdate =      "Tue Nov 23 10:54:34 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.ens-lyon.fr/pub/LIP/Rapports/RR/RR2003/RR2003-01.ps.gz;
                 ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4707.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point testing",
}

@InProceedings{Boullis:2003:SOH,
  author =       "Nicolas Boullis and Arnaud Tisserand",
  title =        "Some optimizations of hardware multiplication by
                 constant matrices",
  crossref =     "Bajard:2003:ISC",
  pages =        "20--27",
  year =         "2003",
  bibdate =      "Wed Nov 26 11:59:51 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Boullis.pdf",
  abstract =     "This paper presents some improvements on the
                 optimization of hardware multiplication by constant
                 matrices. We focus on the automatic generation of
                 circuits that involve constant matrix multiplication
                 (CMM), i.e. multiplication of a vector by a constant
                 matrix. The proposed method, based on number recoding
                 and dedicated common sub-expression factorization
                 algorithms was implemented in a VHDL generator. The
                 obtained results on several applications have been
                 implemented on FPGAs and compared to previous
                 solutions. Up to 40\% area and speed savings are
                 achieved.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@TechReport{Brisebarre:2003:FTP,
  author =       "Nicolas Brisebarre and Jean-Michel Muller",
  title =        "Finding the ``truncated'' polynomial that is closest
                 to a function",
  type =         "Research Report",
  number =       "4787",
  institution =  "INRIA Rhone-Alpes",
  address =      "ZIRST, 655 Avenue de l'Europe, Montbonnot, 38334 Saint
                 Ismier cedex, France",
  year =         "2003",
  bibdate =      "Fri Jun 24 14:41:03 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4787.pdf;
                 ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-4787.ps.gz;
                 http://arxiv.org/pdf/cs.MS/0307009;
                 http://www.inria.fr/rrrt/rr-4787.html",
  abstract =     "When implementing regular enough functions (e.g.,
                 elementary or special functions) on a computing system,
                 we frequently use polynomial approximations. In most
                 cases, the polynomial that best approximates (for a
                 given distance and in a given interval) a function has
                 coefficients that are not exactly representable with a
                 finite number of bits. And yet, the polynomial
                 approximations that are actually implemented do have
                 coefficients that are represented with a finite - and
                 sometimes small - number of bits: this is due to the
                 finiteness of the floating-point representations (for
                 software implementations), and to the need to have
                 small, hence fast and/or inexpensive, multipliers (for
                 hardware implementations). We then have to consider
                 polynomial approximations for which the degree-$i$
                 coefficient has at most $ m_i $ fractional bits (in
                 other words, it is a rational number with denominator $
                 2^{m_i} $). We provide a general method for finding the
                 best polynomial approximation under this constraint.
                 Then, we suggest refinements than can be used to
                 accelerate our method.",
  acknowledgement = ack-nhfb,
}

@Misc{Brown:2003:DPA,
  author =       "Walter E. Brown",
  title =        "A [{DRAFT}] Proposal to Add Mathematical Special
                 Functions to the {C++ Standard Library}",
  howpublished = "World-Wide Web document",
  day =          "3",
  month =        jan,
  year =         "2003",
  bibdate =      "Wed Jan 29 17:15:07 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://home.fnal.gov/~wb/N0000.html",
  acknowledgement = ack-nhfb,
}

@InProceedings{Burgess:2003:SRN,
  author =       "Neil Burgess",
  title =        "Scaling an {RNS} number using the core function",
  crossref =     "Bajard:2003:ISC",
  pages =        "262--269",
  year =         "2003",
  bibdate =      "Wed Nov 26 12:04:40 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Burgess.pdf",
  abstract =     "This paper introduces a method for extracting the core
                 of a Residue Number System (RNS) number within the RNS,
                 this affording a new method for scaling RNS numbers.
                 Suppose an RNS comprises a set of co-prime moduli, $
                 m_i $, with $ \prod m_i = M $. This paper describes a
                 method for approximately scaling such an RNS number by
                 a subset of the moduli, $ \prod m_j = M_J = \sqrt {M}
                 $, with the characteristic that all computations are
                 performed using the original moduli and one other
                 non-maintained short wordlength modulus.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@InProceedings{Cao:2003:DHS,
  author =       "Bin Cao and T. Srikanthan and Chip-Hong Chang",
  booktitle =    "{ISCAS '03}, Proceedings of the 2003 International
                 Symposium on Circuits and Systems, 25--28 May 2003",
  title =        "Design of a high speed reverse converter for a new
                 $4$-moduli set residue number system",
  volume =       "4",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "IV-520--IV-523",
  year =         "2003",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.2003.1205951",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper presents an elegant residue-to-binary
                 algorithm for a new 4-moduli set (2/sup n/ - 1, 2/sup
                 n/, 2/sup n/ + 1, 2/sup 2n/ + 1) Residue Number System.
                 Our reverse conversion algorithm takes advantage of the
                 special number properties of the \ldots{}",
}

@Article{Chaudhuri:2003:DAO,
  author =       "Ranjan Chaudhuri",
  title =        "Do the arithmetic operations really execute in
                 constant time?",
  journal =      j-SIGCSE,
  volume =       "35",
  number =       "2",
  pages =        "43--44",
  month =        jun,
  year =         "2003",
  CODEN =        "SIGSD3",
  DOI =          "https://doi.org/10.1145/782941.782977",
  ISSN =         "0097-8418 (print), 2331-3927 (electronic)",
  ISSN-L =       "0097-8418",
  bibdate =      "Sat Nov 17 16:57:02 MST 2012",
  bibsource =    "DBLP;
                 http://dblp.uni-trier.de/db/journals/sigcse/sigcse35.html#Chaudhuri03;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigcse2000.bib",
  URL =          "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/DBLP/2003.bib",
  abstract =     "The paper emphasizes the need for exposing the
                 undergraduate computer science students to the
                 bit-level analysis of the run-times of certain computer
                 algorithms. These are algorithms where the input(s)
                 consist of one or more integers and only a bit-level
                 analysis yields a more realistic estimate of the
                 run-time behaviors of such algorithms.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGCSE Bulletin (ACM Special Interest Group on
                 Computer Science Education)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J688",
}

@InProceedings{Chaves:2003:RRD,
  author =       "R. Chaves and L. Sousa",
  booktitle =    "Proceedings. Euromicro Symposium on Digital System
                 Design, 2003",
  title =        "{RDSP}: a {RISC} {DSP} based on residue number
                 system",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "128--135",
  year =         "2003",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/DSD.2003.1231911",
  ISBN =         "0-7695-2003-0",
  ISBN-13 =      "978-0-7695-2003-2",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper is focused on low power programmable fast
                 digital signal processors (DSP) design based on a
                 configurable 5-stage RISC core architecture and on
                 residue number systems (RNS). Several innovative
                 aspects are introduced at the control and \ldots{}",
}

@InProceedings{Chen:2003:PIC,
  author =       "Chichyang Chen and Rui-Lin Chen",
  booktitle =    "Proceedings of the {IEEE} International Conference on
                 Application-Specific Systems, Architectures, and
                 Processors, 24--26 June 2003",
  title =        "Performance-improved computation of very large
                 word-length {LNS} addition\slash subtraction using
                 signed-digit arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "337--347",
  year =         "2003",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Pipelined computation of very large word-length LNS
                 addition/subtraction requires a significant amount of
                 hardware and long pipeline latency. We propose a base-e
                 exponential algorithm to simplify the exponential
                 computation and to replace half of \ldots{}",
}

@Article{Chevallier-Mames:2003:FDS,
  author =       "Beno{\^\i}t Chevallier-Mames and Marc Joye and Pascal
                 Paillierinst",
  title =        "Faster Double-Size Modular Multiplication from
                 {Euclidean} Multipliers",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2779",
  pages =        "214--227",
  year =         "2003",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Apr 4 18:12:50 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
  keywords =     "CHES 2003; cryptography",
}

@InProceedings{Ciet:2003:PFI,
  author =       "M. Ciet and M. Neve and E. Peeters and J.-J.
                 Quisquater",
  booktitle =    "{MWSCAS '03}. Proceedings of the 46th {IEEE}
                 International Midwest Symposium on Circuits and
                 Systems",
  title =        "Parallel {FPGA} implementation of {RSA} with residue
                 number systems --- can side-channel threats be
                 avoided?",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "806--810",
  year =         "2003",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/MWSCAS.2003.1562409",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "In this paper, the authors presented a new parallel
                 architecture to avoid side-channel analysis such as:
                 timing attack, simple/differential power analysis,
                 fault induction attack and simple/differential
                 electromagnetic analysis. Montgomery \ldots{}",
}

@Article{Constantinides:2003:BRB,
  author =       "George A. Constantinides",
  title =        "Book Review: {{\booktitle{Computer Arithmetic
                 Algorithms}}, by Israel Koren. A. K. Peters}",
  journal =      j-SIGACT,
  volume =       "34",
  number =       "3",
  pages =        "13--15",
  month =        sep,
  year =         "2003",
  CODEN =        "SIGNDM",
  DOI =          "https://doi.org/10.1145/945526.945532",
  ISSN =         "0163-5700 (print), 1943-5827 (electronic)",
  ISSN-L =       "0163-5700",
  bibdate =      "Wed Mar 21 18:30:26 MDT 2012",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigact.bib",
  note =         "See \cite{Koren:1993:CAA,Koren:2002:CAA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGACT News",
  journal-URL =  "http://dl.acm.org/citation.cfm?id=J697",
}

@Article{Constantinides:2003:SSA,
  author =       "G. A. Constantinides and P. Y. K. Cheung and W. Luk",
  title =        "Synthesis of saturation arithmetic architectures",
  journal =      j-TODAES,
  volume =       "8",
  number =       "3",
  pages =        "334--354",
  month =        jul,
  year =         "2003",
  CODEN =        "ATASFO",
  ISSN =         "1084-4309 (print), 1557-7309 (electronic)",
  ISSN-L =       "1084-4309",
  bibdate =      "Thu Aug 7 11:12:06 MDT 2003",
  bibsource =    "http://www.acm.org/pubs/contents/journals/todaes/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Design Automation of Electronic
                 Systems (TODAES)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J776",
}

@Article{Conway:2003:NCB,
  author =       "R. Conway and J. Nelson",
  title =        "New {CRT}-based {RNS} converter using restricted
                 moduli set",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "52",
  number =       "5",
  pages =        "572--578",
  month =        may,
  year =         "2003",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2003.1197124",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 08:52:48 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1197124",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@TechReport{Cornea:2003:DSR,
  author =       "M. Cornea and J. Harrison and C. Iordache and B. Norin
                 and S. Story",
  title =        "Division, Square Root and Remainder Algorithms for the
                 {Intel Itanium} Architecture",
  type =         "Report",
  institution =  pub-INTEL,
  address =      pub-INTEL:adr,
  month =        nov,
  year =         "2003",
  bibdate =      "Fri Jun 24 12:05:58 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cotofana:2003:CAR,
  author =       "Sorin Cotofana and Casper Lageweg and Stamatis
                 Vassiliadis",
  title =        "On computing addition related arithmetic operations
                 via controlled transport of charge",
  crossref =     "Bajard:2003:ISC",
  pages =        "245--252",
  year =         "2003",
  bibdate =      "Wed Nov 26 12:04:40 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Cotofana.pdf",
  abstract =     "In this paper we investigate the implementation of
                 basic arithmetic functions, such as addition and
                 multiplication, in Single Electron Tunneling (SET)
                 technology. First, we describe the SET equivalents of
                 Boolean CMOS gates and Threshold logic gates. Second,
                 we propose a set of building blocks, which can be
                 utilized for a novel design style, namely arithmetic
                 operations performed by direct manipulation of the
                 location of individual electrons within the system.
                 Using this new set of building blocks, we propose
                 several novel approaches for computing addition related
                 arithmetic operations via the controlled transport of
                 charge (individual electrons). In particular, we prove
                 the following: $n$-bit addition can be implemented with
                 a depth-$2$ network built with $ O(n) $ circuit
                 elements; $n$-input parity can be computed with a
                 depth-$2$ network constructed with $ O(n) $ circuit
                 elements and the same applies for $ n | \log n $
                 counters; multiple operand addition of $ m | n $-bit
                 operands can be implemented with a depth-$2$ network
                 using $ O(m n) $ circuit elements; and finally $n$-bit
                 multiplication can be implemented with a depth-$3$
                 network built with $ O(n) $ circuit elements.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@TechReport{Cowlishaw:2003:DAE,
  author =       "Mike Cowlishaw",
  title =        "Decimal Arithmetic Encoding Strawman 4d",
  type =         "Report",
  number =       "Version 0.96",
  institution =  "IBM UK Laboratories",
  address =      "Hursley, UK",
  day =          "21",
  month =        feb,
  year =         "2003",
  bibdate =      "Fri Mar 03 07:15:51 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www2.hursley.ibm.com/decimal/decbits.pdf",
  abstract =     "This document describes proposed encodings suitable
                 for supporting the general purpose floating-point
                 decimal arithmetic defined in the Decimal Arithmetic
                 Specification, which allows fixed-point and integer
                 decimal arithmetic as subsets.

                 Three formats of decimal numbers are described: (1) a
                 decimal32 number, which is encoded in four consecutive
                 bytes (32 bits); (2) a decimal64 number, which is
                 encoded in eight consecutive bytes (64 bits); (3) a
                 decimal128 number, which is encoded in 16 consecutive
                 bytes (128 bits). The encodings provide ranges of
                 positive normal numbers of approximately $ [1.0 e - 95,
                 1.0 e + 97) $, $ [1.0 e - 383, 1.0 e + 385) $, and $
                 [1.0 e - 6143, 1.0 e6145) $, with precisions of 7, 16,
                 and 34 decimal digits respectively. Subnormals extended
                 the range down to 1.0e-390, 1.0e-398, and 1.0e-6176,
                 respectively.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@InProceedings{Cowlishaw:2003:DFP,
  author =       "Michael F. Cowlishaw",
  title =        "Decimal floating-point: algorism for computers",
  crossref =     "Bajard:2003:ISC",
  pages =        "104--111",
  year =         "2003",
  DOI =          "https://doi.org/10.1109/ARITH.2003.1207666",
  bibdate =      "Fri Nov 28 11:02:29 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Cowlishaw.pdf;
                 http://www.dec.usc.es/arith16/papers/paper-107.pdf;
                 http://www2.hursley.ibm.com/decimal/IEEE-cowlishaw-arith16.pdf",
  abstract =     "Decimal arithmetic is the norm in human calculations,
                 and human-centric applications must use a decimal
                 floating-point arithmetic to achieve the same
                 results.\par

                 Initial benchmarks indicate that some applications
                 spend 50\% to 90\% of their time in decimal processing,
                 because software decimal arithmetic suffers a $ 100
                 \times $ to $ 1000 \times $ performance penalty over
                 hardware. The need for decimal floating-point in
                 hardware is urgent.\par

                 Existing designs, however, either fail to conform to
                 modern standards or are incompatible with the
                 established rules of decimal arithmetic. This paper
                 introduces a new approach to decimal floating-point
                 which not only provides the strict results which are
                 necessary for commercial applications but also meets
                 the constraints and requirements of the IEEE 854
                 standard.\par

                 A hardware implementation of this arithmetic is in
                 development, and it is expected that this will
                 significantly accelerate a wide variety of
                 applications.",
  acknowledgement = ack-nhfb,
  keywords =     "algorism (the decimal system of numeration); ARITH-16;
                 decimal floating-point arithmetic",
}

@InProceedings{Daneshbeh:2003:UBS,
  author =       "Amir.K. Daneshbeh and M. A. Hasan",
  title =        "A unidirectional bit serial systolic architecture for
                 double-basis division over {$ \mathrm {GF}(2^m) $}",
  crossref =     "Bajard:2003:ISC",
  pages =        "174--180",
  year =         "2003",
  bibdate =      "Wed Nov 26 12:04:35 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Daneshbeh.pdf",
  abstract =     "A unidirectional bit serial systolic architecture for
                 division over Galois field $ \mathrm {GF}(2^m) $ is
                 presented which uses both triangular and polynomial
                 basis representations. It is suitable for hardware
                 implementations where the dimension of the field is
                 large and may vary. This is the typical case for
                 cryptographic applications. This architecture is
                 simulated in Verilog-HDL and synthesized for a clock
                 period of $ 1.4 $ ns using Synopsys. The time and area
                 complexities are truly linear, since no carry
                 propagation structures are present, and the complexity
                 measures are equivalent or excel the best designs
                 proposed so far.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@Article{Daumas:2003:FRR,
  author =       "Marc Daumas and David W. Matula",
  title =        "Further Reducing the Redundancy of a Notation Over a
                 Minimally Redundant Digit Set",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "33",
  number =       "1--2",
  pages =        "7--18",
  month =        jan,
  year =         "2003",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1023/A:1021133616373",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Tue Nov 27 14:14:52 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Redundant notations are used implicitly or explicitly
                 in many digital designs. They have been studied in
                 details and a general framework is known to reduce the
                 redundancy of a notation down to the minimally
                 redundant digit set. We present here an operator to
                 further reduce the redundancy of such a representation.
                 It does not reduce the number of allowed digits since
                 removing one digit to a minimally redundant digit set
                 is a conversion to a non redundant digit set and this
                 is an expensive operation. Our operator introduces some
                 correlation between the digits to reduce the number of
                 possible redundant notations for any represented
                 number. This reduction is visible in small useful
                 operators like the elimination of leading zeros. We
                 also present a key application with a CMOS Booth
                 recoded multiplier. Our multiplier is able to accept
                 both a redundant or a non redundant input with very
                 little modifications and almost no penalty in time or
                 space compared to state-of-the-art non redundant
                 multipliers.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
}

@PhdThesis{Defour:2003:FEA,
  author =       "David Defour",
  title =        "Fonctions {{\'E}}l{\'e}mentaires: Algorithmes et
                 Impl{\'e}mentations Efficaces pour {l'Arrondi} Correct
                 en Double Pr{\'e}cision. ({French}) [{Elementary}
                 Functions: Efficient Algorithms and Implementations for
                 Correct Rounding in Double Precision]",
  school =       "L'{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "Lyon, France",
  pages =        "viii + 133",
  day =          "9",
  month =        sep,
  year =         "2003",
  bibdate =      "Tue Dec 02 11:25:16 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://gala.univ-perp.fr/ddefour/research/thesis_dd.pdf;
                 http://www.ens-lyon.fr/LIP/Pub/Rapports/PhD/PhD2003/PhD2003-01.ps.gz;
                 https://theses.hal.science/tel-00006022v1",
  abstract =     "The representation formats and behaviors of floating
                 point arithmetics available in computers are defined by
                 the IEEE-754 standard. This standard imposes the system
                 to return as a result of one of the four basic
                 operations (+, *, /, sqrt), the rounding of the exact
                 result. This property is called <>,this warranties the
                 quality of the result. It enables construction of proof
                 that this particular algorithms can be manipulated
                 independently of the machine. However, due to the <>,
                 elementary functions (sine, cosine, exponential,
                 \ldots{}) are absent in the IEEE-754 standard. Contrary
                 to basic operations, it is difficult to discover the
                 necessary accuracy required to guarantee correct
                 rounding for elementary functions. However if the
                 representation format is set, it is possible that an
                 exhaustive search will help determine this bound: it
                 was Lef{\`e}vre's work for the double
                 precision.\par

                 The objectives of this thesis is to exploit these
                 bounds for each functions and rounding modes, to
                 certify correct rounding in double precision. Thanks to
                 this bound we have defined an evaluation within 2
                 steps: a quick phase which is based on the property of
                 the IEEE standard that often proves satisfactory and an
                 accurate step based on multiprecision operations which
                 is precise all the time. For the second step we have
                 designed a multiprecision library which was optimized
                 in order to acquire precision corresponding to the
                 bound, and the characteristics of processors in 2003.",
  acknowledgement = ack-nhfb,
  keywords =     "correct rounding; floating-point arithmetic",
  language =     "French",
}

@Article{Demmel:2003:AEF,
  author =       "James Demmel and Yozo Hida",
  title =        "Accurate and Efficient Floating Point Summation",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "25",
  number =       "4",
  pages =        "1214--1248",
  day =          "5",
  month =        dec,
  year =         "2003",
  CODEN =        "SJOCE3",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65G50 (65B10)",
  MRnumber =     "MR2045054 (2005b:65055)",
  bibdate =      "Mon Jan 12 19:00:46 MST 2004",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/25/4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/40762",
  abstract =     "We present and analyze several simple algorithms for
                 accurately computing the sum of $n$ floating point
                 numbers using a wider accumulator. Let $f$ and $F$ be
                 the number of significant bits in the summands and the
                 accumulator, respectively. Then assuming gradual
                 underflow, no overflow, and round-to-nearest
                 arithmetic, up to approximately $ 2^{F - f} $ numbers
                 can be added accurately by simply summing the terms in
                 decreasing order of exponents, yielding a sum correct
                 to within about $ 1.5 $ units in the last place (ulps).
                 We apply this result to the floating point formats in
                 the IEEE floating point standard. For example, a dot
                 product of single precision vectors of length at most
                 33 computed using double precision and sorting is
                 guaranteed correct to nearly 1.5 ulps. If
                 double-extended precision is used, the vector length
                 can be as large as 65,537. We also investigate how the
                 cost of sorting can be reduced or eliminated while
                 retaining accuracy.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  keywords =     "accurate floating-point summation",
}

@Article{Demmel:2003:CAF,
  author =       "James Demmel",
  title =        "The complexity of accurate floating point
                 computation",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "1",
  month =        may,
  year =         "2003",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  MRclass =      "65F, 65G50, 65Y20, 68Q25",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Published in Proceedings of the ICM, Beijing 2002,
                 vol. 3, 697--706.",
  URL =          "http://arxiv.org/abs/math/0305004",
  abstract =     "Our goal is to find accurate and efficient algorithms,
                 when they exist, for evaluating rational expressions
                 containing floating point numbers, and for computing
                 matrix factorizations (like LU and the SVD) of matrices
                 with rational expressions as entries. More precisely,
                 {\em accuracy} means the relative error in the output
                 must be less than one (no matter how tiny the output
                 is), and {\em efficiency} means that the algorithm runs
                 in polynomial time. Our goal is challenging because our
                 accuracy demand is much stricter than usual.",
  acknowledgement = ack-nhfb,
  subject =      "Numerical Analysis (math.NA)",
}

@TechReport{Deshmukh:2003:HPS,
  author =       "R. G. Deshmukh and Hatim Ghazi Zaini",
  title =        "High performance signal processing through
                 computational enhancement and hardware integration",
  institution =  "Florida Institute of Technology",
  address =      "Melbourne, FL, USA",
  pages =        "320",
  year =         "2003",
  bibdate =      "Thu Aug 07 18:49:39 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Order Number AAI3099386.",
  abstract =     "Mathematical operations on complex numbers are
                 commonly required in numerous computer applications.
                 The use of complex number computations in the design
                 algorithms for various digital signal processing (DSP)
                 has received considerable attention in recent years.
                 Algorithms in complex orthogonal transformations,
                 correlations, and filtrations are a part of arithmetic
                 computations such as geometric analysis in graphics or
                 signal processing. The digital signal processing
                 algorithms and modern digital communication systems
                 such as equalization, modulation and demodulation are
                 all deal with data streams represented by complex
                 numbers. These applications require efficient
                 representation and manipulation, in addition to
                 treatment of complex numbers. These algorithms usually
                 include arithmetic operations. The digital signal
                 processing demands always increase and higher
                 performance in the implementation of algorithms are
                 investigated. Therefore, the implementations of the
                 arithmetic operations of the complex numbers for
                 high-performance especially for complex number
                 multiplier are of significant interest.\par

                 A novel method for complex numbers representation and
                 the arithmetic operations on them was introduced for
                 computer vision which is a relatively new area. The
                 proposed Redundant Complex Binary Number System (RCBNS)
                 was developed by combining a Redundant Binary Number
                 and a complex number in the base $ ( - 1 + j) $.\par

                 A Redundant Complex Binary Number System consists of
                 both the real and the imaginary parts presented by a
                 radix number system that forms a single redundant
                 integer digit set. This system is formed by using
                 complex radix of $ ( - 1 + j) $ and a digit set of $
                 \alpha = 3 $, where $ \alpha $ assumes a value of $ -
                 3, - 2, - 1, 0, 1, 2, 3 $. The arithmetic operations on
                 these complex numbers treat the real and the imaginary
                 parts as one unit. Carry-free addition is the advantage
                 in the arithmetic operations that uses operands in the
                 Redundant Complex Binary Number System.\par

                 Conversion of decimal complex numbers in the standard
                 binary form to the RCBNS form is accomplished by
                 converting the decimal complex number to the complex
                 binary form and then the real part and the imaginary
                 part to be treated in one unit. Two methods for the
                 conversion to the RCBNS form are presented. These
                 complex numbers in the RCBNS form are used to perform
                 arithmetic operations, addition, subtraction,
                 multiplication and division. The results of arithmetic
                 operations on complex number are available in the RCBNS
                 form. These results in the RCBNS form should be
                 converted back to the Standard Binary Number form. Two
                 methods are presented for the reconversion. Both
                 methods are based on separating the real part and the
                 imaginary part of each row of four digit positions of
                 the RCBNS number and forward them to two dedicated
                 registers. The comparisons of the proposed multiplier
                 with other existing multipliers were done. Finally,
                 methodology and processes of the proposed work were
                 modeled (functional and behavioral) using a hardware
                 description language, VHDL. In this research, the RCBNS
                 form for complex number reduces the number of steps
                 required to perform complex number arithmetic
                 operations, thus enhancing the speed.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal arithmetic",
}

@InProceedings{Detrey:2003:VLL,
  author =       "J{\'e}r{\'e}mie Detrey and Florent de Dinechim",
  title =        "A {VHDL} Library of {LNS} Operators",
  crossref =     "Matthews:2003:PTS",
  pages =        "2227--2231",
  year =         "2003",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://perso.ens-lyon.fr/jeremie.detrey/FPLibrary/;
                 http://perso.ens-lyon.fr/jeremie.detrey/publications/DetDin2003:asilomar.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "logarithmic number system (LNS)",
  summary =      "Not \ldots{}",
}

@Misc{DiBrino:2003:FPP,
  author =       "M. DiBrino and F. Karim",
  title =        "Floating-point pipeline with leading zeros anticipator
                 circuit",
  howpublished = "US Patent 6542915",
  month =        apr,
  year =         "2003",
  bibdate =      "Fri Jun 24 10:46:57 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Ercegovac:2003:CDP,
  author =       "Milo{\v{s}} Ercegovac and Jean-Michel Muller",
  title =        "Complex Division with Prescaling of Operands",
  crossref =     "Deprettere:2003:IIC",
  pages =        "304--314",
  year =         "2003",
  DOI =          "https://doi.org/10.1109/ASAP.2003.1212854",
  bibdate =      "Sat Dec 04 09:09:15 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We adapt the radix-r digit-recurrence division
                 algorithm to complex division. By prescaling the
                 operands, we make the selection of quotient digits
                 simple. This leads to a simple hardware implementation,
                 and allows correct rounding of complex quotient. To
                 reduce large prescaling tables required for radices
                 greater than 4, we adapt the bipartite-table method to
                 multiple-operand functions.",
  acknowledgement = ack-nhfb,
  keywords =     "bipartite-table method; complex division; correct
                 rounding; digital arithmetic; floating-point
                 arithmetic; multiple-operand function; number theory;
                 prescaling table; quotient digit selection; radix-r
                 digit-recurrence division algorithm; table lookup",
}

@InProceedings{Ercegovac:2003:DRA,
  author =       "M. D. Ercegovac and Jean-Michel Muller",
  booktitle =    "Conference Record of the Thirty-Seventh Asilomar
                 Conference on Signals, Systems and Computers, 2003",
  title =        "Digit-recurrence algorithms for division and square
                 root with limited precision primitives",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1440--1444",
  year =         "2003",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "We propose a digit-recurrence algorithm for square
                 root using limited-precision multipliers, adders, and
                 table-lookups. The algorithm, except in the
                 initialization, uses the digit-recurrence algorithm for
                 division with limited-precision primitives \ldots{}",
}

@InProceedings{Erdem:2003:LRV,
  author =       "Serdar S. Erdem and {\c{C}}etin K. Ko{\c{c}}",
  title =        "A less recursive variant of {Karatsuba--Ofman}
                 algorithm for multiplying operands of size a power of
                 two",
  crossref =     "Bajard:2003:ISC",
  pages =        "28--35",
  year =         "2003",
  bibdate =      "Wed Nov 26 11:59:51 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Erdem.pdf",
  abstract =     "We propose a new algorithm for fast multiplication of
                 large integers having a precision of $ 2^k $ computer
                 words, where $k$ is an integer. The algorithm is
                 derived from the Karatsuba--Ofman Algorithm and has the
                 same asymptotic complexity. However, the running time
                 of the new algorithm is slightly better, and it makes
                 one third as many recursive calls.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@InProceedings{Erle:2003:DMC,
  author =       "M. A. Erle and M. J. Schulte",
  title =        "Decimal multiplication via carry-save addition",
  crossref =     "Deprettere:2003:IIC",
  pages =        "348--358",
  year =         "2003",
  bibdate =      "Fri Mar 25 05:52:41 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2003-03.pdf",
  abstract =     "Decimal multiplication is important in many commercial
                 applications including financial analysis, banking, tax
                 calculation, currency conversion, insurance, and
                 accounting. This paper presents two novel designs for
                 fixed-point decimal multiplication that utilize decimal
                 carry-save addition to reduce the critical path delay.
                 First, a multiplier that stores a reduced number of
                 multiplicand multiples and uses decimal carry-save
                 addition in the iterative portion of the design is
                 presented. Then, a second multiplier design is proposed
                 with several notable improvements including fast
                 generation of multiplicand multiples that do not need
                 to be stored, the use of decimal (4:2) compressors, and
                 a simplified decimal carry-propagate addition to
                 produce the final product. When multiplying two
                 $n$-digit operands to produce a $ 2 n $-digit product,
                 the improved multiplier design has a worst-case latency
                 of $ n + 4 $ cycles and an initiation interval of $ n +
                 1 $ cycles. Three data-dependent optimizations, which
                 help reduce the multipliers' average latency, are also
                 described. The multipliers presented can be extended to
                 support decimal floating-point multiplication.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@InProceedings{Even:2003:PEA,
  author =       "Guy Even and Peter-Michael Seidel and Warren E.
                 Ferguson",
  title =        "A parametric error analysis of {Goldschmidt}'s
                 division algorithm",
  crossref =     "Bajard:2003:ISC",
  pages =        "165--171",
  year =         "2003",
  bibdate =      "Wed Nov 26 12:04:35 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Even.pdf",
  abstract =     "Back in the 60's Goldschmidt presented a variation of
                 Newton--Raphson iterations for division that is well
                 suited for pipelining. The problem in using
                 Goldschmidt's division algorithm is to present an error
                 analysis that enables one to save hardware by using
                 just the right amount of precision for intermediate
                 calculations while still providing correct rounding.
                 Previous implementations relied on combining formal
                 proof methods (that span thousands of lines) with
                 millions of test vectors. These techniques yield
                 correct designs but the analysis is hard to follow and
                 is not quite tight.\par

                 We present a simple parametric error analysis of
                 Goldschmidt's division algorithm. This analysis sheds
                 more light on the effect of the different parameters on
                 the error. In addition, we derive closed error formulae
                 that allow to determine optimal parameter choices in
                 four practical settings.\par

                 We apply our analysis to show that a few bits of
                 precision can be saved in the floating-point division
                 (FP-DIV) microarchitecture of the AMD-K7TM
                 microprocessor. These reductions in precision apply to
                 the initial approximation and to the lengths of the
                 multiplicands in the multiplier. When translated to
                 cost, the reductions reflect a savings of $ 10.6 \% $
                 in the overall cost of the FP-DIV micro-architecture.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16; correct rounding; floating-point
                 arithmetic",
}

@InProceedings{Even:2003:PMD,
  author =       "Guy Even and Peter-Michael Seidel",
  booktitle =    "Proceedings of the 21st International Conference on
                 Computer Design",
  title =        "Pipelined multiplicative division with {IEEE}
                 rounding",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "240--245",
  year =         "2003",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICCD.2003.1240901",
  ISBN =         "0-7695-2025-1",
  ISBN-13 =      "978-0-7695-2025-4",
  ISSN =         "1063-6404",
  ISSN-L =       "1063-6404",
  bibdate =      "Sat Jul 16 11:25:05 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "We propose optimized pipelined implementations for
                 Goldschmidt's division algorithm with IEEE rounding
                 based on Booth radix-8 multiplication. Compared to
                 other FP-division algorithms, our implementations
                 require fewer clock cycles and admit shorter periods.
                 The considered optimizations for the quotient
                 approximation are based on a careful general analysis
                 of tight error bounds for the implementation and are
                 accompanied by the utilization of redundant
                 representations, partial compressions, injection-based
                 rounding, and rectangular multipliers for the internal
                 computations. To efficiently achieve IEEE compliant
                 rounding, we introduce the concept of dew-point
                 rounding that allows efficient implementation and
                 reduced requirements for the quotient approximation. On
                 this basis, we propose the implementation of different
                 versions of Goldschmidt's division algorithm with
                 different pipeline depths. None of these
                 implementations requires a full-sized multiplier at any
                 stage of the computations. In this way we reduce
                 latency, cost, and enable increased throughput at a
                 reasonable cost. We suggest a full range of pipelining
                 depths: On one extreme is a 3-stage pipeline with a
                 restart time that simply equals the latency minus the
                 number of pipeline stages. On the other extreme is a
                 fully pipelined design.",
}

@InProceedings{Fahmy:2003:CRF,
  author =       "Hossam A. H. Fahmy and Michael J. Flynn",
  title =        "The case for a redundant format in floating point
                 arithmetic",
  crossref =     "Bajard:2003:ISC",
  pages =        "95--102",
  year =         "2003",
  bibdate =      "Wed Nov 26 11:59:51 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Fahmy.pdf",
  abstract =     "This work uses a partially redundant number system as
                 an internal format for floating point arithmetic
                 operations. The redundant number system enables carry
                 free arithmetic operations to improve performance.
                 Conversion from the proposed internal format back to
                 the standard IEEE format is done only when an operand
                 is written to memory. A detailed discussion of an adder
                 using the proposed format is presented and the specific
                 challenges of the design are explained. A brief
                 description of a multiplier and divider using the
                 proposed format is also presented. The proposed
                 internal format and arithmetic units comply with all
                 the rounding modes of the IEEE 754 floating point
                 standard. Transistor simulation of the adder and
                 multiplier confirm the performance advantage predicted
                 by the analytical model.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@PhdThesis{Fahmy:2003:RDF,
  author =       "Hossam A. H. Fahmy",
  title =        "A redundant digit floating point system",
  type =         "{Ph.D.} dissertation",
  school =       "Department of Computer Science, Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "146",
  month =        nov,
  year =         "2003",
  bibdate =      "Wed Nov 15 07:59:18 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://wwwlib.umi.com/dissertations/fullcit/3090583",
  abstract =     "Arithmetic operations are among the most basic
                 instructions in microprocessors, digital signal
                 processors and graphics accelerators. Addition is the
                 most frequent arithmetic operation in numerically
                 intensive applications. Multiplication follows closely
                 and then division and other elementary functions. The
                 speed of those arithmetic operations is also often
                 directly linked to the overall performance of the
                 computers. The work presented in this thesis proposes
                 several techniques to improve the effectiveness of
                 floating point arithmetic units. A partially redundant
                 number system is used as an internal format for
                 floating point arithmetic operations. The redundant
                 number system is based on signed digits and enables
                 carry free arithmetic operations to improve the
                 performance. Conversion from the proposed internal
                 format back to the standard IEEE format is done only
                 when an operand is written to memory. A detailed
                 discussion of an adder and a multiplier using the
                 proposed format is presented and the specific
                 challenges of the designs are explained. Beside the
                 redundancy, the proposed units include further
                 enhancements that increase the floating point
                 performance such as a hexadecimal based number format
                 and a postponed rounding technique. A time delay model
                 is developed and applied to analytically predict the
                 performance of the floating point units. The predicted
                 delays are then compared to state-of-the-art designs.
                 The comparison is done over a range of operand widths,
                 fan-in and radices to show the merits of each
                 implementation. The proposed system achieves better
                 performance for double precision and larger operand
                 width. Transistor simulation of the complete adder and
                 multiplier confirm the performance advantage predicted
                 by the analytical model. A brief description of a
                 divider using; the proposed format is also presented.
                 The proposed internal format and arithmetic units
                 comply with all the rounding modes of the IEEE 754
                 floating point standard.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Fang:2003:FPE,
  author =       "Claire Fang Fang and Tsuhan Chen and Rob A. Rutenbar",
  title =        "Floating-point error analysis based on affine
                 arithmetic",
  crossref =     "IEEE:2003:IICa",
  pages =        "561--564",
  year =         "2003",
  DOI =          "https://doi.org/10.1109/ICASSP.2003.1202428",
  bibdate =      "Thu Mar 24 20:40:52 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://amp.ece.cmu.edu/Publication/Fang/icassp2003_fang.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Fernandez:2003:FPA,
  author =       "Jos{\'e}-Jes{\'u}s Fern{\'a}ndez and Inmaculada
                 Garc{\'\i}a and Ester M. Garz{\'o}n",
  title =        "Floating point arithmetic teaching for computational
                 science",
  journal =      j-FUT-GEN-COMP-SYS,
  volume =       "19",
  number =       "8",
  pages =        "1321--1334",
  month =        nov,
  year =         "2003",
  CODEN =        "FGSEVI",
  ISSN =         "0167-739X (print), 1872-7115 (electronic)",
  ISSN-L =       "0167-739X",
  bibdate =      "Sat Jan 10 10:03:38 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Computational science is based upon numerical
                 computing and, consequently, requires excellent
                 knowledge of floating point computer arithmetic. In
                 general, the average computational science student has
                 a relatively limited understanding of the implications
                 of floating point computation. This paper presents an
                 initiative to teach floating point number
                 representation and arithmetic in undergraduate courses
                 in computational science. The approach is based on
                 carefully designed practical exercises which highlight
                 the main properties and computational issues of finite
                 length number representation and arithmetic. In
                 conjunction to the exercises, an auxiliary educational
                 tool constitutes a valuable support for students to
                 learn and understand the concepts involved. Simpler
                 formats are used as an introduction to the IEEE 754
                 standard, with the aim of presenting the fundamentals
                 of the floating point computation and emphasizing its
                 limitations. This approach could be included in courses
                 related to computer organization, programming, discrete
                 mathematics, numerical methods or scientific computing
                 in computational science curricula.",
  acknowledgement = ack-nhfb,
  fjournal =     "Future Generation Computer Systems",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0167739X",
  keywords =     "Computational science education; Computer arithmetic;
                 Floating point computation",
  remark =       "Selected papers from the Workshop on Education in
                 Computational Sciences held at the International
                 Conference on Computational Science.",
}

@InProceedings{Fousse:2003:AST,
  author =       "L. Fousse and P. Zimmermann",
  title =        "Accurate Summation: Towards a Simpler and Formal
                 Proof",
  crossref =     "Anonymous:2003:CRN",
  pages =        "97--108",
  year =         "2003",
  bibdate =      "Sat Jun 25 14:56:11 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}

@InProceedings{Frougny:2003:LMR,
  author =       "Christiane Frougny and Athasit Surarerks",
  title =        "On-line multiplication in real and complex base",
  crossref =     "Bajard:2003:ISC",
  pages =        "212--219",
  year =         "2003",
  bibdate =      "Fri Nov 28 11:03:48 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Frougny.pdf",
  abstract =     "Multiplication of two numbers represented in base $
                 \beta $ is shown to be computable by an on-line
                 algorithm when $ \beta $ is a negative integer, a
                 positive non-integer real number, or a complex number
                 of the form $ i \sqrt {r} $, where $r$ is a positive
                 integer.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@Book{Gansner:2003:SMB,
  author =       "Emden R. Gansner and John H. Reppy",
  title =        "The {Standard ML} Basis Manual",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "????",
  year =         "2003",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Wed Jan 29 16:31:52 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
  remark =       "From \cite{Steele:2004:RHP}: ``toDecimal should
                 produce only as many digits as are necessary for
                 fromDecimal to convert back to the same number, i.e.,
                 for any Normal or SubNormal real value r, we have:
                 fromDecimal (toDecimal r) = r \ldots{} Algorithms for
                 accurately and efficiently converting between binary
                 and decimal real representations are readily available,
                 e.g., see the technical report \cite{Gay:1990:CRB}.''",
}

@InCollection{Gavrilova:2003:ESC,
  author =       "M. L. Gavrilova",
  booktitle =    "Computational science and its {applications---ICCSA
                 2003}. Part {III}",
  title =        "An explicit solution for computing the {Euclidean}
                 {$d$}-dimensional {Voronoi} diagram of spheres in a
                 floating-point arithmetic",
  volume =       "2669",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "827--835",
  year =         "2003",
  MRclass =      "68U05 (52B55)",
  MRnumber =     "MR2118360",
  bibdate =      "Thu Nov 8 19:16:14 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Lecture Notes in Computer Science",
  acknowledgement = ack-nhfb,
}

@InProceedings{Geddes:2003:EFH,
  author =       "Keith O. Geddes and Wei Wei Zheng",
  title =        "Exploiting fast hardware floating point in high
                 precision computation",
  crossref =     "Senda:2003:IPI",
  pages =        "111--118",
  year =         "2003",
  DOI =          "https://doi.org/10.1145/860854.860886",
  MRclass =      "65G99",
  MRnumber =     "MR2035201 (2005d:65074)",
  bibdate =      "Sat Dec 13 18:17:28 MST 2003",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We apply an iterative refinement method based on a
                 linear Newton iteration to solve a particular group of
                 high precision computation problems. The method
                 generates an initial solution at hardware floating
                 point precision using a traditional method and then
                 repeatedly refines this solution to higher precision,
                 exploiting hardware floating point computation in each
                 iteration. This is in contrast to direct solution of
                 the high precision problem completely in software
                 floating point. Theoretical cost analysis, as well as
                 experimental evidence, shows a significant reduction in
                 computational cost is achieved by the iterative
                 refinement method on this group of problems.",
  acknowledgement = ack-nhfb,
}

@Article{Geiselmann:2003:RRD,
  author =       "W. Geiselmann and R. Steinwandt",
  title =        "A redundant representation of {$ \mathrm {GF}(q^n) $}
                 for designing arithmetic circuits",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "52",
  number =       "7",
  pages =        "848--853",
  month =        jul,
  year =         "2003",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2003.1214334",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 08:52:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1214334",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Gerwig:2003:HPF,
  author =       "Guenter Gerwig and Holger Wetter and Eric M. Schwarz
                 and Juergen Haess",
  title =        "High performance floating-point unit with 116 bit wide
                 divider",
  crossref =     "Bajard:2003:ISC",
  pages =        "87--94",
  year =         "2003",
  bibdate =      "Wed Nov 26 11:59:51 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Gerwig.pdf",
  abstract =     "The next generation zSeries floating-point unit is
                 unveiled which is the first IBM mainframe with a fused
                 multiply-add dataflow. It supports both S/390
                 hexadecimal floating-point architecture and the IEEE
                 754 binary floating-point architecture which was first
                 implemented in S/390 on the 1998 S/390 G5
                 floating-point unit. The new floating-point unit
                 supports a total of 6 formats including single, double,
                 and quadword formats implemented in hardware. The
                 floating-point pipeline is 5 cycles with a throughput
                 of 1 multiply-add per cycle. Both hexadecimal and
                 binary floating-point instructions are capable of this
                 performance due to a novel way of handling both
                 formats. Other key developments include new methods for
                 handling denormalized numbers and quad precision divide
                 engine dataflow. This divider uses a radix-4 SRT
                 algorithm and is able to handle quad precision divides
                 in multiple floating-point and fixed-point formats. The
                 number of iterations for fixed-point divisions depend
                 on the effective number of quotient bits. It uses a
                 reduced carry-save form for the partial remainder, with
                 only 1 carry bit for every 4 sum bits, to save area and
                 power.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@Misc{Goldberg:2003:WEC,
  author =       "David Goldberg",
  title =        "What Every Computer Scientist Should Know About
                 Floating-Point Arithmetic",
  howpublished = "Oracle Web site.",
  year =         "2003",
  bibdate =      "Wed Jun 19 07:57:39 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "This is a reprint of \cite{Goldberg:1991:WEC} with a
                 new section, \booktitle{Differences Among IEEE 754
                 Implementations}, by Doug Priest.",
  URL =          "https://docs.oracle.com/cd/E19060-01/stud8.compiler/817-0932/ncg_goldberg.html",
  acknowledgement = ack-nhfb,
}

@Book{Grabmeier:2003:CAH,
  editor =       "Johannes Grabmeier and Erich Kaltofen and Volker
                 Weispfenning",
  title =        "Computer algebra handbook: foundations, applications,
                 systems",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xx + 637",
  year =         "2003",
  ISBN =         "3-540-65466-6",
  ISBN-13 =      "978-3-540-65466-7",
  LCCN =         "QA155.7.E4 C64954 2003",
  MRclass =      "68W30, 00B15, 68-06",
  bibdate =      "Tue Nov 22 06:00:25 MST 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Includes CD-ROM.",
  URL =          "http://www.springer.com/sgw/cda/frontpage/0,11855,1-102-22-1477871-0,00.html",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation; Aldor; AXIOM;
                 Derive; exact arithmetic; Macsyma; Magma; Maple
                 Mathematica; MuPAD; REDUCE; TI-92",
  subject =      "Algebra; Data processing",
}

@Article{Grossschadl:2003:ASL,
  author =       "Johann Gro{\ss}sch{\"a}dl",
  title =        "Architectural Support for Long Integer Modulo
                 Arithmetic on {RISC}-Based {Smart Cards}",
  journal =      j-IJHPCA,
  volume =       "17",
  number =       "2",
  pages =        "135--146",
  month =        "Summer",
  year =         "2003",
  CODEN =        "IHPCFL",
  ISSN =         "1094-3420 (print), 1741-2846 (electronic)",
  ISSN-L =       "1094-3420",
  bibdate =      "Fri Nov 28 06:52:13 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://hpc.sagepub.com/content/by/year",
  keywords =     "application-specific instruct set processor (ASIP);
                 coarsely-integrated operand scanning (CIOS);
                 Diffie--Hellman; inner-loop operation; Montgomery
                 multiplication; processor specialization; public-key
                 cryptography; Rivest-Shamir-Adelman",
}

@Article{Hanrot:2003:DRF,
  author =       "G. Hanrot and J. Rivat and G. Tenenbaum and P.
                 Zimmermann",
  title =        "Density results on floating-point invertible numbers",
  journal =      j-THEOR-COMP-SCI,
  volume =       "291",
  number =       "2",
  pages =        "135--141",
  year =         "2003",
  CODEN =        "TCSDIQ",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  MRclass =      "68M07 (65G30)",
  MRnumber =     "MR1957436 (2005b:68028)",
  bibdate =      "Thu Nov 8 19:16:14 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Real numbers and computers (Schloss Dagstuhl, 2000)",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}

@Article{Harrison:2003:FVS,
  author =       "John Harrison",
  title =        "Formal verification of square root algorithms",
  journal =      j-FORM-METHODS-SYST-DES,
  volume =       "22",
  number =       "2",
  pages =        "143--153",
  month =        mar,
  year =         "2003",
  CODEN =        "FMSDE6",
  DOI =          "https://doi.org/10.1023/A:1022973506233",
  ISSN =         "0925-9856 (print), 1572-8102 (electronic)",
  ISSN-L =       "0925-9856",
  bibdate =      "Sat Feb 08 08:47:21 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/intel-ia-64.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1023/A:1022973506233",
  abstract =     "We discuss the formal verification of some low-level
                 mathematical software for the Intel Itanium
                 architecture. A number of important algorithms have
                 been proven correct using the HOL Light theorem prover.
                 After briefly surveying some of our formal verification
                 work, we discuss in more detail the verification of a
                 square root algorithm, which helps to illustrate why
                 some features of HOL Light, in particular
                 programmability, make it especially suitable for these
                 applications.",
  acknowledgement = ack-nhfb,
  fjournal =     "Formal Methods in System Design",
  journal-URL =  "https://dl.acm.org/loi/fmsd",
}

@InProceedings{Harrison:2003:ICC,
  author =       "John Harrison",
  title =        "Isolating critical cases for reciprocals using integer
                 factorization",
  crossref =     "Bajard:2003:ISC",
  pages =        "148--157",
  year =         "2003",
  bibdate =      "Wed Nov 26 12:04:35 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Harrison.pdf",
  abstract =     "One approach to testing and\slash or proving
                 correctness of a floating-point algorithm computing a
                 function $f$ is based on finding input floating-point
                 numbers $ \alpha $ such that the exact result $
                 f(\alpha) $ is very close to a ``rounding boundary'',
                 i.e. a floating-point number or a midpoint between
                 them. In the present paper we show how to do this for
                 the reciprocal function by utilizing prime
                 factorizations. We present the method and show
                 examples, as well as making a fairly detailed study of
                 its expected and worst-case behavior. We point out how
                 this analysis of reciprocals can be useful in analyzing
                 certain reciprocal algorithms, and also show how the
                 approach can be trivially adapted to the reciprocal
                 square root function.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16; correct rounding; floating-point
                 arithmetic",
}

@Article{Holmes:2003:PTC,
  author =       "Neville Holmes",
  title =        "The Profession: Truth and Clarity in Arithmetic",
  journal =      j-COMPUTER,
  volume =       "36",
  number =       "2",
  pages =        "108, 106--107",
  month =        feb,
  year =         "2003",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Fri Dec 12 19:53:54 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://csdl.computer.org/dl/mags/co/2003/02/r2108.htm;
                 http://csdl.computer.org/dl/mags/co/2003/02/r2108.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}

@InProceedings{Huang:2003:HPL,
  author =       "Zhijun Huang and Milo{\v{s}} D. Ercegovac",
  title =        "High-performance left-to-right array multiplier
                 design",
  crossref =     "Bajard:2003:ISC",
  pages =        "4--11",
  year =         "2003",
  bibdate =      "Wed Nov 26 11:59:51 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Huang.pdf",
  abstract =     "We propose a split array multiplier organized in a
                 left-to-right leapfrog (LRLF) structure with reduced
                 delay compared to conventional array multipliers.
                 Moreover, the proposed design shows equivalent
                 performance as tree multipliers for $ n \leq 32 $. An
                 efficient radix-4 recoding logic generates the partial
                 products in a left-to-right order. The partial products
                 are split into upper and lower groups. Each group is
                 reduced using [3:2] adders with optimized signal flows
                 and the carry-save results from two groups are combined
                 using a [4:2] adder. The final product is obtained with
                 a prefix adder optimized to match the non-uniform
                 arrival profile of the inputs. Layout experiments
                 indicate that upper\slash lower split multipliers have
                 slightly less area and power than optimized tree
                 multipliers while keeping the same delay for $ n \leq
                 32 $.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@Misc{Intel:2003:DSR,
  author =       "{Intel}",
  title =        "Divide, Square Root, and Remainder Algorithms for the
                 {Itanium} Architecture",
  howpublished = "Intel Software Development Products",
  day =          "18",
  month =        dec,
  year =         "2003",
  bibdate =      "Tue Nov 18 16:23:36 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.intel.com/cd/software/products/asmo-na/eng/219863.htm",
  acknowledgement = ack-nhfb,
}

@Misc{Intel:2003:NID,
  author =       "{Intel}",
  title =        "Non-{IEEE} Division, Square Root, Reciprocal, and
                 Reciprocal Square Root Algorithms for the {Intel
                 Itanium} Architecture",
  howpublished = "Intel Software Development Products",
  day =          "18",
  month =        dec,
  year =         "2003",
  bibdate =      "Tue Nov 18 16:23:36 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.intel.com/cd/software/products/asmo-na/eng/219864.htm",
  acknowledgement = ack-nhfb,
}

@InProceedings{Iordache:2003:OFP,
  author =       "Cristina Iordache and Ping Tak Peter Tang",
  title =        "An overview of floating-point support and math library
                 on the {Intel XScale} architecture",
  crossref =     "Bajard:2003:ISC",
  pages =        "122--128",
  year =         "2003",
  bibdate =      "Wed Nov 26 12:04:35 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Iordache.pdf",
  abstract =     "New microprocessor architectures often require
                 software support for basic arithmetic operations such
                 as divide, or square root. The Intel\reg{} XScale\TM{}
                 processor, designed for low power mobile devices,
                 provides no hardware support for floating-point. We
                 show that an efficient software implementation of the
                 basic operations and math library routines can achieve
                 competitive performance, and effectively hide the lack
                 of hardware floating-point for most applications.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@InProceedings{Kaihara:2003:VAM,
  author =       "Marcelo E. Kaihara and Naofumi Takagi",
  title =        "A {VLSI} algorithm for modular multiplication\slash
                 division",
  crossref =     "Bajard:2003:ISC",
  pages =        "220--227",
  year =         "2003",
  bibdate =      "Wed Nov 26 12:04:40 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Kaihara.pdf",
  abstract =     "We propose an algorithm for modular
                 multiplication\slash division suitable for VLSI
                 implementation. The algorithm is based on Montgomery's
                 method for modular multiplication and on the extended
                 Binary GCD algorithm for modular division. It can
                 perform either of these operations with a reduced
                 amount of hardware. Both calculations are carried out
                 through iterations of simple operations such as shifts
                 and additions\slash subtractions. The radix-2
                 signed-digit representation is employed so that all
                 additions and subtractions are performed without carry
                 propagation. A modular multiplier\slash divider based
                 on this algorithm has a linear array structure with a
                 bit-slice feature and carries out an n-bit modular
                 multiplication in at most $ \floor {2(n + 2) / 3} + 3 $
                 clock cycles and an $n$-bit modular division in at most
                 $ 2 n + 5 $ clock cycles, where the length of the clock
                 cycle is constant and independent of $n$.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@Article{Kaivola:2003:PEL,
  author =       "Roope Kaivola and Katherine Kohatsu",
  title =        "Proof engineering in the large: formal verification of
                 {Pentium\reg{}4} floating-point divider",
  journal =      j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER,
  volume =       "4",
  number =       "3",
  pages =        "323--334",
  month =        may,
  year =         "2003",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s10009-002-0081-6",
  ISSN =         "1433-2779 (print), 1433-2787 (electronic)",
  ISSN-L =       "1433-2779",
  bibdate =      "Tue Nov 23 15:01:41 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal on Software Tools for Technology
                 Transfer: STTT",
  journal-URL =  "http://link.springer.com/journal/10009",
}

@Article{Katti:2003:LCM,
  author =       "R. Katti and J. Brennan",
  title =        "Low complexity multiplication in a finite field using
                 ring representation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "52",
  number =       "4",
  pages =        "418--427",
  month =        apr,
  year =         "2003",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2003.1190583",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 08:52:46 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1190583",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Koren:2003:SCA,
  author =       "Israel Koren and Yaron Koren and Bejoy G. Oomman",
  title =        "Saturating counters: application and design
                 alternatives",
  crossref =     "Bajard:2003:ISC",
  pages =        "228--235",
  year =         "2003",
  bibdate =      "Wed Nov 26 12:04:40 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Koren.pdf",
  abstract =     "We define a new class of parallel counters, Saturating
                 Counters, which provide the exact count of the inputs
                 that are 1 only if this count is below a given
                 threshold. Such counters are useful in, for example, a
                 self-test and repair unit for embedded memories in a
                 system-on-a-chip. We describe this application and
                 present several alternatives for the design of the
                 saturating counter. We then compare the delay and area
                 of the proposed design alternatives.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@InProceedings{Kornerup:2003:RSQ,
  author =       "Peter Kornerup",
  title =        "Revisiting {SRT} quotient digit selection",
  crossref =     "Bajard:2003:ISC",
  pages =        "38--45",
  year =         "2003",
  bibdate =      "Wed Nov 26 11:59:51 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Kornerup.pdf",
  abstract =     "The quotient digit selection in the SRT division
                 algorithm is based on a few most significant bits of
                 the remainder and divisor, where the remainder is
                 usually represented in a redundant representation. The
                 number of leading bits needed depends on the quotient
                 radix and digit set, and is usually found by an
                 extensive search, to assure that the next quotient
                 digit can be chosen as valid for all points (remainder,
                 divisor) in a set defined by the truncated remainder
                 and divisor, i.e., an ``uncertainty
                 rectangle''.\par

                 This paper presents expressions for the number of bits
                 needed for the truncated remainder and divisor, thus
                 eliminating the need for a search through the
                 truncation parameter space for validation. It also
                 presents simple algorithms to properly map truncated
                 negative divisors and remainders into non-negative
                 values, allowing the quotient selection function only
                 to be defined on the smaller domain of non-negative
                 values.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@InProceedings{Krithivasan:2003:MAM,
  author =       "S. Krithivasan and M. J. Schulte",
  title =        "Multiplier Architectures for Media Processing",
  crossref =     "Matthews:2003:PTS",
  pages =        "2193--2197",
  year =         "2003",
  bibdate =      "Sun Mar 04 17:52:49 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2003-08.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kwon:2003:LCL,
  author =       "Soonhak Kwon",
  title =        "A low complexity and a low latency bit parallel
                 systolic multiplier over {$ \mathrm {GF}(2^m) $} using
                 an optimal normal basis of type {II}",
  crossref =     "Bajard:2003:ISC",
  pages =        "196--202",
  year =         "2003",
  bibdate =      "Wed Nov 26 12:04:35 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Kwon.pdf",
  abstract =     "Using the self duality of an optimal normal basis
                 (ONB) of type II, we present a bit parallel systolic
                 multiplier over $ \mathrm {GF}(2^m) $ which has a low
                 hardware complexity and a low latency. We show that our
                 multiplier has a latency $ m + 1 $ and the basic cell
                 of our circuit design needs 5 latches (flip-flops). On
                 the other hand, most of other multipliers of the same
                 type have latency $ 3 m $ and the basic cell of each
                 multiplier needs 7 latches. Comparing the gates areas
                 in each basic cell, we find that the hardware
                 complexity of our multiplier is 25 percent reduced from
                 the multipliers with 7 latches.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@Article{Lang:2003:RRS,
  author =       "Tom{\'a}s Lang and Elisardo Antelo",
  title =        "Radix-$4$ Reciprocal Square-root and Its Combination
                 with Division and Square Root",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "52",
  number =       "9",
  pages =        "1100--1114",
  month =        sep,
  year =         "2003",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2003.1228508",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 08:52:54 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1228508",
  abstract =     "In this work, we present a reciprocal square root
                 algorithm by digit recurrence and selection by a
                 staircase function and the radix-$4$ implementation. As
                 in similar algorithms for division and square root, the
                 results are obtained correctly rounded in a
                 straightforward manner (in contrast to existing methods
                 to compute the reciprocal square root). Although,
                 apparently, a single selection function can only be
                 used for $ j \geq 2 $ (the selection constants are
                 different for $ j = 0 $, $ j = 1 $, and $ j \geq 2 $),
                 we show that it is possible to use a single selection
                 function for all iterations. We perform a rough
                 comparison with existing methods and we conclude that
                 our implementation is a low hardware complexity
                 solution with moderate latency, especially for exactly
                 rounded results. We also extend the unit to support
                 division and square root with the same selection
                 function and with slight modifications in the
                 initialization of the reciprocal square root unit.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Lee:2003:DPL,
  author =       "B. Lee and N. Burgess",
  title =        "A Dual-Path Logarithmic Number System Addition\slash
                 Subtraction Scheme for {FPGA}",
  crossref =     "Cheung:2003:FPL",
  pages =        "808--817",
  year =         "2003",
  bibdate =      "Fri Jun 24 18:24:42 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Lefevre:2003:FRR,
  author =       "Vincent Lef{\`e}vre and Jean-Michel Muller",
  title =        "On-the-fly Range Reduction",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "33",
  number =       "1--2",
  pages =        "31--35",
  month =        jan,
  year =         "2003",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1023/A:1021137717282",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Sat Jun 25 08:56:19 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In several cases, the input argument of an elementary
                 function evaluation is given bit-serially, most
                 significant bit first. We suggest a solution for
                 performing the first step of the evaluation (namely,
                 the range reduction) on the fly: the computation is
                 overlapped with the reception of the input bits. This
                 algorithm can be used for the trigonometric functions
                 sin, cos, tan as well as for the exponential
                 function.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
  keywords =     "range reduction",
}

@Misc{Lefevre:2003:TMD,
  author =       "Vincent Lef{\`e}vre and Jean-Michel Muller",
  title =        "The {Table Maker's Dilemma}: our search for worst
                 cases",
  howpublished = "World-Wide Web software project archive.",
  day =          "28",
  month =        oct,
  year =         "2003",
  bibdate =      "Fri Jun 24 20:08:53 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://perso.ens-lyon.fr/jean-michel.muller/Intro-to-TMD.htm",
  abstract =     "The Table Maker's Dilemma consists in finding, for a
                 given function and a given domain, the smallest value
                 of $m$ [the relative error is $ 2^{-m} $ ] such that
                 rounding this approximate value $ y* $ always gives the
                 same result as rounding the exact value $y$. This is
                 done by looking for ``worst cases'', that is, in the
                 considered domain, the values $x$ such that $ f(x) $ is
                 closest to an exactly representable number or the
                 mid-point of two exactly representable numbers.",
  acknowledgement = ack-nhfb,
}

@TechReport{Lefevre:2003:WCC,
  author =       "Vincent Lef{\`e}vre and Jean-Michel Muller",
  title =        "Worst Cases for Correct Rounding for the Elementary
                 Functions in Double Precision",
  type =         "Technical report",
  institution =  "INRIA, Projet Spaces, LORIA, Campus Scientifique",
  address =      "B.P. 239, 54506 Vandoeuvre-l{\`e}s-Nancy Cedex,
                 France",
  day =          "14",
  month =        aug,
  year =         "2003",
  bibdate =      "Thu Jul 08 08:27:53 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://perso.ens-lyon.fr/jean-michel.muller/TMDworstcases.pdf",
  abstract =     "We give the results of our search for the worst cases
                 for correct rounding of the major elementary functions
                 in double precision floating-point arithmetic. These
                 results allow the design of reasonably fast routines
                 that will compute these functions with correct
                 rounding, at least in some interval, for any of the
                 four rounding modes specified by the IEEE-754 standard.
                 They will also allow one to easily test libraries that
                 are claimed to provide correctly rounded functions.",
  acknowledgement = ack-nhfb,
  keywords =     "computer arithmetic; correct rounding; elementary
                 functions; floating-point arithmetic; Table Maker's
                 Dilemma",
}

@InProceedings{Li:2003:TEA,
  author =       "Ren-Cang Li and Sylvie Boldo and Marc Daumas",
  title =        "Theorems on efficient argument reductions",
  crossref =     "Bajard:2003:ISC",
  pages =        "129--136",
  year =         "2003",
  bibdate =      "Wed Nov 26 12:04:35 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://csdl.computer.org/comp/proceedings/arith/2003/1894/00/1894toc.htm;
                 http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Li.pdf",
  abstract =     "A commonly used argument reduction technique in
                 elementary function computations begins with two
                 positive floating point numbers $ \alpha $ and $ \gamma
                 $ that approximate (usually irrational but not
                 necessarily) numbers $ 1 / C $ and $C$, e.g., $ C = 2
                 \pi $ for trigonometric functions and $ \ln 2 $ for $
                 e^x $. Given an argument to the function of interest it
                 extracts $z$ as defined by $ x \alpha = z + \zeta $
                 with $ z = k2^{-N} $ and $ | \zeta | \leq 2^{N - 1} $
                 where $k$, $N$ are integers and $ N \geq 0 $ is
                 preselected, and then computes $ u = x - z \gamma $.
                 Usually $ z \gamma $ takes more bits than the working
                 precision provides for storing its significand, and
                 thus exact $ x - z \gamma $ may not be represented
                 exactly by a floating point number of the same
                 precision. This will cause a performance penalty when
                 the working precision is the highest available on the
                 underlying hardware and thus considerable extra work is
                 needed to get all the bits of $ x - z \gamma $ right.
                 This paper presents theorems that show under mild
                 conditions that can be easily met on today's computer
                 hardware and still allow $ \alpha \approx 1 / C $ and $
                 \gamma \approx C $ to almost the full working
                 precision, $ x - z \gamma $ is a floating point number
                 of the same precision. An algorithmic procedure based
                 on the theorems is obtained. The results will enhance
                 performance, in particular on machines that has
                 hardware support for fused multiply-add (fma)
                 instruction(s).",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@InProceedings{Liu:2003:FPC,
  author =       "Z. Liu and K. Dickson and J. V. McCanny",
  booktitle =    "{Proceedings IEEE International Conference on
                 Application-Specific Systems, Architectures, and
                 Processors. ASAP 2003}",
  title =        "A floating-point {CORDIC} based {SVD} processor",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "194--203",
  year =         "2003",
  DOI =          "https://doi.org/10.1109/ASAP.2003.1212843",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer architecture; Concurrent computing; Digital
                 signal processing; Floating-point arithmetic; Hardware;
                 Jacobian matrices; Laboratories; Pipeline processing;
                 Silicon; Singular value decomposition",
}

@InProceedings{Mamidi:2003:AGC,
  author =       "S. Mamidi and M. Senthilvelan and M. J. Schulte and S.
                 Krithivasan",
  title =        "Automated Generation of Configurable Media
                 Processors",
  crossref =     "Matthews:2003:PTS",
  pages =        "339--343",
  year =         "2003",
  bibdate =      "Sun Mar 04 17:51:05 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2003-09.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Markstein:2003:ASC,
  author =       "Peter Markstein",
  title =        "Accelerating sine and cosine evaluation with compiler
                 assistance",
  crossref =     "Bajard:2003:ISC",
  pages =        "137--140",
  year =         "2003",
  bibdate =      "Wed Nov 26 12:04:35 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Markstein.pdf",
  abstract =     "Some software libraries add special entry points to
                 enable both the sine and cosine to be evaluated with
                 one call for performance reasons. This paper proposes
                 another methods which does not involve new function
                 names. By having the compiler front end recognize
                 trigonometric function invocations, and replace them
                 with a call to a common function followed by a short
                 routine to produce the desired computation, it is
                 possible to computer both the sine and the cosine when
                 needed in about the same time as to compute only one of
                 them.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@InProceedings{Markstein:2003:FQP,
  author =       "Peter Markstein",
  title =        "A fast quad precision elementary function library for
                 {Itanium}",
  crossref =     "Anonymous:2003:CRN",
  pages =        "5--12",
  year =         "2003",
  bibdate =      "Fri Jun 24 20:14:39 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This talk will describe Itanium's floating point
                 architecture and how it has been used to produce a high
                 performance, highly accurate quad precision elementary
                 function library.\par

                 Itanium's floating-point features will first be
                 described, from the point of view of a computer
                 architect. Many conflicting requirements vie for
                 consideration during the design of a new computer
                 architecture. These include instruction word size,
                 number of registers, the set of operations, arithmetic
                 precisions supported, and memory access. Some of the
                 trade-offs during the design phase will be
                 discussed.\par

                 One of the objectives of the original Itanium design
                 was to accelerate quad precision arithmetic. The talk
                 will describe how the Itanium elementary function
                 library was constructed, with attention to performance
                 and accuracy. Because a pair of double-extended
                 floating point words are used for internal operations
                 involving quad precision numbers, intermediate results,
                 holding 128 bits, provide 15 guard bits during
                 intermediate calculations, resulting in a very low
                 percentage of misrounded results.",
  acknowledgement = ack-nhfb,
}

@Article{Matula:2003:BFM,
  author =       "David W. Matula and Lee D. McFearin",
  title =        "A $ p \times p $ bit fraction model of binary floating
                 point division and extremal rounding cases",
  journal =      j-THEOR-COMP-SCI,
  volume =       "291",
  number =       "2",
  pages =        "159--182",
  year =         "2003",
  CODEN =        "TCSDIQ",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  MRclass =      "68M07 (65G30)",
  MRnumber =     "MR1957438 (2004e:68004)",
  MRreviewer =   "Jean-Marie Chesneaux",
  bibdate =      "Thu Nov 8 19:16:14 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Real numbers and computers (Schloss Dagstuhl, 2000)",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
  keywords =     "rounding errors",
}

@InProceedings{Matula:2003:CAA,
  author =       "David W. Matula",
  title =        "Computer Arithmetic --- An Algorithm Engineer's
                 Perspective",
  crossref =     "Bajard:2003:ISC",
  pages =        "2--2",
  year =         "2003",
  bibdate =      "Wed Nov 26 11:59:51 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Matula_keynote.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@InProceedings{Matula:2003:PID,
  author =       "David W. Matula and Alex Fit-Florea",
  title =        "Prescaled integer division",
  crossref =     "Bajard:2003:ISC",
  pages =        "63--68",
  year =         "2003",
  bibdate =      "Wed Nov 26 11:59:51 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Matula.pdf",
  abstract =     "We describe a high radix integer division algorithm
                 where the divisor is prescaled and the quotient is
                 post-scaled without modifying the dividend to obtain an
                 identity $ N = Q* \times D + R* $ with the quotient $
                 Q* $ differing from the desired integer quotient $Q$
                 only in its lowest order high radix digit. Here the
                 ``oversized'' partial remainder $ R* $ is bounded by
                 the scaled divisor with at most one additional high
                 radix digit selection needed to reduce the partial
                 remainder and augment the quotient to obtain the
                 desired integer division result $ N = Q \times D + R $
                 with $ 0 \leq R \leq D - 1 $.\par

                 We present a high radix multiplicative version of this
                 algorithm where a $ k \times p $ digit base $ \beta $
                 rectangular aspect ratio multiplier allows quotient
                 digit selection in radix $ \beta^{k - 1} $ with a cost
                 of only one $ k \times p $ digit multiply per high
                 radix digit, plus the fixed pre- and post-scaling
                 operation costs. We also present a Booth radix $4$
                 additive version of this algorithm where appropriately
                 compressed representation of the partial remainder with
                 Booth digits $ \{ - 2, - 1, 0, 1, 2 \} $ allows
                 successive quotient digit selection from the leading
                 partial remainder digit without the iterative table
                 lookups required in SRT division.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@InProceedings{McCann:2003:SDA,
  author =       "Mark McCann and Nicholas Pippenger",
  title =        "{SRT} division algorithms as dynamical systems",
  crossref =     "Bajard:2003:ISC",
  pages =        "46--53",
  year =         "2003",
  bibdate =      "Wed Nov 26 11:59:51 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_McCann.pdf",
  abstract =     "SRT division, as it was discovered in the late 1950s
                 represented an important improvement in the speed of
                 division algorithms for computers at the time. A
                 variant of SRT division is still commonly implemented
                 in computers today. Although some bounds on the
                 performance of the original SRT division method were
                 obtained, a great many questions remained unanswered.
                 In this paper, the original version of SRT division is
                 described as a dynamical system. This enables us to
                 bring modern dynamical systems theory, a relatively new
                 development in mathematics, to bear on an older
                 problem. In doing so, we are able to show that SRT
                 division is ergodic, and is even Bernoulli, for all
                 real divisors and dividends. With the Bernoulli
                 property, we are able to use entropy to prove that the
                 natural extensions of SRT division are isomorphic by
                 way of the Kolmogorov-Ornstein Theorem. We demonstrate
                 how our methods and results can be applied to a much
                 larger class of division algorithms.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@Article{Montgomery:2003:FEC,
  author =       "Peter L. Montgomery {Kirsten Eisentr{\"a}ger, Kristin
                 Lauter}",
  title =        "Fast Elliptic Curve Arithmetic and Improved {Weil}
                 Pairing Evaluation",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2612",
  pages =        "343--354",
  year =         "2003",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Apr 4 18:46:22 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
  keywords =     "cryptology; Topics in Cryptology CT-RSA 2003",
}

@InProceedings{Muller:2003:SRS,
  author =       "Jean-Michel Muller",
  title =        "{``Partially} rounded'' small-order approximations for
                 accurate, hardware-oriented, table-based methods",
  crossref =     "Bajard:2003:ISC",
  pages =        "114--121",
  year =         "2003",
  bibdate =      "Wed Nov 26 12:04:35 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Muller.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
  summary =      "We aim at evaluating elementary and special functions
                 using small tables and small, rectangular, multipliers.
                 To do that, we show how accurate polynomial
                 approximations whose order-1 coefficients are small in
                 size (a few bits only) can be computed. We compare the
                 obtained results with similar work in the recent
                 literature",
}

@InProceedings{Nannarelli:2003:PDT,
  author =       "A. Nannarelli and G. C. Cardarilli and M. Re",
  booktitle =    "{ISCAS '03}, Proceedings of the 2003 International
                 Symposium on Circuits and Systems, 25--28 May 2003",
  title =        "Power-delay tradeoffs in residue number system",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "V-413--V-416",
  year =         "2003",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.2003.1206300",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "In this paper we present some tradeoffs between delay
                 and power consumption in the design of digital
                 processors based on the Residue Number System (RNS). We
                 focus on reducing the switching capacitance, and
                 therefore the power, in modular adders and \ldots{}",
}

@Article{Nievergelt:2003:SFM,
  author =       "Yves Nievergelt",
  title =        "Scalar fused multiply-add instructions produce
                 floating-point matrix arithmetic provably accurate to
                 the penultimate digit",
  journal =      j-TOMS,
  volume =       "29",
  number =       "1",
  pages =        "27--48",
  month =        mar,
  year =         "2003",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/641876.641878",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "68W99 (65Y99 68M99)",
  MRnumber =     "MR2001452",
  bibdate =      "Fri Mar 28 08:17:55 MST 2003",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Combined with doubly compensated summation, scalar
                 fused multiply-add instructions redefine the concept of
                 floating-point arithmetic, because they allow for the
                 computation of sums of real or complex matrix products
                 accurate to the penultimate digit. Particular cases
                 include complex arithmetic, dot products, cross
                 products, residuals of linear systems, determinants of
                 small matrices, discriminants of quadratic, cubic, or
                 quartic equations, and polynomials.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "accurate floating-point summation; algorithms; design;
                 doubly compensated summation; floating-point
                 arithmetic; fused multiply-add instruction; languages;
                 matrix arithmetic; provable accuracy; rounding error;
                 standardization; theory",
  subject =      "Primary Classification: B. Hardware, B.2 ARITHMETIC
                 AND LOGIC STRUCTURES, B.2.0 General;

                 Additional Classification: B. Hardware, B.7 INTEGRATED
                 CIRCUITS B.7.1 Types and Design Styles Subjects:
                 Algorithms implemented in hardware B.8 Performance and
                 Reliability B.8.2 Performance Analysis and Design
                 Aids

                 C. Computer Systems Organization C.0 GENERAL Subjects:
                 Instruction set design (e.g., RISC, CISC, VLIW)

                 F. Theory of Computation F.2 ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY F.2.1 Numerical Algorithms and
                 Problems Subjects: Computations on matrices

                 G. Mathematics of Computing G.1 NUMERICAL ANALYSIS
                 G.1.0 General Subjects: Computer arithmetic; Multiple
                 precision arithmetic; Numerical algorithms; Error
                 analysis G.4 MATHEMATICAL SOFTWARE Subjects: Algorithm
                 design and analysis; Certification and testing;
                 Reliability and robustness",
}

@Article{Okeya:2003:WNM,
  author =       "Katsuyuki Okeya and Tsuyoshi Takagi",
  title =        "The Width-$w$ {NAF} Method Provides Small Memory and
                 Fast Elliptic Scalar Multiplications Secure against
                 Side Channel Attacks",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2612",
  pages =        "328--342",
  year =         "2003",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Apr 4 18:46:22 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
  keywords =     "cryptology; Topics in Cryptology CT-RSA 2003",
}

@InProceedings{Oklobdzija:2003:EDE,
  author =       "Vojin G. Oklobdzija and Bart R. Zeydel and Hoang Dao
                 and Sanu Mathew and Ram Krishnamurthy",
  title =        "Energy-delay estimation technique for high-performance
                 microprocessor {VLSI} adders",
  crossref =     "Bajard:2003:ISC",
  pages =        "272--279",
  year =         "2003",
  bibdate =      "Wed Nov 26 12:04:40 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Oklobdzija.pdf",
  abstract =     "In this paper, we motivate the concept of comparing
                 VLSI adders based on their energy-delay trade-offs and
                 present a technique for estimating the energy-delay
                 space of various high-performance VLSI adder
                 topologies. Further, we show that our estimates
                 accurately represent tradeoffs in the energy-delay
                 space for high-performance 32-bit and 64-bit processor
                 adders in 0.13mm and 0.10mm CMOS technologies, with an
                 accuracy of 8\% in delay estimates and 20\% in energy
                 estimates, compared with simulated data.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@InProceedings{Oklobdzija:2003:TDP,
  author =       "V. G. Oklobdzija and R. Krishnamurthy",
  title =        "Tutorial: Design of power efficient {VLSI} arithmetic:
                 speed and power trade-offs",
  crossref =     "Bajard:2003:ISC",
  pages =        "280--280",
  year =         "2003",
  bibdate =      "Wed Nov 26 12:04:40 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@Article{ORourke:2003:ANM,
  author =       "C. O'Rourke and B. Sunar",
  title =        "Achieving {NTRU} with {Montgomery} multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "52",
  number =       "4",
  pages =        "440--448",
  month =        apr,
  year =         "2003",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2003.1190585",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 08:52:46 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1190585",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Parhami:2003:TUB,
  author =       "B. Parhami",
  title =        "Tight upper bounds on the minimum precision required
                 of the divisor and the partial remainder in high-radix
                 division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "52",
  number =       "11",
  pages =        "1509--1514",
  month =        nov,
  year =         "2003",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2003.1244949",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 08:52:58 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1244949",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Paschalakis:2003:DPF,
  author =       "S. Paschalakis and P. Lee",
  title =        "Double precision floating-point arithmetic on
                 {FPGAs}",
  crossref =     "IEEE:2003:IICb",
  pages =        "352--358",
  year =         "2003",
  DOI =          "https://doi.org/10.1109/FPT.2003.1275775",
  bibdate =      "Sat Oct 9 12:57:30 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present low cost FPGA floating-point arithmetic
                 circuits for all the common operations, i.e.
                 addition/subtraction, multiplication, division and
                 square root. Such circuits can be extremely useful in
                 the FPGA implementation of complex systems that benefit
                 from the reprogrammability and parallelism of the FPGA
                 device but also require a general purpose arithmetic
                 unit. While previous work has considered circuits for
                 low precision floating-point formats, we consider the
                 implementation of 64-bit double precision circuits that
                 also provide rounding and exception handling.",
  acknowledgement = ack-nhfb,
}

@Article{Percival:2003:RMM,
  author =       "Colin Percival",
  title =        "Rapid multiplication modulo the sum and difference of
                 highly composite numbers",
  journal =      j-MATH-COMPUT,
  volume =       "72",
  number =       "241",
  pages =        "387--395",
  month =        jan,
  year =         "2003",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Fri Nov 22 10:22:27 MST 2002",
  bibsource =    "http://www.ams.org/mcom/2003-72-241;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ams.org/journal-getitem?pii=S0025-5718-02-01419-9;
                 http://www.ams.org/mcom/2003-72-241/S0025-5718-02-01419-9/S0025-5718-02-01419-9.dvi;
                 http://www.ams.org/mcom/2003-72-241/S0025-5718-02-01419-9/S0025-5718-02-01419-9.pdf;
                 http://www.ams.org/mcom/2003-72-241/S0025-5718-02-01419-9/S0025-5718-02-01419-9.ps;
                 http://www.ams.org/mcom/2003-72-241/S0025-5718-02-01419-9/S0025-5718-02-01419-9.tex",
  abstract =     "We extend the work of Richard Crandall et al. to
                 demonstrate how the Discrete Weighted Transform (DWT)
                 can be applied to speed up multiplication modulo any
                 number of the form $ a \pm b $ where $ \prod_{p \vert
                 ab}{p} $ is small. In particular this allows rapid
                 computation modulo numbers of the form $ k \cdot 2^n
                 \pm 1 $.\par

                 In addition, we prove tight bounds on the rounding
                 errors which naturally occur in floating-point
                 implementations of FFT and DWT multiplications. This
                 makes it possible for FFT multiplications to be used in
                 situations where correctness is essential, for example
                 in computer algebra packages.",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@InProceedings{Phillips:2003:SRR,
  author =       "B. Phillips",
  booktitle =    "Conference Record of the Thirty-Seventh Asilomar
                 Conference on Signals, Systems and Computers, 2003",
  title =        "Scaling and reduction in the residue number system
                 with pairs of conjugate moduli",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2247--2251",
  year =         "2003",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ACSSC.2003.1292380",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The residue number system (RNS) with pairs of
                 conjugate moduli uses a modulus set containing pairs of
                 moduli of the form {2/sup k/-1, 2/sup k/+1}. This RNS
                 provides a good trade-off between large dynamic range
                 and channel width. It also supports \ldots{}",
}

@InProceedings{Pineiro:2003:HRI,
  author =       "J.-A. Pi{\~n}eiro and M. D. Ercegovac and J. D.
                 Bruguera",
  title =        "High-radix iterative algorithm for powering
                 computation",
  crossref =     "Bajard:2003:ISC",
  pages =        "204--211",
  year =         "2003",
  bibdate =      "Wed Nov 26 12:04:35 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Pineiro.pdf",
  abstract =     "A high-radix composite algorithm for the computation
                 of the powering function ($ X^Y $) is presented in this
                 paper. The algorithm consists of a sequence of
                 overlapped operations: (i) digit-recurrence logarithm,
                 (ii) left-to-right carry-free (LRCF) multiplications,
                 and (iii) on-line exponential. A redundant number
                 system is used, and the selection in (i) and (iii) is
                 done by rounding except from the first iteration, when
                 selection by table look-up is necessary to guarantee
                 the convergence of the recurrences. A sequential
                 implementation of the algorithm is proposed, and the
                 execution times and hardware requirements are estimated
                 for single and double-precision floating-point
                 computations, for radix $ r = 128 $ showing that
                 powering can be computed with similar performance as
                 high-radix CORDIC algorithms.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@InProceedings{Pineiro:2003:LHR,
  author =       "J.-A. Pineiro and J. D. Bruguera and M. D. Ercegovac",
  booktitle =    "2003. {ISCAS '03}. Proceedings of the 2003
                 International Symposium on Circuits and Systems. 25--28
                 May 2003",
  title =        "On-line high-radix exponential with selection by
                 rounding",
  volume =       "4",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "IV-121--IV-124",
  year =         "2003",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:05 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "An on-line high-radix algorithm for computing the
                 exponential function ($e^x$) with arbitrary precision
                 $n$ is presented. Selection by rounding and a redundant
                 digit-set for the digits $e_j$ are used, with selection
                 by table in the first \ldots{}",
}

@Article{Reyhani-Masoleh:2003:EMB,
  author =       "A. Reyhani-Masoleh and M. A. Hasan",
  title =        "Efficient multiplication beyond optimal normal bases",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "52",
  number =       "4",
  pages =        "428--439",
  month =        apr,
  year =         "2003",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2003.1190584",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 08:52:46 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1190584",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Reyhani-Masoleh:2003:FNB,
  author =       "A. Reyhani-Masoleh and M. A. Hasan",
  title =        "Fast normal basis multiplication using general purpose
                 processors",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "52",
  number =       "11",
  pages =        "1379--1390",
  month =        nov,
  year =         "2003",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2003.1244936",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 08:52:57 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1244936",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Reyhani-Masoleh:2003:LCB,
  author =       "Arash Reyhani-Masoleh and M. Anwar Hasan",
  title =        "On Low Complexity Bit Parallel Polynomial Basis
                 Multipliers",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2779",
  pages =        "189--202",
  year =         "2003",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Apr 4 18:12:50 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
  keywords =     "CHES 2003; cryptography",
}

@InProceedings{Reyhani-Masoleh:2003:LCS,
  author =       "Arash Reyhani-Masoleh and M. Anwar Hasan",
  title =        "Low complexity sequential normal basis multipliers
                 over {$ \mathrm {GF}(2^m) $}",
  crossref =     "Bajard:2003:ISC",
  pages =        "188--195",
  year =         "2003",
  bibdate =      "Wed Nov 26 12:04:35 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Reyhani-Masoleh.pdf",
  abstract =     "For efficient hardware implementation of finite field
                 arithmetic units, the use of a normal basis is
                 advantageous. In this article, two architectures for
                 multipliers over the finite field $ \mathrm {GF}(2^m) $
                 are proposed. Both of these multipliers are of
                 sequential type --- after receiving the coordinates of
                 the two input field elements, they go through $m$
                 iterations (or clock cycles) to finally yield all the
                 coordinates of the product in parallel. These
                 multipliers are highly area efficient and require fewer
                 number of logic gates even when compared with the most
                 area efficient multiplier available in the open
                 literature. This makes the proposed multipliers
                 suitable for applications where the value of is large
                 but space is of concern, e.g., resource constrained
                 cryptographic systems. Additionally, the AND gate count
                 for one of the multipliers is $ \floor {m / 2} + 1 $
                 only. This implies that if the multiplication over $
                 \mathrm {GF}(2^m) $ is performed using a suitable
                 subfield $ \mathrm {GF}(2^n) $ where $ n > 1 $ and $ n
                 | m $, then the corresponding multiplier architecture
                 will yield a highly efficient digit or word serial
                 multiplier.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@InProceedings{Rice:2003:NIS,
  author =       "Eric Rice and Richard Hughey",
  title =        "A new iterative structure for hardware division: the
                 parallel paths algorithm",
  crossref =     "Bajard:2003:ISC",
  pages =        "54--62",
  year =         "2003",
  bibdate =      "Wed Nov 26 11:59:51 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Rice.pdf",
  abstract =     "This paper presents a new approach to hardware
                 division --- the parallel paths algorithm. In this
                 approach, prescaling allows the division recurrence to
                 be implemented by three processes which can be
                 calculated in parallel during iterations. While two of
                 the processes must complete in a single iteration, the
                 third --- which includes the most expensive division
                 operations --- can be calculated over multiple
                 iterations. Iteration latency is determined by the
                 slowest of the three paths, and in many cases can be
                 limited to that of carry-save addition and latching. A
                 radix-4 implementation of the algorithm is shown to
                 achieve better performance than other commonly used
                 methods while requiring a modest increase in area.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@Article{Rodriguez-Henriquez:2003:PMB,
  author =       "F. Rodriguez-Henriquez and {\c{C}}. K. Ko{\c{c}}",
  title =        "Parallel multipliers based on special irreducible
                 pentanomials",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "52",
  number =       "12",
  pages =        "1535--1542",
  month =        dec,
  year =         "2003",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2003.1252850",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 08:52:59 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1252850",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Schonfelder:2003:VPA,
  author =       "J. L. Schonfelder",
  title =        "Variable precision arithmetic: a {Fortran 95} module",
  journal =      j-SCI-PROG,
  volume =       "11",
  number =       "1",
  pages =        "67--76",
  year =         "2003",
  CODEN =        "SCIPEV",
  ISSN =         "1058-9244 (print), 1875-919X (electronic)",
  ISSN-L =       "1058-9244",
  bibdate =      "Mon Jan 12 06:28:15 MST 2004",
  bibsource =    "http://www.iospress.nl/site/html/10589244.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientific Programming",
  journal-URL =  "http://iospress.metapress.com/content/1058-9244",
}

@InProceedings{Schulte:2003:CMS,
  author =       "M. J. Schulte and L. P. Marquette and S. Krithivasan
                 and E. G. Walters and J. Glossner",
  title =        "Combined Multiplication and Sum of Squares Units",
  crossref =     "Deprettere:2003:IIC",
  pages =        "204--214",
  year =         "2003",
  bibdate =      "Sun Mar 04 20:46:13 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2003-02.pdf",
  acknowledgement = ack-nhfb,
  remark =       "One of three finalists for the best paper award.",
}

@InProceedings{Schwarz:2003:HID,
  author =       "Eric M. Schwarz and Martin Schmookler and Son Dao
                 Trong",
  title =        "Hardware implementations of denormalized numbers",
  crossref =     "Bajard:2003:ISC",
  pages =        "70--78",
  year =         "2003",
  DOI =          "https://doi.org/10.1109/ARITH.2003.1207662",
  bibdate =      "Wed Nov 26 11:59:51 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Schwarz.pdf",
  abstract =     "Denormalized numbers are the most difficult type of
                 numbers to implement in floating-point units. They are
                 so complex that some designs have elected to handle
                 them in software rather than in hardware. This has
                 results in execution times in the tens of thousands of
                 cycle, which as made denormalized numbers useless to
                 programmers. This does not have to happen. With a small
                 amount of additional hardware, denormalized numbers and
                 underflows can be handled close to the speed of
                 normalized numbers. Most of the techniques discussed
                 here have only been discussed in filed or pending
                 patent applications.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@InProceedings{Schwarz:2003:PRI,
  author =       "E. Schwarz",
  title =        "Panel: Revisions to the {IEEE 754} standard for
                 floating-point arithmetic",
  crossref =     "Bajard:2003:ISC",
  pages =        "112--112",
  year =         "2003",
  bibdate =      "Wed Nov 26 12:04:35 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@InProceedings{Seidel:2003:MPI,
  author =       "Peter-Michael Seidel",
  booktitle =    "{2003 IEEE International Symposium on
                 Micro-NanoMechatronics and Human Science}",
  title =        "Multiple Path {IEEE} Floating-Point Fused
                 Multiply-Add",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1359--1362",
  year =         "2003",
  DOI =          "https://doi.org/10.1109/MWSCAS.2003.1562547",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Fri Jun 24 12:02:41 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We propose optimizations for the IEEE floating-point
                 fused multiply-add operation by considering multiple
                 exclusive parallel computation paths in the
                 implementation. For the proposed design we can show a
                 significant performance improvement over conventional
                 implementations. Considering a variable latency
                 implementation allows for further reduction of the
                 average latency.",
  acknowledgement = ack-nhfb,
  xxbooktitle =  "Proc. 46th Int. IEEE MidWest Symposium on Circuits and
                 Systems (MWSCAS)",
}

@InProceedings{Senthilvelan:2003:FAL,
  author =       "M. Senthilvelan and M. J. Schulte",
  title =        "A Flexible Arithmetic and Logic Unit for Multimedia
                 Processing",
  crossref =     "Luk:2003:PSA",
  pages =        "520--528",
  year =         "2003",
  bibdate =      "Sun Mar 04 20:44:10 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2003-05.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sheldon:2003:SRI,
  author =       "Jeffrey Sheldon and Walter Lee and Ben Greenwald and
                 Saman Amarasinghe",
  title =        "Strength Reduction of Integer Division and Modulo
                 Operations",
  crossref =     "Dietz:2003:LCP",
  pages =        "254--273",
  year =         "2003",
  DOI =          "https://doi.org/10.1007/3-540-35767-X_17",
  bibdate =      "Fri Jun 24 12:09:31 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/link.asp?id=3hfwyuyjxkf23nd2;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=0302-9743&volume=2624&spage=254",
  abstract =     "Integer division, modulo, and remainder operations are
                 expressive and useful operations. They are logical
                 candidates to express complex data accesses such as the
                 wrap-around behavior in queues using ring buffers. In
                 addition, they appear frequently in address
                 computations as a result of compiler optimizations that
                 improve data locality, perform data distribution, or
                 enable parallelization. Experienced application
                 programmers, however, avoid them because they are slow.
                 Furthermore, while advances in both hardware and
                 software have improved the performance of many parts of
                 a program, few are applicable to division and modulo
                 operations. This trend makes these operations
                 increasingly detrimental to program performance. This
                 paper describes a suite of optimizations for
                 eliminating division, modulo, and remainder operations
                 from programs. These techniques are analogous to
                 strength reduction techniques used for multiplications.
                 In addition to some algebraic simplifications, we
                 present a set of optimization techniques that
                 eliminates division and modulo operations that are
                 functions of loop induction variables and loop
                 constants. The optimizations rely on algebra, integer
                 programming, and loop transformations.",
  acknowledgement = ack-nhfb,
}

@Article{Singer:2003:REP,
  author =       "Sanja Singer and Sa{\v{s}}a Singer",
  title =        "Rounding error and perturbation bounds for the
                 symplectic {QR} factorization",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "358",
  number =       "1--3",
  pages =        "255--279",
  day =          "1",
  month =        jan,
  year =         "2003",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Mon Apr 28 07:27:21 MDT 2003",
  bibsource =    "http://www.elsevier.com/locate/laa;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.elsevier.nl/gej-ng/10/30/19/207/25/39/abstract.html;
                 http://www.sciencedirect.com/science?_ob=GatewayURL&_origin=SOCJLA&_urlversion=4&_method=citationSearch&_version=1&_piikey=S002437950200263X&_volkey=00243795%23358%23255&_refkey=Singer%232003%23255%23279&md5=d630d009cc24a902e31bc6f9537af08c",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Article{Smith:2003:UMP,
  author =       "David M. Smith",
  title =        "Using Multiple-Precision Arithmetic",
  journal =      j-COMPUT-SCI-ENG,
  volume =       "5",
  number =       "4",
  pages =        "88--93",
  month =        jul # "\slash " # aug,
  year =         "2003",
  CODEN =        "CSENFA",
  ISSN =         "1521-9615 (print), 1558-366X (electronic)",
  ISSN-L =       "1521-9615",
  bibdate =      "Sat Jan 3 18:25:08 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://csdl.computer.org/dl/mags/cs/2003/04/c4088.htm;
                 http://csdl.computer.org/dl/mags/cs/2003/04/c4088.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing in Science and Engineering",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
  summary =      "High-precision arithmetic is useful in many different
                 computational problems. The most common is a
                 numerically unstable algorithm, for which, say, 53-bit
                 (ANSI/IEEE 754-1985 Standard) double precision would
                 not yield a sufficiently accurate result. \ldots{}",
}

@Article{Sofroniou:2003:IFR,
  author =       "Mark Sofroniou and Giulia Spaletta",
  title =        "Increment formulations for rounding error reduction in
                 the numerical solution of structured differential
                 systems",
  journal =      j-FUT-GEN-COMP-SYS,
  volume =       "19",
  number =       "3",
  pages =        "375--383",
  month =        apr,
  year =         "2003",
  CODEN =        "FGSEVI",
  ISSN =         "0167-739X (print), 1872-7115 (electronic)",
  ISSN-L =       "0167-739X",
  bibdate =      "Sat Jan 10 10:03:32 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Future Generation Computer Systems",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0167739X",
}

@InProceedings{Stehle:2003:WCL,
  author =       "Damien Stehl{\'e} and Vincent Lef{\`e}vre and Paul
                 Zimmermann",
  title =        "Worst cases and lattice reduction",
  crossref =     "Bajard:2003:ISC",
  pages =        "142--147",
  year =         "2003",
  bibdate =      "Wed Nov 26 12:04:35 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Stehle.pdf",
  abstract =     "We propose a new algorithm to find worst cases for
                 correct rounding of an analytic function. We first
                 reduce this problem to the real small value problem ---
                 i.e. for polynomials with real coefficients. Then we
                 show that this second problem can be solved
                 efficiently, by extending Coppersmith's work on the
                 integer small value problem --- for polynomials with
                 integer coefficients --- using lattice reduction [4, 5,
                 6].\par

                 For floating-point numbers with a mantissa less than
                 $N$, and a polynomial approximation of degree $d$, our
                 algorithm finds all worst cases at distance $ < N^{-d^2
                 / (2d + 1)} $ from a machine number in time $ O(N^{(d +
                 1) / (2d + 1) + \epsilon }) $. For $ d = 2 $, this
                 improves on the $ O(N^{2 / 3} + \epsilon) $ complexity
                 from Lef{\'e}vre's algorithm [15, 16] to $ O(N^{3 / 5}
                 + \epsilon) $. We exhibit some new worst cases found
                 using our algorithm, for double-extended and quadruple
                 precision. For larger $d$, our algorithm can be used to
                 check that there exist no worst cases at distance $ <
                 N^{-k} $ in time $ O(N^{1 / 2 + O(1 / k)}) $.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16; correct rounding; floating-point
                 arithmetic",
}

@InProceedings{Sun:2003:NAF,
  author =       "Haiping Sun and Minglun Gao",
  title =        "A novel architecture for floating-point
                 multiply-add-fused operation",
  crossref =     "IEEE:2004:PJC",
  volume =       "3",
  pages =        "1675--1679",
  year =         "2003",
  DOI =          "https://doi.org/10.1109/ICICS.2003.1292753",
  bibdate =      "Sun Feb 20 10:50:21 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Suvakovic:2003:EEA,
  author =       "Dusan Suvakovic and C. Andr{\'e} T. Salama",
  title =        "Energy Efficient Adiabatic Multiplier-Accumulator
                 Design",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "33",
  number =       "1",
  pages =        "83--103",
  month =        jan,
  year =         "2003",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1023/A:1021145919099",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Fri Jun 24 16:00:03 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper presents a strategy for minimizing
                 non-adiabatic dissipation in adiabatic arithmetic
                 units. The non-adiabatic dissipation is minimized by
                 architectural design involving a small number of
                 complex logic gates. Circuit design of complex
                 adiabatic gates, based on ordered binary decision
                 diagrams (OBDD), is introduced. An optimized
                 architecture for adiabatic parallel multipliers is
                 proposed and savings in energy dissipation over
                 competing architectures are estimated. Experimental
                 results obtained from implementation of an adiabatic
                 multiply-accumulate (MAC) unit suggest that the
                 proposed strategy provides substantial improvement in
                 energy efficiency over equivalent non-adiabatic and
                 alternative adiabatic implementations, while achieving
                 a competitive operating speed.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
}

@Article{Swider:2003:EEF,
  author =       "Zbigniew {\'S}wider",
  title =        "Errors of elementary floating-point operations in
                 control algorithms",
  journal =      "Arch. Control Sci.",
  volume =       "13(49)",
  number =       "4",
  pages =        "505--526",
  year =         "2003",
  ISSN =         "0004-072X",
  MRclass =      "65G50 (62J10)",
  MRnumber =     "MR2175804 (2006g:65076)",
  bibdate =      "Thu Nov 8 19:16:14 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Archives of Control Sciences. Polish Academy of
                 Sciences. Committee of Automatic Control and Robotics",
  keywords =     "rounding errors",
}

@InProceedings{Tan:2003:MPF,
  author =       "Dimitri Tan and Albert Danysh and Michael Liebelt",
  title =        "Multiple-precision fixed-point vector
                 multiply-accumulator using shared segmentation",
  crossref =     "Bajard:2003:ISC",
  pages =        "12--19",
  year =         "2003",
  bibdate =      "Wed Nov 26 11:59:51 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Tan.pdf",
  abstract =     "We present a 64-bit fixed-point vector
                 multiply-accumulator (MAC) architecture capable of
                 supporting multiple precisions. The vector MAC can
                 perform one 64$ \times $64, two 32$ \times $32, four
                 16$ \times $16 or eight 8$ \times $8 bit signed\slash
                 unsigned multiply-accumulates using essentially the
                 same hardware as a scalar 64-bit MAC and with only a
                 small increase in delay. The scalar MAC architecture is
                 vectorized by inserting mode-dependent multiplexing
                 into the partial product generation and by inserting
                 mode-dependent kills in the carry chain of the
                 reduction tree and the final carry-propagate adder.
                 This is an example of ``shared segmentation'' in which
                 the existing scalar structure is segmented and then
                 shared between vector modes. The vector MAC is area
                 efficient and can be fully pipelined which makes it
                 suitable for high-performance processors and possibly
                 dynamically reconfigurable processors.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@Article{Tenca:2003:SAM,
  author =       "A. F. Tenca and C. K. Koc",
  title =        "A scalable architecture for modular multiplication
                 based on {Montgomery}'s algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "52",
  number =       "9",
  pages =        "1215--1221",
  month =        sep,
  year =         "2003",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2003.1228516",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 08:52:54 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1228516",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Thomas:2003:IMF,
  author =       "James W. Thomas",
  title =        "Inlining of mathematical functions in {HP-UX} for
                 {Itanium 2}",
  crossref =     "IEEE:2003:PCI",
  pages =        "135--144",
  year =         "2003",
  DOI =          "https://doi.org/10.1109/CGO.2003.1191540",
  bibdate =      "Thu Jun 09 18:37:10 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "HP-UX compilers inline mathematical functions for
                 Itanium Processor Family (IPF) systems to improve
                 throughput 4X--8X versus external library calls,
                 achieving speeds comparable to highly tuned vector
                 functions, without requiring the user to code for a
                 vector interface and without sacrificing accuracy or
                 edge-case behaviors. This paper highlights IPF
                 architectural features that support implementation of
                 high-performance, high-quality math functions for
                 inlining. It discusses strategies for utilizing the
                 features and developing inlineable sequences on a large
                 scale, and it presents requisite compiler features and
                 language extensions. Also, this paper describes
                 compiler mechanisms that produce inlineable code and
                 inline it.",
  acknowledgement = ack-nhfb,
  keywords =     "EPIC; Intel IA-64; Itanium",
}

@Article{Vergos:2003:DRA,
  author =       "H. T. Vergos and D. Nikolos and M. Bellos and C.
                 Efstathiou",
  title =        "Deterministic {BIST} for {RNS} adders",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "52",
  number =       "7",
  pages =        "896--906",
  month =        jul,
  year =         "2003",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2003.1214338",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 08:52:51 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1214338",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Wahid:2003:EFA,
  author =       "K. A. Wahid and V. S. Dimitrov and G. A. Jullien",
  title =        "Error-free arithmetic for discrete wavelet transforms
                 using algebraic integers",
  crossref =     "Bajard:2003:ISC",
  pages =        "238--244",
  year =         "2003",
  bibdate =      "Wed Nov 26 12:04:40 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acsel-lab.com/arithmetic/arith16/papers/ARITH16_Jullien.pdf",
  abstract =     "In this paper a novel encoding scheme is introduced
                 with applications to error-free computation of Discrete
                 Wavelet Transforms (DWT) based on Daubechies wavelets.
                 The encoding scheme is based on an algebraic integer
                 decomposition of the wavelet coefficients. This work is
                 a continuation of our research into error-free
                 computation of DCTs and IDCTs, and this extension is
                 timely since the DWT is part of the new standard for
                 JPEG2000. This encoding technique eliminates the
                 requirements to approximate the transformation matrix
                 elements by obtaining their exact representations. As a
                 result, we achieve error-free calculations up to the
                 final reconstruction step where we are free to choose
                 an approximate substitution precision based on a
                 hardware\slash accuracy trade-off.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@InProceedings{Walters:2003:UTM,
  author =       "E. {Walters III} and M. G. Arnold and M. J. Schulte",
  title =        "Using Truncated Multipliers in {DCT} and {IDCT}
                 Hardware Accelerators",
  crossref =     "Luk:2003:PSA",
  pages =        "573--584",
  year =         "2003",
  bibdate =      "Sun Mar 04 17:56:12 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2003-06.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Wang:2003:TDF,
  author =       "Xiaojun Wang and B. E. Nelson",
  booktitle =    "{FCCM 2003}: 11th Annual {IEEE} Symposium on
                 Field-Programmable Custom Computing Machines, 9--11
                 April 2003",
  title =        "Tradeoffs of designing floating-point division and
                 square root on {Virtex FPGAs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "195--203",
  year =         "2003",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "Low latency, high throughput and small area are three
                 major design considerations of an FPGA (field
                 programmable gate array) design. In this paper, we
                 present a high radix SRT division algorithm and a
                 binary restoring square root algorithm. We \ldots{}",
}

@InCollection{Warren:2003:DLD,
  author =       "Henry S. Warren",
  title =        "The distribution of leading digits",
  crossref =     "Warren:2003:HD",
  chapter =      "15.3",
  pages =        "264--267",
  year =         "2003",
  bibdate =      "Fri Mar 16 08:02:56 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Wei:2003:REE,
  author =       "Musheng Wei and Qiaohua Liu",
  title =        "Roundoff error estimates of the modified
                 {Gram--Schmidt} algorithm with column pivoting",
  journal =      j-BIT-NUM-MATH,
  volume =       "43",
  number =       "3",
  pages =        "627--645",
  month =        sep,
  year =         "2003",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1023/B:BITN.0000007051.49808.04",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65F20 (65G50)",
  MRnumber =     "MR2026721 (2004k:65070)",
  bibdate =      "Wed Jan 4 15:06:06 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=43&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=43&issue=3&spage=627",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT. Numerical Mathematics",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "floating-point arithmetic; rounding errors",
}

@Article{Yan:2003:NSA,
  author =       "Z. Yan and D. V. Sarwate",
  title =        "New systolic architectures for inversion and division
                 in {$ \mathrm {GF}(2^m) $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "52",
  number =       "11",
  pages =        "1514--1519",
  month =        nov,
  year =         "2003",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2003.1244950",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 08:52:58 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1244950",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Zhang:2003:DRV,
  author =       "Chang N. Zhang and Hua Li",
  title =        "Design of Reconfigurable {VLSI} Architecture for
                 Hybrid Arithmetic in {$ G F(2^m) $}",
  journal =      j-COMP-J,
  volume =       "46",
  number =       "4",
  pages =        "449--460",
  month =        jul,
  year =         "2003",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Sun Jun 29 07:07:13 MDT 2003",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_46/Issue_04/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_46/Issue_04/460449.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_46/Issue_04/pdf/460449.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Zielke:2003:GLL,
  author =       "Gerhard Zielke and Volker Drygalla",
  title =        "{Genaue L{\"o}sung linearer Gleichungssysteme}.
                 ({German}) [{Exact} solution of linear systems of
                 equations]",
  journal =      j-GAMM-MIT,
  volume =       "26",
  number =       "??",
  pages =        "7--107",
  month =        "????",
  year =         "2003",
  ISSN =         "0936-7195",
  MRclass =      "65F99 (01A60 65-03 65G50 68-03)",
  MRnumber =     "MR2056620 (2005d:65069)",
  bibdate =      "Fri Jan 06 08:03:49 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  URL =          "http://www.wiley-vch.de/publish/en/journals/alphabeticIndex/2250/",
  acknowledgement = ack-nhfb,
  ajournal =     "GAMM Mitt., Ges. Angew. Math. Mech.",
  fjournal =     "Mitteilungen der Gesellschaft f{\"u}r Angewandte
                 Mathematik und Mechanik",
  keywords =     "accurate floating-point summation",
  language =     "German",
  remark =       "Contains MATLAB code for error-free accumulation of
                 floating-point sums and scalar products.",
  xxnote =       "No electronic copies available yet at publisher site,
                 and cannot find online copy in Web searches.",
}

@Article{Ziv:2003:SGM,
  author =       "Abraham Ziv and Laurent Fournier",
  title =        "Solving the generalized mask constraint for test
                 generation of binary floating point add operation",
  journal =      j-THEOR-COMP-SCI,
  volume =       "291",
  number =       "2",
  pages =        "183--201",
  day =          "27",
  month =        jan,
  year =         "2003",
  CODEN =        "TCSDIQ",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  MRclass =      "68M07 (65G30)",
  MRnumber =     "MR1957439 (2004d:68005)",
  bibdate =      "Thu Nov 8 19:16:14 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Real numbers and computers (Schloss Dagstuhl, 2000)",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
  keywords =     "floating-point testing",
}

@InProceedings{Ziv:2003:SRC,
  author =       "Abraham Ziv and Merav Aharoni and Sigal Asaf",
  title =        "Solving range constraints for binary floating-point
                 instructions",
  crossref =     "Bajard:2003:ISC",
  pages =        "158--164",
  year =         "2003",
  bibdate =      "Wed Nov 26 12:04:35 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present algorithms that solve the following
                 problem: given three ranges of floating-point numbers $
                 R_x $, $ R_y $, $ R_z $, a floating-point operation
                 (op), and a rounding-mode (round), generate three
                 floating-point numbers $ \bar {x} $, $ \bar {y} $, $
                 \bar {z} $ such that $ \bar {x} \in R_x $, $ \bar {y}
                 \in R_y $, $ \bar {z} \in R_z $ and $ \bar {z} =
                 \mathfun {round}(\bar {x} \mathop {op} \bar {y}) $.
                 This problem, although quite simple when dealing with
                 intervals of real numbers, is much more complex when
                 considering ranges of machine numbers. We provide full
                 solutions for add and subtract, and partial solutions
                 for multiply and divide. We use range constraints on
                 the input operands and on the result operand of
                 floating-point instructions to target corner cases when
                 generating test cases for use in verification of
                 floating-point hardware. The algorithms have been
                 implemented in a floating-point test-generator and are
                 currently being used to verify floating-point units of
                 several processors.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
  remark =       "No PDF file at the ARITH-16 Web site, and no DOI for
                 the IEEE Xplore Web site.",
}

@Article{Abbasbandy:2004:USA,
  author =       "S. Abbasbandy and M. A. Fariborzi Araghi",
  title =        "The use of the stochastic arithmetic to estimate the
                 value of interpolation polynomial with optimal degree",
  journal =      j-APPL-NUM-MATH,
  volume =       "50",
  number =       "3--4",
  pages =        "279--290",
  month =        sep,
  year =         "2004",
  CODEN =        "ANMAEL",
  DOI =          "https://doi.org/10.1016/j.apnum.2004.01.003",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Sat May 14 10:50:47 MDT 2005",
  bibsource =    "http://www.sciencedirect.com/science/journal/01689274;
                 https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0168927404000066",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274",
}

@TechReport{Akutin:2004:HOM,
  author =       "Yuri Akutin and Cristina Anderson and Marius Cornea
                 and Alexey Ershov and Eugeny Gladkov and Evgeny Gvozdev
                 and Bob Hanek and John Harrison and Alexander Isaev and
                 Andrey Kolesov and Alexey Kovalev and Elena Luneva and
                 Sergey Maidanov and Andrey Naraikin and Bob Norin and
                 Pavel Shelepugin and Vladimir Sorokin and Shane Story
                 and Ping Tak Peter Tang",
  title =        "Highly Optimized Mathematical Functions for the
                 {IA-64} Architecture",
  type =         "Application note",
  number =       "245410-011",
  institution =  inst-INTEL,
  address =      inst-INTEL:adr,
  pages =        "14",
  day =          "16",
  month =        dec,
  year =         "2004",
  bibdate =      "Tue Nov 18 15:45:26 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://download.intel.com/software/opensource/numerics/libm.pdf;
                 http://www.intel.com/cd/software/products/asmo-na/eng/219868.htm;
                 http://www.intel.com/cd/software/products/asmo-na/eng/219871.htm?prn=y",
  abstract =     "Highly Optimized Mathematical Functions for the Intel
                 Itanium Architecture Intel Corporation is providing
                 Intel Itanium assembler source code to evaluate certain
                 core mathematical support functions for the C and
                 FORTRAN programming languages. The intent is that these
                 should replace less optimized implementations that
                 would normally be provided by the compiler or OS
                 vendor. The functions work well on the Itanium 2
                 processor as well as the original Itanium
                 processor.\par

                 The present document explains the rationale behind this
                 decision and summarizes important information on
                 performance and accuracy of the Intel-provided
                 functions.",
  acknowledgement = ack-nhfb,
}

@Book{Altman:2004:NIS,
  author =       "Micah Altman and Jeff Gill and Michael McDonald",
  title =        "Numerical Issues in Statistical Computing for the
                 Social Scientist",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xv + 323",
  year =         "2004",
  DOI =          "https://doi.org/10.1002/0471475769",
  ISBN =         "0-471-23633-0, 0-471-47574-2 (e-book), 0-471-47576-9
                 (e-book)",
  ISBN-13 =      "978-0-471-23633-7, 978-0-471-47574-3 (e-book),
                 978-0-471-47576-7 (e-book)",
  LCCN =         "QA276.4 .A398 2004",
  bibdate =      "Thu Oct 17 17:33:39 MDT 2019",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 z3950.loc.gov:7090/Voyage",
  abstract =     "At last --- a social scientist's guide through the
                 pitfalls of modern statistical computing. Addressing
                 the current deficiency in the literature on statistical
                 methods as they apply to the social and behavioral
                 sciences, \booktitle{Numerical Issues in Statistical
                 Computing for the Social Scientist} seeks to provide
                 readers with a unique practical guidebook to the
                 numerical methods underlying computerized statistical
                 calculations specific to these fields. The authors
                 demonstrate that knowledge of these numerical methods
                 and how they are used in statistical packages is
                 essential for making accurate inferences.",
  acknowledgement = ack-nhfb,
  subject =      "Estad{\'i}stica; Inform{\`a}tica; Ci{\`e}ncies
                 socials; M{\`e}todes estad{\'i}stics",
  tableofcontents = "1: Introduction: Consequences of Numerical
                 Inaccuracy / 1 \\
                 1.1: Importance of Understanding Computational
                 Statistics / 1 \\
                 1.2: Brief History: Duhem to the Twenty-First Century /
                 3 \\
                 1.3: Motivating Example: Rare Events Counts Models / 6
                 \\
                 2: Sources of Inaccuracy in Statistical Computation /
                 12 \\
                 2.1.1: Revealing Example: Computing the Coefficient
                 Standard Deviation / 12 \\
                 2.1.2: Some Preliminary Conclusions / 13 \\
                 2.2: Fundamental Theoretical Concepts / 15 \\
                 2.2.1: Accuracy and Precision / 15 \\
                 2.2.2: Problems, Algorithms, and Implementations / 15
                 \\
                 2.3: Accuracy and Correct Inference / 18 \\
                 2.3.1: Brief Digression: Why Statistical Inference Is
                 Harder in Practice Than It Appears / 20 \\
                 2.4: Sources of Implementation Errors / 21 \\
                 2.4.1: Bugs, Errors, and Annoyances / 22 \\
                 2.4.2: Computer Arithmetic / 23 \\
                 2.5: Algorithmic Limitations / 29 \\
                 2.5.1: Randomized Algorithms / 30 \\
                 2.5.2: Approximation Algorithms for Statistical
                 Functions / 31 \\
                 2.5.3: Heuristic Algorithms for Random Number
                 Generation / 32 \\
                 2.5.4: Local Search Algorithms / 39 \\
                 3: Evaluating Statistical Software / 44 \\
                 3.1.1: Strategies for Evaluating Accuracy / 44 \\
                 3.1.2: Conditioning / 47 \\
                 3.2: Benchmarks for Statistical Packages / 48 \\
                 3.2.1: NIST Statistical Reference Datasets / 49 \\
                 3.2.2: Benchmarking Nonlinear Problems with StRD / 51
                 \\
                 3.2.3: Analyzing StRD Test Results / 53 \\
                 3.2.4: Empirical Tests of Pseudo-Random Number
                 Generation / 54 \\
                 3.2.5: Tests of Distribution Functions / 58 \\
                 3.2.6: Testing the Accuracy of Data Input and Output /
                 60 \\
                 3.3: General Features Supporting Accurate and
                 Reproducible Results / 63 \\
                 3.4: Comparison of Some Popular Statistical Packages /
                 64 \\
                 3.5: Reproduction of Research / 65 \\
                 3.6: Choosing a Statistical Package / 69 \\
                 4: Robust Inference / 71 \\
                 4.3: Sensitivity Tests / 73 \\
                 4.3.1: Sensitivity to Alternative Implementations and
                 Algorithms / 73 \\
                 4.3.2: Perturbation Tests / 75 \\
                 4.3.3: Tests of Global Optimality / 84 \\
                 4.4: Obtaining More Accurate Results / 91 \\
                 4.4.1: High-Precision Mathematical Libraries / 92 \\
                 4.4.2: Increasing the Precision of Intermediate
                 Calculations / 93 \\
                 4.4.3: Selecting Optimization Methods / 95 \\
                 4.5: Inference for Computationally Difficult Problems /
                 103 \\
                 4.5.1: Obtaining Confidence Intervals with Ill-Behaved
                 Functions / 104 \\
                 4.5.2: Interpreting Results in the Presence of Multiple
                 Modes / 106 \\
                 4.5.3: Inference in the Presence of Instability / 114
                 \\
                 5: Numerical Issues in Markov Chain Monte Carlo
                 Estimation / 118 \\
                 5.2: Background and History / 119 \\
                 5.3: Essential Markov Chain Theory / 120 \\
                 5.3.1: Measure and Probability Preliminaries / 120 \\
                 5.3.2: Markov Chain Properties / 121 \\
                 5.3.3: The Final Word (Sort of) / 125 \\
                 5.4: Mechanics of Common MCMC Algorithms / 126 \\
                 5.4.1: Metropolis--Hastings Algorithm / 126 \\
                 5.4.2: Hit-and-Run Algorithm / 127 \\
                 5.4.3: Gibbs Sampler / 128 \\
                 5.5: Role of Random Number Generation / 129 \\
                 5.5.1: Periodicity of Generators and MCMC Effects / 130
                 \\
                 5.5.2: Periodicity and Convergence / 132 \\
                 5.5.3: Example: The Slice Sampler / 135 \\
                 5.5.4: Evaluating WinBUGS / 137 \\
                 5.6: Absorbing State Problem / 139 \\
                 5.7: Regular Monte Carlo Simulation / 140 \\
                 5.8: So What Can Be Done? / 141 \\
                 6: Numerical Issues Involved in Inverting Hessian
                 Matrices / Jeff Gill, Gary King / 143 \\
                 6.2: Means versus Modes / 145 \\
                 6.3: Developing a Solution Using Bayesian Simulation
                 Tools / 147 \\
                 6.4: What Is It That Bayesians Do? / 148 \\
                 6.5: Problem in Detail: Noninvertible Hessians / 149
                 \\
                 6.6: Generalized Inverse/Generalized Cholesky Solution
                 / 151 \\
                 6.7: Generalized Inverse / 151 \\
                 6.7.1: Numerical Examples of the Generalized Inverse /
                 154 \\
                 6.8: Generalized Cholesky Decomposition / 155 \\
                 6.8.1: Standard Algorithm / 156 \\
                 6.8.2: Gill--Murray Cholesky Factorization / 156 \\
                 6.8.3: Schnabel--Eskow Cholesky Factorization / 158 \\
                 6.8.4: Numerical Examples of the Generalized Cholesky
                 Decomposition / 158 \\
                 6.9: Importance Sampling and Sampling Importance
                 Resampling / 160 \\
                 6.9.1: Algorithm Details / 160 \\
                 6.9.2: SIR Output / 162 \\
                 6.9.3: Relevance to the Generalized Process / 163 \\
                 6.10: Public Policy Analysis Example / 163 \\
                 6.10.1: Texas / 164 \\
                 6.10.2: Florida / 168 \\
                 6.11: Alternative Methods / 171 \\
                 6.11.1: Drawing from the Singular Normal / 171 \\
                 6.11.2: Aliasing / 173 \\
                 6.11.3: Ridge Regression / 173 \\
                 6.11.4: Derivative Approach / 174 \\
                 6.11.5: Bootstrapping / 174 \\
                 6.11.6: Respecification (Redux) / 175 \\
                 7: Numerical Behavior of King's EI Method / 177 \\
                 7.2: Ecological Inference Problem and Proposed
                 Solutions / 179 \\
                 7.3: Numeric Accuracy in Ecological Inference / 180 \\
                 7.3.1: Case Study 1: Examples from King (1997) / 182
                 \\
                 7.3.2: Nonlinear Optimization / 186 \\
                 7.3.3: Pseudo-Random Number Generation / 187 \\
                 7.3.4: Platform and Version Sensitivity / 188 \\
                 7.4: Case Study 2: Burden and Kimball (1998) / 189 \\
                 7.4.1: Data Perturbation / 191 \\
                 7.4.2: Option Dependence / 194 \\
                 7.4.3: Platform Dependence / 195 \\
                 7.4.4: Discussion: Summarizing Uncertainty / 196 \\
                 8: Some Details of Nonlinear Estimation / B. D.
                 McCullough / 199 \\
                 8.2: Overview of Algorithms / 200 \\
                 8.3: Some Numerical Details / 204 \\
                 8.4: What Can Go Wrong? / 206 \\
                 8.5: Four Steps / 210 \\
                 8.5.1 Step 1: Examine the Gradient / 211 \\
                 8.5.2 Step 2: Inspect the Trace / 211 \\
                 8.5.3 Step 3: Analyze the Hessian / 212 \\
                 8.5.4 Step 4: Profile the Objective Function / 212 \\
                 8.6: Wald versus Likelihood Inference / 215 \\
                 9: Spatial Regression Models / James P. LeSage / 219
                 \\
                 9.2: Sample Data Associated with Map Locations / 219
                 \\
                 9.2.1: Spatial Dependence / 219 \\
                 9.2.2: Specifying Dependence Using Weight Matrices /
                 220 \\
                 9.2.3: Estimation Consequences of Spatial Dependence /
                 222 \\
                 9.3: Maximum Likelihood Estimation of Spatial Models /
                 223 \\
                 9.3.1: Sparse Matrix Algorithms / 224 \\
                 9.3.2: Vectorization of the Optimization Problem / 225
                 \\
                 9.3.3: Trade-offs between Speed and Numerical Accuracy
                 / 226 \\
                 9.3.4: Applied Illustrations / 228 \\
                 9.4: Bayesian Spatial Regression Models / 229 \\
                 9.4.1: Bayesian Heteroscedastic Spatial Models / 230
                 \\
                 9.4.2: Estimation of Bayesian Spatial Models / 231 \\
                 9.4.3: Conditional Distributions for the SAR Model /
                 232 \\
                 9.4.4: MCMC Sampler / 234 \\
                 9.4.5: Illustration of the Bayesian Model / 234 \\
                 10: Convergence Problems in Logistic Regression / Paul
                 Allison / 238 \\
                 10.2: Overview of Logistic Maximum Likelihood
                 Estimation / 238 \\
                 10.3: What Can Go Wrong? / 240 \\
                 10.4: Behavior of the Newton--Raphson Algorithm under
                 Separation / 243 \\
                 10.4.1: Specific Implementations / 244 \\
                 10.4.2: Warning Messages / 244 \\
                 10.4.3: False Convergence / 246 \\
                 10.4.4: Reporting of Parameter Estimates and Standard
                 Errors / 247 \\
                 10.4.5: Likelihood Ratio Statistics / 247 \\
                 10.5: Diagnosis of Separation Problems / 247 \\
                 10.6: Solutions for Quasi-Complete Separation / 248 \\
                 10.6.1: Deletion of Problem Variables / 248 \\
                 10.6.2: Combining Categories / 248 \\
                 10.6.3: Do Nothing and Report Likelihood Ratio
                 Chi-Squares / 249 \\
                 10.6.4: Exact Inference / 249 \\
                 10.6.5: Bayesian Estimation / 250 \\
                 10.6.6: Penalized Maximum Likelihood Estimation / 250
                 \\
                 10.7: Solutions for Complete Separation / 251 \\
                 10.8: Extensions / 252 \\
                 11: Recommendations for Replication and Accurate
                 Analysis / 253 \\
                 11.1: General Recommendations for Replication / 253 \\
                 11.1.1: Reproduction, Replication, and Verification /
                 254 \\
                 11.1.2: Recreating Data / 255 \\
                 11.1.3: Inputting Data / 256 \\
                 11.1.4: Analyzing Data / 257 \\
                 11.2: Recommendations for Producing Verifiable Results
                 / 259 \\
                 11.3: General Recommendations for Improving the Numeric
                 Accuracy of Analysis / 260 \\
                 11.4: Recommendations for Particular Statistical Models
                 / 261 \\
                 11.4.1: Nonlinear Least Squares and Maximum Likelihood
                 / 261 \\
                 11.4.2: Robust Hessian Inversion / 262 \\
                 11.4.3: MCMC Estimation / 263 \\
                 11.4.4: Logistic Regression / 265 \\
                 11.4.5: Spatial Regression / 266 \\
                 Where Do We Go from Here? / 266 \\
                 Bibliography / 267 \\
                 Author Index / 303 \\
                 Subject Index / 315",
}

@Article{Assimakopoulos:2004:IRM,
  author =       "C. Assimakopoulos and F.-N. Pavlidou",
  title =        "Integrated rounding method for real number bit
                 distribution over {DMT} systems",
  journal =      j-ELECT-LETTERS,
  volume =       "40",
  number =       "19",
  pages =        "1235--1236",
  day =          "16",
  month =        sep,
  year =         "2004",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Jul 16 11:25:05 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  summary =      "Most bit loading algorithms proposed in the literature
                 originally distribute a non-integer number of bits to
                 the subcarriers of a discrete multitone (DMT) system
                 and then, employing an iterative algorithm they round
                 these assigned numbers to \ldots{}",
}

@Article{Astola:2004:FAE,
  author =       "J. T. Astola and K. Egiazarian and M. Stankovi{\'c}
                 and R. S. Stankovi{\'c}",
  title =        "{Fibonacci} Arithmetic Expressions",
  journal =      j-AUTOMATION-REMOTE-CTL,
  volume =       "65",
  number =       "6",
  pages =        "842--856",
  month =        jun,
  year =         "2004",
  CODEN =        "AURCAT",
  ISSN =         "0005-1179 (print), 1608-3032 (electronic)",
  ISSN-L =       "0005-1179",
  bibdate =      "Thu Aug 07 19:27:43 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this paper, we extend the arithmetic (AR)
                 expressions for functions on finite dyadic groups to
                 functions used in Fibonacci interconnection topologies.
                 We have introduced the Fibonacci-Arithmetic (FibAR)
                 expressions for representation of these functions. We
                 discussed the optimization of FibARs with respect to
                 the number of non-zero coefficients through the
                 Fixed-Polarity FibARs defined by using different
                 polarities for the Fibonacci variables. In this way, we
                 provide a base to extend the application of ARs and
                 related powerful CAD design tools for switching
                 functions to functions in Fibonacci interconnection
                 topologies.",
  acknowledgement = ack-nhfb,
  fjournal =     "Automation and Remote Control",
}

@Article{Avot-Chotin:2004:HID,
  author =       "Roselyne Avot-Chotin and Habib Mehrez",
  title =        "Hardware Implementation of Discrete Stochastic
                 Arithmetic",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "37",
  number =       "1--4",
  pages =        "21--33",
  month =        dec,
  year =         "2004",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Dec 6 07:00:28 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/58/A/3/abstract.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  remark =       "Special Issue: SCAN'2002 International Conference
                 (Guest Editors: Ren {\'e} Alt and Jean-Luc Lamotte)",
}

@InProceedings{Bachega:2004:HPS,
  author =       "L. Bachega and Siddhartha Chatterjee and K. A. Dockser
                 and J. A. Gunnels and Manish Gupta and F. G. Gustavson
                 and C. A. Lapkowski and G. K. Liu and M. P. Mendell and
                 C. D. Wait and T. J. C. Ward",
  booktitle =    "{PACT 2004}. Proceedings. 13th International
                 Conference on Parallel Architecture and Compilation
                 Techniques, 29 Sept.--3 Oct. 2004",
  title =        "A high-performance {SIMD} floating point unit for
                 {BlueGene/L}: architecture, compilation, and algorithm
                 design",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "85--96",
  year =         "2004",
  bibdate =      "Wed Apr 27 18:18:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We describe the design, implementation, and evaluation
                 of a dual-issue SIMD-like extension of the PowerPC 440
                 floating-point unit (FPU) core. This extended FPU is
                 targeted at both IBM's massively parallel BlueGene/L
                 machine as well as more pervasive embedded platforms.",
  acknowledgement = ack-nhfb,
}

@Article{Bajard:2004:FRI,
  author =       "J.-C. Bajard and L. Imbert",
  title =        "A full {RNS} implementation of {RSA}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "53",
  number =       "6",
  pages =        "769--774",
  month =        jun,
  year =         "2004",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2004.2",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 08:12:38 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1288551",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Misc{Bernstein:2004:FPA,
  author =       "Daniel J. Bernstein",
  title =        "Floating-Point Arithmetic and Message Authentication",
  pages =        "21",
  day =          "18",
  month =        sep,
  year =         "2004",
  bibdate =      "Mon May 13 10:25:28 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/hash.bib",
  note =         "To be incorporated into the author's
                 \booktitle{High-Speed Cryptography} book. [As of 13 May
                 2024, this book seems not to have been published.]",
  URL =          "https://cr.yp.to/antiforgery/hash127-20040918.pdf",
  abstract =     "There is a well-known class of message authentication
                 systems guaranteeing that attackers will have a
                 negligible chance of successfully forging a message.
                 This paper shows how one of these systems can hash
                 messages at extremely high speed --- much more quickly
                 than previous systems at the same security level ---
                 using IEEE floating-point arithmetic. This paper also
                 presents a survey of the literature in a unified
                 mathematical framework.",
  acknowledgement = ack-nhfb,
  remark =       "From the first page: ``What distinguishes $ h_r $ is
                 its speed: it is the first high-security system that
                 offers better speed than the MD5-based systems in
                 common use today.'' The section on Priority dates on
                 the second page notes earlier work back to April
                 1999.",
}

@TechReport{Bernstein:2004:RRH,
  author =       "Daniel J. Bernstein",
  title =        "Removing Redundancy in High-Precision {Newton}
                 Iteration",
  type =         "Technical Report",
  institution =  "Department of Mathematics, Statistics, and Computer
                 Science (M/C 249), The University of Illinois at
                 Chicago",
  address =      "Chicago, IL 60607-7045",
  pages =        "2",
  day =          "9",
  month =        mar,
  year =         "2004",
  bibdate =      "Sun Sep 10 07:51:20 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also \cite{Hanrot:2004:NIR}.",
  URL =          "http://cr.yp.to/fastnewton.html;
                 http://cr.yp.to/fastnewton/fastnewton-20040309.pdf",
  abstract =     "This paper presents new algorithms for several
                 high-precision operations in the power series ring $
                 C[[x]] $. Compared to computing $n$ coefficients of a
                 product in $ C[[x]] $, computing $n$ coefficients of a
                 reciprocal in $ C[[x]] $ takes $ 1.5 + o(1) $ times
                 longer; a quotient or logarithm, $ 2.16666 \cdots {} +
                 o(1) $ times longer; a square root, $ 1.83333 \cdots {}
                 + o(1) $ times longer; an exponential, $ 2.83333 \cdots
                 {} + o(1) $ times longer. Previous algorithms had worse
                 constants. The same ideas apply to high-precision
                 computations in $R$, $ Q_p $, etc.",
  acknowledgement = ack-nhfb,
}

@TechReport{Bernstein:2004:SRT,
  author =       "Daniel J. Bernstein",
  title =        "Scaled Remainder Trees",
  type =         "Report",
  institution =  "University of Sydney",
  address =      "Sydney, NSW, Australia",
  day =          "20",
  month =        apr,
  year =         "2004",
  bibdate =      "Tue Oct 15 07:27:53 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Draft for \booktitle{Mathematics of Computation}, but
                 never published in that journal.",
  URL =          "http://cr.yp.to/arith/scaledmod-20040820.pdf",
  abstract =     "It is well known that one can compute $ U \bmod p_1 $,
                 $ U \bmod p_2 $, \ldots{} in time $ n(\lg n)^{2 + o(1)}
                 $ where $n$ is the number of bits in $U$, $ p_1$, $
                 p_2$, \ldots{}. Here $U$, $ p_1$, $ p_2$, \ldots{} can
                 be integers or polynomials over a fixed finite field.
                 Bostan, Lecerf, and Schost recently introduced an
                 algorithm for the polynomial case that takes time $
                 n(\lg n)^{2 + o(1)}$ with a smaller $ o(1)$. They did
                 not claim any similar speedup for integers; their
                 algorithm uses polynomial reversal and
                 coefficient-matrix transposition, neither of which
                 applies to integers. This paper presents a simpler
                 algorithm that achieves the same speedup and that works
                 for both polynomials and integers. This paper then
                 points out several redundancies that can be eliminated
                 from the algorithm, saving even more time.",
  acknowledgement = ack-nhfb,
  remark =       "Paul Zimmermann reported on the gmp-devel mailing list
                 on Tue, 15 Oct 2019 10:40:48 +0200 that the remainder
                 algorithm in this report is rediscovered in
                 \cite{Lemire:2019:FRD}.",
}

@TechReport{Bertin:2004:FPL,
  author =       "C. Bertin and Nicolas Brisebarre and B. Dupont de
                 Dinechin and C.-P. Jeannerod and C. Monat and
                 Jean-Michel Muller and S. Raina and A. Tisserand",
  title =        "A floating-point library for integer processors",
  type =         "Research Report",
  number =       "RR2004-37",
  institution =  "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "69364 Lyon Cedex 07, France",
  pages =        "2 + 11",
  month =        jul,
  year =         "2004",
  bibdate =      "Mon Dec 06 11:02:55 2004",
  bibsource =    "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-37.ps.gz",
  abstract =     "This paper presents a C library for the software
                 support of single precision floating-point (FP)
                 arithmetic on processors without FP hardware units such
                 as VLIW or DSP processor cores for embedded
                 applications. This library provides several levels of
                 compliance to the IEEE 754 FP standard. The complete
                 specifications of the standard can be used or just some
                 relaxed characteristics such as restricted rounding
                 modes or computations without denormal numbers. This
                 library is evaluated on the ST200 VLIW processors from
                 STMicroelectronics.",
  acknowledgement = ack-nhfb,
  keywords =     "addition; Computer arithmetic; division; DSP;
                 floating-point arithmetic; integer processor;
                 multiplication; square-root; VLIW",
  remark =       "Published in ``Advanced Signal Processing Algorithms,
                 Architectures, and Implementations XIV, Spie 2004.''",
}

@TechReport{Beuchat:2004:FMM,
  author =       "Jean-Luc Beuchat",
  title =        "A Family of Modulo $ (2^n + 1) $ Multipliers",
  type =         "Research Report",
  number =       "RR2004-39",
  institution =  "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "69364 Lyon Cedex 07, France",
  pages =        "2 + 13",
  year =         "2004",
  bibdate =      "Mon Dec 06 11:05:32 2004",
  bibsource =    "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-39.ps.gz",
  abstract =     "In this paper, we first describe a novel modulo $ (2^n
                 + 1) $ addition algorithm suited to FPGA and ASIC
                 implementations, and discuss several architectures of
                 multioperand modulo $ (2^n + 1) $ adders. Then, we
                 propose three implementations of a modulo $ (2^n + 1) $
                 multiplication algorithm based on a paper by A.
                 Wrzyszcz and D. Milford. The first operator is based on
                 an $ n \times n $ multiplication and a subsequent
                 modulo $ (2^n + 1) $ correction, and takes advantage of
                 the arithmetic logic embedded in Spartan or Virtex
                 FPGAs. The second operator computes a sum of
                 modulo-reduced partial products by means of a
                 multioperand modulo $ (2^n + 1) $ adder. Then,
                 radix-$4$ modified Booth recoding reduces the number of
                 partial products, while making their generation more
                 complex. Finally, we provide a comparison of this
                 family of algorithms with existing solutions.",
  acknowledgement = ack-nhfb,
  keywords =     "FPGA Implementation; Modular Arithmetic; Modulo
                 $(2^n+1)$ Addition; Modulo $(2^n+1)$ Multiplication",
}

@Article{Boggs:2004:MIP,
  author =       "Darrell Boggs and Aravindh Baktha and Jason Hawkins
                 and Deborah T. Marr and J. Alan Miller and Patrice
                 Roussel and Ronak Singhal and Bret Toll and K. S.
                 Venkatraman",
  title =        "The Microarchitecture of the {Intel{\reg}
                 Pentium{\reg} 4} Processor on 90nm Technology",
  journal =      j-INTEL-TECH-J,
  volume =       "8",
  number =       "1",
  pages =        "1--17",
  month =        feb,
  year =         "2004",
  bibdate =      "Mon Jul 11 08:46:53 2005",
  bibsource =    "http://developer.intel.com/technology/itj/archive/2004.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://developer.intel.com/technology/itj/2004/volume08issue01/foreword.htm",
  acknowledgement = ack-nhfb,
  keywords =     "complex arithmetic; floating-point arithmetic;
                 Hyper-Threading Technology; microarchitecture;
                 Pentium{\reg} 4 processor",
  remark =       "From pp. 10--11: ``Five instructions have been added
                 to significantly accelerate complex arithmetic. Two
                 instructions (addsubps and addsubpd) perform a mix of
                 floating-point addition and subtraction, hence removing
                 the need for changing the sign of some operands. Three
                 others (movsldup, movshdup, movddup), in their memory
                 version, combine loads with some level of duplication,
                 hence saving the need for a shuffle instruction on the
                 loaded data.''",
}

@InProceedings{Boldo:2004:BGB,
  author =       "Sylvie Boldo",
  title =        "Bridging the gap between formal specification and
                 bit-level floating-point arithmetic",
  crossref =     "Frougny:2004:RCR",
  pages =        "22--36",
  year =         "2004",
  bibdate =      "Fri Nov 17 07:00:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_04_boldo.pdf",
  abstract =     "Floating-point arithmetic is defined by the IEEE-754
                 standard and has often been formalized. We propose a
                 new Coq formalization based on the bit-level
                 representation of the standard and we prove strong
                 links between this new formalization and a previous
                 high-level one. In this process, we have defined
                 functions for any rounding mode described by the
                 standard. Our library can now be applied to certify
                 both software and hardware. Developing results in those
                 two dramatically different directions, like no other
                 formal development so far, guarantees that nothing was
                 forgotten or poorly specified in our formalization. It
                 also lets us compare our work with the existing
                 bit-level formalizations developed with other proof
                 assistants.",
  acknowledgement = ack-nhfb,
  keywords =     "Coq; floating-point; formal proof checking; IEEE-754",
}

@PhdThesis{Boldo:2004:PFA,
  author =       "Sylvie Boldo",
  title =        "Preuves formelles en arithm{\'e}tiques {\`a} virgule
                 flottante. ({French}) [Formal proofs in floating-point
                 arithmetic]",
  type =         "{Ph.D.} thesis",
  school =       "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "69364 Lyon Cedex 07, France",
  pages =        "????",
  month =        nov,
  year =         "2004",
  bibdate =      "Tue Nov 23 09:53:06 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "French",
}

@Article{Boldo:2004:PTC,
  author =       "Sylvie Boldo and Marc Daumas",
  title =        "Properties of two's complement floating point
                 notations",
  journal =      j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER,
  volume =       "5",
  number =       "2--3",
  pages =        "237--246",
  month =        mar,
  year =         "2004",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s10009-003-0120-y",
  ISSN =         "1433-2779 (print), 1433-2787 (electronic)",
  ISSN-L =       "1433-2779",
  bibdate =      "Tue Nov 23 09:56:44 2004",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=journal&issn=1433-2779;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://perso.ens-lyon.fr/marc.daumas/SoftArith/BolDau04a.pdf",
  abstract =     "Few designs, mostly those of Texas Instruments,
                 continue to use two's complement floating point units.
                 Such units are simpler to build and to validate, but
                 they do not comply to the dominant IEEE standard for
                 floating point arithmetic. We compare some properties
                 of the two systems in this text. Some features are
                 lost, but others remain unchanged. One strong example
                 is the case of Sterbenz' theorem and our recent
                 extension. We show in the paper that the theorem and
                 its extension hold for the two's complement
                 architecture. Still, users should ensure that results
                 are large enough on circuits that do not implement
                 gradual underflow. Theorems have been proven and
                 validated using the Coq automatic proof checker.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal on Software Tools for Technology
                 Transfer: STTT",
  journal-URL =  "http://link.springer.com/journal/10009",
}

@Article{Boldo:2004:STQ,
  author =       "Sylvie Boldo and Marc Daumas",
  title =        "A Simple Test Qualifying the Accuracy of {Horner}'s
                 Rule for Polynomials",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "37",
  number =       "1--4",
  pages =        "45--60",
  month =        dec,
  year =         "2004",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Dec 6 06:44:22 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 Ingenta database",
  note =         "SCAN2002 International Conference (Guest Editors: Rene
                 Alt and Jean-Luc Lamotte).",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "floating-point testing",
  pagecount =    "16",
}

@TechReport{Boldo:2004:WDR,
  author =       "Sylvie Boldo and Guillaume Melquiond",
  title =        "When double rounding is odd",
  type =         "Research Report",
  number =       "RR2004-48",
  institution =  "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "69364 Lyon Cedex 07, France",
  pages =        "2 + 7",
  month =        nov,
  year =         "2004",
  bibdate =      "Mon Dec 06 11:18:07 2004",
  bibsource =    "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-48.pdf;
                 https://inria.hal.science/inria-00070603v2/file/BolMel.pdf",
  abstract =     "Double rounding consists in a first rounding in an
                 intermediate extended precision and then a second
                 rounding in the working precision. The natural question
                 is then of the precision and correctness of the final
                 result. Unfortunately, the used double rounding
                 algorithms do not obtain a correct rounding of the
                 initial value. We prove an efficient algorithm for the
                 double rounding to give the correct rounding to the
                 nearest value assuming the first rounding is to odd. As
                 this rounding is unusual and this property is
                 surprising, we formally proved this property using the
                 Coq automatic proof checker.",
  acknowledgement = ack-nhfb,
  keywords =     "Coq; correct rounding; double rounding;
                 Floating-point; floating-point arithmetic; formal
                 proof; round-to-odd (RO(x))",
}

@Article{Brisebarre:2004:ACR,
  author =       "Nicolas Brisebarre and Jean-Michel Muller and Saurabh
                 Kumar Raina",
  title =        "Accelerating correctly rounded floating-point division
                 when the divisor is known in advance",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "53",
  number =       "8",
  pages =        "1069--1072",
  month =        aug,
  year =         "2004",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2004.37",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 08:12:41 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1306999",
  abstract =     "We present techniques for accelerating the
                 floating-point computation of $ x / y $ when $y$ is
                 known before $x$. The proposed algorithms are oriented
                 toward architectures with available fused-mac
                 operations. The goal is to get exactly the same result
                 as with \ldots{}",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "We present techniques for accelerating the
                 floating-point computation of x/y when y is known
                 before x. The proposed algorithms are oriented toward
                 architectures with available fused-mac operations. The
                 goal is to get exactly the same result as with
                 \ldots{}",
}

@TechReport{Brisebarre:2004:CRM,
  author =       "Nicolas Brisebarre and Jean-Michel Muller",
  title =        "Correctly rounded multiplication by arbitrary
                 precision constants",
  type =         "Research Report",
  number =       "RR2004-44",
  institution =  "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "69364 Lyon Cedex 07, France",
  pages =        "2 + 14",
  month =        oct,
  year =         "2004",
  bibdate =      "Mon Dec 06 11:11:37 2004",
  bibsource =    "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-44.pdf",
  abstract =     "We introduce an algorithm for multiplying a
                 floating-point number $x$ by a constant $C$ that is not
                 exactly representable in floating-point arithmetic. Our
                 algorithm uses a multiplication and a fused multiply
                 accumulate instruction. We give methods for checking
                 whether, for a given value of $C$ and a given
                 floating-point format, our algorithm returns a
                 correctly rounded result for any $x$. When it does not,
                 our methods give the values $x$ for which the
                 multiplication is not correctly rounded.",
  acknowledgement = ack-nhfb,
  keywords =     "Computer Arithmetic; Correct rounding; Floating-point
                 Arithmetic; Fused-mac; Multiplication by a constant",
}

@TechReport{Bruguera:2004:DDF,
  author =       "Javier D. Bruguera and Tom{\'a}s Lang",
  title =        "Double-Datapath Floating-point multiply-add fused:
                 latency reduction for floating-point addition",
  type =         "Report",
  institution =  "Grupo de Arquitectura de Computadores, Universidad de
                 Santiago de Compostela",
  address =      "Edificio Monte de la Condesa, Campus Sur, 15782
                 Santiago de Compostela, Spain",
  pages =        "24",
  year =         "2004",
  bibdate =      "Fri Jun 24 10:10:03 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www-gpaa.dec.usc.es/arquivos/articulos/2004/gac2004-i03.ps;
                 http://www.ac.usc.es/arquivos/articulos/2004/gac2004-i03.ps",
  acknowledgement = ack-nhfb,
  keywords =     "computer arithmetic; floating-point functional units;
                 multiply-add fused (MAF) operation; VLSI design",
}

@InProceedings{Busaba:2004:DFP,
  author =       "Fadi Busaba and Timothy Slegel and Steven Carlough and
                 Christopher Krygowski and John G. Rell",
  title =        "The design of the fixed point unit for the z990
                 microprocessor",
  crossref =     "ACM:2004:GVN",
  pages =        "364--367",
  year =         "2004",
  bibdate =      "Thu Aug 07 18:08:54 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The paper presents the design of the Fixed Point Unit
                 (FXU) for the IBM eServer z990 microprocessor
                 (announced in 2Q '03) that runs at 1.2 GHz [2]. The FXU
                 is capable of executing two Register-Memory
                 instructions including arithmetic instructions and a
                 branch instruction in a single cycle. The FXU executes
                 a total of 369 instructions that operate on variable
                 size operands (1 to 256 bytes). The instruction set
                 include decimal arithmetic with multiplies and divides,
                 binary arithmetic, shifts and rotates, loads/stores,
                 branches, long moves, logical operations, convert
                 instructions, and other special instructions. The FXU
                 consists of 64-bit dataflow stack that is custom
                 designed and a control stack that is synthesized. The
                 current FXU is the first superscalar design for the
                 CMOS z-series machines, has a new improved decimal
                 unit, and has for the first time a $ 16 \times 64 $ bit
                 binary multiplier.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal arithmetic; microprocessor; superscalar FXU",
}

@InProceedings{Cagnard:2004:ABF,
  author =       "B. Cagnard and P. Simonnet",
  title =        "Automata, {Borel} functions and real numbers in
                 {Pisot} base",
  crossref =     "Frougny:2004:RCR",
  pages =        "37--54",
  year =         "2004",
  bibdate =      "Fri Nov 17 07:00:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_05_cagnard.pdf",
  abstract =     "This note is about functions $ f : A^\omega \to
                 B^\omega $ whose graph is recognized by a B{\"u}chi
                 finite automaton on the product alphabet $ A \times B
                 $. These functions are Baire class 2 in the Baire
                 hierarchy of Borel functions and it is decidable
                 whether such functions are continuous or not. In 1920
                 W. Sierpinski showed that a function $ f : \mathbb {R}
                 \to \mathbb {R} $ is Baire class 1 if and only if both
                 the overgraph and the undergraph of $f$ are $ F_\sigma
                 $. We show that such characterization is also true for
                 functions on infinite words if we replace the real
                 ordering by the lexicographical ordering on $ B^\omega
                 $. From this we deduce that it is decidable whether
                 such functions are of Baire class 1 or not. We extend
                 this result to reals functions definable by automata in
                 Pisot base.",
  acknowledgement = ack-nhfb,
  keywords =     "automata; Borel function; Borel set; sequential
                 machine",
}

@InProceedings{Cao:2004:DRB,
  author =       "B. Cao and T. Srikanthan and Chip-Hong Chang",
  booktitle =    "{ISCAS '04}, Proceedings of the 2004 International
                 Symposium on Circuits and Systems, 23--26 May 2004",
  title =        "Design of residue-to-binary converter for a new
                 $5$-moduli superset residue number system",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "II-841--4",
  year =         "2004",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/IECON.2004.1432111",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper presents an efficient residue-to-binary
                 (R/B) conversion algorithm for a new 5-moduli superset
                 {2/sup n/-1, 2/sup n/, 2/sup n/+1, 2/sup n+1/-1, 2/sup
                 n-1/-1} residue number system (RNS) when n is even. The
                 new moduli set is provided for \ldots{}",
}

@InProceedings{Cardarilli:2004:LPI,
  author =       "G. C. Cardarilli and A. Del Re and A. Nannarelli and
                 M. Re",
  booktitle =    "{ISCAS '04}, Proceedings of the 2004 International
                 Symposium on Circuits and Systems, 23--26 May 2004",
  title =        "Low-power implementation of polyphase filters in
                 {Quadratic Residue Number} system",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "II-725--8",
  year =         "2004",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/TWC.2004.833509",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The aim of this work is the reduction of the power
                 dissipated in digital filters, while maintaining the
                 timing unchanged. A polyphase filter bank in the
                 Quadratic Residue Number System (QRNS) has been
                 implemented and then compared, in terms of \ldots{}",
}

@InProceedings{Chakraborty:2004:GAL,
  author =       "M. Chakraborty and A. Mitra",
  booktitle =    "Proceedings. ({ICASSP '04}). {IEEE} International
                 Conference on Acoustics, Speech, and Signal Processing,
                 17--21 May 2004",
  title =        "The gradient adaptive lattice algorithm in block
                 floating point format",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "II-849--II-852",
  year =         "2004",
  bibdate =      "Wed Apr 27 18:18:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chirca:2004:SLP,
  author =       "K. Chirca and M. Schulte and J. Glossner and S. Mamidi
                 and S. Vassiliadis",
  title =        "A Static Low-Power, High-Performance 32-bit Carry Skip
                 Adder",
  crossref =     "Selvaraj:2004:PES",
  pages =        "615--619",
  year =         "2004",
  bibdate =      "Sun Mar 04 20:52:48 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2004-12.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Clinger:2004:HRF,
  author =       "William D. Clinger",
  title =        "How to read floating point numbers accurately",
  journal =      j-SIGPLAN,
  volume =       "39",
  number =       "4",
  pages =        "360--371",
  month =        apr,
  year =         "2004",
  CODEN =        "SINODQ",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Tue Apr 12 09:38:13 MDT 2005",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}

@Article{Clinger:2004:RHR,
  author =       "William D. Clinger",
  title =        "Retrospective: How to read floating point numbers
                 accurately",
  journal =      j-SIGPLAN,
  volume =       "39",
  number =       "4",
  pages =        "360--371",
  month =        apr,
  year =         "2004",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/989393.989430",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Wed May 26 06:21:19 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Best of PLDI 1979--1999. Reprint of, and retrospective
                 on, \cite{Clinger:1990:HRF}.",
  abstract =     "Converting decimal scientific notation into binary
                 floating point is nontrivial, but this conversion can
                 be performed with the best possible accuracy without
                 sacrificing efficiency. Consider the problem of
                 converting decimal scientific notation for a number
                 into the best binary floating point approximation to
                 that number, for some fixed precision. This problem
                 cannot be solved using arithmetic of any fixed
                 precision. Hence the IEEE Standard for Binary
                 Floating-Point Arithmetic does not require the result
                 of such a conversion to be the best approximation. This
                 paper presents an efficient algorithm that always finds
                 the best approximation. The algorithm uses a few extra
                 bits of precision to compute an IEEE-conforming
                 approximation while testing an intermediate result to
                 determine whether the approximation could be other than
                 the best. If the approximation might not be the best,
                 then the best approximation is determined by a few
                 simple operations on multiple-precision integers, where
                 the precision is determined by the input. When using 64
                 bits of precision to compute IEEE double precision
                 results, the algorithm avoids higher-precision
                 arithmetic over 99\% of the time. The input problem
                 considered by this paper is the inverse of an output
                 problem considered by Steele and White: Given a binary
                 floating point number, print a correctly rounded
                 decimal representation of it using the smallest number
                 of digits that will allow the number to be read without
                 loss of accuracy. The Steele and White algorithm
                 assumes that the input problem is solved; an imperfect
                 solution to the input problem, as allowed by the IEEE
                 standard and ubiquitous in current practice, defeats
                 the purpose of their algorithm.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}

@Article{Cowlishaw:2004:FFE,
  author =       "Mike Cowlishaw and Joshua Bloch and Joseph D. Darcy",
  title =        "Fixed, Floating, and Exact Computation in {Java}'s
                 {{\em BigDecimal\/}}: Calculations just got easier",
  journal =      j-DDJ,
  volume =       "29",
  number =       "7",
  pages =        "22, 24, 26--27",
  month =        jul,
  year =         "2004",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Thu Jun 03 07:31:12 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
  keywords =     "decimal floating-point arithmetic",
}

@Article{Croot:2004:ACC,
  author =       "Ernie Croot and Ren-Cang Li and H. J. Hui June Zhu",
  title =        "The {\em abc\/} conjecture and correctly rounded
                 reciprocal square roots",
  journal =      j-THEOR-COMP-SCI,
  volume =       "315",
  number =       "2--3",
  pages =        "405--417",
  day =          "6",
  month =        may,
  year =         "2004",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Thu Nov 4 10:19:15 MST 2004",
  bibsource =    "http://www.sciencedirect.com/science/journal/03043975;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The reciprocal square root calculation $ \alpha = 1 /
                 \sqrt {x} $ is very common in scientific computations.
                 Having a correctly rounded implementation of it is of
                 great importance in producing numerically predictable
                 code among today's heterogeneous computing environment.
                 Existing results suggest that to get the correctly
                 rounded $ \alpha $ in a floating point number system
                 with $p$ significant bits, we may have to compute up to
                 $ 3 p + 1 $ leading bits of $ \alpha $. However,
                 numerical evidence indicates the actual number may be
                 as small as $ 2 p $ plus a few more bits. This paper
                 attempts to bridge the gap by showing that this is
                 indeed true, assuming the {\em abc\/} conjecture which
                 is widely purported to hold. (But our results do not
                 tell exactly how many more bits beyond the $ 2 p $
                 bits, due to the fact that the constants involved in
                 the conjecture are ineffective.) Along the way, rough
                 bounds which are comparable to the existing ones are
                 also proven. The technique used here is a combination
                 of the classical Liouville's estimation and
                 contemporary number theory.",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}

@TechReport{Daumas:2004:GFCa,
  author =       "Marc Daumas and Guillaume Melquiond",
  title =        "Generating formally certified bounds on values and
                 round-off errors",
  type =         "Research Report",
  number =       "RR2004-36",
  institution =  "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "69364 Lyon Cedex 07, France",
  pages =        "2 + 24",
  month =        jul,
  year =         "2004",
  bibdate =      "Mon Dec 06 10:59:57 2004",
  bibsource =    "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-36.ps.gz",
  abstract =     "We present a new tool that generates bounds on the
                 values and the round-off errors of programs using
                 floating point operations. The tool is based on forward
                 error analysis and interval arithmetic. The novelty of
                 our tool is that it produces a formal proof of the
                 bounds that can be checked independently using an
                 automatic proof checker such as Coq and a complete
                 model of floating point arithmetic. For the first time
                 ever, we can easily certify that simple numerical
                 programs such as the ones usually found in real time
                 applications do not overflow and that round-off errors
                 are below acceptable thresholds. Such level of quality
                 should be compulsory on safety critical applications.
                 As our tool is easy to handle, it could also be used
                 for many pieces of software.",
  acknowledgement = ack-nhfb,
  keywords =     "Certification; Formal proof; Overflow; Round-off
                 error; Safety critical",
}

@InProceedings{Daumas:2004:GFCb,
  author =       "Marc Daumas and Guillaume Melquiond",
  title =        "Generating formally certified bounds on values and
                 round-off errors",
  crossref =     "Frougny:2004:RCR",
  pages =        "55--70",
  year =         "2004",
  bibdate =      "Fri Nov 17 07:00:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_06_daumas.pdf",
  abstract =     "We present a new tool that generates bounds on the
                 values and the round-off errors of programs using
                 floating point operations. The tool is based on forward
                 error analysis and interval arithmetic. The novelty of
                 our tool is that it produces a formal proof of the
                 bounds that can be checked independently using an
                 automatic proof checker such as Coq and a complete
                 model of floating point arithmetic. For the first time
                 ever, we can easily certify that simple numerical
                 programs such as the ones usually found in real time
                 applications do not overflow and that round-off errors
                 are contained. Such level of quality should be
                 compulsory on safety critical applications. As our tool
                 is easy to handle, it could be used for many pieces of
                 software.",
  acknowledgement = ack-nhfb,
  keywords =     "Certification; Formal proof; Overflow; Round-off
                 error; Safety critical",
}

@Misc{deDinechin:2004:C,
  author =       "Florent de Dinechin",
  title =        "crlibm",
  howpublished = "World-Wide Web software project archive.",
  day =          "16",
  month =        apr,
  year =         "2004",
  bibdate =      "Fri Jun 24 14:38:41 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://lipforge.ens-lyon.fr/projects/crlibm/",
  abstract =     "The purpose of this project is to offer a mathematical
                 library (libm) with proven, IEEE-754 compliant, correct
                 rounding in the four rounding modes, and performances
                 comparable to standard libms.",
  acknowledgement = ack-nhfb,
}

@TechReport{deDinechin:2004:FCR,
  author =       "Florent de Dinechin and David Defour and Christoph
                 Lauter",
  title =        "Fast correct rounding of elementary functions in
                 double precision using double-extended arithmetic",
  type =         "Research Report",
  number =       "RR2004-10",
  institution =  "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "69364 Lyon Cedex 07, France",
  pages =        "2 + 12",
  month =        mar,
  year =         "2004",
  bibdate =      "Mon Dec 06 10:49:12 2004",
  bibsource =    "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-10.pdf",
  abstract =     "This article shows that IEEE-754 double-precision
                 correct rounding of the most common elementary
                 functions (exp/log, trigonometric and hyperbolic) is
                 achievable on current processors using only
                 double-double-extended arithmetic. This allows to
                 improve by several orders of magnitude the worst case
                 performance of a correctly-rounded mathematical
                 library, compared to the current state of the art. This
                 article builds up on previous work by Lef{\`e}vre and
                 Muller, who have shown that an intermediate accuracy of
                 up to 158 bits is required for the evaluation of some
                 functions. We show that the practical accuracy required
                 can always be reduced to less than 119 bits, which is
                 easy to obtain using well-known and well-proven
                 techniques of double-double-extended arithmetic. As an
                 example, a prototype implementation of the exponential
                 function on the Itanium has a worst-case time about
                 twice that of the standard, highly optimized libm by
                 Intel, which doesn't offer correct rounding. Such a
                 small performance penalty should allow correct rounding
                 of elementary functions to become the standard.",
  acknowledgement = ack-nhfb,
  keywords =     "Correct Rounding; Double-extended Precision;
                 Elementary Functions; floating-point arithmetic;
                 IEEE-754",
}

@InProceedings{deDinechin:2004:PCR,
  author =       "Florent de Dinechin and Catherine Loirat and
                 Jean-Michel Muller",
  title =        "A proven correctly rounded logarithm in
                 double-precision",
  crossref =     "Frougny:2004:RCR",
  pages =        "71--85",
  year =         "2004",
  bibdate =      "Fri Nov 17 07:00:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_07_dinechin.pdf",
  abstract =     "This article is a case study in the implementation of
                 a proven, portable, and efficient correctly rounded
                 elementary function in double-precision. We describe
                 the methodology used in the implementation of the
                 natural logarithm in the crlibm library. The discipline
                 required to prove a tight bound on the overall
                 evaluation error allows to design a very efficient
                 implementation with moderate effort.",
  acknowledgement = ack-nhfb,
  keywords =     "arithmetic; correct rounding; elementary functions;
                 floating-point; libm; logarithm",
}

@TechReport{deDinechin:2004:TPU,
  author =       "Florent de Dinechin and Nicolas Gast",
  title =        "Towards the post-ultimate {\tt libm}",
  type =         "Research Report",
  number =       "RR2004-47",
  institution =  "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "69364 Lyon Cedex 07, France",
  month =        nov,
  year =         "2004",
  bibdate =      "Mon Dec 06 11:15:40 2004",
  bibsource =    "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-47.pdf",
  abstract =     "This article presents advances in the subject of
                 double-precision correctly rounded elementary functions
                 since the publication of the libultim mathematical
                 library developed by Ziv at IBM. This library
                 demonstrated that the performance overhead of correct
                 rounding could be made negligible in average. However,
                 the worst case execution time was up to 1000 times the
                 average time, and memory consumption was also a
                 problem. To address these questions, a range of new
                 techniques, from the more portable to the more
                 efficient, are presented, and demonstrated on two
                 typical functions, exponential and arctangent. The main
                 result of this paper is to show that the worst-case
                 execution time can be bounded within a factor of 2 to
                 10 of the average time, with memory consumption
                 comparable to current libms. This has in turn
                 implications on the techniques and tradeoffs for
                 correctly rounded functions. This article also shows
                 that these techniques make it much easier to prove the
                 correct rounding property. Thus, this article lifts the
                 last technical obstacles to a widespread use of (at
                 least some) correctly rounded double precision
                 elementary functions.",
  acknowledgement = ack-nhfb,
  keywords =     "correct rounding; Elementary Functions; floating-point
                 arithmetic; IEEE-754",
}

@Article{deFigueiredo:2004:AAC,
  author =       "Luiz Henrique de Figueiredo and Jorge Stolfi",
  title =        "Affine Arithmetic: Concepts and Applications",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "37",
  number =       "1--4",
  pages =        "147--158",
  month =        dec,
  year =         "2004",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Dec 6 07:00:28 MST 2004",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/58/A/10/abstract.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  remark =       "Special Issue: SCAN'2002 International Conference
                 (Guest Editors: Ren{\'e} Alt and Jean-Luc Lamotte)",
}

@Article{Defour:2004:PSM,
  author =       "David Defour and Guillaume Hanrot and Vincent
                 Lef{\`e}vre and Jean-Michel Muller and Nathalie Revol
                 and Paul Zimmermann",
  title =        "Proposal for a Standardization of Mathematical
                 Function Implementation in Floating-Point Arithmetic",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "37",
  number =       "1--4",
  pages =        "367--375",
  month =        dec,
  year =         "2004",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "65D20 (65G50)",
  MRnumber =     "MR2109920",
  bibdate =      "Mon Dec 6 07:00:28 MST 2004",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/58/A/30/abstract.htm;
                 http://perso.ens-lyon.fr/jean-michel.muller/NumAlg04.pdf;
                 http://www.loria.fr/~zimmerma/papers/PropStandFunctions.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  remark =       "Special Issue: SCAN'2002 International Conference
                 (Guest Editors: Ren {\'e} Alt and Jean-Luc Lamotte)",
}

@InProceedings{DelRe:2004:TAG,
  author =       "A. {Del Re} and A. Nannaelli and M. Re",
  booktitle =    "Proc. Design Auto. Test Europe ({DATE}), Vol. 1, Feb.
                 2004",
  title =        "A Tool for Automatic Generation of {RTL}-level {VHDL}
                 Description of {RNS FIR} Filters",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2004",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Fri Jun 24 18:18:50 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Residue Number System (RNS)",
}

@InCollection{Demmel:2004:AEA,
  author =       "James Demmel and Plamen Koev",
  title =        "Accurate and efficient algorithms for floating point
                 computation",
  crossref =     "Hilledt:2004:AME",
  pages =        "73--88",
  year =         "2004",
  MRclass =      "65Gxx (65Fxx)",
  MRnumber =     "MR2296263",
  bibdate =      "Thu Nov 8 19:16:14 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}

@Article{Demmel:2004:FAF,
  author =       "James Demmel and Yozo Hida",
  title =        "Fast and Accurate Floating Point Summation with
                 Application to Computational Geometry",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "37",
  number =       "1--4",
  pages =        "101--112",
  month =        dec,
  year =         "2004",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "65B10 (65D18)",
  MRnumber =     "MR2109897",
  bibdate =      "Mon Dec 6 07:00:28 MST 2004",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/58/A/6/abstract.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "accurate floating-point summation",
  remark =       "Special Issue: SCAN'2002 International Conference
                 (Guest Editors: Ren {\'e} Alt and Jean-Luc Lamotte)",
}

@TechReport{Detrey:2004:SOF,
  author =       "J{\'e}r{\'e}mie Detrey and Florent de Dinechin",
  title =        "Second Order Function Approximation with a Single
                 Small Multiplication",
  type =         "Research Report",
  number =       "RR2004-13",
  institution =  "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "69364 Lyon Cedex 07, France",
  pages =        "2 + 8",
  month =        mar,
  year =         "2004",
  bibdate =      "Mon Dec 06 10:51:35 2004",
  bibsource =    "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-13.ps.gz",
  abstract =     "This paper presents a new scheme for the hardware
                 evaluation of elementary functions, based on a
                 piecewise second order minimax approximation. The
                 novelty is that this evaluation requires only one small
                 rectangular multiplication. Therefore the resulting
                 architecture combines a small table size, thanks to
                 second-order evaluation, with a short critical path:
                 Consisting of one table lookup, the rectangular
                 multiplication, and one addition, the critical path is
                 shorter than that of a plain first-order evaluation.
                 Synthesis results for several functions show that this
                 method outperforms all the previously published methods
                 in both area and speed for precisions ranging from 12
                 to 24 bits.",
  acknowledgement = ack-nhfb,
  keywords =     "Computer Arithmetic; Hardware Elementary Functions
                 Evaluation.",
}

@TechReport{Detrey:2004:TBP,
  author =       "J{\'e}r{\'e}mie Detrey and Florent de Dinechin",
  title =        "Table-based polynomials for fast hardware function
                 evaluation",
  type =         "Research Report",
  number =       "November 2004",
  institution =  "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "69364 Lyon Cedex 07, France",
  pages =        "2 + 11",
  year =         "2004",
  bibdate =      "Mon Dec 06 11:19:55 2004",
  bibsource =    "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-52.ps.gz",
  abstract =     "Many general table-based methods for the evaluation in
                 hardware of elementary functions have been published.
                 The bipartite and multipartite methods implement a
                 first-order approximation of the function using only
                 table lookups and additions. Recently, a
                 single-multiplier second-order method of similar
                 inspiration has also been published. This paper
                 presents a general framework extending such methods to
                 approximations of arbitrary order, using adders, small
                 multipliers, and very small ad-hoc powering units. We
                 obtain implementations that are both smaller and faster
                 than all previously published approaches. This paper
                 also deals with the FPGA implementation of such
                 methods. Previous work have consistently shown that the
                 more complex methods were also faster: The reduction of
                 the table size meant a reduction of its lookup time,
                 which compensated for the addition and multiplication
                 time. A second contribution is therefore to finally
                 create a tradeoff between space and time among
                 table-based methods.",
  acknowledgement = ack-nhfb,
  keywords =     "FPGA; Function evaluation; hardware operators;
                 polynomial approximation; table-based method",
}

@TechReport{Detrey:2004:TUC,
  author =       "J{\'e}r{\'e}mie Detrey and Florent de Dinechin",
  title =        "A tool for unbiased comparison between logarithmic and
                 floating-point arithmetic",
  type =         "Research Report",
  number =       "RR2004-31",
  institution =  "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "69364 Lyon Cedex 07, France",
  pages =        "2 + 16",
  month =        jun,
  year =         "2004",
  bibdate =      "Mon Dec 06 10:56:33 2004",
  bibsource =    "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-31.ps.gz",
  abstract =     "This paper describes two concurrent libraries of
                 parameterized arithmetic operators for manipulating
                 high-dynamic numbers on FPGAs. One of them uses a
                 floating-point representation, the other one uses a
                 logarithmic representation. Along with their direct
                 interest, those two libraries allow
                 application-specific comparisons of those two number
                 representation systems. They are unbiased in the sense
                 that they tend to reflect the state-of-the-art for both
                 number arithmetic systems, and are freely available at
                 \path=http://www.ens-lyon.fr/LIP/Arenaire/=.",
  acknowledgement = ack-nhfb,
  keywords =     "Arithmetic; Floating-Point; FPGA; Hardware Operators;
                 LNS; Logarithmic Number system; VHDL",
}

@InProceedings{Doss:2004:FBI,
  author =       "C. C. Doss and R. L. {Riley, Jr.}",
  booktitle =    "{FCCM 2004}. 12th Annual {IEEE} Symposium on
                 Field-Programmable Custom Computing Machines, 20--23
                 April 2004",
  title =        "{FPGA}-based implementation of a robust {IEEE-754}
                 exponential unit",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "229--238",
  year =         "2004",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 17:14:11 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "This work explores the feasibility of implementing a
                 floating-point exponentiation unit on reconfigurable
                 computing systems. A table-driven exponentiation unit
                 was implemented using synthesizable VHDL. The project
                 included creating pipelined \ldots{}",
}

@Article{Efstathiou:2004:MBM,
  author =       "C. Efstathiou and H. T. Vergos and D. Nikolos",
  title =        "Modified {Booth} modulo $ 2^n - 1 $ multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "53",
  number =       "3",
  pages =        "370--374",
  month =        mar,
  year =         "2004",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2004.1261842",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 08:12:33 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1261842",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Egner:2004:CTN,
  author =       "Sebastian Egner and Richard A. Kelsey and Michael
                 Sperber",
  editor =       "????",
  booktitle =    "Fifth Workshop on Scheme and Functional Programming.
                 {September 22, 2004, Snowbird, Utah, USA}",
  title =        "Cleaning up the Tower: Numbers in {Scheme}",
  publisher =    "????",
  address =      "????",
  pages =        "13",
  day =          "22",
  month =        sep,
  year =         "2004",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Mon Apr 25 06:55:59 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www-pu.informatik.uni-tuebingen.de/users/sperber/papers/numerical-tower.pdf",
  acknowledgement = ack-nhfb,
}

@Article{ElHajji:2004:SIL,
  author =       "Said {El Hajji} and Nathalie Revol and Paul {Van
                 Dooren}",
  title =        "Special Issue on {Linear Algebra and Arithmetic,
                 Proceedings of the ALA'01 Conference held in Rabat,
                 Morocco on May 28--31, 2001}",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "162",
  number =       "1",
  pages =        "ix--x",
  day =          "1",
  month =        jan,
  year =         "2004",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:59:56 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042703007428",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@TechReport{Ercegovac:2004:CSRa,
  author =       "Milo{\v{s}} Ercegovac and Jean-Michel Muller",
  title =        "Complex Square Root with Operand Prescaling",
  type =         "Research Report",
  number =       "RR2004-42",
  institution =  "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "69364 Lyon Cedex 07, France",
  pages =        "2 + 12",
  month =        sep,
  year =         "2004",
  bibdate =      "Mon Dec 06 11:07:40 2004",
  bibsource =    "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-42.pdf",
  abstract =     "We propose a radix-$r$ digit-recurrence algorithm for
                 complex square-root. The operand is prescaled to allow
                 the selection of square-root digits by rounding of the
                 residual. This leads to a simple hardware
                 implementation. Moreover, the use of digit recurrence
                 approach allows correct rounding of the result. The
                 algorithm, compatible with the complex division, and
                 its design are described at a high-level. We also give
                 rough comparisons of its latency and cost with respect
                 to implementation based on standard floating-point
                 instructions as used in software routines for complex
                 square root.",
  acknowledgement = ack-nhfb,
  keywords =     "complex square-root; Computer arithmetic; correct
                 rounding; digit-recurrence algorithm; floating-point
                 arithmetic; operand prescaling.",
}

@InProceedings{Ercegovac:2004:CSRb,
  author =       "Milo{\v{s}} Ercegovac and Jean-Michel Muller",
  booktitle =    "{Proceedings of the 15th IEEE International Conference
                 on Application-Specific Systems, Architectures and
                 Processors, 2004}",
  title =        "Complex square root with operand prescaling",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "52--62",
  year =         "2004",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ASAP.2004.1342458",
  ISBN =         "0-7695-2226-2",
  ISBN-13 =      "978-0-7695-2226-5",
  ISSN =         "1063-6862",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "We propose a radix-r digit-recurrence algorithm for
                 complex square-root. The operand is prescaled to allow
                 the selection of square-root digits by rounding of the
                 residual. This leads to a simple hardware
                 implementation. Moreover, the use of digit \ldots{}",
}

@Book{Ercegovac:2004:DA,
  author =       "Milo{\v{s}} Dragutin Ercegovac and Tom{\'a}s Lang",
  title =        "Digital Arithmetic",
  publisher =    pub-MORGAN-KAUFMANN,
  address =      pub-MORGAN-KAUFMANN:adr,
  pages =        "xxv + 709",
  year =         "2004",
  ISBN =         "1-55860-798-6",
  ISBN-13 =      "978-1-55860-798-9",
  LCCN =         "QA76.9.C62 E72 2004",
  bibdate =      "Thu Jun 20 10:19:42 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "US\$89.95, UK\pounds 59.95",
  URL =          "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/;
                 http://www.loc.gov/catdir/description/els031/2002114337.html;
                 http://www.loc.gov/catdir/toc/els031/2002114337.html",
  acknowledgement = ack-nhfb,
  subject =      "Computer arithmetic",
  tableofcontents = "Preface \\
                 1. Review of Basic Number Representations and
                 Arithmetic Algorithms \\
                 2. Two-Operand Addition \\
                 3. Multi-Operand Addition \\
                 4. Multiplication \\
                 5. Division by Digit Recurrence \\
                 6. Square Root by Digit Recurrence \\
                 7. Reciprocal, Division, Reciprocal Square Root and
                 Square Root by Iterative Approximation \\
                 8. Floating-Point Representation, Algorithms, and
                 Implementations \\
                 9. Digit-Serial Arithmetic \\
                 10. Function Evaluation \\
                 11. CORDIC Algorithm and Implementations",
}

@InProceedings{Ercegovac:2004:DCD,
  author =       "Milo{\v{s}} Ercegovac and Jean-Michel Muller",
  title =        "Design of a complex divider",
  crossref =     "Luk:2004:ASP",
  pages =        "51--59",
  year =         "2004",
  bibdate =      "Sat Dec 04 10:02:00 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Fousse:2004:AST,
  author =       "Laurent Fousse and Paul Zimmermann",
  title =        "Accurate Summation: Towards a Simpler and Formal
                 Proof",
  type =         "Technical Report",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  pages =        "11",
  day =          "6",
  month =        sep,
  year =         "2004",
  bibdate =      "Sun Sep 10 08:08:04 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.loria.fr/~zimmerma/papers/rnc5.pdf",
  abstract =     "This paper provides a simpler proof of the accurate
                 summation algorithm proposed by Demmel and Hida in [1].
                 It also gives improved bounds in some cases, and
                 examples showing that those new bounds are optimal.
                 This simpler proof will be used to obtain a
                 computer-generated proof of Demmel--Hida's algorithm,
                 using a proof assistant like HOL, PVS or Coq.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation; floating-point
                 arithmetic",
}

@InProceedings{Fousse:2004:CPE,
  author =       "L. Fousse and S. Schmitt",
  title =        "A comparison of polynomial evaluation schemes",
  crossref =     "Frougny:2004:RCR",
  pages =        "86--102",
  year =         "2004",
  bibdate =      "Fri Nov 17 07:00:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_08_fousse.pdf",
  abstract =     "The goal of this paper is to analyze two polynomial
                 evaluation schemes for multiple precision floating
                 point arithmetic. Polynomials are used extensively in
                 numerical computations (Taylor series for mathematical
                 functions, root finding) but a rigorous bound of the
                 error on the final result is seldom provided. We
                 provide such an estimate for the two schemes and find
                 how to reduce the number of operations required at
                 run-time by a dynamic error analysis. This work is
                 useful for floating point polynomial arithmetic.",
  acknowledgement = ack-nhfb,
  keywords =     "bounded error; correct rounding; floating-point
                 arithmetic; polynomial evaluation",
}

@TechReport{Fousse:2004:FPD,
  author =       "Laurent Fousse and Paul Zimmermann",
  title =        "A Formal Proof of {Demmel} and {Hida}'s Accurate
                 Summation Algorithm",
  type =         "Technical Report",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  pages =        "12",
  month =        jan,
  year =         "2004",
  bibdate =      "Sun Sep 10 07:58:09 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.loria.fr/~zimmerma/papers/tcs.ps.gz",
  abstract =     "A new proof of the ``accurate summation'' algorithm
                 proposed by Demmel and Hida is presented. The main part
                 of that proof has been written in the Coq language and
                 verified by the Coq proof assistant.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation; bounded error;
                 floating-point arithmetic; formal proof",
}

@InProceedings{Frougny:2004:ICR,
  author =       "Christiane Frougny",
  title =        "Introduction: [6th conference on Real Numbers and
                 Computers]",
  crossref =     "Frougny:2004:RCR",
  pages =        "1--4",
  year =         "2004",
  bibdate =      "Fri Nov 17 07:00:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_00_intro.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Fuchssteiner:2004:ILN,
  author =       "Benno Fuchssteiner",
  title =        "Invited Lecture: New ideas and results for solving
                 Differential equations symbolically [abstract only]",
  crossref =     "Frougny:2004:RCR",
  pages =        "5--5",
  year =         "2004",
  bibdate =      "Fri Nov 17 07:00:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_01_fuchssteiner.pdf",
  abstract =     "The lecture is a report on current research activities
                 of the MuPAD group in the area of symbolic and numeric
                 solutions of ODE (ordinary differential
                 equations).\par

                 Based on a unification of Lie-point-symmetries and
                 Lie--B{\"a}cklund-symmetries the results of classical
                 Lie-symmetry approaches (for example Liouville--Arnold)
                 to ODE are generalized thus opening new avenues for
                 using integrability (around initial values) for wider
                 classes of differential equations.\par

                 Applications and numerical consequences of these
                 results will be discussed and plans how to extend
                 current solution methods, numerical as well as
                 symbolical, to wider classes of transcendents (i.e.
                 Painlev{\'e} transcendents) will be presented",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gaffar:2004:UBW,
  author =       "A. A. Gaffar and O. Mencer and W. Luk",
  booktitle =    "{FCCM 2004}. 12th Annual {IEEE} Symposium on
                 Field-Programmable Custom Computing Machines, 20--23
                 April 2004",
  title =        "Unifying bit-width optimisation for fixed-point and
                 floating-point designs",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "79--88",
  year =         "2004",
  bibdate =      "Wed Apr 27 18:18:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper presents a method that offers a uniform
                 treatment for bit-width optimisation of both
                 fixed-point and floating-point designs. Our work
                 utilises automatic differentiation to compute the
                 sensitivities of outputs to the bit-width of the
                 various operands in the design. \ldots{}",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gebali:2004:EAF,
  author =       "Fayez Gebali and Mohamed Watheq El-Kharashi",
  title =        "{ERL}: an algorithm for fast evaluation of
                 exponential, reciprocal, and logarithmic functions",
  crossref =     "Wahdan:2004:IHE",
  pages =        "269--272",
  year =         "2004",
  bibdate =      "Sat Jul 16 18:04:58 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A fast algorithm (ERL) is proposed for evaluating
                 Exponential, Reciprocal, and Logarithmic functions. The
                 algorithm requires two to three iterations to complete
                 using simple operations such as multiply, accumulate,
                 and table lookup. The algorithm is independent of the
                 number format used by the machine. Thus it can be
                 implemented using the IEEE 754 floating-point standard
                 or any other special format used by special-purpose
                 processors. The dynamic range of the algorithm is
                 limited only by the dynamic range of the machine on
                 which it is implemented Numerical simulations are
                 performed which verifies the speed and accuracy of the
                 algorithm.",
  acknowledgement = ack-nhfb,
}

@Article{Gemignani:2004:REA,
  author =       "Luca Gemignani and Grazia Lotti",
  title =        "Rounding Error Analysis in Solving {$M$}-Matrix Linear
                 Systems of Block {Hessenberg} Form",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "36",
  number =       "2",
  pages =        "157--168",
  month =        jun,
  year =         "2004",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Dec 6 07:00:32 MST 2004",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/54/A/4/abstract.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Article{Gerwig:2004:IEZ,
  author =       "G. Gerwig and H. Wetter and E. M. Schwarz and J. Haess
                 and C. A. Krygowski and B. M. Fleischer and M.
                 Kroener",
  title =        "The {IBM eServer z990} floating-point unit",
  journal =      j-IBM-JRD,
  volume =       "48",
  number =       "3/4",
  pages =        "311--322",
  month =        "????",
  year =         "2004",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.483.0311",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Tue Sep 28 06:50:40 MDT 2004",
  bibsource =    "http://www.research.ibm.com/journal/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.research.ibm.com/journal/rd/483/gerwig.html;
                 http://www.research.ibm.com/journal/rd/483/gerwig.pdf",
  abstract =     "The floating-point unit (FPU) of the IBM z990 eServer
                 is the first one in an IBM mainframe with a fused
                 multiply-add dataflow. It also represents the first
                 time that an SRT divide algorithm (named after Sweeney,
                 Robertson, and Tocher, who independently proposed the
                 algorithm) was used in an IBM mainframe. The FPU
                 supports dual architectures: the zSeries hexadecimal
                 floating-point architecture and the IEEE 754 binary
                 floating-point architecture. Six floating-point formats
                 including short, long, and extended operands are
                 supported in hardware. The throughput of this FPU is
                 one multiply-add operation per cycle. The instructions
                 are executed in five pipeline steps, and there are
                 multiple provisions to avoid stalls in case of data
                 dependencies. It is able to handle denormalized input
                 operands and denormalized results without a stall
                 (except for architectural program exceptions). It has a
                 new extended-precision divide and square-root dataflow.
                 This dataflow uses a radix-4 SRT algorithm (radix-2 for
                 square root) and is able to handle divides and
                 square-root operations in multiple floating-point and
                 fixed-point formats. For fixed-point divisions, a new
                 mechanism improves the performance by using an
                 algorithm with which the number of divide iterations
                 depends on the effective number of quotient bits.",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "decimal floating-point arithmetic",
  ordernumber =  "G322-0240",
}

@Article{Geyer:2004:DFD,
  author =       "Christina Lynn Geyer and Patricia Pepple Williamson",
  title =        "Detecting fraud in data sets using {Benford's Law}",
  journal =      j-COMMUN-STAT-SIMUL-COMPUT,
  volume =       "B33",
  number =       "1",
  pages =        "229--246",
  month =        "????",
  year =         "2004",
  CODEN =        "CSSCDB",
  DOI =          "https://doi.org/10.1081/SAC-120028442",
  ISSN =         "0361-0918",
  ISSN-L =       "0361-0918",
  MRclass =      "62-07",
  MRnumber =     "2044866",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Comm. Statist. Simulation Comput.",
  fjournal =     "Communications in Statistics: Simulation and
                 Computation",
  journal-URL =  "http://www.tandfonline.com/loi/lssp20",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@InProceedings{Gok:2004:DSP,
  author =       "M. Gok and M. J. Schulte and S. Krithivasan",
  editor =       "????",
  booktitle =    "Proceedings of the Workshop on Application Specific
                 Processors, Stockholm, Sweden, August, 2004",
  title =        "Designs for Subword-Parallel Multiplications and Dot
                 Product Operations",
  publisher =    "????",
  address =      "????",
  pages =        "27--31",
  year =         "2004",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sun Mar 04 20:51:24 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Govindu:2004:AHP,
  author =       "Gokul Govindu and L. Zhuo and S. Choi and V.
                 Prasanna",
  booktitle =    "Proceedings. 18th International Parallel and
                 Distributed Processing Symposium, 26--30 April 2004",
  title =        "Analysis of high-performance floating-point arithmetic
                 on {FPGAs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "149--149",
  year =         "2004",
  bibdate =      "Wed Apr 27 18:18:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Govindu:2004:HPE,
  author =       "G. Govindu and S. Choi and V. Prasanna and V. Daga and
                 S. Gangadharpalli and V. Sridhar",
  booktitle =    "Proceedings. 18th International Parallel and
                 Distributed Processing Symposium, 26--30 April 2004",
  title =        "A high-performance and energy-efficient architecture
                 for floating-point based {LU} decomposition on
                 {FPGAs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "149--149",
  year =         "2004",
  bibdate =      "Wed Apr 27 18:18:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Graillat:2004:CRC,
  author =       "Stef Graillat and Philippe Langlois",
  title =        "A comparison of real and complex pseudozero sets for
                 polynomials with real coefficients",
  crossref =     "Frougny:2004:RCR",
  pages =        "103--112",
  year =         "2004",
  MRclass =      "65F35 68W30",
  bibdate =      "Fri Nov 17 07:00:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_09_graillat.pdf",
  abstract =     "Pseudozeros are useful to describe how perturbations
                 of polynomial coefficients affect its zeros. We compare
                 two types of pseudozero sets: the complex and the real
                 pseudozero sets. These sets differ with respect to the
                 type of perturbations. The first set --- complex
                 perturbations of a complex polynomial --- has been
                 intensively studied while the second one --- real
                 perturbations of a real polynomial --- seems to have
                 received no attention. We present a computable formula
                 for the real pseudozero set and a comparison between
                 these two pseudozero sets. We conclude that the complex
                 pseudozero sets have to be preferred except when the
                 perturbed real polynomials admit non-real zeros.",
  acknowledgement = ack-nhfb,
  keywords =     "perturbation; polynomial root; pseudozero set;
                 uncertainty",
}

@Manual{Granlund:2004:GMG,
  author =       "Torbj{\"o}rn Granlund and Gunnar Sj{\"o}din and Hans
                 Riesel and Richard Stallman and Brian Beuning and Doug
                 Lea and John Amanatides and Paul Zimmermann and Ken
                 Weber and Per Bothner and Joachim Hollman and Bennet
                 Yee and Andreas Schwab and Robert Harley and David Seal
                 and Robert Harley and Torsten Ekedahl and Paul
                 Zimmermann and Linus Nordberg and Kent Boortz and Kevin
                 Ryde and Steve Root and Gerardo Ballabio and Hans
                 Thorsen",
  title =        "{GNU MP}: The {GNU} Multiple Precision Arithmetic
                 Library",
  organization = pub-FSF,
  address =      pub-FSF:adr,
  edition =      "Version 4.1.4",
  pages =        "iv + 127",
  day =          "21",
  month =        sep,
  year =         "2004",
  bibdate =      "Wed Nov 24 08:41:48 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "GNUP MP development began in 1991. Earler versions are
                 1.0 (8-Aug-1991), 2.0 (24-Apr-1996), 3.0 (17-Apr-2000),
                 and 4.0 (1-Dec-2001).",
  URL =          "ftp://ftp.gnu.org/gnu/gmp/gmp-4.1.4.tar.gz;
                 http://www.swox.se/gmp/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Groza:2004:DIS,
  author =       "V. Groza and M. Debski and D. Ionescu",
  booktitle =    "{IMTC 04}. Proceedings of the 21st {IEEE}
                 Instrumentation and Measurement Technology Conference,
                 18--20 May 2004",
  title =        "Design and implementation of a self-calibrating
                 floating-point analog-to-digital converter",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "707--710",
  year =         "2004",
  bibdate =      "Wed Apr 27 18:18:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Floating point analog-to-digital converters (FP-ADC)
                 are characterized by a high relative precision, but, in
                 some applications, their absolute precision had to be
                 traded off for speed. This paper presents the
                 architecture, design and implementation of a
                 self-calibrating differential predictive floating point
                 analog-to-digital converter which is characterized by
                 high conversion rates while its precision is kept at
                 high values by additional hardware that periodically
                 performs calibration cycles.\ldots{}",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hack:2004:IPR,
  author =       "Michel Hack",
  title =        "On Intermediate Precision Required for
                 Correctly-Rounding Decimal-to-Binary Floating-Point
                 Conversion",
  crossref =     "Frougny:2004:RCR",
  pages =        "113--134",
  year =         "2004",
  bibdate =      "Thu Apr 28 05:55:01 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_10_hack.pdf",
  abstract =     "The algorithms developed ten years ago in preparation
                 for IBM's support of IEEE Floating-Point on its
                 mainframe S/390 processors use an overly conservative
                 intermediate precision to guarantee correctly-rounded
                 results across the entire exponent range. Here we study
                 the minimal requirement for both bounded and unbounded
                 precision on the decimal side (converting to machine
                 precision on the binary side). An interesting new
                 theorem on Continued Fraction expansions is offered, as
                 well as an open problem on the growth of partial
                 quotients for ratios of powers of two and five.",
  acknowledgement = ack-nhfb,
  keywords =     "base conversion; Continued Fractions; correct
                 rounding; decimal floating-point arithmetic;
                 Floating-Point conversion",
  remark =       "Improvement on \cite{Abbott:1999:ASS}.",
}

@Article{Hanrot:2004:MPA,
  author =       "Guillaume Hanrot and Michel Quercia and Paul
                 Zimmermann",
  title =        "The Middle Product Algorithm {I}. Speeding up the
                 division and square root of power series",
  journal =      j-APPL-ALGEBRA-ENG-COMMUN-COMPUT,
  volume =       "14",
  number =       "6",
  pages =        "415--438",
  month =        mar,
  year =         "2004",
  CODEN =        "AAECEW",
  DOI =          "https://doi.org/10.1007/s00200-003-0144-2",
  ISSN =         "0938-1279 (print), 1432-0622 (electronic)",
  ISSN-L =       "0938-1279",
  bibdate =      "Sun Sep 10 08:12:01 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://springerlink.metapress.com/content/57p2fta5k71085wm/fulltext.pdf",
  abstract =     "We present new algorithms for the inverse, division,
                 and square root of power series. The key trick is a new
                 algorithm --- MiddleProduct or, for short, MP ---
                 computing the $n$ middle coefficients of a $ (2 n - 1)
                 \times n $ full product in the same number of
                 multiplications as a full $ n \times n $ product. This
                 improves previous work of Brent, Mulders, Karp and
                 Markstein, Burnikel and Ziegler. These results apply
                 both to series and polynomials.",
  acknowledgement = ack-nhfb,
  fjournal =     "Applicable algebra in engineering, communication and
                 computing",
}

@TechReport{Hanrot:2004:NIR,
  author =       "Guillaume Hanrot and Paul Zimmermann",
  title =        "{Newton} Iteration Revisited",
  type =         "Technical Report",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  pages =        "2",
  month =        mar,
  year =         "2004",
  bibdate =      "Sun Sep 10 07:46:53 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Bernstein:2004:RRH}.",
  URL =          "http://www.loria.fr/~zimmerma/papers/fastnewton.ps.gz",
  abstract =     "On March 10, 2004, Dan Bernstein announced a revised
                 draft of his paper {\em Removing redundancy in
                 high-precision Newton iteration}
                 (\path=http://cr.yp.to/fastnewton.html=) with
                 algorithms that compute a reciprocal of order $n$ over
                 $ C[[x]] 1.5 + o(1) $ times longer than a product; a
                 quotient or logarithm $ 2.16666 \ldots {} + o(1) $
                 times longer; a square root $ 1.83333 \ldots {} + o(1)
                 $ times longer; an exponential $ 2.83333 \ldots {} +
                 o(1) $ times longer. We give better algorithms.",
  acknowledgement = ack-nhfb,
  remark =       "Note added on March 24, 2004: the $ 1.5 + o(1) $
                 reciprocal algorithm was already published by
                 Sch{\"o}nhage ({\tm Information Processing Letters} 74,
                 2000, pp. 41--46).",
}

@Article{Herbst:2004:RWS,
  author =       "Klaus-Dieter Herbst",
  title =        "{Rezension: \booktitle{Wilhelm Schickard ---
                 Briefwechsel} von Friedrich Seck}",
  journal =      j-BER-WISSENSCHAFTGESCH,
  volume =       "27",
  number =       "4",
  pages =        "315--317",
  month =        dec,
  year =         "2004",
  CODEN =        "BEWID8",
  DOI =          "https://doi.org/10.1002/bewi.200490037",
  ISSN =         "0170-6233 (print), 1522-2365 (electronic)",
  ISSN-L =       "0170-6233",
  bibdate =      "Sun Aug 4 10:12:45 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/berwissenschaftgesch.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "{Ber. Wissenschaftgesch.}",
  fjournal =     "{Berichte zur Wissenschaftsgeschichte}",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2365/",
  language =     "German",
  onlinedate =   "3 Jan 2005",
}

@Article{Hiasat:2004:SFR,
  author =       "Ahmad A. Hiasat",
  title =        "A Suggestion for a Fast Residue Multiplier for a
                 Family of Moduli of the Form $ (2 n - (2 p \pm 1)) $",
  journal =      j-COMP-J,
  volume =       "47",
  number =       "1",
  pages =        "93--??",
  month =        jan,
  year =         "2004",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Thu Feb 26 06:22:27 2004",
  bibsource =    "http://www3.oup.co.uk/computer_journal/hdb/Volume_47/Issue_01/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_47/Issue_01/470093.sgm.abs.html;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_47/Issue_01/pdf/470093.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Hormigo:2004:CPV,
  author =       "Javier Hormigo and Julio Villalba and Emilio L.
                 Zapata",
  title =        "{CORDIC} Processor for Variable-Precision Interval
                 Arithmetic",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "37",
  number =       "1",
  pages =        "21--39",
  month =        may,
  year =         "2004",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1023/B:VLSI.0000017001.88149.f4",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Thu Aug 07 19:16:20 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this paper we present a specific CORDIC processor
                 for variable-precision coordinates. This system allows
                 us to specify the precision to perform the CORDIC
                 operation, and control the accuracy of the result, in
                 such a way that re-computation of inaccurate results
                 can be carried out with higher precision. It permits a
                 reliable and accurate evaluation of a wide range of
                 elementary functions. The specific architecture
                 designed greatly improves the computational time of
                 previous solutions based on classic polynomial
                 approximation. For controlling error in numerical
                 computation (where intervals are normally narrow) the
                 proposed design performs an interval operation in a
                 time close to that of a point operation.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
}

@Manual{IBM:2004:ZAP,
  author =       "{IBM}",
  title =        "{z/Architecture} Principles of Operation",
  organization = "IBM Corporation",
  address =      "Department 55JA Mail Station P384, 2455 South Road
                 Poughkeepsie, NY, 12601-5400, USA",
  edition =      "Fourth",
  pages =        "xxvi + 1124",
  month =        may,
  year =         "2004",
  bibdate =      "Sat Mar 11 17:19:27 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IBM order number SA22-7832-03.",
  URL =          "http://publibz.boulder.ibm.com/cgi-bin/bookmgr_OS390/download/DZ9ZR003.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
  remark =       "This manual continues a tradition of that began with
                 the publication in 1964 of the IBM System/360
                 Principles of Operation, long considered a classic and
                 a landmark description of the oldest computer
                 architecture in continuous use. Chapter 9 provides an
                 overview of the floating-point support, Chapter 18
                 describes the hexadecimal floating-point instructions,
                 and Chapter 19 the binary (IEEE 754) floating-point
                 instructions. Both hexadecimal and binary sets support
                 32-bit, 64-bit, and 128-bit formats, all in hardware on
                 the IBM G5 processors. However, the
                 recently-implemented decimal floating-point arithmetic
                 is not described in this edition.",
}

@Article{Jeong:2004:CEP,
  author =       "Jong-Chul Jeong and Woo-Chan Park and Woong Jeong and
                 Tack-Don Han and Moon-Key Lee",
  title =        "A cost-effective pipelined divider with a small lookup
                 table",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "53",
  number =       "4",
  pages =        "489--495",
  month =        apr,
  year =         "2004",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2004.1268407",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 08:12:35 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1268407",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Misc{Kahan:2004:CFP,
  author =       "W. Kahan",
  title =        "On the Cost of Floating-Point Computation Without
                 Extra-Precise Arithmetic",
  howpublished = "World-Wide Web document",
  pages =        "21",
  day =          "20",
  month =        nov,
  year =         "2004",
  bibdate =      "Mon Apr 25 17:44:03 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Boldo:2009:KAC} for a proof of this
                 algorithm for accurate computation of the discriminant
                 needed for the solution of quadratic equations.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Qdrtcs.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2004:HFM,
  author =       "W. Kahan",
  title =        "How Futile are Mindless Assessments of Roundoff in
                 Floating-Point Computation?",
  howpublished = "World-Wide Web document",
  pages =        "37",
  day =          "1",
  month =        nov,
  year =         "2004",
  bibdate =      "Mon Apr 25 17:41:28 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Mind1ess.pdf;
                 http://www.cs.berkeley.edu/~wkahan/Mindless.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; rounding errors",
}

@Misc{Kahan:2004:SSR,
  author =       "W. Kahan",
  title =        "$ 128 $ Squares of $ 128 $ Square Roots",
  howpublished = "World-Wide Web document",
  pages =        "3",
  day =          "29",
  month =        jan,
  year =         "2004",
  bibdate =      "Mon Apr 25 18:25:57 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Lecture notes for Math 128.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Math128/SqSqrts.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kahn:2004:CEA,
  author =       "Ken Kahn",
  title =        "The child-engineering of arithmetic in {ToonTalk}",
  crossref =     "Druin:2004:IDC",
  pages =        "141--142",
  year =         "2004",
  DOI =          "https://doi.org/10.1145/1017833.1017860",
  bibdate =      "Fri Aug 08 09:04:34 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Providing a child-appropriate interface to an
                 arithmetic package with large numbers and exact
                 fractions is surprisingly challenging. We discuss
                 solutions to problems ranging from how to present
                 fractions such as 1/3 to how to deal with numbers with
                 tens of thousands of digits. As with other objects in
                 ToonTalk, we strive to make the enhanced numbers work
                 in a concrete and playful manner.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kenney:2004:HFD,
  author =       "R. D. Kenney and M. J. Schulte and M. A. Erle",
  title =        "A high-frequency decimal multiplier",
  crossref =     "IEEE:2004:IICa",
  pages =        "26--29",
  year =         "2004",
  bibdate =      "Fri Mar 25 05:54:22 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2004-05.pdf",
  abstract =     "Decimal arithmetic is regaining popularity in the
                 computing community due to the growing importance of
                 commercial, financial, and Internet-based applications,
                 which process decimal data. This paper presents an
                 iterative decimal multiplier, which is operates at high
                 clock frequencies and scales well to large operand
                 sizes. The multiplier uses a new decimal representation
                 for intermediate products, which allows for a very fast
                 two- stage iterative multiplier design. Decimal
                 multipliers, which are synthesized using a 0.11 micron
                 CMOS standard cell library, operate at clock
                 frequencies close to 2 GHz. The latency of the proposed
                 design to multiply two n-digit BCD operands is $ (n +
                 8) $ cycles with a new multiplication able to begin
                 every $ (n + 1) $ cycles.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@InProceedings{Kenney:2004:MDA,
  author =       "Robert D. Kenney and Michael J. Schulte and Mark A.
                 Erle",
  title =        "Multioperand Decimal Addition",
  crossref =     "Smailagic:2004:ETV",
  pages =        "251--253",
  year =         "2004",
  bibdate =      "Wed May 04 07:51:51 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2004-07.pdf",
  abstract =     "This paper introduces and analyzes four techniques for
                 performing fast decimal addition on multiple binary
                 coded decimal (BCD) operands. Three of the techniques
                 speculate BCD correction values and use chaining to
                 correct intermediate results. The first speculates over
                 one addition. The second speculates over two additions.
                 The third employs multiple instances of the second
                 technique in parallel and then merges the results. The
                 fourth technique uses a binary carry-save adder tree
                 and produces a binary sum. Combinational logic is then
                 used to correct the sum and determine the carry into
                 the next digit. Multioperand adder designs are
                 constructed and synthesized for four to sixteen input
                 operands. Analyses are performed on the synthesis
                 results and the merits of each technique are discussed.
                 Finally, these techniques are compared to previous
                 attempts made at speeding up decimal addition.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
  pagecount =    "10",
}

@Article{Kim:2004:AAA,
  author =       "Hyun-Sung Kim and Kee-Young Yoo",
  title =        "{AOP} arithmetic architectures over {$ \mathrm
                 {GF}(2^m) $}",
  journal =      j-APPL-MATH-COMP,
  volume =       "158",
  number =       "1",
  pages =        "7--18",
  day =          "25",
  month =        oct,
  year =         "2004",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Mon Jul 4 09:15:36 MDT 2005",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Ko:2004:CCF,
  author =       "Sangho Ko and Robert R. Bitmead",
  title =        "Covariance calculation for floating-point state-space
                 realizations",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "52",
  number =       "12",
  pages =        "3370--3377",
  month =        dec,
  year =         "2004",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  MRclass =      "93B15 (94A12)",
  MRnumber =     "MR2107918 (2005h:93033)",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper provides a new method for analyzing
                 floating-point roundoff error for digital filters by
                 using ``finite signal-to-noise'' models whose noise
                 sources have variances proportional to the variance or
                 power of the corrupted signals.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
  summary =      "This paper provides a new method for analyzing
                 floating-point roundoff error for digital filters by
                 using ``finite signal-to-noise'' models whose noise
                 sources have variances proportional to the variance or
                 power of the corrupted signals. With this model
                 \ldots{}",
}

@InProceedings{Kobayashi:2004:SHC,
  author =       "S. Kobayashi and I. Kozuka and W. H. Tang and D.
                 Landmann",
  title =        "A software\slash hardware codesigned hands free system
                 on a ``resizable'' block-floating-point {DSP}",
  crossref =     "IEEE:2004:IICc",
  volume =       "5",
  pages =        "V-149--V-152",
  year =         "2004",
  bibdate =      "Wed Apr 27 18:18:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Kornerup:2004:RCN,
  author =       "Peter Kornerup and Jean-Michel Muller",
  title =        "{RN}-coding of numbers: definition and some
                 properties",
  type =         "Research Report",
  number =       "RR2004-43",
  institution =  "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "69364 Lyon Cedex 07, France",
  pages =        "2 + 9",
  month =        sep,
  year =         "2004",
  bibdate =      "Mon Dec 06 11:09:46 2004",
  bibsource =    "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-43.pdf",
  abstract =     "We define RN-codings as radix-$ \beta $ signed
                 representations of numbers for which rounding to the
                 nearest is always identical to truncation. After giving
                 characterizations of such representations, we
                 investigate some of their properties, and we suggest
                 algorithms for conversion to and from these codings.",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic; number systems",
}

@InProceedings{Krithivasan:2004:SPM,
  author =       "S. Krithivasan and M. J. Schulte and J. Glossner",
  title =        "A Subword-Parallel Multiplication and Sum-of-Squares
                 Unit",
  crossref =     "Smailagic:2004:ETV",
  pages =        "273--274",
  year =         "2004",
  bibdate =      "Sun Mar 04 20:59:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2004-03.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Krueger:2004:DLI,
  author =       "S. D. Krueger and Peter-Michael Seidel",
  booktitle =    "{FCCM 2004}. 12th Annual {IEEE} Symposium on
                 Field-Programmable Custom Computing Machines, 20--23
                 April 2004",
  title =        "Design of an on-line {IEEE} floating-point addition
                 unit for {FPGAs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "239--246",
  year =         "2004",
  bibdate =      "Wed Apr 27 18:18:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present the design of an on-line IEEE
                 floating-point (FP) adder. In on-line arithmetic a
                 result is computed as a digit serial output stream from
                 digit serial input streams. The result digits begin to
                 be produced a short delay after the first input arrive
                 and before all the input digits have been received.
                 \ldots{}",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kucukkabak:2004:DIR,
  author =       "U. Kucukkabak and A. Akkas",
  editor =       "Henry Selvaraj",
  booktitle =    "{DSD 2004: Euromicro Symposium on Digital System
                 Design: Architectures, Methods and Tools. Rennes,
                 France, August 31--September 2, 2004}",
  title =        "Design and implementation of reciprocal unit using
                 table look-up and {Newton--Raphson} iteration",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  bookpages =    "xiii + 631",
  pages =        "249--253",
  year =         "2004",
  DOI =          "https://doi.org/10.1109/dsd.2004.1333284",
  ISBN =         "0-7695-2203-3",
  ISBN-13 =      "978-0-7695-2203-6",
  LCCN =         "QA76.9.S88 E97 2004; TK7868.D5 E93 2004",
  bibdate =      "Thu Apr 10 14:57:55 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kwon:2004:SMI,
  author =       "Taek-Jun Kwon and Joong-Seok Moon and J. Sondeen and
                 J. Draper",
  booktitle =    "{ISCAS '04}. Proceedings of the 2004 International
                 Symposium on Circuits and Systems, 23--26 May 2004",
  title =        "A 0.18 /spl $ \mu $ /m implementation of a
                 floating-point unit for a processing-in-memory system",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "II-453--II-456",
  year =         "2004",
  bibdate =      "Wed Apr 27 18:18:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Lang:2004:FPM,
  author =       "T. Lang and J. D. Bruguera",
  title =        "Floating-point multiply-add-fused with reduced
                 latency",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "53",
  number =       "8",
  pages =        "988--1003",
  month =        aug,
  year =         "2004",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2004.44",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 08:12:40 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://www.ac.usc.es/arquivos/articulos/2004/gac2004-j06.ps;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1306992",
  abstract =     "We propose architecture for the computation of the
                 double-precision floating-point multiply-add-fused
                 (MAP) operation $ A + (B \times C) $. This architecture
                 is based on the combined addition and rounding (using a
                 dual adder) and in the anticipation of the
                 normalization step before the addition. Because the
                 normalization is performed before the addition, it is
                 not possible to overlap the leading-zero-anticipator
                 with the adder. Consequently, to avoid the increase in
                 delay, we modify the design of the LZA so that the
                 leading bits of its output are produced first and can
                 be used to begin the normalization. Moreover, parts of
                 the addition are also anticipated. We have estimated
                 the delay of the resulting architecture considering the
                 load introduced by long connections, and we estimate a
                 delay reduction of between 15 percent and 20 percent,
                 with respect to previous implementations.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "We propose architecture for the computation of the
                 double-precision floating-point multiply-add-fused
                 (MAP) operation A + (B $\times$ C). This architecture
                 is based on the combined addition and rounding (using a
                 dual adder) and in the anticipation \ldots{}",
}

@TechReport{Lefevre:2004:AFF,
  author =       "Vincent Lef{\`e}vre and Paul Zimmermann",
  title =        "Arithm{\'e}tique flottante. ({French})
                 [{Floating-point} arithmetic]",
  type =         "Technical Report",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  pages =        "60",
  month =        feb,
  year =         "2004",
  bibdate =      "Sun Sep 10 08:03:11 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-5105.pdf;
                 ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-5105.ps.gz",
  abstract =     "This document releases lecture notes given during 2003
                 at University Henri Poincar{\'e} (Nancy, France). These
                 notes are mainly based on the book {\em Elementary
                 Functions. Algorithms and Implementation\/} by
                 Jean-Michel Muller.",
  acknowledgement = ack-nhfb,
  keywords =     "arbitrary precision; correct rounding; fixed
                 precision; floating-point number; IEEE 754 standard",
  language =     "French",
}

@InProceedings{Lefevre:2004:GMP,
  author =       "Vincent Lef{\`e}vre",
  title =        "The Generic Multiple-Precision Floating-Point Addition
                 With Exact Rounding (as in the {MPFR} Library)",
  crossref =     "Frougny:2004:RCR",
  pages =        "135--145",
  year =         "2004",
  bibdate =      "Fri Nov 17 07:00:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_11_lefevre.pdf",
  abstract =     "We study the multiple-precision addition of two
                 positive floating-point numbers in base 2, with exact
                 rounding, as specified in the MPFR library, i.e. where
                 each number has its own precision. We show how the best
                 possible complexity (up to a constant factor that
                 depends on the implementation) can be obtain.",
  acknowledgement = ack-nhfb,
  keywords =     "addition; exact rounding; floating point; multiple
                 precision",
}

@InProceedings{Leyva:2004:GHS,
  author =       "G. Leyva and G. Caffarena and C. Carreras and O.
                 Nieto-Taladriz",
  booktitle =    "{FCCM 2004}. 12th Annual {IEEE} Symposium on
                 Field-Programmable Custom Computing Machines, 20--23
                 April 2004",
  title =        "A generator of high-speed floating-point modules",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "306--307",
  year =         "2004",
  bibdate =      "Wed Apr 27 18:18:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Hardware implementation of arithmetic modules is a
                 time-consuming task. Consequently, there is a demand
                 for CAD tools that help the designer in reducing design
                 times. This paper presents a floating-point module
                 generator that allows user specification of the
                 mantissa, exponent bit-width and clock period.
                 \ldots{}",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lin:2004:SFP,
  author =       "Hung-Yueh Lin and Tay-Jyi Lin and Chie-Min Chao and
                 Yen-Chin Liao and Chih-Wei Liu and Chein-Wei Jen",
  booktitle =    "{ISCAS '04}. Proceedings of the 2004 International
                 Symposium on Circuits and Systems, 23--26 May 2004",
  title =        "Static floating-point unit with implicit exponent
                 tracking for embedded {DSP}",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "II-821--II-824",
  year =         "2004",
  bibdate =      "Wed Apr 27 18:18:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{Lu:2004:ALC,
  author =       "Mi Lu",
  title =        "Arithmetic and logic in computer systems",
  volume =       "169",
  publisher =    pub-WILEY-INTERSCIENCE,
  address =      pub-WILEY-INTERSCIENCE:adr,
  pages =        "xxi + 246",
  year =         "2004",
  ISBN =         "0-471-46945-9 (cloth)",
  ISBN-13 =      "978-0-471-46945-2 (cloth)",
  LCCN =         "QA76.9.C62 L8 2004",
  bibdate =      "Thu Nov 18 08:57:10 MST 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "iley Series in Microwave and Optical Engineering",
  URL =          "http://www.loc.gov/catdir/bios/wiley046/2003062036.html;
                 http://www.loc.gov/catdir/description/wiley041/2003062036.html;
                 http://www.loc.gov/catdir/toc/wiley041/2003062036.html",
  acknowledgement = ack-nhfb,
  subject =      "Computer arithmetic; Logic programming",
  tableofcontents = "Addition and Subtraction 29 \\
                 High-Speed Adder 53 \\
                 Sequential Multiplication 77 \\
                 Parallel Multiplication 103 \\
                 Sequential Division 135 \\
                 Fast Array Dividers 167 \\
                 Floating Point Operations 183 \\
                 Residue Number Operations 199 \\
                 Operations through Logarithms 221 \\
                 Signed-Digit Number Operations 235 \\
                 Index 245",
}

@InProceedings{Lutz:2004:NFP,
  author =       "D. R. Lutz and C. N. Hinds",
  booktitle =    "Conference Record of the Thirty-Eighth Asilomar
                 Conference on Signals, Systems and Computers, Nov.
                 7--10, 2004",
  title =        "A new floating-point architecture for wireless {$3$D}
                 graphics",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1879--1883",
  year =         "2004",
  bibdate =      "Wed Apr 27 18:18:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Madhukumar:2004:EAR,
  author =       "A. S. Madhukumar and F. Chin",
  title =        "Enhanced architecture for residue number system-based
                 {CDMA} for high-rate data transmission",
  journal =      j-IEEE-TRANS-WIREL-COMMUN,
  volume =       "3",
  number =       "5",
  pages =        "1363--1368",
  month =        sep,
  year =         "2004",
  CODEN =        "ITWCAX",
  DOI =          "https://doi.org/10.1109/TWC.2004.833509",
  ISSN =         "1536-1276 (print), 1558-2248 (electronic)",
  ISSN-L =       "1536-1276",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=29589",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Wirel. Commun.",
  fjournal =     "IEEE Transactions on Wireless Communications",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7693",
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper presents an advanced architecture for
                 residue number system (RNS)-based code-division
                 multiple-access (CDMA) system for high-rate data
                 transmission by combining RNS representation, phase
                 shift keying/quadrature amplitude modulation (PSK/
                 \ldots{})",
}

@InProceedings{Marcus:2004:FSS,
  author =       "G. Marcus and P. Hinojosa and A. Avila and J.
                 Nolazco-Flores",
  booktitle =    "Proceedings of the Fifth {IEEE} International Caracas
                 Conference on Devices, Circuits and Systems, November
                 3--5, 2004",
  title =        "A fully synthesizable single-precision, floating-point
                 adder\slash subtractor and multiplier in {VHDL} for
                 general and educational use",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "319--323",
  year =         "2004",
  bibdate =      "Wed Apr 27 18:18:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Markov:2004:SAA,
  author =       "Svetoslav Markov and Rene Alt",
  title =        "Stochastic arithmetic: Addition and multiplication by
                 scalars",
  journal =      j-APPL-NUM-MATH,
  volume =       "50",
  number =       "3--4",
  pages =        "475--488",
  month =        sep,
  year =         "2004",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Sat May 14 10:50:47 MDT 2005",
  bibsource =    "http://www.sciencedirect.com/science/journal/01689274;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274",
}

@Article{Markov:2004:SAS,
  author =       "Svetoslav Markov and Rene Alt and Jean-Luc Lamotte",
  title =        "Stochastic Arithmetic: $s$-spaces and Some
                 Applications",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "37",
  number =       "1--4",
  pages =        "275--284",
  month =        dec,
  year =         "2004",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Dec 6 07:00:28 MST 2004",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/58/A/22/abstract.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  remark =       "Special Issue: SCAN'2002 International Conference
                 (Guest Editors: Ren {\'e} Alt and Jean-Luc Lamotte)",
}

@InProceedings{Markstein:2004:SDS,
  author =       "Peter Markstein",
  title =        "Software Division and Square Root Using
                 {Goldschmidt}'s Algorithms",
  crossref =     "Frougny:2004:RCR",
  pages =        "146--157",
  year =         "2004",
  bibdate =      "Fri Nov 17 07:00:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_12_markstein.pdf",
  abstract =     "Goldschmidt's Algorithms for division and square root
                 are often characterized as being useful for hardware
                 implementation, and lacking self-correction. A
                 reexamination of these algorithms show that there are
                 good software counterparts that retain the speed
                 advantage of Goldschmidt's Algorithm over the
                 Newton--Raphson iteration. A final step is needed,
                 however, to get the last bit rounded correctly.",
  acknowledgement = ack-nhfb,
  keywords =     "correct rounding; division; floating-point arithmetic;
                 Goldschmidt; square root",
}

@Article{McIvor:2004:IMM,
  author =       "C. McIvor and M. McLoone and J. V. McCanny",
  title =        "Improved {Montgomery} modular inverse algorithm",
  journal =      j-ELECT-LETTERS,
  volume =       "40",
  number =       "18",
  pages =        "1110--1112",
  day =          "2",
  month =        sep,
  year =         "2004",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:20045610",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Wed Dec 28 18:13:01 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "https://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1335002",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}

@Article{McKenzie:2004:ACP,
  author =       "Pierre McKenzie and Heribert Vollmer and Klaus W.
                 Wagner",
  title =        "Arithmetic Circuits and Polynomial Replacement
                 Systems",
  journal =      j-SIAM-J-COMPUT,
  volume =       "33",
  number =       "6",
  pages =        "1513--1531",
  month =        dec,
  year =         "2004",
  CODEN =        "SMJCAT",
  ISSN =         "0097-5397 (print), 1095-7111 (electronic)",
  ISSN-L =       "0097-5397",
  bibdate =      "Sat Apr 16 10:19:28 MDT 2005",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/33/6;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/39207",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Computing",
  journal-URL =  "http://epubs.siam.org/sicomp",
}

@Article{McLaughlin:2004:NFM,
  author =       "Philip B. {McLaughlin, Jr.}",
  title =        "New frameworks for {Montgomery}'s modular
                 multiplication method",
  journal =      j-MATH-COMPUT,
  volume =       "73",
  number =       "246",
  pages =        "899--906",
  month =        apr,
  year =         "2004",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Wed Aug 11 08:23:05 MDT 2004",
  bibsource =    "http://www.ams.org/mcom/2004-73-246;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ams.org/mcom/2004-73-246/S0025-5718-03-01543-6/home.html;
                 http://www.ams.org/mcom/2004-73-246/S0025-5718-03-01543-6/S0025-5718-03-01543-6.dvi;
                 http://www.ams.org/mcom/2004-73-246/S0025-5718-03-01543-6/S0025-5718-03-01543-6.pdf;
                 http://www.ams.org/mcom/2004-73-246/S0025-5718-03-01543-6/S0025-5718-03-01543-6.ps;
                 http://www.ams.org/mcom/2004-73-246/S0025-5718-03-01543-6/S0025-5718-03-01543-6.tex",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Mitra:2004:NAB,
  author =       "A. Mitra and M. Chakraborty",
  title =        "The {NLMS} algorithm in block floating-point format",
  journal =      j-IEEE-SIGNAL-PROCESS-LETT,
  volume =       "11",
  number =       "3",
  pages =        "301--304",
  month =        mar,
  year =         "2004",
  CODEN =        "ISPLEM",
  ISSN =         "1070-9908 (print), 1558-2361 (electronic)",
  ISSN-L =       "1070-9908",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present a novel scheme to implement the normalized
                 least mean square algorithm in block floating-point
                 (BFP) format, which permits processing of data over a
                 wide dynamic range, at a cost significantly less than
                 that of a floating-point processor.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Signal Processing Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=97",
  summary =      "We present a novel scheme to implement the normalized
                 least mean square algorithm in block floating-point
                 (BFP) format, which permits processing of data over a
                 wide dynamic range, at a cost significantly less than
                 that of a floating-point processor. \ldots{}",
}

@Manual{MPFRTeam:2004:MMP,
  author =       "{The MPFR Team}",
  title =        "{MPFR}: {The} {Multiple Precision Floating-Point
                 Reliable Library}: Edition 2.1.0: {November 2004}",
  pages =        "ii + 35",
  year =         "2004",
  bibdate =      "Thu Dec 15 18:49:26 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mpfr.org/mpfr-current/mpfr.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Muller:2004:CSR,
  author =       "Siguna M{\"u}ller",
  title =        "On the Computation of Square Roots in Finite Fields",
  journal =      j-DESIGNS-CODES-CRYPTOGR,
  volume =       "31",
  number =       "3",
  pages =        "301--312",
  month =        mar,
  year =         "2004",
  CODEN =        "DCCREC",
  ISSN =         "0925-1022 (print), 1573-7586 (electronic)",
  ISSN-L =       "0925-1022",
  bibdate =      "Tue Aug 3 16:38:18 MDT 2004",
  bibsource =    "http://www.wkap.nl/jrnltoc.htm/0925-1022;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ipsapp008.kluweronline.com/IPS/content/ext/x/J/4630/I/61/A/8/abstract.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Designs, codes, and cryptography",
  journal-URL =  "http://link.springer.com/journal/10623",
}

@TechReport{Muller:2004:DCS,
  author =       "Jean-Michel Muller and A. Tisserand and B. Dupont de
                 Dinechin and C. Monat",
  title =        "Division by Constant for the {ST100} {DSP}
                 Microprocessor",
  type =         "Research Report",
  number =       "RR2004-45",
  institution =  "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "69364 Lyon Cedex 07, France",
  pages =        "2 + 10",
  month =        oct,
  year =         "2004",
  bibdate =      "Mon Dec 06 11:14:04 2004",
  bibsource =    "http://www.ens-lyon.fr/LIP/Pub/rr2004.php;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2004/RR2004-45.ps.gz",
  abstract =     "Algorithms for Euclidean (i.e., integer) division by a
                 constant operation are presented. They allow fast
                 computation for some values of the divisor (known at
                 compile time) or also when both quotient and modulus
                 are required. These algorithms are based on the
                 multiply-accumulate instruction and the 40-bit
                 arithmetic available in many DSPs. The results are
                 demonstrated on the ST100 DSP from STMicroelectronics
                 in the case of standard speech coding applications.",
  acknowledgement = ack-nhfb,
  keywords =     "Compiler; Computer Arithmetic; Division by Constant;
                 DSP; Euclidean Division; Software Division",
}

@Article{Nguyen:2004:LDL,
  author =       "P. Nguyen and D. Stehle",
  title =        "Low-dimensional lattice basis reduction revisited
                 (extended abstract)",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "3076",
  pages =        "338--357",
  year =         "2004",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/b98210",
  ISBN =         "3-540-22156-5",
  ISBN-13 =      "978-3-540-22156-2",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Fri Jun 24 14:49:07 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Nievergelt:2004:AAP,
  author =       "Yves Nievergelt",
  title =        "Analysis and applications of {Priest}'s distillation",
  journal =      j-TOMS,
  volume =       "30",
  number =       "4",
  pages =        "402--433",
  month =        dec,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1039813.1039815",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 12 06:34:31 MDT 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Correcting an infinite loop in Douglas M. Priest's
                 renormalization algorithm, the theory proved here
                 supports streamlined algorithms to resolve the
                 tablemaker's dilemma for the floating-point computation
                 of real and complex sums and dot-products, properly
                 rounded to the ultimate digit. Applications include
                 computations of areas, volumes, and intersections.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "accurate floating-point summation; correct rounding;
                 floating-point arithmetic",
}

@Article{Ogasawara:2004:OPO,
  author =       "Takeshi Ogasawara and Hideaki Komatsu and Toshio
                 Nakatani",
  title =        "Optimizing precision overhead for x86 processors",
  journal =      j-SPE,
  volume =       "34",
  number =       "9",
  pages =        "875--893",
  day =          "25",
  month =        jul,
  year =         "2004",
  CODEN =        "SPEXBL",
  DOI =          "https://doi.org/10.1002/spe.596",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Sat Apr 16 07:26:31 MDT 2005",
  bibsource =    "http://www.interscience.wiley.com/jpages/0038-0644;
                 http://www3.interscience.wiley.com/journalfinder.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "It is a major challenge for a Java JIT compiler to
                 perform single-precision floating-point operations
                 efficiently for the x86 processors. In previous
                 research, the double-precision mode is set as the
                 default precision mode when methods are invoked.
                 Sophisticated approaches then use heuristic approaches
                 to optimization by considering the trade-offs between
                 roundings and mode switches. However, this convention
                 introduces redundant mode switches across method
                 boundaries. Furthermore, methods that include both
                 single- and double-precision operations cannot switch
                 the mode, even if single-precision operations are
                 dominant. We propose a new approach to these problems.
                 We eliminate redundant mode switches by ignoring the
                 default precision mode and calling a method in the same
                 precision mode as the caller. For methods that include
                 both single- and double-precision methods, we reduce
                 the overhead of rounding by isolating code segments of
                 a given method that should be executed in the
                 single-precision mode. We implemented our approach in
                 IBM's Just-in-Time compiler, and obtained experimental
                 results demonstrating that, in SPECjvm98, it
                 consistently shows the best performance in any
                 configuration of benchmark programs, inline policies,
                 and processor architectures compared with previous
                 research approaches.",
  acknowledgement = ack-nhfb,
  fjournal =     "Software---Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  keywords =     "floating-point operations; Java; precision control;
                 x86 processors",
  onlinedate =   "27 Apr 2004",
}

@TechReport{Ogita:2004:ASDa,
  author =       "Takeshi Ogita and Siegfried M. Rump and Shin'ichi
                 Oishi",
  title =        "Accurate Sum and Dot Product",
  type =         "Technical Report",
  number =       "04.1",
  institution =  "Forschungsschwerpunkt Informations- und
                 Kommunikationstechnik, Technical University
                 Hamburg-Harburg",
  address =      "Hamburg, Germany",
  pages =        "4",
  year =         "2004",
  bibdate =      "Fri Nov 26 15:58:09 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation; distillation",
}

@InProceedings{Ogita:2004:ASDb,
  author =       "Takeshi Ogita and Siegfried M. Rump and Shin'ichi
                 Oishi",
  title =        "Accurate Sum and Dot Product with Applications",
  crossref =     "IEEE:2004:IIS",
  pages =        "152--155",
  year =         "2004",
  bibdate =      "Fri Nov 26 15:55:22 2004",
  bibsource =    "http://www.oishi.info.waseda.ac.jp/~ogita/index.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://citeseer.ist.psu.edu/cache/papers/cs2/255/http:zSzzSzwww.oishi.info.waseda.ac.jpzSz~ogitazSzdoczSzsum040921.pdf/accurate-sum-and-dot.pdf;
                 http://www.ti3.tu-harburg.de/paper/rump/OgRuOi04a.pdf",
  abstract =     "In a recent paper the authors presented a new and very
                 fast algorithm for accurate computation and inclusion
                 of the sum and dot product of floating point numbers.
                 In this paper we show that the algorithms can be used
                 to compute a very accurate inclusion of the solution of
                 systems of linear equations. As a basic building block,
                 accurate solution of linear equations has applications
                 in very many areas.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}

@InProceedings{Olausson:2004:RFP,
  author =       "M. Olausson and A. Ehliar and J. Eilert and D. Liu",
  booktitle =    "{ISCAS '04}. Proceedings of the 2004 International
                 Symposium on Circuits and Systems, 23--26 May 2004",
  title =        "Reduced floating point for {MPEG1/2} layer {III}
                 decoding",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "V-209--V-212",
  year =         "2004",
  bibdate =      "Wed Apr 27 18:18:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A new approach to decode MPEG 1/2-layer III, mp3, is
                 presented. Instead of converting the algorithm to fixed
                 point, we propose a 16-bit floating point
                 implementation. These 16 bits include 1 sign bit and 15
                 bits of both mantissa and exponent. \ldots{}",
  acknowledgement = ack-nhfb,
}

@InProceedings{Ortiz:2004:SPI,
  author =       "I. Ortiz and M. Jimenez",
  booktitle =    "{MWSCAS '04}. The 2004 47th Midwest Symposium on
                 Circuits and Systems. 25--28 July 2004",
  title =        "Scalable pipeline insertion in floating-point division
                 and square root units",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "II-225--II-228",
  year =         "2004",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Division and square root are important operations in a
                 number of data processing algorithms. They are
                 inherently time consuming operations and can require a
                 significant amount of resources when implemented in
                 hardware. This work reports the development of
                 scalable, floating-point (FP) division and square root
                 operators with adjustable precision, range, and
                 pipeline granularity. An algorithm for pipeline
                 insertion was used for both operators, enabling speeds
                 up to 204MFLOPS when implemented on a Xilinx Virtex II
                 FPGA.",
  acknowledgement = ack-nhfb,
  summary =      "Division and square root are important operations in a
                 number of data processing algorithms. They are
                 inherently time consuming operations and can require a
                 significant amount of resources when implemented in
                 hardware. This work reports the \ldots{}",
}

@Article{Pace:2004:ERL,
  author =       "L. Pace and A. Salvan and L. Ventura",
  title =        "The Effects of Rounding on Likelihood Procedures",
  journal =      j-J-APPL-STAT,
  volume =       "31",
  number =       "1",
  pages =        "29--48",
  month =        jan,
  year =         "2004",
  CODEN =        "????",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  bibdate =      "Sat Dec 4 12:10:37 MST 2004",
  bibsource =    "http://www.tandf.co.uk/journals/routledge/02664763.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
}

@Article{Page:2004:PCA,
  author =       "D. Page and N. P. Smart",
  title =        "Parallel cryptographic arithmetic using a redundant
                 {Montgomery} representation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "53",
  number =       "11",
  pages =        "1474--1482",
  month =        nov,
  year =         "2004",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2004.100",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 08:12:46 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1336767",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Paul:2004:SMR,
  author =       "L. J. Paul and P. H. Bauer and C. Lorand and K.
                 Premaratne",
  booktitle =    "{MWSCAS '04}. The 2004 47th Midwest Symposium on
                 Circuits and Systems, 25--28 July 2004",
  title =        "Stabilizing mantissa rates in feedback systems with
                 floating-point quantization",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "II-501--II-504",
  year =         "2004",
  bibdate =      "Wed Apr 27 18:18:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Petkovic:2004:GCS,
  author =       "M. S. Petkovi{\'c} and L. Ranci{\'c}",
  title =        "On the guaranteed convergence of the square-root
                 iteration method",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "170",
  number =       "1",
  pages =        "169--179",
  day =          "1",
  month =        sep,
  year =         "2004",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:00:00 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042704000184",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Pineiro:2004:AAL,
  author =       "J. A. Pi{\~n}eiro and M. D. Ercegovac and J. D.
                 Bruguera",
  title =        "Algorithm and Architecture for Logarithm, Exponential
                 and Powering Computation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "53",
  number =       "9",
  pages =        "1085--1096",
  year =         "2004",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2004.53",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jun 24 10:05:48 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://www.ac.usc.es/arquivos/articulos/2004/gac2004-j05.ps",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Plouffe:2004:ILS,
  author =       "Simon Plouffe",
  title =        "Invited Lecture: A survey of Integer Relations
                 algorithms and rational numbers [abstract only]",
  crossref =     "Frougny:2004:RCR",
  pages =        "",
  year =         "2004",
  bibdate =      "Fri Nov 17 07:00:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_02_plouffe.pdf",
  abstract =     "It is widely believed that Integer Relations
                 algorithms such as LLL, Lattice reduction or PSLQ which
                 are implemented in most computer algebra systems are
                 generalizations of the Euclidian algorithm or the
                 continued fraction algorithm.\par

                 We give simple examples of cases where the programs
                 fails to find a solution and in general examples of
                 problem that could hardly be solved using such
                 tools.\par

                 Most of the examples are either large rational numbers
                 or near rational numbers, the difference being so small
                 that even very high precision do not guarantee to have
                 results",
  acknowledgement = ack-nhfb,
  keywords =     "Algebraic numbers; Coordination sequences; Golden
                 ratio; Integer Relations; Lattice Reduction; LLL; Pisot
                 sequences; PSLQ; Zeolites",
}

@Article{Priest:2004:ESC,
  author =       "Douglas M. Priest",
  title =        "Efficient scaling for complex division",
  journal =      j-TOMS,
  volume =       "30",
  number =       "4",
  pages =        "389--401",
  month =        dec,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1039813.1039814",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 12 06:34:31 MDT 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We develop a simple method for scaling to avoid
                 overflow and harmful underflow in complex division. The
                 method guarantees that no overflow will occur unless at
                 least one component of the quotient must overflow,
                 otherwise the normwise error in the computed result is
                 at most a few units in the last place. Moreover, the
                 scaling requires only four floating point
                 multiplications and a small amount of integer
                 arithmetic to compute the scale factor. Thus, on many
                 modern CPUs, our method is both safer and faster than
                 Smith's widely used algorithm.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "complex division",
}

@Article{Putot:2004:SAB,
  author =       "Sylvie Putot and Eric Goubault and Matthieu Martel",
  title =        "Static Analysis-Based Validation of Floating-Point
                 Computations",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2991",
  pages =        "306--313",
  year =         "2004",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Wed Mar 10 06:51:00 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springeronline.com/3-540-21260-4",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Quach:2004:SIR,
  author =       "N. T. Quach and N. Takagi and M. J. Flynn",
  title =        "Systematic {IEEE} rounding method for high-speed
                 floating-point multipliers",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "12",
  number =       "5",
  pages =        "511--521",
  month =        may,
  year =         "2004",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/TVLSI.2004.825860",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Sat Jul 16 11:25:05 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "For performance reasons, many high-speed
                 floating-point multipliers today precompute multiple
                 significand values (SVs) in advance. The final
                 normalization and rounding steps are then performed by
                 selecting the appropriate SV. While having speed
                 advantages, this integrated rounding method complicates
                 the development of the rounding logic significantly,
                 hence, requiring a systematic rounding method.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
  summary =      "For performance reasons, many high-speed
                 floating-point multipliers today precompute multiple
                 significand values (SVs) in advance. The final
                 normalization and rounding steps are then performed by
                 selecting the appropriate SV. While having speed
                 advantages \ldots{}",
}

@Article{Radecka:2004:DVT,
  author =       "K. Radecka and Z. Zilic",
  title =        "Design verification by test vectors and arithmetic
                 transform universal test set",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "53",
  number =       "5",
  pages =        "628--640",
  month =        may,
  year =         "2004",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2004.1275301",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 08:12:36 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1275301",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Rettinger:2004:FAJ,
  author =       "R. Rettinger",
  title =        "A Fast Algorithm for {Julia} Sets of Hyperbolic
                 Rational Functions",
  crossref =     "Frougny:2004:RCR",
  pages =        "158--171",
  year =         "2004",
  bibdate =      "Fri Nov 17 07:00:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_13_rettinger.pdf",
  abstract =     "Although numerous computer programs have been written
                 to compute sets of points which claim to approximate
                 Julia sets, no reliable high precision pictures of
                 nontrivial Julia sets are currently known. Usually, no
                 error estimates are added and even those algorithms
                 which work reliable in theory, become unreliable in
                 practice due to rounding errors and the use of fixed
                 length floating point numbers.\par

                 In this paper we prove the existence of polynomial time
                 algorithms to approximate the Julia sets of given
                 hyperbolic rational functions. We will give a strict
                 computable error estimation w.r.t. the Hausdorff metric
                 on the complex sphere. This extends a result on
                 polynomials $ z \to z^2 + c $, where $ |c| < 1 / 4 $,
                 in [RW03] and an earlier result in [Zho98] on the
                 recursiveness of the Julia sets of hyperbolic
                 polynomials.\par

                 The algorithm given in this paper computes Julia sets
                 locally in time $ O(k \cdot M(k)) $ (where $ M(k) $
                 denotes the time needed to multiply two $k$-bit
                 numbers). Roughly speaking, the local time complexity
                 is the number of Turing machine steps to decide a set
                 of disks of spherical diameter $ 2^{-k}$ so that the
                 union of these disks has Hausdorff distance at most $
                 2^{-k + 2}$. This allows to give reliable pictures of
                 Julia sets to arbitrary precision.",
  acknowledgement = ack-nhfb,
  keywords =     "Computational Complexity; Julia Sets",
}

@Article{Reyhani-Masoleh:2004:EDS,
  author =       "Arash Reyhani-Masoleh and M. Anwar Hasan",
  title =        "Efficient digit-serial normal basis multipliers over
                 binary extension fields",
  journal =      j-TECS,
  volume =       "3",
  number =       "3",
  pages =        "575--592",
  month =        aug,
  year =         "2004",
  CODEN =        "????",
  ISSN =         "1539-9087 (print), 1558-3465 (electronic)",
  ISSN-L =       "1539-9087",
  bibdate =      "Fri Oct 29 06:35:47 MDT 2004",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Embedded Computing Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?&idx=J840",
}

@Article{Reyhani-Masoleh:2004:LCB,
  author =       "A. Reyhani-Masoleh and M. A. Hasan",
  title =        "Low complexity bit parallel architectures for
                 polynomial basis multiplication over {$ {\rm GF}(2^m)
                 $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "53",
  number =       "8",
  pages =        "945--959",
  month =        aug,
  year =         "2004",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2004.47",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 08:12:40 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1306989",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Riley:2004:HAE,
  author =       "Joseph Riley and Michael J. Schulte",
  title =        "A Hardware Accelerator for Elliptic Curve Cryptography
                 over {$ \mathrm {GF}(2^m) $}",
  journal =      j-INT-J-COMP-RESEARCH,
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  year =         "2004",
  ISSN =         "1535-6698",
  bibdate =      "Sun Mar 04 20:54:26 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Special Issue on Cryptographic Hardware and Embedded
                 Systems",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2004-10.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Computer Research",
}

@InProceedings{Roy:2004:ACF,
  author =       "S. Roy and P. Banerjee",
  booktitle =    "Proceedings. 41st Design Automation Conference, June
                 7--11, 2004",
  title =        "An algorithm for converting floating-point
                 computations to fixed-point in {MATLAB} based {FPGA}
                 design",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "484--487",
  year =         "2004",
  bibdate =      "Wed Apr 27 18:18:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sadaghdar:2004:BFP,
  author =       "M. Sadaghdar and K. Iniewski and M. Syrzycki",
  booktitle =    "Canadian Conference on Electrical and Computer
                 Engineering, 2--5 May 2004",
  title =        "11-bit floating-point pipelined analog to digital
                 converter in 0.18$ \mu $ m {CMOS}",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1503--1506",
  year =         "2004",
  bibdate =      "Wed Apr 27 18:18:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Schimmler:2004:BSF,
  author =       "Manfred Schimmler and Bertil Schmidt and Hans-Werner
                 Lang",
  title =        "A bit-serial floating-point unit for a massively
                 parallel system on a chip",
  journal =      j-PARALLEL-ALGORITHMS-APPL,
  volume =       "19",
  number =       "2-3",
  pages =        "79--95",
  year =         "2004",
  CODEN =        "PAAPEC",
  ISSN =         "1063-7192",
  ISSN-L =       "1026-7689",
  MRclass =      "Database Expansion Item",
  MRnumber =     "MR2113359",
  bibdate =      "Thu Nov 8 19:16:14 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Parallel Algorithms and Applications",
  journal-URL =  "http://www.tandfonline.com/loi/gpaa20",
}

@InProceedings{Schirra:2004:ILR,
  author =       "Stefan Schirra",
  title =        "Invited Lecture: Real Numbers and Robustness in
                 Computational Geometry",
  crossref =     "Frougny:2004:RCR",
  pages =        "7--21",
  year =         "2004",
  bibdate =      "Fri Nov 17 07:00:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_03_schirra.pdf",
  abstract =     "Robustness issues due to imprecise arithmetic used in
                 place of exact real number computation are a notorious
                 problem in the implementation of geometric algorithms.
                 We briefly address some robustness issues and discuss
                 approaches to resolve them.",
  acknowledgement = ack-nhfb,
  keywords =     "computational geometry; exact geometric computation;
                 robustness",
}

@TechReport{Schulte:2004:DED,
  author =       "Michael J. Schulte and Eric Schwarz",
  title =        "Design Exploration for Decimal Floating-Point
                 Arithmetic {IBM} University Partnership Program
                 Proposal",
  type =         "Technical report",
  institution =  "University of Wisconsin-Madison and IBM Systems and
                 Technology Group",
  address =      "Madison, WI, USA",
  pages =        "4",
  day =          "11",
  month =        mar,
  year =         "2004",
  bibdate =      "Sat Mar 03 19:24:05 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://domino.research.ibm.com/acas/w3www_acas.nsf/images/proposals_04.05/%24FILE/schulte.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@InProceedings{Schulte:2004:LPC,
  author =       "M. J. Schulte and K. Chirca and J. Glossner and H.
                 Wang and S. Mamidi and P. I. Balzola and S.
                 Vassiliadis",
  title =        "A Low-Power Carry Skip Adder with Fast Saturation",
  crossref =     "IEEE:2004:IICb",
  pages =        "269--279",
  year =         "2004",
  bibdate =      "Sun Mar 04 20:56:38 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2004-11.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Seidel:2004:DOI,
  author =       "Peter-Michael Seidel and Guy Even",
  title =        "Delay-optimized implementation of {IEEE}
                 floating-point addition",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "53",
  number =       "2",
  pages =        "97--113",
  month =        feb,
  year =         "2004",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2004.1261822",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 08:12:30 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1261822",
  abstract =     "We present an IEEE floating-point adder (FP-adder)
                 design. The adder accepts normalized numbers, supports
                 all four IEEE rounding modes, and outputs the correctly
                 normalized rounded sum\slash difference in the format
                 required by the IEEE Standard.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "We present an IEEE floating-point adder (FP-adder)
                 design. The adder accepts normalized numbers, supports
                 all four IEEE rounding modes, and outputs the correctly
                 normalized rounded sum/difference in the format
                 required by the IEEE Standard. The FP-adder \ldots{}",
}

@InProceedings{Seidel:2004:LIF,
  author =       "Peter-Michael Seidel",
  booktitle =    "Conference Record of the Thirty-Eighth Asilomar
                 Conference on Signals, Systems and Computers, Nov.
                 7--10, 2004",
  title =        "On-line {IEEE} floating-point multiplication and
                 division for reduced power dissipation",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "498--502",
  year =         "2004",
  bibdate =      "Wed Apr 27 18:18:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Shi:2004:FPF,
  author =       "Changchun Shi and R. W. Brodersen",
  title =        "Floating-point to fixed-point conversion with decision
                 errors due to quantization",
  crossref =     "IEEE:2004:IICc",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "V-41--V-44",
  year =         "2004",
  bibdate =      "Wed Apr 27 18:18:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Steele:2004:RHP,
  author =       "Guy L. {Steele Jr.} and Jon L. White",
  title =        "Retrospective: How to Print Floating-Point Numbers
                 Accurately",
  journal =      j-SIGPLAN,
  volume =       "39",
  number =       "4",
  pages =        "372--389",
  month =        apr,
  year =         "2004",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/989393.989431",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Tue Jun 15 10:00:43 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Best of PLDI 1979--1999. Reprint of, and retrospective
                 on, \cite{Steele:1990:HPF}.",
  abstract =     "We present algorithms for accurately converting
                 floating-point numbers to decimal representation. The
                 key idea is to carry along with the computation an
                 explicit representation of the required rounding
                 accuracy. We begin with the simpler problem of
                 converting fixed-point fractions. A modification of the
                 well-known algorithm for radix-conversion of
                 fixed-point fractions by multiplication explicitly
                 determines when to terminate the conversion process; a
                 variable number of digits are produced. The algorithm
                 has these properties: (*) No information is lost; the
                 original fraction can be recovered from the output by
                 rounding. (*) No ``garbage digits'' are produced. (*)
                 The output is correctly rounded. (*) It is never
                 necessary to propagate carries on rounding. We then
                 derive two algorithms for free-format out-put of
                 floating-point numbers. The first simply scales the
                 given floating-point number to an appropriate
                 fractional range and then applies the algorithm for
                 fractions. This is quite fast and simple to code but
                 has inaccuracies stemming from round-off errors and
                 oversimplification. The second algorithm guarantees
                 mathematical accuracy by using multiple-precision
                 integer arithmetic and handling special cases. Both
                 algorithms produce no more digits than necessary
                 (intuitively, the ``1.3 prints as 1.2999999'' problem
                 does not occur). Finally, we modify the free-format
                 conversion algorithm for use in fixed-format
                 applications. Information may be lost if the fixed
                 format provides too few digit positions, but the output
                 is always correctly rounded. On the other hand, no
                 ``garbage digits'' are ever produced, even if the fixed
                 format specifies too many digit positions (intuitively,
                 the ``4/3 prints as 1.333333328366279602'' problem does
                 not occur).",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}

@PhdThesis{Stehle:2004:ARR,
  author =       "Damien Stehl{\'e}",
  title =        "Algorithmique de la r{\'e}duction de r{\'e}seaux et
                 application {\`a} la recherche de pires cas pour
                 l'arrondi de fonctions math{\'e}matiques. ({French})
                 [{Algorithmics} of network reduction and application to
                 the search for worst cases for rounding of mathematical
                 functions]",
  type =         "Doctorat de {l'Universit{\'e} Henri Poincar{\'e} ---
                 Nancy 1 (sp{\'e}cialit{\'e} informatique)}",
  school =       "Universit{\'e} Henri Poincar{\'e} --- Nancy",
  address =      "Nancy, France",
  pages =        "xvi + 252",
  year =         "2004",
  bibdate =      "Fri Dec 08 09:38:41 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://theses.hal.science/tel-01748080/",
  abstract =     "Euclidean lattices are a powerful tool for several
                 algorithmic topics, among which are cryptography and
                 algorithmic number theory. The contributions of this
                 thesis are twofold: we improve lattice basis reduction
                 algorithms, and we introduce a new application of
                 lattice reduction, in computer arithmetic. Concerning
                 lattices, we consider both small dimensions and
                 arbitrary dimensions, for which we improve the
                 classical LLL algorithm. Concerning the application, we
                 make use of Coppersmith's method for computing the
                 small roots of multivariate modular polynomials, in
                 order to find the worst cases for the rounding of
                 mathematical functions, when the function, the rounding
                 mode and the precision are fixed. We also generalise
                 our technique to find input numbers that are
                 simultaneously bad for two functions. These two methods
                 are expensive pre-computations, but once performed,
                 they help speeding up the implementations of elementary
                 mathematical functions in fixed precision.",
  acknowledgement = ack-nhfb,
}

@Misc{Stehle:2004:GAT,
  author =       "D. Stehl{\'e} and P. Zimmermann",
  title =        "{Gal}'s Accurate Tables Method Revisited",
  howpublished = "World-Wide Web document",
  year =         "2004",
  bibdate =      "Fri Jun 24 14:56:03 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.loria.fr/~stehle/downloads/2x-double.txt;
                 http://www.loria.fr/~stehle/downloads/sincos-double.txt;
                 http://www.loria.fr/~stehle/IMPROVEDGAL.html",
  abstract =     "Gal's accurate tables algorithm aims at providing an
                 efficient implementation of elementary functions with
                 correct rounding as often as possible. This method
                 requires an expensive pre-computation of a table made
                 of the values taken by the function --- or by several
                 related functions --- at some distinguished points. Our
                 improvements of Gal's method are two-fold: on the one
                 hand we describe what is the arguably best set of
                 distinguished values and how it improves the efficiency
                 and correctness of the implementation of the function,
                 and on the other hand we give an algorithm which
                 drastically decreases the cost of the pre-computation.
                 These improvements are related to the worst cases for
                 the correct rounding of mathematical functions and to
                 the algorithms for finding them. We show that the whole
                 method can be turned into practice by giving complete
                 tables for $ 2^x $ and $ \sin x $ for $x$ in $ [1 / 2,
                 1) $, in double precision.\par

                 Here are the two tables mentioned in the article: the $
                 \sin x $ table and the $ 2^x $ table.\par

                 Erratum in the final version of the paper: in Section
                 4, the simultaneous worst case for sin and cos is t0 =
                 1f09c0c6cde5e3 and not t0 = 31a93fddd45e3.",
  acknowledgement = ack-nhfb,
}

@Book{Stine:2004:DCA,
  author =       "James E. Stine",
  title =        "Digital computer arithmetic datapath design using
                 {Verilog HDL}",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "xi + 180",
  year =         "2004",
  ISBN =         "1-4020-7710-6",
  ISBN-13 =      "978-1-4020-7710-4",
  LCCN =         "TK7868.D5 S75 2004",
  bibdate =      "Thu Nov 18 09:03:42 MST 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0820/2003064036-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0820/2003064036-t.html",
  acknowledgement = ack-nhfb,
  keywords =     "computer arithmetic; computers / cad-cam; computers /
                 hardware / personal computers / general; computers /
                 logic design; computers / programming languages /
                 general; computers / systems architecture / general;
                 digital electronics; mathematics / discrete
                 mathematics; technology \& engineering / electrical;
                 technology \& engineering / electronics / circuits /
                 general; technology \& engineering / electronics /
                 digital; Verilog (computer hardware description
                 language)",
  subject =      "Digital electronics; Verilog (Computer hardware
                 description language); Computer arithmetic",
}

@Misc{Sun:2004:LBR,
  author =       "{Sun Microsystems, Inc.}",
  title =        "Libmcr 0.9 beta: a reference correctly-rounded library
                 of basic double-precision transcendental elementary
                 functions",
  howpublished = "World-Wide Web software project archive",
  year =         "2004",
  bibdate =      "Fri Jun 24 14:59:44 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sun.com/download/products.xml?id=41797765",
  acknowledgement = ack-nhfb,
}

@Article{Sunar:2004:GMC,
  author =       "B. Sunar",
  title =        "A generalized method for constructing subquadratic
                 complexity {$ \mathrm {GF}(2^k) $} multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "53",
  number =       "9",
  pages =        "1097--1105",
  month =        sep,
  year =         "2004",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2004.52",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jun 24 21:17:30 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Sypniewski:2004:IAU,
  author =       "M. Sypniewski and W. K. Gwarek",
  booktitle =    "2004 {IEEE} {MTT-S} International Microwave Symposium
                 Digest. 6--11 June 2004",
  title =        "On the influence of arithmetic underflow rounding
                 standard on the speed of {FDTD} modeling",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1795--1798",
  year =         "2004",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:06 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper presents the influence of arithmetic
                 underflow rounding operations on the speed of FDTD
                 analysis. It is shown that the underflow treatment
                 according to the IEEE standard 754 (commonly accepted
                 and implemented in modern arithmetic \ldots{}).",
}

@InProceedings{Tadaki:2004:ECH,
  author =       "Kohtaro Tadaki",
  title =        "An extension of Chaitin's halting probability {$
                 \Omega $} to measurement operator in infinite
                 dimensional quantum system",
  crossref =     "Frougny:2004:RCR",
  pages =        "172--191",
  year =         "2004",
  bibdate =      "Fri Nov 17 07:00:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_14_tadaki.pdf",
  abstract =     "This paper proposes an extension of Chaitin's halting
                 probability $ \Omega $ to measurement operator in
                 infinite dimensional quantum system. Chaitin's $ \Omega
                 $ is defined as the probability that the universal
                 self-delimiting Turing machine $U$ halts, and plays a
                 central role in the development of algorithmic
                 information theory. In the theory, there are two
                 equivalent ways to define the program-size complexity $
                 H(s)$ of a given finite binary string s. In the
                 standard way, $ H(s)$ is defined as the length of the
                 shortest input string for U to output s. In the other
                 way, the so-called universal probability $m$ is
                 introduced first, and then $ H(s)$ is defined as $ -
                 \log_2 m(s)$ without reference to the concept of
                 program-size.\par

                 Mathematically, the statistics of outcomes in a quantum
                 measurement are described by a positive operator-valued
                 measure (POVM) in the most general setting. Based on
                 the theory of computability structures on a Banach
                 space developed by Pour-El and Richards, we extend the
                 universal probability to an analogue of POVM in
                 infinite dimensional quantum system, called universal
                 semi-POVM. We also give another characterization of
                 Chaitin's $ \Omega $ numbers by universal
                 probabilities. Then, based on this characterization, we
                 propose to define an extension of $ \Omega $ as a sum
                 of the POVM elements of a universal semi-POVM. The
                 validity of this definition is discussed.\par

                 In what follows, we introduce an operator version $
                 \hat {H}(s)$ of $ H(s) $ in a Hilbert space of infinite
                 dimension using universal semi-POVM, and study the
                 properties of $ \hat {H}(s)$.",
  acknowledgement = ack-nhfb,
  keywords =     "algorithmic information theory; Chaitin's $\Omega$;
                 computability in analysis; POVM; quantum measurement;
                 universal probability",
}

@TechReport{Thomas:2004:LLF,
  author =       "James W. Thomas and Jon P. Okada and Peter Markstein
                 and Ren-Cang Li",
  title =        "The {{\tt Libm}} Library and Floating-Point Arithmetic
                 in {HP-UX} for {Itanium}-Based Systems: Updated for
                 {HP-UX 11i v2}",
  type =         "Technical report",
  institution =  "Hewlett--Packard Company",
  address =      "Palo Alto, CA, USA",
  pages =        "26",
  day =          "3",
  month =        dec,
  year =         "2004",
  bibdate =      "Fri Jun 24 20:12:09 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://h21007.www2.hp.com/dspp/ddl/ddl_Download_File_TRX/1,1249,942,00.pdf",
  abstract =     "The HP-UX libm library provides mathematical functions
                 for C, C++, and Fortran 90. The HP-UX libm library and
                 compilers for Itanium-based systems provide a leading
                 combination of functionality, quality, and
                 performance.With inlining and software pipelining,
                 commonly used math functions can achieve throughput
                 comparable to hand-tuned vector routines without
                 requiring user code to be written for a vector
                 interface, and with no loss of accuracy or edge-case
                 behavior: For example, the single precision exponential
                 can exceed 400 million evaluations per second on a 1.5
                 GHz Itanium 2 system. The math API encompasses C99,
                 X/Open, and other popular functionality and offers four
                 fully supported IEEE floating types. The libm library
                 and compilers provide features that facilitate
                 programming techniques that have not been practical
                 heretofore. The libm implementation for Itanium-based
                 systems, introduced in 2001 in HP-UX B.11.20 (11i
                 v1.5), has been upgraded in B.11.22 (11i v1.6), B.11.23
                 (11i v2), and most recently in B.11.23 AR1204 and the
                 associated Math Library Cumulative Patch PHSS\_31853
                 with improved performance and overall quality and with
                 a few new functions. The AR1204 compilers are available
                 as patches for B.11.22; the associated Math patch for
                 B.11.22 is PHSS_32066. This paper (1) describes the
                 latest libm library (including sequences the compilers
                 inline) in terms of functionality, speed, accuracy,
                 standards, and special-case behavior; (2) discusses
                 programming techniques that exploit the floating-point
                 capabilities of HP-UX on Itanium- based systems; and
                 (3) describes motivations, goals, and development
                 strategies for the libm library and the compiler
                 floating-point facilities.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Thompson:2004:BDF,
  author =       "J. Thompson and N. Karra and M. J. Schulte",
  booktitle =    "Proceedings. {IEEE Computer Society Annual Symposium
                 on VLSI, 19--20 February 2004}",
  title =        "A 64-bit decimal floating-point adder",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "297--298",
  year =         "2004",
  bibdate =      "Wed Apr 27 18:18:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2004-08.pdf",
  abstract =     "Due to rapid growth in financial, commercial, and
                 Internet-based applications, there is an increasing
                 desire to allow computers to operate on both binary and
                 decimal floating-point numbers. Consequently,
                 specifications for decimal floating-point support are
                 being added to the IEEE-754 Standard for Floating-Point
                 Arithmetic. In this paper, we present the design and
                 implementation of a decimal floating-point adder that
                 is compliant with the current draft revision of this
                 standard. The adder supports operations on 64-bit
                 (16-digit) decimal floating-point operands. We provide
                 synthesis results indicating the estimated area and
                 delay for our design when it is pipelined to various
                 depths.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@Manual{TI:2004:TUG,
  title =        "{TMS320C3x} User's Guide",
  organization = "Texas Instruments",
  address =      "Post Office box 655303, Dallas, TX 75265, USA",
  pages =        "770",
  year =         "2004",
  bibdate =      "Wed Nov 24 09:20:17 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Literature Number: SPRU031F 2558539-9761 revision L
                 March 2004",
  URL =          "http://www-s.ti.com/sc/psheets/spru031f/spru031f.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "digital signal processor (DSP)",
}

@InProceedings{Tsoi:2004:ALA,
  author =       "K. H. Tsoi and C. H. Ho and H. C. Yeung and P. H. W.
                 Leong",
  title =        "An Arithmetic Library and its Application to the
                 {$N$}-body Problem",
  crossref =     "Arnold:2004:PAI",
  pages =        "68--78",
  year =         "2004",
  DOI =          "https://doi.org/10.1109/FCCM.2004.14",
  bibdate =      "Sat Jun 25 12:45:15 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cse.cuhk.edu.hk/~phwl/mt/public/archives/papers/cast_fccm04.pdf",
  abstract =     "Computer arithmetic is a specialist field of study,
                 and it is very difficult for designers to choose the
                 most efficient method for implementing a given
                 algorithm due to the large number of design choices
                 available. In this paper, an object oriented arithmetic
                 library is presented which can be used to simulate and
                 generate designs which use fixed, floating, logarithmic
                 and hybrid number representations. The advantages of
                 this approach are that a user can explore tradeoffs
                 concerning precision, accuracy and speed from single
                 high level description. Furthermore, users need not be
                 intimately familiar with the implementation details of
                 the underlying libraries, thus allowing users to
                 develop systems employing advanced computer arithmetic
                 without detailed knowledge of its implementation. The
                 application of this library to a coprocessor which
                 implements the force pipeline for an N-body solver is
                 described.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Underwood:2004:CGC,
  author =       "K. D. Underwood and K. S. Hemmert",
  booktitle =    "{FCCM 2004}. 12th Annual {IEEE} Symposium on
                 Field-Programmable Custom Computing Machines, 20--23
                 April 2004",
  title =        "Closing the gap: {CPU} and {FPGA} trends in
                 sustainable floating-point {BLAS} performance",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "219--228",
  year =         "2004",
  bibdate =      "Wed Apr 27 18:18:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Field programmable gate arrays (FPGAs) have long been
                 an attractive alternative to microprocessors for
                 computing tasks--as long as floating-point arithmetic
                 is not required. Fueled by the advance of Moore's law,
                 FPGAs are rapidly reaching sufficient densities to
                 enhance peak floating-point performance as well. The
                 question, however, is how much of this peak performance
                 can be sustained. This paper examines three of the
                 basic linear algebra subroutine (BLAS) functions:
                 vector dot product, matrix-vector multiply, and matrix
                 multiply. A comparison of microprocessors, FPGAs, and
                 reconfigurable computing platforms is performed for
                 each operation. The analysis highlights the amount of
                 memory bandwidth and internal storage needed to sustain
                 peak performance with FPGAs. This analysis considers
                 the historical context of the last six years and is
                 extrapolated for the next six years.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Underwood:2004:FVC,
  author =       "Keith D. Underwood",
  title =        "{FPGAs} vs. {CPUs}: Trends in peak floating-point
                 performance",
  crossref =     "ACM:2004:FAS",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "171--180",
  year =         "2004",
  DOI =          "https://doi.org/10.1145/968280.968305",
  bibdate =      "Sat Oct 9 13:06:11 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Moore's Law states that the number of transistors on a
                 device doubles every two years; however, it is often
                 (mis)quoted based on its impact on CPU performance.
                 This important corollary of Moore's Law states that
                 improved clock frequency plus improved architecture
                 yields a doubling of CPU performance every 18 months.
                 This paper examines the impact of Moore's Law on the
                 peak floating-point performance of FPGAs. Performance
                 trends for individual operations are analyzed as well
                 as the performance trend of a common instruction mix
                 (multiply accumulate). The important result is that
                 peak FPGA floating-point performance is growing
                 significantly faster than peak floating-point
                 performance for a CPU.",
  acknowledgement = ack-nhfb,
}

@Article{Vignes:2004:DSA,
  author =       "Jean Vignes",
  title =        "Discrete Stochastic Arithmetic for Validating Results
                 of Numerical Software",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "37",
  number =       "1--4",
  pages =        "377--390",
  month =        dec,
  year =         "2004",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Dec 6 07:00:28 MST 2004",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ipsapp009.kluweronline.com/IPS/content/ext/x/J/5058/I/58/A/31/abstract.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  remark =       "Special Issue: SCAN'2002 International Conference
                 (Guest Editors: Ren {\'e} Alt and Jean-Luc Lamotte).",
}

@Article{vonzurGathen:2004:FAG,
  author =       "J. Joachim von zur Gathen and Michael N{\"o}cker",
  title =        "Fast arithmetic with general {Gau{\ss}} periods",
  journal =      j-THEOR-COMP-SCI,
  volume =       "315",
  number =       "2--3",
  pages =        "419--452",
  day =          "6",
  month =        may,
  year =         "2004",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Thu Nov 4 10:19:15 MST 2004",
  bibsource =    "http://www.sciencedirect.com/science/journal/03043975;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We show how to apply fast arithmetic in conjunction
                 with general Gau{\ss} periods in finite fields. This is
                 an essential ingredient for some efficient
                 exponentiation algorithms.",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
  keywords =     "Efficient arithmetic; Exponentiation; Finite fields;
                 Gau{\ss} period; Normal basis",
}

@InProceedings{Voronenko:2004:AGI,
  author =       "Y. Voronenko and M. Puschel",
  title =        "Automatic generation of implementations for {DSP}
                 transforms on fused multiply-add architectures",
  crossref =     "IEEE:2004:IICc",
  volume =       "5",
  pages =        "V-101--V-104",
  year =         "2004",
  DOI =          "https://doi.org/10.1109/ICASSP.2004.1327057",
  bibdate =      "Sun Feb 20 10:05:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Many modern computer architectures feature fused
                 multiply-add (FMA) instructions, which offer
                 potentially faster performance for numerical
                 applications. For DSP transforms, compilers can only
                 generate FMA code to a very limited extent because
                 optimal use of FMAs requires modifying the chosen
                 algorithm. In this paper, we present a framework for
                 automatically generating FMA code for every linear DSP
                 transform, which we implemented as an extension to the
                 SPIRAL code generation system. We show that for many
                 transforms and transform sizes, our generated FMA code
                 matches the best-known hand-derived FMA algorithms in
                 terms of arithmetic cost. Further, we present actual
                 runtime results that show the speed-up obtained by
                 using FMA instructions.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Walters:2004:TSC,
  author =       "E. G. Walters and M. J. Schulte and M. G. Arnold",
  title =        "Truncated Squarers with Constant and Variable
                 Correction",
  crossref =     "Luk:2004:ASP",
  year =         "2004",
  bibdate =      "Sun Mar 04 20:49:55 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2004-14.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Wang:2004:DFP,
  author =       "Liang-Kai Wang and M. J. Schulte",
  booktitle =    "Proceedings. 15th {IEEE} International Conference on
                 Application-Specific Systems, Architectures and
                 Processors, 27--29 Sept. 2004",
  title =        "Decimal floating-point division using
                 {Newton--Raphson} iteration",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "84--95",
  year =         "2004",
  bibdate =      "Wed Apr 27 18:18:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2004-06.pdf",
  abstract =     "Decreasing feature sizes allow additional
                 functionality to be added to future microprocessors to
                 improve the performance of important application
                 domains. As a result of rapid growth in financial,
                 commercial, and Internet-based applications, hardware
                 support for decimal floating-point arithmetic is now
                 being considered by various computer manufacturers and
                 specifications for decimal floating-point arithmetic
                 have been added to the draft revision of the IEEE-754
                 Standard for Floating-Point Arithmetic (IEEE-754R).
                 This work presents an efficient arithmetic algorithm
                 and hardware design for decimal floating-point
                 division. \ldots{}",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@InProceedings{Weaver:2004:MFD,
  author =       "B. J. Weaver and Y. V. Zakharov and T. C. Tozer",
  title =        "Multiplication-free division of complex numbers",
  crossref =     "Anonymous:2004:ICM",
  pages =        "211--214",
  year =         "2004",
  bibdate =      "Sat Dec 04 09:59:02 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Wu:2004:HSL,
  author =       "Chien-Hsing Wu and Chien-Ming Wu and Ming-Der Shieh
                 and Yin-Tsung Hwang",
  title =        "High-speed, low-complexity systolic designs of novel
                 iterative division algorithms in {$ \mathrm {GF}(2^m)
                 $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "53",
  number =       "3",
  pages =        "375--380",
  month =        mar,
  year =         "2004",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2004.1261843",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jul 5 08:12:33 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1261843",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Wu:2004:ORF,
  author =       "Jun Wu and Sheng Chen and James F. Whidborne and Jian
                 Chu",
  title =        "Optimal realizations of floating-point implemented
                 digital controllers with finite word length
                 considerations",
  journal =      j-INT-J-CONTROL,
  volume =       "77",
  number =       "5",
  pages =        "427--440",
  year =         "2004",
  CODEN =        "IJCOAZ",
  ISSN =         "0020-7179 (print), 1366-5820 (electronic)",
  ISSN-L =       "0020-7179",
  MRclass =      "93B15 (93C57)",
  MRnumber =     "MR2052876",
  bibdate =      "Thu Nov 8 19:16:14 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Control",
  journal-URL =  "http://www.tandfonline.com/loi/tcon20",
}

@InProceedings{Yang:2004:EEP,
  author =       "Xiao Yang and S. K. Valia and M. J. Schulte and R. B.
                 Lee",
  booktitle =    "Conference Record of the Thirty-Eighth Asilomar
                 Conference on Signals, Systems and Computers, Nov.
                 7--10, 2004",
  title =        "Exploration and evaluation of {PLX} floating-point
                 instructions and implementations for {$3$D} graphics",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1873--1878",
  year =         "2004",
  bibdate =      "Wed Apr 27 18:18:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2004-18.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Yang:2004:PFE,
  author =       "Xiao Yang and R. B. Lee",
  booktitle =    "{ICME '04}. 2004 {IEEE} International Conference on
                 Multimedia and Expo, 27--30 June 2004",
  title =        "{PLX FP}: an efficient floating-point instruction set
                 for {$3$D} graphics",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "137--140",
  year =         "2004",
  bibdate =      "Wed Apr 27 18:18:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "3D graphics is an important component in the workload
                 of today's computing platforms. Many ISA extensions for
                 3D graphics have been proposed and implemented. We
                 describe PLX FP, a new floating-point extension to the
                 PLX architecture, designed to support very efficiently
                 the essential operations needed for the 3D graphics
                 pipeline. Very high performance floating-point 3D
                 graphics processing is achieved, using a low-cost PLX
                 processor.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Yoon:2004:IPT,
  author =       "Han-Ul Yoon and Kyoung-Taik Park and Kwee-Bo Sim",
  booktitle =    "{IECON 2004}, 30th Annual Conference of {IEEE}
                 Industrial Electronics Society",
  title =        "Improvement of processing time using residue number
                 system and sorting network in controller design",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2046--2051",
  year =         "2004",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/IECON.2004.1432111",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper presents and proposes two approaches to
                 speed up for the controller unit. One is a residue
                 number system (RNS), the other is a sorting network.
                 Using an RNS reduces the total bit size of adder and
                 carry-propagation delays. Also, using \ldots{}",
}

@InProceedings{Zhang:2004:PBL,
  author =       "W. Zhang and G. A. Jullien and V. S. Dimitrov",
  booktitle =    "Proceedings of the 2004 International Symposium on
                 Circuits and Systems: {ISCAS '04}, 23--26 May 2004",
  title =        "A programmable base {$2$D}-{LNS} {MAC} with
                 self-generated look-up tables",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "II-789--92",
  year =         "2004",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 16:14:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper presents a new architecture for a
                 programmable second base 2-dimensional logarithmic
                 number system (2D LNS) Multiply Accumulator Cell (MAC)
                 using DRAMs to store the conversion look-up tables
                 (LUTs). It uses a direct mapping from non- \ldots{}",
}

@InProceedings{Zheng:2004:HRN,
  author =       "Xizhong Zheng",
  title =        "On the Hierarchy of {$ \Delta_2^0 $}-Real Numbers",
  crossref =     "Frougny:2004:RCR",
  pages =        "192--215",
  year =         "2004",
  bibdate =      "Fri Nov 17 07:00:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6_15_zheng.pdf",
  abstract =     "A real number x is called $ \Delta_2^0 $ if its binary
                 expansion corresponds to a $ \Delta_2^0 $-set of
                 natural numbers. Such reals are just the limits of
                 computable sequences of rational numbers and hence also
                 called computably approximable. Depending on how fast
                 the sequences converge, $ \Delta_2^0 $-reals have
                 different levels of effectiveness. This leads to
                 various hierarchies of $ \Delta_2^0 $ reals. In this
                 paper we summarize several recent developments related
                 to such kind of hierarchies",
  acknowledgement = ack-nhfb,
  keywords =     "$ \Delta_2^0 $-reals; Computably approximable reals;
                 hierarchy",
}

@Article{Zhu:2004:ISR,
  author =       "Hufei Zhu and Zhongding Lei and F. P. S. Chin",
  title =        "An improved square-root algorithm for {BLAST}",
  journal =      j-IEEE-SIGNAL-PROCESS-LETT,
  volume =       "11",
  number =       "9",
  pages =        "772--775",
  month =        sep,
  year =         "2004",
  CODEN =        "ISPLEM",
  ISSN =         "1070-9908 (print), 1558-2361 (electronic)",
  ISSN-L =       "1070-9908",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Signal Processing Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=97",
  summary =      "In this letter, an improved square-root algorithm for
                 Bell Labs Layered Space-Time (BLAST) system is
                 proposed. It speeds up the original square-root
                 algorithm by 36\% in terms of the number of
                 multiplications and additions. Compared with the
                 \ldots{}",
}

@InProceedings{Zhuo:2004:SMA,
  author =       "L. Zhuo and V. K. Prasanna",
  booktitle =    "Proceedings. 18th International Parallel and
                 Distributed Processing Symposium, 26--30 April 2004",
  title =        "Scalable and modular algorithms for floating-point
                 matrix multiplication on {FPGAs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "92--92",
  year =         "2004",
  bibdate =      "Wed Apr 27 18:18:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Zimmerman:2004:DCI,
  author =       "T. Zimmerman and J. R. Hoff",
  title =        "The design of a charge-integrating modified
                 floating-point {ADC} chip",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "39",
  number =       "6",
  pages =        "895--905",
  month =        jun,
  year =         "2004",
  CODEN =        "IJSCBC",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  summary =      "One of the challenges posed by calorimeters in
                 high-energy physics experiments is digitizing wide
                 dynamic range charge signals at high rate to a
                 specified precision. One response to this challenge is
                 the development of the QIE (charge integrator and
                 \ldots{}).",
}

@Article{Abdallah:2005:MRN,
  author =       "M. Abdallah and A. Skavantzos",
  title =        "On {MultiModuli} residue number systems with moduli of
                 forms $ r^a $, $ r^b - 1 $, $ r^c + 1 $",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-1,
  volume =       "52",
  number =       "7",
  pages =        "1253--1266",
  month =        jul,
  year =         "2005",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/TCSI.2005.851388",
  ISSN =         "????",
  ISSN-L =       "1549-8328",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=32002",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems I: Regular
                 Papers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8919",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The residue number system (RNS) is an integer system
                 appropriate for implementing fast digital signal
                 processors since it can support parallel, carry-free,
                 high-speed arithmetic. One of the most important
                 considerations when designing RNS systems is \ldots{}",
}

@Article{Abtahi:2005:CFR,
  author =       "M. Abtahi and P. Siy",
  title =        "Core function of an {RNS} number with no ambiguity",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "50",
  number =       "3--4",
  pages =        "459--470",
  month =        aug,
  year =         "2005",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:49:46 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122105002890",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@InProceedings{Adharapurapu:2005:LSO,
  author =       "Pavan Adharapurapu and Milo{\v{s}} Ercegovac",
  title =        "A Linear-System Operator based Scheme for Evaluation
                 of Multinomials",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-178.pdf",
  abstract =     "We present a radix-2 online computational scheme for
                 evaluating multinomials in a fixed-point number
                 representation system. Its main advantage is that it
                 can adapt to any evaluation graph representing the
                 multinomial. Evaluation graphs are efficient
                 representations of multinomials in a factored form. The
                 proposed scheme maps subgraphs of the evaluation graph
                 using linear-system operators. These operators
                 transform the expressions represented by the subgraphs
                 into systems of linear equations. The linear equations
                 are then solved in an online,
                 most-significant-digit-first fashion. The scheme
                 produces, after an initial delay, one output digit per
                 iteration for inputs within range. The iteration time
                 is equal to the sum of the delays of a redundant adder,
                 multiplexer, register and a selection unit and is
                 independent of the size of the multinomial and the
                 precision of the inputs/outputs. The initial delay is
                 proportional to the diameter of the evaluation graph
                 and the maximum number of children of any addition node
                 in the graph. The proposed method lends itself to
                 implementation using simple, highly regular hardware
                 with serial interconnections between modules.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17",
  pagecount =    "8",
}

@InProceedings{Aharoni:2005:SCI,
  author =       "Merav Aharoni and Sigal Asaf and Ron Maharik and Ilan
                 Nehama and Ilya Nikulshin and Abraham Ziv",
  title =        "Solving Constraints on the Invisible Bits of the
                 Intermediate Result for Floating-Point Verification",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-136.pdf",
  abstract =     "Test generation for datapath floating-point
                 verification involves targeting intricate corner cases,
                 which can often be solved only through complex
                 constraint solving.\par

                 In the process of calculating the result, we use an
                 intermediate result whose significand comprises a
                 finite number of bits and a sticky bit that is 0 if and
                 only if the intermediate result is exact. We refer to
                 all the bits beyond those represented in the final
                 result as the invisible bits. We deal with corner cases
                 that can only be defined via constraints on the
                 intermediate result.\par

                 Our work investigates the following problem: Given a
                 floating-point operation, and constraints on the
                 invisible bits and the sticky bit, find two inputs for
                 the operation that yield an intermediate result
                 compatible with the constraints.\par

                 The paper supplies a deterministic solution for
                 addition and subtraction, and probabilistic solutions
                 for multiplication and division. It also discusses the
                 application of these algorithms to the verification of
                 floating-point implementations.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17",
  pagecount =    "8",
}

@Article{Alvarez:2005:FMF,
  author =       "C. Alvarez and J. Corbal and M. Valero",
  title =        "Fuzzy Memoization for Floating-Point Multimedia
                 Applications",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "7",
  pages =        "922--927",
  month =        jul,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.119",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 16:17:17 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1432675",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "Instruction memoization is a promising technique to
                 reduce the power consumption and increase the
                 performance of future low-end/mobile multimedia
                 systems. Power and performance efficiency can be
                 improved by reusing instances of an already executed
                 \ldots{}",
}

@Misc{Anonymous:2005:HAP,
  author =       "Anonymous",
  title =        "How to Avoid Performance Penalties for
                 Gradual-Underflow Behavior",
  howpublished = "World-Wide Web document",
  year =         "2005",
  bibdate =      "Fri Oct 14 17:01:56 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.intel.com/cd/ids/developer/asmo-na/eng/dc/pentium4/knowledgebase/90575.htm",
  abstract =     "The Pentium 4 processor supports calculation involving
                 sub-normals with special code stored in 'Read Only
                 Memory', which is not pipelined as are calculations in
                 the normalized range. In order to avoid the performance
                 penalty, such processors often support an
                 abrupt-underflow mode, where sub-normals are
                 ``flushed'' immediately to zero. Where an Intel
                 processor supports FTZ, it is possible to set the mode
                 at run-time and to change it to suit the requirements
                 of a program that may require full protection of
                 accuracy in certain code sequences and fast execution
                 in others.",
  acknowledgement = ack-nhfb,
  remark =       "Discusses mechanisms for selecting flush-to-zero
                 behavior on Pentium 4 processors in Microsoft Windows
                 and GNU/Linux.",
}

@Misc{Anonymous:2005:TMF,
  author =       "Anonymous",
  title =        "Test of Mathematical Functions of the {Standard C
                 Library}",
  howpublished = "World-Wide Web software project archive",
  month =        jun,
  year =         "2005",
  bibdate =      "Fri Jun 24 19:55:16 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.vinc17.org/research/testlibm/",
  abstract =     "Some of the mathematical functions of the standard C
                 library have been tested on worst cases for the exact
                 rounding in double precision. The following table gives
                 the ratio or the number of incorrect roundings for
                 various machines, in the rounding to nearest mode.",
  acknowledgement = ack-nhfb,
  xxnote =       "LOOK AT THIS MORE!!!",
}

@Article{Antelo:2005:DRD,
  author =       "E. Antelo and T. Lang and P. Montuschi and A.
                 Nannarelli",
  title =        "Digit-recurrence dividers with reduced logical depth",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "7",
  pages =        "837--851",
  month =        jul,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.115",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 16:17:17 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1432667",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Antelo:2005:LLD,
  author =       "Elisardo Antelo and Tom{\'a}s Lang and Paolo Montuschi
                 and Alberto Nannarelli",
  title =        "Low Latency Digit-Recurrence Reciprocal and
                 Square-Root Reciprocal Algorithm and Architecture",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-116.pdf",
  abstract =     "The reciprocal and square-root reciprocal operations
                 are important in several applications. For the
                 operations, we present algorithms that combine a
                 digit-by-digit module and one iteration of a
                 quadratic-convergence approximation. The latter is
                 implemented by a digit-recurrence, which uses the
                 digits produced by the digit-by-digit part. In this
                 way, both parts execute in an overlapped manner, so
                 that the total number of cycles is about half the
                 number that would be required by the digit-by-digit
                 part alone. Because of the approximation, correct
                 rounding of the result cannot be obtained directly in
                 all cases; we propose a variable-time implementation
                 that produces the correctly rounded result with a small
                 average overhead. Radix-4 implementations are described
                 and have been synthesized. They achieve the same cycle
                 time as the standard digit-by-digit implementation,
                 resulting in a speed-up of about 2 and, because of the
                 approximation part, the area factor is also about 2. We
                 also show a combined implementation for both operations
                 that has essentially the same complexity as that for
                 square-root reciprocal alone.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17; correct rounding; floating-point
                 arithmetic",
  pagecount =    "8",
}

@InProceedings{Antelo:2005:LLP,
  author =       "Elisardo Antelo and Julio Villalba",
  title =        "Low Latency Pipelined Circular {CORDIC}",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-132.pdf",
  abstract =     "The pipelined CORDIC with linear approximation to
                 rotation has been proposed to achieve reductions in
                 delay, power and area; however, the schemes for
                 rotation (multiplication) and vectoring (division)
                 complicate implementation in a single unit. In this
                 work, we improve the linear approximation scheme,
                 leading to a unified implementation for rotation and
                 vectoring where fully parallel tree multipliers are
                 used instead of the second half of CORDIC iterations.
                 We also combine the linear approximation to rotation
                 with the scale factor compensation so that the
                 compensation is performed concurrently with the
                 rotation process. Comparison with other designs is also
                 provided.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17",
  pagecount =    "8",
}

@InProceedings{Arnold:2005:BIR,
  author =       "M. G. Arnold and J. Ruan",
  title =        "Bipartite Implementation of the Residue Logarithmic
                 Number System",
  crossref =     "Luk:2005:ASP",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Fri Jun 24 18:11:43 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Accepted for publication.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Arnold:2005:RLN,
  author =       "Mark Arnold",
  title =        "The Residue Logarithmic Number System: Theory and
                 Implementation",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-163.pdf;
                 http://www.cse.lehigh.edu/~caar/rlns.pdf",
  abstract =     "The Residue Logarithmic Number System (RLNS)
                 represents real values as quantized logarithms which,
                 in turn, are represented using the Residue Number
                 System (RNS). Compared to the conventional Logarithmic
                 Number System (LNS) in which quantized logarithms are
                 represented as binary integers, RLNS offers faster
                 multiplication and division times. RLNS and LNS use a
                 table lookup involving all bits for addition. The
                 width, dynamic range, precision and na{\"\i}ve table
                 size of RLNS (with careful moduli selection) is as good
                 as those for conventional LNS.\par

                 Conventional LNS can be more efficient than na{\"\i}ve
                 addition lookup. First, commutativity allows
                 interchanging arguments. Second, the addition function
                 is often essentially zero, and does not have to be
                 tabulated. In binary, comparisons are easy. In residue,
                 comparisons are slow. Although RLNS inherently demands
                 comparison, this paper shows a novel way comparisons
                 can be performed in parallel to the lookup from a small
                 table. This paper also describes a novel tool that
                 generates synthesizable Verilog, making RLNS viable in
                 practical applications that can benefit from shorter
                 multiply and divide times.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17; Logarithmic Number System; Residue Number
                 System",
  pagecount =    "10",
}

@Misc{Bailey:2005:DFDa,
  author =       "David H. Bailey",
  title =        "{DDFUN90}: {Fortran-90} double-double package",
  howpublished = "World-Wide Web site with software archives.",
  day =          "11",
  month =        mar,
  year =         "2005",
  bibdate =      "Tue Nov 22 05:48:53 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://crd.lbl.gov/~dhbailey/mpdist/;
                 http://crd.lbl.gov/~dhbailey/mpdist/ddfun90.tar.gz",
  abstract =     "This package contains software for performing
                 double-double arithmetic (approximately 32 decimal
                 digits). It is similar to the qd package above in
                 functionality, and in fact, an application program
                 written for one should be compatible with the other.
                 However this is entirely written in Fortran-90.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}

@Misc{Bailey:2005:DFDb,
  author =       "David H. Bailey",
  title =        "{DSFUN90}: {Fortran-90} double-single package",
  howpublished = "World-Wide Web site with software archives.",
  day =          "11",
  month =        mar,
  year =         "2005",
  bibdate =      "Tue Nov 22 05:48:53 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://crd.lbl.gov/~dhbailey/mpdist/;
                 http://crd.lbl.gov/~dhbailey/mpdist/dsfun90.tar.gz",
  abstract =     "This package contains software for performing
                 double-single arithmetic (approximately 15 decimal
                 digits). It is entirely written in Fortran-90. It is
                 targeted to systems, such as game systems, that do not
                 support IEEE 64-bit floating-point arithmetic.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}

@Article{Bailey:2005:HPF,
  author =       "David H. Bailey",
  title =        "High-Precision Floating-Point Arithmetic in Scientific
                 Computation",
  journal =      j-COMPUT-SCI-ENG,
  volume =       "7",
  number =       "3",
  pages =        "54--61",
  month =        may # "\slash " # jun,
  year =         "2005",
  CODEN =        "CSENFA",
  DOI =          "https://doi.org/10.1109/MCSE.2005.52",
  ISSN =         "1521-9615 (print), 1558-366X (electronic)",
  ISSN-L =       "1521-9615",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computscieng.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://csdl.computer.org/comp/mags/cs/2005/03/c3054abs.htm;
                 http://csdl.computer.org/dl/mags/cs/2005/03/c3054.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing in Science and Engineering",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
  summary =      "IEEE 64-bit floating-point arithmetic is sufficient
                 for most scientific applications, but a rapidly growing
                 body of scientific computing applications requires a
                 higher level of numeric precision. Software packages
                 have yielded interesting scientific \ldots{}",
}

@Misc{Bailey:2005:QDD,
  author =       "David H. Bailey",
  title =        "{QD}: double-double and quad double package",
  howpublished = "World-Wide Web site with software archives.",
  day =          "24",
  month =        aug,
  year =         "2005",
  bibdate =      "Tue Nov 22 05:48:53 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://crd.lbl.gov/~dhbailey/mpdist/;
                 http://crd.lbl.gov/~dhbailey/mpdist/qd.tar.gz",
  abstract =     "This package supports both a double-double datatype
                 (approx. 32 decimal digits) and a quad-double datatype
                 (approx. 64 decimal digits). The computational library
                 is written in C++. Both C++ and Fortran-90 high-level
                 language interfaces are provided to permit one to use
                 convert an existing C++ or Fortran-90 program to use
                 the library with only minor changes to the source code.
                 In most cases only a few type statements and (for
                 Fortran-90 programs) read\slash write statements need
                 to be changed. PSLQ and numerical quadrature programs
                 are included.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bajard:2005:AOP,
  author =       "Jean-Claude Bajard and Laurent Imbert and Thomas
                 Plantard",
  title =        "Arithmetic Operations in the Polynomial Modular Number
                 System",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-168.pdf",
  abstract =     "We propose a new number representation and arithmetic
                 for the elements of the ring of integers modulo p. The
                 so-called Polynomial Modular Number System (PMNS)
                 allows for fast polynomial arithmetic and easy
                 parallelization. The most important contribution of
                 this paper is the fundamental theorem of a Modular
                 Number System, which provides a bound for the
                 coefficients of the polynomials used to represent the
                 set $ \mathbb {Z}_p $. However, we also propose a
                 complete set of algorithms to perform the arithmetic
                 operations over a PMNS, which make this system of
                 practical interest for people concerned about efficient
                 implementation of modular arithmetic.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17; Lattice theory; Modular arithmetic; Number
                 system; Table-based methods",
  pagecount =    "8",
}

@InProceedings{Bajard:2005:PMM,
  author =       "Jean-Claude Bajard and Laurent Imbert and Graham
                 Jullien",
  title =        "Parallel {Montgomery} Multiplication in {$ \mathrm
                 {GF}(2^k) $} using Trinomial Residue Arithmetic",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-169.pdf",
  abstract =     "We propose the first general multiplication algorithm
                 in $ \mathrm {GF}(2^k) $ with a subquadratic area
                 complexity of $ \mathcal {O}(k^{8 / 5}) = \mathcal
                 {O}(k^{1.6}) $. Using the Chinese Remainder Theorem, we
                 represent the elements of $ \mathrm {GF}(2^k) $; i.e.,
                 the polynomials in $ \mathrm {GF}(2)[X] $ of degree at
                 most $ k - 1 $, by the remainder modulo a set of $n$
                 pairwise prime trinomials, $ T_1, \ldots {}, T_n $, of
                 degree $d$ and such that $ n d \geq k $. Our algorithm
                 is based on Montgomery's multiplication applied to the
                 ring formed by the direct product of the trinomials.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17",
  pagecount =    "8",
}

@Misc{Beebe:2005:MPA,
  author =       "Nelson H. F. Beebe",
  title =        "Multiple-precision arithmetic {FAQ}",
  howpublished = "World-Wide Web frequently-asked question document.",
  month =        sep,
  year =         "2005",
  bibdate =      "Wed Aug 30 17:46:43 2006",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "This report is updated frequently.",
  URL =          "https://www.math.utah.edu/faq/mp/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Beuchat:2005:MAR,
  author =       "Jean-Luc Beuchat and Jean-Michel Muller",
  editor =       "Stamatis Vassiliadis and Nikitas J. Dimopoulos and
                 Sanjay Vishnu Rajopadhye",
  booktitle =    "{Proceedings of the 16th IEEE International Conference
                 on Application-Specific Systems, Architectures, and
                 Processors (ASAP 2005), 23--25 July 2005, Samos,
                 Greece}",
  title =        "Multiplication algorithms for Radix-2 {RN}-codings and
                 two's complement numbers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  bookpages =    "xiii + 419",
  pages =        "303--308",
  year =         "2005",
  DOI =          "https://doi.org/10.1109/ASAP.2005.45",
  ISBN =         "0-7695-2407-9",
  ISBN-13 =      "978-0-7695-2407-8",
  ISSN =         "1063-6862",
  LCCN =         "",
  bibdate =      "Sun Jun 19 14:52:45 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=10334",
  acknowledgement = ack-nhfb,
}

@Article{Blanck:2005:EEC,
  author =       "J. Blanck",
  title =        "Efficient exact computation of iterated maps",
  journal =      j-J-LOGIC-ALG-PROG,
  volume =       "64",
  number =       "1",
  pages =        "41--59",
  month =        jul,
  year =         "2005",
  DOI =          "https://doi.org/10.1016/j.jlap.2004.07.004",
  ISSN =         "1567-8326 (print), 1873-5940 (electronic)",
  ISSN-L =       "1567-8326",
  bibdate =      "Thu Oct 17 10:09:18 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Logic and Algebraic Programming",
  journal-URL =  "http://www.sciencedirect.com/science/journal/15678326",
  remark =       "Special issue on Practical development of exact real
                 number computation.",
}

@Article{Boehm:2005:CRJ,
  author =       "Hans-J. Boehm",
  title =        "The constructive reals as a {Java Library}",
  journal =      j-J-LOGIC-ALG-PROG,
  volume =       "64",
  number =       "1",
  pages =        "3--11",
  month =        jul,
  year =         "2005",
  DOI =          "https://doi.org/10.1016/j.jlap.2004.07.002",
  ISSN =         "1567-8326 (print), 1873-5940 (electronic)",
  ISSN-L =       "1567-8326",
  bibdate =      "Wed Oct 16 18:43:22 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/java2000.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/S1567832604000736",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Logic and Algebraic Programming",
  journal-URL =  "http://www.sciencedirect.com/science/journal/15678326",
  remark =       "Special issue on Practical development of exact real
                 number computation.",
}

@InProceedings{Boldo:2005:SFC,
  author =       "Sylvie Boldo and Jean-Michel Muller",
  title =        "Some Functions Computable with a Fused-mac",
  crossref =     "Montuschi:2005:PIS",
  pages =        "52--58",
  year =         "2005",
  DOI =          "https://doi.org/10.1109/ARITH.2005.39",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-106.pdf",
  abstract =     "The fused multiply accumulate instruction (fused-mac)
                 that is available on some current processors such as
                 the Power PC or the Itanium eases some calculations. We
                 give examples of some floating-point functions (such as
                 ulp(x) or Nextafter(x, y)), or some useful tests, that
                 are easily computable using a fused-mac. Then, we show
                 that, with rounding to the nearest, the error of a
                 fused-mac instruction is exactly representable as the
                 sum of two floating-point numbers. We give an algorithm
                 that computes that error.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17",
  pagecount =    "7",
}

@Article{Bowman:2005:AVS,
  author =       "K. O. Bowman and L. R. Shenton",
  title =        "The asymptotic variance and skewness of maximum
                 likelihood estimators using {Maple}",
  journal =      j-J-STAT-COMPUT-SIMUL,
  volume =       "75",
  number =       "12",
  pages =        "975--986",
  year =         "2005",
  CODEN =        "JSCSAJ",
  DOI =          "https://doi.org/10.1080/00949650412331321142",
  ISSN =         "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
  ISSN-L =       "0094-9655",
  bibdate =      "Tue Apr 22 09:12:30 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Computation and Simulation",
  journal-URL =  "http://www.tandfonline.com/loi/gscs20",
}

@InProceedings{Brisebarre:2005:CRM,
  author =       "Nicolas Brisebarre and Jean-Michel Muller",
  title =        "Correctly Rounded Multiplication by Arbitrary
                 Precision Constants",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-122.pdf",
  abstract =     "We introduce an algorithm for multiplying a
                 floating-point number $x$ by a constant $C$ that is not
                 exactly representable in floating-point arithmetic. Our
                 algorithm uses a multiplication and a fused multiply
                 and add instruction. We give methods for checking
                 whether, for a given value of $C$ and a given
                 floating-point format, our algorithm returns a
                 correctly rounded result for any $x$. When it does not,
                 our methods give the values $x$ for which it does
                 not.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17; correct rounding; floating-point
                 arithmetic",
  pagecount =    "8",
}

@Article{Brisebarre:2005:NRR,
  author =       "Nicolas Brisebarre and David Defour and Peter Kornerup
                 and Jean-Michel Muller and Nathalie Revol",
  title =        "A New Range-Reduction Algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "3",
  pages =        "331--339",
  month =        mar,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.36",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue May 30 12:14:00 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://csdl.computer.org/comp/trans/tc/2005/03/t0331abs.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0331.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0331.pdf;
                 http://ieeexplore.ieee.org/iel5/12/30205/01388197.pdf;
                 http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205;
                 http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388197",
  abstract =     "Range-reduction is a key point for getting accurate
                 elementary function routines. We introduce a new
                 algorithm that is fast for input arguments belonging to
                 the most common domains, yet accurate over the full
                 double-precision range.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-16; range reduction",
  remark =       "Special issue on computer arithmetic: selected papers
                 from ARITH-16.",
}

@InProceedings{Bruguera:2005:FPF,
  author =       "Javier Bruguera and Tom{\'a}s Lang",
  title =        "Floating-point Fused Multiply-Add: Reduced Latency for
                 Floating-Point Addition",
  crossref =     "Montuschi:2005:PIS",
  pages =        "42--51",
  year =         "2005",
  DOI =          "https://doi.org/10.1109/ARITH.2005.22",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-102.pdf",
  abstract =     "In this paper we propose an architecture for the
                 computation of the double precision floating point
                 multiply add fused (MAF) operation $ A + (B \times C) $
                 that permits to compute the floating point addition
                 with lower latency than floating point multiplication
                 and MAF. While previous MAF architectures compute the
                 three operations with the same latency, the proposed
                 architecture permits to skip the first pipeline stages,
                 those related with the multiplication $ B \times C $,
                 in case of an addition. For instance, for a MAF unit
                 pipelined into three or five stages, the latency of the
                 floating point addition is reduced to two or three
                 cycles, respectively. To achieve the latency reduction
                 for floating-point addition, the alignment shifter,
                 which in previous organizations is in parallel with the
                 multiplication, is moved so that the multiplication can
                 be bypassed. To avoid that this modification increases
                 the critical path, a double-datapath organization is
                 used, in which the alignment and normalization are in
                 separate paths. Moreover, we use the techniques
                 developed previously of combining the addition and the
                 rounding and of performing the normalization before the
                 addition.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17",
  pagecount =    "10",
}

@Article{Burgess:2005:PRI,
  author =       "N. Burgess",
  title =        "Prenormalization rounding in {IEEE} floating-point
                 operations using a flagged prefix adder",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "13",
  number =       "2",
  pages =        "266--277",
  month =        feb,
  year =         "2005",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/TVLSI.2004.840764",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper demonstrates how IEEE 754 floating-point
                 standard compliant rounding can be merged with
                 carry-propagate addition in floating-point unit (FPU)
                 designs by using a novel adaptation of the prefix
                 adder. The paper considers add/subtract, multiply,
                 \ldots{}",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
  summary =      "This paper demonstrates how IEEE 754 floating-point
                 standard compliant rounding can be merged with
                 carry-propagate addition in floating-point unit (FPU)
                 designs by using a novel adaptation of the prefix
                 adder. The paper considers add/subtract, multiply
                 \ldots{}",
}

@Article{Chakraborty:2005:BFP,
  author =       "M. Chakraborty and A. Mitra",
  title =        "A block floating-point realization of the gradient
                 adaptive lattice filter",
  journal =      j-IEEE-SIGNAL-PROCESS-LETT,
  volume =       "12",
  number =       "4",
  pages =        "265--268",
  month =        apr,
  year =         "2005",
  CODEN =        "ISPLEM",
  ISSN =         "1070-9908 (print), 1558-2361 (electronic)",
  ISSN-L =       "1070-9908",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Signal Processing Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=97",
  summary =      "We present a novel scheme to implement the gradient
                 adaptive lattice (GAL) algorithm using block floating
                 point (BFP) arithmetic that permits processing of data
                 over a wide dynamic range at a cost significantly less
                 than that of a floating point (FP) \ldots{}",
}

@Article{Chang:2005:LCB,
  author =       "Ku-Young Chang and Dowon Hong and Hyun-Sook Cho",
  title =        "Low complexity bit-parallel multiplier for {$ {\rm
                 GF}(2^m) $} defined by all-one polynomials using
                 redundant representation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "12",
  pages =        "1628--1630",
  month =        dec,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.199",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 16:17:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1524942",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Chaniotakis:2005:LNB,
  author =       "Eleftherios Chaniotakis and Paraskevas Kalivas and
                 Kiamal Pekmestzi",
  title =        "Long Number Bit-Serial Squarers",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-162.pdf",
  abstract =     "New bit serial squarers for long numbers in LSB first
                 form, are presented in this paper. The first presented
                 scheme is a 50\% operational efficient squarer than has
                 the half number of cells compared to the traditional
                 squarers. The second scheme is a 100\% operational
                 efficient squarer. In this scheme, the number of the
                 cells remain unchanged compared to other proposed
                 schemes but the number of the required registers is
                 reduced significantly. Both schemes are presented in
                 non-systolic and systolic form and are compared against
                 other squarers presented in the bibliography from the
                 aspect of hardware complexity.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17",
  pagecount =    "8",
}

@Article{Chatterjee:2005:DEH,
  author =       "S. Chatterjee and L. R. Bachega and P. Bergner and K.
                 A. Dockser and J. A. Gunnels and M. Gupta and F. G.
                 Gustavson and C. A. Lapkowski and G. K. Liu and M.
                 Mendell and R. Nair and C. D. Wait and T. J. C. Ward
                 and P. Wu",
  title =        "Design and exploitation of a high-performance {SIMD}
                 floating-point unit for {Blue Gene/L}",
  journal =      j-IBM-JRD,
  volume =       "49",
  number =       "2/3",
  pages =        "377--391",
  month =        "????",
  year =         "2005",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Wed Jun 1 08:14:41 MDT 2005",
  bibsource =    "http://www.research.ibm.com/journal/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.research.ibm.com/journal/rd/492/chatterjee.pdf",
  abstract =     "We describe the design of a dual-issue
                 single-instruction, multiple-data-like (SIMD-like)
                 extension of the IBM PowerPC 440 floating-point unit
                 (FPU) core and the compiler and algorithmic techniques
                 to exploit it. This extended FPU is targeted at both
                 the IBM massively parallel Blue Gene/L machine and the
                 more pervasive embedded platforms. We discuss the
                 hardware and software codesign that was essential in
                 order to fully realize the performance benefits of the
                 FPU when constrained by the memory bandwidth
                 limitations and high penalties for misaligned data
                 access imposed by the memory hierarchy on a Blue Gene/L
                 node. Using both hand-optimized and compiled code for
                 key linear algebraic kernels, we validate the
                 architectural design choices, evaluate the success of
                 the compiler, and quantify the effectiveness of the
                 novel algorithm design techniques. Our measurements
                 show that the combination of algorithm, compiler, and
                 hardware delivers a significant fraction of peak
                 floating-point performance for compute-bound-kernels,
                 such as matrix multiplication, and delivers a
                 significant fraction of peak memory bandwidth for
                 memory-bound kernels, such as DAXPY, while remaining
                 largely insensitive to data alignment.",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  ordernumber =  "G322-0240",
}

@InProceedings{Choi:2005:PPA,
  author =       "Youngmoon Choi and Earl Swartzlander",
  title =        "Parallel Prefix Adder Design with Matrix
                 Representation",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-107.pdf",
  abstract =     "This paper presents a one-shot batch process that
                 generates a wide range of designs for a group of
                 parallel prefix adders. The prefix adders are
                 represented by two two-dimensional matrixes and two
                 vectors. This matrix representation makes it possible
                 to compose two functions for gate sizing which
                 calculate the delay and the total transistor width of
                 the carry propagation graph of adders. After gate
                 sizing, the critical path net-lists of the carry
                 propagation graph are generated from the matrix
                 representation for spice delay calculation. The process
                 is illustrated by generating sets of delay and total
                 transistor width pairs for 32-bit and 64-bit cases.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17",
  pagecount =    "9",
}

@Article{Cotofana:2005:ARA,
  author =       "Sorin Cotofana and Casper Lageweg and Stamatis
                 Vassiliadis",
  title =        "Addition Related Arithmetic Operations via Controlled
                 Transport of Charge",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "3",
  pages =        "243--256",
  month =        mar,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.40",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 16:17:15 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://csdl.computer.org/comp/trans/tc/2005/03/t0243abs.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0243.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0243.pdf;
                 http://ieeexplore.ieee.org/iel5/12/30205/01388190.pdf?isnumber=30205&prod=JNL&arnumber=1388190&arSt=+243&ared=+256&arAuthor=Cotofana%2C+S.%3B+Lageweg%2C+C.%3B+Vassiliadis%2C+S.;
                 http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388190&count=13&index=1;
                 http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388190",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-16",
  remark =       "Special issue on computer arithmetic: selected papers
                 from ARITH-16.",
}

@TechReport{Cowlishaw:2005:GDA,
  author =       "Mike Cowlishaw",
  title =        "General Decimal Arithmetic Specification",
  type =         "Report",
  number =       "Version 1.50",
  institution =  "IBM UK Laboratories",
  address =      "Hursley, UK",
  pages =        "iii + 63",
  day =          "9",
  month =        dec,
  year =         "2005",
  bibdate =      "Thu Mar 02 10:58:02 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www2.hursley.ibm.com/decimal/decarith.pdf;
                 http://www2.hursley.ibm.com/decimal/decarith.ps",
  abstract =     "This document defines a general purpose decimal
                 arithmetic. A correct implementation of this
                 specification is a decimal arithmetic which conforms to
                 the requirements of the IEEE standard 854-1987, while
                 supporting integer and unrounded floating-point
                 arithmetic as subsets.

                 Appendix A describes a simplified subset of the full
                 arithmetic which implements the decimal floating-point
                 arithmetic defined in ANSI Standard X3.274-1996 (the
                 REXX programming language) (this provides the model for
                 the unrounded floating-point rules). Appendix B
                 summarizes the design concepts behind the decimal
                 arithmetic. Appendix C lists the changes to this
                 specification.",
  acknowledgement = ack-nhfb,
  keywords =     "correct rounding; decimal floating-point arithmetic",
}

@Article{Daneshbeh:2005:CUB,
  author =       "Amir K. Daneshbeh and M. Anwar Hasan",
  title =        "A Class of Unidirectional Bit Serial Systolic
                 Architectures for Multiplicative Inversion and Division
                 over {$ \mathrm {GF}(2^m) $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "3",
  pages =        "370--380",
  month =        mar,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.35",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue May 30 12:14:00 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://csdl.computer.org/comp/trans/tc/2005/03/t0370abs.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0370.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0370.pdf;
                 http://ieeexplore.ieee.org/iel5/12/30205/01388201.pdf?isnumber=30205&prod=JNL&arnumber=1388201&arSt=+370&ared=+380&arAuthor=Daneshbeh%2C+A.K.%3B+Hasan%2C+M.A.;
                 http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388201&count=13&index=12;
                 http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388201",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-16",
  remark =       "Special issue on computer arithmetic: selected papers
                 from ARITH-16.",
}

@Article{Danysh:2005:AIV,
  author =       "Albert Danysh and Dimitri Tan",
  title =        "Architecture and Implementation of a Vector\slash
                 {SIMD} Multiply-Accumulate Unit",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "3",
  pages =        "284--293",
  month =        mar,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.41",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue May 30 12:14:00 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://csdl.computer.org/comp/trans/tc/2005/03/t0284abs.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0284.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0284.pdf;
                 http://ieeexplore.ieee.org/iel5/12/30205/01388193.pdf?isnumber=30205&prod=JNL&arnumber=1388193&arSt=+284&ared=+293&arAuthor=Danysh%2C+A.%3B+Tan%2C+D.;
                 http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388193&count=13&index=4;
                 http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388193",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-16",
  remark =       "Special issue on computer arithmetic: selected papers
                 from ARITH-16.",
}

@Manual{Daramy-Loirat:2005:CLL,
  author =       "Catherine Daramy-Loirat and David Defour and Florent
                 de Dinechin and Matthieu Gallet and Nicolas Gast and
                 Jean-Michel Muller",
  title =        "{CR-LIBM}: a library of correctly rounded elementary
                 functions in double-precision",
  organization = "Laboratoire de l'Informatique du Parall{\'e}lisme",
  address =      "Lyon, France",
  pages =        "138",
  day =          "16",
  month =        sep,
  year =         "2005",
  bibdate =      "Thu Dec 15 16:27:30 2005",
  bibsource =    "http://lipforge.ens-lyon.fr/projects/crlibm/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://lipforge.ens-lyon.fr/frs/download.php/11/crlibm.pdf",
  abstract =     "The crlibm project aims at developing a portable,
                 proven, correctly rounded, and efficient mathematical
                 library ({\tt libm}) for double precision. Current libm
                 implementations do not always return the floating-point
                 number that is closest to the exact mathematical
                 result. As a consequence, different libm
                 implementations will return different results for the
                 same input, which prevents full portability of
                 floating-point applications. In addition, few libraries
                 support but the round-to-nearest mode of the
                 IEEE754/IEC 60559 standard for floating-point
                 arithmetic (hereafter usually referred to as the
                 IEEE-754 standard). crlibm provides the four rounding
                 modes: To nearest, to $ + \infty $, to $ - \infty $ and
                 to zero.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Daumas:2005:GPU,
  author =       "Marc Daumas and Guillaume Melquiond and C{\'e}sar
                 Mu{\~n}oz",
  title =        "Guaranteed Proofs Using Interval Arithmetic",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-155.pdf",
  abstract =     "This paper presents a set of tools for mechanical
                 reasoning of numerical bounds using interval
                 arithmetic. The tools implement two techniques for
                 reducing decorrelation: interval splitting and Taylor's
                 series expansions. Although the tools are designed for
                 the proof assistant system PVS, expertise on PVS is not
                 required. The ultimate goal of the tools is to provide
                 guaranteed proofs of numerical properties with a
                 minimal human-theorem prover interaction.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17",
  pagecount =    "8",
}

@Article{deDinechin:2005:MTM,
  author =       "Florent de Dinechin and Arnaud Tisserand",
  title =        "Multipartite Table Methods",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "3",
  pages =        "319--330",
  month =        mar,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.54",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue May 30 12:14:00 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://csdl.computer.org/comp/trans/tc/2005/03/t0319abs.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0319.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0319.pdf;
                 http://ieeexplore.ieee.org/iel5/12/30205/01388196.pdf?isnumber=30205&prod=JNL&arnumber=1388196&arSt=+319&ared=+330&arAuthor=de+Dinechin%2C+F.%3B+Tisserand%2C+A.;
                 http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388196&count=13&index=7;
                 http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388196",
  abstract =     "A unified view of most previous
                 table-lookup-and-addition methods (bipartite tables,
                 SBTM, STAM, and multipartite methods) is presented.
                 This unified view allows a more accurate computation of
                 the error entailed by these methods, which enables a
                 wider design space exploration, leading to tables
                 smaller than the best previously published ones by up
                 to 50 percent. The synthesis of these multipartite
                 architectures on Virtex FPGAs is also discussed.
                 Compared to other methods involving multipliers, the
                 multipartite approach offers the best speed/area
                 tradeoff for precisions up to 16 bits. A reference
                 implementation is available at
                 http://www.ens-lyon.fr/LIP/Arenaire/.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-16",
  remark =       "Special issue on computer arithmetic: selected papers
                 from ARITH-16.",
}

@InProceedings{deDinechin:2005:TPU,
  author =       "Florent de Dinechin and Alexey Ershov and Nicolas
                 Gast",
  title =        "Towards the Post-ultimate {\tt libm}",
  crossref =     "Montuschi:2005:PIS",
  pages =        "288--295",
  year =         "2005",
  DOI =          "https://doi.org/10.1109/ARITH.2005.46",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-165.pdf",
  abstract =     "This article presents advances on the subject of
                 correctly rounded elementary functions since the
                 publication of the {\tt libultim} mathematical library
                 developed by Ziv at IBM. This library showed that the
                 average performance and memory overhead of correct
                 rounding could be made negligible. However, the
                 worst-case overhead was still a factor 1000 or more. It
                 is shown here that, with current processor technology,
                 this worst-case overhead can be kept within a factor of
                 2 to 10 of current best libms. This low overhead has
                 very positive consequences on the techniques for
                 implementing and proving correctly rounded functions,
                 which are also studied. These results lift the last
                 technical obstacles to a generalisation of (at least
                 some) correctly rounded double precision elementary
                 functions.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17; correct rounding; floating-point
                 arithmetic",
  pagecount =    "8",
}

@InProceedings{Dou:2005:BFP,
  author =       "Y. Dou and S. Vassiliadis and G. K. Kuzmanov and G. N.
                 Gaydadjiev",
  title =        "64-bit floating-point {FPGA} matrix multiplication",
  crossref =     "ACM:2005:FAS",
  pages =        "86--95",
  year =         "2005",
  DOI =          "https://doi.org/10.1145/1046192.1046204",
  bibdate =      "Sat Oct 9 12:38:44 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We introduce a 64-bit ANSI/IEEE Std 754-1985 floating
                 point design of a hardware matrix multiplier optimized
                 for FPGA implementations. A general block matrix
                 multiplication algorithm, applicable for an arbitrary
                 matrix size is proposed. The algorithm potentially
                 enables optimum performance by exploiting the data
                 locality and reusability incurred by the general matrix
                 multiplication scheme and considering the limitations
                 of the I/O bandwidth and the local storage volume. We
                 implement a scalable linear array of processing
                 elements (PE) supporting the proposed algorithm in the
                 Xilinx Virtex II Pro technology. Synthesis results
                 confirm a superior performance-area ratio compared to
                 related recent works. Assuming the same FPGA chip, the
                 same amount of local memory, and the same I/O
                 bandwidth, our design outperforms related proposals by
                 at least 1.7X and up to 18X consuming the least
                 reconfigurable resources. A total of 39 PEs can be
                 integrated into the xc2vp125-7 FPGA, reaching
                 performance of, e.g., 15.6 GFLOPS with 1600 KB local
                 memory and 400 MB/s external memory bandwidth.",
  acknowledgement = ack-nhfb,
}

@Article{Efstathiou:2005:EDM,
  author =       "C. Efstathiou and H. T. Vergos and G. Dimitrakopoulos
                 and D. Nikolos",
  title =        "Efficient diminished-$1$ modulo $ 2^n + 1 $
                 multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "4",
  pages =        "491--496",
  month =        apr,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.63",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 16:17:16 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1401868",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Eggert:2005:PEN,
  author =       "P. R. Eggert and D. S. Parker",
  title =        "Perturbing and evaluating numerical programs without
                 recompilation --- the wonglediff way",
  journal =      j-SPE,
  volume =       "35",
  number =       "4",
  pages =        "313--322",
  day =          "10",
  month =        apr,
  year =         "2005",
  CODEN =        "SPEXBL",
  DOI =          "https://doi.org/10.1002/spe.637",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Sat Apr 16 07:26:37 MDT 2005",
  bibsource =    "http://www.interscience.wiley.com/jpages/0038-0644;
                 http://www3.interscience.wiley.com/journalfinder.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "wonglediff is a program that tests the sensitivity of
                 arbitrary program executables or processes to changes
                 that are introduced by a process that runs in parallel.
                 On Unix and Linux kernels, wonglediff creates a
                 supervisor process that runs applications and, on the
                 fly, introduces desired changes to their process state.
                 When execution terminates, it then summarizes the
                 resulting changes in the output files. The technique
                 employed has a variety of uses. This paper describes an
                 implementation of wonglediff that checks the
                 sensitivity of programs to random changes in the
                 floating-point rounding modes. It runs a program
                 several times, wongling it each time: randomly toggling
                 the IEEE-754 rounding mode of the program as it
                 executes. By comparing the resulting output, one gets a
                 poor man's numerical stability analysis for the
                 program. Although the analysis does not give any kind
                 of guarantee about a program's stability, it can reveal
                 genuine instability, and it does serve as a
                 particularly useful and revealing idiot light. In our
                 implementation, differences among the output files from
                 the program's multiple runs are summarized in a report.
                 This report is in fact an HTML version of the output
                 file, with inline mark-up summarizing individual
                 differences among the multiple instances. When viewed
                 with a browser, the differences can be highlighted or
                 rendered in many different ways.",
  acknowledgement = ack-nhfb,
  fjournal =     "Software---Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  keywords =     "diff; IEEE-754 floating point arithmetic; numerical
                 instability checking; random rounding; rounding modes;
                 sensitivity analysis",
  onlinedate =   "21 Dec 2004",
}

@Article{Eleftheriou:2005:SFF,
  author =       "M. Eleftheriou and B. G. Fitch and A. Rayshubskiy and
                 T. J. C. Ward and R. S. Germain",
  title =        "Scalable framework for {$3$D} {FFTs} on the {Blue
                 Gene/L} supercomputer: Implementation and early
                 performance measurements",
  journal =      j-IBM-JRD,
  volume =       "49",
  number =       "2/3",
  pages =        "457--464",
  month =        "????",
  year =         "2005",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Wed Jun 1 08:14:41 MDT 2005",
  bibsource =    "http://www.research.ibm.com/journal/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.research.ibm.com/journal/rd/492/eleftheriou.pdf",
  abstract =     "This paper presents results on a
                 communications-intensive kernel, the three-dimensional
                 fast Fourier transform (3D FFT), running on the
                 2,048-node Blue Gene/L (BG/L) prototype. Two
                 implementations of the volumetric FFT algorithm were
                 characterized, one built on the Message Passing
                 Interface library and another built on an active packet
                 Application Program Interface supported by the hardware
                 bring-up environment, the BG/L advanced diagnostics
                 environment. Preliminary performance experiments on the
                 BG/L prototype indicate that both of our
                 implementations scale well up to 1,024 nodes for $3$D
                 FFTs of size $ 128 \time 128 \times 128 $. The
                 performance of the volumetric FFT is also compared with
                 that of the Fastest Fourier Transform in the West
                 (FFTW) library. In general, the volumetric FFT
                 outperforms a port of the FFTW Version 2.1.5 library on
                 large-node-count partitions.",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  ordernumber =  "G322-0240",
}

@Article{Enenkel:2005:CMF,
  author =       "R. F. Enenkel and B. G. Fitch and R. S. Germain and F.
                 G. Gustavson and A. Martin and M. Mendell and J. W.
                 Pitera and M. C. Pitman and A. Rayshubskiy and F. Suits
                 and W. C. Swope and T. J. C. Ward",
  title =        "Custom math functions for molecular dynamics",
  journal =      j-IBM-JRD,
  volume =       "49",
  number =       "2/3",
  pages =        "465--474",
  month =        "????",
  year =         "2005",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Wed Jun 1 08:14:41 MDT 2005",
  bibsource =    "http://www.research.ibm.com/journal/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.research.ibm.com/journal/rd/492/enenkel.pdf",
  abstract =     "While developing the protein folding application for
                 the IBM Blue Gene/L supercomputer, some frequently
                 executed computational kernels were encountered. These
                 were significantly more complex than the linear algebra
                 kernels that are normally provided as tuned libraries
                 with modern machines. Using regular library functions
                 for these would have resulted in an application that
                 exploited only 5--10\% of the potential floating-point
                 throughput of the machine. This paper is a tour of the
                 functions encountered; they have been expressed in C++
                 (and could be expressed in other languages such as
                 Fortran or C). With the help of a good optimizing
                 compiler, floating-point efficiency is much closer to
                 100\%. The protein folding application was initially
                 run by the life science researchers on IBM POWER3e
                 machines while the computer science researchers were
                 designing and bringing up the Blue Gene/L hardware.
                 Some of the work discussed resulted in enhanced
                 compiler optimizations, which now improve the
                 performance of floating-point-intensive applications
                 compiled by the IBM VisualAgent series of compilers for
                 POWER3, POWER4e, POWER4+, and POWER5. The
                 implementations are offered in the hope that they may
                 help in other implementations of molecular dynamics or
                 in other fields of endeavor, and in the hope that
                 others may adapt the ideas presented here to deliver
                 additional mathematical functions at high throughput.",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  ordernumber =  "G322-0240",
}

@InProceedings{Erle:2005:DME,
  author =       "Mark Erle and Eric Schwarz and Michael Schulte",
  title =        "Decimal Multiplication With Efficient Partial Product
                 Generation",
  crossref =     "Montuschi:2005:PIS",
  pages =        "21--28",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-183.pdf;
                 http://mesa.ece.wisc.edu/publications/cp_2005-07.pdf",
  abstract =     "Decimal multiplication is important in many commercial
                 applications including financial analysis, banking, tax
                 calculation, currency conversion, insurance, and
                 accounting. This paper presents a novel design for
                 fixed-point decimal multiplication that utilizes a
                 simple recoding scheme to produce signed-magnitude
                 representations of the operands thereby greatly
                 simplifying the process of generating partial products
                 for each multiplier digit. The partial products are
                 generated using a digit-by-digit multiplier on a
                 word-by-digit basis, first in a signed-digit form with
                 two digits per position, and then combined via a
                 combinational circuit. As the signed-digit partial
                 products are developed one at a time while traversing
                 the recoded multiplier operand from the least
                 significant digit to the most significant digit, each
                 partial product is added along with the accumulated sum
                 of previous partial products via a signed-digit adder.
                 This work is significantly different from other work
                 employing digit-by-digit multipliers due to the
                 efficiency gained by restricting the range of digits
                 throughout the multiplication process.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17; decimal floating-point arithmetic",
  pagecount =    "8",
}

@InProceedings{Etiemble:2005:CBF,
  author =       "D. Etiemble and S. Bouaziz and L. Lacassagne",
  title =        "Customizing 16-bit floating point instructions on a
                 {NIOS II} processor for {FPGA} image and media
                 processing",
  crossref =     "IEEE:2005:PWE",
  pages =        "61--66",
  year =         "2005",
  DOI =          "https://doi.org/10.1109/ESTMED.2005.1518073",
  bibdate =      "Sat Oct 9 12:40:19 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We have implemented customized SIMD 16-bit floating
                 point instructions on a NIOS II processor. On several
                 image processing and media benchmarks for which the
                 accuracy and dynamic range of this format is
                 sufficient, a speed-up ranging from 1.5 to more than 2
                 is obtained versus the integer implementation. The
                 hardware overhead remains limited and is compatible
                 with the capacities of today's FPGAs.",
  acknowledgement = ack-nhfb,
}

@Article{Even:2005:PEA,
  author =       "Guy Even and Peter-Michael Seidel and Warren E.
                 Ferguson",
  title =        "A parametric error analysis of {Goldschmidt}'s
                 division algorithm",
  journal =      j-J-COMP-SYS-SCI,
  volume =       "70",
  number =       "1",
  pages =        "118--139",
  month =        feb,
  year =         "2005",
  CODEN =        "JCSSBM",
  DOI =          "https://doi.org/10.1016/j.jcss.2004.08.004",
  ISSN =         "0022-0000 (print), 1090-2724 (electronic)",
  ISSN-L =       "0022-0000",
  bibdate =      "Tue Jan 29 15:26:56 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcompsyssci.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022000004000960",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computer and System Sciences",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00220000",
}

@Article{Fan:2005:FBP,
  author =       "Haining Fan and Yiqi Dai",
  title =        "Fast bit-parallel {$ \mathrm {GF}(2^n) $} multiplier
                 for all trinomials",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "4",
  pages =        "485--490",
  month =        apr,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.64",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 16:17:16 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1401867",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Fit-Florea:2005:ABE,
  author =       "A. Fit-Florea and D. W. Matula and M. A. Thornton",
  title =        "Addition-based exponentiation modulo $ 2^k $",
  journal =      j-ELECT-LETTERS,
  volume =       "41",
  number =       "2",
  pages =        "56--57",
  day =          "20",
  month =        jan,
  year =         "2005",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:20057538",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Fri Jun 24 15:17:52 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/iel5/2220/30332/01393468.pdf",
  abstract =     "A novel method for performing exponentiation modulo $
                 2^k $ is described. The algorithm has a critical path
                 consisting of $k$ dependent shift-and-add modulo $ 2^k
                 $ operations. Although $3$ is the preferred exponent
                 base, the algorithm can be extended easily in order to
                 perform the general binary powering operation.",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
}

@TechReport{Fousse:2005:MMP,
  author =       "Laurent Fousse and Guillaume Hanrot and Vincent
                 Lef{\`e}vre and Patrick P{\'e}lissier and Paul
                 Zimmermann",
  title =        "{MPFR}: a Multiple-Precision Binary Floating-Point
                 Library With Correct Rounding",
  type =         "Technical Report",
  number =       "RR-5753",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  pages =        "15",
  month =        nov,
  year =         "2005",
  bibdate =      "Sun Sep 10 07:26:55 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-5753.pdf;
                 ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-5753.ps.gz;
                 http://www.inria.fr/rrrt/rr-5753.html",
  abstract =     "This paper presents a multiple-precision binary
                 floating-point library, written in the ISO C language,
                 and based on the GNU MP library. Its particularity is
                 to extend ideas from the IEEE-754 standard to arbitrary
                 precision, by providing correct rounding",
  acknowledgement = ack-nhfb,
}

@Article{Fraysse:2005:ASG,
  author =       "Val{\'r}ie Frayss{\'e} and Luc Giraud and Serge
                 Gratton and Julien Langou",
  title =        "{Algorithm 842}: a set of {GMRES} routines for real
                 and complex arithmetics on high performance computers",
  journal =      j-TOMS,
  volume =       "31",
  number =       "2",
  pages =        "228--238",
  month =        jun,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1067967.1067970",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Jun 21 16:55:57 MDT 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this article we describe our implementations of the
                 GMRES algorithm for both real and complex, single and
                 double precision arithmetics suitable for serial,
                 shared memory and distributed memory computers. For the
                 sake of portability, simplicity, flexibility and
                 efficiency the GMRES solvers have been implemented in
                 Fortran 77 using the reverse communication mechanism
                 for the matrix-vector product, the preconditioning and
                 the dot product computations. For distributed memory
                 computation, several orthogonalization procedures have
                 been implemented to reduce the cost of the dot product
                 calculation, which is a well-known bottleneck of
                 efficiency for the Krylov methods. Either implicit or
                 explicit calculation of the residual at restart are
                 possible depending on the actual cost of the
                 matrix-vector product. Finally the implemented stopping
                 criterion is based on a normwise backward error.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@TechReport{Giles:2005:BLN,
  author =       "David E. Giles",
  title =        "{Benford's Law} and Naturally Occurring Prices in
                 Certain {ebaY} Auctions",
  type =         "Econometrics Working Paper",
  number =       "EWP0505",
  institution =  "Department of Economics, University of Victoria",
  address =      "Victoria, BC, Canada",
  month =        may,
  year =         "2005",
  ISSN =         "1485-6441",
  bibdate =      "Thu Feb 15 16:24:39 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://web.uvic.ca/econ/ewp0505.pdf",
  abstract =     "We show that certain the winning bids for certain ebaY
                 auctions obey Benford's Law. One implication of this is
                 that it is unlikely that these bids are subject to
                 collusion among bidders, or ``shilling'' on the part of
                 sellers. Parenthetically, we also show that numbers
                 from the naturally occurring Fibonacci and Lucas
                 sequences also obey Benford's Law.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Giraud:2005:REA,
  author =       "Luc Giraud and Julien Langou and Miroslav
                 Rozlozn{\'\i}k and Jasper van den Eshof",
  title =        "Rounding error analysis of the classical
                 {Gram--Schmidt} orthogonalization process",
  journal =      j-NUM-MATH,
  volume =       "101",
  number =       "1",
  pages =        "87--100",
  month =        jul,
  year =         "2005",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/s00211-005-0615-4",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65F25, 65G50, 15A23",
  bibdate =      "Tue Oct 11 18:59:06 MDT 2005",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0029-599X&volume=101&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0029-599X&volume=101&issue=1&spage=87",
  abstract =     "This paper provides two results on the numerical
                 behavior of the classical Gram--Schmidt algorithm. The
                 first result states that, provided the normal equations
                 associated with the initial vectors are numerically
                 nonsingular, the loss of orthogonality of the vectors
                 computed by the classical Gram--Schmidt algorithm
                 depends quadratically on the condition number of the
                 initial vectors. The second result states that,
                 provided the initial set of vectors has numerical full
                 rank, two iterations of the classical Gram--Schmidt
                 algorithm are enough for ensuring the orthogonality of
                 the computed vectors to be close to the unit roundoff
                 level.",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Glusker:2005:TCM,
  author =       "Mark Glusker and David M. Hogan and Pamela Vass",
  title =        "The Ternary Calculating Machine of {Thomas Fowler}",
  journal =      j-IEEE-ANN-HIST-COMPUT,
  volume =       "27",
  number =       "3",
  pages =        "4--22",
  month =        jul # "\slash " # sep,
  year =         "2005",
  CODEN =        "IAHCEX",
  DOI =          "https://doi.org/10.1109/MAHC.2005.49",
  ISSN =         "1058-6180 (print), 1934-1547 (electronic)",
  ISSN-L =       "1058-6180",
  bibdate =      "Mon Nov 7 18:51:49 MST 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In 1840, Thomas Fowler, a self-taught English
                 mathematician and inventor, created a unique ternary
                 calculating machine. Until recently, all detail of this
                 machine was lost. A research project begun in 1997
                 uncovered sufficient information to enable the
                 recreation of a physical concept model of Fowler's
                 machine. The next step is to create a historically
                 accurate replica.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Annals of the History of Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85",
  keywords =     "19th century; Augustus De Morgan; balanced ternary;
                 base-3; calculating machine; historical reconstruction;
                 signed ternary; ternary; Thomas Fowler",
}

@TechReport{Graillat:2005:CHS,
  author =       "S. Graillat and P. Langlois and N. Louvet",
  title =        "Compensated {Horner} Scheme",
  type =         "Research Report",
  number =       "RR2005-04",
  institution =  "{\'E}quipe de Recherche DALI, Laboratoire LP2A,
                 Universit{\'e} de Perpignan, Via Domitia",
  address =      "Perpignan, France",
  pages =        "ii + 25",
  day =          "24",
  month =        jul,
  year =         "2005",
  bibdate =      "Fri Jan 06 07:45:03 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://gala.univ-perp.fr/~graillat/papers/rr2005-04.pdf",
  abstract =     "We present a compensated Horner scheme, that is an
                 accurate and fast algorithm to evaluate univariate
                 polynomials in floating point arithmetic. The accuracy
                 of the computed result is similar to the one given by
                 the Horner scheme computed in twice the working
                 precision. This compensated Horner scheme runs at least
                 as fast as existing implementations producing the same
                 output accuracy. We also propose to compute in pure
                 floating point arithmetic a valid error estimate that
                 bound the actual accuracy of the compensated
                 evaluation. Numerical experiments involving
                 ill-conditioned polynomials illustrate these results.
                 All algorithms are performed at a given working
                 precision and are portable assuming the floating point
                 arithmetic satisfies the IEEE-754 standard.",
  acknowledgement = ack-nhfb,
  amsclass =     "65G, 65Y99",
  keywords =     "compensated Horner scheme; error-free transformations;
                 extended precision; IEEE-754 floating point arithmetic;
                 polynomial evaluation; running error bound",
}

@TechReport{Graillat:2005:ICH,
  author =       "S. Graillat and P. Langlois and N. Louvet",
  title =        "Improving the compensated {Horner} scheme with a fused
                 multiply and add",
  type =         "Research Report",
  number =       "RR2005-05",
  institution =  "{\'E}quipe de Recherche DALI, Laboratoire LP2A,
                 Universit{\'e} de Perpignan, Via Domitia",
  address =      "Perpignan, France",
  month =        nov,
  year =         "2005",
  bibdate =      "Sat Feb 26 18:45:17 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Guizzo:2005:IRS,
  author =       "E. Guizzo",
  title =        "{IBM} reclaims supercomputer lead",
  journal =      j-IEEE-SPECTRUM,
  volume =       "42",
  number =       "2",
  pages =        "15--16",
  month =        feb,
  year =         "2005",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.2005.1389501",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Thu Sep 01 16:25:09 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "70 Tflops; floating-point arithmetic; IBM Glue
                 Gene/L",
}

@InProceedings{Haijun:2005:ROT,
  author =       "Sun Haijun and Shao Zhibiao and Zom Gang and Zhao
                 Ning",
  booktitle =    "Proceedings of {2005 IEEE International Workshop on
                 VLSI Design and Video Technology, 28--30 May 2005}",
  title =        "The research on optimization techniques of 32-bit
                 floating-point {RISC} microprocessor",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "63--66",
  year =         "2005",
  DOI =          "https://doi.org/10.1109/iwvdvt.2005.1504465",
  bibdate =      "Wed Dec 13 09:49:47 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "XJ-1 processor",
}

@Book{Hally:2005:EBS,
  author =       "Mike Hally",
  title =        "Electronic Brains: Stories from the Dawn of the
                 Computer Age",
  publisher =    pub-JOSEPH-HENRY,
  address =      pub-JOSEPH-HENRY:adr,
  pages =        "xxiii + 275",
  year =         "2005",
  ISBN =         "0-309-09630-8 (hardcover)",
  ISBN-13 =      "978-0-309-09630-0 (hardcover)",
  LCCN =         "QA76.17 .H35 2005",
  bibdate =      "Wed Aug 9 07:02:58 MDT 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://catdir.loc.gov/catdir/toc/ecip0514/2005016583.html;
                 http://library.ccsu.edu/help/spcoll/oconnell/index.htm",
  abstract =     "By the 1960s, IBM, once a manufacturer of mechanical
                 tabulators, had beaten all rivals and dominated the
                 world computer market. But IBM came late to the race.
                 From the 1930s to the 1950s, small independent teams on
                 four continents worked on the development of the very
                 first modern computers --- practical, electronic,
                 multipurpose, digital machines with memory for data and
                 programs. From interviews with surviving members of
                 those original pioneering teams, the author builds up a
                 picture of the eccentric, obsessive and fiercely loyal
                 men and women who laid the foundations for the
                 computerized world we now live in, and re-creates the
                 atmosphere of those early days.",
  acknowledgement = ack-nhfb,
  subject =      "Computers; History; Ordinateurs; Histoire; Computers.;
                 Computers.",
  tableofcontents = "From ABC to ENIAC \\
                 UNIVAC \\
                 Saviour of the Census \\
                 Saluting the Moose \\
                 When Britain Led the Computing World \\
                 LEO the Lyons Computer \\
                 So Then We Took the Roof Off \\
                 Wizards of Oz \\
                 Water on the Brain \\
                 It's Not About Being First: the Rise and Rise of IBM
                 \\
                 Arithmetic \\
                 Technical bits",
}

@Book{Hanss:2005:AFA,
  author =       "Michael Hanss",
  title =        "Applied fuzzy arithmetic: an introduction with
                 engineering applications",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xiii + 256",
  year =         "2005",
  ISBN =         "3-540-24201-5",
  ISBN-13 =      "978-3-540-24201-7",
  LCCN =         "QA248.5 .H36 2005",
  bibdate =      "Mon Oct 29 18:21:47 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0662/2004117177-d.html",
  acknowledgement = ack-nhfb,
  subject =      "Fuzzy arithmetic; Fuzzy logic",
}

@InProceedings{Hariri:2005:SMS,
  author =       "A. Hariri and K. Navi and R. Rastegar",
  booktitle =    "{EUROCON 2005, The International Conference on
                 ``Computer as a Tool'': proceedings: Belgrade, Serbia
                 and Montenegro: November 21--24, 2005}",
  title =        "A Simplified Modulo $ (2^n - 1) $ Squaring Scheme for
                 Residue Number System",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "615--618",
  year =         "2005",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/EURCON.2005.1630004",
  ISBN =         "1-4244-0049-X",
  ISBN-13 =      "978-1-4244-0049-2",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Residue Number System (RNS) is a valuable tool for
                 fast and parallel arithmetic and has a variety of
                 applications in digital signal processing, fault
                 tolerant systems, etc. One of the most fundamental
                 moduli in Residue Number System is modulo (2
                 \ldots{})",
}

@InProceedings{Harris:2005:IUS,
  author =       "David Harris and Ram Krishnamurthy and Mark Anders and
                 Sanu Mathew and Steven Hsu",
  title =        "An Improved Unified Scalable Radix-$2$ {Montgomery}
                 Multiplier",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-109.pdf",
  abstract =     "This paper describes an improved version of the
                 Tenca-Ko{\c{c}} unified scalable radix-2 Montgomery
                 multiplier with half the latency for small and moderate
                 precision operands and half the queue memory
                 requirement. Like the Tenca-Ko{\c{c}} multiplier, this
                 design is reconfigurable to accept any input precision
                 in either $ \mathrm {GF}(p) $ or $ \mathrm {GF}(2 n) $
                 up to the size of the on-chip memory. An FPGA
                 implementation can perform 1024-bit modular
                 exponentiation in 16 ms using 5598 4-input lookup
                 tables, making it the fastest unified scalable design
                 yet reported.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17",
  pagecount =    "7",
}

@InProceedings{He:2005:MAF,
  author =       "Hu He and Zheng Li and Yihe Sun",
  title =        "Multiply-add fused float point unit with on-fly
                 denormalized number processing",
  crossref =     "IEEE:2005:MSC",
  pages =        "1466--1468",
  year =         "2005",
  DOI =          "https://doi.org/10.1109/MWSCAS.2005.1594389",
  bibdate =      "Sun Feb 20 10:45:46 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Denormalized numbers are the most difficult type of
                 numbers to implement in float-point units. They are so
                 complex that many designs avoid handling them in
                 hardware. The denormalized number processing cost two
                 much extra clock cycle in software implementation. In
                 this paper, an on-fly floating point denormalized
                 number processing implemented in a multiply-add-fused
                 (MAF) with little extra latency is presented. The
                 denormalized number processing is embedded in a popular
                 MAF data path and fused with the MAF smoothly by
                 representing the denormalized number. The extra latency
                 introduced by the denormalized number processing is
                 cost by the denormalized number detection.",
  acknowledgement = ack-nhfb,
}

@Article{Hernandez:2005:ACN,
  author =       "M. A. Hern{\'a}ndez and N. Romero",
  title =        "Accelerated convergence in {Newton}'s method for
                 approximating square roots",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "177",
  number =       "1",
  pages =        "225--229",
  day =          "1",
  month =        may,
  year =         "2005",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:00:04 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042704004315",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Hsiao:2005:EVI,
  author =       "Shen-Fu Hsiao and Yu Hen Hu and T.-B. Juang and
                 Chung-Han Lee",
  title =        "Efficient {VLSI} implementations of fast
                 multiplierless approximated {DCT} using parameterized
                 hardware modules for silicon intellectual property
                 design",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-1,
  volume =       "52",
  number =       "8",
  pages =        "1568--1579",
  year =         "2005",
  DOI =          "https://doi.org/10.1109/TCSI.2005.851709",
  ISSN =         "1549-8328 (print), 1558-0806 (electronic)",
  ISSN-L =       "1549-8328",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems I: Regular
                 Papers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8919",
  keywords =     "binDCT; Computer architecture; CORDIC; Discrete cosine
                 transform (DCT); Discrete cosine transforms; Discrete
                 Fourier transforms; Embedded computing; Hardware;
                 integer DCT (IDCT); Intellectual property; shifted
                 discrete Fourier transform (SDFT); Silicon;
                 System-on-a-chip; Two dimensional displays; Very large
                 scale integration; very large-scale integration (VLSI)
                 design",
}

@InCollection{Huang:2005:EMP,
  author =       "Liusheng Huang and Hong Zhong and Hong Shen and
                 Yonglong Luo",
  editor =       "Hong Shen and Koji Nakano",
  booktitle =    "{Sixth International Conference on Parallel and
                 Distributed Computing, Applications and Technologies,
                 2005. PDCAT 2005: 5--8 December 2005, Dalian, China}",
  title =        "An Efficient Multiple-Precision Division Algorithm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  bookpages =    "xxvi + 1091",
  pages =        "971--974",
  year =         "2005",
  DOI =          "https://doi.org/10.1109/PDCAT.2005.79",
  ISBN =         "0-7695-2405-2",
  ISBN-13 =      "978-0-7695-2405-4",
  LCCN =         "QA76.58 .I5752 2005",
  bibdate =      "Mon Dec 09 14:30:16 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/infoproc2010.bib",
  note =         "The authors present an integer-division algorithm that
                 runs three to five times faster than Knuth's 1981
                 original. However, there is an error in the
                 renormalization algorithm that is corrected in
                 \cite{Mukhopadhyay:2014:EMP}, while retaining the
                 speedup.",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/servlet/opac?punumber=10544",
}

@Article{Huang:2005:HPL,
  author =       "Zhijun Huang and Milo{\v{s}} D. Ercegovac",
  title =        "High-Performance Low-Power Left-to-Right Array
                 Multiplier Design",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "3",
  pages =        "272--283",
  month =        mar,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.51",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 16:17:15 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://csdl.computer.org/comp/trans/tc/2005/03/t0272abs.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0272.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0272.pdf;
                 http://ieeexplore.ieee.org/iel5/12/30205/01388192.pdf?isnumber=30205&prod=JNL&arnumber=1388192&arSt=+272&ared=+283&arAuthor=Zhijun+Huang%3B+Ercegovac%2C+M.D.;
                 http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388192&count=13&index=3;
                 http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388192",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-16",
  remark =       "Special issue on computer arithmetic: selected papers
                 from ARITH-16.",
}

@InProceedings{Jacobi:2005:AFV,
  author =       "C. Jacobi and K. Weber and V. Paruthi and J.
                 Baumgartner",
  title =        "Automatic formal verification of fused-multiply-add
                 {FPUs}",
  crossref =     "IEEE:2005:DAT",
  volume =       "2",
  pages =        "1298--1303",
  year =         "2005",
  DOI =          "https://doi.org/10.1109/DATE.2005.75",
  bibdate =      "Sun Feb 20 09:57:04 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this paper we describe a fully-automated
                 methodology for formal verification of
                 fused-multiply-add floating point units (FPU). Our
                 methodology verifies an implementation FPU against a
                 simple reference model derived from the processor's
                 architectural specification, which may include all
                 aspects of the IEEE specification including denormal
                 operands and exceptions. Our strategy uses a
                 combination of BDD- and SAT-based symbolic simulation.
                 To make this verification task tractable, we use a
                 combination of case-splitting, multiplier isolation,
                 and automatic model reduction techniques. The
                 case-splitting is defined only in terms of the
                 reference model, which makes this approach easily
                 portable to new designs. The methodology is directly
                 applicable to multi-GHz industrial implementation
                 models (e.g., HDL or gate-level circuit
                 representations) that contain all details of the
                 high-performance transistor-level model, such as
                 aggressive pipelining, clocking, etc. Experimental
                 results are provided to demonstrate the computational
                 efficiency of this approach.",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2005:BTG,
  author =       "William Kahan",
  title =        "A Brief Tutorial on Gradual Underflow",
  howpublished = "World-Wide Web lecture notes.",
  pages =        "15",
  day =          "8",
  month =        jul,
  year =         "2005",
  bibdate =      "Fri Jul 15 11:38:13 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Prepared for ARITH 17, Tues. 28 June 2005, and
                 subsequently augmented.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ARITH_17U.pdf",
  acknowledgement = ack-nhfb,
}

@Manual{Kahan:2005:DP,
  author =       "William Kahan",
  title =        "A Demonstration of Presubstitution for $ \infty /
                 \infty $",
  pages =        "10",
  day =          "5",
  month =        jul,
  year =         "2005",
  bibdate =      "Fri Jul 15 11:47:46 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.berkeley.edu/~wkahan/Grail.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Kahan:2005:FPA,
  author =       "William Kahan",
  title =        "Floating-Point Arithmetic Besieged by {``Business}
                 Decisions''",
  howpublished = "World-Wide Web lecture notes.",
  pages =        "28",
  day =          "5",
  month =        jul,
  year =         "2005",
  bibdate =      "Fri Jul 15 12:07:31 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "A Keynote Address, prepared for the IEEE-Sponsored
                 ARITH 17 Symposium on Computer Arithmetic, delivered on
                 Mon. 27 June 2005 in Hyannis, Massachusetts.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/ARITH_17.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Kahan:2005:OQD,
  author =       "William Kahan and Dan Zuras",
  title =        "An Open Question to Developers of Numerical Software",
  journal =      j-COMPUTER,
  volume =       "38",
  number =       "5",
  pages =        "91--94",
  month =        may,
  year =         "2005",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Wed May 04 15:33:06 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://csdl.computer.org/comp/mags/co/2005/05/r5091abs.htm;
                 http://csdl.computer.org/comp/mags/co/2005/05/r5toc.htm;
                 http://csdl.computer.org/dl/mags/co/2005/05/r5091.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
  subject =      "Are signaling NaNs needed?",
}

@Article{Kaihara:2005:HAM,
  author =       "M. E. Kaihara and N. Takagi",
  title =        "A hardware algorithm for modular multiplication\slash
                 division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "1",
  pages =        "12--21 54",
  month =        jan,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.1(410)",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 16:17:14 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1362636",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Misc{Karlsson:2005:IIL,
  author =       "Kent Karlsson",
  title =        "{ISO\slash IEC 10967, Language Independent Arithmetic
                 (LIA)}",
  howpublished = "Wikipedia article",
  day =          "31",
  month =        oct,
  year =         "2005",
  bibdate =      "Sat Dec 17 10:42:52 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://en.wikipedia.org/wiki/ISO/IEC_10967;
                 http://www.open-std.org/JTC1/SC22/WG11/docs/n364.pdf;
                 http://www.open-std.org/JTC1/SC22/WG11/docs/n462.pdf;
                 http://www.open-std.org/jtc1/sc22/wg11/docs/n490.pdf",
  abstract =     "ISO/IEC 10967, Language independent arithmetic (LIA),
                 is a series of standards on computer arithmetic. It is
                 compatible with IEC 60559 (more known as IEEE 754 or
                 IEC 559), and indeed much of the specifications in
                 parts 2 and 3 are for IEEE 754 special values (though
                 such values are not required).\par

                 LIA currently consists of three parts:\par
                 \begin{itemize}

                 \item[Part 1] Integer and floating point arithmetic,
                 first edition published 1994.

                 \item[Part 2] Elementary numerical functions, first
                 edition published 2001.

                 \item[Part 3] Complex integer and floating point
                 arithmetic and complex elementary numerical functions,
                 first edition is now (2005) in FDIS
                 stage.

                 \end{itemize}",
  acknowledgement = ack-nhfb,
}

@Article{Kenney:2005:HSM,
  author =       "R. D. Kenney and M. J. Schulte",
  title =        "High-Speed Multioperand Decimal Adders",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "8",
  pages =        "953--963",
  month =        aug,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.129",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 16:17:18 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2005-04.pdf;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1453497",
  abstract =     "There is increasing interest in hardware support for
                 decimal arithmetic as a result of recent growth in
                 commercial, financial, and Internet-based applications.
                 Consequently, new specifications for decimal
                 floating-point arithmetic have been added to the draft
                 revision of the IEEE-754 Standard for Floating-Point
                 Arithmetic. This paper introduces and analyzes three
                 techniques for performing fast decimal addition on
                 multiple binary coded decimal (BCD) operands. Two of
                 the techniques speculate BCD correction values and
                 correct intermediate results while adding the input
                 operands. The first speculates over one addition. The
                 second speculates over two additions. The third
                 technique uses a binary carry-save adder tree and
                 produces a binary sum. Combinational logic is then used
                 to correct the sum and determine the carry into the
                 next more significant digit. Multioperand adder designs
                 are constructed and synthesized for four to 16 input
                 operands. Analyses are performed on the synthesis
                 results and the merits of each technique are discussed.
                 Finally, these techniques are compared to several
                 previous techniques for high-speed decimal addition.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "computer arithmetic; decimal arithmetic; decimal
                 floating-point arithmetic; hardware designs;
                 multioperand adders",
}

@Article{Khabbazian:2005:NMA,
  author =       "M. Khabbazian and T. A. Gulliver and V. K. Bhargava",
  title =        "A new minimal average weight representation for
                 left-to-right point multiplication methods",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "11",
  pages =        "1454--1459",
  month =        nov,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.173",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 16:17:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1514423",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@TechReport{Klarer:2005:DTC,
  author =       "Robert Klarer",
  title =        "Decimal Types for {C++}: Second Draft",
  type =         "Report",
  number =       "C22/WG21/N1839 J16/05-0099",
  institution =  "IBM Canada, Ltd.",
  address =      "Toronto, ON, Canada",
  day =          "24",
  month =        jun,
  year =         "2005",
  bibdate =      "Thu Mar 02 10:47:15 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2005/n1839.html",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@Article{Kornerup:2005:DSS,
  author =       "Peter Kornerup",
  title =        "Digit Selection for {SRT} Division and Square Root",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "3",
  pages =        "294--303",
  month =        mar,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.47",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 16:17:15 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://csdl.computer.org/comp/trans/tc/2005/03/t0294abs.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0294.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0294.pdf;
                 http://ieeexplore.ieee.org/iel5/12/30205/01388194.pdf?isnumber=30205&prod=JNL&arnumber=1388194&arSt=+294&ared=+303&arAuthor=Kornerup%2C+P.;
                 http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388194&count=13&index=5;
                 http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388194",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-16",
  remark =       "Special issue on computer arithmetic: selected papers
                 from ARITH-16.",
  summary =      "The quotient digit selection in the SRT division
                 algorithm is based on a few most significant bits of
                 the remainder and divisor, where the remainder is
                 usually represented in a redundant representation. The
                 number of leading bits needed depends on \ldots{}",
}

@InProceedings{Kornerup:2005:LGD,
  author =       "Peter Kornerup and Jean-Michel Muller",
  title =        "Leading Guard Digits in Finite Precision Redundant
                 Representations",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Fri Jun 24 20:32:32 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.imada.sdu.dk/~kornerup/papers/red-add.pdf",
  abstract =     "Redundant number representations are generally used to
                 allow constant time additions, based on the fact that
                 only bounded carry-ripples take place. But carries may
                 ripple out into positions which may not be needed to
                 represent the final value of the result, and thus a
                 certain amount of leading guard digits are needed to
                 correctly determine the result. Also when cancellation
                 during subtractions occur, there may be nonzero digits
                 in positions not needed to represent the result of the
                 calculation. It is shown here that for normal redundant
                 digit sets with radix greater than two, a single guard
                 digit is sufficient to determine the value of such an
                 arbitrary length prefix of leading non-zero digits.
                 This is also the case for the unsigned carry-save
                 representation, whereas two guard digits are necessary
                 and sufficient for additions in the binary signed-digit
                 and 2's complement carry-save representations.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17; Leading guard digits; Multi-operand
                 additions; Redundant representations",
  pagecount =    "6",
}

@InProceedings{Kornerup:2005:RCN,
  author =       "Peter Kornerup and Jean-Michel Muller",
  booktitle =    "Proceedings of the International Meeting on Automated
                 Compliance Systems ({IMACS'05}), July 2005",
  title =        "{RN}-coding of numbers: Definition and some
                 properties",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Sun Jun 19 14:24:12 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.researchgate.net/publication/243786550_RN-coding_of_numbers_definition_and_some_properties",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kornerup:2005:SPR,
  author =       "Peter Kornerup and David Matula",
  title =        "Single Precision Reciprocals by Multipartite Table
                 Lookup",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-177.pdf",
  abstract =     "We develop the foundations for confirming monotonicity
                 of a multi-term reciprocal function approximation. We
                 introduce the concept of operand recoding to improve
                 the accuracy of multipartite approximation. The results
                 are applied to provide a proposed four-partite
                 reciprocal implementation with total table size $
                 \approx 27 $ Kbytes, that yields an IEEE standard,
                 single precision sized format (24 bit) reciprocal
                 instruction, that is a one-ulp monotonic reciprocal.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17",
  pagecount =    "9",
}

@Article{Kulikova:2005:CAS,
  author =       "A. A. Kulikova and Yu. V. Prokhorov",
  title =        "Completely Asymmetric Stable Laws and {Benford's
                 Law}",
  journal =      j-THEORY-PROBAB-APPL,
  volume =       "49",
  number =       "1",
  pages =        "163--169",
  month =        mar,
  year =         "2005",
  CODEN =        "TPRBAU",
  ISSN =         "0040-585X (print), 1095-7219 (electronic)",
  ISSN-L =       "0040-585X",
  bibdate =      "Thu Jul 7 19:15:48 MDT 2005",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/TVP/49/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/98094",
  acknowledgement = ack-nhfb,
  fjournal =     "Theory of Probability and its Applications",
  journal-URL =  "http://epubs.siam.org/tvp",
  keywords =     "Benford's Law; Zipf's Law",
}

@Article{Lang:2005:HTC,
  author =       "Tom{\'a}s Lang and Elisardo Antelo",
  title =        "High-Throughput {CORDIC}-Based Geometry Operations for
                 {$3$D} Computer Graphics",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "3",
  pages =        "347--361",
  month =        mar,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.53",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue May 30 12:14:00 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://csdl.computer.org/comp/trans/tc/2005/03/t0347abs.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0347.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0347.pdf;
                 http://ieeexplore.ieee.org/iel5/12/30205/01388199.pdf?isnumber=30205&prod=JNL&arnumber=1388199&arSt=+347&ared=+361&arAuthor=Lang%2C+T.%3B+Antelo%2C+E.;
                 http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388199&count=13&index=10;
                 http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388199",
  abstract =     "Graphics processors require strong arithmetic support
                 to perform computational kernels over data streams.
                 Because of the current implementation using the basic
                 arithmetic operations, the algorithms are given in
                 algebraic terms. However, since the operations are
                 really of a geometric nature, it seems to us that more
                 flexibility in the implementation is obtained if the
                 description is given in a high-level geometrical form.
                 As a consequence of this line of thought, this paper is
                 an attempt to reconsider some kernels in a graphics
                 processor to obtain implementations that are
                 potentially more scalable than just replicating the
                 modules used in conventional implementations. We
                 present the formulation of representative 3D computer
                 graphics operations in terms of CORDIC-type primitives.
                 Then, we briefly outline a stream processor based on
                 CORDIC-type modules to efficiently implement these
                 graphic operations. We perform a rough comparison with
                 current implementations and conclude that the
                 CORDIC-based alternative might be attractive.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-16",
  remark =       "Special issue on computer arithmetic: selected papers
                 from ARITH-16.",
}

@TechReport{Langlois:2005:STS,
  author =       "P. Langlois and N. Louvet",
  title =        "Solving Triangular Systems More Accurately and
                 Efficiently",
  type =         "Research Report",
  number =       "RR2005-02",
  institution =  "{\'E}quipe de Recherche DALI, Laboratoire LP2A,
                 Universit{\'e} de Perpignan, Via Domitia",
  address =      "Perpignan, France",
  pages =        "15",
  day =          "9",
  month =        may,
  year =         "2005",
  bibdate =      "Fri Jan 06 07:54:13 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://webdali.univ-perp.fr/RR/rr2005-02.pdf",
  abstract =     "We present a new algorithm that solves linear
                 triangular systems accurately and efficiently. By
                 accurately, we mean that this algorithm should yield a
                 solution as accurate as the one computed in twice the
                 working precision. By efficiently, we mean that its
                 implementation should run faster than the corresponding
                 XBLAS routine with the same output accuracy.",
  acknowledgement = ack-nhfb,
  keywords =     "error-free transformations; extended precision;
                 IEEE-754 floating point arithmetic; substitution
                 algorithm; triangular linear system; XBLAS",
}

@TechReport{Lauter:2005:BBB,
  author =       "Christoph Quirin Lauter",
  title =        "Basic building blocks for a triple-double intermediate
                 format",
  type =         "Technical Report",
  number =       "RR-5702",
  institution =  "Inria",
  address =      "????",
  pages =        "iii + 67 + i",
  year =         "2005",
  bibdate =      "Sat Apr 01 08:05:25 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://hal.inria.fr/inria-00070314;
                 https://hal.inria.fr/inria-00070314/document",
  abstract =     "The implementation of correctly rounded elementary
                 functions needs high intermediate accuracy before final
                 rounding. This accuracy can be provided by (pseudo-)
                 expansions of size three, i.e. a triple-double format.
                 The report presents all basic operators for such a
                 format. Triple-double numbers can be redundant. A
                 renormalization procedure is presented and proven.
                 Elementary functions' implementations need addition and
                 multiplication sequences. These operators must take
                 operands in double, double-double and triple-double
                 format. The results must be accordingly in one of the
                 formats. Several procedures are presented. Proofs are
                 given for their accuracy bounds. Intermediate
                 triple-double results must finally be correctly rounded
                 to double precision. Two effective rounding sequences
                 are presented, one for round-to-nearest mode, one for
                 the directed rounding modes. Their complete proofs
                 constitute half of the report.",
  acknowledgement = ack-nhfb,
  keywords =     "correct rounding; floating-point arithmetic",
}

@Misc{Lawlor:2005:PDP,
  author =       "Orion Lawlor and Hari Govind and Isaac Dooley and
                 Michael Breitenfeld and Laxmikant Kale",
  title =        "Performance Degradation in the Presence of Subnormal
                 Floating-Point Values",
  howpublished = "World-Wide Web slides from the Workshop on Operating
                 System Interfaces in High Performance Applications
                 2005",
  year =         "2005",
  bibdate =      "Sat Mar 04 17:10:07 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://charm.cs.uiuc.edu/presentations/OSIHPA/html/",
  acknowledgement = ack-nhfb,
}

@Article{Lee:2005:LCB,
  author =       "Chiou-Yng Lee and Jenn-Shyong Horng and I-Chang Jou
                 and Erl-Huei Lu",
  title =        "Low-complexity bit-parallel systolic {Montgomery}
                 multipliers for special classes of {$ \mathrm {GF}(2^m)
                 $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "9",
  pages =        "1061--1070",
  month =        sep,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.147",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 16:17:18 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1471668",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Lee:2005:OHF,
  author =       "D.-U. Lee and A. A. Gaffar and O. Mencer and W. Luk",
  title =        "Optimizing hardware function evaluation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "12",
  pages =        "1520--1531",
  month =        dec,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.201",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue May 30 12:04:26 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  abstract =     "We present a methodology and an automated system for
                 function evaluation unit generation. Our system selects
                 the best function evaluation hardware for a given
                 function, accuracy requirements, technology mapping,
                 and optimization metrics, such as area, throughput, and
                 latency. Function evaluation $ f(x) $ typically
                 consists of range reduction and the actual evaluation
                 on a small convenient interval such as $ [0, \pi / 2) $
                 for $ \sin (x) $. We investigate the impact of hardware
                 function evaluation with range reduction for a given
                 range and precision of $x$ and $ f(x) $ on area and
                 speed. An automated bit-width optimization technique
                 for minimizing the sizes of the operators in the data
                 paths is also proposed. We explore a vast design space
                 for fixed-point $ \sin (x) $, $ \log (x) $, and $ \sqrt
                 {x} $ accurate to one unit in the last place using
                 MATLAB and ASC, a stream compiler for
                 field-programmable gate arrays (FPGAs). In this study,
                 we implement over 2,000 placed-and-routed FPGA designs,
                 resulting in over 100 million application-specific
                 integrated circuit (ASIC) equivalent gates. We provide
                 optimal function evaluation results for range and
                 precision combinations between 8 and 48 bits.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "application specific integrated circuits;
                 application-specific integrated circuit equivalent
                 gates; ASC; ASIC; automated bit-width optimization
                 technique; circuit optimisation; computer arithmetic;
                 elementary function approximation; field programmable
                 gate arrays; field-programmable gate arrays; fixed
                 point arithmetic; fixed-point arithmetic; FPGA;
                 hardware function evaluation optimisation; logic
                 design; MATLAB; minimax approximation; range reduction;
                 stream compiler",
}

@Article{Lefevre:2005:GMP,
  author =       "Vincent Lef{\`e}vre",
  title =        "The Generic Multiple-Precision Floating-Point Addition
                 With Exact Rounding (as in the {MPFR} Library)",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "11",
  month =        may,
  year =         "2005",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/cs/0505027",
  abstract =     "We study the multiple-precision addition of two
                 positive floating-point numbers in base 2, with exact
                 rounding, as specified in the MPFR library, i.e. where
                 each number has its own precision. We show how the best
                 possible complexity (up to a constant factor that
                 depends on the implementation) can be obtain.",
  acknowledgement = ack-nhfb,
  subject =      "Data Structures and Algorithms (cs.DS)",
}

@InProceedings{Lefevre:2005:NRD,
  author =       "Vincent Lef{\`e}vre",
  title =        "New Results on the Distance Between a Segment and {$
                 \mathbb {Z}^2 $}. Application to the Exact Rounding",
  crossref =     "Montuschi:2005:PIS",
  pages =        "68--75",
  year =         "2005",
  DOI =          "https://doi.org/10.1109/ARITH.2005.32",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-147.pdf",
  abstract =     "This paper presents extensions to Lef{\'e}vre's
                 algorithm that computes a lower bound on the distance
                 between a segment and a regular grid $ Z^2 $. This
                 algorithm and, in particular, the extensions are useful
                 in the search for worst cases for the exact rounding of
                 unary elementary functions or base-conversion
                 functions. The proof that is presented here is simpler
                 and less technical than the original proof. This paper
                 also gives benchmark results with various optimization
                 parameters, explanations of these results, and an
                 application to base conversion.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17",
  pagecount =    "8",
}

@InProceedings{Li:2005:HIA,
  author =       "L. Li and A. Fit-Florea and M. A. Thornton and D. W.
                 Matula",
  title =        "Hardware Implementation of an Additive Bit-Serial
                 Algorithm for the Discrete Logarithm Modulo-$ 2^k $",
  crossref =     "IEEE:2005:ICS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Fri Jun 24 15:56:30 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Li:2005:NBI,
  author =       "L. Li and A. Fit-Florea and M. A. Thornton and D. W.
                 Matula",
  title =        "A New Binary Integer Number System with Simplified
                 Hardware Support",
  crossref =     "IEEE:2005:PII",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Fri Jun 24 15:58:49 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Submitted.",
  acknowledgement = ack-nhfb,
}

@Article{Li:2005:RPE,
  author =       "C. Li and S. Pion and C. K. Yap",
  title =        "Recent progress in exact geometric computation",
  journal =      j-J-LOGIC-ALG-PROG,
  volume =       "64",
  number =       "1",
  pages =        "85--111",
  month =        jul,
  year =         "2005",
  DOI =          "https://doi.org/10.1016/j.jlap.2004.07.006",
  ISSN =         "1567-8326 (print), 1873-5940 (electronic)",
  ISSN-L =       "1567-8326",
  bibdate =      "Thu Oct 17 10:09:18 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Logic and Algebraic Programming",
  journal-URL =  "http://www.sciencedirect.com/science/journal/15678326",
  remark =       "Special issue on Practical development of exact real
                 number computation.",
}

@Article{Lorencz:2005:SFA,
  author =       "R{\'o}bert L{\'o}rencz and Josef Hlav{\'a}{\v{c}}",
  title =        "Subtraction-free {Almost Montgomery Inverse}
                 algorithm",
  journal =      j-INFO-PROC-LETT,
  volume =       "94",
  number =       "1",
  pages =        "11--14",
  day =          "15",
  month =        apr,
  year =         "2005",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Thu Mar 31 18:41:00 MDT 2011",
  bibsource =    "http://www.sciencedirect.com/science/journal/00200190;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}

@Article{Lorenz:2005:VTB,
  author =       "J. Lorenz and S. Kral and F. Franchetti and C. W.
                 Ueberhuber",
  title =        "Vectorization techniques for the {Blue Gene/L} double
                 {FPU}",
  journal =      j-IBM-JRD,
  volume =       "49",
  number =       "2/3",
  pages =        "437--446",
  month =        "????",
  year =         "2005",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Wed Jun 1 08:14:41 MDT 2005",
  bibsource =    "http://www.research.ibm.com/journal/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.research.ibm.com/journal/rd/492/lorenz.pdf",
  abstract =     "This paper presents vectorization techniques tailored
                 to meet the specifics of the two-way single-instruction
                 multiple-data (SIMD) double-precision floating-point
                 unit (FPU), which is a core element of the node
                 application-specific integrated circuit (ASIC) chips of
                 the IBM 360-teraflops Blue Gene/L supercomputer. This
                 paper focuses on the general-purpose basic-block
                 vectorization and optimization methods as they are
                 incorporated in the Vienna MAP vectorizer and
                 optimizer. The innovative technologies presented here,
                 which have consistently delivered superior performance
                 and portability across a wide range of platforms, were
                 carried over to prototypes of Blue Gene/L and joined
                 with the automatic performance-tuning system known as
                 Fastest Fourier Transform in the West (FFTW). FFTW
                 performance-optimization facilities working with the
                 compiler technologies presented in this paper are able
                 to produce vectorized fast Fourier transform (FFT)
                 codes that are tuned automatically to single Blue
                 Gene/L processors and are up to 80\% faster than the
                 best-performing scalar FFT codes generated by FFTW.",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  ordernumber =  "G322-0240",
}

@InProceedings{Macchetti:2005:QPH,
  author =       "Marco Macchetti and Luigi Dadda",
  title =        "Quasi-Pipelined Hash Circuits",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-149.pdf",
  abstract =     "Hash functions are an important cryptographic
                 primitive. They are used to obtain a fixed-size
                 fingerprint, or hash value, of an arbitrary long
                 message. We focus particularly on the class of
                 dedicated hash functions, whose general construction is
                 presented; the peculiar arrangement of sequential and
                 combinational units makes the application of pipelining
                 techniques to these constructions not trivial. We
                 formalize here an optimization technique called
                 quasipipelining, whose goal is to optimize the critical
                 path and thus to increase the clock frequency in
                 dedicated hardware implementations. The SHA-2 algorithm
                 has been previously examined by Dadda et al., with
                 specific versions of quasipipelining; here, a full
                 generalization of the technique is presented, along
                 with application to the SHA-1 algorithm.
                 Quasi-pipelining could be as well applied to future
                 hashing algorithms, provided they are designed along
                 the same lines as those of the SHA family.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17",
  pagecount =    "8",
}

@InProceedings{Markstein:2005:FSM,
  author =       "Peter Markstein",
  title =        "A Fast-Start Method for Computing the Inverse
                 Tangent",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-112.pdf",
  abstract =     "In a search for an algorithm to compute $ \atan (x) $
                 which has both low latency and few floating point
                 instructions, an interesting variant of familiar
                 trigonometry formulas was discovered that allow the
                 start of argument reduction to commence before any
                 references to tables stored in memory are needed. Low
                 latency makes the method suitable for a closed
                 subroutine, and few floating point operations make the
                 method advantageous for a software-pipelined
                 implementation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17; IA-64; Itanium-2",
  pagecount =    "6",
}

@TechReport{Marques:2005:BIF,
  author =       "Osni A. Marques and E. Jason Riedy and Christof
                 V{\"o}mel",
  title =        "Benefits of {IEEE-754} Features in Modern Symmetric
                 Tridiagonal Eigensolvers",
  type =         "LAPACK Working Note",
  number =       "172",
  institution =  "Computer Science Division, University of California,
                 Berkeley",
  address =      "Berkeley, CA, USA",
  pages =        "22",
  day =          "30",
  month =        sep,
  year =         "2005",
  MRclass =      "15A18, 15A23.",
  bibdate =      "Mon Mar 20 12:18:56 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Also issued as Technical Report UCB//CSD-05-1414.",
  URL =          "http://www.netlib.org/lapack/lawnspdf/lawn172.pdf",
  abstract =     "Bisection is one of the most common methods used to
                 compute the eigenvalues of symmetric tridiagonal
                 matrices. Bisection relies on the Sturm count: for a
                 given shift $ \sigma $, the number of negative pivots
                 in the factorization $ T \sigma I = L D L^T $ equals
                 the number of eigenvalues of $T$ that are smaller than
                 $ \sigma $. In IEEE-754 arithmetic, the value $ \infty
                 $ permits the computation to continue past a zero
                 pivot, producing a correct Sturm count when $T$ is
                 unreduced. Demmel and Li showed in the 90s that using $
                 \infty $ rather than testing for zero pivots within the
                 loop could improve performance significantly on certain
                 architectures.

                 When eigenvalues are to be computed to high relative
                 accuracy, it is often preferable to work with $ L D L^T
                 $ factorizations instead of the original tridiagonal
                 $T$, see for example the MRRR algorithm. In these
                 cases, the Sturm count has to be computed from $ L D
                 L^T $. The differential stationary and progressive qds
                 algorithms are the methods of choice.

                 While it seems trivial to replace $T$ by $ L D L^T $,
                 in reality these algorithms are more complicated: in
                 IEEE-754 arithmetic, a zero pivot produces an overflow,
                 followed by an invalid exception (NaN), that renders
                 the Sturm count incorrect.

                 We present alternative, safe formulations that are
                 guaranteed to produce the correct result.

                 Benchmarking these algorithms on a variety of platforms
                 shows that the original formulation without tests is
                 always faster provided no exception occurs. The
                 transforms see speed-ups of up to $ 2.6 \times $ over
                 the careful formulations.

                 Tests on industrial matrices show that encountering
                 exceptions in practice is rare. This leads to the
                 following design: First, compute the Sturm count by the
                 fast but unsafe algorithm. Then, if an exception
                 occurred, recompute the count by a safe, slower
                 alternative. The new Sturm count algorithms improve the
                 speed of bisection by up to $ 2 \times $ on our test
                 matrices. Furthermore, unlike the traditional
                 tiny-pivot substitution, proper use of IEEE-754
                 features provides a careful formulation that imposes no
                 input range restrictions.",
  acknowledgement = ack-nhfb,
  keywords =     "differential qds algorithms; IEEE-754 arithmetic;
                 IEEE-754 performance; LAPACK; MRRR algorithm; NaN
                 arithmetic",
}

@InProceedings{Matula:2005:TLS,
  author =       "David Matula and Alex Fit-Florea and Mitchell
                 Thornton",
  title =        "Table Lookup Structures for Multiplicative Inverses
                 Modulo $ 2^k $",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-160.pdf",
  abstract =     "We introduce an inheritance property and related table
                 lookup structures applicable to simplified evaluation
                 of the modular operations ``multiplicative inverse'',
                 ``discrete log'', and ``exponential residue'' in the
                 particular modulus $ 2^k $. Regarding applications, we
                 describe an integer representation system of Benschop
                 for transforming integer multiplications into additions
                 which benefits from our table lookup function
                 evaluation procedures.\par We focus herein on the
                 multiplicative inverse modulo $ 2^k $ to exhibit
                 simplifications in hardware implementations realized
                 from the inheritance property. A table lookup structure
                 given by a bit string that can be interpreted with
                 reference to a binary tree is described and analyzed.
                 Using observed symmetries, the lookup structure size is
                 reduced allowing a novel direct lookup process for
                 multiplicative inverses for all 16-bit odd integers to
                 be obtained from a table of size less than two KBytes.
                 The 16-bit multiplicative inverse operation is also
                 applicable for providing a seed inverse for obtaining
                 32/64-bit multiplicative inverses by one/two iterations
                 of a known quadratic refinement algorithm.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17",
  pagecount =    "8",
}

@Article{McCann:2005:SDA,
  author =       "Mark McCann and Nicholas Pippenger",
  title =        "{SRT} Division Algorithms as Dynamical Systems",
  journal =      j-SIAM-J-COMPUT,
  volume =       "34",
  number =       "6",
  pages =        "1279--1301",
  month =        dec,
  year =         "2005",
  CODEN =        "SMJCAT",
  DOI =          "https://doi.org/10.1137/S009753970444106X",
  ISSN =         "0097-5397 (print), 1095-7111 (electronic)",
  ISSN-L =       "0097-5397",
  MRclass =      "68W40, 37E05",
  bibdate =      "Fri Dec 30 06:20:35 MST 2005",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/34/6;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/44106",
  abstract =     "Sweeney--Robertson--Tocher (SRT) division, as it was
                 discovered in the late 1950s, represented an important
                 improvement in the speed of division algorithms for
                 computers at the time. A variant of SRT division is
                 still commonly implemented in computers today. Although
                 some bounds on the performance of the original SRT
                 division method were obtained, a great many questions
                 remained unanswered. In this paper, the original
                 version of SRT division is described as a dynamical
                 system. This enables us to bring modern dynamical
                 systems theory, a relatively new development in
                 mathematics, to bear on an older problem. In doing so,
                 we are able to show that SRT division is ergodic, and
                 is even Bernoulli, for all real divisors and dividends.
                 With the Bernoulli property, we are able to use entropy
                 to prove that the natural extensions of SRT division
                 are isomorphic by way of the Kolmogorov--Ornstein
                 theorem. We demonstrate how our methods and results can
                 be applied to a much larger class of division
                 algorithms.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Computing",
  journal-URL =  "http://epubs.siam.org/sicomp",
  keywords =     "SRT division, ergodic, Bernoulli, dynamical systems,
                 entropy",
}

@InProceedings{Mei:2005:LZA,
  author =       "Xiao-Lu Mei",
  title =        "Leading zero anticipation for latency improvement in
                 floating-point fused multiply-add units",
  crossref =     "Tang:2005:AIC",
  pages =        "53--56",
  year =         "2005",
  DOI =          "https://doi.org/10.1109/ICASIC.2005.1611267",
  bibdate =      "Sun Feb 20 09:52:59 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The leading zero anticipation (LZA) is vital in the
                 floating-point fused multiply-add (FMA) units. The
                 general LZA algorithms can only deal with 2 operands.
                 It increases the critical path delay of high
                 performance floating-point FMA units. The paper
                 presents a novel LZA algorithm to deal with 3 operands
                 directly and implemented the 106-bit leading zero
                 anticipator in the high performance floating-point FMA
                 with the general LZA algorithm and the proposed LZA
                 algorithm respectively. Compared with the general
                 leading zero anticipator, the proposed leading zero
                 anticipator can reduce the delay of the critical path
                 by 16.67\% and reduce the area by 19.63\%
                 approximately.",
  acknowledgement = ack-nhfb,
}

@Article{Menissier-Morain:2005:APR,
  author =       "Val{\'e}rie M{\'e}nissier-Morain",
  title =        "Arbitrary precision real arithmetic: design and
                 algorithms",
  journal =      j-J-LOGIC-ALG-PROG,
  volume =       "64",
  number =       "1",
  pages =        "13--39",
  month =        jul,
  year =         "2005",
  DOI =          "https://doi.org/10.1016/j.jlap.2004.07.003",
  ISSN =         "1567-8326 (print), 1873-5940 (electronic)",
  ISSN-L =       "1567-8326",
  bibdate =      "Thu Oct 17 10:09:18 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Logic and Algebraic Programming",
  journal-URL =  "http://www.sciencedirect.com/science/journal/15678326",
  remark =       "Special issue on Practical development of exact real
                 number computation.",
}

@Article{Mitra:2005:BFP,
  author =       "Abhijit Mitra and Mrityunjoy Chakraborty and Hideaki
                 Sakai",
  title =        "A block floating-point treatment to the {LMS}
                 algorithm: efficient realization and a roundoff error
                 analysis",
  journal =      j-IEEE-TRANS-SIG-PROC,
  volume =       "53",
  number =       "12",
  pages =        "4536--4544",
  year =         "2005",
  CODEN =        "ITPRED",
  ISSN =         "1053-587X (print), 1941-0476 (electronic)",
  ISSN-L =       "1053-587X",
  MRclass =      "Database Expansion Item",
  MRnumber =     "MR2246666",
  bibdate =      "Thu Nov 8 19:16:14 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=78",
}

@Book{Mitzenmacher:2005:PCI,
  author =       "Michael Mitzenmacher and Eli Upfal",
  title =        "Probability and Computing: an Introduction to
                 Randomized Algorithms and Probabilistic Analysis",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xvi + 352",
  year =         "2005",
  DOI =          "https://doi.org/10.1017/cbo9780511813603",
  ISBN =         "0-521-83540-2 (print), 0-511-81360-0 (e-book)",
  ISBN-13 =      "978-0-521-83540-4 (print), 978-0-511-81360-3
                 (e-book)",
  LCCN =         "QA274 .M574 2005",
  bibdate =      "Fri Sep 22 17:57:47 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  subject =      "Algorithms; Probabilities; Stochastic analysis;
                 Algorithmes; Probabilit{\'e}s; Analyse stochastique",
  tableofcontents = "Events and probability \\
                 Discrete random variables and expectation \\
                 Moments and deviations \\
                 Chernoff bounds \\
                 Balls, bins and random graphs \\
                 The probabilistic method \\
                 Markov chains and random walks \\
                 Continuous distributions and the Poisson process \\
                 Entropy, randomness, and information \\
                 The Monte Carlo method \\
                 Coupling of Markov chains \\
                 Martingales \\
                 Pairwise independence and universal hash functions \\
                 Balanced allocations",
}

@Article{Montgomery:2005:FSS,
  author =       "Peter L. Montgomery",
  title =        "Five, Six, and Seven-Term {Karatsuba}-Like Formulae",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "3",
  pages =        "362--369",
  month =        mar,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.49",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue May 30 12:14:00 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://csdl.computer.org/comp/trans/tc/2005/03/t0362abs.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0362.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0362.pdf;
                 http://ieeexplore.ieee.org/iel5/12/30205/01388200.pdf?isnumber=30205&prod=JNL&arnumber=1388200&arSt=+362&ared=+369&arAuthor=Montgomery%2C+P.L.;
                 http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388200&count=13&index=11;
                 http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388200",
  abstract =     "The Karatsuba--Ofman algorithm starts with a way to
                 multiply two 2-term (i.e., linear) polynomials using
                 three scalar multiplications. There is also a way to
                 multiply two 3-term (i.e., quadratic) polynomials using
                 six scalar multiplications. These are used within
                 recursive constructions to multiply two higher-degree
                 polynomials in subquadratic time. We present
                 division-free formulae, which multiply two 5-term
                 polynomials with 13 scalar multiplications, two 6-term
                 polynomials with 17 scalar multiplications, and two
                 7-term polynomials with 22 scalar multiplications.
                 These formulae may be mixed with the 2-term and 3-term
                 formulae within recursive constructions, leading to
                 improved bounds for many other degrees. Using only the
                 6-term formula leads to better asymptotic performance
                 than standard Karatsuba. The new formulae work in any
                 characteristic, but simplify in characteristic 2. We
                 describe their application to elliptic curve arithmetic
                 over binary fields. We include some timing data.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-16",
  remark =       "Special issue on computer arithmetic: selected papers
                 from ARITH-16.",
}

@InProceedings{Morris:2005:FBF,
  author =       "G. Morris and V. Prasanna",
  title =        "An {FPGA}-based floating-point {Jacobi} iterative
                 solver",
  crossref =     "Bein:2005:PIS",
  pages =        "420--427",
  year =         "2005",
  DOI =          "https://doi.org/10.1109/ISPAN.2005.18",
  bibdate =      "Sat Oct 9 12:54:52 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Within the parallel computing domain, field
                 programmable gate arrays (FPGA) are no longer
                 restricted to their traditional role as substitutes for
                 application-specific integrated circuits --- as
                 hardware `hidden' from the end user. Several high
                 performance computing vendors offer parallel
                 reconfigurable computers employing user-programmable
                 FPGAs. These exciting new architectures allow end-users
                 to, in effect, create reconfigurable coprocessors
                 targeting the computationally intensive parts of each
                 problem. The increased capability of contemporary FPGAs
                 coupled with the embarrassingly parallel nature of the
                 Jacobi iterative method make the Jacobi method an ideal
                 candidate for hardware acceleration. This paper
                 introduces a parameterized design for a deeply
                 pipelined, highly parallelized IEEE 64-bit
                 floating-point version of the Jacobi method. A Jacobi
                 circuit is implemented using a Xilinx Virtex-II Pro as
                 the target FPGA device. Implementation statistics and
                 performance estimates are presented.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mueller:2005:VFP,
  author =       "Silvia M. Mueller and Christian Jacobi and Hwa-Joon Oh
                 and Kevin D. Tran and Cottier Scott and Brad W. Michael
                 and Hiroo Nishikawa and Yonetaro Totsuka and Tatsuya
                 Namatame and Naoka Yano and Takashi Machida and Sang H.
                 Dhong",
  title =        "The Vector Floating-Point Unit in a Synergistic
                 Processor Element of a {CELL} Processor",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-151.pdf",
  abstract =     "The floating-point unit in the Synergistic Processor
                 Element of the 1st generation multi-core CELL Processor
                 is described. The FPU supports 4-way SIMD single
                 precision and integer operations and 2-way SIMD double
                 precision operations. The design required a
                 high-frequency, low latency, power and area efficiency
                 with primary application to the multimedia streaming
                 workloads, such as 3D graphics. The FPU has 3 different
                 latencies, optimizing the performance critical single
                 precision FMA operations, which are executed with a
                 6-cycle latency at an 11FO4 cycle time. The latency
                 includes the global forwarding of the result. These
                 challenging performance, power, and area goals were
                 achieved through the co-design of architecture and
                 implementation with optimizations at all levels of the
                 design. This paper focuses on the logical and
                 algorithmic aspects of the FPU we developed, to achieve
                 these goals.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17",
  pagecount =    "9",
}

@TechReport{Muller:2005:D,
  author =       "Jean-Michel Muller",
  title =        "On the Definition of {\tt ulp(x)}",
  type =         "Rapport de recherche",
  number =       "LIP RR2005-09, INRIA RR-5504",
  institution =  "Laboratoire de l'Informatique du Parall{\'e}lisme",
  address =      "Lyon, France",
  pages =        "19",
  month =        feb,
  year =         "2005",
  ISSN =         "0249-6399",
  bibdate =      "Wed Jun 24 22:44:21 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-5504.pdf",
  abstract =     "Function ulp (acronym for \emph{unit in the last
                 place}) is frequently used for expressing errors in
                 floating-point computations. We present several
                 previously suggested definitions of that function, and
                 analyse some of their properties.",
  acknowledgement = ack-nhfb,
  keywords =     "computer arithmetic; floating-point arithmetic; ULP;
                 unit in the last place",
}

@InProceedings{Muller:2005:DCS,
  author =       "Jean-Michel Muller and Arnaud Tisserand and Benoit de
                 Dinechin and Christophe Monat",
  title =        "Division by Constant for the {ST100 DSP}
                 Microprocessor",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-133.pdf",
  abstract =     "Algorithms for Euclidean (i.e., integer) division by a
                 constant operation are presented. They allow fast
                 computation for some values of the divisor (known at
                 compile time) or also when both quotient and modulus
                 are required. These algorithms are based on the
                 multiply-accumulate instruction and the 40-bit
                 arithmetic available in DSPs such as the ST100 DSP from
                 STMicroelectronics. The results are demonstrated in the
                 case of standard speech coding applications.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17",
  pagecount =    "7",
}

@Article{Muller:2005:GEI,
  author =       "Norbert M{\"u}ller and Martin Escardo and Paul
                 Zimmermann",
  title =        "Guest editors' introduction: Special issue on
                 practical development of exact real number
                 computation",
  journal =      j-J-LOGIC-ALG-PROG,
  volume =       "64",
  number =       "1",
  pages =        "1--2",
  month =        jul,
  year =         "2005",
  DOI =          "https://doi.org/10.1016/j.jlap.2004.07.001",
  ISSN =         "1567-8326 (print), 1873-5940 (electronic)",
  ISSN-L =       "1567-8326",
  bibdate =      "Thu Oct 17 10:09:18 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Logic and Algebraic Programming",
  journal-URL =  "http://www.sciencedirect.com/science/journal/15678326",
  remark =       "Special issue on Practical development of exact real
                 number computation.",
}

@Article{Muscedere:2005:ETB,
  author =       "Roberto Muscedere and Vassil Dimitrov and Graham A.
                 Jullien and William C. Miller",
  title =        "Efficient Techniques for Binary-to-Multidigit
                 Multidimensional Logarithmic Number System Conversion
                 Using Range-Addressable Look-Up Tables",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "3",
  pages =        "257--271",
  month =        mar,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.48",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue May 30 12:14:00 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://csdl.computer.org/comp/trans/tc/2005/03/t0257abs.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0257.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0257.pdf;
                 http://ieeexplore.ieee.org/iel5/12/30205/01388191.pdf?isnumber=30205&prod=JNL&arnumber=1388191&arSt=+257&ared=+271&arAuthor=Muscedere%2C+R.%3B+Dimitrov%2C+V.%3B+Jullien%2C+G.A.%3B+Miller%2C+W.C.;
                 http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388191&count=13&index=2;
                 http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388191",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-16",
  remark =       "Special issue on computer arithmetic: selected papers
                 from ARITH-16.",
}

@Article{Muscedere:2005:LPT,
  author =       "Roberto Muscedere and Vassil Dimitrov and Graham
                 Jullien and William Miller",
  title =        "A low-power two-digit multi-dimensional logarithmic
                 number system filterbank architecture for a digital
                 hearing aid",
  journal =      j-EURASIP-J-ADV-SIGNAL-PROCESS,
  volume =       "1",
  pages =        "3015--3025",
  year =         "2005",
  DOI =          "https://doi.org/10.1155/ASP.2005.3015",
  ISSN =         "1110-8657 (print), 1687-0433 (electronic)",
  ISSN-L =       "1110-8657",
  bibdate =      "Fri Aug 8 08:37:33 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper addresses the implementation of a
                 filterbank for digital hearing aids using a
                 multi-dimensional logarithmic number system (MDLNS).
                 The MDLNS, which has similar properties to the
                 classical logarithmic number system (LNS), provides
                 more degrees of freedom than the LNS by virtue of
                 having two, or more, orthogonal bases and the ability
                 to use multiple MDLNS components or digits. The
                 logarithmic properties of the MDLNS also allow for
                 reduced complexity multiplication and large dynamic
                 range, and a multiple-digit MDLNS provides a
                 considerable reduction in hardware complexity compared
                 to a conventional LNS approach. We discuss an improved
                 design for a two-digit 2D MDLNS filterbank
                 implementation which reduces power and area by over two
                 times compared to the original design.",
  acknowledgement = ack-nhfb,
  ajournal =     "EURASIP J. Appl. Signal Process.",
  articleno =    "326504",
  fjournal =     "EURASIP Journal on Advances in Signal Processing",
  journal-URL =  "https://asp-eurasipjournals.springeropen.com/",
}

@Article{Newman:2005:PLP,
  author =       "M. E. J. Newman",
  title =        "Power laws, {Pareto} distributions and {Zipf}'s law",
  journal =      j-CONTEMP-PHYS,
  volume =       "46",
  number =       "5",
  pages =        "323--351",
  month =        sep,
  year =         "2005",
  CODEN =        "CTPHAF",
  DOI =          "https://doi.org/10.1080/00107510500052444",
  ISSN =         "0010-7514 (print), 1366-5812 (electronic)",
  ISSN-L =       "0010-7514",
  bibdate =      "Thu Feb 18 20:07:22 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/contempphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "When the probability of measuring a particular value
                 of some quantity varies inversely as a power of that
                 value, the quantity is said to follow a power law, also
                 known variously as Zipf's law or the Pareto
                 distribution. Power laws appear widely in physics,
                 biology, earth and planetary sciences, economics and
                 finance, computer science, demography and the social
                 sciences. For instance, the distributions of the sizes
                 of cities, earthquakes, forest fires, solar flares,
                 moon craters and people's personal fortunes all appear
                 to follow power laws. The origin of power-law behaviour
                 has been a topic of debate in the scientific community
                 for more than a century. Here we review some of the
                 empirical evidence for the existence of power-law forms
                 and the theories proposed to explain them.",
  acknowledgement = ack-nhfb,
  fjournal =     "Contemporary Physics",
  journal-URL =  "http://www.tandfonline.com/loi/tcph20",
  keywords =     "Benford's Law; critical phenomena; Legendre beta
                 function; Pareto distribution; percolation; phase
                 transitions; power-law distributions; random walks;
                 Riemann zeta function; scale-free distributions; Yule
                 process; Zipf's Law",
  remark =       "This article is an excellent survey of continuous and
                 discrete distributions that follow a power law, and
                 some that do not. It is well worth reading.",
  subject =      "astrophysics; atomic and nuclear physics; chemical
                 physics; computational physics; condensed matter
                 physics; environmental physics; experimental physics;
                 general physics; particle and high energy physics;
                 plasma physics; space science; theoretical physics",
}

@Article{Nguyen:2005:FPL,
  author =       "P. Nguyen and D. Stehle",
  title =        "Floating-Point {LLL} Revisited",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "3494",
  pages =        "215--233",
  year =         "2005",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/11426639_13",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Fri Jun 24 14:51:11 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Lenstra-Lenstra-Lov{\'a}sz lattice basis reduction
                 algorithm (LLL or $ L^3 $) is a very popular tool in
                 public-key cryptanalysis and in many other fields.
                 Given an integer $d$-dimensional lattice basis with
                 vectors of norm less than $B$ in an $n$-dimensional
                 space, $ L^3 $ outputs a so-called $ L^3 $-reduced
                 basis in polynomial time $ O(d^5 n \log^3 B) $, using
                 arithmetic operations on integers of bit-length $ O(d l
                 o g B) $. This worst-case complexity is problematic for
                 lattices arising in cryptanalysis where $d$ or/and $
                 \log B $ are often large. As a result, the original $
                 L^3 $ is almost never used in practice. Instead, one
                 applies floating-point variants of $ L^3 $, where the
                 long-integer arithmetic required by Gram--Schmidt
                 orthogonalisation (central in $ L^3 $) is replaced by
                 floating-point arithmetic. Unfortunately, this is known
                 to be unstable in the worst-case: the usual
                 floating-point $ L^3 $ is not even guaranteed to
                 terminate, and the output basis may not be $ L^3
                 $-reduced at all. In this article, we introduce the $
                 L^2 $ algorithm, a new and natural floating-point
                 variant of $ L^3 $ which provably outputs $ L^3
                 $-reduced bases in polynomial time $ O(d^4 n (d + \log
                 B) \log B) $. This is the first $ L^3 $ algorithm whose
                 running time (without fast integer arithmetic) provably
                 grows only quadratically with respect to $ \log B $,
                 like the well-known Euclidean and Gaussian algorithms,
                 which it generalizes.",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
  keywords =     "$L^3$; Lattice Reduction; LLL; Public-Key
                 Cryptanalysis",
}

@InProceedings{Oberman:2005:HPA,
  author =       "Stuart Oberman and Michael Siu",
  title =        "A High-Performance Area-Efficient Multifunction
                 Interpolator",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-164.pdf",
  abstract =     "This paper presents the algorithms and implementation
                 of a high-performance functional unit used for multiple
                 interpolation applications. Graphics processing units
                 (GPUs) frequently perform two classes of floating point
                 interpolation within programmable shaders: per-pixel
                 attribute interpolation and transcendental function
                 approximation. We present a design that efficiently
                 performs both classes of interpolation on a shared
                 functional unit. Enhanced minimax approximations with
                 quadratic interpolation minimize lookup-table sizes and
                 datapath widths for fully-pipelined function
                 approximation. Rectangular multipliers support both
                 sign-magnitude and two's complement inputs of variable
                 widths. Superpipelining is used throughout the design
                 to increase operating frequency and interpolation
                 throughput while maximizing area efficiency.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17",
  pagecount =    "8",
}

@Article{Ogita:2005:ASD,
  author =       "Takeshi Ogita and Siegfried M. Rump and Shin'ichi
                 Oishi",
  title =        "Accurate Sum and Dot Product",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "26",
  number =       "6",
  pages =        "1955--1988",
  month =        nov,
  year =         "2005",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/030601818",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "5-04, 65G99, 65-04",
  bibdate =      "Mon Nov 21 14:52:48 MST 2005",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/26/6;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/60181",
  abstract =     "Algorithms for summation and dot product of
                 floating-point numbers are presented which are fast in
                 terms of measured computing time. We show that the
                 computed results are as accurate as if computed in
                 twice or K-fold working precision, $ K \ge 3 $. For
                 twice the working precision our algorithms for
                 summation and dot product are some 40\% faster than the
                 corresponding XBLAS routines while sharing similar
                 error estimates. Our algorithms are widely applicable
                 because they require only addition, subtraction, and
                 multiplication of floating-point numbers in the same
                 working precision as the given data. Higher precision
                 is unnecessary, algorithms are straight loops without
                 branch, and no access to mantissa or exponent is
                 necessary.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  keywords =     "accurate dot product; accurate floating-point
                 summation; fast algorithms; high precision; verified
                 error bounds",
}

@InProceedings{Oh:2005:FPS,
  author =       "H.-J. Oh and S. M. Mueller and C. Jacobi and K. D.
                 Tran and S. R. Cottier and B. W. Michael and H.
                 Nishikawa and Y. Totsuka and T. Namatame and N. Yano
                 and T. Machida and S. H. Dhong",
  booktitle =    "{2005 Symposium on VLSI Circuits, June 16--18th, 2005,
                 Rhiga Royal Hotel Kyoto, Kyoto, Japan}",
  title =        "A Fully-Pipelined Single-Precision Floating Point Unit
                 in the Synergistic Processor Element of a {CELL}
                 Processor",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "??--??",
  year =         "2005",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Fri Jun 24 14:35:04 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Paper 2.4",
  URL =          "http://www.vlsisymposium.org/circuits/technical.html",
  abstract =     "The floating point unit in the synergistic processor
                 element of a CELL processor is a fully-pipelined 4-way
                 SIMD unit designed to accelerate media and data
                 streaming. It supports 32-bit single-precision floating
                 point and 16-bit integer operands with two different
                 latencies, optimizing the performance of critical
                 single-precision multiply-add operations. It employs
                 fine-grained clock gating for power saving.
                 Architecture, logic, circuits and integration are
                 co-designed to meet the performance, power, and area
                 goals.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Pareto:2005:GAL,
  author =       "Lena Pareto",
  title =        "Graphical arithmetic for learners with dyscalculia",
  crossref =     "ACM:2005:ASI",
  pages =        "214--215",
  year =         "2005",
  DOI =          "https://doi.org/10.1145/1090785.1090836",
  bibdate =      "Thu Aug 07 18:43:59 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We propose a model for arithmetic, based on graphical
                 representations, to complement the symbolic language of
                 mathematics. The focus is conceptual understanding of
                 arithmetic. We argue that the graphical model supports
                 understanding concepts known to be difficult for
                 learners with dyscalculia, such as number-sense and
                 decimal system. The proposed graphical representation
                 share properties of the decimal system, but is closer
                 to the semantic representation of numbers vital to the
                 number-sense. The model is evaluated with
                 school-children, but needs to be further tested by
                 learners with dyscalculia.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal arithmetic",
}

@InProceedings{Phatak:2005:FMR,
  author =       "Dhananjay Phatak and Tom Goff",
  title =        "Fast Modular Reduction for Large Wordlengths via One
                 Linear and One Cyclic Convolution",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-156.pdf",
  abstract =     "Modular reduction is a fundamental operation in
                 cryptographic systems. Most well known modular
                 reduction methods including Barrett's and Montgomery's
                 algorithms leverage some-pre computations to avoid
                 divisions so that the main complexity of these methods
                 lies in a sequence of two long multiplications. For
                 large wordlengths a multiplication which is tantamount
                 to a linear convolution is performed via the Fast
                 Fourier Transform (FFT) or other transform-based
                 techniques as in the Schonhage-Strassen multiplication
                 algorithm.\par

                 We show a fundamental property (the separation
                 principle): in a modular reduction based on long
                 multiplications, the linear convolution required by one
                 of the two long multiplications can be replaced by a
                 cyclic convolution, and the halves can be separated
                 using other information available due to the intrinsic
                 redundancy of the operations. This reduces the number
                 of operations by about 25\%. We demonstrate that both
                 Barrett's and Montgomery's methods can be sped up by
                 using the aforementioned fundamental principle. It is
                 shown that a direct application of this algorithm to
                 modular exponentiation (either using Barrett's or
                 Montgomery's methods) can be expected to yield about
                 17\% speedup.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17; cryptography; cyclic convolution;
                 elliptic-curve; fast modular reduction; FFT multiply;
                 large wordlength; linear convolution; number theoretic
                 transforms; principle of separation",
  pagecount =    "8",
}

@Article{Pineiro:2005:HSF,
  author =       "Jose-Alejandro Pi{\~n}eiro and Stuart F. Oberman and
                 Jean-Michel Muller and Javier D. Bruguera",
  title =        "High-Speed Function Approximation Using a Minimax
                 Quadratic Interpolator",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "3",
  pages =        "304--318",
  month =        mar,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.52",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue May 30 12:14:00 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://csdl.computer.org/comp/trans/tc/2005/03/t0304abs.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0304.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0304.pdf;
                 http://ieeexplore.ieee.org/iel5/12/30205/01388195.pdf?isnumber=30205&prod=JNL&arnumber=1388195&arSt=+304&ared=+318&arAuthor=Pineiro%2C+J.-A.%3B+Oberman%2C+S.F.%3B+Muller%2C+J.-M.%3B+Bruguera%2C+J.D.;
                 http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388195&count=13&index=6;
                 http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388195",
  abstract =     "A table-based method for high-speed function
                 approximation in single-precision floating-point format
                 is presented in this paper. Our focus is the
                 approximation of reciprocal, square root, square root
                 reciprocal, exponentials, logarithms, trigonometric
                 functions, powering (with a fixed exponent $p$), or
                 special functions. The algorithm presented here
                 combines table look-up, an enhanced minimax quadratic
                 approximation, and an efficient evaluation of the
                 second-degree polynomial (using a specialized squaring
                 unit, redundant arithmetic, and multioperand addition).
                 The execution times and area costs of an architecture
                 implementing our method are estimated, showing the
                 achievement of the fast execution times of linear
                 approximation methods and the reduced area requirements
                 of other second-degree interpolation algorithms.
                 Moreover, the use of an enhanced minimax approximation
                 which, through an iterative process, takes into account
                 the effect of rounding the polynomial coefficients to a
                 finite size allows for a further reduction in the size
                 of the look-up tables to be used, making our method
                 very suitable for the implementation of an elementary
                 function generator in state-of-the-art DSPs or graphics
                 processing units (GPUs).",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-16",
  remark =       "Special issue on computer arithmetic: selected papers
                 from ARITH-16.",
}

@Article{Revol:2005:TMF,
  author =       "N. Revol and K. Makino and M. Berz",
  title =        "{Taylor} models and floating-point arithmetic: proof
                 that arithmetic operations are validated in {COSY}",
  journal =      j-J-LOGIC-ALG-PROG,
  volume =       "64",
  number =       "1",
  pages =        "135--154",
  month =        jul,
  year =         "2005",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/j.jlap.2004.07.008",
  ISSN =         "1567-8326 (print), 1873-5940 (electronic)",
  ISSN-L =       "1567-8326",
  MRclass =      "65G20",
  MRnumber =     "MR2137738 (2006a:65071)",
  bibdate =      "Thu Oct 17 10:09:18 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://bt.pa.msu.edu/pub/papers/TMJLAP03/TMJLAP03.pdf",
  abstract =     "The goal of this paper is to prove that the
                 implementation of Taylor models in COSY, based on
                 floating-point arithmetic, computes results satisfying
                 the ``containment property'', i.e., guaranteed
                 results.\par

                 First, Taylor models are defined and their
                 implementation in the COSY software by Makino and Berz
                 is detailed. Afterwards IEEE-754 floating-point
                 arithmetic is introduced. Then the core of this paper
                 is given: the algorithms implemented in COSY for
                 multiplying a Taylor model by a scalar, for adding or
                 multiplying two Taylor models are given and are proven
                 to return Taylor models satisfying the containment
                 property.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Logic and Algebraic Programming",
  journal-URL =  "http://www.sciencedirect.com/science/journal/15678326",
  keywords =     "Containment property; COSY software; Floating-point
                 operation; Rounding error; Taylor model; Validated
                 result",
  remark =       "Special issue on Practical development of exact real
                 number computation.",
}

@Article{Reyhani-Masoleh:2005:LCW,
  author =       "A. Reyhani-Masoleh and M. A. Hasan",
  title =        "Low complexity word-level sequential normal basis
                 multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "2",
  pages =        "98--110",
  month =        feb,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.29",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 16:17:15 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1377149",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Robison:2005:BUD,
  author =       "Arch Robison",
  title =        "{$N$}-Bit Unsigned Division Via {$N$}-Bit
                 Multiply-Add",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-104.pdf",
  abstract =     "Integer division on modern processors is expensive
                 compared to multiplication. Previous algorithms for
                 performing unsigned division by an invariant divisor,
                 via reciprocal approximation, suffer in the worst case
                 from a common requirement for $ n + 1 $ bit
                 multiplication, which typically must be synthesized
                 from $n$-bit multiplication and extra arithmetic
                 operations. This paper presents, and proves, a hybrid
                 of previous algorithms that replaces $ n + 1 $ bit
                 multiplication with a single fused multiply-add
                 operation on $n$-bit operands, thus reducing any
                 $n$-bit unsigned division to the upper $n$ bits of a
                 multiply-add, followed by a single right shift. An
                 additional benefit is that the prerequisite
                 calculations are simple and fast. On the Itanium 2
                 processor, the technique is advantageous for as few as
                 two quotients that share a common run-time divisor.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17",
  pagecount =    "9",
}

@TechReport{Rump:2005:AFP,
  author =       "Siegfried M. Rump and Takeshi Ogita and Shin'ichi
                 Oishi",
  title =        "Accurate Floating-Point Summation",
  type =         "Technical Report",
  number =       "05.12",
  institution =  "Faculty for Information- and Communication Sciences,
                 Hamburg University of Technology",
  address =      "Hamburg, Germany",
  day =          "13",
  month =        nov,
  year =         "2005",
  bibdate =      "Wed Jan 04 12:31:28 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ti3.tu-harburg.de/paper/rump/Ru05d.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation; distillation",
}

@Article{Savas:2005:CFA,
  author =       "E. Savas",
  title =        "A carry-free architecture for {Montgomery} inversion",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "12",
  pages =        "1508--1519",
  month =        dec,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.188",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 16:17:19 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1524933",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Misc{Sax:2005:FPN,
  author =       "Jeffrey Sax",
  title =        "Floating Point in {.NET} part 1: {Concepts} and
                 Formats",
  howpublished = "World-Wide Web document",
  day =          "18",
  month =        apr,
  year =         "2005",
  bibdate =      "Wed Mar 15 06:07:27 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.codeproject.com/dotnet/ExtremeFloatingPoint1.asp;
                 http://www.codeproject.com/dotnet/ExtremeFloatingPoint1/ExtremeFloatingPoint1.zip",
  acknowledgement = ack-nhfb,
  remark =       "Introductory tutorial on floating-point formats.
                 Cannot find parts 2 and 3.",
}

@Article{Schulte:2005:GEI,
  author =       "Michael J. Schulte and Jean-Claude Bajard",
  title =        "{Guest Editors}' Introduction: Special Issue on
                 Computer Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "3",
  pages =        "241--242",
  month =        mar,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.50",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Apr 27 18:04:38 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://csdl.computer.org/comp/trans/tc/2005/03/t0241.pdf;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0241.htm",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  remark =       "From the article: ``This special issue presents recent
                 high-quality research in computer arithmetic. The 12
                 papers included in this special issue were selected
                 from 36 papers submitted in response to an open call
                 for papers. This call for papers followed the 16th IEEE
                 International Symposium on Computer Arithmetic, which
                 took place in Santiago de Compostella in June 2003.
                 Each paper received at least three reviews and the top
                 papers were selected for inclusion in this special
                 issue. Six papers are expanded versions of the papers
                 presented at the 16th IEEE Symposium on Computer
                 Arithmetic, three are expanded versions of papers
                 presented at other conferences, and three are original
                 contributions.''",
}

@InProceedings{Schulte:2005:PED,
  author =       "M. J. Schulte and N. Lindberg and A. Laxminarain",
  booktitle =    "Proceedings of the 6th {IBM} Austin Center for
                 Advanced Studies Conference, Austin, {TX}, February,
                 2005",
  title =        "Performance Evaluation of Decimal Floating-Point
                 Arithmetic",
  publisher =    pub-IBM,
  address =      pub-IBM:adr,
  pages =        "??--??",
  year =         "2005",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sun Mar 04 10:14:56 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://domino.watson.ibm.com/acas/w3www_acas.nsf/images/conf05/%24FILE/schulte.pdf;
                 http://mesa.ece.wisc.edu/publications/cp_2005-14.pdf",
  abstract =     "The prominence of decimal data in commercial and
                 financial applications has led researchers to pursue
                 efficient techniques for performing decimal
                 floating-point arithmetic. While several software
                 implementations of decimal floating-point arithmetic
                 have been implemented, there is a growing need to
                 provide hardware support for decimal floating-point
                 arithmetic to keep up with the processing demands of
                 emerging commercial and financial applications. This
                 paper evaluates and compares the performance of decimal
                 floating-point arithmetic operations when implemented
                 on superscalar processors using either software
                 libraries or specialized hardware designs. Our
                 comparisons show that hardware implementations of
                 decimal floating-point arithmetic operations are one to
                 two orders of magnitude faster than software
                 implementations.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@InProceedings{Seidel:2005:HRI,
  author =       "Peter-Michael Seidel",
  title =        "High-Radix Implementation of {IEEE} Floating-Point
                 Addition",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-192.pdf",
  abstract =     "We are proposing a micro-architecture for
                 high-performance IEEE floating-point addition that is
                 based on a (non-redundant) high-radix representation of
                 the floating-point operands. The main improvement of
                 the proposed IEEE FP addition implementation is
                 achieved by avoiding the computation of full alignment
                 and normalization shifts which impose major delays in
                 conventional implementations of IEEE FP addition. This
                 reduction is achieved at the cost of wider operand
                 interfaces and an increased complexity for IEEE
                 compliant rounding. We present a detailed discussion of
                 an IEEE FP adder implementation using the proposed
                 high-radix format and explain the specific benefits and
                 challenges of the design.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17",
  pagecount =    "8",
}

@Article{Seidel:2005:SRR,
  author =       "Peter-Michael Seidel and L. D. McFearin and D. W. Matula",
  title =        "Secondary radix recodings for higher radix
                 multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "2",
  pages =        "111--123",
  month =        feb,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.32",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 16:17:15 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1377150",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Serebrenik:2005:TFP,
  author =       "Alexander Serebrenik and Danny {De Schreye}",
  title =        "Termination of Floating-Point Computations",
  journal =      j-J-AUTOM-REASON,
  volume =       "34",
  number =       "2",
  pages =        "141--177",
  month =        dec,
  year =         "2005",
  CODEN =        "JAREEW",
  DOI =          "https://doi.org/10.1007/s10817-005-6546-z",
  ISSN =         "0168-7433 (print), 1573-0670 (electronic)",
  ISSN-L =       "0168-7433",
  MRclass =      "68N17 (65G99 68Q60)",
  MRnumber =     "MR2213571 (2007d:68022)",
  MRreviewer =   "Andrzej Kozlowski",
  bibdate =      "Sat Apr 2 10:50:29 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
  URL =          "http://link.springer.com/article/10.1007/s10817-005-6546-z",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Autom. Reason.",
  fjournal =     "Journal of Automated Reasoning",
  journal-URL =  "http://link.springer.com/journal/10817",
}

@InProceedings{Setiaarif:2005:NMS,
  author =       "E. Setiaarif and P. Siy",
  booktitle =    "{NAFIPS 2005}, Annual Meeting of the North American
                 Fuzzy Information Processing Society, 26--28 June
                 2005",
  title =        "A new moduli set selection technique to improve sign
                 detection and number comparison in residue number
                 system ({RNS})",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "766--768",
  year =         "2005",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/NAFIPS.2005.1548635",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "Residue number system (RNS) offers a promising future
                 because its carry-free operations in addition,
                 subtraction and multiplication. This inherent property
                 of RNS can be used to reduce the complexity of
                 calculation in many applications, such as \ldots{}",
}

@InProceedings{Soderstrand:2005:RNS,
  author =       "M. A. Soderstrand and G. Y. Cho and L. G. Johnson",
  booktitle =    "{ISCAS 2005}, {IEEE} International Symposium on
                 Circuits and Systems, 23--26 May 2005",
  title =        "Residue number system implementations of complex
                 heterodyne tunable filters",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "548--551",
  year =         "2005",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.2005.1464646",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "The heterodyne signals for a complex heterodyne filter
                 based upon M/2 equally-spaced heterodyne frequencies
                 between DC and the Nyquist frequency can be generated
                 from taking integer powers of the M/sup th/ root of
                 one. In residue number systems (RNS) \ldots{}",
}

@Article{Sofroniou:2005:PNC,
  author =       "Mark Sofroniou and Giulia Spaletta",
  title =        "Precise numerical computation",
  journal =      j-J-LOGIC-ALG-PROG,
  volume =       "64",
  number =       "1",
  pages =        "113--134",
  month =        jul,
  year =         "2005",
  DOI =          "https://doi.org/10.1016/j.jlap.2004.07.007",
  ISSN =         "1567-8326 (print), 1873-5940 (electronic)",
  ISSN-L =       "1567-8326",
  bibdate =      "Thu Oct 17 10:09:18 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1567832604000785",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Logic and Algebraic Programming",
  journal-URL =  "http://www.sciencedirect.com/science/journal/15678326",
  keywords =     "accuracy and precision; computer algebra systems;
                 computer aspects of numerical algorithms; condition
                 number; error analysis; floating-point arithmetic;
                 interval arithmetic; Mathematica; significance
                 arithmetic; symbolic algebra",
  remark =       "Special issue on Practical development of exact real
                 number computation. Paper dedicated to Jerry B. Keiper
                 (1953--1995) and Nicholas C. Metropolis (1915--1999).
                 It is primarily about describing Mathematica's
                 significance arithmetic.",
}

@Article{Sofronioua:2005:PNC,
  author =       "Mark Sofronioua and Giulia Spalettab",
  title =        "Precise numerical computation",
  journal =      j-J-LOGIC-ALG-PROG,
  volume =       "64",
  number =       "1",
  pages =        "113--134",
  month =        jul,
  year =         "2005",
  DOI =          "https://doi.org/10.1016/j.jlap.2004.07.007",
  ISSN =         "1567-8326 (print), 1873-5940 (electronic)",
  ISSN-L =       "1567-8326",
  bibdate =      "Fri Apr 04 08:12:14 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1567832604000785",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Logic and Algebraic Programming",
  journal-URL =  "http://www.sciencedirect.com/science/journal/15678326",
  keywords =     "accuracy and precision; computer algebra systems;
                 computer aspects of numerical algorithms; condition
                 number; error analysis; floating-point arithmetic;
                 interval arithmetic; Mathematica; significance
                 arithmetic; symbolic algebra",
}

@Misc{Steele:2005:SME,
  author =       "Guy L. {Steele Jr.}",
  title =        "System and method for extracting the high part of a
                 floating point operand",
  howpublished = "US Patent 6976050",
  day =          "13",
  month =        dec,
  year =         "2005",
  bibdate =      "Tue Dec 23 15:06:47 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/6976050/fulltext.html",
  abstract =     "A method and system determine a high part of a
                 floating point operand. Exponent field bits and
                 fraction field bits of a result are set to a zero if
                 the determined format is an infinity format or an
                 overflow format. The exponent field bits and the
                 fraction field bits of the result are set to
                 corresponding exponent field bits and corresponding
                 fraction field bits of the floating point operand if
                 the determined format is a not-a-number (NaN) format.
                 At least one of the fraction field bits of the result
                 is adaptively cleared if the determined format is a
                 denormalized format or a delimited format.",
  acknowledgement = ack-nhfb,
  patentdate =   "12/13/2005",
}

@Misc{Steele:2005:SMF,
  author =       "Guy L. {Steele Jr.}",
  title =        "System and method for forcing floating point status
                 information to selected values",
  howpublished = "US Patent 6970898",
  day =          "29",
  month =        nov,
  year =         "2005",
  bibdate =      "Tue Dec 23 15:06:47 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/6970898/fulltext.html",
  abstract =     "A floating point flag forcing circuit comprising an
                 circuit and a result assembler. The circuit receives a
                 plurality of floating point operands, analyzes the
                 floating point operand, receives one or more control
                 input signals, determines one or more predetermined
                 formats in which the plurality of operands are
                 represented, and generates one or more control signals.
                 The result assembler receives the control signals from
                 the circuit, along with one or more inputs, and
                 assembles a result.",
  acknowledgement = ack-nhfb,
}

@Misc{Steele:2005:SMG,
  author =       "Guy L. {Steele Jr.}",
  title =        "System and method for generating an integer part of a
                 logarithm of a floating point operand",
  howpublished = "US Patent 6961744",
  day =          "01",
  month =        nov,
  year =         "2005",
  bibdate =      "Tue Dec 23 15:06:47 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/6961744/fulltext.html",
  abstract =     "A logarithm unit computes an integer part of a
                 logarithm of a floating point operand according to an
                 embodiment of the present invention. The logarithm unit
                 analyzes a format of the floating point operand and
                 generates at least one signal representative of the
                 format. The logarithm unit determines a magnitude of an
                 unbiased exponent of the floating point operand as an
                 intermediate result based on the at least one signal,
                 wherein the unbiased exponent is represented by
                 unbiased exponent bits. Still further, the logarithm
                 unit determines an exponent field and a fraction field
                 high part of the intermediate result. A result is
                 assembled equaling the integer part of the logarithm of
                 the floating point operand based on the at least one
                 signal wherein, if the floating point operand is in at
                 least one of a denormalized format, a normalized
                 non-zero format, and a delimited format, an exponent
                 field of the result equals the exponent field of the
                 intermediate result and a fraction field high part of
                 the result equals the fraction field high part of the
                 intermediate result.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Stehle:2005:GAT,
  author =       "Damien Stehl{\'e} and Paul Zimmermann",
  title =        "{Gal}'s Accurate Tables Method Revisited",
  crossref =     "Montuschi:2005:PIS",
  pages =        "275--264",
  year =         "2005",
  DOI =          "https://doi.org/10.1109/ARITH.2005.24",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-152.pdf",
  abstract =     "Gal's accurate tables algorithm aims at providing an
                 efficient implementation of mathematical functions with
                 correct rounding as often as possible. This method
                 requires an expensive pre-computation of the values
                 taken by the function or by several related functions
                 at some distinguished points. Our improvements of Gal's
                 method are two-fold: on the one hand we describe what
                 is the arguably best set of distinguished values and
                 how it improves the efficiency and accuracy of the
                 function implementation, and on the other hand we give
                 an algorithm which drastically decreases the cost of
                 the pre-computation. These improvements are related to
                 the worst cases for the correct rounding of
                 mathematical functions and to the algorithms for
                 finding them. We demonstrate how the whole method can
                 be turned into practice for $ 2^x $ and $ \sin x $ for
                 $ x \in [1 / 2, 1) $, in double precision.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17; correct rounding; floating-point
                 arithmetic",
  pagecount =    "8",
}

@Article{Stehle:2005:SWC,
  author =       "Damien Stehl{\'e} and Vincent Lef{\`e}vre and Paul
                 Zimmermann",
  title =        "Searching Worst Cases of a One-Variable Function Using
                 Lattice Reduction",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "54",
  number =       "3",
  pages =        "340--346",
  month =        mar,
  year =         "2005",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2005.55",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue May 30 12:14:00 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://csdl.computer.org/comp/trans/tc/2005/03/t0340abs.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0340.htm;
                 http://csdl.computer.org/dl/trans/tc/2005/03/t0340.pdf;
                 http://ieeexplore.ieee.org/iel5/12/30205/01388198.pdf?isnumber=30205&prod=JNL&arnumber=1388198&arSt=+340&ared=+346&arAuthor=Stehle%2C+D.%3B+Lefevre%2C+V.%3B+Zimmermann%2C+P.;
                 http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=30205&arnumber=1388198&count=13&index=9;
                 http://ieeexplore.ieee.org/xpls/references.jsp?arnumber=1388198",
  abstract =     "We propose a new algorithm to find worst cases for the
                 correct rounding of a mathematical function of one
                 variable. We first reduce this problem to the real
                 small value problem---i.e., for polynomials with real
                 coefficients. Then, we show that this second problem
                 can be solved efficiently by extending Coppersmith's
                 work on the integer small value problem---for
                 polynomials with integer coefficients---using lattice
                 reduction. For floating-point numbers with a mantissa
                 less than $N$ and a polynomial approximation of degree
                 $d$, our algorithm finds all worst cases at distance
                 less than $ N^{\frac {-d^2}{2d + 1}} $ from a machine
                 number in time $ O(N^{{\frac {d + 12d + 1}} +
                 \varepsilon }) $. For $ d = 2 $, a detailed study
                 improves on the $ O(N^{2 / 3 + \varepsilon }) $
                 complexity from Lef{\`e}vre's algorithm to $ O(N^{4 / 7
                 + \varepsilon }) $. For larger $d$, our algorithm can
                 be used to check that there exist no worst cases at
                 distance less than $ N^{-k} $ in time $ O(N^{1 / 2 +
                 \varepsilon }) $.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "ARITH-16; Computer arithmetic; correct rounding;
                 multiple precision arithmetic; special function
                 approximations",
  remark =       "Special issue on computer arithmetic: selected papers
                 from ARITH-16.",
}

@InProceedings{Stine:2005:CTC,
  author =       "J. E. Stine and M. J. Schulte",
  title =        "A Combined Two's Complement and Floating-Point
                 Comparator",
  crossref =     "IEEE:2005:IIS",
  pages =        "89--92",
  year =         "2005",
  bibdate =      "Sun Mar 04 21:02:35 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2005-09.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Takagi:2005:HAI,
  author =       "Naofumi Takagi and Shunsuke Kadowaki and Kazuyoshi
                 Takagi",
  title =        "A Hardware Algorithm for Integer Division",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-113.pdf",
  abstract =     "A hardware algorithm for integer division is proposed.
                 It is based on the digit-recurrence, non-restoring
                 division algorithm. Fast computation is achieved by the
                 use of the radix-2 signed-digit representation. The
                 algorithm does not require normalization of the
                 divisor, and hence, does not require area-consuming
                 leading one (or zero) detection nor shifts of
                 variable-amount. Combinational (unfolded)
                 implementation of the algorithm yields a regularly
                 structured array divider, where pipelining is possible
                 for increasing the throughput. Sequential
                 implementation yields a compact divider.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17",
  pagecount =    "7",
}

@Article{Takahashi:2005:AMP,
  author =       "Daisuke Takahashi",
  title =        "An algorithm for multiple-precision floating-point
                 multiplication",
  journal =      j-APPL-MATH-COMP,
  volume =       "166",
  number =       "2",
  pages =        "291--298",
  day =          "15",
  month =        jul,
  year =         "2005",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  MRclass =      "65G99",
  MRnumber =     "MR2143788 (2006a:65075)",
  bibdate =      "Mon Jul 4 09:15:46 MDT 2005",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present an algorithm for multiple-precision
                 floating-point multiplication. The conventional
                 algorithms based on the fast Fourier transform (FFT)
                 multiply two $n$-bit numbers to obtain a $ 2 n $-bit
                 result. In multiple-precision floating-point
                 multiplication, we need only the returned result whose
                 precision is equal to the multiple-precision
                 floating-point number. We show that the overall
                 arithmetic operations for FFT-based multiple-precision
                 floating-point multiplication are reduced by
                 decomposition of the full-length multiplication into
                 shorter-length multiplication.",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  keywords =     "Fast Fourier transform; Multiple-precision arithmetic;
                 Multiplication; Program derivation",
}

@TechReport{Tang:2005:BBI,
  author =       "Ping Tak Peter Tang",
  title =        "{BID} --- Binary-Integer Decimal Encoding for Decimal
                 Floating Point: a Format Friendly to Software Emulation
                 and Compiler Native Support",
  type =         "Technical report",
  institution =  "Intel Corporation",
  address =      "San Jose, CA, USA",
  day =          "17",
  month =        jun,
  year =         "2005",
  bibdate =      "Thu Oct 14 14:50:39 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "BID (Binary-Integer Decimal) Encoding; decimal
                 floating point arithmetic",
  remark =       "Last Updated: July 12, 2005. Minor Modifications:
                 January 3, 2006",
}

@TechReport{Tang:2005:GBE,
  author =       "Ping Tak Peter Tang",
  title =        "On Generalized {BCD} Encodings for Decimal Floating
                 Point",
  type =         "Technical comment",
  institution =  "Software and Solutions Group, Intel Corporation",
  address =      "San Jose, CA, USA",
  day =          "7",
  month =        mar,
  year =         "2005",
  bibdate =      "Sat Nov 05 21:19:43 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@Article{Tsuiki:2005:RNC,
  author =       "Hideki Tsuiki",
  title =        "Real number computation with committed choice logic
                 programming languages",
  journal =      j-J-LOGIC-ALG-PROG,
  volume =       "64",
  number =       "1",
  pages =        "61--84",
  month =        jul,
  year =         "2005",
  DOI =          "https://doi.org/10.1016/j.jlap.2004.07.005",
  ISSN =         "1567-8326 (print), 1873-5940 (electronic)",
  ISSN-L =       "1567-8326",
  bibdate =      "Thu Oct 17 10:09:18 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Logic and Algebraic Programming",
  journal-URL =  "http://www.sciencedirect.com/science/journal/15678326",
  remark =       "Special issue on Practical development of exact real
                 number computation.",
}

@InCollection{Turing:2005:PEC,
  author =       "Alan M. Turing",
  title =        "Proposed Electronic Calculator (1945)",
  crossref =     "Copeland:2005:ATA",
  pages =        "??--??",
  year =         "2005",
  DOI =          "https://doi.org/10.1093/acprof:oso/9780198565932.003.0021",
  bibdate =      "Mon Nov 01 18:47:26 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This chapter presents Alan M. Turing's report,
                 `Proposed Electronic Calculator'. The report was
                 submitted to the Executive Committee of the National
                 Physical Laboratory in February 1946, under the
                 description `Report by Dr. A. M. Turing on Proposals
                 for the Development of an Automatic Computing Engine
                 (ACE)'. The design set out in `Proposed Electronic
                 Calculator' was the basis for all the ACE computers.",
  acknowledgement = ack-nhfb,
  author-dates = "Alan Mathison Turing (23 June 1912--7 June 1954)",
}

@InProceedings{Usevitch:2005:JCL,
  author =       "B. Usevitch",
  booktitle =    "Proceedings. {DCC 2005} Data Compression Conference,
                 29--31 March 2005",
  title =        "{JPEG2000} Compliant Lossless Coding of Floating Point
                 Data",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "484--484",
  year =         "2005",
  bibdate =      "Wed Apr 27 18:18:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Verdonk:2005:BSI,
  author =       "B. Verdonk and J. Vervloet and A. Cuyt",
  title =        "Blending Set and Interval Arithmetic for Maximal
                 Reliability",
  journal =      j-COMPUTING,
  volume =       "74",
  number =       "1",
  pages =        "41--65",
  month =        feb,
  year =         "2005",
  CODEN =        "CMPTA2",
  DOI =          "https://doi.org/10.1007/s00607-004-0090-2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Jul 5 09:25:15 MDT 2005",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=74&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=74&issue=1&spage=41",
  abstract =     "In both [3] and [8], the authors review the
                 implementation of the basic operations in interval
                 arithmetic, and in particular discuss the different
                 approaches given in the literature for interval
                 division when the divisor interval contains zero. In
                 these papers, and in the references therein, the basic
                 operations are defined for real or extended real
                 interval operands.\par

                 Division by an interval containing zero is a special
                 case of an interval function for which the input
                 arguments contain points outside the domain of the
                 underlying point function. A number of approaches exist
                 in the literature, [7], [12], to remove restrictions on
                 the domain of interval functions and hence obtain a
                 closed, exception-free interval system.\par

                 In this paper, we present an alternative approach to
                 remove restrictions on the domain of interval functions
                 and to guarantee the inclusion property in all
                 situations, even when some input intervals contain
                 points that lie outside the domain of the underlying
                 point function. To achieve this, we allow for the
                 (efficient) set-based representation of non-real
                 results. The computed intervals are sharp, yet contain
                 more information and the resulting interval system is
                 closed and exception-free. We also show how the
                 presented ideas can be implemented in an interval
                 arithmetic library. The performance overhead is
                 negligible compared to the fact that the implementation
                 using the new approach offers 100\% reliability in
                 return.\par

                 The structure of the paper is as follows. We set off
                 with a motivating example in Sect. 1. In Sect. 2, we
                 review various approaches to interval division and then
                 introduce vset-division of real intervals, based on the
                 newly introduced concept of value set or vset. In Sect.
                 3, we give a formal definition of real vset-intervals
                 and arithmetic on these intervals. We prove a number of
                 essential properties and point out the likenesses and
                 differences with other approaches. Finally, in Sect. 4,
                 we discuss the implementation of vset-interval
                 arithmetic in a floating-point context.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "inclusion property; Interval arithmetic",
}

@InProceedings{Wahid:2005:EFC,
  author =       "Khan Wahid and Vassil Dimitrov and Graham Jullien",
  title =        "Error-Free Computation of $ 8 \times 8 $ {$2$-D} {DCT}
                 and {IDCT} using Two-Dimensional Algebraic Integer
                 Quantization",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-138.pdf",
  abstract =     "This paper presents a novel error-free
                 (infinite-precision) architecture for the fast
                 implementation of both $ 8 \times 8 $ $2$-D Discrete
                 Cosine Transform and Inverse DCT. The architecture uses
                 a new algebraic integer quantization of a $1$-D radix-8
                 DCT that allows the separable computation of a $2$-D $
                 8 \times 8 $ DCT without any intermediate number
                 representation conversions. This is a considerable
                 improvement on previously introduced algebraic integer
                 encoding techniques to compute both DCT and IDCT which
                 eliminates the requirements to approximate the
                 transformation matrix elements by obtaining their exact
                 representations and hence mapping the transcendental
                 functions without any errors. Using this encoding
                 scheme, an entire $ 8 \times 8 $ $1$-D DCT-SQ (scalar
                 quantization) algorithm can be implemented with only 24
                 adders. Apart from the multiplication-free nature, this
                 new mapping scheme fits to this algorithm, eliminating
                 any computational or quantization errors and resulting
                 short-word-length and high-speed-design.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17",
  pagecount =    "8",
}

@Article{Wait:2005:IPF,
  author =       "C. D. Wait",
  title =        "{IBM PowerPC 440 FPU} with complex-arithmetic
                 extensions",
  journal =      j-IBM-JRD,
  volume =       "49",
  number =       "2/3",
  pages =        "249--254",
  month =        "????",
  year =         "2005",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Wed Jun 1 08:14:41 MDT 2005",
  bibsource =    "http://www.research.ibm.com/journal/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.research.ibm.com/journal/rd/492/wait.pdf",
  abstract =     "The PowerPC 440 floating-point unit (FPU) with
                 complex-arithmetic extensions is an embedded
                 application-specific integrated circuit (ASIC) core
                 designed to be used with the IBM PowerPC 440 processor
                 core on the Blue Gene/L compute chip. The FPU core
                 implements the floating-point instruction set from the
                 PowerPC Architecture and the floating-point instruction
                 extensions created to aid in matrix and
                 complex-arithmetic operations. The FPU instruction
                 extensions de ne double-precision operations that are
                 primarily single-instruction multiple-data (SIMD) and
                 require two (primary and secondary) arithmetic
                 pipelines and floating-point register files. However,
                 to aid complex-arithmetic routines, some FPU extensions
                 actually perform different (yet closely related)
                 operations while executing in the arithmetic pipelines.
                 The FPU core implements an operand crossbar between the
                 primary and secondary arithmetic datapaths to enable
                 each pipeline operand access from the primary or
                 secondary register file. The PowerPC 440 processor core
                 provides 128-bit storage buses and simultaneous issue
                 of an arithmetic instruction with a storage
                 instruction, allowing the FPU core to fully utilize the
                 parallel arithmetic pipes.",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  ordernumber =  "G322-0240",
}

@InProceedings{Walter:2005:DDP,
  author =       "Colin Walter and David Samyde",
  title =        "Data Dependent Power Use in Multipliers",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-126.pdf",
  abstract =     "Recent research has demonstrated the vulnerability of
                 certain smart card architectures to power and
                 electromagnetic analysis when multiplier operations are
                 insufficiently shielded from external monitoring. Here
                 several standard multipliers are investigated in more
                 detail in order to provide the foundation for
                 understanding potential weaknesses and enabling the
                 subsequent successful repair of those systems. A model
                 is built which accurately predicts power use as a
                 function of the Hamming weights of inputs without the
                 combinatorial explosion of exhaustive simulation. This
                 confirms that power use is indeed data dependent at
                 least for those multipliers. Laboratory experiments
                 confirm that EMR also corresponds closely to these
                 power predictions over a wide range of frequencies.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17; Differential power analysis; DPA; EMA;
                 multiplication; multiplier; RSA cryptosystem.; smart
                 card",
  pagecount =    "9",
}

@InProceedings{Walters:2005:EFA,
  author =       "George Walters and Michael Schulte",
  title =        "Efficient Function Approximation Using Truncated
                 Multipliers and Squarers",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-190.pdf",
  abstract =     "This paper presents a technique for designing linear
                 and quadratic interpolators for function approximation
                 using truncated multipliers and squarers. Initial
                 coefficient values are found using a Chebyshev series
                 approximation, and then adjusted through exhaustive
                 simulation to minimize the maximum absolute error of
                 the interpolator output. This technique is suitable for
                 any function and any precision up to 24-bits (IEEE
                 single precision). Designs for linear and quadratic
                 interpolators that implement the reciprocal function, $
                 f(x) = 1 / x, $ are presented and analyzed as an
                 example. We show that a 24-bit truncated reciprocal
                 quadratic interpolator with a design specification of $
                 \pm 1 $ ulp error requires 24.1\% fewer partial
                 products to implement than a comparable standard
                 interpolator with the same error specification.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17",
  pagecount =    "8",
}

@InProceedings{Wang:2005:DFPa,
  author =       "L.-K. Wang and M. J. Schulte",
  title =        "Decimal Floating-Point Square Root Using
                 {Newton--Raphson} Iteration",
  crossref =     "Vassiliadis:2005:IIC",
  pages =        "309--315",
  year =         "2005",
  bibdate =      "Sun Mar 04 10:19:28 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_2005-05.pdf",
  abstract =     "With continued reductions in feature size, additional
                 functionality may be added to future microprocessors to
                 boost the performance of important application domains.
                 Due to growth in commercial, financial, and
                 Internet-based applications, decimal floating point
                 arithmetic is now attracting more attention and
                 hardware support for decimal operations is being
                 considered by various computer manufacturers. In order
                 to standardize decimal number formats and operations,
                 specifications for decimal floating-point arithmetic
                 have been added to the draft revision of the IEEE-754
                 Standard for Floating-Point Arithmetic (IEEE-754R).
                 This paper presents an efficient arithmetic algorithm
                 and hardware design for decimal floating-point square
                 root. This design uses an optimized piecewise linear
                 approximation, a modified Newton--Raphson iteration, a
                 specialized rounding technique, and a modified decimal
                 multiplier. Synthesis results show that a 64-bit
                 (16-digit) implementation of decimal square root, which
                 is compliant with IEEE-754R, has an estimated critical
                 path delay of 0.95 ns and a maximum latency of 210
                 clock cycles when implemented using a sequential
                 multiplier and LSI Logic's 0.11 micron Gflx-P standard
                 cell library.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@Article{Whidborne:2005:OCF,
  author =       "James F. Whidborne and Da-Wei Gu and Jun Wu and Sheng
                 Chen",
  title =        "Optimal controller and filter realizations using
                 finite-precision, floating-point arithmetic",
  journal =      j-INT-J-SYST-SCI,
  volume =       "36",
  number =       "7",
  pages =        "405--413",
  year =         "2005",
  CODEN =        "IJSYA9",
  ISSN =         "0020-7721 (print), 1464-5319 (electronic)",
  ISSN-L =       "0020-7721",
  MRclass =      "93B50 (93B40 93E11)",
  MRnumber =     "MR2152458",
  bibdate =      "Thu Nov 8 19:16:14 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Systems Science. Principles
                 and Applications of Systems and Integration",
  journal-URL =  "http://www.tandfonline.com/loi/tsys20",
}

@InCollection{Wilkinson:2005:PAN,
  author =       "James H. Wilkinson",
  title =        "The {Pilot ACE} at the {National Physical
                 Laboratory}",
  crossref =     "Copeland:2005:ATA",
  pages =        "93--105",
  year =         "2005",
  DOI =          "https://doi.org/10.1093/acprof:oso/9780198565932.003.0005",
  bibdate =      "Mon Nov 01 18:18:06 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ingentaconnect.com/content/oso/2353639/2005/00000001/00000001/art00006",
  abstract =     "This chapter discusses the pilot Automatic Computing
                 Engine (ACE) project at the National Physical
                 Laboratory. The Pilot ACE had been designed purely as
                 an experimental machine to demonstrate the competence
                 of the team as computer engineers. It was originally
                 intended that when it was successfully completed a
                 full-scale computer would be built. However, when it
                 was successful, it was the only electronic computer in
                 a government department and the engineers came under
                 very heavy pressure to use the Pilot ACE for serious
                 computing. They implemented a small set of
                 modifications which included the addition of an
                 automatic multiplier and improvements to the control
                 unit which made programming a little less arduous. The
                 computer was then put into general use and did yeoman
                 service for a number of years.",
  acknowledgement = ack-nhfb,
  remark =       "Reprint of article in {\em The Radio and Electronic
                 Engineer, Vol. 45, No. 7, pp. 336--340, July 1975}.
                 From the article:\par

                 ``A great deal of quite detailed coding was done by the
                 ACE team in the period from 1946--1948. It included
                 basic subroutines for such things as multi-length
                 arithmetic (including multiplication, division and
                 square roots), floating-point arithmetic (both
                 single-precision and double-precision) and interval
                 arithmetic. The subroutines for floating-point
                 arithmetic were particularly detailed; they were coded
                 by G. G. Alway and myself in 1947 and were for both
                 Version V and Version VII. They were almost certainly
                 the earliest floating-point subroutines and it is
                 interesting that those for the Version V were
                 essentially the same as the subroutines which were
                 subsequently used on the Pilot ACE itself. At a time
                 when the arithmetic provided on modern computers is
                 often so disappointing it is interesting to recall that
                 the subroutines included provision for accumulating
                 inner-products in double-precision floating-point
                 arithmetic and all rounding was
                 immaculate.''\par

                 ``Even double precision and triple precision
                 floating-point routines were reasonably fast and we
                 gained extensive experience with such computation long
                 before it was much used elsewhere. I think it is not
                 unreasonable to claim that the development of
                 floating-point error analysis at NPL, which was well in
                 advance of that elsewhere, was an indirect consequence
                 of our use of optimum coding.''",
}

@InProceedings{Wo:2005:SSC,
  author =       "Zhaojun Wo and Israel Koren",
  title =        "Synthesis of Saturating Counters Using Traditional and
                 Non-traditional Basic Counters",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-191.pdf",
  abstract =     "Saturating counters are a newly defined class of
                 generalized parallel counters that provide the exact
                 number of inputs which are equal to 1 only if this
                 number is below a given threshold. Such counters are
                 useful in, for example, self-test and repair units for
                 embedded memories. This paper defines saturating
                 counters for arbitrary threshold values and presents
                 several alternatives for their implementation. The
                 delay and area of the proposed design alternatives are
                 then estimated using a 0.25$ \mu $ m cell library.
                 Finally, we study the behavior of saturating counters
                 when the threshold approaches the number of input bits,
                 i.e., the special case of non-saturating parallel
                 counters.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17",
  pagecount =    "8",
}

@Article{Yang:2005:IMM,
  author =       "Jen-Ho Yang and Chin-Chen Chang and Chih-Hung Wang",
  title =        "An iterative modular multiplication algorithm in
                 {RNS}",
  journal =      j-APPL-MATH-COMP,
  volume =       "171",
  number =       "1",
  pages =        "637--645",
  day =          "1",
  month =        dec,
  year =         "2005",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Sat Jul 12 09:02:51 MDT 2008",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@InProceedings{Yatskiv:2005:MAB,
  author =       "V. Yatskiv and N. Yatskiv",
  booktitle =    "Proceedings of The Third Workshop 2005 {IEEE}
                 Intelligent Data Acquisition and Advanced Computing
                 Systems: Technology and Applications",
  title =        "Multiple Access on the Basis of Residue Number System
                 Transformation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "527--530",
  year =         "2005",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/IDAACS.2005.283039",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "In this paper research of efficiency channelizing
                 methods on the basis of residue number of classes of
                 transformation is conducted. Research is conducted on
                 the basis of calculation of delay mean time before
                 transmission. The results of \ldots{}",
}

@InProceedings{Zeydel:2005:EMA,
  author =       "Bart Zeydel and Theo Kluter and Vojin Oklobdzija",
  title =        "Efficient Mapping of Addition Recurrence Algorithms in
                 {CMOS}",
  crossref =     "Montuschi:2005:PIS",
  pages =        "??--??",
  year =         "2005",
  bibdate =      "Wed Jun 22 07:02:55 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arith17.polito.it/final/paper-181.pdf",
  abstract =     "Efficient adder design requires proper selection of a
                 recurrence algorithm and its realization. Each of the
                 algorithms: Weinberger's, Ling's and Doran's were
                 analyzed for its flexibility in representation and
                 suitability for realization in CMOS. We describe
                 general techniques for developing efficient
                 realizations based on CMOS technology constraints when
                 using Ling's algorithm. From these techniques we
                 propose two high-performance realizations that achieve
                 1 FO4 delay improvement at the same energy and 50\%
                 energy reduction at the same delay than existing Ling
                 and Weinberger designs.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17",
  pagecount =    "7",
}

@Article{Zhu:2005:NDA,
  author =       "Yong-Kang Zhu and Jun-Hai Yong and Guo-Qin Zheng",
  title =        "A New Distillation Algorithm for Floating-Point
                 Summation",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "26",
  number =       "6",
  pages =        "2066--2078",
  month =        nov,
  year =         "2005",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/030602009",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65G05, 65B10",
  MRnumber =     "MR2196589 (2006i:65078)",
  bibdate =      "Mon Nov 21 14:52:48 MST 2005",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/26/6;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/60200",
  abstract =     "The summation of $n$ floating-point numbers is
                 ubiquitous in numerical computations. We present a new
                 distillation algorithm for floating-point summation
                 which is stable, efficient, and accurate. The algorithm
                 iteratively ``distills'' the summands without
                 discarding any significant digit until the partial sums
                 cannot change the whole sum. It uses standard
                 floating-point arithmetic and does not rely on the
                 choice of radix or any other specific assumption.
                 Furthermore, the error bound of our algorithm is
                 independent of $n$ and less than 1 ulp.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  keywords =     "accurate floating-point summation; distillation;
                 rounding error",
}

@InProceedings{Zhuo:2005:DSF,
  author =       "Ling Zhuo and G. R. Morris and V. K. Prasanna",
  booktitle =    "Proceedings. 19th {IEEE} International Parallel and
                 Distributed Processing Symposium, 04--08 April 2005",
  title =        "Designing Scalable {FPGA}-Based Reduction Circuits
                 Using Pipelined Floating-Point Cores",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "147a-147a",
  year =         "2005",
  bibdate =      "Wed Apr 27 18:18:12 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The use of pipelined floating-point arithmetic cores
                 to create high-performance FPGA-based computational
                 kernels has introduced a new class of problems that do
                 not exist when using single-cycle arithmetic cores.
                 \ldots{}",
  acknowledgement = ack-nhfb,
}

@Misc{Zimmermann:2005:EBC,
  author =       "Paul Zimmermann and Richard Brent and Colin Percival",
  title =        "Error bounds on complex floating-point
                 multiplication",
  howpublished = "World-Wide Web slides",
  day =          "14",
  month =        dec,
  year =         "2005",
  bibdate =      "Wed Dec 14 09:56:25 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.loria.fr/~zimmerma/talks/cm.pdf",
  abstract =     "Providing that no overflow or underflow occur, no
                 denormal values are produced, arithmetic results are
                 correctly rounded to a nearest representable value, $
                 z_0 z_1 \neq 0 $, and $ \epsilon \leq 2^{-5} $, the
                 relative error $ |z_2 (z_0 z_1)^{-1} - 1 | $ is less
                 than $ \epsilon \sqrt {5} = (1 / 2) \beta^{1 - t} \sqrt
                 {5} $.",
  acknowledgement = ack-nhfb,
  keywords =     "complex floating-point arithmetic; correct rounding;
                 floating-point arithmetic",
  remark =       "Article submitted to Mathematics of Computation
                 (2005), 12 pages.",
}

@Misc{Zimmermann:2005:MPT,
  author =       "Paul Zimmermann and Nathalie Revol and Patrick
                 P{\'e}lissier",
  title =        "{{\tt mpcheck}}: a program to test the accuracy of
                 elementary functions",
  howpublished = "World-Wide Web software archive",
  year =         "2005",
  bibdate =      "Sat Nov 05 21:16:00 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.loria.fr/~zimmerma/free/mpcheck-1.1.0.tar.gz;
                 http://www.loria.fr/~zimmerma/mpcheck/",
  acknowledgement = ack-nhfb,
}

@TechReport{Zimmermann:2005:MVC,
  author =       "Paul Zimmermann",
  title =        "{MPFR}: vers un calcul flottant correct ? ({French})
                 [{MPFR}: Towards correct floating-point arithmetic?]",
  type =         "Online interactive report.",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  year =         "2005",
  bibdate =      "Sun Sep 10 07:38:21 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://interstices.info/display.jsp?id=c_9345",
  abstract =     "Obtenir un seul r{\'e}sultat pour un calcul donn{\'e}:
                 {\`a} premi{\`e}re vue, cela semble une {\'e}vidence;
                 c'est en fait un vaste sujet de recherche auquel les
                 chercheurs apportent petit {\`a} petit leurs
                 contributions. Une nouvelle {\'e}tape est franchie
                 aujourd'hui gr{\^a}ce {\`a} MPFR, une biblioth{\`e}que
                 de calcul multi-pr{\'e}cision sur les nombres
                 flottants. ({French}) [Getting a single result for a
                 given calculation seems obvious at first sight. In
                 fact, it is a vast area of research to which
                 researchers are adding their contributions little by
                 little. A new level is reached today thanks to MPFR, a
                 multiple-precision library for floating-point
                 arithmetic.]",
  acknowledgement = ack-nhfb,
  language =     "French",
}

@Misc{Zimmermann:2005:WTA,
  author =       "Paul Zimmermann",
  title =        "Why transcendentals and arbitrary precision?",
  howpublished = "World-Wide Web slides",
  day =          "15",
  month =        dec,
  year =         "2005",
  bibdate =      "Thu Dec 15 15:03:09 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.loria.fr/~zimmerma/talks/why.pdf",
  acknowledgement = ack-nhfb,
  summary =      "This talk surveys the state of the computation of
                 transcendental functions on current hardware platforms,
                 and discusses the cost of implementing
                 correctly-rounded results.",
}

@TechReport{Zimmermann:2005:XXX,
  author =       "Paul Zimmermann",
  title =        "5,341,321",
  type =         "Technical report",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  pages =        "2",
  day =          "8",
  month =        jun,
  year =         "2005",
  bibdate =      "Sun Sep 10 07:32:04 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.loria.fr/~zimmerma/papers/5341321.ps.gz",
  abstract =     "This short note shows the nasty effects of patents for
                 the development of free software, even for patents that
                 were not written with software applications in mind.",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point division; Karp--Markstein patent on
                 modified Newton--Raphson iteration",
  remark =       "The title is the number of the U.S. Patent on the
                 algorithm described in the article, which is a
                 completely trivial modification of Newton--Raphson
                 iteration, published in \cite{Karp:1997:HPD}. The
                 patent itself is \cite{Karp:1994:FPA}, and it expired
                 on 5 May 2013.",
}

@InProceedings{Anderson:2006:AMF,
  author =       "Cristina S. Anderson and Shane Story and Nikita
                 Astafiev",
  title =        "Accurate Math Functions on the {Intel IA-32}
                 Architecture: a Performance-Driven Design",
  crossref =     "Anonymous:2006:PCR",
  pages =        "??--??",
  year =         "2006",
  bibdate =      "Tue Jun 27 10:28:05 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "elementary functions",
}

@Article{Anguita:2006:FFS,
  author =       "D. Anguita and S. Pischiutta and S. Ridella and D.
                 Sterpi",
  title =        "Feed-Forward Support Vector Machine Without
                 Multipliers",
  journal =      j-IEEE-TRANS-NEURAL-NETW,
  volume =       "17",
  number =       "5",
  pages =        "1328--1331",
  year =         "2006",
  CODEN =        "ITNNEP",
  DOI =          "https://doi.org/10.1109/TNN.2006.877537",
  ISSN =         "1045-9227 (print), 1941-0093 (electronic)",
  ISSN-L =       "1045-9227",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Neural Networks",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=72",
  keywords =     "Algorithm design and analysis; Coordinate rotation
                 digital computer (CORDIC); Embedded computing; Embedded
                 system; embedded systems; Feedforward systems;
                 Fixed-point arithmetic; fixed-point arithmetic;
                 Hardware; Kernel; Machine learning algorithms; support
                 vector machine (SVM); Support vector machine
                 classification; Support vector machines",
}

@Misc{Anonymous:2006:IFPa,
  author =       "Anonymous",
  title =        "{Intel} and Floating Point: Updating One of the
                 Industry's Most Successful Standards",
  howpublished = "World-Wide Web document",
  day =          "20",
  month =        jul,
  year =         "2006",
  bibdate =      "Wed Nov 22 21:51:25 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.intel.com/standards/floatingpoint.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@Misc{Anonymous:2006:IFPb,
  author =       "Anonymous",
  title =        "{IBM}'s forthcoming {Power6} processor can count to
                 10",
  howpublished = "World-Wide Web document",
  month =        oct,
  year =         "2006",
  bibdate =      "Wed Oct 11 07:44:23 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://news.zdnet.com/2100-9584_22-6124451.html",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
  remark =       "Reports that the 5GHz Power6 is due in mid-2007, and
                 adds hardware support for decimal floating-point
                 arithmetic.",
}

@Misc{Anonymous:2006:RSI,
  author =       "Anonymous",
  title =        "Reference Software Implementation of the {IEEE 754R}
                 Decimal Floating-Point Arithmetic",
  howpublished = "World-Wide Web document",
  year =         "2006",
  bibdate =      "Wed Nov 22 21:40:41 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://cache-www.intel.com/cd/00/00/29/43/294339_294339.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "BID encoding; decimal floating-point arithmetic",
  remark =       "Describes new rounding algorithms that eliminate the
                 need to convert a binary integer decimal representation
                 to decimal, round, and convert back. The article claims
                 median speedups of 6 to 60 over the IBM densely packed
                 format used in the decNumber package. However, no
                 information is given about the availability of this
                 reference implementation. See also
                 \cite{Cornea:2006:SII}.",
}

@Article{Avanzi:2006:SMK,
  author =       "Roberto M. Avanzi and Clemens Heuberger and Helmut
                 Prodinger",
  title =        "Scalar Multiplication on {Koblitz} Curves Using the
                 {Frobenius} Endomorphism and Its Combination with Point
                 Halving: Extensions and Mathematical Analysis",
  journal =      j-ALGORITHMICA,
  volume =       "46",
  number =       "3--4",
  pages =        "249--270",
  month =        nov,
  year =         "2006",
  CODEN =        "ALGOEJ",
  DOI =          "https://doi.org/10.1007/s00453-006-0105-9",
  ISSN =         "0178-4617 (print), 1432-0541 (electronic)",
  ISSN-L =       "0178-4617",
  bibdate =      "Wed Jul 9 22:25:03 MDT 2008",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0178-4617&volume=46&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0178-4617&volume=46&issue=3&spage=249",
  acknowledgement = ack-nhfb,
  fjournal =     "Algorithmica",
  journal-URL =  "http://link.springer.com/journal/453",
}

@Article{Bajard:2006:AOF,
  author =       "J.-C. Bajard and L. Imbert and C. Negre",
  title =        "Arithmetic Operations in Finite Fields of Medium Prime
                 Characteristic Using the {Lagrange} Representation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "55",
  number =       "9",
  pages =        "1167--1177",
  month =        sep,
  year =         "2006",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2006.136",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 15:35:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1668044",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Bartzis:2006:EBB,
  author =       "Constantinos Bartzis and Tevfik Bultan",
  title =        "Efficient {BDDs} for bounded arithmetic constraints",
  journal =      j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER,
  volume =       "8",
  number =       "1",
  pages =        "26--36",
  month =        feb,
  year =         "2006",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s10009-004-0171-8",
  ISSN =         "1433-2779 (print), 1433-2787 (electronic)",
  ISSN-L =       "1433-2779",
  bibdate =      "Wed Jul 9 18:12:21 MDT 2008",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1433-2779&volume=8&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=1433-2779&volume=8&issue=1&spage=26",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal on Software Tools for Technology
                 Transfer: STTT",
  journal-URL =  "http://link.springer.com/journal/10009",
  keywords =     "BDD; Integer arithmetic; Model checking; SMV",
}

@Article{Bernal:2006:IRD,
  author =       "Javier Bernal and Christoph J. Witzgall",
  title =        "Integer Representation of Decimal Numbers for Exact
                 Computations",
  journal =      j-J-RES-NATL-BUR-STAND,
  volume =       "111",
  number =       "2",
  pages =        "79--88",
  month =        mar # "\slash " # apr,
  year =         "2006",
  DOI =          "https://doi.org/10.6028/jres.111.006",
  bibdate =      "Tue Nov 05 15:32:18 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://nvlpubs.nist.gov/nistpubs/jres/111/2/V111.N02.A02.pdf",
  abstract =     "A scheme is presented and software is documented for
                 representing as integers input decimal numbers that
                 have been stored in a computer as double precision
                 floating point numbers and for carrying out
                 multiplications, additions and subtractions based on
                 these numbers in an exact manner. The input decimal
                 numbers must not have more than nine digits to the left
                 of the decimal point. The decimal fractions of their
                 floating point representations are all first rounded
                 off at a prespecified location, a location no more than
                 nine digits away from the decimal point. The number of
                 digits to the left of the decimal point for each input
                 number besides not being allowed to exceed nine must
                 then be such that the total number of digits from the
                 leftmost digit of the number to the location where
                 round-off is to occur does not exceed fourteen.",
  acknowledgement = ack-nhfb,
  keywords =     "computational geometry; Delaunay triangulation; exact
                 integer arithmetic; power diagram; regular
                 triangulation; robustness; Voronoi diagram",
}

@TechReport{Bertot:2006:PGS,
  author =       "Yves Bertot and Nicolas Magaud and Paul Zimmermann",
  title =        "A proof of {GMP} square root using the {Coq}
                 assistant",
  type =         "Research Report",
  number =       "RR-4475",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  pages =        "28",
  year =         "2006",
  bibdate =      "Sun Sep 10 08:34:35 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4475.pdf;
                 ftp://ftp.inria.fr/INRIA/publication/publi-ps-gz/RR/RR-4475.ps.gz;
                 http://www.inria.fr/rrrt/rr-4475.html",
  abstract =     "We present a formal proof (at the implementation
                 level) of an efficient algorithm proposed in to compute
                 square roots of arbitrarily large integers. This
                 program, which is part of the GNU Multiple Precision
                 Arithmetic Library (GMP), is completely proven within
                 the system. Proofs are developed using the Correctness
                 tool to deal with imperative features of the program.
                 The formalization is rather large (more than 13000
                 lines) and requires some advanced techniques for proof
                 management and reuse.",
  acknowledgement = ack-nhfb,
}

@Article{Bik:2006:MVF,
  author =       "Aart J. C. Bik and Xinmin Tian and Milind B. Girkar",
  title =        "Multimedia vectorization of floating-point {MIN\slash
                 MAX} reductions",
  journal =      j-CCPE,
  volume =       "18",
  number =       "9",
  pages =        "997--1007",
  day =          "10",
  month =        aug,
  year =         "2006",
  CODEN =        "CCPEBO",
  DOI =          "https://doi.org/10.1002/cpe.1009",
  ISSN =         "1532-0626 (print), 1532-0634 (electronic)",
  ISSN-L =       "1532-0626",
  bibdate =      "Mon Dec 5 10:08:04 MST 2011",
  bibsource =    "http://www.interscience.wiley.com/jpages/1532-0626;
                 https://www.math.utah.edu/pub/tex/bib/ccpe.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Concurrency and Computation: Prac\-tice and
                 Experience",
  journal-URL =  "http://www.interscience.wiley.com/jpages/1532-0626",
  onlinedate =   "12 Jan 2006",
}

@Article{Boldo:2006:PFF,
  author =       "S. Boldo",
  title =        "Pitfalls of a full floating-point proof: example on
                 the formal proof of the {Veltkamp\slash Dekker}
                 algorithms",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "4130",
  pages =        "52--66",
  year =         "2006",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/11814771_6",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  MRnumber =     "MR2354672",
  bibdate =      "Sun Feb 19 07:32:26 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Misc{Bonten:2006:ACF,
  author =       "J. H. M. Bonten",
  title =        "Arithmetic Computer Formats",
  howpublished = "Web document",
  day =          "5",
  month =        oct,
  year =         "2006",
  bibdate =      "Tue Oct 30 11:08:12 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://home.hetnet.nl/mr_1/81/jhm.bonten/computers/bitsandbytes/wordsizes/",
  abstract =     "This map contains a set of descriptions of the
                 memory-word formats for the floating point numbers used
                 in some extinct, old and modern species of the
                 computer-fauna. Also it contains some theory about the
                 storage of these numbers. And it gives some proposals
                 to improve the use of decimal numbers, both in Cobol
                 and in Fortran/C/C++.",
  acknowledgement = ack-nhfb,
  keywords =     "Burroughs 6700; Burroughs 7700; Burroughs 7900; Cray
                 1; DEC Alpha; DEC PDP-10; DEC PDP-11; DEC VAX; IBM
                 7094; IEEE-754; Unisys-A; Univac 1100; Univac 418",
}

@Article{Briggs:2006:IER,
  author =       "Keith Briggs",
  title =        "Implementing exact real arithmetic in {\tt python},
                 {C++} and {C}",
  journal =      j-THEOR-COMP-SCI,
  volume =       "351",
  number =       "1",
  pages =        "74--81",
  day =          "14",
  month =        feb,
  year =         "2006",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Tue Mar 29 06:48:55 MDT 2011",
  bibsource =    "http://www.sciencedirect.com/science/journal/03043975;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "I discuss the design and performance issues arising in
                 the efficient implementation of the scaled-integer
                 exact real arithmetic model introduced by Boehm and
                 others. This system represents a real number with a
                 automatically controlled level of precision by a
                 rational with implicit denominator. I describe three
                 practical codes, in python, C++ and C. These allow the
                 convenient use of this computational paradigm in
                 commonly used imperative languages.",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}

@InProceedings{Castellanos:2006:BDF,
  author =       "I. D. Castellanos and J. E. Stine",
  title =        "A 64-bit Decimal Floating-Point Comparator",
  crossref =     "Dimopoulos:2006:IIC",
  pages =        "138--144",
  year =         "2006",
  DOI =          "https://doi.org/10.1109/ASAP.2006.2",
  bibdate =      "Mon Mar 19 10:17:28 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Decimal arithmetic is growing in importance as
                 scientific studies reveal that current financial and
                 commercial applications spend a high percentage
                 overhead in this type of calculations. Typically,
                 software is utilized to emulate decimal floating point
                 arithmetic in these applications. On the other hand,
                 functional units that employ decimal floating point
                 hardware can improve performance by two or three orders
                 of magnitude. This paper presents the design and
                 implementation of a novel decimal floating-point
                 comparator compliant with the current draft revision of
                 the IEEE-754 Standard for floating-point arithmetic. It
                 utilizes a novel BCD magnitude comparator with
                 logarithmic delay and it supports 64-bit decimal
                 floating-point numbers. Area and delay results are
                 examined for an implementation in TSMC SCN6M SCMOS
                 technology.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@Article{Chang:2006:DAR,
  author =       "Chin-Chen Chang and Yeu-Pong Lai",
  title =        "A division algorithm for residue numbers",
  journal =      j-APPL-MATH-COMP,
  volume =       "172",
  number =       "1",
  pages =        "368--378",
  day =          "1",
  month =        jan,
  year =         "2006",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2005.02.008",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Sat Jul 12 09:02:52 MDT 2008",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In the residue number system, modular multiplication,
                 modular addition, and modular subtraction are closure
                 operations. However, modular division is also important
                 for applying the residue number system. Inspired by
                 Gamberger's work, we create a division operation to be
                 used in residue number system. In Gamberger's scheme,
                 the transformation from residues to a binary integer is
                 required for keeping the remainder. To eliminate the
                 overhead in transformation, our scheme uses only the
                 residues so that the computing efficiency can be
                 improved. Besides, we also provide an efficient way to
                 find a multiplicative inverse.",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@InProceedings{Choi:2006:DCB,
  author =       "Sung Woo Choi and Sung-il Pae and Hyungju Park and
                 Chee Yap",
  title =        "Decidability of Collision between a Helical Motion and
                 an Algebraic Motion",
  crossref =     "Anonymous:2006:PCR",
  pages =        "??--??",
  year =         "2006",
  bibdate =      "Tue Jun 27 10:28:05 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Misc{Cornea:2006:SII,
  author =       "Marius Cornea and Cristina Anderson",
  title =        "Software Implementation of the {IEEE 754R} Decimal
                 Floating-Point Architecture",
  howpublished = "World-Wide Web slides",
  day =          "10--12",
  month =        jul,
  year =         "2006",
  bibdate =      "Wed Nov 22 21:47:16 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also \cite{Anonymous:2006:RSI}.",
  URL =          "http://rnc7.loria.fr/cornea_poster.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "BID encoding; decimal floating-point arithmetic",
}

@Manual{Cowlishaw:2006:DCL,
  author =       "Mike Cowlishaw",
  title =        "The {decNumber C} library",
  organization = pub-IBM,
  address =      pub-IBM:adr,
  day =          "22",
  month =        nov,
  year =         "2006",
  bibdate =      "Fri Apr 20 08:02:33 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Version 3.37",
  URL =          "http://download.icu-project.org/ex/files/decNumber/decNumber-icu-337.zip",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic; DPD encoding",
}

@Article{Dahab:2006:SMU,
  author =       "R. Dahab and D. Hankerson and F. Hu and M. Long and J.
                 Lopez and A. Menezes",
  title =        "Software multiplication using {Gaussian} normal
                 bases",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "55",
  number =       "8",
  pages =        "974--984",
  month =        aug,
  year =         "2006",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2006.132",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 15:35:55 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1650195",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{deDinechin:2006:STP,
  author =       "Florent de Dinechin and Sergey Maidanov",
  title =        "Software techniques for perfect elementary functions
                 in floating-point interval arithmetic",
  crossref =     "Anonymous:2006:PCR",
  pages =        "??--??",
  year =         "2006",
  bibdate =      "Tue Jun 27 10:28:05 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "elementary functions",
}

@Article{Demmel:2006:EBE,
  author =       "James Demmel and Yozo Hida and William Kahan and
                 Xiaoye S. Li and Sonil Mukherjee and E. Jason Riedy",
  title =        "Error bounds from extra-precise iterative refinement",
  journal =      j-TOMS,
  volume =       "32",
  number =       "2",
  pages =        "325--351",
  month =        jun,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1141885.1141894",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Aug 23 10:29:48 MDT 2006",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present the design and testing of an algorithm for
                 iterative refinement of the solution of linear
                 equations where the residual is computed with extra
                 precision. This algorithm was originally proposed in
                 1948 and analyzed in the 1960s as a means to compute
                 very accurate solutions to all but the most
                 ill-conditioned linear systems. However, two obstacles
                 have until now prevented its adoption in standard
                 subroutine libraries like LAPACK: (1) There was no
                 standard way to access the higher precision arithmetic
                 needed to compute residuals, and (2) it was unclear how
                 to compute a reliable error bound for the computed
                 solution. The completion of the new BLAS Technical
                 Forum Standard has essentially removed the first
                 obstacle. To overcome the second obstacle, we show how
                 the application of iterative refinement can be used to
                 compute an error bound in any norm at small cost and
                 use this to compute both an error bound in the usual
                 infinity norm, and a componentwise relative error
                 bound. We report extensive test results on over $ 6.2 $
                 million matrices of dimensions $5$, $ 10$, $ 100$, and
                 $ 1000$. As long as a normwise (componentwise)
                 condition number computed by the algorithm is less than
                 $ 1 / m a x \{ 10, \sqrt {n} \} \varepsilon_w$, the
                 computed normwise (componentwise) error bound is at
                 most $ 2 m a x \{ 10, \sqrt {n} \} \cdot
                 \varepsilon_w$, and indeed bounds the true error. Here,
                 $n$ is the matrix dimension and $ \varepsilon_w =
                 2^{-24}$ is the working precision. Residuals were
                 computed in double precision (53 bits of precision). In
                 other words, the algorithm always computed a tiny error
                 at negligible extra cost for most linear systems. For
                 worse conditioned problems (which we can detect using
                 condition estimation), we obtained small correct error
                 bounds in over 90\% of cases.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Deng:2006:IMM,
  author =       "Rui Deng and Yujie Zhou",
  title =        "Improvement to {Montgomery} Modular Inverse
                 Algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "55",
  number =       "9",
  pages =        "1207--1210",
  month =        sep,
  year =         "2006",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2006.150",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 15:35:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1668048",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Book{Deschamps:2006:SAC,
  author =       "Jean-Pierre Deschamps and G{\'e}ry Jean Antoine Bioul
                 and Gustavo D. Sutter",
  title =        "Synthesis of arithmetic circuits: {FPGA}, {ASIC}, and
                 embedded systems",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xix + 556",
  year =         "2006",
  ISBN =         "0-471-68783-9 (hardcover)",
  ISBN-13 =      "978-0-471-68783-2 (hardcover)",
  LCCN =         "TK7895.A65 D47 2006",
  bibdate =      "Wed Oct 1 10:16:56 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0621/2005003237-b.html;
                 http://www.loc.gov/catdir/enhancements/fy0621/2005003237-d.html;
                 http://www.loc.gov/catdir/toc/ecip057/2005003237.html",
  acknowledgement = ack-nhfb,
  author-dates = "1945--",
  subject =      "Computer arithmetic and logic units; Digital
                 electronics; Embedded computer systems",
  tableofcontents = "Mathematical background \\
                 Number representation \\
                 Arithmetic operations: addition and subtraction \\
                 Arithmetic operations: multiplication \\
                 Arithmetic operations: division \\
                 Other arithmetic operations \\
                 Finite field operations \\
                 Hardware platforms \\
                 Circuit synthesis: general principles \\
                 Adders and subtractors \\
                 Multipliers \\
                 Dividers \\
                 Other arithmetic operators \\
                 Circuits for finite field operations \\
                 Floating-point unit",
}

@Misc{Detrey:2006:FVL,
  author =       "J{\'e}r{\'e}mie Detrey and Florent de Dinechin",
  title =        "{FPLibrary}. {A} {VHDL} library of parametrisable
                 floating-point and {LNS} operators for {FPGA}",
  howpublished = "Web site and source code.",
  year =         "2006",
  bibdate =      "Sat Oct 9 12:42:00 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "The FPLibrary has been superceded by the FloPoCo
                 project \cite{deDinechin:2010:FGA}.",
  URL =          "http://www.ens-lyon.fr/LIP/Arenaire/Ware/FPLibrary/",
  acknowledgement = ack-nhfb,
}

@Article{Dietz:2006:FPC,
  author =       "Hank Dietz and Bill Dieter and Randy Fisher and
                 Kungyen Chang",
  title =        "Floating-Point Computation with Just Enough Accuracy",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "3991",
  pages =        "226--233",
  year =         "2006",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Wed Jan 06 09:42:37 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "ICCS 2006, Part I, conference proceedings.",
  URL =          "http://aggregate.org/NPAR/iccs2006.pdf",
  abstract =     "Most mathematical formulae are defined in terms of
                 operations on real numbers, but computers can only
                 operate on numeric values with finite precision and
                 range. Using floating-point values as real numbers does
                 not clearly identify the precision with which each
                 value must be represented. Too little precision yields
                 inaccurate results; too much wastes computational
                 resources.\par

                 The popularity of multimedia applications has made fast
                 hardware support for low-precision floating-point
                 arithmetic common in Digital Signal Processors (DSPs),
                 SIMD Within A Register (SWAR) instruction set
                 extensions for general purpose processors, and in
                 Graphics Processing Units (GPUs). In this paper, we
                 describe a simple approach by which the speed of these
                 low-precision operations can be speculatively employed
                 to meet user-specified accuracy constraints. Where the
                 native precision(s) yield insufficient accuracy, a
                 simple technique is used to efficiently synthesize
                 enhanced precision using pairs of native values.",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
  keywords =     "Digital Signal Processors (DSPs); double-double
                 arithmetic; native pair; pair-precision arithmetic;
                 SIMD Within A Register (SWAR)",
}

@InProceedings{Diniz:2006:DFP,
  author =       "P. C. Diniz and G. Govindu",
  title =        "Design of field-programmable dual-precision
                 floating-point arithmetic units",
  crossref =     "Bertels:2006:FPI",
  pages =        "1--4",
  year =         "2006",
  DOI =          "https://doi.org/10.1109/FPL.2006.311302",
  bibdate =      "Sat Oct 9 12:37:10 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The growth in FPGA capacity and the inclusion of
                 embedded arithmetic cores has enabled the use of these
                 devices for general purpose floating-point computing.
                 Despite their clock rate handicap with respect to
                 contemporary general-purpose processors, these devices
                 can be field-programmable to meet the precision
                 requirements and operator-level parallelism of a
                 specific computation. In this paper we describe and
                 evaluate the performance of dual-precision, pipelined,
                 floating-point arithmetic cores for addition,
                 multiplication and division. Each of these arithmetic
                 cores can be switched at run-time to perform either one
                 double-precision operation, or with the same hardware
                 resources, perform two single-precision operations. We
                 also implemented quad-precision cores which can be
                 switched to perform either one quad-precision operation
                 or two double-precision operations. As an application
                 of these cores, we describe and evaluate the
                 performance potential of a custom, but flexible, vector
                 processing units as part of a system-level architecture
                 targeting a Xilinx Virtex-II Prom 100 FPGA device
                 connected to multiple SRAM banks.",
  acknowledgement = ack-nhfb,
  xxpages =      "733--736",
}

@Article{Enge:2006:CCP,
  author =       "Andreas Enge",
  title =        "The complexity of class polynomial computation via
                 floating point approximations",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "24",
  month =        jan,
  year =         "2006",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Published in Mathematics of Computation 78, {\bf 266}
                 (2009) 1089--1107.",
  URL =          "http://arxiv.org/abs/cs/0601104",
  abstract =     "We analyse the complexity of computing class
                 polynomials, that are an important ingredient for CM
                 constructions of elliptic curves, via complex floating
                 point approximations of their roots. The heart of the
                 algorithm is the evaluation of modular functions in
                 several arguments. The fastest one of the presented
                 approaches uses a technique devised by Dupont to
                 evaluate modular functions by Newton iterations on an
                 expression involving the arithmetic-geometric mean. It
                 runs in time $ O (|D| \log^5 |D| \log \log |D|) = O
                 (|D|^{1 + \epsilon }) = O (h^{2 + \epsilon }) $ for any
                 $ \epsilon > 0 $, where $D$ is the CM discriminant and
                 $h$ is the degree of the class polynomial. Another fast
                 algorithm uses multipoint evaluation techniques known
                 from symbolic computation; its asymptotic complexity is
                 worse by a factor of $ \log |D|$. Up to logarithmic
                 factors, this running time matches the size of the
                 constructed polynomials. The estimate also relies on a
                 new result concerning the complexity of enumerating the
                 class group of an imaginary-quadratic order and on a
                 rigorously proven upper bound for the height of class
                 polynomials.",
  acknowledgement = ack-nhfb,
  subject =      "Numerical Analysis (cs.NA); Symbolic Computation
                 (cs.SC); Number Theory (math.NT)",
}

@Article{Fan:2006:RBM,
  author =       "H. Fan and M. A. Hasan",
  title =        "Relationship between {$ \mathrm {GF}(2^m) $}
                 {Montgomery} and Shifted Polynomial Basis
                 Multiplication Algorithms",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "55",
  number =       "9",
  pages =        "1202--1206",
  month =        sep,
  year =         "2006",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2006.152",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 15:35:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1668047",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Feldstein:2006:GTO,
  author =       "Alan Feldstein and Peter R. Turner",
  title =        "Gradual and tapered overflow and underflow: a
                 functional differential equation and its
                 approximation",
  journal =      j-APPL-NUM-MATH,
  volume =       "56",
  number =       "3--4",
  pages =        "517--532",
  month =        mar # "\slash " # apr,
  year =         "2006",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Tue Aug 24 11:17:20 MDT 2010",
  bibsource =    "http://www.sciencedirect.com/science/journal/01689274;
                 https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274",
}

@Article{Gandhi:2006:DRA,
  author =       "Rajiv Gandhi and Samir Khuller and Srinivasan
                 Parthasarathy and Aravind Srinivasan",
  title =        "Dependent rounding and its applications to
                 approximation algorithms",
  journal =      j-J-ACM,
  volume =       "53",
  number =       "3",
  pages =        "324--360",
  month =        may,
  year =         "2006",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/1147954.1147956",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Wed Aug 23 06:38:20 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}

@Article{Gochman:2006:IIC,
  author =       "Simcha Gochman and Avi Mendelson and Alon Naveh and
                 Efraim Rotem",
  title =        "Introduction to {Intel Core Duo} Processor
                 Architecture",
  journal =      j-INTEL-TECH-J,
  volume =       "10",
  number =       "2",
  pages =        "89--97",
  day =          "15",
  month =        may,
  year =         "2006",
  DOI =          "https://doi.org/10.1535/itj.1002",
  ISSN =         "1535-766X",
  bibdate =      "Tue Jun 20 07:47:25 2006",
  bibsource =    "ftp://download.intel.com/technology/itj/2006/volume10issue02/vol10_iss02.pdf;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://developer.intel.com/technology/itj/2006/volume10issue02/art01_Intro_to_Core_Duo/p01_abstract.htm",
  acknowledgement = ack-nhfb,
  remark =       "From p. 91: ``Another bottleneck that was discovered
                 was the handling of the floating point (FP) Control
                 Word (CW). The FP CW is part of the x87 state and was
                 usually viewed as `constant'; namely it is loaded once
                 at the beginning and stays constant throughout the
                 program. This is indeed the way the FP CW is used by
                 most of the programs. However there are some FP
                 applications that manipulate the `rounding control'
                 which is located in this register: the default rounding
                 mode is `rounding to nearest even' but before
                 converting results to fixed point, some applications
                 change the round control to `chop' (this is the rule
                 with C programs for example). Such behavior was treated
                 rather inefficiently by the Pentium M core: each
                 manipulation of the FP CW was effectively stalling the
                 pipeline until its completion. The Intel Core Duo core
                 introduced a new renaming mechanism for the FP CW so
                 that four different versions of this register can
                 coexist on the fly without stalling the machine.''",
}

@Article{Gok:2006:IMO,
  author =       "M. Gok and M. J. Schulte and M. G. Arnold",
  title =        "Integer multipliers with overflow detection",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "55",
  number =       "8",
  pages =        "1062--1066",
  month =        aug,
  year =         "2006",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2006.126",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 15:35:55 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1650203",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Goubault:2006:SAN,
  author =       "Eric Goubault and Sylvie Putot",
  title =        "Static analysis of numerical algorithms",
  crossref =     "Yi:2006:SAI",
  pages =        "18--34",
  year =         "2006",
  DOI =          "https://doi.org/10.1007/11823230_3",
  bibdate =      "Sat Apr 01 08:03:10 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer.com/chapter/10.1007/11823230_3",
  acknowledgement = ack-nhfb,
}

@InProceedings{Graa:2006:IFF,
  author =       "Guillaume Da Gra{\c{c}}a and David Defour",
  title =        "Implementation of float-float operators on graphics
                 hardware",
  crossref =     "Anonymous:2006:PCR",
  pages =        "??--??",
  year =         "2006",
  bibdate =      "Tue Jun 27 10:28:05 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Graca:2006:ODE,
  author =       "Daniel S. Gra{\c{c}}a and Ning Zhong and Jorge
                 Buescu",
  title =        "The ordinary differential equation defined by a
                 computable function whose maximal interval of existence
                 is non-computable",
  crossref =     "Anonymous:2006:PCR",
  pages =        "??--??",
  year =         "2006",
  bibdate =      "Tue Jun 27 10:28:05 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Graillat:2006:ICH,
  author =       "Stef Graillat and Philippe Langlois and Nicolas
                 Louvet",
  title =        "Improving the Compensated {Horner} Scheme with a Fused
                 Multiply and Add",
  crossref =     "Haddad:2006:ACP",
  pages =        "1323--1327",
  year =         "2006",
  DOI =          "https://doi.org/10.1145/1141277.1141585",
  bibdate =      "Sat Feb 26 18:19:47 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Several different techniques and softwares intend to
                 improve the accuracy of results computed in a fixed
                 finite precision. Here we focus on a method to improve
                 the accuracy of the polynomial evaluation. It is well
                 known that the use of the Fused Multiply and Add
                 operation available on some microprocessors like Intel
                 Itanium improves slightly the accuracy of the Horner
                 scheme. In this paper, we propose an accurate
                 compensated Horner scheme specially designed to take
                 advantage of the Fused Multiply and Add. We prove that
                 the computed result is as accurate as if computed in
                 twice the working precision. The algorithm we present
                 is fast since it only requires well optimizable
                 floating point operations, performed in the same
                 working precision as the given data.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Harrison:2006:FPV,
  author =       "John Harrison",
  title =        "Floating-point verification using theorem proving",
  crossref =     "Cimatti:2006:FMH",
  pages =        "211--242",
  year =         "2006",
  DOI =          "https://doi.org/10.1007/11757283_8",
  bibdate =      "Wed Nov 26 22:40:10 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Hars:2006:MIA,
  author =       "Laszlo Hars",
  title =        "Modular Inverse Algorithms Without Multiplications for
                 Cryptographic Applications",
  journal =      j-EURASIP-J-EMBED-SYS,
  volume =       "2006",
  pages =        "1--13",
  year =         "2006",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1155/ES/2006/32192",
  ISSN =         "1687-3955 (print), 1687-3963 (electronic)",
  ISSN-L =       "1687-3955",
  bibdate =      "Wed Dec 28 09:54:06 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  note =         "Article ID 32192.",
  URL =          "http://downloads.hindawi.com/journals/es/2006/032192.pdf",
  abstract =     "Hardware and algorithmic optimization techniques are
                 presented to the left-shift, right-shift, and the
                 traditional Euclidean-modular inverse algorithms.
                 Theoretical arguments and extensive simulations
                 determined the resulting expected running time. On many
                 computational platforms these turn out to be the
                 fastest known algorithms for moderate operand lengths.
                 They are based on variants of Euclidean-type extended
                 GCD algorithms. On the considered computational
                 platforms for operand lengths used in cryptography, the
                 fastest presented modular inverse algorithms need about
                 twice the time of modular multiplications, or even
                 less. Consequently, in elliptic curve cryptography
                 delaying modular divisions is slower (affine
                 coordinates are the best) and the RSA and ElGamal
                 cryptosystems can be accelerated.",
  acknowledgement = ack-nhfb,
  fjournal =     "EURASIP Journal on Embedded Systems",
}

@Article{Hill:2006:QUB,
  author =       "M. Hill and I. Robinson",
  title =        "Quadrature using 64-bit {IEEE} arithmetic for
                 integrands over $ [0, 1] $ with a singularity at $1$",
  journal =      j-THEOR-COMP-SCI,
  volume =       "351",
  number =       "1",
  pages =        "82--100",
  day =          "14",
  month =        feb,
  year =         "2006",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Tue Mar 29 06:48:55 MDT 2011",
  bibsource =    "http://www.sciencedirect.com/science/journal/03043975;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present a detailed study of some problems
                 encountered when quadrature over $ [0, 1] $ is
                 attempted with integrands that have a singularity at
                 $1$. Methods designed to increase the accuracy of such
                 quadratures, for example, the application of
                 periodising transformations, are examined in the
                 context of the representational limitations of 64-bit
                 IEEE arithmetic near $1$ in $ [0, 1] $. A heuristic is
                 proposed for the forecasting of a lower bound on the
                 irremovable error due to these limitations. We conclude
                 by affirming the commonly accepted procedure that where
                 possible, integrals should be symbolically transformed
                 so that any remaining singularity occurs at $0$.",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}

@Article{How:2006:RRN,
  author =       "H. T. How and T. H. Liew and Ee-Lin Kuan and Lie-Liang
                 Yang and L. Hanzo",
  title =        "A redundant residue number system coded burst-by-burst
                 adaptive joint-detection based {CDMA} speech
                 transceiver",
  journal =      j-IEEE-TRANS-VEH-TECHNOL,
  volume =       "55",
  number =       "1",
  pages =        "387--396",
  month =        jan,
  year =         "2006",
  CODEN =        "ITUTAB",
  DOI =          "https://doi.org/10.1109/TVT.2005.861175",
  ISSN =         "0018-9545 (print), 1939-9359 (electronic)",
  ISSN-L =       "0018-9545",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=33430",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Vehicular Technology",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=25",
  keywords =     "residue arithmetic; residue number system",
  summary =      "A burst-by-burst (BbB) adaptive speech transceiver is
                 proposed, which can drop its source coding rate and
                 speech quality under transceiver control in order to
                 invoke a more error resilient modem mode among less
                 favorable channel conditions. The \ldots{}",
}

@TechReport{Hurlimann:2006:BLB,
  author =       "Werner H{\"u}rlimann",
  title =        "{Benford's Law} from 1881 to 2006: a bibliography",
  type =         "Report",
  address =      "Feldstrasse 145, CH-8004 Z{\"u}rich, Switzerland",
  pages =        "15",
  day =          "5",
  month =        jul,
  year =         "2006",
  bibdate =      "Fri Mar 30 11:32:30 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/pdf/math.ST/0607168",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  remark =       "This bibliography lists 325 references on the title
                 subject, with these (years) and counts: (1881) 1,
                 (1912) 1, (1916) 1, (1917) 1, (1936) 1, (1938) 1,
                 (1944) 1, (1945) 1, (1948) 2, (1950) 1, (1952) 1,
                 (1953) 1, (1954) 1, (1957) 3, (1960) 1, (1961) 2,
                 (1963) 1, (1964) 2, (1965) 2, (1966) 1, (1967) 1,
                 (1968) 2, (1969) 5, (1970) 1, (1971) 4, (1972) 2,
                 (1973) 7, (1974) 2, (1975) 1, (1976) 5, (1977) 3,
                 (1978) 3, (1979) 2, (1981) 6, (1982) 3, (1983) 4,
                 (1984) 7, (1985) 2, (1986) 7, (1987) 5, (1988) 1,
                 (1988) 5, (1989) 2, (1990) 1, (1991) 4, (1992) 6,
                 (1993) 5, (1994) 5, (1995) 1, (1995) 2, (1996) 4,
                 (1997) 1, (1997) 9, (1998) 1, (1998) 6, (1999) 12,
                 (2000) 10, (2001) 19, (2002) 30, (2003) 22, (2004) 29,
                 (2005) 34, (2006) 18.",
}

@Manual{IBM:2006:PDF,
  author =       "{IBM Corporation}",
  title =        "Preliminary Decimal-Floating-Point Architecture",
  publisher =    pub-IBM,
  address =      pub-IBM:adr,
  pages =        "viii + 52",
  month =        nov,
  year =         "2006",
  bibdate =      "Sat Apr 07 12:13:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Form number SA23-2232-00.",
  URL =          "http://publibz.boulder.ibm.com/epubs/pdf/a2322320.pdf;
                 http://www-03.ibm.com/servers/eserver/zseries/zos/bkserv/r3pdf/zarchpops.html",
  abstract =     "This is a preliminary description of the
                 decimal-floating-point (DFP) facility and the
                 floating-point support-enhancement facility. It will be
                 superseded by the next published version of the {\em
                 IBM z/Architecture Principles of Operation\/}
                 (SA22-7832).",
  acknowledgement = ack-nhfb,
}

@Article{Imana:2006:BPF,
  author =       "J. L. Imana and J. M. Sanchez and F. Tirado",
  title =        "Bit-parallel finite field multipliers for irreducible
                 trinomials",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "55",
  number =       "5",
  pages =        "520--533",
  month =        may,
  year =         "2006",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2006.69",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 15:35:54 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1613833",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@TechReport{Intel:2006:IFP,
  author =       "{Intel}",
  title =        "{Intel} and Floating Point: Updating One of the
                 Industry's Most Successful Standards",
  type =         "{Web} report",
  institution =  "Intel Corporation",
  address =      "San Jose, CA, USA",
  pages =        "11",
  day =          "17",
  month =        jul,
  year =         "2006",
  bibdate =      "Thu Oct 14 14:43:38 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.intel.com/standards/floatingpoint.pdf",
  acknowledgement = ack-nhfb,
  remark =       "Includes mention of some major historical systems
                 failures due to faulty handling of floating-point
                 arithmetic, and discusses future directions for decimal
                 arithmetic.",
}

@Book{ISO:2006:IIIa,
  author =       "{ISO}",
  title =        "{ISO\slash IEC 10967-3}: {Information} technology ---
                 {Language} independent arithmetic --- {Part} 3:
                 {Complex} integer and floating point arithmetic and
                 complex elementary numerical functions",
  publisher =    pub-ISO,
  address =      pub-ISO:adr,
  pages =        "viii + 149",
  day =          "15",
  month =        aug,
  year =         "2006",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sun Mar 15 11:09:44 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://standards.iso.org/ittf/PubliclyAvailableStandards/c037994_ISO_IEC_10967-3_2006(E).zip;
                 http://www.iso.ch/cate/d24427.html",
  acknowledgement = ack-nhfb,
}

@Misc{ISO:2006:IIJa,
  author =       "{ISO}",
  title =        "{ISO\slash IEC JTC1 SC22 WG14 N1154}: Extension for
                 the programming language {C} to support decimal
                 floating-point arithmetic",
  howpublished = "World-Wide Web document",
  day =          "27",
  month =        feb,
  year =         "2006",
  bibdate =      "Tue Mar 07 18:23:45 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1154.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@Misc{ISO:2006:IIJb,
  author =       "{ISO}",
  title =        "{ISO\slash IEC JTC1 SC22 WG14 N1161}: Rationale for
                 {TR 24732}: Extension to the programming language {C}:
                 Decimal Floating-Point Arithmetic",
  howpublished = "World-Wide Web document",
  day =          "27",
  month =        feb,
  year =         "2006",
  bibdate =      "Tue Mar 07 18:23:45 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1161.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@Misc{ISO:2006:IIJc,
  author =       "{ISO}",
  title =        "{ISO\slash IEC JTC1 SC22 WG14 N1176}: Extension for
                 the programming language {C} to support decimal
                 floating-point arithmetic",
  howpublished = "World-Wide Web document",
  pages =        "iii + 33",
  day =          "24",
  month =        may,
  year =         "2006",
  bibdate =      "Sat Feb 24 20:00:36 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://open-std.org/jtc1/sc22/wg14/www/docs/n1176.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@Misc{Kahan:2006:AIR,
  author =       "William Kahan",
  title =        "Applications of {IEEE 754r}'s Rounding Modes",
  howpublished = "World-Wide Web document.",
  day =          "16",
  month =        feb,
  year =         "2006",
  bibdate =      "Fri Feb 17 17:54:50 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://nonabelian.com/754/RNDGMODE.TXT",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kaivani:2006:RID,
  author =       "A. Kaivani and A. Zaker Alhosseini and S. Gorgin and
                 M. Fazlali",
  title =        "Reversible Implementation of Densely-Packed-Decimal
                 Converter to and from Binary-Coded-Decimal Format Using
                 in {IEEE-754R}",
  crossref =     "Mohanty:2006:IIC",
  pages =        "273--276",
  year =         "2006",
  bibdate =      "Thu Aug 07 18:12:35 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Binary Coded Decimal (BCD) encoding has always
                 dominated the decimal arithmetic algorithms and their
                 hardware implementation. Due to importance of decimal
                 arithmetic, the decimal format defined in lEEE 754
                 floating point standard has been revisited. It uses
                 Densely Packed Decimal (DPD) encoding to store
                 significand part of a decimal floating point number.
                 Furthermore in recent years reversible logic has
                 attracted the attention of engineers for designing low
                 power CMOS circuits, as it is not possible to realize
                 quantum computing without reversible logic
                 implementation. This paper derives the reversible
                 implementation of DPD converter to and from
                 conventional BCD format using in IEEE 754R.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@Article{Kang:2006:SHS,
  author =       "J.-Y. Kang and J.-L. Gaudiot",
  title =        "A Simple High-Speed Multiplier Design",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "55",
  number =       "10",
  pages =        "1253--1258",
  month =        oct,
  year =         "2006",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2006.156",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 15:35:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1683756",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Kettani:2006:CBN,
  author =       "Houssain Kettani",
  title =        "On the Conversion Between Number Systems",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-2,
  volume =       "53",
  number =       "11",
  pages =        "1255--1258",
  month =        nov,
  year =         "2006",
  CODEN =        "ICSPE5",
  DOI =          "https://doi.org/10.1109/TCSII.2006.882856",
  ISSN =         "1057-7130 (print), 1558-125X (electronic)",
  ISSN-L =       "1057-7130",
  bibdate =      "Mon Mar 19 10:05:23 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This brief revisits the problem of conversion between
                 number systems and asks the following question: given a
                 nonnegative decimal number, what is the value of the
                 digit at position in the corresponding base number?
                 Thus, we do not require the knowledge of other digits
                 except the one we are interested in. Accordingly, we
                 present a conversion function that relates each digit
                 in a base system to the decimal value that is equal to
                 the base number in question. We also show some
                 applications of this new algorithm in the areas of
                 parallel computing and cryptography.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems. 2, Analog
                 and Digital Signal Processing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=82",
  keywords =     "Algorithm's efficiency; base numbers; conversion",
}

@Article{Kong:2006:IGA,
  author =       "Fanyu Kong and Zhun Cai and Jia Yu and Daxing Li",
  title =        "Improved generalized {Atkin} algorithm for computing
                 square roots in finite fields",
  journal =      j-INFO-PROC-LETT,
  volume =       "98",
  number =       "1",
  pages =        "1--5",
  day =          "15",
  month =        apr,
  year =         "2006",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Thu Mar 31 18:41:08 MDT 2011",
  bibsource =    "http://www.sciencedirect.com/science/journal/00200190;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}

@Article{Kornerup:2006:CSV,
  author =       "Peter Kornerup and Jean-Michel Muller",
  title =        "Choosing starting values for certain {Newton--Raphson}
                 iterations",
  journal =      j-THEOR-COMP-SCI,
  volume =       "351",
  number =       "1",
  pages =        "101--110",
  day =          "14",
  month =        feb,
  year =         "2006",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Tue Mar 29 06:48:55 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tcs2005.bib",
  abstract =     "We aim at finding the best possible seed values when
                 computing $ a^{1 / p} $ using the Newton--Raphson
                 iteration in a given interval. A natural choice of the
                 seed value would be the one that best approximates the
                 expected result. It turns out that in most cases, the
                 best seed value can be quite far from this natural
                 choice. When we evaluate a monotone function $ f(a) $
                 in the interval $ [a_\mathrm {min}, a_\mathrm {max}] $,
                 by building the sequence $ x_n $ defined by the
                 Newton--Raphson iteration, the natural choice consists
                 in choosing $ x_0 $ equal to the arithmetic mean of the
                 endpoint values. This minimizes the maximum possible
                 distance between $ x_0 $ and $ f(a) $. And yet, if we
                 perform $n$ iterations, what matters is to minimize the
                 maximum possible distance between $ x_n $ and $ f(a) $.
                 In several examples, the value of the best starting
                 point varies rather significantly with the number of
                 iterations.",
  acknowledgement = ack-nhfb,
  ajournal =     "Theor. Comput. Sci.",
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975/",
}

@InProceedings{Kornerup:2006:RCN,
  author =       "Peter Kornerup and Jean-Michel Muller",
  title =        "{RN}-Codings: New Insights and Some Applications",
  crossref =     "Anonymous:2006:PCR",
  pages =        "??--??",
  year =         "2006",
  bibdate =      "Tue Jun 27 10:28:05 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Kulikova:2006:HFD,
  author =       "A. A. Kulikova and Yu. V. Prokhorov and V. I.
                 Khokhlov",
  title =        "{H.F.D.} ({$H$}-function Distribution) and {Benford's
                 Law}. {I}",
  journal =      j-THEORY-PROBAB-APPL,
  volume =       "50",
  number =       "2",
  pages =        "311--315",
  month =        jan,
  year =         "2006",
  CODEN =        "TPRBAU",
  DOI =          "https://doi.org/10.1137/S0040585X97981706",
  ISSN =         "0040-585X (print), 1095-7219 (electronic)",
  ISSN-L =       "0040-585X",
  bibdate =      "Wed May 19 18:14:51 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/TVP/50/2;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Theory of Probability and its Applications",
  journal-URL =  "http://epubs.siam.org/tvp",
}

@Article{Kumar:2006:ODS,
  author =       "Sandeep Kumar and T. Wollinger and C. Paar",
  title =        "Optimum Digit Serial {$ \mathrm {GF}(2^m) $}
                 Multipliers for Curve-Based Cryptography",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "55",
  number =       "10",
  pages =        "1306--1311",
  month =        oct,
  year =         "2006",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2006.165",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 15:35:57 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1683761",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Kushner:2006:I,
  author =       "David Kushner",
  title =        "The Insomniacs",
  journal =      j-IEEE-SPECTRUM,
  volume =       "43",
  number =       "12",
  pages =        "24--29",
  month =        dec,
  year =         "2006",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.2006.253405",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Thu Sep 01 16:23:03 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "floating-point arithmetic; IBM Cell processor; Sony
                 Playstation 3",
}

@InProceedings{Lang:2006:SRI,
  author =       "Tomas Lang and Javier D. Bruguera",
  title =        "The sunity representation to improve the accuracy of
                 some computations",
  crossref =     "Anonymous:2006:PCR",
  pages =        "??--??",
  year =         "2006",
  bibdate =      "Tue Jun 27 10:28:05 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Langou:2006:EPBa,
  author =       "Julie Langou and Julien Langou and Piotr Luszczek and
                 Jakub Kurzak and Alfredo Buttari and Jack Dongarra",
  title =        "Exploiting the Performance of 32 bit Floating Point
                 Arithmetic in Obtaining 64 bit Accuracy (Revisiting
                 Iterative Refinement for Linear Systems)",
  type =         "LAPACK Working Note",
  number =       "175",
  institution =  inst-UT-CS,
  address =      inst-UT-CS:adr,
  pages =        "17",
  month =        jun,
  year =         "2006",
  bibdate =      "Mon Oct 09 12:05:43 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.netlib.org/lapack/lawnspdf/lawn175.pdf;
                 http://www.netlib.org/lapack/lawnspdf/lawn175.ps",
  abstract =     "Recent versions of microprocessors exhibit performance
                 characteristics for 32 bit floating point arithmetic
                 (single precision) that is substantially higher than 64
                 bit floating point arithmetic (double precision).
                 Examples include the Intel's Pentium IV and M
                 processors, AMD's Opteron architectures and the IBM's
                 Cell Broad Engine processor. When working in single
                 precision, floating point operations can be performed
                 up to two times faster on the Pentium and up to ten
                 times faster on the Cell over double precision. The
                 performance enhancements in these architectures are
                 derived by accessing extensions to the basic
                 architecture, such as SSE2 in the case of the Pentium
                 and the vector functions on the IBM Cell. The
                 motivation for this paper is to exploit single
                 precision operations whenever possible and resort to
                 double precision at critical stages while attempting to
                 provide the full double precision results. The results
                 described here are fairly general and can be applied to
                 various problems in linear algebra such as solving
                 large sparse systems, using direct or iterative methods
                 and some eigenvalue problems. There are limitations to
                 the success of this process, such as when the
                 conditioning of the problem exceeds the reciprocal of
                 the accuracy of the single precision computations. In
                 that case the double precision algorithm should be
                 used.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Langou:2006:EPBb,
  author =       "Julie Langou and Julien Langou and Piotr Luszczek and
                 Jakub Kurzak and Alfredo Buttari and Jack Dongarra",
  title =        "Exploiting the performance of 32 bit floating point
                 arithmetic in obtaining 64 bit accuracy (revisiting
                 iterative refinement for linear systems)",
  crossref =     "ACM:2006:SCH",
  pages =        "??--??",
  year =         "2006",
  DOI =          "https://doi.org/10.1145/1188455.1188573",
  bibdate =      "Thu Nov 08 20:00:17 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Recent versions of microprocessors exhibit performance
                 characteristics for 32 bit floating point arithmetic
                 (single precision) that is substantially higher than 64
                 bit floating point arithmetic (double precision).
                 Examples include the Intel's Pentium IV and M
                 processors, AMD's Opteron architectures and the IBM's
                 Cell Broad Engine processor. When working in single
                 precision, floating point operations can be performed
                 up to two times faster on the Pentium and up to ten
                 times faster on the Cell over double precision. The
                 performance enhancements in these architectures are
                 derived by accessing extensions to the basic
                 architecture, such as SSE2 in the case of the Pentium
                 and the vector functions on the IBM Cell. The
                 motivation for this paper is to exploit single
                 precision operations whenever possible and resort to
                 double precision at critical stages while attempting to
                 provide the full double precision results. The results
                 described here are fairly general and can be applied to
                 various problems in linear algebra such as solving
                 large sparse systems, using direct or iterative methods
                 and some eigenvalue problems. There are limitations to
                 the success of this process, such as when the
                 conditioning of the problem exceeds the reciprocal of
                 the accuracy of the single precision computations. In
                 that case the double precision algorithm should be
                 used.",
  acknowledgement = ack-nhfb,
  articleno =    "113",
}

@TechReport{Lefevre:2006:WCE,
  author =       "Vincent Lef{\`e}vre and Damien Stehl{\'e} and Paul
                 Zimmermann",
  title =        "Worst Cases for the Exponential Function in the {IEEE
                 754r} {{\tt decimal64}} Format",
  type =         "Technical report",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  pages =        "14",
  month =        sep,
  year =         "2006",
  bibdate =      "Wed Sep 06 07:31:38 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "To appear in a special LNCS issue following the
                 Dagstuhl seminar 06021: Reliable Implementation of Real
                 Number Algorithms: Theory and Practice.",
  URL =          "http://www.loria.fr/~zimmerma/papers/decimalexp-lncs-final.pdf;
                 http://www.loria.fr/~zimmerma/wc/decimal32.html;
                 http://www.loria.fr/~zimmerma/wc/decimal64.html",
  abstract =     "We searched for the worst cases for correct rounding
                 of the exponential function in the IEEE 754r decimal64
                 format, and computed all the bad cases whose distance
                 from a breakpoint (for all rounding modes) is less than
                 $ 10^{-15} $ ulp, and we give the worst ones. In
                 particular, the worst case for $ |x| \geq 3 \times
                 10^{-11} $ is $ \exp (9.407822313572878 \times 10^{-2})
                 = 1.098645682066338 \, 50000000000000000 \, 278 \ldots
                 {} $. This work can be extended to other elementary
                 functions in the decimal64 format and allows the design
                 of reasonably fast routines that will evaluate these
                 functions with correct rounding, at least in some
                 domains.",
  acknowledgement = ack-nhfb,
  keywords =     "correct rounding; decimal floating-point arithmetic",
}

@Article{Liew:2006:SRR,
  author =       "T. H. Liew and Lie-Liang Yang and L. Hanzo",
  title =        "Systematic redundant residue number system codes:
                 analytical upper bound and iterative decoding
                 performance over {AWGN} and {Rayleigh} channels",
  journal =      j-IEEE-TRANS-COMM,
  volume =       "54",
  number =       "6",
  pages =        "1006--1016",
  month =        jun,
  year =         "2006",
  CODEN =        "IECMBT",
  DOI =          "https://doi.org/10.1109/TCOMM.2006.876843",
  ISSN =         "0090-6778 (print), 1558-0857 (electronic)",
  ISSN-L =       "0090-6778",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=34443",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Communications",
  keywords =     "residue arithmetic; residue number system",
  summary =      "The novel family of redundant residue number system
                 (RRNS) codes is studied. RRNS codes constitute
                 maximum-minimum distance block codes, exhibiting
                 identical distance properties to Reed--Solomon codes.
                 Binary to RRNS symbol-mapping methods are \ldots{}",
}

@Article{Lindstrom:2006:FEC,
  author =       "Peter Lindstrom and Martin Isenburg",
  title =        "Fast and Efficient Compression of Floating-Point
                 Data",
  journal =      j-IEEE-TRANS-VIS-COMPUT-GRAPH,
  volume =       "12",
  number =       "5",
  pages =        "1245--1250",
  month =        sep # "\slash " # oct,
  year =         "2006",
  CODEN =        "ITVGEA",
  DOI =          "https://doi.org/10.1109/TVCG.2006.143",
  ISSN =         "1077-2626 (print), 1941-0506 (electronic), 2160-9306",
  ISSN-L =       "1077-2626",
  bibdate =      "Thu Jul 3 15:20:21 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Visualization and Computer
                 Graphics",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2945",
}

@Article{Mahalingam:2006:IAM,
  author =       "Venkatraman Mahalingam and Nagarajan Ranganathan",
  title =        "Improving Accuracy in {Mitchell}'s Logarithmic
                 Multiplication Using Operand Decomposition",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "55",
  number =       "12",
  pages =        "1523--1535",
  month =        dec,
  year =         "2006",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2006.198",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 15:35:57 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1717385",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  remark =       "See \cite{Mitchell:1962:CMD}.",
}

@Article{Marques:2006:BIF,
  author =       "Osni A. Marques and E. Jason Riedy and Christof
                 V{\"o}mel",
  title =        "Benefits of {IEEE-754} Features in Modern Symmetric
                 Tridiagonal Eigensolvers",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "28",
  number =       "5",
  pages =        "1613--1633",
  month =        jan,
  year =         "2006",
  CODEN =        "SJOCE3",
  DOI =          "",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Wed May 19 10:43:43 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/28/5;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}

@InProceedings{Maslennikowa:2006:DFB,
  author =       "N. Maslennikowa and O. Maslennikow and R. Berezowski
                 and J.-P. Lienou",
  booktitle =    "{MIXDES 2006}, Proceedings of the International
                 Conference Mixed Design of Integrated Circuits and
                 System, 22--24 June 2006",
  title =        "Design of {FPGA}-based Multi-operand Modular Adders
                 for Residue Number System Converters",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "264--268",
  year =         "2006",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.2006.1693181",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
}

@PhdThesis{Melquiond:2006:AIC,
  author =       "Guillaume Melquiond",
  title =        "De l'arithm{\'e}tique d'intervalles {\`a} la
                 certification de programmes. ({French}) [{From}
                 interval arithmetic to program certification]",
  type =         "Ph.D. dissertation",
  school =       "{\'E}cole normale sup{\'e}rieure de Lyon",
  address =      "Lyon, France",
  pages =        "vi + 126",
  day =          "21",
  month =        nov,
  year =         "2006",
  bibdate =      "Fri Sep 22 16:41:05 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://theses.hal.science/tel-01094485/file/06-these.pdf",
  abstract =     "Computer numbers are usually limited, both in range
                 and in precision. As a consequence, a careful
                 certification has to be performed for applications that
                 compute with these sets of numbers. Unfortunately,
                 performing such a certification by hand is error-prone.
                 Formal methods can ensure that the certification is
                 correct, but making use of them is usually long and
                 tedious, even for experts. This thesis aims at
                 improving the availability of these methods to
                 developers by automatizing their implementation. The
                 key concepts are the use of interval arithmetic, a
                 database of theorems on computer arithmetics, and a
                 system for rewriting expressions in order to compute
                 tight bounds on rounding errors.\par

                 This approach has led to the development of the Gappa
                 tool. It is designed to verify the numeric properties
                 of programs relying on floating-point or fixed-point
                 arithmetic. When verifying these properties, the tool
                 also generates formal proofs of their correctness.
                 These proofs can later be mechanically checked by the
                 Coq proof assistant. Gappa has been successfully used
                 for certifying some functions of the CRlibm, CGAL, and
                 FLIP libraries, among others",
  acknowledgement = ack-nhfb,
  keywords =     "Coq proof assistant; correct rounding; fixed-point
                 arithmetic; floating-point arithmetic; formal methods;
                 interval arithmetic; program certification",
}

@Article{Meurant:2006:LCG,
  author =       "G{\'e}rard Meurant and Zden{\v{e}}k Strako{\v{s}}",
  title =        "The {Lanczos} and conjugate gradient algorithms in
                 finite precision arithmetic",
  journal =      j-ACTA-NUMERICA,
  volume =       "15",
  pages =        "471--542",
  year =         "2006",
  CODEN =        "ANUMFU",
  DOI =          "https://doi.org/10.1017/S096249290626001X",
  ISBN =         "0-521-86815-7",
  ISBN-13 =      "978-0-521-86815-0",
  ISSN =         "0962-4929 (print), 1474-0508 (electronic)",
  ISSN-L =       "0962-4929",
  MRclass =      "65F15 (65F10 65G50)",
  MRnumber =     "2269746 (2007m:65031)",
  MRreviewer =   "A. Bultheel",
  bibdate =      "Sat Sep 24 10:35:17 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 https://www.math.utah.edu/pub/tex/bib/actanumerica.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Lanczos and conjugate gradient algorithms were
                 introduced more than five decades ago as tools for
                 numerical computation of dominant eigenvalues of
                 symmetric matrices and for solving linear algebraic
                 systems with symmetric positive definite matrices,
                 respectively. Because of their fundamental relationship
                 with the theory of orthogonal polynomials and Gauss
                 quadrature of the Riemann--Stieltjes integral, the
                 Lanczos and conjugate gradient algorithms represent
                 very interesting general mathematical objects, with
                 highly nonlinear properties which can be conveniently
                 translated from algebraic language into the language of
                 mathematical analysis, and vice versa. The algorithms
                 are also very interesting numerically, since their
                 numerical behaviour can be explained by an elegant
                 mathematical theory, and the interplay between analysis
                 and algebra is useful there too.\par

                 Motivated by this view, the present contribution wishes
                 to pay a tribute to those who have made an
                 understanding of the Lanczos and conjugate gradient
                 algorithms possible through their pioneering work, and
                 to review recent solutions of several open problems
                 that have also contributed to knowledge of the
                 subject.",
  acknowledgement = ack-nhfb,
  ajournal =     "Acta Numer.",
  fjournal =     "Acta Numerica",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=ANU",
  onlinedate =   "16 May 2006",
}

@Misc{Muller:2006:CLA,
  author =       "Jean-Michel Muller",
  title =        "{CR-LIBM}, and {Arenaire}'s results on function
                 implementation",
  howpublished = "World-Wide Web slides.",
  pages =        "92",
  month =        nov,
  year =         "2006",
  bibdate =      "Wed Nov 15 07:54:31 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://grouper.ieee.org/groups/754/email/pdfNTnWzhjsBA.pdf",
  acknowledgement = ack-nhfb,
}

@Book{Muller:2006:EFA,
  author =       "Jean-Michel Muller",
  booktitle =    "Elementary Functions: Algorithms and Implementation",
  title =        "Elementary Functions: Algorithms and Implementation",
  publisher =    pub-BIRKHAUSER,
  address =      pub-BIRKHAUSER:adr,
  edition =      "Second",
  pages =        "xxii + 266",
  year =         "2006",
  ISBN =         "0-8176-4372-9",
  ISBN-13 =      "978-0-8176-4372-0",
  LCCN =         "QA331 .M866 2006",
  bibdate =      "Fri Jul 25 12:00:55 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "US\$59.95",
  URL =          "http://perso.ens-lyon.fr/jean-michel.muller/SecondEdition.html;
                 http://www.springer.com/sgw/cda/frontpage/0,,4-40109-22-72377986-0,00.html",
  acknowledgement = ack-nhfb,
  subject =      "Functions; Data processing; Algorithms",
  tableofcontents = "Preface to the second edition \\
                 Preface to the first edition \\
                 Introduction / 1--7 \\
                 Some basic things about computer arithmetic / 9--24 \\
                 Part I. Algorithms based on polynomial approximation
                 and/or table lookup, multiple-precision evaluation of
                 functions / 25--25 \\
                 Polynomial or rational approximations / 27--66 \\
                 Table-based methods / 67--87 \\
                 Multiple-precision evaluation of functions / 89--100
                 \\
                 Part II. Shift-and-add algorithms / 101--101 \\
                 Introduction to shift-and-add algorithms / 103--131 \\
                 The CORDIC algorithm / 133--156 \\
                 Some other shift-and-add algorithms / 157--169 \\
                 Part III. Range reduction, final rounding and
                 exceptions / 171--171 \\
                 Range reduction / 173--191 \\
                 Final rounding / 193--216 \\
                 Miscellaneous / 217--223 \\
                 Examples of implementation / 225--232 \\
                 Bibliography / 233--259 \\
                 Index / 261--265",
}

@Article{Nievergelt:2006:EPD,
  author =       "Yves Nievergelt",
  title =        "Extensions of {Priest}'s Double-Precision Summation",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "28",
  number =       "5",
  pages =        "1837--1850",
  month =        jan,
  year =         "2006",
  CODEN =        "SJOCE3",
  DOI =          "",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Wed May 19 10:43:43 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/28/5;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  keywords =     "accurate floating-point summation",
}

@Article{Nikmehr:2006:FDF,
  author =       "H. Nikmehr and B. Phillips and C.-C. Lim",
  title =        "Fast Decimal Floating-Point Division",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "14",
  number =       "9",
  pages =        "951--961",
  month =        sep,
  year =         "2006",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/TVLSI.2006.884047",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Mon Mar 19 10:15:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A new implementation for decimal floating-point (DFP)
                 division is introduced. The algorithm is based on
                 high-radix SRT division The SRT division algorithm is
                 named after D. Sweeney, J. E. Robertson, and T. D.
                 Tocher. with the recurrence in a new decimal
                 signed-digit format. Quotient digits are selected using
                 comparison multiples, where the magnitude of the
                 quotient digit is calculated by comparing the truncated
                 partial remainder with limited precision multiples of
                 the divisor. The sign is determined concurrently by
                 investigating the polarity of the truncated partial
                 remainder. A timing evaluation using a logic synthesis
                 shows a significant decrease in the division execution
                 time in contrast with one of the fastest DFP dividers
                 reported in the open literature",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
  keywords =     "decimal floating-point arithmetic",
}

@Article{OLeary:2006:CMA,
  author =       "Dianne P. O'Leary",
  title =        "Computer Memory and Arithmetic: a Look under the
                 Hood",
  journal =      j-COMPUT-SCI-ENG,
  volume =       "8",
  number =       "3",
  pages =        "54--59",
  month =        may # "\slash " # jun,
  year =         "2006",
  CODEN =        "CSENFA",
  DOI =          "https://doi.org/10.1109/MCSE.2006.39",
  ISSN =         "1521-9615 (print), 1558-366X (electronic)",
  ISSN-L =       "1521-9615",
  bibdate =      "Thu Jul 3 11:16:38 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Computers have a hierarchy of storage units. Memory
                 management systems try to store information that you
                 will soon need in a unit that gives fast access. This
                 means that large vectors and arrays are broken up and
                 moved piece by piece as needed. You can write a correct
                 computer program without ever knowing about memory
                 management, but attention to memory management allows
                 you to consistently write programs that don't have
                 excessive memory delays. In this paper, we consider a
                 model of computer memory organization. We hide some
                 detail but give enough information to let us make
                 decisions about how to organize our computations for
                 efficiency. We use mathematical modeling to estimate a
                 typical computer's memory parameters, and then we see
                 how important these parameters are relative to the
                 speed of floating-point arithmetic.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing in Science and Engineering",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
}

@Article{Ou:2006:DSE,
  author =       "Jingzhao Ou and Viktor K. Prasanna",
  title =        "Design space exploration using arithmetic-level
                 hardware--software cosimulation for configurable
                 multiprocessor platforms",
  journal =      j-TECS,
  volume =       "5",
  number =       "2",
  pages =        "355--382",
  month =        may,
  year =         "2006",
  CODEN =        "????",
  ISSN =         "1539-9087 (print), 1558-3465 (electronic)",
  ISSN-L =       "1539-9087",
  bibdate =      "Wed Aug 23 05:26:43 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Embedded Computing Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?&idx=J840",
}

@Article{Ozban:2006:NMA,
  author =       "Ahmet Ya{\c{s}}ar {\"O}zban",
  title =        "New methods for approximating square roots",
  journal =      j-APPL-MATH-COMP,
  volume =       "175",
  number =       "1",
  pages =        "532--540",
  day =          "1",
  month =        apr,
  year =         "2006",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Sat Jul 12 09:02:54 MDT 2008",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Park:2006:EBP,
  author =       "Sun-Mi Park and Ku-Young Chang and Dowon Hong",
  title =        "Efficient Bit-Parallel Multiplier for Irreducible
                 Pentanomials Using a Shifted Polynomial Basis",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "55",
  number =       "9",
  pages =        "1211--1215",
  month =        sep,
  year =         "2006",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2006.146",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 15:35:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1668049",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Parks:2006:UTS,
  author =       "Michael Parks",
  title =        "Unifying Tests for Square Root",
  crossref =     "Anonymous:2006:PCR",
  pages =        "??--??",
  year =         "2006",
  bibdate =      "Tue Jun 27 10:28:05 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "elementary functions; floating-point testing",
}

@Article{Perry:2006:BSF,
  author =       "Tekla S. Perry",
  title =        "Building a supercomputer in a flash",
  journal =      j-IEEE-SPECTRUM,
  volume =       "41",
  number =       "6",
  pages =        "24--25",
  month =        jun,
  year =         "2006",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.2004.1303368",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Thu Sep 01 16:21:26 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "floating-point arithmetic",
  remark =       "Flash mob linked 669 PCs at UCSF in six hours to
                 produce a LINPACK speed of 180 Gflops (below the 500
                 Gflops goal).",
}

@InProceedings{Persson:2006:RCA,
  author =       "A. Persson and L. Bengtsson",
  booktitle =    "{ISCAS 2006}, Proceedings, 2006 {IEEE} International
                 Symposium on Circuits and Systems, 21--24 May 2006",
  title =        "Reverse conversion architectures for signed-digit
                 residue number systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "4",
  year =         "2006",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ISCAS.2006.1693181",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "This paper presents circuits for conversion from
                 radix-2 signed-digit residue numbers to binary form.
                 Four reverse converters for combined RNS/SD number
                 systems based on different moduli sets are presented.
                 Implementations are compared with respect \ldots{}",
}

@InProceedings{Piso:2006:OMD,
  author =       "D. Piso and J. D. Bruguera",
  editor =       "????",
  booktitle =    "Proceedings of the {XXI} Conference on Design of
                 Circuits and Integrated Systems ({DSIS2006, Barcelona,
                 2006})",
  title =        "Optimizing the Multiplier Design for {Goldschmidt}'s
                 Division and Reciprocal Units",
  publisher =    "????",
  address =      "????",
  pages =        "1C.3--??",
  year =         "2006",
  bibdate =      "Sun Dec 10 14:00:32 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "TO DO: [11-Dec-2023] I cannot yet locate this
                 article.",
}

@Article{Pryce:2006:IAC,
  author =       "J. D. Pryce and G. F. Corliss",
  title =        "Interval Arithmetic with Containment Sets",
  journal =      j-COMPUTING,
  volume =       "78",
  number =       "3",
  pages =        "251--276",
  month =        nov,
  year =         "2006",
  CODEN =        "CMPTA2",
  DOI =          "https://doi.org/10.1007/s00607-006-0180-4",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "54D35; 65-02; 65G30; 65G40",
  bibdate =      "Tue Jul 8 22:32:47 MDT 2008",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=78&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=78&issue=3&spage=251",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "containment set; cset; division by zero; infinity;
                 interval arithmetic; validated computation",
}

@Article{Qian:2006:HMP,
  author =       "Jianbo Qian and Cao An Wang",
  title =        "How much precision is needed to compare two sums of
                 square roots of integers?",
  journal =      j-INFO-PROC-LETT,
  volume =       "100",
  number =       "5",
  pages =        "194--198",
  day =          "16",
  month =        dec,
  year =         "2006",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Thu Mar 31 15:52:31 MDT 2011",
  bibsource =    "http://www.sciencedirect.com/science/journal/00200190;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}

@Article{Rajagopal:2006:TOA,
  author =       "S. Rajagopal and J. R. Cavallaro",
  title =        "Truncated Online Arithmetic with Applications to
                 Communication Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "55",
  number =       "10",
  pages =        "1240--1252",
  month =        oct,
  year =         "2006",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2006.168",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 15:35:56 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1683755",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Shen:2006:TAS,
  author =       "Xunyang Shen and Peter R. Turner",
  title =        "{Taylor} approximation for symmetric level-index
                 arithmetic processing",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "26",
  number =       "3",
  pages =        "584--603",
  month =        jul,
  year =         "2006",
  CODEN =        "IJNADH",
  DOI =          "https://doi.org/10.1093/imanum/drl004",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  bibdate =      "Tue Jun 24 12:23:09 MDT 2008",
  bibsource =    "http://imanum.oxfordjournals.org/content/vol26/issue3/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/cgi/content/abstract/26/3/584;
                 http://comjnl.oxfordjournals.org/cgi/reprint/26/3/584",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
}

@Article{Shou:2006:MAA,
  author =       "Huahao Shou and Hongwei Lin and Ralph R. Martin and
                 Guojin Wang",
  title =        "Modified affine arithmetic in tensor form for
                 trivariate polynomial evaluation and algebraic surface
                 plotting",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "195",
  number =       "1--2",
  pages =        "155--171",
  day =          "15",
  month =        oct,
  year =         "2006",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:12:01 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042705004814",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Singh:2006:IEE,
  author =       "S. B. Singh and H. S. Kasana",
  title =        "Improved estimates for error in floating point
                 representation analysis",
  journal =      j-BULL-CALCUTTA-MATH-SOC,
  volume =       "98",
  number =       "2",
  pages =        "117--124",
  year =         "2006",
  CODEN =        "BCMSA5",
  ISSN =         "0008-0659",
  MRclass =      "65G50",
  MRnumber =     "MR2217971 (2006k:65128)",
  bibdate =      "Thu Nov 8 19:16:14 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Bulletin of the Calcutta Mathematical Society",
  journal-URL =  "http://bulletin.calmathsoc.org/database.php",
  keywords =     "rounding errors",
}

@Article{Solymosi:2006:APS,
  author =       "J{\'o}zsef Solymosi",
  title =        "Arithmetic Progressions in Sets with Small Sumsets",
  journal =      j-COMBIN-PROBAB-COMPUT,
  volume =       "15",
  number =       "4",
  pages =        "597--603",
  month =        jul,
  year =         "2006",
  CODEN =        "CPCOFG",
  DOI =          "https://doi.org/10.1017/S0963548306007516",
  ISSN =         "0963-5483 (print), 1469-2163 (electronic)",
  ISSN-L =       "0963-5483",
  bibdate =      "Mon Jul 7 15:38:18 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://journals.cambridge.org/action/displayIssue?jid=CPC&volumeId=15&issueId=04",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=CPC",
}

@Book{StDenis:2006:BMH,
  author =       "Tom {St Denis} and Greg Rose",
  title =        "{BigNum} Math: Implementing Cryptographic Multiple
                 Precision Arithmetic",
  publisher =    pub-SYNGRESS,
  address =      pub-SYNGRESS:adr,
  pages =        "xviii + 296",
  year =         "2006",
  ISBN =         "1-59749-112-8",
  ISBN-13 =      "978-1-59749-112-9",
  LCCN =         "QA402.5 2006",
  bibdate =      "Fri Jun 12 07:26:51 MDT 2009",
  bibsource =    "clas.caltech.edu:210/INNOPAC;
                 https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 z3950.bibsys.no:2100/BIBSYS",
  URL =          "http://www.oreilly.com/catalog/1597491128/index.html",
  acknowledgement = ack-nhfb,
  keywords =     "Karatsuba multiplication; modular exponentiation;
                 Montgomery reduction",
  tableofcontents = "Introduction \\
                 Multiple Precision Arithmetic \\
                 Exercises \\
                 Portability and Stability \\
                 Getting Started \\
                 Maintenance Algorithms \\
                 Basic Operations \\
                 Sign Manipulation \\
                 Basic Arithmetic \\
                 Multiplication and Squaring \\
                 The Multipliers \\
                 Multiplication \\
                 Modular Reduction \\
                 Basics of Modular Reduction \\
                 Exponentiation \\
                 Exponentiation Basics \\
                 Higher Level Algorithms \\
                 Number Theoretic Algorithms",
}

@Book{StDenis:2006:BMI,
  author =       "Tom {St. Denis}",
  title =        "{BigNum} Math: Implementing Cryptographic Multiple
                 Precision Arithmetic",
  publisher =    pub-SYNGRESS,
  address =      pub-SYNGRESS:adr,
  pages =        "xviii + 296",
  year =         "2006",
  ISBN =         "1-59749-112-8",
  ISBN-13 =      "978-1-59749-112-9",
  LCCN =         "QA402.5 .S73 2006",
  bibdate =      "Thu Oct 19 19:07:57 2006",
  bibsource =    "clas.caltech.edu:210/INNOPAC;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$49.95",
  URL =          "http://www.oreilly.com/catalog/1597491128/index.html",
  acknowledgement = ack-nhfb,
  keywords =     "Karatsuba multiplication; modular exponentiation;
                 Montgomery reduction",
}

@Misc{Steele:2006:FPM,
  author =       "Guy L. {Steele Jr.}",
  title =        "Floating point multiplier for delimited operands",
  howpublished = "US Patent 7003540",
  day =          "21",
  month =        feb,
  year =         "2006",
  bibdate =      "Tue Dec 23 15:06:47 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/7003540/fulltext.html",
  abstract =     "A method for providing a floating point product
                 consistent with the present invention includes
                 multiplying a subprecise operand and a non-subprecise
                 operand using a plurality of intermediate stages. The
                 method further includes correcting an error introduced
                 by the subprecise operand by performing an operation in
                 conjunction with a one of the plurality of intermediate
                 stages utilizing a compensating summand.",
  acknowledgement = ack-nhfb,
}

@Misc{Steele:2006:FPSa,
  author =       "Guy L. {Steele Jr.}",
  title =        "Floating point system with improved support of
                 interval arithmetic",
  howpublished = "US Patent 7069288",
  day =          "27",
  month =        jun,
  year =         "2006",
  bibdate =      "Tue Dec 23 15:06:47 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/7069288/fulltext.html",
  abstract =     "Embodiments consistent with the principles of the
                 present invention provide improved results, compared to
                 IEEE Std. 754, for floating point operations used in
                 interval arithmetic calculations. One embodiment
                 consistent with the principles of the present invention
                 provides a method of enhancing support of an interval
                 computation when performing a floating point arithmetic
                 operation, comprising the steps, performed by a
                 processor, of receiving a first floating point operand,
                 receiving a second floating point operand, executing
                 the floating point arithmetic operation on the first
                 floating point operand and the second floating point
                 operand, determining whether a NaN substitution is
                 necessary, producing a floating point result if the NaN
                 substitution is determined to be unnecessary, and
                 substituting an alternative value as the floating point
                 result if the NaN substitution is determined to be
                 necessary.",
  acknowledgement = ack-nhfb,
}

@Misc{Steele:2006:FPSb,
  author =       "Guy L. {Steele Jr.}",
  title =        "Floating point status information testing circuit",
  howpublished = "US Patent 7016928",
  day =          "21",
  month =        mar,
  year =         "2006",
  bibdate =      "Tue Dec 23 15:06:47 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/7016928/fulltext.html",
  abstract =     "A floating point operand testing circuit includes an
                 analysis circuit and a result generator circuit coupled
                 to the analysis circuit. The analysis circuit
                 determines the status of a floating point operand based
                 upon data within the operand. An operand buffer may
                 supply the operand to the analysis circuit. The result
                 generator circuit is responsive to at least one control
                 signal and asserts a result signal if the floating
                 point analysis circuit matches the floating point
                 status to a predetermined format specified by the
                 control signal. The result signal can condition the
                 outcome of a floating point instruction. The result
                 generator may also respond to multiple control signals
                 asserted when testing a single operand for different
                 formats, such as not-a-number (NaN), infinity,
                 normalized, denormalized, invalid operation, overflow,
                 underflow, division by zero, exact, and inexact.",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point testing",
}

@Misc{Steele:2006:FPU,
  author =       "Guy L. {Steele Jr.}",
  title =        "Floating point unit for detecting and representing
                 inexact computations without flags or traps",
  howpublished = "US Patent 7069289",
  day =          "27",
  month =        jun,
  year =         "2006",
  bibdate =      "Tue Dec 23 15:06:47 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/7069289/fulltext.html",
  abstract =     "A method and system perform a rounding step of a
                 floating point computation on at least one floating
                 point operand to preserve an inexact status. Inexact
                 status information generated from the rounding step may
                 be encoded within the result, instead of requiring a
                 separate floating point status register for the inexact
                 status information. In one embodiment, inexact status
                 information is preserved by determining whether the at
                 least one operand is inexact. Further, an intermediate
                 result of the floating point computation is analyzed to
                 determine whether it is inexact. Finally, the
                 intermediate result is rounded based on whether the at
                 least one operand is inexact and whether the
                 intermediate result is inexact to preserve an inexact
                 status of the at least one operand and the intermediate
                 result.",
  acknowledgement = ack-nhfb,
}

@Misc{Steele:2006:SMP,
  author =       "Guy L. {Steele Jr.}",
  title =        "System and method for performing floating point
                 operations involving extended exponents",
  howpublished = "US Patent 6993549",
  day =          "31",
  month =        jan,
  year =         "2006",
  bibdate =      "Tue Dec 23 15:06:47 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/6993549/fulltext.html",
  abstract =     "An extended exponent floating point unit performs an
                 extended exponent floating point operation on a
                 plurality of operands to produce a product of the
                 plurality of operands. The extended exponent floating
                 point unit groups the plurality of operands into at
                 least one group, determines a plurality of scale
                 factors for the plurality of operands, respectively,
                 and provides a running sum of the plurality of scale
                 factors. The extended exponent floating point unit
                 further scales the plurality of operands to obtain a
                 plurality of scaled operands, multiplies the plurality
                 of scaled operands to obtain a group product, and
                 scales the group product to obtain a scaled group
                 product. The scaled group product is adjusted based on
                 the running sum. The plurality of operands are grouped
                 such that when all the plurality of scaled operands in
                 the at least one group are multiplied an overflow or
                 underflow will not occur.",
  acknowledgement = ack-nhfb,
}

@Misc{Steele:2006:TOC,
  author =       "Guy L. {Steele Jr.}",
  title =        "Total order comparator unit for comparing values of
                 two floating point operands",
  howpublished = "US Patent 7133890",
  day =          "07",
  month =        nov,
  year =         "2006",
  bibdate =      "Tue Dec 23 15:06:47 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/7133890/fulltext.html",
  abstract =     "A floating point total order comparator circuit for
                 comparing a first floating point operand and a second
                 floating point operand includes a first analysis
                 circuit for determining a format of the first floating
                 point operand based upon floating point status
                 information encoded within the first floating point
                 operand, a second analysis circuit for determining a
                 format of the second floating point operand based upon
                 floating point status information encoded within the
                 second floating point operand, and a result generator
                 circuit coupled to the analysis circuits for producing
                 a result indicating a total order comparative
                 relationship between the first floating point operand
                 and the second floating point operand based on the
                 format of the first floating point operand and the
                 format of the second floating point operand. The result
                 can condition the outcome of a floating point
                 instruction. The floating point total order comparator
                 circuit may recognize several predetermined operand
                 formats, such as not-a-number (NaN), infinity,
                 normalized, denormalized, invalid operation, overflow,
                 underflow, division by zero, positive zero, negative
                 zero, exact, and inexact.",
  acknowledgement = ack-nhfb,
}

@Article{Strzebonski:2006:CAD,
  author =       "Adam W. Strzebo{\'n}ski",
  title =        "{Cylindrical Algebraic Decomposition} using validated
                 numerics",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "41",
  number =       "9",
  pages =        "1021--1038",
  month =        sep,
  year =         "2006",
  CODEN =        "JSYCEH",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  bibdate =      "Wed Aug 25 20:13:18 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171/",
}

@InProceedings{Strzodka:2006:PMP,
  author =       "R. Strzodka and D. Goddeke",
  title =        "Pipelined mixed precision algorithms on {FPGAs} for
                 fast and accurate {PDE} solvers from low precision
                 components",
  crossref =     "Pocek:2006:FAI",
  pages =        "259--270",
  year =         "2006",
  bibdate =      "Sat Oct 9 13:03:16 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sung:2006:HEV,
  author =       "Tze-yun Sung and Yaw-shih Shieh and Chun-wang Yu and
                 Hsi-chin Hsin",
  booktitle =    "{2006 Seventh International Conference on Parallel and
                 Distributed Computing, Applications and Technologies
                 (PDCAT'06)}",
  title =        "A High-Efficiency Vector Interpolator Using Redundant
                 {CORDIC} Arithmetic in Power-Aware 3-D Graphics
                 Rendering",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "44--49",
  year =         "2006",
  DOI =          "https://doi.org/10.1109/PDCAT.2006.7",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "3-D vector interpolation; Algorithm design and
                 analysis; Arithmetic; CORDIC algorithm; Delay;
                 Graphics; Hardware; high-throughput.; Interpolation;
                 Pipeline processing; Redundant CORDIC arithmetic;
                 Rendering (computer graphics); Throughput; Very large
                 scale integration",
}

@InProceedings{Taylor:2006:IAI,
  author =       "Paul Taylor",
  title =        "Interval Analysis Without Intervals",
  crossref =     "Anonymous:2006:PCR",
  pages =        "??--??",
  year =         "2006",
  bibdate =      "Tue Jun 27 10:28:05 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Thakkar:2006:PDP,
  author =       "Anuja J. Thakkar and Abdel Ejnioui",
  title =        "Pipelining of double precision floating point division
                 and square root operations",
  crossref =     "Menezes:2006:PAS",
  pages =        "488--493",
  year =         "2006",
  DOI =          "https://doi.org/10.1145/1185448.1185555",
  bibdate =      "Sat Oct 9 13:04:49 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Space applications rely increasingly on high data rate
                 DSP algorithms. These algorithms use double precision
                 floating point arithmetic operations. While most DSP
                 applications can be compiled on DSP processors, high
                 data rate DSP computations require novel implementation
                 technologies to support their high throughputs. Only
                 recently, gate densities in FPGAs have reached a level
                 which makes them attractive platforms to implement
                 compute-intensive DSP applications. In this context,
                 this paper presents the sequential and pipelined
                 designs of a double precision floating point divider
                 and square root unit on FPGAs. Contrary to pipelined
                 parallel implementations, the pipelining of these units
                 is based on unrolling the iterations in low-radix digit
                 recurrence algorithms. These units are mapped on
                 generic FPGA reconfigurable fabric without taking
                 advantage of any advanced architectural components
                 available in high capacity FPGAs. The implementations
                 of these designs show that their performances are
                 comparable to, and sometimes higher than, the
                 performances of non-iterative designs based of high
                 radix numbers. The iterative divider and square root
                 unit occupy less than 1\% of an XC2V6000 FPGA chip
                 while their pipelined counterparts can produce
                 throughputs that reach the 100 MFLOPS mark by consuming
                 a modest 8\% of the chip area.",
  acknowledgement = ack-nhfb,
}

@Article{Thapliyal:2006:CIF,
  author =       "Himanshu Thapliyal and Hamid R. Arabnia and A. P.
                 Vinod",
  title =        "Combined Integer and Floating Point Multiplication
                 Architecture ({CIFM}) for {FPGAs} and Its Reversible
                 Logic Implementation",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "14",
  month =        oct,
  year =         "2006",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/cs/0610090",
  abstract =     "In this paper, the authors propose the idea of a
                 combined integer and floating point multiplier(CIFM)
                 for FPGAs. The authors propose the replacement of
                 existing 18x18 dedicated multipliers in FPGAs with
                 dedicated 24x24 multipliers designed with small 4x4 bit
                 multipliers. It is also proposed that for every
                 dedicated 24x24 bit multiplier block designed with 4x4
                 bit multipliers, four redundant 4x4 multiplier should
                 be provided to enforce the feature of self
                 repairability (to recover from the faults). In the
                 proposed CIFM reconfigurability at run time is also
                 provided resulting in low power. The major source of
                 motivation for providing the dedicated 24x24 bit
                 multiplier stems from the fact that single precision
                 floating point multiplier requires 24x24 bit integer
                 multiplier for mantissa multiplication. A
                 reconfigurable, self-repairable 24x24 bit multiplier
                 (implemented with 4x4 bit multiply modules) will
                 ideally suit this purpose, making FPGAs more suitable
                 for integer as well floating point operations. A
                 dedicated 4x4 bit multiplier is also proposed in this
                 paper. Moreover, in the recent years, reversible logic
                 has emerged as a promising technology having its
                 applications in low power CMOS, quantum computing,
                 nanotechnology, and optical computing. It is not
                 possible to realize quantum computing without
                 reversible logic. Thus, this paper also paper provides
                 the reversible logic implementation of the proposed
                 CIFM. The reversible CIFM designed and proposed here
                 will form the basis of the completely reversible
                 FPGAs.",
  acknowledgement = ack-nhfb,
  subject =      "Hardware Architecture (cs.AR)",
}

@InProceedings{Thapliyal:2006:DNR,
  author =       "Himanshu Thapliyal and Sumedha K. Gupta",
  title =        "Design of Novel Reversible Carry Look-Ahead {BCD}
                 Subtractor",
  crossref =     "Mohanty:2006:IIC",
  pages =        "253--258",
  year =         "2006",
  DOI =          "https://doi.org/10.1109/ICIT.2006.44",
  bibdate =      "Thu Aug 07 19:09:50 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "IEEE 754r is the ongoing revision to the IEEE 754
                 floating point standard. A major enhancement to the
                 standard is the addition of decimal format, thus the
                 design of BCD arithmetic units is likely to get
                 significant attention. Firstly, this paper introduces a
                 novel carry look-ahead BCD adder and then builds a
                 novel carry look-ahead BCD subtractor based on it.
                 Secondly, it introduces the reversible logic
                 implementation of the proposed carry look-ahead BCD
                 subtractor. We have tried to design the reversible
                 logic implementation of the BCD Subtractor optimal in
                 terms of number of reversible gates used and garbage
                 outputs produced. Thus, the proposed work will be of
                 significant value as the technologies mature.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Thapliyal:2006:NBA,
  author =       "H. Thapliyal and S. Kotiyal and M. B. Srinivas",
  title =        "Novel {BCD} adders and their reversible logic
                 implementation for {IEEE 754R} format",
  crossref =     "IEEE:2006:ICV",
  year =         "2006",
  DOI =          "https://doi.org/10.1109/VLSID.2006.122",
  bibdate =      "Mon Mar 19 10:19:57 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "IEEE 754r is the ongoing revision to the IEEE 754
                 floating point standard and a major enhancement to the
                 standard is the addition of decimal format. This paper
                 proposes two novel BCD adders called carry skip and
                 carry look-ahead BCD adders respectively. Furthermore,
                 in the recent years, reversible logic has emerged as a
                 promising technology having its applications in low
                 power CMOS, quantum computing, nanotechnology, and
                 optical computing. It is not possible to realize
                 quantum computing without reversible logic. Thus, this
                 paper also paper provides the reversible logic
                 implementation of the conventional BCD adder as the
                 well as the proposed carry skip BCD adder using a
                 recently proposed TSG gate. Furthermore, a new
                 reversible gate called TS-3 is also being proposed and
                 it has been shown that the proposed reversible logic
                 implementation of the BCD adders is much better
                 compared to recently proposed one, in terms of number
                 of reversible gates used and garbage outputs produced.
                 The reversible BCD circuits designed and proposed here
                 form the basis of the decimal ALU of a primitive
                 quantum CPU.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@Article{Toivonen:2006:VFF,
  author =       "T. Toivonen and J. Heikkila",
  title =        "Video filtering with {Fermat} number theoretic
                 transforms using residue number system",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-VIDEO-TECH,
  volume =       "16",
  number =       "1",
  pages =        "92--101",
  month =        jan,
  year =         "2006",
  CODEN =        "ITCTEM",
  DOI =          "https://doi.org/10.1109/TCSVT.2005.858612",
  ISSN =         "1051-8215 (print), 1558-2205 (electronic)",
  ISSN-L =       "1051-8215",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=33196",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems for Video
                 Technology",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=76",
  keywords =     "residue arithmetic; residue number system",
  summary =      "We investigate image and video convolutions based on
                 Fermat number transform (FNT) modulo q=2/sup M/+1 where
                 M is an integer power of two. These transforms are
                 found to be ideal for image convolutions, except that
                 the choices for the word length, \ldots{}",
}

@Book{Trott:2006:MGN,
  author =       "Michael Trott",
  title =        "The {Mathematica} guidebook for numerics",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xxxvi + 1208",
  year =         "2006",
  ISBN =         "0-387-95011-7",
  ISBN-13 =      "978-0-387-95011-2",
  LCCN =         "QA76.95 .T773 2006",
  MRclass =      "65-00",
  MRnumber =     "MR2174594 (2006m:65001)",
  bibdate =      "Thu Nov 8 19:02:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "With 1 DVD (Windows, Macintosh, Mac, UNIX)",
  acknowledgement = ack-nhfb,
}

@Article{VanMeter:2006:DAQ,
  author =       "Rodney {Van Meter} and Kae Nemoto and W. J. Munro and
                 Kohei M. Itoh",
  title =        "Distributed Arithmetic on a Quantum Multicomputer",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "34",
  number =       "2",
  pages =        "354--365",
  year =         "2006",
  CODEN =        "CANED2",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Mon Aug 21 15:00:05 MDT 2006",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
}

@InProceedings{Vazquez:2006:CSD,
  author =       "Alvaro Vazquez and Elisardo Antelo",
  title =        "Conditional Speculative Decimal Addition",
  crossref =     "Anonymous:2006:PCR",
  pages =        "??--??",
  year =         "2006",
  bibdate =      "Tue Jun 27 10:28:05 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@Article{Villalba:2006:DRM,
  author =       "J. Villalba and T. Lang and M. A. Gonzalez",
  title =        "Double-residue modular range reduction for
                 floating-point hardware implementations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "55",
  number =       "3",
  pages =        "254--267",
  month =        mar,
  year =         "2006",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2006.38",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 15:35:53 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1583556",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Wang:2006:ACV,
  author =       "X. Wang and S. Braganza and M. Leeser",
  title =        "Advanced components in the variable precision
                 floating-point library",
  crossref =     "Pocek:2006:FAI",
  pages =        "249--258",
  year =         "2006",
  DOI =          "https://doi.org/10.1109/FCCM.2006.21",
  bibdate =      "Sat Oct 9 13:07:28 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Optimal reconfigurable hardware implementations may
                 require the use of arbitrary floating-point formats
                 that do not necessarily conform to IEEE specified
                 sizes. The authors have previously presented a variable
                 precision floating-point library for use with
                 reconfigurable hardware. The authors recently added
                 three advanced components: floating-point division,
                 floating-point square root and floating-point
                 accumulation to our library. These advanced components
                 use algorithms that are well suited to FPGA
                 implementations and exhibit a good tradeoff between
                 area, latency and throughput. The floating-point format
                 of our library is both general and flexible. All IEEE
                 formats, including 64-bit double-precision format, are
                 a subset of our format. All previously published
                 floating-point formats for reconfigurable hardware are
                 a subset of our format as well. The generic
                 floating-point format supported by all of our library
                 components makes it easy and convenient to create a
                 pipelined, custom data path with optimal bitwidth for
                 each operation. Our library can be used to achieve more
                 parallelism and less power dissipation than adhering to
                 a standard format. To further increase parallelism and
                 reduce power dissipation, our library also supports
                 hybrid fixed and floating point operations in the same
                 design. The division and square root designs are based
                 on table lookup and Taylor series expansion, and make
                 use of memories and multipliers embedded on the FPGA
                 chip. The iterative accumulator utilizes the library
                 addition module as well as buffering and control logic
                 to achieve performance similar to that of the addition
                 by itself. They are all fully pipelined designs with
                 clock speed comparable to that of other library
                 components to aid the designer in implementing fast,
                 complex, pipelined designs.",
  acknowledgement = ack-nhfb,
}

@Article{Wang:2006:PAN,
  author =       "Chengpu Wang",
  title =        "Precision Arithmetic: A New Floating-Point
                 Arithmetic",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "25",
  month =        jun,
  year =         "2006",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  MRclass =      "65Y04, 65T50",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/cs/0606103",
  abstract =     "A new deterministic floating-point arithmetic called
                 precision arithmetic is developed to track precision
                 for arithmetic calculations. It uses a novel rounding
                 scheme to avoid excessive rounding error propagation of
                 conventional floating-point arithmetic. Unlike interval
                 arithmetic, its uncertainty tracking is based on
                 statistics and the central limit theorem, with a much
                 tighter bounding range. Its stable rounding error
                 distribution is approximated by a truncated normal
                 distribution. Generic standards and systematic methods
                 for validating uncertainty-bearing arithmetics are
                 discussed. The precision arithmetic is found to be
                 better than interval arithmetic in both
                 uncertainty-tracking and uncertainty-bounding for
                 normal usages. The precision arithmetic is available
                 publicly at
                 \url{http://precisionarithm.sourceforge.net/}",
  acknowledgement = ack-nhfb,
  remark =       "This document has been updated 21 times from 25 Jun
                 2006 to 3 Apr 2014.",
  subject =      "Discrete Mathematics (cs.DM); Data Structures and
                 Algorithms (cs.DS); Numerical Analysis (cs.NA)",
}

@Article{Wires:2006:RRS,
  author =       "Kent E. Wires and Michael J. Schulte",
  title =        "Reciprocal and Reciprocal Square Root Units with
                 Operand Modification and Multiplication",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "42",
  number =       "3",
  pages =        "257--272",
  month =        mar,
  year =         "2006",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1007/s11265-006-4186-0",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Mon Mar 05 08:26:23 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://springerlink.metapress.com/content/t6027p6713727606/fulltext.pdf",
  abstract =     "Reciprocals and reciprocal square roots are used in
                 several digital signal processing, multimedia, and
                 scientific computing applications. This paper presents
                 high-speed methods for computing reciprocals and
                 reciprocal square roots. These methods use a table
                 lookup, operand modification, and multiplication to
                 obtain an initial approximation. This is followed by a
                 modified Newton--Raphson iteration, which improves the
                 accuracy of the initial approximation. The initial
                 approximation and Newton--Raphson iteration employ
                 specialized hardware to reduce the delay, area, and
                 power dissipation. The application of these methods is
                 illustrated through the design of reciprocal and
                 reciprocal square root units for operands in the IEEE
                 single precision format. These designs are pipelined to
                 produce a new result every clock cycle.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
  keywords =     "computer arithmetic; function approximation;
                 Newton--Raphson iteration; reciprocal; reciprocal
                 square root; table lookup",
}

@Article{Wong:2006:FES,
  author =       "K. W. Wong and Edward C. W. Lee and L. M. Cheng and
                 Xiaofeng Liao",
  title =        "Fast elliptic scalar multiplication using new
                 double-base chain and point halving",
  journal =      j-APPL-MATH-COMP,
  volume =       "183",
  number =       "2",
  pages =        "1000--1007",
  day =          "15",
  month =        dec,
  year =         "2006",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Sat Jul 12 09:03:00 MDT 2008",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Xenoulis:2006:TAS,
  author =       "G. Xenoulis and M. Psarakis and D. Gizopoulos and A.
                 Paschalis",
  title =        "Testability Analysis and Scalable Test Generation for
                 High-Speed Floating-Point Units",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "55",
  number =       "11",
  pages =        "1449--1457",
  month =        nov,
  year =         "2006",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2006.187",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 15:35:57 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1705453",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Xia:2006:RSI,
  author =       "Bican Xia and Ting Zhang",
  title =        "Real solution isolation using interval arithmetic",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "52",
  number =       "6--7",
  pages =        "853--860",
  month =        sep # "\slash " # oct,
  year =         "2006",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:49:55 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122106002896",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Manual{XILINX:2006:XLF,
  author =       "{XILINX}",
  title =        "{XILINX LogiCORE} floating-point operator v3.0 product
                 specification",
  organization = "Xilinx, Inc.",
  day =          "28",
  month =        sep,
  year =         "2006",
  bibdate =      "Sat Oct 9 13:09:37 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.xilinx.com/bvdocs/ipcenter/data_sheet/floating_point_ds335.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{You:2006:DDA,
  author =       "Younggap You and Yong Dae Kim and Jong Hwa Choi",
  title =        "Dynamic Decimal Adder Circuit Design by using the
                 Carry Lookahead",
  crossref =     "IEEE:2006:PIW",
  pages =        "242--244",
  year =         "2006",
  bibdate =      "Mon Mar 19 11:11:29 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/iel5/10974/34591/01649627.pdf",
  abstract =     "This paper presents a carry lookahead (CLA) circuitry
                 design based on dynamic circuit aiming at delay
                 reduction in addition of BCD coded decimal numbers. The
                 performance of the proposed dynamic decimal adder is
                 analyzed demonstrating its speed improvement. Timing
                 simulation on the proposed decimal addition circuit
                 employing 0.25 $ \mu $ m CMOS technology yields the
                 worst case delay of 622ns.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@InProceedings{Zhu:2006:FGA,
  author =       "Yong-Kang Zhu and Wayne Hayes",
  title =        "Fast, guaranteed-accurate sums of many floating-point
                 numbers",
  crossref =     "Anonymous:2006:PCR",
  pages =        "??--??",
  year =         "2006",
  bibdate =      "Tue Jun 27 10:28:05 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}

@TechReport{Zimmermann:2006:AFD,
  author =       "Paul Zimmermann",
  title =        "Asymptotically Fast Division for {GMP}",
  type =         "Technical report",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  day =          "31",
  month =        aug,
  year =         "2006",
  bibdate =      "Sun Sep 10 07:18:34 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.loria.fr/~zimmerma/papers/invert.pdf",
  abstract =     "Until version 4.2.1, GNU MP (GMP for short) division
                 has complexity O(M(n) log n), which is not
                 asymptotically optimal. We propose here some division
                 algorithms that achieve O(M(n)) with small constants.",
  acknowledgement = ack-nhfb,
}

@TechReport{Zimmermann:2006:EBC,
  author =       "Paul Zimmermann and Richard Brent and Colin Percival",
  title =        "Errors Bounds on Complex Floating-Point
                 Multiplication",
  type =         "Technical report",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  pages =        "????",
  year =         "2006",
  bibdate =      "Sun Sep 10 07:21:42 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.loria.fr/~zimmerma/papers/index.html",
  abstract =     "Given floating-point arithmetic with $t$-digit base-$
                 \beta $ significands in which all arithmetic operations
                 are performed as if calculated to infinite precision
                 and rounded to a nearest representable value, we prove
                 that the product of complex values $ z_0 $ and $ z_1 $
                 can be computed with maximum absolute error $ |z_0 |
                 |z_1 | (1 / 2) \beta^{1 - t} \sqrt {5} $. In
                 particular, this provides relative error bounds of $ {2
                 - 24} \sqrt {5} $ and $ {2 - 53} \sqrt {5} $ for IEEE
                 754 single and double precision arithmetic
                 respectively, provided that overflow, underflow, and
                 denormals do not occur. We also provide the numerical
                 worst cases for IEEE 754 single and double precision
                 arithmetic.",
  acknowledgement = ack-nhfb,
  xxnote =       "Check author order?? Paper not yet online.",
}

@Misc{Zimmermann:2006:WC,
  author =       "Paul Zimmermann",
  title =        "Worst Cases for $ \sin (\hbox {BIG}) $",
  howpublished = "World-Wide Web slides.",
  day =          "2",
  month =        nov,
  year =         "2006",
  bibdate =      "Wed Nov 15 07:56:07 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.loria.fr/~zimmerma/talks/sinbig.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Zimmermann:2006:YE,
  author =       "Paul Zimmermann and Bruce Dodson",
  title =        "20 Years of {ECM}",
  crossref =     "Hess:2006:ANT",
  pages =        "525--541",
  year =         "2006",
  DOI =          "https://doi.org/10.1007/11792086_37",
  bibdate =      "Mon May 31 12:31:07 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://members.loria.fr/PZimmermann/papers/40760525.pdf",
  abstract =     "The Elliptic Curve Method for integer factorization
                 (ECM) was invented by H. W. Lenstra, Jr., in 1985 [14].
                 In the past 20 years, many improvements of ECM were
                 proposed on the mathematical, algorithmic, and
                 implementation sides. This paper summarizes the current
                 state-of-the-art, as implemented in the GMP-ECM
                 software.",
  acknowledgement = ack-nhfb,
  keywords =     "assembly code; elliptic curve; Fermat number; modular
                 multiplication; quadratic domain",
}

@Article{Abtahi:2007:FSD,
  author =       "M. Abtahi and P. Siy",
  title =        "The Factor-2 Sign Detection Algorithm using a core
                 function for {RNS} numbers",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "53",
  number =       "9",
  pages =        "1455--1463",
  month =        may,
  year =         "2007",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:50:01 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122107001150",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@InProceedings{Aharoni:2007:SCI,
  author =       "Merav Aharoni and Ron Maharik and Abraham Ziv",
  title =        "Solving Constraints on the Intermediate Result of
                 Decimal Floating-Point Operations",
  crossref =     "Kornerup:2007:PIS",
  pages =        "38--45",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.33",
  bibdate =      "Tue Oct 9 16:32:41 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.lirmm.fr/arith18/papers/aharoni-DecimalConstraints.pdf",
  abstract =     "The draft revision of the IEEE Standard for Floating-
                 Point Arithmetic (IEEE P754) includes a definition for
                 decimal floating-point (FP) in addition to the widely
                 used binary FP specification. The decimal standard
                 raises new concerns with regard to the verification of
                 hardware- and software-based designs. The verification
                 process normally emphasizes intricate corner cases and
                 uncommon events. The decimal format introduces several
                 new classes of such events in addition to those
                 characteristic of binary FP. Our work addresses the
                 following problem: Given a decimal floating-point
                 operation, a constraint on the intermediate result, and
                 a constraint on the representation selected for the
                 result, find random inputs for the operation that yield
                 an intermediate result compatible with these
                 specifications. The paper supplies efficient analytic
                 solutions for addition and for some cases of
                 multiplication and division. We provide probabilistic
                 algorithms for the remaining cases. These algorithms
                 prove to be efficient in the actual implementation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}

@InProceedings{Anonymous:2007:AI,
  author =       "Anonymous",
  title =        "Author Index",
  crossref =     "Kornerup:2007:PIS",
  pages =        "269--269",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.12",
  bibdate =      "Tue Oct 9 17:16:03 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}

@Article{Anonymous:2007:CPSa,
  author =       "Anonymous",
  title =        "Call for Papers for Special Issue on Computer
                 Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "56",
  number =       "1",
  pages =        "144--144",
  month =        jan,
  year =         "2007",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2007.250631",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 15:03:37 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Anonymous:2007:CPSb,
  author =       "Anonymous",
  title =        "Call for Papers for Special Section on Computer
                 Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "56",
  number =       "2",
  pages =        "287--287",
  month =        feb,
  year =         "2007",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2007.22",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 15:03:37 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Balasubramaniam:2007:ECS,
  author =       "P. Balasubramaniam and E. Karthikeyan",
  title =        "Elliptic curve scalar multiplication algorithm using
                 complementary recoding",
  journal =      j-APPL-MATH-COMP,
  volume =       "190",
  number =       "1",
  pages =        "51--56",
  day =          "1",
  month =        jul,
  year =         "2007",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Sat Jul 12 09:03:06 MDT 2008",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Balasubramaniam:2007:FSS,
  author =       "P. Balasubramaniam and E. Karthikeyan",
  title =        "Fast simultaneous scalar multiplication",
  journal =      j-APPL-MATH-COMP,
  volume =       "192",
  number =       "2",
  pages =        "399--404",
  day =          "15",
  month =        sep,
  year =         "2007",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Sat Jul 12 09:03:08 MDT 2008",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Beebe:2007:ETM,
  author =       "Nelson H. F. Beebe",
  title =        "Extending {\TeX} and {\MF} with floating-point
                 arithmetic",
  journal =      j-TUGboat,
  volume =       "28",
  number =       "3",
  pages =        "319--328",
  year =         "2007",
  ISSN =         "0896-3207",
  ISSN-L =       "0896-3207",
  bibdate =      "Tue Oct 23 19:13:23 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/index-table-t.html#tugboat;
                 https://www.math.utah.edu/pub/tex/bib/tugboat.bib;
                 https://www.tug.org/tug2007/",
  URL =          "https://tug.org/TUGboat/tb28-3/tb90beebe.pdf",
  abstract =     "The article surveys the state of arithmetic in \TeX{}
                 and \MF{}, suggests that they could usefully be
                 extended to support floating-point arithmetic, and
                 shows how this could be done with a relatively small
                 effort, \emph{without} loss of the important feature of
                 platform-independent results from those programs, and
                 \emph{without} invalidating any existing documents, or
                 software written for those programs, including output
                 drivers.",
  acknowledgement = ack-bnb # " and " # ack-nhfb,
  confnote =     "TUG 2007 Proceedings (San Diego, CA, USA).",
  errata =       "P. 502, column 1, bottom of page: ``use a'' -> ``use
                 as a''; \\
                 p. 504, column 1, middle of page: ``beeen'' ->
                 ``been''; \\
                 p. 505, column 1, top of page: ``power of base'' ->
                 ``power of the base''",
  fjournal =     "TUGboat",
  issue =        "90",
  journal-URL =  "https://tug.org/TUGboat/",
  ORCID-numbers = "Beebe, Nelson H. F./0000-0001-7281-4263",
  remark =       "Advanced{\Dash}floating-point history, problems, and
                 futures.",
}

@InProceedings{Beebe:2007:NDF,
  author =       "Nelson H. F. Beebe",
  title =        "New directions in floating-point arithmetic",
  crossref =     "Simos:2007:CMS",
  volume =       "2A",
  publisher =    pub-AIP,
  address =      pub-AIP:adr,
  pages =        "155--158",
  year =         "2007",
  bibdate =      "Thu Feb 21 14:34:40 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Beuchat:2007:ANP,
  author =       "Jean-Luc Beuchat and Masaaki Shirase and Tsuyoshi
                 Takagi and Eiji Okamoto",
  title =        "An Algorithm for the {$ \eta T $} Pairing Calculation
                 in Characteristic Three and its Hardware
                 Implementation",
  crossref =     "Kornerup:2007:PIS",
  pages =        "97--104",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.10",
  bibdate =      "Tue Oct 9 16:32:41 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this paper, we propose a modified $ \eta T $
                 pairing algorithm in characteristic three which does
                 not need any cube root extraction. We also discuss its
                 implementation on a low cost platform which hosts an
                 Altera Cyclone II FPGA device. Our pairing accelerator
                 is ten times faster than previous known FPGA
                 implementations in characteristic three",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18; characteristic three; elliptic curve; eta T
                 pairing; FPGA; hardware accelerator; Tate pairing",
}

@InProceedings{Bodrato:2007:IPM,
  author =       "Marco Bodrato and Alberto Zanoni",
  title =        "Integer and polynomial multiplication: towards optimal
                 {Toom--Cook} matrices",
  crossref =     "Brown:2007:PIS",
  pages =        "17--24",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277552",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Karatsuba and Toom--Cook are well-known methods used
                 to multiply efficiently long integers. There have been
                 different proposal about the interpolating values used
                 to determine the matrix to be inverted and the sequence
                 of operations to invert it. A definitive word about
                 which is the optimal matrix (values) and the (number
                 of) basic operations to invert it seems still not to
                 have been said. In this paper we present some
                 particular examples of useful matrices and a method to
                 generate automatically, by means of optimised
                 exhaustive searches on a graph, the best sequence of
                 basic operations to invert them.",
  acknowledgement = ack-nhfb,
  keywords =     "integer and polynomial multiplication; interpolation;
                 Karatsuba; matrix inversion; squaring; Toom--Cook",
}

@Article{Boldo:2007:FPD,
  author =       "Sylvie Boldo and Marc Daumas and Pascal Giorgi",
  title =        "Formal proof for delayed finite field arithmetic using
                 floating point operators",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "6",
  month =        mar,
  year =         "2007",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/cs/0703026",
  abstract =     "Formal proof checkers such as Coq are capable of
                 validating proofs of correction of algorithms for
                 finite field arithmetics but they require extensive
                 training from potential users. The delayed solution of
                 a triangular system over a finite field mixes
                 operations on integers and operations on floating point
                 numbers. We focus in this report on verifying proof
                 obligations that state that no round off error occurred
                 on any of the floating point operations. We use a tool
                 named Gappa that can be learned in a matter of minutes
                 to generate proofs related to floating point arithmetic
                 and hide technicalities of formal proof checkers. We
                 found that three facilities are missing from existing
                 tools. The first one is the ability to use in Gappa new
                 lemmas that cannot be easily expressed as rewriting
                 rules. We coined the second one ``variable
                 interchange'' as it would be required to validate loop
                 interchanges. The third facility handles massive loop
                 unrolling and argument instantiation by generating
                 traces of execution for a large number of cases. We
                 hope that these facilities may sometime in the future
                 be integrated into mainstream code validation.",
  acknowledgement = ack-nhfb,
  subject =      "Symbolic Computation (cs.SC)",
}

@InProceedings{Boldo:2007:FVF,
  author =       "Sylvie Boldo and Jean-Christophe Filliatre",
  title =        "Formal Verification of Floating-Point Programs",
  crossref =     "Kornerup:2007:PIS",
  pages =        "187--194",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.20",
  bibdate =      "Tue Oct 9 17:16:03 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.lri.fr/~filliatr/ftp/publis/caduceus-floats.pdf",
  abstract =     "This paper introduces a methodology to perform formal
                 verification of floating-point C programs. It extends
                 an existing tool for the verification of C programs,
                 Caduceus, with new annotations specific to
                 floating-point arithmetic. The Caduceus first-order
                 logic model for C programs is extended accordingly.
                 Then verification conditions expressing the correctness
                 of the programs are obtained in the usual way and can
                 be discharged interactively with the Coq proof
                 assistant, using an existing Coq formalization of
                 floating-point arithmetic. This methodology is already
                 implemented and has been successfully applied to
                 several short floating-point programs, which are
                 presented in this paper.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}

@InProceedings{Boldo:2007:PCA,
  author =       "Sylvie Boldo and Marc Daumas and William Kahan and
                 Guillaume Melquiond",
  title =        "Proof and certification of an accurate discriminant",
  crossref =     "Luther:2007:GII",
  pages =        "??--??",
  year =         "2007",
  bibdate =      "Wed Jun 24 22:27:02 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Brent:2007:EBC,
  author =       "Richard Brent and Colin Percival and Paul Zimmermann",
  title =        "Error bounds on complex floating-point
                 multiplication",
  journal =      j-MATH-COMPUT,
  volume =       "76",
  number =       "259",
  pages =        "1469--1481",
  year =         "2007",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-07-01931-X",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65G50",
  MRnumber =     "MR2299783 (2008b:65062)",
  bibdate =      "Thu Nov 8 19:16:14 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Given floating-point arithmetic with $t$-digit base-$
                 \beta $ significands in which all arithmetic operations
                 are performed as if calculated to infinite precision
                 and rounded to a nearest representable value, we prove
                 that the product of complex values $ z_0 $ and $ z_1 $
                 can be computed with maximum absolute error $ \vert z_0
                 \Vert z_1 \vert \frac {1}{2} \beta^{1 - t} \sqrt {5} $.
                 In particular, this provides relative error bounds of $
                 2^{-24} \sqrt {5} $ and $ 2^{-53} \sqrt {5} $ for IEEE
                 754 single and double precision arithmetic
                 respectively, provided that overflow, underflow, and
                 denormals do not occur. We also provide the numerical
                 worst cases for IEEE 754 single and double precision
                 arithmetic.",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "rounding errors",
}

@Article{Brisebarre:2007:CRA,
  author =       "Nicolas Brisebarre and Jean-Michel Muller",
  title =        "Correct rounding of algebraic functions",
  journal =      j-INFORM-THEOR-APPL,
  volume =       "41",
  number =       "1",
  pages =        "71--83",
  month =        jan,
  year =         "2007",
  CODEN =        "RSITD7, RITAE4",
  DOI =          "https://doi.org/10.1051/ita:2007002",
  ISSN =         "0988-3754 (print), 1290-385X (electronic)",
  ISSN-L =       "0988-3754",
  bibdate =      "Fri Dec 8 09:49:12 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "RAIRO. Informatique th{\'e}orique et applications :=
                 Theoretical informatics and applications",
}

@InProceedings{Brisebarre:2007:EPA,
  author =       "Nicolas Brisebarre and Sylvain Chevillard",
  title =        "Efficient polynomial {$ L^\infty $}-approximations",
  crossref =     "Kornerup:2007:PIS",
  pages =        "169--176",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.17",
  bibdate =      "Tue Oct 9 17:16:03 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We address the problem of computing a good
                 floating-point-coefficient polynomial approximation to
                 a function, with respect to the supremum norm. This is
                 a key step in most processes of evaluation of a
                 function. We present a fast and efficient method, based
                 on lattice basis reduction, that often gives the best
                 polynomial possible and most of the time returns a very
                 good approximation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}

@InProceedings{Brisebarre:2007:FPA,
  author =       "Nicolas Brisebarre and Guillaume Hanrot",
  title =        "Floating-point {$ L^2 $}-approximations to functions",
  crossref =     "Kornerup:2007:PIS",
  pages =        "177--186",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.38",
  bibdate =      "Tue Oct 9 17:16:03 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In the present paper, we investigate the approximation
                 of a function by a polynomial with floating-point
                 coefficients; we are looking for the best approximation
                 in the $ L^2 $ sense. Finding a best polynomial $ L^2
                 $-approximation with real coefficients is an easy
                 exercise about orthogonal projections. However,
                 truncating the coefficients to floating-point numbers,
                 which is needed for further computations, makes the
                 approximation way worse. Hence, we study the problem of
                 computing best approximations under the constraint that
                 coefficients are floating-point numbers. We show that
                 the corresponding problem is NP-hard, by reduction to
                 the CVP problem. We investigate the practical behaviour
                 of exact and approximate algorithms for this problem.
                 The conclusion is that it is possible in a short amount
                 of time to obtain a relative or absolute best $ L^2
                 $-approximation. The main applications are for large
                 dimension, as a preliminary step of finding
                 $L$-approximations and for functions with large
                 variations, for which relative best approximation is by
                 far more interesting than absolute.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}

@InProceedings{Burgess:2007:DAV,
  author =       "Neil Burgess and Chris N. Hinds",
  title =        "Design of the {ARM VFP11} Divide and Square Root
                 Synthesisable Macrocell",
  crossref =     "Kornerup:2007:PIS",
  pages =        "87--96",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.15",
  bibdate =      "Tue Oct 9 16:32:41 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper presents the detailed design of the ARM
                 VFP11 Divide and Square Root synthesisable macrocell.
                 The macrocell was designed using the minimum-redundancy
                 radix-4 SRT digit recurrence algorithm, and this paper
                 describes a novel acceleration technique employed to
                 achieve the required processor clock frequency of up to
                 750MHz in 90nm CMOS. Logical Effort theory is used to
                 provide a delay analysis of the unit, which
                 demonstrates the balanced nature of the two critical
                 paths therein.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}

@Article{Ceberio:2007:ITA,
  author =       "Martine Ceberio and Vladik Kreinovich and Sanjeev
                 Chopra and Luc Longpr{\'e} and Hung T. Nguyen and
                 Bertram Lud{\"a}scher and Chitta Baral",
  title =        "Interval-type and affine arithmetic-type techniques
                 for handling uncertainty in expert systems",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "199",
  number =       "2",
  pages =        "403--410",
  day =          "15",
  month =        feb,
  year =         "2007",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:12:04 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037704270500779X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Chaves:2007:IRN,
  author =       "R. Chaves and L. Sousa",
  title =        "Improving residue number system multiplication with
                 more balanced moduli sets and enhanced modular
                 arithmetic structures",
  journal =      "IET Computers \& Digital Techniques",
  volume =       "1",
  number =       "5",
  pages =        "472--480",
  month =        sep,
  year =         "2007",
  CODEN =        "ICDTEA, ICDTEX",
  DOI =          "https://doi.org/10.1049/iet-cdt:20060059",
  ISSN =         "1751-8601 (print), 1751-861X (electronic)",
  ISSN-L =       "1751-8601",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnumber=4312767;
                 https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4117424",
  acknowledgement = ack-nhfb,
  ajournal =     "IEE Proc.-Comput. Digit. Tech",
  journal-URL =  "https://digital-library.theiet.org/content/journals/iet-cdt;jsessionid=1s2tx6k4du6p5.x-iet-live-01",
  keywords =     "residue arithmetic; residue number system",
}

@Article{Chen:2007:NSA,
  author =       "Gang Chen and Guoqiang Bai and Hongyi Chen",
  title =        "A New Systolic Architecture for Modular Division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "56",
  number =       "2",
  pages =        "282--286",
  month =        feb,
  year =         "2007",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2007.20",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 15:03:37 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4042687",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Cho:2007:BBL,
  author =       "Wendy K. Tam Cho and Brian J. Gaines",
  title =        "Breaking the {(Benford) Law}",
  journal =      j-AMER-STAT,
  volume =       "61",
  number =       "3",
  pages =        "218--223",
  month =        aug,
  year =         "2007",
  CODEN =        "ASTAAJ",
  DOI =          "https://doi.org/10.1198/000313007X223496",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Thu Aug 26 21:48:27 MDT 2010",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 https://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@InProceedings{Cho:2007:SPM,
  author =       "Heumpil Cho and Earl E. {Swartzlander, Jr.}",
  title =        "Serial Parallel Multiplier Design in Quantum-dot
                 Cellular Automata",
  crossref =     "Kornerup:2007:PIS",
  pages =        "7--15",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.32",
  bibdate =      "Tue Oct 9 16:32:41 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "An emerging nanotechnology, quantum-dot cellular
                 automata (QCA), has the potential for attractive
                 features such as faster speed, smaller size, and lower
                 power consumption than transistor based technology.
                 Quantum-dot cellular automata has a simple cell as the
                 basic element. The cell is used as a building block to
                 construct gates, wires, and memories. Several adder
                 designs have been proposed, but multiplier design in
                 QCA is a rather unexplored research area. This paper
                 utilizes the QCA characteristics to design serial
                 parallel multipliers. Two types of serial parallel
                 multipliers are designed and simulated with several
                 different operand sizes. Those designs are compared in
                 terms of complexity, area, and latency. The serial
                 parallel multipliers have simple and regular
                 structures.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}

@InProceedings{Chung:2007:ASF,
  author =       "Jaewook Chung and M. Anwar Hasan",
  title =        "Asymmetric Squaring Formulae",
  crossref =     "Kornerup:2007:PIS",
  pages =        "113--122",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.11",
  bibdate =      "Tue Oct 9 16:32:41 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present efficient squaring formulae based on the
                 Toom--Cook multiplication algorithm. The latter always
                 requires at least one non-trivial constant division in
                 the interpolation step. We show such non-trivial
                 divisions are not needed in the case two operands are
                 equal for three, four and five-way squarings. Our
                 analysis shows that our 3-way squaring algorithms have
                 much less overhead than the best known 3-way Toom--Cook
                 algorithm. Our experimental results show that one of
                 our new 3-way squaring methods performs faster than
                 mpz\_mul() in GNU multiple precision library (GMP) for
                 squaring integers of approximately 2400-6700 bits on
                 Pentium IV Prescott 3.2GHz. For squaring in $ Z[x] $,
                 our 3-way squaring algorithms are much superior to
                 other known squaring algorithms for small input size.
                 In addition, we present 4-way and 5-way squaring
                 formulae which do not require any constant divisions by
                 integers other than a power of 2. Under some reasonable
                 assumptions, our 5-way squaring formula is faster than
                 the recently proposed Montgomery's 5-way Karatsuba-like
                 formulae.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18; Cook multiplication algorithm; Karatsuba
                 algorithm; Karatsuba-like formulae; Montgomery's
                 Squaring; Toom-multiple-precision arithmetic",
}

@Article{Chung:2007:LWP,
  author =       "Jaewook Chung and M. Anwar Hasan",
  title =        "Low-Weight Polynomial Form Integers for Efficient
                 Modular Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "56",
  number =       "1",
  pages =        "44--57",
  month =        jan,
  year =         "2007",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2007.250622",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 15:03:36 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4016496",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Chung:2007:MRA,
  author =       "Jaewook Chung and M. Anwar Hasan",
  title =        "{Montgomery} Reduction Algorithm for Modular
                 Multiplication Using Low-Weight Polynomial Form
                 Integers",
  crossref =     "Kornerup:2007:PIS",
  pages =        "230--239",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.23",
  bibdate =      "Tue Oct 9 17:16:03 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this paper, we extend a recent piece of work on
                 low-weight polynomial form integers (LWPFIs). We
                 present a new coefficient reduction algorithm based on
                 the Montgomery reduction algorithm and provide its
                 detailed analysis results. We give a condition for
                 eliminating the final subtractions at the end of our
                 Montgomery reduction algorithm adapted to perform the
                 coefficient reduction. Our experimental results show
                 that a new coefficient reduction algorithm is indeed
                 more efficient than the one presented in [1].",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}

@InProceedings{Cornea:2007:SII,
  author =       "Marius Cornea and Cristina Anderson and John Harrison
                 and Ping Tak Peter Tang and Eric Schneider and Charles
                 Tsen",
  title =        "A Software Implementation of the {IEEE 754R} Decimal
                 Floating-Point Arithmetic Using the Binary Encoding
                 Format",
  crossref =     "Kornerup:2007:PIS",
  pages =        "29--37",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.7",
  bibdate =      "Tue Oct 09 12:00:30 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.lirmm.fr/arith18/papers/CorneaM_Decimal_ARITH18.pdf",
  abstract =     "The IEEE Standard 754-1985 for Binary Floating-Point
                 Arithmetic [1] was revised [2], and an important
                 addition is the definition of decimal floating-point
                 arithmetic. This is intended mainly to provide a
                 robust, reliable framework for financial applications
                 that are often subject to legal requirements concerning
                 rounding and precision of the results, because the
                 binary floating-point arithmetic may introduce small
                 but unacceptable errors. Using binary floating-point
                 calculations to emulate decimal calculations in order
                 to correct this issue has led to the existence of
                 numerous proprietary software packages, each with its
                 own characteristics and capabilities. IEEE 754R decimal
                 arithmetic should unify the ways decimal floating-point
                 calculations are carried out on various platforms. New
                 algorithms and properties are presented in this paper
                 which are used in a software implementation of the IEEE
                 754R decimal floating-point arithmetic, with emphasis
                 on using binary operations efficiently. The focus is on
                 rounding techniques for decimal values stored in binary
                 format, but algorithms for the more important or
                 interesting operations of addition, multiplication,
                 division, and conversions between binary and decimal
                 floating-point formats are also outlined. Performance
                 results are included for a wider range of operations,
                 showing promise that our approach is viable for
                 applications that require decimal floating-point
                 calculations",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18; BID rounding; correct rounding;
                 floating-point arithmetic",
}

@Manual{Cowlishaw:2007:DCL,
  author =       "Mike Cowlishaw",
  title =        "The {decNumber C} library",
  organization = pub-IBM,
  address =      pub-IBM:adr,
  day =          "18",
  month =        apr,
  year =         "2007",
  bibdate =      "Fri Apr 20 08:02:33 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Version 3.40",
  URL =          "http://download.icu-project.org/ex/files/decNumber/decNumber-icu-340.zip",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic; DPD encoding",
}

@Article{Dadda:2007:MPD,
  author =       "Luigi Dadda",
  title =        "Multioperand Parallel Decimal Adder: a Mixed Binary
                 and {BCD} Approach",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "56",
  number =       "10",
  pages =        "1320--1328",
  month =        oct,
  year =         "2007",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2007.1067",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Aug 07 17:48:41 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  abstract =     "Decimal arithmetic has been in recent years revived
                 due to the large amount of data in commercial
                 applications. We consider the problem of Multi Operand
                 Parallel Decimal Addition with an approach that uses
                 binary arithmetic, suggested by the adoption of BCD
                 numbers. This involves corrections in order to obtain
                 the BCD result, or a binary to decimal conversion. We
                 adopt the latter approach, particularly efficient for a
                 large number of addends. Conversion requires a
                 relatively small area and can afford fast operation.
                 The BD conversion, moreover, allows an easy alignment
                 of the sums of adjacent columns. We treat the design of
                 BCD digit adders using fast carry free adders and the
                 conversion problem through a known parallel scheme
                 using elementary conversion cells. Spreadsheets have
                 been developed for adding several BCD digits and for
                 simulating the binary to decimal conversion as design
                 tool.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  author-dates = "29 April 1923--26 October 2012",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "decimal floating-point arithmetic",
}

@Article{David:2007:HCM,
  author =       "J. P. David and K. Kalach and N. Tittley",
  title =        "Hardware Complexity of Modular Multiplication and
                 Exponentiation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "56",
  number =       "10",
  pages =        "1308--1319",
  month =        oct,
  year =         "2007",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2007.1084",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 15:03:41 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4302704",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{deDinechin:2007:FCR,
  author =       "Florent de Dinechin and Christoph Lauter and
                 Jean-Michel Muller",
  title =        "Fast and correctly rounded logarithms in
                 double-precision",
  journal =      j-INFORM-THEOR-APPL,
  volume =       "41",
  number =       "1",
  pages =        "85--102",
  month =        jan,
  year =         "2007",
  CODEN =        "RSITD7, RITAE4",
  DOI =          "https://doi.org/10.1051/ita:2007003",
  ISSN =         "0988-3754 (print), 1290-385X (electronic)",
  ISSN-L =       "0988-3754",
  bibdate =      "Fri Dec 8 09:46:23 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "RAIRO. Informatique th{\'e}orique et applications :=
                 Theoretical informatics and applications",
}

@InProceedings{Detrey:2007:RHF,
  author =       "Jeremie Detrey and Florent de Dinechin and Xavier
                 Pujol",
  title =        "Return of the hardware floating-point elementary
                 function",
  crossref =     "Kornerup:2007:PIS",
  pages =        "161--168",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.29",
  bibdate =      "Tue Oct 9 17:16:03 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The study of specific hardware circuits for the
                 evaluation of floating-point elementary functions was
                 once an active research area, until it was realized
                 that these functions were not frequent enough to
                 justify dedicating silicon to them. Research then
                 turned to software functions. This situation may be
                 about to change again with the advent of reconfigurable
                 co-processors based on field-programmable gate arrays.
                 Such co-processors now have a capacity that allows them
                 to accommodate double-precision floating-point
                 computing. Hardware operators for elementary functions
                 targeted to such platforms have the potential to vastly
                 outperform software functions, and will not permanently
                 waste silicon resources. This article studies the
                 optimization, for this target technology, of operators
                 for the exponential and logarithm functions up to
                 double-precision. These operators are freely available
                 from http://www.ens-lyon.fr/LIP/Arenaire/.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}

@Article{Detrey:2007:TUC,
  author =       "J{\'e}r{\'e}mie Detrey and Florent Dinechin",
  title =        "A Tool for Unbiased Comparison between Logarithmic and
                 Floating-point Arithmetic",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "49",
  number =       "1",
  pages =        "161--175",
  month =        oct,
  year =         "2007",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1007/s11265-007-0048-7",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Mon Nov 05 19:20:45 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "For applications requiring a large dynamic, real
                 numbers may be represented either in floating-point, or
                 in the logarithm number system (LNS). Which system is
                 best for a given application is difficult to know in
                 advance, because the cost and performance of LNS
                 operators depend on the target accuracy in a highly non
                 linear way. Therefore, a comparison of the pros and
                 cons of both number systems in terms of cost,
                 performance and overall accuracy is only relevant on a
                 per-application basis. To make such a comparison
                 possible, two concurrent libraries of parameterized
                 arithmetic operators, targeting recent
                 field-programmable gate arrays, are presented. They are
                 unbiased in the sense that they strive to reflect the
                 state-of-the-art for both number systems. These
                 libraries are freely available at
                 http://www.ens-lyon.fr/LIP/Arenaire/.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
}

@Article{Diekmann:2007:FDU,
  author =       "Andreas Diekmann",
  title =        "Not the First Digit! {Using} {Benford's Law} to Detect
                 Fraudulent Scientific Data",
  journal =      j-J-APPL-STAT,
  volume =       "34",
  number =       "3",
  pages =        "321--329",
  year =         "2007",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/02664760601004940",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  bibdate =      "Wed Aug 25 11:41:54 MDT 2010",
  bibsource =    "http://www.tandf.co.uk/journals/routledge/02664763.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Digits in statistical data produced by natural or
                 social processes are often distributed in a manner
                 described by 'Benford's law'. Recently, a test against
                 this distribution was used to identify fraudulent
                 accounting data. This test is based on the supposition
                 that first, second, third, and other digits in real
                 data follow the Benford distribution while the digits
                 in fabricated data do not. Is it possible to apply
                 Benford tests to detect fabricated or falsified
                 scientific data as well as fraudulent financial data?
                 We approached this question in two ways. First, we
                 examined the use of the Benford distribution as a
                 standard by checking the frequencies of the nine
                 possible first and ten possible second digits in
                 published statistical estimates. Second, we conducted
                 experiments in which subjects were asked to fabricate
                 statistical estimates (regression coefficients). The
                 digits in these experimental data were scrutinized for
                 possible deviations from the Benford distribution.
                 There were two main findings. First, both digits of the
                 published regression coefficients were approximately
                 Benford distributed or at least followed a pattern of
                 monotonic decline. Second, the experimental results
                 yielded new insights into the strengths and weaknesses
                 of Benford tests. Surprisingly, first digits of faked
                 data also exhibited a pattern of monotonic decline,
                 while second, third, and fourth digits were distributed
                 less in accordance with Benford's law. At least in the
                 case of regression coefficients, there were indications
                 that checks for digit-preference anomalies should focus
                 less on the first (i.e. leftmost) and more on later
                 digits.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
  keywords =     "Benford's Law; data fabrication; digital analysis;
                 distribution of digits from regression coefficients;
                 first digit law; Zipf's Law",
}

@Article{Dieter:2007:LCM,
  author =       "W. R. Dieter and A. Kaveti and H. G. Dietz",
  title =        "Low-Cost Microarchitectural Support for Improved
                 Floating-Point Accuracy",
  journal =      j-IEEE-COMPUT-ARCHIT-LETT,
  volume =       "6",
  number =       "1",
  pages =        "13--16",
  month =        jan,
  year =         "2007",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/L-CA.2007.1",
  ISSN =         "1556-6056 (print), 1556-6064 (electronic)",
  ISSN-L =       "1556-6056",
  bibdate =      "Fri Jun 21 05:49:19 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeecomputarchitlett.bib",
  abstract =     "Some processors designed for consumer applications,
                 such as graphics processing units (CPUs) and the CELL
                 processor, promise outstanding floating-point
                 performance for scientific applications at commodity
                 prices. However, IEEE single precision is the most
                 precise floating-point data type these processors
                 directly support in hardware. Pairs of native
                 floating-point numbers can be used to represent a base
                 result and a residual term to increase accuracy, but
                 the resulting order of magnitude slowdown dramatically
                 reduces the price/performance advantage of these
                 systems. By adding a few simple microarchitectural
                 features, acceptable accuracy can be obtained with
                 relatively little performance penalty. To reduce the
                 cost of native-pair arithmetic, a residual register is
                 used to hold information that would normally have been
                 discarded after each floating-point computation. The
                 residual register dramatically simplifies the code,
                 providing both lower latency and better
                 instruction-level parallelism.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Computer Architecture Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=10208",
  keywords =     "Application software; B Hardware; B.2 Arithmetic and
                 Logic Structures; B.2.4 High-Speed Arithmetic; B.2.4.b
                 Cost/performance; C Computer Systems Organization; C.0
                 General; C.0.b Hardware/software interfaces; C.1
                 Processor Architectures; C.1.5 Micro-architecture
                 implementation considerations; CELL processor; computer
                 architecture; Costs; floating point arithmetic;
                 floating-point accuracy; Floating-point arithmetic; G
                 Mathematics of Computing; G.1 Numerical Analysis; G.1.0
                 General; G.1.0.e Multiple precision arithmetic;
                 Graphics; graphics processing units; Hardware; I
                 Computing Methodologies; I.3 Computer Graphics; I.3.1
                 Hardware Architecture; I.3.1.a Graphics processors;
                 IEEE single precision; instruction-level parallelism;
                 microarchitectural support; Microarchitecture; parallel
                 processing; Pipelines; Registers; Software algorithms;
                 Software performance",
}

@InProceedings{Dimitrov:2007:MCS,
  author =       "Vassil Dimitrov and Laurent Imbert and Andrew
                 Zakaluzny",
  title =        "Multiplication by a Constant is Sublinear",
  crossref =     "Kornerup:2007:PIS",
  pages =        "261--268",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.24",
  bibdate =      "Tue Oct 9 17:16:03 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper explores the use of the double-base number
                 system (DBNS) for constant integer multiplication. The
                 DBNS recoding scheme represents integers --- in this
                 case constants --- in a multiple-radix way in the hope
                 of minimizing the number of additions to be performed
                 during constant multiplication. On the theoretical
                 side, we propose a formal proof which shows that our
                 recoding technique diminishes the number of additions
                 in a sublinear way. Therefore, we prove Lef{\`e}vre's
                 conjecture that the multiplication by an integer
                 constant is achievable in sublinear time. In a second
                 part, we investigate various strategies and we provide
                 numerical data showcasing the potential interest of our
                 approach.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18; Double-Based Number System (DBNS)",
}

@Article{Doornik:2007:CHP,
  author =       "Jurgen A. Doornik",
  title =        "Conversion of high-period random numbers to floating
                 point",
  journal =      j-TOMACS,
  volume =       "17",
  number =       "1",
  pages =        "??--??",
  month =        jan,
  year =         "2007",
  CODEN =        "ATMCEZ",
  DOI =          "https://doi.org/10.1145/1189756.1189759",
  ISSN =         "1049-3301 (print), 1558-1195 (electronic)",
  ISSN-L =       "1049-3301",
  bibdate =      "Sat Apr 14 09:34:46 MDT 2007",
  bibsource =    "http://www.acm.org/pubs/contents/journals/tomacs/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  articleno =    "3",
  fjournal =     "ACM Transactions on Modeling and Computer Simulation",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?&idx=J781",
}

@Article{Duale:2007:DFP,
  author =       "A. Y. Duale and M. H. Decker and H.-G. Zipperer and M.
                 Aharoni and T. J. Bohizic",
  title =        "Decimal floating-point in {z9}: An implementation and
                 testing perspective",
  journal =      j-IBM-JRD,
  volume =       "51",
  number =       "1/2",
  pages =        "217--227",
  month =        jan # " \slash " # mar,
  year =         "2007",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.511.0217",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Fri Feb 9 20:31:06 MST 2007",
  bibsource =    "http://www.research.ibm.com/journal/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.research.ibm.com/journal/rd/511/duale.html",
  abstract =     "Although decimal arithmetic is widely used in
                 commercial and financial applications, the related
                 computations are handled in software. As a result,
                 applications that use decimal data may experience
                 performance degradations. Use of the newly defined
                 decimal floating-point (DFP) format instead of binary
                 floating-point is expected to significantly improve the
                 performance of such applications. System z9 is the
                 first IBM machine to support the DFP instructions. We
                 present an overview of this implementation and provide
                 some measurement of the performance gained using
                 hardware assists. Various tools and techniques employed
                 for the DFP verification on unit, element, and system
                 levels are presented in detail. Several groups within
                 IBM collaborated on the verification of the new DFP
                 facility, using a common reference model to predict DFP
                 results.",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "decimal floating-point arithmetic",
  ordernumber =  "????",
}

@Article{Eisen:2007:IPA,
  author =       "L. Eisen and J. W. {Ward III} and H.-W. Tast and N.
                 M{\"a}ding and J. Leenstra and S. M. Mueller and C.
                 Jacobi and J. Preiss and E. M. Schwarz and S. R.
                 Carlough",
  title =        "{IBM POWER6} accelerators: {VMX} and {DFU}",
  journal =      j-IBM-JRD,
  volume =       "51",
  number =       "6",
  pages =        "663--683",
  month =        nov,
  year =         "2007",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Mon Jul 7 21:49:07 MDT 2008",
  bibsource =    "http://www.research.ibm.com/journal/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.research.ibm.com/journal/rd/516/eisen.html",
  abstract =     "The IBM POWER6 microprocessor core includes two
                 accelerators for increasing performance of specific
                 workloads. The vector multimedia extension (VMX)
                 provides a vector acceleration of graphic and
                 scientific workloads. It provides single instructions
                 that work on multiple data elements. The instructions
                 separate a 128-bit vector into different components
                 that are operated on concurrently. The decimal
                 floating-point unit (DFU) provides acceleration of
                 commercial workloads, more specifically, financial
                 transactions. It provides a new number system that
                 performs implicit rounding to decimal radix points, a
                 feature essential to monetary transactions. The IBM
                 POWER processor instruction set is substantially
                 expanded with the addition of these two accelerators.
                 The VMX architecture contains 176 instructions, while
                 the DFU architecture adds 54 instructions to the base
                 architecture. The IEEE 754R Binary Floating-Point
                 Arithmetic Standard defines decimal floating-point
                 formats, and the POWER6 processor---on which a
                 substantial amount of area has been devoted to
                 increasing performance of both scientific and
                 commercial workloads---is the first commercial hardware
                 implementation of this format.",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "decimal floating-point arithmetic",
}

@Article{Eisinberg:2007:AFP,
  author =       "A. Eisinberg and G. Fedele",
  title =        "Accurate floating-point summation: a new approach",
  journal =      j-APPL-MATH-COMP,
  volume =       "189",
  number =       "1",
  pages =        "410--424",
  year =         "2007",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  MRclass =      "65B10",
  MRnumber =     "MR2330219",
  bibdate =      "Thu Nov 8 19:16:14 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The aim of this paper is to find an accurate and
                 efficient algorithm for evaluating the summation of
                 large sets of floating-point numbers. We present a new
                 representation of the floating-point number system in
                 which a number is represented as a linear combination
                 of integers and the coefficients are powers of the base
                 of the floating-point system. The approach allows to
                 build up an accurate floating-point summation algorithm
                 based on the fact that no rounding error occurs
                 whenever two integer numbers are summed or a
                 floating-point number is multiplied by powers of the
                 base of the floating-point system. The proposed
                 algorithm seems to be competitive in terms of
                 computational effort and, under some assumptions, the
                 computed sum is greatly accurate. With such
                 assumptions, less-conservative in the practical
                 applications, we prove that the relative error of the
                 computed sum is bounded by the unit roundoff.",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  keywords =     "accurate floating-point summation",
}

@Article{Ercegovac:2007:CSR,
  author =       "Milo{\v{s}} D. Ercegovac and Jean-Michel Muller",
  title =        "Complex Square Root with Operand Prescaling",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "49",
  number =       "1",
  pages =        "19--30",
  month =        oct,
  year =         "2007",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1007/s11265-006-0029-2",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Mon Nov 05 19:24:36 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We propose a radix-$r$ digit-recurrence algorithm for
                 complex square-root. The operand is prescaled to allow
                 the selection of square-root digits by rounding of the
                 residual. This leads to a simple hardware
                 implementation of digit selection. Moreover, the use of
                 digit recurrence approach allows correct rounding of
                 the result if needed. The algorithm, compatible with
                 the complex division presented in Ercegovac and Muller
                 (``Complex Division with Prescaling of the Operands,''
                 in Proc. Application-Specific Systems, Architectures,
                 and Processors (ASAP'03), The Hague, The Netherlands,
                 June 24---26, 2003), and its design are described. We
                 also give rough estimates of its latency and cost with
                 respect to implementation based on standard
                 floating-point instructions as used in software
                 routines for complex square root.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
}

@InProceedings{Ercegovac:2007:HOM,
  author =       "Milo{\v{s}} D. Ercegovac and Jean-Michel Muller",
  editor =       "{IEEE}",
  booktitle =    "{2007 IEEE International Conference on
                 Application-specific Systems, Architectures and
                 Processors (ASAP), Montr{\'e}al, Canada, July 8--11,
                 2007}",
  title =        "A Hardware-Oriented Method for Evaluating Complex
                 Polynomials",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "122--127",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ASAP.2007.4429968",
  ISBN =         "1-4244-1027-4",
  ISBN-13 =      "978-1-4244-1027-9",
  bibdate =      "Fri Sep 29 10:42:47 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Erle:2007:DFP,
  author =       "Mark A. Erle and Michael J. Schulte and Brian J.
                 Hickmann",
  title =        "Decimal Floating-Point Multiplication Via Carry-Save
                 Addition",
  crossref =     "Kornerup:2007:PIS",
  pages =        "46--55",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.14",
  bibdate =      "Tue Oct 9 16:32:41 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.lirmm.fr/arith18/papers/erlem-DFPmultiplication-v2.pdf",
  abstract =     "Decimal multiplication is important in many commercial
                 applications including financial analysis, banking, tax
                 calculation, currency conversion, insurance, and
                 accounting. This paper presents the design of a decimal
                 floating-point multiplier that complies with
                 specifications for decimal multiplication given in the
                 draft revision of the IEEE 754 Standard for
                 Floating-point Arithmetic (IEEE 754R). This multiplier
                 extends a previously published decimal fixedpoint
                 multiplier design by adding several features including
                 exponent generation, sticky bit generation, shifting of
                 the intermediate product, rounding, and exception
                 detection and handling. The core of the decimal
                 multiplication algorithm is an iterative scheme of
                 partial product accumulation employing decimal
                 carry-save addition to reduce the critical path delay.
                 Novel features of the proposed multiplier include
                 support for decimal floating-point numbers, on-the-fly
                 generation of the sticky bit, early estimation of the
                 shift amount, and efficient decimal rounding. Area and
                 delay estimates are provided for a verified Verilog
                 register transfer level model of the multiplier.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}

@Article{Fan:2007:NAS,
  author =       "Haining Fan and M. Anwar Hasan",
  title =        "A New Approach to Subquadratic Space Complexity
                 Parallel Multipliers for Extended Binary Fields",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "56",
  number =       "2",
  pages =        "224--233",
  month =        feb,
  year =         "2007",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2007.19",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 15:03:37 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4042682",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Fan:2007:SCC,
  author =       "Haining Fan and M. Anwar Hasan",
  title =        "Subquadratic Computational Complexity Schemes for
                 Extended Binary Field Multiplication Using Optimal
                 Normal Bases",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "56",
  number =       "10",
  pages =        "1435--1437",
  month =        oct,
  year =         "2007",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2007.1076",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 15:03:42 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4302715",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Fousse:2007:AMP,
  author =       "Laurent Fousse",
  title =        "Accurate Multiple-Precision {Gauss--Legendre}
                 Quadrature",
  crossref =     "Kornerup:2007:PIS",
  pages =        "150--160",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.8",
  bibdate =      "Tue Oct 9 16:32:41 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Numerical integration is an operation that is
                 frequently available in multiple precision numerical
                 software packages. The different quadrature schemes
                 used are considered well studied but the rounding
                 errors that result from the computation are often
                 neglected, and the actual accuracy of the results are
                 therefore seldom rigorously proven. We propose an
                 implementation of the Gauss--Legendre quadrature scheme
                 with bounded error: given a bound on the derivatives of
                 a function we are able to compute an interval
                 containing the true value of the integral, in arbitrary
                 precision. The error analysis is given as well as
                 experimental error measurements and timings, and a
                 complete quadrature example.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}

@Article{Fousse:2007:MMP,
  author =       "Laurent Fousse and Guillaume Hanrot and Vincent
                 Lef{\`e}vre and Patrick P{\'e}lissier and Paul
                 Zimmermann",
  title =        "{MPFR}: a multiple-precision binary floating-point
                 library with correct rounding",
  journal =      j-TOMS,
  volume =       "33",
  number =       "2",
  pages =        "1--15",
  month =        jun,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1236463.1236468",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65G99",
  MRnumber =     "MR2326955",
  bibdate =      "Thu Jul 26 17:36:59 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article presents a multiple-precision binary
                 floating-point library, written in the ISO C language,
                 and based on the GNU MP library. Its particularity is
                 to extend to arbitrary-precision, ideas from the IEEE
                 754 standard, by providing correct rounding and
                 exceptions. We demonstrate how these strong semantics
                 are achieved---with no significant slowdown with
                 respect to other arbitrary-precision tools---and
                 discuss a few applications where such a library can be
                 useful.",
  acknowledgement = ack-nhfb,
  articleno =    "13",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fousse:2007:MPC,
  author =       "Laurent Fousse",
  title =        "Multiple-Precision Correctly rounded {Newton--Cotes}
                 quadrature",
  journal =      j-INFORM-THEOR-APPL,
  volume =       "41",
  number =       "1",
  pages =        "103--121",
  month =        jan,
  year =         "2007",
  CODEN =        "RSITD7, RITAE4",
  DOI =          "https://doi.org/10.1051/ita:2007004",
  ISSN =         "0988-3754 (print), 1290-385X (electronic)",
  ISSN-L =       "0988-3754",
  bibdate =      "Fri Dec 8 09:50:26 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "RAIRO. Informatique th{\'e}orique et applications :=
                 Theoretical informatics and applications",
}

@Article{Frommer:2007:PEZ,
  author =       "A. Frommer and F. Hoxha and B. Lang",
  title =        "Proving the existence of zeros using the topological
                 degree and interval arithmetic",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "199",
  number =       "2",
  pages =        "397--402",
  day =          "15",
  month =        feb,
  year =         "2007",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:12:04 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042705007788",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Furer:2007:FIM,
  author =       "Martin F{\"u}rer",
  title =        "Faster integer multiplication",
  crossref =     "ACM:2007:SPA",
  pages =        "57--66",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1250790.1250800",
  bibdate =      "Fri Jun 20 18:28:53 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "For more than 35 years, the fastest known method for
                 integer multiplication has been the
                 Sch{\"o}nhage-Strassen algorithm running in time $ O(n
                 \log n \log \log n) $. Under certain restrictive
                 conditions there is a corresponding $ \Omega (n \log n)
                 $ lower bound. The prevailing conjecture has always
                 been that the complexity of an optimal algorithm is $
                 \Theta (n \log n) $. We present a major step towards
                 closing the gap from above by presenting an algorithm
                 running in time $ n \log n, 2^{O(\log * n)} $.\par

                 The main result is for Boolean circuits as well as for
                 multitape Turing machines, but it has consequences to
                 other models of computation as well.",
  acknowledgement = ack-nhfb,
  keywords =     "complexity; computer arithmetic; discrete Fourier
                 transform; FFT; integer multiplication",
}

@InProceedings{Gaudry:2007:GBI,
  author =       "Pierrick Gaudry and Alexander Kruppa and Paul
                 Zimmermann",
  title =        "A {\tt gmp}-based implementation of
                 {Sch{\"o}nhage--Strassen}'s large integer
                 multiplication algorithm",
  crossref =     "Brown:2007:PIS",
  pages =        "167--174",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277572",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Sch{\"o}nhage--Strassen's algorithm is one of the best
                 known algorithms for multiplying large integers.
                 Implementing it efficiently is of utmost importance,
                 since many other algorithms rely on it as a subroutine.
                 We present here an improved implementation, based on
                 the one distributed within the GMP library. The
                 following ideas and techniques were used or tried:
                 faster arithmetic modulo $ 2^n + 1 $, improved cache
                 locality, Mersenne transforms, Chinese Remainder
                 Reconstruction, the $ \sqrt 2 $ trick, Harley's and
                 Granlund's tricks, improved tuning.",
  acknowledgement = ack-nhfb,
  keywords =     "integer multiplication; multiprecision arithmetic",
}

@Article{Goel:2007:RMS,
  author =       "S. Goel and S. K. Dash",
  title =        "Response of model simulated weather parameters to
                 round-off-errors on different systems",
  journal =      "Environmental Modelling \& Software",
  volume =       "22",
  number =       "8",
  pages =        "1164--1174",
  month =        aug,
  year =         "2007",
  CODEN =        "EMSOFT",
  DOI =          "https://doi.org/10.1016/j.envsoft.2006.06.011",
  ISSN =         "1364-8152 (print), 1873-6726 (electronic)",
  ISSN-L =       "1364-8152",
  bibdate =      "Fri Aug 08 08:49:37 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this study, the weather forecasting model of the
                 National Centre for Medium Range Weather Forecasting
                 (NCMRWF) is used for examining the characteristics of
                 round-off-errors on three different computer
                 architectures --- PARAM 10K, SUNFIRE 6800 and Dec Alpha
                 for several meteorological parameters such as
                 precipitation, temperature at the surface and
                 mid-atmosphere, and upper and lower level winds. It is
                 well known that the implementation of floating point
                 arithmetic varies from one computing system to another.
                 As a result, meteorological parameters simulated by
                 numerical models on two different systems may deviate
                 from each other and the difference field becomes larger
                 as the model is integrated for longer time, for
                 example, in the scale of several months. This paper
                 focuses on the reduction of such round-off-errors by a
                 simple method of modifying the format representation of
                 the initial data supplied to the model. In all the
                 three systems, the model has been integrated for 4
                 months starting from 4th May, 1996. It is found that
                 after 5 days of model integration with the modified
                 data, the round-off-errors become insignificant. The
                 rate of reduction of round-off-errors is fast up to a
                 month of model integration and thereafter the rate
                 slows down and stabilises. It is further noticed that
                 at the end of four months of integration, the reduction
                 in round-off-errors over the tropical region and oceans
                 is much more than over the rest of the globe.",
  acknowledgement = ack-nhfb,
  ajournal =     "Environ. Model. Softw.",
  journal-URL =  "https://www.sciencedirect.com/journal/environmental-modelling-and-software",
  keywords =     "round-off error; rounding error",
}

@InProceedings{Goldberg:2007:FIP,
  author =       "Ronen Goldberg and Guy Even and Peter-Michael Seidel",
  title =        "An {FPGA} implementation of pipelined multiplicative
                 division with {IEEE} rounding",
  crossref =     "Pocek:2007:PAI",
  pages =        "185--196",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/FCCM.2007.59",
  bibdate =      "Sat Oct 9 12:43:39 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We report the results of an FPGA implementation of
                 double precision floating-point division with IEEE
                 rounding. We achieve a total latency (i.e., cycles
                 times clock period) that is 2:6 times smaller than the
                 latency of the fastest previous implementation on
                 FPGAs. The amount of hardware, on the other hand, is
                 comparable to commercial cores. The division circuit is
                 based on Goldschmidt's algorithm. All IEEE rounding
                 modes are supported and are implemented using dewpoint
                 rounding. The precision of the initial approximation of
                 the reciprocal is 14 bits. To save hardware and reduce
                 the critical path, a half-sized 62x30 Booth radix-8
                 multiplier is used. This multiplier can receive both
                 the multiplicand and the multiplier in carry-save
                 representation. The division circuit is partitioned
                 into four pipeline stages, has a latency of 11 cycles,
                 and may restart a new double precision division
                 operation after 8 cycles. Synthesis results of an
                 implementation (not including the computation of the
                 initial approximation of the reciprocal and the
                 exponent path) guarantee a clock frequency of 131 MHz
                 on an Altera Stratix II using 3592 ALMs. The
                 implementation was successfully tested with over 10
                 million random vectors as well as over a million
                 hard-to-round vectors.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hanrot:2007:WCP,
  author =       "Guillaume Hanrot and Vincent Lef{\`e}vre and Damien
                 Stehle and Paul Zimmermann",
  title =        "Worst Cases of a Periodic Function for Large
                 Arguments",
  crossref =     "Kornerup:2007:PIS",
  pages =        "133--140",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.37",
  bibdate =      "Tue Oct 9 16:32:41 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "One considers the problem of finding hard to round
                 cases of a periodic function for large floating-point
                 inputs, more precisely when the function cannot be
                 efficiently approximated by a polynomial. This is one
                 of the last few issues that prevents from guaranteeing
                 an efficient computation of correctly rounded
                 transcendentals for the whole IEEE-754 double precision
                 format. The first non-naive algorithm for that problem
                 is presented, with a heuristic complexity of O(20.676p)
                 for a precision of p bits. The efficiency of the
                 algorithm is shown on the largest IEEE-754 double
                 precision binade for the sine function, and some
                 corresponding bad cases are given. We can hope that all
                 the worst cases of the trigonometric functions in their
                 whole domain will be found within a few years, a task
                 that was considered out of reach until now.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18; correct rounding; floating-point
                 arithmetic",
}

@Article{Harrison:2007:FPV,
  author =       "J. Harrison",
  title =        "Floating-Point Verification",
  journal =      j-J-UCS,
  volume =       "13",
  number =       "5",
  pages =        "629--638",
  month =        "????",
  year =         "2007",
  CODEN =        "????",
  ISSN =         "0948-6968",
  ISSN-L =       "0948-6968",
  bibdate =      "Thu Jul 10 06:41:41 MDT 2008",
  bibsource =    "http://www.jucs.org/jucs;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.jucs.org/jucs_13_5/floating_point_verification",
  abstract =     "This paper overviews the application of formal
                 verification techniques to hardware in general, and to
                 floating-point hardware in particular. A specific
                 challenge is to connect the usual mathematical view of
                 continuous arithmetic operations with the discrete
                 world, in a credible and verifiable way.",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
}

@InProceedings{Hasenplaugh:2007:FMR,
  author =       "William Hasenplaugh and Gunnar Gaubatz and Vinodh
                 Gopal",
  title =        "Fast Modular Reduction",
  crossref =     "Kornerup:2007:PIS",
  pages =        "225--229",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.18",
  bibdate =      "Tue Oct 9 17:16:03 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "It is widely acknowledged that efficient modular
                 multiplication is a key to high-performance
                 implementation of public-key cryptography, be it
                 classical RSA, Diffie--Hellman, or (hyper-) elliptic
                 curve algorithms. In the recent decade, practitioners
                 have relied mainly on two popular methods: Montgomery
                 Multiplication and regular long-integer multiplication
                 in combination with Barrett's modular reduction
                 technique. In this paper, we propose a modification to
                 Barrett's algorithm that leads to a significant
                 reduction (25\% to 75\%) in multiplications and
                 additions.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}

@Article{Hernandez:2007:MPO,
  author =       "M. A. Hern{\'a}ndez and N. Romero",
  title =        "Methods with prefixed order for approximating square
                 roots with global and general convergence",
  journal =      j-APPL-MATH-COMP,
  volume =       "194",
  number =       "2",
  pages =        "346--353",
  day =          "15",
  month =        dec,
  year =         "2007",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Sat Jul 12 09:03:09 MDT 2008",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@InProceedings{Hilewitz:2007:PAB,
  author =       "Yedidya Hilewitz and Ruby B. Lee",
  title =        "Performing Advanced Bit Manipulations Efficiently in
                 General-Purpose Processors",
  crossref =     "Kornerup:2007:PIS",
  pages =        "251--260",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.27",
  bibdate =      "Tue Oct 9 17:16:03 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper describes a new basis for the
                 implementation of a shifter functional unit. We present
                 a design based on the inverse butterfly and butterfly
                 datapath circuits that performs the standard shift and
                 rotate operations, as well as more advanced extract,
                 deposit and mix operations found in some processors.
                 Additionally, it also supports important new classes of
                 even more advanced bit manipulation instructions
                 recently proposed: these include arbitrary bit
                 permutations, bit scatter and bit gather instructions.
                 The new functional unit's datapath is comparable in
                 latency to that of the classic barrel shifter. It
                 replaces two existing functional units --- shifter and
                 mix --- with a much more powerful one.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}

@Article{Holmes:2007:BA,
  author =       "Neville Holmes",
  title =        "Binary Arithmetic",
  journal =      j-COMPUTER,
  volume =       "40",
  number =       "6",
  pages =        "90--93",
  month =        jun,
  year =         "2007",
  CODEN =        "CPTRB4",
  DOI =          "https://doi.org/10.1109/MC.2007.196",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Fri Jun 29 14:19:11 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
  keywords =     "complete arithmetic; interval arithmetic",
}

@Article{Homann:2007:IFPa,
  author =       "Holger Homann and J{\"u}rgen Dreher and Rainer
                 Grauer",
  title =        "Impact of the floating-point precision and
                 interpolation scheme on the results of {DNS} of
                 turbulence by pseudo-spectral codes",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "22",
  month =        may,
  year =         "2007",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Published in \cite{Homann:2007:IFPb}.",
  URL =          "http://arxiv.org/abs/0705.3144",
  abstract =     "In this paper we investigate the impact of the
                 floating-point precision and interpolation scheme on
                 the results of direct numerical simulations (DNS) of
                 turbulence by pseudo-spectral codes. Three different
                 types of floating-point precision configurations show
                 no differences in the statistical results. This implies
                 that single precision computations allow for increased
                 Reynolds numbers due to the reduced amount of memory
                 needed. The interpolation scheme for obtaining velocity
                 values at particle positions has a noticeable impact on
                 the Lagrangian acceleration statistics. A tri-cubic
                 scheme results in a slightly broader acceleration
                 probability density function than a tri-linear scheme.
                 Furthermore the scaling behavior obtained by the cubic
                 interpolation scheme exhibits a tendency towards a
                 slightly increased degree of intermittency compared to
                 the linear one.",
  acknowledgement = ack-nhfb,
  subject =      "Computational Physics (physics.comp-ph); Fluid
                 Dynamics (physics.flu-dyn)",
}

@Article{Homann:2007:IFPb,
  author =       "Holger Homann and J{\"u}rgen Dreher and Rainer
                 Grauer",
  title =        "Impact of the floating-point precision and
                 interpolation scheme on the results of {DNS} of
                 turbulence by pseudo-spectral codes",
  journal =      j-COMP-PHYS-COMM,
  volume =       "177",
  number =       "7",
  pages =        "560--565",
  day =          "1",
  month =        oct,
  year =         "2007",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2007.05.019",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 23:42:25 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465507002998",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Hosangadi:2007:AMO,
  author =       "Anup Hosangadi and Farzan Fallah and Ryan Kastner",
  title =        "Algebraic Methods for Optimizing Constant
                 Multiplications in Linear Systems",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "49",
  number =       "1",
  pages =        "31--50",
  month =        oct,
  year =         "2007",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1007/s11265-007-0137-7",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Mon Nov 05 19:29:43 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Constant multiplications can be efficiently
                 implemented in hardware by converting them into a
                 sequence of nested additions and shift operations. They
                 can be optimized further by finding common
                 subexpressions among these operations. In this work, we
                 present algebraic methods for eliminating common
                 subexpressions. Algebraic techniques are established in
                 multi-level logic synthesis for the minimization of the
                 number of literals and hence gates to implement Boolean
                 logic. In this work we use the concepts of two of these
                 methods, namely rectangle covering and fast extract
                 (FX) and adapt them to the problem of optimizing linear
                 arithmetic expressions. The main advantage of using
                 such methods is that we can optimize systems consisting
                 of multiple variables, which is not possible using the
                 conventional optimization techniques. Our optimizations
                 are aimed at reducing the area and power consumption of
                 the hardware, and experimental results show up to
                 30.3\% improvement in the number of operations over
                 conventional techniques. Synthesis and simulation
                 results show up to 30\% area reduction and up to 27\%
                 power reduction. We also modified our algorithm to
                 perform delay aware optimization, where we perform
                 common subexpression elimination such that the delay is
                 not exceeded beyond a particular value.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
}

@InProceedings{Hosseinzadeh:2007:NMS,
  author =       "M. Hosseinzadeh and K. Navi and S. Gorgin",
  booktitle =    "{ICEE '07}, International Conference on Electrical
                 Engineering, 11--12 April 2007",
  title =        "A New Moduli Set for Residue Number System: $ \{ r^n -
                 2, r^n - 1, r^n \} $",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--6",
  year =         "2007",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/ICEE.2007.4287306",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "In this paper a new moduli set is for Residue Number
                 System: introduced where $r = 2k + 1$ and $k = 1, 2, 3,
                 \ldots{}$. This moduli set includes pair wise
                 relatively prime moduli, so it offers the maximum
                 possible dynamic range. For this moduli set, the
                 related circuits are simply realizable in the Multiple
                 Valued Logic (MVL) and arithmetic in this moduli set
                 enjoys very high speed operations and simple
                 reverse\slash forward conversion (RNS to MVL\slash MVL
                 to RNS).\par

                 After introducing the new moduli set, we design its
                 related circuits and converters. Finally, we compare
                 the results of those of similar moduli sets and show
                 that our moduli set significantly improves the time
                 complexity while offering greater dynamic range.",
}

@InProceedings{Huang:2007:NAM,
  author =       "Libo Huang and Li Shen and Kui Dai and Zhiying Wang",
  title =        "A New Architecture for Multiple-Precision
                 Floating-Point Multiply-Add Fused Unit Design",
  crossref =     "Kornerup:2007:PIS",
  pages =        "69--76",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.5",
  bibdate =      "Tue Oct 9 16:32:41 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The floating-point multiply-add fused (MAF) unit sets
                 a new trend in the processor design to speed up
                 floating-point performance in scientific and multimedia
                 applications. This paper proposes a new architecture
                 for the MAF unit that supports multiple IEEE precisions
                 multiply-add operation (A*B+C) with Single Instruction
                 Multiple Data (SIMD) feature. The proposed MAF unit can
                 perform either one double-precision or two parallel
                 single-precision operations using about 18\% more
                 hardware than a conventional double-precision MAF unit
                 and with 9\% increase in delay. To accommodate the
                 simultaneous computation of two single-precision MAF
                 operations, several basic modules of double-precision
                 MAF unit are redesigned. They are either segmented by
                 precision mode dependent multiplexers or attached by
                 the duplicated hardware. The proposed MAF unit can be
                 fully pipelined and the experimental results show that
                 it is suitable for processors with floating-point unit
                 (FPU).",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}

@InProceedings{Iguchi:2007:DRC,
  author =       "Yukihiro Iguchi and Tsutomu Sasao and Munehiro
                 Matsuura",
  title =        "On Designs of Radix Converters Using Arithmetic
                 Decompositions---Binary to Decimal Converters---",
  crossref =     "IEEE:2007:IPI",
  pages =        "32--32",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ISMVL.2007.39",
  bibdate =      "Thu Aug 07 17:34:11 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In digital signal processing, radixes other than two
                 are often used for high-speed computation. In the
                 computation for finance, decimal numbers are used
                 instead of binary numbers. In such cases, radix
                 converters are necessary. This paper considers design
                 methods for binary to $q$-nary converters. It
                 introduces a new design technique based on weighted-sum
                 (WS) functions. The method computes a WS function for
                 each digit by an LUT cascade and a binary adder, then
                 adds adjacent digits with $q$-nary adders. A 16-bit
                 binary to decimal converter is designed to show the
                 method.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@Article{Ihsberner:2007:REA,
  author =       "Katja Ihsberner",
  title =        "Roundoff error analysis of fast {DCT} algorithms in
                 fixed point arithmetic",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "46",
  number =       "1",
  pages =        "1--22",
  month =        sep,
  year =         "2007",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-007-9123-1",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  MRclass =      "subject classification (2000); 65T50; 65G50",
  bibdate =      "Tue Jul 8 19:14:29 MDT 2008",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=46&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=46&issue=1&spage=1",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "Discrete cosine transform; Factorization of cosine
                 matrix; Fast cosine transform; Fixed point arithmetic;
                 Numerical stability; Roundoff error",
}

@InProceedings{James:2007:QAD,
  author =       "Rekha K. James and Shahana T. K. and K. Poulose Jacob
                 and Sreela Sasi",
  title =        "Quick Addition of Decimals Using Reversible
                 Conservative Logic",
  crossref =     "IEEE:2007:API",
  pages =        "191--195",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ADCOM.2007.108",
  bibdate =      "Thu Aug 07 18:33:41 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In recent years, reversible logic has emerged as one
                 of the most important approaches for power optimization
                 with its application in low power CMOS, nanotechnology
                 and quantum computing. This research proposes quick
                 addition of decimals (QAD) suitable for multi-digit BCD
                 addition, using reversible conservative logic. The
                 design makes use of reversible fault tolerant Fredkin
                 gates only. The implementation strategy is to reduce
                 the number of levels of delay there by increasing the
                 speed, which is the most important factor for high
                 speed circuits.",
  acknowledgement = ack-nhfb,
  keywords =     "decimal arithmetic; delay reduction; fault detection;
                 reversible logic",
}

@InProceedings{Kapre:2007:OPF,
  author =       "Nachiket Kapre and Andre DeHon",
  title =        "Optimistic Parallelization of Floating-Point
                 Accumulation",
  crossref =     "Kornerup:2007:PIS",
  pages =        "205--216",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.25",
  bibdate =      "Tue Oct 9 17:16:03 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Floating-point arithmetic is notoriously
                 nonassociative due to the limited precision
                 representation which demands intermediate values be
                 rounded to fit in the available precision. The
                 resulting cyclic dependency in floating-point
                 accumulation inhibits parallelization of the
                 computation, including efficient use of pipelining. In
                 practice, however, we observe that floating-point
                 operations are ``mostly'' associative. This observation
                 can be exploited to parallelize floating-point
                 accumulation using a form of optimistic concurrency. In
                 this scheme, we first compute an optimistic associative
                 approximation to the sum and then relax the computation
                 by iteratively propagating errors until the correct sum
                 is obtained. We map this computation to a network of 16
                 statically-scheduled, pipelined, double-precision
                 floating-point adders on the Virtex-4 LX160 (-12)
                 device where each floating-point adder runs at 296MHz
                 and has a pipeline depth of 10. On this 16 PE design,
                 we demonstrate an average speedup of 6{\AA} -- with
                 randomly generated data and 3-7{\AA} --- with
                 summations extracted from Conjugate Gradient
                 benchmarks.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}

@Article{Kechagias:2007:CME,
  author =       "P. S. Kechagias and Basil K. Papadopoulos",
  title =        "Computational method to evaluate fuzzy arithmetic
                 operations",
  journal =      j-APPL-MATH-COMP,
  volume =       "185",
  number =       "1",
  pages =        "169--177",
  day =          "1",
  month =        feb,
  year =         "2007",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Sat Jul 12 09:03:01 MDT 2008",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Khabbazian:2007:DPC,
  author =       "M. Khabbazian and T. A. Gulliver and V. K. Bhargava",
  title =        "Double Point Compression with Applications to Speeding
                 Up Random Point Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "56",
  number =       "3",
  pages =        "305--313",
  month =        mar,
  year =         "2007",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2007.47",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 15:03:37 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4079514",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Knowles:2007:RSE,
  author =       "Simon Knowles",
  title =        "The Return of Silicon Efficiency",
  crossref =     "Kornerup:2007:PIS",
  pages =        "3--3",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.36",
  bibdate =      "Tue Oct 9 16:32:41 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The economic and physical forces which have always
                 shaped the business of digital chip design are again
                 evolving to change the priorities of designers. Key
                 physical trends include the end of gate oxide thickness
                 scaling, and the effect of small dopant populations on
                 threshold voltage variance. Key economic trends include
                 the need to tolerate specification shift and design
                 error, and the need to amortise chip development cost
                 over multiple market sockets.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}

@InProceedings{Kobayashi:2007:AIG,
  author =       "Katsuki Kobayashi and Naofumi Takagi and Kazuyoshi
                 Takagi",
  title =        "An Algorithm for Inversion in {$ \mathrm {GF}(2^m) $}
                 Suitable for Implementation Using a Polynomial Multiply
                 Instruction on {$ \mathrm {GF}(2) $}",
  crossref =     "Kornerup:2007:PIS",
  pages =        "105--112",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.9",
  bibdate =      "Tue Oct 9 16:32:41 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "An algorithm for inversion in $ \mathrm {GF}(2^m) $
                 suitable for implementation using a polynomial multiply
                 instruction on $ \mathrm {GF}(2) $ is proposed. It is
                 based on the extended Euclid's algorithm. In the
                 algorithm, operations corresponding to several
                 contiguous iterations of the VLSI algorithm proposed by
                 Brunner et al. is represented as a matrix. They are
                 calculated at once through the matrix efficiently by
                 means of a polynomial multiply instruction on $ \mathrm
                 {GF}(2) $. For example, in the case where the word size
                 of a processor and $m$ are $ 32 $ and $ 571 $,
                 respectively, the algorithm calculates inversion with
                 about the half number of instructions of the
                 conventional algorithm on the average.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}

@Article{Kornerup:2007:CIPa,
  author =       "Peter Kornerup and Vincent Lef{\`e}vre and Jean-Michel
                 Muller",
  title =        "Computing Integer Powers in Floating-Point
                 Arithmetic",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "30",
  month =        may,
  year =         "2007",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Published in \cite{Kornerup:2007:CIPb}.",
  URL =          "http://arxiv.org/abs/0705.4369",
  abstract =     "We introduce two algorithms for accurately evaluating
                 powers to a positive integer in floating-point
                 arithmetic, assuming a fused multiply-add (fma)
                 instruction is available. We show that our log-time
                 algorithm always produce faithfully-rounded results,
                 discuss the possibility of getting correctly rounded
                 results, and show that results correctly rounded in
                 double precision can be obtained if extended-precision
                 is available with the possibility to round into double
                 precision (with a single rounding).",
  acknowledgement = ack-nhfb,
  keywords =     "correct rounding; floating-point arithmetic",
  subject =      "Numerical Analysis (cs.NA); Mathematical Software
                 (cs.MS)",
}

@InProceedings{Kornerup:2007:CIPb,
  author =       "Peter Kornerup and Vincent Lefevre and Jean-Michel
                 Muller",
  editor =       "Michael B. Matthews",
  booktitle =    "{2007 Conference Record of the Forty-First Asilomar
                 Conference on Signals, Systems and Computers, November
                 4--7, 2007. Pacific Grove, California}",
  title =        "Computing Integer Powers in Floating-Point
                 Arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "343--347",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ACSSC.2007.4487226",
  ISBN =         "1-4244-2110-1",
  ISBN-13 =      "978-1-4244-2110-7",
  ISSN =         "1058-6393",
  ISSN-L =       "1058-6393",
  bibdate =      "Fri Sep 29 10:55:50 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We introduce two algorithms for accurately evaluating
                 powers to a positive integer in floating-point
                 arithmetic, assuming a fused multiply-add (fma)
                 instruction is available. We show that our log-time
                 algorithm always produce faithfully-rounded results,
                 discuss the possibility of getting correctly rounded
                 results, and show that results correctly rounded in
                 double precision can be obtained if extended precision
                 is available with the possibility to round into double
                 precision (with a single rounding).",
  acknowledgement = ack-nhfb,
}

@Article{Kuliamin:2007:STI,
  author =       "V. V. Kuliamin",
  title =        "Standardization and testing of implementations of
                 mathematical functions in floating point numbers",
  journal =      j-PROG-COMP-SOFT,
  volume =       "33",
  number =       "3",
  pages =        "154--173",
  year =         "2007",
  CODEN =        "PCSODA",
  DOI =          "https://doi.org/10.1134/S036176880703005X",
  ISSN =         "0361-7688 (print), 1608-3261 (electronic)",
  ISSN-L =       "0361-7688",
  bibdate =      "Fri Aug 08 09:01:30 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Requirements definition and test suites development
                 for implementations of mathematical functions in
                 floating point arithmetic in the framework of the IEEE
                 754 standard are considered. A method based on this
                 standard is proposed for defining requirements for such
                 functions. This method can be used for the
                 standardization of implementations of such functions;
                 this kind of standardization extends IEEE 754. A method
                 for designing test suites for the verification of those
                 requirements is presented. The proposed methods are
                 based on specific properties of the representation of
                 floating point numbers and on some features of the
                 functions under examination.",
  acknowledgement = ack-nhfb,
  fjournal =     "Programming and Computer Software; translation of
                 Programmirovaniye (Moscow, USSR) Plenum",
  journal-URL =  "http://link.springer.com/journal/11086",
  keywords =     "floating-point function testing and verification",
}

@Article{Lambov:2007:REI,
  author =       "Branimir Lambov",
  title =        "{RealLib}: An efficient implementation of exact real
                 arithmetic",
  journal =      "Mathematical Structures in Computer Science",
  volume =       "17",
  number =       "1",
  pages =        "81--98",
  month =        feb,
  year =         "2007",
  ISSN =         "0960-1295",
  bibdate =      "Thu Aug 07 19:25:30 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.brics.dk/~barnie/RealPractical.pdf",
  abstract =     "This paper is an introduction to the RealLib package
                 for exact real number computations. The library
                 provides certified accuracy, but tries to achieve this
                 at performance close to the performance of hardware
                 floating point for problems that do not require higher
                 precision. The paper gives the motivation and features
                 of the design of the library and compares it with other
                 packages for exact real arithmetic.",
  acknowledgement = ack-nhfb,
}

@Article{Lang:2007:RDR,
  author =       "Tomas Lang and Alberto Nannarelli",
  title =        "A Radix-10 Digit-Recurrence Division Unit: Algorithm
                 and Architecture",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "56",
  number =       "6",
  pages =        "727--739",
  month =        jun,
  year =         "2007",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2007.1038",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 15:03:39 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4167785",
  abstract =     "In this work, we present a radix-10 division unit that
                 is based on the digit-recurrence algorithm. The
                 previous decimal division designs do not include recent
                 developments in the theory and practice of this type of
                 algorithm, which were developed for radix-$ 2^k $
                 dividers. In addition to the adaptation of these
                 features, the radix-10 quotient digit is decomposed
                 into a radix-2 digit and a radix-5 digit in such a way
                 that only five and two times the divisor are required
                 in the recurrence. Moreover, the most significant slice
                 of the recurrence, which includes the selection
                 function, is implemented in radix-2, avoiding the
                 additional delay introduced by the radix--10 carry-save
                 additions and allowing the balancing of the paths to
                 reduce the cycle delay. The results of the
                 implementation of the proposed radix-10 division unit
                 show that its latency is close to that of radix-16
                 division units (comparable dynamic range of
                 significands) and it has a shorter latency than a
                 radix-10 unit based on the Newton--Raphson
                 approximation.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "algorithms and architectures for floating-point
                 arithmetic; decimal arithmetic; decimal division;
                 decimal floating-point arithmetic; digit-recurrence
                 division",
}

@InProceedings{Langlois:2007:HEF,
  author =       "Philippe Langlois and Nicolas Louvet",
  title =        "How to Ensure a Faithful Polynomial Evaluation with
                 the Compensated {Horner} Algorithm",
  crossref =     "Kornerup:2007:PIS",
  pages =        "141--149",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.21",
  bibdate =      "Tue Oct 9 16:32:41 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The compensated Horner algorithm improves the accuracy
                 of polynomial evaluation in IEEE-754 floating point
                 arithmetic: the computed result is as accurate as if it
                 was computed with the classic Horner algorithm in twice
                 the working precision. Since the condition number still
                 governs the accuracy of this computation, it may return
                 an arbitrary number of inexact digits. We address here
                 how to compute a faithfully rounded result, that is one
                 of the two floating point neighbors of the exact
                 evaluation. We propose an a priori sufficient condition
                 on the condition number to ensure that the compensated
                 evaluation is faithfully rounded. We also propose a
                 validated and dynamic method to test at the running
                 time if the compensated result is actually faithfully
                 rounded. Numerical experiments illustrate the behavior
                 of these two conditions and that the associated running
                 time over-cost is really interesting.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}

@TechReport{Langlois:2007:MIL,
  author =       "Philippe Langlois and Nicolas Louvet",
  title =        "More Instruction Level Parallelism Explains the Actual
                 Efficiency of Compensated Algorithms",
  institution =  "Laboratoire de Physique Appliqu{\'e}e et
                 d'Automatique",
  address =      "Perpignan, France",
  pages =        "11",
  year =         "2007",
  bibdate =      "Sat Apr 01 07:54:10 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://hal.archives-ouvertes.fr/hal-00165020;
                 https://hal.archives-ouvertes.fr/hal-00165020/document",
  abstract =     "The compensated Horner algorithm and the Horner
                 algorithm with double-double arithmetic improve the
                 accuracy of polynomial evaluation in IEEE-754 floating
                 point arithmetic. Both yield a polynomial evaluation as
                 accurate as if it was computed with the classic Horner
                 algorithm in twice the working precision. Both
                 algorithms also share the same low-level computation of
                 the floating point rounding errors and cost a similar
                 number of floating point operations. We report
                 numerical experiments to exhibit that the compensated
                 algorithm runs at least twice as fast as the
                 double-double one on modern processors. We propose to
                 explain such efficiency by identifying more instruction
                 level parallelism in the compensated implementation.
                 Such property also applies to other compensated
                 algorithms for summation, dot product and triangular
                 linear system solving. More generally this paper
                 illustrates how this kind of performance analysis may
                 be useful to highlight the actual efficiency of
                 numerical algorithms.",
  acknowledgement = ack-nhfb,
}

@Article{Laurie:2007:VPA,
  author =       "Dirk Laurie",
  title =        "Variable-precision arithmetic considered perilous ---
                 a detective story",
  journal =      j-ELECTRON-TRANS-NUMER-ANAL,
  volume =       "28",
  pages =        "168--173",
  year =         "2007\slash 2008",
  CODEN =        "????",
  ISSN =         "1068-9613 (print), 1097-4067 (electronic)",
  ISSN-L =       "1068-9613",
  bibdate =      "Mon Sep 6 12:28:30 MDT 2010",
  bibsource =    "http://etna.mcs.kent.edu/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Special volume for Gene Golub.",
  URL =          "http://etna.mcs.kent.edu/vol.28.2007-2008/pp168-173.dir/pp168-173.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronic Transactions on Numerical Analysis",
  journal-URL =  "http://etna.mcs.kent.edu/",
}

@TechReport{Lefevre:2007:SNP,
  author =       "Vincent Lef{\'e}vre and Jean-Michel Muller",
  title =        "Some notes on the possible under\slash overflow of the
                 most common elementary functions",
  type =         "Report",
  institution =  "LIP, {\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "Lyon, France",
  pages =        "7",
  year =         "2007",
  bibdate =      "Fri May 25 16:18:32 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://prunel.ccsd.cnrs.fr/ensl-00149414",
  abstract =     "The purpose of this short note is not to describe when
                 underflow or overflow must be signalled (it is quite
                 clear that the rules are the same as for the basic
                 arithmetic operations). We just want to show that for
                 some of the most common functions and floating-point
                 formats, in many cases, we can know in advance that the
                 results will always lie in the range of the numbers
                 that are representable by normal floating-point
                 numbers, so that in these cases there is no need to
                 worry about underflow or overflow. Note that when it is
                 not the case, an implementation is still possible using
                 a run-time test.",
  acknowledgement = ack-nhfb,
  keywords =     "elementary functions; floating-point arithmetic;
                 overflow; underflow",
}

@InProceedings{Li:2007:DDP,
  author =       "Zhaolin Li and Gongqiong Li",
  title =        "Design of a Double-Precision Floating-Point
                 Multiply-Add-Fused Unit with Consideration of Data
                 Dependence",
  crossref =     "Becker:2007:EVT",
  pages =        "492--497",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ISVLSI.2007.37",
  bibdate =      "Sun Feb 20 10:48:57 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Li:2007:DEF,
  author =       "Zhaolin Li and Gongqiong Li",
  title =        "Design of an Extended Floating-Point
                 Multiply-Add-Fused Unit for Exploiting
                 Instruction-Level Parallelism",
  crossref =     "IEEE:2007:ICI",
  pages =        "17--20",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ISICIR.2007.4441785",
  bibdate =      "Sun Feb 20 10:13:02 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper presents an extended single-precision
                 floating-point multiply-add-fused unit, called EMAF
                 unit, which is designed for exploiting
                 instruction-level parallelism. Concurrent addition and
                 multiplication instructions can be executed in parallel
                 besides traditional multiply-add-fused instructions.
                 Moreover, some other kinds of two consecutive but
                 dependent instructions can also be accelerated without
                 stalling anyone. At the same time the accuracy is also
                 increased over the traditional multiply-add-fused
                 units. The EMAF unit is implemented with three pipeline
                 stages. Experiment results show that compared with the
                 traditional multiply-add-fused unit up to 26\% cycle
                 reduction is gained at the cost of 0.1 ns time
                 penalty.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Li:2007:DFP,
  author =       "Gongqiong Li and Zhaolin Li",
  title =        "Design of a Fully Pipelined Single-Precision
                 Multiply-Add-Fused Unit",
  crossref =     "IEEE:2007:ICV",
  pages =        "318--323",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/VLSID.2007.64",
  bibdate =      "Sun Feb 20 10:15:37 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The floating point multiply-add operation A+BtimesC is
                 fundamental in many scientific and multimedia
                 applications. This paper presents a fully pipelined
                 single-precision multiply-add fused unit, which is
                 based on the combination of the final addition with
                 rounding. Normalization is performed before the final
                 addition to determine the rounding position. A
                 three-step normalization method is proposed for
                 attaining latency reduction. Moreover, this paper
                 presents a method to eliminate a one-bit error of the
                 multiply result for increasing the precision. Finally,
                 a new technique to deal with the number of 1, which is
                 added in the LSB of the operand to get 2's complement,
                 is proposed to reduce logic complexity and time delay.
                 The overall MAF unit has a latency of 5 cycles, a
                 throughput of 1 cycle, and a cycle time of 1.82 ns in
                 0.18 mum CMOS technology.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Li:2007:FAT,
  author =       "Xin Li and Marc Moreno Maza and {\'E}ric Schost",
  title =        "Fast arithmetic for triangular sets: from theory to
                 practice",
  crossref =     "Brown:2007:PIS",
  pages =        "269--276",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277548.1277585",
  bibdate =      "Fri Jun 20 08:46:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We study arithmetic operations for triangular families
                 of polynomials, concentrating on multiplication in
                 dimension zero. By a suitable extension of fast
                 univariate Euclidean division, we obtain theoretical
                 and practical improvements over a direct recursive
                 approach; for a family of special cases, we reach
                 quasi-linear complexity. The main outcome we have in
                 mind is the acceleration of higher-level algorithms, by
                 interfacing our low-level implementation with languages
                 such as AXIOM or Maple We show the potential for huge
                 speed-ups, by comparing two AXIOM implementations of
                 van Hoeij and Monagan's modular GCD algorithm.",
  acknowledgement = ack-nhfb,
  keywords =     "high-performance; multiplication; triangular set",
}

@InProceedings{Lopez:2007:EIF,
  author =       "Guillermo A. Lopez and Michela Taufer and Patricia J.
                 Teller",
  title =        "Evaluation of {IEEE 754} floating-point arithmetic
                 compliance across a wide range of heterogeneous
                 computers",
  crossref =     "Morales:2007:TRT",
  pages =        "1--4",
  year =         "2007",
  bibdate =      "Fri Aug 08 08:39:30 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Scientific applications rely heavily on floating-point
                 arithmetic and, therefore, are affected by the
                 precision and implementation of floating-point
                 operations. Although the computers we use are IEEE
                 compliant, this only assures the same representation of
                 floating-point numbers; it does not guarantee that
                 floating-point operations will be performed in the same
                 way on all computers. As a result the same program run
                 on different computers may yield different results.
                 This paper is a first step in understanding the reason
                 for this, in particular, different results for the
                 execution of the application Charmm on different
                 computers. We report on our use of a well-known test
                 suite, IeeeCC754, to evaluate IEEE 754 compliance
                 across a wide range of heterogeneous computers with
                 different architectures, operating systems, precisions,
                 and compilers.",
  acknowledgement = ack-nhfb,
}

@PhdThesis{Louvet:2007:ACA,
  author =       "Nicolas Louvet",
  title =        "Algorithmes compens{\'e}s en arithm{\'e}tique
                 flottante: pr{\'e}cision, validation, performances",
  type =         "{Docteur de l'universit{\'e} de Perpignan
                 sp{\'e}cialit{\'e}: Informatique}",
  school =       "Laboratoire ELIAUS: {\'E}lectronique, Informatique,
                 Automatique et Syst{\`e}mes, Universit{\'e} de
                 Perpignan Via Domitia",
  address =      "Perpignan, France",
  pages =        "vi + 188",
  day =          "27",
  month =        nov,
  year =         "2007",
  bibdate =      "Mon Mar 19 14:32:15 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://tel.archives-ouvertes.fr/tel-01315543/en",
  abstract =     "Rounding error may totally corrupt the result of a
                 floating point computation. How to improve and validate
                 the accuracy of a floating point computation, without
                 large computing time overheads? We consider two case
                 studies: polynomial evaluation and linear triangular
                 system solving. In both cases we use compensation of
                 the rounding errors to improve the accuracy of the
                 computed result. The contributions of this work are
                 divided into three levels. (1) Improving the accuracy.
                 We propose a compensated Horner scheme that computes
                 polynomial evaluation with the same accuracy as the
                 classic Horner algorithm performed in twice the working
                 precision. Generalizing this algorithm, we present
                 another compensated version of the Horner scheme
                 simulating $K$ times the working precision ($ K > 1$).
                 We also show how to compensate the rounding errors
                 generated by the substitution algorithm for triangular
                 system solving. (2) Validating the computed result. We
                 show how to validate the quality of the compensated
                 polynomial evaluation. We propose a method to compute
                 an ``a posteriori'' error bound together with the
                 compensated result. This error bound is computed using
                 only basic floating point operations, which ensures
                 portability and efficiency of the method. (3)
                 Performances of compensated algorithms. Our computing
                 time measures show the interest of compensated
                 algorithms compared to other software solutions that
                 provide the same output accuracy. We also justify good
                 practical performances of compensated algorithms thanks
                 to a detailed study of the instruction-level
                 parallelism they contain.",
  acknowledgement = ack-nhfb,
  keywords =     "compensated algorithms; Computer arithmetic; efficient
                 algorithms; IEEE-754 standard; numerical algorithms",
}

@Misc{Lundvall:2007:CDF,
  author =       "Shawn D. Lundvall and Eric M. Schwarz and Ronald M.
                 {Smith, Sr.} and Phil C. Yeh",
  title =        "Composition of decimal floating point data, and
                 methods therefor",
  howpublished = "US Patent 8060545B2.",
  day =          "26",
  month =        apr,
  year =         "2007",
  bibdate =      "Thu Mar 15 09:28:54 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://patents.google.com/patent/US8060545",
  abstract =     "A decimal floating point finite number in a decimal
                 floating point format is composed from the number in a
                 different format. A decimal floating point format
                 includes fields to hold information relating to the
                 sign, exponent and significand of the decimal floating
                 point finite number. Other decimal floating point data,
                 including infinities and NaNs (not a number), are also
                 composed. Decimal floating point data are also
                 decomposed from the decimal floating point format to a
                 different format.",
  acknowledgement = ack-nhfb,
}

@Misc{Lundvall:2007:DDF,
  author =       "Shawn D. Lundvall and Eric M. Schwarz and Ronald M.
                 {Smith, Sr.} and Phil C. Yeh",
  title =        "Decomposition of decimal floating point data",
  howpublished = "US Patent 9690580B2.",
  day =          "26",
  month =        apr,
  year =         "2007",
  bibdate =      "Thu Mar 15 09:31:05 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://patents.google.com/patent/US9690580B2/en",
  abstract =     "A decimal floating point finite number in a decimal
                 floating point format is composed from the number in a
                 different format. A decimal floating point format
                 includes fields to hold information relating to the
                 sign, exponent and significand of the decimal floating
                 point finite number. Other decimal floating point data,
                 including infinities and NaNs (not a number), are also
                 composed. Decimal floating point data are also
                 decomposed from the decimal floating point format to a
                 different format.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Maslennikow:2007:DFB,
  author =       "Oleg Maslennikow and Natalia Maslennikowa and
                 Magdalena Rajewska and Dariusz Gretkowski and
                 Jean-Pierre Lienou",
  booktitle =    "{CADSM '07}. 9th International Conference --- The
                 Experience of Designing and Applications of {CAD}
                 Systems in Microelectronics",
  title =        "Design of {FPGA}-based Residue Number System
                 Converters for Digital Signal Processing Systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "194--201",
  year =         "2007",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/CADSM.2007.4297523",
  ISSN =         "????",
  bibdate =      "Fri Nov 9 11:38:59 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "residue arithmetic; residue number system",
  summary =      "In this paper, two new and simple structures of the
                 q-operands multi-operand modular adder have been
                 proposed, which are adapted to realization in the
                 Xilinx FPGA devices. The main purpose of new MOMA
                 designs has been the reduction of hardware \ldots{}",
}

@Article{Melquiond:2007:FCF,
  author =       "Guillaume Melquiond and Sylvain Pion",
  title =        "Formally certified floating-point filters for
                 homogeneous geometric predicates",
  journal =      j-INFORM-THEOR-APPL,
  volume =       "41",
  number =       "1",
  pages =        "57--69",
  year =         "2007",
  CODEN =        "RSITD7, RITAE4",
  DOI =          "https://doi.org/10.1051/ita:2007005",
  ISSN =         "0988-3754 (print), 1290-385X (electronic)",
  ISSN-L =       "0988-3754",
  MRclass =      "68U05 (65G50)",
  MRnumber =     "MR2330043",
  bibdate =      "Thu Nov 08 19:16:32 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Informatics and Applications. Informatique
                 Th{\'e}orique et Applications",
}

@Article{Mine:2007:RAD,
  author =       "Antoine Min{\'e}",
  title =        "Relational Abstract Domains for the Detection of
                 Floating-Point Run-Time Errors",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "15",
  month =        mar,
  year =         "2007",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Published in European Symposium on Programming (ESOP)
                 (03/2004) 3--17.",
  URL =          "http://arxiv.org/abs/cs/0703077",
  abstract =     "We present a new idea to adapt relational abstract
                 domains to the analysis of IEEE 754-compliant
                 floating-point numbers in order to statically detect,
                 through abstract Interpretation-based static analyses,
                 potential floating-point run-time exceptions such as
                 overflows or invalid operations. In order to take the
                 non-linearity of rounding into account, expressions are
                 modeled as linear forms with interval coefficients. We
                 show how to extend already existing numerical abstract
                 domains, such as the octagon abstract domain, to
                 efficiently abstract transfer functions based on
                 interval linear forms. We discuss specific fixpoint
                 stabilization techniques and give some experimental
                 results.",
  acknowledgement = ack-nhfb,
  subject =      "Programming Languages (cs.PL)",
}

@TechReport{Mitchell:2007:MFP,
  author =       "D. Mitchell and S. Noble",
  title =        "Multiprecision floating-point arithmetic on {Apple}
                 systems",
  type =         "Report",
  institution =  "Advanced Computation Group, Apple Computer",
  address =      "Cupertino, CA, USA",
  pages =        "23",
  day =          "13",
  month =        mar,
  year =         "2007",
  bibdate =      "Tue Mar 19 10:22:50 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://images.apple.com/acg/pdf/MP_Floating_Point_20070313.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARPREC; GMP",
}

@Article{Miyajima:2007:ETS,
  author =       "Shinya Miyajima and Masahide Kashiwagi",
  title =        "Existence test for solution of nonlinear systems
                 applying affine arithmetic",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "199",
  number =       "2",
  pages =        "304--309",
  day =          "15",
  month =        feb,
  year =         "2007",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:12:04 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037704270500765X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Monniaux:2007:AZT,
  author =       "David Monniaux",
  title =        "Applying the {$Z$}-transform for the static analysis
                 of floating-point numerical filters",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "2",
  month =        jun,
  year =         "2007",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/0706.0252",
  abstract =     "Digital linear filters are used in a variety of
                 applications (sound treatment, control/command, etc.),
                 implemented in software, in hardware, or a combination
                 thereof. For safety-critical applications, it is
                 necessary to bound all variables and outputs of all
                 filters. We give a compositional, effective abstraction
                 for digital linear filters expressed as block diagrams,
                 yielding sound, precise bounds for fixed-point or
                 floating-point implementations of the filters.",
  acknowledgement = ack-nhfb,
  subject =      "Programming Languages (cs.PL); Numerical Analysis
                 (cs.NA)",
}

@TechReport{Monniaux:2007:PVFa,
  author =       "David Monniaux",
  title =        "The pitfalls of verifying floating-point
                 computations",
  type =         "Technical report",
  number =       "HAL-00128124",
  institution =  "CNRS\slash {\'E}cole Normale Sup{\'e}rieure",
  address =      "45, rue d'Ulm 75230 Paris cedex 5, France",
  pages =        "44",
  day =          "29",
  month =        jun,
  year =         "2007",
  bibdate =      "Fri Jul 06 18:10:00 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Published in \cite{Monniaux:2008:PVF}.",
  URL =          "http://hal.archives-ouvertes.fr/docs/00/15/88/63/PDF/floating-point.pdf",
  abstract =     "Current critical systems often use a lot of
                 floating-point computations, and thus the testing or
                 static analysis of programs containing floating-point
                 operators has become a priority. However, correctly
                 defining the semantics of common implementations of
                 floating-point is tricky, because semantics may change
                 according to many factors beyond source-code level,
                 such as choices made by compilers. We here give
                 concrete examples of problems that can appear and
                 solutions for implementing in analysis software",
  acknowledgement = ack-nhfb,
}

@Article{Monniaux:2007:PVFb,
  author =       "David Monniaux",
  title =        "The pitfalls of verifying floating-point
                 computations",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "30",
  month =        jan,
  year =         "2007",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Published in \cite{Monniaux:2008:PVF}.",
  URL =          "http://arxiv.org/abs/cs/0701192",
  abstract =     "Current critical systems commonly use a lot of
                 floating-point computations, and thus the testing or
                 static analysis of programs containing floating-point
                 operators has become a priority. However, correctly
                 defining the semantics of common implementations of
                 floating-point is tricky, because semantics may change
                 with many factors beyond source-code level, such as
                 choices made by compilers. We here give concrete
                 examples of problems that can appear and solutions to
                 implement in analysis software.",
  acknowledgement = ack-nhfb,
  subject =      "Programming Languages (cs.PL); Numerical Analysis
                 (cs.NA)",
}

@Article{Montuschi:2007:DDA,
  author =       "P. Montuschi and J. D. Bruguera and L. Ciminiera and
                 J.-A. Pieiro",
  title =        "A Digit-by-Digit Algorithm for $m$ th Root
                 Extraction",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "56",
  number =       "12",
  pages =        "1696--1706",
  month =        dec,
  year =         "2007",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2007.70764",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 15:03:43 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4358221",
  abstract =     "A general digit-recurrence algorithm for the
                 computation of the $m$ th root (with an $m$ integer) is
                 presented in this paper. Based on the concept of
                 completing the mth root, a detailed analysis of the
                 convergence conditions is performed and iteration-
                 independent digit-selection rules are obtained for any
                 radix and redundant digit set. A radix-2 version for
                 mth rooting is also studied, together with closed
                 formulas for both the digit selection rules and the
                 number of bits required to perform correct
                 selections.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Muller-Olm:2007:AMA,
  author =       "Markus M{\"u}ller-Olm and Helmut Seidl",
  title =        "Analysis of modular arithmetic",
  journal =      j-TOPLAS,
  volume =       "29",
  number =       "5",
  pages =        "29:1--29:27",
  month =        aug,
  year =         "2007",
  CODEN =        "ATPSDT",
  DOI =          "https://doi.org/10.1145/1275497.1275504",
  ISSN =         "0164-0925 (print), 1558-4593 (electronic)",
  ISSN-L =       "0164-0925",
  bibdate =      "Wed Jun 11 19:22:40 MDT 2008",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toplas/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We consider integer arithmetic modulo a power of 2 as
                 provided by mainstream programming languages like Java
                 or standard implementations of C. The difficulty here
                 is that, for $ w > 1 $, the ring $ Z_m $ of integers
                 modulo $ m = 2^w $ has zero divisors and thus cannot be
                 embedded into a field. Not withstanding that, we
                 present intra- and interprocedural algorithms for
                 inferring for every program point u affine relations
                 between program variables valid at $u$. If conditional
                 branching is replaced with nondeterministic branching,
                 our algorithms are not only sound but also complete in
                 that they detect all valid affine relations in a
                 natural class of programs. Moreover, they run in time
                 linear in the program size and polynomial in the number
                 of program variables and can be implemented by using
                 the same modular integer arithmetic as the target
                 language to be analyzed. We also indicate how our
                 analysis can be extended to deal with equality guards,
                 even in an interprocedural setting.",
  acknowledgement = ack-nhfb,
  articleno =    "29",
  fjournal =     "ACM Transactions on Programming Languages and
                 Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J783",
}

@Article{Nikmehr:2007:FRF,
  author =       "Hooman Nikmehr and Braden Phillips and Cheng-Chew
                 Lim",
  title =        "A Fast Radix-4 Floating-Point Divider with Quotient
                 Digit Selection by Comparison Multiples",
  journal =      j-COMP-J,
  volume =       "50",
  number =       "1",
  pages =        "81--92",
  month =        jan,
  year =         "2007",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/bxl048",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Wed Apr 28 14:33:32 MDT 2010",
  bibsource =    "http://comjnl.oxfordjournals.org/content/vol50/issue1/index.dtl;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/cgi/content/abstract/50/1/81;
                 http://comjnl.oxfordjournals.org/cgi/content/full/50/1/81;
                 http://comjnl.oxfordjournals.org/cgi/reprint/50/1/81",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@InProceedings{Osborne:2007:AAG,
  author =       "W. Osborne and R. Cheung and J. Coutinho and W. Luk
                 and O. Mencer",
  title =        "Automatic accuracy-guaranteed bit-width optimization
                 for fixed and floating-point systems",
  crossref =     "Bertels:2007:PIC",
  pages =        "617--620",
  year =         "2007",
  bibdate =      "Thu Mar 24 20:53:04 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=4380601",
  acknowledgement = ack-nhfb,
}

@TechReport{Pan:2007:EFS,
  author =       "V. Y. Pan and B. Murphy and G. Qian and R. E.
                 Rosholt",
  title =        "Error-free summations via floating-point operations",
  type =         "Report",
  number =       "2007010 and 2007013",
  institution =  "CUNY Ph.D. Program in Computer Science, Graduate
                 Center, City University of New York",
  address =      "New York, NY, USA",
  year =         "2007",
  bibdate =      "Mon Mar 06 17:24:08 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Pan:2007:SAS,
  author =       "V. Y. Pan and B. Murphy and R. E. Rosholt and M.
                 Tabanjeh",
  editor =       "Jan Verschelde and Stephen M. Watt",
  booktitle =    "{SNC'07: proceedings of the 2007 International
                 Workshop on Symbolic--Numeric Computation, London
                 (Ontario, Canada), July 25--27, 2007}",
  title =        "The {Schur} aggregation for solving linear systems of
                 equations",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  bookpages =    "viii + 299",
  pages =        "142--151",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1277500.1277522",
  ISBN =         "1-59593-744-7 (paperback)",
  ISBN-13 =      "978-1-59593-744-5 (paperback)",
  LCCN =         "QA9.59 .S53 2007",
  bibdate =      "Mon Mar 06 17:26:18 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  abstract =     "According to our previous theoretical and experimental
                 study, additive preconditioners can be readily computed
                 for ill conditioned matrices, but application of such
                 preconditioners to facilitating matrix computations is
                 not straight-forward. In the present paper we develop
                 some nontrivial techniques for this task.They enabled
                 us to confine the original numerical problems to the
                 computation of the Schur aggregates of smaller sizes.
                 We overcome these problems by extending the Wilkinson's
                 iterative refinement and applying some advanced
                 semi-symbolic algorithms for multiplication and
                 summation.In particular with these techniques we
                 control precision throughout our computations.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation; Additive
                 preconditioning; Determinants; Iterative refinement;
                 Linear systems of equations; Sherman Morrison Woodbury
                 formula",
  subject =      "Computable functions; Data processing; Congresses;
                 Numerical analysis; Logic, Symbolic and mathematical",
}

@Article{Patel:2007:FMA,
  author =       "R. A. Patel and M. Benaissa and S. Boussakta",
  title =        "Fast Modulo $ 2^n - (2^{n - 2} + 1) $ Addition: a New
                 Class of Adder for {RNS}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "56",
  number =       "4",
  pages =        "572--576",
  month =        apr,
  year =         "2007",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2007.1001",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 15:03:38 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4118680",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "residue number system (RNS)",
}

@InProceedings{Patil:2007:REE,
  author =       "Dinesh Patil and Omid Azizi and Mark Horowitz and Ron
                 Ho and Rajesh Ananthraman",
  title =        "Robust Energy-Efficient Adder Topologies",
  crossref =     "Kornerup:2007:PIS",
  pages =        "16--28",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.31",
  bibdate =      "Tue Oct 9 16:32:41 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this paper we explore the relationship between
                 adder topology and energy efficiency. We compare the
                 energy-delay tradeoff curves of selected 32-bit adder
                 topologies, to determine how architectural features and
                 design techniques affect energy efficiency. Optimizing
                 different adders for the supply and threshold voltages,
                 and transistor sizing, we show that topologies with the
                 least number of logic stages having an average fanin of
                 two per stage, and fewest wires are most energy
                 efficient. While a design with fully custom sizes can
                 be extremely tedious to layout, we show that custom
                 sizing can be used as a guide to group different gates
                 in the design, resulting in a manageable layout
                 overhead without significant loss of energy
                 efficiency.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}

@Article{Pearce:2007:MLH,
  author =       "Roman Pearce and Michael Monagan",
  title =        "A {Maple} library for high performance sparse
                 polynomial arithmetic",
  journal =      j-ACM-COMM-COMP-ALGEBRA,
  volume =       "41",
  number =       "3",
  pages =        "110--111",
  month =        sep,
  year =         "2007",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/1358190.1358203",
  ISSN =         "1932-2232 (print), 1932-2240 (electronic)",
  ISSN-L =       "1932-2232",
  bibdate =      "Wed Jun 18 09:23:01 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We have developed a library for sparse polynomial
                 arithmetic to supplement Maple's internal routines.
                 Along the way we identified three common sources of
                 inefficiency in existing implementations.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Communications in Computer Algebra",
  issue =        "161",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}

@Article{Rauh:2007:ROI,
  author =       "Andreas Rauh and Marco Kletting and Harald Aschemann
                 and Eberhard P. Hofer",
  title =        "Reduction of overestimation in interval arithmetic
                 simulation of biological wastewater treatment
                 processes",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "199",
  number =       "2",
  pages =        "207--212",
  day =          "15",
  month =        feb,
  year =         "2007",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:12:04 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2005.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042705007521",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Saldamli:2007:SME,
  author =       "Gokay Saldamli and Cetin K. Koc",
  title =        "Spectral Modular Exponentiation",
  crossref =     "Kornerup:2007:PIS",
  pages =        "123--132",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.34",
  bibdate =      "Tue Oct 9 16:32:41 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We describe a new method to perform the modular
                 exponentiation operation, i.e., the computation of $ c
                 = m e \bmod n $, where $c$, $m$, $e$ and $n$ are large
                 integers. The new method uses the discrete Fourier
                 transform over a finite ring, and relies on new
                 techniques to perform multiplication and reduction
                 operations. The method yields efficient and highly
                 parallel architectures for hardware realizations of
                 public-key cryptosystems requiring the modular
                 exponentiation as the core computation, such as the RSA
                 and Diffie--Hellman algorithms.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}

@Article{Saqib:2007:CAI,
  author =       "Nazar Abbas Saqib",
  title =        "Complexity Analysis for 4-Input\slash 1-Output {FPGAs}
                 Applied to Multiplier Designs",
  journal =      j-SCPE,
  volume =       "8",
  number =       "4",
  pages =        "411--422",
  month =        dec,
  year =         "2007",
  CODEN =        "????",
  ISSN =         "1895-1767",
  bibdate =      "Thu Sep 2 11:55:11 MDT 2010",
  bibsource =    "http://www.scpe.org/content/8/4.toc;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.scpe.org/vols/vol08/no4/SCPE_8_4_07.pdf;
                 http://www.scpe.org/vols/vol08/no4/SCPE_8_4_07.zip",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.scpe.org/",
}

@InProceedings{Schulte:2007:FPD,
  author =       "M. J. Schulte and D. Tan and C. E. Lemonds",
  editor =       "{IEEE}",
  booktitle =    "Proceedings of the 25th {IEEE} International
                 Conference on Computer Design: {7--10 October 2007}",
  title =        "Floating-Point Division Algorithms for an x86
                 Microprocessor with a Rectangular Multiplier",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "304--310",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ICCD.2007.4601917",
  bibdate =      "Sun Dec 10 14:03:42 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Floating-point division is an important operation in
                 scientific computing and multimedia applications. This
                 paper presents and compares two division algorithms for
                 an x86 microprocessor, which utilizes a rectangular
                 multiplier that is optimized for multimedia
                 applications. The proposed division algorithms are
                 based on Goldschmidt's division algorithm and provide
                 correctly rounded results for IEEE 754 single, double,
                 and extended precision floating-point numbers. Compared
                 to a previous Goldschmidt division algorithm, the
                 fastest proposed algorithm requires 25\% to 37\% fewer
                 cycles, while utilizing a multiplier that is roughly
                 2.5 times smaller.",
  acknowledgement = ack-nhfb,
}

@Article{Scott:2007:NHC,
  author =       "N. S. Scott and F. J{\'e}z{\'e}quel and C. Denis and
                 J.-M. Chesneaux",
  title =        "Numerical `health check' for scientific codes: the
                 {CADNA} approach",
  journal =      j-COMP-PHYS-COMM,
  volume =       "176",
  number =       "8",
  pages =        "507--521",
  day =          "15",
  month =        apr,
  year =         "2007",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2007.01.005",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 23:42:15 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465507000331",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@InProceedings{Shams:2007:EHA,
  author =       "R. Shams and R. Kennedy",
  editor =       "????",
  booktitle =    "{Proceedings of the International Conference on Signal
                 Processing and Communications Systems (ICSPCS), Gold
                 Coast, Australia, 2007}",
  title =        "Efficient histogram algorithms for {NVIDIA CUDA}
                 compatible devices",
  publisher =    "????",
  address =      "????",
  pages =        "418--422",
  year =         "2007",
  bibdate =      "Sat Oct 31 07:03:20 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Shpilka:2007:IDA,
  author =       "Amir Shpilka",
  title =        "Interpolation of depth-3 arithmetic circuits with two
                 multiplication gates",
  crossref =     "ACM:2007:SPA",
  pages =        "284--293",
  year =         "2007",
  DOI =          "https://doi.org/10.1145/1250790.1250833",
  bibdate =      "Fri Jun 20 18:28:53 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "arithmetic circuits; depth-3; exact learning;
                 interpolation",
}

@InProceedings{Sousa:2007:EMM,
  author =       "Leonel Sousa",
  title =        "Efficient Method for Magnitude Comparison in {RNS}
                 Based on Two Pairs of Conjugate Moduli",
  crossref =     "Kornerup:2007:PIS",
  pages =        "240--250",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.16",
  bibdate =      "Tue Oct 9 17:16:03 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The non-positional nature of Residue Number Systems
                 (RNS) is very useful to achieve carry free arithmetic.
                 However it makes the comparison of numbers more
                 difficult than in the traditional weighted number
                 systems: there is no any efficient general method for
                 magnitude comparison in RNS. Moreover, magnitude
                 comparison for RNS that rely on pairs of conjugate
                 moduli, which are not relatively prime moduli sets
                 recently proposed because of the large dynamic ranges
                 and the simplicity of the arithmetic units, is a new
                 unsolved problem. In this paper an efficient method and
                 a VLSI architecture is proposed for magnitude
                 comparison in RNS based on sets formed by two pairs of
                 conjugate moduli. This proposed method is much more
                 efficient than the other known ones and is the only one
                 valid for moduli sets not formed by relatively prime
                 integers. The method has been applied to design a very
                 fast Sum-of-Absolute Differences (SAD) unit for motion
                 estimation in video sequences that performs the
                 function entirely within the RNS channels. Experimental
                 results show that this new SAD unit, implemented in the
                 internal memory blocks of the xc2vp50-7 FPGA, is
                 capable of achieving the high throughput required to
                 perform real-time motion estimation in high resolution
                 images.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}

@Misc{Steele:2007:CSP,
  author =       "Guy L. {Steele Jr.}",
  title =        "Circuit for selectively providing maximum or minimum
                 of a pair of floating point operands",
  howpublished = "US Patent 7228324",
  day =          "05",
  month =        jun,
  year =         "2007",
  bibdate =      "Tue Dec 23 15:06:47 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/7228324/fulltext.html",
  abstract =     "A floating point max/min circuit for determining the
                 maximum or minimum of two floating point operands
                 includes a first analysis circuit configured to
                 determine a format of a first floating point operand of
                 the two floating point operands based upon floating
                 point tatus information encoded within the first
                 floating point operand, a second analysis circuit
                 configured to determine a format of a second floating
                 point operand of the two floating point operands based
                 upon floating point status information encoded within
                 the second floating point operand, a decision circuit,
                 coupled to the first analysis circuit and to the second
                 analysis circuit and responding to a function control
                 signal that indicates the threshold condition is one of
                 a maximum of the two floating point operands and a
                 minimum of the two floating point operands, for
                 generating at least one assembly control signal based
                 on the format of a first floating point operand, the
                 format of a second floating point operand, and the
                 function control signal, and a result assembler
                 circuit, coupled to the decision circuit, for producing
                 a result indicating which of the first floating point
                 operand and the second floating point operand meet the
                 threshold condition, based on the at least one assembly
                 control signal. The format of the floating point
                 operands may be from a group comprising: not-a-number
                 (NaN), positive infinity, negative infinity,
                 normalized, denormalized, positive overflow, negative
                 overflow, positive underflow, negative underflow,
                 inexact, exact, division by zero, invalid operation,
                 positive zero, and negative zero. The result produced
                 may be a third floating point operand having encoded
                 floating point status information, and at least part of
                 the encoded floating point status information in the
                 result may come from either the first floating point
                 operand or the second floating point operand.",
  acknowledgement = ack-nhfb,
}

@Misc{Steele:2007:CUC,
  author =       "Guy L. {Steele Jr.}",
  title =        "Comparator unit for comparing values of floating point
                 operands",
  howpublished = "US Patent 7191202",
  day =          "13",
  month =        mar,
  year =         "2007",
  bibdate =      "Tue Dec 23 15:06:47 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/7191202/fulltext.html",
  abstract =     "A floating point comparator circuit for comparing a
                 plurality of floating point operands includes a
                 plurality of analysis circuits, one for each of the
                 floating point operands, configured to determine a
                 format of each of the floating point operands based
                 upon floating point status information encoded within
                 each of the floating point operands, and a result
                 generator circuit coupled to the analysis circuits, the
                 result generator circuit configured to generate a
                 result signal based on the format determined by each
                 analysis circuit and based on a comparative
                 relationship among the floating point operands. The
                 format of each of the floating point operands may be
                 from a group including: not-a-number (NaN), infinity,
                 normalized, denormalized, zero, invalid operation,
                 overflow, underflow, division by zero, exact, and
                 inexact. The result generator circuit may ignore the
                 encoded floating point statuses of the plurality of
                 floating point operands when comparing just the
                 magnitudes of the plurality of floating point
                 operands.",
  acknowledgement = ack-nhfb,
}

@Misc{Steele:2007:MSCa,
  author =       "Guy L. {Steele Jr.}",
  title =        "Methods and systems for computing the quotient of
                 floating-point intervals",
  howpublished = "US Patent 7236999",
  day =          "26",
  month =        jun,
  year =         "2007",
  bibdate =      "Tue Dec 23 15:06:47 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/7236999/fulltext.html",
  abstract =     "Computing an output interval includes producing a
                 first result from a conditional selection using a first
                 operand, a second operand, and a third operand, the
                 operands respectively including a second input interval
                 upper-point, a first input interval upper-point, and a
                 first input interval lower-point. Next, computing an
                 output interval includes producing a second result from
                 the conditional selection, the operands respectively
                 including a second input interval upper-point, the
                 first input interval upper-point, and the first input
                 interval lower-point. Furthermore, computing an output
                 interval includes producing a third result from a
                 conditional division using the first operand, the
                 second operand, and the third operand, the operands
                 respectively including the first result, the second
                 input interval upper-point, and the second input
                 interval lower-point. And finally, a fourth result is
                 produced from the conditional division, the operands
                 respectively including the second result, the second
                 input interval lower-point, and the second input
                 interval upper-point.",
  acknowledgement = ack-nhfb,
}

@Misc{Steele:2007:MSCb,
  author =       "Guy L. {Steele Jr.}",
  title =        "Methods and systems for computing floating-point
                 intervals",
  howpublished = "US Patent 7219117",
  day =          "15",
  month =        may,
  year =         "2007",
  bibdate =      "Tue Dec 23 15:06:47 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/7219117/fulltext.html",
  abstract =     "Computing an output interval includes producing a
                 first product resulting from a conditional
                 multiplication using a first operand, a second operand,
                 and a third operand. Next a second product is produced
                 resulting from the conditional multiplication using the
                 first operand, the second operand, and the third
                 operand. Then a third product is produced resulting
                 from the conditional multiplication using the first
                 operand, the second operand, and the third operand.
                 Next a fourth product is produced resulting from the
                 conditional multiplication using the first operand, the
                 second operand, and the third operand. And finally, the
                 output interval is produced including an output
                 interval lower-point and an output interval
                 upper-point, the output interval lower-point being the
                 minimum of the first product and the third product, and
                 the output interval upper-point being the maximum of
                 the second product and the fourth product.",
  acknowledgement = ack-nhfb,
}

@Article{Stern:2007:MLA,
  author =       "Richard Stern",
  title =        "Micro Law: Antitrust Division Gives {IEEE Standard}
                 Setters the Okay to Ask Patentees How {RAND} They Are",
  journal =      j-IEEE-MICRO,
  volume =       "27",
  number =       "3",
  pages =        "106--109",
  month =        may # "\slash " # jun,
  year =         "2007",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.2007.47",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Wed Jul 2 21:58:03 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}

@Article{Stoutemyer:2007:UCN,
  author =       "David R. Stoutemyer",
  title =        "Useful Computations Need Useful Numbers",
  journal =      j-ACM-COMM-COMP-ALGEBRA,
  volume =       "41",
  number =       "3",
  pages =        "75--99",
  month =        sep,
  year =         "2007",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/1358190.1358192",
  ISSN =         "1932-2232 (print), 1932-2240 (electronic)",
  ISSN-L =       "1932-2232",
  bibdate =      "Wed Jun 18 09:23:01 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Most of us have taken the exact rational and
                 approximate numbers in our computer algebra systems for
                 granted for a long time, not thinking to ask if they
                 could be significantly better. With exact rational
                 arithmetic and adjustable-precision floating-point
                 arithmetic to precision limited only by the total
                 computer memory or our patience, what more could we
                 want for such numbers? It turns out that there is much
                 more that can be done that permits us to obtain exact
                 results more often, more intelligible results,
                 approximate results guaranteed to have requested error
                 bounds, and recovery of exact results from approximate
                 ones.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Communications in Computer Algebra",
  issue =        "161",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
  keywords =     "interval arithmetic",
}

@Article{Swartzlander:2007:NTC,
  author =       "Earl E. {Swartzlander, Jr.}",
  title =        "The Negative Two's Complement Number System",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "49",
  number =       "1",
  pages =        "177--183",
  month =        oct,
  year =         "2007",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1007/s11265-007-0052-y",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Mon Nov 05 19:26:21 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The two's complement fractional fixed-point number
                 system is widely used to implement digital signal
                 processing on VLSI chips. It has a range of values from
                 $ - 1 $ to one least significant bit below +1. Either
                 the multiplication of $ - 1 $ - $ - 1 $ or taking the
                 absolute value of $ - 1 $ produces a result ($ + 1 $)
                 that cannot be represented. A new system, the negative
                 two's complement number system, is described here that
                 has a range of one least significant bit above $ - 1 $
                 to $ + 1 $ which eliminates the problem. This paper
                 presents the new number system and describes algorithms
                 for the basic arithmetic operations.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
  xxnote =       "Check math in abstract??",
}

@InProceedings{Tang:2007:MMU,
  author =       "Ping Tak Peter Tang",
  title =        "Modular Multiplication using Redundant Digit
                 Division",
  crossref =     "Kornerup:2007:PIS",
  pages =        "217--224",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.22",
  bibdate =      "Tue Oct 9 17:16:03 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Most implementations of the modular exponentiation, $
                 M E \bmod N $, computation in cryptographic algorithms
                 employ Montgomery multiplication, $ (A B R - 1) \bmod N
                 $, instead of modular multiplication, $ A B \bmod N $,
                 even the former requires some transformational
                 overheads. This is so because a state-of-the-art
                 Montgomery multiplication implementation has a
                 performance advantage over direct modular
                 multiplication based on the Barrett algorithm that more
                 than compensates for the overhead. In this paper, we
                 present a direct modular multiplication method that is
                 comparable in speed to Montgomery multiplication. One
                 consequence is that when the exponent in small, direct
                 computation (which does not incur the transformational
                 overhead) using the modular multiplication algorithm
                 presented here results in practical performance gain.
                 For the exponent 17, for instance, which requires five
                 modular multiplication, a saving of up to 40\% can be
                 achieved.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}

@Article{Thapliyal:2007:CIV,
  author =       "Himanshu Thapliyal and Hamid R. Arabnia and Rajnish
                 Bajpai and Kamal K. Sharma",
  title =        "Combined Integer and Variable Precision ({CIVP})
                 Floating Point Multiplication Architecture for
                 {FPGAs}",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "16",
  month =        nov,
  year =         "2007",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/0711.2671",
  abstract =     "In this paper, we propose an architecture/methodology
                 for making FPGAs suitable for integer as well as
                 variable precision floating point multiplication. The
                 proposed work will of great importance in applications
                 which requires variable precision floating point
                 multiplication such as multi-media processing
                 applications. In the proposed architecture/methodology,
                 we propose the replacement of existing 18x18 bit and
                 25x18 bit dedicated multipliers in FPGAs with dedicated
                 24x24 bit and 24x9 bit multipliers, respectively. We
                 have proved that our approach of providing the
                 dedicated 24x24 bit and 24x9 bit multipliers in FPGAs
                 will make them efficient for performing integer as well
                 as single precision, double precision, and Quadruple
                 precision floating point multiplications.",
  acknowledgement = ack-nhfb,
  subject =      "Hardware Architecture (cs.AR)",
}

@InProceedings{Trong:2007:PBF,
  author =       "Son Dao Trong and Martin Schmookler and Eric. M.
                 Schwarz and Michael Kroener",
  title =        "{P6} Binary Floating-Point Unit",
  crossref =     "Kornerup:2007:PIS",
  pages =        "77--86",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.26",
  bibdate =      "Tue Oct 9 16:32:41 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The floating point unit of the next generation PowerPC
                 is detailed. It has been tested at over 5 GHz. The
                 design supports an extremely aggressive cycle time of
                 13 FO4 using a technology independent measure. For most
                 dependent instructions, its fused multiply-add dataflow
                 has only 6 effective pipeline stages. This is nearly
                 equivalent to its predecessor, the Power 5, even though
                 its technology independent frequency has increased over
                 70\%. Overall the frequency has improved over 100\%. It
                 achieves this high performance through aggressive
                 feedback paths, circuit design and layout. The pipeline
                 has 7 stages but data may be fed back to dependent
                 operations prior to rounding and complete
                 normalization. Division and square root algorithms are
                 also described which take advantage of high-precision
                 linear approximation hardware for obtaining a
                 reciprocal or reciprocal square root approximation",
  acknowledgement = ack-nhfb,
  keywords =     "aggressive data forwarding; ARITH-18; data processing
                 without stalls; denormal result handling;
                 floating-point unit; high-frequency design",
}

@InProceedings{Tsen:2007:HDBa,
  author =       "C. Tsen and S. Gonzalez-Navarro and M. Schulte",
  title =        "Hardware Design of a Binary Integer Decimal-based
                 Floating-point Adder",
  crossref =     "IEEE:2007:ICC",
  pages =        "288--295",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ICCD.2007.4601915",
  bibdate =      "Sat Dec 04 10:20:58 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Because of the growing importance of decimal
                 floating-point (DFP) arithmetic, specifications for it
                 are included in the IEEE Draft Standard for
                 Floating-point Arithmetic (IEEE P754). In this paper,
                 we present a novel algorithm and hardware design for a
                 DFP adder. The adder performs addition and subtraction
                 on 64-bit operands that use the IEEE P754 binary
                 encoding of DFP numbers, widely known as the binary
                 integer decimal (BID) encoding. The BID adder uses a
                 novel hardware component for decimal digit counting and
                 an enhanced version of a previously published BID
                 rounding unit. By adding more sophisticated control,
                 operations are performed with variable latency to
                 optimize for common cases. We show that a BID-based DFP
                 adder design can be achieved with a modest area
                 increase compared to a single 2-stage pipelined 64-bit
                 fixed-point multiplier. Over 70\% of the BID adder's
                 area is due to the 64-bit fixed-point multiplier, which
                 can be shared with a binary floating-point multiplier
                 and hardware for other DFP operations. To our
                 knowledge, this is the first hardware design for adding
                 and subtracting IEEE P754 BID-encoded DFP numbers",
  acknowledgement = ack-nhfb,
}

@InProceedings{Tsen:2007:HDBb,
  author =       "Charles Tsen and Michael Schulte and Sonia
                 Gonzalez-Navarro",
  title =        "Hardware Design of a Binary Integer Decimal-based
                 {IEEE P754} Rounding Unit",
  crossref =     "IEEE:2007:ACP",
  pages =        "115--121",
  year =         "2007",
  bibdate =      "Sun Feb 20 17:42:56 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Because of the growing importance of decimal
                 floating-point (DFP) arithmetic, specifications for it
                 were recently added to the draft revision of the IEEE
                 754 Standard (IEEE P754). In this paper, we present a
                 hardware design for a rounding unit for 64-bit DFP
                 numbers (decimal 64) that use the IEEE P754 binary
                 encoding of DFP numbers, which is widely known as the
                 Binary Integer Decimal (BID) encoding. We summarize the
                 technique used for rounding, present the theory and
                 design of the BID rounding unit, and evaluate its
                 critical path delay, latency, and area for
                 combinational and pipelined designs. Over 86\% of the
                 rounding unit's area is due to a 55-bit by 54-bit
                 binary multiplier, which can be shared with a
                 double-precision binary floating-point multiplier. To
                 our knowledge, this is the first hardware design for
                 rounding IEEE P754 BID-encoded DFP numbers.",
  acknowledgement = ack-nhfb,
  keywords =     "BID rounding; binary integer decimal encoding; decimal
                 floating-point arithmetic; double-precision binary
                 floating-point multiplier; hardware design; IEEE 754
                 standard; IEEE P754 binary encoding; IEEE P754 rounding
                 unit",
}

@Article{Vasudevan:2007:AVA,
  author =       "S. Vasudevan and V. Viswanath and R. W. Sumners and J.
                 A. Abraham",
  title =        "Automatic Verification of Arithmetic Circuits in {RTL}
                 Using Stepwise Refinement of Term Rewriting Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "56",
  number =       "10",
  pages =        "1401--1414",
  month =        oct,
  year =         "2007",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2007.1073",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 15:03:42 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4302711",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Vazquez:2007:NFH,
  author =       "Alvaro Vazquez and Elisardo Antelo and Paolo
                 Montuschi",
  title =        "A New Family of High-Performance Parallel Decimal
                 Multipliers",
  crossref =     "Kornerup:2007:PIS",
  pages =        "195--204",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.6",
  bibdate =      "Tue Oct 9 17:16:03 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.lirmm.fr/arith18/papers/vazquez-DecimalMultiplier.pdf",
  abstract =     "This paper introduces two novel architectures for
                 parallel decimal multipliers. Our multipliers are based
                 on a new algorithm for decimal carry-save multioperand
                 addition that uses a novel BCD-4221 recoding for
                 decimal digits. It significantly improves the area and
                 latency of the partial product reduction tree with
                 respect to previous proposals. We also present three
                 schemes for fast and efficient generation of partial
                 products in parallel. The recoding of the BCD-8421
                 multiplier operand into minimally redundant
                 signed-digit radix-10, radix-4 and radix-5
                 representations using new recoders reduces the
                 complexity of partial product generation. In addition,
                 SD radix-4 and radix-5 recodings allow the reuse of a
                 conventional parallel binary radix-4 multiplier to
                 perform combined binary/ decimal multiplications.
                 Evaluation results show that the proposed architectures
                 have interesting area-delay figures compared to
                 conventional Booth radix-4 and radix-8 parallel binary
                 multipliers and other representative alternatives for
                 decimal multiplication.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}

@InProceedings{Veeramachaneni:2007:NHS,
  author =       "Sreehari Veeramachaneni and M. Kirthi Krishna and
                 Lingamneni Avinash and Reddy P. Sreekanth and M. B.
                 Srinivas",
  title =        "Novel, High-Speed 16-Digit {BCD} Adders Conforming to
                 {IEEE 754r} Format",
  crossref =     "Becker:2007:EVT",
  pages =        "343--350",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ISVLSI.2007.71",
  bibdate =      "Thu Aug 07 18:55:05 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In view of increasing prominence of commercial,
                 financial and Internet-based applications that process
                 data in decimal format, there is a renewed interest in
                 providing hardware support to handle decimal data. In
                 this paper, a new architecture for efficient 1-digit
                 decimal addition of binary coded decimal (BCD)
                 operands, which is the core of high speed multi-operand
                 adders and floating decimal-point arithmetic, is
                 proposed. Based on this 1-digit BCD adder, novel
                 architectures for higher order (n-digit) BCD adders
                 such as ripple carry adder and carry look-ahead adder
                 are derived. The proposed circuits are compared (both
                 qualitatively as well as quantitatively) with the
                 existing circuits in literature and are shown to
                 perform better. Simulation results show that the
                 proposed 1-digit BCD adder achieves an improvement of
                 40\% in delay. The 16-digit BCD lookahead adder using
                 prefix logic is shown to perform at least 80\% faster
                 than the existing ripple carry one.",
  acknowledgement = ack-nhfb,
}

@Article{Voronenko:2007:MMC,
  author =       "Yevgen Voronenko and Markus P{\"u}schel",
  title =        "Multiplierless multiple constant multiplication",
  journal =      j-TALG,
  volume =       "3",
  number =       "2",
  pages =        "11:1--11:??",
  month =        may,
  year =         "2007",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/1240233.1240234",
  ISSN =         "1549-6325 (print), 1549-6333 (electronic)",
  ISSN-L =       "1549-6325",
  bibdate =      "Mon Jun 16 11:54:42 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A variable can be multiplied by a given set of
                 fixed-point constants using a multiplier block that
                 consists exclusively of additions, subtractions, and
                 shifts. The generation of a multiplier block from the
                 set of constants is known as the multiple constant
                 multiplication (MCM) problem. Finding the optimal
                 solution, namely, the one with the fewest number of
                 additions and subtractions, is known to be NP-complete.
                 We propose a new algorithm for the MCM problem, which
                 produces solutions that require up to 20\% less
                 additions and subtractions than the best previously
                 known algorithm. At the same time our algorithm, in
                 contrast to the closest competing algorithm, is not
                 limited by the constant bitwidths. We present our
                 algorithm using a unifying formal framework for the
                 best, graph-based MCM algorithms and provide a detailed
                 runtime analysis and experimental evaluation. We show
                 that our algorithm can handle problem sizes as large as
                 100 32-bit constants in a time acceptable for most
                 applications. The implementation of the new algorithm
                 is available at \url{www.spiral.net}.",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  fjournal =     "ACM Transactions on Algorithms (TALG)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J982",
  keywords =     "Addition chains; directed graph; FIR filter;
                 fixed-point arithmetic; strength reduction",
}

@InProceedings{Vouzis:2007:MCL,
  author =       "P. Vouzis and M. Arnold and S. Collange and M.
                 Kothare",
  title =        "{Monte Carlo} logarithmic number system for model
                 predictive control",
  crossref =     "Bertels:2007:PIC",
  pages =        "453--458",
  year =         "2007",
  bibdate =      "Thu Mar 24 20:58:01 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Wang:2007:DFPa,
  author =       "Liang-Kai Wang and Michael J. Schulte",
  title =        "Decimal Floating-Point Adder and Multifunction Unit
                 with Injection-Based Rounding",
  crossref =     "Kornerup:2007:PIS",
  pages =        "56--68",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/ARITH.2007.13",
  bibdate =      "Tue Oct 9 16:32:41 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.lirmm.fr/arith18/papers/wang_schulte-multifunction_unit.pdf",
  abstract =     "Shrinking feature sizes gives more headroom for
                 designers to extend the functionality of
                 microprocessors. The IEEE 754R working group has
                 revised the IEEE 754-1985 Standard for Binary
                 Floating-Point Arithmetic to include specifications for
                 decimal floating-point arithmetic and IBM recently
                 announced incorporating a decimal floating-point unit
                 into their POWER6 processor. As processor support for
                 decimal floating-point arithmetic emerges, it is
                 important to investigate efficient algorithms and
                 hardware designs for common decimal floating-point
                 arithmetic algorithms. This paper presents novel
                 designs for a decimal floating-point adder and a
                 decimal floating-point multifunction unit. To reduce
                 their delay, both the adder and the multifunction unit
                 use decimal injection-based rounding, a new form of
                 decimal operand alignment, and a fast flag-based method
                 for rounding and overflow detection. Synthesis results
                 indicate that the proposed adder is roughly 21\% faster
                 and 1.6\% smaller than a previous decimal
                 floating-point adder design, when implemented in the
                 same technology. Compared to the decimal floating-point
                 adder, the decimal floating-point multifunction unit
                 provides six additional operations, yet only has
                 2.8\%more delay and 9.7\% more area.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}

@Article{Wang:2007:DFPb,
  author =       "Liang-Kai Wang and Michael J. Schulte",
  title =        "A Decimal Floating-Point Divider Using
                 {Newton--Raphson} Iteration",
  journal =      j-J-VLSI-SIGNAL-PROC,
  volume =       "49",
  number =       "1",
  pages =        "3--18",
  month =        oct,
  year =         "2007",
  CODEN =        "JVSPED",
  DOI =          "https://doi.org/10.1007/s11265-007-0058-5",
  ISSN =         "0922-5773 (print), 1573-109x (electronic)",
  ISSN-L =       "0922-5773",
  bibdate =      "Mon Nov 05 19:17:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Increasing chip densities and transistor counts
                 provide more room for designers to add functionality
                 for important application domains into future
                 microprocessors. As a result of rapid growth in
                 financial, commercial, and Internet-based applications,
                 hardware support for decimal floating-point arithmetic
                 is now being considered by various computer
                 manufacturers and specifications for decimal
                 floating-point arithmetic have been added to the draft
                 revision of the IEEE-754 Standard for Floating-Point
                 Arithmetic (IEEE P754). In this paper, we presents an
                 efficient arithmetic algorithm and hardware design for
                 decimal floating-point division. The design uses an
                 efficient piecewise linear approximation, a modified
                 Newton---Raphson iteration, a specialized rounding
                 technique, and a simplified decimal incrementer and
                 decrementer. Synthesis results show that a 64-bit
                 (16-digit) implementation of the decimal divider, which
                 is compliant with the current version of IEEE P754, has
                 an estimated critical path delay of 0.69 ns (around 13
                 FO4 inverter delays) when implemented using LSI Logic's
                 0.11 micron Gflx-P standard cell library.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of VLSI Signal Processing",
}

@PhdThesis{Wang:2007:PSD,
  author =       "Liang-Kai Wang",
  title =        "Processor support for decimal floating-point
                 arithmetic",
  type =         "{Ph.D.} thesis",
  school =       "The University of Wisconsin --- Madison",
  address =      "Madison, WI, USA",
  pages =        "157",
  year =         "2007",
  ISBN =         "0-549-19463-0",
  ISBN-13 =      "978-0-549-19463-7",
  bibdate =      "Thu Aug 07 16:22:03 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Decimal data permeates society, as humans most
                 commonly use base-ten numbers. Although microprocessors
                 normally use base-two binary arithmetic to obtain
                 faster execution times and simpler circuitry, binary
                 numbers cannot represent decimal fractions exactly.
                 This leads to large errors being accumulated after
                 several decimal operations. Furthermore, binary
                 floating-point arithmetic operations perform binary
                 rounding instead of decimal rounding. Consequently,
                 applications, such as financial, commercial, tax, and
                 Internet-based applications, which are sensitive to
                 representation and rounding errors, often require
                 decimal arithmetic. Due to the increasing importance of
                 and demand for decimal arithmetic, its formats and
                 operations have been specified in the IEEE Draft
                 Standard for Floating-point Arithmetic (IEEE
                 P754).\par

                 Most decimal applications use software routines and
                 binary arithmetic to emulate decimal operations.
                 Although this approach eliminates errors due to
                 converting between binary and decimal numbers and
                 provides decimal rounding to mirror manual
                 calculations, it results in long latencies for
                 numerically intensive commercial applications. This is
                 because software emulation of decimal floating-point
                 (DFP) arithmetic has significant overhead due to
                 function calls, dealing with decimal formats, operand
                 alignment, decimal rounding, and special case and
                 exception handling.\par

                 This dissertation investigates processor support for
                 decimal floating-point arithmetic. It first reviews
                 recent progress in decimal arithmetic, including
                 decimal encodings, the IEEE P754 Draft Standard, and
                 software packages, hardware designs, and benchmark
                 suites for decimal arithmetic. Next, this dissertation
                 presents novel arithmetic algorithms and hardware
                 designs for basic DFP operations, including DFP
                 addition, subtraction, division, square root, and
                 others. Most of the hardware designs presented in this
                 dissertation are the first published designs compliant
                 with the IEEE P754 Draft Standard. Finally, to study
                 the performance impact of DFP instructions and
                 hardware, this dissertation presents the first publicly
                 available benchmark suite for DFP arithmetic. This
                 benchmark suite, along with instruction set extensions
                 and a decimal-enhanced processor simulator, are used to
                 demonstrate that providing fast hardware support for
                 DFP operations leads to significant performance
                 benefits to DFP-intensive applications.",
  acknowledgement = ack-nhfb,
  advisor =      "Michael J. Schulte",
}

@Article{Wu:2007:FBM,
  author =       "Chia-Long Wu and Der-Chyuan Lou and Te-Jen Chang",
  title =        "Fast binary multiplication by performing dot counting
                 and complement recoding",
  journal =      j-APPL-MATH-COMP,
  volume =       "191",
  number =       "1",
  pages =        "132--139",
  day =          "1",
  month =        aug,
  year =         "2007",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Sat Jul 12 09:03:07 MDT 2008",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Wu:2007:FMM,
  author =       "Chia-Long Wu and Der-Chyuan Lou and Jui-Chang Lai and
                 Te-Jen Chang",
  title =        "Fast modular multi-exponentiation using modified
                 complex arithmetic",
  journal =      j-APPL-MATH-COMP,
  volume =       "186",
  number =       "2",
  pages =        "1065--1074",
  day =          "15",
  month =        mar,
  year =         "2007",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Sat Jul 12 09:03:03 MDT 2008",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Xu:2007:HWP,
  author =       "Fei Xu and Chip-Hong Chang and Ching-Chuen Jong",
  title =        "{Hamming} weight pyramid --- a new insight into
                 canonical signed digit representation and its
                 applications",
  journal =      j-COMPUT-ELECTR-ENG,
  volume =       "33",
  number =       "3",
  pages =        "195--207",
  month =        may,
  year =         "2007",
  CODEN =        "CPEEBQ",
  DOI =          "https://doi.org/10.1016/j.compeleceng.2006.09.001",
  ISSN =         "0045-7906 (print), 1879-0755 (electronic)",
  ISSN-L =       "0045-7906",
  bibdate =      "Thu Aug 07 19:18:35 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Signed-power-of-two terms are widely used in design
                 automation algorithms for digital filter synthesis and
                 optimization, linear transformation and other multiple
                 constant multiplication problems. In these
                 applications, the computation efficiency or solution
                 quality tends to degrade with the number of nonzero
                 digits in the signed digit representation of the a
                 priori fixed coefficients. This paper provides a new
                 perspective to interpret the hamming weights of
                 fixed-point coefficients represented in
                 signed-power-of-two terms with minimal number of
                 nonzero digits, called the minimal signed digit (MSD)
                 representation. A new hamming weight pyramid (HWP) is
                 proposed to succinctly compress the information about
                 the distribution of the hamming weights of canonical
                 signed digit (CSD) representation in a visually
                 appealing manner for analysis and synthesis. CSD is a
                 unique and popularly used subset of the general MSD
                 representation. Many interesting properties of CSD are
                 uncovered in this regularly structured HWP. These
                 properties are exploited to develop a novel and elegant
                 algorithm for the direct conversion of decimal number
                 to CSD representation. We also show that the HWP can
                 also be employed to overcome the limit imposed on the
                 word length of the coefficients for the reduced adder
                 graph (RAG) algorithm and filter coefficient
                 synthesis.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Electrical Engineering",
}

@Article{Yen:2007:ICM,
  author =       "Sung-Ming Yen and Wei-Chih Lien and SangJae Moon",
  title =        "Inefficiency of common-multiplicand multiplication and
                 exponentiation algorithms by performing binary
                 complements",
  journal =      j-APPL-MATH-COMP,
  volume =       "189",
  number =       "1",
  pages =        "285--290",
  day =          "1",
  month =        jun,
  year =         "2007",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Sat Jul 12 09:03:05 MDT 2008",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@PhdThesis{Yu:2007:DPE,
  author =       "Xian-Yan Yu",
  title =        "Design of Power-Efficient Floating-Point Adder
                 Blocks",
  type =         "{Ph.D.} thesis",
  school =       "Advanced Computer Systems Engineering Laboratory,
                 University of California, Davis",
  address =      "Davis, CA, USA",
  pages =        "????",
  month =        may,
  year =         "2007",
  bibdate =      "Tue Oct 09 18:04:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "IBM Power6",
}

@Article{Zhuo:2007:SMA,
  author =       "Ling Zhuo and Viktor K. Prasanna",
  title =        "Scalable and Modular Algorithms for Floating-Point
                 Matrix Multiplication on Reconfigurable Computing
                 Systems",
  journal =      j-IEEE-TRANS-PAR-DIST-SYS,
  volume =       "18",
  number =       "4",
  pages =        "433--448",
  month =        apr,
  year =         "2007",
  CODEN =        "ITDSEO",
  DOI =          "https://doi.org/10.1109/TPDS.2007.1001",
  ISSN =         "1045-9219 (print), 1558-2183 (electronic)",
  ISSN-L =       "1045-9219",
  bibdate =      "Thu Jul 3 14:26:52 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Parallel Distrib. Syst.",
  fjournal =     "IEEE Transactions on Parallel and Distributed
                 Systems",
  journal-URL =  "http://www.computer.org/tpds/archives.htm",
}

@Article{Aamodt:2008:CTI,
  author =       "Tor M. Aamodt and Paul Chow",
  title =        "Compile-time and instruction-set methods for improving
                 floating- to fixed-point conversion accuracy",
  journal =      j-TECS,
  volume =       "7",
  number =       "3",
  pages =        "26:1--26:??",
  month =        apr,
  year =         "2008",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/1347375.1347379",
  ISSN =         "1539-9087 (print), 1558-3465 (electronic)",
  ISSN-L =       "1539-9087",
  bibdate =      "Thu Jun 12 15:22:21 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper proposes and evaluates compile time and
                 instruction-set techniques for improving the accuracy
                 of signal-processing algorithms run on fixed-point
                 embedded processors. These techniques are proposed in
                 the context of a profile guided floating- to
                 fixed-point compiler-based conversion process. A novel
                 fixed-point scaling algorithm (IRP) is introduced that
                 exploits correlations between values in a program by
                 applying fixed-point scaling, retaining as much
                 precision as possible without causing overflow. This
                 approach is extended into a more aggressive scaling
                 algorithm (IRP-SA) by leveraging the modulo nature of
                 2's complement addition and subtraction to discard most
                 significant bits that may not be redundant
                 sign-extension bits. A complementary scaling technique
                 (IDS) is then proposed that enables the fixed-point
                 scaling of a variable to be parameterized, depending
                 upon the context of its definitions and uses. Finally,
                 a novel instruction-set enhancement--- fractional
                 multiplication with internal left shift (FMLS)---is
                 proposed to further leverage interoperand correlations
                 uncovered by the IRP-SA scaling algorithm. FMLS
                 preserves a different subset of the full product's bits
                 than traditional fractional fixed-point or integer
                 multiplication. On average, FMLS combined with IRP-SA
                 improves accuracy on processors with uniform bitwidth
                 register architectures by the equivalent of 0.61 bits
                 of additional precision for a set of signal-processing
                 benchmarks (up to 2 bits). Even without employing FMLS,
                 the IRP-SA scaling algorithm achieves additional
                 accuracy over two previous fixed-point scaling
                 algorithms by averages of 1.71 and 0.49 bits.
                 Furthermore, as FMLS combines multiplication with a
                 scaling shift, it reduces execution time by an average
                 of 9.8\%. An implementation of IDS, specialized to
                 single-nested loops, is found to improve accuracy of a
                 lattice filter benchmark by the equivalent of more than
                 16-bits of precision.",
  acknowledgement = ack-nhfb,
  articleno =    "26",
  fjournal =     "ACM Transactions on Embedded Computing Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?&idx=J840",
  keywords =     "compilation; digital signal processing; fixed-point;
                 fractional multiplication; scaling; signal-to-noise
                 ratio",
}

@Article{Ahmadi:2008:PFS,
  author =       "O. Ahmadi and D. Hankerson and F.
                 Rodr{\'\i}guez-Henr{\'\i}quez",
  title =        "Parallel Formulations of Scalar Multiplication on
                 {Koblitz} Curves",
  journal =      j-J-UCS,
  volume =       "14",
  number =       "3",
  pages =        "481--504",
  month =        "????",
  year =         "2008",
  CODEN =        "????",
  ISSN =         "0948-6968",
  ISSN-L =       "0948-6968",
  bibdate =      "Thu Jul 10 06:41:41 MDT 2008",
  bibsource =    "http://www.jucs.org/jucs;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.jucs.org/jucs_14_3/parallel_formulations_of_scalar",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
  keywords =     "cryptography",
}

@Book{ASTM:2008:AES,
  author =       "{ASTM}",
  title =        "{ASTM E29-08}: Standard Practice for Using Significant
                 Digits in Test Data to Determine Conformance with
                 Specifications",
  publisher =    "ASTM International",
  address =      "West Conshohocken, PA, USA",
  year =         "2008",
  DOI =          "https://doi.org/10.1520/E0029",
  bibdate =      "Mon May 21 17:19:21 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.astm.org/Standards/E29.htm",
  abstract =     "This practice is intended to assist the various
                 technical committees in the use of uniform methods of
                 indicating the number of digits which are to be
                 considered significant in specification limits, for
                 example, specified maximum values and specified minimum
                 values. Its aim is to outline methods which should aid
                 in clarifying the intended meaning of specification
                 limits with which observed values or calculated test
                 results are compared in determining conformance with
                 specifications. Two commonly accepted methods of
                 rounding data, identified as the absolute method and
                 the rounding method are described. The guidelines for
                 retaining significant figures in calculation and
                 reporting of test results are presented in details.",
  acknowledgement = ack-nhfb,
}

@Article{Bapst:2008:SIO,
  author =       "Frederic Bapst and Fran{\c{c}}ois Kilchoer",
  title =        "Signalling Integer Overflows in {Java}: a tool for
                 checking overflows in {Java} code",
  journal =      j-DDJ,
  volume =       "33",
  number =       "9",
  pages =        "54--58",
  month =        sep,
  year =         "2008",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Tue Aug 12 18:02:50 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://home.hefr.ch/bapst/cojac",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
  keywords =     "integer overflow detection; Java",
  remark =       "The COJAC (Checking Overflows in JAva Code) tool
                 instruments a compiled {\tt .class} file, replacing
                 integer instructions subject to overflow with calls to
                 routines that report any overflow.",
}

@Article{Beuchat:2008:AGM,
  author =       "Jean-Luc Beuchat and Jean-Michel Muller",
  title =        "Automatic Generation of Modular Multipliers for {FPGA}
                 Applications",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "57",
  number =       "12",
  pages =        "1600--1613",
  month =        dec,
  year =         "2008",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2008.102",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 12:17:44 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4564441",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Boldo:2008:EFC,
  author =       "Sylvie Boldo and Guillaume Melquiond",
  title =        "Emulation of a {FMA} and Correctly Rounded Sums:
                 Proved Algorithms Using Rounding to Odd",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "57",
  number =       "4",
  pages =        "462--471",
  month =        apr,
  year =         "2008",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2007.70819",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 12:17:40 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ens-lyon.hal.science/inria-00080427/file/odd-rounding.pdf;
                 https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4358278",
  abstract =     "Rounding to odd is a nonstandard rounding on
                 floating-point numbers. By using it for some
                 intermediate values instead of rounding to nearest,
                 correctly rounded results can be obtained at the end of
                 computations. We present an algorithm for emulating the
                 fused multiply-and-add operator. We also present an
                 iterative algorithm for computing the correctly rounded
                 sum of a set of floating-point numbers under mild
                 assumptions. A variation on both previous algorithms is
                 the correctly rounded sum of any three floating-point
                 numbers. This leads to efficient implementations, even
                 when this rounding is not available. In order to
                 guarantee the correctness of these properties and
                 algorithms, we formally proved them by using the Coq
                 proof checker.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keyword =      "double rounding; round-to-odd (RO(x))",
}

@Article{Brisebarre:2008:CRM,
  author =       "Nicolas Brisebarre and Jean-Michel Muller",
  title =        "Correctly Rounded Multiplication by Arbitrary
                 Precision Constants",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "57",
  number =       "2",
  pages =        "165--174",
  month =        feb,
  year =         "2008",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2007.70813",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 12:17:40 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4358257",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Brisebarre:2008:EME,
  author =       "Nicolas Brisebarre and Sylvain Chevillard and
                 Milo{\v{s}} D. Ercegovac and Jean-Michel Muller and
                 Serge Torres",
  title =        "An Efficient Method for Evaluating Polynomial and
                 Rational Function Approximations",
  crossref =     "IEEE:2008:ICA",
  pages =        "233--238",
  year =         "2008",
  DOI =          "https://doi.org/10.1109/ASAP.2008.4580185",
  bibdate =      "Mon Feb 10 07:28:25 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Brisebarre:2008:IFP,
  author =       "Nicolas Brisebarre and Florent de Dinechin and
                 Jean-Michel Muller",
  title =        "Integer and floating-point constant multipliers for
                 {FPGAs}",
  crossref =     "IEEE:2008:ICA",
  pages =        "239--244",
  year =         "2008",
  DOI =          "https://doi.org/10.1109/ASAP.2008.4580184",
  bibdate =      "Mon Feb 10 08:12:58 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Buttari:2008:UMP,
  author =       "Alfredo Buttari and Jack Dongarra and Jakub Kurzak and
                 Piotr Luszczek and Stanimir Tomov",
  title =        "Using Mixed Precision for Sparse Matrix Computations
                 to Enhance the Performance while Achieving 64-bit
                 Accuracy",
  journal =      j-TOMS,
  volume =       "34",
  number =       "4",
  pages =        "17:1--17:22",
  month =        jul,
  year =         "2008",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1377596.1377597",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 16 11:30:01 MDT 2008",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "By using a combination of 32-bit and 64-bit floating
                 point arithmetic, the performance of many sparse linear
                 algebra algorithms can be significantly enhanced while
                 maintaining the 64-bit accuracy of the resulting
                 solution. These ideas can be applied to sparse
                 multifrontal and supernodal direct techniques and
                 sparse iterative techniques such as Krylov subspace
                 methods. The approach presented here can apply not only
                 to conventional processors but also to exotic
                 technologies such as Field Programmable Gate Arrays
                 (FPGA), Graphical Processing Units (GPU), and the Cell
                 BE processor.",
  acknowledgement = ack-nhfb,
  articleno =    "17",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "floating point; iterative refinement; linear systems;
                 precision",
}

@Article{Carnicer:2008:REP,
  author =       "J. M. Carnicer and T. N. T. Goodman and J. M.
                 Pe{\~n}a",
  title =        "Roundoff errors for polynomial evaluation by a family
                 of formulae",
  journal =      j-COMPUTING,
  volume =       "82",
  number =       "2--3",
  pages =        "199--215",
  month =        jul,
  year =         "2008",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Sun Oct 31 11:09:47 MDT 2010",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=82&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=82&issue=2&spage=199",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Article{Castaldo:2008:RFP,
  author =       "Anthony M. Castaldo and R. Clint Whaley and Anthony T.
                 Chronopoulos",
  title =        "Reducing Floating Point Error in Dot Product Using the
                 Superblock Family of Algorithms",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "31",
  number =       "2",
  pages =        "1156--1174",
  month =        "????",
  year =         "2008",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/070679946",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Wed May 19 10:44:14 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/31/2;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper discusses both the theoretical and
                 statistical errors obtained by various well-known dot
                 products, from the canonical to pairwise algorithms,
                 and introduces a new and more general framework that we
                 have named superblock which subsumes them and permits a
                 practitioner to make trade-offs between computational
                 performance, memory usage, and error behavior. We show
                 that algorithms with lower error bounds tend to behave
                 noticeably better in practice. Unlike many such
                 error-reducing algorithms, superblock requires no
                 additional floating point operations and should be
                 implementable with little to no performance loss,
                 making it suitable for use as a performance-critical
                 building block of a linear algebra kernel.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  keywords =     "accurate floating-point summation; floating-point dot
                 product",
}

@InProceedings{Castellanos:2008:CTD,
  author =       "Ivan D. Castellanos and James E. Stine",
  title =        "Compressor trees for decimal partial product
                 reduction",
  crossref =     "ACM:2008:GPA",
  pages =        "107--110",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1366110.1366137",
  bibdate =      "Thu Aug 07 17:39:02 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Decimal multiplication has grown in interest due to
                 the recent announcement of new IEEE 754R standards and
                 the availability of high-speed decimal computation
                 hardware. Prior research enabled partial products to be
                 coded more efficiently for their use in radix 10
                 architectures. This paper clarifies previous techniques
                 for partial product reduction using carry-save adders
                 and presents a new 4:2 compressor structure. This new
                 structure improves performance at the expense of more
                 gates, however, regularity is introduced into the
                 circuit to promote implementations in Very Large Scale
                 Integration (VLSI) Designs. Results are presented and
                 compared for several designs using a TSMC SCN6M $ 0.18
                 \mu $ m feature size.",
  acknowledgement = ack-nhfb,
}

@Article{Cavagnino:2008:EAI,
  author =       "D. Cavagnino and A. E. Werbrouck",
  title =        "Efficient Algorithms for Integer Division by Constants
                 Using Multiplication",
  journal =      j-COMP-J,
  volume =       "51",
  number =       "4",
  pages =        "470--480",
  month =        jul,
  year =         "2008",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/bxm082",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Wed Apr 28 14:33:34 MDT 2010",
  bibsource =    "http://comjnl.oxfordjournals.org/content/vol51/issue4/index.dtl;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/cgi/content/abstract/51/4/470;
                 http://comjnl.oxfordjournals.org/cgi/content/full/51/4/470;
                 http://comjnl.oxfordjournals.org/cgi/reprint/51/4/470",
  abstract =     "We present a complete analysis of the integer division
                 of a single unsigned dividend word by a single unsigned
                 divisor word based on double-word multiplication of the
                 dividend by an inverse of the divisor. The well-known
                 advantage of this method yields run-time efficiency, if
                 the inverse of the divisor can be calculated at compile
                 time, since multiplication is much faster than division
                 in arithmetic units. Our analysis leads to the
                 discovery of a limit to the straightforward application
                 of this method in the form of a critical dividend,
                 which fortunately associates with a minority of the
                 possible divisors (20\%) and defines only a small upper
                 part of the available dividend space. We present two
                 algorithms for ascertaining whether a critical dividend
                 exists and, if so, its value along with a circumvention
                 of this limit. For completeness, we include an
                 algorithm for integer division of a unsigned
                 double-word dividend by an unsigned single-word divisor
                 in which the quotient is not limited to a single word
                 and the remainder is an intrinsic part of the result.",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "division by multiplication; efficiency; integer
                 constants; integer division; multiplicative inverse",
  remark =       "See \cite{Cavagnino:2011:AAD}.",
}

@Article{Colon-Bonet:2008:MEF,
  author =       "Glenn Col{\'o}n-Bonet and Paul {Winterrowd, Jr.}",
  title =        "Multiplier Evolution: a Family of Multiplier {VLSI}
                 Implementations",
  journal =      j-COMP-J,
  volume =       "51",
  number =       "5",
  pages =        "585--594",
  month =        sep,
  year =         "2008",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/bxm123",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Wed Apr 28 14:33:34 MDT 2010",
  bibsource =    "http://comjnl.oxfordjournals.org/content/vol51/issue5/index.dtl;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/cgi/content/abstract/51/5/585;
                 http://comjnl.oxfordjournals.org/cgi/content/full/51/5/585;
                 http://comjnl.oxfordjournals.org/cgi/reprint/51/5/585",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Cordeiro:2008:MSI,
  author =       "Gauss M. Cordeiro and Borko D. Stosi{\'c}",
  title =        "{Maple} script for improving test statistics",
  journal =      j-J-STAT-COMPUT-SIMUL,
  volume =       "78",
  number =       "11",
  pages =        "1045--1053",
  year =         "2008",
  CODEN =        "JSCSAJ",
  DOI =          "https://doi.org/10.1080/00949650701490969",
  ISSN =         "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
  ISSN-L =       "0094-9655",
  bibdate =      "Tue Apr 22 09:12:46 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Computation and Simulation",
  journal-URL =  "http://www.tandfonline.com/loi/gscs20",
}

@InProceedings{De:2008:FIM,
  author =       "Anindya De and Piyush P. Kurur and Chandan Saha and
                 Ramprasad Saptharishi",
  title =        "Fast integer multiplication using modular arithmetic",
  crossref =     "ACM:2008:SPA",
  pages =        "499--506",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1374376.1374447",
  bibdate =      "Fri Jun 20 18:31:53 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We give an $ O(N \log N 2^{O(\log *N)}) $ algorithm
                 for multiplying two $N$-bit integers that improves the
                 $ O(N \log N \log \log N) $ algorithm by
                 Sch{\"o}nhage--Strassen. Both these algorithms use
                 modular arithmetic. Recently, F{\"u}rer gave an $ O(N
                 \log N 2^{O(\log *N)}) $ algorithm which however uses
                 arithmetic over complex numbers as opposed to modular
                 arithmetic. In this paper, we use multivariate
                 polynomial multiplication along with ideas from
                 F{\"u}rer's algorithm to achieve this improvement in
                 the modular setting. Our algorithm can also be viewed
                 as a $p$-adic version of F{\"u}rer's algorithm. Thus,
                 we show that the two seemingly different approaches to
                 integer multiplication, modular and complex arithmetic,
                 are similar.",
  acknowledgement = ack-nhfb,
  keywords =     "computational algebra; integer multiplication; modular
                 arithmetic",
}

@Article{DeDinechin:2008:CFP,
  author =       "Florent {De Dinechin} and Christoph Quirin Lauter and
                 Guillaume Melquiond",
  title =        "Certifying floating-point implementations using
                 {Gappa}",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "3",
  month =        jan,
  year =         "2008",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/0801.0523",
  abstract =     "High confidence in floating-point programs requires
                 proving numerical properties of final and intermediate
                 values. One may need to guarantee that a value stays
                 within some range, or that the error relative to some
                 ideal value is well bounded. Such work may require
                 several lines of proof for each line of code, and will
                 usually be broken by the smallest change to the code
                 (e.g. for maintenance or optimization purpose).
                 Certifying these programs by hand is therefore very
                 tedious and error-prone. This article discusses the use
                 of the Gappa proof assistant in this context. Gappa has
                 two main advantages over previous approaches: Its input
                 format is very close to the actual C code to validate,
                 and it automates error evaluation and propagation using
                 interval arithmetic. Besides, it can be used to
                 incrementally prove complex mathematical properties
                 pertaining to the C code. Yet it does not require any
                 specific knowledge about automatic theorem proving, and
                 thus is accessible to a wide community. Moreover, Gappa
                 may generate a formal proof of the results that can be
                 checked independently by a lower-level proof assistant
                 like Coq, hence providing an even higher confidence in
                 the certification of the numerical code. The article
                 demonstrates the use of this tool on a real-size
                 example, an elementary function with correctly rounded
                 output.",
  acknowledgement = ack-nhfb,
  subject =      "Numerical Analysis (cs.NA); Mathematical Software
                 (cs.MS)",
}

@Article{DeDinechin:2008:OPF,
  author =       "Florent {De Dinechin} and Christoph Quirin Lauter",
  title =        "Optimizing polynomials for floating-point
                 implementation",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--12",
  day =          "4",
  month =        mar,
  year =         "2008",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/0803.0439",
  abstract =     "The floating-point implementation of a function on an
                 interval often reduces to polynomial approximation, the
                 polynomial being typically provided by Remez algorithm.
                 However, the floating-point evaluation of a Remez
                 polynomial sometimes leads to catastrophic
                 cancellations. This happens when some of the polynomial
                 coefficients are very small in magnitude with respects
                 to others. In this case, it is better to force these
                 coefficients to zero, which also reduces the operation
                 count. This technique, classically used for odd or even
                 functions, may be generalized to a much larger class of
                 functions. An algorithm is presented that forces to
                 zero the smaller coefficients of the initial polynomial
                 thanks to a modified Remez algorithm targeting an
                 incomplete monomial basis. One advantage of this
                 technique is that it is purely numerical, the function
                 being used as a numerical black box. This algorithm is
                 implemented within a larger polynomial implementation
                 tool that is demonstrated on a range of examples,
                 resulting in polynomials with less coefficients than
                 those obtained the usual way.",
  acknowledgement = ack-nhfb,
  subject =      "Numerical Analysis (cs.NA); Mathematical Software
                 (cs.MS)",
}

@Article{Dimitrov:2008:PSP,
  author =       "V. S. Dimitrov and K. U. Jarvinen and M. J. Jacobson
                 and W. Chan and Zhun Huang",
  title =        "Provably Sublinear Point Multiplication on {Koblitz}
                 Curves and Its Hardware Implementation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "57",
  number =       "11",
  pages =        "1469--1481",
  month =        nov,
  year =         "2008",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2008.65",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 12:17:44 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  note =         "See comments \cite{Lee:2012:CPS}.",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4487060",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Dvir:2008:HRT,
  author =       "Zeev Dvir and Amir Shpilka and Amir Yehudayoff",
  title =        "Hardness-randomness tradeoffs for bounded depth
                 arithmetic circuits",
  crossref =     "ACM:2008:SPA",
  pages =        "741--748",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1374376.1374482",
  bibdate =      "Fri Jun 20 18:31:53 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this paper we show that lower bounds for bounded
                 depth arithmetic circuits imply derandomization of
                 polynomial identity testing for bounded depth
                 arithmetic circuits. More formally, if there exists an
                 explicit polynomial $ f(x_1, \ldots {}, x_m) $ that
                 cannot be computed by a depth $d$ arithmetic circuit of
                 small size then there exists an efficient deterministic
                 algorithm to test whether a given depth $ d - 8 $
                 circuit is identically zero or not (assuming the
                 individual degrees of the tested circuit are not too
                 high). In particular, if we are guaranteed that the
                 circuit computes a multilinear polynomial then we can
                 perform the identity test efficiently. To the best of
                 our knowledge this is the first hardness-randomness
                 tradeoff for bounded depth arithmetic circuits. The
                 above results are obtained using the arithmetic
                 Nisan-Wigderson generator of Impagliazzo and Kabanets
                 together with a new theorem on bounded depth circuits,
                 which is the main technical contribution of our work.
                 This theorem deals with polynomial equations of the
                 form $ P(x_1, \ldots {}, x_n, y) \equiv 0 $ and shows
                 that if $P$ has a circuit of depth $d$ and size $s$ and
                 if the polynomial $ f(x_1, \ldots {}, x_n) $ satisfies
                 $ P(x_1, \ldots {}, x_n, f(x_1, \ldots {}, x_n)) \equiv
                 0 $ then $f$ has a circuit of depth $ d + 3 $ and size
                 $ O(s \times r + m^r) $, where $m$ is the degree of $f$
                 and $r$ is the highest degree of the variable $y$
                 appearing in $P$. In the other direction we observe
                 that the methods of Impagliazzo and Kabanets imply that
                 if we can derandomize polynomial identity testing for
                 bounded depth circuits then NEXP does not have bounded
                 depth arithmetic circuits. That is, either NEXP $ \not
                 \subset $ P/poly or the Permanent is not computable by
                 polynomial size bounded depth arithmetic circuits.",
  acknowledgement = ack-nhfb,
  keywords =     "arithmetic circuits; bounded depth circuits;
                 hardness-randomness tradeoffs; identity testing; lower
                 bounds",
}

@Article{Edmonson:2008:ISS,
  author =       "W. W. Edmonson and M. H. van Emden",
  title =        "Interval Semantics for Standard Floating-Point
                 Arithmetic",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--10",
  day =          "23",
  month =        oct,
  year =         "2008",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/0810.4196",
  abstract =     "If the non-zero finite floating-point numbers are
                 interpreted as point intervals, then the effect of
                 rounding can be interpreted as computing one of the
                 bounds of the result according to interval arithmetic.
                 We give an interval interpretation for the signed zeros
                 and infinities, so that the undefined operations 0*inf,
                 inf - inf, inf/inf, and 0/0 become defined. In this way
                 no operation remains that gives rise to an error
                 condition. Mathematically questionable features of the
                 floating-point standard become well-defined sets of
                 reals. Interval semantics provides a basis for the
                 verification of numerical algorithms. We derive the
                 results of the newly defined operations and consider
                 the implications for hardware implementation.",
  acknowledgement = ack-nhfb,
  subject =      "Numerical Analysis (cs.NA); Hardware Architecture
                 (cs.AR)",
}

@PhdThesis{Erle:2008:AHD,
  author =       "Mark A. Erle",
  title =        "Algorithms and Hardware Designs for Decimal
                 Multiplication",
  type =         "{Ph.D.} Thesis",
  school =       "Department of Computer Engineering, Lehigh
                 University",
  address =      "Bethlehem, PA, USA",
  pages =        "xviii + 221",
  day =          "21",
  month =        nov,
  year =         "2008",
  bibdate =      "Tue Mar 01 19:53:02 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://speleotrove.com/decimal/erle2008-decimal-multipliers-dissertation-duplex.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gonzalez-Navarro:2008:BID,
  author =       "S. Gonzalez-Navarro and C. Tsen and M. Schulte",
  title =        "Binary Integer Decimal-based Multiplier for Decimal
                 Floating-Point Arithmetic",
  crossref =     "Matthews:2008:CRF",
  pages =        "353--357",
  year =         "2008",
  DOI =          "https://doi.org/10.1109/ACSSC.2007.4487228",
  bibdate =      "Sat Dec 04 10:25:08 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Demand for decimal floating-point (DFP) arithmetic is
                 increasing because global business, e-commerce,
                 financial applications, and the standards and laws that
                 govern them require it. The IEEE P754 draft standard
                 for floating-point arithmetic specifies formats and
                 operations for DFP numbers. In this paper, we present
                 an IEEE P754-compliant multiplier that operates on
                 values that use the binary encoding of DFP numbers,
                 commonly referred to as the binary integer decimal
                 (BID) encoding. Our BID-based DFP multiplier uses
                 high-speed binary hardware, has variable latency, and
                 is optimized for the common case that the product does
                 not need to be rounded. Our multiplier also uses a
                 novel technique that estimates the number of product
                 digits that needed to be rounded in parallel with the
                 significant multiplication. In this design, a single
                 multiplier is used to multiply the significants and
                 round the product. We believe this the first hardware
                 design of a DFP multiplier for BID-encoded numbers.",
  acknowledgement = ack-nhfb,
}

@Article{Graillat:2008:ASZ,
  author =       "Stef Graillat",
  title =        "Accurate simple zeros of polynomials in floating point
                 arithmetic",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "56",
  number =       "4",
  pages =        "1114--1120",
  month =        aug,
  year =         "2008",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:50:16 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122108001120",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Book{Hardy:2008:ITN,
  author =       "G. H. (Godfrey Harold) Hardy and Edward Maitland
                 Wright and D. R. Heath-Brown and Joseph H. Silverman",
  title =        "An introduction to the theory of numbers",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  edition =      "Sixth",
  pages =        "xxi + 621",
  year =         "2008",
  ISBN =         "0-19-921985-0 (hardcover), 0-19-921986-9 (paperback)",
  ISBN-13 =      "978-0-19-921985-8 (hardcover), 978-0-19-921986-5
                 (paperback)",
  LCCN =         "QA241 .H28 2008",
  bibdate =      "Thu Nov 18 09:18:59 MST 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 library.ox.ac.uk:210/ADVANCE",
  series =       "Oxford mathematics",
  acknowledgement = ack-nhfb,
  author-dates = "G. H. Hardy (1877--1947)",
  remark =       "Previous (fifth) edition 1979.",
  subject =      "Number theory",
}

@Article{Homma:2008:SAD,
  author =       "N. Homma and T. Aoki and T. Higuchi",
  title =        "A Systematic Approach for Designing Redundant
                 Arithmetic Adders Based on Counter Tree Diagrams",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "57",
  number =       "12",
  pages =        "1633--1646",
  month =        dec,
  year =         "2008",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2008.106",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 12:17:44 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4569835",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Hsiao:2008:EDF,
  author =       "Shen-Fu Hsiao and Hsin-Mau Lee and Yen-Chun Cheng and
                 Ming-Yu Tsai",
  booktitle =    "{APCCAS 2008 --- 2008 IEEE Asia Pacific Conference on
                 Circuits and Systems}",
  title =        "Efficient designs of floating-point {CORDIC} rotation
                 and vectoring operations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1422--1425",
  year =         "2008",
  DOI =          "https://doi.org/10.1109/APCCAS.2008.4746297",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer architecture; Computer science; Costs; Delay;
                 Design engineering; Fixed-point arithmetic;
                 Floating-point arithmetic; Graphics; High performance
                 computing; Process design",
}

@Article{Jager:2008:DAD,
  author =       "Hendrik Jager and Pierre Liardet",
  title =        "Distributions arithm{\'e}tiques des d{\'e}nominateurs
                 de convergents de fractions continues. ({French})
                 [Arithmetic distributions of the denominators of
                 continued fractions]",
  journal =      "Proceedings of the Koninklijke Nederlandse Akademie
                 van Wetenschappen, Series A, Indagationes
                 mathematicae",
  volume =       "91",
  number =       "2",
  pages =        "181--197",
  day =          "20",
  month =        jun,
  year =         "2008",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/S1385-7258(88)80026-X",
  ISSN =         "1385-7258 (print), 1878-5972 (electronic)",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "http://www.sciencedirect.com/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S138572588880026X",
  acknowledgement = ack-nhfb,
  fjournal =     "Indagationes Mathematicae (Proceedings)",
  keywords =     "Benford's Law",
  language =     "French",
  xxjournal =    "Indagationes Mathematicae (Proceedings)",
}

@Article{Jezequel:2008:CLE,
  author =       "Fabienne J{\'e}z{\'e}quel and Jean-Marie Chesneaux",
  title =        "{CADNA}: a library for estimating round-off error
                 propagation",
  journal =      j-COMP-PHYS-COMM,
  volume =       "178",
  number =       "12",
  pages =        "933--955",
  day =          "15",
  month =        jun,
  year =         "2008",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2008.02.003",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 23:42:31 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465508000775",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Jimeno:2008:BBA,
  author =       "Antonio Jimeno and Higinio Mora and Jose L. Sanchez
                 and Francisco Pujol",
  title =        "A {BCD}-based architecture for fast coordinate
                 rotation",
  journal =      j-J-SYST-ARCH,
  volume =       "54",
  number =       "8",
  pages =        "829--840",
  month =        aug,
  year =         "2008",
  CODEN =        "JSARFB",
  DOI =          "https://doi.org/10.1016/j.sysarc.2008.02.001",
  ISSN =         "1383-7621 (print), 1873-6165 (electronic)",
  ISSN-L =       "1383-7621",
  bibdate =      "Thu Aug 07 18:04:43 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Although radix 10 based arithmetic has been gaining
                 renewed importance over the last few years, decimal
                 systems are not efficient enough and techniques are
                 still under development. In this paper, an improvement
                 of the CORDIC (coordinate rotation digital computer)
                 method for decimal representation is proposed and
                 applied to produce fast rotations. The algorithm uses
                 BCD operands as inputs, combining the advantages of
                 both decimal and binary systems. The result is a
                 reduction of 50\% in the number of iterations if
                 compared with the original Decimal CORDIC method.
                 Finally, we present a hardware architecture useful to
                 produce BCD coordinates rotations accurately and fast,
                 and different experiments demonstrating the advantages
                 of the new method are shown. A reduction of 75\% in a
                 single stage delay is obtained, whereas the circuit
                 area just increases in about 5\%.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Systems Architecture: the EUROMICRO
                 Journal",
  keywords =     "binary coded decimals; computer performance; CORDIC;
                 decimal arithmetic; digital arithmetic",
}

@Misc{Kahan:2008:BFU,
  author =       "William Kahan",
  title =        "Back to the Future of Undebuggable Floating-Point
                 Computation in Science and Engineering",
  howpublished = "Web document",
  day =          "30",
  month =        mar,
  year =         "2008",
  bibdate =      "Mon Mar 31 16:50:19 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "The Bay Area Scientific Computing Day, BASCD08,
                 honoring Profs. Kahan and Parlett, 29--30 March,
                 2008.",
  URL =          "http://math.berkeley.edu/bascd08;
                 http://www.eecs.berkeley.edu/~wkahan/BASCD08K.pdf",
  abstract =     "When I began to program an electronic computer in
                 1953, von Neumann was still disparaging floating-point
                 computation, which was generally deemed impervious to
                 error-analysis. Occasional anomalous results were
                 expected. Often they were attributed wrongly to
                 ``Ill-Condition''. Putting one's data through several
                 numerical methods some of whose results might agree was
                 a prudent policy. Those days are back. Their challenges
                 will be illustrated by a program like some used by
                 structural engineers for forty years. To cope, we need
                 debugging aids like those in Section 14 of my web
                 page's {\tt Mindless.pdf}. Help can come only from the
                 designers of hardware, compilers and software
                 development systems after they are persuaded that the
                 demand for such aids is commercially significant.",
  acknowledgement = ack-nhfb,
}

@Article{Kaihara:2008:BMM,
  author =       "M. E. Kaihara and N. Takagi",
  title =        "Bipartite Modular Multiplication Method",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "57",
  number =       "2",
  pages =        "157--164",
  month =        feb,
  year =         "2008",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2007.70793",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 12:17:40 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4358245",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Khalid:2008:NRE,
  author =       "M. S. Khalid and M. R. Amin and M. M. Hossain and M.
                 Anwer",
  editor =       "{IEEE}",
  booktitle =    "{Proceedings of 10th International Conference on
                 Computer and Information Technology (ICCIT 2007),
                 27-29, December 2007, United International University,
                 Dhanmondi, Dhaka-1209, Bangladesh}",
  title =        "Numerical round-off error in cellular phone services
                 billing system",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  bookpages =    "534 + 7",
  pages =        "1--5",
  year =         "2008",
  DOI =          "https://doi.org/10.1109/ICCITECHN.2007.4579417",
  ISBN =         "1-4244-1550-0, 1-4244-1551-9",
  ISBN-13 =      "978-1-4244-1550-2, 978-1-4244-1551-9",
  LCCN =         "QA75.5 .I574 2007",
  bibdate =      "Wed Jul 06 19:14:16 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Cellular phone services billing for per minute tariff
                 plan and 1-second pulse involve floating point division
                 and multiplication operation to calculate per call
                 bill. Monthly customer billing involves addition
                 operations on per call bills, which are floating point
                 numbers. Round-off errors occur due to floating point
                 numberspsila computer representation limitations and
                 for storing limited significant figures during billing.
                 The study analyzed post-paid itemized bills of a
                 cellular phone service operator in Bangladesh and
                 identified that accumulated round-off error for active
                 post-paid subscribers is significantly high for
                 subscriber group of large number. The research
                 recommends a per second tariff plan to completely
                 eliminate round-off error which also reduces floating
                 point number operations.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kong:2008:RMI,
  author =       "I. Kong and E. E. {Swartzlander, Jr.}",
  editor =       "Michael B. Matthews",
  booktitle =    "42nd Asilomar Conference on Signals, Systems and
                 Computers: {October 26--29, 2008, Pacific Grove,
                 California}",
  title =        "A Rounding Method with Improved Error Tolerance for
                 Division by Convergence",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1814--1818",
  year =         "2008",
  DOI =          "https://doi.org/10.1109/ACSSC.2008.5074740",
  ISBN =         "1-4244-2941-2",
  ISBN-13 =      "978-1-4244-2941-7",
  ISSN =         "1058-6393",
  ISSN-L =       "1058-6393",
  LCCN =         "TK7801 .A83 2008",
  bibdate =      "Sun Dec 10 14:05:54 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A new rounding method for division by convergence is
                 presented. It allows twice the error tolerance of
                 current methods, so it allows the multiplier of a
                 3-iteration Goldschmidt divider to be implemented using
                 only 3 extra bits. The new rounding method applies
                 special truncation methods at the final iteration step,
                 and it requires a minor modification in rounding
                 constants of the multiplier. It has been verified using
                 a SystemC model of the Goldschmidt divider supporting
                 variable precision. The verification consists of two
                 parts: the maximum error of approximate quotients and
                 the rounding result correctness. The maximum error of
                 approximate quotients is checked by analysis and via
                 simulation. The final rounding results are checked with
                 both random double precision floating-point
                 significands and exhaustive 17-bit precision test
                 vectors",
  acknowledgement = ack-nhfb,
}

@Book{Kulisch:2008:CAV,
  author =       "Ulrich Kulisch",
  title =        "Computer Arithmetic and Validity --- Theory,
                 Implementation, and Applications",
  publisher =    pub-GRUYTER,
  address =      pub-GRUYTER:adr,
  pages =        "410 (est.)",
  year =         "2008",
  ISBN =         "3-11-020318-9 (hardcover)",
  ISBN-13 =      "978-3-11-020318-9 (hardcover)",
  ISSN =         "0179-0986",
  LCCN =         "????",
  bibdate =      "Wed Jun 11 14:53:52 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$108.00",
  series =       "De Gruyter Studies in Mathematics",
  abstract =     "A New Approach to Scientific Computation is a
                 collection of papers delivered at a symposium held at
                 the IBM Thomas J. Watson Research Center on August 3,
                 1982. The symposium provided a forum for reviewing
                 various aspects of an approach to scientific
                 computation based on a systematic theory of computer
                 arithmetic. Computer demonstration packages for
                 standard problems of numerical mathematics are
                 considered. Comprised of 12 chapters, this volume
                 begins by summarizing an extensive research activity in
                 scientific computation as well as the experience gained
                 through various implementations \ldots{}",
  acknowledgement = ack-nhfb,
}

@PhdThesis{Lauter:2008:ACF,
  author =       "Christoph Quirin Lauter",
  title =        "Arrondi correct de fonctions math{\'e}matiques ---
                 Fonctions univari{\'e}es et bivari{\'e}es,
                 certification et automatisation. ({French}) [{Correct}
                 rounding of mathematical functions --- univariate and
                 bivariate functions, certification and automation]",
  type =         "{Ph.D.} dissertation",
  school =       "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "Lyon, France",
  pages =        "xiii + 197 + 3",
  month =        oct,
  year =         "2008",
  bibdate =      "Fri Dec 08 10:03:47 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.christoph-lauter.org/these.pdf",
  acknowledgement = ack-nhfb,
  advisor =      "Florent de Dinechin and Jean-Michel Muller",
}

@Article{Lefevre:2008:WCE,
  author =       "Vincent Lef{\`e}vre and Damien Stehl{\'e} and Paul
                 Zimmermann",
  title =        "Worst Cases for the Exponential Function in the {IEEE
                 754r decimal64} Format",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "5045",
  pages =        "114--126",
  year =         "2008",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-540-85521-7_7",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Thu Oct 1 11:29:36 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs2008a.bib",
  URL =          "http://link.springer.com/content/pdf/10.1007/978-3-540-85521-7_7.pdf",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-540-85521-7",
  book-URL =     "http://www.springerlink.com/content/978-3-540-85521-7",
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
  remark =       "From the abstract: ``the worst case for $ |x| \geq 3
                 \times 10^{-11} $ is exp(9.407822313572878e-2) =
                 1.09864568206633850000000000000000278.''",
}

@Article{Li:2008:MLB,
  author =       "Xin Li and Marc Moreno Maza and Raqeeb Rasheed and
                 {\'E}ric Schost",
  title =        "The {\tt modpn} library: bringing fast polynomial
                 arithmetic into {MAPLE}",
  journal =      j-ACM-COMM-COMP-ALGEBRA,
  volume =       "42",
  number =       "3",
  pages =        "172--174",
  month =        sep,
  year =         "2008",
  CODEN =        "????",
  ISSN =         "1932-2232 (print), 1932-2240 (electronic)",
  ISSN-L =       "1932-2232",
  bibdate =      "Fri Feb 13 18:17:36 MST 2009",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Communications in Computer Algebra",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}

@Article{Liu:2008:FIM,
  author =       "J. Liu and B. Weaver and Y. Zakharov",
  title =        "{FPGA} implementation of multiplication-free complex
                 division",
  journal =      j-ELECT-LETTERS,
  volume =       "44",
  number =       "2",
  pages =        "5--96",
  day =          "17",
  month =        jan,
  year =         "2008",
  CODEN =        "ELLEAK",
  DOI =          "https://doi.org/10.1049/el:20082567",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Fri Dec 03 14:53:57 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The FPGA implementation of a new complex division
                 algorithm is described. It is based on the dichotomous
                 co-ordinate descent method and requires only bit-shift
                 and addition operations. Consequently, the footprint of
                 the new complex division core is remarkably small.",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  keyword =      "FPGA; bit-shift; dichotomous coordinate descent
                 method; multiplication-free complex division; field
                 programmable gate arrays; signal processing",
}

@Misc{Melquiond:2008:DRA,
  author =       "Guillaume Melquiond and Sylvain Pion",
  title =        "Directed Rounding Arithmetic Operations",
  howpublished = "Web document",
  day =          "05",
  month =        dec,
  year =         "2008",
  bibdate =      "Mon Dec 08 14:57:52 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "ISO WG21 Document N2811=08-0321, posted to the
                 stds-1788 mailing list on 8-Dec-2008.",
  acknowledgement = ack-nhfb,
}

@Article{Monniaux:2008:PVF,
  author =       "David Monniaux",
  title =        "The pitfalls of verifying floating-point
                 computations",
  journal =      j-TOPLAS,
  volume =       "30",
  number =       "3",
  pages =        "12:1--12:41",
  month =        may,
  year =         "2008",
  CODEN =        "ATPSDT",
  DOI =          "https://doi.org/10.1145/1353445.1353446",
  ISSN =         "0164-0925 (print), 1558-4593 (electronic)",
  ISSN-L =       "0164-0925",
  bibdate =      "Wed Jun 11 19:14:53 MDT 2008",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toplas/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Current critical systems often use a lot of
                 floating-point computations, and thus the testing or
                 static analysis of programs containing floating-point
                 operators has become a priority. However, correctly
                 defining the semantics of common implementations of
                 floating-point is tricky, because semantics may change
                 according to many factors beyond source-code level,
                 such as choices made by compilers. We here give
                 concrete examples of problems that can appear and
                 solutions for implementing in analysis software.",
  acknowledgement = ack-nhfb,
  articleno =    "12",
  fjournal =     "ACM Transactions on Programming Languages and
                 Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J783",
}

@Article{Moore:2008:IMB,
  author =       "Samuel K. Moore",
  title =        "{Intel} Makes A Big Jump In Computer Math",
  journal =      j-IEEE-SPECTRUM,
  volume =       "45",
  number =       "2",
  pages =        "14--15",
  month =        feb,
  year =         "2008",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/SPEC.2008.4445770",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Sat Jan 18 12:29:46 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum2000.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "45-nanometer processors; Clocks; Computer
                 architecture; computer math; Convergence; Crops;
                 Digital arithmetic; financial computing; Frequency
                 conversion; Intel; Intel Pentium; Loans and mortgages;
                 microprocessor chips; Microprocessors; Penryn; Penryn
                 chip; Programming profession; scientific computing;
                 Scientific computing; size 45 nm; SRT Radix-4 (Sweeney,
                 Robertson, Tocher) division",
}

@Article{Morris:2008:PLC,
  author =       "Gerald R. Morris and Viktor K. Prasanna",
  title =        "A pipelined-loop-compatible architecture and algorithm
                 to reduce variable-length sets of floating-point data
                 on a reconfigurable computer",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "68",
  number =       "7",
  pages =        "913--921",
  month =        jul,
  year =         "2008",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Fri Jul 11 20:32:36 MDT 2008",
  bibsource =    "http://www.sciencedirect.com/science/journal/07437315;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
}

@Article{Nakamori:2008:SRA,
  author =       "S. Nakamori",
  title =        "Square-root algorithms of {RLS Wiener} filter and
                 fixed-point smoother in linear discrete stochastic
                 systems",
  journal =      j-APPL-MATH-COMP,
  volume =       "203",
  number =       "1",
  pages =        "186--193",
  day =          "1",
  month =        sep,
  year =         "2008",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Fri Sep 3 10:53:23 MDT 2010",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Namin:2008:NFF,
  author =       "A. H. Namin and Huapeng Wu and M. Ahmadi",
  title =        "A New Finite-Field Multiplier Using Redundant
                 Representation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "57",
  number =       "5",
  pages =        "716--720",
  month =        may,
  year =         "2008",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2007.70834",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 12:17:41 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4378354",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Book{P754:2008:ISF,
  author =       "{IEEE Task P754}",
  title =        "{IEEE 754-2008, Standard for Floating-Point
                 Arithmetic}",
  publisher =    pub-IEEE-STD,
  address =      pub-IEEE-STD:adr,
  pages =        "58",
  day =          "29",
  month =        aug,
  year =         "2008",
  DOI =          "https://doi.org/10.1109/IEEESTD.2008.4610935",
  ISBN =         "0-7381-5753-8 (paper), 0-7381-5752-X (electronic)",
  ISBN-13 =      "978-0-7381-5753-5 (paper), 978-0-7381-5752-8
                 (electronic)",
  LCCN =         "????",
  bibdate =      "Thu Sep 25 09:50:30 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeestd.bib",
  URL =          "http://en.wikipedia.org/wiki/IEEE_754-2008;
                 http://ieeexplore.ieee.org/servlet/opac?punumber=4610933",
  abstract =     "This standard specifies interchange and arithmetic
                 formats and methods for binary and decimal
                 floating-point arithmetic in computer programming
                 environments. This standard specifies exception
                 conditions and their default handling. An
                 implementation of a floating-point system conforming to
                 this standard may be realized entirely in software,
                 entirely in hardware, or in any combination of software
                 and hardware. For operations specified in the normative
                 part of this standard, numerical results and exceptions
                 are uniquely determined by the values of the input
                 data, sequence of operations, and destination formats,
                 all under user control.",
  acknowledgement = ack-nhfb,
}

@Article{Pan:2008:SAL,
  author =       "V. Y. Pan and D. Grady and B. Murphy and G. Qian and
                 R. E. Rosholt and A. D. Ruslanov",
  title =        "{Schur} aggregation for linear systems and
                 determinants",
  journal =      j-THEOR-COMP-SCI,
  volume =       "409",
  number =       "2",
  pages =        "255--268",
  day =          "17",
  month =        dec,
  year =         "2008",
  CODEN =        "TCSCDI",
  DOI =          "https://doi.org/10.1016/j.tcs.2008.09.005",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Mon Mar 28 21:21:44 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tcs2005.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975/",
  keywords =     "accurate floating-point summation; Additive
                 preconditioning; Determinants; Iterative refinement;
                 Linear systems of equations; Sherman Morrison Woodbury
                 formula",
}

@InCollection{Patterson:2008:AC,
  author =       "David A. Patterson and John L. Hennessy",
  title =        "Arithmetic for Computers",
  crossref =     "Patterson:2008:COD",
  chapter =      "3",
  pages =        "222--297",
  year =         "2008",
  bibdate =      "Thu Dec 04 18:36:00 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic",
}

@InCollection{Patterson:2008:GCG,
  author =       "David A. Patterson and John L. Hennessy",
  title =        "Graphics and Computing {GPUs}",
  crossref =     "Patterson:2008:COD",
  chapter =      "A",
  pages =        "A-1--A-77",
  year =         "2008",
  bibdate =      "Thu Dec 04 18:36:00 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; GPU",
}

@Article{Pineiro:2008:RDD,
  author =       "J.-A. Pineiro and J. D. Bruguera and F. Lamberti and
                 P. Montuschi",
  title =        "A Radix-2 Digit-by-Digit Architecture for Cube Root",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "57",
  number =       "4",
  pages =        "562--566",
  month =        apr,
  year =         "2008",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2007.70848",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 12:17:41 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4407683",
  abstract =     "A radix-2 digit-recurrence algorithm and architecture
                 for the computation of the cube root are presented in
                 this paper. The original recurrence based on the
                 concept of completing the cube is modified to allow an
                 efficient implementation of the algorithm and the cycle
                 time and area cost of the resulting architecture are
                 estimated as 7.5 times the delay of a full adder and
                 around 9,000 nand2 cells, respectively, for
                 double-precision computations.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Piso:2008:FOS,
  author =       "D. Piso and J. D. Bruguera",
  editor =       "Michael B. Matthews",
  booktitle =    "42nd Asilomar Conference on Signals, Systems and
                 Computers: {October 26--29, 2008, Pacific Grove,
                 California}",
  title =        "Forcing {\em one-sided\/} results in {Goldschmidt}
                 algorithm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1830--1833",
  month =        oct,
  year =         "2008",
  DOI =          "https://doi.org/10.1109/acssc.2008.5074743",
  ISBN =         "1-4244-2941-2",
  ISBN-13 =      "978-1-4244-2941-7",
  ISSN =         "1058-6393",
  ISSN-L =       "1058-6393",
  LCCN =         "TK7801 .A83 2008",
  bibdate =      "Mon Dec 11 08:10:00 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper presents a method to obtain one-sided error
                 results from Goldschmidt (GLD) algorithm. In some
                 applications is useful to obtain a one-sided error
                 result. This is done introducing error bias in the
                 intermediate iterations. An error analysis permits to
                 obtain expressions to estimate the loss of precision
                 and to compensate it. In this way, the one-sided error
                 results are obtained without significant additional
                 hardware requirement.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Piso:2008:NRA,
  author =       "D. Piso and J. D. Bruguera",
  editor =       "Luca Fanucci",
  booktitle =    "Proceedings: {11th Euromicro Symposium on Digital
                 Systems Design: Architectures, Methods and Tools (DSD
                 2008), Parma, Italy, September 3--5, 2008}",
  title =        "A New Rounding Algorithm for Variable Latency Division
                 and Square Root Implementations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "760--767",
  year =         "2008",
  DOI =          "https://doi.org/10.1109/DSD.2008.28.",
  ISBN =         "0-7695-3277-2",
  ISBN-13 =      "978-0-7695-3277-6",
  bibdate =      "Sun Dec 10 13:55:38 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The aim of this work is to present a method for
                 rounding quadratically converging algorithms that
                 improves their performance. This method is able to
                 reduce significantly the number of cases where the
                 remainder calculation is necessary. It is based on
                 previous methods and incorporates additional bits of
                 the result approximation to be checked. This work
                 includes the result of exhaustive simulations that
                 permit us to measure exactly how many calculations are
                 avoided. Using these simulations, it is concluded that
                 the presented method is able to reduce by half the
                 number of remainder calculations. Using adequate result
                 approximations the remainder calculation is necessary
                 in only 5\% of the total cases",
  acknowledgement = ack-nhfb,
}

@Article{Quinnell:2008:BFP,
  author =       "E. Quinnell and E. E. Swartzlander and C. Lemonds",
  title =        "Bridge Floating-Point Fused Multiply-Add Design",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "16",
  number =       "12",
  pages =        "1727--1731",
  year =         "2008",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/TVLSI.2008.2001944",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Sat Feb 19 18:54:07 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
}

@InProceedings{Quinnell:2008:FPF,
  author =       "E. Quinnell and E. E. Swartzlander and C. Lemonds",
  title =        "Floating-Point Fused Multiply-Add Architectures",
  crossref =     "Matthews:2008:CRF",
  pages =        "331--337",
  year =         "2008",
  DOI =          "https://doi.org/10.1109/ACSSC.2007.4487224",
  bibdate =      "Sat Feb 19 18:56:18 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Two new floating-point fused multiply-add
                 architectures for the single instruction execution of $
                 (A \times B) + C $ are presented. The three-path
                 architecture uses parallel hardware paths similar to
                 those in dual-path floating-point adders. The new
                 bridge architecture re-uses common floating-point
                 components to add a fused multiply-add instruction.
                 Each new architecture as well as a collection of
                 floating-point arithmetic units and a classic fused
                 multiplier-adder have been designed using the Advanced
                 Micro Devices 65 nanometer silicon on insulator CMOS
                 technology to fairly compare the new architectures.",
  acknowledgement = ack-nhfb,
}

@Article{Rahaman:2008:CTB,
  author =       "H. Rahaman and J. Mathew and D. K. Pradhan and A. M.
                 Jabir",
  title =        "{C}-testable bit parallel multipliers over {$ {\rm
                 GF}(2^m) $}",
  journal =      j-TODAES,
  volume =       "13",
  number =       "1",
  pages =        "5:1--5:??",
  month =        jan,
  year =         "2008",
  CODEN =        "ATASFO",
  DOI =          "https://doi.org/10.1145/1297666.1297671",
  ISSN =         "1084-4309 (print), 1557-7309 (electronic)",
  ISSN-L =       "1084-4309",
  bibdate =      "Thu Jun 12 18:10:00 MDT 2008",
  bibsource =    "http://www.acm.org/pubs/contents/journals/todaes/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present a C-testable design of polynomial basis
                 (PB) bit-parallel (BP) multipliers over GF(2 m) for
                 100\% coverage of stuck-at faults. Our design method
                 also includes the method for test vector generation,
                 which is simple and efficient. C-testability is
                 achieved with three control inputs and approximately
                 6\% additional hardware. Only 8 constant vectors are
                 required irrespective of the sizes of the fields and
                 primitive polynomial. We also present a Built-In
                 Self-Test (BIST) architecture for generating the test
                 vectors efficiently, which eliminates the need for the
                 extra control inputs. Since these circuits have
                 critical applications as parts of cryptography (e.g.,
                 Elliptic Curve Crypto (ECC) systems) hardware, the BIST
                 architecture may provide with added level of security,
                 as the tests would be done internally and without the
                 requirement of probing by external testing equipment.
                 Finally we present experimental results comprising the
                 area, delay and power of the testable multipliers of
                 various sizes with the help of the Synopsys{\reg} tools
                 using UMC 0. 18 micron CMOS technology library.",
  acknowledgement = ack-nhfb,
  articleno =    "5",
  fjournal =     "ACM Transactions on Design Automation of Electronic
                 Systems (TODAES)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J776",
  keywords =     "built-in self-test; C-testable; cryptography; digital
                 signal processing; error control code; fault;
                 floating-point testing; Galois field; multiplier;
                 polynomials; stuck-at fault; testing; TPG; VLSI
                 design",
}

@Article{Rahaman:2008:DRT,
  author =       "H. Rahaman and J. Mathew and D. K. Pradhan and A. M.
                 Jabir",
  title =        "Derivation of Reduced Test Vectors for Bit-Parallel
                 Multipliers over {$ \mathrm {GF}(2^m) $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "57",
  number =       "9",
  pages =        "1289--1294",
  month =        sep,
  year =         "2008",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2008.63",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 12:17:43 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4487058",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Ravikumar:2008:BND,
  author =       "Bala Ravikumar",
  title =        "The {Benford--Newcomb} Distribution and Unambiguous
                 Context-Free Languages",
  journal =      j-INT-J-FOUND-COMP-SCI,
  volume =       "19",
  number =       "3",
  pages =        "717--727",
  month =        jun,
  year =         "2008",
  CODEN =        "IFCSEN",
  DOI =          "https://doi.org/10.1142/S0129054108005905",
  ISSN =         "0129-0541 (print), 1793-6373 (electronic)",
  ISSN-L =       "0129-0541",
  bibdate =      "Tue Aug 31 07:37:14 MDT 2010",
  bibsource =    "http://ejournals.wspc.com.sg/ijfcs/mkt/archive.shtml;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Foundations of Computer
                 Science (IJFCS)",
  journal-URL =  "http://www.worldscientific.com/loi/ijfcs",
}

@InProceedings{Raz:2008:EFL,
  author =       "Ran Raz",
  title =        "Elusive functions and lower bounds for arithmetic
                 circuits",
  crossref =     "ACM:2008:SPA",
  pages =        "711--720",
  year =         "2008",
  DOI =          "https://doi.org/10.1145/1374376.1374479",
  bibdate =      "Fri Jun 20 18:31:53 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A basic fact in linear algebra is that the image of
                 the curve $ f(x) = (x^1, x^2, x^3, \ldots {}, x^m) $,
                 say over $C$, is not contained in any $ m - 1 $
                 dimensional affine subspace of $ C^m $. In other words,
                 the image of $f$ is not contained in the image of any
                 polynomial-mapping $ \Gamma : C^{m - 1} \rightarrow C^m
                 $ of degree 1 (that is, an affine mapping). Can one
                 give an explicit example for a polynomial curve $ f : C
                 \rightarrow C^m $, such that, the image of $f$ is not
                 contained in the image of any polynomial-mapping $
                 \Gamma : C^{m - 1} \rightarrow C^m $ of degree 2? In
                 this paper, we show that problems of this type are
                 closely related to proving lower bounds for the size of
                 general arithmetic circuits. For example, any explicit
                 $f$ as above (with the right notion of explicitness)
                 implies super-polynomial lower bounds for computing the
                 permanent over $C$. More generally, we say that a
                 polynomial-mapping $ f : F^n \rightarrow F^m $ is $ (s,
                 r) $-elusive, if for every polynomial-mapping $ \Gamma
                 : F^s \rightarrow F^m $ of degree $r$, $ I m(f) \not
                 \subset I m(\Gamma) $. We show that for many settings
                 of the parameters $ n, m, s, r $, explicit
                 constructions of elusive polynomial-mappings imply
                 strong (up to exponential) lower bounds for general
                 arithmetic circuits. Finally, for every $r$, of degree
                 $ O(r) $, that is $ (s, r) $-elusive for $ s = n^{1 +
                 \Omega (1 / r)} $. We use this to construct for any
                 $r$, an explicit example for an $n$-variate polynomial
                 of total-degree $ O(r) $, with coefficients in $ \{ 0,
                 1, \} $ such that, any depth $r$ arithmetic circuit for
                 this polynomial (over any field) is of size $ \geq n^{1
                 + \Omega (1 / r)} $. In particular, for any constant
                 $r$, this gives a constant degree polynomial, such
                 that, any depth $r$ arithmetic circuit for this
                 polynomial is of size $ \geq n^{1 + \Omega (1)} $.
                 Previously, only lower bounds of the type $ \Omega (n
                 \lambda_r (n)) $, where $ \lambda_r (n) $ are extremely
                 slowly growing functions (e.g., $ \lambda_5 (n) = \log
                 n $, and $ \lambda_7 (n) = \log * \log * n $), were
                 known for constant-depth arithmetic circuits for
                 polynomials of constant degree.",
  acknowledgement = ack-nhfb,
  keywords =     "arithmetic circuits; bounded depth circuits; circuit
                 complexity; lower bounds",
}

@Article{Raz:2008:LBS,
  author =       "Ran Raz and Amir Shpilka and Amir Yehudayoff",
  title =        "A Lower Bound for the Size of Syntactically
                 Multilinear Arithmetic Circuits",
  journal =      j-SIAM-J-COMPUT,
  volume =       "38",
  number =       "4",
  pages =        "1624--1647",
  month =        "????",
  year =         "2008",
  CODEN =        "SMJCAT",
  DOI =          "",
  ISSN =         "0097-5397 (print), 1095-7111 (electronic)",
  ISSN-L =       "0097-5397",
  bibdate =      "Tue May 18 08:22:01 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/38/4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Computing",
  journal-URL =  "http://epubs.siam.org/sicomp",
}

@Article{Rodriguez-Henriquez:2008:LCB,
  author =       "F. Rodriguez-Henriquez and G. Morales-Luna and J.
                 Lopez",
  title =        "Low-Complexity Bit-Parallel Square Root Computation
                 over {$ \mathrm {GF}(2^m) $} for All Trinomials",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "57",
  number =       "4",
  pages =        "472--480",
  month =        apr,
  year =         "2008",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2007.70822",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 12:17:40 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4358282",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Ruiz:2008:EIR,
  author =       "Gustavo A. Ruiz and Mercedes Granda",
  title =        "Efficient implementation of {3X} for radix-8
                 encoding",
  journal =      j-MICROELECT-J,
  volume =       "39",
  number =       "1",
  pages =        "152--159",
  month =        jan,
  year =         "2008",
  CODEN =        "MICEB9",
  DOI =          "https://doi.org/10.1016/j.mejo.2007.10.006",
  ISSN =         "0026-2692 (print), 1879-2391 (electronic)",
  ISSN-L =       "0026-2692",
  bibdate =      "Wed Dec 13 09:54:52 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Microelectronics Journal",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00262692",
  keywords =     "Booth-3 encoding; computation of $3 x$; Goldschmidt
                 division algorithm",
}

@Article{Rump:2008:AFPa,
  author =       "Siegfried M. Rump and Takeshi Ogita and Shin'ichi
                 Oishi",
  title =        "Accurate Floating-Point Summation. {Part I}: Faithful
                 Rounding",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "31",
  number =       "1",
  pages =        "189--224",
  month =        "????",
  year =         "2008",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/050645671",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Wed May 19 10:44:12 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/31/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Given a vector of floating-point numbers with exact
                 sum $s$, we present an algorithm for calculating a
                 faithful rounding of $s$, i.e., the result is one of
                 the immediate floating-point neighbors of $s$. If the
                 sum $s$ is a floating-point number, we prove that this
                 is the result of our algorithm. The algorithm adapts to
                 the condition number of the sum, i.e., it is fast for
                 mildly conditioned sums with slowly increasing
                 computing time proportional to the logarithm of the
                 condition number. All statements are also true in the
                 presence of underflow. The algorithm does not depend on
                 the exponent range. Our algorithm is fast in terms of
                 measured computing time because it allows good
                 instruction-level parallelism, it neither requires
                 special operations such as access to mantissa or
                 exponent, it contains no branch in the inner loop, nor
                 does it require some extra precision: The only
                 operations used are standard floating-point addition,
                 subtraction, and multiplication in one working
                 precision, for example, double precision. Certain
                 constants used in the algorithm are proved to be
                 optimal.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  keywords =     "accurate floating-point summation; distillation",
}

@Article{Rump:2008:AFPb,
  author =       "Siegfried M. Rump and Takeshi Ogita and Shin'ichi
                 Oishi",
  title =        "Accurate Floating-Point Summation. {Part II}: Sign,
                 {$K$}-Fold Faithful and Rounding to Nearest",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "31",
  number =       "2",
  pages =        "1269--1302",
  month =        "????",
  year =         "2008",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/07068816X",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Wed May 19 10:44:14 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/31/2;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In Part II of this paper we first refine the analysis
                 of error-free vector transformations presented in Part
                 I. Based on that we present an algorithm for
                 calculating the rounded-to-nearest result of $ s :=
                 \sum p_i $ for a given vector of floating-point numbers
                 $ p_i $, as well as algorithms for directed rounding. A
                 special algorithm for computing the sign of $s$ is
                 given, also working for huge dimensions. Assume a
                 floating-point working precision with relative rounding
                 error unit eps. We define and investigate a $K$-fold
                 faithful rounding of a real number $r$. Basically the
                 result is stored in a vector $ \mathtt {Res}_{\nu } $
                 of $K$ nonoverlapping floating-point numbers such that
                 $ \sum \mathtt {Res}_{\nu } $ approximates $r$ with
                 relative accuracy $ \mathtt {eps}^K $, and replacing $
                 \mathtt {Res}_K $ by its floating-point neighbors in $
                 \sum \mathtt {Res}_{\nu } $ forms a lower and upper
                 bound for $r$. For a given vector of floating-point
                 numbers with exact sum $s$, we present an algorithm for
                 calculating a $K$-fold faithful rounding of $s$ using
                 solely the working precision. Furthermore, an algorithm
                 for calculating a faithfully rounded result of the sum
                 of a vector of huge dimension is presented. Our
                 algorithms are fast in terms of measured computing time
                 because they allow good instruction-level parallelism,
                 they neither require special operations such as access
                 to mantissa or exponent, they contain no branch in the
                 inner loop, nor do they require some extra precision.
                 The only operations used are standard floating-point
                 addition, subtraction, and multiplication in one
                 working precision, for example, double precision.
                 Certain constants used in the algorithms are proved to
                 be optimal.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  keywords =     "accurate floating-point summation; distillation",
}

@TechReport{Rump:2008:UFA,
  author =       "Siegfried M. Rump",
  title =        "Ultimately Fast Accurate Summation",
  type =         "Technical Report",
  institution =  "Institute for Reliable Computing, Technische
                 Universit{\"a}t Hamburg",
  address =      "Hamburg, Germany",
  pages =        "28",
  day =          "19",
  month =        oct,
  year =         "2008",
  MRclass =      "15-04, 65G99, 65-04",
  bibdate =      "Sat Oct 25 15:15:14 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ti3.tu-harburg.de/paper/rump/Ru08b.pdf",
  abstract =     "We present two new algorithms FastAccSum and
                 FastPrecSum, one to compute a faithful rounding of the
                 sum of floating-point numbers, and the other for a
                 result ``as if'' computed in $K$-fold precision.
                 Faithful rounding means the result is one of the
                 immediate floating-point neighbors of the exact result,
                 or the exact sum if it is a floating-point number. The
                 algorithms are based on our previous algorithms AccSum
                 and PrecSum and improve them by up to 25\%. The first
                 algorithm adapts to the condition number of the sum,
                 i.e., the computing time is proportional to the
                 logarithm of the condition number. The second algorithm
                 does not need extra memory, and the computing time
                 depends only on the dimension and $K$. Both algorithms
                 are the fastest known in terms of flops. They allow
                 good instruction-level parallelism so that they are
                 also fast in terms of measured computing time. The
                 algorithms require only standard floating-point
                 addition, subtraction and multiplication in one working
                 precision, for example double precision.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation; distillation; error
                 analysis; error-free transformation; faithful rounding;
                 high accuracy; K-fold precision; maximally accurate
                 summation; XBLAS",
  remark =       "Submitted for publication.",
}

@Article{Russell:2008:BOR,
  author =       "Craig Russell",
  title =        "Bridging the Object-Relational Divide",
  journal =      j-QUEUE,
  volume =       "6",
  number =       "3",
  pages =        "18--28",
  month =        may # "\slash " # jun,
  year =         "2008",
  CODEN =        "AQCUAE",
  DOI =          "https://doi.org/10.1145/1394127.1394139",
  ISSN =         "1542-7730 (print), 1542-7749 (electronic)",
  ISSN-L =       "1542-7730",
  bibdate =      "Tue Aug 5 19:04:31 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "ORM technologies can simplify data access, but be
                 aware of the challenges that come with introducing this
                 new layer of abstraction.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Queue: Tomorrow's Computing Today",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J882",
}

@Article{Schreppers:2008:ACC,
  author =       "Walter Schreppers and Annie Cuyt",
  title =        "{Algorithm 871}: a {C\slash C++} precompiler for
                 autogeneration of multiprecision programs",
  journal =      j-TOMS,
  volume =       "34",
  number =       "1",
  pages =        "5:1--5:20",
  month =        jan,
  year =         "2008",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1322436.1322441",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Mar 12 17:39:58 MDT 2008",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In the past decade a number of libraries for
                 multiprecision floating-point arithmetic have been
                 developed. We describe an easy to use, generic C/C++
                 transcription program or precompiler for the conversion
                 of C or C++ source code into new code that uses a C++
                 multiprecision library of choice. The precompiler can
                 convert any type in the input source code to another
                 type in the output source code. The input source can be
                 either C or C++, while the output code generated by the
                 precompiler and using the new types, is C++. The type
                 conversion is based on a simple XML configuration file
                 which is provided by either the developer of the
                 multiprecision library or by the user of the
                 precompiler. The precompiler can also convert to data
                 types with additional features, which are not supported
                 in the types of the source code. Applicability of the
                 precompiler is shown with the successful conversion of
                 large subsets of the GNU Scientific Library and
                 Numerical Recipes.",
  acknowledgement = ack-nhfb,
  articleno =    "5",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Misc{Steele:2008:FPA,
  author =       "Guy L. {Steele Jr.}",
  title =        "Floating point adder with embedded status
                 information",
  howpublished = "US Patent 7366749",
  day =          "29",
  month =        apr,
  year =         "2008",
  bibdate =      "Tue Dec 23 15:06:47 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/7366749/fulltext.html",
  abstract =     "A system for providing a floating point sum includes
                 an analyzer circuit configured to determine a first
                 status of a first floating point operand and a second
                 status of a second floating point operand based upon
                 data within the first floating point operand and data
                 with the second floating point operand respectively. In
                 addition, the system includes a results circuit coupled
                 to the analyzer circuit. The results circuit is
                 configured to assert a resulting floating point operand
                 containing the sum of the first floating point operand
                 and the second floating point operand and a resulting
                 status embedded within the resulting floating point
                 operand.",
  acknowledgement = ack-nhfb,
}

@Misc{Steele:2008:FPD,
  author =       "Guy L. {Steele Jr.}",
  title =        "Floating point divider with embedded status
                 information",
  howpublished = "US Patent 7363337",
  day =          "22",
  month =        apr,
  year =         "2008",
  bibdate =      "Tue Dec 23 15:06:47 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/7363337/fulltext.html",
  abstract =     "A system for providing floating point division
                 includes an analyzer circuit configured to determine a
                 first status of a first floating point operand and a
                 second status of a second floating point operand based
                 upon data within the first floating point operand and
                 data within the second floating point operand
                 respectively. In addition, the system includes a
                 results circuit coupled to the analyzer circuit. The
                 results circuit is configured to assert a resulting
                 floating point operand containing the result of the
                 division of the first floating point operand by the
                 second floating point operand. Additionally, the
                 results circuit provides resulting status embedded
                 within the resulting floating point operand.",
  acknowledgement = ack-nhfb,
}

@Misc{Steele:2008:FPSa,
  author =       "Guy L. {Steele Jr.}",
  title =        "Floating point status information accumulation
                 circuit",
  howpublished = "US Patent 7444367",
  day =          "28",
  month =        oct,
  year =         "2008",
  bibdate =      "Tue Dec 23 15:05:52 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/7444367/fulltext.html",
  abstract =     "A floating point flag combining or accumulating
                 circuit includes an analysis circuit that receives a
                 plurality of floating point operands, each having
                 encoded status flag information, and a result
                 assembler. The analysis circuit analyzes the plurality
                 of floating point operands and provides an indication
                 of one or more predetermined formats in which the
                 plurality of floating point operands are represented.
                 The result assembler receives the indication from the
                 analysis circuit and assembles an accumulated result
                 that represents a value and combines the encoded status
                 flag information from at least two of the plurality of
                 floating point operands.",
  acknowledgement = ack-nhfb,
}

@Misc{Steele:2008:FPSb,
  author =       "Guy L. {Steele Jr.}",
  title =        "Floating point square root provider with embedded
                 status information",
  howpublished = "US Patent 7430576",
  day =          "30",
  month =        sep,
  year =         "2008",
  bibdate =      "Tue Dec 23 15:06:43 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/7430576/fulltext.html",
  abstract =     "A system for providing a floating point square root
                 comprises an analyzer circuit configured to determine a
                 first status of a first floating point operand based
                 upon data within the first floating point operand. In
                 addition, the system comprises a results circuit
                 coupled to the analyzer circuit. The results circuit is
                 configured to assert a resulting floating point operand
                 containing the square root of the first floating point
                 operand and a resulting status embedded within the
                 resulting floating point operand.",
  acknowledgement = ack-nhfb,
}

@Misc{Steele:2008:FPSc,
  author =       "Guy L. {Steele Jr.}",
  title =        "Floating point system that represents status flag
                 information within a floating point operand",
  howpublished = "US Patent 7395297",
  day =          "01",
  month =        jul,
  year =         "2008",
  bibdate =      "Tue Dec 23 15:06:47 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.patentstorm.us/patents/7395297/fulltext.html",
  abstract =     "A floating point unit generates results in which
                 status information generated for an operation is
                 encoded within the resulting operand, instead of
                 requiring a separate floating point status register for
                 the status information. In one embodiment, a floating
                 point operand data structure includes a first portion
                 having floating point operand data and a second portion
                 having embedded status information associated with at
                 least one status condition of the operand data. The
                 status condition may be determined from only the
                 embedded status information. The status condition may
                 also be associated with at least one floating point
                 operation that generated the operand data structure.
                 The outcome of a conditional floating point instruction
                 may be based on the embedded status information without
                 regard to contents of the floating point status
                 register. The second portion of the data structure may
                 also have at least one bit indicative of the status
                 condition, such as an invalid operation status, an
                 overflow status, an underflow status, a division by
                 zero status, an infinity status, and an inexact
                 status.",
  acknowledgement = ack-nhfb,
}

@Article{Sun:2008:HPM,
  author =       "Junqing Sun and G. D. Peterson and O. O. Storaasli",
  title =        "High-Performance Mixed-Precision Linear Solver for
                 {FPGAs}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "57",
  number =       "12",
  pages =        "1614--1623",
  month =        dec,
  year =         "2008",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2008.89",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 12:17:44 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4531732",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Terauds:2008:CFP,
  author =       "Maris Terauds and Gatis Valters and Uldis Derums and
                 Nauris Vasilevskis and Peteris Misans",
  booktitle =    "{2008 NORCHIP}",
  title =        "Comparison of Fixed-Point Arithmetic Errors for the
                 {FPGA}-based {CRAIMOT} Basis Function Generators",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "108--113",
  year =         "2008",
  DOI =          "https://doi.org/10.1109/NORCHP.2008.4738293",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithm design and analysis; CORDIC algorithm;
                 Discrete cosine transforms; Error analysis; Field
                 programmable gate arrays; Fixed-point arithmetic;
                 Fixed-point errors; FPGA; Generation of basis
                 functions; Interpolation; Quantization; Signal
                 generators; Signal synthesis; Speech synthesis",
}

@Article{Thill:2008:EMP,
  author =       "M. Thill",
  title =        "Erratum: a more precise rounding algorithm for
                 rational numbers",
  journal =      j-COMPUTING,
  volume =       "82",
  number =       "4",
  pages =        "261--262",
  month =        sep,
  year =         "2008",
  CODEN =        "CMPTA2",
  DOI =          "https://doi.org/10.1007/s00607-008-0013-8",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Sun Oct 31 11:09:49 MDT 2010",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=82&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Thill:2008:MPR}.",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=82&issue=4&spage=261",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Article{Thill:2008:MPR,
  author =       "M. Thill",
  title =        "A more precise rounding algorithm for rational
                 numbers",
  journal =      j-COMPUTING,
  volume =       "82",
  number =       "2--3",
  pages =        "189--198",
  month =        jul,
  year =         "2008",
  CODEN =        "CMPTA2",
  DOI =          "https://doi.org/10.1007/s00607-008-0006-7",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Sun Oct 31 11:09:47 MDT 2010",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=82&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See erratum \cite{Thill:2008:EMP}.",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=82&issue=2&spage=189",
  abstract =     "We adjoin a more precise companion to the classical
                 mediant rounding algorithm for rational numbers.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Article{Tsigaridas:2008:CRR,
  author =       "Elias P. Tsigaridas and Ioannis Z. Emiris",
  title =        "On the complexity of real root isolation using
                 continued fractions",
  journal =      j-THEOR-COMP-SCI,
  volume =       "392",
  number =       "1--3",
  pages =        "158--173",
  day =          "28",
  month =        feb,
  year =         "2008",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Mon Mar 28 21:49:12 MDT 2011",
  bibsource =    "http://www.sciencedirect.com/science/journal/03043975;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}

@Article{VanMeter:2008:ADM,
  author =       "Rodney {Van Meter} and W. J. Munro and Kae Nemoto and
                 Kohei M. Itoh",
  title =        "Arithmetic on a distributed-memory quantum
                 multicomputer",
  journal =      j-JETC,
  volume =       "3",
  number =       "4",
  pages =        "2:1--2:??",
  month =        jan,
  year =         "2008",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/1324177.1324179",
  ISSN =         "1550-4832 (print), 1550-4840 (electronic)",
  ISSN-L =       "1550-4832",
  bibdate =      "Fri Jun 20 11:04:00 MDT 2008",
  bibsource =    "http://www.acm.org/pubs/contents/journals/jetc/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We evaluate the performance of quantum arithmetic
                 algorithms run on a distributed quantum computer (a
                 quantum multicomputer). We vary the node capacity and
                 I/O capabilities, and the network topology. The
                 tradeoff of choosing between gates executed remotely,
                 through ``teleported gates'' on entangled pairs of
                 qubits (telegate), versus exchanging the relevant
                 qubits via quantum teleportation, then executing the
                 algorithm using local gates (teledata), is examined. We
                 show that the teledata approach performs better, and
                 that carry-ripple adders perform well when the
                 teleportation block is decomposed so that the key
                 quantum operations can be parallelized. A node size of
                 only a few logical qubits performs adequately provided
                 that the nodes have two transceiver qubits. A linear
                 network topology performs acceptably for a broad range
                 of system sizes and performance parameters. We
                 therefore recommend pursuing small, high-I/O bandwidth
                 nodes and a simple network. Such a machine will run
                 Shor's algorithm for factoring large numbers
                 efficiently.",
  acknowledgement = ack-nhfb,
  articleno =    "2",
  fjournal =     "ACM Journal on Emerging Technologies in Computing
                 Systems (JETC)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J967",
  keywords =     "quantum computer architecture; Quantum computing",
}

@Article{Webb:2008:IZN,
  author =       "Charles F. Webb",
  title =        "{IBM z10}: The Next-Generation Mainframe
                 Microprocessor",
  journal =      j-IEEE-MICRO,
  volume =       "28",
  number =       "2",
  pages =        "19--29",
  month =        mar # "\slash " # apr,
  year =         "2008",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.2008.26",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Wed Jul 2 21:58:04 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The IBM system z10 includes four microprocessor cores
                 --- each with a private 3-Mbyte cache --- and
                 integrated accelerators for decimal floating-point
                 computation, cryptography, and data compression. A
                 separate SMP hub chip provides a shared third-level
                 cache and interconnect fabric for multiprocessor
                 scaling. This article focuses on the high-frequency
                 design techniques used to achieve a 4.4-GHz system, and
                 on the pipeline design that optimizes z10's CPU
                 performance.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  keywords =     "decimal floating-point arithmetic",
}

@TechReport{Wirth:2008:ND,
  author =       "Niklaus Wirth",
  title =        "A Note on Division",
  type =         "Note",
  institution =  inst-ETH,
  address =      inst-ETH:adr,
  pages =        "4",
  day =          "20",
  month =        aug,
  year =         "2008",
  bibdate =      "Tue Jan 09 07:42:36 2024",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/w/wirth-niklaus.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://people.inf.ethz.ch/wirth/Miscellaneous/Division.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Niklaus Wirth (15 February 1934--1 January 2024)",
}

@Article{Yamanaka:2008:PAA,
  author =       "Naoya Yamanaka and Takeshi Ogita and Siegfried M. Rump
                 and Shin'ichi Oishi",
  title =        "A parallel algorithm for accurate dot product",
  journal =      j-PARALLEL-COMPUTING,
  volume =       "34",
  number =       "6--8",
  pages =        "392--410",
  month =        jul,
  year =         "2008",
  CODEN =        "PACOEJ",
  DOI =          "https://doi.org/10.1016/j.parco.2008.02.002",
  ISSN =         "0167-8191 (print), 1872-7336 (electronic)",
  ISSN-L =       "0167-8191",
  bibdate =      "Thu Sep 2 17:51:09 MDT 2010",
  bibsource =    "http://www.sciencedirect.com/science/journal/01678191;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Parallel algorithms for accurate summation and dot
                 product are proposed. They are parallelized versions of
                 fast and accurate algorithms of calculating sum and dot
                 product using error-free transformations which are
                 recently proposed by Ogita et al. [T. Ogita, S. M.
                 Rump, S. Oishi, Accurate sum and dot product, SIAM J.
                 Sci. Comput. 26(6) (2005) 1955--1988]. They have shown
                 their algorithms are fast in terms of measured
                 computing time. However, due to the strong data
                 dependence in the process of their algorithms, it is
                 difficult to parallelize them. Similarly to their
                 algorithms, the proposed parallel algorithms in this
                 paper are designed to achieve the results as if
                 computed in K-fold working precision with keeping the
                 fastness of their algorithms. Numerical results are
                 presented showing the performance of the proposed
                 parallel algorithm of calculating dot product.",
  acknowledgement = ack-nhfb,
  fjournal =     "Parallel Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01678191",
  keywords =     "accurate dot product; accurate summation; DotK; higher
                 precision; parallel algorithm; PDotK; PSumK; SumK",
  remark =       "See \cite{Ogita:2005:ASD} for the cited paper.",
}

@InProceedings{Zhou:2008:DCF,
  author =       "Jie Zhou and Yazhuo Dong and Yong Dou and Yuanwu Lei",
  booktitle =    "{2008 International Conference on Embedded Software
                 and Systems}",
  title =        "Dynamic Configurable Floating-Point {FFT} Pipelines
                 and Hybrid-Mode {CORDIC} on {FPGA}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "616--620",
  year =         "2008",
  DOI =          "https://doi.org/10.1109/ICESS.2008.95",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Azimuth; Clocks; CORDIC; Dynamic configurable
                 pipeline; FFT; Field programmable gate arrays;
                 Floating-point; FPGA; Lead; Pipelines; Process control;
                 Table lookup",
}

@InProceedings{Zhou:2008:DPH,
  author =       "Jie Zhou and Yong Dou and Yuanwu Lei and Jinbo Xu and
                 Yazhuo Dong",
  booktitle =    "{2008 10th IEEE International Conference on High
                 Performance Computing and Communications}",
  title =        "Double Precision Hybrid-Mode Floating-Point {FPGA}
                 {CORDIC} Co-processor",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "182--189",
  year =         "2008",
  DOI =          "https://doi.org/10.1109/HPCC.2008.14",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithm design and analysis; Convergence; CORDIC;
                 double precision; Equations; Field programmable gate
                 arrays; floating-point; FPGA; Hardware; hybrid-mode;
                 Mathematical model; Pipelines",
}

@InProceedings{Zhou:2008:HMF,
  author =       "Jie Zhou and Yong Dou and Yuanwu Lei and Yazhuo Dong",
  title =        "Hybrid-Mode Floating-Point {FPGA} {CORDIC}
                 Co-processor",
  crossref =     "Woods:2008:RCA",
  pages =        "256--261",
  year =         "2008",
  DOI =          "https://doi.org/10.1007/978-3-540-78610-8_25",
  bibdate =      "Tue Oct 28 07:04:09 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Adikari:2009:HBT,
  author =       "Jithra Adikari and Vassil Dimitrov and Laurent
                 Imbert",
  title =        "Hybrid Binary-Ternary Joint Form and Its Application
                 in Elliptic Curve Cryptography",
  crossref =     "Bruguera:2009:PIS",
  pages =        "76--83",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Multi-exponentiation is a common and time consuming
                 operation in public-key cryptography. Its elliptic
                 curve counterpart, called multi-scalar multiplication
                 is extensively used for digital signature verification.
                 Several algorithms have been proposed to speed-up those
                 critical computations. They are based on simultaneously
                 recoding a set of integers in order to minimize the
                 number of general multiplications or point additions.
                 When signed-digit recoding techniques can be used, as
                 in the world of elliptic curves, Joint Sparse Form
                 (JSF) and interleaving w-NAF are the most efficient
                 algorithms. In this paper, a novel recoding algorithm
                 for a pair of integers is proposed, based on a
                 decomposition that mixes powers of 2 and powers of 3.
                 The so-called Hybrid Binary-Ternary Joint Form require
                 fewer digits and is sparser than the JSF and the
                 interleaving w-NAF. Its advantages are illustrated for
                 elliptic curve double-scalar multiplication; the
                 operation counts show a gain of up to 19\%.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19",
}

@InProceedings{Amaricai:2009:DFP,
  author =       "A. Amaricai and M. Vladutiu and O. Boncalo",
  title =        "Design of floating point units for interval
                 arithmetic",
  crossref =     "IEEE:2009:PDR",
  year =         "2009",
  DOI =          "https://doi.org/10.1109/RME.2009.5201307",
  bibdate =      "Thu Mar 24 21:37:47 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this paper, hardware units for interval addition,
                 multiplication and divide-add fused are presented.
                 Regarding interval addition, a new architecture of
                 double path adder, is presented. This architecture
                 exploits the parallel structure of double path adder.
                 Regarding multiplication, the proposed architecture is
                 based on a dual result multiplier (floating point
                 multiplication unit with two differently rounded
                 results for the same pair of operands) and two floating
                 point comparators. The goal of the divide-add fused
                 unit is to increase the performance of the interval
                 Newton's method. Algorithm and architecture for this
                 operation, inspired by the ones used for multiply-add
                 fused, are proposed.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Anderson:2009:PAD,
  author =       "Michael J. Anderson and Charles Tsen and Liang-Kai
                 Wang and Katherine Compton and Michael J. Schulte",
  title =        "Performance analysis of decimal floating-point
                 libraries and its impact on decimal hardware and
                 software solutions",
  crossref =     "IEEE:2009:IICb",
  pages =        "465--471",
  year =         "2009",
  DOI =          "https://doi.org/10.1109/ICCD.2009.5413114",
  bibdate =      "Thu Feb 17 08:05:14 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The IEEE Standards Committee recently approved the
                 IEEE 754-2008 Standard for Floating-point Arithmetic,
                 which includes specifications for decimal
                 floating-point (DFP) arithmetic. A growing number of
                 DFP solutions have emerged, and developers now have
                 many DFP design choices including arbitrary or fixed
                 precision, binary or decimal significand encodings,
                 64-bit or 128-bit DFP operands, and software or
                 hardware implementations.\par

                 There is a need for accurate analysis of these
                 solutions on representative DFP benchmarks. In this
                 paper, we expand previous DFP benchmark and performance
                 analysis research. We employ a DFP benchmark suite that
                 currently supports several DFP solutions and is easily
                 extendable. We also present performance analysis that
                 (1) provides execution profiles for various DFP
                 encodings and types, (2) gives the average number
                 cycles for common DFP operations and the total number
                 of each DFP operation in each benchmark, and (3)
                 highlights the tradeoffs between using 64-bit and
                 128-bit DFP operands for both binary and decimal
                 significand encodings. This analysis can help guide the
                 design of future DFP hardware and software solutions.",
  acknowledgement = ack-nhfb,
  keywords =     "binary significand encodings; decimal floating-point
                 arithmetic; decimal floating-point libraries; decimal
                 significand encodings; DFP encodings; DFP hardware
                 solutions; DFP operands; DFP software solutions; IEEE
                 754-2008 standard; IEEE Standards Committee;
                 performance analysis",
}

@InProceedings{Anonymous:2009:AI,
  author =       "Anonymous",
  title =        "Author Index",
  crossref =     "Bruguera:2009:PIS",
  pages =        "235--235",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19",
}

@Article{Anonymous:2009:CPC,
  author =       "Anonymous",
  title =        "Call-for-Papers on Computer Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "5",
  pages =        "719--719",
  month =        may,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2009.47",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 11:37:41 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Arnold:2009:DPR,
  author =       "Mark G. Arnold and Sylvain Collange",
  title =        "A Dual-Purpose Real\slash Complex Logarithmic Number
                 System {ALU}",
  crossref =     "Bruguera:2009:PIS",
  pages =        "15--24",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The real Logarithmic Number System (LNS) allows fast
                 and inexpensive multiplication and division but more
                 expensive addition and subtraction as precision
                 increases. Recent advances in higher-order and
                 multipartite table methods, together with
                 cotransformation, allow real LNS ALUs to be implemented
                 effectively on FPGAs for a wide variety of
                 medium-precision special-purpose applications. The
                 Complex LNS (CLNS) is a generalization of LNS which
                 represents complex values in log-polar form. CLNS is a
                 more compact representation than traditional
                 rectangular methods, reducing the cost of busses and
                 memory in intensive complex-number applications like
                 the FFT; however, prior CLNS implementations were
                 either slow CORDIC-based or expensive 2D-table-based
                 approaches. This paper attempts to leverage the recent
                 advances made in real-valued LNS units for the more
                 specialized context of CLNS. This paper proposes a
                 novel approach to reduce the cost of CLNS addition by
                 re-using a conventional real-valued LNS ALU with
                 specialized CLNS hardware that is smaller than the
                 real-valued LNS ALU to which it is attached. The
                 resulting ALU is much less expensive than prior fast
                 CLNS units at the cost of some extra delay. The extra
                 hardware added to the ALU is for trigonometric-related
                 functions, and may be useful in LNS applications other
                 than CLNS. The novel algorithm proposed here is
                 implemented using the FloPoCo library (which
                 incorporates recent HOTBM advances in function-unit
                 generation), and FPGA synthesis results are reported.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19; complex arithmetic; FPGA; hardware function
                 evaluation; logarithmic number system",
}

@Article{Baboulin:2009:ASC,
  author =       "Marc Baboulin and Alfredo Buttari and Jack Dongarra
                 and Jakub Kurzak and Julie Langou and Julien Langou and
                 Piotr Luszczek and Stanimire Tomov",
  title =        "Accelerating scientific computations with mixed
                 precision algorithms",
  journal =      j-COMP-PHYS-COMM,
  volume =       "180",
  number =       "12",
  pages =        "2526--2533",
  month =        dec,
  year =         "2009",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2008.11.005",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 23:42:47 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465508003846",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@InProceedings{Bajard:2009:SRB,
  author =       "J. C. Bajard and M. Kaihara and T. Plantard",
  title =        "Selected {RNS} Bases for Modular Multiplication",
  crossref =     "Bruguera:2009:PIS",
  pages =        "25--31",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The selection of the elements of the bases in an RNS
                 modular multiplication method is crucial and has a
                 great impact in the overall performance. This work
                 proposes specific sets of optimal RNS moduli with
                 elements of Hamming weight three whose inverses used in
                 the MRS reconstruction have very small Hamming weight.
                 This property is exploited in RNS bases conversions, to
                 completely remove and replace the products by few
                 additions/subtractions and shifts, reducing the time
                 complexity of modular multiplication. These bases are
                 specially crafted to computation with operands of sizes
                 256 or more and are suitable for cryptographic
                 applications such as the ECC protocols.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19",
}

@Article{Barsi:2009:ECP,
  author =       "Ferruccio Barsi and Maria Cristina Pinotti",
  title =        "Error control by product codes in arithmetic units",
  journal =      j-INT-J-PAR-EMER-DIST-SYS,
  volume =       "24",
  number =       "5",
  pages =        "407--419",
  year =         "2009",
  CODEN =        "????",
  ISSN =         "1744-5760 (print), 1744-5779 (electronic)",
  ISSN-L =       "1744-5760",
  bibdate =      "Thu Sep 2 08:12:37 MDT 2010",
  bibsource =    "http://www.informaworld.com/smpp/title~content=t713729127~link=cover;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.tandfonline.com/loi/gpaa20",
}

@Article{Bayat-Sarmadi:2009:CED,
  author =       "S. Bayat-Sarmadi and M. A. Hasan",
  title =        "Concurrent Error Detection in Finite-Field Arithmetic
                 Operations Using Pipelined and Systolic Architectures",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "11",
  pages =        "1553--1567",
  month =        nov,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2009.62",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 11:37:44 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4815219",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Beebe:2009:NML,
  author =       "Nelson H. F. Beebe",
  title =        "A new math library",
  journal =      j-IJQC,
  volume =       "109",
  number =       "13",
  pages =        "3008--3025",
  day =          "5",
  month =        nov,
  year =         "2009",
  CODEN =        "IJQCB2",
  DOI =          "https://doi.org/10.1002/qua.22266",
  ISSN =         "0020-7608 (print), 1097-461X (electronic)",
  ISSN-L =       "0020-7608",
  bibdate =      "Tue Sep 08 18:56:33 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The design and development of a new mathematical
                 function library is described. The library extends
                 programming support to decimal, as well as binary,
                 arithmetic, and aims to influence the future evolution
                 of floating-point support in programming languages,
                 libraries, and hardware. It encourages and facilitates
                 research in new computer-arithmetic designs, and the
                 analysis and comparison of historical ones.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Quantum Chemistry",
  journal-URL =  "http://www.interscience.wiley.com/jpages/0020-7608/",
  keywords =     "binary arithmetic; computer arithmetic; decimal
                 arithmetic; elementary functions; floating-point
                 arithmetic; hexadecimal arithmetic; input/output
                 conversions; integer arithmetic; interpreted languages;
                 mathematical software library; number bases;
                 octuple-precision arithmetic; pair-precision
                 arithmetic; programming languages; scripting languages;
                 special functions; wobbling precision",
  pagecount =    "15",
  remark =       "Submitted 28 January 2009; accepted 17 March 2009.",
}

@Article{Blomquist:2009:MSC,
  author =       "Frithjof Blomquist and Werner Hofschuster and Walter
                 Kr{\"a}mer",
  title =        "A Modified Staggered Correction Arithmetic with
                 Enhanced Accuracy and Very Wide Exponent Range",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "5492",
  pages =        "41--67",
  year =         "2009",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-642-01591-5_4",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Apr 10 08:32:19 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/content/k038294004403504/",
  acknowledgement = ack-nhfb,
  author-dates = "1952--2014 (WK)",
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
  keywords =     "C-XSC; complex interval functions; interval
                 computation; multiple precision; reliable numerical
                 computations; staggered correction; wide exponent
                 range",
  remark =       "Conference on Numerical Validation in Current Hardware
                 Architectures",
  remark-2 =     "Includes algorithms for division, $\exp(x)$, $(1 +
                 x)^n$, $\log(x)$, $\log(1 + x)$, and $\sqrt{x}$.
                 Staggered arithmetic represents numbers with tuples
                 $(e, x_1, x_2, \ldots{}, x_n)$ where $e$ is either
                 integer or a floating-point whole number, the $x_k$ are
                 floating-point, and a number has the value $2^e \sum_{k
                 = 1}^n x_k$. For interval arithmetic, the last element
                 is a pair of lower and upper bounds.",
}

@Article{Boldo:2009:CCG,
  author =       "Sylvie Boldo and Jean-Christophe Filli{\^a}tre and
                 Guillaume Melquiond",
  title =        "Combining {Coq} and {Gappa} for Certifying
                 Floating-Point Programs",
  journal =      j-LECT-NOTES-COMP-SCI,
  pages =        "59--74",
  year =         "2009",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-642-02614-0_10",
  ISBN =         "3-642-02614-1",
  ISBN-13 =      "978-3-642-02614-0",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Jun 8 08:31:22 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
  keywords =     "Intelligent Computer Mathematics",
}

@Article{Boldo:2009:FRC,
  author =       "Sylvie Boldo",
  title =        "Floats and Ropes: a Case Study for Formal Numerical
                 Program Verification",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "5556",
  pages =        "91--102",
  year =         "2009",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-642-02930-1_8",
  ISBN =         "3-642-02930-2",
  ISBN-13 =      "978-3-642-02930-1",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Jun 8 08:25:53 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
  keywords =     "Automata, Languages and Programming. ICALP 2009",
}

@Article{Boldo:2009:FVA,
  author =       "S. Boldo and Marc Daumas and Ren-Cang Li",
  title =        "Formally Verified Argument Reduction with a Fused
                 Multiply-Add",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "8",
  pages =        "1139--1145",
  month =        aug,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2008.216",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 11:37:43 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4711042",
  abstract =     "The Cody and Waite argument reduction technique works
                 perfectly for reasonably large arguments, but as the
                 input grows, there are no bits left to approximate the
                 constant with enough accuracy. Under mild assumptions,
                 we show that the result computed with a fused
                 multiply-add provides a fully accurate result for many
                 possible values of the input with a constant almost
                 accurate to the full working precision. We also present
                 an algorithm for a fully accurate second reduction step
                 to reach full double accuracy (all the significand bits
                 of two numbers are accurate) even in the worst cases of
                 argument reduction. Our work recalls the common
                 algorithms and presents proofs of correctness. All the
                 proofs are formally verified using the Coq automatic
                 proof checker.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Boldo:2009:KAC,
  author =       "S. Boldo",
  title =        "{Kahan}'s Algorithm for a Correct Discriminant
                 Computation at Last Formally Proven",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "2",
  pages =        "220--225",
  month =        feb,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2008.200",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jun 12 08:51:00 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  note =         "See \cite{Kahan:2004:CFP} for the original
                 algorithm.",
  abstract =     "This article tackles Kahan's algorithm to compute
                 accurately the discriminant. This is a known difficult
                 problem, and this algorithm leads to an error bounded
                 by 2 ulps of the floating-point result. The proofs
                 involved are long and tricky and even trickier than
                 expected as the test involved may give a result
                 different from the result of the same test without
                 rounding. We give here the total demonstration of the
                 validity of this algorithm, and we provide sufficient
                 conditions to guarantee that neither overflow nor
                 underflow will jeopardize the result. The IEEE-754
                 double-precision program is annotated using the Why
                 platform and the proof obligations are done using the
                 Coq automatic proof checker.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Coq; correct rounding; discriminant; floating point;
                 formal proof; Why platform",
  remark =       "Extended version of ARITH-18 article
                 \cite{Boldo:2007:FVF}.",
}

@Article{Bryant:2009:ABD,
  author =       "Randal E. Bryant and Daniel Kroening and Jo{\"e}l
                 Ouaknine and Sanjit A. Seshia and Ofer Strichman and
                 Bryan Brady",
  title =        "An abstraction-based decision procedure for bit-vector
                 arithmetic",
  journal =      j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER,
  volume =       "11",
  number =       "2",
  pages =        "95--104",
  month =        apr,
  year =         "2009",
  CODEN =        "????",
  ISSN =         "1433-2779 (print), 1433-2787 (electronic)",
  ISSN-L =       "1433-2779",
  bibdate =      "Sat Sep 11 07:13:37 MDT 2010",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1433-2779&volume=11&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=1433-2779&volume=11&issue=2&spage=95",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal on Software Tools for Technology
                 Transfer: STTT",
  journal-URL =  "http://link.springer.com/journal/10009",
}

@Article{Bullynck:2009:MAB,
  author =       "Maarten Bullynck",
  title =        "Modular arithmetic before {C. F. Gauss}:
                 Systematizations and discussions on remainder problems
                 in {18th-Century Germany}",
  journal =      j-HIST-MATH,
  volume =       "36",
  number =       "1",
  pages =        "48--72",
  month =        feb,
  year =         "2009",
  CODEN =        "HIMADS",
  ISSN =         "0315-0860 (print), 1090-249X (electronic)",
  ISSN-L =       "0315-0860",
  bibdate =      "Wed Jun 26 06:21:00 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/histmath.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0315086008000670",
  acknowledgement = ack-nhfb,
  fjournal =     "Historia Mathematica",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03150860/",
}

@Article{Burtscher:2009:FHS,
  author =       "M. Burtscher and P. Ratanaworabhan",
  title =        "{FPC}: a High-Speed Compressor for Double-Precision
                 Floating-Point Data",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "1",
  pages =        "18--31",
  month =        jan,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2008.131",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 11:37:39 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4589203",
  abstract =     "Many scientific programs exchange large quantities of
                 double-precision data between processing nodes and with
                 mass storage devices. Data compression can reduce the
                 number of bytes that need to be transferred and stored.
                 However, data compression is only likely to be employed
                 in high-end computing environments if it does not
                 impede the throughput. This paper describes and
                 evaluates FPC, a fast lossless compression algorithm
                 for linear streams of 64-bit floating-point data. FPC
                 works well on hard-to-compress scientific data sets and
                 meets the throughput demands of high-performance
                 systems. A comparison with five lossless compression
                 schemes, BZIP2, DFCM, FSD, GZIP, and PLMI, on 4
                 architectures and 13 data sets shows that FPC
                 compresses and decompresses one to two orders of
                 magnitude faster than the other algorithms at the same
                 geometric-mean compression ratio. Moreover, FPC
                 provides a guaranteed throughput as long as the
                 prediction tables fit into the L1 data cache. For
                 example, on a 1.6-GHz Itanium 2 server, the throughput
                 is 670 Mbytes/s regardless of what data are being
                 compressed.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "BZIP2; data compression; DFCM; double-precision
                 floating-point data; floating point compression; FSD;
                 geometric-mean compression ratio; GZIP; linear streams;
                 lossless compression algorithm; PLMI; scientific data
                 sets compression; scientific programs",
}

@InProceedings{Cenk:2009:PMF,
  author =       "Murat Cenk and {\c{C}}etin Kaya Ko{\c{c}} and Ferruh
                 {\"O}zbudak",
  title =        "Polynomial Multiplication over Finite Fields Using
                 Field Extensions and Interpolation",
  crossref =     "Bruguera:2009:PIS",
  pages =        "84--91",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A method for polynomial multiplication over finite
                 fields using field extensions and polynomial
                 interpolation is introduced. The proposed method uses
                 polynomial interpolation as Toom--Cook method together
                 with field extensions. Furthermore, the proposed method
                 can be used when Toom--Cook method cannot be applied
                 directly. Explicit formulae improving the previous
                 results in many cases are obtained.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19; correct rounding; floating-point
                 arithmetic",
}

@Article{Chabert:2009:PEA,
  author =       "Gilles Chabert and Luc Jaulin",
  title =        "A Priori Error Analysis and Spring Arithmetic",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "31",
  number =       "3",
  pages =        "2214--2230",
  month =        "????",
  year =         "2009",
  CODEN =        "SJOCE3",
  DOI =          "",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Wed May 19 10:44:16 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/31/3;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}

@InProceedings{Chen:2009:BDF,
  author =       "Dongdong Chen and Yu Zhang and Younhee Choi and Moon
                 Ho Lee and Seok-Bum Ko",
  title =        "A 32-bit Decimal Floating-Point Logarithmic
                 Converter",
  crossref =     "Bruguera:2009:PIS",
  pages =        "195--203",
  year =         "2009",
  DOI =          "https://doi.org/10.1109/ARITH.2009.22",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper presents a new design and implementation of
                 a 32-bit decimal floating-point (DFP) logarithmic
                 converter based on the digit-recurrence algorithm. The
                 converter can calculate accurate logarithms of 32-bit
                 DFP numbers which are defined in the IEEE 754-2008
                 standard. Redundant digit $ e_1 $ is obtained by
                 look-up table in the first iteration and the rest
                 redundant digits $ e_j $ are selected by rounding the
                 scaled remainder during the succeeding iterations. The
                 sequential architecture of the proposed 32-bit DFP
                 logarithmic converter is implemented on Xilinx
                 Virtex-II Pro P30 FPGA device and then synthesized with
                 TMSC 0.18-$ \mu $ m standard cell library. The
                 implementation results indicate that the maximum
                 frequency of the proposed architecture is 47.7 MHz in
                 FPGA and 107.9 MHz in TMSC 0.18-$ \mu $ m technology.
                 The faithful 32-bit DFP logarithm results can be
                 obtained in 18 cycles.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19; decimal floating-point; decimal logarithmic
                 converter; digit-recurrence algorithm; selection by
                 rounding.",
}

@InProceedings{Chen:2009:NDA,
  author =       "Dongdong Chen and Yu Zhang and D. Teng and K. Wahid
                 and Moon Ho Lee and Seok-Bum Ko",
  title =        "A new decimal antilogarithmic converter",
  crossref =     "IEEE:2009:IIS",
  pages =        "445--448",
  year =         "2009",
  DOI =          "https://doi.org/10.1109/ISCAS.2009.5117781",
  bibdate =      "Thu Feb 17 08:34:31 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cheng:2009:DSE,
  author =       "Chung-Kuan Cheng",
  title =        "Design Space Exploration for Power-Efficient
                 Mixed-Radix {Ling} Adders",
  crossref =     "Bruguera:2009:PIS",
  pages =        "212--212",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present an integer linear programming (ILP) method
                 that optimizes generalized prefix Ling adders in terms
                 of area, delay, and power. The contribution is listed
                 in the following.\par

                 (1) We devise an ILP formulation based on logical
                 effort models so that we can use ILP solver, CPLEX, to
                 produce minimum power solutions with given structural,
                 area and timing constraints. The formulation allows the
                 adjustment of parameters and constraints, e.g. the
                 radix numbers and the ratio of static and dynamic
                 power. We implement the flow for the users to
                 automatically synthesize the adders.\par

                 (2) We engineer sets of integer decision variables and
                 linear constraints to depict the prefix topology,
                 signal delay, and power characterization. Since the
                 design space of prefix adders is large, optimal
                 solutions are usually hard to generate without good
                 formulations. We generate redundant constraints to
                 prune the search space. The approach significantly
                 reduces the execution time.\par

                 (3) We explore mixed radices for prefix topologies,
                 i.e. GP cells have radices 2, 3, or 4, and a prefix
                 network can contain cells of different radices. This
                 mixed-radix feature expands the design space for better
                 solutions. High-radix adders reduce logic levels and
                 thus can serve for high performance applications. On
                 the other hand, high-radix cells take more logical
                 effort, longer parasitic delay, and more power
                 consumption. These factors are all taken care of in the
                 devised ILP formulation.\par

                 (4) We adopt the structure of Ling adders to produce
                 faster sum and carry responses. The experiments show
                 that Ling adders achieve better results than normal
                 prefix adders.\par

                 (5) We apply hierarchical design methods to handle high
                 bit-width modules. One weakness of ILP solver is the
                 scaleability of computational time with the bit-width.
                 We use a divide-and-conquer strategy to synthesize
                 64-bit adders.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19",
  remark =       "Only abstract published.",
}

@InProceedings{Chevillard:2009:CFC,
  author =       "Sylvain Chevillard and Mioara Joldes and Christoph
                 Lauter",
  title =        "Certified and Fast Computation of Supremum Norms of
                 Approximation Errors",
  crossref =     "Bruguera:2009:PIS",
  pages =        "169--176",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In many numerical programs there is a need for a
                 high-quality floating-point approximation of useful
                 functions $f$, such as such as $ \exp $, $ \sin $, $
                 \erf $. In the actual implementation, the function is
                 replaced by a polynomial $p$, which leads to an
                 approximation error (absolute or relative) $ \epsilon =
                 p - f $ or $ \epsilon = p / f - 1 $. The tight yet
                 certain bounding of this error is an important step
                 towards safe implementations. The problem is difficult
                 mainly because that approximation error is very small
                 and the difference $ p - f $ is subject to high
                 cancellation. Previous approaches for computing the
                 supremum norm in this degenerate case, have proven to
                 be unsafe, not sufficiently tight or too tedious in
                 manual work. We present a safe and fast algorithm that
                 computes a tight lower and upper bound for the supremum
                 norms of approximation errors. The algorithm is based
                 on a combination of several techniques, including
                 enhanced interval arithmetic, automatic differentiation
                 and isolation of the roots of a polynomial. We have
                 implemented our algorithm and give timings on several
                 examples.",
  acknowledgement = ack-nhfb,
  keywords =     "approximation error; ARITH-19; automatic/algorithmic
                 differentiation; certified computation; elementary
                 function; interval arithmetic; roots isolation
                 technique.; supremum/infinity norm",
}

@Article{Cho:2009:AMD,
  author =       "H. Cho and E. E. Swartzlander",
  title =        "Adder and Multiplier Design in Quantum-Dot Cellular
                 Automata",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "6",
  pages =        "721--727",
  month =        jun,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2009.21",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 11:37:41 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4760137",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Chouliaras:2009:CLF,
  author =       "V. A. Chouliaras and K. Manolopoulos and D. Reisis",
  title =        "A configurable length, Fused Multiply-Add floating
                 point unit for a {VLIW} processor",
  crossref =     "Sezer:2009:IIS",
  pages =        "93--96",
  year =         "2009",
  DOI =          "https://doi.org/10.1109/SOCCON.2009.5398088",
  bibdate =      "Sun Feb 20 10:03:30 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The efficiency of fused multiply add units plays a key
                 role in the processor's performance for a variety of
                 applications. A design keeping the advantages of the
                 FMA regarding the latency and the hardware utilization
                 and also improving the result's accuracy in both
                 normalized and denormalized numbers is the subject of
                 this work. The FMA unit has configurable latency and it
                 is integrated in a VLIW processor. The VLSI TSMC 0.13
                 implementation achieved an operating frequency of 232.6
                 MHz and a final post-routed area of 121900.478 $ \mu $
                 m$^2$.",
  acknowledgement = ack-nhfb,
}

@Article{Cilardo:2009:EBP,
  author =       "A. Cilardo",
  title =        "Efficient Bit-Parallel {$ \mathrm {GF}(2^m) $}
                 Multiplier for a Large Class of Irreducible
                 Pentanomials",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "7",
  pages =        "1001--1008",
  month =        jul,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2009.16",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 11:37:42 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4752811",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Colberg:2009:HAS,
  author =       "Peter H. Colberg and Felix H{\"o}fling",
  title =        "Highly accelerated simulations of glassy dynamics
                 using {GPUs}: caveats on limited floating-point
                 precision",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--12",
  day =          "20",
  month =        dec,
  year =         "2009",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Published in Comp. Phys. Comm. {\bf 182}, 1120
                 (2011).",
  URL =          "http://arxiv.org/abs/0912.3824",
  abstract =     "Modern graphics processing units (GPUs) provide
                 impressive computing resources, which can be accessed
                 conveniently through the CUDA programming interface. We
                 describe how GPUs can be used to considerably speed up
                 molecular dynamics (MD) simulations for system sizes
                 ranging up to about 1 million particles. Particular
                 emphasis is put on the numerical long-time stability in
                 terms of energy and momentum conservation, and caveats
                 on limited floating-point precision are issued. Strict
                 energy conservation over $ 10^8 $ MD steps is obtained
                 by double-single emulation of the floating-point
                 arithmetic in accuracy-critical parts of the algorithm.
                 For the slow dynamics of a supercooled binary
                 Lennard-Jones mixture, we demonstrate that the use of
                 single-floating point precision may result in
                 quantitatively and even physically wrong results. For
                 simulations of a Lennard-Jones fluid, the described
                 implementation shows speedup factors of up to 80
                 compared to a serial implementation for the CPU, and a
                 single GPU was found to compare with a parallelised MD
                 simulation using 64 distributed cores.",
  acknowledgement = ack-nhfb,
  subject =      "Computational Physics (physics.comp-ph); Soft
                 Condensed Matter (cond-mat.soft); Distributed,
                 Parallel, and Cluster Computing (cs.DC)",
}

@InProceedings{Cornea:2009:IDF,
  author =       "Marius Cornea",
  title =        "{IEEE 754-2008} Decimal Floating-Point for {Intel}
                 Architecture Processors",
  crossref =     "Bruguera:2009:PIS",
  pages =        "225--228",
  year =         "2009",
  DOI =          "https://doi.org/10.1109/ARITH.2009.35",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A brief description is provided of the decimal
                 floating-point support available for Intel Architecture
                 processors, compliant with the IEEE Standard 754-2008
                 for Floating-Point Arithmetic [1]. Some performance
                 results are included.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19",
}

@Article{Cornea:2009:SII,
  author =       "M. Cornea and J. Harrison and C. Anderson and P. Tang
                 and E. Schneider and E. Gvozdev",
  title =        "A Software Implementation of the {IEEE 754R} Decimal
                 Floating-Point Arithmetic Using the Binary Encoding
                 Format",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "2",
  pages =        "148--162",
  month =        feb,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2008.209",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 11:37:39 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4674342",
  abstract =     "The IEEE Standard 754-1985 for Binary Floating-Point
                 Arithmetic [19] was revised [20], and an important
                 addition is the definition of decimal floating-point
                 arithmetic [8], [24]. This is intended mainly to
                 provide a robust reliable framework for financial
                 applications that are often subject to legal
                 requirements concerning rounding and precision of the
                 results, because the binary floating-point arithmetic
                 may introduce small but unacceptable errors. Using
                 binary floating-point calculations to emulate decimal
                 calculations in order to correct this issue has led to
                 the existence of numerous proprietary software
                 packages, each with its own characteristics and
                 capabilities. The IEEE 754R decimal arithmetic should
                 unify the ways decimal floating-point calculations are
                 carried out on various platforms. New algorithms and
                 properties are presented in this paper, which are used
                 in a software implementation of the IEEE 754R decimal
                 floating-point arithmetic, with emphasis on using
                 binary operations efficiently. The focus is on rounding
                 techniques for decimal values stored in binary format,
                 but algorithms are outlined for the more important or
                 interesting operations of addition, multiplication, and
                 division, including the case of nonhomogeneous
                 operands, as well as conversions between binary and
                 decimal floating-point formats. Performance results are
                 included for a wider range of operations, showing
                 promise that our approach is viable for applications
                 that require decimal floating-point calculations. This
                 paper extends an earlier publication [6].",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "binary-decimal conversion.; computer arithmetic;
                 correct rounding; decimal floating-point;
                 floating-point arithmetic; multiple-precision
                 arithmetic",
  remark =       "Extended version of ARITH-18 article
                 \cite{Cornea:2007:SII}.",
}

@Article{Csuros:2009:ACF,
  author =       "Miklos Csuros",
  title =        "Approximate counting with a floating-point counter",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "20",
  month =        apr,
  year =         "2009",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/0904.3062",
  abstract =     "Memory becomes a limiting factor in contemporary
                 applications, such as analyses of the Webgraph and
                 molecular sequences, when many objects need to be
                 counted simultaneously. Robert Morris [Communications
                 of the ACM, 21:840--842, 1978] proposed a probabilistic
                 technique for approximate counting that is extremely
                 space-efficient. The basic idea is to increment a
                 counter containing the value $X$ with probability $
                 2^{-X}$. As a result, the counter contains an
                 approximation of $ \lg n$ after $n$ probabilistic
                 updates stored in $ \lg \lg n$ bits. Here we revisit
                 the original idea of Morris, and introduce a binary
                 floating-point counter that uses a $d$-bit significand
                 in conjunction with a binary exponent. The counter
                 yields a simple formula for an unbiased estimation of
                 $n$ with a standard deviation of about $ 0.6 \cdot
                 n2^{-d / 2}$, and uses $ d + \lg \lg n$ bits. We
                 analyze the floating-point counter's performance in a
                 general framework that applies to any probabilistic
                 counter, and derive practical formulas to assess its
                 accuracy.",
  acknowledgement = ack-nhfb,
  subject =      "Data Structures and Algorithms (cs.DS)",
}

@Article{Daumas:2009:VRN,
  author =       "Marc Daumas and D. Lester and C. Muoz",
  title =        "Verified Real Number Calculations: a Library for
                 Interval Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "2",
  pages =        "226--237",
  month =        feb,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2008.213",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 11:37:39 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4685896",
  abstract =     "Real number calculations on elementary functions are
                 remarkably difficult to handle in mechanical proofs. In
                 this paper, we show how these calculations can be
                 performed within a theorem prover or proof assistant in
                 a convenient and highly automated as well as
                 interactive way. First, we formally establish upper and
                 lower bounds for elementary functions. Then, based on
                 these bounds, we develop a rational interval arithmetic
                 where real number calculations take place in an
                 algebraic setting. In order to reduce the dependency
                 effect of interval arithmetic, we integrate two
                 techniques: interval splitting and Taylor series
                 expansions. This pragmatic approach has been developed,
                 and formally verified, in a theorem prover. The formal
                 development also includes a set of customizable
                 strategies to automate proofs involving explicit
                 calculations over real numbers. Our ultimate goal is to
                 provide guaranteed proofs of numerical properties with
                 minimal human theorem-prover interaction.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "interval arithmetic; proof checking; real number
                 calculations; theorem proving",
  remark =       "Extended version of ARITH-18 article
                 \cite{Daumas:2009:VRN}.",
}

@Article{Davida:2009:FAU,
  author =       "George Davida and Bruce Litow and Guangwu Xu",
  title =        "Fast arithmetics using {Chinese} remaindering",
  journal =      j-INFO-PROC-LETT,
  volume =       "109",
  number =       "13",
  pages =        "660--662",
  day =          "15",
  month =        jun,
  year =         "2009",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Thu Mar 31 15:53:33 MDT 2011",
  bibsource =    "http://www.sciencedirect.com/science/journal/00200190;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}

@Article{DeCaro:2009:DSM,
  author =       "Davide {De Caro} and Nicola Petra and Antonio G. M.
                 Strollo",
  title =        "Digital Synthesizer\slash Mixer With Hybrid {CORDIC}
                 Multiplier Architecture: Error Analysis and
                 Optimization",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-1,
  volume =       "56",
  number =       "2",
  pages =        "364--373",
  year =         "2009",
  DOI =          "https://doi.org/10.1109/TCSI.2008.2001370",
  ISSN =         "1549-8328 (print), 1558-0806 (electronic)",
  ISSN-L =       "1549-8328",
  MRclass =      "99-01",
  MRnumber =     "3030492",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "1469.94241",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems. I. Regular
                 Papers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8919",
  keywords =     "94C30; Angle rotator; Circuits; CMOS technology;
                 Computer architecture; CORDIC algorithm; Delay; digital
                 downconverter; digital mixer; digital synthesizer;
                 digital tuner; digital upconverter; direct digital
                 frequency synthesizer (DDFS); Equations; Error
                 analysis; Frequency synthesizers; mixer; modulator;
                 quadrature modulator; Signal processing algorithms;
                 Table lookup; Tuners",
  ZBmath =       "7390012",
}

@Book{Deschamps:2009:HIF,
  author =       "Jean-Pierre Deschamps and Jos{\'e} Luis Ima{\~n}a and
                 Gustavo D. Sutter",
  title =        "Hardware implementation of finite-field arithmetic",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "xiii + 347",
  year =         "2009",
  ISBN =         "0-07-154581-6 (hardcover)",
  ISBN-13 =      "978-0-07-154581-5 (hardcover)",
  LCCN =         "TK7895.E42 D466 2009",
  bibdate =      "Sat Sep 20 16:04:08 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Electronic engineering",
  abstract =     "Master cutting-edge electronic circuit synthesis and
                 design with help from this detailed guide. Hardware
                 Implementation of Finite-Field Arithmetic describes
                 algorithms and circuits for executing finite-field
                 operations, including addition, subtraction,
                 multiplication, squaring, exponentiation, and
                 division.\par

                 This comprehensive resource begins with an overview of
                 mathematics, covering algebra, number theory, finite
                 fields, and cryptography. The book then presents
                 algorithms which can be executed and verified with
                 actual input data. Logic schemes and VHDL models are
                 described in such a way that the corresponding circuits
                 can be easily simulated and synthesized. The book
                 concludes with a real-world example of a finite-field
                 application --- elliptic-curve cryptography. This is an
                 essential guide for hardware engineers involved in the
                 development of embedded systems.",
  acknowledgement = ack-nhfb,
  author-dates = "1945--",
  subject =      "Embedded computer systems; Design and construction;
                 Field programmable gate arrays; Application-specific
                 integrated circuits; Computer arithmetic",
  tableofcontents = "1. Mathematical background / 1--24 \\
                 2. Mod $m$ reduction / 25--60 \\
                 3. Mod $m$ operations / 61--90 \\
                 4. Operations over ${\rm GF}(p)$ / 91--116 \\
                 5. Operations over $Z_p[x] / f(x)$ / 117--138 \\
                 6. Operations over ${\rm GF}(p^n)$ / 139--162 \\
                 7. Operations over ${\rm GF}(2^m)$ --- Polynomial bases
                 / 163--234 \\
                 8. Operations over ${\rm GF}(2^m)$ --- Normal bases /
                 235--268 \\
                 9. Operations over ${\rm GF}(2^m)$ --- Other bases /
                 269--286 \\
                 10. An Example of Application --- Elliptic curve
                 cryptography / 287--312 \\
                 Appendix A. $p = 2^{192} - 2^{64} - 1$ / 313--318 \\
                 Appendix B. Optical Extension Fields / 319--330 \\
                 Appendix C. Binary Fields / 331--334 \\
                 Appendix D. Ada versus VHDL / 337--340 \\
                 Index / 341--347",
}

@InProceedings{Dormiani:2009:DIR,
  author =       "P. Dormiani and M. D. Ercegovac and Jean-Michel
                 Muller",
  title =        "Design and Implementation of a Radix-4 Complex
                 Division Unit with Prescaling",
  crossref =     "IEEE:2009:IICa",
  pages =        "83--90",
  year =         "2009",
  DOI =          "https://doi.org/10.1109/ASAP.2009.32",
  bibdate =      "Fri Dec 03 15:01:28 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present a design and implementation of a radix-4
                 complex division unit with prescaling of the operands.
                 Specifically, we extend the treatment of the residual
                 bound and errors due to the use of truncated redundant
                 representation. The requirements for prescaling tables
                 are simplified and a detailed specification of the
                 table design is given. All principal components used in
                 the design are described and the proposed optimizations
                 are explained. The target platform for implementation
                 was an Altera Stratix II FPGA for which we report
                 timing and area requirements. For a precision of 36
                 bits, the implementation uses 1185 ALUTs, achieving a
                 latency of 157 ns. The maximum clock frequency is
                 173.49 MHz.",
  acknowledgement = ack-nhfb,
  keywords =     "Altera Stratix II FPGA; digital arithmetic; field
                 programmable gate arrays; frequency 173.49 MHz;
                 integrated circuit design; logic design; operand
                 prescaling; prescalers; prescaling tables; radix-4
                 complex division unit; table design",
}

@InProceedings{Dormiani:2009:LPT,
  author =       "Pouya Dormiani and Milo D. Ercegovac and Jean-Michel
                 Muller",
  editor =       "Michael B. Matthews",
  booktitle =    "{2009 Conference Record of the Forty-Third Asilomar
                 Conference on Signals, Systems and Computers. November
                 1--4, 2009. Pacific Grove, California}",
  title =        "Low precision table based complex reciprocal
                 approximation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1803--1807",
  year =         "2009",
  DOI =          "https://doi.org/10.1109/ACSSC.2009.5470209",
  ISBN =         "1-4244-5827-7",
  ISBN-13 =      "978-1-4244-5827-1",
  ISSN =         "1058-6393",
  ISSN-L =       "1058-6393",
  bibdate =      "Fri Sep 29 10:50:54 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Duff:2009:GMA,
  author =       "Bob Duff",
  title =        "Gem \#26: the {\tt mod} attribute",
  journal =      j-SIGADA-LETTERS,
  volume =       "29",
  number =       "1",
  pages =        "33--34",
  month =        apr,
  year =         "2009",
  CODEN =        "AALEE5",
  DOI =          "https://doi.org/10.1145/1541788.1541795",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Mon Jun 21 14:03:13 MDT 2010",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  abstract =     "Ada Gem \#26 --- T'Mod can be used to convert signed
                 integers to modular integers using modular (wraparound)
                 arithmetic.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
}

@InProceedings{Edmonson:2009:IIS,
  author =       "William Edmonson and Guillaume Melquiond",
  title =        "{IEEE Interval Standard Working Group --- P1788}:
                 Current Status",
  crossref =     "Bruguera:2009:PIS",
  pages =        "231--234",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Late 2008, at SCAN 2008 in El Paso, TX, an effort to
                 standardize interval computations was started by a
                 working group of the IEEE Microprocessor Standards
                 Committee, titled the Interval Arithmetic Working Group
                 of the IEEE P1788 Standard. This paper describes the
                 goals of this effort, the history of the working group,
                 and how it relates to the IEEE 754 Standard. It gives a
                 brief overview of the policies and procedures for
                 constructing the standard, and its expected structure.
                 It also presents some of the questions the group may
                 have to solve in the future.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19",
}

@Article{Enge:2009:CCP,
  author =       "Andreas Enge",
  title =        "The complexity of class polynomial computation via
                 floating point approximations",
  journal =      j-MATH-COMPUT,
  volume =       "78",
  number =       "266",
  pages =        "1089--1107",
  month =        apr,
  year =         "2009",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Fri May 14 06:20:58 MDT 2010",
  bibsource =    "http://www.ams.org/mcom/2009-78-266;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ams.org/journals/mcom/2009-78-266/S0025-5718-08-02200-X/home.html;
                 http://www.ams.org/journals/mcom/2009-78-266/S0025-5718-08-02200-X/S0025-5718-08-02200-X.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "roots of elliptic curves",
}

@Manual{Enge:2009:MLM,
  author =       "Andreas Enge and Philippe Th{\'e}veny and Paul
                 Zimmermann",
  title =        "{\texttt{mpc}} --- a library for multiprecision
                 complex arithmetic with exact rounding",
  organization = "INRIA",
  address =      "France",
  edition =      "0.8.1",
  month =        dec,
  year =         "2009",
  bibdate =      "Sun May 2 09:31:32 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://mpc.multiprecision.org/",
  acknowledgement = ack-nhfb,
}

@Article{Erle:2009:DFP,
  author =       "Mark A. Erle and Brian J. Hickmann and Michael J.
                 Schulte",
  title =        "Decimal Floating-Point Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "7",
  pages =        "902--916",
  month =        jul,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2008.218",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 11:37:42 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4711044",
  abstract =     "Decimal multiplication is important in many commercial
                 applications including financial analysis, banking, tax
                 calculation, currency conversion, insurance, and
                 accounting. This paper presents the design of two
                 decimal floating-point multipliers: one whose partial
                 product accumulation strategy employs decimal
                 carry-save addition and one that employs binary
                 carry-save addition. The multiplier based on decimal
                 carry-save addition favors a nonpipelined iterative
                 implementation. The multiplier utilizing binary
                 carry-save addition allows for an efficient pipelined
                 implementation when latency and throughput are
                 considered more important than area. Both designs
                 comply with specifications for decimal multiplication
                 given in the IEEE 754 Standard for Floating-Point
                 Arithmetic (IEEE 754-2008). The multipliers extend
                 previously published decimal fixed-point multipliers by
                 adding several features, including exponent generation,
                 sticky bit generation, shifting of the intermediate
                 product, rounding, and exception detection and
                 handling. Novel features of the multipliers include
                 support for decimal floating-point numbers, on-the-fly
                 generation of the sticky bit in the iterative design,
                 early estimation of the shift amount, and efficient
                 decimal rounding. Iterative and parallel decimal
                 fixed-point and floating-point multipliers are compared
                 in terms of their area, delay, latency, and throughput
                 based on verified Verilog register-transfer-level
                 models.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "arithmetic and logic units; binary coded decimal;
                 computer arithmetic; decimal multiplication;
                 floating-point arithmetic; general high-speed
                 arithmetic; parallel multiplication; pipelined
                 multiplication; serial multiplication",
}

@InProceedings{Fahmy:2009:EDI,
  author =       "Hossam A. H. Fahmy and Ramy Raafat and Amira M.
                 Abdel-Majeed and Rodina Samy and Tarek ElDeeb and
                 Yasmin Farouk",
  title =        "Energy and Delay Improvement via Decimal Floating
                 Point Units",
  crossref =     "Bruguera:2009:PIS",
  pages =        "221--224",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Interest in decimal arithmetic increased considerably
                 in recent years. This paper presents new designs for
                 decimal floating point (DFP) addition, multiplication,
                 fused multiply-add, division, and square root. It
                 stresses the importance of energy savings achieved by
                 hardware implementations of the IEEE standard for
                 decimal floating point. To the best of the authors
                 knowledge, this is the first work to discuss energy
                 savings in DFP and the first to present a hardware
                 implementation of a fused multiply-add. Our
                 Newton--Raphson based divider is over three times
                 faster than the similar design previously reported.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19",
}

@Article{Fewster:2009:SEB,
  author =       "R. M. Fewster",
  title =        "A Simple Explanation of {Benford's Law}",
  journal =      j-AMER-STAT,
  volume =       "63",
  number =       "1",
  pages =        "26--32",
  month =        feb,
  year =         "2009",
  CODEN =        "ASTAAJ",
  DOI =          "https://doi.org/10.1198/tast.2009.0005",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Thu Aug 26 21:48:27 MDT 2010",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 https://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@Article{Fit-Florea:2009:DLN,
  author =       "A. Fit-Florea and L. Li and M. A. Thornton and D. W.
                 Matula",
  title =        "A Discrete Logarithm Number System for Integer
                 Arithmetic Modulo $ 2^k $: Algorithms and Lookup
                 Structures",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "2",
  pages =        "163--174",
  month =        feb,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2008.204",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 11:37:39 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4663061",
  abstract =     "We present a $k$-bit encoding of the $k$-bit binary
                 integers based on a discrete logarithm representation.
                 The representation supports a discrete logarithm number
                 system (DLS) that allows integer multiplication to be
                 reduced to addition and integer exponentiation to be
                 reduced to multiplication. We introduce right-to-left
                 bit serial conversion, deconversion, and unified
                 conversion/deconversion algorithms between binary and
                 DLS. The conversion algorithms utilize $ O(k) $
                 additions, do not require the use of a multiplier, and
                 are applicable at least up to 128-bit integers. We
                 illustrate the use of the representation in determining
                 a novel and efficient integer power modulo $ 2^k $
                 operation $ |x^y|_{2k} $ and compare hardware
                 performance with a current state-of-the-art method.
                 Furthermore, we describe properties of the conversion
                 mappings that allow compact table lookup structures to
                 be employed for direct conversion to and deconversion
                 from the DLS encoding. Our lookup architecture allows
                 16-bit conversion and deconversion mappings to be
                 realized with table sizes of order 2--8 Kbytes, which
                 is up to a $ 64 \times $ size reduction of the 128
                 Kbytes of an arbitrary 16-bits-in, 16-bits-out function
                 table. Performance and area results that demonstrate
                 the effectiveness of the table lookup architecture are
                 given. The lookup methodology extends to other 16-bit
                 integer functions such as multiplicative inverse and
                 squaring operations.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "arithmetic and logic units; bit serial; computer
                 arithmetic; conversions; discrete logarithm; high-speed
                 arithmetic; integer power; number encodings; table
                 lookup",
}

@Article{Fraysse:2009:ASF,
  author =       "Val{\'e}rie Frayss{\'e} and Luc Giraud and Serge
                 Gratton",
  title =        "{Algorithm 881}: a Set of Flexible {GMRES} Routines
                 for Real and Complex Arithmetics on High-Performance
                 Computers",
  journal =      j-TOMS,
  volume =       "35",
  number =       "2",
  pages =        "13:1--13:12",
  month =        jul,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1377612.1377617",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 5 18:13:00 MDT 2008",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this article we describe our implementations of the
                 FGMRES algorithm for both real and complex, single and
                 double precision arithmetics suitable for serial,
                 shared-memory, and distributed-memory computers. For
                 the sake of portability, simplicity, flexibility, and
                 efficiency, the FGMRES solvers have been implemented in
                 Fortran 77 using the reverse communication mechanism
                 for the matrix-vector product, the preconditioning, and
                 the dot-product computations. For distributed-memory
                 computation, several orthogonalization procedures have
                 been implemented to reduce the cost of the dot-product
                 calculation, which is a well-known bottleneck of
                 efficiency for Krylov methods. Furthermore, either
                 implicit or explicit calculation of the residual at
                 restart is possible depending on the actual cost of the
                 matrix-vector product. Finally, the implemented
                 stopping criterion is based on a normwise backward
                 error.",
  acknowledgement = ack-nhfb,
  articleno =    "13",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "distributed memory; FGMRES; flexible Krylov methods;
                 high-performance computing; linear systems; reverse
                 communication",
}

@Article{Furer:2009:FIM,
  author =       "Martin F{\"u}rer",
  title =        "Faster Integer Multiplication",
  journal =      j-SIAM-J-COMPUT,
  volume =       "39",
  number =       "3",
  pages =        "979--1005",
  month =        "????",
  year =         "2009",
  CODEN =        "SMJCAT",
  DOI =          "",
  ISSN =         "0097-5397 (print), 1095-7111 (electronic)",
  ISSN-L =       "0097-5397",
  bibdate =      "Tue May 18 08:22:12 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/39/3;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Computing",
  journal-URL =  "http://epubs.siam.org/sicomp",
}

@InProceedings{Ganai:2009:EDP,
  author =       "Malay K. Ganai and Franjo Ivan{\v{c}}i{\'c}",
  booktitle =    "{2009 Formal Methods in Computer-Aided Design}",
  title =        "Efficient decision procedure for non-linear arithmetic
                 constraints using {CORDIC}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "61--68",
  year =         "2009",
  DOI =          "https://doi.org/10.1109/FMCAD.2009.5351140",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Constraint theory; Control systems; Floating-point
                 arithmetic; Laboratories; National electric code;
                 Nonlinear control systems; Numerical stability;
                 Operations research; Search engines; Surface-mount
                 technology",
}

@Article{Gavrilova:2009:ESC,
  author =       "Marina L. Gavrilova",
  title =        "An Explicit Solution for Computing the Vertices of the
                 {Euclidean} $d$-Dimensional {Voronoi} Diagram of
                 Spheres in a Floating-Point Arithmetic",
  journal =      j-INT-J-COMPUT-GEOM-APPL,
  volume =       "19",
  number =       "5",
  pages =        "415--424",
  month =        oct,
  year =         "2009",
  CODEN =        "IJCAEV",
  DOI =          "https://doi.org/10.1142/S0218195909003040",
  ISSN =         "0218-1959",
  bibdate =      "Mon Aug 30 10:25:06 MDT 2010",
  bibsource =    "http://ejournals.wspc.com.sg/ijcga/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International journal of computational geometry and
                 applications",
  journal-URL =  "http://www.worldscientific.com/loi/ijcga",
}

@InCollection{Gentle:2009:CSA,
  author =       "James E. Gentle",
  booktitle =    "Computational Statistics",
  title =        "Computer Storage and Arithmetic",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "xxi + 727",
  pages =        "85--105",
  year =         "2009",
  DOI =          "https://doi.org/10.1007/978-0-387-98144-4_2",
  ISBN =         "0-387-98143-8 (print), 0-387-98144-6 (electronic)",
  ISBN-13 =      "978-0-387-98143-7 (print), 978-0-387-98144-4
                 (electronic)",
  LCCN =         "QA276.4 .G46 2009",
  bibdate =      "Mon May 06 17:36:21 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Statistics and Computing",
  URL =          "http://link.springer.com/chapter/10.1007/978-0-387-98144-4_2",
  acknowledgement = ack-nhfb,
  tableofcontents = "Part I, Preliminaries. Mathematical and statistical
                 preliminaries \\
                 Part II, Statistical computing \\
                 Computer storage and arithmetic \\
                 algorithm and programming \\
                 Approximation of functions and numerical quadrature \\
                 Numerical linear algebra \\
                 Solution of nonlinear equations and optimization \\
                 Generation of random numbers \\
                 Part III, Methods of computational statistics \\
                 Graphical methods in computational statistics \\
                 Tools for identification of structure in data \\
                 Estimation of functions \\
                 Monte Carlo methods for statistical inference \\
                 Data randomization, partitioning, and augmentation \\
                 Bootstrap methods \\
                 Part IV, Exploring data density and relationships \\
                 Estimation of probability density functions using
                 parametric models \\
                 Nonparametric estimation of probability density
                 functions \\
                 Statistical learning and data mining \\
                 Statistical models of dependencies",
}

@InProceedings{Gonzalez-Navarro:2009:CDB,
  author =       "Sonia Gonzalez-Navarro and Alberto Nannarelli and
                 Michael J. Schulte and Charles Tsen",
  title =        "A combined decimal and binary floating-point divider",
  crossref =     "Matthews:2009:CRF",
  pages =        "930--934",
  year =         "2009",
  DOI =          "https://doi.org/10.1109/ACSSC.2009.5470014",
  bibdate =      "Thu Feb 17 08:16:50 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this paper, we present the hardware design of a
                 combined decimal and binary floating-point divider,
                 based on specifications in the IEEE 754-2008 Standard
                 for Floating-point Arithmetic. In contrast to most
                 recent decimal divider designs, which are based on the
                 Binary Coded Decimal (BCD) encoding, our divider
                 operates on either 64-bit binary encoded decimal
                 floating-point (DFP) numbers or 64-bit binary
                 floating-point (BFP) numbers. The division approach
                 implemented in our design is based on a
                 digit-recurrence algorithm. We describe the hardware
                 resources shared between the two floating-point
                 datatypes and demonstrate that hardware sharing is
                 advantageous. Compared to a standalone DFP divider, the
                 combined divider has the same worst case delay and 17\%
                 more area.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gorgin:2009:FRD,
  author =       "Saeid Gorgin and Ghassem Jaberipur",
  title =        "Fully Redundant Decimal Arithmetic",
  crossref =     "Bruguera:2009:PIS",
  pages =        "145--152",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Hardware implementation of all the basic radix-10
                 arithmetic operations is evolving as a new trend in the
                 design and implementation of general purpose digital
                 processors. Redundant representation of partial
                 products and remainders is common in the multiplication
                 and division hardware algorithms, respectively.
                 Carry-free implementation of the more frequent
                 add/subtract operations, with the byproduct of
                 enhancing the speed of multiplication and division, is
                 possible with redundant number representation. However,
                 conversion of redundant results to conventional
                 representations entails slow carry propagation that can
                 be avoided if the results are kept in redundant format
                 for later use as operands of other arithmetic
                 operations. Given that redundant decimal
                 representations, contrary to redundant binary, do not
                 necessarily require extra storage, we are motivated to
                 develop a framework for fully redundant decimal
                 arithmetic, where all operands and results belong to
                 the same redundant decimal number system and can be
                 stored and later used as operands of further decimal
                 operations. In this paper, we present a new faster
                 decimal signed digit add/sub unit and show how it can
                 be efficiently used in the design of decimal
                 multipliers and dividers, where all operands and
                 results are represented with the same redundant digit
                 set $ [ - 7, 7] $.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19",
}

@Article{Graillat:2009:AAV,
  author =       "Stef Graillat and Philippe Langlois and Nicolas
                 Louvet",
  title =        "Algorithms for accurate, validated and fast polynomial
                 evaluation",
  journal =      j-JAPAN-J-INDUST-APPL-MATH,
  volume =       "26",
  number =       "2--3",
  pages =        "191--214",
  year =         "2009",
  CODEN =        "JAPJI7",
  ISSN =         "0916-7005 (print), 1868-937x (electronic)",
  bibdate =      "Sat Jun 4 17:41:42 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Japan Journal of Industrial and Applied Mathematics",
}

@Article{Graillat:2009:AFP,
  author =       "Stef Graillat",
  title =        "Accurate Floating-Point Product and Exponentiation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "7",
  pages =        "994--1000",
  month =        jul,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2008.215",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 11:37:42 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4711041",
  abstract =     "Several different techniques and softwares intend to
                 improve the accuracy of results computed in a fixed
                 finite precision. Here, we focus on a method to improve
                 the accuracy of the product of floating-point numbers.
                 We show that the computed result is as accurate as if
                 computed in twice the working precision. The algorithm
                 is simple since it only requires addition, subtraction,
                 and multiplication of floating-point numbers in the
                 same working precision as the given data. Such an
                 algorithm can be useful for example to compute the
                 determinant of a triangular matrix and to evaluate a
                 polynomial when represented by the root product form.
                 It can also be used to compute the integer power of a
                 floating-point number.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "accurate product; computer arithmetic; error analysis;
                 error-free transformations; exponentiation; faithful
                 rounding; finite precision; floating-point arithmetic;
                 numerical algorithms",
}

@Article{Gu:2009:SDB,
  author =       "Haihua Gu and Dawu Gu",
  title =        "Speeding Up the Double-Base Recoding Algorithm of
                 Scalar Multiplication",
  journal =      j-CRYPTOLOGIA,
  volume =       "33",
  number =       "4",
  pages =        "315--320",
  year =         "2009",
  CODEN =        "CRYPE6",
  ISSN =         "0161-1194 (print), 1558-1586 (electronic)",
  ISSN-L =       "0161-1194",
  bibdate =      "Tue Aug 31 11:44:06 MDT 2010",
  bibsource =    "http://www.tandf.co.uk/journals/titles/01611194.asp;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Cryptologia",
  journal-URL =  "http://www.tandfonline.com/loi/ucry20",
}

@InProceedings{Guralnik:2009:ISV,
  author =       "Elena Guralnik and Ariel J. Birnbaum and Anatoly
                 Koyfman and Avi Kaplan",
  title =        "Implementation Specific Verification of Divide and
                 Square Root Instructions",
  crossref =     "Bruguera:2009:PIS",
  pages =        "114--121",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Floating point operations such as divide and square
                 root are typically implemented in microcode rather than
                 dedicated logic. Bugs in these operations missed by
                 generic black-box verification tools, were analyzed.
                 This led to the conclusion that the corner cases, in
                 addition to being implementation dependent, could not
                 be characterized in terms of special input or output
                 values in a straightforward manner.\par

                 However, many of those cases can be easily generalized
                 for many known implementations. The typical
                 implementation uses a known iterative approximation
                 algorithm, such as the Newton--Raphson method, to
                 calculate the desired result; thus, it is sufficient to
                 produce the corner cases associated with the specific
                 algorithm.\par

                 We investigated the following problem: given an
                 iterative algorithm to compute a binary floating point
                 operation, the iteration number, and an interval, find
                 random inputs for the operation that, after the
                 requested iteration, yield a relative error within the
                 specified interval. This paper describes a method to
                 solve this problem. This method was implemented in a
                 floating-point test generator and is currently being
                 used to verify the floating-point units of several
                 processors.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19",
}

@Article{Han:2009:ICS,
  author =       "Dong-Guk Han and Dooho Choi and Howon Kim",
  title =        "Improved Computation of Square Roots in Specific
                 Finite Fields",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "2",
  pages =        "188--196",
  month =        feb,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2008.201",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 11:37:39 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4663058",
  abstract =     "In this paper, we study exponentiation in the specific
                 finite fields $ F_q $ with very special exponents such
                 as those that occur in algorithms for computing square
                 roots. Here, $q$ is a prime power, $ q = p^k $, where $
                 k > 1 $, and $k$ is odd. Our algorithmic approach
                 improves the corresponding exponentiation resulted from
                 the better rewritten exponent. To the best of our
                 knowledge, it is the first major improvement to the
                 Tonelli--Shanks algorithm, for example, the number of
                 multiplications can be reduced to at least 60 percent
                 on the average when $ p \equiv 1 \pmod 16 $. Several
                 numerical examples are given that show the speedup of
                 the proposed methods.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "cryptography; efficient computation; finite fields;
                 square roots",
}

@Article{Hariri:2009:BSB,
  author =       "A. Hariri and A. Reyhani-Masoleh",
  title =        "Bit-Serial and Bit-Parallel {Montgomery}
                 Multiplication and Squaring over {$ \mathrm {GF}(2^m)
                 $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "10",
  pages =        "1332--1345",
  month =        oct,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2009.70",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 11:37:43 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4912195",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Harrison:2009:DTB,
  author =       "John Harrison",
  title =        "Decimal Transcendentals via Binary",
  crossref =     "Bruguera:2009:PIS",
  pages =        "187--194",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We describe the design and implementation of a
                 comprehensive library of transcendental functions for
                 the new IEEE decimal floating-point formats. In
                 principle, such functions are very much analogous to
                 their binary counterparts, though with a few additional
                 subtleties connected with `scale' (preferred exponent).
                 But our approach has been not to employ direct
                 techniques, but rather to re-use existing binary
                 functions as much as possible, both for greater
                 efficiency and ease of implementation. For some
                 functions the most straightforward approach (convert
                 from decimal to binary, perform binary operation,
                 convert back) works well. In many cases, however, these
                 are insufficiently accurate, and subtler approaches
                 must be used.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19",
}

@InProceedings{Harrison:2009:FAB,
  author =       "John Harrison",
  title =        "Fast and Accurate {Bessel} Function Computation",
  crossref =     "Bruguera:2009:PIS",
  pages =        "104--113",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Bessel functions are considered relatively
                 difficult to compute. Although they have a simple power
                 series expansion that is everywhere convergent, they
                 exhibit approximately periodic behavior which makes the
                 direct use of the power series impractically slow and
                 numerically unstable. We describe an alternative method
                 based on systematic expansion around the zeros,
                 refining existing techniques based on Hankel
                 expansions, which mostly avoids the use of
                 multiprecision arithmetic while yielding accurate
                 results.",
  acknowledgement = ack-nhfb,
  keywords =     "$J0(x), J1(1), Y0(x), Y1(1)$; ARITH-19; ordinary
                 Bessel functions of the first and second kinds",
}

@InProceedings{Hasan:2009:SSC,
  author =       "M. A. Hasan and C. Negre",
  title =        "Subquadratic Space Complexity Multiplier for a Class
                 of Binary Fields Using {Toeplitz} Matrix Approach",
  crossref =     "Bruguera:2009:PIS",
  pages =        "67--75",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In the recent past, subquadratic space complexity
                 multipliers have been proposed for binary fields
                 defined by irreducible trinomials and some specific
                 pentanomials. For such multipliers, alternative
                 irreducible polynomials can also be used, in
                 particular, nearly all one polynomials (NAOPs) seem to
                 be better than pentanomials (see [7]). For improved
                 efficiency, multiplication modulo an NAOP is performed
                 via modulo a quadrinomial whose degree is one more than
                 that of the original NAOP. In this paper, we present a
                 Toeplitz matrix-vector product based approach for
                 multiplication modulo a quadrinomial. We obtain a fully
                 parallel (nonsequential) multiplier with a subquadratic
                 space complexity, which has the same order of space
                 complexity as that of Fan and Hasan [4].\par

                 The Toeplitz matrix-vector product based approach is
                 also interesting in the design of sequential
                 multipliers. In this paper, we present two such
                 multipliers: one with bit serial output and the other
                 bit parallel output.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19; binary field; double basis; multiplication;
                 subquadratic complexity",
}

@Article{Hinek:2009:ALS,
  author =       "M. Jason Hinek and Charles C. Y. Lam",
  title =        "Another look at some fast modular arithmetic methods",
  journal =      j-J-MATH-CRYPTOL,
  volume =       "3",
  number =       "2",
  pages =        "165--174",
  year =         "2009",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1515/JMC.2009.008",
  ISSN =         "1862-2976 (print), 1862-2984 (electronic)",
  ISSN-L =       "1862-2976",
  MRclass =      "68W40 (94A60)",
  MRnumber =     "2590262",
  bibdate =      "Fri Mar 17 08:36:49 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathcryptol.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Cryptology",
  journal-URL =  "http://www.degruyter.com/view/j/jmc",
}

@Article{Ho:2009:FPF,
  author =       "C. H. Ho and C. W. Yu and P. Leong and W. Luk and S.
                 J. E. Wilton",
  title =        "Floating-point {FPGA}: architecture and modeling",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "17",
  number =       "12",
  pages =        "1709--1718",
  year =         "2009",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/TVLSI.2008.2006616",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Thu Mar 24 20:51:13 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
}

@Book{ISO:2009:IIT,
  author =       "{International Organization for Standardization}",
  title =        "{ISO/IEC TR 24732:2009} Information technology ---
                 Programming languages, their environments and system
                 software interfaces --- Extension for the programming
                 language {C} to support decimal floating-point
                 arithmetic",
  publisher =    pub-ISO,
  address =      pub-ISO:adr,
  year =         "2009",
  LCCN =         "????",
  bibdate =      "Thu Nov 25 08:56:44 2010",
  bibsource =    "http://www.iso.org/iso/search.htm;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Technical report",
  URL =          "http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=38842",
  acknowledgement = ack-nhfb,
  subject =      "programming languages (electronic computers)",
}

@Article{Jaberipur:2009:ISP,
  author =       "G. Jaberipur and A. Kaivani",
  title =        "Improving the Speed of Parallel Decimal
                 Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "11",
  pages =        "1539--1552",
  month =        nov,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2009.110",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 11:37:44 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5184812",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Jaberipur:2009:UAD,
  author =       "Ghassem Jaberipur and Behrooz Parhami",
  title =        "Unified Approach to the Design of Modulo-$ (2^n \pm 1)
                 $ Adders Based on Signed-{LSB} Representation of
                 Residues",
  crossref =     "Bruguera:2009:PIS",
  pages =        "57--64",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Moduli of the form $ 2 n \pm 1 $, which greatly
                 simplify certain arithmetic operations in residue
                 number systems (RNS), have been of longstanding
                 interest. A steady stream of designs for modulo-$ 2 n
                 \pm 1 $ adders has rendered the latency of such adders
                 quite competitive with ordinary adders. The next
                 logical step is to approach the problem in a unified
                 and systematic manner that does not require each design
                 to be taken up from scratch and to undergo the
                 error-prone and labor-intensive optimization for high
                 speed and low power dissipation. Accordingly, we devise
                 a new redundant representation of mod-$ 2 n \pm 1 $
                 residues that allows ordinary fast adders and a small
                 amount of peripheral logic to be used for mod-$ 2 n \pm
                 1 $ addition. Advantages of the building-block approach
                 include shorter design time, easier exploration of the
                 design space (area\slash speed\slash power tradeoffs),
                 and greater confidence in the correctness of the
                 resulting circuits. Advantages of the unified design
                 include the possibility of fault-tolerant and
                 gracefully degrading RNS circuit realizations with
                 fairly low hardware redundancy.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19",
}

@InProceedings{James:2009:HPL,
  author =       "R. K. James and K. P. Jacob and S. Sasi",
  title =        "High performance, low latency double digit decimal
                 multiplier on {ASIC} and {FPGA}",
  crossref =     "Abraham:2009:WCN",
  pages =        "1445--1450",
  year =         "2009",
  DOI =          "https://doi.org/10.1109/NABIC.2009.5393703",
  bibdate =      "Thu Feb 17 08:43:10 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Decimal multiplication is an integral part of
                 financial, commercial, and Internet-based computations.
                 This paper presents a novel double digit decimal
                 multiplication (DDDM) technique that offers low latency
                 and high throughput. This design performs two digit
                 multiplications simultaneously in one clock cycle.
                 Double digit fixed point decimal multipliers for
                 7digit, 16 digit and 34 digit are simulated using
                 Leonardo Spectrum from Mentor Graphics Corporation
                 using ASIC Library. The paper also presents area and
                 delay comparisons for these fixed point multipliers on
                 Xilinx, Altera, Actel and Quick logic FPGAs. This
                 multiplier design can be extended to support decimal
                 floating point multiplication for IEEE 754-2008
                 standard.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Jeannerod:2009:NBF,
  author =       "Claude-Pierre Jeannerod and Herv{\'e} Knochel and
                 Christophe Monat and Guillaume Revy and Gilles
                 Villard",
  title =        "A New Binary Floating-Point Division Algorithm and Its
                 Software Implementation on the {ST231} Processor",
  crossref =     "Bruguera:2009:PIS",
  pages =        "95--103",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper deals with the design and implementation of
                 low latency software for binary floating-point division
                 with correct rounding to nearest. The approach we
                 present here targets a VLIW integer processor of the
                 ST200 family, and is based on fast and accurate
                 programs for evaluating some particular bivariate
                 polynomials. We start by giving approximation and
                 evaluation error conditions that are sufficient to
                 ensure correct rounding. Then we describe the
                 heuristics used to generate such evaluation programs,
                 as well as those used to automatically validate their
                 accuracy. Finally, we propose, for the binary32 format,
                 a complete C implementation of the resulting division
                 algorithm. With the ST200 compiler and compared to
                 previous implementations, the speed-up observed with
                 our approach is by a factor of almost 1.8.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19; binary floating-point division; code
                 generation and validation; correct rounding; polynomial
                 evaluation; VLIW integer processor",
}

@Article{Jiang:2009:FPA,
  author =       "D. Jiang and N. F. Stewart",
  title =        "Floating-Point Arithmetic for Computational Geometry
                 Problems with Uncertain Data",
  journal =      j-INT-J-COMPUT-GEOM-APPL,
  volume =       "19",
  number =       "4",
  pages =        "371--385",
  month =        aug,
  year =         "2009",
  CODEN =        "IJCAEV",
  DOI =          "https://doi.org/10.1142/S0218195909003015",
  ISSN =         "0218-1959",
  bibdate =      "Mon Aug 30 10:25:06 MDT 2010",
  bibsource =    "http://ejournals.wspc.com.sg/ijcga/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International journal of computational geometry and
                 applications",
  journal-URL =  "http://www.worldscientific.com/loi/ijcga",
  xxnote =       "Check downcased title string??",
}

@InProceedings{Kaivola:2009:RTF,
  author =       "Roope Kaivola and Rajnish Ghughal and Naren Narasimhan
                 and Amber Telfer and Jesse Whittemore and Sudhindra
                 Pandav and Anna Slobodov{\'a} and Christopher Taylor
                 and Vladimir Frolov and Erik Reeber and Armaghan Naik",
  title =        "Replacing Testing with Formal Verification in
                 {Intel{\reg} Core{\TM} i7} Processor Execution Engine
                 Validation",
  crossref =     "Bouajjani:2009:CAV",
  pages =        "414--429",
  year =         "2009",
  DOI =          "https://doi.org/10.1007/978-3-642-02658-4_32",
  ISBN =         "3-642-02658-3",
  ISBN-13 =      "978-3-642-02658-4",
  bibdate =      "Fri Dec 8 13:33:33 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Keaton:2009:IIR,
  author =       "David Keaton and Thomas Plum and Robert C. Seacord and
                 David Svoboda and Alex Volkovitsky and Timothy Wilson",
  title =        "As-if Infinitely Ranged Integer Model",
  type =         "Technical Note",
  number =       "CMU/SEI-2009-TN-023",
  institution =  "Carnegie-Mellon University Software Engineering
                 Institute",
  address =      "Pittsburgh, PA, USA",
  month =        jul,
  year =         "2009",
  bibdate =      "Fri Aug 23 08:27:41 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://resources.sei.cmu.edu/asset_files/TechnicalNote/2009_004_001_15074.pdf;
                 https://resources.sei.cmu.edu/library/asset-view.cfm?assetid=9019",
  abstract =     "Integer overflow and wraparound are major causes of
                 software vulnerabilities in the C and C++ programming
                 languages. In this paper we present the as-if
                 infinitely ranged (AIR) integer model, which provides a
                 largely automated mechanism for eliminating integer
                 overflow and integer truncation. The AIR integer model
                 either produces a value equivalent to one that would
                 have been obtained using infinitely ranged integers or
                 results in a runtime constraint violation. Unlike
                 previous integer models, AIR integers do not require
                 precise traps, and consequently do not break or inhibit
                 most existing optimizations.",
  acknowledgement = ack-nhfb,
  keywords =     "integer overflow; integer wraparound",
}

@InProceedings{Khare:2009:HEA,
  author =       "Kavita Khare and Nilay Khare and Supriya Aggarwal",
  booktitle =    "{2009 IEEE International Advance Computing
                 Conference}",
  title =        "Hardware Efficient Algorithm for Complex Arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "209--213",
  year =         "2009",
  DOI =          "https://doi.org/10.1109/IADCC.2009.4809008",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithm design and analysis; Application software;
                 Computer architecture; CORDIC; Digital arithmetic;
                 Digital signal processing; FPGA; Hardware; ISE
                 Simulator; Recursive Architecture; Signal processing
                 algorithms; Taylor series; Throughput; Very large scale
                 integration; Xilinx9.2i",
}

@Article{Kim:2009:FPU,
  author =       "Donghyun Kim and Lee-Sup Kim",
  title =        "A Floating-Point Unit for {$4$D} Vector Inner Product
                 with Reduced Latency",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "7",
  pages =        "890--901",
  month =        jul,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2008.210",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 11:37:42 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4674343",
  abstract =     "This paper presents the algorithm and implementation
                 of a new high-performance functional unit for
                 floating-point four-dimensional vector inner product
                 (4D dot product; DP4), which is most frequently
                 performed in 3D graphics application. The proposed
                 IEEE-compliant DP4 unit computes $ {\rm Z} = {\rm AB} +
                 {rm CD} + {\rm EF} + {\rm GH} $ in one path and keeps
                 the intermediate rounding by IEEE-754 rounding to
                 nearest even. The intermediate rounding is merged with
                 shift alignment, and intermediate carry-propagated
                 addition and normalization are omitted to reduce
                 latency in the proposed architecture. The proposed DP4
                 unit is implemented with 0.18-$ \mu $ m CMOS technology
                 and has 12.8-ns critical path delay, which is reduced
                 by 45.5 percent compared to a previous DP4
                 implementation using discrete multipliers and adders.
                 The proposed DP4 unit also reduces the cycle time of 3D
                 graphics applications by 12.4 percent on the average
                 compared to the usual 3D graphics FPU based on four-way
                 multiply-add-fused units.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "3D graphics; DP4; floating point arithmetic; graphics
                 processors; vector inner product",
}

@InProceedings{Kornerup:2009:CCR,
  author =       "P. Kornerup and V. Lef{\`e}vre and N. Louvet and
                 Jean-Michel Muller",
  title =        "On the Computation of Correctly-Rounded Sums",
  crossref =     "Bruguera:2009:PIS",
  pages =        "155--160",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper presents a study of some basic blocks
                 needed in the design of floating-point summation
                 algorithms. In particular, we show that among the set
                 of the algorithms with no comparisons performing only
                 floating-point additions\slash subtractions, the 2Sum
                 algorithm introduced by Knuth is minimal, both in terms
                 of number of operations and depth of the dependency
                 graph. Under reasonable conditions, we also prove that
                 no algorithms performing only round-to-nearest
                 additions\slash subtractions exist to compute the
                 round-to-nearest sum of at least three floating-point
                 numbers. Starting from an algorithm due to Boldo and
                 Melquiond, we also present new results about the
                 computation of the correctly-rounded sum of three
                 floating-point numbers.",
  acknowledgement = ack-nhfb,
  keywords =     "2Sum and Fast2Sum algorithms; accurate floating-point
                 summation; ARITH-19; correct rounding; floating-point
                 arithmetic; summation algorithms",
}

@Article{Kornerup:2009:GEI,
  author =       "Peter Kornerup and Paolo Montuschi and Jean-Michel
                 Muller and Eric Schwarz",
  title =        "{Guest Editors}' Introduction: Special Section on
                 Computer Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "2",
  pages =        "145--147",
  month =        feb,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2009.11",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 11:37:39 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4740165",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Lang:2009:DUB,
  author =       "T. Lang and A. Nannarelli",
  title =        "Division Unit for Binary Integer Decimals",
  crossref =     "IEEE:2009:IICa",
  pages =        "1--7",
  year =         "2009",
  DOI =          "https://doi.org/10.1109/ASAP.2009.42",
  bibdate =      "Sat Dec 04 06:56:17 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this work, we present a radix-10 division unit that
                 is based on the digit-recurrence algorithm and
                 implements binary encodings (binary integer decimal or
                 BID) for significands. Recent decimal division designs
                 are all based on the binary coded decimal (BCD)
                 encoding. We adapt the radix-10 digit-recurrence
                 algorithm to BID representation and implement the
                 division unit in standard cell technology. The
                 implementation of the proposed BID division unit is
                 compared to that of a BCD based unit implementing the
                 same algorithm. The comparison shows that for
                 normalized operands the BID unit has the same latency
                 as the BCD unit and reduced area, but the normalization
                 is more expensive when implemented in BID.",
  acknowledgement = ack-nhfb,
  keywords =     "adders; BID floating-point adder; BID floating-point
                 multiplier; binary coded decimal encoding; binary
                 integer decimals; computer arithmetic; decimal
                 arithmetic; decimal division designs; digit-recurrence
                 algorithm; digital arithmetic; division; multiplying
                 circuits; radix-10 digit-recurrence algorithm; radix-10
                 division unit",
}

@Article{Lauter:2009:ERB,
  author =       "C. Q. Lauter and V. Lefevre",
  title =        "An Efficient Rounding Boundary Test for {\tt pow(x,
                 y)} in Double Precision",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "2",
  pages =        "197--207",
  month =        feb,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2008.202",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 11:37:39 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4663059",
  abstract =     "The correct rounding of the function $ \textrm {pow} :
                 (x, y) \rightarrow x^y $ is currently based on Ziv's
                 iterative approximation process. In order to ensure its
                 termination, cases when $ x^y $ falls on a
                 rounding-boundary must be filtered out. Such
                 rounding-boundaries are floating-point numbers and
                 midpoints between two consecutive floating-point
                 numbers. Detecting rounding-boundaries for pow is a
                 difficult problem. Previous approaches use repeated
                 square root extraction followed by repeated square and
                 multiply. This paper presents a new rounding-boundary
                 test for pow in double precision, which reduces this to
                 a few comparisons with precomputed constants. These
                 constants are deduced from worst cases for the Table
                 Maker's Dilemma, searched over a small subset of the
                 input domain. This is a novel use of such worst-case
                 bounds. The resulting algorithm has been designed for a
                 fast-on-average correctly rounded implementation of
                 pow, considering the scarcity of rounding-boundary
                 cases. It does not stall average computations for
                 rounding-boundary detection. This paper includes its
                 correctness proof and experimental results.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "correct rounding; floating-point arithmetic; power
                 function.",
}

@Article{Li:2009:FAT,
  author =       "Xin Li and Marc Moreno Maza and {\'E}ric Schost",
  title =        "Fast arithmetic for triangular sets: From theory to
                 practice",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "44",
  number =       "7",
  pages =        "891--907",
  month =        jul,
  year =         "2009",
  CODEN =        "JSYCEH",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  bibdate =      "Wed Aug 25 20:13:19 MDT 2010",
  bibsource =    "http://www.sciencedirect.com/science/journal/07477171;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171",
}

@TechReport{Maclaren:2009:HCH,
  author =       "N. M. Maclaren",
  title =        "How Computers Handle Numbers: a.k.a. Computer
                 Arithmetic Uncovered",
  type =         "Course notes",
  institution =  "Cambridge University Computing Service",
  address =      "Cambridge, UK",
  month =        jul,
  year =         "2009",
  bibdate =      "Tue Apr 27 09:48:59 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www-uxsup.csx.cam.ac.uk/courses/Arithmetic/notes.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Martel:2009:PTN,
  author =       "Matthieu Martel",
  editor =       "Germ{\'a}n Puebla",
  booktitle =    "{Proceedings of the 2009 ACM SIGPLAN Workshop on
                 Partial Evaluation and Program Manipulation ---
                 PEPM'09: Savannah, Georgia, USA, January 19--20,
                 2009}",
  title =        "Program transformation for numerical precision",
  publisher =    "{ACM} Press",
  pages =        "101--110",
  year =         "2009",
  DOI =          "https://doi.org/10.1145/1480945.1480960",
  ISBN =         "1-60558-327-8",
  ISBN-13 =      "978-1-60558-327-3",
  bibdate =      "Thu Oct 17 05:52:02 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://dl.acm.org/citation.cfm?doid=1480945.1480960",
  abstract =     "This article introduces a new program transformation
                 in order to enhance the numerical accuracy of
                 floating-point computations. We consider that a program
                 would return an exact result if the computations were
                 carried out using real numbers. In practice, roundoff
                 errors due to the finite representation of values arise
                 during the execution. These errors are closely related
                 to the way formulas are evaluated. Indeed,
                 mathematically equivalent formulas, obtained using laws
                 like associativity, distributivity, etc., may lead to
                 very different numerical results in the computer
                 arithmetic. We propose a semantics-based transformation
                 in order to optimize the numerical accuracy of
                 programs. This transformation is expressed in the
                 abstract interpretation framework and it aims at
                 rewriting pieces of numerical codes in order to obtain
                 results closer to what the computer would output if it
                 used the exact arithmetic.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Matula:2009:HRS,
  author =       "David W. Matula",
  title =        "Higher Radix Squaring Operations Employing
                 Left-to-Right Dual Recoding",
  crossref =     "Bruguera:2009:PIS",
  pages =        "39--47",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We introduce a novel left-to-right leading digit first
                 dual recoding of an operand for the purpose of
                 designing the squaring operation on that operand. Our
                 dual recoding yields an array of non-negative partial
                 squares of size essentially one half that of a
                 comparable multiplier partial product array for both
                 radix-4 and radix-8 designs. For radix-8 design the
                 128-bit square of a 64-bit operand can be obtained from
                 a consolidated partial square array of just 11 rows. We
                 describe advantages of our left-to-right recoding
                 compared to a previous right-to-left Booth-folding
                 encoding applicable to radix-4. We also show
                 simplifications available to the designs of a rounded
                 floating point square operation and to a low precision
                 approximate square.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19; Booth multiplier recoding; Booth-folding;
                 partial products; partial squares; sign extension.;
                 squarer",
}

@InProceedings{Mazor:2009:HPC,
  author =       "Stanley Mazor",
  title =        "A Historical Perspective on Computer Arithmetic",
  crossref =     "Bruguera:2009:PIS",
  pages =        "35--35",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19; Intel 4004; Intel 8080",
  remark =       "Only abstract published.",
}

@Book{Miller:2009:RNR,
  editor =       "Frederic P. Miller and Agnes F. Vandome and John
                 McBrewster",
  title =        "Roman Numerals: Roman numeral analysis, Roman
                 arithmetic, Roman abacus, {Kharosthi}, {Unicode}
                 numerals, {Etruscan} numerals, Positional notation,
                 Arabic numerals, Districts of {Turku}",
  publisher =    "Alphascript Publishing",
  address =      "17 Rue Meldrum, Beau Bassin, 1713-01 Mauritius",
  pages =        "88 (est.)",
  year =         "2009",
  ISBN =         "613-0-06480-2",
  ISBN-13 =      "978-613-0-06480-8",
  LCCN =         "????",
  bibdate =      "Wed Oct 28 09:06:59 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$50",
  acknowledgement = ack-nhfb,
}

@InProceedings{Minchola:2009:FID,
  author =       "C. Minchola and G. Sutter",
  title =        "A {FPGA} {IEEE-754-2008} {Decimal64} Floating-Point
                 Multiplier",
  crossref =     "Cumplido:2009:RPI",
  pages =        "59--64",
  year =         "2009",
  DOI =          "https://doi.org/10.1109/ReConFig.2009.34",
  bibdate =      "Thu Feb 17 08:36:13 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Monniaux:2009:UFPa,
  author =       "David Monniaux",
  title =        "On using floating-point computations to help an exact
                 linear arithmetic decision procedure",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "22",
  month =        apr,
  year =         "2009",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/0904.3525",
  abstract =     "We consider the decision problem for quantifier-free
                 formulas whose atoms are linear inequalities
                 interpreted over the reals or rationals. This problem
                 may be decided using satisfiability modulo theory
                 (SMT), using a mixture of a SAT solver and a
                 simplex-based decision procedure for conjunctions.
                 State-of-the-art SMT solvers use simplex
                 implementations over rational numbers, which perform
                 well for typical problems arising from model-checking
                 and program analysis (sparse inequalities, small
                 coefficients) but are slow for other applications
                 (denser problems, larger coefficients). We propose a
                 simple preprocessing phase that can be adapted on
                 existing SMT solvers and that may be optionally
                 triggered. Despite using floating-point computations,
                 our method is sound and complete --- it merely affects
                 efficiency. We implemented the method and provide
                 benchmarks showing that this change brings a naive and
                 slow decision procedure (''textbook simplex'' with
                 rational numbers) up to the efficiency of recent SMT
                 solvers, over test cases arising from model-checking,
                 and makes it definitely faster than state-of-the-art
                 SMT solvers on dense examples.",
  acknowledgement = ack-nhfb,
  subject =      "Logic in Computer Science (cs.LO); Numerical Analysis
                 (cs.NA)",
}

@InProceedings{Monniaux:2009:UFPb,
  author =       "David Monniaux",
  title =        "On Using Floating-Point Computations to Help an Exact
                 Linear Arithmetic Decision Procedure",
  crossref =     "Bouajjani:2009:CAV",
  pages =        "570--583",
  year =         "2009",
  DOI =          "https://doi.org/10.1007/978-3-642-02658-4_42",
  bibdate =      "Fri Dec 8 14:29:46 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Mosbach:2009:QPI,
  author =       "Sebastian Mosbach and Amanda G. Turner",
  title =        "A quantitative probabilistic investigation into the
                 accumulation of rounding errors in numerical {ODE}
                 solution",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "57",
  number =       "7",
  pages =        "1157--1167",
  month =        apr,
  year =         "2009",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:50:24 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122109000431",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Murakami:2009:CFT,
  author =       "Hiroshi Murakami",
  title =        "A continued fraction type method to find a rational
                 number in a given closed interval whose denominator is
                 minimal",
  journal =      j-ACM-COMM-COMP-ALGEBRA,
  volume =       "43",
  number =       "3",
  pages =        "88--90",
  month =        sep,
  year =         "2009",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/1823931.1823943",
  ISSN =         "1932-2232 (print), 1932-2240 (electronic)",
  ISSN-L =       "1932-2232",
  bibdate =      "Tue Jul 6 14:14:27 MDT 2010",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We show a fast algorithm to find a rational number in
                 a given real interval whose denominator is minimal. The
                 algorithm is similar to the regular continued fraction
                 expansion for a real number.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Communications in Computer Algebra",
  issue =        "169",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
  keywords =     "approximation; continued fraction; interval; rational
                 number",
}

@Article{Pan:2009:NEF,
  author =       "V. Y. Pan and B. Murphy and G. Qian and R. E.
                 Rosholt",
  title =        "A new error-free floating-point summation algorithm",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "57",
  number =       "4",
  pages =        "560--564",
  month =        feb,
  year =         "2009",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/j.camwa.2008.09.051",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:50:22 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122108006718",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Papadantonakis:2009:PSA,
  author =       "K. Papadantonakis and N. Kapre and S. Chan and A.
                 DeHon",
  title =        "Pipelining Saturated Accumulation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "2",
  pages =        "208--219",
  month =        feb,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2008.110",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jun 12 08:51:00 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  abstract =     "Aggressive pipelining and spatial parallelism allow
                 integrated circuits (e.g., custom VLSI, ASICs, and
                 FPGAs) to achieve high throughput on many Digital
                 Signal Processing applications. However, cyclic data
                 dependencies in the computation can limit parallelism
                 and reduce the efficiency and speed of an
                 implementation. Saturated accumulation is an important
                 example where such a cycle limits the throughput of
                 signal processing applications. We show how to
                 reformulate saturated addition as an associative
                 operation so that we can use a parallel-prefix
                 calculation to perform saturated accumulation at any
                 data rate supported by the device. This allows us, for
                 example, to design a 16-bit saturated accumulator which
                 can operate at 280 MHz on a Xilinx Spartan-3
                 (XC3S-5000-4) FPGA, the maximum frequency supported by
                 the component's DCM.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "accumulation; high-speed arithmetic; parallel prefix.;
                 pipeline and parallel arithmetic and logic structures;
                 saturated arithmetic",
  remark =       "Extended version of ARITH-18 article \cite{}.",
}

@InProceedings{Preiss:2009:ACS,
  author =       "Jochen Preiss and Maarten Boersma and Silvia Melitta
                 Mueller",
  title =        "Advanced Clockgating Schemes for
                 Fused-Multiply-Add-Type Floating-Point Units",
  crossref =     "Bruguera:2009:PIS",
  pages =        "48--56",
  year =         "2009",
  DOI =          "https://doi.org/10.1109/ARITH.2009.17",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The paper introduces fine-grain clockgating schemes
                 for fused multiply-add-type floating-point units (FPU).
                 The clockgating is based on instruction type, precision
                 and operand values. The presented schemes focus on
                 reducing the power at peak performance, where each FPU
                 stage is used in nearly every cycle and conventional
                 schemes have little impact on the power consumption.
                 Depending on the instruction mix, the schemes allow to
                 turn off 18\% to 74\% of the register bits. Even for
                 the worst case instruction 18\% to 37\% of the FPU are
                 shut down depending on the data patterns.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19; clockgating; floating-point hardware; fused
                 multiply-add; IEEE 754 Standard; power reduction",
}

@Article{Rump:2009:CPS,
  author =       "Siegfried M. Rump and Paul Zimmermann and Sylvie Boldo
                 and Guillaume Melquiond",
  title =        "Computing predecessor and successor in rounding to
                 nearest",
  journal =      j-BIT-NUM-MATH,
  volume =       "49",
  number =       "2",
  pages =        "419--431",
  month =        jun,
  year =         "2009",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/s10543-009-0218-z",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Mon May 24 15:36:43 MDT 2010",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=49&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=49&issue=2&spage=419",
  abstract =     "We give simple and efficient methods to compute and/or
                 estimate the predecessor and successor of a
                 floating-point number using only floating-point
                 operations in rounding to nearest. This may be used to
                 simulate interval operations, in which case the quality
                 in terms of the diameter of the result is significantly
                 improved compared to existing approaches.",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT. Numerical Mathematics",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "directed rounding; floating-point arithmetic;
                 predecessor; rounding to nearest; successor",
}

@Article{Rump:2009:UFA,
  author =       "Siegfried M. Rump",
  title =        "Ultimately Fast Accurate Summation",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "31",
  number =       "5",
  pages =        "3466--3502",
  month =        "????",
  year =         "2009",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/080738490",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Wed May 19 10:44:20 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/31/5;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present two new algorithms FastAccSum and
                 FastPrecSum, one to compute a faithful rounding of the
                 sum of floating-point numbers and the other for a
                 result ``as if'' computed in $K$-fold precision.
                 Faithful rounding means the computed result either is
                 one of the immediate floating-point neighbors of the
                 exact result or is equal to the exact sum if this is a
                 floating-point number. The algorithms are based on our
                 previous algorithms AccSum and PrecSum and improve them
                 by up to 25\%. The first algorithm adapts to the
                 condition number of the sum; i.e., the computing time
                 is proportional to the difficulty of the problem. The
                 second algorithm does not need extra memory, and the
                 computing time depends only on the number of summands
                 and $K$. Both algorithms are the fastest known in terms
                 of flops. They allow good instruction-level parallelism
                 so that they are also fast in terms of measured
                 computing time. The algorithms require only standard
                 floating-point addition, subtraction, and
                 multiplication in one working precision, for example,
                 double precision.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  keywords =     "accurate floating-point summation; distillation",
}

@Article{Schwarz:2009:DFP,
  author =       "E. M. Schwarz and J. S. Kapernick and M. F.
                 Cowlishaw",
  title =        "Decimal floating-point support on the {IBM System z10}
                 processor",
  journal =      j-IBM-JRD,
  volume =       "53",
  number =       "1",
  pages =        "4:1--4:10",
  month =        jan # "\slash " # feb,
  year =         "2009",
  CODEN =        "IBMJAE",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Thu Jan 29 14:25:32 MST 2009",
  bibsource =    "http://www.research.ibm.com/journal/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.research.ibm.com/journal/rd/531/schwarz.pdf",
  abstract =     "The latest IBM zSeries processor, the IBM System z10
                 processor, provides hardware support for the decimal
                 floating-point (DFP) facility that was introduced on
                 the IBM System z9 processor. The z9 processor
                 implements the facility with a mixture of low-level
                 software and hardware assists. Recently, the IBM POWER6
                 processor-based System p 570 server introduced a
                 hardware implementation of the DFP facility. The latest
                 zSeries processor includes a decimal floating-point
                 unit based on the POWER6 processor DFP unit that has
                 been enhanced to also support the traditional zSeries
                 decimal fixed-point instruction set. This paper
                 explains the hardware implementation to support both
                 decimal fixed point and DFP and the new software
                 support for the DFP facility, including IBM z/OS, Java
                 JIT, and C/C++ compilers, as well as support in IBM DB2
                 and middleware.",
  acknowledgement = ack-nhfb,
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "ARITH-19",
  remark =       "Extended version of ARITH-18 article \cite{}.",
}

@InProceedings{Shaw:2009:ASM,
  author =       "David E. Shaw",
  title =        "{Anton}: a Specialized Machine for Millisecond-Scale
                 Molecular Dynamics Simulations of Proteins",
  crossref =     "Bruguera:2009:PIS",
  pages =        "3--3",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19",
}

@Article{Shpilka:2009:IDA,
  author =       "Amir Shpilka",
  title =        "Interpolation of Depth-3 Arithmetic Circuits with Two
                 Multiplication Gates",
  journal =      j-SIAM-J-COMPUT,
  volume =       "38",
  number =       "6",
  pages =        "2130--2161",
  month =        "????",
  year =         "2009",
  CODEN =        "SMJCAT",
  DOI =          "",
  ISSN =         "0097-5397 (print), 1095-7111 (electronic)",
  ISSN-L =       "0097-5397",
  bibdate =      "Tue May 18 08:22:06 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/38/6;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Computing",
  journal-URL =  "http://epubs.siam.org/sicomp",
}

@TechReport{Stewart:2009:FMP,
  author =       "G. W. Stewart",
  title =        "{Flap}: a {Matlab} Package for Adjustable Precision
                 Floating-Point Arithmetic",
  type =         "Report",
  institution =  "Department of Computer Science, University of
                 Maryland",
  address =      "College Park, MD, USA",
  year =         "2009",
  bibdate =      "Sun Jun 19 13:11:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.umd.edu/~stewart/flap/flap.html",
  abstract =     "Flap is a package to implement floating-point
                 arithmetic with adjustable precision. Specifically,
                 operations are performed on Matlab doubles but are
                 rounded to a user specified number of decimal digits
                 after each operation. The number can be changed
                 dynamically. Flap is intended to make it easy to
                 generate examples of the effects of rounding error for
                 classroom use.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Tajallipour:2009:FCD,
  author =       "R. Tajallipour and D. Teng and Seok-Bum Ko and K.
                 Wahid",
  title =        "On the fast computation of decimal logarithm",
  crossref =     "ICCIT:2009:ICC",
  pages =        "32--36",
  year =         "2009",
  DOI =          "https://doi.org/10.1109/ICCIT.2009.5407171",
  bibdate =      "Thu Feb 17 08:28:37 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The paper presents a new and fast algorithm to
                 efficiently compute radix-10 logarithm of a decimal
                 number. The algorithm uses 32-bit floating-point
                 arithmetic, and is based on a digit-by-digit iterative
                 computation that does not require look-up tables, curve
                 fitting, decimal-binary conversion, or division
                 operations; the number of iterations depends on the
                 user defined precision. The algorithm produces
                 error-free (infinite precision) results up to 7 decimal
                 digits. A numerical example is shown for the purpose of
                 illustration. The accuracy is analyzed for several
                 decimal digits showing compliance with the IEEE
                 754-2008 Standard. When implemented on to the Xilinx
                 VirtexII FPGA, the architecture costs only 1,053 logic
                 cells, runs at a maximum frequency of 44 MHz, and
                 consumes 79 mW of power.",
  acknowledgement = ack-nhfb,
}

@Article{Tan:2009:LPM,
  author =       "D. Tan and C. E. Lemonds and Michael J. Schulte",
  title =        "Low-Power Multiple-Precision Iterative Floating-Point
                 Multiplier with {SIMD} Support",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "2",
  pages =        "175--187",
  month =        feb,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2008.203",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 11:37:39 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4663060",
  abstract =     "The demand for improved SIMD floating-point
                 performance on general-purpose x86-compatible
                 microprocessors is rising. At the same time, there is a
                 conflicting demand in the low-power computing market
                 for a reduction in power consumption. Along with this,
                 there is the absolute necessity of backward
                 compatibility for x86-compatible microprocessors, which
                 includes the support of x87 scientific floating-point
                 instructions. The combined effect is that there is a
                 need for low-power, low-cost floating-point units that
                 are still capable of delivering good SIMD performance
                 while maintaining full x86 functionality. This paper
                 presents the design of an x86-compatible floating-point
                 multiplier (FPM) that is compliant with the IEEE-754
                 Standard for Binary Floating-Point Arithmetic [12] and
                 is specifically tailored to provide good SIMD
                 performance in a low-cost, low-power solution while
                 maintaining full x87 backward compatibility. The FPM
                 efficiently supports multiple precisions using an
                 iterative rectangular multiplier. The FPM can perform
                 two parallel single-precision multiplies every cycle
                 with a latency of two cycles, one double-precision
                 multiply every two cycles with a latency of four
                 cycles, or one extended-double-precision multiply every
                 three cycles with a latency of five cycles. The
                 iterative FPM also supports division, square-root, and
                 transcendental functions. Compared to a previous design
                 with similar functionality, the proposed iterative FPM
                 has 60 percent less area and 59 percent less dynamic
                 power dissipation.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Computer arithmetic; floating-point arithmetic;
                 low-power; multimedia; multiplying circuits;
                 rectangular multiplier; very-large-scale integration",
}

@InProceedings{Tenca:2009:MOF,
  author =       "Alexandre F. Tenca",
  title =        "Multi-operand Floating-Point Addition",
  crossref =     "Bruguera:2009:PIS",
  pages =        "161--168",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The design of a component to perform parallel addition
                 of multiple floating-point (FP) operands is explored in
                 this work. In particular, a 3-input FP adder is
                 discussed in more detail, but the main concepts and
                 ideas presented in this work are valid for FP adders
                 with more inputs. The proposed design is more accurate
                 than conventional FP addition using a network of
                 2-operand FP adders and it may have competitive area
                 and delay depending on the number of input operands.
                 Implementation results of a 3-operand FP adder are
                 presented to compare its performance to a network of
                 2-input FP adders.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19",
}

@InProceedings{Tsen:2009:CDB,
  author =       "Charles Tsen and Sonia Gonzalez-Navarro and Michael J.
                 Schulte and Brian Hickmann and Katherine Compton",
  title =        "A Combined Decimal and Binary Floating-Point
                 Multiplier",
  crossref =     "IEEE:2009:IICa",
  pages =        "8--15",
  year =         "2009",
  DOI =          "https://doi.org/10.1109/ASAP.2009.28",
  bibdate =      "Sat Dec 04 07:01:08 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this paper, we describe the first hardware design
                 of a combined binary and decimal floating-point
                 multiplier, based on specifications in the IEEE
                 754-2008 floating-point standard. The multiplier design
                 operates on either (1) 64-bit binary encoded decimal
                 floating-point (DFP) numbers or (2) 64-bit binary
                 floating-point (BFP) numbers. It returns properly
                 rounded results for the rounding modes specified in
                 IEEE 754-2008. The design shares the following hardware
                 resources between the two floating-point datatypes: a
                 54-bit by 54-bit binary multiplier, portions of the
                 operand encoding/decoding, a 54-bit right shifter,
                 exponent calculation logic, and rounding logic. Our
                 synthesis results show that hardware sharing is
                 feasible and has a reasonable impact on area, latency,
                 and delay. The combined BFP and DFP multiplier occupies
                 only 58\% of the total area that would be required by
                 separate BFP and DFP units. Furthermore, the critical
                 path delay of a combined multiplier has a negligible
                 increase over a standalone DFP multiplier, without
                 increasing the number of cycles to perform either BFP
                 or DFP multiplication.",
  acknowledgement = ack-nhfb,
  keywords =     "binary encoded decimal floating-point; binary
                 floating-point multiplier; combined decimal
                 floating-point multiplier design; Commercial
                 Applications; Computer Arithmetic; Decimal
                 Floating-point; exponent calculation logic; floating
                 point arithmetic; Floating-point; Hardware; hardware
                 design; Hardware Reuse; IEEE 754-2008; IEEE 754-2008
                 floating-point standard; logic design; Multiplication;
                 multiplying circuits; Register-Transfer-Level
                 Implementation; right shifter; rounding logic",
}

@TechReport{Tydeman:2009:CMC,
  author =       "Fred J. Tydeman",
  title =        "Complex Multiply and Complex Divide, taking into
                 account {IEEE-754 (IEC 60559)} signed zeros, signed
                 infinities, {NaN}, and {C99 \_Imaginary\_I}",
  type =         "Report",
  number =       "WG14 N1399",
  institution =  "????",
  address =      "????",
  day =          "25",
  month =        sep,
  year =         "2009",
  bibdate =      "Mon Sep 30 09:48:02 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.open-std.org/jtc1/sc22/wg14/www/docs/n1399.htm",
  acknowledgement = ack-nhfb,
}

@TechReport{Usselmann:2009:FPU,
  author =       "R. Usselmann",
  title =        "Floating point unit",
  type =         "Web report",
  institution =  "Algotronix Ltd.",
  address =      "Edinburgh EH8 8YB, UK",
  day =          "20",
  month =        dec,
  year =         "2009",
  bibdate =      "Thu Mar 24 21:02:16 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://opencores.org/project,fpu",
  abstract =     "This is a single precision floating point unit. It is
                 fully IEEE 754 compliant. It can currently perform
                 Add\slash Sub, Mul and Divide operations, as well as
                 integer to floating point and floating point to integer
                 conversions. It supports four rounding modes: Round to
                 Nearest Even, Round to Zero, Round to +INF and Round to
                 INF. There is now also a separate FP compare unit. It
                 is located in the {\tt fpu/fcmp} directory.",
  acknowledgement = ack-nhfb,
  remark =       "Creatred 25-Sep-2001",
}

@Article{Van:2009:PEP,
  author =       "Lan-Da Van and Jin-Hao Tu",
  title =        "Power-Efficient Pipelined Reconfigurable Fixed-Width
                 {Baugh--Wooley} Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "10",
  pages =        "1346--1355",
  month =        oct,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2009.89",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 11:37:43 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5156495",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{VanDenDries:2009:AC,
  author =       "Lou {Van Den Dries} and Yiannis N. Moschovakis",
  title =        "Arithmetic complexity",
  journal =      j-TOCL,
  volume =       "10",
  number =       "1",
  pages =        "2:1--2:??",
  month =        jan,
  year =         "2009",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/1459010.1459012",
  ISSN =         "1529-3785 (print), 1557-945X (electronic)",
  ISSN-L =       "1529-3785",
  bibdate =      "Mon Jan 26 18:05:23 MST 2009",
  bibsource =    "http://www.acm.org/pubs/contents/journals/tocl/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We obtain {\em lower bounds\/} on the cost of
                 computing various arithmetic functions and deciding
                 various arithmetic relations from specified primitives.
                 This includes lower bounds for computing the greatest
                 common divisor and deciding coprimeness of two
                 integers, from primitives like addition, subtraction,
                 division with remainder and multiplication. Some of our
                 results are in terms of recursive programs, but they
                 generalize directly to most (plausibly all) algorithms
                 from the specified primitives. Our methods involve some
                 elementary number theory as well as the development of
                 some basic notions and facts about recursive
                 algorithms.",
  acknowledgement = ack-nhfb,
  articleno =    "2",
  fjournal =     "ACM Transactions on Computational Logic",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J773",
  keywords =     "coprimeness; greatest common divisor; Lower bounds for
                 arithmetical problems; recursive programs",
}

@InProceedings{Vazquez:2009:CDT,
  author =       "{\'A}lvaro V{\'a}zquez and Julio Villalba and Elisardo
                 Antelo",
  title =        "Computation of Decimal Transcendental Functions Using
                 the {CORDIC} Algorithm",
  crossref =     "Bruguera:2009:PIS",
  pages =        "179--186",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this work we propose new decimal floating-point
                 CORDIC algorithms for transcendental function
                 evaluation. We show how these algorithms are mapped to
                 a state of the art Decimal Floating-Point Unit (DFPU),
                 both considering the use of a carry-propagate adder or
                 a carry-save redundant adder. We compared with previous
                 decimal CORDIC proposals and with table-driven
                 algorithms, and we concluded that our approach have
                 significant potential advantages for transcendental
                 function evaluation in state of the art DFPUs with
                 minor modifications of the hardware.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19",
}

@InProceedings{Vazquez:2009:HPS,
  author =       "{\'A}lvaro V{\'a}zquez and Elisardo Antelo",
  title =        "A High-Performance Significand {BCD} Adder with {IEEE
                 754-2008} Decimal Rounding",
  crossref =     "Bruguera:2009:PIS",
  pages =        "135--144",
  year =         "2009",
  DOI =          "https://doi.org/10.1109/ARITH.2009.30",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present a new method and architecture to merge
                 efficiently IEEE 754-2008 decimal rounding with
                 significand BCD addition and subtraction. This is a key
                 component to improve several decimal floating-point
                 operations such as addition, multiplication and fused
                 multiply-add. The decimal rounding unit is based on a
                 direct implementation of the IEEE 754-2008 rounding
                 modes. We show that the resultant implementations for
                 IEEE 754-2008 Decimal64 (16 precision digits) and
                 Decimal128 (34 precision digits) formats reduce
                 significantly the area and latency required for
                 significand BCD addition/subtraction and decimal
                 rounding in previous high-performance decimal
                 floating-point adders.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19",
}

@InProceedings{Verma:2009:CAO,
  author =       "Ajay K. Verma and Philip Brisk and Paolo Ienne",
  title =        "Challenges in Automatic Optimization of Arithmetic
                 Circuits",
  crossref =     "Bruguera:2009:PIS",
  pages =        "213--218",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Despite the impressive progress of logic synthesis in
                 the past decade, finding the best architecture for a
                 given circuit still remains an open and largely
                 unsolved problem, especially for arithmetic circuits.
                 In many cases, the outcome of even the most advanced
                 synthesis techniques is highly dependent on the input
                 description of the circuit, and the optimizations
                 themselves barely modify the architecture of the
                 circuit itself. Once the input description is converted
                 to an appropriate architecture, logic synthesis
                 performs local optimizations quite effectively;
                 however, finding the best architecture up front is a
                 nontrivial problem. This paper reviews recent results
                 in arithmetic logic synthesis that the authors have
                 published in recent years. Progress has clearly been
                 made, but much further work is still needed to narrow
                 the gap between the effectiveness of logic synthesis
                 techniques for arithmetic and control-oriented
                 circuits.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19",
}

@InProceedings{Vuillemin:2009:EDS,
  author =       "Jean E. Vuillemin",
  title =        "Efficient Data Structure and Algorithms for Sparse
                 Integers, Sets and Predicates",
  crossref =     "Bruguera:2009:PIS",
  pages =        "7--14",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We construct a natural number $ n > 1 $ by trichotomy
                 $$ n = g + x_p d, x_p = 2^{2^p}, 0 \leq g < x_p, 0 < d
                 < x_p $$ applied recursively, and by systematically
                 sharing nodes with equal integer value. The resulting
                 Integer Decision Diagram IDD is a directed acyclic
                 graph DAG which represents $n$ by $ S(n) $ nodes in
                 computer memory. IDDs compete with bit-arrays, which
                 represent the consecutive bits of $n$ within roughly $
                 l(n) $ contiguous bits in memory. Unlike the binary
                 length $ l(n) $, the size $ S(n) $ is not monotonic.
                 Most integers are dense: their size is near worst &
                 average. The IDD size of sparse integers is arbitrarily
                 smaller.\par

                 Over dense numbers, the worst\slash average time\slash
                 space complexity of IDDs arithmetic operations is
                 proportional to that of bit-arrays. Yet, equality
                 testing is performed in unit time with IDDs and the
                 time\slash space complexity of some operations (e.g. $
                 \textrm {sign}(n - m), n \pm 2^m, 2^{2^n} $) are (at
                 least) exponentially better with IDDs than with
                 bit-arrays, even over dense operands.

                 Over sparse operands, the time and space complexity of
                 all ALU operations $ \{ \cap, \cup, \oplus, +, - \} $
                 are (in general) arbitrarily better with IDDs than
                 bit-arrays.\par

                 The coding powers of integers lets IDDs implement
                 integer sets and predicates as well as arithmetics. The
                 IDD package is a one-shop alternative to 3 (and more)
                 successful yet rather different packages for processing
                 large numbers, dictionaries and Boolean functions.
                 Performance levels are comparable over dense
                 structures, and IDDs prove best in class over sparse
                 structures.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19; boolean functions; decision diagrams
                 IDD/BDD/BMD/ZDD; dictionaries; integer dichotomy and
                 trichotomy; sparse numbers; store/compute/code once",
}

@InProceedings{Wang:2009:DFP,
  author =       "Liang-Kai Wang and Michael J. Schulte",
  title =        "A Decimal Floating-Point Adder with Decoded Operands
                 and a Decimal Leading-Zero Anticipator",
  crossref =     "Bruguera:2009:PIS",
  pages =        "125--134",
  year =         "2009",
  DOI =          "https://doi.org/10.1109/ARITH.2009.9",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The IEEE 754-2008 Standard for Floating-Point
                 Arithmetic was of officially approved this year. One of
                 the most important revisions to IEEE 754-1985 is the
                 introduction of decimal floating-point (DFP) formats
                 and operations. Since IEEE 754-1985 was revised, major
                 microprocessor vendors have been working on hardware
                 designs and software libraries for decimal arithmetic.
                 Because the new standard has been approved, many
                 software vendors are planning to adapt the new decimal
                 formats into their applications. Therefore, it is
                 important to investigate efficient algorithms and
                 hardware designs for common DFP arithmetic operations
                 to improve the performance of these applications. This
                 paper presents a novel DFP adder with decoded operands
                 and a decimal leading-zero anticipator (LZA). The DFP
                 adder is based on a previous DFP adder design with
                 several new features, including a new internal format,
                 an improved operand pre-correction stage, and a novel
                 decimal LZA to obtain better timing for decimal
                 addition and subtraction. Synthesis results show that
                 the new DFP adder is roughly 14\% faster than the
                 previous design.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19",
}

@Article{Wang:2009:HDD,
  author =       "Liang-Kai Wang and Michael J. Schulte and J. D.
                 Thompson and N. Jairam",
  title =        "Hardware Designs for Decimal Floating-Point Addition
                 and Related Operations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "58",
  number =       "3",
  pages =        "322--335",
  month =        mar,
  year =         "2009",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2008.147",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 4 11:37:40 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4599577",
  abstract =     "Decimal arithmetic is often used in commercial,
                 financial, and Internet-based applications. Due to the
                 growing importance of decimal floating-point (DFP)
                 arithmetic, the IEEE 754-2008 Standard for
                 Floating-Point Arithmetic (IEEE 754-2008) includes
                 specifications for DFP arithmetic. IBM recently
                 announced adding DFP instructions to their POWER6, z9,
                 and z10 microprocessor architectures. As processor
                 support for DFP arithmetic emerges, it is important to
                 investigate efficient arithmetic algorithms and
                 hardware designs for common DFP arithmetic operations.
                 This paper gives an overview of DFP arithmetic in IEEE
                 754-2008 and discusses previous research on decimal
                 fixed-point and floating-point addition. It also
                 presents novel designs for a DFP adder and a DFP
                 multifunction unit (DFP MFU) that comply with IEEE
                 754-2008. To reduce their delay, the DFP adder and MFU
                 use decimal injection-based rounding, a new form of
                 decimal operand alignment, and a fast flag-based method
                 for rounding and overflow detection. Synthesis results
                 indicate that the proposed DFP adder is roughly 21
                 percent faster and 1.6 percent smaller than a previous
                 DFP adder design, when implemented in the same
                 technology. Compared to the DFP adder, the DFP MFU
                 provides six additional operations, yet only has 2.8
                 percent more delay and 9.7 percent more area. A
                 pipelined version of the DFP MFU has a latency of six
                 cycles, a throughput of one result per cycle, an
                 estimated critical path delay of 12.9 fanout-of-four
                 (FO4) inverter delays, and an estimated area of 45,681
                 NAND2 equivalent gates.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "addition; computer arithmetic; Decimal;
                 floating-point; logic design; multifunction unit;
                 subtraction",
}

@InProceedings{Wang:2009:RCD,
  author =       "Dong Wang and M. D. Ercegovac and Nanning Zheng",
  title =        "A radix-8 complex divider for {FPGA} implementation",
  crossref =     "IEEE:2009:ICF",
  pages =        "236--241",
  year =         "2009",
  DOI =          "https://doi.org/10.1109/FPL.2009.5272300",
  bibdate =      "Fri Dec 03 15:33:08 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present a design of a radix-8 complex division for
                 fixed-point operands suitable for FPGA implementation.
                 The design, consisting of operands' prescaling and
                 digit recurrence, shares logic resources and optimizes
                 the use of 6-input LUTs of FPGA devices for efficient
                 design. An optimized single table for prescaling
                 factors is developed. The design is implemented in
                 Altera Stratix-II FPGA for several operands precisions
                 and compared in cost, latency and power with a design
                 using non-shared resources and with an IP-based design.
                 The results show advantages of the proposed design in
                 cost, delay, and power.",
  acknowledgement = ack-nhfb,
  keywords =     "Altera Stratix-II FPGA; digit recurrence; dividing
                 circuits; field programmable gate arrays; IP-based
                 design; logic resources; non-shared resources; operand
                 prescaling; radix-8 complex divider",
}

@Manual{XILINX:2009:XLF,
  author =       "{XILINX}",
  title =        "{XILINX LogiCORE} floating-point operator v5.0 product
                 specification",
  organization = "Xilinx, Inc.",
  day =          "24",
  month =        jun,
  year =         "2009",
  bibdate =      "Sat Oct 9 13:09:37 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.xilinx.com/support/documentation/ip_documentation/floating_point_ds335.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Zhu:2009:CRH,
  author =       "Yong-Kang Zhu and Wayne B. Hayes",
  title =        "Correct Rounding and a Hybrid Approach to Exact
                 Floating-Point Summation",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "31",
  number =       "4",
  pages =        "2981--3001",
  month =        "????",
  year =         "2009",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/070710020",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Wed May 19 10:44:18 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/31/4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present two algorithms for computing correctly
                 rounded sums of arrays of floating-point numbers.
                 First, iFastSum improves upon our previous FastSum by
                 requiring no additional space beyond the original
                 array, which is destroyed. It runs about 20\% faster
                 than FastSum in the general case and two times faster
                 when extremely ill-conditioned data are used. The
                 second algorithm is HybridSum, which combines three
                 summation ideas together: splitting the mantissa, radix
                 sorting, and using iFastSum. The result is that when
                 the number of summands is greater than about $ 10^4 $,
                 for a given $n$ its running time is almost a constant,
                 independent of the condition number. It runs almost as
                 fast as iFastSum in the general case and much faster
                 than iFastSum when ill-conditioned data are used.
                 HybridSum requires only one pass through the input
                 array and uses constant storage, and it is thus
                 suitable for exact summation as an ``online''
                 algorithm. Neither algorithm requires extra precision
                 accumulators, and both work in any base. Their accuracy
                 is guaranteed independent of the condition number and
                 the number of summands.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  keywords =     "accurate floating-point summation; correct rounding;
                 floating-point arithmetic",
}

@InProceedings{Zimmermann:2009:DSS,
  author =       "Reto Zimmermann",
  title =        "Datapath Synthesis for Standard-Cell Design",
  crossref =     "Bruguera:2009:PIS",
  pages =        "207--211",
  year =         "2009",
  bibdate =      "Fri Jun 12 12:34:25 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Datapath synthesis for standard-cell design goes
                 through extraction of arithmetic operations from RTL
                 code, high-level arithmetic optimizations and netlist
                 generation. Numerous architectures and optimization
                 strategies exist that result in circuit implementations
                 with very different performance characteristics. This
                 work summarizes the circuit architectures and
                 techniques used in a commercial synthesis tool to
                 optimize cell-based datapath netlists for timing, area
                 and power.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19",
}

@Article{Akbarpour:2010:VSI,
  author =       "Behzad Akbarpour and Amr T. Abdel-Hamid and
                 Sofi{\`e}ne Tahar and John Harrison",
  title =        "Verifying a Synthesized Implementation of {IEEE-754}
                 Floating-Point Exponential Function using {HOL}",
  journal =      j-COMP-J,
  volume =       "53",
  number =       "4",
  pages =        "465--488",
  month =        may,
  year =         "2010",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/bxp023",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Wed Apr 28 14:33:36 MDT 2010",
  bibsource =    "http://comjnl.oxfordjournals.org/content/vol53/issue4/index.dtl;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/cgi/content/abstract/53/4/465;
                 http://comjnl.oxfordjournals.org/cgi/reprint/53/4/465",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Aldous:2010:WCO,
  author =       "David Aldous and Tung Phan",
  title =        "When Can One Test an Explanation? {Compare} and
                 Contrast {Benford's Law} and the Fuzzy {CLT}",
  journal =      j-AMER-STAT,
  volume =       "64",
  number =       "3",
  pages =        "221--227",
  month =        aug,
  year =         "2010",
  CODEN =        "ASTAAJ",
  DOI =          "https://doi.org/10.1198/tast.2010.09098",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Thu Aug 26 21:48:27 MDT 2010",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 https://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@Article{Alimohammad:2010:UAA,
  author =       "A. Alimohammad and S. F. Fard and B. F. Cockburn",
  title =        "A Unified Architecture for the Accurate and
                 High-Throughput Implementation of Six Key Elementary
                 Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "59",
  number =       "4",
  pages =        "449--456",
  month =        "????",
  year =         "2010",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2009.169",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 3 11:52:27 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5313801",
  abstract =     "This paper presents a unified architecture for the
                 compact implementation of several key elementary
                 functions, including reciprocal, square root, and
                 logarithm, in single-precision floating-point
                 arithmetic. The proposed high-throughput design is
                 based on uniform domain segmentation and curve fitting
                 techniques. Numerically accurate least-squares
                 regression is utilized to calculate the polynomial
                 coefficients. The architecture is optimized by
                 analyzing the trade-off between the size of the
                 required memory and the precision of intermediate
                 variables to achieve the minimum 23-bit accuracy
                 required for single-precision floating-point
                 representation. The efficiency of the proposed unified
                 data path is demonstrated on a common
                 field-programmable gate array.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Amin:2010:HRM,
  author =       "Alaaeldin Amin and Waleed Shinwari",
  title =        "High-Radix Multiplier-Dividers: Theory, Design, and
                 Hardware",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "59",
  number =       "8",
  pages =        "1009--1022",
  month =        "????",
  year =         "2010",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.78",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 3 11:52:30 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5453337",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Banescu:2010:MFP,
  author =       "Sebastian Banescu and Florent de Dinechin and Bogdan
                 Pasca and Radu Tudoran",
  title =        "Multipliers for floating-point double precision and
                 beyond on {FPGAs}",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "38",
  number =       "4",
  pages =        "73--79",
  month =        sep,
  year =         "2010",
  CODEN =        "CANED2",
  DOI =          "https://doi.org/10.1145/1926367.1926380",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Thu Jan 20 14:27:03 MST 2011",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The implementation of high-precision floating-point
                 applications on reconfigurable hardware requires large
                 multipliers. Full multipliers are the core of
                 floating-point multipliers. Truncated multipliers,
                 trading resources for a well-controlled accuracy
                 degradation, are useful building blocks in situations
                 where a full multiplier is not needed.\par

                 This work studies the automated generation of such
                 multipliers using the embedded multipliers and adders
                 present in the DSP blocks of current FPGAs. The
                 optimization of such multipliers is expressed as a
                 tiling problem, where a tile represents a hardware
                 multiplier, and super-tiles represent combinations of
                 several hardware multipliers and adders, making
                 efficient use of the DSP internal resources. This
                 tiling technique is shown to adapt to full or truncated
                 multipliers. It addresses arbitrary precisions
                 including single, double but also the quadruple
                 precision introduced by the IEEE-754-2008 standard and
                 currently unsupported by processor hardware. An
                 open-source implementation is provided in the FloPoCo
                 project.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
}

@Article{Block:2010:GEB,
  author =       "Henry W. Block and Thomas H. Savits",
  title =        "A General Example for {Benford} Data",
  journal =      j-AMER-STAT,
  volume =       "64",
  number =       "4",
  pages =        "335--339",
  month =        nov,
  year =         "2010",
  CODEN =        "ASTAAJ",
  DOI =          "https://doi.org/10.1198/tast.2010.09169",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Wed Nov 9 17:20:17 MST 2011",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 https://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Benford's Law deals, among other things, with the
                 proportion of numbers whose first significant digit is
                 a $1$ (e.g., $ 0.00131 $ and $ 19668 $ both have first
                 significant digit $1$) in a variety of datasets. In
                 these datasets, which arise in various compendiums or
                 as mixtures of various sets of numbers, the proportion
                 of numbers with first significant digit one is $ 0.3010
                 $ which is much higher than the commonsense value of $
                 1 / 9 $. The reasons for this occurrence have been
                 elusive. Mathematical attempts to explain this
                 phenomenon have been relatively fruitless. Methods
                 involving probability have been somewhat more
                 successful. In this article we give some simple reasons
                 for this occurrence and also give an example of a
                 general mixture of distributions which exactly
                 satisfies this Law. Various other examples and
                 counterexamples are also given.",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@Article{Brent:2010:PAV,
  author =       "Richard P. Brent",
  title =        "On the precision attainable with various
                 floating-point number systems",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "20",
  month =        apr,
  year =         "2010",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  MRclass =      "65Y04",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/1004.3374",
  abstract =     "For scientific computations on a digital computer the
                 set of real number is usually approximated by a finite
                 set $F$ of ``floating-point'' numbers. We compare the
                 numerical accuracy possible with difference choices of
                 $F$ having approximately the same range and requiring
                 the same word length. In particular, we compare
                 different choices of base (or radix) in the usual
                 floating-point systems. The emphasis is on the choice
                 of $F$, not on the details of the number representation
                 or the arithmetic, but both rounded and truncated
                 arithmetic are considered. Theoretical results are
                 given, and some simulations of typical floating-point
                 computations (forming sums, solving systems of linear
                 equations, finding eigenvalues) are described. If the
                 leading fraction bit of a normalized base 2 number is
                 not stored explicitly (saving a bit), and the criterion
                 is to minimize the mean square roundoff error, then
                 base 2 is best. If unnormalized numbers are allowed, so
                 the first bit must be stored explicitly, then base 4
                 (or sometimes base 8) is the best of the usual
                 systems.",
  acknowledgement = ack-nhfb,
  remark =       "Published in IEEE Transactions on Computers {\bf C-22}
                 (1973), 601--607.",
  subject =      "Numerical Analysis (cs.NA); Numerical Analysis
                 (math.NA)",
}

@InProceedings{Brisebarre:2010:IDF,
  author =       "Nicolas Brisebarre and Nicolas Louvet and {\'E}rik
                 Martin-Dorel and Jean-Michel Muller and Adrien
                 Panhaleux and Milo D. Ercegovac",
  editor =       "Fran{\c{c}}ois Charot and Frank Hannig and J{\"u}rgen
                 Teich and Christophe Wolinski",
  booktitle =    "{ASAP 2010 --- 21st IEEE International Conference on
                 Application-specific Systems, Architectures and
                 Processors. July 7--9, 2010. Rennes, France}",
  title =        "Implementing decimal floating-point arithmetic through
                 binary: Some suggestions",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "317--320",
  year =         "2010",
  DOI =          "https://doi.org/10.1109/ASAP.2010.5540969",
  ISBN =         "1-4244-6967-8",
  ISBN-13 =      "978-1-4244-6967-3",
  ISSN =         "1063-6862",
  ISSN-L =       "1063-6862",
  bibdate =      "Fri Sep 29 10:41:24 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic",
}

@Article{Chapoutot:2010:ISN,
  author =       "Alexandre Chapoutot",
  title =        "Interval Slopes as Numerical Abstract Domain for
                 Floating-Point Variables",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "1",
  month =        apr,
  year =         "2010",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/1004.0202",
  abstract =     "The design of embedded control systems is mainly done
                 with model-based tools such as Matlab/Simulink.
                 Numerical simulation is the central technique of
                 development and verification of such tools.
                 Floating-point arithmetic, that is well-known to only
                 provide approximated results, is omnipresent in this
                 activity. In order to validate the behaviors of
                 numerical simulations using abstract
                 interpretation-based static analysis, we present,
                 theoretically and with experiments, a new partially
                 relational abstract domain dedicated to floating-point
                 variables. It comes from interval expansion of
                 non-linear functions using slopes and it is able to
                 mimic all the behaviors of the floating-point
                 arithmetic. Hence it is adapted to prove the absence of
                 run-time errors or to analyze the numerical precision
                 of embedded control systems.",
  acknowledgement = ack-nhfb,
  subject =      "Programming Languages (cs.PL); Numerical Analysis
                 (cs.NA)",
}

@Article{Cheng:2010:BSS,
  author =       "Qi Cheng and Xianmeng Meng and Celi Sun and Jiazhe
                 Chen",
  title =        "Bounding the sum of square roots via lattice
                 reduction",
  journal =      j-MATH-COMPUT,
  volume =       "79",
  number =       "270",
  pages =        "1109--1122",
  month =        apr,
  year =         "2010",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Fri May 14 06:21:06 MDT 2010",
  bibsource =    "http://www.ams.org/mcom/2010-79-270;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  URL =          "http://www.ams.org/journals/mcom/2010-79-270/S0025-5718-09-02304-7/home.html;
                 http://www.ams.org/journals/mcom/2010-79-270/S0025-5718-09-02304-7/S0025-5718-09-02304-7.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@InProceedings{Chevillard:2010:SED,
  author =       "Sylvain Chevillard and Mioara Jolde and Christoph
                 Lauter",
  title =        "{Sollya}: An Environment for the Development of
                 Numerical Codes",
  crossref =     "Fukuda:2010:MSI",
  pages =        "28--31",
  year =         "2010",
  DOI =          "https://doi.org/10.1007/978-3-642-15582-6_5",
  bibdate =      "Sat Sep 23 06:20:46 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs2010a.bib",
  URL =          "http://link.springer.com/content/pdf/10.1007/978-3-642-15582-6_5.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cuyt:2010:VSF,
  author =       "Annie Cuyt and Franky Backeljauw and Stefan Becuwe and
                 Joris {Van Deun}",
  title =        "Validated Special Functions Software",
  crossref =     "Fukuda:2010:MSI",
  pages =        "32--34",
  year =         "2010",
  DOI =          "https://doi.org/10.1007/978-3-642-15582-6_6",
  bibdate =      "Sat Sep 23 06:20:46 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Daumas:2010:CBE,
  author =       "Marc Daumas and Guillaume Melquiond",
  title =        "Certification of bounds on expressions involving
                 rounded operators",
  journal =      j-TOMS,
  volume =       "37",
  number =       "1",
  pages =        "2:1--2:20",
  month =        jan,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1644001.1644003",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Mar 15 10:45:33 MDT 2010",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Gappa is a tool designed to formally verify the
                 correctness of numerical software and hardware. It uses
                 interval arithmetic and forward error analysis to bound
                 mathematical expressions that involve rounded as well
                 as exact operators. It then generates a theorem and its
                 proof for each verified enclosure. This proof can be
                 automatically checked with a proof assistant, such as
                 Coq or HOL Light. It relies on a large companion
                 library of facts that we have developed. This Coq
                 library provides theorems dealing with addition,
                 multiplication, division, and square root, for both
                 fixed- and floating-point arithmetics. Gappa uses
                 multiple-precision dyadic fractions for the endpoints
                 of intervals and performs forward error analysis on
                 rounded operators when necessary. When asked, Gappa
                 reports the best bounds it is able to reach for a given
                 expression in a given context. This feature can be used
                 to identify where the set of facts and automatic
                 techniques implemented in Gappa becomes insufficient.
                 Gappa handles seamlessly additional properties
                 expressed as interval properties or rewriting rules in
                 order to establish more intricate bounds. Recent work
                 showed that Gappa is suited to discharge proof
                 obligations generated for small pieces of software.
                 They may be produced by third-party tools and the first
                 applications of Gappa use proof obligations written by
                 designers or obtained from traces of execution.",
  acknowledgement = ack-nhfb,
  articleno =    "2",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Coq; correct rounding; dyadic fraction; floating-point
                 arithmetic; Forward error analysis; HOL Light; interval
                 arithmetic; proof obligation; proof system; PVS",
}

@InProceedings{deDinechin:2010:AGP,
  author =       "Florent de Dinechin and Mioara Joldes and Bogdan
                 Pasca",
  booktitle =    "{ASAP 2010} --- {21st IEEE International Conference on
                 Application-specific Systems, Architectures and
                 Processors}",
  title =        "Automatic generation of polynomial-based hardware
                 architectures for function evaluation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "216--222",
  month =        jul,
  year =         "2010",
  DOI =          "https://doi.org/10.1109/asap.2010.5540952",
  bibdate =      "Thu Apr 10 13:04:38 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Misc{deDinechin:2010:FGA,
  author =       "Florent de Dinechin and Bogdan Pasca",
  title =        "{FloPoCo}: generator of arithmetic cores
                 ({Floating-Point Cores}, but not only) for {FPGAs} (but
                 not only)",
  howpublished = "Web site and source code.",
  day =          "10",
  month =        aug,
  year =         "2010",
  bibdate =      "Sat Oct 9 14:27:50 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The purpose of the FloPoCo project is to explore the
                 many ways in which the flexibility of the FPGA target
                 can be exploited in the arithmetic realm, with a focus
                 on floating-point.\par

                 The philosophy of FloPoCo is that floating-point on
                 FPGAs should not rely on operators that mimick those
                 available in processors. By designing radically new
                 operators, one may obtain more accurate results with
                 less hardware in less time. This thesis is detailed in
                 this document.\par

                 Therefore FloPoCo focuses on exotic operators and
                 exotic precisions. However it also provides basic
                 operators (+,-,*,/ and square root) whose performance
                 matches vendor-supplied operators while offering more
                 flexibility.\par

                 FloPoCo is not a library of operators, but a generator
                 of operators written in C++. It inputs operator
                 specifications, and outputs synthesizable VHDL. This
                 approach allows much better optimization and
                 customization than what VHDL alone permits. In
                 addition, FloPoCo is to our knowledge the easiest way
                 to design complex operators with flexible
                 pipeline.\par

                 FloPoCo supersedes FPLibrary, and is compatible with
                 it.",
  acknowledgement = ack-nhfb,
}

@InProceedings{deDinechin:2010:FPE,
  author =       "Florent de Dinechin and Bogdan Pasca",
  editor =       "Jinian Bian and Qiang Zhou and Kang Zhao",
  booktitle =    "{Proceedings 2010 International Conference on
                 Field-Programmable Technology, 8--10 December 2010,
                 Beijing, China}",
  title =        "Floating-point exponential functions for {DSP}-enabled
                 {FPGAs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "110--117",
  month =        dec,
  year =         "2010",
  DOI =          "https://doi.org/10.1109/FPT.2010.5681764",
  bibdate =      "Sat Feb 08 09:35:06 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{deDinechin:2010:MSR,
  author =       "Florent de Dinechin and Mioara Joldes and Bogdan Pasca
                 and Guillaume Revy",
  editor =       "Fabrizio Ferrandi and Jari Nurmi and Marco D.
                 Santambrogio",
  booktitle =    "2010 International Conference on Field Programmable
                 Logic and Applications: {FPL 2010, 31 August--2
                 September 2010, Milano, Italy}",
  title =        "Multiplicative Square Root Algorithms for {FPGAs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "547--577",
  year =         "2010",
  DOI =          "https://doi.org/10.1109/FPL.2010.112",
  ISBN =         "0-7695-4179-8",
  ISBN-13 =      "978-0-7695-4179-2",
  bibdate =      "Sat Nov 08 11:18:48 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ens-lyon.hal.science/ensl-00475779v2/document",
  acknowledgement = ack-nhfb,
  remark =       "LIP Research Report RR2010-17",
}

@InProceedings{Digeser:2010:ISE,
  author =       "P. Digeser and M. Tubolino and M. Klemm and D. Shapiro
                 and M. Bolic",
  title =        "Instruction set extension in the {NIOS II}: a floating
                 point divider for complex numbers",
  crossref =     "IEEE:2010:CCE",
  year =         "2010",
  DOI =          "https://doi.org/10.1109/CCECE.2010.5575173",
  bibdate =      "Fri Dec 03 15:43:03 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "As increasing the clock frequency leads to
                 unmanageable heat and power dissipation the search is
                 on for another way to get more power efficient and
                 faster embedded systems. Given that chip area is also a
                 constraint, we investigate the addition of a custom
                 instruction to the processor instruction set which
                 enables the execution of an efficient complex division.
                 The instruction we designed is a hardware divider for
                 complex numbers which receives four input values and
                 returns two output values. The data bandwidth
                 constraint of 2 inputs and 1 output is loosened by
                 making the instruction multicycle as described in
                 previous work. We uses the custom instruction interface
                 of the NIOS II soft processor and achieve a speedup of
                 up to $ 3 \tines $ over the unmodified instruction
                 set.",
  acknowledgement = ack-nhfb,
  keywords =     "clock frequency; complex numbers; custom instruction;
                 embedded systems; floating point arithmetic; floating
                 point divider; instruction multicycle; instruction set
                 extension; instruction sets; microprocessor chips; NIOS
                 II soft processor; processor instruction set",
}

@Article{Dvir:2010:HRT,
  author =       "Zeev Dvir and Amir Shpilka and Amir Yehudayoff",
  title =        "Hardness-Randomness Tradeoffs for Bounded Depth
                 Arithmetic Circuits",
  journal =      j-SIAM-J-COMPUT,
  volume =       "39",
  number =       "4",
  pages =        "1279--1293",
  month =        "????",
  year =         "2010",
  CODEN =        "SMJCAT",
  DOI =          "",
  ISSN =         "0097-5397 (print), 1095-7111 (electronic)",
  ISSN-L =       "0097-5397",
  bibdate =      "Tue May 18 08:22:14 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/39/4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Computing",
  journal-URL =  "http://epubs.siam.org/sicomp",
}

@InProceedings{El-Hariry:2010:MCM,
  author =       "Yassmeen M. El-Hariry and Ahmed H. Madian",
  booktitle =    "{2010 International Conference on Microelectronics}",
  title =        "{MOS} current mode logic realization of digital
                 arithmetic circuits",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "128--131",
  year =         "2010",
  DOI =          "https://doi.org/10.1109/ICM.2010.5696090",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; Capacitors; Clocks; CMOS integrated circuits;
                 CORDIC; Current mode logic; Delay; four-bit Multiplier;
                 low power dissipation; Power dissipation; Transistors",
}

@Article{Emmart:2010:HPI,
  author =       "Niall Emmart and Charles Weems",
  title =        "High Precision Integer Addition, Subtraction and
                 Multiplication with a Graphics Processing Unit",
  journal =      j-PARALLEL-PROCESS-LETT,
  volume =       "20",
  number =       "4",
  pages =        "293--306",
  month =        dec,
  year =         "2010",
  CODEN =        "PPLTEE",
  DOI =          "https://doi.org/10.1142/S0129626410000259",
  ISSN =         "0129-6264 (print), 1793-642X (electronic)",
  bibdate =      "Tue Feb 28 11:32:05 MST 2012",
  bibsource =    "http://ejournals.wspc.com.sg/ppl/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/parallelprocesslett.bib",
  note =         "See later improvements \cite{Emmart:2011:HPI}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Parallel Processing Letters",
  journal-URL =  "http://www.worldscientific.com/loi/ppl",
  keywords =     "GNU GMP multiple precision package; graphics
                 processing unit; Karatsuba multiplication algorithm;
                 multiple precision arithmetic; parallel algorithm;
                 Strassen FFT multiplication algorithm",
  remark =       "The abstract reports improvements (GPU compared to
                 GMP) of 3x for multiplication, and 8x for addition and
                 subtraction, with very long operands (32KB or
                 greater).",
}

@InProceedings{Fahmy:2010:DFP,
  author =       "H. A. H. Fahmy and T. ElDeeb and M. Y. Hassan and Y.
                 Farouk and R. R. Eissa",
  title =        "Decimal floating point for future processors",
  crossref =     "IEEE:2010:ICM",
  pages =        "443--446",
  year =         "2010",
  DOI =          "https://doi.org/10.1109/ICM.2010.5696183",
  bibdate =      "Thu Feb 17 08:30:56 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Many new designs for Decimal Floating Point (DFP)
                 hardware units have been proposed in the last few
                 years. To date, only the IBM POWER6 and POWER7
                 processors include internal units for decimal floating
                 point processing. We have designed and tested several
                 DFP units including an adder, multiplier, divider,
                 square root, and fused multiply-add compliant with the
                 IEEE 754-2008 standard. This paper presents the results
                 of using our units as part of a vector co-processor and
                 the anticipated gains once the units are moved on chip
                 with the main processor.",
  acknowledgement = ack-nhfb,
}

@MastersThesis{Fang:2010:DFP,
  author =       "Zhao Fang",
  title =        "The design of {FFT} processor based on {CORDIC}
                 arithmetic",
  type =         "{Master's} thesis",
  school =       "Beijing Institute of Technology",
  address =      "Beijing (People's Republic of China)",
  year =         "2010",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://login.ezproxy.lib.utah.edu/login?url=https://www.proquest.com/dissertations-theses/design-fft-processor-based-on-cordic-arithmetic/docview/1868432799/se-2",
  acknowledgement = ack-nhfb,
  advisor =      "Ying Tao Ding",
  keywords =     "(UMI)AAI10350426; 0544:Electrical engineering; Applied
                 sciences; Electrical engineering",
  ris-m1 =       "10350426",
}

@Misc{Fiedler:2010:GGF,
  author =       "Glenn Fiedler",
  title =        "Gaffer on Games --- Floating Point Determinism",
  howpublished = "Web site",
  day =          "24",
  month =        feb,
  year =         "2010",
  bibdate =      "Mon Dec 04 07:07:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Comments on the problem of reproducing game behavior
                 on different platforms because of floating-point
                 issues.",
  acknowledgement = ack-nhfb,
  remark =       "See also \cite{Dickinson:2001:IRB}.",
}

@Article{Frey:2010:ABC,
  author =       "Gerhard Frey",
  title =        "The Arithmetic Behind Cryptography",
  journal =      j-NAMS,
  volume =       "57",
  number =       "3",
  pages =        "366--374",
  month =        mar,
  year =         "2010",
  CODEN =        "AMNOAN",
  ISSN =         "0002-9920 (print), 1088-9477 (electronic)",
  ISSN-L =       "0002-9920",
  bibdate =      "Mon Feb 22 15:35:29 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ams.org/notices/201003/",
  acknowledgement = ack-nhfb,
  ajournal =     "Notices Amer. Math. Soc.",
  fjournal =     "Notices of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/notices/",
}

@Article{Fu:2010:FDO,
  author =       "Haohuan Fu and O. Mencer and W. Luk",
  title =        "{FPGA} Designs with Optimized Logarithmic Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "59",
  number =       "7",
  pages =        "1000--1006",
  month =        "????",
  year =         "2010",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.51",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 3 12:14:07 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5416693",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Ghazi:2010:WHU,
  author =       "Kaveh R. Ghazi and Vincent Lef{\`e}vre and Philippe
                 Theveny and Paul Zimmermann",
  title =        "Why and How to Use Arbitrary Precision",
  journal =      j-COMPUT-SCI-ENG,
  volume =       "12",
  number =       "3",
  pages =        "5",
  month =        may # "\slash " # jun,
  year =         "2010",
  CODEN =        "CSENFA",
  DOI =          "https://doi.org/10.1109/MCSE.2010.73",
  ISSN =         "0740-7475 (print), 1558-1918 (electronic)",
  ISSN-L =       "1521-9615",
  bibdate =      "Thu May 13 11:08:14 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing in Science and Engineering",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
}

@InProceedings{Habegger:2010:EHI,
  author =       "Andreas Habegger and Andreas Stahel and Josef Goette
                 and Marcel Jacomet",
  editor =       "{IEEE}",
  booktitle =    "{2010 Fifth IEEE International Symposium on Electronic
                 Design, Test \& Applications: 13--15 January 2010 Ho
                 Chi Minh City, Vietnam}",
  title =        "An Efficient Hardware Implementation for a Reciprocal
                 Unit",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "183--187",
  year =         "2010",
  DOI =          "https://doi.org/10.1109/delta.2010.65",
  bibdate =      "Thu Apr 10 13:16:33 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Hemmert:2010:FEF,
  author =       "K. Scott Hemmert and Keith D. Underwood",
  title =        "Fast, Efficient Floating-Point Adders and Multipliers
                 for {FPGAs}",
  journal =      j-TRETS,
  volume =       "3",
  number =       "3",
  pages =        "11:1--11:??",
  month =        sep,
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/1839480.1839481",
  ISSN =         "1936-7406 (print), 1936-7414 (electronic)",
  ISSN-L =       "1936-7406",
  bibdate =      "Fri Oct 8 18:26:34 MDT 2010",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Floating-point applications are a growing trend in the
                 FPGA community. As such, it has become critical to
                 create floating-point units optimized for standard FPGA
                 technology. Unfortunately, the FPGA design space is
                 very different from the VLSI design space; thus,
                 optimizations for FPGAs can differ significantly from
                 optimizations for VLSI. In particular, the FPGA
                 environment constrains the design space such that only
                 limited parallelism can be effectively exploited to
                 reduce latency. Obtaining the right balances between
                 clock speed, latency, and area in FPGAs can be
                 particularly challenging. This article presents
                 implementation details for an IEEE-754 standard
                 floating-point adder and multiplier for FPGAs. The
                 designs presented here enable a Xilinx Virtex4 FPGA
                 (-11 speed grade) to achieve 270 MHz IEEE compliant
                 double precision floating-point performance with a
                 9-stage adder pipeline and 14-stage multiplier
                 pipeline. The area requirement is approximately 500
                 slices for the adder and under 750 slices for the
                 multiplier.",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  fjournal =     "ACM Transactions on Reconfigurable Technology and
                 Systems (TRETS)",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J1151",
  keywords =     "floating point; FPGA; HPC; reconfigurable computing",
}

@InProceedings{Hsiao:2010:IFP,
  author =       "Shen-Fu Hsiao and Chia-Shen Wen and Hsin-Mau Lee",
  booktitle =    "{2010 International Symposium on Next Generation
                 Electronics}",
  title =        "Implementation of floating-point {CORDIC} rotation and
                 vectoring based on look up tables and multipliers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "44--47",
  year =         "2010",
  DOI =          "https://doi.org/10.1109/ISNE.2010.5669143",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Adders; arithmetic; CMOS integrated
                 circuits; CORDIC; floating-point operations; function
                 approximation; Lead; look up table",
}

@InProceedings{Hsiao:2010:LCD,
  author =       "Shen-Fu Hsiao and Chia-Sheng Wen and Ming-Yu Tsai",
  editor =       "????",
  booktitle =    "{2010 International Symposium on Next Generation
                 Electronics: 18--19 November 2010}",
  title =        "Low-cost design of reciprocal function units using
                 shared multipliers and adders for polynomial
                 approximation and {Newton--Raphson} interpolation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "40--43",
  month =        nov,
  year =         "2010",
  DOI =          "https://doi.org/10.1109/isne.2010.5669204",
  bibdate =      "Thu Apr 10 13:30:38 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Jaberipur:2010:RDF,
  author =       "G. Jaberipur and B. Parhami and S. Gorgin",
  title =        "Redundant-Digit Floating-Point Addition Scheme Based
                 on a Stored Rounding Value",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "59",
  number =       "5",
  pages =        "694--706",
  month =        "????",
  year =         "2010",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2009.152",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 3 11:52:28 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5278659",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Jiang:2010:AEP,
  author =       "Hao Jiang and Shengguo Li and Lizhi Cheng and Fang
                 Su",
  title =        "Accurate evaluation of a polynomial and its derivative
                 in {Bernstein} form",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "60",
  number =       "3",
  pages =        "744--755",
  month =        aug,
  year =         "2010",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:50:42 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122110003706",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Misc{Kahan:2010:PUC,
  author =       "W. Kahan",
  title =        "{Pete}'s unsung contribution to {IEEE Standard 754}
                 for binary floating-point: a talk at a conference to
                 celebrate {G. W. ``Pete'' Stewart}'s 70th Birthday",
  howpublished = "Lecture slides",
  pages =        "18",
  day =          "19",
  month =        jul,
  year =         "2010",
  bibdate =      "Wed Aug 07 15:43:36 2024",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://people.eecs.berkeley.edu/~wkahan/19July10.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Kalla:2010:PIN,
  author =       "Ron Kalla and Balaram Sinharoy and William J. Starke
                 and Michael Floyd",
  title =        "{Power7}: {IBM}'s Next-Generation Server Processor",
  journal =      j-IEEE-MICRO,
  volume =       "30",
  number =       "2",
  pages =        "7--15",
  month =        mar # "\slash " # apr,
  year =         "2010",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.2010.38",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Fri Apr 23 06:37:18 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  keywords =     "decimal floating-point arithmetic; fused multiply-add
                 (FMA); IEEE 754-2008 arithmetic; subnormal numbers in
                 hardware; underflow",
}

@Book{Kastner:2010:AOT,
  author =       "Ryan Kastner and Anup Hosangadi and Farzan Fallah",
  title =        "Arithmetic optimization techniques for hardware and
                 software design",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "vii + 187",
  year =         "2010",
  ISBN =         "0-521-88099-8",
  ISBN-13 =      "978-0-521-88099-2",
  LCCN =         "QA76.9.C62 K37 2010; QA76.9.C62 KAS 2010",
  bibdate =      "Mon Jul 12 14:32:42 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 library.ox.ac.uk:210/ADVANCE",
  URL =          "http://assets.cambridge.org/97805218/80992/cover/9780521880992.jpg",
  abstract =     "Obtain better system performance, lower energy
                 consumption, and avoid hand-coding arithmetic functions
                 with this concise guide to automated optimization
                 techniques for hardware and software design. High-level
                 compiler optimizations and high-speed architectures for
                 implementing FIR filters are covered, which can improve
                 performance in communications, signal processing,
                 computer graphics, and cryptography. Clearly explained
                 algorithms and illustrative examples throughout make it
                 easy to understand the techniques and write software
                 for their implementation. Background information on the
                 synthesis of arithmetic expressions and computer
                 arithmetic is also included, making the book ideal for
                 newcomers to the subject. This is an invaluable
                 resource for researchers, professionals, and graduate
                 students working in system level design and automation,
                 compilers, and VLSI CAD.",
  acknowledgement = ack-nhfb,
  subject =      "computer arithmetic; electronic digital computers;
                 design and construction; computer software;
                 development; mathematical optimization",
  tableofcontents = "1. Introduction; \\
                 2. Use of arithmetic expressions\\
                 3. Software compilation\\
                 4. Hardware synthesis\\
                 5. Fundamentals of digital arithmetic\\
                 6. Polynomial expressions\\
                 7. Linear systems",
}

@Book{Kirk:2010:PMP,
  author =       "David B. Kirk and Wen-mei W. Hwu",
  title =        "Programming Massively Parallel Processors: a Hands-on
                 Approach",
  publisher =    pub-MORGAN-KAUFMANN,
  address =      pub-MORGAN-KAUFMANN:adr,
  pages =        "xviii + 258",
  year =         "2010",
  ISBN =         "0-12-381472-3",
  ISBN-13 =      "978-0-12-381472-2",
  LCCN =         "QA76.642 .K57 2010",
  bibdate =      "Thu Jul 29 13:33:50 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/pvm.bib;
                 https://www.math.utah.edu/pub/tex/bib/scpe.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib;
                 z3950.bibsys.no:2100/BIBSYS;
                 z3950.loc.gov:7090/Voyager",
  note =         "Chapter 7 (pages 125--140) discusses GPU
                 floating-point considerations.",
  acknowledgement = ack-nhfb,
  keywords =     "CUDA; nVIDIA",
  libnote =      "Not yet in my library.",
  subject =      "parallel programming (computer science); parallel
                 processing (electronic computers); multiprocessors;
                 computer architecture",
  tableofcontents = "1: Introduction \\
                 1.1 GPUs as Parallel Computers \\
                 1.2 Architecture of a Modern GPU \\
                 1.3 Why More Speed or Parallelism? \\
                 1.4 Parallel Programming Languages and Models \\
                 1.5 Overarching Goals \\
                 1.6 Organization of the Book \\
                 2: History of GPU Computing \\
                 2.1. Evolution of Graphics Pipelines The Era of Fixed
                 Function Graphics Pipeline Evolution of Programmable
                 Real-Time Graphics Unified Graphics and Computing
                 Processors \\
                 2.2. GPGPU: an Intermediate Step Scalable GPUs Recent
                 Developments Future Trends \\
                 3: Introduction to CUDA \\
                 3.1. Data Parallelism \\
                 3.2. CUDA Program Structure \\
                 3.3. A Matrix--Matrix Multiplication Example \\
                 3.4. Device Memories and Data Transfer \\
                 3.5. Kernel Functions and Threading \\
                 3.6. Summary Function Declarations Kernel Launch
                 Predefined Variables Runtime API \\
                 4: CUDA Threads \\
                 4.1. CUDA Thread Organization \\
                 4.2. More on BlockIdx and ThreadIdx \\
                 4.3. Synchronization and Transparent Scalability \\
                 4.4. Thread Assignment \\
                 4.5. Thread Scheduling and Latency Tolerance \\
                 4.6. Summary \\
                 5: CUDA Memories \\
                 5.1. Importance of Memory Access Efficiency \\
                 5.2. CUDA Device Memory Types \\
                 5.3. A Strategy for Reducing Global Memory Traffic \\
                 5.4. Memory as a Limiting Factor to Parallelism \\
                 5.5. Summary \\
                 6: Performance Considerations \\
                 6.1. More on Thread Execution \\
                 6.2. Global Memory Bandwidth \\
                 6.3. Dynamic Partitioning of SM Resources \\
                 6.4. Data Prefetching \\
                 6.5. Instruction Mix \\
                 6.6. Thread Granularity \\
                 6.7. Measured Performance and Summary \\
                 \\
                 7: Floating-Point Considerations \\
                 7.1. Floating-Point Format Normalized representation of
                 M Excess encoding of E \\
                 7.2. Representable Numbers \\
                 7.3. Special Bit Patterns and Precision \\
                 7.4. Arithmetic Accuracy and Rounding \\
                 7.5. Algorithm Considerations \\
                 7.6. Summary \\
                 8: Application Case Study I \\
                 Advanced MRI Reconstruction \\
                 8.1. Application Background \\
                 8.2. Iterative Reconstruction \\
                 8.3. Computing FHd \\
                 Step 1: Determine the Kernel Parallelism Structure \\
                 Step 2: Getting Around the Memory Bandwidth Limitation
                 \\
                 Step 3: Use Hardware Trigonometry Functions \\
                 Step 4: Experimental Performance Testing \\
                 8.4. Final Evaluation \\
                 9: Application Case Study II \\
                 Molecular Visualization and Analysis \\
                 9.1. Application Background \\
                 9.2. A Simple Kernel Implementation \\
                 9.3. Instruction Execution Efficiency \\
                 9.4. Memory Coalescing \\
                 9.5. Additional Performance Comparisons \\
                 9.6. Using Multiple GPUs \\
                 10: Parallel Programming and Computational Thinking \\
                 10.1. Goals of Parallel Programming \\
                 10.2. Problem Decomposition \\
                 10.3. Algorithm Selection \\
                 10.4. Computational Thinking \\
                 11: A Brief Introduction to OpenCL? \\
                 11.1. Background \\
                 11.2. Data Parallelism Model \\
                 11.3. Device Architecture \\
                 11.4. Kernel Functions \\
                 11.5. Device Management and Kernel Launch \\
                 11.6. Electrostatic Potential Map in OpenCL \\
                 11.7. Summary \\
                 12: Conclusion and Future Outlook \\
                 12.1. Goals Revisited \\
                 12.2. Memory Architecture Evolution \\
                 12.3. Kernel Execution Control Evolution \\
                 12.4. Core Performance \\
                 12.5. Programming Environment \\
                 12.6. A Bright Outlook \\
                 Appendix A: Matrix Multiplication Example Code \\
                 Appendix B: Speed and feed of current generation CUDA
                 devices",
}

@Article{Knezevic:2010:FIM,
  author =       "M. Knezevic and F. Vercauteren and I. Verbauwhede",
  title =        "Faster Interleaved Modular Multiplication Based on
                 {Barrett} and {Montgomery} Reduction Methods",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "59",
  number =       "12",
  pages =        "1715--1721",
  month =        "????",
  year =         "2010",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.93",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 3 11:52:34 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5453352",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Kong:2010:RMR,
  author =       "Inwook Kong and E. E. Swartzlander",
  title =        "A Rounding Method to Reduce the Required Multiplier
                 Precision for {Goldschmidt} Division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "59",
  number =       "12",
  pages =        "1703--1708",
  month =        dec,
  year =         "2010",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.86",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 3 11:52:34 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5453345",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@TechReport{Kornerup:2010:CCRa,
  author =       "Peter Kornerup and Vincent Lef{\`e}vre and Nicholas
                 Louvet and Jean-Michel Muller",
  title =        "On the computation of correctly-rounded sums",
  type =         "Research report",
  number =       "RR-7262",
  institution =  "INRIA",
  address =      "Lyon, France",
  pages =        "28",
  month =        apr,
  year =         "2010",
  bibdate =      "Tue Dec 26 14:47:39 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://hal.inria.fr/inria-00475279",
  abstract =     "This paper presents a study of some basic blocks
                 needed in the design of floating-point summation
                 algorithms. In particular, we show that among the set
                 of the algorithms with no comparisons performing only
                 floating-point additions\slash subtractions, the 2Sum
                 algorithm introduced by Knuth is minimal, both in terms
                 of number of operations and depth of the dependency
                 graph. We investigate the possible use of another
                 algorithm, Dekker's Fast2Sum algorithm, in radix-10
                 arithmetic. We give methods for computing, in radix 10,
                 the floating-point number nearest the average value of
                 two floating-point numbers. Under reasonable
                 conditions, we also prove that no algorithms performing
                 only round-to-nearest additions\slash subtractions
                 exist to compute the round-to-nearest sum of at least
                 three floating-point numbers. Starting from an
                 algorithm due to Boldo and Melquiond, we also present
                 new results about the computation of the
                 correctly-rounded sum of three floating-point
                 numbers.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}

@Article{Kornerup:2010:CCRb,
  author =       "Peter Kornerup and Christoph Lauter and Vincent
                 Lef{\`e}vre and Nicolas Louvet and Jean-Michel Muller",
  title =        "Computing correctly rounded integer powers in
                 floating-point arithmetic",
  journal =      j-TOMS,
  volume =       "37",
  number =       "1",
  pages =        "4:1--4:23",
  month =        jan,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1644001.1644005",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Mar 15 10:45:33 MDT 2010",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We introduce several algorithms for accurately
                 evaluating powers to a positive integer in
                 floating-point arithmetic, assuming a {\em fused
                 multiply-add\/} (fma) instruction is available. For
                 bounded, yet very large values of the exponent, we aim
                 at obtaining correctly rounded results in
                 round-to-nearest mode, that is, our algorithms return
                 the floating-point number that is nearest the exact
                 value.",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "correct rounding; floating-point arithmetic; integer
                 power function",
}

@Book{Kornerup:2010:FPN,
  author =       "Peter Kornerup and David W. Matula",
  title =        "Finite Precision Number Systems and Arithmetic",
  volume =       "133",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xv + 699",
  year =         "2010",
  ISBN =         "0-521-76135-2 (hardcover)",
  ISBN-13 =      "978-0-521-76135-2 (hardcover)",
  LCCN =         "QA248 .K627 2010",
  bibdate =      "Sun Jun 19 14:21:37 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Encyclopedia of mathematics and its applications",
  URL =          "http://assets.cambridge.org/97805217/61352/cover/9780521761352.jpg;
                 http://catdir.loc.gov/catdir/enhancements/fy1011/2010030521-b.html;
                 http://catdir.loc.gov/catdir/enhancements/fy1011/2010030521-d.html;
                 http://catdir.loc.gov/catdir/enhancements/fy1011/2010030521-t.html",
  abstract =     "Fundamental arithmetic operations support virtually
                 all of the engineering, scientific, and financial
                 computations required for practical applications, from
                 cryptography, to financial planning, to rocket science.
                 This comprehensive reference provides researchers with
                 the thorough understanding of number representations
                 that is a necessary foundation for designing efficient
                 arithmetic algorithms. Using the elementary foundations
                 of radix number systems as a basis for arithmetic, the
                 authors develop and compare alternative algorithms for
                 the fundamental operations of addition, multiplication,
                 division, and square root with precisely defined
                 roundings. Various finite precision number systems are
                 investigated, with the focus on comparative analysis of
                 practically efficient algorithms for closed arithmetic
                 operations over these systems. Each chapter begins with
                 an introduction to its contents and ends with
                 bibliographic notes and an extensive bibliography. The
                 book may also be used for graduate teaching: problems
                 and exercises are scattered throughout the text and a
                 solutions manual is available for instructors.",
  acknowledgement = ack-nhfb,
  subject =      "Arithmetic; Foundations",
  tableofcontents = "Preface / xi \\
                 1. Radix polynomial representations / 1 \\
                 2. Base and digit set conversion / 59 \\
                 3. Addition / \\
                 4. Multiplication / \\
                 5. Division / 275 \\
                 6. Square root / 398 \\
                 7. Floating-point number systems / 447 \\
                 8. Modular arithmetic and residue number systems / 528
                 \\
                 9. Rational arithmetic / 63 \\
                 Author index / 691 \\
                 Index / 693",
}

@TechReport{KrusemanAretz:2010:DCP,
  author =       "F. E. J. {Kruseman Aretz}",
  title =        "Design and correctness proof of an emulation of the
                 floating-point operations of the {Electrologica X8}: a
                 case study",
  type =         "Computer Science Report",
  number =       "1002",
  institution =  "Technische Universiteit Eindhoven",
  address =      "Eindhoven, The Netherlands",
  pages =        "58",
  day =          "30",
  month =        mar,
  year =         "2010",
  bibdate =      "Mon Oct 17 16:37:56 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://repository.tue.nl/674735",
  abstract =     "Some time ago I decided to write an emulator for a
                 Dutch computer from the sixties of the previous
                 century, the Electrologica X8, in order to be able to
                 run its ALGOL 60 implementation and to do some
                 measurements with it. That emulator was written in
                 (standard ISO) Pascal.",
  acknowledgement = ack-nhfb,
  remark-1 =     "From page 2: ``Electrologica was a Dutch computer
                 factory, founded in 1956. It produced the Electrologica
                 X1 (from 1958) and its successor, the Electrologica X8
                 (from 1965). The latter was more or less upwards
                 compatible with the former, about a factor of 12
                 faster, and in addition it had floating-point hardware:
                 an additional register F and instructions for
                 floating-point addition, subtraction, multiplication,
                 and division.''",
  remark-2 =     "From page 3: ``the floating-point operations `+', `-',
                 `*', and `/' all delivered the best possible result,
                 i.e. that floating-point number in standard form whose
                 value is closest to the exact result. In case that the
                 exact result of the operation was precisely midway two
                 consecutive floating-point numbers, the result was
                 rounded upwards for positive results and downwards for
                 negative results.''",
  remark-3 =     "From page 29: ``The number representation of the EL X8
                 was in one-complement, with preference for $-0$ over
                 $+0$ (I have not analyzed whether an implementation
                 directly in the one-complement representation needs
                 more, or perhaps less guarding bits).",
  remark-4 =     "Page 56 presents the four-step Newton--Raphson
                 algorithm used to implement the square-root operation
                 on the EL8, producing results with a maximum error of
                 0.90 bit.",
}

@Article{Lamotte:2010:CVC,
  author =       "Jean-Luc Lamotte and Jean-Marie Chesneaux and Fabienne
                 J{\'e}z{\'e}quel",
  title =        "{CADNA\_C}: a version of {CADNA} for use with {C} or
                 {C++} programs",
  journal =      j-COMP-PHYS-COMM,
  volume =       "181",
  number =       "11",
  pages =        "1925--1926",
  month =        nov,
  year =         "2010",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2010.07.006",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 11 09:54:31 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465510002353",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Lefevre:2010:LTL,
  author =       "Vincent Lef{\'e}vre and Philippe Th{\'e}veny and
                 Florent de Dinechin and Claude-Pierre Jeannerod and
                 Christophe Mouilleron and David Pfannholzer and
                 Nathalie Revol",
  title =        "{LEMA}: towards a language for reliable arithmetic",
  journal =      j-ACM-COMM-COMP-ALGEBRA,
  volume =       "44",
  number =       "2",
  pages =        "41--52",
  month =        jun,
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/1838599.1838622",
  ISSN =         "1932-2232 (print), 1932-2240 (electronic)",
  ISSN-L =       "1932-2232",
  bibdate =      "Mon Aug 2 13:47:24 MDT 2010",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Generating certified and efficient numerical codes
                 requires information ranging from the mathematical
                 level to the representation of numbers. Even though the
                 mathematical semantics can be expressed using the
                 content part of MathML, this language does not
                 encompass the implementation on computers. Indeed
                 various arithmetics may be involved, like
                 floating-point or fixed-point, in fixed precision or
                 arbitrary precision, and current tools do not handle
                 all of these.\par

                 Therefore we propose in this paper LEMA (Langage pour
                 les Expressions Math{\'e}matiques Annot{\'e}es), a
                 descriptive language based on MathML with additional
                 expressiveness. LEMA will be used during the automatic
                 generation of certified numerical codes. Such a
                 generation process typically involves several steps,
                 and LEMA would thus act as a glue to represent and
                 store the information at every stage.\par

                 First, we specify in the language the characteristics
                 of the arithmetic as described in the IEEE 754
                 floating-point standard: formats, exceptions, rounding
                 modes. This can be generalized to other arithmetics.
                 Then, we use annotations to attach a specific
                 arithmetic context to an expression tree. Finally,
                 considering the evaluation of the expression in this
                 context allows us to deduce several properties on the
                 result, like being exact or being an exception. Other
                 useful properties include numerical ranges and error
                 bounds.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Communications in Computer Algebra",
  issue =        "172",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}

@Article{Lima:2010:KBA,
  author =       "J. B. Lima and D. Panario and Qiang Wang",
  title =        "A {Karatsuba}-Based Algorithm for Polynomial
                 Multiplication in {Chebyshev} Form",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "59",
  number =       "6",
  pages =        "835--841",
  month =        "????",
  year =         "2010",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.45",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 3 11:52:29 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5416688",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Loitsch:2010:PFP,
  author =       "Florian Loitsch",
  title =        "Printing floating-point numbers quickly and accurately
                 with integers",
  journal =      j-SIGPLAN,
  volume =       "45",
  number =       "6",
  pages =        "233--243",
  month =        jun,
  year =         "2010",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/1809028.1806623",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Fri Oct 8 17:53:18 MDT 2010",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present algorithms for accurately converting
                 floating-point numbers to decimal representation. They
                 are fast (up to 4 times faster than commonly used
                 algorithms that use high-precision integers) and
                 correct: any printed number will evaluate to the same
                 number, when read again.\par

                 Our algorithms are fast, because they require only
                 fixed-size integer arithmetic. The sole requirement for
                 the integer type is that it has at least two more bits
                 than the significand of the floating-point number.
                 Hence, for IEEE 754 double-precision numbers (having a
                 53-bit significand) an integer type with 55 bits is
                 sufficient. Moreover we show how to exploit additional
                 bits to improve the generated output.\par

                 We present three algorithms with different properties:
                 the first algorithm is the most basic one, and does not
                 take advantage of any extra bits. It simply shows how
                 to perform the binary-to-decimal transformation with
                 the minimal number of bits. Our second algorithm
                 improves on the first one by using the additional bits
                 to produce a shorter (often the shortest)
                 result.\par

                 Finally we propose a third version that can be used
                 when the shortest output is a requirement. The last
                 algorithm either produces optimal decimal
                 representations (with respect to shortness and
                 rounding) or rejects its input. For IEEE 754
                 double-precision numbers and 64-bit integers roughly
                 99.4\% of all numbers can be processed efficiently. The
                 remaining 0.6\% are rejected and need to be printed by
                 a slower complete algorithm.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "correct rounding; dtoa; floating-point printing",
}

@InProceedings{Louvet:2010:NRA,
  author =       "Nicolas Louvet and Jean-Michel Muller and Adrien
                 Panhaleux",
  title =        "{Newton--Raphson} algorithms for floating-point
                 division using an {FMA}",
  crossref =     "Charot:2010:API",
  pages =        "200--207",
  year =         "2010",
  DOI =          "https://doi.org/10.1109/ASAP.2010.5540948",
  bibdate =      "Thu Feb 17 08:21:17 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "When implementing a function $f$ in floating-point
                 arithmetic, if we wish correct rounding and good
                 performance, it is important to know if there are input
                 floating-point values $x$ such that $ f(x) $ is either
                 the middle of two consecutive floating-point numbers
                 (assuming rounded-to-nearest arithmetic), or a
                 floating-point number (assuming rounded toward $ \pm
                 \infty $ or toward $0$ arithmetic). In the first case,
                 we say that $ f(x) $ is a midpoint, and in the second
                 case, we say that $ f(x) $ is an exact point. For some
                 usual algebraic functions and various floating-point
                 formats, we prove whether or not there exist midpoints
                 or exact points. When there exist midpoints or exact
                 points, we characterize them or list all of them (if
                 there are not too many). The results and the techniques
                 presented in this paper can be used in particular to
                 deal with both the binary and the decimal formats
                 defined in the IEEE 754-2008 standard for
                 floating-point arithmetic.",
  acknowledgement = ack-nhfb,
}

@Article{Maruyama:2010:SVN,
  author =       "Takumi Maruyama and Toshio Yoshida and Ryuji Kan and
                 Iwao Yamazaki and Shuji Yamamura and Noriyuki Takahashi
                 and Mikio Hondou and Hiroshi Okano",
  title =        "{Sparc64 VIIIfx}: a New-Generation Octocore Processor
                 for Petascale Computing",
  journal =      j-IEEE-MICRO,
  volume =       "30",
  number =       "2",
  pages =        "30--40",
  month =        mar # "\slash " # apr,
  year =         "2010",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.2010.40",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Fri Apr 23 06:37:18 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  keywords =     "fused multiply-add (FMA); IEEE 754-2008 arithmetic",
}

@Article{Mathews:2010:AOE,
  author =       "Deborah Mathews",
  title =        "Abstract only: an empirical study of parallel big
                 number arithmetic",
  journal =      j-ACM-COMM-COMP-ALGEBRA,
  volume =       "44",
  number =       "2",
  pages =        "25--25",
  month =        jun,
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/1838599.1838615",
  ISSN =         "1932-2232 (print), 1932-2240 (electronic)",
  ISSN-L =       "1932-2232",
  bibdate =      "Mon Aug 2 13:47:24 MDT 2010",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "To capitalize on multi-core processing, it would be
                 good to perform big number arithmetic in parallel.
                 While a performance increase equal to the number of
                 processors is theoretically possible, our experiments
                 show that in practice the likelihood of gaining any
                 performance increase for big number arithmetic through
                 parallel processing is low. A speed-up approaching the
                 number of processors was not achieved for
                 multiplication until the operands had at least 215
                 bits. No performance gain was realized for addition.
                 The base algorithm used for multiplication was O(n2)
                 and, therefore, suboptimal. The expected performance
                 gain achieved when parallelizing a more efficient base
                 algorithm should be even smaller.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Communications in Computer Algebra",
  issue =        "172",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}

@Article{Mehrotra:2010:SLR,
  author =       "Sanjay Mehrotra and Zhifeng Li",
  title =        "Segment {LLL} Reduction of Lattice Bases Using Modular
                 Arithmetic",
  journal =      j-ALGORITHMS-BASEL,
  volume =       "3",
  number =       "3",
  pages =        "224--243",
  month =        sep,
  year =         "2010",
  CODEN =        "ALGOCH",
  DOI =          "https://doi.org/10.3390/a3030224",
  ISSN =         "1999-4893 (electronic)",
  ISSN-L =       "1999-4893",
  bibdate =      "Fri May 3 13:50:12 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/algorithms.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.mdpi.com/1999-4893/3/3/224",
  acknowledgement = ack-nhfb,
  fjournal =     "Algorithms (Basel)",
  journal-URL =  "https://www.mdpi.com/journal/algorithms",
  pubdates =     "Received: 28 May 2010 / Accepted: 29 June 2010 /
                 Published: 12 July 2010",
}

@Article{Meyer:2010:CGT,
  author =       "Quirin Meyer and Jochen S{\"u}{\ss}muth and Gerd
                 Su{\ss}ner and Marc Stamminger and G{\"u}nther
                 Greiner",
  title =        "Computer Graphics Theory: On Floating-Point Normal
                 Vectors",
  journal =      j-CGF,
  volume =       "29",
  number =       "4",
  pages =        "1405--1409",
  month =        jun,
  year =         "2010",
  CODEN =        "CGFODY",
  DOI =          "https://doi.org/10.1111/j.1467-8659.2010.01737.x",
  ISSN =         "0167-7055 (print), 1467-8659 (electronic)",
  ISSN-L =       "0167-7055",
  bibdate =      "Sat May 11 13:28:01 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cgf.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Com{\-}pu{\-}ter Graphics Forum",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-8659/",
  onlinedate =   "26 Aug 2010",
}

@TechReport{Moller:2010:IDI,
  author =       "Niels M{\"o}ller and Torbj{\"o}rn Granlund",
  title =        "Improved division by invariant integers",
  type =         "Report",
  institution =  "Centre for Industrial and Applied Mathematics, KTH",
  address =      "Stockholm, Sweden",
  pages =        "10",
  day =          "13",
  month =        apr,
  year =         "2010",
  bibdate =      "Mon Oct 14 15:57:19 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://gmplib.org/~tege/division-paper.pdf",
  abstract =     "This paper considers the problem of dividing a
                 two-word integer by a single-word integer, together
                 with a few extensions and applications. Due to lack of
                 efficient division instructions in current processors,
                 the division is performed as a multiplication using a
                 precomputed single-word approximation of the reciprocal
                 of the divisor, followed by a couple of adjustment
                 steps. There are three common types of unsigned
                 multiplication instructions; we define full word
                 multiplication (umul) which produces the two-word
                 product of two single-word integers, low multiplication
                 (umullo) which produces only the least significant word
                 of the product, and high multiplication (umulhi), which
                 produces only the most significant word. We describe an
                 algorithm which produces a quotient and remainder using
                 one umul and one umullo. This is an improvement over
                 earlier methods, since the new method uses cheaper
                 multiplication operations. It turns out we also get
                 some additional savings from simpler adjustment
                 conditions. The algorithm has been implemented in
                 version 4.3 of the GMP library. When applied to the
                 problem of dividing a large integer by a single word,
                 the new algorithm gives a speedup of roughly 30\%,
                 benchmarked on AMD and Intel processors in the x86-64
                 family.",
  acknowledgement = ack-nhfb,
}

@Article{Morisita:2010:IEA,
  author =       "Hirokazu Morisita and Kenta Inakagata and Yasunori
                 Osana and Naoyuki Fujita and Hideharu Amano",
  title =        "Implementation and evaluation of an arithmetic
                 pipeline on {FLOPS-$2$D}: multi-{FPGA} system",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "38",
  number =       "4",
  pages =        "8--13",
  month =        sep,
  year =         "2010",
  CODEN =        "CANED2",
  DOI =          "https://doi.org/10.1145/1926367.1926370",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Thu Jan 20 14:27:03 MST 2011",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "UPACS (Unified Platform for Aerospace Computational
                 Simulation) is one of the practical CFD (Computational
                 Fluid Dynamics) packages supporting various
                 selectability. A custom machine for efficient execution
                 of MUSCL; a core functions of UPACS is implemented on
                 FLOPS-2D (Flexibly Linkable Object for Programmable
                 System); multi-FPGA reconfigurable system. The deep and
                 complicated pipeline structure generated from MUSCL
                 dataflow is divided and optimized into two FPGA boards
                 by using a tuning tool called RER. With optimization of
                 the order of operations and pipeline structure, about
                 60\% utilization of the pipeline is achieved even by
                 using serial links between two boards.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
}

@Article{Mukherjee:2010:NAC,
  author =       "Manideepa Mukherjee and Amitabha Sinha",
  title =        "A novel architecture for conversion of binary to
                 single digit double base numbers",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "38",
  number =       "5",
  pages =        "1--6",
  month =        dec,
  year =         "2010",
  CODEN =        "CANED2",
  DOI =          "https://doi.org/10.1145/1978907.1978909",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Fri May 13 11:25:46 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Double base number systems are increasingly attractive
                 for many compute intensive applications especially in
                 signal processing because of their capabilities of
                 handling arithmetic operations efficiently. However,
                 the complexity involved in converting binary to DBNS
                 becomes a major bottleneck and the efficiency of
                 performance goes down drastically due to the complexity
                 involved in conversion. Since complexity of multi digit
                 DBNS multiplications and additions increases with the
                 number of digits (index i,j), in this paper a novel
                 conversion scheme has been proposed where a given
                 binary number will be converted to a single digit
                 (index i,j) double base number. The proposed scheme not
                 only reduces the hardware complexity of the arithmetic
                 operations but also reduces the time of execution.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
  keywords =     "Double-Based Number System (DBNS)",
}

@Book{Muller:2010:HFP,
  author =       "Jean-Michel Muller and Nicolas Brisebarre and Florent
                 de Dinechin and Claude-Pierre Jeannerod and Vincent
                 Lef{\`e}vre and Guillaume Melquiond and Nathalie Revol
                 and Damien Stehl{\'e} and Serge Torres",
  title =        "Handbook of Floating-Point Arithmetic",
  publisher =    pub-BIRKHAUSER-BOSTON,
  address =      pub-BIRKHAUSER-BOSTON:adr,
  pages =        "xxiii + 572",
  year =         "2010",
  DOI =          "https://doi.org/10.1007/978-0-8176-4705-6",
  ISBN =         "0-8176-4704-X (hardcover), 0-8176-4705-8 (e-book)",
  ISBN-13 =      "978-0-8176-4704-9 (hardcover), 978-0-8176-4705-6
                 (e-book)",
  LCCN =         "QA76.9.C62 H36 2010",
  MRnumber =     "MR2568265",
  bibdate =      "Thu Jan 27 16:18:58 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  price =        "US\$90 (est.)",
  acknowledgement = ack-nhfb,
  tableofcontents = "Preface \\
                 List of Figures \\
                 List of Tables \\
                 I Introduction, Basic Definitions, and Standards \\
                 1 Introduction \\
                 2 Definitions and Basic Notions \\
                 3 Floating-Point Formats and Environment \\
                 II Cleverly Using Floating-Point Arithmetic \\
                 4 Basic Properties and Algorithms \\
                 5 The Fused Multiply-Add Instruction \\
                 6 Enhanced Floating-Point Sums, Dot Products, and
                 Polynomial Values \\
                 7 Languages and Compilers \\
                 III Implementing Floating-Point Operators \\
                 8 Algorithms for the Five Basic Operations \\
                 9 Hardware Implementation of Floating-Point Arithmetic
                 \\
                 10 Software Implementation of Floating-Point
                 Arithmetic",
}

@InProceedings{Munoz:2010:FBF,
  author =       "Daniel M. Mu{\~n}oz and Diego F. Sanchez and Carlos H.
                 Llanos and Mauricio Ayala-Rinc{\'o}n",
  booktitle =    "{2010 VI Southern Programmable Logic Conference
                 (SPL)}",
  title =        "{FPGA} based floating-point library for {CORDIC}
                 algorithms",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "55--60",
  year =         "2010",
  DOI =          "https://doi.org/10.1109/SPL.2010.5483002",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Application software; Computer architecture;
                 Concurrent computing; Costs; Dynamic range; Error
                 analysis; Field programmable gate arrays; Hardware;
                 Libraries; Signal processing algorithms",
}

@Article{Nickolls:2010:GCE,
  author =       "John Nickolls and William J. Dally",
  title =        "The {GPU} Computing Era",
  journal =      j-IEEE-MICRO,
  volume =       "30",
  number =       "2",
  pages =        "56--69",
  month =        mar # "\slash " # apr,
  year =         "2010",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.2010.41",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Fri Apr 23 06:37:18 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  keywords =     "fused multiply-add (FMA); IEEE 754-2008 arithmetic;
                 subnormal numbers in hardware; underflow",
  remark =       "From page 64 of the article:\par

                 IEEE 754-2008 floating-point arithmetic\par

                 The Fermi CUDA core floating-point unit implements the
                 IEEE 754-2008 floating-point arithmetic standard for
                 32-bit single-precision and 64-bit double-precision
                 results, including fused multiply-add (FMA)
                 instructions. FMA computes $ D = A \times B + C $ with
                 no loss of precision by retaining full precision in the
                 intermediate product and addition, then rounding the
                 final sum to form the result. Using FMA enables fast
                 division and square-root operations with exactly
                 rounded results.\par

                 Fermi raises the throughput of 64-bit double-precision
                 operations to half that of single-precision operations,
                 a dramatic improvement over the T10 GPU. This
                 performance level enables broader deployment of GPUs in
                 high-performance computing. The floating-point
                 instructions handle subnormal numbers at full speed in
                 hardware, allowing small values to retain partial
                 precision rather than flushing them to zero or
                 calculating subnormal values in multicycle software
                 exception handlers as most CPUs do.\par

                 The SFUs execute 32-bit floating-point instructions for
                 fast approximations of reciprocal, reciprocal square
                 root, sin, cos, exp, and log functions. The
                 approximations are precise to better than 22 mantissa
                 bits.",
}

@Misc{NURCL:2010:VNV,
  author =       "{Northeastern University Reconfigurable Computing
                 Laboratory}",
  title =        "{Vfloat}: The {Northeastern Variable precision
                 FLOATing point library}",
  howpublished = "Web site.",
  year =         "2010",
  bibdate =      "Sat Oct 9 12:56:05 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ece.neu.edu/groups/rcl/projects/floatingpoint/",
  acknowledgement = ack-nhfb,
}

@Book{Parhami:2010:CAA,
  author =       "Behrooz Parhami",
  title =        "Computer arithmetic: algorithms and hardware designs",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  edition =      "Second",
  pages =        "xxv + 641",
  year =         "2010",
  ISBN =         "0-19-532848-5 (hardcover)",
  ISBN-13 =      "978-0-19-532848-6 (hardcover)",
  LCCN =         "QA76.9.C62 P37 2010",
  bibdate =      "Sat Sep 20 16:57:27 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "The Oxford series in electrical and computer
                 engineering",
  URL =          "http://www.loc.gov/catdir/enhancements/fy1006/2009034155-d.html;
                 http://www.loc.gov/catdir/enhancements/fy1006/2009034155-t.html",
  abstract =     "Ideal for graduate and senior undergraduate courses in
                 computer arithmetic and advanced digital design,
                 Computer Arithmetic: Algorithms and Hardware Designs,
                 Second Edition, provides a balanced, comprehensive
                 treatment of computer arithmetic. It covers topics in
                 arithmetic unit design and circuit implementation that
                 complement the architectural and algorithmic speedup
                 techniques used in high-performance computer
                 architecture and parallel processing. Using a unified
                 and consistent framework, the text begins with number
                 representation and proceeds through basic arithmetic
                 operations, floating-point arithmetic, and function
                 evaluation methods. Later chapters cover broad design
                 and implementation topics --- including techniques for
                 high-throughput, low-power, fault-tolerant, and
                 reconfigurable arithmetic. An appendix provides a
                 historical view of the field and speculates on its
                 future. An indispensable resource for instruction,
                 professional development, and research, Computer
                 Arithmetic: Algorithms and Hardware Designs, Second
                 Edition, combines broad coverage of the underlying
                 theories of computer arithmetic with numerous examples
                 of practical designs, worked-out examples, and a large
                 collection of meaningful problems. This second edition
                 includes a new chapter on reconfigurable arithmetic, in
                 order to address the fact that arithmetic functions are
                 increasingly being implemented on field-programmable
                 gate arrays (FPGAs) and FPGA-like configurable devices.
                 Updated and thoroughly revised, the book offers new and
                 expanded coverage of saturating adders and multipliers,
                 truncated multipliers, fused multiply-add units,
                 overlapped quotient digit selection, bipartite and
                 multipartite tables, reversible logic, dot notation,
                 modular arithmetic, Montgomery modular reduction,
                 division by constants, IEEE floating-point standard
                 formats, and interval arithmetic.",
  acknowledgement = ack-nhfb,
  subject =      "Computer arithmetic; Computer algorithms; Computer
                 algorithms.; Computer arithmetic.",
  tableofcontents = "Part I: Number representation \\
                 Numbers and Arithmetic \\
                 Representing Signed Numbers \\
                 Redundant Number Systems \\
                 Residue Number Systems \\
                 Part II: Addition\slash Subtraction. Basic Addition and
                 Counting \\
                 Carry-Lookahead Adders \\
                 Variations in Fast Adders \\
                 Multioperand Addition \\
                 Part III: Multiplication. Basic Multiplication Schemes
                 \\
                 High-Radix Multipliers \\
                 Tree and Array Multipliers \\
                 Variations in Multipliers \\
                 Part IV: Division. Basic Division Schemes \\
                 High-Radix Dividers \\
                 Variations in Dividers \\
                 Division by Convergence \\
                 Part V: Real arithmetic. Floating-Point Representations
                 \\
                 Floating-Point Operations \\
                 Errors and Error Control \\
                 Precise and Certifiable Arithmetic \\
                 Part VI: Function evaluation. Square-Rooting Methods
                 \\
                 The CORDIC Algorithms \\
                 Variations in Function Evaluation \\
                 Arithmetic by Table Lookup \\
                 High-Throughput Arithmetic \\
                 Part VII: Implementation topics \\
                 Low-Power Arithmetic \\
                 Fault-Tolerant Arithmetic \\
                 Reconfigurable Arithmetic",
}

@Article{Pence:2010:OCF,
  author =       "W. D. Pence and R. L. White and R. Seaman",
  title =        "Optimal Compression of Floating-point Astronomical
                 Images Without Significant Loss of Information",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "7",
  month =        jul,
  year =         "2010",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/datacompression.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Published in PASP {\bf 122}, 1096 (2010).",
  URL =          "http://arxiv.org/abs/1007.1179",
  abstract =     "We describe a compression method for floating-point
                 astronomical images that gives compression ratios of
                 $6$--$ 10$ while still preserving the scientifically
                 important information in the image. The pixel values
                 are first preprocessed by quantizing them into scaled
                 integer intensity levels, which removes some of the
                 uncompressible noise in the image. The integers are
                 then losslessly compressed using the fast and efficient
                 Rice algorithm and stored in a portable FITS format
                 file. Quantizing an image more coarsely gives greater
                 image compression, but it also increases the noise and
                 degrades the precision of the photometric and
                 astrometric measurements in the quantized image.
                 Dithering the pixel values during the quantization
                 process can greatly improve the precision of
                 measurements in the images. This is especially
                 important if the analysis algorithm relies on the mode
                 or the median which would be similarly quantized if the
                 pixel values are not dithered. We perform a series of
                 experiments on both synthetic and real astronomical CCD
                 images to quantitatively demonstrate that the
                 magnitudes and positions of stars in the quantized
                 images can be measured with the predicted amount of
                 precision. In order to encourage wider use of these
                 image compression methods, we have made available a
                 pair of general-purpose image compression programs,
                 called fpack and funpack, which can be used to compress
                 any FITS format image.",
  acknowledgement = ack-nhfb,
  subject =      "Instrumentation and Methods for Astrophysics
                 (astro-ph.IM)",
}

@Article{Purohit:2010:EIA,
  author =       "G. N. Purohit and Asmita Singh Rawat",
  title =        "Efficient Implementation of Arithmetic Operations in
                 {ECC} over Binary Fields",
  journal =      j-INT-J-COMP-APPL,
  volume =       "6",
  number =       "??",
  pages =        "5--9",
  month =        sep,
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.5120/1056-1376",
  ISSN =         "0975-8887",
  ISSN-L =       "0975-8887",
  bibdate =      "Fri Jan 24 08:33:30 MST 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/intjcompappl.bib",
  URL =          "https://www.ijcaonline.org/archives/volume6/number2/1056-1376/",
  acknowledgement = ack-nhfb,
  ajournal =     "Intern. J. of Computer Applications",
  articleno =    "2",
  fjournal =     "International Journal of Computer Applications",
  journal-URL =  "https://www.ijcaonline.org/",
}

@InProceedings{Qi:2010:DLC,
  author =       "Zichu Qi and Qi Guo and Ge Zhang and Xiangku Li and
                 Weiwu Hu",
  title =        "Design of Low-Cost High-Performance Floating-Point
                 Fused Multiply-Add with Reduced Power",
  crossref =     "IEEE:2010:ICV",
  pages =        "206--211",
  year =         "2010",
  DOI =          "https://doi.org/10.1109/VLSI.Design.2010.41",
  bibdate =      "Sun Feb 20 10:01:52 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper presents a floating-point fused
                 multiply-add (FMA) unit with low-cost and low power
                 techniques. To improve the performance, two
                 single-precision operations can be performed
                 concurrently with one double-precision datapath, which
                 is very useful in multimedia and even scientific
                 applications. Moreover, to reduce the additional area
                 costs for supporting two single-precision operations in
                 parallel, multiple double-precision units, i.e., the
                 multiplier, shifter and adder, are reused as much as
                 possible. A modified dual-path algorithm is proposed by
                 classifying the exponent difference into three cases
                 and implementing them with close and far paths, which
                 can reduce latency and facilitate lowering power
                 consumption by enabling only one of the two paths. In
                 addition, in case of FADD instructions, the multiplier
                 in the first stage is bypassed and kept in stable mode,
                 which can significantly improve FADD instruction
                 performance and lower power consumption. The overall
                 FMA unit has a latency of 4 cycles while the FADD
                 operation has 3 cycles. Each cycle has a time delay of
                 about 0.66 ns in the ST 65 nm CMOS technology. Compared
                 with the conventional double-precision FMA, about 13\%
                 delay is reduced and about 22\% area is increased,
                 which is acceptable since two single-precision results
                 can be generated simultaneously.",
  acknowledgement = ack-nhfb,
}

@Article{Roldao:2010:HTF,
  author =       "Antonio Roldao and George A. Constantinides",
  title =        "A High Throughput {FPGA}-Based Floating Point
                 Conjugate Gradient Implementation for Dense Matrices",
  journal =      j-TRETS,
  volume =       "3",
  number =       "1",
  pages =        "1:1--1:??",
  month =        jan,
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/1661438.1661439",
  ISSN =         "1936-7406 (print), 1936-7414 (electronic)",
  ISSN-L =       "1936-7406",
  bibdate =      "Tue Mar 16 09:47:03 MDT 2010",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  articleno =    "1",
  fjournal =     "ACM Transactions on Reconfigurable Technology and
                 Systems (TRETS)",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J1151",
}

@InProceedings{Rummer:2010:IPI,
  author =       "Philipp R{\"u}mmer and Thomas Wahl",
  editor =       "An smt-lib theory of binary floating-point
                 arithmetic",
  booktitle =    "????",
  title =        "Informal proceedings of {8th International Workshop on
                 Satisfiability Modulo Theories (SMT) at FLoC,
                 Edinburgh, Scotland}",
  publisher =    "????",
  address =      "??",
  pages =        "??--??",
  year =         "2010",
  DOI =          "",
  ISBN =         "",
  ISBN-13 =      "",
  LCCN =         "",
  bibdate =      "Sat Apr 02 09:57:20 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "",
  acknowledgement = ack-nhfb,
}

@InProceedings{Rump:2010:ARC,
  author =       "Siegfried M. Rump",
  title =        "Accurate and Reliable Computing in Floating-Point
                 Arithmetic",
  crossref =     "Fukuda:2010:MSI",
  pages =        "105--108",
  year =         "2010",
  DOI =          "https://doi.org/10.1007/978-3-642-15582-6_22",
  bibdate =      "Sat Sep 23 06:20:46 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs2010a.bib",
  URL =          "http://link.springer.com/content/pdf/10.1007/978-3-642-15582-6_22.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Rump:2010:FHP,
  author =       "Siegfried M. Rump and T. Ogita and S. Oishi",
  title =        "Fast high precision summation",
  journal =      "Nonlinear Theory and Its Applications ({NOLTA})",
  volume =       "1",
  number =       "1",
  pages =        "2--24",
  month =        "????",
  year =         "2010",
  DOI =          "https://doi.org/10.1587/nolta.1.2",
  bibdate =      "Wed Oct 12 18:34:53 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate dot product; accurate summation",
}

@InProceedings{Rump:2010:VMRa,
  author =       "Siegfried M. Rump",
  title =        "Verification methods: rigorous results using
                 floating-point arithmetic",
  crossref =     "Watt:2010:IPI",
  pages =        "3--4",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837937",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The classical mathematical proof is performed by
                 pencil and paper. However, there are many ways in which
                 computers may be used in a mathematical proof. But
                 `proofs by computers' or even the use of computers in
                 the course of a proof are not so readily accepted (the
                 December 2008 issue of the Notices of the American
                 Mathematical Society is devoted to formal proofs by
                 computers).\par

                 In this talk we discuss how verification methods may
                 assist in achieving a mathematically rigorous result.
                 In particular we emphasize how floating-point
                 arithmetic is used.\par

                 The goal of verification methods is ambitious: For a
                 given problem it is proved, with the aid of a computer,
                 that there exists a (unique) solution within computed
                 bounds. The methods are constructive, and the results
                 are rigorous in every respect. Verification methods
                 apply to data with tolerances as well.\par

                 Rigorous results are the main goal in computer algebra.
                 However, verification methods use solely floating-point
                 arithmetic, so that the total computational effort is
                 not too far from that of a purely (approximate)
                 numerical method. Nontrivial problems have been solved
                 using verification methods. For example:\par

                 Tucker (1999) received the 2004 EMS prize awarded by
                 the European Mathematical Society for (citation)
                 `giving a rigorous proof that the Lorenz attractor
                 exists for the parameter values provided by Lorenz.
                 This was a long standing challenge to the dynamical
                 system community, and was included by Smale in his list
                 of problems for the new millennium. The proof uses
                 computer estimates with rigorous bounds based on higher
                 dimensional interval arithmetics.'\par

                 Sahinidis and Tawaralani (2005) received the 2006
                 Beale-Orchard-Hays Prize for their package BARON which
                 (citation) `incorporates techniques from automatic
                 differentiation, interval arithmetic, and other areas
                 to yield an automatic, modular, and relatively
                 efficient solver for the very difficult area of global
                 optimization'.\par

                 A main goal of this talk is to introduce the principles
                 of how to design verification algorithms, and how these
                 principles differ from those for traditional numerical
                 algorithms.\par

                 We begin with a brief discussion of the working tools
                 of verification methods, in particular floating-point
                 and interval arithmetic. In particular the development
                 and limits of verification methods for finite
                 dimensional problems are discussed in some detail;
                 problems include dense systems of linear equations,
                 sparse linear systems, systems of nonlinear equations,
                 semi-definite programming and other special linear and
                 nonlinear problems including M-matrices, simple and
                 multiple roots of polynomials, bounds for simple and
                 multiple eigenvalues or clusters, and quadrature. We
                 mention that automatic differentiation tools to compute
                 the range of gradients, Hessians, Taylor coefficients,
                 and slopes are necessary. If time permits, verification
                 methods for continuous problems, namely two-point
                 boundary value problems and semilinear elliptic
                 boundary value problems are presented.\par

                 Throughout the talk, a number of examples of the wrong
                 use of interval operations are given. In the past such
                 examples contributed to the dubious reputation of
                 interval arithmetic, whereas they are, in fact, just a
                 misuse.\par

                 Some algorithms are presented in executable
                 Matlab/INTLAB-code. INTLAB, the Matlab toolbox for
                 reliable computing and free for academic use, is
                 developed and written by Rump (1999). It was, for
                 example, used by Bornemann, Laurie, Wagon, and
                 Waldvogel (2004) in the solution of half of the
                 problems of the $ 10 \times 10 $-digit challenge by
                 Trefethen (2002).",
  acknowledgement = ack-nhfb,
}

@Article{Rump:2010:VMRb,
  author =       "Siegfried M. Rump",
  title =        "Verification methods: Rigorous results using
                 floating-point arithmetic",
  journal =      j-ACTA-NUMERICA,
  volume =       "19",
  pages =        "287--449",
  year =         "2010",
  CODEN =        "ANUMFU",
  DOI =          "https://doi.org/10.1017/S096249291000005X",
  ISBN =         "0-521-19284-6",
  ISBN-13 =      "978-0-521-19284-2",
  ISSN =         "0962-4929 (print), 1474-0508 (electronic)",
  ISSN-L =       "0962-4929",
  MRclass =      "65G20 (03B35 68T05)",
  MRnumber =     "2652784 (2011j:65093)",
  MRreviewer =   "Ljiljana Petkovi{\'c}",
  bibdate =      "Sat Sep 24 10:35:17 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/actanumerica.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ti3.tu-harburg.de/paper/rump/Ru10.pdf",
  abstract =     "This review article is devoted to verification methods
                 and consists of three parts of similar length. In Part
                 1 the working tools of verification methods are
                 discussed, in particular floating-point and interval
                 arithmetic; my findings in Section 1.5 (Historical
                 remarks) seem new, even to experts in the field.\par

                 In Part 2, the development and limits of verification
                 methods for finite-dimensional problems are discussed
                 in some detail. In particular, we discuss how
                 verification is {\em not\/} working. For example, we
                 give a probabilistic argument that the so-called
                 interval Gaussian elimination (IGA) does not work even
                 for (well-conditioned) random matrices of small size.
                 Verification methods are discussed for problems such as
                 dense systems of linear equations, sparse linear
                 systems, systems of nonlinear equations, semi-definite
                 programming and other special linear and nonlinear
                 problems, including M-matrices, finding simple and
                 multiple roots of polynomials, bounds for simple and
                 multiple eigenvalues or clusters, and quadrature. The
                 necessary automatic differentiation tools to compute
                 the range of gradients, Hessians, Taylor coefficients,
                 and slopes are also introduced.\par

                 Concerning the important area of optimization, Neumaier
                 (2004) gave in his Acta Numerica article an overview on
                 global optimization and constraint satisfaction
                 methods. In view of the thorough treatment there,
                 showing the essential role of interval methods in this
                 area, we restrict our discussion to a few recent,
                 complementary issues.\par

                 Finally, in Part 3, verification methods for
                 infinite-dimensional problems are presented, namely
                 two-point boundary value problems and semilinear
                 elliptic boundary value problems.\par

                 Throughout the article, many examples of the
                 inappropriate use of interval operations are given. In
                 the past such examples contributed to the dubious
                 reputation of interval arithmetic (see Section 1.3),
                 whereas they are, in fact, simply a misuse.\par

                 One main goal of this review article is to introduce
                 the principles of the design of verification
                 algorithms, and how these principles differ from those
                 for traditional numerical algorithms (see Section
                 1.4).\par

                 Many algorithms are presented in executable
                 MATLAB/INTLAB code, providing the opportunity to test
                 the methods directly. INTLAB, the MATLAB toolbox for
                 reliable computing, was, for example, used by
                 Bornemann, Laurie, Wagon and Waldvogel (2004) in the
                 solution of half of the problems of the SIAM $ 10
                 \times 10 $-digit challenge by Trefethen (2002).",
  acknowledgement = ack-nhfb,
  ajournal =     "Acta Numer.",
  fjournal =     "Acta Numerica",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=ANU",
  onlinedate =   "10 May 2010",
}

@Article{Ryden:2010:EIR,
  author =       "Jesper Ryd{\'e}n and Sven Erick Alm",
  title =        "The effect of interaction and rounding error in
                 two-way {ANOVA}: example of impact on testing for
                 normality",
  journal =      j-J-APPL-STAT,
  volume =       "37",
  number =       "10",
  pages =        "1695--1701",
  month =        oct,
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/02664760903143925",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  bibdate =      "Mon Sep 5 18:53:08 MDT 2011",
  bibsource =    "http://www.tandf.co.uk/journals/routledge/02664763.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
  onlinedate =   "21 Sep 2010",
}

@Article{Saito:2010:DQP,
  author =       "Tsubasa Saito and Emiko Ishiwata and Hidehiko
                 Hasegawa",
  title =        "Development of quadruple precision arithmetic toolbox
                 {QuPAT} on {Scilab}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "6017",
  pages =        "60--70",
  year =         "2010",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-642-12165-4_5",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Apr 01 07:57:10 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-3-642-12165-4_5",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
  keywords =     "floating-point arithmetic; QuPAT (Quadruple Precision
                 Arithmetic Toolbox)",
  remark =       "International Conference on Computational Science and
                 Its Applications, ICCSA 2010",
}

@InProceedings{Samy:2010:DFP,
  author =       "R. Samy and H. A. H. Fahmy and R. Raafat and A.
                 Mohamed and T. ElDeeb and Y. Farouk",
  title =        "A decimal floating-point fused-multiply-add unit",
  crossref =     "Delgado-Frias:2010:IIM",
  pages =        "529--532",
  year =         "2010",
  DOI =          "https://doi.org/10.1109/MWSCAS.2010.5548746",
  bibdate =      "Thu Feb 17 08:38:22 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper presents the first hardware implementation
                 of a fully parallel decimal floating-point
                 fused-multiply-add unit performing the operation $ \pm
                 (A \times B) \pm C $ on decimal floating-point
                 operands. The proposed design is fully compliant with
                 the IEEE 754-2008 standard and supports the two
                 standard formats decimal64 and decimal128. Furthermore,
                 the proposed design may be controlled to perform the
                 multiplication or the addition\slash subtraction as
                 standalone operations. Our decimal floating-point FMA
                 may be pipelined so that a complete resultant decimal
                 floating-point is available each clock cycle.",
  acknowledgement = ack-nhfb,
}

@Article{Sasaki:2010:CFP,
  author =       "Tateaki Sasaki and Fujio Kako",
  title =        "Computing floating-point {Gr{\"o}bner} bases
                 accurately",
  journal =      j-ACM-COMM-COMP-ALGEBRA,
  volume =       "44",
  number =       "3",
  pages =        "142--143",
  month =        sep,
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/1940475.1940504",
  ISSN =         "1932-2232 (print), 1932-2240 (electronic)",
  ISSN-L =       "1932-2232",
  bibdate =      "Thu Mar 31 10:24:16 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We propose a new method for floating-point Gr{\"o}bner
                 basis computation. The idea is to improve the
                 accuracies of the coefficients of polynomials of
                 intermediate bases computed by our previous method, by
                 reducing coefficient matrices by Gaussian
                 elimination.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Communications in Computer Algebra",
  issue =        "173",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}

@Book{Schertz:2010:CM,
  author =       "Reinhard Schertz",
  title =        "Complex Multiplication",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xiii + 361",
  year =         "2010",
  ISBN =         "0-521-76668-0",
  ISBN-13 =      "978-0-521-76668-5",
  LCCN =         "QA564 .S294 2010",
  bibdate =      "Thu Mar 04 18:34:14 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "This is a self-contained account of the state of the
                 art in classical complex multiplication that includes
                 recent results on rings of integers and applications to
                 cryptography using elliptic curves. The author is
                 exhaustive in his treatment, giving a thorough
                 development of the theory of elliptic functions,
                 modular functions and quadratic number fields and
                 providing a concise summary of the results from class
                 field theory. The main results are accompanied by
                 numerical examples, equipping any reader with all the
                 tools and formulas they need. Topics covered include:
                 the construction of class fields over quadratic
                 imaginary number fields by singular values of the
                 modular invariant $j$ and Weber's tau-function;
                 explicit construction of rings of integers in ray class
                 fields and Galois module structure; the construction of
                 cryptographically relevant elliptic curves over finite
                 fields; proof of Berwick's congruences using division
                 values of the Weierstrass $p$-function; relations
                 between elliptic units and class numbers.",
  subject =      "Multiplication, Complex",
  tableofcontents = "Preface \\
                 1. Elliptic functions \\
                 2. Modular functions \\
                 3. Basic facts from number theory \\
                 4. Factorisation of singular values \\
                 5. The reciprocity law \\
                 6. Generation of ring class fields and ray class fields
                 \\
                 7. Integral basis in ray class fields \\
                 8. Galois module structure \\
                 9. Berwick's congruences \\
                 10. Cryptographically relevant elliptic curves \\
                 11. The class number formulas of Curt Meyer \\
                 12. Arithmetic interpretation of class number formulas
                 \\
                 References \\
                 Index of notation \\
                 Index",
}

@Article{Schneeweiss:2010:SAR,
  author =       "H. Schneeweiss and J. Komlos and A. S. Ahmad",
  title =        "Symmetric and asymmetric rounding: a review and some
                 new results",
  journal =      j-ASTA-ADV-STAT-ANAL,
  volume =       "94",
  number =       "3",
  pages =        "247--271",
  month =        sep,
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s10182-010-0125-2",
  ISSN =         "1863-8171 (print), 1863-818X (electronic)",
  ISSN-L =       "1863-8171",
  bibdate =      "Thu Feb 5 09:35:46 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/asta.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer.com/article/10.1007/s10182-010-0125-2",
  acknowledgement = ack-nhfb,
  fjournal =     "AStA. Advances in Statistical Analysis",
  journal-URL =  "http://link.springer.com/journal/10182",
}

@InProceedings{Sheikh:2010:OOA,
  author =       "Basit Riaz Sheikh and Rajit Manohar",
  editor =       "IEEE",
  booktitle =    "{ASYNC 2010: 16th IEEE Symposium on Asynchronous
                 Circuits and Systems, 3--6 May 2010, Grenoble, France,
                 Proceedings}",
  title =        "An Operand-Optimized Asynchronous {IEEE 754}
                 Double-Precision Floating-Point Adder",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  bookpages =    "xviii + 197",
  pages =        "151--162",
  year =         "2010",
  DOI =          "https://doi.org/10.1109/ASYNC.2010.24",
  ISBN =         "0-7695-4032-5",
  ISBN-13 =      "978-0-7695-4032-0",
  LCCN =         "????",
  bibdate =      "Sat Apr 02 16:34:52 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=5476966;
                 https://www.semanticscholar.org/paper/An-Operand-Optimized-Asynchronous-IEEE-754-Double-Sheikh-Manohar/3e30463d11ba059f19c5959e0acc66709390475e",
  acknowledgement = ack-nhfb,
}

@Article{Shieh:2010:WBM,
  author =       "Ming-Der Shieh and Wen-Ching Lin",
  title =        "Word-Based {Montgomery} Modular Multiplication
                 Algorithm for Low-Latency Scalable Architectures",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "59",
  number =       "8",
  pages =        "1145--1151",
  month =        "????",
  year =         "2010",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.72",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 3 11:52:31 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5441286",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Shuster:2010:ECN,
  author =       "John A. Shuster and Jens K{\"o}plinger",
  title =        "Elliptic complex numbers with dual multiplication",
  journal =      j-APPL-MATH-COMP,
  volume =       "216",
  number =       "12",
  pages =        "3497--3514",
  day =          "15",
  month =        aug,
  year =         "2010",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Fri Sep 3 10:53:27 MDT 2010",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Book{Smiley:2010:MWI,
  author =       "Jane Smiley",
  title =        "The man who invented the computer: the biography of
                 {John Atanasoff}, digital pioneer",
  publisher =    pub-DOUBLEDAY,
  address =      pub-DOUBLEDAY:adr,
  pages =        "246 + 8",
  year =         "2010",
  ISBN =         "0-385-52713-6, 0-385-53372-1 (e-book), 1-299-11995-6
                 (e-book)",
  ISBN-13 =      "978-0-385-52713-2, 978-0-385-53372-0 (e-book),
                 978-1-299-11995-6 (e-book)",
  LCCN =         "QA76.2.A75 S64 2010",
  bibdate =      "Mon Oct 25 10:49:42 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/t/teller-edward.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\$25.95",
  abstract =     "One night in the late 1930s, in a bar on the
                 Illinois--Iowa border, John Vincent Atanasoff, a
                 professor of physics at Iowa State University, after a
                 frustrating day performing tedious mathematical
                 calculations in his lab, hit on the idea that the
                 binary number system and electronic switches, combined
                 with an array of capacitors on a moving drum to serve
                 as memory, could yield a computing machine that would
                 make his life easier. Then he went back and built the
                 machine. It worked, but he never patented the device,
                 and the developers of the far-better-known ENIAC almost
                 certainly stole critical ideas from him. But in 1973 a
                 court declared that the patent on that Sperry Rand
                 device was invalid, opening the gates to the computer
                 revolution. Biographer Jane Smiley makes the race to
                 develop digital computing as gripping as a real-life
                 techno-thriller.",
  acknowledgement = ack-nhfb,
  keywords =     "ABC computer; Alan Turing; Charles Babbage; Clifford
                 Berry; J. Presper Eckert; John V (John Vincent)
                 Atanasoff; John von Neumann; John W. Mauchly; Konrad
                 Zuse; Max Newman",
  remark-1 =     "This book contains discussions of the patent battles
                 over early computer designs (pp 131--133 and Chapter
                 9), and some limited information about arithmetic
                 choices, such as on pp. 162--163 ``Howard Aiken, who
                 was still advocating for decimal numbers for
                 computers''. It also contains statements of how Konrad
                 Zuse's early work on electromechanical computers was
                 finally made known in the 1950s in the US (see p.
                 159).",
  remark-2 =     "The chapters are numbered, but without titles, so
                 there is no tableofcontents field in this entry.",
  remark-3 =     "Chapters 10--12 on the Honeywell vs Sperry lawsuit
                 (1968--1971) over who discovered the computer present a
                 strong rebuttal to the views in
                 \cite{McCartney:2001:ETT}.",
  remark-4 =     "Pages 188--189 mention Edward Teller's testimony in
                 August 1971 in the Honeywell vs Sperry lawsuit that the
                 ENIAC had been used for calculations by Los Alamos
                 scientists in 1945--1945, almost two years before the
                 Mauchly and Eckert (i.e., Sperry) patent claims on
                 ENIAC technology. That is `prior art' that led to
                 Sperry losing its patent claims for ENIAC.",
  subject =      "Atanasoff, John V (John Vincent); Computer scientists;
                 United States; Biography; Inventors; Physicists; Iowa;
                 College teachers; Electronic digital computers;
                 History; 20th century; Patents; Intellectual property",
}

@Article{Smith:2010:AFA,
  author =       "Alastair M. Smith and George A. Constantinides and
                 Peter Y. K. Cheung",
  title =        "An Automated Flow for Arithmetic Component Generation
                 in Field-Programmable Gate Arrays",
  journal =      j-TRETS,
  volume =       "3",
  number =       "3",
  pages =        "13:1--13:??",
  month =        sep,
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/1839480.1839483",
  ISSN =         "1936-7406 (print), 1936-7414 (electronic)",
  ISSN-L =       "1936-7406",
  bibdate =      "Fri Oct 8 18:26:34 MDT 2010",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "State-of-the-art configurable logic platforms, such as
                 Field-Programmable Gate Arrays (FPGAs), consist of a
                 heterogeneous mixture of different component types.
                 Compared to traditional homogeneous configurable
                 platforms, heterogeneity provides speed and density
                 advantages. This is due to the replacement of
                 inefficient programmable logic and routing with
                 specialized logic and fixed interconnect in components
                 such as memories, embedded processor units, and fused
                 arithmetic units. Given the increasing complexity of
                 these components, this article introduces a method to
                 automatically propose and explore the benefits of
                 different types of fused arithmetic units. The methods
                 are based on common subgraph extraction techniques,
                 meaning that it is possible to explore different
                 subcircuits that occur frequently across a set of
                 benchmarks. A quantitative analysis is performed of the
                 various fused arithmetic circuits identified by our
                 tool, which are then automatically synthesized to an
                 ASIC process, providing a study of the speed and area
                 benefits of the components. The results of this study
                 provide bounds on the performance of heterogeneous
                 FPGAs: by incorporating coarse-grain components which
                 match the specific needs of a set of benchmarks we show
                 that significant improvements in circuit speed and area
                 can be made.",
  acknowledgement = ack-nhfb,
  articleno =    "13",
  fjournal =     "ACM Transactions on Reconfigurable Technology and
                 Systems (TRETS)",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J1151",
  keywords =     "common subgraph; FPGA; reconfigurable logic",
}

@InProceedings{Sze:2010:TQB,
  author =       "Tsz-Wo Sze",
  editor =       "{IEEE}",
  booktitle =    "{2010 IEEE Second International Conference on Cloud
                 Computing Technology and Science (CloudCom)}",
  title =        "The Two Quadrillionth Bit of Pi is $0$ ! {Distributed}
                 Computation of Pi with {Apache Hadoop}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "727",
  year =         "2010",
  DOI =          "https://doi.org/10.1109/CloudCom.2010.57",
  ISBN =         "1-4244-9405-2",
  ISBN-13 =      "978-1-4244-9405-7",
  LCCN =         "????",
  bibdate =      "Mon Apr 25 18:16:05 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present a new record on computing specific bits of
                 Pi, the mathematical constant, and discuss performing
                 such computations on Apache Hadoop clusters. The
                 specific bits represented in hexadecimal are 0E6C1294
                 AED40403 F56D2D76 4026265B CA98511D 0FCFFAA1 0F4D28B1
                 BB5392B8. These 256 bits end at the
                 2,000,000,000,000,252nd bit position, which doubles the
                 position and quadruples the precision of the previous
                 known record. The position of the first bit is
                 1,999,999,999,999,997 and the value of the two
                 quadrillionth bit is 0. The computation is carried out
                 by a MapReduce program called DistBbp. To effectively
                 utilize available cluster resources without
                 monopolizing the whole cluster, we develop an elastic
                 computation framework that automatically schedules
                 computation slices, each a DistBbp job, as either
                 map-side or reduce-side computation based on changing
                 cluster load condition. We have calculated Pi at
                 varying bit positions and precisions, and one of the
                 largest computations took 23 days of wall clock time
                 and 503 years of CPU time on a 1000-node cluster.",
  acknowledgement = ack-nhfb,
  remark =       "This paper contains a good discussion of
                 floating-point rounding errors in the BBP algorithm,
                 and of the optimal way to distribute computations over
                 multiple independent systems sharing a common
                 filesystem (needed to permit restart after node
                 failure).",
}

@Article{Szewczak:2010:LTR,
  author =       "Zbigniew S. Szewczak",
  title =        "A limit theorem for random sums modulo $1$",
  journal =      j-STAT-PROB-LETT,
  volume =       "80",
  number =       "9 10",
  pages =        "747--751",
  year =         "2010",
  CODEN =        "SPLTDC",
  DOI =          "https://doi.org/10.1016/j.spl.2010.01.005",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167715210000106",
  abstract =     "Residues of partial sums in a class of dependent
                 random variables, including functionals of uniformly
                 recurrent Markov chains, are in the domain of
                 attraction of the uniform distribution. These types of
                 limit theorems arise for example in the multiplication
                 of floating-point numbers.",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01677152",
  keywords =     "Benford's Law",
}

@Article{Takahashi:2010:PIM,
  author =       "Daisuke Takahashi",
  title =        "Parallel implementation of multiple-precision
                 arithmetic and $ 2, 576, 980, 370, 000 $ decimal digits
                 of $ \pi $ calculation",
  journal =      j-PARALLEL-COMPUTING,
  volume =       "36",
  number =       "8",
  pages =        "439--448",
  month =        aug,
  year =         "2010",
  CODEN =        "PACOEJ",
  DOI =          "https://doi.org/10.1016/j.parco.2010.02.007",
  ISSN =         "0167-8191 (print), 1872-7336 (electronic)",
  ISSN-L =       "0167-8191",
  bibdate =      "Thu Sep 2 17:51:13 MDT 2010",
  bibsource =    "http://www.sciencedirect.com/science/journal/01678191;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present efficient parallel algorithms for
                 multiple-precision arithmetic operations of more than
                 several million decimal digits on distributed-memory
                 parallel computers. A parallel implementation of
                 floating-point real FFT-based multiplication is used,
                 since the key operation for fast multiple-precision
                 arithmetic is multiplication. The operation for
                 releasing propagated carries and borrows in
                 multiple-precision addition, subtraction and
                 multiplication was also parallelized. More than 2.576
                 trillion decimal digits of $ \pi $ were computed on 640
                 nodes of Appro Xtreme-X3 (648 nodes, 147.2 GFlops/node,
                 95.4 TFlops peak performance) with a computing elapsed
                 time of 73 h 36 min which includes the time required
                 for verification.",
  acknowledgement = ack-nhfb,
  fjournal =     "Parallel Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01678191",
  keywords =     "distributed-memory parallel computer; Fast Fourier
                 transform; multiple-precision arithmetic",
}

@Article{Tichy:2010:GAF,
  author =       "Milan Tichy and Jan Schier and David Gregg",
  title =        "{GSFAP} adaptive filtering using log arithmetic for
                 resource-constrained embedded systems",
  journal =      j-TECS,
  volume =       "9",
  number =       "3",
  pages =        "29:1--29:??",
  month =        feb,
  year =         "2010",
  CODEN =        "????",
  ISSN =         "1539-9087 (print), 1558-3465 (electronic)",
  ISSN-L =       "1539-9087",
  bibdate =      "Mon Mar 15 18:41:02 MDT 2010",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  articleno =    "29",
  fjournal =     "ACM Transactions on Embedded Computing Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?&idx=J840",
}

@Article{Vazquez:2010:IDH,
  author =       "A. Vazquez and E. Antelo and P. Montuschi",
  title =        "Improved Design of High-Performance Parallel Decimal
                 Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "59",
  number =       "5",
  pages =        "679--693",
  month =        "????",
  year =         "2010",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2009.167",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 3 11:52:28 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5313798",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Vestias:2010:PDM,
  author =       "M. P. V{\'e}stias and H. C. Neto",
  title =        "Parallel decimal multipliers using binary
                 multipliers",
  crossref =     "Santos:2010:PVS",
  pages =        "73--78",
  year =         "2010",
  DOI =          "https://doi.org/10.1109/SPL.2010.5483001",
  bibdate =      "Thu Feb 17 08:10:02 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Human-centric applications, like financial and
                 commercial, depend on decimal arithmetic since the
                 results must match exactly those obtained by human
                 calculations. The IEEE-754 2008 standard for floating
                 point arithmetic has definitely recognized the
                 importance of decimal for computer arithmetic. A number
                 of hardware approaches have already been proposed for
                 decimal arithmetic operations, including addition,
                 subtraction, multiplication and division. However, few
                 efforts have been done to develop decimal IP cores able
                 to take advantage of the binary multipliers available
                 in most reconfigurable computing architectures. In this
                 paper, we analyze the tradeoffs involved in the design
                 of a parallel decimal multiplier, for decimal operands
                 with 8 and 16 digits, using existent coarse-grained
                 embedded binary arithmetic blocks. The proposed
                 circuits were implemented in a Xilinx Virtex 4 FPGA.
                 The results indicate that the proposed parallel
                 multipliers are very competitive when compared to
                 decimal multipliers implemented with direct
                 manipulation of BCD numbers.",
  acknowledgement = ack-nhfb,
}

@Article{Viswanadham:2010:ULI,
  author =       "Y. K. Viswanadham and Ch. D. V. Subba Rao and T. V.
                 Subrahmanyam",
  title =        "Ultra Long Integer Multiplication on {GDPS}",
  journal =      j-INT-J-COMP-APPL,
  volume =       "7",
  number =       "??",
  pages =        "22--25",
  month =        oct,
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.5120/1271-1751",
  ISSN =         "0975-8887",
  ISSN-L =       "0975-8887",
  bibdate =      "Fri Jan 24 08:33:46 MST 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/intjcompappl.bib",
  URL =          "https://www.ijcaonline.org/archives/volume7/number8/1271-1751/",
  acknowledgement = ack-nhfb,
  ajournal =     "Intern. J. of Computer Applications",
  articleno =    "8",
  fjournal =     "International Journal of Computer Applications",
  journal-URL =  "https://www.ijcaonline.org/",
}

@Article{Wang:2010:AOB,
  author =       "Chih-Yueh Wang and Chen-Yang Yin and Hong-Yu Chen and
                 Yung-Ko Chen",
  title =        "Arithmetic Operations Beyond Floating Point Number
                 Precision",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "29",
  month =        sep,
  year =         "2010",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/1009.5911",
  abstract =     "In basic computational physics classes, students often
                 raise the question of how to compute a number that
                 exceeds the numerical limit of the machine. While
                 technique of avoiding overflow/underflow has practical
                 application in the electrical and electronics
                 engineering industries, it is not commonly utilized in
                 scientific computing, because scientific notation is
                 adequate in most cases. We present an undergraduate
                 project that deals with such calculations beyond a
                 machine's numerical limit, known as arbitrary precision
                 arithmetic. The assignment asks students to investigate
                 the approach of calculating the exact value of a large
                 number beyond the floating point number precision,
                 using the basic scientific programming language
                 Fortran. The basic concept is to utilize arrays to
                 decompose the number and allocate finite memory.
                 Examples of the successive multiplication of even
                 number and the multiplication and division of two
                 overflowing floats are presented. The multiple
                 precision scheme has been applied to hardware and
                 firmware design for digital signal processing (DSP)
                 systems, and is gaining importance to scientific
                 computing. Such basic arithmetic operations can be
                 integrated to solve advanced mathematical problems to
                 almost arbitrarily-high precision that is limited by
                 the memory of the host machine.",
  acknowledgement = ack-nhfb,
  subject =      "Computational Physics (physics.comp-ph); Physics
                 Education (physics.ed-ph)",
}

@InProceedings{Wang:2010:DAH,
  author =       "Dong Wang and M. D. Ercegovac and Nanning Zheng",
  title =        "Design and analysis of high radix complex dividers",
  crossref =     "IEEE:2010:ICC",
  pages =        "V1--84--V1--88",
  year =         "2010",
  DOI =          "https://doi.org/10.1109/ICCET.2010.5486287",
  bibdate =      "Fri Dec 03 15:18:03 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper evaluates FPGA-based high radix hardware
                 architecture for complex division. The architecture
                 uses the digit-recurrence algorithm with prescaling of
                 complex operands. It efficiently executes the
                 prescaling and recurrence procedures in shared logic
                 resources. Thirty independent designs of different
                 radices from 4 to 64 and input precisions from 16 to 64
                 are implemented in Stratix-II FPGA and results on cost
                 and performance provide a broad space of design
                 parameters. Moreover, methods for estimating logic
                 resource consumption and timing performance are also
                 given so that one could make quick evaluations on the
                 design before any actual implementations. The proposed
                 architecture and design can be used as standalone
                 arithmetic units for systems-on-chip implementations,
                 in embedded processors, or as IP for VLSI
                 implementation in general.",
  acknowledgement = ack-nhfb,
  keywords =     "design parameter; digit-recurrence algorithm; digital
                 arithmetic; embedded processor; field programmable gate
                 arrays; high radix complex dividers; IP implementation;
                 logic design; shared logic resource consumption;
                 standalone arithmetic unit; Stratix-II FPGA-based high
                 radix hardware architecture; system-on-chip;
                 systems-on-chip implementation; VLSI implementation",
}

@Article{Wang:2010:SHD,
  author =       "Liang-Kai Wang and Mark A. Erle and Charles Tsen and
                 Eric M. Schwarz and Michael J. Schulte",
  title =        "A survey of hardware designs for decimal arithmetic",
  journal =      j-IBM-JRD,
  volume =       "54",
  number =       "2",
  pages =        "8:1--8:15",
  month =        "????",
  year =         "2010",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/JRD.2010.2040930",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  bibdate =      "Sat May 1 17:44:14 MDT 2010",
  bibsource =    "http://www.research.ibm.com/journal/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.research.ibm.com/journal/abstracts/rd/542/wang-schwarz.html",
  abstract =     "Decimal data and decimal arithmetic operations are
                 ubiquitous in daily life. Although microprocessors
                 normally use binary arithmetic for computations,
                 decimal arithmetic is often required in financial and
                 commercial applications. Due to the increasing
                 importance of and demand for decimal arithmetic,
                 decimal floating-point (DFP) formats and operations are
                 specified in the revised IEEE Standard for
                 Floating-Point Arithmetic (IEEE 754-2008). This paper
                 provides a survey of hardware designs for decimal
                 arithmetic. It gives an overview of DFP arithmetic in
                 IEEE 754-2008, describes processors that provide
                 hardware and instruction set support for decimal
                 arithmetic, and provides a survey of hardware designs
                 for decimal addition, subtraction, multiplication, and
                 division. Finally, it describes potential areas for
                 future research.",
  acknowledgement = ack-nhfb,
  articleno =    "8",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  keywords =     "decimal floating-point arithmetic",
}

@Article{Wang:2010:VVP,
  author =       "Xiaojun Wang and Miriam Leeser",
  title =        "{VFloat}: a Variable Precision Fixed- and
                 Floating-Point Library for Reconfigurable Hardware",
  journal =      j-TRETS,
  volume =       "3",
  number =       "3",
  pages =        "16:1--16:??",
  month =        sep,
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/1839480.1839486",
  ISSN =         "1936-7406 (print), 1936-7414 (electronic)",
  ISSN-L =       "1936-7406",
  bibdate =      "Fri Oct 8 18:26:34 MDT 2010",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/trets.bib",
  abstract =     "Optimal reconfigurable hardware implementations may
                 require the use of arbitrary floating-point formats
                 that do not necessarily conform to IEEE specified
                 sizes. We present a variable precision floating-point
                 library (VFloat) that supports general floating-point
                 formats including IEEE standard formats. Most
                 previously published floating-point formats for use
                 with reconfigurable hardware are subsets of our format.
                 Custom datapaths with optimal bitwidths for each
                 operation can be built using the variable precision
                 hardware modules in the VFloat library, enabling a
                 higher level of parallelism. The VFloat library
                 includes three types of hardware modules for format
                 control, arithmetic operations, and conversions between
                 fixed-point and floating-point formats. The format
                 conversions allow for hybrid fixed- and floating-point
                 operations in a single design. This gives the designer
                 control over a large number of design possibilities
                 including format as well as number range within the
                 same application. In this article, we give an overview
                 of the components in the VFloat library and demonstrate
                 their use in an implementation of the K-means
                 clustering algorithm applied to multispectral satellite
                 images.",
  acknowledgement = ack-nhfb,
  articleno =    "16",
  fjournal =     "ACM Transactions on Reconfigurable Technology and
                 Systems (TRETS)",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J1151",
  keywords =     "clustering; floating-point; Reconfigurable hardware",
}

@Article{Waters:2010:RCW,
  author =       "Ron S. Waters and Earl E. Swartzlander",
  title =        "A Reduced Complexity {Wallace} Multiplier Reduction",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "59",
  number =       "8",
  pages =        "1134--1137",
  month =        "????",
  year =         "2010",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.103",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Jul 3 11:52:31 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5467045",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Ye:2010:FIC,
  author =       "Min Ye and Taijun Liu and Yan Ye and Gaoming Xu and
                 Tiefeng Xu",
  booktitle =    "{2010 6th International Conference on Wireless
                 Communications Networking and Mobile Computing
                 (WiCOM)}",
  title =        "{FPGA} Implementation of {CORDIC}-based Square Root
                 Operation for Parameter Extraction of Digital
                 Pre-Distortion for Power Amplifiers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--4",
  year =         "2010",
  DOI =          "https://doi.org/10.1109/WICOM.2010.5600929",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Arrays; Field programmable gate arrays; Hardware;
                 Parameter extraction; Power amplifiers; Software;
                 Software algorithms",
}

@InProceedings{Zanoni:2010:ITC,
  author =       "Alberto Zanoni",
  title =        "Iterative {Toom--Cook} methods for very unbalanced
                 long integer multiplication",
  crossref =     "Watt:2010:IPI",
  pages =        "319--323",
  year =         "2010",
  DOI =          "https://doi.org/10.1145/1837934.1837995",
  bibdate =      "Fri Jun 17 08:06:37 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We consider the multiplication of long integers when
                 one factor is much larger than the other one. We
                 describe an iterative approach using Toom--Cook
                 unbalanced methods, which results in the evaluation of
                 the smaller integer only once. The particular case of
                 Toom-2.5 is considered in full detail. A further
                 optimization depending on the parity of the shortest
                 operand evaluation in 1 is also described. A comparison
                 with GMP library is also presented.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Zhao:2010:GMP,
  author =       "Kaiyong Zhao and Xiaowen Chu",
  editor =       "{IEEE}",
  booktitle =    "{IEEE 10th International Conference on Computer and
                 Information Technology (CIT), 2010: June 29, 2010--July
                 1, 2010, Bradford, West Yorkshire, UK}",
  title =        "{GPUMP}: a Multiple-Precision Integer Library for
                 {GPUs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  bookpages =    "xcix + 2987 (est.)",
  pages =        "1164--1168",
  year =         "2010",
  DOI =          "https://doi.org/10.1109/CIT.2010.211",
  ISBN =         "0-7695-4108-9 (print), 1-4244-7547-3",
  ISBN-13 =      "978-0-7695-4108-2 (print), 978-1-4244-7547-6",
  LCCN =         "????",
  bibdate =      "Thu Jan 16 10:33:01 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/pvm.bib",
  note =         "IEEE Computer Society Order Number E4108. BMS Part
                 Number: CFP10355-CDR",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/servlet/opac?punumber=5575291",
  keywords =     "CUDA; GPU; multiple-precision algorithm;
                 multiple-precision comparison; multiple-precision
                 division; multiple-precision exponentiation;
                 multiple-precision modular addition; multiple-precision
                 modular multiplication; multiple-precision Montgomery
                 exponentiation; multiple-precision Montgomery
                 multiplication; multiple-precision Montgomery
                 reduction; multiple-precision multiplication; nVidia
                 GT200 GPU",
}

@Article{Zhu:2010:AOE,
  author =       "Yong-Kang Zhu and Wayne B. Hayes",
  title =        "{Algorithm 908}: Online Exact Summation of
                 Floating-Point Streams",
  journal =      j-TOMS,
  volume =       "37",
  number =       "3",
  pages =        "37:1--37:13",
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1824801.1824815",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 27 10:15:50 MDT 2010",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present a novel, online algorithm for exact
                 summation of a stream of floating-point numbers. By
                 ``online'' we mean that the algorithm needs to see only
                 one input at a time, and can take an arbitrary length
                 input stream of such inputs while requiring only
                 constant memory. By ``exact'' we mean that the sum of
                 the internal array of our algorithm is exactly equal to
                 the sum of all the inputs, and the returned result is
                 the correctly-rounded sum. The proof of correctness is
                 valid for all inputs (including nonnormalized numbers
                 but modulo intermediate overflow), and is independent
                 of the number of summands or the condition number of
                 the sum. The algorithm asymptotically needs only 5
                 FLOPs per summand, and due to instruction-level
                 parallelism runs only about 2--3 times slower than the
                 obvious, fast-but-dumb ``ordinary recursive summation''
                 loop when the number of summands is greater than
                 10,000. Thus, to our knowledge, it is the fastest, most
                 accurate, and most memory efficient among known
                 algorithms. Indeed, it is difficult to see how a faster
                 algorithm or one requiring significantly fewer FLOPs
                 could exist without hardware improvements. An
                 application for a large number of summands is
                 provided.",
  acknowledgement = ack-nhfb,
  articleno =    "37",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "accurate floating-point summation; correct rounding;
                 floating-point arithmetic; rounding error",
}

@InProceedings{Zimmermann:2010:RCG,
  author =       "Paul Zimmermann",
  title =        "Reliable Computing with {GNU MPFR}",
  crossref =     "Fukuda:2010:MSI",
  pages =        "42--45",
  year =         "2010",
  DOI =          "https://doi.org/10.1007/978-3-642-15582-6_8",
  bibdate =      "Sat Sep 23 06:20:46 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Adikari:2011:HBT,
  author =       "Jithra Adikari and Vassil S. Dimitrov and Laurent
                 Imbert",
  title =        "Hybrid Binary-Ternary Number System for Elliptic Curve
                 Cryptosystems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  number =       "2",
  pages =        "254--265",
  month =        feb,
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.138",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Feb 20 19:15:33 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Al-Ashrafy:2011:EIF,
  author =       "M. Al-Ashrafy and A. Salem and W. Anis",
  booktitle =    "{2011 Saudi International Electronics, Communications
                 and Photonics Conference (SIECPC)}",
  title =        "An efficient implementation of floating point
                 multiplier",
  publisher =    "pub-IEEE",
  address =      "pub-IEEE:adr",
  pages =        "1--5",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/SIECPC.2011.5876905",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5876905",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5783968",
}

@InProceedings{Anderson:2011:GVD,
  author =       "Timothy Anderson and Duc Bui and Shriram Moharil and
                 Soujanya Narnur and Mujibur Rahman and Anthony Lell and
                 Eric Biscondi and Ashish Shrivastava and Peter Dent and
                 Mingjian Yan and Hasan Mahmood",
  title =        "A {1.5 Ghz VLIW DSP CPU} with Integrated Floating
                 Point and Fixed Point Instructions in 40 nm {CMOS}",
  crossref =     "Schwarz:2011:PIS",
  pages =        "82--86",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.20",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992112",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20",
}

@Article{Anonymous:2011:CPSa,
  author =       "Anonymous",
  title =        "Call for Papers: Special Section on Computer
                 Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  number =       "6",
  pages =        "910--910",
  month =        jun,
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2011.88",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jun 29 10:26:18 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Book{Antelo:2011:IIFa,
  editor =       "Elisardo Antelo",
  title =        "Industrial Implementations of Floating-Point Units",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2011",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Thu Aug 18 08:02:12 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Filename ES0000033.",
  tableofcontents = "Editor's Introduction \\
                 Related Videos \\
                 ``P6 Binary Floating-Point Unit,'' by Son Dao Trong,
                 Martin Schmookler, Eric M. Schwarz, and Michael Kroener
                 \\
                 ``FPU Implementations with Denormalized Numbers,'' by
                 Eric M. Schwarz, Martin Schmookler, and Son Dao Trong
                 \\
                 ``1-GHz HAL SPARC64 Dual Floating Point Unit with RAS
                 Features,'' by Ajay Naini, Atul Dhablania, Warren
                 James, and Debjit Das Sarma \\
                 ``Low-Power Multiple-Precision Iterative Floating-Point
                 Multiplier with SIMD Support,'' by Dimitri Tan, Carl E.
                 Lemonds, and Michael J. Schulte \\
                 ``The Vector Floating-Point Unit in a Synergistic
                 Processor Element of a CELL Processor,'' by Silvia M.
                 Mueller, Christian Jacobi, Hwa-Joon Oh, Kevin D. Tran,
                 Scott R. Cottier, Brad W. Michael, Hiroo Nishikawa,
                 Yonetaro Totsuka, Tatsuya Namatame, Naoka Yano, Takashi
                 Machida, and Sang H. Dhong \\
                 ``A High-Performance SIMD Floating Point Unit for
                 BlueGene/L: Architecture, Compilation, and Algorithm
                 Design,'' by Leonardo Bachega, Siddhartha Chatterjee,
                 Kenneth A. Dockser, John A. Gunnels, Manish Gupta, Fred
                 G. Gustavson, Christopher A. Lapkowski, Gary K. Liu,
                 Mark P. Mendell, Charles D. Wait, and T. J. Chris Ward
                 \\
                 ``Design of the ARM VFP11 Divide and Square Root
                 Synthesisable Macrocell,'' by Neil Burgess and Chris N.
                 Hinds \\
                 ``Correctness Proofs Outline for Newton-Raphson Based
                 Floating-Point Divide and Square Root Algorithms,'' by
                 Marius A. Cornea-Hasegan, Roger A. Golliver, and Peter
                 Markstein \\
                 Recommended Resources \\
                 About the Editor",
}

@Book{Antelo:2011:IIFb,
  editor =       "Elisardo Antelo",
  title =        "Industrial Implementations of Floating-Point Units",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2011",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Thu Aug 18 08:02:12 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Filename ES0000034.",
  tableofcontents = "Editor's Introduction \\
                 Related Videos \\
                 ``A High-Performance Area-Efficient Multifunction
                 Interpolator,'' by Stuart F. Oberman and Michael Y. Siu
                 \\
                 ``New Algorithms for Improved Transcendental Functions
                 on IA-64,'' by Shane Story and Ping Tak Peter Tang \\
                 ``Energy-Delay Estimation Technique for
                 High-Performance Microprocessor VLSI Adders,'' by Vojin
                 G. Oklobdzija, Bart R. Zeydel, Hoang Dao, Sanu Mathew,
                 and Ram Krishnamurthy \\
                 ``Advanced Clockgating Schemes for
                 Fused-Multiply-Add-Type Floating-Point Units,'' by
                 Jochen Preiss, Maarten Boersma, and Silvia Melitta
                 Mueller \\
                 ``Design of Low-Cost High-Performance Floating-Point
                 Fused Multiply-Add with Reduced Power,'' by Zichu Qi,
                 Qi Guo, Ge Zhang, Xiangku Li, and Weiwu Hu \\
                 ``Decimal Floating-Point: Algorism for Computers,'' by
                 Michael F. Cowlishaw \\
                 ``A Software Implementation of the IEEE 754R Decimal
                 Floating-Point Arithmetic Using the Binary Encoding
                 Format,'' by Marius Cornea, John Harrison, Cristina
                 Anderson, Ping Tak Peter Tang, Eric Schneider, and
                 Evgeny Gvozdev \\
                 Recommended Resources \\
                 About the Editor",
}

@InProceedings{Arias-Garcia:2011:SFI,
  author =       "J. Arias-Garcia and R. Pezzuol Jacobi and C. H. Llanos
                 and M. Ayala-Rincon",
  booktitle =    "{2011 VII Southern Conference on Programmable Logic
                 (SPL)}",
  title =        "A suitable {FPGA} implementation of floating-point
                 matrix inversion based on {Gauss--Jordan} elimination",
  publisher =    "pub-IEEE",
  address =      "pub-IEEE:adr",
  pages =        "263--268",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/SPL.2011.5782659",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5782659",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5771182",
}

@Article{Arnold:2011:RCL,
  author =       "Mark G. Arnold and Sylvain Collange",
  title =        "A Real\slash Complex Logarithmic Number System {ALU}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  number =       "2",
  pages =        "202--213",
  month =        feb,
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.154",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Feb 20 19:15:33 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Arnold:2011:TQC,
  author =       "Mark G. Arnold and John Cowles and Vassilis Paliouras
                 and Ioannis Kouretas",
  title =        "Towards a Quaternion Complex Logarithmic Number
                 System",
  crossref =     "Schwarz:2011:PIS",
  pages =        "33--42",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.14",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992106",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20; logarithmic number system (LNS)",
}

@Article{Badin:2011:IAM,
  author =       "Matthew Badin and Lubomir Bic and Michael Dillencourt
                 and Alexandru Nicolau",
  title =        "Improving accuracy for matrix multiplications on
                 {GPUs}",
  journal =      j-SCI-PROG,
  volume =       "19",
  number =       "1",
  pages =        "3--11",
  month =        "????",
  year =         "2011",
  CODEN =        "SCIPEV",
  DOI =          "https://doi.org/10.3233/SPR-2011-0315",
  ISSN =         "1058-9244 (print), 1875-919X (electronic)",
  ISSN-L =       "1058-9244",
  bibdate =      "Tue Dec 13 19:01:37 MST 2011",
  bibsource =    "http://www.iospress.nl/journal/scientific-programming/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sciprogram.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientific Programming",
  journal-URL =  "http://iospress.metapress.com/content/1058-9244",
}

@TechReport{Bailey:2011:GMD,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "The Greatest Mathematical Discovery?",
  type =         "Report",
  institution =  "Lawrence Berkeley National Laboratory and Centre for
                 Computer Assisted RMA, University of Newcastle",
  address =      "Berkeley, CA 94720, USA and Callaghan, NSW 2308,
                 Australia",
  pages =        "10",
  day =          "8",
  month =        may,
  year =         "2011",
  bibdate =      "Fri Aug 12 18:29:28 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.davidhbailey.com/dhbpapers/decimal.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "decimal arithmetic history",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
}

@TechReport{Baudin:2011:EBC,
  author =       "M. Baudin",
  title =        "Error bounds of complex arithmetic",
  type =         "Report",
  number =       "??",
  institution =  "????",
  address =      "????",
  month =        jun,
  year =         "2011",
  bibdate =      "Sun Feb 19 07:29:34 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://forge.scilab.org/upload/compdiv/files/complexerrorbounds_v0.2.pdf",
  acknowledgement = ack-nhfb,
}

@TechReport{Beebe:2011:BPAb,
  author =       "Nelson H. F. Beebe",
  title =        "A Bibliography of Publications about {Benford's Law},
                 {Heaps' Law}, and {Zipf's Law}",
  institution =  inst-CSC,
  address =      inst-CSC:adr,
  pages =        "62",
  day =          "12",
  month =        nov,
  year =         "2011",
  bibdate =      "Thu Nov 10 12:15:06 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.math.utah.edu/pub/tex/bib/index-table-b.html#benfords-law",
  acknowledgement = ack-nhfb,
}

@Article{Berger:2011:FSM,
  author =       "Arno Berger and Theodore P. Hill and Bahar Kaynar and
                 Ad Ridder",
  title =        "Finite-state {Markov} Chains Obey {Benford's Law}",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "32",
  number =       "3",
  pages =        "665--684",
  month =        "????",
  year =         "2011",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/100789890",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Wed Aug 24 11:18:18 MDT 2011",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/32/3;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  URL =          "http://epubs.siam.org/simax/resource/1/sjmael/v32/i3/p665_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
  onlinedate =   "July 21, 2011",
}

@Article{Beuchat:2011:FAP,
  author =       "Jean-Luc Beuchat and Jeremie Detrey and Nicolas
                 Estibals and Eiji Okamoto and Francisco
                 Rodriguez-Henriquez",
  title =        "Fast Architectures for the {$ \eta_T $} Pairing over
                 Small-Characteristic Supersingular Elliptic Curves",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  number =       "2",
  pages =        "266--281",
  month =        feb,
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.163",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Feb 20 19:15:33 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Bhakthavatchalu:2011:CRF,
  author =       "Ramesh Bhakthavatchalu and Nisha Abdul Kareem and J.
                 Arya",
  booktitle =    "{2011 IEEE Recent Advances in Intelligent
                 Computational Systems}",
  title =        "Comparison of reconfigurable {FFT} processor
                 implementation using {CORDIC} and multipliers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "343--347",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/RAICS.2011.6069331",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithm design and analysis; Computer architecture;
                 CORDIC; digital signal processor (DSP); Discrete
                 Fourier transforms; Equations; Fast Fourier transform
                 (FFT); Fast Fourier transforms; FPGA; Integrated
                 circuit modeling; Signal processing algorithms",
}

@InProceedings{Bodrato:2011:HDT,
  author =       "Marco Bodrato",
  title =        "High Degree {Toom'n'Half} for Balanced and Unbalanced
                 Multiplication",
  crossref =     "Schwarz:2011:PIS",
  pages =        "15--22",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.12",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992104",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20",
}

@InProceedings{Boersma:2011:PBF,
  author =       "Maarten Boersma and Michael Kroner and Christophe
                 Layer and Petra Leber and Silvia M. Muller and Kerstin
                 Schelm",
  title =        "The {POWER7} Binary Floating-Point Unit",
  crossref =     "Schwarz:2011:PIS",
  pages =        "87--91",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.21",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992113",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20",
}

@Article{Boldo:2011:EAE,
  author =       "Sylvie Boldo and Jean-Michel Muller",
  title =        "Exact and Approximated Error of the {FMA}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  number =       "2",
  pages =        "157--164",
  month =        feb,
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.139",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Feb 20 19:15:33 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  abstract =     "The fused multiply accumulate-add (FMA) instruction,
                 specified by the IEEE 754-2008 Standard for
                 Floating-Point Arithmetic, eases some calculations, and
                 is already available on some current processors such as
                 the Power PC or the Itanium. We first extend an earlier
                 work on the computation of the exact error of an FMA
                 (by giving more general conditions and providing a
                 formal proof). Then, we present a new algorithm that
                 computes an approximation to the error of an FMA, and
                 provide error bounds and a formal proof for that
                 algorithm.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Boldo:2011:FUL,
  author =       "Sylvie Boldo and Guillaume Melquiond",
  title =        "{Flocq}: a Unified Library for Proving Floating-Point
                 Algorithms in {Coq}",
  crossref =     "Schwarz:2011:PIS",
  pages =        "243--252",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.40",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992132",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20",
}

@Article{Boldo:2011:FVN,
  author =       "Sylvie Boldo and Claude March{\'e}",
  title =        "Formal Verification of Numerical Programs: From {C}
                 Annotated Programs to Mechanical Proofs",
  journal =      j-MATH-COMPUT-SCI,
  volume =       "5",
  number =       "4",
  pages =        "377--393",
  month =        dec,
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s11786-011-0099-9",
  ISSN =         "1661-8270 (print), 1661-8289 (electronic)",
  ISSN-L =       "1661-8270",
  bibdate =      "Tue Nov 6 10:16:23 MST 2012",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1661-8270&volume=5&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/math-comput-sci.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=1661-8270&volume=5&issue=4&spage=377",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics in Computer Science",
  journal-URL =  "http://www.springerlink.com/content/1661-8270/",
  keywords =     "Alt-Ergo; automated reasoning; C program; Coq; CVC3;
                 floating-point arithmetic; formal specification;
                 Frama-C; Gappa; Jessie plugin; Why; Z3",
}

@InProceedings{Bos:2011:ESA,
  author =       "Joppe W. Bos and Thorsten Kleinjung and Arjen K.
                 Lenstra and Peter L. Montgomery",
  title =        "Efficient {SIMD} Arithmetic Modulo a {Mersenne}
                 Number",
  crossref =     "Schwarz:2011:PIS",
  pages =        "213--221",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.37",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992129",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20",
}

@Book{Brent:2011:MCA,
  author =       "Richard P. Brent and Paul Zimmermann",
  title =        "Modern Computer Arithmetic",
  volume =       "18",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xvi + 221",
  year =         "2011",
  DOI =          "https://doi.org/10.1017/CBO9780511921698",
  ISBN =         "0-521-19469-5 (hardcover)",
  ISBN-13 =      "978-0-521-19469-3 (hardcover)",
  LCCN =         "QA76.9.C62 BRE 2011",
  bibdate =      "Sat Jan 15 12:25:22 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigact.bib;
                 library.ox.ac.uk:210/ADVANCE",
  series =       "Cambridge monographs on applied and computational
                 mathematics",
  URL =          "http://www.loria.fr/~zimmerma/mca/pub226.html",
  acknowledgement = ack-nhfb,
  subject =      "Computer arithmetic",
  tableofcontents = "Preface / ix \\
                 Acknowledgements / xi \\
                 Notation / xiii \\
                 Integer arithmetic / 1 \\
                 1.1 Representation and notations / 1 \\
                 1.2 Addition and subtraction / 2 \\
                 1.3 Multiplication / J \\
                 i.3.1 Naive multiplication / 4 \\
                 1.3.2 Karatsuba's algorithm / 5 \\
                 1.3.3 Toom--Cook multiplication / 6 \\
                 1.3.4 Use of the fast Fourier transform (FFT) / 8 \\
                 1.3.5 Unbalanced multiplication / 8 \\
                 1.3.6 Squaring / 11 \\
                 1.3.7 Multiplication by a constant / 13 \\
                 1.4 Division / 14 \\
                 1.4.1 Naive division / 14 \\
                 1.4.2 Divisor preconditioning / 16 \\
                 1.4.3 Divide and conquer division / 18 \\
                 1.4.4 Newton's method / 21 \\
                 1.4.5 Exact division / 21 \\
                 1.4.6 Only quotient or remainder wanted / 22 \\
                 1.4.7 Division by a single word / 23 \\
                 1.4.8 Hensel's division / 24 \\
                 1.5 Roots / 25 \\
                 1.5.1 Square root / 25 \\
                 1.5.2 $k$th root / 27 \\
                 1.5.3 Exact root / 28 \\
                 1.6 Greatest common divisor / 29 \\
                 1.6.1 Naive GCD / 29 \\
                 1.6.2 Extended GCD / 32 \\
                 1.6.3 Half binary GCD, divide and conquer GCD / 33 \\
                 1.7 Base conversion / 37 \\
                 1.7.1 Quadratic algorithms / 37 \\
                 1.7.2 Subquadratic algorithms / 38 \\
                 1.8 Exercises / 39 \\
                 1.9 Notes and references / 44 \\
                 Modular arithmetic and the FFT / 47 \\
                 2.1 Representation / 47 \\
                 2.1.1 Classical representation / 47 \\
                 2.1.2 Montgomery's form / 48 \\
                 2.1.3 Residue number systems / 48 \\
                 2.1.4 MSB vs LSB algorithms / 49 \\
                 2.1.5 Link with Polynomials / 49 \\
                 2.2 Modular addition and subtraction / 50 \\
                 2.3 The Fourier transform / 50 \\
                 2.3.1 Theoretical setting / 50 \\
                 2.3.2 The fast Fourier transform / 51 \\
                 2.3.3 The Sch{\"o}nhage--Strassen algorithm / 55 \\
                 2.4 Modular multiplication / 58 \\
                 2.4.1 Barrett's algorithm / 58 \\
                 2.4.2 Montgomery's multiplication / 60 \\
                 2.4.3 McLaughlin's algorithm / 63 \\
                 2.4.4 Special moduli / 65 \\
                 2.5 Modular division and inversion / 65 \\
                 2.5.1 Several inversions at once / 61 \\
                 2.6 Modular exponentiation / 68 \\
                 2.6.1 Binary exponentiation / 70 \\
                 2.6.2 Exponentiation with a larger base / 70 \\
                 2.6.3 Sliding window and redundant representation / 72
                 \\
                 2.7 Chinese remainder theorem / 75 \\
                 2.8 Exercises / 75 \\
                 2.9 Notes and references / 77 \\
                 Floating-point arithmetic / 79 \\
                 3.1 Representation / 79 \\
                 3.1.1 Radix choice / 80 \\
                 3.1.2 Exponent range / 81 \\
                 3.1.3 Special values / 82 \\
                 3.1.4 Subnormal numbers / 82 \\
                 3.1.5 Encoding / 83 \\
                 3.1.6 Precision: local, global, operation, operand / 84
                 \\
                 3.1.7 Link to integers / 86 \\
                 3.1.8 Ziv's algorithm and error analysis / 86 \\
                 3.1.9 Rounding / 87 \\
                 3.1.10 Strategies / 90 \\
                 3.2 Addition, subtraction, comparison / 91 \\
                 3.2.1 Floating-point addition / 92 \\
                 3.2.2 Floating-point subtraction / 93 \\
                 3.3 Multiplication / 95 \\
                 3.3.1 Integer multiplication via complex FFT / 98 \\
                 3.3.2 The middle product / 99 \\
                 3.4 Reciprocal and division / 101 \\
                 3.4.1 Reciprocal / 102 \\
                 3.4.2 Division / 106 \\
                 3.5 Square root / 111 \\
                 3.5.1 Reciprocal square root / 112 \\
                 3.6 Conversion / 114 \\
                 3.6.1 Floating-point output / 115 \\
                 3.6.2 Floating-point input / 117 \\
                 3.7 Exercises / 118 \\
                 3.8 Notes and references / 120 \\
                 Elementary and special function evaluation / 125 \\
                 4.1 Introduction / 125 \\
                 4.2 Newton's method / 126 \\
                 4.2.1 Newton's method for inverse roots / 127 \\
                 4.2.2 Newton's method for reciprocals / 128 \\
                 4.2.3 Newton's method for (reciprocal) square roots /
                 129 \\
                 4.2.4 Newton's method for formal power series / 129 \\
                 4.2.5 Newton's method for functional inverses / 130 \\
                 4.2.6 Higher-order Newton-like methods / 131 \\
                 4.3 Argument reduction / 132 \\
                 4.3.1 Repeated use of a doubling formula / 134 \\
                 4.3.2 Loss of precision / 134 \\
                 4.3.3 Guard digits / 135 \\
                 4.3.4 Doubling versus tripling / 136 \\
                 4.4 Power series / 136 \\
                 4.4.1 Direct power series evaluation / 140 \\
                 4.4.2 Power series with argument reduction / 140 \\
                 4.4.3 Rectangular series splitting / 141 \\
                 4.5 Asymptotic expansions / 144 \\
                 4.6 Continued fractions / 150 \\
                 4.7 Recurrence relations / 152 \\
                 4.7.1 Evaluation of Bessel functions / 153 \\
                 4.7.2 Evaluation of Bernoulli and tangent numbers / 154
                 \\
                 4.8 Arithmetic--geometric mean / 158 \\
                 4.8.1 Elliptic integrals / 158 \\
                 4.8.2 First AGM algorithm for the logarithm / 159 \\
                 4.8.3 Theta functions / 160 \\
                 4.8.4 Second AGM algorithm for the logarithm / 162 \\
                 4.8.5 The complex AGM / 163 \\
                 4.9 Binary splitting / 163 \\
                 4.9.1 A binary splitting algorithm for sin, cos / 166
                 \\
                 4.9.2 The bit-burst algorithm / 161 \\
                 4.10 Contour integration / 169 \\
                 4.11 Exercises / 171 \\
                 4.12 Notes and references / 179 \\
                 Implementations and pointers / 185 \\
                 5.1 Software tools / 185 \\
                 5.1.1 CLN / 185 \\
                 5.1.2 GNUMP (GMP) / 185 \\
                 5.1.3 MPFQ / 186 \\
                 5.1.4 GNU MPFR / 187 \\
                 5.1.5 Other multiple-precision packages / 187 \\
                 5.1.6 Computational algebra packages / 188 \\
                 5.2 Mailing lists / 189 \\
                 5.2.1 The GMP lists / 189 \\
                 5.2.2 The MPFR list / 190 \\
                 5.3 Online documents / 190 \\
                 References / 191 \\
                 Index / 207",
}

@InProceedings{Brisebarre:2011:APS,
  author =       "Nicolas Brisebarre and Mioara Joldes and Peter
                 Kornerup and {\'E}rik Martin-Dorel and Jean-Michel
                 Muller",
  title =        "Augmented Precision Square Roots and {$2$-D} Norms,
                 and Discussion on Correctly Rounding $ \sqrt {x^2 +
                 y^2} $",
  crossref =     "Schwarz:2011:PIS",
  pages =        "23--30",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.13",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992105",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20; correct rounding; floating-point arithmetic;
                 hypotenuse",
}

@Article{Bruguera:2011:GEI,
  author =       "Javier Bruguera and Marius Cornea and Debjit Das
                 Sarma",
  title =        "{Guest Editors}' Introduction: Special Section on
                 Computer Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  number =       "2",
  pages =        "145--147",
  month =        feb,
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2011.15",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Feb 20 19:15:33 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Brumley:2011:BSB,
  author =       "Billy Bob Brumley and Dan Page",
  title =        "Bit-Sliced Binary Normal Basis Multiplication",
  crossref =     "Schwarz:2011:PIS",
  pages =        "205--212",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.36",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992128",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20; correct rounding; floating-point
                 arithmetic",
}

@InProceedings{Brunie:2011:MPF,
  author =       "Nicolas Brunie and Florent de Dinechin and Benoit de
                 Dinechin",
  booktitle =    "2011 Conference Record of the {Forty Fifth Asilomar
                 Conference on Signals, Systems and Computers
                 (ASILOMAR)}",
  title =        "A mixed-precision fused multiply and add",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  month =        nov,
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ACSSC.2011.6189977",
  bibdate =      "Wed Aug 7 14:09:53 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Brusentsov:2011:TCS,
  author =       "Nikolay Petrovich Brusentsov and Jos{\'e} Ramil
                 Alvarez",
  title =        "Ternary Computers: The {Setun} and the {Setun 70}",
  crossref =     "Impagliazzo:2011:PSR",
  pages =        "74--80",
  year =         "2011",
  DOI =          "https://doi.org/10.1007/978-3-642-22816-2_10",
  bibdate =      "Sun Aug 16 19:31:45 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer.com/openurl?genre=book%26isbn=978-3-642-22815-5",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-642-22816-2",
  remark =       "The Setun computer series was unusual in being
                 proposed to use base-3 (ternary) floating-point
                 arithmetic.",
}

@InProceedings{Burgess:2011:FRC,
  author =       "Neil Burgess",
  title =        "Fast Ripple-Carry Adders in Standard-Cell {CMOS
                 VLSI}",
  crossref =     "Schwarz:2011:PIS",
  pages =        "103--111",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.23",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992115",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20",
}

@InProceedings{Butts:2011:RDR,
  author =       "J. Adam Butts and Ping Tak Peter Tang and Ron O. Dror
                 and David E. Shaw",
  title =        "Radix-8 Digit-by-Rounding: Achieving High-Performance
                 Reciprocals, Square Roots, and Reciprocal Square
                 Roots",
  crossref =     "Schwarz:2011:PIS",
  pages =        "149--158",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.28",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992120",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20",
}

@Article{Calamia:2011:CGG,
  author =       "J. Calamia",
  title =        "{China}'s {Godson} gamble",
  journal =      j-IEEE-SPECTRUM,
  volume =       "48",
  number =       "5",
  pages =        "14--16",
  month =        may,
  year =         "2011",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.2011.5753229",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Fri Jan 17 18:54:05 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/super.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "American born chip; China; Chinese researcher; country
                 homegrown high end processor; energy conservation;
                 energy efficiency; floating point operation; Godson-3B;
                 mainframes; Mesh networks; multiprocessing systems;
                 supercomputer; Supercomputers; The Dawning",
}

@InProceedings{Carlough:2011:IZD,
  author =       "Steven Carlough and Adam Collura and Silvia Mueller
                 and Michael Kroener",
  title =        "The {IBM zEnterprise-196} Decimal Floating-Point
                 Accelerator",
  crossref =     "Schwarz:2011:PIS",
  pages =        "139--146",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.27",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992119",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20; decimal floating-point arithmetic",
}

@Article{Cavagnino:2011:AAD,
  author =       "D. Cavagnino and A. E. Werbrouck",
  title =        "An Analysis of Associated Dividends in the {DBM}
                 Algorithm for Division by Constants Using
                 Multiplication",
  journal =      j-COMP-J,
  volume =       "54",
  number =       "1",
  pages =        "148--156",
  month =        jan,
  year =         "2011",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/bxp117",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 21 19:26:47 MST 2010",
  bibsource =    "http://comjnl.oxfordjournals.org/content/54/1.toc;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/54/1/148.full.pdf+html",
  abstract =     "When a compiler encounters a fixed integer divisor,
                 which is not a power of 2, it can calculate its inverse
                 to be multiplied by the run-time integer dividends to
                 obtain the quotients, using our very efficient,
                 recently published [Cavagnino, D. and Werbrouck, A. E.
                 (2008) {\em Efficient algorithms for integer division
                 by constants using multiplication}. Comp. J., 51,
                 470--480] division by multiplication algorithms.
                 Essentially our algorithms permit a complete partition
                 of a defined number space into non-adverse and adverse
                 divisors on the basis of whether a dividend associated
                 with each divisor is, or is not, greater than the
                 maximum dividend size. In this paper, we demonstrate
                 useful relations between the dividends associated with
                 all divisors and with their multiples by positive
                 powers",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "dividend distribution; division by multiplication
                 (DBM); integer division; multiplicative division",
  onlinedate =   "December 30, 2009",
  remark =       "See \cite{Cavagnino:2008:EAI}.",
}

@Article{Cenk:2011:EM,
  author =       "Murat Cenk and Ferruh {\"O}zbudak",
  title =        "Efficient multiplications in {$ \mathbb {F}_{5^{5n}}
                 $} and {$ \mathbb {F}_{7^{7n}} $}",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "236",
  number =       "2",
  pages =        "177--183",
  day =          "15",
  month =        aug,
  year =         "2011",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/j.cam.2011.06.016",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "11Y16 (11T99 12E20)",
  MRnumber =     "2827399",
  bibdate =      "Sat Feb 25 13:24:37 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042711003396",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  xxtitle =      "Efficient multiplications in {[??IMAGE??]} and
                 {[??IMAGE??]}",
}

@Article{Chakraborty:2011:CBS,
  author =       "Anindita Chakraborty and Amitabha Sinha",
  title =        "Conversion of binary to single-term triple base
                 numbers for {DSP} applications",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "39",
  number =       "5",
  pages =        "5--11",
  month =        dec,
  year =         "2011",
  CODEN =        "CANED2",
  DOI =          "https://doi.org/10.1145/2093339.2093342",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Thu Mar 15 14:07:10 MDT 2012",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
  abstract =     "In this paper high speed Residue Number System (RNS)
                 based FIR filter using Distributed Arithmetic (DA) is
                 proposed. The proposed architecture uses the module set
                 having the value of numbers as small as possible. In
                 case of using Distributed Arithmetic in FIR filter; the
                 size of LUTs gets increased exponentially with the
                 increase of tap of the filter. Here care has been taken
                 so that sizes of LUTs do not get increased. The
                 proposed architecture is designed using verilog HDL; a
                 popular hardware description language [9]. The design
                 is synthesized with ISE 10.1 and implemented on
                 Xilinx's Virtex-4. The proposed architecture is also
                 compared with conventional RNS-DA FIR filter. The
                 results show that the proposed architecture can
                 implement FIR filter with high speed.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
}

@Article{Chang:2011:CGR,
  author =       "Harry M. Chang",
  title =        "Constructing $n$-gram rules for natural language
                 models through exploring the limitation of the
                 {Zipf--Mandelbrot} law",
  journal =      j-COMPUTING,
  volume =       "91",
  number =       "3",
  pages =        "241--264",
  month =        mar,
  year =         "2011",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Sep 6 19:14:24 MDT 2011",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=91&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=91&issue=3&spage=241",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Article{Chen:2011:PIM,
  author =       "Zhimin Chen and Patrick Schaumont",
  title =        "A Parallel Implementation of {Montgomery}
                 Multiplication on Multicore Systems: Algorithm,
                 Analysis, and Prototype",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  number =       "12",
  pages =        "1692--1703",
  month =        dec,
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.256",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Nov 6 07:52:27 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5669278",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Chen:2011:TSA,
  author =       "Jianxun Chen and Yongzhong Huang and Shaozhong Guo and
                 Shimiao Chen and Wei Wang",
  booktitle =    "{2011 Third International Conference on Measuring
                 Technology and Mechatronics Automation (ICMTMA)}",
  title =        "Test Standardization and Analyse Model of Mathematical
                 Functions for Precision",
  volume =       "3",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "652--655",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ICMTMA.2011.734",
  ISBN =         "0-7695-4296-4",
  ISBN-13 =      "978-0-7695-4296-6",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5721571",
  abstract =     "This article describes problems of meet the
                 requirements to implementations of mathematical
                 functions working with floating-point numbers, and so
                 facilitate the comprehensive testing of mathematical
                 functions. Inconsistency and incompleteness of
                 available standards in the domain is demonstrated.
                 Correct rounding requirement is suggested to guarantee
                 preservation of all important properties of functions
                 and to support high level of interoperability between
                 different mathematical libraries and software using
                 them. The article also concerns precision analyse of
                 mathematical functions. Conformance test construction
                 method is proposed based on different sources of test
                 data.",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5720445",
  remark =       "This paper contains unattributed plagiaristic copying
                 of material from
                 \url{https://www.math.utah.edu/~beebe/software/ieee/index.html}.",
}

@InProceedings{Chevillard:2011:AGC,
  author =       "Sylvain Chevillard",
  title =        "Automatic Generation of Code for the Evaluation of
                 Constant Expressions at Any Precision with a Guaranteed
                 Error Bound",
  crossref =     "Schwarz:2011:PIS",
  pages =        "225--232",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.38",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992130",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20",
}

@Article{Colberg:2011:HAS,
  author =       "Peter H. Colberg and Felix H{\"o}fling",
  title =        "Highly accelerated simulations of glassy dynamics
                 using {GPUs}: Caveats on limited floating-point
                 precision",
  journal =      j-COMP-PHYS-COMM,
  volume =       "182",
  number =       "5",
  pages =        "1120--1129",
  month =        may,
  year =         "2011",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2011.01.009",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Sat Feb 11 10:10:57 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465511000294",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Corless:2011:RCA,
  author =       "Robert Corless and Erik Postma and David R.
                 Stoutemyer",
  title =        "Rounding coefficients and artificially underflowing
                 terms in non-numeric expressions",
  journal =      j-ACM-COMM-COMP-ALGEBRA,
  volume =       "45",
  number =       "1",
  pages =        "17--48",
  month =        mar,
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2016567.2016570",
  ISSN =         "1932-2232 (print), 1932-2240 (electronic)",
  ISSN-L =       "1932-2232",
  bibdate =      "Wed Aug 17 08:55:07 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This article takes an analytical viewpoint to address
                 the following questions: 1. How can we justifiably
                 beautify an input or result sum of non-numeric terms
                 that has some approximate coefficients by deleting some
                 terms and/or rounding some coefficients to simpler
                 floating-point or rational numbers? 2. When we add two
                 expressions, how can we justifiably delete more
                 non-zero result terms and/or round some result
                 coefficients to even simpler floating-point, rational
                 or irrational numbers? The methods considered in this
                 paper provide a justifiable scale-invariant way to
                 attack these problems for subexpressions that are
                 multivariate sums of monomials with real exponents.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Communications in Computer Algebra",
  issue =        "175",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
  keywords =     "floating-point arithmetic; rounding; symbolic
                 algebra",
}

@InProceedings{Cui:2011:TDB,
  author =       "Mingyi Cui",
  booktitle =    "{2011 International Conference on Electronic and
                 Mechanical Engineering and Information Technology
                 (EMEIT)}",
  title =        "A threshold denoising based floating point
                 representation genetic algorithm",
  volume =       "7",
  publisher =    "pub-IEEE",
  address =      "pub-IEEE:adr",
  pages =        "3305--3308",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/EMEIT.2011.6023063",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6023063",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5996364",
}

@Article{Curran:2011:ZSM,
  author =       "Brian W. Curran and Lee E. Eisen and Eric M. Schwarz
                 and Pak-kin Mak and James Warnock and Patrick J. Meaney
                 and Michael Fee",
  title =        "The {zEnterprise 196} System and Microprocessor",
  journal =      j-IEEE-MICRO,
  volume =       "31",
  number =       "2",
  pages =        "26--40",
  month =        mar # "\slash " # apr,
  year =         "2011",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.2011.34",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Tue Apr 26 13:50:28 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The zEnterprise 196 is the latest IBM System zSeries
                 mainframe computer, which builds on IBM's 46-year
                 heritage of compatible enterprise-class machines. This
                 design advances the prior z10 processor pipeline with
                 out-of-order execution to achieve considerable
                 performance gains in legacy online transaction
                 processing and computationally intensive workloads.
                 This article describes the system structure and details
                 of this new high-frequency microprocessor.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
  keywords =     "correct rounding; floating-point arithmetic; Hot Chips
                 22 conference proceedings",
  remark =       "From page 34: ``IEEE Std 754-2008 (IEEE Standard for
                 Floating-Point Arithmetic) adds the requirement to
                 support heterogeneous operations on operands with
                 different precisions. In light of this standard, z196
                 added a new rounding mode called round to prepare for
                 shorter precision to all binary floating-point
                 instructions. Using this new rounding mode allows an
                 addition with a double-precision addend and a
                 single-precision augend to produce a single-precision
                 sum with correct rounding.''",
}

@Article{Daisaka:2011:GMS,
  author =       "Hiroshi Daisaka and Naohito Nakasato and Junichiro
                 Makino and Fukuko Yuasa and Tadashi Ishikawa",
  title =        "{GRAPE-MP}: An {SIMD} Accelerator Board for
                 Multi-precision Arithmetic",
  journal =      "Procedia Computer Science",
  volume =       "4",
  pages =        "878--887",
  month =        may,
  year =         "2011",
  DOI =          "https://doi.org/10.1016/j.procs.2011.04.093",
  ISSN =         "1877-0509",
  ISSN-L =       "1877-0509",
  bibdate =      "Wed Jun 12 16:47:38 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Proc. Comput. Sci.",
}

@Article{Das:2011:HSR,
  author =       "Malay Das and Amitabha Sinha and Nishant Kumar Giri",
  title =        "High speed residue number system ({RNS}) based {FIR}
                 filter using distributed arithmetic ({DA})",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "39",
  number =       "5",
  pages =        "1--4",
  month =        dec,
  year =         "2011",
  CODEN =        "CANED2",
  DOI =          "https://doi.org/10.1145/2093339.2093341",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Thu Mar 15 14:07:10 MDT 2012",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
}

@InProceedings{deDinechin:2011:AOY,
  author =       "Florent de Dinechin",
  title =        "The Arithmetic Operators You Will Never See in a
                 Microprocessor",
  crossref =     "Schwarz:2011:PIS",
  pages =        "189--190",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.33",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992125",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20",
}

@Article{deDinechin:2011:CFP,
  author =       "Florent de Dinechin and Christoph Lauter and Guillaume
                 Melquiond",
  title =        "Certifying the Floating-Point Implementation of an
                 Elementary Function Using {Gappa}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  number =       "2",
  pages =        "242--253",
  month =        feb,
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.128",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Feb 20 19:15:33 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  abstract =     "High confidence in floating-point programs requires
                 proving numerical properties of final and intermediate
                 values. One may need to guarantee that a value stays
                 within some range, or that the error relative to some
                 ideal value is well bounded. This certification may
                 require a time-consuming proof for each line of code,
                 and it is usually broken by the smallest change to the
                 code, e.g., for maintenance or optimization purpose.
                 Certifying floating-point programs by hand is,
                 therefore, very tedious and error-prone. The Gappa
                 proof assistant is designed to make this task both
                 easier and more secure, due to the following novel
                 features: It automates the evaluation and propagation
                 of rounding errors using interval arithmetic. Its input
                 format is very close to the actual code to validate. It
                 can be used incrementally to prove complex mathematical
                 properties pertaining to the code. It generates a
                 formal proof of the results, which can be checked
                 independently by a lower level proof assistant like
                 Coq. Yet it does not require any specific knowledge
                 about automatic theorem proving, and thus, is
                 accessible to a wide community. This paper demonstrates
                 the practical use of this tool for a widely used class
                 of floating-point programs: implementations of
                 elementary functions in a mathematical library.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{DelVento:2011:SLM,
  author =       "Davide {Del Vento} and Thomas Engel and Siddhartha S.
                 Ghosh and David L. Hart and Rory Kelly and Si Liu and
                 Richard Valent",
  title =        "System-level monitoring of floating-point performance
                 to improve effective system utilization",
  crossref =     "ACM:2011:SSP",
  pages =        "5:1--5:6",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/2063348.2063355",
  bibdate =      "Fri Dec 16 11:19:26 MST 2011",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/supercomputing2011.bib",
  acknowledgement = ack-nhfb,
  articleno =    "5",
}

@Article{Dimitrov:2011:AEM,
  author =       "Vassil S. Dimitrov and Kimmo U. Jarvinen and Jithra
                 Adikari",
  title =        "Area-Efficient Multipliers Based on Multiple-Radix
                 Representations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  number =       "2",
  pages =        "189--201",
  month =        feb,
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.200",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Feb 20 19:15:33 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Dimond:2011:ALS,
  author =       "Rob Dimond and Sebastien Racani{\`e}re and Oliver
                 Pell",
  title =        "Accelerating Large-Scale {HPC} Applications Using
                 {FPGAs}",
  crossref =     "Schwarz:2011:PIS",
  pages =        "191--192",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.34",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992126",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20",
}

@Article{Emmart:2011:HPI,
  author =       "Niall Emmart and Charles C. Weems",
  title =        "High Precision Integer Multiplication with a {GPU}
                 Using {Strassen}'s Algorithm with Multiple {FFT}
                 Sizes",
  journal =      j-PARALLEL-PROCESS-LETT,
  volume =       "21",
  number =       "3",
  pages =        "359--375",
  month =        sep,
  year =         "2011",
  CODEN =        "PPLTEE",
  DOI =          "https://doi.org/10.1142/S0129626411000266",
  ISSN =         "0129-6264 (print), 1793-642X (electronic)",
  bibdate =      "Tue Feb 28 11:32:08 MST 2012",
  bibsource =    "http://ejournals.wspc.com.sg/ppl/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/parallelprocesslett.bib",
  note =         "See earlier work \cite{Emmart:2010:HPI}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Parallel Processing Letters",
  journal-URL =  "http://www.worldscientific.com/loi/ppl",
  remark =       "The abstract reports an improvement (GPU compared to
                 GMP) of 13.9x to 19x for multiplication with operands
                 of 255Kbits to 16320Kbits, compared to earlier work
                 \cite{Emmart:2010:HPI}.",
}

@InProceedings{Fischer:2011:HIC,
  author =       "Ralf Fischer",
  title =        "High Intelligence Computing: The New Era of High
                 Performance Computing",
  crossref =     "Schwarz:2011:PIS",
  pages =        "3--3",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.42",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992102",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20",
}

@Article{Galal:2011:EEF,
  author =       "Sameh Galal and Mark Horowitz",
  title =        "Energy-Efficient Floating-Point Unit Design",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  number =       "7",
  pages =        "913--922",
  month =        jul,
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.121",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jun 29 10:26:18 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Galal:2011:LSF,
  author =       "Sameh Galal and Mark Horowitz",
  title =        "Latency Sensitive {FMA} Design",
  crossref =     "Schwarz:2011:PIS",
  pages =        "129--138",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.26",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992118",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20",
}

@InProceedings{Gandino:2011:GAI,
  author =       "Filippo Gandino and Fabrizio Lamberti and Paolo
                 Montuschi and Jean-Claude Bajard",
  title =        "A General Approach for Improving {RNS Montgomery}
                 Exponentiation Using Pre-processing",
  crossref =     "Schwarz:2011:PIS",
  pages =        "195--204",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.35",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992127",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20; residue number system (RNS)",
}

@Article{Garofalo:2011:ACM,
  author =       "Valeria Garofalo and Nicola Petra and Ettore Napoli",
  title =        "Analytical Calculation of the Maximum Error for a
                 Family of Truncated Multipliers Providing Minimum Mean
                 Square Error",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  number =       "9",
  pages =        "1366--1371",
  month =        sep,
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.236",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Aug 22 09:18:06 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5669274",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Gebali:2011:FPA,
  author =       "Fayez Gebali",
  booktitle =    "{Proceedings of the 2011 IEEE National Aerospace and
                 Electronics Conference (NAECON)}",
  title =        "Floating-point adaptive {CORDIC} ({FPA-CORDIC})
                 algorithm for elementary function calculation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "46--50",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/NAECON.2011.6183075",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Adaptive algorithms; Computers; Convergence; CORDIC;
                 DSP applications; Educational institutions; Elementary
                 function calculation; Equations; Mathematical model;
                 Merged scaling; Noise; Scientific calculations;
                 Vectors",
}

@InProceedings{Gonzalez-Espin:2011:ECA,
  author =       "Fran Gonz{\'a}lez-Esp{\'\i}n and Emilio Figueres and
                 Gabriel Garcer{\'a} and Iv{\'a}n Patrao",
  booktitle =    "{2011 IEEE International Symposium on Industrial
                 Electronics}",
  title =        "An efficient {CORDIC} arithmetic unit for 3-phase
                 voltage grid synchronization",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "125--130",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ISIE.2011.5984144",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Calculus; Harmonic analysis; Low pass filters; Power
                 harmonic filters; Synchronization; Topology",
}

@InProceedings{Gopikiran:2011:FIF,
  author =       "G. Gopikiran and R. Thilagavathy",
  booktitle =    "{2011 International Conference on Signal Processing,
                 Communication, Computing and Networking Technologies
                 (ICSCCN)}",
  title =        "{FPGA} implementation of floating-point rotation mode
                 {CORDIC} algorithm",
  publisher =    "pub-IEEE",
  address =      "pub-IEEE:adr",
  pages =        "506--508",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ICSCCN.2011.6024604",
  bibdate =      "Tue Sep 27 08:11:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6024604",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6016617",
}

@InProceedings{Gorgin:2011:FHR,
  author =       "Saeid Gorgin and Ghassem Jaberipur",
  title =        "A Family of High Radix Signed Digit Adders",
  crossref =     "Schwarz:2011:PIS",
  pages =        "112--120",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.24",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992116",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20",
}

@InProceedings{Goubault:2011:SAF,
  author =       "Eric Goubault and Sylvie Putot",
  editor =       "Ranjit Jhala and David A. Schmidt",
  booktitle =    "{VMCAI'11: Proceedings of the 12th international
                 conference on verification, model checking, and
                 abstract interpretation. Austin, TX, USA --- January
                 23--25, 2011}",
  title =        "Static Analysis of Finite Precision Computations",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "232--247",
  year =         "2011",
  ISBN =         "3-642-18274-7",
  ISBN-13 =      "978-3-642-18274-7",
  bibdate =      "Thu Oct 17 05:33:04 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=1946284.1946301",
  abstract =     "We define several abstract semantics for the static
                 analysis of finite precision computations, that bound
                 not only the ranges of values taken by numerical
                 variables of a program, but also the difference with
                 the result of the same sequence of operations in an
                 idealized real number semantics. These domains point
                 out with more or less detail (control point, block,
                 function for instance) sources of numerical errors in
                 the program and the way they were propagated by further
                 computations, thus allowing to evaluate not only the
                 rounding error, but also sensitivity to inputs or
                 parameters of the program. We describe two classes of
                 abstractions, a non relational one based on intervals,
                 and a weakly relational one based on parametrized
                 zonotopic abstract domains called affine sets,
                 especially well suited for sensitivity analysis and
                 test generation. These abstract domains are implemented
                 in the Fluctuat static analyzer, and we finally present
                 some experiments.",
  acknowledgement = ack-nhfb,
}

@Article{Graillat:2011:SAM,
  author =       "Stef Graillat and Fabienne J{\'e}z{\'e}quel and Shiyue
                 Wang and Yuxiang Zhu",
  title =        "Stochastic Arithmetic in Multiprecision",
  journal =      j-MATH-COMPUT-SCI,
  volume =       "5",
  number =       "4",
  pages =        "359--375",
  month =        dec,
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s11786-011-0103-4",
  ISSN =         "1661-8270 (print), 1661-8289 (electronic)",
  ISSN-L =       "1661-8270",
  bibdate =      "Tue Nov 6 10:16:23 MST 2012",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1661-8270&volume=5&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/math-comput-sci.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=1661-8270&volume=5&issue=4&spage=359",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics in Computer Science",
  journal-URL =  "http://www.springerlink.com/content/1661-8270/",
  keywords =     "interval arithmetic; MPFI; MPFR; multiprecision;
                 Stochastic Arithmetic in Multiprecision (SAM)",
}

@Article{Grcar:2011:JNA,
  author =       "Joseph F. Grcar",
  title =        "{John von Neumann}'s Analysis of {Gaussian}
                 Elimination and the Origins of Modern Numerical
                 Analysis",
  journal =      j-SIAM-REVIEW,
  volume =       "53",
  number =       "4",
  pages =        "607--682",
  month =        "????",
  year =         "2011",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/080734716",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "01-08, 65-03, 65F05, 65F35, 65G50, 65M12, 68-03, 65-03
                 (01A60 65F35 68-03)",
  MRnumber =     "2861262 (2012m:65001)",
  MRreviewer =   "Ilse C. F. Ipsen",
  bibdate =      "Fri Jun 21 11:25:02 MDT 2013",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/53/4;
                 http://epubs.siam.org/toc/siread/53/4;
                 https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "http://epubs.siam.org/sirev/resource/1/siread/v53/i4/p607_s1",
  abstract =     "Just when modern computers (digital, electronic, and
                 programmable) were being invented, John von Neumann and
                 Herman Goldstine wrote a paper to illustrate the
                 mathematical analyses that they believed would be
                 needed to use the new machines effectively and to guide
                 the development of still faster computers. Their
                 foresight and the congruence of historical events made
                 their work the first modern paper in numerical
                 analysis. Von Neumann once remarked that to found a
                 mathematical theory one had to prove the first theorem,
                 which he and Goldstine did for the accuracy of
                 mechanized Gaussian elimination --- but their paper was
                 about more than that. Von Neumann and Goldstine
                 described what they surmized would be the significant
                 questions once computers became available for
                 computational science, and they suggested enduring ways
                 to answer them.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  keywords =     "backward error, CFL condition, computer architecture,
                 computer arithmetic, computer programming, condition
                 number, decomposition paradigm, Gaussian elimination,
                 history, matrix norms, numerical analysis, rounding
                 error analysis, stability, stochastic linear algebra,
                 von Neumann",
  onlinedate =   "November 07, 2011",
}

@InProceedings{Gupta:2011:LPP,
  author =       "A. Gupta and S. Mandavalli and V. J. Mooney and
                 Keck-Voon Ling and A. Basu and H. Johan and B.
                 Tandianus",
  booktitle =    "{2011 IEEE Computer Society Annual Symposium on VLSI
                 (ISVLSI)}",
  title =        "Low Power Probabilistic Floating Point Multiplier
                 Design",
  publisher =    "pub-IEEE",
  address =      "pub-IEEE:adr",
  pages =        "182--187",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ISVLSI.2011.54",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992502",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5992458",
}

@Article{Guralnik:2011:SBV,
  author =       "Elena Guralnik and Merav Aharoni and Ariel J. Birnbaum
                 and Anatoly Koyfman",
  title =        "Simulation-Based Verification of Floating-Point
                 Division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  number =       "2",
  pages =        "176--188",
  month =        feb,
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.165",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Feb 20 19:15:33 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  abstract =     "Floating-point division is known to exhibit an
                 exceptionally wide array of corner cases, making its
                 verification a difficult challenge. Despite the
                 remarkable advances in formal methods, the intricacies
                 of this operation and its implementation often render
                 these inapplicable. Simulation-based methods remain the
                 primary means for verification of division. FPgen is a
                 test generation framework targeted at the floating
                 point datapath. It has been successfully used in the
                 simulation-based verification of a variety of hardware
                 designs. FPgen comprises a comprehensive test plan and
                 a powerful test generator. A proper response to the
                 difficulties posed by division constitutes a major part
                 of FPgen's capabilities. We present an overview of the
                 relevant verification tasks supplied with FPgen and the
                 underlying algorithms used to target them.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Han:2011:NDS,
  author =       "Liu Han and Dongdong Chen and Khan A. Wahid and
                 Seok-Bum Ko",
  booktitle =    "{2011 IEEE International Symposium on Circuits and
                 Systems (ISCAS)}",
  title =        "Nonspeculative decimal signed digit adder",
  publisher =    "pub-IEEE",
  address =      "pub-IEEE:adr",
  pages =        "1053--1056",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ISCAS.2011.5937750",
  bibdate =      "Tue Sep 27 08:11:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5937750",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5910713",
}

@Article{Hariri:2011:CED,
  author =       "Arash Hariri and Arash Reyhani-Masoleh",
  title =        "Concurrent Error Detection in {Montgomery}
                 Multiplication over Binary Extension Fields",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  number =       "9",
  pages =        "1341--1353",
  month =        sep,
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.258",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Aug 22 09:18:06 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5669280",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Haron:2011:RRN,
  author =       "Nor Zaidi Haron and Said Hamdioui",
  title =        "Redundant Residue Number System Code for
                 Fault-Tolerant Hybrid Memories",
  journal =      j-JETC,
  volume =       "7",
  number =       "1",
  pages =        "4:1--4:??",
  month =        jan,
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/1899390.1899394",
  ISSN =         "1550-4832 (print), 1550-4840 (electronic)",
  ISSN-L =       "1550-4832",
  bibdate =      "Mon Mar 28 12:17:03 MDT 2011",
  bibsource =    "http://www.acm.org/pubs/contents/journals/jetc/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  fjournal =     "ACM Journal on Emerging Technologies in Computing
                 Systems (JETC)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J967",
}

@Article{Harvey:2011:FAS,
  author =       "David Harvey",
  title =        "Faster algorithms for the square root and reciprocal
                 of power series",
  journal =      j-MATH-COMPUT,
  volume =       "80",
  number =       "273",
  pages =        "387--394",
  month =        jan,
  year =         "2011",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Wed Oct 13 16:46:42 MDT 2010",
  bibsource =    "http://www.ams.org/mcom/2011-80-273;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  URL =          "http://www.ams.org/journals/mcom/2011-80-273/S0025-5718-2010-02392-0/home.html;
                 http://www.ams.org/journals/mcom/2011-80-273/S0025-5718-2010-02392-0/S0025-5718-2010-02392-0.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@InProceedings{Harvey:2011:SDL,
  author =       "David Harvey and Paul Zimmermann",
  title =        "Short Division of Long Integers",
  crossref =     "Schwarz:2011:PIS",
  pages =        "7--14",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.11",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992103",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20",
}

@InProceedings{Holanda:2011:FBA,
  author =       "B. Holanda and R. Pimentel and J. Barbosa and R.
                 Camarotti and A. Silva-Filho and L. Joao and V. Souza
                 and J. Ferraz and M. Lima",
  booktitle =    "{2011 IEEE International Symposium on Parallel and
                 Distributed Processing Workshops and Phd Forum
                 (IPDPSW)}",
  title =        "An {FPGA}-Based Accelerator to Speed-Up Matrix
                 Multiplication of Floating Point Operations",
  publisher =    "pub-IEEE",
  address =      "pub-IEEE:adr",
  pages =        "306--309",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/IPDPS.2011.165",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6008910",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6008655",
}

@Article{Hong:2011:EOS,
  author =       "Wonhak Hong and Rajashekhar Modugu and Minsu Choi",
  title =        "Efficient Online Self-Checking Modulo $ 2^n + 1 $
                 Multiplier Design",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  number =       "9",
  pages =        "1354--1365",
  month =        sep,
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.49",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Aug 22 09:18:06 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5962404",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Hsiao:2011:DLC,
  author =       "Shen-Fu Hsiao and Chan-Feng Chiu and Chia-Sheng Wen",
  booktitle =    "{2011 IEEE International Conference on IC Design \&
                 Technology (ICICDT)}",
  title =        "Design of a low-cost floating-point programmable
                 vertex processor for mobile graphics applications based
                 on hybrid number system",
  publisher =    "pub-IEEE",
  address =      "pub-IEEE:adr",
  pages =        "1--4",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ICICDT.2011.5783231",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5783231",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5773347",
}

@Article{Huang:2011:LCB,
  author =       "L. Huang and S. Ma and L. Shen and Z. Wang and N.
                 Xiao",
  title =        "Low Cost {Binary128} floating-point {FMA} Unit Design
                 with {SIMD} Support",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "PP",
  number =       "99",
  pages =        "1",
  month =        "????",
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2011.77",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5740858",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  book-URL =     "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Huang:2011:NHA,
  author =       "Miaoqing Huang and Kris Gaj and Tarek El-Ghazawi",
  title =        "New Hardware Architectures for {Montgomery} Modular
                 Multiplication Algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  number =       "7",
  pages =        "923--936",
  month =        jul,
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.247",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jun 29 10:26:18 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Huynh:2011:EAP,
  author =       "Thang Viet Huynh and Manfred Mucke",
  booktitle =    "{2011 International Conference on Advanced
                 Technologies for Communications (ATC)}",
  title =        "Error analysis and precision estimation for
                 floating-point dot-products using affine arithmetic",
  publisher =    "pub-IEEE",
  address =      "pub-IEEE:adr",
  pages =        "319--322",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ATC.2011.6027495",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6027495",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6022617",
}

@Article{Ibrahim:2011:PAA,
  author =       "Atef Ibrahim and Fayez Gebali and Hamed Elsimary and
                 Amin Nassar",
  title =        "Processor Array Architectures for Scalable Radix $4$
                 {Montgomery} Modular Multiplication Algorithm",
  journal =      j-IEEE-TRANS-PAR-DIST-SYS,
  volume =       "22",
  number =       "7",
  pages =        "1142--1149",
  month =        jul,
  year =         "2011",
  CODEN =        "ITDSEO",
  DOI =          "https://doi.org/10.1109/TPDS.2010.196",
  ISSN =         "1045-9219 (print), 1558-2183 (electronic)",
  ISSN-L =       "1045-9219",
  bibdate =      "Fri Jul 22 07:54:38 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranspardistsys.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Parallel Distrib. Syst.",
  fjournal =     "IEEE Transactions on Parallel and Distributed
                 Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=71",
}

@Article{Ikhile:2011:RBD,
  author =       "M. N. O. Ikhile",
  title =        "The root and {Bell}'s disk iteration methods are of
                 the same error propagation characteristics in the
                 simultaneous determination of the zeros of a
                 polynomial, Part {II}: Round-off error analysis by use
                 of interval arithmetic",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "61",
  number =       "11",
  pages =        "3191--3217",
  month =        jun,
  year =         "2011",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:50:47 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122111002860",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@InProceedings{Ismail:2011:RLL,
  author =       "R. Che Ismail and J. N. Coleman",
  title =        "{ROM}-less {LNS}",
  crossref =     "Schwarz:2011:PIS",
  pages =        "43--51",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.15",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992107",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20; logarithmic number system (LNS)",
}

@Book{ISO:2011:III,
  author =       "{ISO}",
  title =        "{ISO/IEC/IEEE 60559:2011 Information technology ---
                 Microprocessor Systems --- Floating-Point arithmetic}",
  publisher =    pub-ISO,
  address =      pub-ISO:adr,
  pages =        "58",
  year =         "2011",
  bibdate =      "Fri Jul 15 12:50:32 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=57469",
  abstract =     "ISO/IEC/IEEE 60559:2011(E) specifies formats and
                 methods for floating-point arithmetic in computer
                 systems --- standard and extended functions with
                 single, double, extended, and extendable precision and
                 recommends formats for data interchange. Exception
                 conditions are defined and standard handling of these
                 conditions is specified. It provides a method for
                 computation with floating-point numbers that will yield
                 the same result whether the processing is done in
                 hardware, software, or a combination of the two. The
                 results of the computation will be identical,
                 independent of implementation, given the same input
                 data. Errors, and error conditions, in the mathematical
                 processing will be reported in a consistent manner
                 regardless of implementation. This first edition,
                 published as ISO/IEC/IEEE 60559, replaces the second
                 edition of IEC 60559.",
  acknowledgement = ack-nhfb,
  xxISBN =       "????",
  xxLCCN =       "????",
}

@Article{Izsak:2011:CPM,
  author =       "Alexander Izsak and Nicholas Pippenger",
  title =        "Carry propagation in multiplication by constants",
  journal =      j-TALG,
  volume =       "7",
  number =       "4",
  pages =        "54:1--54:??",
  month =        sep,
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2000807.2000822",
  ISSN =         "1549-6325 (print), 1549-6333 (electronic)",
  ISSN-L =       "1549-6325",
  bibdate =      "Sat Oct 22 09:20:09 MDT 2011",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/talg.bib",
  acknowledgement = ack-nhfb,
  articleno =    "54",
  fjournal =     "ACM Transactions on Algorithms (TALG)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J982",
}

@Article{Jaime:2011:HSA,
  author =       "F. J. Jaime and M. A. S{\'a}nchez and J. Hormigo and
                 J. Villalba and E. L. Zapata",
  title =        "High-Speed Algorithms and Architectures for Range
                 Reduction Computation",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "19",
  number =       "3",
  pages =        "512--516",
  month =        "????",
  year =         "2011",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/TVLSI.2009.2033932",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5308221",
  abstract =     "Range reduction is a crucial step for accuracy in
                 trigonometric functions evaluation. This paper shows
                 and compares a set of algorithms for additive range
                 reduction computation and their corresponding
                 application-specific integrated circuit implementations
                 (ensuring an accuracy of one unit in the last place). A
                 word-serial architecture implementation has been used
                 as a reference for clearer comparisons. Besides, a new
                 table-based pipelined architecture for range reduction
                 has also been proposed.",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=92",
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
}

@Article{Jaiswal:2011:HPF,
  author =       "Manish Kumar Jaiswal and Ray C. C. Cheung",
  title =        "High Performance {FPGA} Implementation of Double
                 Precision Floating Point Adder\slash Subtractor",
  journal =      "International Journal of Hybrid Information
                 Technology: IJHIT",
  volume =       "4",
  number =       "4",
  pages =        "71--80",
  month =        oct,
  year =         "2011",
  DOI =          "https://doi.org/10.14257/ijhit.2011.4.4.06",
  ISSN =         "1738-9968 (print), 2652-2233 (electronic)",
  bibdate =      "Mon Apr 20 10:04:06 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://gvpress.com/journals/IJHIT/vol4_no4/6.pdf",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://gvpress.com/journals/IJHIT/",
}

@Article{Janhunen:2011:FFP,
  author =       "J. Janhunen and T. Pitkanen and O. Silven and M.
                 Juntti",
  title =        "Fixed- and floating-point Processor Comparison for
                 {MIMO--OFDM} Detector",
  journal =      "IEEE Journal of Selected Topics in Signal Processing",
  volume =       "5",
  number =       "8",
  pages =        "1588--1598",
  month =        dec,
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/JSTSP.2011.2165830",
  ISSN =         "1932-4553 (print), 1941-0484 (electronic)",
  ISSN-L =       "1932-4553",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5995137",
  acknowledgement = ack-nhfb,
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4200690",
}

@InProceedings{Janhunen:2011:FVF,
  author =       "J. Janhunen and P. Salmela and O. Silven and M.
                 Juntti",
  booktitle =    "{2011 IEEE International Conference on Acoustics,
                 Speech and Signal Processing (ICASSP)}",
  title =        "Fixed- versus floating-point implementation of
                 {MIMO--OFDM} detector",
  publisher =    "pub-IEEE",
  address =      "pub-IEEE:adr",
  pages =        "3276--3279",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ICASSP.2011.5946721",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5946721",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5916934",
}

@Article{Jeannerod:2011:CFP,
  author =       "Claude-Pierr Jeannerod and Herv{\'e} Knochel and
                 Christophe Monat and Guillaume Revy",
  title =        "Computing Floating-Point Square Roots via Bivariate
                 Polynomial Evaluation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  number =       "2",
  pages =        "214--227",
  month =        feb,
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.152",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Feb 20 19:15:33 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  abstract =     "In this paper, we show how to reduce the computation
                 of correctly rounded square roots of binary
                 floating-point data to the fixed-point evaluation of
                 some particular integer polynomials in two variables.
                 By designing parallel and accurate evaluation schemes
                 for such bivariate polynomials, we show further that
                 this approach allows for high instruction-level
                 parallelism (ILP) exposure, and thus, potentially
                 low-latency implementations. Then, as an illustration,
                 we detail a C implementation of our method in the case
                 of IEEE 754-2008 binary32 floating-point data (formerly
                 called single precision in the 1985 version of the IEEE
                 754 standard). This software implementation, which
                 assumes 32-bit unsigned integer arithmetic only, is
                 almost complete in the sense that it supports special
                 operands, subnormal numbers, and all rounding-direction
                 attributes, but not exception handling (that is, status
                 flags are not set). Finally, we have carried out
                 experiments with this implementation on the ST231, an
                 integer processor from the STMicroelectronics' ST200
                 family, using the ST200 family VLIW compiler. The
                 results obtained demonstrate the practical interest of
                 our approach in that context: for all
                 rounding-direction attributes, the generated assembly
                 code is optimally scheduled and has indeed low latency
                 (23 cycles).",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Jeannerod:2011:HSF,
  author =       "Claude-Pierre Jeannerod and Jingyan Jourdan-Lu and
                 Christophe Monat and Guillaume Revy",
  title =        "How to Square Floats Accurately and Efficiently on the
                 {ST231} Integer Processor",
  crossref =     "Schwarz:2011:PIS",
  pages =        "77--81",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.19",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992111",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20",
}

@Article{Jeannerod:2011:MEP,
  author =       "Claude-Pierre Jeannerod and Nicolas Louvet and
                 Jean-Michel Muller and Adrien Panhaleux",
  title =        "Midpoints and Exact Points of Some Algebraic Functions
                 in Floating-Point Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  number =       "2",
  pages =        "228--241",
  month =        feb,
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.144",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Feb 20 19:15:33 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  abstract =     "When implementing a function $f$ in floating-point
                 arithmetic, if we wish correct rounding and good
                 performance, it is important to know if there are input
                 floating-point values $x$ such that $ f(x) $ is either
                 the middle of two consecutive floating-point numbers
                 (assuming rounded-to-nearest arithmetic), or a
                 floating-point number (assuming rounded toward $ \pm
                 \infty $ or toward $0$ arithmetic). In the first case,
                 we say that $ f(x) $ is a midpoint, and in the second
                 case, we say that $ f(x) $ is an exact point. For some
                 usual algebraic functions and various floating-point
                 formats, we prove whether or not there exist midpoints
                 or exact points. When there exist midpoints or exact
                 points, we characterize them or list all of them (if
                 there are not too many). The results and the techniques
                 presented in this paper can be used in particular to
                 deal with both the binary and the decimal formats
                 defined in the IEEE 754-2008 standard for
                 floating-point arithmetic.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Jiang:2011:AEP,
  author =       "Hao Jiang and Roberto Barrio and Housen Li and Xiangke
                 Liao and Lizhi Cheng and Fang Su",
  title =        "Accurate evaluation of a polynomial in {Chebyshev}
                 form",
  journal =      j-APPL-MATH-COMP,
  volume =       "217",
  number =       "23",
  pages =        "9702--9716",
  day =          "1",
  month =        aug,
  year =         "2011",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2011.04.054",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Oct 25 12:05:42 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300311006242",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Kainuma:2011:DIC,
  author =       "T. Kainuma and Y. Shimamura and F. Miyaoka and Y.
                 Yamanashi and N. Yoshikawa and A. Fujimaki and K.
                 Takagi and N. Takagi and S. Nagasawa",
  title =        "Design and Implementation of Component Circuits of an
                 {SFQ} Half-Precision floating-point Adder Using
                 {10-kA\slash cm$^2$ Nb} Process",
  journal =      j-IEEE-TRANS-APPL-SUPERCOND,
  volume =       "21",
  number =       "3",
  pages =        "827--830",
  month =        "????",
  year =         "2011",
  CODEN =        "ITASE9",
  DOI =          "https://doi.org/10.1109/TASC.2010.2096374",
  ISSN =         "1051-8223 (print), 1558-2515 (electronic)",
  ISSN-L =       "1051-8223",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5680618",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=77",
  fjournal =     "IEEE Transactions on Applied Superconductivity",
}

@Article{Kaivani:2011:DCR,
  author =       "Amir Kaivani and Ghassem Jaberipur",
  title =        "Decimal {CORDIC} Rotation based on Selection by
                 Rounding: Algorithm and Architecture",
  journal =      j-COMP-J,
  volume =       "54",
  number =       "11",
  pages =        "1798--1809",
  month =        nov,
  year =         "2011",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/bxr012",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Oct 28 10:35:35 MDT 2011",
  bibsource =    "http://comjnl.oxfordjournals.org/content/54/11.toc;
                 https://www.math.utah.edu/pub/tex/bib/compj2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Hardware implementation of decimal floating-point
                 arithmetic is a topic of great interest among the
                 researchers in computer arithmetic and also the digital
                 processor industry. Software packages for decimal
                 arithmetic are actually being challenged by decimal
                 hardware units. This spreading trend seems to include
                 hardware implementation of elementary functions. The
                 (Coordinate Rotation Digital Computer) CORDIC
                 algorithm, due to its simplicity, is one of the most
                 efficient methods for computing elementary functions.
                 In this work, we develop a decimal CORDIC scheme with
                 almost half number of equally long cycles with respect
                 to the best previous design. This is achieved via
                 retiming of the conventional CORDIC architecture and
                 selection of the microrotation factors by rounding.
                 However, the proposed design does not lead to a
                 predetermined constant scaling factor. The solution
                 that we use is to iteratively compute the logarithm of
                 the scaling factor followed by a decimal
                 exponentiation. The same CORDIC hardware is reused for
                 performing the latter. The proposed CORDIC method
                 requires $ 2 n + 3 $ cycles for $n$-digit decimal
                 operands vs. $ 4 n $ cycles of the previous methods.
                 Evaluations with 16-digit operands based on logical
                 effort analysis conclude that the proposed architecture
                 shows 82\% speed advantage, at the cost of 60\% more
                 area and 2.5 KB more ROM.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  onlinedate =   "March 11, 2011",
}

@InProceedings{Kathiara:2011:AVS,
  author =       "J. Kathiara and M. Leeser",
  booktitle =    "{2011 IEEE 19th Annual International Symposium on
                 Field-Programmable Custom Computing Machines (FCCM)}",
  title =        "An Autonomous Vector\slash Scalar Floating Point
                 Coprocessor for {FPGAs}",
  publisher =    "pub-IEEE",
  address =      "pub-IEEE:adr",
  pages =        "33--36",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/FCCM.2011.14",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5771244",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5771180",
}

@Article{Kim:2011:ZAS,
  author =       "SeongKi Kim and HaYoon Song and SangYong Han",
  title =        "{ZipfAllocation}: an algorithm for static allocation
                 of movies in a cluster of video servers",
  journal =      j-SPE,
  volume =       "41",
  number =       "6",
  pages =        "695--716",
  month =        may,
  year =         "2011",
  CODEN =        "SPEXBL",
  DOI =          "https://doi.org/10.1002/spe.1027",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Tue Jun 21 17:09:57 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Software---Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  onlinedate =   "25 Nov 2010",
}

@Article{Kong:2011:GDM,
  author =       "Inwook Kong and Earl E. Swartzlander",
  title =        "A {Goldschmidt} Division Method With Faster Than
                 Quadratic Convergence",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "19",
  number =       "4",
  pages =        "696--700",
  month =        apr,
  year =         "2011",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/tvlsi.2009.2036926",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Mon Dec 11 08:01:22 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A new method to implement faster than quadratic
                 convergence for Goldschmidt division using simple logic
                 circuits is presented. While the approximate quotient
                 converges quadratically in conventional Goldschmidt
                 division, the new method achieves nearly cubic
                 convergence. Although division with cubic convergence
                 has been regarded as impractical due to its complexity,
                 the proposed method reduces the logic complexity and
                 the delay by using an approximate squarer with a simple
                 logic implementation and a redundant binary Booth
                 recoder. It is especially effective in a system that
                 already has a radix-8 multiplier. As a result, the
                 effective area for the reciprocal table can be reduced
                 by 25.4\%. The proposed method has been verified by
                 SystemC and Verilog models. The final results are
                 confirmed by simulation with both random double
                 precision numbers and an exhaustive suite of 17-bit
                 test vectors.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
}

@Article{Kornerup:2011:PAO,
  author =       "Peter Kornerup and Jean-Michel Muller and Adrien
                 Panhaleux",
  title =        "Performing Arithmetic Operations on Round-to-Nearest
                 Representations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  number =       "2",
  pages =        "282--291",
  month =        feb,
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.134",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Feb 20 19:15:33 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  abstract =     "During any composite computation, there is a constant
                 need for rounding intermediate results before they can
                 participate in further processing. Recently, a class of
                 number representations denoted RN-Codings were
                 introduced, allowing an unbiased rounding-to-nearest to
                 take place by a simple truncation, with the property
                 that problems with double-roundings are avoided. In
                 this paper, we first investigate a particular encoding
                 of the binary representation. This encoding is
                 generalized to any radix and digit set; however, radix
                 complement representations for even values of the radix
                 turn out to be particularly feasible. The encoding is
                 essentially an ordinary radix complement representation
                 with an appended round-bit, but still allowing
                 rounding-to-nearest by truncation, and thus avoiding
                 problems with double-roundings. Conversions from radix
                 complement to these round-to-nearest representations
                 can be performed in constant time, whereas conversion
                 the other way, in general, takes at least logarithmic
                 time. Not only is rounding-to-nearest a constant time
                 operation, but so is also sign inversion, both of which
                 are at best log-time operations on ordinary two's
                 complement representations. Addition and multiplication
                 on such fixed-point representations are first analyzed
                 and defined in such a way that rounding information can
                 be carried along in a meaningful way, at minimal cost.
                 The analysis is carried through for a compact
                 (canonical) encoding using two's complement
                 representation, supplied with a round-bit. Based on the
                 fixed-point encoding, it is shown possible to define
                 floating-point representations, and a sketch of the
                 implementation of an FPU is presented.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Kulisch:2011:EDP,
  author =       "Ulrich Kulisch and Van Snyder",
  title =        "The exact dot product as basic tool for long interval
                 arithmetic",
  journal =      j-COMPUTING,
  volume =       "91",
  number =       "3",
  pages =        "307--313",
  month =        mar,
  year =         "2011",
  CODEN =        "CMPTA2",
  DOI =          "https://doi.org/10.1007/s00607-010-0127-7",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Sep 6 19:14:24 MDT 2011",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=91&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=91&issue=3&spage=307",
  abstract =     "Computing with guarantees is based on two arithmetical
                 features. One is fixed (double) precision interval
                 arithmetic. The other one is dynamic precision interval
                 arithmetic, here also called long interval arithmetic.
                 The basic tool to achieve high speed dynamic precision
                 arithmetic for real and interval data is an exact
                 multiply and accumulate operation and with it an exact
                 dot product. Pipelining allows to compute it at the
                 same high speed as vector operations on conventional
                 vector processors. Long interval arithmetic fully
                 benefits from such high speed. Exactitude brings very
                 high accuracy, and thereby stability into computation.
                 This document, which has been incorporated into the
                 draft standard for interval arithmetic being developed
                 by IEEE P1788, specifies the implementation of an exact
                 multiply and accumulate operation.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "arithmetic standard; computer arithmetic; exact dot
                 product; floating-point arithmetic; scientific
                 computing",
  remark =       "This document is an identical copy of a motion
                 accepted by the international standards committee IEEE
                 P1788 on interval arithmetic. Its contents will be
                 published in a few years when the development of the
                 standard is completed. The new floating-point
                 arithmetic standard IEEE 754 (available since 2008)
                 provides a function for accumulation of the dot product
                 of two vectors with no accuracy requirement.
                 Manufacturers who support the dot product by hardware
                 should be aware that IEEE P1788 requires the exact
                 result. Once a weak solution has been put into hardware
                 it may be difficult to change it later. It is therefore
                 important to bring this decision to public attention as
                 soon as possible. Actually the simplest and fastest way
                 for computing a dot product is to compute it exactly
                 [4].",
}

@Article{Kulisch:2011:VFE,
  author =       "Ulrich Kulisch",
  title =        "Very fast and exact accumulation of products",
  journal =      j-COMPUTING,
  volume =       "91",
  number =       "4",
  pages =        "397--405",
  month =        apr,
  year =         "2011",
  CODEN =        "CMPTA2",
  DOI =          "https://doi.org/10.1007/s00607-010-0131-y",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Sep 6 19:14:31 MDT 2011",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=91&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=91&issue=4&spage=397",
  abstract =     "The IFIP Working Group on Numerical Software and other
                 scientists repeatedly requested that a future
                 arithmetic standard should consider and specify an
                 exact dot product (EDP) [The IFIP WG IEEE 754R letter,
                 dated September 4 (2007), The IFIP WG IEEE P1788
                 letter, dated September 9 (2009)]. On 18 November 2009
                 the IEEE standards committee P1788 on interval
                 arithmetic accepted a motion [Kulisch and Snyder (The
                 exact dot product as basic tool for long interval
                 arithmetic, passed on Nov 18, 2009 as official IEEE
                 P1788 document)] for including the EDP into a future
                 interval arithmetic standard. Actually the simplest and
                 fastest way for computing a dot product is to compute
                 it exactly. By pipelining, it can be computed in the
                 time the processor needs to read the data, i.e., it
                 comes with utmost speed. A hardware implementation of
                 the EDP exceeds any approximate computation of the dot
                 product in software by several orders of magnitude. By
                 a sample illustration the paper informally specifies
                 the implementation of the EDP on computers. While
                 [Kulisch and Snyder (The exact dot product as basic
                 tool for long interval arithmetic, passed on Nov 18,
                 2009 as official IEEE P1788 document)] defines what has
                 to be provided, how to embed the EDP into the new
                 standard IEEE 754, [IEEE Floating-Point Arithmetic
                 Standard 754 (2008)] and how exceptions like NaN are to
                 be dealt with, this article illustrates how the EDP can
                 be implemented on computers. There is indeed no simpler
                 way of accumulating a dot product. Any method that just
                 computes an approximation also has to consider the
                 relative values of the summands. This results in a more
                 complicated method. The hardware needed for the EDP is
                 comparable to that for a fast multiplier by an adder
                 tree, accepted years ago and now standard technology in
                 every modern processor. The EDP brings the same speedup
                 for accumulations at comparable costs. In Numerical
                 Analysis the dot product is ubiquitous. It is not
                 merely a fundamental operation in all vector and matrix
                 spaces. It is the EDP which makes residual correction
                 effective. This has a direct and positive influence on
                 all iterative solvers of systems of equations. The EDP
                 is essential for fast long real and long interval
                 arithmetic, as well as for assessing and managing
                 uncertainty in computing. By operator overloading
                 variable precision interval arithmetic is very easy to
                 use. With it the result of every arithmetic expression
                 can be guaranteed to a number of correct digits.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "arithmetic standards; computer arithmetic; exact dot
                 product; floating-point arithmetic; scientific
                 computing",
}

@Article{Lamberti:2011:RCT,
  author =       "Fabrizio Lamberti and Nikos Andrikos and Elisardo
                 Antelo and Paolo Montuschi",
  title =        "Reducing the Computation Time in (Short Bit-Width)
                 Two's Complement Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  number =       "2",
  pages =        "148--156",
  month =        feb,
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.156",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Feb 20 19:15:33 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Langhammer:2011:TFD,
  author =       "Martin Langhammer",
  title =        "Teraflop {FPGA} Design",
  crossref =     "Schwarz:2011:PIS",
  pages =        "187--188",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.32",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992124",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20",
}

@TechReport{Lefevre:2011:SSI,
  author =       "Vincent Lef{\`e}vre",
  title =        "{SIPE}: Small Integer Plus Exponent",
  institution =  "INRIA",
  address =      "Lyon, France",
  pages =        "25",
  year =         "2011",
  bibdate =      "Tue Dec 26 14:57:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://hal.inria.fr/hal-00650659",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lei:2011:FIV,
  author =       "Yuanwu Lei and Yong Dou and Song Guo and Jie Zhou",
  editor =       "Olivier Temam and Pen-Chung Yew and Binyu Zang",
  booktitle =    "Advanced Parallel Processing Technologies: {9th
                 International Symposium, APPT 2011, Shanghai, China,
                 September 26--27, 2011, Proceedings}",
  title =        "{FPGA} Implementation of Variable-Precision
                 Floating-Point Arithmetic",
  volume =       "6965",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "127--141",
  year =         "2011",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-642-24151-2_10",
  ISBN =         "3-642-24151-4",
  ISBN-13 =      "978-3-642-24151-2",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Wed Jun 12 16:52:47 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
}

@InProceedings{Lei:2011:VSP,
  author =       "Yuanwu Lei and Yong Dou and Jie Zhou and Sufeng Wang",
  editor =       "Peter Athanas and Dionisios Pnevmatikatos and Nicolas
                 Sklavos",
  booktitle =    "21st International Conference on Field Programmable
                 Logic and Applications: {FPL 2011, 5--7 September 2011,
                 Chania, Greece}",
  title =        "{VPFPAP}: A Special-Purpose {VLIW} Processor for
                 Variable-Precision Floating-Point Arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "252--257",
  month =        sep,
  year =         "2011",
  DOI =          "https://doi.org/10.1109/fpl.2011.51",
  bibdate =      "Wed Jun 12 16:41:42 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  book-URL =     "https://ieeexplore.ieee.org/xpl/conhome/6044763/proceeding",
}

@InProceedings{Lipetz:2011:SCC,
  author =       "Daniel Lipetz and Eric Schwarz",
  title =        "Self Checking in Current Floating-Point Units",
  crossref =     "Schwarz:2011:PIS",
  pages =        "73--76",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.18",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992110",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20",
}

@Article{Liu:2011:FAH,
  author =       "Feng Liu and Xiaoyu Song and Qingping Tan and Gang
                 Chen",
  title =        "Formal Analysis of Hybrid Prefix\slash Carry-Select
                 Arithmetic Systems",
  journal =      j-COMP-J,
  volume =       "54",
  number =       "6",
  pages =        "894--904",
  month =        jun,
  year =         "2011",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/bxq048",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Wed Jun 1 18:54:12 MDT 2011",
  bibsource =    "content/54/6.toc;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/54/6/894.full.pdf+html",
  abstract =     "Arithmetic circuits play an important role in
                 high-performance digital systems. The paper considers a
                 generic architecture of hybrid prefix\slash
                 carry-select arithmetic systems. A novel proof
                 methodology is proposed to model and verify hybrid
                 addition systems. Algebraic structures and first-order
                 recursive equations are harnessed in proof derivations.
                 Case studies on several typical classes of hybrid
                 prefix\slash carry-select adders and special cases with
                 pseudo-carries such as Ling's carry demonstrate the
                 effectiveness of the proposed approach.",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "carry-select adders; computer arithmetic; formal
                 methods; parallel prefix adders",
  onlinedate =   "May 25, 2010",
}

@InProceedings{Liu:2011:ILC,
  author =       "Yuanlong Liu and Bateer and Wen Zhong",
  booktitle =    "{2011 International Conference on Computer Science and
                 Service System (CSSS)}",
  title =        "Implementation of a low complexity divider for
                 {ILUT}-based {FPGAs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "464--466",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/CSSS.2011.5974453",
  bibdate =      "Tue Sep 27 08:11:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5974453",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5959270",
}

@InProceedings{Lutz:2011:FMA,
  author =       "David R. Lutz",
  title =        "Fused Multiply-Add Microarchitecture Comprising
                 Separate Early-Normalizing Multiply and Add Pipelines",
  crossref =     "Schwarz:2011:PIS",
  pages =        "123--128",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.25",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992117",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20",
}

@InProceedings{Malone:2011:FBI,
  author =       "A. N. Malone and G. R. Morris and K. H. Abed",
  booktitle =    "{Southeastcon, 2011 Proceedings of IEEE}",
  title =        "{FPGA}-based implementation of {Horner}'s rule on a
                 high performance heterogeneous computer",
  publisher =    "pub-IEEE",
  address =      "pub-IEEE:adr",
  pages =        "277--282",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/SECON.2011.5752949",
  bibdate =      "Tue Sep 27 08:11:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5752949",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5746658",
}

@Article{Masakova:2011:ANS,
  author =       "Z. Mas{\'a}kov{\'a} and E. Pelantov{\'a} and T.
                 V{\'a}vra",
  title =        "Arithmetics in number systems with a negative base",
  journal =      j-THEOR-COMP-SCI,
  volume =       "412",
  number =       "8--10",
  pages =        "835--845",
  day =          "4",
  month =        mar,
  year =         "2011",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Aug 31 10:15:30 MDT 2011",
  bibsource =    "http://www.sciencedirect.com/science/journal/03043975;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}

@InProceedings{Matula:2011:PLP,
  author =       "David W. Matula and Mihai T. Panu",
  title =        "A Prescale-Lookup-Postscale Additive Procedure for
                 Obtaining a Single Precision Ulp Accurate Reciprocal",
  crossref =     "Schwarz:2011:PIS",
  pages =        "177--183",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.31",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992123",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20",
}

@InProceedings{Mauer:2011:FPS,
  author =       "V. Mauer and M. Parker",
  booktitle =    "{Radar Conference (RADAR), 2011 IEEE}",
  title =        "Floating point {STAP} implementation on {FPGAs}",
  publisher =    "pub-IEEE",
  address =      "pub-IEEE:adr",
  pages =        "901--904",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/RADAR.2011.5960667",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5960667",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5941184",
}

@InProceedings{Minchola:2011:FID,
  author =       "C. Minchola and M. Vazquez and G. Sutter",
  booktitle =    "{2011 VII Southern Conference on Programmable Logic
                 (SPL)}",
  title =        "A {FPGA} {IEEE-754-2008} decimal64 floating-point
                 adder\slash subtractor",
  publisher =    "pub-IEEE",
  address =      "pub-IEEE:adr",
  pages =        "251--256",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/SPL.2011.5782657",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5782657",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5771182",
  keywords =     "decimal floating-point arithmetic",
}

@Article{Moller:2011:IDI,
  author =       "Niels M{\"o}ller and Torbj{\"o}rn Granlund",
  title =        "Improved Division by Invariant Integers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  number =       "2",
  pages =        "165--175",
  month =        feb,
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.143",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sun Feb 20 19:15:33 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  abstract =     "This paper considers the problem of dividing a
                 two-word integer by a single-word integer, together
                 with a few extensions and applications. Due to lack of
                 efficient division instructions in current processors,
                 the division is performed as a multiplication using a
                 precomputed single-word approximation of the reciprocal
                 of the divisor, followed by a couple of adjustment
                 steps. There are three common types of unsigned
                 multiplication instructions: we define full word
                 multiplication (umul), which produces the two-word
                 product of two single-word integers; low multiplication
                 (umullo), which produces only the least significant
                 word of the product; and high multiplication (umulhi),
                 which produces only the most significant word. We
                 describe an algorithm that produces a quotient and
                 remainder using one umul and one umullo. This is an
                 improvement over earlier methods, since the new method
                 uses cheaper multiplication operations. It turns out
                 that we also get some additional savings from simpler
                 adjustment conditions. The algorithm has been
                 implemented in version 4.3 of the gmp library. When
                 applied to the problem of dividing a large integer by a
                 single word, the new algorithm gives a speedup of
                 roughly 30 percent, benchmarked on AMD and Intel
                 processors in the x86\_64 family.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Mouilleron:2011:AGF,
  author =       "Christophe Mouilleron and Guillaume Revy",
  title =        "Automatic Generation of Fast and Certified Code for
                 Polynomial Evaluation",
  crossref =     "Schwarz:2011:PIS",
  pages =        "233--242",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.39",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992131",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20",
}

@InProceedings{Nannarelli:2011:RCD,
  author =       "Alberto Nannarelli",
  title =        "Radix-16 Combined Division and Square Root Unit",
  crossref =     "Schwarz:2011:PIS",
  pages =        "169--176",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.30",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992122",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20; sqrt(x); square root",
}

@InCollection{Nguyen:2011:FSA,
  author =       "Hong Diep Nguyen and Bogdan Pasca and Thomas B.
                 Preu{\ss}er",
  editor =       "Peter Athanas and Dionisios Pnevmatikatos and Nicolas
                 Sklavos",
  booktitle =    "{21st International Conference on Field Programmable
                 Logic and Applications: FPL 2011: proceedings: 5--7
                 September 2011, Chania, Greece}",
  title =        "{FPGA}-specific arithmetic optimizations of
                 short-latency adders",
  publisher =    "pub-IEEE",
  address =      "pub-IEEE:adr",
  bookpages =    "xxviii + 560",
  pages =        "232--237",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/FPL.2011.49",
  ISBN =         "0-7695-4529-7",
  ISBN-13 =      "978-0-7695-4529-5",
  LCCN =         "TK7895.G36",
  bibdate =      "Sat Feb 08 09:55:40 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/document/6044770",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/servlet/opac?punumber=6044763",
}

@Article{Ozaki:2011:TEE,
  author =       "Katsuhisa Ozaki and Takeshi Ogita and Shin'ichi
                 Oishi",
  title =        "Tight and efficient enclosure of matrix multiplication
                 by using optimized {BLAS}",
  journal =      j-NUM-LIN-ALG-APPL,
  volume =       "18",
  number =       "2",
  pages =        "237--248",
  month =        mar,
  year =         "2011",
  CODEN =        "NLAAEM",
  DOI =          "https://doi.org/10.1002/nla.724",
  ISSN =         "1070-5325 (print), 1099-1506 (electronic)",
  ISSN-L =       "1070-5325",
  bibdate =      "Wed Mar 16 10:14:59 MDT 2011",
  bibsource =    "http://www.interscience.wiley.com/jpages/1070-5325;
                 http://www3.interscience.wiley.com/journalfinder.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper is concerned with the tight enclosure of
                 matrix multiplication $ A B $ for two floating-point
                 matrices $A$ and $B$. The aim of this paper is to
                 compute component-wise upper and lower bounds of the
                 exact result $C$ of the matrix multiplication $ A B $
                 by floating-point arithmetic. Namely, an interval
                 matrix enclosing $C$ is obtained. In this paper, new
                 algorithms for enclosing $C$ are proposed. The proposed
                 algorithms are designed to mainly exploit the level 3
                 operations in BLAS. Although the proposed algorithms
                 take around twice as much costs as a standard algorithm
                 promoted by Oishi and Rump, the accuracy of the result
                 by the proposed algorithms is better than that of the
                 standard algorithm. At the end of this paper, we
                 present numerical examples showing the efficiency of
                 the proposed algorithms",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical linear algebra with applications",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
  keywords =     "interval arithmetic; matrix multiplication; verified
                 numerical computation",
  onlinedate =   "19 May 2010",
}

@InProceedings{Park:2011:LPS,
  author =       "Daejin Park and Tag Gon Kim and Changmin Kim and
                 Sungho Kwak",
  title =        "A low-power sync processor with a floating-point timer
                 and universal edge tracer for {3DTV} active shutter
                 glasses",
  crossref =     "IEEE:2011:ICC",
  pages =        "1--3",
  year =         "2011",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/COOLCHIPS.2011.5890924",
  ISSN =         "0367-9950",
  ISSN-L =       "0367-9950",
  bibdate =      "Wed Dec 21 14:34:51 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cool-chips.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5890924",
  acknowledgement = ack-nhfb,
}

@InProceedings{Peay:2011:IQW,
  author =       "N. S. Peay and G. R. Morris and K. H. Abed",
  booktitle =    "{2011 Proceedings of IEEE Southeastcon}",
  title =        "Integrating {Quartus Wizard}-based {VHDL}
                 floating-point components into a high performance
                 heterogeneous computing environment",
  publisher =    "pub-IEEE",
  address =      "pub-IEEE:adr",
  pages =        "413--417",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/SECON.2011.5752977",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5752977",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5746658",
}

@Article{Piso:2011:VLG,
  author =       "Daniel Piso and Javier D. Bruguera",
  title =        "Variable Latency {Goldschmidt} Algorithm Based on a
                 New Rounding Method and a Remainder Estimate",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  number =       "11",
  pages =        "1535--1546",
  month =        nov,
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.269",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Sep 27 07:57:50 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5669291",
  abstract =     "A new variable latency Goldschmidt algorithm is
                 presented. The algorithm is based on a new rounding
                 method for division, square root, and their reciprocals
                 that avoids the conventional remainder calculation in
                 most of cases and improves previous proposals. The
                 rounding decision is taken by checking the least
                 significant bits of the output of the last Goldschmidt
                 iteration without any other transformation. This helps
                 to reduce the number of cases which need the
                 calculation of the remainder. Additionally, we avoid
                 the calculation of the remainder for most of those
                 cases by using a remainder estimate that can be easily
                 obtained from the Goldschmidt iteration. The
                 calculation of the estimate is much simpler and less
                 time consuming than the calculation of the remainder
                 and this contributes to reducing the number of cases
                 which need a large latency. The combination of both
                 techniques allows us to define a variable latency
                 algorithm which needs to compute the remainder in just
                 nine percent of the total number of cases for
                 reciprocal and division and in 12 percent for square
                 root and square root reciprocal.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "accuracy; approximation algorithms; approximation
                 methods; computers; division; equations; Goldschmidt
                 algorithm; hardware; mathematical model; reciprocal;
                 rounding; square root; square root reciprocal; variable
                 latency.",
}

@InProceedings{Preusser:2011:ACF,
  author =       "Thomas B. Preu{\ss}er and Martin Zabel and Rainer G.
                 Spallek",
  title =        "Accelerating Computations on {FPGA} Carry Chains by
                 Operand Compaction",
  crossref =     "Schwarz:2011:PIS",
  pages =        "95--102",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.22",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992114",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20",
}

@InProceedings{Ramakrishnan:2011:AFP,
  author =       "A. Ramakrishnan and J. M. Conrad",
  booktitle =    "{2011 Proceedings of IEEE Southeastcon}",
  title =        "Analysis of floating point operations in
                 microcontrollers",
  publisher =    "pub-IEEE",
  address =      "pub-IEEE:adr",
  pages =        "97--100",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/SECON.2011.5752913",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5752913",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5746658",
}

@Article{Romano:2011:NLR,
  author =       "Paul K. Romano and Harry McLaughlin",
  title =        "On Non-Linear Recursive Sequences and {Benford's
                 Law}",
  journal =      j-FIB-QUART,
  volume =       "49",
  number =       "2",
  pages =        "134--138",
  month =        may,
  year =         "2011",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:04:45 MDT 2011",
  bibsource =    "http://www.fq.math.ca/49-2.html;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.fq.math.ca/Abstracts/49-2/romano.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Romanovski:2011:ASS,
  author =       "Valery G. Romanovski and Mateja Presern",
  title =        "An approach to solving systems of polynomials via
                 modular arithmetics with applications",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "236",
  number =       "2",
  pages =        "196--208",
  day =          "15",
  month =        aug,
  year =         "2011",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:24:37 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042711003542",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Rupp:2011:SBF,
  author =       "Benjamin Rupp and Howard Lovatt and Andrea Vezzini",
  booktitle =    "{Proceedings of the 2011 14th European Conference on
                 Power Electronics and Applications (EPE 2011)}",
  title =        "Simulink-based floating-point {DSP} Control Platform",
  publisher =    "pub-IEEE",
  address =      "pub-IEEE:adr",
  pages =        "1--7",
  year =         "2011",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6020132",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6014782",
}

@InProceedings{Samman:2011:RSP,
  author =       "F. A. Samman and P. Surapong and M. Glesner",
  booktitle =    "{2011 6th International Workshop on Reconfigurable
                 Communication-centric Systems-on-Chip (ReCoSoC)}",
  title =        "Reconfigurable streaming processor core with
                 interconnected floating-point arithmetic units for
                 multicore adaptive signal processing systems",
  publisher =    "pub-IEEE",
  address =      "pub-IEEE:adr",
  pages =        "1--6",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ReCoSoC.2011.5981539",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5981539",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5967008",
}

@InProceedings{Sarbishei:2011:FPA,
  author =       "Omid Sarbishei and Katarzyna Radecka",
  title =        "On the Fixed-Point Accuracy Analysis and Optimization
                 of {FFT} Units with {CORDIC} Multipliers",
  crossref =     "Schwarz:2011:PIS",
  pages =        "62--69",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.17",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992109",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20",
}

@Article{Seidel:2011:FVI,
  author =       "Peter-Michael Seidel",
  title =        "Formal Verification of an Iterative Low-Power x86
                 Floating-Point Multiplier with Redundant Feedback",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "21",
  month =        oct,
  year =         "2011",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Published in EPTCS 70, 2011, pp. 70--83.",
  URL =          "http://arxiv.org/abs/1110.4675",
  abstract =     "We present the formal verification of a low-power x86
                 floating-point multiplier. The multiplier operates
                 iteratively and feeds back intermediate results in
                 redundant representation. It supports x87 and SSE
                 instructions in various precisions and can block the
                 issuing of new instructions. The design has been
                 optimized for low-power operation and has not been
                 constrained by the formal verification effort.
                 Additional improvements for the implementation were
                 identified through formal verification. The formal
                 verification of the design also incorporates the
                 implementation of clock-gating and control logic. The
                 core of the verification effort was based on ACL2
                 theorem proving. Additionally, model checking has been
                 used to verify some properties of the floating-point
                 scheduler that are relevant for the correct operation
                 of the unit.",
  acknowledgement = ack-nhfb,
  subject =      "Logic in Computer Science (cs.LO); Hardware
                 Architecture (cs.AR); Mathematical Software (cs.MS)",
}

@Article{Seo:2011:GDP,
  author =       "Young-Hun Seo and Seon-Kyoo Lee and Jae-Yoon Sim",
  title =        "A {1-GHz} Digital {PLL} with a 3-ps resolution
                 floating-point-number {TDC} in a 0.18-{CMOS}",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
  volume =       "58",
  number =       "2",
  pages =        "70--74",
  month =        "????",
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/TCSII.2011.2106315",
  ISSN =         "1549-7747 (print), 1558-3791 (electronic)",
  ISSN-L =       "1549-7747",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5713246",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8920",
  fjournal =     "IEEE Transactions on Circuits and Systems II: Express
                 Briefs",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
}

@Article{Siegel:2011:LAL,
  author =       "Stefan Siegel and J{\"u}rgen Wolff von Gudenberg",
  title =        "A long accumulator like a carry-save adder",
  journal =      j-COMPUTING,
  volume =       "93",
  number =       "??",
  pages =        "??--??",
  month =        "????",
  year =         "2011",
  CODEN =        "CMPTA2",
  DOI =          "https://doi.org/10.1007/s00607-011-0164-x",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Fri Nov 18 15:08:38 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing: Archiv f{\"u}r informatik und numerik",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "accurate floating-point summation",
  pagecount =    "11",
  remark =       "Online on 12 November 2011, but not yet assigned to a
                 journal issue.",
}

@InProceedings{Singh:2011:VEF,
  author =       "R. R. Singh and A. Tiwari and V. K. Singh and G. S.
                 Tomar",
  booktitle =    "{2011 International Conference on Communication
                 Systems and Network Technologies (CSNT)}",
  title =        "{VHDL} Environment for Floating Point Arithmetic Logic
                 Unit-{ALU} Design and Simulation",
  publisher =    "pub-IEEE",
  address =      "pub-IEEE:adr",
  pages =        "469--472",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/CSNT.2011.167",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5966491",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5963767",
}

@Article{Singha:2011:NAF,
  author =       "Satrughna Singha and Aniruddha Ghosh and Amitabha
                 Sinha",
  title =        "A new architecture for {FPGA} based implementation of
                 conversion of binary to double base number system
                 ({DBNS}) using parallel search technique",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "39",
  number =       "5",
  pages =        "12--18",
  month =        dec,
  year =         "2011",
  CODEN =        "CANED2",
  DOI =          "https://doi.org/10.1145/2093339.2093343",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Thu Mar 15 14:07:10 MDT 2012",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
  abstract =     "Non-binary number systems are increasingly gaining
                 popularity in signal processing applications for their
                 capabilities of handling arithmetic operations
                 efficiently. One such number system, ``Double Base
                 Number System (DBNS)'' has gained attention to many
                 researchers for it's capability of performing
                 multiplication operation efficiently. Recently,
                 ``Triple Base Number System (TBNS)'' has been
                 introduced which shows better performance over DBNS for
                 higher bit operations in terms of speed, hardware
                 complexity and power dissipation. However, the
                 advantages of TBNS systems cannot be exploited due to
                 substantial overhead of conversion from binary to TBNS.
                 Keeping this issue in view, in this paper, a novel
                 architecture has been proposed for high performance
                 binary to TBNS conversion. Efficiency of this
                 conversion scheme has been dealt with in details and
                 experimental results and analysis clearly indicate the
                 novelty of the architecture.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
}

@InProceedings{Surapong:2011:PFP,
  author =       "Pongyupinpanich Surapong and Manfred Glesner",
  booktitle =    "{2011 21st International Conference on Field
                 Programmable Logic and Applications}",
  title =        "Pipelined Floating-Point Architecture for a Phase and
                 Magnitude Detector Based on {CORDIC}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "382--384",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/FPL.2011.74",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer architecture; Control systems; CORDIC;
                 Detectors; Field programmable gate arrays;
                 floating-point computation; Hardware; phase and
                 magnitude detector; Pipeline processing; Silicon",
}

@InProceedings{Tang:2011:TCT,
  author =       "Ping Tak Peter Tang and J. Adam Butts and Ron O. Dror
                 and David E. Shaw",
  title =        "Tight Certification Techniques for Digit-by-Rounding
                 Algorithms with Application to a New $ 1 / \sqrt {x} $
                 Design",
  crossref =     "Schwarz:2011:PIS",
  pages =        "159--168",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.29",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992121",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20; reciprocal square root; rsqrt(x)",
}

@Article{Tsen:2011:HDB,
  author =       "Charles Tsen and Sonia Gonzalez-Navarro and Michael J.
                 Schulte and Katherine Compton",
  title =        "Hardware Designs for Binary Integer Decimal-Based
                 Rounding",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "60",
  number =       "5",
  pages =        "614--627",
  month =        may,
  year =         "2011",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.268",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jun 29 10:26:18 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  abstract =     "Decimal floating-point (DFP) arithmetic is becoming
                 increasingly important, and specifications for it are
                 included in the revised IEEE 754 Standard for
                 Floating-Point Arithmetic (IEEE 754-2008). The binary
                 encoding of DFP numbers specified in IEEE 754-2008 is
                 commonly referred to as Binary-Integer Decimal (BID).
                 BID uses a binary integer to encode the significand,
                 which allows it to leverage existing high-speed binary
                 circuits. However, performing decimal rounding on these
                 binary significands is challenging. In this paper, we
                 propose and evaluate several approaches to perform
                 decimal rounding in hardware for DFP numbers that use
                 the BID encoding. We summarize several rounding
                 techniques, present the theory and design of each
                 proposed rounding unit, and use synthesis results to
                 evaluate the critical path delay, latency, and area of
                 rounding units for 64-bit BID numbers. Our results
                 indicate that the bulk of each rounder design is
                 occupied by a binary fixed-point multiplier that can be
                 shared with other integer and floating-point
                 operations. This is the first paper to present and
                 compare a variety of techniques for BID-based rounding
                 hardware. These techniques are valuable to designers of
                 BID-based DFP solutions.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Arithmetic algorithms; BID rounding; binary integer
                 decimal; computer arithmetic; decimal floating-point;
                 hardware designs; IEEE 754-2008; rounding",
}

@InProceedings{Vazquez:2011:CIA,
  author =       "{\'A}lvaro V{\'a}zquez and Javier D. Bruguera",
  title =        "Composite Iterative Algorithm and Architecture for
                 $q$-th Root Calculation",
  crossref =     "Schwarz:2011:PIS",
  pages =        "52--61",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH.2011.16",
  bibdate =      "Sat Aug 20 09:00:00 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5992108",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20",
}

@InProceedings{Vestias:2011:IDM,
  author =       "M. P. Vestias and H. C. Neto",
  booktitle =    "{2011 VII Southern Conference on Programmable Logic
                 (SPL)}",
  title =        "Iterative decimal multiplication using binary
                 arithmetic",
  publisher =    "pub-IEEE",
  address =      "pub-IEEE:adr",
  pages =        "257--262",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/SPL.2011.5782658",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5782658",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5771182",
  keywords =     "decimal floating-point arithmetic",
}

@InProceedings{Vigliar:2011:MFB,
  author =       "Mario Vigliar and Giancarlo Raiconi and Amedeo D'Auria
                 and Giuseppe Del Mastro",
  booktitle =    "{2011 IEEE 54th International Midwest Symposium on
                 Circuits and Systems (MWSCAS)}",
  title =        "Modelling a fast {BLAS} level-1 inspired vectorized
                 {FPU} for {ARM} devices",
  publisher =    "pub-IEEE",
  address =      "pub-IEEE:adr",
  pages =        "1--4",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/MWSCAS.2011.6026644",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6026644",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6019810",
}

@InProceedings{Wang:2011:DFB,
  author =       "Mulan Wang and Xinghua Zhu and Baosheng Wang and
                 Xiaoxia Li",
  booktitle =    "{2011 International Conference on Mechatronic Science,
                 Electric Engineering and Computer (MEC)}",
  title =        "Development of {FPGA}-based arithmetic module in {CNC}
                 system",
  publisher =    "pub-IEEE",
  address =      "pub-IEEE:adr",
  pages =        "494--497",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/MEC.2011.6025510",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6025510",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6020827",
}

@Article{Wang:2011:RCM,
  author =       "Xiaofang Wang and Pallav Gupta",
  title =        "Resource-constrained multiprocessor synthesis for
                 floating-point applications on {FPGAs}",
  journal =      j-TODAES,
  volume =       "16",
  number =       "4",
  pages =        "41:1--41:??",
  month =        oct,
  year =         "2011",
  CODEN =        "ATASFO",
  DOI =          "https://doi.org/10.1145/2003695.2003701",
  ISSN =         "1084-4309 (print), 1557-7309 (electronic)",
  ISSN-L =       "1084-4309",
  bibdate =      "Sat Oct 22 09:25:48 MDT 2011",
  bibsource =    "http://www.acm.org/pubs/contents/journals/todaes/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/todaes.bib",
  acknowledgement = ack-nhfb,
  articleno =    "41",
  fjournal =     "ACM Transactions on Design Automation of Electronic
                 Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J776",
}

@TechReport{Whitehead:2011:PPF,
  author =       "Nathan Whitehead and Alex Fit-Florea",
  title =        "Precision \& Performance: Floating Point and {IEEE
                 754} Compliance for {NVIDIA GPUs}",
  type =         "Report",
  institution =  "nVidia Corporation",
  address =      "Santa Clara, CA, USA",
  pages =        "7",
  day =          "21",
  month =        jun,
  year =         "2011",
  bibdate =      "Tue Sep 04 09:13:29 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://developer.download.nvidia.com/assets/cuda/files/NVIDIA-CUDA-Floating-Point.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Xu:2011:DLF,
  author =       "Jun Xu and Hong Wang",
  booktitle =    "{2011 IEEE International Symposium on Circuits and
                 Systems (ISCAS)}",
  title =        "Desynchronize a legacy floating-point adder with
                 operand-dependant delay elements",
  publisher =    "pub-IEEE",
  address =      "pub-IEEE:adr",
  pages =        "1427--1430",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ISCAS.2011.5937841",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5937841",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=5910713",
}

@MastersThesis{Yang:2011:CMD,
  author =       "Yu Chen Yang",
  title =        "{C} model design and verification of floating-point
                 {CORDIC} for hardware implementation",
  type =         "{Master's} thesis",
  school =       "Xian Jiaotong University",
  address =      "Xian, People's Republic of China",
  year =         "2011",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://login.ezproxy.lib.utah.edu/login?url=https://www.proquest.com/dissertations-theses/c-model-design-verification-floating-point-cordic/docview/1874930256/se-2",
  acknowledgement = ack-nhfb,
  advisor =      "Kui Zhi Mei",
  keywords =     "(UMI)AAI10542507; 0984:Computer science; Applied
                 sciences; Computer science",
  ris-m1 =       "10542507",
}

@InProceedings{Yeung:2011:MCF,
  author =       "Jackson H. C. Yeung and Evangeline F. Y. Young and
                 Philip H. W. Leong",
  booktitle =    "{FPGA '11: Proceedings of the 19th ACM\slash SIGDA
                 International Symposium on Field Programmable Gate
                 Arrays, Monterey, CA, USA, February 27--March 01,
                 2011}",
  title =        "A {Monte-Carlo} floating-point unit for
                 self-validating arithmetic",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "199--208",
  year =         "2011",
  DOI =          "https://doi.org/10.1145/1950413.1950453",
  ISBN =         "1-4503-0554-7",
  ISBN-13 =      "978-1-4503-0554-9",
  bibdate =      "Tue Sep 27 08:57:51 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Monte-Carlo arithmetic is a form of self-validating
                 arithmetic that accounts for the effect of rounding
                 errors. We have implemented a floating point unit that
                 can perform either IEEE 754 or Monte-Carlo floating
                 point computation, allowing hardware accelerated
                 validation of results during execution. Experiments
                 show that our approach has a modest hardware overhead
                 and allows the propagation of rounding error to be
                 accurately estimated.",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point; FPGA; FPU; Monte Carlo arithmetic",
  numpages =     "10",
}

@Article{Yu:2011:OFP,
  author =       "C. Yu and A. M. Smith and W. Luk and P. H. W. Leong
                 and S. J. E. Wilton",
  title =        "Optimizing Floating Point Units in Hybrid {FPGAs}",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "PP",
  number =       "99",
  pages =        "1--10",
  month =        "????",
  year =         "2011",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/TVLSI.2011.2153883",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Tue Sep 27 08:11:02 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5893965",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=92",
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
}

@Article{Zalaket:2011:PFU,
  author =       "Joseph Zalaket and Joseph Hajj-Boutros",
  title =        "Prime factorization using square root approximation",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "61",
  number =       "9",
  pages =        "2463--2467",
  month =        may,
  year =         "2011",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:50:54 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122111001131",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Abbott:2012:TFA,
  author =       "John Abbott",
  title =        "Twin-float arithmetic",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "47",
  number =       "5",
  pages =        "536--551",
  month =        may,
  year =         "2012",
  CODEN =        "JSYCEH",
  DOI =          "https://doi.org/10.1016/j.jsc.2011.12.005",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  bibdate =      "Sat Feb 25 10:12:47 MST 2012",
  bibsource =    "http://www.sciencedirect.com/science/journal/07477171;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0747717111001970",
  abstract =     "We present a heuristically certified form of
                 floating-point arithmetic and its implementation in
                 CoCoALib. This arithmetic is intended to act as a fast
                 alternative to exact rational arithmetic, and is
                 developed from the idea of paired floats expounded by
                 Traverso and Zanoni (2002). As prerequisites we need a
                 source of (pseudo-)random numbers, and an underlying
                 floating-point arithmetic system where the user can set
                 the precision. Twin-float arithmetic can be used only
                 where the input data are exact, or can be obtained at
                 high enough precision. Our arithmetic includes a total
                 cancellation heuristic for sums and differences, and so
                 can be used in classical algebraic algorithms such as
                 Buchberger's algorithm. We also present a (new)
                 algorithm for recovering an exact rational value from a
                 twin-float, so in some cases an exact answer can be
                 obtained from an approximate computation.\par

                 The ideas presented here are implemented as a ring in
                 CoCoALib, called RingTwinFloat, allowing them to be
                 used easily in a wide variety of algebraic computations
                 (including Gr{\"o}bner bases).",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171",
}

@Article{Adam:2012:FPD,
  author =       "Sanda Adam and Gheorghe Adam",
  title =        "Floating Point Degree of Precision in Numerical
                 Quadrature",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "7125",
  pages =        "189--194",
  year =         "2012",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-642-28212-6_19",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Wed Dec 19 15:24:39 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs2012b.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-3-642-28212-6_19/",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-642-28212-6",
  book-URL =     "http://www.springerlink.com/content/978-3-642-28212-6",
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Aharony:2012:IFP,
  author =       "Merav Aharony and Emanuel Gofman and Elena Guralnik
                 and Anatoly Koyfman",
  title =        "Injecting Floating-Point Testing Knowledge into Test
                 Generators",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "7261",
  pages =        "234--241",
  year =         "2012",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-642-34188-5_20",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Wed Dec 19 15:18:42 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs2012d.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-3-642-34188-5_20/",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-642-34188-5",
  book-URL =     "http://www.springerlink.com/content/978-3-642-34188-5",
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Akleylek:2012:MRR,
  author =       "Sedat Akleylek and Ferruh Ozbudak",
  title =        "Modified Redundant Representation for Designing
                 Arithmetic Circuits with Small Complexity",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "61",
  number =       "3",
  pages =        "427--432",
  month =        mar,
  year =         "2012",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2011.29",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Feb 3 07:35:03 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Al-Mohy:2012:MAB,
  author =       "Awad H. Al-Mohy",
  title =        "A more accurate {Briggs} method for the logarithm",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "59",
  number =       "??",
  pages =        "??--??",
  month =        "????",
  year =         "2012",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-011-9496-z",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Wed Nov 30 06:36:53 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/content/4110609h521kg66m/",
  abstract =     "A new approach for computing an expression of the form
                 $ a^{1 / 2^k} - 1 $ is presented that avoids the danger
                 of subtractive cancellation in floating point
                 arithmetic, where $a$ is a complex number not belonging
                 to the closed negative real axis and $k$ is a
                 nonnegative integer. We also derive a condition number
                 for the problem. The algorithm therefore allows highly
                 accurate numerical calculation of $ \log (a) $ using
                 Briggs' method.",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "Briggs' method; Briggs' tables; Inverse scaling and
                 squaring method; Logarithm function",
}

@Misc{Anonymous:2012:FIS,
  author =       "Anonymous",
  title =        "Fast inverse square root",
  howpublished = "Wikipedia article.",
  day =          "20",
  month =        mar,
  year =         "2012",
  bibdate =      "Mon Apr 02 17:03:18 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "This article describes an algorithm for the inverse
                 square root. The only novel feature is use of two
                 IEEE-754 specific magic constants for 32-bit and 64-bit
                 binary arithmetic that allow obtaining fast starting
                 estimates for Newton--Raphson iterations by
                 manipulating the floating-point representations as
                 integers. The code fails to handle signed zero,
                 Infinity, and NaN arguments, uses too few iterations,
                 and does not adjust for rounding errors to obtain
                 correctly-rounded results. See \cite{Blinn:1997:JBC}.",
  URL =          "http://en.wikipedia.org/wiki/Fast_inverse_square_root",
  acknowledgement = ack-nhfb,
}

@Article{Antao:2012:RBE,
  author =       "Samuel Ant{\~a}o and Jean-Claude Bajard and Leonel
                 Sousa",
  title =        "{RNS}-Based Elliptic Curve Point Multiplication for
                 Massive Parallel Architectures",
  journal =      j-COMP-J,
  volume =       "55",
  number =       "5",
  pages =        "629--647",
  month =        may,
  year =         "2012",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/bxr119",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Wed May 2 11:34:42 MDT 2012",
  bibsource =    "http://comjnl.oxfordjournals.org/content/55/5.toc;
                 https://www.math.utah.edu/pub/tex/bib/compj2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/55/5/629.full.pdf+html",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "Residue Number System (RNS)",
  onlinedate =   "November 30, 2011",
}

@Article{Antelo:2012:GEI,
  author =       "Elisardo Antelo and David Hough and Paolo Ienne",
  title =        "{Guest Editors}' Introduction: Special Section on
                 Computer Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "61",
  number =       "8",
  pages =        "1057--1058",
  month =        aug,
  year =         "2012",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2012.153",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jul 27 08:30:49 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Book{Antelo:2012:IIFa,
  author =       "Elisardo Antelo",
  title =        "Industrial Implementations of Floating-Point Units:
                 Vol. 1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "103 (est.)",
  year =         "2012",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Thu Dec 06 11:34:04 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Product ID ES0000033.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Editor's Introduction \\
                 Related Videos \\
                 P6 Binary Floating-Point Unit / Son Dao Trong, Martin
                 Schmookler, Eric M. Schwarz, and Michael Kroener \\
                 FPU Implementations with Denormalized Numbers / Eric M.
                 Schwarz, Martin Schmookler, and Son Dao Trong \\
                 1-GHz HAL SPARC64{\TM} Dual Floating Point Unit with
                 RAS Features / Ajay Naini, Atul Dhablania, Warren
                 James, and Debjit Das Sarma \\
                 Low-Power Multiple-Precision Iterative Floating-Point
                 Multiplier with SIMD Support / Dimitri Tan, Carl E.
                 Lemonds, and Michael J. Schulte \\
                 The Vector Floating-Point Unit in a Synergistic
                 Processor Element of a CELL Processor / Silvia M.
                 Mueller, Christian Jacobi, Hwa-Joon Oh, Kevin D. Tran,
                 Scott R. Cottier, Brad W. Michael, Hiroo Nishikawa,
                 Yonetaro Totsuka, Tatsuya Namatame, Naoka Yano, Takashi
                 Machida, and Sang H. Dhong \\
                 A High-Performance SIMD Floating Point Unit for
                 BlueGene/L: Architecture, Compilation, and Algorithm
                 Design / Leonardo Bachega, Siddhartha Chatterjee,
                 Kenneth A. Dockser, John A. Gunnels, Manish Gupta, Fred
                 G. Gustavson, Christopher A. Lapkowski, Gary K. Liu,
                 Mark P. Mendell, Charles D. Wait, and T. J. Chris Ward
                 \\
                 Design of the ARM VFP11 Divide and Square Root
                 Synthesisable Macrocell / Neil Burgess and Chris N.
                 Hinds \\
                 Correctness Proofs Outline for Newton--Raphson Based
                 Floating-Point Divide and Square Root Algorithms /
                 Marius A. Cornea-Hasegan, Roger A. Golliver, and Peter
                 Markstein \\
                 Recommended Resources \\
                 About the Editor",
}

@Book{Antelo:2012:IIFb,
  author =       "Elisardo Antelo",
  title =        "Industrial Implementations of Floating-Point Units:
                 Vol. 2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "79 (est.)",
  year =         "2012",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Thu Dec 06 11:34:04 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Product ID ES0000034.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Table of Contents \\
                 Editor Bio \\
                 Editor's Introduction \\
                 Related Videos \\
                 A High-Performance Area-Efficient Multifunction
                 Interpolator / Stuart F. Oberman and Michael Y. Siu \\
                 New Algorithms for Improved Transcendental Functions on
                 IA-64 / Shane Story and Ping Tak Peter Tang \\
                 Energy-Delay Estimation Technique for High-Performance
                 Microprocessor VLSI Adders / Vojin G. Oklobdzija, Bart
                 R. Zeydel, Hoang Dao, Sanu Mathew, and Ram
                 Krishnamurthy \\
                 Advanced Clockgating Schemes for
                 Fused-Multiply-Add-Type Floating-Point Units / Jochen
                 Preiss, Maarten Boersma, and Silvia Melitta Mueller \\
                 Design of Low-Cost High-Performance Floating-Point
                 Fused Multiply-Add with Reduced Power / Zichu Qi, Qi
                 Guo, Ge Zhang, Xiangku Li, and Weiwu Hu \\
                 Decimal Floating-Point: Algorism for Computers /
                 Michael F. Cowlishaw \\
                 A Software Implementation of the IEEE 754R Decimal
                 Floating-Point Arithmetic Using the Binary Encoding
                 Format / Marius Cornea, John Harrison, Cristina
                 Anderson, Ping Tak Peter Tang, Eric Schneider, and
                 Evgeny Gvozdev \\
                 Recommended Resources \\
                 About the Editor",
}

@Article{Aswal:2012:BFD,
  author =       "Abhilasha Aswal and M. Ganesh Perumal and G. N.
                 Srinivasa Prasanna",
  title =        "On Basic Financial Decimal Operations on Binary
                 Machines",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "61",
  number =       "8",
  pages =        "1084--1096",
  month =        aug,
  year =         "2012",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2012.89",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jul 27 08:30:49 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Bailey:2012:AIS,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "Ancient {Indian} Square Roots: An Exercise in Forensic
                 Paleo-Mathematics",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "119",
  number =       "8",
  pages =        "646--657",
  month =        oct,
  year =         "2012",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.4169/amer.math.monthly.119.08.646",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Thu Nov 8 07:34:21 MST 2012",
  bibsource =    "http://www.jstor.org/journals/00029890.html;
                 http://www.jstor.org/stable/10.4169/amermathmont.119.issue-8;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.jstor.org/stable/pdfplus/10.4169/amer.math.monthly.119.08.646.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Article{Bailey:2012:HPC,
  author =       "David H. Bailey and Roberto Barrio and Jonathan M.
                 Borwein",
  title =        "High-precision computation: Mathematical physics and
                 dynamics",
  journal =      j-APPL-MATH-COMP,
  volume =       "218",
  number =       "20",
  pages =        "10106--10121",
  day =          "15",
  month =        jun,
  year =         "2012",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2012.03.087",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  MRclass =      "65Y04 (68M07)",
  MRnumber =     "2921767",
  bibdate =      "Thu Aug 11 10:27:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://docserver.carma.newcastle.edu.au/775/;
                 http://www.sciencedirect.com/science/article/pii/S0096300312003505",
  abstract =     "At the present time, IEEE 64-bit floating-point
                 arithmetic is sufficiently accurate for most scientific
                 applications. However, for a rapidly growing body of
                 important scientific computing applications, a higher
                 level of numeric precision is required. Such
                 calculations are facilitated by high-precision software
                 packages that include high-level language translation
                 modules to minimize the conversion effort. This paper
                 presents an overview of recent applications of these
                 techniques and provides some analysis of their
                 numerical requirements. We conclude that high-precision
                 arithmetic facilities are now an indispensable
                 component of a modern large-scale scientific computing
                 environment.",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
  keywords =     "Dynamical systems; Experimental mathematics;
                 High-precision computation; Mathematical physics",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  researcherid-numbers = "Barrio, Roberto/L-4983-2014",
}

@Article{Baudin:2012:RCD,
  author =       "Michael Baudin and Robert L. Smith",
  title =        "A Robust Complex Division in {Scilab}",
  journal =      "CoRR",
  volume =       "abs/1210.4539",
  year =         "2012",
  bibdate =      "Tue Apr 16 08:18:25 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  URL =          "http://arxiv.org/abs/1210.4539",
  abstract =     "The most widely used algorithm for floating point
                 complex division, known as Smith's method, may fail
                 more often than expected. This document presents two
                 improved complex division algorithms. We present a
                 proof of the robustness of the first improved
                 algorithm. Numerical simulations show that this
                 algorithm performs well in practice and is
                 significantly more robust than other known
                 implementations. By combining additional scaling
                 methods with this first algorithm, we were able to
                 create a second algorithm, which rarely fails.",
  acknowledgement = ack-nhfb,
}

@Article{Benz:2012:DPA,
  author =       "Florian Benz and Andreas Hildebrandt and Sebastian
                 Hack",
  title =        "A dynamic program analysis to find floating-point
                 accuracy problems",
  journal =      j-SIGPLAN,
  volume =       "47",
  number =       "6",
  pages =        "453--462",
  month =        jun,
  year =         "2012",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/2345156.2254118",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Mon Aug 6 16:31:49 MDT 2012",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
  note =         "PLDI '12 proceedings.",
  abstract =     "Programs using floating-point arithmetic are prone to
                 accuracy problems caused by rounding and catastrophic
                 cancellation. These phenomena provoke bugs that are
                 notoriously hard to track down: the program does not
                 necessarily crash and the results are not necessarily
                 obviously wrong, but often subtly inaccurate. Further
                 use of these values can lead to catastrophic errors. In
                 this paper, we present a dynamic program analysis that
                 supports the programmer in finding accuracy problems.
                 Our analysis uses binary translation to perform every
                 floating-point computation side by side in higher
                 precision. Furthermore, we use a lightweight slicing
                 approach to track the evolution of errors. We evaluate
                 our analysis by demonstrating that it catches
                 well-known floating-point accuracy problems and by
                 analyzing the Spec CFP2006 floating-point benchmark. In
                 the latter, we show how our tool tracks down a
                 catastrophic cancellation that causes a complete loss
                 of accuracy leading to a meaningless program result.
                 Finally, we apply our program to a complex, real-world
                 bioinformatics application in which our program
                 detected a serious cancellation. Correcting the
                 instability led not only to improved quality of the
                 result, but also to an improvement of the program's run
                 time.In this paper, we present a dynamic program
                 analysis that supports the programmer in finding
                 accuracy problems. Our analysis uses binary translation
                 to perform every floating-point computation side by
                 side in higher precision. Furthermore, we use a
                 lightweight slicing approach to track the evolution of
                 errors. We evaluate our analysis by demonstrating that
                 it catches well-known floating-point accuracy problems
                 and by analyzing the SpecfiCFP2006 floating-point
                 benchmark. In the latter, we show how our tool tracks
                 down a catastrophic cancellation that causes a complete
                 loss of accuracy leading to a meaningless program
                 result. Finally, we apply our program to a complex,
                 real-world bioinformatics application in which our
                 program detected a serious cancellation. Correcting the
                 instability led not only to improved quality of the
                 result, but also to an improvement of the program's run
                 time.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}

@InProceedings{Bohlender:2012:CFE,
  author =       "G. Bohlender and U. Kulisch",
  title =        "Comments on fast and exact accumulation of products",
  crossref =     "Jonasson:2012:APSb",
  pages =        "148--156",
  year =         "2012",
  DOI =          "https://doi.org/10.1007/978-3-642-28145-7_15",
  bibdate =      "Sat Oct 31 07:09:45 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Boldo:2012:AOP,
  author =       "Sylvie Boldo and Guillaume Melquiond",
  title =        "Arithm{\'e}tique des ordinateurs et preuves formelles.
                 ({French}) [{Computer} arithmetic and formal proofs]",
  institution =  "{\'E}cole des Jeunes Chercheurs en Informatique
                 Math{\'e}matique",
  address =      "????",
  pages =        "31",
  day =          "22",
  month =        mar,
  year =         "2012",
  bibdate =      "Fri Sep 22 17:09:39 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://inria.hal.science/hal-00755333/file/main.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Brisebarre:2012:MPK,
  author =       "Nicolas Brisebarre and Milo D. Ercegovac and
                 Jean-Michel Muller",
  editor =       "{IEEE}",
  booktitle =    "{2012 IEEE 23rd International Conference on
                 Application-Specific Systems, Architectures and
                 Processors, 9--11 July 2012. Delft, The Netherlands}",
  title =        "{$ (M, p, k) $}-Friendly Points: a Table-Based Method
                 for Trigonometric Function Evaluation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "46--52",
  year =         "2012",
  DOI =          "https://doi.org/10.1109/ASAP.2012.17",
  ISBN =         "0-7695-4768-0",
  ISBN-13 =      "978-0-7695-4768-8",
  ISSN =         "1063-6862",
  ISSN-L =       "1063-6862",
  bibdate =      "Fri Sep 29 10:49:22 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Bruintjes:2012:SLA,
  author =       "Tom M. Bruintjes and Karel H. G. Walters and Sabih H.
                 Gerez and Bert Molenkamp and Gerard J. M. Smit",
  title =        "{Sabrewing}: a lightweight architecture for combined
                 floating-point and integer arithmetic",
  journal =      j-TACO,
  volume =       "8",
  number =       "4",
  pages =        "41:1--41:??",
  month =        jan,
  year =         "2012",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2086696.2086720",
  ISSN =         "1544-3566 (print), 1544-3973 (electronic)",
  ISSN-L =       "1544-3566",
  bibdate =      "Sat Jan 21 07:49:49 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/taco.bib",
  abstract =     "In spite of the fact that floating-point arithmetic is
                 costly in terms of silicon area, the joint design of
                 hardware for floating-point and integer arithmetic is
                 seldom considered. While components like multipliers
                 and adders can potentially be shared, floating-point
                 and integer units in contemporary processors are
                 practically disjoint. This work presents a new
                 architecture which tightly integrates floating-point
                 and integer arithmetic in a single datapath. It is
                 mainly intended for use in low-power embedded digital
                 signal processors and therefore the following design
                 constraints were important: limited use of pipelining
                 for the convenience of the compiler; maintaining
                 compatibility with existing technology; minimal area
                 and power consumption for applicability in embedded
                 systems.",
  acknowledgement = ack-nhfb,
  articleno =    "41",
  fjournal =     "ACM Transactions on Architecture and Code Optimization
                 (TACO)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J924",
}

@Article{Chen:2012:IDF,
  author =       "Dongdong Chen and Liu Han and Younhee Choi and
                 Seok-Bum Ko",
  title =        "Improved Decimal Floating-Point Logarithmic Converter
                 Based on Selection by Rounding",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "61",
  number =       "5",
  pages =        "607--621",
  month =        may,
  year =         "2012",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2011.43",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Apr 6 18:50:40 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  abstract =     "This paper presents the algorithm and architecture of
                 the decimal floating-point (DFP) logarithmic converter,
                 based on the digit-recurrence algorithm with selection
                 by rounding. The proposed approach can compute faithful
                 DFP logarithm results for any one of the three DFP
                 formats specified in the IEEE 754-2008 standard. In
                 order to optimize the latency for the proposed design,
                 we mainly integrate the following novel features: (1)
                 using the redundant carry-save representation of the
                 data-path; (2) reducing the number of iterations by
                 determining the number of initial iteration; and (3)
                 retiming and balancing the delay of the proposed
                 architecture. The proposed architecture is synthesized
                 with STM 90-nm standard cell library and the results
                 show that the critical path delay and the number of
                 clock cycles of the proposed Decimal64 logarithmic
                 converter are 1.55 ns (34.4 FO4) and 19 respectively,
                 and the total hardware complexity is 43572 NAND2 gates.
                 The delay estimation results of the proposed
                 architecture show that its latency is close to that of
                 the binary radix-16 logarithmic converter, and that it
                 has a significant decrease on latency compared with a
                 recently published high performance CORDIC
                 implementation.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Cleemput:2012:CMT,
  author =       "Jeroen V. Cleemput and Bart Coppens and Bjorn {De
                 Sutter}",
  title =        "Compiler mitigations for time attacks on modern x86
                 processors",
  journal =      j-TACO,
  volume =       "8",
  number =       "4",
  pages =        "23:1--23:??",
  month =        jan,
  year =         "2012",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2086696.2086702",
  ISSN =         "1544-3566 (print), 1544-3973 (electronic)",
  ISSN-L =       "1544-3566",
  bibdate =      "Sat Jan 21 07:49:49 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/taco.bib",
  abstract =     "This paper studies and evaluates the extent to which
                 automated compiler techniques can defend against
                 timing-based side channel attacks on modern x86
                 processors. We study how modern x86 processors can leak
                 timing information through side channels that relate to
                 data flow. We study the efficiency, effectiveness,
                 portability, predictability and sensitivity of several
                 mitigating code transformations that eliminate or
                 minimize key-dependent execution time variations.
                 Furthermore, we discuss the extent to which compiler
                 backends are a suitable tool to provide automated
                 support for the proposed mitigations.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Archit. Code Optim.",
  articleno =    "23",
  fjournal =     "ACM Transactions on Architecture and Code Optimization
                 (TACO)",
  journal-URL =  "https://dl.acm.org/loi/taco",
}

@Article{Das:2012:AAT,
  author =       "Subrata Das and Partha Sarathi Dasgupta and Samar
                 Sensarma",
  title =        "Arithmetic Algorithms for Ternary Number System",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "7373",
  pages =        "111--120",
  year =         "2012",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-642-31494-0_13",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Wed Dec 19 15:21:09 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs2012f.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-3-642-31494-0_13/",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-642-31494-0",
  book-URL =     "http://www.springerlink.com/content/978-3-642-31494-0",
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{deDinechin:2012:MRC,
  author =       "Florent de Dinechin",
  title =        "Multiplication by rational constants",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
  volume =       "52",
  number =       "2",
  pages =        "98--102",
  month =        feb,
  year =         "2012",
  DOI =          "https://doi.org/10.1109/TCSII.2011.2177706",
  ISSN =         "1549-7747 (print), 1558-3791 (electronic)",
  ISSN-L =       "1549-7747",
  bibdate =      "Sat Feb 08 09:46:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/document/6126071",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE trans. circuits syst., II Express briefs",
  fjournal =     "IEEE Transactions on Circuits and Systems II: Express
                 Briefs",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
}

@Article{deDinechin:2012:TBD,
  author =       "Florent de Dinechin and Laurent-St{\'e}phane Didier",
  title =        "Table-Based Division by Small Integer Constants",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "7199",
  pages =        "53--63",
  year =         "2012",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-642-28365-9_5",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Wed Dec 19 15:26:07 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs2012b.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-3-642-28365-9_5/",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-642-28365-9",
  book-URL =     "http://www.springerlink.com/content/978-3-642-28365-9",
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Book{Deschamps:2012:GFI,
  author =       "Jean-Pierre Deschamps and Gustavo D. Sutter and
                 Enrique Cant{\'o}",
  title =        "Guide to {FPGA} implementation of arithmetic
                 functions",
  volume =       "95",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xv + 469",
  year =         "2012",
  DOI =          "https://doi.org/10.1007/978-94-007-2987-2",
  ISBN =         "94-007-2986-3 (hardcover), 94-007-2987-1 (e-book)",
  ISBN-13 =      "978-94-007-2986-5 (hardcover), 978-94-007-2987-2
                 (e-book)",
  LCCN =         "TK7895.G36",
  bibdate =      "Wed Oct 1 10:19:58 MDT 2014",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  series =       "Lecture notes in electrical engineering",
  abstract =     "This book is designed both for FPGA users interested
                 in developing new, specific components --- generally
                 for reducing execution times and IP core designers
                 interested in extending their catalog of specific
                 components. The main focus is circuit synthesis and the
                 discussion shows, for example, how a given algorithm
                 executing some complex function can be translated to a
                 synthesizable circuit description, as well as which are
                 the best choices the designer can make to reduce the
                 circuit cost, latency, or power consumption. This is
                 not a book on algorithms. It is a book that shows how
                 to translate efficiently an algorithm to a circuit,
                 using techniques such as parallelism, pipeline, loop
                 unrolling, and others. Numerous examples of FPGA
                 implementation are described throughout this book and
                 the circuits are modeled in VHDL. Complete and
                 synthesizable source files are available for
                 download.",
  acknowledgement = ack-nhfb,
  author-dates = "1945--",
  subject =      "Field programmable gate arrays; Programming;
                 Arithmetic functions",
  tableofcontents = "Basic Building Blocks \\
                 Architecture of Digital Circuits \\
                 Special Topics of Data Path Synthesis \\
                 Control Unit Synthesis \\
                 Electronic Aspects of Digital Design \\
                 EDA Tools \\
                 Adders \\
                 Multipliers \\
                 Dividers \\
                 Other Operations \\
                 Decimal Operations \\
                 Floating Point Arithmetic \\
                 Finite-Field Arithmetic \\
                 Systems on Chip \\
                 Embedded Systems Development: Case Studies \\
                 Partial Reconfiguration on Xilinx FPGAs",
}

@Article{Diethelm:2012:LRN,
  author =       "Kai Diethelm",
  title =        "The Limits of Reproducibility in Numerical
                 Simulation",
  journal =      j-COMPUT-SCI-ENG,
  volume =       "14",
  number =       "1",
  pages =        "64--72",
  month =        jan # "\slash " # feb,
  year =         "2012",
  CODEN =        "CSENFA",
  DOI =          "https://doi.org/10.1109/MCSE.2011.21",
  ISSN =         "1521-9615 (print), 1558-366X (electronic)",
  ISSN-L =       "1521-9615",
  bibdate =      "Tue Jan 31 12:29:01 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computscieng.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing in Science and Engineering",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
  remark =       "This paper discusses the problem of reproducible, and
                 accurate, computation of long floating-point dot
                 products in parallel computing environments, and how
                 nonreproducibility leads to user confusion.",
}

@InProceedings{Dong:2012:ISP,
  author =       "Chen Dong and Chen He and Sun Xing and Pang Long",
  booktitle =    "{2012 International Conference on Control Engineering
                 and Communication Technology}",
  title =        "Implementation of Single-Precision Floating-Point
                 Trigonometric Functions with Small Area",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "589--592",
  year =         "2012",
  DOI =          "https://doi.org/10.1109/ICCECT.2012.186",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithm design and analysis; Computer architecture;
                 CORDIC; Equations; Field programmable gate arrays;
                 floating-point; FPGA; Hardware; Mathematical model;
                 Transforms; trigonometric functions",
}

@Article{Dumas:2012:NRI,
  author =       "Jean-Guillaume Dumas",
  title =        "On {Newton--Raphson} iteration for multiplicative
                 inverses modulo prime powers",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--11",
  day =          "28",
  month =        sep,
  year =         "2012",
  DOI =          "https://doi.org/10.48550/arXiv.1209.6626",
  bibdate =      "Mon Feb 09 05:55:11 2026",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See journal article \cite{Dumas:2014:NRI}, corrections
                 \cite{Walther:2019:VNR}, and later work
                 \cite{Hurchalla:2022:IIM}.",
  URL =          "https://arxiv.org/abs/1209.6626",
  abstract =     "We study algorithms for the fast computation of
                 modular inverses. Newton--Raphson iteration over
                 $p$-adic numbers gives a recurrence relation computing
                 modular inverse modulo $ p^m$, that is logarithmic in
                 $m$. We solve the recurrence to obtain an explicit
                 formula for the inverse. Then we study different
                 implementation variants of this iteration and show that
                 our explicit formula is interesting for small exponent
                 values but slower for large exponent, say of more than
                 700 bits. Overall we thus propose a hybrid combination
                 of our explicit formula and the best asymptotic
                 variants. This hybrid combination yields then a
                 constant factor improvement, also for large
                 exponents.",
  acknowledgement = ack-nhfb,
}

@Article{Fan:2012:EHI,
  author =       "Junfeng Fan and Frederik Vercauteren and Ingrid
                 Verbauwhede",
  title =        "Efficient Hardware Implementation of {FP}-Arithmetic
                 for Pairing-Friendly Curves",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "61",
  number =       "5",
  pages =        "676--685",
  month =        may,
  year =         "2012",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2011.78",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Apr 6 18:50:40 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Fout:2012:APB,
  author =       "Nathaniel Fout and Kwan-Liu Ma",
  title =        "An Adaptive Prediction-Based Approach to Lossless
                 Compression of Floating-Point Volume Data",
  journal =      j-IEEE-TRANS-VIS-COMPUT-GRAPH,
  volume =       "18",
  number =       "12",
  pages =        "2295--2304",
  month =        dec,
  year =         "2012",
  CODEN =        "ITVGEA",
  DOI =          "https://doi.org/10.1109/TVCG.2012.194",
  ISSN =         "1077-2626 (print), 1941-0506 (electronic), 2160-9306",
  ISSN-L =       "1077-2626",
  bibdate =      "Mon Oct 22 07:55:05 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransviscomputgraph.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Visualization and Computer
                 Graphics",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2945",
}

@Article{G:2012:DOR,
  author =       "Rangaraju H G and Aakash Babu Suresh and Muralidhara K
                 N",
  title =        "Design and Optimization of Reversible Multiplier
                 Circuit",
  journal =      j-INT-J-COMP-APPL,
  volume =       "52",
  number =       "??",
  pages =        "44--50",
  month =        aug,
  year =         "2012",
  CODEN =        "????",
  DOI =          "https://doi.org/10.5120/8242-1523",
  ISSN =         "0975-8887",
  ISSN-L =       "0975-8887",
  bibdate =      "Fri Jan 24 08:48:11 MST 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/intjcompappl.bib",
  URL =          "https://www.ijcaonline.org/archives/volume52/number10/8242-1523/",
  acknowledgement = ack-nhfb,
  ajournal =     "Intern. J. of Computer Applications",
  articleno =    "10",
  fjournal =     "International Journal of Computer Applications",
  journal-URL =  "https://www.ijcaonline.org/",
}

@Article{Gandino:2012:AAS,
  author =       "Filippo Gandino and Fabrizio Lamberti and Gianluca
                 Paravati and Jean-Claude Bajard and Paolo Montuschi",
  title =        "An Algorithmic and Architectural Study on {Montgomery}
                 Exponentiation in {RNS}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "61",
  number =       "8",
  pages =        "1071--1083",
  month =        aug,
  year =         "2012",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2012.84",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jul 27 08:30:49 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Gazeau:2012:NLM,
  author =       "Ivan Gazeau and Dale Miller and Catuscia Palamidessi",
  title =        "A non-local method for robustness analysis of floating
                 point programs",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "3",
  month =        feb,
  year =         "2012",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/1202.0693",
  abstract =     "Robustness is a standard correctness property which
                 intuitively means that if the input to the program
                 changes less than a fixed small amount then the output
                 changes only slightly. This notion is useful in the
                 analysis of rounding error for floating point programs
                 because it helps to establish bounds on output errors
                 introduced by both measurement errors and by floating
                 point computation. Compositional methods often do not
                 work since key constructs---like the conditional and
                 the while-loop---are not robust. We propose a method
                 for proving the robustness of a while-loop. This method
                 is non-local in the sense that instead of breaking the
                 analysis down to single lines of code, it checks
                 certain global properties of its structure. We show the
                 applicability of our method on two standard algorithms:
                 the CORDIC computation of the cosine and Dijkstra's
                 shortest path algorithm.",
  acknowledgement = ack-nhfb,
  subject =      "Programming Languages (cs.PL)",
}

@Article{Ghosh:2012:FPR,
  author =       "Aniruddha Ghosh and Satrughna Singha and Amitabha
                 Sinha",
  title =        "{``Floating point RNS''}: a new concept for designing
                 the {MAC} unit of digital signal processor",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "40",
  number =       "2",
  pages =        "39--43",
  month =        may,
  year =         "2012",
  CODEN =        "CANED2",
  DOI =          "https://doi.org/10.1145/2234336.2234343",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Fri Jun 1 17:06:51 MDT 2012",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
  abstract =     "Execution of arithmetic operations at a very high
                 speed in real time is the major concern in compute
                 intensive digital signal processing (DSP) algorithms
                 Residue Number Systems are being considered as
                 alternative to binary number system because of their
                 capabilities of performing ``carry free'' arithmetic
                 operations. However, RNS systems have so far been used
                 to handle integer numbers only. Floating Point RNS
                 arithmetic units have obvious advantages over fixed
                 point multiply {\&} accumulate (MAC) units which are
                 the key units in Digital Signal Processors. Keeping
                 this in view, in this paper, the architecture of a
                 floating point MAC unit is presented.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
}

@Article{Giessing:2012:FRB,
  author =       "Sarah Giessing",
  title =        "Flexible Rounding Based on Consistent Post-tabular
                 Stochastic Noise",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "7556",
  pages =        "22--34",
  year =         "2012",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-642-33627-0_3",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Wed Dec 19 15:24:52 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs2012j.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-3-642-33627-0_3/",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-642-33627-0",
  book-URL =     "http://www.springerlink.com/content/978-3-642-33627-0",
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InCollection{Goldberg:2012:CA,
  author =       "David Goldberg",
  title =        "Computer Arithmetic",
  crossref =     "Hennessy:2012:CAQ",
  chapter =      "J",
  pages =        "J-1--J-74",
  year =         "2012",
  bibdate =      "Mon Nov 11 05:34:58 2019",
  bibsource =    "http://www.mkp.com/CA3;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "The complete Appendix J is not in the printed book; it
                 is available only at the book's Web site.",
  URL =          "http://booksite.mkp.com/9780123838728/references/appendix_j.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Goossens:2012:CTS,
  author =       "Bernard Goossens and Philippe [Gr{\'e}goire] Langlois
                 and David Parello and Kathy Porada",
  booktitle =    "Numerical Sofware: Design, Analysis and Verification,
                 Santander, Spain, 4--6 July 2012",
  title =        "Computing time for summation algorithm: Less hazard
                 and more scientific research",
  publisher =    "????",
  address =      "????",
  pages =        "i + 34",
  year =         "2012",
  bibdate =      "Sat Apr 01 08:09:42 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://hal-lirmm.ccsd.cnrs.fr/lirmm-00835508",
  abstract =     "Several accurate algorithms to sum IEEE-754 floating
                 point numbers have been recently published. The
                 contributions by Rump, Ogita and Oishi [3, 4, 2] and
                 the newest ones proposed by Zhu and Hayes [5, 6] are
                 examples of accurate summation algorithms. Some of
                 these actually compute the correct rounding of the
                 exact sum, i.e., the most accurate value with respect
                 to the finite precision of the floating point
                 arithmetic. This computed sum does not suffer anymore
                 from the condition number of the summation. In such
                 cases, the run-time performances and the memory print
                 become the discriminant properties to decide which
                 algorithm to choose. In this talk we focus the problem
                 of presenting reliable measures of the run-time
                 performances of such core algorithms. As Rump writes in
                 [2], Measuring the computing time of summation
                 algorithms in a high-level language on today's
                 architectures is more of a hazard than scientific
                 research. We introduced PerPI, a software tool that
                 automatizes an almost machine independent analysis
                 based on the instruction-level parallelism of the
                 algorithm [1]. We analyze the previously mentioned
                 accurate summation algorithms. We discuss whether PerPI
                 provides a more reliable performance analysis and how
                 to improve the confidence level of future contributions
                 in this area.",
  acknowledgement = ack-nhfb,
  keywords =     "correct rounding; faithful summation; floating-point
                 arithmetic, accurate summation; instruction level
                 parallelism; performance evaluation; PerPI;
                 reproducibility",
  remark =       "Lecture slides",
}

@Article{Grcar:2012:JNA,
  author =       "Joseph F. Grcar",
  title =        "{John von Neumann}'s Analysis of {Gaussian}
                 Elimination and the Origins of Modern Numerical
                 Analysis",
  journal =      j-SIAM-REVIEW,
  volume =       "53",
  number =       "4",
  pages =        "607--682",
  month =        "????",
  year =         "2012",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/080734716",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  MRclass =      "01-08, 65-03, 65F05, 65F35, 65G50, 65M12, 68-03",
  bibdate =      "Thu Jan 12 12:42:30 MST 2012",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/53/4;
                 https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "http://epubs.siam.org/sirev/resource/1/siread/v53/i4/p607_s1",
  abstract =     "Just when modern computers (digital, electronic, and
                 programmable) were being invented, John von Neumann and
                 Herman Goldstine wrote a paper to illustrate the
                 mathematical analyses that they believed would be
                 needed to use the new machines effectively and to guide
                 the development of still faster computers. Their
                 foresight and the congruence of historical events made
                 their work the first modern paper in numerical
                 analysis. Von Neumann once remarked that to found a
                 mathematical theory one had to prove the first theorem,
                 which he and Goldstine did for the accuracy of
                 mechanized Gaussian elimination --- but their paper was
                 about more than that. Von Neumann and Goldstine
                 described what they surmised would be the significant
                 questions once computers became available for
                 computational science, and they suggested enduring ways
                 to answer them.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  keywords =     "backward error, CFL condition, computer architecture,
                 computer arithmetic, computer programming, condition
                 number, decomposition paradigm, Gaussian elimination,
                 history, matrix norms, numerical analysis, rounding
                 error analysis, stability, stochastic linear algebra,
                 von Neumann",
  onlinedate =   "November 07, 2011",
}

@InProceedings{Haller:2012:DFP,
  author =       "L. Haller and A. Griggio and M. Brain and D.
                 Kroening",
  booktitle =    "{Formal Methods in Computer-Aided Design (FMCAD),
                 2012}",
  title =        "Deciding floating-point logic with systematic
                 abstraction",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "131--140",
  month =        oct,
  year =         "2012",
  ISBN =         "1-4673-4832-5",
  ISBN-13 =      "978-1-4673-4832-4",
  bibdate =      "Sat Jun 4 18:09:21 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "abstract interpretation; Abstracts; Algorithm design
                 and analysis; Analytical models; binary floating-point
                 arithmetic; bit-precise decision procedure; bit-vector
                 encoding; computability; conflict analysis algorithm;
                 conflict driven clause learning algorithm; decision
                 procedures; Design automation; encoding; Encoding;
                 floating point; floating point arithmetic;
                 floating-point interval abstraction; floating-point
                 logic; floating-point satisfiability checking;
                 lattice-based abstraction; Lattices; MATHSAT5;
                 natural-domain SMT approach; propositional solver; SAT
                 solver; Standards; systematic abstraction",
}

@Article{Huang:2012:LCB,
  author =       "Libo Huang and Sheng Ma and Li Shen and Zhiying Wang
                 and Nong Xiao",
  title =        "Low-Cost {Binary128} Floating-Point {FMA} Unit Design
                 with {SIMD} Support",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "61",
  number =       "5",
  pages =        "745--751",
  month =        may,
  year =         "2012",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2011.77",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Apr 6 18:50:40 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Hyman:2012:LF,
  author =       "Paul Hyman",
  title =        "Lost and found",
  journal =      j-CACM,
  volume =       "55",
  number =       "7",
  pages =        "21--21",
  month =        jul,
  year =         "2012",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/2209249.2209258",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Tue Jul 3 13:54:33 MDT 2012",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Researchers discover computer pioneer Konrad Zuse's
                 long-forgotten Z9, the world's first program-controlled
                 binary relay calculator using floating-point
                 arithmetic.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@TechReport{Kahan:2012:DNR,
  author =       "W. Kahan",
  title =        "Desperately Needed Remedies for the Undebuggability of
                 Large Floating-Point Computations in Science and
                 Engineering",
  type =         "Report",
  institution =  inst-BERKELEY-EECS,
  address =      inst-BERKELEY-EECS:adr,
  pages =        "90",
  day =          "24",
  month =        apr,
  year =         "2012",
  bibdate =      "Mon Aug 26 10:36:06 2024",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://people.eecs.berkeley.edu/~wkahan/Boulder.pdf",
  acknowledgement = ack-nhfb,
}

@TechReport{Katranov:2012:DRN,
  author =       "A. Katranov",
  title =        "Deterministic Reduction: a new Community Preview
                 Feature in {Intel Threading Building Blocks}",
  type =         "Report",
  institution =  pub-INTEL,
  address =      pub-INTEL:adr,
  pages =        "????",
  year =         "2012",
  bibdate =      "Sat Oct 31 06:58:31 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Koiran:2012:ACC,
  author =       "Pascal Koiran",
  title =        "Arithmetic circuits: the chasm at depth four gets
                 wider",
  journal =      j-THEOR-COMP-SCI,
  volume =       "448",
  number =       "1",
  pages =        "56--65",
  day =          "24",
  month =        aug,
  year =         "2012",
  CODEN =        "TCSCDI",
  DOI =          "https://doi.org/10.1016/j.tcs.2012.03.041",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Sat Jun 30 13:07:21 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tcs2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0304397512003131",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975/",
}

@Article{Kornerup:2012:CCR,
  author =       "Peter Kornerup and Vincent Lef{\`e}vre and Nicolas
                 Louvet and Jean-Michel Muller",
  title =        "On the Computation of Correctly Rounded Sums",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "61",
  number =       "3",
  pages =        "289--298",
  month =        mar,
  year =         "2012",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2011.27",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Feb 3 07:35:03 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  abstract =     "This paper presents a study of some basic blocks
                 needed in the design of floating-point summation
                 algorithms. In particular, in radix-2 floating-point
                 arithmetic, we show that among the set of the
                 algorithms with no comparisons performing only
                 floating-point additions/subtractions, the 2Sum
                 algorithm introduced by Knuth is minimal, both in terms
                 of number of operations and depth of the dependency
                 graph. We investigate the possible use of another
                 algorithm, Dekker's Fast2Sum algorithm, in radix-10
                 arithmetic. We give methods for computing, in radix 10,
                 the floating-point number nearest the average value of
                 two floating-point numbers. We also prove that under
                 reasonable conditions, an algorithm performing only
                 round-to-nearest additions/subtractions cannot compute
                 the round-to-nearest sum of at least three
                 floating-point numbers. Starting from an algorithm due
                 to Boldo and Melquiond, we also present new results
                 about the computation of the correctly-rounded sum of
                 three floating-point numbers. For a few of our
                 algorithms, we assume new operations defined by the
                 recent IEEE 754-2008 Standard are available.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "accurate floating-point summation; correct rounding;
                 floating-point arithmetic",
}

@Article{Kornerup:2012:FPA,
  author =       "Peter Kornerup and Jean-Michel Muller and Adrien
                 Panhaleux",
  title =        "Floating-Point Arithmetic on Round-to-Nearest
                 Representations",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "18",
  month =        jan,
  year =         "2012",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/1201.3914",
  abstract =     "Recently we introduced a class of number
                 representations denoted RN-representations, allowing an
                 un-biased rounding-to-nearest to take place by a simple
                 truncation. In this paper we briefly review the binary
                 fixed-point representation in an encoding which is
                 essentially an ordinary 2's complement representation
                 with an appended round-bit. Not only is this rounding a
                 constant time operation, so is also sign inversion,
                 both of which are at best log-time operations on
                 ordinary 2's complement representations. Addition,
                 multiplication and division is defined in such a way
                 that rounding information can be carried along in a
                 meaningful way, at minimal cost. Based on the
                 fixed-point encoding we here define a floating point
                 representation, and describe to some detail a possible
                 implementation of a floating point arithmetic unit
                 employing this representation, including also the
                 directed roundings.",
  acknowledgement = ack-nhfb,
  subject =      "Numerical Analysis (cs.NA)",
}

@Article{Kramer:2012:MAP,
  author =       "Walter Kr{\"a}mer",
  title =        "Multiple\slash arbitrary precision interval
                 computations in {C-XSC}",
  journal =      j-COMPUTING,
  volume =       "94",
  number =       "2--4",
  pages =        "229--241",
  month =        mar,
  year =         "2012",
  CODEN =        "CMPTA2",
  DOI =          "https://doi.org/10.1007/s00607-011-0174-8",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Mon Apr 9 16:41:18 MDT 2012",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=94&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=94&issue=2&spage=229",
  acknowledgement = ack-nhfb,
  author-dates = "1952--2014",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  remark =       "Special Issue on GAMM--IMACS International Symposium
                 on Scientific Computing, Computer Arithmetic and
                 Validated Numerics (SCAN2010).",
}

@InProceedings{Kumm:2012:RCS,
  author =       "Martin Kumm and Katharina Liebisch and Peter Zipf",
  editor =       "????",
  booktitle =    "{IEEE 22nd International Conference on Field
                 Programmable Logic and Application (FPL), 2012}",
  title =        "Reduced Complexity Single and Multiple Constant
                 Multiplication in Floating Point Precision",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "255--261",
  year =         "2012",
  DOI =          "https://doi.org/10.1109/FPL.2012.6339190",
  bibdate =      "Sat Feb 08 09:39:36 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/document/6339190/",
  acknowledgement = ack-nhfb,
}

@Article{Kurka:2012:FAA,
  author =       "Petr K{\r{u}}rka",
  title =        "Fast Arithmetical Algorithms in {M{\"o}bius} Number
                 Systems",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "61",
  number =       "8",
  pages =        "1097--1109",
  month =        aug,
  year =         "2012",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2012.87",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jul 27 08:30:49 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Langlois:2012:ACT,
  author =       "Philippe Langlois and Matthieu Martel and Laurent
                 Th{\'e}venoux",
  editor =       "????",
  booktitle =    "{Proceedings of the 15th GAMM--IMACS International
                 Symposium on Scientific Computing, Computer Arithmetic
                 and Validated Numerics, Novosibirsk, Russia}",
  title =        "Automatic code transformation to optimize accuracy and
                 speed in floating-point arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "??--??",
  year =         "2012",
  bibdate =      "Sat Apr 01 07:42:30 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://hal.archives-ouvertes.fr/hal-00821667",
  abstract =     "We want to allow the standard software developer to
                 automatically transform his/her code in order to
                 increase the accuracy of floating-point computations.
                 This transformation is actually an optimization since
                 we aim to take into account two opposite criteria:
                 accuracy and execution time. A first step towards this
                 automatic optimization is presented in this work. We
                 propose to automatically introduce at the compile-time
                 compensation steps in (parts of) the floating-point
                 computations. We present a tool to parse C codes and to
                 insert compensated floating-point operations. This
                 provides a compensated computation that improves the
                 accuracy of specific computing patterns.",
  acknowledgement = ack-nhfb,
}

@TechReport{Langlois:2012:CTS,
  author =       "Philippe Langlois and David Parello and Bernard
                 Goossens and Kathy Porada",
  title =        "Computing time for summation algorithm: Less hazard
                 and more scientific research",
  type =         "Research Report",
  number =       "RR-12021",
  institution =  "LIRMM, Universit{\'e} Montpellier 2",
  address =      "CNRS UMR 5506, France",
  pages =        "i + 34",
  year =         "2012",
  bibdate =      "Sat Apr 01 08:09:42 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://personales.unican.es/segurajj/numsoft12/;
                 https://hal-lirmm.ccsd.cnrs.fr/lirmm-00737617;
                 https://hal-lirmm.ccsd.cnrs.fr/lirmm-00737617/document",
  abstract =     "Several accurate algorithms to sum IEEE-754
                 floating-point numbers have been recently published.
                 The recent contributions by Rump, Ogita and Oishi and
                 the newest ones proposed by Zhu and Hayes are examples
                 of accurate summation algorithms. Some of these even
                 compute the faithful or the correct rounding of the
                 exact sum, i.e. the most accurate value with respect to
                 the finite precision of the floating-point arithmetic.
                 This computed sum does not suffer anymore from the
                 condition number of the summation. In such cases, the
                 run-time performances and the memory prints become the
                 discriminant properties to decide which algorithm is
                 best.\par

                 In this paper we focus on the reliability of the
                 run-time performance measure of such core algorithms.
                 We explain how right Rump when he writes ``Measuring
                 the computing time of summation algorithms in a
                 high-level language on today's architectures is more of
                 a hazard than scientific research.'' Neither the
                 classical flop count nor hardware counter based
                 measures are satisfactory here. We propose to analyze
                 the instruction level parallelism of these algorithms
                 to reliably evaluate their performance potential. We
                 use PerPI, a software tool that automatizes an almost
                 machine independent instruction-level parallelism
                 analysis. We study recent accurate summation algorithms
                 with a detailed focus on the two newest faithful ones.
                 We illustrate and discuss why PerPI provides a more
                 reliable performance analysis, the remaining weakness
                 and how to improve confidence for future contributions
                 in this area.",
  acknowledgement = ack-nhfb,
  keywords =     "correct rounding; faithful summation; floating-point
                 arithmetic, accurate summation; instruction level
                 parallelism; performance evaluation; PerPI;
                 reproducibility",
}

@Article{Lee:2012:CPS,
  author =       "Mun-Kyu Lee",
  title =        "Comments on {``Provably Sublinear Point Multiplication
                 on Koblitz Curves and Its Hardware Implementation''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "61",
  number =       "4",
  pages =        "591--592",
  month =        apr,
  year =         "2012",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2011.109",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Mar 10 16:19:08 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  note =         "See \cite{Dimitrov:2008:PSP}.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Lee:2012:DHP,
  author =       "Yong-Hwan Lee and Young-Sung Cho and Sangook Moon",
  title =        "Design of a high precision logarithmic converter in a
                 binary floating point divider",
  journal =      j-CCPE,
  volume =       "24",
  number =       "4",
  pages =        "342--353",
  month =        "????",
  year =         "2012",
  CODEN =        "CCPEBO",
  DOI =          "https://doi.org/10.1002/cpe.1569",
  ISSN =         "1532-0626 (print), 1532-0634 (electronic)",
  ISSN-L =       "1532-0626",
  bibdate =      "Wed Apr 4 09:18:01 MDT 2012",
  bibsource =    "http://www.interscience.wiley.com/jpages/1532-0626;
                 https://www.math.utah.edu/pub/tex/bib/ccpe.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Concurrency and Computation: Prac\-tice and
                 Experience",
  journal-URL =  "http://www.interscience.wiley.com/jpages/1532-0626",
  onlinedate =   "1 Apr 2010",
}

@Article{Li:2012:ENE,
  author =       "Wenbin Li and Sven Simon and Steffen Kie{\ss}",
  title =        "On the estimation of numerical error bounds in linear
                 algebra based on discrete stochastic arithmetic",
  journal =      j-APPL-NUM-MATH,
  volume =       "62",
  number =       "5",
  pages =        "536--555",
  month =        may,
  year =         "2012",
  CODEN =        "ANMAEL",
  DOI =          "https://doi.org/10.1016/j.apnum.2012.01.001",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Thu Mar 8 07:24:49 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0168927412000086",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
}

@Article{Liedel:2012:SDC,
  author =       "Manuel Liedel",
  title =        "Secure Distributed Computation of the Square Root and
                 Applications",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "7232",
  pages =        "277--288",
  year =         "2012",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-642-29101-2_19",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Mon Dec 24 07:23:24 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs2012c.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-3-642-29101-2_19/;
                 http://link.springer.com/content/pdf/10.1007/978-3-642-29101-2_19",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-642-29101-2",
  book-URL =     "http://www.springerlink.com/content/978-3-642-29101-2",
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Liu:2012:PED,
  author =       "Wei Liu and Alberto Nannarelli",
  title =        "Power Efficient Division and Square Root Unit",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "61",
  number =       "8",
  pages =        "1059--1070",
  month =        aug,
  year =         "2012",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2012.82",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jul 27 08:30:49 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Mahapatra:2012:FIS,
  author =       "Chinmaya Mahapatra and Saad Mahboob and Victor C. M.
                 Leung and Thanos Stouraitis",
  booktitle =    "{2012 International Conference on Control Engineering
                 and Communication Technology}",
  title =        "Fast Inverse Square Root Based Matrix Inverse for
                 {MIMO-LTE} Systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "321--324",
  year =         "2012",
  DOI =          "https://doi.org/10.1109/ICCECT.2012.253",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Arrays; CORDIC; Fast inverse square root; Field
                 programmable gate arrays; Hardware; Matrix
                 decomposition; MIMO; MIMO LTE; Pipeline processing;
                 Pipelining; QR decomposition; Systolic array; Xilinx
                 virtex6 FPGA",
}

@Article{Maitra:2012:NAC,
  author =       "Subhashis Maitra and Amitabha Sinha",
  title =        "A new algorithm for computing triple-base number
                 system",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "40",
  number =       "4",
  pages =        "3--9",
  month =        sep,
  year =         "2012",
  CODEN =        "CANED2",
  DOI =          "https://doi.org/10.1145/2411116.2411119",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Tue Dec 11 08:06:57 MST 2012",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
  abstract =     "We introduce here a generalized method a new Algorithm
                 to find Triple-Base number system and Triple-Base chain
                 and hence in turn Single Digit Triple-Base number
                 system(SDTBNS). The proposed method is not only simpler
                 and faster than the Algorithms to find Double-Base
                 number system or Double-Base chain, experimentally it
                 also returns a shorter length of Triple-Base chain
                 which in turn reduces the size of the look-up-table to
                 find out SDTBNS. The complexity analysis and
                 experimental results shows the novelty of the proposed
                 Algorithm. Moreover when the proposed method is applied
                 to find scalar multiplication in case of Elliptic Curve
                 Cryptography and coefficient multiplication in case of
                 designing digital filter, its efficiency also proves
                 its novelty. Here we have used third base as $5$
                 because when it is multiplied by $2$ gives $ 10 $ which
                 can be efficiently used for decimal shifting, i.e. if
                 an integer '$n$' can be represented in SDTBNS form,
                 then $ n / 10_x $ or $ n \times 10_x $ can also
                 represented in SDTBNS only by diving or multiplying
                 '$n$' by $ 10 $.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
}

@InBook{Markovi:2012:CDS,
  author =       "Dejan Markovi and Robert W. Brodersen",
  booktitle =    "{DSP} Architecture Design Essentials",
  title =        "{CORDIC}, Divider, Square Root",
  publisher =    "Springer US",
  pages =        "91--110",
  year =         "2012",
  DOI =          "https://doi.org/10.1007/978-1-4419-9660-2_6",
  ISBN =         "1-4419-9660-5",
  ISBN-13 =      "978-1-4419-9660-2",
  bibdate =      "Tue Oct 28 07:04:09 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Masotti:2012:FPN,
  author =       "Glauco Masotti",
  title =        "Floating-Point Numbers with Error Estimates
                 (revised)",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--45",
  day =          "28",
  month =        jan,
  year =         "2012",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/1201.5975",
  abstract =     "The study addresses the problem of precision in
                 floating-point (FP) computations. A method for
                 estimating the errors which affect intermediate and
                 final results is proposed and a summary of many
                 software simulations is discussed. The basic idea
                 consists of representing FP numbers by means of a data
                 structure collecting value and estimated error
                 information. Under certain constraints, the estimate of
                 the absolute error is accurate and has a compact
                 statistical distribution. By monitoring the estimated
                 relative error during a computation (an ad-hoc
                 definition of relative error has been used), the
                 validity of results can be ensured. The error estimate
                 enables the implementation of robust algorithms, and
                 the detection of ill-conditioned problems. A dynamic
                 extension of number precision, under the control of
                 error estimates, is advocated, in order to compute
                 results within given error bounds. A reduced time
                 penalty could be achieved by a specialized FP
                 processor. The realization of a hardwired processor
                 incorporating the method, with current technology,
                 should not be anymore a problem and would make the
                 practical adoption of the method feasible for most
                 applications.",
  acknowledgement = ack-nhfb,
  subject =      "Numerical Analysis (cs.NA)",
}

@Misc{McCalpin:2012:OSH,
  author =       "J. D. McCalpin",
  title =        "Is ``ordered summation'' a hard problem to speed up?",
  howpublished = "Web document",
  day =          "28",
  month =        may,
  year =         "2012",
  bibdate =      "Sat Oct 31 07:16:11 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://blogs.utexas.edu/jdm4372/2012/02/15/is-ordered-summation-a-hard-problem-to-speed-up/",
  acknowledgement = ack-nhfb,
}

@Article{Milicevic:2012:PAO,
  author =       "Aleksandar Milicevic and Daniel Jackson",
  title =        "Preventing Arithmetic Overflows in {Alloy}",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "7316",
  pages =        "108--121",
  year =         "2012",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-642-30885-7_8",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Mon Dec 24 07:32:30 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs2012e.bib",
  URL =          "http://link.springer.com/content/pdf/10.1007/978-3-642-30885-7_8",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-642-30885-7",
  book-URL =     "http://www.springerlink.com/content/978-3-642-30885-7",
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InProceedings{Mine:2012:ADB,
  author =       "Antoine Min{\'e}",
  editor =       "Gudmund Grov",
  booktitle =    "{WING'12 --- 4th International Workshop on Invariant
                 Generation, held on June 30, 2012 in Manchester, UK}",
  title =        "Abstract domains for bit-level machine integer and
                 floating-point operations",
  publisher =    pub-ELSEVIER,
  address =      pub-ELSEVIER:adr,
  pages =        "16",
  year =         "2012",
  bibdate =      "Sat Jun 4 17:14:37 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mukunoki:2012:PCD,
  author =       "Daichi Mukunoki and Daisuke Takahashi",
  editor =       "????",
  booktitle =    "{ATIP '12: Proceedings of the ATIP\slash A*CRC
                 Workshop on Accelerator Technologies for
                 High-Performance Computing: Does Asia Lead the Way?}",
  title =        "Performance Comparison of Double, Triple and Quadruple
                 Precision Real and Complex {BLAS} Subroutines on {GPUs}
                 (extended abstract)",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "788--790",
  year =         "2012",
  ISBN =         "1-4503-1644-1",
  ISBN-13 =      "978-1-4503-1644-6",
  LCCN =         "????",
  bibdate =      "Wed Nov 14 11:07:15 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "doubled double precision; quad-double precision;
                 triple precision",
  remark =       "From page 788: ``\ldots{} the computation cost of the
                 quadruple precision BLAS subroutines is approximately
                 20 times more than the double precision
                 subroutines.''",
}

@Article{Muller:2012:SSV,
  author =       "Norbert Th. M{\"u}ller and Christian Uhrhan",
  title =        "Some Steps into Verification of Exact Real
                 Arithmetic",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "7226",
  pages =        "168--173",
  year =         "2012",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-642-28891-3_17",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Wed Dec 19 15:18:01 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs2012c.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-3-642-28891-3_17/",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-642-28891-3",
  book-URL =     "http://www.springerlink.com/content/978-3-642-28891-3",
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Nehmeier:2012:SHI,
  author =       "M. Nehmeier and S. Siegel and J. Wolff von Gudenberg",
  title =        "Specification of hardware for interval arithmetic",
  journal =      j-COMPUTING,
  volume =       "94",
  number =       "2--4",
  pages =        "243--255",
  month =        mar,
  year =         "2012",
  CODEN =        "CMPTA2",
  DOI =          "https://doi.org/10.1007/s00607-012-0185-0",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Mon Apr 9 16:41:18 MDT 2012",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=94&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=94&issue=2&spage=243",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "Hardware design; Interval arithmetic; Interval
                 standardization",
  remark =       "Special Issue on GAMM--IMACS International Symposium
                 on Scientific Computing, Computer Arithmetic and
                 Validated Numerics (SCAN2010).",
}

@Article{Neron:2012:FPS,
  author =       "Pierre Neron",
  title =        "A Formal Proof of Square Root and Division Elimination
                 in Embedded Programs",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "7679",
  pages =        "256--272",
  year =         "2012",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-642-35308-6_20",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sun Dec 16 12:08:25 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs2012l.bib",
  URL =          "http://www.springerlink.com//chapter/10.1007/978-3-642-35308-6_20/",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-642-35308-6Certified
                 Programs and Proofs",
  book-URL =     "http://www.springerlink.com/content/978-3-642-35308-6",
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Oudjida:2012:NHR,
  author =       "A. K. Oudjida and N. Chaillet and M. L. Berrandjia and
                 A. Liacha",
  title =        "A new high radix-2 $r$ ($ r \geq 8 $) multibit
                 recoding algorithm for large operand size ({$ N \geq 32
                 $}) multipliers",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "40",
  number =       "4",
  pages =        "32--43",
  month =        sep,
  year =         "2012",
  CODEN =        "CANED2",
  DOI =          "https://doi.org/10.1145/2411116.2411122",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Tue Dec 11 08:06:57 MST 2012",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
  abstract =     "This paper addresses the problem of multiplication
                 with large operand sizes ($ N \geq 32 $). We propose a
                 new recursive recoding algorithm that shortens the
                 critical path of the multiplier and reduces the
                 hardware complexity of partial-product-generators as
                 well. The new recoding algorithm provides an optimal
                 space/time partitioning of the multiplier architecture
                 for any size $N$ of the operands. As a result, the
                 critical path is drastically reduced to $ 3^3 \sqrt N /
                 2 - 3 $ with no area overhead in comparison to modified
                 Booth algorithm that shows a critical path of $ N / 2 $
                 in adder stages. For instance, only $7$ adder stages
                 are needed for a 64-bit two's complement multiplier.
                 Confronted to reference algorithms for $ N = 64 $,
                 important gain ratios of $ 1.62 $, $ 1.71 $, $ 2.64 $
                 are obtained in terms of multiply-time, energy
                 consumption per multiply operation, and total gate
                 count, respectively.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
}

@Article{Ozaki:2012:FAF,
  author =       "Katsuhisa Ozaki and Takeshi Ogita and Siegfried M.
                 Rump and Shin'ichi Oishi",
  title =        "Fast algorithms for floating-point interval matrix
                 multiplication",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "236",
  number =       "7",
  pages =        "1795--1814",
  month =        jan,
  year =         "2012",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:24:38 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042711005449",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@PhdThesis{Panhaleux:2012:CFP,
  author =       "A. Panhaleux",
  title =        "Contributions to floating-point arithmetic: Coding and
                 correct rounding of algebraic functions",
  type =         "{Ph.D.} dissertation",
  school =       "{\'E}cole Normale Sup{\'e}rieure de Lyon",
  address =      "Lyon, France",
  year =         "2012",
  bibdate =      "Sun Jun 19 15:08:09 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://theses.hal.science/tel-00744373v1",
  abstract =     "Efficient and reliable computer arithmetic is a key
                 requirement to perform fast and reliable numerical
                 computations. The choice of the number system and the
                 choice of the arithmetic algorithms are important. We
                 present a new representation of numbers, the
                 ``RN-codings'', such that truncating a RN-coded number
                 to some position is equivalent to rounding it to the
                 nearest. We give some arithmetic algorithms for
                 manipulating RN-codings and introduce the concept of
                 ``floating-point RN-codings''. When implementing a
                 function f in floating-point arithmetic, if we wish to
                 always return the floating-point number nearest $ f(x)
                 $, one must be able to determine if $ f(x) $ is above
                 or below the closest ``midpoint'', where a midpoint is
                 the middle of two consecutive floating-point numbers.
                 This determination is first done with some given
                 precision, and if it does not suffice, we start again
                 with higher precision, and so on. This process may not
                 terminate if $ f(x) $ can be a midpoint. Given an
                 algebraic function $f$, we try either to show that
                 there are no floating-point numbers $x$ such that $
                 f(x)$ is a midpoint, or we try to enumerate or
                 characterize them. Since the IBM PowerPC, binary
                 division has frequently been implemented using variants
                 of the Newton-Raphson iteration due to Peter Markstein.
                 This iteration is very fast, but much care is needed if
                 we aim at always returning the floating-point number
                 nearest the exact quotient. We investigate a way of
                 efficiently merging Markstein iterations with faster
                 yet less accurate iterations called Goldschmidt
                 iterations. We also investigate whether those
                 iterations can be used for decimal floating-point
                 arithmetic. We provide sure and tight error bounds for
                 these algorithms.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Petrovsky:2012:CIL,
  author =       "Nicolai A. Petrovsky and Marek Parfieniuk",
  booktitle =    "{2012 International Conference on Signals and
                 Electronic Systems (ICSES)}",
  title =        "The {CORDIC-inside-lifting} architecture for
                 constant-coefficient hardware quaternion multipliers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--6",
  year =         "2012",
  DOI =          "https://doi.org/10.1109/ICSES.2012.6382236",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Approximation algorithms; Approximation methods; Field
                 programmable gate arrays; Hardware; Pipeline
                 processing; Quaternions; Vectors",
}

@InProceedings{Pongyupinpanich:2012:DEF,
  author =       "S. Pongyupinpanich and F. A. Samman and M. Glesner and
                 S. Singhaniyom",
  booktitle =    "{2012 9th International Conference on Electrical
                 Engineering/Electronics, Computer, Telecommunications
                 and Information Technology}",
  title =        "Design and evaluation of a floating-point division
                 operator based on {CORDIC} algorithm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--4",
  year =         "2012",
  DOI =          "https://doi.org/10.1109/ECTICon.2012.6254331",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithm design and analysis; Computer architecture;
                 Convergence; Field programmable gate arrays; Hardware;
                 MATLAB; Signal processing algorithms",
}

@InProceedings{Raj:2012:RLC,
  author =       "Krishna Raj and Praveen Kumar Singh and Rajkumar
                 Tomar",
  booktitle =    "{2012 2nd International Conference on Power, Control
                 and Embedded Systems}",
  title =        "A review of low cost multiplier using {CORDIC}
                 subsystem",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--5",
  year =         "2012",
  DOI =          "https://doi.org/10.1109/ICPCES.2012.6508092",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; Artificial intelligence; Clocks; Complex
                 multiplication; Costs; Hardware; Logic; Parallel
                 multiplier; Pipelined rotator; Recursive rotator;
                 Serial multiplier; Shift registers; Signal processing
                 algorithms; Sonar applications; Throughput",
}

@Article{Rodriguez:2012:RRE,
  author =       "Marcos Rodr{\'\i}guez and Roberto Barrio",
  title =        "Reducing rounding errors and achieving {Brouwer}'s law
                 with {Taylor Series Method}",
  journal =      j-APPL-NUM-MATH,
  volume =       "62",
  number =       "8",
  pages =        "1014--1024",
  month =        aug,
  year =         "2012",
  CODEN =        "ANMAEL",
  DOI =          "https://doi.org/10.1016/j.apnum.2012.03.008",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Sat Apr 28 09:37:06 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0168927412000645",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
}

@Article{Rump:2012:EEF,
  author =       "Siegfried M. Rump",
  title =        "Error estimation of floating-point summation and dot
                 product",
  journal =      j-BIT-NUM-MATH,
  volume =       "52",
  number =       "1",
  pages =        "201--220",
  month =        mar,
  year =         "2012",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/s10543-011-0342-4",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Mon Apr 9 17:00:06 MDT 2012",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=52&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=52&issue=1&spage=201",
  abstract =     "We improve the well-known Wilkinson-type estimates for
                 the error of standard floating-point recursive
                 summation and dot product by up to a factor 2. The
                 bounds are valid when computed in rounding to nearest,
                 no higher order terms are necessary, and they are best
                 possible. For summation there is no restriction on the
                 number of summands. The proofs are short by using a new
                 tool for the estimation of errors in floating-point
                 computations which cures drawbacks of the ``unit in the
                 last place (ulp)''. The presented estimates are nice
                 and simple, and closer to what one may expect.",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT Numerical Mathematics",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "accurate floating-point dot product; accurate
                 floating-point summation",
}

@Article{Rump:2012:FIM,
  author =       "Siegfried M. Rump",
  title =        "Fast interval matrix multiplication",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "61",
  number =       "1",
  pages =        "1--34",
  month =        sep,
  year =         "2012",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Wed Mar 6 09:10:18 MST 2013",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1017-1398&volume=61&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=1017-1398&volume=61&issue=1&spage=1",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Article{Saha:2012:DHS,
  author =       "Prabir Saha and Arindam Banerjee and Anup Dandapat and
                 Partha Bhattacharyya",
  title =        "Design of High Speed {Vedic} Multiplier for Decimal
                 Number System",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "7373",
  pages =        "79--88",
  year =         "2012",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-642-31494-0_10",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Wed Dec 19 15:21:09 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs2012f.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-3-642-31494-0_10/",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-642-31494-0",
  book-URL =     "http://www.springerlink.com/content/978-3-642-31494-0",
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Saito:2012:AGM,
  author =       "Tsubasa Saito and Emiko Ishiwata and Hidehiko
                 Hasegawa",
  title =        "Analysis of the {GCR} method with mixed precision
                 arithmetic using {QuPAT}",
  journal =      j-J-COMPUT-SCI,
  volume =       "3",
  number =       "3",
  pages =        "87--91",
  month =        may,
  year =         "2012",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/j.jocs.2011.05.001",
  ISSN =         "1877-7503 (print), 1877-7511 (electronic)",
  ISSN-L =       "1877-7503",
  bibdate =      "Tue Sep 19 13:53:15 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputsci.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/S1877750311000329",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Comput. Sci.",
  fjournal =     "Journal of Computational Science",
  journal-URL =  "https://www.sciencedirect.com/journal/journal-of-computational-science",
}

@Article{Seo:2012:MPM,
  author =       "Hwajeong Seo and Howon Kim",
  title =        "Multi-precision Multiplication for Public-Key
                 Cryptography on Embedded Microprocessors",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "7690",
  pages =        "55--67",
  year =         "2012",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-642-35416-8_5",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Wed Dec 19 15:18:58 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs2012l.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-3-642-35416-8_5/",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-642-35416-8",
  book-URL =     "http://www.springerlink.com/content/978-3-642-35416-8",
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@InProceedings{Sheikh:2012:AFP,
  author =       "Basit Riaz Sheikh and Rajit Manohar",
  editor =       "{IEEE}",
  booktitle =    "{2012 IEEE International Symposium on Asynchronous
                 Circuits and Systems: proceedings, ASYNC 2012: 7--9 May
                 2012, Copenhagen, Denmark}",
  title =        "An Asynchronous Floating-Point Multiplier",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "89--96",
  year =         "2012",
  DOI =          "https://doi.org/10.1109/ASYNC.2012.19",
  ISBN =         "1-4673-1360-2, 0-7695-4688-9",
  ISBN-13 =      "978-1-4673-1360-5, 978-0-7695-4688-9",
  ISSN =         "1522-8681",
  ISSN-L =       "1522-8681",
  LCCN =         "TK7868.A79",
  bibdate =      "Sat Apr 02 16:30:48 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=6242773",
  acknowledgement = ack-nhfb,
}

@InProceedings{Shi:2012:DPM,
  author =       "Jiangyi Shi and Mingxing Wang and Yinghui Tian and Zhe
                 Yang",
  booktitle =    "{2012 Second International Conference on Intelligent
                 System Design and Engineering Application}",
  title =        "Design of Plural-Multiplier Based on {CORDIC}
                 Algorithm for {FFT} Application",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1220--1223",
  year =         "2012",
  DOI =          "https://doi.org/10.1109/ISdea.2012.500",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; Agricultural machinery; Algorithm design and
                 analysis; CORDIC algorithm; FFT; Hardware; Pipeline
                 processing; Pipeline structure; Plural-Multiplier;
                 Signal processing algorithms; Simulation",
}

@Article{Siegel:2012:LAL,
  author =       "Stefan Siegel and J{\"u}rgen Wolff von Gudenberg",
  title =        "A long accumulator like a carry-save adder",
  journal =      j-COMPUTING,
  volume =       "94",
  number =       "2--4",
  pages =        "203--213",
  month =        mar,
  year =         "2012",
  CODEN =        "CMPTA2",
  DOI =          "https://doi.org/10.1007/s00607-011-0164-x",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Mon Apr 9 16:41:18 MDT 2012",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=94&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=94&issue=2&spage=203",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "accurate floating-point dot product; accurate
                 floating-point summation",
  remark =       "Special Issue on GAMM--IMACS International Symposium
                 on Scientific Computing, Computer Arithmetic and
                 Validated Numerics (SCAN2010).",
}

@Article{Su:2012:IIN,
  author =       "Chen Su and Haining Fan",
  title =        "Impact of {Intel}'s new instruction sets on software
                 implementation of {$ {\rm GF}(2)[x] $} multiplication",
  journal =      j-INFO-PROC-LETT,
  volume =       "112",
  number =       "12",
  pages =        "497--502",
  day =          "30",
  month =        jun,
  year =         "2012",
  CODEN =        "IFPLAT",
  DOI =          "https://doi.org/10.1016/j.ipl.2012.03.012",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Mon May 21 07:13:00 MDT 2012",
  bibsource =    "http://www.sciencedirect.com/science/journal/00200190;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/infoproc2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0020019012000804",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  keywords =     "AVX; Cryptography; GF(2)[x] multiplication; Karatsuba
                 algorithm; PCLMULQDQ; SSE",
}

@Article{Sudha:2012:NMC,
  author =       "J. Sudha and M. C. Hanumantharaju and V.
                 Venkateswarulu and Jayalaxmi H",
  title =        "A Novel Method for Computing Exponential Function
                 Using {CORDIC} Algorithm",
  journal =      "Procedia Engineering",
  volume =       "30",
  pages =        "519--528",
  year =         "2012",
  DOI =          "https://doi.org/10.1016/j.proeng.2012.01.893",
  ISSN =         "1877-7058",
  ISSN-L =       "1877-7058",
  bibdate =      "Sat Oct 18 15:38:59 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Swartzlander:2012:FIF,
  author =       "Earl E. Swartzlander and Hani H. M. Saleh",
  title =        "{FFT} Implementation with Fused Floating-Point
                 Operations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "61",
  number =       "2",
  pages =        "284--288",
  month =        feb,
  year =         "2012",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.271",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Jan 13 17:55:10 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5669293",
  abstract =     "This paper applies two fused floating-point operations
                 to the implementation of fast Fourier transform
                 butterfly units. The operations are a fused two-term
                 dot product and a fused add-subtract unit. The FFT
                 `butterfly' operations consist of complex
                 multiplications, additions and subtractions. Both
                 radix-2 and radix-4 butterflies are implemented
                 efficiently with the two fused floating-point
                 operations. When placed and routed using a high
                 performance standard cell technology, the fused FFT
                 butterflies are about 15\% faster and 30\% smaller than
                 a conventional implementation. Also the numerical
                 results of the fused implementations are slightly more
                 accurate since they use fewer rounding operations.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  book-URL =     "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Thome:2012:SRA,
  author =       "Emmanuel Thom{\'e}",
  title =        "Square Root Algorithms for the Number Field Sieve",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "7369",
  pages =        "208--224",
  year =         "2012",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-642-31662-3_15",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Mon Dec 24 07:44:06 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-3-642-31662-3_15/;
                 http://link.springer.com/content/pdf/10.1007/978-3-642-31662-3_15",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-642-31662-3",
  book-URL =     "http://www.springerlink.com/content/978-3-642-31662-3",
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Vazquez:2012:RFP,
  author =       "Alvaro Vazquez and Julio Villalba-Moreno and Elisardo
                 Antelo and Emilio L. Zapata",
  title =        "Redundant Floating-Point Decimal {CORDIC} Algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "61",
  number =       "11",
  pages =        "1551--1562",
  month =        nov,
  year =         "2012",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2011.217",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Oct 22 08:22:47 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Wang:2012:EMB,
  author =       "Zhen Wang and Shuqin Fan",
  title =        "Efficient {Montgomery}-Based Semi-Systolic Multiplier
                 for Even-Type {GNB} of {$ {\rm GF}(2^m) $}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "61",
  number =       "3",
  pages =        "415--419",
  month =        mar,
  year =         "2012",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2010.272",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Feb 3 07:35:03 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Wang:2012:RCC,
  author =       "Dong Wang and Milo{\v{s}} D. Ercegovac",
  title =        "A Radix-16 Combined Complex Division\slash Square Root
                 Unit with Operand Prescaling",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "61",
  number =       "9",
  pages =        "1243--1255",
  month =        sep,
  year =         "2012",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2011.143",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Aug 29 17:48:10 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Wang:2012:UBW,
  author =       "Xi Wang and Haogang Chen and Alvin Cheung and Zhihao
                 Jia and Nickolai Zeldovich and M. Frans Kaashoek",
  editor =       "{ACM}",
  booktitle =    "Proceedings of the {Asia--Pacific Workshop on Systems:
                 APSys '12, July 23--24, 2012, Seoul, South Korea}",
  title =        "Undefined Behavior: What Happened to My Code?",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "101",
  year =         "2012",
  DOI =          "https://doi.org/10.1145/2349896.2349905",
  ISBN =         "1-4503-1669-7",
  ISBN-13 =      "978-1-4503-1669-9",
  LCCN =         "QA75.5",
  bibdate =      "Thu Feb 18 06:30:11 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2349896",
  abstract =     "System programming languages such as C grant compiler
                 writers freedom to generate efficient code for a
                 specific instruction set by defining certain language
                 constructs as undefined behavior. Unfortunately, the
                 rules for what is undefined behavior are subtle and
                 programmers make mistakes that sometimes lead to
                 security vulnerabilities. This position paper argues
                 that the research community should help address the
                 problems that arise from undefined behavior, and not
                 dismiss them as esoteric C implementation issues. We
                 show that these errors do happen in real-world systems,
                 that the issues are tricky, and that current practices
                 to address the issues are insufficient.",
  acknowledgement = ack-nhfb,
  remark =       "This article exhibits several small code snippets
                 where, because of C's rules of undefined behavior,
                 compilers are free to change, order, or even eliminate,
                 code in unexpected ways. Several of the examples are
                 protective code intended to detect errors, such as
                 division by zero and pointer dereferencing.",
}

@Article{Yan:2012:RBC,
  author =       "Song Yan",
  title =        "Review of {{\booktitle{Modern Computer Arithmetic}},
                 by Richard Brent and Paul Zimmermann}",
  journal =      j-SIGACT,
  volume =       "43",
  number =       "4",
  pages =        "49--51",
  month =        dec,
  year =         "2012",
  CODEN =        "SIGNDM",
  DOI =          "https://doi.org/10.1145/2421119.2421130",
  ISSN =         "0163-5700 (print), 1943-5827 (electronic)",
  ISSN-L =       "0163-5700",
  bibdate =      "Sun May 5 10:25:40 MDT 2013",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigact.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGACT News",
  journal-URL =  "http://dl.acm.org/citation.cfm?id=J697",
}

@Article{Yan:2012:RMC,
  author =       "Song Yan",
  title =        "Review of {{\booktitle{Modern Computer Arithmetic}},
                 by Richard Brent and Paul Zimmermann}",
  journal =      j-SIGACT,
  volume =       "43",
  number =       "4",
  pages =        "49--51",
  month =        dec,
  year =         "2012",
  CODEN =        "SIGNDM",
  DOI =          "https://doi.org/10.1145/2421119.2421130",
  ISSN =         "0163-5700 (print), 1943-5827 (electronic)",
  ISSN-L =       "0163-5700",
  bibdate =      "Sun May 5 10:25:40 MDT 2013",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigact.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGACT News",
  journal-URL =  "http://dl.acm.org/citation.cfm?id=J697",
}

@InProceedings{Yang:2012:CDS,
  author =       "Bohan Yang and Dong Wang and Leibo Liu",
  booktitle =    "{2012 2nd International Conference on Consumer
                 Electronics, Communications and Networks (CECNet)}",
  title =        "Complex division and square-root using {CORDIC}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2464--2468",
  year =         "2012",
  DOI =          "https://doi.org/10.1109/CECNet.2012.6201840",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Adders; Algorithm design and analysis;
                 Complex; Computer architecture; CORDIC; Division; Field
                 programmable gate arrays; FPGA; Hardware; Registers;
                 Square-root",
}

@Article{Anguita:2013:EES,
  author =       "D. Anguita and A. Ghio and L. Oneto and X. Parra and
                 J. L. Reyes-Ortiz",
  title =        "Energy Efficient {Smartphone}-Based Activity
                 Recognition using Fixed-Point Arithmetic",
  journal =      j-J-UCS,
  volume =       "19",
  number =       "9",
  pages =        "1295--??",
  month =        "????",
  year =         "2013",
  CODEN =        "????",
  ISSN =         "0948-695X (print), 0948-6968 (electronic)",
  ISSN-L =       "0948-6968",
  bibdate =      "Fri Sep 13 11:19:07 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jucs.bib",
  URL =          "http://www.jucs.org/jucs_19_9/energy_efficient_smartphone_based",
  acknowledgement = ack-nhfb,
  fjournal =     "J.UCS: Journal of Universal Computer Science",
  journal-URL =  "http://www.jucs.org/jucs",
}

@InProceedings{Anonymous:2013:DML,
  author =       "Anonymous",
  title =        "Dedication: In memory of {Luigi Ciminiera} 1954--2012
                 and In memory of {Luigi Dadda} 1923--2012",
  crossref =     "IEEE:2013:PIS",
  pages =        "ix--xi",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.11",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-21; Biographies; Ciminiera, Luigi; Dadda, Luigi;
                 Obituaries",
}

@Misc{Anonymous:2013:IOF,
  author =       "Anonymous",
  title =        "{Intel} overstates {FPU} accuracy",
  howpublished = "Web document",
  day =          "1",
  month =        jun,
  year =         "2013",
  bibdate =      "Sat Jun 04 16:53:16 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.notabs.org/fpuaccuracy/",
  abstract =     "For nearly 20 years Intel has claimed high accuracy
                 for the transcendental floating point instructions in
                 its PC processor products. Intel documentation for the
                 1993 Pentium states: On the Pentium processor, the
                 worst case error on functions is less than 1 ulp when
                 rounding to the nearest-even and less than 1.5 ulps
                 when rounding in other modes. This claim has never been
                 true for the instructions fsin, fcos, fsincos, and
                 fptan. The red in the plots below show ranges where the
                 error exceeds 1.0 ulp.",
  acknowledgement = ack-nhfb,
}

@Article{Antao:2013:CFA,
  author =       "Samuel Ant{\~a}o and Leonel Sousa",
  title =        "The {CRNS} framework and its application to
                 programmable and reconfigurable cryptography",
  journal =      j-TACO,
  volume =       "9",
  number =       "4",
  pages =        "33:1--33:??",
  month =        jan,
  year =         "2013",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2400682.2400692",
  ISSN =         "1544-3566 (print), 1544-3973 (electronic)",
  ISSN-L =       "1544-3566",
  bibdate =      "Fri Jan 18 10:57:16 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/taco.bib",
  abstract =     "This article proposes the Computing with the Residue
                 Number System (CRNS) framework, which aims at the
                 design automation of accelerators for Modular
                 Arithmetic (MA). The framework provides a comprehensive
                 set of tools ranging from a programming language and
                 respective compiler to back-ends targeting parallel
                 computation platforms such as Graphical Processing
                 Units (GPUs) and reconfigurable hardware. Given an
                 input algorithm described with a high-level programming
                 language, the CRNS can be used to obtain in a few
                 seconds the corresponding optimized Parallel Thread
                 Execution (PTX) program ready to be run on GPUs or the
                 Hardware Description Language (HDL) specification of a
                 fully functional accelerator suitable for
                 reconfigurable hardware and embedded systems. The
                 resulting framework's implementations benefit from the
                 Residue Number System (RNS) arithmetic's
                 parallelization properties in a fully automated way.
                 Designers do not need to be familiar with the
                 mathematical details concerning the employed
                 arithmetic, namely the RNS representation. In order to
                 thoroughly describe and evaluate the proposed
                 framework, experimental results obtained for the
                 supported back-ends (GPU and HDL) are presented
                 targeting the implementation of the modular
                 exponentiation used in the Rivest--Shamir--Adleman
                 (RSA) algorithm and Elliptic Curve (EC) point
                 multiplication. Results suggest competitive latency and
                 throughput with minimum design effort and overcoming
                 all the development issues that arise in the
                 specification and verification of dedicated
                 solutions.",
  acknowledgement = ack-nhfb,
  articleno =    "33",
  fjournal =     "ACM Transactions on Architecture and Code Optimization
                 (TACO)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J924",
}

@InProceedings{Arnold:2013:DLN,
  author =       "Mark G. Arnold and Sylvain Collange",
  editor =       "{IEEE}",
  booktitle =    "{24th IEEE International Conference on
                 Application-Specific Systems, Architectures and
                 Processors (ASAP), 5--7 June 2013}",
  title =        "The denormal logarithmic number system",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "117--124",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ASAP.2013.6567564",
  ISBN =         "1-4799-0493-7, 1-4799-0494-5 (paperback),
                 1-4799-0492-9",
  ISBN-13 =      "978-1-4799-0493-8, 978-1-4799-0494-5 (paperback),
                 978-1-4799-0492-1",
  LCCN =         "QA76.5",
  bibdate =      "Mon May 30 07:23:44 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=6558539",
  acknowledgement = ack-nhfb,
}

@Article{Bagnara:2013:EBF,
  author =       "Roberto Bagnara and Matthieu Carlier and Roberta Gori
                 and Arnaud Gotlieb",
  title =        "Exploiting Binary Floating-Point Representations for
                 Constraint Propagation: The Complete Unabridged
                 Version",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--51",
  day =          "18",
  month =        aug,
  year =         "2013",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/1308.3847",
  abstract =     "Floating-point computations are quickly finding their
                 way in the design of safety- and mission-critical
                 systems, despite the fact that designing floating-point
                 algorithms is significantly more difficult than
                 designing integer algorithms. For this reason,
                 verification and validation of floating-point
                 computations is a hot research topic. An important
                 verification technique, especially in some industrial
                 sectors, is testing. However, generating test data for
                 floating-point intensive programs proved to be a
                 challenging problem. Existing approaches usually resort
                 to random or search-based test data generation, but
                 without symbolic reasoning it is almost impossible to
                 generate test inputs that execute complex paths
                 controlled by floating-point computations. Moreover, as
                 constraint solvers over the reals or the rationals do
                 not natively support the handling of rounding errors,
                 the need arises for efficient constraint solvers over
                 floating-point domains. In this paper, we present and
                 fully justify improved algorithms for the propagation
                 of arithmetic IEEE 754 binary floating-point
                 constraints. The key point of these algorithms is a
                 generalization of an idea by B. Marre and C. Michel
                 that exploits a property of the representation of
                 floating-point numbers.",
  acknowledgement = ack-nhfb,
  subject =      "Artificial Intelligence (cs.AI); Software Engineering
                 (cs.SE)",
}

@InProceedings{Bailey:2013:KHP,
  author =       "David H. Bailey",
  title =        "Keynote {I}: High-precision computation: Applications
                 and challenges",
  crossref =     "IEEE:2013:PIS",
  pages =        "3--3",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.39",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-21",
}

@InProceedings{Bajard:2013:FDR,
  author =       "Jean-Claude Bajard and Julien Eynard and Filippo
                 Gandino",
  title =        "Fault Detection in {RNS} {Montgomery} Modular
                 Multiplication",
  crossref =     "IEEE:2013:PIS",
  pages =        "119--126",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.31",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-21; Base Conversions; Computer architecture;
                 cryptographic functions; Cryptography; cryptography;
                 fault attacks; Fault detection; fault detection; Fault
                 Detection; fault diagnosis; fault injection; field
                 programmable gate arrays; FPGA; GPU; Hardware; leak
                 resistant arithmetic; modular arithmetic; Montgomery
                 Reduction; Redundancy; Residue Number System; residue
                 number systems; Resistance; RNS; RNS Montgomery modular
                 multiplication; side channel attacks; Standards",
}

@Article{Bao:2013:FDI,
  author =       "Tao Bao and Xiangyu Zhang",
  title =        "On-the-fly detection of instability problems in
                 floating-point program execution",
  journal =      j-SIGPLAN,
  volume =       "48",
  number =       "10",
  pages =        "817--832",
  month =        oct,
  year =         "2013",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/2544173.2509526",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Mon Dec 9 09:19:33 MST 2013",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
  note =         "OOPSLA '13 conference proceedings.",
  abstract =     "The machine representation of floating point values
                 has limited precision such that errors may be
                 introduced during execution. These errors may get
                 propagated and magnified by the following operations,
                 leading to instability problems, e.g., control flow
                 path may be undesirably altered and faulty output may
                 be emitted. In this paper, we develop an on-the-fly
                 efficient monitoring technique that can predict if an
                 execution is stable. The technique does not explicitly
                 compute errors as doing so incurs high overhead.
                 Instead, it detects possible places where an error
                 becomes substantially inflated regarding the
                 corresponding value, and then tags the value with one
                 bit to denote that it has an inflated error. It then
                 tracks inflation bit propagation, taking care of
                 operations that may cut off such propagation. It
                 reports instability if any inflation bit reaches a
                 critical execution point, such as a predicate, where
                 the inflated error may induce substantial execution
                 difference, such as different execution paths. Our
                 experiment shows that with appropriate thresholds, the
                 technique can correctly detect that over 99.999996\% of
                 the inputs of all the programs we studied are stable
                 while a traditional technique relying solely on
                 inflation detection mistakenly classifies majority of
                 the inputs as unstable for some of the programs.
                 Compared to the state of the art technique that is
                 based on high precision computation and causes several
                 hundred times slowdown, our technique only causes 7.91
                 times slowdown on average and can report all the true
                 unstable executions with the appropriate thresholds.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}

@Article{Barr:2013:ADF,
  author =       "Earl T. Barr and Thanh Vo and Vu Le and Zhendong Su",
  title =        "Automatic detection of floating-point exceptions",
  journal =      j-SIGPLAN,
  volume =       "48",
  number =       "1",
  pages =        "549--560",
  month =        jan,
  year =         "2013",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/2480359.2429133",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Mon Jul 1 17:15:03 MDT 2013",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
  abstract =     "It is well-known that floating-point exceptions can be
                 disastrous and writing exception-free numerical
                 programs is very difficult. Thus, it is important to
                 automatically detect such errors. In this paper, we
                 present Ariadne, a practical symbolic execution system
                 specifically designed and implemented for detecting
                 floating-point exceptions. Ariadne systematically
                 transforms a numerical program to explicitly check each
                 exception triggering condition. Ariadne symbolically
                 executes the transformed program using real arithmetic
                 to find candidate real-valued inputs that can reach and
                 trigger an exception. Ariadne converts each candidate
                 input into a floating-point number, then tests it
                 against the original program. In general, approximating
                 floating-point arithmetic with real arithmetic can
                 change paths from feasible to infeasible and vice
                 versa. The key insight of this work is that, for the
                 problem of detecting floating-point exceptions, this
                 approximation works well in practice because, if one
                 input reaches an exception, many are likely to, and at
                 least one of them will do so over both floating-point
                 and real arithmetic. To realize Ariadne, we also
                 devised a novel, practical linearization technique to
                 solve nonlinear constraints. We extensively evaluated
                 Ariadne over 467 scalar functions in the widely used
                 GNU Scientific Library (GSL). Our results show that
                 Ariadne is practical and identifies a large number of
                 real runtime exceptions in GSL. The GSL developers
                 confirmed our preliminary findings and look forward to
                 Ariadne's public release, which we plan to do in the
                 near future.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  remark =       "POPL '13 conference proceedings.",
}

@InProceedings{Boldo:2013:FVC,
  author =       "Sylvie Boldo and Jacques-Henri Jourdan and Xavier
                 Leroy and Guillaume Melquiond",
  title =        "A Formally-Verified {C} Compiler Supporting
                 Floating-Point Arithmetic",
  crossref =     "IEEE:2013:PIS",
  pages =        "107--115",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.30",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-21; ARM microprocessor; C compiler; Comp Cert
                 compilation; Computer architecture; floating point
                 arithmetic; floating-point arithmetic; floating-point
                 semantic preservation; formal proof; formal
                 verification; IEEE standards; IEEE-754 standard; Java;
                 Libraries; mathematical specification; microprocessor
                 chips; Optimization; PowerPC microprocessor; program
                 compilers; Program processors; programming language;
                 Semantics; Standards; verified compilation; x86-SSE2
                 microprocessor",
}

@InProceedings{Boldo:2013:HCA,
  author =       "Sylvie Boldo",
  title =        "How to Compute the Area of a Triangle: A Formal
                 Revisit",
  crossref =     "IEEE:2013:PIS",
  pages =        "91--98",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.29",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Algorithm design and analysis; algorithm
                 proof; algorithm theory; ARITH-21; Coq; Digital
                 arithmetic; Electronic mail; Error analysis; floating
                 point arithmetic; floating-point arithmetic; formal
                 proof; Kahan algorithm; Libraries; mathematical value;
                 Standards; theorem proving; triangle; triangle area;
                 underflow",
}

@Article{Boldo:2013:WEN,
  author =       "Sylvie Boldo and Fran{\c{c}}ois Cl{\'e}ment and
                 Jean-Christophe Filli{\^a}tre and Micaela Mayero and
                 Guillaume Melquiond and Pierre Weis",
  title =        "Wave Equation Numerical Resolution: a Comprehensive
                 Mechanized Proof of a {C} Program",
  journal =      j-J-AUTOM-REASON,
  volume =       "50",
  number =       "4",
  pages =        "423--456",
  month =        apr,
  year =         "2013",
  CODEN =        "JAREEW",
  DOI =          "https://doi.org/10.1007/s10817-012-9255-4",
  ISSN =         "0168-7433 (print), 1573-0670 (electronic)",
  ISSN-L =       "0168-7433",
  bibdate =      "Sat Apr 2 10:51:04 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
  URL =          "http://link.springer.com/article/10.1007/s10817-012-9255-4",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Autom. Reason.",
  fjournal =     "Journal of Automated Reasoning",
  journal-URL =  "http://link.springer.com/journal/10817",
  keywords =     "floating-point error analysis",
}

@InProceedings{Brisebarre:2013:CBB,
  author =       "Nicolas Brisebarre and Marc Mezzarobba and Jean-Michel
                 Muller and Christof Lauter",
  title =        "Comparison between {Binary64} and {Decimal64}
                 Floating-Point Numbers",
  crossref =     "IEEE:2013:PIS",
  pages =        "145--152",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.23",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Approximation methods; ARITH-21; binary
                 encoding; Binary64 floating-point numbers; binary64 FP
                 number; Decimal Floating-Point; Decimal64
                 floating-point numbers; decimal64 FP number; Digital
                 arithmetic; Encoding; encoding; first pass; floating
                 point arithmetic; Floating-Point Arithmetic;
                 Floating-Point Comparisons; FP arithmetic; Hardware;
                 IEEE 754-2008 standard; IEEE standards; second pass;
                 software-oriented algorithm; Standards; Testing;
                 two-step algorithm",
}

@Article{Carter:2013:ESF,
  author =       "Ashley R. Carter",
  title =        "Evolution of the Significant Figure Rules",
  journal =      j-PHYS-TEACHER,
  volume =       "51",
  number =       "6",
  pages =        "340--343",
  month =        sep,
  year =         "2013",
  CODEN =        "PHTEAH",
  DOI =          "https://doi.org/10.1119/1.4818368",
  ISSN =         "0031-921X (print), 1943-4928 (electronic)",
  ISSN-L =       "0031-921X",
  bibdate =      "Mon May 21 11:31:50 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Physics Teacher",
  journal-URL =  "http://scitation.aip.org/content/aapt/journal/tpt",
}

@InProceedings{Chabrier:2013:FMB,
  author =       "Thomas Chabrier and Arnaud Tisserand",
  title =        "On-the-Fly Multi-base Recoding for {ECC} Scalar
                 Multiplication without Pre-computations",
  crossref =     "IEEE:2013:PIS",
  pages =        "219--228",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.17",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-21; base point multiples; cheap divisibility
                 tests; Clocks; Cryptography; curve-level operations;
                 DBNS; digital arithmetic; divisibility test;
                 double-base number system; ECC scalar multiplication;
                 elliptic curve cryptography; exact division by
                 constant; fast recoding methods; field programmable
                 gate arrays; Field programmable gate arrays; FPGA
                 implementation; greedy algorithm; greedy algorithms;
                 Hardware; MBNS; multibase number system; nonadjacent
                 form; off-line conversion; on-the-fly multibase
                 recoding; public key cryptography; scalar
                 multiplication; scalar recoding; Standards; Table
                 lookup",
}

@Article{Chen:2013:PGF,
  author =       "Doris Chen and Deshanand Singh",
  title =        "Profile-guided floating- to fixed-point conversion for
                 hybrid {FPGA}-processor applications",
  journal =      j-TACO,
  volume =       "9",
  number =       "4",
  pages =        "43:1--43:??",
  month =        jan,
  year =         "2013",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2400682.2400702",
  ISSN =         "1544-3566 (print), 1544-3973 (electronic)",
  ISSN-L =       "1544-3566",
  bibdate =      "Fri Jan 18 10:57:16 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/taco.bib",
  abstract =     "The key to enabling widespread use of FPGAs for
                 algorithm acceleration is to allow programmers to
                 create efficient designs without the time-consuming
                 hardware design process. Programmers are used to
                 developing scientific and mathematical algorithms in
                 high-level languages (C/C++) using floating point data
                 types. Although easy to implement, the dynamic range
                 provided by floating point is not necessary in many
                 applications; more efficient implementations can be
                 realized using fixed point arithmetic. While this topic
                 has been studied previously [Han et al. 2006; Olson et
                 al. 1999; Gaffar et al. 2004; Aamodt and Chow 1999],
                 the degree of full automation has always been lacking.
                 We present a novel design flow for cases where FPGAs
                 are used to offload computations from a microprocessor.
                 Our LLVM-based algorithm inserts value profiling code
                 into an unmodified C/C++ application to guide its
                 automatic conversion to fixed point. This allows for
                 fast and accurate design space exploration on a host
                 microprocessor before any accelerators are mapped to
                 the FPGA. Through experimental results, we demonstrate
                 that fixed-point conversion can yield resource savings
                 of up to 2x--3x reductions. Embedded RAM usage is
                 minimized, and 13\%--22\% higher $ F_{\rm max} $ than
                 the original floating-point implementation is observed.
                 In a case study, we show that 17\% reduction in logic
                 and 24\% reduction in register usage can be realized by
                 using our algorithm in conjunction with a High-Level
                 Synthesis (HLS) tool.",
  acknowledgement = ack-nhfb,
  articleno =    "43",
  fjournal =     "ACM Transactions on Architecture and Code Optimization
                 (TACO)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J924",
}

@InProceedings{Chevillard:2013:MPE,
  author =       "Sylvain Chevillard and Marc Mezzarobba",
  title =        "Multiple-Precision Evaluation of the {Airy} {Ai}
                 Function with Reduced Cancellation",
  crossref =     "IEEE:2013:PIS",
  pages =        "175--182",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.33",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Airy Ai function; algorithm; Algorithm
                 design and analysis; Approximation algorithms;
                 Approximation methods; arbitrary precision; ARITH-21;
                 asymptotics; cancellation reduction; classical Miller
                 algorithm; correct rounding; differential equations;
                 Equations; error bounds; ill-conditioned three-term
                 recurrence; linear ordinary differential equation;
                 Miller method; multiple-precision evaluation;
                 nonnegative Taylor expansions; numerical evaluation;
                 series (mathematics); series expansion; Shape; Special
                 functions; Taylor coefficients; Taylor series",
}

@Article{Cleveland:2013:OIR,
  author =       "Mathew A. Cleveland and Thomas A. Brunner and Nicholas
                 A. Gentile and Jeffrey A. Keasler",
  title =        "Obtaining identical results with double precision
                 global accuracy on different numbers of processors in
                 parallel particle {Monte Carlo} simulations",
  journal =      j-J-COMPUT-PHYS,
  volume =       "251",
  number =       "??",
  pages =        "223--236",
  day =          "15",
  month =        oct,
  year =         "2013",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/j.jcp.2013.05.041",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Tue Aug 6 11:36:34 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0021999113004075",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991",
  keywords =     "accurate floating-point summation",
}

@TechReport{Corden:2013:DFP,
  author =       "Martyn Corden",
  title =        "Differences in Floating-Point Arithmetic Between
                 {Intel Xeon} Processors and the {Intel Xeon Phi}
                 Coprocessor",
  type =         "Report",
  institution =  inst-INTEL,
  address =      inst-INTEL:adr,
  pages =        "6",
  year =         "2013",
  bibdate =      "Sat Oct 31 06:56:03 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://software.intel.com/en-us/articles/differences-in-floating-point-arithmetic-between-intel-xeon-processors-and-the-intel-xeon;
                 https://software.intel.com/file/420203/download",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cornea:2013:PAR,
  author =       "Marius Cornea",
  title =        "Precision, Accuracy, and Rounding Error Propagation in
                 Exascale Computing",
  crossref =     "IEEE:2013:PIS",
  pages =        "231--234",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.42",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; ARITH-21; Computational modeling; computer
                 architects; Digital arithmetic; exascale computing;
                 exascale level computers; Hardware; parallel machines;
                 Parallel processing; rounding error propagation;
                 supercomputers; Supercomputers",
}

@Article{De:2013:FIM,
  author =       "Anindya De and Piyush P. Kurur and Chandan Saha and
                 Ramprasad Saptharishi",
  title =        "Fast Integer Multiplication Using Modular Arithmetic",
  journal =      j-SIAM-J-COMPUT,
  volume =       "42",
  number =       "2",
  pages =        "685--699",
  month =        "????",
  year =         "2013",
  CODEN =        "SMJCAT",
  DOI =          "https://doi.org/10.1137/100811167",
  ISSN =         "0097-5397 (print), 1095-7111 (electronic)",
  ISSN-L =       "0097-5397",
  bibdate =      "Tue Feb 11 17:21:19 MST 2014",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SICOMP/42/2;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjcomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Computing",
  journal-URL =  "http://epubs.siam.org/sicomp",
  onlinedate =   "January 2013",
}

@Article{deDinechin:2013:FPE,
  author =       "Florent de Dinechin and Pedro Echeverr{\'\i}a and
                 Marisa L{\'o}pez-Vallejo and Bogdan Pasca",
  title =        "Floating-Point Exponentiation Units for Reconfigurable
                 Computing",
  journal =      j-TRETS,
  volume =       "6",
  number =       "1",
  pages =        "4:1--4:??",
  month =        may,
  year =         "2013",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2457443.2457447",
  ISSN =         "1936-7406 (print), 1936-7414 (electronic)",
  ISSN-L =       "1936-7406",
  bibdate =      "Thu Mar 13 08:09:42 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/trets.bib",
  abstract =     "The high performance and capacity of current FPGAs
                 makes them suitable as acceleration co-processors. This
                 article studies the implementation, for such
                 accelerators, of the floating-point power function $
                 x^y $ as defined by the C99 and IEEE 754-2008
                 standards, generalized here to arbitrary exponent and
                 mantissa sizes. Last-bit accuracy at the smallest
                 possible cost is obtained thanks to a careful study of
                 the various subcomponents: a floating-point logarithm,
                 a modified floating-point exponential, and a truncated
                 floating-point multiplier. A parameterized architecture
                 generator in the open-source FloPoCo project is
                 presented in details and evaluated.",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  fjournal =     "ACM Transactions on Reconfigurable Technology and
                 Systems (TRETS)",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J1151",
}

@Article{deDinechin:2013:FPT,
  author =       "Florent de Dinechin and Matei Istoan and Guillaume
                 Sergent",
  title =        "Fixed-point trigonometric functions on {FPGAs}",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "41",
  number =       "5",
  pages =        "83--88",
  month =        dec,
  year =         "2013",
  CODEN =        "CANED2",
  DOI =          "https://doi.org/10.1145/2641361.2641375",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Mon Aug 18 17:12:43 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
  abstract =     "Three approaches for computing sines and cosines on
                 FPGAs are studied in this paper, with a focus of
                 high-throughput pipelined architecture, and
                 state-of-the-art implementation techniques. The first
                 approach is the classical CORDIC iteration, for which
                 we suggest a reduced iteration technique and fine
                 optimizations in datapath width and latency. The second
                 is an ad-hoc architecture specifically designed around
                 trigonometric identities. The third uses a generic
                 table- and DSP-based polynomial approximator. These
                 three architectures are implemented and compared in the
                 FloPoCo framework.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
  keywords =     "CORDIC; cosine; sine",
}

@Article{deDinechin:2013:ZRT,
  author =       "Florent de Dinechin and Christoph Lauter and
                 Jean-Michel Muller and Serge Torres",
  title =        "On {Ziv}'s rounding test",
  journal =      j-TOMS,
  volume =       "39",
  number =       "4",
  pages =        "25:1--25:19",
  month =        jul,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2491491.2491495",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jul 19 17:20:56 MDT 2013",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A very simple test, introduced by Ziv, allows one to
                 determine if an approximation to the value $ f(x) $ of
                 an elementary function at a given point x suffices to
                 return the floating-point number nearest $ f(x) $. The
                 same test may be used when implementing floating-point
                 operations with input and output operands of different
                 formats, using arithmetic operators tailored for
                 manipulating operands of the same format. That test
                 depends on a ``magic constant'' $e$. We show how to
                 choose that constant $e$ to make the test reliable and
                 efficient. Various cases are considered, depending on
                 the availability of an fma instruction, and on the
                 range of $ f(x)$.",
  acknowledgement = ack-nhfb,
  articleno =    "25",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Misc{Demmel:2013:ERF,
  author =       "James Demmel and Hong Diep Nguyen",
  title =        "Efficient Reproducible Floating-Point Reduction
                 Operations on Large Scale Systems",
  howpublished = "SIAM AN13 talk slides.",
  day =          "8--12",
  month =        jul,
  year =         "2013",
  bibdate =      "Mon Jan 04 15:49:09 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://bebop.cs.berkeley.edu/reproblas/docs/talks/SIAM_AN13.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Demmel:2013:FRF,
  author =       "James Demmel and Hong Diep Nguyen",
  title =        "Fast Reproducible Floating-Point Summation",
  crossref =     "IEEE:2013:PIS",
  pages =        "163--172",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.9",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.eecs.berkeley.edu/~hdnguyen/public/papers/ARITH21_Fast_Sum.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Algorithm design and analysis; ARITH-21;
                 correct rounding; correctness check; debugging; dynamic
                 scheduling; Educational institutions; error-free vector
                 transformation; floating point arithmetic; floating
                 point nonassociativity; floating-point; floating-point
                 operation; floating-point summation; Numerical
                 analysis; parallel computing resource; Parallel
                 processing; parallel processing; parallelism; Program
                 processors; reduction operation; reproducibility;
                 reproducibility property; rounding error; rounding
                 mode; Rump algorithm; scheduling; summation; summation
                 order; Vectors",
}

@InProceedings{Demmel:2013:NRA,
  author =       "James Demmel and Hong Diep Nguyen",
  title =        "Numerical Reproducibility and Accuracy at Exascale",
  crossref =     "IEEE:2013:PIS",
  pages =        "235--237",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.43",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://bebop.cs.berkeley.edu/reproblas/docs/talks/ARITH21_ExaScale.pdf;
                 http://www.eecs.berkeley.edu/~hdnguyen/public/papers/ARITH21_ExaScale.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; addition; ARITH-21; Computational modeling;
                 Digital arithmetic; dynamic scheduling; Educational
                 institutions; exascale computing; floating point
                 arithmetic; floating point operations; Hardware;
                 hardware heterogeneity; hardware trends; intermittent
                 failures; numerical accuracy; numerical
                 reproducibility; parallel processing; Program
                 processors; Shape",
}

@Misc{Demmel:2013:RRB,
  author =       "James Demmel and Hong Diep Nguyen",
  title =        "{ReproBLAS}: Reproducible {BLAS}",
  howpublished = "SC'13 talk slides.",
  day =          "22",
  month =        nov,
  year =         "2013",
  bibdate =      "Mon Jan 04 15:49:09 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://bebop.cs.berkeley.edu/reproblas/docs/talks/SC13.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Detrey:2013:RCF,
  author =       "J{\'e}r{\'e}mie Detrey and Pierrick Gaudry and Marion
                 Videau",
  title =        "Relation Collection for the Function Field Sieve",
  crossref =     "IEEE:2013:PIS",
  pages =        "201--210",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.28",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "algorithmic techniques; ARITH-21; Arrays; cache
                 storage; cache-aware sieving algorithms; cryptographic
                 size; Cryptography; discrete logarithm; FFS;
                 finite-field arithmetic; Function Field Sieve; function
                 field sieve; Lattices; low-degree prime ideals;
                 medium-to record-sized computations; polynomial
                 arithmetic; polynomial arithmetic technique;
                 polynomials; Polynomials; public key cryptography;
                 record-sized discrete-logarithm computations; relation
                 collection step; small-characteristic finite fields;
                 Vectors",
}

@InProceedings{Dimitrov:2013:ALI,
  author =       "Vassil Dimitrov and Kimmo J{\"a}rvinen",
  title =        "Another Look at Inversions over Binary Fields",
  crossref =     "IEEE:2013:PIS",
  pages =        "211--218",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.25",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithm design and analysis; ARITH-21; binary
                 fields; binary Galois fields; double-base
                 representations; Galois fields; hardware
                 implementations; inversion algorithms; Itoh-Tsujii
                 algorithm; NIST; Polynomials; Prediction algorithms;
                 public key cryptography; public key cryptosystems;
                 Signal processing algorithms; Software; Software
                 algorithms; software implementations; squaring
                 computation; triple-base representations",
}

@Article{Dingle:2013:RIT,
  author =       "Nicholas J. Dingle and Nicholas J. Higham",
  title =        "Reducing the influence of tiny normwise relative
                 errors on performance profiles",
  journal =      j-TOMS,
  volume =       "39",
  number =       "4",
  pages =        "24:1--24:11",
  month =        jul,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2491491.2491494",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jul 19 17:20:56 MDT 2013",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "It is a widespread but little-noticed phenomenon that
                 the normwise relative error $ || x - y || / || x || $
                 of vectors $x$ and $y$ of floating point numbers of the
                 same precision, where $y$ is an approximation to x, can
                 be many orders of magnitude smaller than the unit
                 roundoff. We analyze this phenomenon and show that in
                 the $ \infty $-norm it happens precisely when $x$ has
                 components of widely varying magnitude and every
                 component of $x$ of largest magnitude agrees with the
                 corresponding component of $y$. Performance profiles
                 are a popular way to compare competing algorithms
                 according to particular measures of performance. We
                 show that performance profiles based on normwise
                 relative errors can give a misleading impression due to
                 the influence of zero or tiny normwise relative errors.
                 We propose a transformation that reduces the influence
                 of these extreme errors in a controlled manner, while
                 preserving the monotonicity of the underlying data and
                 leaving the performance profile unchanged at its left
                 end-point. Numerical examples with both artificial and
                 genuine data illustrate the benefits of the
                 transformation.",
  acknowledgement = ack-nhfb,
  articleno =    "24",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@TechReport{Doertel:2013:BKM,
  author =       "K. Doertel",
  title =        "Best Known Method: Avoid heterogeneous precision in
                 control flow calculations",
  type =         "Report",
  institution =  pub-INTEL,
  address =      pub-INTEL:adr,
  pages =        "????",
  year =         "2013",
  bibdate =      "Sat Oct 31 07:00:07 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Edmunds:2013:AME,
  author =       "Michael G. Edmunds",
  title =        "Keynote {II}: The {Antikythera Mechanism} and the
                 early history of mechanical computing",
  crossref =     "IEEE:2013:PIS",
  pages =        "79--79",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.40",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-21",
}

@Article{ElWazeer:2013:SVD,
  author =       "Khaled ElWazeer and Kapil Anand and Aparna Kotha and
                 Matthew Smithson and Rajeev Barua",
  title =        "Scalable variable and data type detection in a binary
                 rewriter",
  journal =      j-SIGPLAN,
  volume =       "48",
  number =       "6",
  pages =        "51--60",
  month =        jun,
  year =         "2013",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/2499370.2462165",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Mon Jul 1 17:15:38 MDT 2013",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
  abstract =     "We present scalable static analyses to recover
                 variables, data types, and function prototypes from
                 stripped x86 executables (without symbol or debug
                 information) and obtain a functional intermediate
                 representation (IR) for analysis and rewriting
                 purposes. Our techniques on average run $ 352 \times $
                 faster than current techniques and still have the same
                 precision. This enables analyzing executables as large
                 as millions of instructions in minutes which is not
                 possible using existing techniques. Our techniques can
                 recover variables allocated to the floating point
                 stack, unlike current techniques. We have integrated
                 our techniques to obtain a compiler level IR that works
                 correctly if recompiled and produces the same output as
                 the input executable. We demonstrate scalability,
                 precision and correctness of our proposed techniques by
                 evaluating them on the complete SPEC2006 benchmarks
                 suite.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  remark =       "PLDI '13 conference proceedings.",
}

@InProceedings{Engels:2013:NLL,
  author =       "Susanne Engels and Elif Bilge Kavun and Christof Paar
                 and Tolga Yalcin and Hristina Mihajloska",
  title =        "A Non-Linear\slash Linear Instruction Set Extension
                 for Lightweight Ciphers",
  crossref =     "IEEE:2013:PIS",
  pages =        "67--75",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.36",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic normal form; ANF; ARITH-21; binary matrix
                 multiply-and-add form; bit permutation; Ciphers;
                 cryptographic operation; cryptography; embedded CPU;
                 embedded microcontroller; Hardware; instruction set
                 extension; lightweight cipher; lightweight ciphers;
                 lightweight cryptographic algorithm; linear instruction
                 set extension; linear operation; matrix algebra;
                 microcontrollers; modular architecture; nonlinear
                 instruction set extension; nonlinear operation;
                 Registers; s-box; Silicon; Software; Standards",
}

@InProceedings{Galal:2013:FGD,
  author =       "Sameh Galal and Ofer Shacham and John S. Brunhaver and
                 Jing Pu and Artem Vassiliev and Mark Horowitz",
  title =        "{FPU} Generator for Design Space Exploration",
  crossref =     "IEEE:2013:PIS",
  pages =        "25--34",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.27",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "adder; ARITH-21; Booth encoder; Booth-2 cascade
                 multiply-add architecture; Booth-3 fused multiply-add
                 architecture; Delays; design space exploration;
                 Encoding; energy efficiency; fair apples-to-apples
                 methodology; floating point; floating point arithmetic;
                 floating point unit; FPU generator; Fused multiply add;
                 Generators; latency-sensitive design; logic design;
                 Logic gates; multipliers; optimisation; Optimization;
                 optimization technique; power efficiency; Radiation
                 detectors; summation tree; throughput-optimized design;
                 Vegetation; Wallace combining tree",
}

@InProceedings{Giorgi:2013:PMM,
  author =       "Pascal Giorgi and Laurent Imbert and Thomas Izard",
  title =        "Parallel Modular Multiplication on Multi-core
                 Processors",
  crossref =     "IEEE:2013:PIS",
  pages =        "135--142",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.20",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithm design and analysis; ARITH-21; Barrett;
                 bipartite; Complexity theory; digital arithmetic; k-ary
                 multipartite algorithms; k-ary multipartite
                 multiplication; low level arithmetic operations;
                 microprocessor chips; Modular multiplication;
                 Montgomery; multi-core; multicore processors;
                 multiprocessing systems; parallel arithmetic; parallel
                 modular multiplications; Parallel processing; parallel
                 processing; Program processors; Software algorithms;
                 software parallelism; Synchronization; tripartite",
}

@Article{Gonzalez-Navarro:2013:BID,
  author =       "Sonia Gonzalez-Navarro and Charles Tsen and Michael J.
                 Schulte",
  title =        "Binary Integer Decimal-Based Floating-Point
                 Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "62",
  number =       "7",
  pages =        "1460--1466",
  month =        jul,
  year =         "2013",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2012.79",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jun 17 15:07:53 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Misc{Gustafson:2013:UCN,
  author =       "John Gustafson",
  title =        "Unleashed Computing: The need to right-size precision
                 to save energy, bandwidth, storage, and electrical
                 power",
  howpublished = "Web slides (64).",
  day =          "19",
  month =        mar,
  year =         "2013",
  bibdate =      "Sat Apr 02 16:24:25 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://sites.ieee.org/scv-cs/files/2013/03/Right-SizingPrecision1.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Han:2013:HSP,
  author =       "Liu Han and Seok-Bum Ko",
  title =        "High-Speed Parallel Decimal Multiplication with
                 Redundant Internal Encodings",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "62",
  number =       "5",
  pages =        "956--968",
  month =        may,
  year =         "2013",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2012.35",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jan 21 09:06:31 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  note =         "See comment \cite{Gorgin:2015:CXH}.",
  abstract =     "The decimal multiplication is one of the most
                 important decimal arithmetic operations which have a
                 growing demand in the area of commercial, financial,
                 and scientific computing. In this paper, we propose a
                 parallel decimal multiplication algorithm with three
                 components, which are a partial product generation, a
                 partial product reduction, and a final digit-set
                 conversion. First, a redundant number system is applied
                 to recode not only the multiplier, but also multiples
                 of the multiplicand in signed-digit (SD) numbers.
                 Furthermore, we present a multioperand SD addition
                 algorithm to reduce the partial product array. Finally,
                 a digit-set conversion algorithm with a hybrid prefix
                 network to decrease the number of the logic gates on
                 the critical path is discussed. An analysis of the
                 timing delay and an HDL model synthesized under 90 nm
                 technology show that by considering the tradeoff of
                 designs among three components, the overall delay of
                 the proposed $ 16 \times 16$-digit multiplier takes
                 about 11 percent less timing delay with 2 percent less
                 area compared to the current fastest design.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Adders; Algorithm design and analysis; Arrays;
                 critical path; Decimal arithmetic; decimal arithmetic
                 operations; Delay; digit-set conversion algorithm;
                 Encoding; HDL model synthesis; high-speed parallel
                 decimal multiplication algorithm; hybrid prefix
                 network; logic design; logic gate number reduction;
                 logic gates; Logic gates; multioperand SD adder;
                 multioperand SD addition algorithm; multiplier
                 recoding; multiplying circuits; parallel
                 multiplication; partial-product array reduction;
                 partial-product generation; partial-product reduction;
                 redundant internal encodings; redundant number system;
                 redundant number systems; SD numbers; signed-digit
                 numbers; timing delay analysis",
}

@InProceedings{Hilaire:2013:RIL,
  author =       "Thibault Hilaire and Benoit Lopez",
  booktitle =    "{SiPS 2013} Proceedings",
  title =        "Reliable implementation of linear filters with
                 fixed-point arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  bookpages =    "xv + 428",
  pages =        "401--406",
  month =        oct,
  year =         "2013",
  DOI =          "https://doi.org/10.1109/sips.2013.6674540",
  ISBN =         "1-4673-6236-0 (print), 1-4673-6238-7 (e-book)",
  ISBN-13 =      "978-1-4673-6236-8 (print), 978-1-4673-6238-2
                 (e-book)",
  LCCN =         "TK5102.9 .I578 2013",
  bibdate =      "Sat Jun 8 08:50:15 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.gbv.de/dms/tib-ub-hannover/791452751.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Ioualalen:2013:SAF,
  author =       "Arnault Ioualalen and Matthieu Martel",
  editor =       "????",
  booktitle =    "{Proceedings of the 24th IEEE International Conference
                 on Application-Specific Systems, Architectures and
                 Processors, June, 2013}",
  title =        "Synthesizing accurate floating-point formulas",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "113--116",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ASAP.2013.6567563",
  bibdate =      "Sat Apr 01 08:00:40 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://hal.archives-ouvertes.fr/hal-00835736",
  acknowledgement = ack-nhfb,
}

@Article{Jaffer:2013:EAR,
  author =       "Aubrey Jaffer",
  title =        "Easy Accurate Reading and Writing of Floating-Point
                 Numbers",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--7",
  day =          "28",
  month =        oct,
  year =         "2013",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  MRclass =      "65G04",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/java2010.bib",
  URL =          "http://arxiv.org/abs/1310.8121",
  abstract =     "Presented here are algorithms for converting between
                 (decimal) scientific-notation and (binary) IEEE-754
                 double-precision floating-point numbers. By employing a
                 rounding integer quotient operation these algorithms
                 are much simpler than those previously published. The
                 values are stable under repeated conversions between
                 the formats. Unlike Java-1.6, the scientific
                 representations generated use only the minimum number
                 of mantissa digits needed to convert back to the
                 original binary values. Implemented in Java these
                 algorithms execute as fast or faster than Java's native
                 conversions over nearly all of the IEEE-754
                 double-precision range.",
  acknowledgement = ack-nhfb,
  keywords =     "base conversion; input-output conversion; radix
                 conversion; round-trip base conversion",
  subject =      "Numerical Analysis (cs.NA)",
}

@InProceedings{Jeannerod:2013:CAC,
  author =       "Claude-Pierre Jeannerod and Nicolas Louvet and
                 Jean-Michel Muller",
  title =        "On the Componentwise Accuracy of Complex
                 Floating-Point Division with an {FMA}",
  crossref =     "IEEE:2013:PIS",
  pages =        "83--90",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.8",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  acknowledgement = ack-nhfb,
  keywords =     "2 determinants; absolute errors; Accuracy; Algorithm
                 design and analysis; Approximation algorithms;
                 Approximation methods; ARITH-21; compensation; complex
                 division; complex floating-point division;
                 componentwise accuracy; componentwise relative error;
                 Digital arithmetic; division algorithms; Error
                 analysis; error analysis; floating point arithmetic;
                 floating-point arithmetic; FMA instruction; fused
                 multiply-add (FMA); fused multiply-add instruction;
                 Kahan compensated algorithm; nonnegative products;
                 radix-two floating-point arithmetic; relative errors;
                 rounding error analysis; Standards; straight-line
                 program; unit roundoff",
}

@Article{Jeannerod:2013:FAK,
  author =       "Claude-Pierre Jeannerod and Nicolas Louvet and
                 Jean-Michel Muller",
  title =        "Further analysis of {Kahan}'s algorithm for the
                 accurate computation of $ 2 \times 2 $ determinants",
  journal =      j-MATH-COMPUT,
  volume =       "82",
  number =       "284",
  pages =        "2245--2264",
  month =        "",
  year =         "2013",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-2013-02679-8",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRnumber =     "MR3073198",
  bibdate =      "Mon Jul 15 12:07:58 MDT 2013",
  bibsource =    "http://www.ams.org/mcom/2013-82-284;
                 https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  URL =          "http://www.ams.org/journals/mcom/2013-82-284/S0025-5718-2013-02679-8;
                 http://www.ams.org/journals/mcom/2013-82-284/S0025-5718-2013-02679-8/S0025-5718-2013-02679-8.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Article{Jeannerod:2013:IEB,
  author =       "Claude-Pierre Jeannerod and Siegfried M. Rump",
  title =        "Improved Error Bounds for Inner Products in
                 Floating-Point Arithmetic",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "34",
  number =       "2",
  pages =        "338--344",
  month =        "????",
  year =         "2013",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/120894488",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Fri Apr 5 06:24:05 MDT 2013",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/34/2;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
  onlinedate =   "January 2013",
}

@Article{Jiang:2013:AED,
  author =       "Hao Jiang and Stef Graillat and Canbin Hu and Shengguo
                 Li and Xiangke Liao and Lizhi Cheng and Fang Su",
  title =        "Accurate evaluation of the $k$-th derivative of a
                 polynomial and its application",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "243",
  number =       "??",
  pages =        "28--47",
  day =          "1",
  month =        may,
  year =         "2013",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/j.cam.2012.11.008",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "65D25",
  MRnumber =     "3003371",
  MRreviewer =   "Ana Maria Acu",
  bibdate =      "Sat Feb 25 13:26:16 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042712005018",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "compensated algorithm; derivative evaluation;
                 error-free transformation; floating-point arithmetic;
                 rounding error",
}

@InProceedings{Jiang:2013:AFE,
  author =       "Hao Jiang and Stef Graillat and Roberto Barrio",
  title =        "Accurate and Fast Evaluation of Elementary Symmetric
                 Functions",
  crossref =     "IEEE:2013:PIS",
  pages =        "183--190",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.18",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; accurate algorithm; Algorithm design and
                 analysis; ARITH-21; compensated algorithm;
                 double-double library; elementary symmetric functions;
                 error-free transformation; error-free transformations;
                 floating point arithmetic; floating-point arithmetic;
                 forward roundoff error bound; Libraries; mathematics
                 computing; MATLAB poly function; Polynomials;
                 psychological measurement; Rasch model; roundoff error;
                 Roundoff errors; running error bound; shaper bound;
                 summation algorithm; Vectors",
}

@InProceedings{Kadric:2013:APF,
  author =       "Edin Kadric and Paul Gurniak and Andr{\'e} DeHon",
  title =        "Accurate Parallel Floating-Point Accumulation",
  crossref =     "IEEE:2013:PIS",
  pages =        "153--162",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.19",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "$O(\log N)$ depth; Accumulation; Accurate; accurate
                 parallel floating-point accumulation; accurate
                 summation; Adders; arbitrary throughput; ARITH-21;
                 Clocks; conservative termination detection;
                 Convergence; field programmable gate arrays; floating
                 point arithmetic; Floating-Point Arithmetic;
                 floating-point sums; FPGA; Hardware; IEEE standards;
                 IEEE-754; Indexes; iterative algorithm; iterative
                 methods; iterative refinement; Moore law scaling;
                 Parallel; parallel associative reduction; Parallel
                 processing; residue-preserving IEEE-754
                 double-precision floating-point adder; Rounding;
                 standard adder; streaming accurate floating-point
                 accumulation unit; tree reduce parallelism; Upper
                 bound; Virtex 6 FPGA",
}

@Article{Khanna:2013:HPN,
  author =       "Gaurav Khanna",
  title =        "High-Precision Numerical Simulations on a {CUDA GPU}:
                 {Kerr} Black Hole Tails",
  journal =      j-J-SCI-COMPUT,
  volume =       "56",
  number =       "2",
  pages =        "366--380",
  month =        aug,
  year =         "2013",
  CODEN =        "JSCOEB",
  DOI =          "https://doi.org/10.1007/s10915-012-9679-3",
  ISSN =         "0885-7474 (print), 1573-7691 (electronic)",
  ISSN-L =       "0885-7474",
  bibdate =      "Sat Mar 8 11:16:21 MST 2014",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0885-7474&volume=56&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jscicomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/pvm.bib",
  URL =          "http://link.springer.com/article/10.1007/s10915-012-9679-3;
                 http://link.springer.com/content/pdf/10.1007/s10915-012-9679-3.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Scientific Computing",
  journal-URL =  "http://link.springer.com/journal/10915",
}

@Article{Kouretas:2013:LPL,
  author =       "Ioannis Kouretas and Charalambos Basetas and Vassilis
                 Paliouras",
  title =        "Low-Power Logarithmic Number System Addition\slash
                 Subtraction and Their Impact on Digital Filters",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "62",
  number =       "11",
  pages =        "2196--2209",
  month =        nov,
  year =         "2013",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2012.111",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 15 08:54:34 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Book{Kulisch:2013:CAV,
  author =       "Ulrich Kulisch",
  title =        "Computer Arithmetic and Validity",
  volume =       "33",
  publisher =    pub-GRUYTER,
  address =      pub-GRUYTER:adr,
  edition =      "Second",
  pages =        "xxii + 434",
  year =         "2013",
  DOI =          "https://doi.org/10.1515/9783110301793",
  ISBN =         "3-11-030173-3, 3-11-030179-2 (e-book), 3-11-030180-6
                 (set)",
  ISBN-13 =      "978-3-11-030173-1, 978-3-11-030179-3 (e-book),
                 978-3-11-030180-9 (set)",
  ISSN =         "0179-0986",
  ISSN-L =       "0179-0986",
  LCCN =         "QA76.9.C62 K853 2013",
  bibdate =      "Sat May 18 08:56:52 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "De Gruyter studies in mathematics",
  abstract =     "This is the revised and extended second edition of the
                 successful basic book on computer arithmetic. It is
                 consistent with the newest recent standard developments
                 in the field. The book shows how the arithmetic
                 capability of the computer can be enhanced. The work is
                 motivated by the desire and the need to improve the
                 accuracy of numerical computing and to control the
                 quality of the computed results (validity). The
                 accuracy requirements for the elementary floating-point
                 operations are extended to the customary product spaces
                 of computations including interval spaces. The
                 mathematical properties of these models are extracted
                 and lead to a general theory of computer arithmetic.
                 Detailed methods and circuits for the implementation of
                 this advanced computer arithmetic are developed in the
                 book. It illustrates how the extended arithmetic can be
                 used to compute highly accurate and mathematically
                 verified results. The book can be used as a high-level
                 undergraduate textbook but also as reference work for
                 research in computer arithmetic and applied
                 mathematics.",
  acknowledgement = ack-nhfb,
  subject =      "computer arithmetic; computer arithmetic and logic
                 units; floating-point arithmetic",
  tableofcontents = "Foreword to the second edition vii \\
                 Preface / ix \\
                 Introduction / 1 \\
                 I Theory of computer arithmetic \\
                 1 First concepts 13 \\
                 1.1 Ordered sets / 13 \\
                 1.2 Complete lattices and complete subnets / 18 \\
                 1.3 Screens and roundings / 24 \\
                 1.4 Arithmetic operations and roundings / 35 \\
                 2 Ringoids and vectoids 43 \\
                 2.1 Ringoids / 43 \\
                 2.2 Vectoids / 54 \\
                 3 Definition of computer arithmetic 62 \\
                 3.1 Introduction / 62 \\
                 3.2 Preliminaries / 65 \\
                 3.3 The traditional definition of computer arithmetic /
                 69 \\
                 3.4 Definition of computer arithmetic by semimorphisms
                 / 70 \\
                 3.5 A remark about roundings / 78 \\
                 3.6 Uniqueness of the minus operator / 79 \\
                 3.7 Rounding near zero / 81 \\
                 4 Interval arithmetic 87 \\
                 4.1 Interval sets and arithmetic / 88 \\
                 4.2 Interval arithmetic over a linearly ordered set /
                 97 \\
                 4.3 Interval matrices / 101 \\
                 4.4 Interval vectors / 107 \\
                 4.5 Interval arithmetic on a screen / 110 \\
                 7.2 Arithmetic interval operations / 237 \\
                 7.2.1 Algebraic operations / 238 \\
                 7.2.2 Comments on the algebraic operations / 240 \\
                 7.3 Circuitry for the arithmetic interval operations /
                 241 \\
                 7.4 Comparisons and lattice operations / 242 \\
                 7.4.1 Comments on comparisons and lattice operations /
                 243 \\
                 7.4.2 Hardware support for comparisons and lattice
                 operations / 243 \\
                 7.5 Alternative circuitry for interval operations and
                 comparisons / 244 \\
                 7.5.1 Hardware support for interval arithmetic on
                 x86-processors 245 \\
                 7.5.2 Accurate evaluation of interval scalar products /
                 247 \\
                 8 Scalar products and complete arithmetic 249 \\
                 8.1 Introduction and motivation / 250 \\
                 8.2 Historical remarks / 252 \\
                 8.3 The ubiquity of the scalar product in numerical
                 analysis / 257 \\
                 8.4 Implementation principles / 260 \\
                 8.4.1 Long adder and long shift / 262 \\
                 8.4.2 Short adder with local memory on the arithmetic
                 unit / 262 \\
                 8.4.3 Remarks / 263 \\
                 8.4.4 Fast carry resolution / 265 \\
                 8.5 Informal sketch for computing an exact dot product
                 / 267 \\
                 8.6 Scalar product computation units (SPUs) / 267 \\
                 8.6.1 SPU for computers with a 32 bit data bus / 269
                 \\
                 8.6.2 A coprocessor chip for the exact scalar product /
                 272 \\
                 8.6.3 SPU for computers with a 64 bit data bus / 275
                 \\
                 8.7 Comments / 278 \\
                 8.7.1 Rounding / 278 \\
                 8.7.2 How much local memory should be provided on an
                 SPU? / 279 \\
                 8.8 The data format complete and complete arithmetic /
                 281 \\
                 8.8.1 Low level instructions for complete arithmetic /
                 282 \\
                 8.8.2 Complete arithmetic in high level programming
                 languages / 283 \\
                 8.9 Top speed scalar product units / 287 \\
                 8.9.1 SPU with long adder for 64 bit data word / 287
                 \\
                 8.9.2 SPU with long adder for 32 bit data word / 292
                 \\
                 8.9.3 An FPGA coprocessor for the exact scalar product
                 / 295 \\
                 8.9.4 SPU with short adder and complete register / 295
                 \\
                 8.9.5 Carry-free accumulation of products in redundant
                 arithmetic 301 \\
                 8.10 Hardware complete register window / 302 \\
                 III Principles of verified computing \\
                 9 Sample applications 307 \\
                 9.1 Basic properties of interval mathematics / 309 \\
                 9.1.1 Interval arithmetic, a powerful calculus to deal
                 with inequalities / 309 \\
                 9.1.2 Interval arithmetic as executable set operations
                 / 310 \\
                 9.1.3 Enclosing the range of function values / 316 \\
                 9.1.4 Nonzero property of a function, global
                 optimization / 319 \\
                 9.2 Differentiation arithmetic, enclosures of
                 derivatives / 321 \\
                 9.3 The interval Newton method / 329 \\
                 9.4 The extended interval Newton method / 332 \\
                 9.5 Verified solution of systems of linear equations /
                 333 \\
                 9.6 Accurate evaluation of arithmetic expressions / 340
                 \\
                 9.6.1 Complete expressions / 341 \\
                 9.6.2 Accurate evaluation of polynomials / 342 \\
                 9.6.3 Arithmetic expressions / 346 \\
                 9.7 Multiple precision arithmetics / 347 \\
                 9.7.1 Multiple precision floating-point arithmetic /
                 348 \\
                 9.7.2 Multiple precision interval arithmetic / 351 \\
                 9.7.3 Applications / 356 \\
                 9.7.4 Adding an exponent part as a scaling factor to
                 complete \\
                 arithmetic / 358 \\
                 9.8 Remarks on Kaucher arithmetic / 360 \\
                 9.8.1 The basic operations of Kaucher arithmetic / 364
                 \\
                 A Frequently used symbols 367 \\
                 B On homomorphism 369 \\
                 Bibliography 371 \\
                 List of figures 421 \\
                 List of tables 425 \\
                 Index 427",
}

@Article{Kupriianova:2013:RCIa,
  author =       "O. Kupriianova and Ch. Lauter and Jean-Michel Muller",
  title =        "Radix Conversion for {IEEE754-2008} Mixed Radix
                 Floating-Point Arithmetic",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "2",
  month =        dec,
  year =         "2013",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/1312.0455",
  abstract =     "Conversion between binary and decimal floating-point
                 representations is ubiquitous. Floating-point radix
                 conversion means converting both the exponent and the
                 mantissa. We develop an atomic operation for FP radix
                 conversion with simple straight-line algorithm,
                 suitable for hardware design. Exponent conversion is
                 performed with a small multiplication and a lookup
                 table. It yields the correct result without error.
                 Mantissa conversion uses a few multiplications and a
                 small lookup table that is shared amongst all types of
                 conversions. The accuracy changes by adjusting the
                 computing precision.",
  acknowledgement = ack-nhfb,
  subject =      "Mathematical Software (cs.MS)",
}

@InProceedings{Kupriianova:2013:RCIb,
  author =       "Olga Kupriianova and Christoph Lauter and Jean-Michel
                 Muller",
  editor =       "Michael B. Matthews",
  booktitle =    "{The Forty-Seventh Asilomar Conference on Signals,
                 Systems and Computers. November 3--6, 2013. Pacific
                 Grove, California}",
  title =        "Radix conversion for {IEEE754-2008} mixed radix
                 floating-point arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1134--1138",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ACSSC.2013.6810471",
  ISBN =         "1-4799-2390-7",
  ISBN-13 =      "978-1-4799-2390-8",
  bibdate =      "Fri Sep 29 10:52:22 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kurka:2013:UAA,
  author =       "Petr K{\r{u}}rka and Martin Delacourt",
  title =        "The Unary Arithmetical Algorithm in Bimodular Number
                 Systems",
  crossref =     "IEEE:2013:PIS",
  pages =        "127--134",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.10",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Absorption; ARITH-21; bimodular number system; binary
                 signed system; computational complexity; Convergence;
                 Electronic mail; exact real arithmetic; expansion
                 subshifts; linear average time complexity; Moebius
                 number systems; Moebius transformation; Random
                 variables; residue number systems; statistical
                 analysis; statistical evidence; Time complexity;
                 Transducers; unary arithmetical algorithm; Vectors",
}

@Article{Lam:2013:DFP,
  author =       "Michael O. Lam and Jeffrey K. Hollingsworth and G. W.
                 Stewart",
  title =        "Dynamic floating-point cancellation detection",
  journal =      j-PARALLEL-COMPUTING,
  volume =       "39",
  number =       "3",
  pages =        "146--155",
  month =        mar,
  year =         "2013",
  CODEN =        "PACOEJ",
  ISSN =         "0167-8191 (print), 1872-7336 (electronic)",
  ISSN-L =       "0167-8191",
  bibdate =      "Wed Mar 27 07:19:15 MDT 2013",
  bibsource =    "http://www.sciencedirect.com/science/journal/01678191;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/parallelcomputing.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167819112000622",
  acknowledgement = ack-nhfb,
  fjournal =     "Parallel Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01678191",
}

@Misc{Lefevre:2013:HRC,
  author =       "Vincent Lef{\`e}vre",
  title =        "Hardest-to-Round Cases: Part 2",
  howpublished = "Lecture slides from ENS-Lyon, France.",
  pages =        "30",
  day =          "8",
  month =        oct,
  year =         "2013",
  bibdate =      "Wed Oct 09 09:40:50 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "From the slides: `After 13,812,778 CPU core hours ($
                 \approx $ 1576 years) for the first step'', the hardest
                 cases for correct rounding in the IEEE 754 binary64
                 format were found for $ e^x $, $ 2^x $, $ 10^x $, $
                 \sinh $, $ \cosh $, $ \sin (2 \pi x) $, $ \cos (2 \pi
                 x) $, $ \tan (2 \pi x) $; for $ x^n $ for $ n \in [ -
                 180, - 2] $ and $ n \in [3, 5188] $; for $ \sin (x) $,
                 $ \cos (x) $, and $ \tan (x) $ for $ x \in [ - \pi / 2,
                 + \pi / 2] $; and for their inverse functions.",
}

@TechReport{Lefevre:2013:SML,
  author =       "Vincent Lef{\`e}vre",
  title =        "{Sipe}: a mini-library for very low precision
                 computations with correct rounding.",
  type =         "Report",
  number =       "hal-00864580",
  institution =  "INRIA, LIP / CNRS / ENS Lyon / Universit{\'e} de
                 Lyon",
  address =      "Lyon, France",
  pages =        "13",
  day =          "22",
  month =        sep,
  year =         "2013",
  bibdate =      "Sat Dec 23 12:04:45 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://inria.hal.science/hal-00864580",
  abstract =     "Sipe is a mini-library in the form of a C header file,
                 to perform radix-2 floating-point computations in very
                 low precisions with correct rounding, either to nearest
                 or toward zero. The goal of such a tool is to do proofs
                 of algorithms\slash properties or computations of tight
                 error bounds in these precisions by exhaustive tests,
                 in order to try to generalize them to higher
                 precisions. The currently supported operations are
                 addition, subtraction, multiplication (possibly with
                 the error term), fused multiply-add\slash subtract
                 (FMA\slash FMS), and miscellaneous comparisons and
                 conversions. sipe provides two implementations of these
                 operations, with the same API and the same behavior:
                 one based on integer arithmetic, and a new one based on
                 floating-point arithmetic. Timing comparisons have been
                 done with hardware IEEE-754 floating point and with GNU
                 MPFR.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lefevre:2013:SSI,
  author =       "Vincent Lef{\`e}vre",
  title =        "{SIPE}: Small Integer Plus Exponent",
  crossref =     "IEEE:2013:PIS",
  pages =        "99--106",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.22",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://hal.inria.fr/hal-00763954",
  acknowledgement = ack-nhfb,
  keywords =     "addition; Algorithm design and analysis; ARITH-21;
                 arithmetic operations; C header file; Computers;
                 Context; correct rounding; floating point arithmetic;
                 floating-point computations; FMA; GNU MPFR; Hardware;
                 hardware IEEE-754 floating point; IEEE standards;
                 Libraries; low precision; mini-library; multiplication;
                 radix 2; SIPE; small integer plus exponent; Standards;
                 subtraction; Timing; timing comparisons",
}

@Article{Lei:2013:FIE,
  author =       "Yuanwu Lei and Yong Dou and Yazhuo Dong and Jie Zhou
                 and Fei Xia",
  title =        "{FPGA} implementation of an exact dot product and its
                 application in variable-precision floating-point
                 arithmetic",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "64",
  number =       "2",
  pages =        "580--605",
  month =        may,
  year =         "2013",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1007/s11227-012-0860-0",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Sat Feb 8 10:21:14 MST 2014",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0920-8542&volume=64&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsuper.bib",
  URL =          "http://link.springer.com/article/10.1007/s11227-012-0860-0",
  acknowledgement = ack-nhfb,
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
}

@Article{Lei:2013:VCI,
  author =       "Yuanwu Lei and Yong Dou and Lei Guo and Jinbo Xu and
                 Jie Zhou and Yazhuo Dong and Hongjian Li",
  title =        "{VLIW} coprocessor for {IEEE-754} quadruple-precision
                 elementary functions",
  journal =      j-TACO,
  volume =       "10",
  number =       "3",
  pages =        "12:1--12:??",
  month =        sep,
  year =         "2013",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2512430",
  ISSN =         "1544-3566 (print), 1544-3973 (electronic)",
  ISSN-L =       "1544-3566",
  bibdate =      "Mon Sep 16 17:20:12 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/taco.bib",
  abstract =     "In this article, a unified VLIW coprocessor, based on
                 a common group of atomic operation units, for Quad
                 arithmetic and elementary functions (QP\_VELP) is
                 presented. The explicitly parallel scheme of VLIW
                 instruction and Estrin's evaluation scheme for
                 polynomials are used to improve the performance. A
                 two-level VLIW instruction RAM scheme is introduced to
                 achieve high scalability and customizability, even for
                 more complex key program kernels. Finally, the Quad
                 arithmetic accelerator (QAA) with the QP\_VELP array is
                 implemented on ASIC. Compared with hyper-thread
                 software implementation on an Intel Xeon E5620, QAA
                 with 8 QP\_VELP units achieves improvement by a factor
                 of 18X.",
  acknowledgement = ack-nhfb,
  articleno =    "12",
  fjournal =     "ACM Transactions on Architecture and Code Optimization
                 (TACO)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J924",
}

@Article{Lowery:2013:RED,
  author =       "Bradley R. Lowery",
  title =        "Relative error due to a single bit-flip in
                 floating-point arithmetic",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--6",
  day =          "15",
  month =        apr,
  year =         "2013",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/1304.4292",
  abstract =     "We consider the error due to a single bit-flip in a
                 floating point number. We assume IEEE 754 double
                 precision arithmetic, which encodes binary floating
                 point numbers in a 64-bit word. We assume that the
                 bit-flip happens randomly so it has equi-probability
                 (1/64) to hit any of the 64 bits. Since we want to
                 mitigate the assumption on our initial floating-point
                 number, we assume that it is uniformly picked among all
                 normalized number. With this framework, we can
                 summarize our findings as follows. The probability for
                 a single bit flip to cause a relative error less than $
                 10^{-11} $ in a normalized floating-point number is
                 above 25\%; The probability for a single bit flip to
                 cause a relative error less than $ 10^{-6} $ in a
                 normalized floating-point number is above 50\%; Etc.",
  acknowledgement = ack-nhfb,
  subject =      "Numerical Analysis (cs.NA)",
}

@Article{Maitra:2013:DSM,
  author =       "Subhashis Maitra and Amitabha Sinha",
  title =        "Design and simulation of {MAC} unit using
                 combinational circuit and adder",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "41",
  number =       "5",
  pages =        "25--33",
  month =        dec,
  year =         "2013",
  CODEN =        "CANED2",
  DOI =          "https://doi.org/10.1145/2641361.2641365",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Mon Aug 18 17:12:43 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
  abstract =     "Hardware and timing complexities of MAC unit to
                 perform arithmetic operation like addition or
                 multiplication especially in the field of Digital
                 Signal Processing (DSP) or Elliptic Curve Cryptography
                 (ECC) are the major issues to the designer. The
                 multiplication operation is essential and abundant in
                 DSP Applications. In order to achieve maximum
                 implementation efficiency and timing performance,
                 designing a DSP systems is critical and frequently
                 presents a significant challenge to hardware engineers.
                 There are certain multipliers that simplify this
                 challenge by abstracting away FPGA device specifics,
                 while maintaining the required maximum performance and
                 resource efficiency. These multipliers are able to
                 perform parallel multiplication and hence constant
                 coefficient multiplication, both with differing
                 implementation styles. Again with the aid of
                 instantaneous resource estimation, hardware engineers
                 can rapidly select the optimal solution for their
                 system. The latest additions to the IP provide fine
                 control over the latency using the concept of
                 pipelining of the multipliers that are purely
                 combinatorial to be fully pipelined. Here a new
                 compensation method that reduces both the hardware and
                 timing complexities of the multiplier used for DSP
                 application or ECC application has been proposed. The
                 design of the MAC unit based on the proposed
                 compensation method has been dealt here properly using
                 Xilinx 13.2 and compared with array multiplier, Booth
                 multiplier and Vedic multiplier to show its novelty
                 over them. The hardware complexity is reduced to about
                 60\% of the original multiplier. Design results show
                 that the proposed architecture has lower hardware
                 overhead, lower error and fast operating speed as
                 compared with array, Booth and Vedic multiplier.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
}

@Article{Maniatakos:2013:LCC,
  author =       "Michail Maniatakos and Prabhakar Kudva and Bruce M.
                 Fleischer and Yiorgos Makris",
  title =        "Low-Cost Concurrent Error Detection for Floating-Point
                 Unit ({FPU}) Controllers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "62",
  number =       "7",
  pages =        "1376--1388",
  month =        jul,
  year =         "2013",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2012.81",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jun 17 15:07:53 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Martin-Dorel:2013:SIR,
  author =       "{\'E}rik Martin-Dorel and Guillaume Melquiond and
                 Jean-Michel Muller",
  title =        "Some issues related to double rounding",
  journal =      j-BIT-NUM-MATH,
  volume =       "53",
  number =       "4",
  pages =        "897--924",
  month =        dec,
  year =         "2013",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/s10543-013-0436-2",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Mon Dec 2 16:05:03 MST 2013",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=53&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer.com/article/10.1007/s10543-013-0436-2",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT Numerical Mathematics",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "double rounding",
}

@InProceedings{Muller:2013:ADR,
  author =       "Jean-Michel Muller",
  editor =       "Michael B. Matthews",
  booktitle =    "{The Forty-Seventh Asilomar Conference on Signals,
                 Systems and Computers. November 3--6, 2013. Pacific
                 Grove, California}",
  title =        "Avoiding double roundings in scaled {Newton--Raphson}
                 division",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "396--399",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ACSSC.2013.6810304",
  ISBN =         "1-4799-2390-7",
  ISBN-13 =      "978-1-4799-2390-8",
  bibdate =      "Fri Sep 29 10:48:21 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "double rounding",
}

@Article{Nathan:2013:REB,
  author =       "Ralph Nathan and Bryan Anthonio and Shih-Lien Lu and
                 Helia Naeimi and Daniel J. Sorin and Xiaobai Sun",
  title =        "Recycled Error Bits: Energy-Efficient Architectural
                 Support for Higher Precision Floating Point",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "27",
  month =        sep,
  year =         "2013",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/1309.7321",
  abstract =     "In this work, we provide energy-efficient
                 architectural support for floating point accuracy. Our
                 goal is to provide accuracy that is far greater than
                 that provided by the processor's hardware floating
                 point unit (FPU). Specifically, for each floating point
                 addition performed, we ``recycle'' that operation's
                 error: the difference between the finite-precision
                 result produced by the hardware and the result that
                 would have been produced by an infinite-precision FPU.
                 We make this error architecturally visible such that it
                 can be used, if desired, by software. Experimental
                 results on physical hardware show that software that
                 exploits architecturally recycled error bits can
                 achieve accuracy comparable to a 2B-bit FPU with
                 performance and energy that are comparable to a B-bit
                 FPU.",
  acknowledgement = ack-nhfb,
  subject =      "Hardware Architecture (cs.AR)",
}

@Article{Nguyen:2013:SED,
  author =       "Trung Duc Nguyen and Rodney {Van Meter}",
  title =        "A Space-Efficient Design for Reversible Floating Point
                 Adder in Quantum Computing",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--11",
  day =          "17",
  month =        jun,
  year =         "2013",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/1306.3760",
  abstract =     "Reversible logic has applications in low-power
                 computing and quantum computing. However, there are few
                 existing designs for reversible floating-point adders
                 and none suitable for quantum computation. In this
                 paper we propose a space-efficient reversible
                 floating-point adder, suitable for binary quantum
                 computation, improving the design of Nachtigal et al.
                 Our work focuses on improving the reversible designs of
                 the alignment unit and the normalization unit, which
                 are the most expensive parts. By changing a few
                 elements of the existing algorithm, including the
                 circuit designs of the RLZC (reversible leading zero
                 counter) and converter, we have reduced the cost about
                 68\%. We also propose fault-tolerant designs for the
                 circuits. The KQ for our fault-tolerant design is
                 almost sixty times as expensive as for a 32-bit
                 fixed-point addition. We note that the floating-point
                 representation makes in-place, truly reversible
                 arithmetic impossible, requiring us to retain both
                 inputs, which limits the sustainability of its use for
                 quantum computation.",
  acknowledgement = ack-nhfb,
  subject =      "Quantum Physics (quant-ph); Emerging Technologies
                 (cs.ET)",
}

@Article{Nikolajsen:2013:FSD,
  author =       "Jorgen L. Nikolajsen",
  title =        "Fractional Significant Digits",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "35",
  number =       "2",
  pages =        "A561--A576",
  month =        "????",
  year =         "2013",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/110828435",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Fri Jul 19 07:43:46 MDT 2013",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SISC/35/2;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  onlinedate =   "January 2013",
}

@Article{Ould-Bachir:2013:SAS,
  author =       "Tarek Ould-Bachir and Jean Pierre David",
  title =        "Self-Alignment Schemes for the Implementation of
                 Addition-Related Floating-Point Operators",
  journal =      j-TRETS,
  volume =       "6",
  number =       "1",
  pages =        "1:1--1:??",
  month =        may,
  year =         "2013",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2457443.2457444",
  ISSN =         "1936-7406 (print), 1936-7414 (electronic)",
  ISSN-L =       "1936-7406",
  bibdate =      "Thu Mar 13 08:09:42 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/trets.bib",
  abstract =     "Advances in semiconductor technology brings to the
                 market incredibly dense devices, capable of handling
                 tens to hundreds floating-point operators on a single
                 chip; so do the latest field programmable gate arrays
                 (FPGAs). In order to alleviate the complexity of
                 resorting to these devices in computationally intensive
                 applications, this article proposes hardware schemes
                 for the realization of addition-related floating-point
                 operators based on the self-alignment technique (SAT).
                 The article demonstrates that the schemes guarantee an
                 accuracy as if summation was computed accurately in the
                 precision of operator's internal mantissa, then
                 faithfully rounded to working precision. To achieve
                 such performance, the article adopts the redundant high
                 radix carry-save (HRCS) format for the rapid addition
                 of wide mantissas. Implementation results show that
                 combining the SAT and the HRCS format allows the
                 implementation of complex operators with reduced area
                 and latency, more so when a fused-path approach is
                 adopted. The article also proposes a new hardware
                 operator for performing endomorphic HRCS additions and
                 presents a new technique for speeding up the conversion
                 from the redundant HRCS to a conventional binary
                 format.",
  acknowledgement = ack-nhfb,
  articleno =    "1",
  fjournal =     "ACM Transactions on Reconfigurable Technology and
                 Systems (TRETS)",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J1151",
}

@Article{Ozaki:2013:GEF,
  author =       "Katsuhisa Ozaki and Takeshi Ogita and Shin'ichi Oishi
                 and Siegfried M. Rump",
  title =        "Generalization of error-free transformation for matrix
                 multiplication and its application",
  journal =      j-NONLINEAR-THEORY-APPL,
  volume =       "4",
  number =       "1",
  pages =        "2--11",
  year =         "2013",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1587/nolta.4.2",
  ISSN =         "2185-4106",
  ISSN-L =       "2185-4106",
  bibdate =      "Sat Feb 8 19:02:28 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.jstage.jst.go.jp/article/nolta/4/1/4_2/_article",
  acknowledgement = ack-nhfb,
  fjournal =     "Nonlinear Theory and Its Applications, {IEICE}",
  journal-URL =  "https://www.jstage.jst.go.jp/browse/nolta/",
}

@InProceedings{Pedram:2013:FPA,
  author =       "Ardavan Pedram and Andreas Gerstlauer and Robert A.
                 van de Geijn",
  title =        "Floating Point Architecture Extensions for Optimized
                 Matrix Factorization",
  crossref =     "IEEE:2013:PIS",
  pages =        "49--58",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.21",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithm design and analysis; application specific
                 integrated circuits; architectural modifications;
                 architecture complexity; ARITH-21; Cholesky; Complexity
                 theory; computational complexity; Computer
                 architecture; custom linear algebra processor; dense
                 linear systems; design trade-offs; floating point;
                 floating point architecture extensions; floating point
                 arithmetic; floating point units; full-custom ASIC
                 designs; least mean squares methods; linear algebra;
                 linear least-squares problems; low power; LU
                 factorization; MAC units; Matrix decomposition; matrix
                 decomposition; matrix factorization; optimized matrix
                 factorization; QR factorizations; Registers; Vectors",
}

@Article{Pontarelli:2013:LCC,
  author =       "Salvatore Pontarelli and Pedro Reviriego and Chris J.
                 Bleakley and Juan Antonio Maestro",
  title =        "Low Complexity Concurrent Error Detection for Complex
                 Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "62",
  number =       "9",
  pages =        "1899--1903",
  month =        sep,
  year =         "2013",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2012.246",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 15 08:54:34 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Rodriguez-Garcia:2013:FFP,
  author =       "A. Rodriguez-Garcia and L. Pizano-Escalante and R.
                 Parra-Michel and O. Longoria-Gandara and J. Cortez",
  editor =       "Ren{\'e} Cumplido and Eduardo de la Torre and Mike
                 Wirthlin",
  booktitle =    "{2013 International Conference on Reconfigurable
                 Computing and FPGAs (ReConFig): Cancun, Mexico,
                 December 9--11, 2013}",
  title =        "Fast fixed-point divider based on {Newton--Raphson}
                 method and piecewise polynomial approximation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--6",
  month =        dec,
  year =         "2013",
  DOI =          "https://doi.org/10.1109/reconfig.2013.6732291",
  ISBN =         "1-4799-2079-7",
  ISBN-13 =      "978-1-4799-2079-2",
  bibdate =      "Thu Apr 10 15:12:10 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Rubio-Gonzalez:2013:PTA,
  author =       "Cindy Rubio-Gonz{\'a}lez and Cuong Nguyen and Hong
                 Diep Nguyen and James Demmel and William Kahan and
                 Koushik Sen and David H. Bailey and Costin Iancu and
                 David Hough",
  booktitle =    "Proceedings of the {SC13's} International Conference
                 on High Performance Computing, Networking, Storage and
                 Analysis, Denver, {CO}, {USA}",
  title =        "{Precimonious}: Tuning assistant for floating-point
                 precision",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "27",
  year =         "2013",
  bibdate =      "Sat Jun 4 17:18:19 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Rump:2013:ASDa,
  author =       "Siegfried M. Rump",
  title =        "Accurate solution of dense linear systems, {Part I}:
                 Algorithms in rounding to nearest",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "242",
  number =       "??",
  pages =        "157--184",
  month =        apr,
  year =         "2013",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:26:15 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042712004360",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Rump:2013:ASDb,
  author =       "Siegfried M. Rump",
  title =        "Accurate solution of dense linear systems, Part {II}:
                 Algorithms using directed rounding",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "242",
  number =       "??",
  pages =        "185--212",
  month =        apr,
  year =         "2013",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:26:15 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042712003974",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Rupley:2013:FPU,
  author =       "Jeff Rupley and John King and Eric Quinnell and Frank
                 Galloway and Ken Patton and Peter-Michael Seidel and
                 James Dinh and Hai Bui and Anasua Bhowmik",
  title =        "The Floating-Point Unit of the {Jaguar} x86 Core",
  crossref =     "IEEE:2013:PIS",
  pages =        "7--16",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.24",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; AES; AES instruction set; AMD Jaguar; AMD
                 Jaguar x86 core; ARITH-21; arithmetic and logic unit;
                 AVX; AVX instruction set; bypass network; CLMUL; CLMUL
                 instruction set; CMOS process; complimentary metal
                 oxide semiconductor; coprocessor model; coprocessors;
                 Decoding; dedicated renamer; dual-issue scheduler;
                 execution pipe; F16C; F16C instruction set; floating
                 point arithmetic; floating-point adder; floating-point
                 iterative multiplier; floating-point unit; formal
                 verification; formal verification technique; FPU; free
                 list; industry implementation; instruction sets;
                 low-power design; Microarchitecture; MMX; native
                 floating-point unit; Optimization; Out of order;
                 physical register file; PRF; pseudorandom verification
                 technique; Registers; retire queue; scheduling; size 28
                 nm; SSE; SSE4.2 instruction set; vector integer ALU;
                 vector integer MUL unit; Vectors; x86 ISA extension;
                 x87",
}

@Article{Russinoff:2013:CFV,
  author =       "David M. Russinoff",
  title =        "Computation and Formal Verification of {SRT} Quotient
                 and Square Root Digit Selection Tables",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "62",
  number =       "5",
  pages =        "900--913",
  month =        may,
  year =         "2013",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2012.40",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Apr 30 12:26:22 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Saha:2013:PAF,
  author =       "Amrita Saha and Manideepa Mukherjee and Debanjana
                 Datta and Sangita Saha and Amitabha Sinha",
  title =        "Performance analysis of a {FPGA} based novel binary
                 and {DBNS} multiplier",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "41",
  number =       "2",
  pages =        "9--16",
  month =        may,
  year =         "2013",
  CODEN =        "CANED2",
  DOI =          "https://doi.org/10.1145/2490302.2490305",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Sat Jun 1 11:00:26 MDT 2013",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
  abstract =     "Designing high performance Software Defined Radio
                 (SDR) with low power and flexibility is a major
                 challenge. While the high performance DSP processors
                 are unable to meet the speed requirements of these
                 SDRs, System on chips (SOCs) are also not suitable
                 because of their limited flexibility. Recently
                 dynamically reconfigurable FPGAs have emerged as high
                 performance programmable hardware to execute highly
                 parallel, computationally intensive signal processing
                 functions efficiently. Since basic intention of an SDR
                 is to implement different modulation / demodulation
                 schemes and basic building blocks for such schemes are
                 signal processing functions, FPGAs have become an
                 important component for implementing these. However,
                 the effectiveness of such an approach with respect to
                 cost, performance and flexibility need to be examined.
                 Double Base Number Systems (DBNS) have been gaining
                 attention for compute intensive applications in signal
                 processing because of their higher performance in
                 arithmetic operations in general and particularly
                 multiplication. Keeping these issues in view, this
                 paper aims to present a new Software defined Radio. To
                 Enhance the performance of the proposed architecture,
                 analysis have been done employing both single index and
                 multiple indices DBNS multipliers. Experiments and
                 analysis on performance have also been done with its
                 binary counterpart. Both DBNS and binary based
                 architecture were implemented on Xilinx virtex iv FPGA
                 using xilinx ISE 9.1 i.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
}

@Article{SaiToh:2013:ZCL,
  author =       "Akira SaiToh",
  title =        "{ZKCM}: a {C++} library for multiprecision matrix
                 computation with applications in quantum information",
  journal =      j-COMP-PHYS-COMM,
  volume =       "184",
  number =       "8",
  pages =        "2005--2020",
  month =        aug,
  year =         "2013",
  CODEN =        "CPHCBZ",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Wed May 15 07:02:08 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/gnu.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465513001306",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  keywords =     "GNU GMP library; MPFR library",
}

@Article{Shen:2013:SCC,
  author =       "Tao Shen and Zhugang Yuan",
  title =        "Stability criterion for a class of fixed-point digital
                 filters using two's complement arithmetic",
  journal =      j-APPL-MATH-COMP,
  volume =       "219",
  number =       "9",
  pages =        "4880--4883",
  day =          "1",
  month =        jan,
  year =         "2013",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2012.10.064",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Mon Dec 17 14:08:35 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300312010806",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@InProceedings{Sohn:2013:IAF,
  author =       "Jongwook Sohn and Earl E. {Swartzlander, Jr.}",
  title =        "Improved Architectures for a Floating-Point Fused Dot
                 Product Unit",
  crossref =     "IEEE:2013:PIS",
  pages =        "41--48",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.26",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; alignment scheme; ARITH-21; complex
                 multiplication; Computer architecture; data flow
                 analysis; DCT butterfly operations; Digital signal
                 processing; digital signal processing; Digital signal
                 processing (DSP); discrete cosine transform butterfly
                 operations; DSP applications; dual-path algorithm;
                 early normalization; fast Fourier transform; FFT;
                 floating point arithmetic; floating-point arithmetic;
                 floating-point fused operations; floating-point fused
                 two-term dot product unit; four-input leading zero
                 anticipation; high-speed computer arithmetic;
                 libraries; nonpipelined dual-path design; pipeline
                 processing; Pipeline processing; pipelining; Power
                 demand; signal processing; size 45 nm; standard cell
                 library; Standards; two-term dot product unit;
                 Vectors",
}

@InProceedings{Srinivasan:2013:SPF,
  author =       "Suresh Srinivasan and Ketan Bhudiya and Rajaraman
                 Ramanarayanan and P. Sahit Babu and Tiju Jacob and Sanu
                 K. Mathew and Ram Krishnamurthy and Vasantha
                 Errgauntla",
  title =        "Split-Path Fused Floating Point Multiply Accumulate
                 ({FPMAC})",
  crossref =     "IEEE:2013:PIS",
  pages =        "17--24",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.32",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; ARITH-21; AVX ISA; contemporary client
                 microprocessor; critical path computation; Delays;
                 Double precision floating point multiply-accumulate;
                 exponent difference; floating point arithmetic; FPMAC
                 design; Hardware; IBM Power6; IEEE Rounding; IEEE
                 standard; IEEE standards; instruction set architecture;
                 instruction sets; ISA support; logic design; Logic
                 gates; microprocessor area; microprocessor chips;
                 microprocessor frequency; microprocessor power;
                 Microprocessors; near path critical logic;
                 Normalization; Program processors; server processor;
                 split-path fused floating point multiply accumulate;
                 SSE ISA; timing design; Wallace tree",
}

@InProceedings{Sullivan:2013:TLA,
  author =       "Michael B. Sullivan and Earl E. {Swartzlander, Jr.}",
  title =        "Truncated Logarithmic Approximation",
  crossref =     "IEEE:2013:PIS",
  pages =        "191--198",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.34",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithm design and analysis; Analytical models;
                 anti-logarithm generation; Approximation algorithms;
                 approximation theory; ARITH-21; binary logarithm;
                 computer arithmetic; Delays; Linear approximation;
                 linear approximation algorithm; logarithm generation;
                 logarithmic approximation; Logic gates; Mitchell
                 approximation algorithm; mixed precision; resource
                 utilization; Truncated approximate binary logarithms;
                 truncated approximate logarithm",
}

@Article{Suri:2013:DHP,
  author =       "Lakshay Suri and Devesh Lamba and Kunwar Kritarth and
                 Bhavna Ghai and Geetanjali Sharma",
  title =        "Design of High Performance and Power Efficient 16-bit
                 Square Root Carry Select Adder using Hybrid {PTL\slash
                 CMOS} Logic",
  journal =      j-INT-J-COMP-APPL,
  volume =       "69",
  number =       "??",
  pages =        "32--35",
  month =        may,
  year =         "2013",
  CODEN =        "????",
  DOI =          "https://doi.org/10.5120/11881-7696",
  ISSN =         "0975-8887",
  ISSN-L =       "0975-8887",
  bibdate =      "Fri Jan 24 08:56:30 MST 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/intjcompappl.bib",
  URL =          "https://www.ijcaonline.org/archives/volume69/number10/11881-7696/",
  acknowledgement = ack-nhfb,
  ajournal =     "Intern. J. of Computer Applications",
  articleno =    "10",
  fjournal =     "International Journal of Computer Applications",
  journal-URL =  "https://www.ijcaonline.org/",
}

@InProceedings{Tao:2013:CRA,
  author =       "Yao Tao and Gao Deyuan and Fan Xiaoya and Jari Nurmi",
  booktitle =    "{2013 IEEE 24th International Conference on
                 Application-Specific Systems, Architectures and
                 Processors}",
  title =        "Correctly rounded architectures for floating-point
                 multi-operand addition and dot-product computation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "346--355",
  month =        jun,
  year =         "2013",
  DOI =          "https://doi.org/10.1109/asap.2013.6567600",
  bibdate =      "Wed Feb 25 14:17:18 2026",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation; correct rounding;
                 floating-point arithmetic; rounding errors",
}

@Article{Tolmachev:2013:MFP,
  author =       "Alex Tolmachev and Igor Tselniker and Maxim Meltsin
                 and Itzik Sigron and David Dahan and Aviv Shalom and
                 Moshe Nazarathy",
  title =        "Multiplier-Free Phase Recovery With Polar-domain
                 Multisymbol-Delay-Detector",
  journal =      j-LIGHTWAVE-TECHNOL,
  volume =       "31",
  number =       "23",
  pages =        "3638--3650",
  year =         "2013",
  CODEN =        "JLTEDG",
  DOI =          "https://doi.org/10.1109/JLT.2013.2283635",
  ISSN =         "0733-8724 (print), 1558-2213 (electronic)",
  ISSN-L =       "0733-8724",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Lightwave Technology",
  keywords =     "Adders; Approximation algorithms; Approximation
                 methods; Complexity theory; CORDIC; FPGA; hardware
                 parallelization; multisymbol delay detection (MSDD);
                 multisymbol phase estimation (MSPE); Optical noise;
                 optically coherent detection; phase estimation; phase
                 recovery; Phase shift keying; real-time demonstration;
                 Signal to noise ratio",
}

@Article{Vazquez:2013:IAA,
  author =       "Alvaro Vazquez and Javier D. Bruguera",
  title =        "Iterative Algorithm and Architecture for Exponential,
                 Logarithm, Powering, and Root Extraction",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "62",
  number =       "9",
  pages =        "1721--1731",
  month =        sep,
  year =         "2013",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2012.247",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 15 08:54:34 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Book{Warren:2013:HD,
  author =       "Henry S. Warren",
  title =        "Hacker's Delight",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Second",
  pages =        "xvi + 494",
  year =         "2013",
  ISBN =         "0-321-84268-5 (hardcover)",
  ISBN-13 =      "978-0-321-84268-8 (hardcover)",
  LCCN =         "QA76.6 .W375 2013",
  bibdate =      "Mon Sep 23 11:53:48 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.pearsonhighered.com/educator/product/Hackers-Delight/9780321842688.page",
  acknowledgement = ack-nhfb,
  subject =      "Computer programming",
  tableofcontents = "Foreword / xiii \\
                 Preface / xv \\
                 Chapter 1: Introduction / 1 \\
                 1-1 Notation / 1 \\
                 1-2 Instruction Set and Execution Time Model / 5 \\
                 Chapter 2: Basics / 11 \\
                 2-1 Manipulating Rightmost Bits / 11 \\
                 2-2 Addition Combined with Logical Operations / 16 \\
                 2-3 Inequalities among Logical and Arithmetic
                 Expressions / 17 \\
                 2-4 Absolute Value Function / 18 \\
                 2-5 Average of Two Integers / 19 \\
                 2-6 Sign Extension / 19 \\
                 2-7 Shift Right Signed from Unsigned / 20 \\
                 2-8 Sign Function / 20 \\
                 2-9 Three-Valued Compare Function / 21 \\
                 2-10 Transfer of Sign Function / 22 \\
                 2-11 Decoding a Zero Means 2**n Field / 22 \\
                 2-12 Comparison Predicates / 23 \\
                 2-13 Overflow Detection / 28 \\
                 2-14 Condition Code Result of Add, Subtract, and
                 Multiply / 36 \\
                 2-15 Rotate Shifts / 37 \\
                 2-16 Double-Length Add/Subtract / 38 \\
                 2-17 Double-Length Shifts / 39 \\
                 2-18 Multibyte Add, Subtract, AbsoluteValue / 40 \\
                 2-19 Doz, Max, Min / 41 \\
                 2-20 Exchanging Registers / 45 \\
                 2-21 Alternating among Two or More Values / 48 \\
                 2-22 A Boolean Decomposition Formula / 51 \\
                 2-23 Implementing Instructions for all 16 Binary
                 Boolean Operations / 53 \\
                 Chapter 3: Power-of-2 Boundaries / 59 \\
                 3-1 Rounding Up/Down to a Multiple of a Known Power of
                 2 / 59 \\
                 3-2 Rounding Up/Down to the Next Power of 2 / 60 \\
                 3-3 Detecting a Power-of-2 Boundary Crossing / 63 \\
                 Chapter 4: Arithmetic Bounds / 67 \\
                 4-1 Checking Bounds of Integers / 67 \\
                 4-2 Propagating Bounds through Adds and Subtracts / 70
                 \\
                 4-3 Propagating Bounds through Logical Operations / 73
                 \\
                 Chapter 5: Counting Bits / 81 \\
                 5-1 Counting 1-Bits / 81 \\
                 5-2 Parity / 96 \\
                 5-3 Counting Leading 0's / 99 \\
                 5-4 Counting Trailing 0's / 107 \\
                 Chapter 6: Searching Words / 117 \\
                 6-1 Find First 0-Byte / 117 \\
                 6-2 Find First String of 1-Bits of a Given Length / 123
                 \\
                 6-3 Find Longest String of 1-Bits / 125 \\
                 6-4 Find Shortest String of 1-Bits / 126 \\
                 Chapter 7: Rearranging Bits And Bytes / 129 \\
                 7-1 Reversing Bits and Bytes / 129 \\
                 7-2 Shuffling Bits / 139 \\
                 7-3 Transposing a Bit Matrix / 141 \\
                 7-4 Compress, or GeneralizedExtract / 150 \\
                 7-5 Expand, or GeneralizedInsert / 156 \\
                 7-6 Hardware Algorithms for Compress and Expand / 157
                 \\
                 7-7 General Permutations, Sheep and Goats Operation /
                 161 \\
                 7-8 Rearrangements and Index Transformations / 165 \\
                 7-9 An LRU Algorithm / 166 \\
                 Chapter 8: Multiplication / 171 \\
                 8-1 Multiword Multiplication / 171 \\
                 8-2 High-Order Half of 64-Bit Product / 173 \\
                 8-3 High-Order Product Signed from/to Unsigned / 174
                 \\
                 8-4 Multiplication by Constants / 175 \\
                 Chapter 9: Integer Division / 181 \\
                 9-1 Preliminaries / 181 \\
                 9-2 Multiword Division / 184 \\
                 9-3 Unsigned Short Division from Signed Division / 189
                 \\
                 9-4 Unsigned Long Division / 192 \\
                 9-5 Doubleword Division from Long Division / 197 \\
                 Chapter 10: Integer Division by Constants / 205 \\
                 10-1 Signed Division by a Known Power of 2 / 205 \\
                 10-2 Signed Remainder from Division by a Known Power of
                 2 / 206 \\
                 10-3 Signed Division and Remainder by Non-Powers of 2 /
                 207 \\
                 10-4 Signed Division by Divisors 2 / 210 \\
                 10-5 Signed Division by Divisors 2 / 218 \\
                 10-6 Incorporation into a Compiler / 220 \\
                 10-7 Miscellaneous Topics / 223 \\
                 10-8 Unsigned Division / 227 \\
                 10-9 Unsigned Division by Divisors 1 / 230 \\
                 10-10 Incorporation into a Compiler (Unsigned) / 232
                 \\
                 10-11 Miscellaneous Topics (Unsigned) / 234 \\
                 10-12 Applicability to Modulus and Floor Division / 237
                 \\
                 10-13 Similar Methods / 237 \\
                 10-14 Sample Magic Numbers / 238 \\
                 10-15 Simple Code in Python / 240 \\
                 10-16 Exact Division by Constants / 240 \\
                 10-17 Test for Zero Remainder after Division by a
                 Constant / 248 \\
                 10-18 Methods Not Using Multiply High / 251 \\
                 10-19 Remainder by Summing Digits / 262 \\
                 10-20 Remainder by Multiplication and Shifting Right /
                 268 \\
                 10-21 Converting to Exact Division / 274 \\
                 10-22 A Timing Test / 276 \\
                 10-23 A Circuit for Dividing by 3 / 276 \\
                 Chapter 11: Some Elementary Functions / 279 \\
                 11-1 Integer Square Root / 279 \\
                 11-2 Integer Cube Root / 287 \\
                 11-3 Integer Exponentiation / 288 \\
                 11-4 Integer Logarithm / 291 \\
                 Chapter 12: Unusual Bases For Number Systems / 299 \\
                 12-1 Base 2 / 299 \\
                 12-2 Base 1 + i / 306 \\
                 12-3 Other Bases / 308 \\
                 12-4 What Is the Most Efficient Base? / 309 \\
                 Chapter 13: Gray Code / 311 \\
                 13-1 Gray Code / 311 \\
                 13-2 Incrementing a Gray-Coded Integer / 313 \\
                 13-3 Negabinary Gray Code / 315 \\
                 13-4 Brief History and Applications / 315 \\
                 Chapter 14: Cyclic Redundancy Check / 319 \\
                 14-1 Introduction / 319 \\
                 14-2 Theory / 320 \\
                 14-3 Practice / 323 \\
                 Chapter 15: Error-Correcting Codes / 331 \\
                 15-1 Introduction / 331 \\
                 15-2 The Hamming Code / 332 \\
                 15-3 Software for SEC-DED on 32 Information Bits / 337
                 \\
                 15-4 Error Correction Considered More Generally / 342
                 \\
                 Chapter 16: Hilbert's Curve / 355 \\
                 16-1 A Recursive Algorithm for Generating the Hilbert
                 Curve / 356 \\
                 16-2 Coordinates from Distance along the Hilbert Curve
                 / 358 \\
                 16-3 Distance from Coordinates on the Hilbert Curve /
                 366 \\
                 16-4 Incrementing the Coordinates on the Hilbert Curve
                 / 368 \\
                 16-5 Non-Recursive Generating Algorithms / 371 \\
                 16-6 Other Space-Filling Curves / 371 \\
                 16-7 Applications / 372 \\
                 Chapter 17: Floating-Point / 375 \\
                 17-1 IEEE Format / 375 \\
                 17-2 Floating-Point To/From Integer Conversions / 377
                 \\
                 17-3 Comparing Floating-Point Numbers Using Integer
                 Operations / 381 \\
                 17-4 An Approximate Reciprocal Square Root Routine /
                 383 \\
                 17-5 The Distribution of Leading Digits / 385 \\
                 17-6 Table of Miscellaneous Values / 387 \\
                 Chapter 18: Formulas for Primes / 391 \\
                 18-1 Introduction / 391 \\
                 18-2 Willans's Formulas / 393 \\
                 18-3 Wormell's Formula / 397 \\
                 18-4 Formulas for Other Difficult Functions / 398 \\
                 Answers to Exercises: / 405 \\
                 Appendix A: Arithmetic Tables for a 4-Bit Machine / 453
                 \\
                 Appendix B: Newton's Method / 457 \\
                 Appendix C: A Gallery of Graphs of Discrete Functions /
                 459 \\
                 C-1 Plots of Logical Operations on Integers / 459 \\
                 C-2 Plots of Addition, Subtraction, and Multiplication
                 / 461 \\
                 C-3 Plots of Functions Involving Division / 463 \\
                 C-4 Plots of the Compress, SAG, and Rotate Left
                 Functions / 464 \\
                 C-5 2D Plots of Some Unary Functions / 466 \\
                 Bibliography / 471 \\
                 Index / 481",
}

@Article{Wiebe:2013:FPR,
  author =       "Nathan Wiebe and Vadym Kliuchnikov",
  title =        "Floating Point Representations in Quantum Circuit
                 Synthesis",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "23",
  month =        may,
  year =         "2013",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/1305.5528",
  abstract =     "We provide a non-deterministic quantum protocol that
                 approximates the single qubit rotations $ R_x(2 a^2
                 b^2) $ using $ R_x(2 a) $ and $ R_x(2 b) $ and a
                 constant number of Clifford and T operations. We then
                 use this method to construct a ``floating point''
                 implementation of a small rotation wherein we use the
                 aforementioned method to construct the exponent part of
                 the rotation and also to combine it with a mantissa.
                 This causes the cost of the synthesis to depend more
                 strongly on the relative (rather than absolute)
                 precision required. We analyze the mean and variance of
                 the T-count required to use our techniques and provide
                 new lower bounds for the T-count for ancilla free
                 synthesis of small single-qubit axial rotations. We
                 further show that our techniques can use ancillas to
                 beat these lower bounds with high probability. We also
                 discuss the T-depth of our method and see that the vast
                 majority of the cost of the resultant circuits can be
                 shifted to parallel computation paths.",
  acknowledgement = ack-nhfb,
  subject =      "Quantum Physics (quant-ph)",
}

@Article{Yabuki:2013:DPC,
  author =       "Michiro Yabuki and Takashi Tsuchiya",
  title =        "Double Precision Computation of the Logistic Map
                 Depends on Computational Modes of the Floating-point
                 Processing Unit",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--10",
  day =          "14",
  month =        may,
  year =         "2013",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/1305.3128",
  abstract =     "Today's most popular CPU can operate in two different
                 computational modes for double precision computations.
                 This fact is not very widely recognized among
                 scientific computer users. The present paper reports
                 the differences the modes bring about using the most
                 thoroughly studied system in chaos theory, the logistic
                 map. Distinct virtual periods due to finite precision
                 come about depending on the computational modes for the
                 parameter value corresponding to fully developed chaos.
                 For other chaotic regime various virtual periods emerge
                 depending on the computational modes and the
                 mathematical expressions of the map. Differences in the
                 bifurcation diagrams due to the modes and the
                 expressions are surveyed exhaustively. A quantity to
                 measure those differences is defined and calculated.",
  acknowledgement = ack-nhfb,
  subject =      "Chaotic Dynamics (nlin.CD)",
}

@InProceedings{Yuce:2013:FCT,
  author =       "Bilgiday Yuce and H. Fatih Ugurdag and Sezer Goren and
                 Gunham Dundar",
  title =        "A Fast Circuit Topology for Finding the Maximum of
                 {$N$} $k$-bit Numbers",
  crossref =     "IEEE:2013:PIS",
  pages =        "59--66",
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ARITH.2013.35",
  ISSN =         "1063-6889",
  bibdate =      "Sat Aug 1 09:38:32 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "AB; area complexity; Area-timing product; ARITH-21;
                 arithmetic operation; array-based maximum finder;
                 Arrays; binary search; Binary trees; Circuit topology;
                 computational complexity; Computer arithmetic; Delays;
                 digital arithmetic; fast circuit topology; iterative
                 methods; k-bit binary numbers; Logic gates; Logic
                 synthesis; Maximum finder; Minimum finder; network
                 topology; program compilers; RTL code generators;
                 standard-cell based iterative synthesis flow; Time
                 complexity; time complexity; Timing optimization;
                 Topology",
}

@Article{Zhang:2013:BAF,
  author =       "Yiwei Zhang and Joseph P. Mcgeehan and Edward M. Regan
                 and Stephen Kelly and Jose Luis Nunez-Yanez",
  title =        "Biophysically Accurate Floating Point Neuroprocessors
                 for Reconfigurable Logic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "62",
  number =       "3",
  pages =        "599--608",
  month =        mar,
  year =         "2013",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2011.257",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Apr 30 12:26:22 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Akleylek:2014:AOF,
  author =       "S. Akleylek and F. {\"O}zbudak and C. {\"O}zel",
  title =        "On the arithmetic operations over finite fields of
                 characteristic three with low complexity",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "259 (part B)",
  number =       "??",
  pages =        "546--554",
  day =          "15",
  month =        mar,
  year =         "2014",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:34:02 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042713004160",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Misc{Anonymous:2014:CLL,
  author =       "Anonymous",
  title =        "{CR-Libm} --- a library of correctly rounded
                 elementary functions in double-precision",
  howpublished = "Web site",
  year =         "2014",
  bibdate =      "Sat Oct 31 07:21:21 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://lipforge.ens-lyon.fr/www/crlibm/",
  abstract =     "CRlibm is a free mathematical library (libm) that
                 provides: (1) implementations of the double-precision
                 C99 standard elementary functions; (2) correctly
                 rounded in the four IEEE-754 rounding modes; (3) with a
                 comprehensive proof of both the algorithms used and
                 their implementation; (4) sufficiently efficient in
                 average time, worst-case time, and memory consumption
                 to replace existing libms transparently.",
  acknowledgement = ack-nhfb,
  keywords =     "correct rounding; CR-Libm; floating-point arithmetic;
                 scslib (software carry save library)",
}

@Article{Area:2014:ACS,
  author =       "Iv{\'a}n Area and Dimitar K. Dimitrov and Eduardo
                 Godoy and Vanessa Paschoa",
  title =        "Approximate Calculation of Sums {I}: Bounds for the
                 Zeros of {Gram} Polynomials",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "52",
  number =       "4",
  pages =        "1867--1886",
  month =        "????",
  year =         "2014",
  CODEN =        "SJNAAM",
  DOI =          "https://doi.org/10.1137/120887278",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  bibdate =      "Sat Sep 13 09:22:34 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/sjnaam/52/4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjnumeranal2010.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
  onlinedate =   "January 2014",
}

@InProceedings{Arteaga:2014:DBR,
  author =       "A. Arteaga and O. Fuhrer and T. Hoefler",
  booktitle =    "{Proceedings of the 2014 IEEE 28th International
                 Parallel and Distributed Processing Symposium}",
  title =        "Designing bit-reproducible portable high-performance
                 applications",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1235--1244",
  year =         "2014",
  DOI =          "https://doi.org/10.1109/IPDPS.2014.127",
  bibdate =      "Sat Oct 31 07:13:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Ballard:2014:CLB,
  author =       "G. Ballard and E. Carson and J. Demmel and M. Hoemmen
                 and N. Knight and O. Schwartz",
  title =        "Communication lower bounds and optimal algorithms for
                 numerical linear algebra",
  journal =      j-ACTA-NUMERICA,
  volume =       "23",
  pages =        "1--155",
  year =         "2014",
  CODEN =        "ANUMFU",
  DOI =          "https://doi.org/10.1017/S0962492914000038",
  ISSN =         "0962-4929 (print), 1474-0508 (electronic)",
  ISSN-L =       "0962-4929",
  bibdate =      "Mon May 12 19:01:04 MDT 2014",
  bibsource =    "http://journals.cambridge.org/action/displayIssue?jid=ANU&volumeId=23&issueId=00;
                 https://www.math.utah.edu/pub/tex/bib/actanumerica.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Acta Numer.",
  fjournal =     "Acta Numerica",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=ANU",
  keywords =     "accurate floating-point summation",
}

@Article{BasiriM:2014:EHB,
  author =       "Mohamed Asan {Basiri M.} and Noor Mahammad Sk",
  title =        "An Efficient Hardware-Based Higher Radix Floating
                 Point {MAC} Design",
  journal =      j-TODAES,
  volume =       "20",
  number =       "1",
  pages =        "15:1--15:??",
  month =        nov,
  year =         "2014",
  CODEN =        "ATASFO",
  DOI =          "https://doi.org/10.1145/2667224",
  ISSN =         "1084-4309 (print), 1557-7309 (electronic)",
  ISSN-L =       "1084-4309",
  bibdate =      "Wed Nov 19 11:18:40 MST 2014",
  bibsource =    "http://www.acm.org/pubs/contents/journals/todaes/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/todaes.bib",
  abstract =     "This article proposes an effective way of implementing
                 a multiply accumulate circuit (MAC) for high-speed
                 floating point arithmetic operations. The real-world
                 applications related to digital signal processing and
                 the like demand high-performance computation with
                 greater accuracy. In general, digital signals are
                 represented as a sequence of signed/unsigned
                 fixed/floating point numbers. The final result of a MAC
                 operation can be computed by feeding the mantissa of
                 the previous MAC result as one of the partial products
                 to a Wallace tree multiplier or Braun multiplier. Thus,
                 the separate accumulation circuit can be avoided by
                 keeping the circuit depth still within the bounds of
                 the Wallace tree multiplier, namely $ O (\log_2 n) $,
                 or Braun multiplier, namely $ O (n) $. In this article,
                 three kinds of floating point MACs are proposed. The
                 experimental results show 48.54\% of improvement in
                 worst path delay achieved by the proposed floating
                 point MAC using a radix-2 Wallace structure compared
                 with a conventional floating point MAC without a
                 pipeline using a 45nm technology library. The same
                 proposed design gives 39.92\% of improvement in worst
                 path delay without a pipeline using a radix-4 Braun
                 structure as compared with a conventional design. In
                 this article, a radix-32 $ Q_{32.32}$-format-based
                 floating point MAC is proposed using a Wallace
                 tree/Braun multiplier. Also this article discusses the
                 msb prediction problem and its solution in floating
                 point arithmetic that is not available in modern fused
                 multiply-add designs. The performance results show
                 comparisons between the proposed floating point MAC
                 with various floating point MAC designs for radix-2,
                 -4, -8, and -16. The proposed design has lesser depth
                 than a conventional floating point MAC as well as a
                 lower area requirement than other ways of floating
                 point MAC implementation, both with/without a
                 pipeline.",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  fjournal =     "ACM Transactions on Design Automation of Electronic
                 Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J776",
}

@PhdThesis{Boldo:2014:DFV,
  author =       "Sylvie Boldo",
  title =        "Deductive formal verification: How to make your
                 floating-point programs behave",
  type =         "Th{\`e}se d habilitation",
  school =       "Universit{\b{e}} Paris-Sud",
  address =      "Paris, France",
  pages =        "iv + 80",
  month =        oct,
  year =         "2014",
  bibdate =      "Fri Jan 31 15:49:31 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.lri.fr/~sboldo/files/hdr.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Bouvier:2014:DFB,
  author =       "Cyril Bouvier and Paul Zimmermann",
  title =        "Division-Free Binary-to-Decimal Conversion",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "63",
  number =       "8",
  pages =        "1895--1901",
  month =        aug,
  year =         "2014",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2014.2315621",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Aug 25 08:24:32 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://members.loria.fr/PZimmermann/papers/get_str.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Chiang:2014:ESI,
  author =       "Wei-Fan Chiang and Ganesh Gopalakrishnan and Zvonimir
                 Rakamari{\'c} and Alexey Solovyev",
  editor =       "{ACM}",
  booktitle =    "{PPoPP '14: Proceedings of the 19th ACM SIGPLAN
                 symposium on Principles and practice of parallel
                 programming}",
  title =        "Efficient Search for Inputs Causing High
                 Floating-point Errors",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "43--52",
  year =         "2014",
  DOI =          "https://doi.org/10.1145/2555243.2555265",
  ISBN =         "1-4503-2656-0",
  ISBN-13 =      "978-1-4503-2656-8",
  LCCN =         "????",
  bibdate =      "Tue Mar 18 14:32:45 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://dl.acm.org/citation.cfm?doid=2555243.2555265",
  acknowledgement = ack-nhfb,
}

@Article{Cibikdiken:2014:CMM,
  author =       "Ali Osman {\c{C}}ibikdiken and Kemal Aydin",
  title =        "Computation of the monodromy matrix in floating point
                 arithmetic with the {Wilkinson} Model",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "67",
  number =       "5",
  pages =        "1186--1194",
  month =        mar,
  year =         "2014",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:51:31 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122113006706",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}

@Article{Darulova:2014:SCR,
  author =       "Eva Darulova and Viktor Kuncak",
  title =        "Sound compilation of reals",
  journal =      j-SIGPLAN,
  volume =       "49",
  number =       "1",
  pages =        "235--248",
  month =        jan,
  year =         "2014",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/2578855.2535874",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Tue Mar 4 17:04:57 MST 2014",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
  note =         "POPL '14 conference proceedings.",
  abstract =     "Writing accurate numerical software is hard because of
                 many sources of unavoidable uncertainties, including
                 finite numerical precision of implementations. We
                 present a programming model where the user writes a
                 program in a real-valued implementation and
                 specification language that explicitly includes
                 different types of uncertainties. We then present a
                 compilation algorithm that generates a finite-precision
                 implementation that is guaranteed to meet the desired
                 precision with respect to real numbers. Our compilation
                 performs a number of verification steps for different
                 candidate precisions. It generates verification
                 conditions that treat all sources of uncertainties in a
                 unified way and encode reasoning about finite-precision
                 roundoff errors into reasoning about real numbers. Such
                 verification conditions can be used as a standardized
                 format for verifying the precision and the correctness
                 of numerical programs. Due to their non-linear nature,
                 precise reasoning about these verification conditions
                 remains difficult and cannot be handled using
                 state-of-the art SMT solvers alone. We therefore
                 propose a new procedure that combines exact SMT solving
                 over reals with approximate and sound affine and
                 interval arithmetic. We show that this approach
                 overcomes scalability limitations of SMT solvers while
                 providing improved precision over affine and interval
                 arithmetic. Our implementation gives promising results
                 on several numerical models, including dynamical
                 systems, transcendental functions, and controller
                 implementations.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}

@Article{Darulova:2014:TCR,
  author =       "Eva Darulova and Viktor Kuncak",
  title =        "Towards a Compiler for Reals",
  journal =      "arxiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--24",
  day =          "1",
  month =        oct,
  year =         "2014",
  bibdate =      "Sat Apr 02 15:52:17 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/1410.0198",
  abstract =     "Numerical software, common in scientific computing or
                 embedded systems, inevitably uses an approximation of
                 the real arithmetic in which most algorithms are
                 designed. In many domains, roundoff errors are not the
                 only source of inaccuracy and measurement and other
                 input errors further increase the uncertainty of the
                 computed results. Adequate tools are needed to help
                 users select suitable approximations, especially for
                 safety-critical applications. We present the
                 source-to-source compiler Rosa which takes as input a
                 real-valued program with error specifications and
                 synthesizes code over an appropriate floating-point or
                 fixed-point data type. The main challenge of such a
                 compiler is a fully automated, sound and yet accurate
                 enough numerical error estimation. We present a unified
                 technique for floating-point and fixed-point arithmetic
                 of various precisions which can handle nonlinear
                 arithmetic, determine closed- form symbolic invariants
                 for unbounded loops and quantify the effects of
                 discontinuities on numerical errors. We evaluate Rosa
                 on a number of benchmarks from scientific computing and
                 embedded systems and, comparing it to state-of-the-art
                 in automated error estimation, show it presents an
                 interesting trade-off between accuracy and
                 performance.",
  acknowledgement = ack-nhfb,
}

@Article{DelBarrio:2014:ULP,
  author =       "Alberto A. {Del Barrio} and Nader Bagherzadeh and
                 Rom{\'a}n Hermida",
  title =        "Ultra-low-power adder stage design for exascale
                 floating point units",
  journal =      j-TECS,
  volume =       "13",
  number =       "3s",
  pages =        "105:1--105:??",
  month =        mar,
  year =         "2014",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2567932",
  ISSN =         "1539-9087 (print), 1558-3465 (electronic)",
  ISSN-L =       "1539-9087",
  bibdate =      "Mon Mar 24 17:17:02 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tecs.bib",
  abstract =     "Currently, the most powerful supercomputers can
                 provide tens of petaflops. Future many-core systems are
                 estimated to provide an exaflop. However, the power
                 budget limitation makes these machines still infeasible
                 and unaffordable. Floating Point Units (FPUs) are
                 critical from both the power consumption and
                 performance points of view of today's microprocessors
                 and supercomputers. Literature offers very different
                 designs. Some of them are focused on increasing
                 performance no matter the penalty, and others on
                 decreasing power at the expense of lower performance.
                 In this article, we propose a novel approach for
                 reducing the power of the FPU without degrading the
                 rest of parameters. Concretely, this power reduction is
                 also accompanied by an area reduction and a performance
                 improvement. Hence, an overall energy gain will be
                 produced. According to our experiments, our proposed
                 unit consumes 17.5\%, 23\% and 16.5\% less energy for
                 single, double and quadruple precision, with an
                 additional 15\%, 21.5\% and 14.5\% delay reduction,
                 respectively. Furthermore, area is also diminished by
                 4\%, 4.5\% and 5\%.",
  acknowledgement = ack-nhfb,
  articleno =    "105",
  fjournal =     "ACM Transactions on Embedded Computing Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?&idx=J840",
}

@Misc{Demmel:2014:THS,
  author =       "James Demmel and Hong Diep Nguyen",
  title =        "Toward hardware support for Reproducible {BLAS}",
  howpublished = "SCAN 2014 talk slides.",
  day =          "24",
  month =        sep,
  year =         "2014",
  bibdate =      "Mon Jan 04 15:49:09 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://bebop.cs.berkeley.edu/reproblas/img/pdf.png",
  acknowledgement = ack-nhfb,
}

@Article{Doerr:2014:RRP,
  author =       "Benjamin Doerr and Magnus Wahlstr{\"o}m",
  title =        "Randomized Rounding in the Presence of a Cardinality
                 Constraint",
  journal =      j-ACM-J-EXP-ALGORITHMICS,
  volume =       "19",
  number =       "1",
  pages =        "1.2:1--1.2:??",
  month =        may,
  year =         "2014",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2594409",
  ISSN =         "1084-6654",
  ISSN-L =       "1084-6654",
  bibdate =      "Wed May 21 14:36:05 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jea.bib",
  abstract =     "We consider the problem of generating randomized
                 roundings that satisfy a single cardinality constraint
                 and admit Chernoff-type large deviation bounds for
                 weighted sums of the variables. That this can be done
                 efficiently was proven by Srinivasan [2001], a
                 different approach was later given by the first author
                 [Doerr 2006]. In this work, we (a) present an improved
                 version of the bitwise derandomization given by Doerr,
                 (b) give the first derandomization of Srinivasan's
                 tree-based randomized approach and prove its
                 correctness, and (c) experimentally compare the
                 resulting algorithms. Our experiments show that adding
                 a single cardinality constraint typically reduces the
                 rounding errors and only moderately increases the
                 running times. In general, our derandomization of the
                 tree-based approach is superior to the derandomized
                 bitwise one, while the two randomized versions produce
                 very similar rounding errors. When implementing the
                 derandomized tree-based approach, however, the choice
                 of the tree is important.",
  acknowledgement = ack-nhfb,
  articleno =    "1.2",
  fjournal =     "Journal of Experimental Algorithmics (JEA)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J430",
}

@Article{Drane:2014:SCF,
  author =       "T. A. Drane and T. M. Rose and G. A. Constantinides",
  title =        "On the Systematic Creation of Faithfully Rounded
                 Truncated Multipliers and Arrays",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "63",
  number =       "10",
  pages =        "2513--2525",
  month =        oct,
  year =         "2014",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2013.126",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Nov 06 07:29:34 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "arbitrary array; bit vectors; correct rounding;
                 correct-by-construction; Data-path design; elemental
                 semiconductors; faithfully rounded truncated arrays;
                 faithfully rounded truncated multipliers; fixed point
                 arithmetic; fixed-point multiplication; floating-point
                 arithmetic; hardware description languages; HDL code;
                 heuristically inspired schemes; high-speed arithmetic;
                 Monte Carlo methods; Monte Carlo simulation;
                 multiplying circuits; parallel circuits; partial
                 product array; Si; silicon; silicon area; systematic
                 creation; truncated multiplier schemes; word length 32
                 bit; worst-case analysis; worst-case error",
}

@Article{Du:2014:AEP,
  author =       "Peibing Du and Hao Jiang and Lizhi Cheng",
  title =        "Accurate Evaluation of Polynomials in {Legendre}
                 Basis",
  journal =      j-J-APPL-MATH,
  volume =       "2014",
  pages =        "742538:1--742538:13",
  year =         "2014",
  DOI =          "https://doi.org/10.1155/2014/742538",
  ISSN =         "1110-757X (print), 1687-0042 (electronic)",
  ISSN-L =       "1110-757X",
  bibdate =      "Mon Mar 19 14:19:47 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.hindawi.com/journals/jam/2014/742538/",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Mathematics",
  journal-URL =  "http://www.hindawi.com/journals/jam/",
}

@Article{Dumas:2014:NRI,
  author =       "Jean-Guillaume Dumas",
  title =        "On {Newton--Raphson} Iteration for Multiplicative
                 Inverses Modulo Prime Powers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "63",
  number =       "8",
  pages =        "2106--2109",
  month =        aug,
  year =         "2014",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2013.94",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Aug 25 08:24:32 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See original work \cite{Dumas:2012:NRI}, corrections
                 \cite{Walther:2019:VNR}, and later work
                 \cite{Hurchalla:2022:IIM}.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Duracz:2014:PFI,
  author =       "Jan Duracz and Michal Kone{\v{c}}n{\'y}",
  title =        "Polynomial function intervals for floating-point
                 software verification",
  journal =      j-ANN-MATH-ARTIF-INTELL,
  volume =       "70",
  number =       "4",
  pages =        "351--398",
  month =        apr,
  year =         "2014",
  CODEN =        "AMAIEC",
  DOI =          "https://doi.org/10.1007/s10472-014-9409-7",
  ISSN =         "1012-2443 (print), 1573-7470 (electronic)",
  ISSN-L =       "1012-2443",
  bibdate =      "Sat Jun 8 08:22:14 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Mathematics and Artificial Intelligence",
  journal-URL =  "http://link.springer.com/journal/10472",
  keywords =     "PolyPaver open-source software tool",
}

@Article{Gilani:2014:EEP,
  author =       "Syed Zohaib Gilani and Nam Sung Kim and Michael
                 Schulte",
  title =        "Energy-Efficient Pixel-Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "63",
  number =       "8",
  pages =        "1--1",
  month =        aug,
  year =         "2014",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2014.2325827",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Aug 25 08:24:32 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Gladshtein:2014:DBP,
  author =       "Michael Gladshtein",
  title =        "Delay-based processing-in-wire for design of {QCA}
                 serial decimal arithmetic units",
  journal =      j-JETC,
  volume =       "10",
  number =       "2",
  pages =        "13:1--13:??",
  month =        feb,
  year =         "2014",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2564927",
  ISSN =         "1550-4832 (print), 1550-4840 (electronic)",
  ISSN-L =       "1550-4832",
  bibdate =      "Fri Feb 28 17:06:25 MST 2014",
  bibsource =    "http://www.acm.org/pubs/contents/journals/jetc/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jetc.bib",
  abstract =     "Quantum-dot cellular automata (QCA) technology is now
                 considered to be one of the prospective technologies
                 for a nanocomputer creation. The physical properties of
                 QCA and its expanding range of computer applications
                 make it expedient to use the novel paradigm of
                 nanocomputer architecture: serial decimal
                 storage-transfer-processing. The delay-based encoding
                 of decimal digits allows the use a delay element as a
                 main element of QCA serial arithmetic units. The simple
                 implementation of the delay element by a short length
                 of QCA wire results in reduction of complexity and of
                 the area required for a QCA circuit. The theoretical
                 basics of delay-based processing-in-wire and design
                 examples of QCA serial decimal arithmetic units are
                 presented.",
  acknowledgement = ack-nhfb,
  articleno =    "13",
  fjournal =     "ACM Journal on Emerging Technologies in Computing
                 Systems (JETC)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J967",
}

@Article{Goualard:2014:HDY,
  author =       "Fr{\'e}d{\'e}ric Goualard",
  title =        "How do you compute the midpoint of an interval?",
  journal =      j-TOMS,
  volume =       "40",
  number =       "2",
  pages =        "11:1--11:25",
  month =        feb,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2493882",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 14 06:30:41 MDT 2014",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The algorithm that computes the midpoint of an
                 interval with floating-point bounds requires some
                 careful devising to handle all possible inputs
                 correctly. We review several implementations from
                 prominent C/C++ interval arithmetic packages and
                 analyze their potential failure to deliver the expected
                 results. We then show how to amend them to avoid common
                 pitfalls. The results presented are also relevant to
                 noninterval arithmetic computation such as the
                 implementation of bisection methods. Enough background
                 on IEEE 754 floating-point arithmetic is provided for
                 this article to serve as a practical introduction to
                 the analysis of floating-point computation.",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Graillat:2014:MRE,
  author =       "Stef Graillat and Vincent Lef{\`e}vre and Jean-Michel
                 Muller",
  title =        "On the maximum relative error when computing $ x^n $
                 in floating-point arithmetic",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "11",
  month =        feb,
  year =         "2014",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/1402.2991",
  abstract =     "In this paper, we improve the usual relative error
                 bound for the computation of $ x^n $ through iterated
                 multiplications by x in binary floating-point
                 arithmetic. The obtained error bound is only slightly
                 better than the usual one, but it is simpler. We also
                 discuss the more general problem of computing the
                 product of n terms.",
  acknowledgement = ack-nhfb,
  subject =      "Numerical Analysis (cs.NA); Numerical Analysis
                 (math.NA)",
}

@InProceedings{Hormigo:2014:ODC,
  author =       "J. Hormigo and J. Villalba",
  editor =       "Michael B. Matthews",
  booktitle =    "{Proceedings of the 48th Asilomar Conference on
                 Signals, Systems, and Computers, November 2--5, 2014,
                 Pacific Grove, California}",
  title =        "Optimizing {DSP} circuits by a new family of
                 arithmetic operators",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "871--875",
  year =         "2014",
  DOI =          "https://doi.org/10.1109/ACSSC.2014.7094576",
  ISBN =         "1-4799-8297-0, 1-4799-8298-9, 1-4799-8295-4",
  ISBN-13 =      "978-1-4799-8297-4",
  ISSN =         "1058-6393",
  LCCN =         "TK7801",
  bibdate =      "Sun Jun 19 14:59:21 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Jeannerod:2014:REF,
  author =       "Claude-Pierre Jeannerod and Siegfried M. Rump",
  title =        "On relative errors of floating-point operations:
                 optimal bounds and applications",
  type =         "Preprint",
  number =       "??",
  institution =  "????",
  address =      "????",
  month =        "????",
  year =         "2014",
  bibdate =      "Mon May 30 07:31:09 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Misc{Johansson:2014:PMP,
  author =       "Fredrik Johansson and {The mpmath Development Team}",
  title =        "\pkg{mpmath}: a {Python} library for
                 arbitrary-precision floating-point arithmetic",
  howpublished = "Web site",
  year =         "2014",
  bibdate =      "Wed Apr 24 13:50:47 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/python.bib",
  URL =          "http://mpmath.org/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Joldes:2014:CRF,
  author =       "Mioara Joldes and Jean-Michel Muller and Valentina
                 Popescu",
  editor =       "{IEEE}",
  booktitle =    "{2014 IEEE 25th International Conference on
                 Application-Specific Systems, Architectures and
                 Processors. 18-20 June 2014. Z{\"u}rich, Switzerland}",
  title =        "On the computation of the reciprocal of floating point
                 expansions using an adapted {Newton--Raphson}
                 iteration",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "63--67",
  year =         "2014",
  DOI =          "https://doi.org/10.1109/ASAP.2014.6868632",
  ISBN =         "1-4799-3608-1",
  ISBN-13 =      "978-1-4799-3608-3",
  bibdate =      "Fri Sep 29 10:47:32 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Joldes:2014:SSH,
  author =       "Mioara Joldes and Valentina Popescu and Warwick
                 Tucker",
  title =        "Searching for Sinks for the {H{\'e}non} Map using a
                 Multiple-precision {GPU} Arithmetic Library",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "42",
  number =       "4",
  pages =        "63--68",
  year =         "2014",
  CODEN =        "CANED2",
  DOI =          "https://doi.org/10.1145/2693714.2693726",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Wed Dec 3 16:18:50 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
  abstract =     "Today, GPUs represent an important hardware
                 development platform for many problems in dynamical
                 systems, where massive parallel computations are
                 needed. Beside that, many numerical studies of chaotic
                 dynamical systems require a computing precision higher
                 than common floating point (FP) formats. One such
                 application is locating invariant sets for chaotic
                 dynamical systems. In particular, we focus on
                 rigorously proving the existence of stable periodic
                 orbits for the H{\'e}non map for parameter values close
                 to the classical ones. For that, we present a
                 multiple-precision floating-point arithmetic library in
                 CUDA programming language for the NVIDIA GPU platform.
                 Our library extends the precision using so-called FP
                 expansions, where a number is represented as the
                 unevaluated sum of standard machine precision FP
                 numbers. This format offers the advantage of using
                 directly available and highly optimized hardware FP
                 operations. We generalize algorithms used by
                 multiple-precisions libraries such as Bailey's QD, or
                 the analogue GPU version, GQD.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
  remark =       "HEART '14 conference proceedings.",
}

@InProceedings{Kasliwal:2014:HRD,
  author =       "Prabha S. Kasliwal and Gaurav Bhand and B. P. Patil",
  booktitle =    "{2014 Science and Information Conference}",
  title =        "Hardware realization of discrete convolution using
                 {CORDIC} and {Vedic} multiplier",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "850--854",
  year =         "2014",
  DOI =          "https://doi.org/10.1109/SAI.2014.6918284",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer architecture; Convolution; CORDIC; Discrete
                 linear convolution; Equations; Field programmable gate
                 arrays; Finite element analysis; FPGA; Signal
                 processing algorithms; Vectors; Vedic",
}

@Article{Korzen:2014:PPP,
  author =       "Marcin Korze{\'n} and Szymon Jaroszewicz",
  title =        "{PaCAL}: A {Python} Package for Arithmetic
                 Computations with Random Variables",
  journal =      j-J-STAT-SOFT,
  volume =       "57",
  number =       "10",
  pages =        "??--??",
  month =        may,
  year =         "2014",
  CODEN =        "JSSOBK",
  ISSN =         "1548-7660",
  ISSN-L =       "1548-7660",
  bibdate =      "Mon Jun 16 11:01:52 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatsoft.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://www.jstatsoft.org/v57/i10",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Software",
  journal-URL =  "http://www.jstatsoft.org/",
  pubdates =     "Submitted 2012-02-14; Accepted 2013-07-21",
}

@InProceedings{Leeser:2014:MIR,
  author =       "Miriam Leeser and Sayan Mukherjee and Jaideep
                 Ramachandran and Thomas Wahl",
  editor =       "{IEEE}",
  booktitle =    "{Design, Automation and Test in Europe Conference and
                 Exhibition (DATE), Dresden, Germany March 24--28,
                 2014}",
  title =        "Make it real: Effective floating-point reasoning via
                 exact arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--4",
  year =         "2014",
  DOI =          "https://doi.org/10.7873/DATE.2014.130",
  ISBN =         "1-4799-3297-3, 3-9815370-2-5",
  ISBN-13 =      "978-1-4799-3297-9, 978-3-9815370-2-4",
  LCCN =         "TK7870 .D467 2014",
  bibdate =      "Sat Jun 4 17:09:03 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=6784162",
  acknowledgement = ack-nhfb,
}

@Article{Lei:2014:FIS,
  author =       "Yuanwu Lei and Lei Guo and Yong Dou and Sheng Ma and
                 Jinbo Xu",
  title =        "{FPGA} Implementation of a Special-Purpose {VLIW}
                 Structure for Double-Precision Elementary Function",
  journal =      j-TRETS,
  volume =       "7",
  number =       "2",
  pages =        "8:1--8:??",
  month =        jun,
  year =         "2014",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2617594",
  ISSN =         "1936-7406 (print), 1936-7414 (electronic)",
  ISSN-L =       "1936-7406",
  bibdate =      "Mon Jun 30 18:26:23 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/trets.bib",
  abstract =     "In the current article, the capability and flexibility
                 of field programmable gate-arrays (FPGAs) to implement
                 IEEE-754 double-precision floating-point elementary
                 functions are explored. To perform various elementary
                 functions on the unified hardware efficiently, we
                 propose a special-purpose very long instruction word
                 (VLIW) processor, called DP\_VELP. This processor is
                 equipped with multiple basic units, and its performance
                 is improved through an explicitly parallel technique.
                 Pipelined evaluation of polynomial approximation with
                 Estrin's scheme is proposed, by scheduling basic
                 components in an optimal order to avoid data hazard
                 stalls and achieve minimal latency. The custom VLIW
                 processor can achieve high scalability. Under the
                 control of specific VLIW instructions, the basic units
                 are combined into special-purpose hardware for
                 elementary functions. Common elementary functions are
                 presented as examples to illustrate the design of
                 elementary function in DP_VELP in detail. Minimax
                 approximation scheme is used to reduce degree of
                 polynomial. Compromise between the size of lookup table
                 and the latency is discussed, and the internal
                 precision is carefully planned to guarantee accuracy of
                 the result. Finally, we create a prototype of the
                 DP_VELP unit and an FPGA accelerator based on the
                 DP_VELP unit on a Xilinx XC6VLX760 FPGA chip to
                 implement the SGP4/SDP4 application. Compared with
                 previous researches, the proposed design can achieve
                 low latency with a reasonable amount of resources and
                 evaluate a variety of elementary functions with the
                 unified hardware to satisfy the demands in scientific
                 applications. Experimental results show that the
                 proposed design guarantees more than 99\% of correct
                 rounding. Moreover, the SGP4/SDP4 accelerator, which is
                 equipped with 39 DP_VELP units and runs at 200 MHz,
                 outperforms the parallel software approach with
                 hyper-thread technology on an Intel Xeon Quad E5620 CPU
                 at 2.40 GHz by a factor of 7X.",
  acknowledgement = ack-nhfb,
  articleno =    "8",
  fjournal =     "ACM Transactions on Reconfigurable Technology and
                 Systems (TRETS)",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J1151",
}

@Article{Lindstrom:2014:FRC,
  author =       "Peter Lindstrom",
  title =        "Fixed-Rate Compressed Floating-Point Arrays",
  journal =      j-IEEE-TRANS-VIS-COMPUT-GRAPH,
  volume =       "20",
  number =       "12",
  pages =        "2674--2683",
  month =        dec,
  year =         "2014",
  CODEN =        "ITVGEA",
  DOI =          "https://doi.org/10.1109/TVCG.2014.2346458",
  ISSN =         "1077-2626 (print), 1941-0506 (electronic), 2160-9306",
  ISSN-L =       "1077-2626",
  bibdate =      "Thu Feb 12 16:40:54 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/datacompression.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransviscomputgraph.bib",
  URL =          "http://csdl.computer.org/csdl/trans/tg/2014/12/06876024-abs.html",
  abstract-URL = "http://csdl.computer.org/csdl/trans/tg/2014/12/06876024-abs.html",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Visualization and Computer
                 Graphics",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2945",
}

@Article{Long:2014:SIF,
  author =       "Fan Long and Stelios Sidiroglou-Douskos and Deokhwan
                 Kim and Martin Rinard",
  title =        "Sound input filter generation for integer overflow
                 errors",
  journal =      j-SIGPLAN,
  volume =       "49",
  number =       "1",
  pages =        "439--452",
  month =        jan,
  year =         "2014",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/2578855.2535888",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Tue Mar 4 17:04:57 MST 2014",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
  note =         "POPL '14 conference proceedings.",
  abstract =     "We present a system, SIFT, for generating input
                 filters that nullify integer overflow errors associated
                 with critical program sites such as memory allocation
                 or block copy sites. SIFT uses a static program
                 analysis to generate filters that discard inputs that
                 may trigger integer overflow errors in the computations
                 of the sizes of allocated memory blocks or the number
                 of copied bytes in block copy operations. Unlike all
                 previous techniques of which we are aware, SIFT is
                 sound --- if an input passes the filter, it will not
                 trigger an integer overflow error at any analyzed site.
                 Our results show that SIFT successfully analyzes (and
                 therefore generates sound input filters for) 56 out of
                 58 memory allocation and block memory copy sites in
                 analyzed input processing modules from five
                 applications (VLC, Dillo, Swfdec, Swftools, and GIMP).
                 These nullified errors include six known integer
                 overflow vulnerabilities. Our results also show that
                 applying these filters to 62895 real-world inputs
                 produces no false positives. The analysis and filter
                 generation times are all less than a second.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
}

@Article{Lupon:2014:SHS,
  author =       "Marc Lupon and Enric Gibert and Grigorios Magklis and
                 Sridhar Samudrala and Ra{\'u}l Mart{\'\i}nez and
                 Kyriakos Stavrou and David R. Ditzel",
  title =        "Speculative hardware\slash software co-designed
                 floating-point multiply-add fusion",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "42",
  number =       "1",
  pages =        "623--638",
  month =        mar,
  year =         "2014",
  CODEN =        "CANED2",
  DOI =          "https://doi.org/10.1145/2654822.2541978",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Thu Sep 4 07:12:13 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
  abstract =     "A Fused Multiply-Add (FMA) instruction is currently
                 available in many general-purpose processors. It
                 increases performance by reducing latency of dependent
                 operations and increases precision by computing the
                 result as an indivisible operation with no intermediate
                 rounding. However, since the arithmetic behavior of a
                 single-rounding FMA operation is different than
                 independent FP multiply followed by FP add
                 instructions, some algorithms require significant
                 revalidation and rewriting efforts to work as expected
                 when they are compiled to operate with FMA --- a cost
                 that developers may not be willing to pay. Because of
                 that, abundant legacy applications are not able to
                 utilize FMA instructions. In this paper we propose a
                 novel HW/SW collaborative technique that is able to
                 efficiently execute workloads with increased
                 utilization of FMA, by adding the option to get the
                 same numerical result as separate FP multiply and FP
                 add pairs. In particular, we extended the host ISA of a
                 HW/SW co-designed processor with a new Combined
                 Multiply-Add (CMA) instruction that performs an FMA
                 operation with an intermediate rounding. This new
                 instruction is used by a transparent dynamic
                 translation software layer that uses a speculative
                 instruction-fusion optimization to transform FP
                 multiply and FP add sequences into CMA instructions.
                 The FMA unit has been slightly modified to support both
                 single-rounding and double-rounding fused instructions
                 without increasing their latency and to provide a
                 conservative fall-back path in case of misspeculation.
                 Evaluation on a cycle-accurate timing simulator showed
                 that CMA improved SPECfp performance by 6.3\% and
                 reduced executed instructions by 4.7\%.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
  remark =       "ASPLOS '14 conference proceedings.",
}

@Article{Marche:2014:VFB,
  author =       "Claude March{\'e}",
  title =        "Verification of the functional behavior of a
                 floating-point program: an industrial case study",
  journal =      j-SCI-COMPUT-PROGRAM,
  volume =       "96 (part 3)",
  number =       "??",
  pages =        "279--296",
  day =          "15",
  month =        dec,
  year =         "2014",
  CODEN =        "SCPGD4",
  ISSN =         "0167-6423 (print), 1872-7964 (electronic)",
  ISSN-L =       "0167-6423",
  bibdate =      "Fri Oct 24 05:57:57 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/scicomputprogram.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167642314001671",
  acknowledgement = ack-nhfb,
  fjournal =     "Science of Computer Programming",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01676423/",
}

@Article{Milicevic:2014:PAO,
  author =       "Aleksandar Milicevic and Daniel Jackson",
  title =        "Preventing arithmetic overflows in {Alloy}",
  journal =      j-SCI-COMPUT-PROGRAM,
  volume =       "94 (part 2)",
  number =       "??",
  pages =        "203--216",
  day =          "15",
  month =        nov,
  year =         "2014",
  CODEN =        "SCPGD4",
  DOI =          "https://doi.org/10.1016/j.scico.2014.05.009",
  ISSN =         "0167-6423 (print), 1872-7964 (electronic)",
  ISSN-L =       "0167-6423",
  bibdate =      "Mon Sep 22 08:04:04 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/scicomputprogram.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167642314002470",
  acknowledgement = ack-nhfb,
  fjournal =     "Science of Computer Programming",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01676423/",
}

@Misc{Moler:2014:CCFa,
  author =       "Cleve Moler",
  title =        "{Cleve's Corner}: Floating Point Numbers",
  howpublished = "MathWorks Web site.",
  day =          "7",
  month =        jul,
  year =         "2014",
  bibdate =      "Sat Jan 19 18:59:13 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://blogs.mathworks.com/cleve/2014/07/07/floating-point-numbers/",
  acknowledgement = ack-nhfb,
}

@Misc{Moler:2014:CCFb,
  author =       "Cleve Moler",
  title =        "{Cleve's Corner}: Floating Point Denormals,
                 Insignificant But Controversial",
  howpublished = "MathWorks Web site.",
  day =          "21",
  month =        jul,
  year =         "2014",
  bibdate =      "Sat Jan 19 18:38:12 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://blogs.mathworks.com/cleve/2014/07/21/floating-point-denormals-insignificant-but-controversial-2/",
  acknowledgement = ack-nhfb,
}

@Article{Mukhopadhyay:2014:EMP,
  author =       "Debapriyay Mukhopadhyay and Subhas C. Nandy",
  title =        "Efficient multiple-precision integer division
                 algorithm",
  journal =      j-INFO-PROC-LETT,
  volume =       "114",
  number =       "3",
  pages =        "152--157",
  month =        mar,
  year =         "2014",
  CODEN =        "IFPLAT",
  DOI =          "https://doi.org/10.1016/j.ipl.2013.10.005",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Mon Dec 9 09:33:47 MST 2013",
  bibsource =    "http://www.sciencedirect.com/science/journal/00200190;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/infoproc2010.bib",
  note =         "This paper provides a correction to the algorithm
                 presented in \cite{Huang:2005:EMP}, and also supplies a
                 complicated correctness proof.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0020019013002627",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  keywords =     "computational arithmetic; cryptography; division
                 algorithm; normalization",
}

@InProceedings{Muller:2014:MRE,
  author =       "Jean-Michel Muller",
  editor =       "????",
  booktitle =    "{INVA} Conference Proceedings, Tokyo, Japan, 2014",
  title =        "On the maximum relative error when computing iterated
                 integer powers in floating-point arithmetic",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2014",
  bibdate =      "Mon May 30 10:37:15 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "See later paper \cite{Graillat:2015:MRE}.",
}

@Article{Murakami:2014:CRN,
  author =       "Hiroshi Murakami",
  title =        "Calculation of Rational Numbers in an Interval Whose
                 Denominator is the Smallest by using {FP} Interval
                 Arithmetic",
  journal =      j-ACM-COMM-COMP-ALGEBRA,
  volume =       "48",
  number =       "3/4",
  pages =        "134--136",
  month =        sep,
  year =         "2014",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2733693.2733711",
  ISSN =         "1932-2232 (print), 1932-2240 (electronic)",
  ISSN-L =       "1932-2232",
  bibdate =      "Thu Feb 5 17:11:08 MST 2015",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
  abstract =     "The continued fraction expansion method is a fast
                 solver to find a rational number in a given real
                 interval whose denominator is the smallest. A simple
                 implementation of the CF expansion method which uses
                 floating point numbers as real numbers has a
                 possibility to give a wrong answer by the effect of
                 numerical round-off errors. In this paper, we show a
                 modification of the algorithm of the CF expansion
                 method so that it uses floating point (FP) intervals as
                 replacements of real numbers. By this modified
                 algorithm, the answer is obtained only when its
                 correctness is guaranteed and the possibility to give a
                 wrong answer is eliminated.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Communications in Computer Algebra",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}

@Article{Nannarelli:2014:GEI,
  author =       "Alberto Nannarelli and Peter-Michael Seidel and Ping
                 Tak Peter Tang",
  title =        "{Guest Editors}' Introduction: Special Section on
                 Computer Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "63",
  number =       "8",
  pages =        "1852--1853",
  month =        aug,
  year =         "2014",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2014.2331711",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Aug 25 08:24:32 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Neto:2014:PUP,
  author =       "Joao Carlos Neto and Alexandre Ferreira Tenca and
                 Wilson Vicente Ruggiero",
  title =        "A Parallel and Uniform $k$-Partition Method for
                 {Montgomery} Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "63",
  number =       "9",
  pages =        "2122--2133",
  month =        sep,
  year =         "2014",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2013.89",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Sep 9 06:54:10 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Nguyen:2014:RED,
  author =       "Trung Duc Nguyen and Rodney {Van Meter}",
  title =        "A Resource-Efficient Design for a Reversible Floating
                 Point Adder in Quantum Computing",
  journal =      j-JETC,
  volume =       "11",
  number =       "2",
  pages =        "13:1--13:??",
  month =        nov,
  year =         "2014",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2629525",
  ISSN =         "1550-4832 (print), 1550-4840 (electronic)",
  ISSN-L =       "1550-4832",
  bibdate =      "Wed Nov 5 18:01:28 MST 2014",
  bibsource =    "http://www.acm.org/pubs/contents/journals/jetc/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jetc.bib",
  abstract =     "Reversible logic has applications in low-power
                 computing and quantum computing. However, there are few
                 existing designs for reversible floating-point adders
                 and none suitable for quantum computation. In this
                 article, we propose a resource-efficient reversible
                 floating-point adder, suitable for binary quantum
                 computation, improving the design of Nachtigal et al.
                 [2011]. Our work focuses on improving the reversible
                 designs of the alignment unit and the normalization
                 unit, which are the most expensive parts. By changing a
                 few elements of the existing algorithm, including the
                 circuit designs of the RLZC (reversible leading zero
                 counter) and converter, we have reduced the cost by
                 about 68\%. We also propose quantum designs adapted to
                 use gates from fault-tolerant libraries. The KQ for our
                 fault-tolerant design is almost 60 times as expensive
                 as for a 32-bit fixed-point addition. We note that the
                 floating-point representation makes in-place, truly
                 reversible arithmetic impossible, requiring us to
                 retain both inputs, which limits the sustainability of
                 its use for quantum computation.",
  acknowledgement = ack-nhfb,
  articleno =    "13",
  fjournal =     "ACM Journal on Emerging Technologies in Computing
                 Systems (JETC)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J967",
}

@Article{Pedram:2014:AAF,
  author =       "Ardavan Pedram and Andreas Gerstlauer and Robert A.
                 van de Geijn",
  title =        "Algorithm, Architecture, and Floating-Point Unit
                 Codesign of a Matrix Factorization Accelerator",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "63",
  number =       "8",
  pages =        "1854--1867",
  month =        aug,
  year =         "2014",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2014.2315627",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Aug 25 08:24:32 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Piso:2014:OAE,
  author =       "D. Piso and J. D. Bruguera",
  title =        "Obtaining Accurate Error Expressions and Bounds for
                 Floating-Point Multiplicative Algorithms",
  journal =      j-COMP-J,
  volume =       "57",
  number =       "2",
  pages =        "319--331",
  month =        feb,
  year =         "2014",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/bxs170",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Mon Feb 3 17:03:04 MST 2014",
  bibsource =    "http://comjnl.oxfordjournals.org/content/57/2.toc;
                 https://www.math.utah.edu/pub/tex/bib/compj2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/57/2/319.full.pdf+html",
  acknowledgement = ack-nhfb,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  onlinedate =   "January 17, 2013",
}

@Misc{Regan:2014:GAD,
  author =       "Rick Regan",
  title =        "{GCC} Avoids Double Rounding Errors With
                 Round-To-Odd",
  howpublished = "Web site",
  day =          "15",
  month =        jan,
  year =         "2014",
  bibdate =      "Fri Dec 08 14:41:07 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/gnu.bib",
  URL =          "https://www.exploringbinary.com/gcc-avoids-double-rounding-errors-with-round-to-odd/",
  acknowledgement = ack-nhfb,
  keywords =     "correct rounding; floating-point arithmetic; round to
                 odd",
}

@Article{Revol:2014:NRP,
  author =       "Nathalie Revol and Philippe Theveny",
  title =        "Numerical Reproducibility and Parallel Computations:
                 Issues for Interval Algorithms",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "63",
  number =       "8",
  pages =        "1915--1924",
  month =        aug,
  year =         "2014",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2014.2322593",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Aug 25 08:24:32 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "floating-point arithmetic; reproducible arithmetic",
}

@Article{Riemens:2014:TSA,
  author =       "Danny P. Riemens and Georgi N. Gaydadjiev and Chris I.
                 de Zeeuw and Christos Strydis",
  title =        "Towards scalable arithmetic units with graceful
                 degradation",
  journal =      j-TECS,
  volume =       "13",
  number =       "4",
  pages =        "87:1--87:??",
  month =        feb,
  year =         "2014",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2499367",
  ISSN =         "1539-9087 (print), 1558-3465 (electronic)",
  ISSN-L =       "1539-9087",
  bibdate =      "Tue Mar 11 18:33:06 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tecs.bib",
  abstract =     "This article presents a new family of scalable
                 arithmetic units (ScAUs) targeting
                 resource-constrained, embedded devices. We, first,
                 study the performance, power, area and scalability
                 properties of general adders. Next, suitable
                 error-detection schemes for low-power embedded systems
                 are discussed. As a result, our ScAUs are enhanced with
                 a suitable error-detection scheme, resulting in a
                 Parity-Checked ScAU (PCScAU) design. The PCScAU strikes
                 a flexible trade-off between space and time redundancy,
                 offering dependability similar to high-end techniques
                 for the area and power cost of low-end approaches. An
                 alternative design, the Precision-Scalable Arithmetic
                 Unit (PScAU) maintains throughput with degraded
                 precision in case of hardware failures. The PScAU is
                 targeting dependable applications where latency rather
                 than numerical accuracy is more important. The PScAU's
                 downscaled mode is also interesting for runtime thermal
                 management due to its advantageous power consumption.
                 We implemented and synthesized the PCScAU, PScAU and a
                 few important reference designs (double-, triple- and
                 quadruple-modular-redundancy adders with/without input
                 gating) in 90- nm UMC technology. Overall, the PC-ScAU
                 ranks first in 9 out of 10 power-delay-area
                 (PDA)-product variants. It exhibits 16\% area savings
                 and 12\% performance speedup for 7\% increase in total
                 power consumption, compared to the cheapest form of
                 conventional hardware replication with the same fault
                 coverage. The PDA product of the PCScAU is, thus,
                 reduced by 21\%. It is interesting that, while total
                 power slightly increases, the PCScAU static power in
                 fact decreases by 14\%. Therefore, for newer technology
                 nodes where the static power component is significant,
                 the PCScAU can also achieve-next to performance and
                 area --- significant power improvements.",
  acknowledgement = ack-nhfb,
  articleno =    "87",
  fjournal =     "ACM Transactions on Embedded Computing Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?&idx=J840",
}

@Article{Rohn:2014:VLD,
  author =       "Jiri Rohn",
  title =        "Verification of Linear (In){Dependence} in Finite
                 Precision Arithmetic",
  journal =      j-MATH-COMPUT-SCI,
  volume =       "8",
  number =       "3--4",
  pages =        "323--328",
  month =        sep,
  year =         "2014",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s11786-014-0196-7",
  ISSN =         "1661-8270 (print), 1661-8289 (electronic)",
  ISSN-L =       "1661-8270",
  bibdate =      "Fri Feb 13 07:10:04 MST 2015",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1661-8270&volume=8&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/math-comput-sci.bib",
  URL =          "http://link.springer.com/article/10.1007/s11786-014-0196-7",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics in Computer Science",
  journal-URL =  "http://link.springer.com/journal/11786",
}

@Article{Roux:2014:IDR,
  author =       "Pierre Roux",
  title =        "Innocuous Double Rounding of Basic Arithmetic
                 Operations",
  journal =      "Journal of Formalized Reasoning",
  volume =       "7",
  number =       "1",
  year =         "2014",
  DOI =          "https://doi.org/10.6092/issn.1972-5787/4359",
  ISSN =         "1972-5787",
  ISSN-L =       "1972-5787",
  bibdate =      "Mon Jan 11 08:08:43 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://hal.archives-ouvertes.fr/hal-01091186",
  abstract =     "Double rounding occurs when a floating-point value is
                 first rounded to an intermediate precision before being
                 rounded to a final precision. The result of two such
                 consecutive roundings can differ from the result
                 obtained when directly rounding to the final precision.
                 Double rounding practically happens, for instance, when
                 implementing the IEEE 754 binary32 format with an
                 arithmetic unit performing operations only in the
                 larger binary64 format, such as done in the PowerPC or
                 x87 floating-point units. It belongs to the folklore in
                 the floating-point arithmetic community that double
                 rounding is innocuous for the basic arithmetic
                 operations (addition, division, multiplication, and
                 square root) as soon as the final precision is about
                 twice larger than the intermediate one. This paper
                 addresses the formal proof of this fact considering
                 underflow cases and its extension to radices other than
                 two.",
  acknowledgement = ack-nhfb,
  keywords =     "double rounding",
}

@Article{Rump:2014:IBE,
  author =       "Siegfried M. Rump and Claude-Pierre Jeannerod",
  title =        "Improved Backward Error Bounds for {$ L U $} and
                 {Cholesky} Factorizations",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "35",
  number =       "2",
  pages =        "684--698",
  month =        "????",
  year =         "2014",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/130927231",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Sat Sep 13 12:06:56 MDT 2014",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/35/2;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "SIAM J. Matrix Anal. Appl.",
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
  keywords =     "$L U$ factorization; backward error; Cholesky
                 factorization; floating-point summation; rounding error
                 analysis; triangular system solving; unit in the first
                 place (ufp)",
  onlinedate =   "January 2014",
}

@Article{Schkufza:2014:SOF,
  author =       "Eric Schkufza and Rahul Sharma and Alex Aiken",
  title =        "Stochastic optimization of floating-point programs
                 with tunable precision",
  journal =      j-SIGPLAN,
  volume =       "49",
  number =       "6",
  pages =        "53--64",
  month =        jun,
  year =         "2014",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/2666356.2594302",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Fri Sep 26 07:38:28 MDT 2014",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
  abstract =     "The aggressive optimization of floating-point
                 computations is an important problem in
                 high-performance computing. Unfortunately,
                 floating-point instruction sets have complicated
                 semantics that often force compilers to preserve
                 programs as written. We present a method that treats
                 floating-point optimization as a stochastic search
                 problem. We demonstrate the ability to generate reduced
                 precision implementations of Intel's handwritten C
                 numeric library which are up to 6 times faster than the
                 original code, and achieve end-to-end speedups of over
                 30\% on a direct numeric simulation and a ray tracer by
                 optimizing kernels that can tolerate a loss of
                 precision while still remaining correct. Because these
                 optimizations are mostly not amenable to formal
                 verification using the current state of the art, we
                 present a stochastic search technique for
                 characterizing maximum error. The technique comes with
                 an asymptotic guarantee and provides strong evidence of
                 correctness.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  received =     "PLDI '14 conference proceedings.",
}

@Article{Shukla:2014:LLH,
  author =       "R. Shukla and K. C. Ray",
  title =        "Low Latency Hybrid {CORDIC} Algorithm",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "63",
  number =       "12",
  pages =        "3066--3078",
  month =        dec,
  year =         "2014",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2013.173",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Dec 4 10:36:57 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "adders; Approximation algorithms; communication
                 systems; Computer architecture; coordinate rotational
                 digital computer; CORDIC algorithm; Delays; digital
                 arithmetic; Digital computers; digital computers;
                 double step branching; fast adders; first order
                 hardware architecture; hardware complexity; hybrid
                 CORDIC algorithm; image processing; low latency; low
                 latency hybrid CORDIC algorithm; Mathematical model;
                 radix-4; redundant arithmetic; scale factor
                 calculation; signal processing; Signal processing
                 algorithms",
}

@Article{Sultana:2014:RAC,
  author =       "Sayeeda Sultana and Katarzyna Radecka",
  title =        "Reversible Architecture of Computer Arithmetic",
  journal =      j-INT-J-COMP-APPL,
  volume =       "93",
  number =       "??",
  pages =        "6--14",
  month =        may,
  year =         "2014",
  CODEN =        "????",
  DOI =          "https://doi.org/10.5120/16281-5852",
  ISSN =         "0975-8887",
  ISSN-L =       "0975-8887",
  bibdate =      "Fri Jan 24 09:07:16 MST 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/intjcompappl.bib",
  URL =          "https://www.ijcaonline.org/archives/volume93/number14/16281-5852/",
  acknowledgement = ack-nhfb,
  ajournal =     "Intern. J. of Computer Applications",
  articleno =    "14",
  fjournal =     "International Journal of Computer Applications",
  journal-URL =  "https://www.ijcaonline.org/",
}

@InProceedings{Szydzik:2014:PRM,
  author =       "Tomasz Szydzik and David Moloney",
  booktitle =    "{2014 IEEE Hot Chips 26 Symposium (HCS)}",
  title =        "Precision refinement for media-processor {SoCs}: fp32
                 $ \to $ fp64 on Myriad",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--1",
  year =         "2014",
  DOI =          "https://doi.org/10.1109/HOTCHIPS.2014.7478834",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Hybrid power systems; Matrix decomposition; Media;
                 Microelectronics; Parallel processing; Program
                 processors; Random access memory",
}

@Article{Toronto:2014:PAF,
  author =       "Neil Toronto and Jay McCarthy",
  title =        "Practically Accurate Floating-Point Math",
  journal =      j-COMPUT-SCI-ENG,
  volume =       "16",
  number =       "4",
  pages =        "80--95",
  month =        jul # "\slash " # aug,
  year =         "2014",
  CODEN =        "CSENFA",
  DOI =          "https://doi.org/10.1109/MCSE.2014.90",
  ISSN =         "1521-9615 (print), 1558-366x (electronic)",
  ISSN-L =       "1521-9615",
  bibdate =      "Thu Sep 4 08:43:09 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computscieng.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing in Science and Engineering",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
}

@Article{Vazquez:2014:FRM,
  author =       "Alvaro Vazquez and Elisardo Antelo and Javier D.
                 Bruguera",
  title =        "Fast Radix-$ 10 $ Multiplication Using Redundant {BCD}
                 Codes",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "63",
  number =       "8",
  pages =        "1902--1914",
  month =        aug,
  year =         "2014",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2014.2315626",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Aug 25 08:24:32 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Wang:2014:CFA,
  author =       "Dong Wang and Milo{\v{s}} D. Ercegovac and Yang Xiao",
  title =        "Complex Function Approximation Using Two-Dimensional
                 Interpolation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "63",
  number =       "12",
  pages =        "2948--2960",
  month =        dec,
  year =         "2014",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2013.181",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Dec 4 10:36:57 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "2D convolution algorithm; 2D interpolation;
                 Approximation error; ASIC; bipartite schemes; bivariate
                 functions; coefficient table; complex exponential;
                 complex function approximation; complex function
                 evaluation; complex reciprocal; Complex reciprocal;
                 Computational complexity; cubic interpolation;
                 exponential functions; field programmable gate arrays;
                 FPGA; Function approximation; generic hardware
                 architecture; interpolation; interpolation degree;
                 interpolation kernels; Lagrange interpolation;
                 Lagrangian functions; linear interpolation; lookup
                 tables; memory requirements; multipartite schemes;
                 quadratic interpolation; Quadratic programming; table
                 lookup; tabulated function; two-dimensional
                 interpolation",
}

@Article{Wang:2014:RBR,
  author =       "PengFei Wang and JianPing Li",
  title =        "On the relation between reliable computation time,
                 float-point precision and the {Lyapunov} exponent in
                 chaotic systems",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--8",
  day =          "18",
  month =        oct,
  year =         "2014",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/1410.4919",
  abstract =     "The relation among reliable computation time, Tc,
                 float-point precision, K, and the Lyapunov exponent,
                 {\lambda}, is obtained as Tc= (lnB/{\lambda})K+C, where
                 B is the base of the float-point system and C is a
                 constant dependent only on the chaotic equation. The
                 equation shows good agreement with numerical
                 experimental results, especially the scale factors.",
  acknowledgement = ack-nhfb,
  subject =      "Chaotic Dynamics (nlin.CD); Numerical Analysis
                 (cs.NA)",
}

@Article{Yao:2014:NRP,
  author =       "Gavin Xiaoxu Yao and Junfeng Fan and Ray C. C. Cheung
                 and Ingrid Verbauwhede",
  title =        "Novel {RNS} Parameter Selection for Fast Modular
                 Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "63",
  number =       "8",
  pages =        "2099--2105",
  month =        aug,
  year =         "2014",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2013.92",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Aug 25 08:24:32 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Zafar:2014:HAD,
  author =       "Saad Zafar and Raviteja Adapa",
  booktitle =    "2014 International Conference on Advances in
                 Electrical Engineering ({ICAEE})",
  title =        "Hardware architecture design and mapping of ``{Fast
                 Inverse Square Root}'' algorithm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--4",
  month =        jan,
  year =         "2014",
  DOI =          "https://doi.org/10.1109/icaee.2014.6838433",
  bibdate =      "Wed Dec 20 07:29:37 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Fast Inverse Square Root algorithm has been used
                 in 3D games of past for lighting and reflection
                 calculations, because it offers up to four times
                 performance gains. This paper presents a hardware
                 implementation of the algorithm on an FPGA board by
                 designing the complete architecture and successfully
                 mapping it on Xilinx Spartan 3E after thorough
                 functional verification. The results show that this
                 implementation provides a very efficient
                 single-precision floating point inverse square root
                 calculator with practically accurate results being made
                 available after just 12 short clock cycles. This
                 performance measure is far superior to the software
                 counterpart of the algorithm, and is not processor
                 dependent like rsqrtss of x86 SSE instruction set.
                 Results of this work can aid FPGA based vector
                 processors or graphic processing units with 3D
                 rendering. The hardware design can also form part of a
                 larger floating point arithmetic unit for dedicated
                 reciprocal square root calculations.",
  acknowledgement = ack-nhfb,
}

@Article{Ahmadifar:2015:NRN,
  author =       "H. Ahmadifar and G. Jaberipur",
  title =        "A New Residue Number System with $5$-Moduli Set: $
                 2^{2 q}$, $ 2^q \pm 3$, $ 2^q \pm 1$",
  journal =      j-COMP-J,
  volume =       "58",
  number =       "7",
  pages =        "1548--1565",
  month =        jul,
  year =         "2015",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/bxu084",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Jul 28 10:40:55 MDT 2015",
  bibsource =    "http://comjnl.oxfordjournals.org/content/58/7.toc;
                 https://www.math.utah.edu/pub/tex/bib/compj2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/58/7/1548",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  onlinedate =   "September 2, 2014",
}

@TechReport{Ahrens:2015:ERF,
  author =       "P. Ahrens and H. D. Nguyen and J. Demmel",
  title =        "Efficient Reproducible Floating Point Summation and
                 {BLAS}",
  type =         "Report",
  number =       "UCB/EECS-2015-229",
  institution =  "EECS Department, University of California, Berkeley",
  address =      "Berkeley, CA, USA",
  day =          "8",
  month =        dec,
  year =         "2015",
  bibdate =      "Mon Jan 04 15:39:44 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.eecs.berkeley.edu/Pubs/TechRpts/2015/EECS-2015-229.html",
  abstract =     "We define reproducibility to mean getting bitwise
                 identical results from multiple runs of the same
                 program, perhaps with different hardware resources or
                 other changes that should ideally not change the
                 answer. Many users depend on reproducibility for
                 debugging or correctness. However, dynamic scheduling
                 of parallel computing resources, combined with
                 nonassociativity of floating point addition, makes
                 attaining reproducibility a challenge even for simple
                 operations like summing a vector of numbers, or more
                 complicated operations like the Basic Linear Algebra
                 Subprograms (BLAS). We describe an algorithm that
                 computes a reproducible sum of floating point numbers,
                 independent of the order of summation. The algorithm
                 depends only on a subset of the IEEE Floating Point
                 Standard 754-2008. It is communication-optimal, in the
                 sense that it does just one pass over the data in the
                 sequential case, or one reduction operation in the
                 parallel case, requiring an ``accumulator'' represented
                 by just 6 floating point words (more can be used if
                 higher precision is desired). The arithmetic cost with
                 a 6-word accumulator is $ 7 n $ floating point
                 additions to sum $n$ words, and (in IEEE double
                 precision) the final error bound can be up to $
                 10^{-8}$ times smaller than the error bound for
                 conventional summation. We describe the basic summation
                 algorithm, the software infrastructure used to build
                 reproducible BLAS (ReproBLAS), and performance results.
                 For example, when computing the dot product of 4096
                 double precision floating point numbers, we get an $ 4
                 \times $ slowdown compared to Intel Math Kernel Library
                 (MKL) running on an Intel Core i7-2600 CPU operating at
                 3.4 GHz and 256 KB L2 Cache.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate dot product; accurate summation",
}

@TechReport{Ahrens:2015:RPM,
  author =       "Peter Ahrens",
  title =        "Reproducible Parallel Matrix-Vector Multiply",
  type =         "{CS 267} final report",
  institution =  "Department of Computer Science, University of
                 California, Berkeley",
  address =      "Berkeley, CA, USA",
  day =          "11",
  month =        may,
  year =         "2015",
  bibdate =      "Mon Jan 04 15:55:37 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://bebop.cs.berkeley.edu/reproblas/docs/reports/PeterAhrensCS267FinalReport.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Aktan:2015:MEA,
  author =       "Mustafa Aktan and Dursun Baran and Vojin G.
                 Oklobdzija",
  title =        "Minimizing Energy by Achieving Optimal Sparseness in
                 Parallel Adders",
  crossref =     "Muller:2015:ISC",
  pages =        "10--17",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.13",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2015; ARITH-22",
}

@InProceedings{Andrysco:2015:SFP,
  author =       "Marc Andrysco and David Kohlbrenner and Keaton Mowery
                 and Ranjit Jhala and Sorin Lerner and Hovav Shacham",
  title =        "On subnormal floating point and abnormal timing",
  crossref =     "IEEE:2015:ISS",
  pages =        "623--639",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/SP.2015.44",
  bibdate =      "Mon Feb 10 08:54:26 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://github.com/kmowery/libfixedtimefixedpoint",
  abstract =     "We identify a timing channel in the floating point
                 instructions of modern x86 processors: the running time
                 of floating point addition and multiplication
                 instructions can vary by two orders of magnitude
                 depending on their operands. We develop a benchmark
                 measuring the timing variability of floating point
                 operations and report on its results. We use floating
                 point data timing variability to demonstrate practical
                 attacks on the security of the Firefox browser
                 (versions 23 through 27) and the Fuzz differentially
                 private database. Finally, we initiate the study of
                 mitigations to floating point data timing channels with
                 libfixedtimefixedpoint, a new fixed-point,
                 constant-time math library. Modern floating point
                 standards and implementations are sophisticated,
                 complex, and subtle, a fact that has not been
                 sufficiently recognized by the security community. More
                 work is needed to assess the implications of the use of
                 floating point instructions in security-relevant
                 software.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Aneesh:2015:HHM,
  author =       "R. Aneesh and Patil Vinayak and M. P. Sobham and A.
                 David Selvakumar",
  booktitle =    "{2015 International Conference on VLSI Systems,
                 Architecture, Technology and Applications
                 (VLSI-SATA)}",
  title =        "{HMFPCC}: --- Hybrid-mode floating point conversion
                 co-processor",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  month =        jan,
  year =         "2015",
  DOI =          "https://doi.org/10.1109/vlsi-sata.2015.7050482",
  bibdate =      "Sat Jun 4 17:15:13 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Misc{Anonymous:2015:EFP,
  author =       "Anonymous",
  title =        "The Evils of Floating Point, and the Joys of Unum",
  howpublished = "Web document",
  day =          "24",
  month =        mar,
  year =         "2015",
  bibdate =      "Sat Apr 02 16:43:03 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://vrworld.com/2015/03/24/the-evils-of-floating-point-and-the-joys-of-unum/",
  acknowledgement = ack-nhfb,
}

@Article{Bailey:2015:HPA,
  author =       "David H. Bailey and Jonathan M. Borwein",
  title =        "High-precision arithmetic in mathematical physics",
  journal =      "Mathematics",
  volume =       "3",
  number =       "2",
  publisher =    "Multidisciplinary Digital Publishing Institute",
  pages =        "337--367",
  year =         "2015",
  bibdate =      "Sat Jun 4 17:21:23 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Misc{Bailey:2015:NRH,
  author =       "David H. Bailey",
  title =        "Numerical reproducibility in high-performance
                 computing",
  howpublished = "24 lecture slides",
  day =          "19",
  month =        nov,
  year =         "2015",
  bibdate =      "Tue Nov 05 15:38:26 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.nist.gov/sites/default/files/documents/itl/ssd/is/NRE-2015-02-dhb-num-repro.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bajard:2015:RAA,
  author =       "Jean-Claude Bajard and Julien Eynard and Nabil
                 Merkiche and Thomas Plantard",
  title =        "{RNS} Arithmetic Approach in Lattice-Based
                 Cryptography: Accelerating the {``Rounding-off''} Core
                 Procedure",
  crossref =     "Muller:2015:ISC",
  pages =        "113--120",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.30",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2015; ARITH-22",
}

@Article{Bankas:2015:NMA,
  author =       "Edem Kwedzo Bankas and Kazeem Alagbe Gbolagade",
  title =        "New {MRC} Adder-Based Reverse Converter for the Moduli
                 Set $ 2^n $, $ 2^{2 n + 1} - 1 $, $ 2^{2 n + 2} - 1 $",
  journal =      j-COMP-J,
  volume =       "58",
  number =       "7",
  pages =        "1566--1572",
  month =        jul,
  year =         "2015",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/bxu089",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Jul 28 10:40:55 MDT 2015",
  bibsource =    "http://comjnl.oxfordjournals.org/content/58/7.toc;
                 https://www.math.utah.edu/pub/tex/bib/compj2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/58/7/1566",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  onlinedate =   "October 9, 2014",
}

@TechReport{Biancolin:2015:HAE,
  author =       "David Biancolin and Jack Koenig",
  title =        "Hardware Accelerator for Exact Dot Product",
  type =         "Report",
  number =       "??",
  institution =  "ASPIRE Laboratory, University of California,
                 Berkeley",
  address =      "Berkeley, CA, USA",
  day =          "19",
  month =        jun,
  year =         "2015",
  bibdate =      "Fri Jun 19 14:30:46 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this paper we present a coprocessor capable of
                 computing a dot product exactly by use of a ``complete
                 register'' (CR) that encodes a fixed point
                 representation of the complete IEEE754 double precision
                 space. We explore the design space of the coprocessor
                 by running simulations on large numbers of distinct
                 configurations. Since only the accumulation register is
                 represented exactly, we demonstrate that EDP is
                 realizable in silicon, requiring additional 11\% over
                 Rocket's area. In addition, the accelerator showed
                 speedups of $3$--$ 6 \times $ over a conventional dot
                 product and matrix multiplication while providing both
                 exactness and reproducibility.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point dot product; accurate
                 floating-point summation",
}

@Article{Bobade:2015:SOM,
  author =       "Sunil Devidas Bobade and Vijay R. Mankar",
  title =        "Space Optimized Multiplier Architecture for Embedded
                 Cryptoprocessor",
  journal =      j-INT-J-COMP-APPL,
  volume =       "113",
  number =       "??",
  pages =        "26--32",
  month =        mar,
  year =         "2015",
  CODEN =        "????",
  DOI =          "https://doi.org/10.5120/19897-1982",
  ISSN =         "0975-8887",
  ISSN-L =       "0975-8887",
  bibdate =      "Fri Jan 24 09:16:05 MST 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/intjcompappl.bib",
  URL =          "https://www.ijcaonline.org/archives/volume113/number14/19897-1982/",
  acknowledgement = ack-nhfb,
  ajournal =     "Intern. J. of Computer Applications",
  articleno =    "14",
  fjournal =     "International Journal of Computer Applications",
  journal-URL =  "https://www.ijcaonline.org/",
}

@InProceedings{Boldo:2015:FVP,
  author =       "Sylvie Boldo and Guillaume Melquiond",
  title =        "Formal Verification of Programs Computing the
                 Floating-Point Average",
  crossref =     "Butler:2015:FMS",
  number =       "9407",
  pages =        "17--32",
  year =         "2015",
  DOI =          "https://doi.org/10.1007/978-3-319-25423-4_2",
  bibdate =      "Fri Jan 31 15:41:04 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://hal.inria.fr/hal-01174892;
                 https://link.springer.com/chapter/10.1007/978-3-319-25423-4_2",
  acknowledgement = ack-nhfb,
}

@Article{Boldo:2015:SSD,
  author =       "Sylvie Boldo",
  editor =       "Sergiy Bogomolov and Matthieu Martel",
  booktitle =    "Proceedings of the Seventh and Eighth International
                 Workshop on Numerical Software Verification, volume 317
                 of Electronic Notes in Theoretical Computer Science,
                 Seattle, 2015",
  title =        "Stupid is as Stupid Does: Taking the Square Root of
                 the Square of a Floating-Point Number",
  journal =      j-ELECT-NOTES-THEOR-COMP-SCI,
  volume =       "317",
  pages =        "50--55",
  day =          "18",
  month =        nov,
  year =         "2015",
  DOI =          "https://doi.org/10.1016/j.entcs.2015.10.004",
  ISSN =         "1571-0661",
  ISSN-L =       "1571-0661",
  bibdate =      "Sat Jun 04 16:01:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronic Notes in Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/15710661",
  remark =       "The author proves in Coq that the square root of the
                 square of a floating-point number $x$ is always $ |x|$,
                 and thus, that $ x / \sqrt {x^2 + y^2}$ lies in $ [ -
                 1, 1]$, PROVIDED that the base is $ \beta = 2$, the
                 precision is $ p > 1$, and rounding is either the IEEE
                 754 default of round-to-nearest-ties-to-even, or
                 round-to-nearest-ties-away-from-zero. She gives simple
                 examples for bases 10 and 1000 where the result lies
                 outside $ [ - 1, 1]$.",
}

@Article{Boldo:2015:VCF,
  author =       "Sylvie Boldo and Jacques-Henri Jourdan and Xavier
                 Leroy and Guillaume Melquiond",
  title =        "Verified Compilation of Floating-Point Computations",
  journal =      j-J-AUTOM-REASON,
  volume =       "54",
  number =       "2",
  pages =        "135--163",
  month =        feb,
  year =         "2015",
  CODEN =        "JAREEW",
  DOI =          "https://doi.org/10.1007/s10817-014-9317-x",
  ISSN =         "0168-7433 (print), 1573-0670 (electronic)",
  ISSN-L =       "0168-7433",
  bibdate =      "Sat Apr 2 10:51:13 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
  URL =          "http://link.springer.com/article/10.1007/s10817-014-9317-x",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Autom. Reason.",
  fjournal =     "Journal of Automated Reasoning",
  journal-URL =  "http://link.springer.com/journal/10817",
}

@InProceedings{Brain:2015:AFS,
  author =       "Martin Brain and Cesare Tinelli and Philipp Ruemmer
                 and Thomas Wahl",
  title =        "An Automatable Formal Semantics for {IEEE-754}
                 Floating-Point Arithmetic",
  crossref =     "Muller:2015:ISC",
  pages =        "160--167",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.26",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2015; ARITH-22",
}

@InProceedings{Brunie:2015:CGM,
  author =       "Nicolas Brunie and Florent de Dinechin and Olga
                 Kupriianova and Christoph Lauter",
  title =        "Code Generators for Mathematical Functions",
  crossref =     "Muller:2015:ISC",
  pages =        "66--73",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.22",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2015; ARITH-22",
}

@Article{Chiang:2015:UFP,
  author =       "Wei-Fan Chiang and Ganesh Gopalakrishnan and Zvonimir
                 Rakamari{\'c}",
  title =        "Unsafe Floating-point to Unsigned Integer Casting
                 Check for {GPU} Programs",
  journal =      j-ELECT-NOTES-THEOR-COMP-SCI,
  volume =       "317",
  number =       "??",
  pages =        "1--12",
  day =          "18",
  month =        nov,
  year =         "2015",
  DOI =          "https://doi.org/10.1016/j.entcs.2015.10.005",
  ISSN =         "1571-0661",
  ISSN-L =       "1571-0661",
  bibdate =      "Fri Apr 17 18:06:24 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Also presented at NSV 2015: 8th International Workshop
                 on Numerical Software Verification 2015, Seattle, WA,
                 USA.",
  URL =          "http://formalverification.cs.utah.edu/papers/nsv15-unsafe-fp2ui.pdf;
                 http://nsv2015.informatik.uni-freiburg.de/",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronic Notes in Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/15710661",
  remark =       "Not yet listed at journal Web site (up to volume 311
                 5-Jan-2015).",
  xxjournal-url = "http://www.elsevier.nl/locate/entcs",
}

@Article{Collange:2015:NRP,
  author =       "Sylvain Collange and David Defour and Stef Graillat
                 and Roman Iakymchuk",
  title =        "Numerical reproducibility for the parallel reduction
                 on multi- and many-core architectures",
  journal =      j-PARALLEL-COMPUTING,
  volume =       "49",
  number =       "??",
  pages =        "83--97",
  month =        nov,
  year =         "2015",
  CODEN =        "PACOEJ",
  DOI =          "https://doi.org/10.1016/j.parco.2015.09.001",
  ISSN =         "0167-8191 (print), 1872-7336 (electronic)",
  ISSN-L =       "0167-8191",
  bibdate =      "Thu Oct 29 17:53:44 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/parallelcomputing.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167819115001155",
  acknowledgement = ack-nhfb,
  fjournal =     "Parallel Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01678191/",
  keywords =     "accuracy; correct rounding; correctly-rounded
                 floating-point sums; CPU; error-free transformations;
                 floating-point arithmetic; GPU; long accumulator;
                 multi- and many-core architectures; parallel
                 floating-point summation; reproducibility; Xeon Phi",
}

@Misc{Cowlishaw:2015:GDA,
  author =       "Mike Cowlishaw",
  title =        "General Decimal Arithmetic",
  howpublished = "Web site.",
  year =         "2015",
  bibdate =      "Mon Apr 25 17:12:00 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://speleotrove.com/decimal/",
  acknowledgement = ack-nhfb,
  remark =       "Previous versions 1981, 1997, 2008.",
}

@Article{Coxon:2015:MMP,
  author =       "Nicholas Coxon",
  title =        "{Montgomery}'s method of polynomial selection for the
                 number field sieve",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "485",
  number =       "??",
  pages =        "72--102",
  day =          "15",
  month =        nov,
  year =         "2015",
  CODEN =        "LAAPAW",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Sat Oct 10 17:54:20 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/linala2015.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0024379515004395",
  acknowledgement = ack-nhfb,
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795/",
}

@Article{Damouche:2015:TPC,
  author =       "N. Damouche and M. Martel and A. Chapoutot",
  title =        "Transformation of a {PID} Controller for Numerical
                 Accuracy",
  journal =      j-ELECT-NOTES-THEOR-COMP-SCI,
  volume =       "317",
  pages =        "47--54",
  month =        nov,
  year =         "2015",
  DOI =          "https://doi.org/10.1016/j.entcs.2015.10.006",
  ISSN =         "1571-0661",
  bibdate =      "Wed Oct 16 18:53:52 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Numerical programs performing floating-point
                 computations are very sensitive to the way formulas are
                 written. Several techniques have been proposed
                 concerning the transformation of expressions in order
                 to improve their accuracy and now we aim at going a
                 step further by automatically transforming larger
                 pieces of code containing several assignments and
                 control structures. This article presents a case study
                 in this direction. We consider a PID controller and we
                 transform its code in order to improve its accuracy.
                 The experimental data obtained when we compare the
                 different versions of the code (which are
                 mathematically equivalent) show that those
                 transformations have a significant impact on the
                 accuracy of the computations.",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronic Notes in Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/15710661",
  remark =       "Creative Commons license.",
}

@TechReport{deDinechin:2015:FPH,
  author =       "Florent de Dinechin",
  title =        "On fixed-point hardware polynomials",
  type =         "Technical Report",
  institution =  "INSA, CITI Lab, Universit{\'e} de Lyon",
  address =      "Lyon, France",
  month =        oct,
  year =         "2015",
  bibdate =      "Mon Feb 10 07:54:27 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://hal.inria.fr/hal-01214739",
  abstract =     "Polynomial approximation is a general technique for
                 the evaluation of numerical functions of one variable.
                 This article addresses the automatic construction of
                 fixed-point hardware polynomial evaluators. By
                 systematically trying to balance the accuracy of all
                 the steps that lead to an architecture, it simplifies
                 and improves the previous body of work covering
                 polynomial approximation, polynomial evaluation, and
                 range reduction. This work is supported by an
                 open-source implementation.",
  acknowledgement = ack-nhfb,
}

@InProceedings{deDinechin:2015:HIF,
  author =       "Florent de Dinechin and Matei Istoan",
  title =        "Hardware Implementations of Fixed-Point {Atan2}",
  crossref =     "Muller:2015:ISC",
  pages =        "34--41",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.23",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2015; ARITH-22; atan; atan2; atan2pi; CORDIC;
                 hypot; hypotenuse",
  remark-1 =     "From page 35: ``This work essentially focuses on
                 FPGAs. An unexpected result is that, even on modern
                 FPGAs enhanced with DSP blocks and memories, CORDIC is
                 a clear winner.''",
  remark-2 =     "From page 37, on $w$-bit computation: ``We therefore
                 need $g_\alpha = 1 + \lceil \log_2 ((w - 1) \times 0.5)
                 \rceil$ guard bits to absorb all these errors.'' For
                 the four IEEE 754 binary formats, that is 5, 6, 6, and
                 7 extra bits, respectively.",
  remark-3 =     "From page 40: ``On the other hand, the latency of
                 CORDIC does not seem quadratic, it seems linear in w.
                 This is explained by the fact that the carry
                 propagation delay is about 30 times faster than the
                 standard routing used between two iterations. It
                 justifies a posteriori the choice of ignoring redundant
                 versions of CORDIC''.",
  remark-4 =     "From page 41: ``To make things even better for CORDIC,
                 it should be noted that it may also compute the module
                 $\sqrt{x^2 + y^2}$ along with the angle [1]. This costs
                 only one additional constant multiplication by $1 /
                 K$.",
}

@Misc{Demmel:2015:CFP,
  author =       "James Demmel and Hong Diep Nguyen and Peter Ahrens",
  title =        "Cost of Floating-Point Reproducibility",
  howpublished = "33 lecture slides",
  day =          "20",
  month =        nov,
  year =         "2015",
  bibdate =      "Tue Nov 05 15:43:15 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.nist.gov/sites/default/files/documents/itl/ssd/is/NRE-2015-07-Nguyen_slides.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Demmel:2015:PRS,
  author =       "J. Demmel and Hong Diep Nguyen",
  title =        "Parallel Reproducible Summation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "64",
  number =       "7",
  pages =        "2060--2070",
  month =        jul,
  year =         "2015",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2014.2345391",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Aug 1 08:53:41 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Denis:2015:VCF,
  author =       "Christophe Denis and Pablo {De Oliveira Castro} and
                 Eric Petit",
  title =        "{Verificarlo}: checking floating point accuracy
                 through {Monte Carlo} Arithmetic",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "4",
  month =        sep,
  year =         "2015",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/1509.01347",
  abstract =     "Numerical accuracy of floating point computation is a
                 well studied topic, but which has not made its way to
                 the end-user in scientific computing. With the recent
                 requirements for code modernization to exploit new
                 highly parallel hardware and perform higher resolution
                 computation, this has become one of the critical issues
                 to address. To democratize numerical accuracy analysis,
                 it is important to propose tools and methodologies to
                 study large use cases in a reliable and automatic way.
                 In this paper, we propose verificarlo, an extension to
                 the LLVM compiler to automatically use Monte Carlo
                 Arithmetic in a transparent way for the end-user. It
                 supports all the major languages including C, C++ and
                 Fortran. We also illustrate the fact that unlike
                 source-to-source approaches, our implementation
                 captures the influence of compiler optimizations on the
                 numerical accuracy. Finally, we illustrate on various
                 use cases how Monte Carlo Arithmetic using the
                 verificarlo tool outperforms the existing approaches
                 and is a step toward automatic numerical analysis of
                 large scientific applications.",
  acknowledgement = ack-nhfb,
  subject =      "Mathematical Software (cs.MS); Numerical Analysis
                 (cs.NA)",
}

@Article{Dietz:2015:UIO,
  author =       "Will Dietz and Peng Li and John Regehr and Vikram
                 Adve",
  title =        "Understanding Integer Overflow in {C\slash C++}",
  journal =      j-TOSEM,
  volume =       "25",
  number =       "1",
  pages =        "2:1--2:29",
  month =        dec,
  year =         "2015",
  CODEN =        "ATSMER",
  DOI =          "https://doi.org/10.1145/2743019",
  ISSN =         "1049-331X (print), 1557-7392 (electronic)",
  ISSN-L =       "1049-331X",
  bibdate =      "Thu Dec 3 09:54:19 MST 2015",
  bibsource =    "http://www.acm.org/pubs/contents/journals/tosem/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tosem.bib",
  abstract =     "Integer overflow bugs in C and C++ programs are
                 difficult to track down and may lead to fatal errors or
                 exploitable vulnerabilities. Although a number of tools
                 for finding these bugs exist, the situation is
                 complicated because not all overflows are bugs. Better
                 tools need to be constructed, but a thorough
                 understanding of the issues behind these errors does
                 not yet exist. We developed IOC, a dynamic checking
                 tool for integer overflows, and used it to conduct the
                 first detailed empirical study of the prevalence and
                 patterns of occurrence of integer overflows in C and
                 C++ code. Our results show that intentional uses of
                 wraparound behaviors are more common than is widely
                 believed; for example, there are over 200 distinct
                 locations in the SPEC CINT2000 benchmarks where
                 overflow occurs. Although many overflows are
                 intentional, a large number of accidental overflows
                 also occur. Orthogonal to programmers' intent,
                 overflows are found in both well-defined and undefined
                 flavors. Applications executing undefined operations
                 can be, and have been, broken by improvements in
                 compiler optimizations. Looking beyond SPEC, we found
                 and reported undefined integer overflows in SQLite,
                 PostgreSQL, SafeInt, GNU MPC and GMP, Firefox, LLVM,
                 Python, BIND, and OpenSSL; many of these have since
                 been fixed.",
  acknowledgement = ack-nhfb,
  articleno =    "2",
  fjournal =     "ACM Transactions on Software Engineering and
                 Methodology",
  journal-URL =  "https://dl.acm.org/loi/cacm0",
}

@Article{Ebergen:2015:RDA,
  author =       "J. Ebergen and N. Jamadagni",
  title =        "Radix-$2$ Division Algorithms with an Over-Redundant
                 Digit Set",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "64",
  number =       "9",
  pages =        "2652--2663",
  month =        "????",
  year =         "2015",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2014.2366738",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Sep 28 12:03:47 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{El-Razouk:2015:NBL,
  author =       "Hayssam El-Razouk and Arash Reyhani-Masoleh",
  title =        "New Bit-Level Serial {$ {\rm GF} (2^m) $}
                 Multiplication Using Polynomial Basis",
  crossref =     "Muller:2015:ISC",
  pages =        "129--136",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.11",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2015; ARITH-22",
}

@Article{Elsayed:2015:NPE,
  author =       "Essam Elsayed and Hatem M. El-Boghdadi",
  title =        "A novel power-efficient multi-operand digit-multiplier
                 using reconfiguration and clock gating",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "71",
  number =       "7",
  pages =        "2539--2564",
  month =        jul,
  year =         "2015",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1007/s11227-015-1403-2",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Sat Aug 8 12:23:11 MDT 2015",
  bibsource =    "http://link.springer.com/journal/11227/71/7;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsuper.bib",
  URL =          "http://link.springer.com/article/10.1007/s11227-015-1403-2",
  acknowledgement = ack-nhfb,
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
}

@Article{Flocke:2015:AAE,
  author =       "N. Flocke",
  title =        "{Algorithm 954}: an Accurate and Efficient Cubic and
                 Quartic Equation Solver for Physical Applications",
  journal =      j-TOMS,
  volume =       "41",
  number =       "4",
  pages =        "30:1--30:24",
  month =        oct,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2699468",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Oct 26 17:31:15 MDT 2015",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We report on an accurate and efficient algorithm for
                 obtaining all roots of general real cubic and quartic
                 polynomials. Both the cubic and quartic solvers give
                 highly accurate roots and place no restrictions on the
                 magnitude of the polynomial coefficients. The key to
                 the algorithm is a proper rescaling of both
                 polynomials. This puts upper bounds on the magnitude of
                 the roots and is very useful in stabilizing the root
                 finding process. The cubic solver is based on dividing
                 the cubic polynomial into six classes. By analyzing the
                 root surface for each class, a fast convergent
                 Newton--Raphson starting point for a real root is
                 obtained at a cost no higher than three additions and
                 four multiplications. The quartic solver uses the cubic
                 solver in getting information about stationary points
                 and, when the quartic has real roots, stable
                 Newton--Raphson iterations give one of the extreme real
                 roots. The remaining roots follow by composite
                 deflation to a cubic. If the quartic has only complex
                 roots, the present article shows that a stable
                 Newton--Raphson iteration on a derived symmetric sixth
                 degree polynomial can be formulated for the real parts
                 of the complex roots. The imaginary parts follow by
                 solving suitable quadratics.",
  acknowledgement = ack-nhfb,
  articleno =    "30",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Frechtling:2015:MMS,
  author =       "Michael Frechtling and Philip H. W. Leong",
  title =        "{MCALIB}: Measuring Sensitivity to Rounding Error with
                 {Monte Carlo} Programming",
  journal =      j-TOPLAS,
  volume =       "37",
  number =       "2",
  pages =        "5:1--5:??",
  month =        apr,
  year =         "2015",
  CODEN =        "ATPSDT",
  DOI =          "https://doi.org/10.1145/2665073",
  ISSN =         "0164-0925 (print), 1558-4593 (electronic)",
  ISSN-L =       "0164-0925",
  bibdate =      "Thu Apr 16 18:32:12 MDT 2015",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toplas/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toplas.bib",
  abstract =     "Runtime analysis provides an effective method for
                 measuring the sensitivity of programs to rounding
                 errors. To date, implementations have required
                 significant changes to source code, detracting from
                 their widespread application. In this work, we present
                 an open source system that automates the quantitative
                 analysis of floating point rounding errors through the
                 use of C-based source-to-source compilation and a Monte
                 Carlo arithmetic library. We demonstrate its
                 application to the comparison of algorithms, detection
                 of catastrophic cancellation, and determination of
                 whether single precision floating point provides
                 sufficient accuracy for a given application. Methods
                 for obtaining quantifiable measurements of sensitivity
                 to rounding error are also detailed.",
  acknowledgement = ack-nhfb,
  articleno =    "5",
  fjournal =     "ACM Transactions on Programming Languages and
                 Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J783",
}

@Article{Froggatt:2015:EAU,
  author =       "Terry Froggatt",
  title =        "An Error in the {Ada} Universal Arithmetic Package",
  journal =      j-SIGADA-LETTERS,
  volume =       "35",
  number =       "2",
  pages =        "14--14",
  month =        aug,
  year =         "2015",
  CODEN =        "AALEE5",
  DOI =          "https://doi.org/10.1145/2903260.2903263",
  ISSN =         "1094-3641 (print), 1557-9476 (electronic)",
  ISSN-L =       "1094-3641",
  bibdate =      "Mon Jun 20 18:46:44 MDT 2016",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigada.bib",
  note =         "See \cite{Fisher:1984:UAP}. The 32-year-old error is a
                 test with digit $t$ that has {\tt if (t > BASE)}, but
                 the operator should instead be {\tt >=}.",
  abstract =     "An Ada Universal Arithmetic package was published over
                 three decades ago in Ada Letters. It was incorporated
                 into several Ada compilers, and it is one of the few
                 compiler components which will have required no change
                 as the Ada language has evolved. The purpose if this
                 note is to draw attention to an error in that package,
                 which may or may not have been corrected in the
                 compilers, but which has never subsequently been
                 corrected within Ada Letters.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGAda Ada Letters",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J32",
}

@Article{Fu:2015:ABE,
  author =       "Zhoulai Fu and Zhaojun Bai and Zhendong Su",
  title =        "Automated backward error analysis for numerical code",
  journal =      j-SIGPLAN,
  volume =       "50",
  number =       "10",
  pages =        "639--654",
  month =        oct,
  year =         "2015",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/2858965.2814317",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Tue Feb 16 12:01:43 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
  abstract =     "Numerical code uses floating-point arithmetic and
                 necessarily suffers from roundoff and truncation
                 errors. Error analysis is the process to quantify such
                 uncertainty in the solution to a problem. Forward error
                 analysis and backward error analysis are two popular
                 paradigms of error analysis. Forward error analysis is
                 more intuitive and has been explored and automated by
                 the programming languages (PL) community. In contrast,
                 although backward error analysis is more preferred by
                 numerical analysts and the foundation for numerical
                 stability, it is less known and unexplored by the PL
                 community. To fill the gap, this paper presents an
                 automated backward error analysis for numerical code to
                 empower both numerical analysts and application
                 developers. In addition, we use the computed backward
                 error results to also compute the condition number, an
                 important quantity recognized by numerical analysts for
                 measuring how sensitive a function is to changes or
                 errors in the input. Experimental results on Intel X87
                 FPU functions and widely-used GNU C Library functions
                 demonstrate that our analysis is effective at analyzing
                 the accuracy of floating-point programs.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  remark =       "OOPSLA '15 conference proceedings.",
}

@InProceedings{Fukushima:2015:PFCc,
  author =       "Toshio Fukushima",
  title =        "Precise and Fast Computation of Elliptic Integrals and
                 Functions",
  crossref =     "Muller:2015:ISC",
  pages =        "50--57",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.15",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2015; ARITH-22",
}

@InProceedings{Gerard:2015:CDR,
  author =       "Beno{\^\i}t G{\'e}rard and Jean-Gabriel Kammerer and
                 Nabil Merkiche",
  title =        "Contributions to the Design of Residue Number System
                 Architectures",
  crossref =     "Muller:2015:ISC",
  pages =        "105--112",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.25",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2015; ARITH-22",
}

@Article{Gorgin:2015:CXH,
  author =       "S. Gorgin and G. Jaberipur",
  title =        "Comment on {``High-Speed Parallel Decimal
                 Multiplication With Redundant Internal Encodings''}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "64",
  number =       "1",
  pages =        "293--294",
  month =        jan,
  year =         "2015",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2013.160",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jan 21 08:56:46 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  note =         "See \cite{Han:2013:HSP}.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Adders; Computer science; Computers; critical delay
                 path; Decimal arithmetic; Delays; digital arithmetic;
                 Educational institutions; Encoding; high speed parallel
                 decimal multiplication; Logic gates; matrix
                 multiplication; parallel decimal multiplication;
                 parallel processing; redundant internal encodings;
                 redundant partial products; redundant representation;
                 signed-digit partial product",
}

@InProceedings{Gouicem:2015:MMD,
  author =       "Mourad Gouicem",
  title =        "Modular Multiplication and Division Algorithms Based
                 on Continued Fraction Expansion",
  crossref =     "Muller:2015:ISC",
  pages =        "137--143",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.21",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2015; ARITH-22",
}

@Article{Graillat:2015:ECF,
  author =       "Stef Graillat and Christoph Lauter and Ping Tak Peter
                 Tang and Naoya Yamanaka and Shin'ichi Oishi",
  title =        "Efficient Calculations of Faithfully Rounded $
                 l_2$-Norms of $n$-Vectors",
  journal =      j-TOMS,
  volume =       "41",
  number =       "4",
  pages =        "24:1--24:20",
  month =        oct,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2699469",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Oct 26 17:31:15 MDT 2015",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In this article, we present an efficient algorithm to
                 compute the faithful rounding of the $ l_2 $-norm of a
                 floating-point vector. This means that the result is
                 accurate to within 1 bit of the underlying
                 floating-point type. This algorithm does not generate
                 overflows or underflows spuriously, but does so when
                 the final result calls for such a numerical exception
                 to be raised. Moreover, the algorithm is well suited
                 for parallel implementation and vectorization. The
                 implementation runs up to 3 times faster than the
                 netlib version on current processors.",
  acknowledgement = ack-nhfb,
  articleno =    "24",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Graillat:2015:MRE,
  author =       "Stef Graillat and Vincent Lef{\`e}vre and Jean-Michel
                 Muller",
  title =        "On the maximum relative error when computing integer
                 powers by iterated multiplications in floating-point
                 arithmetic",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "70",
  number =       "3",
  pages =        "653--667",
  month =        nov,
  year =         "2015",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-015-9967-8",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Sun Oct 25 07:27:50 MDT 2015",
  bibsource =    "http://link.springer.com/journal/11075/70/3;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "http://link.springer.com/article/10.1007/s11075-015-9967-8",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  remark =       "The authors show via a complex multipage proof that
                 the iterated product for $ x^n $ in p-bit binary
                 arithmetic with default IEEE 754 rounding (to nearest
                 with ties to even) produces a worst-case relative error
                 in the product that is no larger than $ (n - 1) u $,
                 where $ u = 2^{-p} $ is the rounding unit.",
}

@Article{Graillat:2015:NVC,
  author =       "Stef Graillat and Fabienne J{\'e}z{\'e}quel and Romain
                 Picot",
  title =        "Numerical validation of compensated summation
                 algorithms with stochastic arithmetic",
  journal =      j-ELECT-NOTES-THEOR-COMP-SCI,
  volume =       "317",
  pages =        "55--69",
  day =          "18",
  month =        nov,
  year =         "2015",
  DOI =          "https://doi.org/10.1016/j.entcs.2015.10.007",
  ISSN =         "1571-0661",
  ISSN-L =       "1571-0661",
  bibdate =      "Sat Jun 4 17:40:10 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronic Notes in Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/15710661",
}

@InProceedings{Gupta:2015:DLL,
  author =       "Suyog Gupta and Ankur Agrawal and Kailash
                 Gopalakrishnan and Pritish Narayanan",
  editor =       "Francis Bach and David Blei",
  booktitle =    "{ICML'15: Proceedings of the 32nd International
                 Conference on International Conference on Machine
                 Learning: Lille, France, July 6--11, 2015}",
  title =        "Deep learning with limited numerical precision",
  publisher =    "JMLR.org",
  address =      "????",
  pages =        "1737--1746",
  year =         "2015",
  bibdate =      "Fri Sep 22 17:39:05 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{Gustafson:2015:EEU,
  author =       "John L. Gustafson",
  title =        "The End of Error: Unum Computing",
  publisher =    pub-CHAPMAN-HALL,
  address =      pub-CHAPMAN-HALL:adr,
  pages =        "xx + 416",
  year =         "2015",
  ISBN =         "1-4822-3986-8, 1-4822-3987-6",
  ISBN-13 =      "978-1-4822-3986-7, 978-1-4822-3987-4",
  LCCN =         "QA275 .G928 2015",
  bibdate =      "Thu Jan 18 06:44:33 2018",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Written by one of the foremost experts in
                 high-performance computing and the inventor of
                 Gustafson's Law, The End of Error: Unum Computing
                 explains a new approach to computer arithmetic: the
                 universal number (unum). The unum encompasses all IEEE
                 floating-point formats as well as fixed-point and exact
                 integer arithmetic. This new number type obtains more
                 accurate answers than floating-point arithmetic yet
                 uses fewer bits in many cases, saving memory,
                 bandwidth, energy, and power. Richly illustrated in
                 color, this groundbreaking book is accessible to anyone
                 who uses computers for technical calculations.",
  acknowledgement = ack-nhfb,
  xxabstract =   "In this groundbreaking book, the author --- a
                 world-renowned expert in high-performance computing
                 (HPC) and inventor of Gustafson's Law --- presents his
                 new approach to computer arithmetic: the unum. The
                 universal number, or unum format, encompasses all IEEE
                 floating-point formats as well as fixed-point and exact
                 integer arithmetic. This approach obtains more accurate
                 answers than floating-point arithmetic yet uses fewer
                 bits in many cases, saving memory, bandwidth, energy,
                 and power. Accessible to researchers in HPC and related
                 areas, the book provides a Mathematica\TM{} notebook
                 for the code examples.",
  xxtitle =      "A New Number Format: The Unum",
}

@InProceedings{Gustafson:2015:KTE,
  author =       "John Gustafson",
  title =        "Keynote Talk: The End of Numerical Error",
  crossref =     "Muller:2015:ISC",
  pages =        "74--74",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.22",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Abstract only.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2015; ARITH-22",
}

@InCollection{Hamming:2015:DN,
  author =       "R. W. Hamming",
  title =        "On the distribution of numbers",
  crossref =     "Swartzlander:2015:CAa",
  pages =        "321--337",
  year =         "2015",
  DOI =          "https://doi.org/10.1142/9789814651578",
  bibdate =      "Tue Aug 7 07:53:59 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/hamming-richard-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper examines the distribution of the mantissas
                 of floating-point numbers and shows how the arithmetic
                 operations of a computer transform various
                 distributions toward the limiting distribution $$ r(x)
                 = 1 / (x \ln b) \qquad (1 / b \leq x \leq 1) $$ (where
                 $b$ is the base of the number system). The paper also
                 gives a number of applications to hardware, software,
                 and general computing which show that this distribution
                 is not merely an amusing curiosity. A brief examination
                 of the distribution of exponents is included.",
  acknowledgement = ack-nhfb,
  author-dates = "Richard Wesley Hamming (1915--1998)",
  keywords =     "Digital arithmetic; Floating point numbers; Limiting
                 distributions; Number system, Application programs;
                 Numbering systems, Arithmetic operations",
}

@InProceedings{Hart:2015:EDC,
  author =       "William Bruce Hart",
  title =        "Efficient Divide-and-Conquer Multiprecision Integer
                 Division",
  crossref =     "Muller:2015:ISC",
  pages =        "90--95",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.19",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2015; ARITH-22; division; multiple-precision
                 arithmetic",
}

@Misc{Higham:2015:MCT,
  author =       "Nicholas J. Higham",
  title =        "Matrix Computation Toolbox",
  howpublished = "Web site.",
  year =         "2015",
  bibdate =      "Sat Apr 01 08:14:19 2017",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  URL =          "http://www.ma.man.ac.uk/~higham/mctoolbox",
  abstract =     "The Matrix Computation Toolbox is a collection of
                 MATLAB M-files containing functions for constructing
                 test matrices, computing matrix factorizations,
                 visualizing matrices, and carrying out direct search
                 optimization. Various other miscellaneous functions are
                 also included. This toolbox supersedes the author's
                 earlier Test Matrix Toolbox (final release
                 1995).\par

                 The toolbox was developed in conjunction with the book
                 Accuracy and Stability of Numerical Algorithms (SIAM,
                 Second edition, August 2002, xxx+680 pp.). That book is
                 the primary documentation for the toolbox: it describes
                 much of the underlying mathematics and many of the
                 algorithms and matrices (it also describes many of the
                 matrices provided by MATLAB's gallery function).",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; MATLAB",
}

@Article{Holzmann:2015:B,
  author =       "Gerard J. Holzmann",
  title =        "Out of Bounds",
  journal =      j-IEEE-SOFTWARE,
  volume =       "32",
  number =       "6",
  pages =        "24--26",
  month =        nov # "\slash " # dec,
  year =         "2015",
  CODEN =        "IESOEG",
  DOI =          "https://doi.org/10.1109/MS.2015.147",
  ISSN =         "0740-7459 (print), 1937-4194 (electronic)",
  ISSN-L =       "0740-7459",
  bibdate =      "Tue Nov 17 07:21:14 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeesoft.bib",
  URL =          "http://csdl.computer.org/csdl/mags/so/2015/06/mso2015060024.html",
  abstract-URL = "http://csdl.computer.org/csdl/mags/so/2015/06/mso2015060024-abs.html",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Software",
  journal-URL =  "http://www.computer.org/portal/web/csdl/magazines/software",
  journalabr =   "IEEE Software",
  remark =       "This article discusses three cases of serious impact
                 of undetected integer overflow: (a) the loss of control
                 of the Deep Impact mission space probe to visit an
                 asteroid; (b) the Boeing 787 Dreamliner (composite
                 materials) generator control unit (GCU) that must now
                 be rebooted at least every 248 days to avoid possibly
                 causing a plane crash; (c) the Planetary Society's
                 LightSail project to test a solar sail in space. It
                 also discusses a failure of NASA's Mars lander, the
                 Curiosity rover, due to storage overflow. Reprinted in
                 \booktitle{Computing Edge}, January 2016, pp. 50--52.",
}

@Article{Hsiao:2015:TSR,
  author =       "Shen-Fu Hsiao and Po-Han Wu and Chia-Sheng Wen and
                 Pramod Kumar Meher",
  title =        "Table Size Reduction Methods for Faithfully Rounded
                 Lookup-Table-Based Multiplierless Function Evaluation",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
  volume =       "62",
  number =       "5",
  pages =        "466--470",
  month =        may,
  year =         "2015",
  DOI =          "https://doi.org/10.1109/TCSII.2014.2386232",
  ISSN =         "1549-7747 (print), 1558-3791 (electronic)",
  ISSN-L =       "1549-7747",
  bibdate =      "Sat Feb 08 10:23:05 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/abstract/document/6998028",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems II: Express
                 Briefs",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
  keywords =     "Accuracy; Adders; adders; Approximation methods;
                 Bipartite; Computer Arithmetic; computer arithmetic;
                 Function Evaluation; function evaluation; graph theory;
                 Indexes; lookup-table-based multiplierless function
                 evaluation; multioperand adder; Multipartite;
                 multipartite; multipartite method; performance
                 evaluation; precision width; Silicon compounds; table
                 decomposition; table lookup; Table lookup; table size;
                 table size reduction method; Table-Based Design;
                 table-based design; table-lookup-and-addition methods",
}

@Article{Hutter:2015:MMA,
  author =       "Michael Hutter and Peter Schwabe",
  title =        "Multiprecision multiplication on {AVR} revisited",
  journal =      j-J-CRYPTO-ENG,
  volume =       "5",
  number =       "3",
  pages =        "201--214",
  month =        sep,
  year =         "2015",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s13389-015-0093-2",
  ISSN =         "2190-8508 (print), 2190-8516 (electronic)",
  ISSN-L =       "2190-8508",
  bibdate =      "Sat Aug 8 10:42:46 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcryptoeng.bib",
  URL =          "http://link.springer.com/article/10.1007/s13389-015-0093-2",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Cryptographic Engineering",
  journal-URL =  "http://link.springer.com/journal/13389",
  keywords =     "AVR ATmega 8-bit microcontroller; Karatsuba
                 multiplication; microcontroller; multiprecision
                 multiplication",
}

@Misc{Iakymchuk:2015:EEB,
  author =       "Roman Iakymchuk and Sylvain Collange and David Defour
                 and Stef Graillat",
  title =        "{ExBLAS} --- Exact {BLAS}",
  howpublished = "Web site.",
  year =         "2015",
  bibdate =      "Sat Oct 31 07:25:14 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://exblas.lip6.fr/;
                 https://www.nist.gov/sites/default/files/documents/itl/ssd/is/NRE-2015-04-iakymchuk.pdf",
  abstract =     "ExBLAS stands for Exact (fast, accurate, and
                 reproducible) Basic Linear Algebra Subprograms.\par

                 The increasing power of current computers enables one
                 to solve more and more complex problems. This,
                 therefore, requires to perform a high number of
                 floating-point operations, each one leading to a
                 round-off error. Because of round-off error
                 propagation, some problems must be solved with a longer
                 floating-point format.\par

                 As Exascale computing is likely to be reached within a
                 decade, getting accurate results in floating-point
                 arithmetic on such computers will be a challenge.
                 However, another challenge will be the reproducibility
                 of the results --- meaning getting a bitwise identical
                 floating-point result from multiple runs of the same
                 code --- due to non-associativity of floating-point
                 operations and dynamic scheduling on parallel
                 computers.\par

                 ExBLAS aims at providing new algorithms and
                 implementations for fundamental linear algebra
                 operations --- like those included in the BLAS library
                 --- that deliver reproducible and accurate results with
                 small or without losses to their performance on modern
                 parallel architectures such as Intel Xeon Phi many-core
                 processors and GPU accelerators. We construct our
                 approach in such a way that it is independent from data
                 partitioning, order of computations, thread scheduling,
                 or reduction tree schemes.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Iakymchuk:2015:ERA,
  author =       "Roman Iakymchuk and Sylvain Collange and David Defour
                 and Stef Graillat",
  editor =       "????",
  booktitle =    "{NRE: Numerical Reproducibility at Exascale, Austin,
                 TX, USA, November 2015}",
  title =        "{ExBLAS}: Reproducible and Accurate {BLAS} Library",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2015",
  bibdate =      "Mon Feb 10 06:22:16 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{IEEE:2015:ISI,
  author =       "{IEEE}",
  title =        "1788-2015 --- {IEEE} Standard for Interval
                 Arithmetic",
  publisher =    pub-IEEE-STD,
  address =      pub-IEEE-STD:adr,
  pages =        "xiv + 79",
  day =          "30",
  month =        jun,
  year =         "2015",
  DOI =          "https://doi.org/10.1109/IEEESTD.2015.7140721",
  ISBN =         "0-7381-9721-1 (PDF), 0-7381-9720-3 (electronic)",
  ISBN-13 =      "978-0-7381-9721-0 (PDF), 978-0-7381-9720-3
                 (electronic)",
  LCCN =         "????",
  bibdate =      "Mon Jan 16 18:28:35 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeestd.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  note =         "Approved 11 June 2015 by IEEE-SA Standards Board.",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=7140719",
  abstract =     "Abstract: This standard species basic interval
                 arithmetic (IA) operations selecting and following one
                 of the commonly used mathematical interval models. This
                 standard supports the IEEE 755 floating-point formats
                 of practical use in interval computations. Exception
                 conditions are defined, and standard handling of these
                 conditions is specified. Consistency with the interval
                 model is tempered with practical considerations based
                 on input from representatives of vendors, developers
                 and maintainers of existing systems. The standard
                 provides a layer between the hardware and the
                 programming language levels. It does not mandate that
                 any operations be implemented in hardware. It does not
                 define any realization of the basic operations as
                 functions in a programming language.",
  acknowledgement = ack-nhfb,
  keywords =     "arithmetic; computing; decoration; enclosure; hull;
                 IEEE 1788; interval; operation; verified",
}

@Article{Jacobsen:2015:PFP,
  author =       "Charles Jacobsen and Alexey Solovyev and Ganesh
                 Gopalakrishnan",
  title =        "A Parameterized Floating-Point Formalizaton in {HOL
                 Light}",
  journal =      j-ELECT-NOTES-THEOR-COMP-SCI,
  volume =       "317",
  number =       "??",
  pages =        "1--6",
  day =          "18",
  month =        nov,
  year =         "2015",
  DOI =          "https://doi.org/10.1016/j.entcs.2015.10.010",
  ISSN =         "1571-0661",
  ISSN-L =       "1571-0661",
  bibdate =      "Fri Apr 17 18:06:24 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Also presented at NSV 2015: 8th International Workshop
                 on Numerical Software Verification 2015, Seattle, WA,
                 USA.",
  URL =          "http://formalverification.cs.utah.edu/papers/nsv15-fp-hol-light.pdf;
                 http://nsv2015.informatik.uni-freiburg.de/",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronic Notes in Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/15710661",
  remark =       "Not yet listed at journal Web site (up to volume 311
                 5-Jan-2015).",
  xxjournal-url = "http://www.elsevier.nl/locate/entcs",
}

@TechReport{Johansson:2015:ADR,
  author =       "Fredrik Johansson",
  title =        "{Arb} Documentation Release 2.6.0",
  type =         "Report",
  institution =  "????",
  address =      "Softwarepark 23, Austria 4113",
  day =          "19",
  month =        apr,
  year =         "2015",
  bibdate =      "Wed Apr 22 09:04:21 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://fredrikj.net/arb/",
  abstract =     "Arb is a C library for arbitrary-precision
                 floating-point ball arithmetic, developed by Fredrik
                 Johansson ({\tt fredrik.johansson@gmail.com}). It
                 supports real and complex numbers, polynomials, power
                 series, matrices, and evaluation of many transcendental
                 functions. All is done with automatic, rigorous error
                 bounds.",
  acknowledgement = ack-nhfb,
  remark =       "From the Feature Overview: ``Ball arithmetic, also
                 known as mid-rad interval arithmetic, is an extension
                 of floating-point arithmetic in which an error bound is
                 attached to each variable. This allows doing rigorous
                 computations over the real numbers, while avoiding the
                 overhead of traditional (inf-sup) interval arithmetic
                 at high precision, and eliminating much of the need for
                 time-consuming and bug-prone manual error analysis
                 associated with standard floating-point arithmetic.''",
}

@InProceedings{Johansson:2015:EIE,
  author =       "Fredrik Johansson",
  title =        "Efficient Implementation of Elementary Functions in
                 the Medium-Precision Range",
  crossref =     "Muller:2015:ISC",
  pages =        "83--89",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.16",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2015; ARITH-22",
}

@Article{Kamm:2015:SFP,
  author =       "Liina Kamm and Jan Willemson",
  title =        "Secure floating point arithmetic and private satellite
                 collision analysis",
  journal =      j-INT-J-INFO-SEC,
  volume =       "14",
  number =       "6",
  pages =        "531--548",
  month =        nov,
  year =         "2015",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s10207-014-0271-8",
  ISSN =         "1615-5262 (print), 1615-5270 (electronic)",
  ISSN-L =       "1615-5262",
  bibdate =      "Tue Jan 23 16:01:44 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/intjinfosec.bib",
  URL =          "http://link.springer.com/article/10.1007/s10207-014-0271-8;
                 http://link.springer.com/content/pdf/10.1007/s10207-014-0271-8.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Information Security",
  journal-URL =  "https://link.springer.com/journal/10207",
}

@Article{Kornerup:2015:RHR,
  author =       "P. Kornerup",
  title =        "Reviewing High-Radix Signed-Digit Adders",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "64",
  number =       "5",
  pages =        "1502--1505",
  month =        may,
  year =         "2015",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2014.2329678",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jun 4 19:46:44 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@TechReport{Kulisch:2015:HSA,
  author =       "Ulrich Kulisch and Gerd Bohlender",
  title =        "High Speed Associative Accumulation of Floating-point
                 Numbers and Floating-point Intervals",
  type =         "Report",
  institution =  "Institut f{\"u}r Angewandte und Numerische Mathematik,
                 Karlsruher Institut f{\"u}r Technologie",
  address =      "D-76128 Karlsruhe, Germany",
  pages =        "8",
  day =          "21",
  month =        dec,
  year =         "2015",
  bibdate =      "Sat Jan 02 12:26:31 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Distributed to stds-1788 mailing list on Fri, 1 Jan
                 2016 09:22:19 +0100; as yet unpublished.",
}

@InProceedings{Kumm:2015:ESM,
  author =       "Martin Kumm and Shahid Abbas and Peter Zipf",
  title =        "An Efficient Softcore Multiplier Architecture for
                 {Xilinx FPGAs}",
  crossref =     "Muller:2015:ISC",
  pages =        "18--25",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.17",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2015; ARITH-22",
}

@PhdThesis{Kupriianova:2015:TMF,
  author =       "Olga Kupriianova",
  title =        "Towards a modern floating-point environment",
  type =         "Th{\`e}se de doctorat",
  school =       "Universit{\'e} Pierre et Marie Curie --- Paris VI",
  address =      "Paris, France",
  pages =        "xi + 130",
  year =         "2015",
  bibdate =      "Fri Jan 31 14:59:32 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://pdfs.semanticscholar.org/94ca/770b22739bdcf22fb9f131d9d4665dc28031.pdf",
  abstract =     "This work investigates two ways of enlarging the
                 current floating-point environment. The first is to
                 support several implementation versions of each
                 mathematical function (elementary such as $ \exp $ or $
                 \log $ and special such as $ \erf $ or $ \Gamma $), the
                 second one is to provide IEEE754 operations that mix
                 the inputs and the output of different radixes. As the
                 number of various implementations for each mathematical
                 function is large, this work is focused on code
                 generation. Our code generator supports the huge
                 variety of functions: it generates parametrized
                 implementations for the user-specified functions. So it
                 may be considered as a black-box function generator.
                 This work contains a novel algorithm for domain
                 splitting and an approach to replace branching on
                 reconstruction by a polynomial. This new domain
                 splitting algorithm produces less subdomains and the
                 polynomial degrees on adjacent subdomains do not change
                 much. To produce vectorizable implementations, if-else
                 statements on the reconstruction step have to be
                 avoided. Since the revision of the IEEE754 Standard in
                 2008 it is possible to mix numbers of different
                 precisions in one operation. However, there is no
                 mechanism that allows users to mix numbers of different
                 radices in one operation. This research starts an
                 examination of mixed-radix arithmetic with the worst
                 cases search for FMA. A novel algorithm to convert a
                 decimal character sequence of arbitrary length to a
                 binary floating-point number is presented. It is
                 independent of currently-set rounding mode and produces
                 correctly-rounded results.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kurka:2015:ERA,
  author =       "Petr K{\r{u}}rka",
  title =        "The Exact Real Arithmetical Algorithm in Binary
                 Continued Fractions",
  crossref =     "Muller:2015:ISC",
  pages =        "168--175",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.20",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2015; ARITH-22",
}

@InProceedings{Langhammer:2015:DIE,
  author =       "Martin Langhammer and Bogdan Pasca",
  title =        "Design and Implementation of an Embedded {FPGA}
                 Floating Point {DSP} Block",
  crossref =     "Muller:2015:ISC",
  pages =        "26--33",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.18",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2015; ARITH-22",
}

@InProceedings{Langroudi:2015:MPP,
  author =       "Seyed Hamed Fatemi Langroudi and Ghassem Jaberipur",
  title =        "Modulo-$ (2^n 2^q 1) $ Parallel Prefix Addition via
                 Excess-Modulo Encoding of Residues",
  crossref =     "Muller:2015:ISC",
  pages =        "121--128",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.9",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2015; ARITH-22",
}

@InProceedings{Laskar:2015:KTN,
  author =       "Jacques Laskar",
  title =        "Keynote Talk: Numerical Challenges in Long Term
                 Integrations of the Solar System",
  crossref =     "Muller:2015:ISC",
  pages =        "104--104",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.35",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Abstract only.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2015; ARITH-22; multiple-precision arithmetic",
}

@InProceedings{Lauter:2015:SAF,
  author =       "Christoph Lauter and Marc Mezzarobba",
  title =        "Semi-Automatic Floating-Point Implementation of
                 Special Functions",
  crossref =     "Muller:2015:ISC",
  pages =        "58--65",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.12",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2015; ARITH-22",
}

@Article{Lee:2015:RRA,
  author =       "Wen-Chuan Lee and Tao Bao and Yunhui Zheng and Xiangyu
                 Zhang and Keval Vora and Rajiv Gupta",
  title =        "{RAIVE}: runtime assessment of floating-point
                 instability by vectorization",
  journal =      j-SIGPLAN,
  volume =       "50",
  number =       "10",
  pages =        "623--638",
  month =        oct,
  year =         "2015",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/2858965.2814299",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Tue Feb 16 12:01:43 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
  abstract =     "Floating point representation has limited precision
                 and inputs to floating point programs may also have
                 errors. Consequently, during execution, errors are
                 introduced, propagated, and accumulated, leading to
                 unreliable outputs. We call this the instability
                 problem. We propose RAIVE, a technique that identifies
                 output variations of a floating point execution in the
                 presence of instability. RAIVE transforms every
                 floating point value to a vector of multiple values ---
                 the values added to create the vector are obtained by
                 introducing artificial errors that are upper bounds of
                 actual errors. The propagation of artificial errors
                 models the propagation of actual errors. When values in
                 vectors result in discrete execution differences (e.g.,
                 following different paths), the execution is forked to
                 capture the resulting output variations. Our evaluation
                 shows that RAIVE can precisely capture output
                 variations. Its overhead (340\%) is 2.43 times lower
                 than the state of the art",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  remark =       "OOPSLA '15 conference proceedings.",
}

@Article{Liu:2015:IBI,
  author =       "L. Liu and S. Peng and C. Zhang and R. Li and B. Wang
                 and C. Sun and Q. Liu and L. Dong and L. Li and Y. Shi
                 and Y. He and W. Zhao and G. Yang",
  title =        "Importance of bitwise identical reproducibility in
                 earth system modeling and status report",
  journal =      "Geoscientific Model Development Discussions",
  volume =       "8",
  number =       "6",
  pages =        "4375--4400",
  month =        jun,
  year =         "2015",
  DOI =          "https://doi.org/10.5194/gmdd-8-4375-2015",
  ISSN =         "1991-959X (print), 1991-9603 (electronic)",
  ISSN-L =       "1991-959X",
  bibdate =      "Mon Feb 10 17:57:24 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.geosci-model-dev-discuss.net/gmd-2015-83/",
  abstract =     "Reproducibility is a fundamental principle of
                 scientific research. Bitwise identical reproducibility,
                 i.e., bitwise computational results can be reproduced,
                 guarantees the reproduction of exactly the same
                 results. Here we show the importance of bitwise
                 identical reproducibility to Earth system modeling but
                 the importance has not yet been widely recognized.
                 Modeled mean climate states, variability and trends at
                 different scales may be significantly changed or even
                 lead to opposing results due to a slight change in the
                 original simulation setting during a reproduction. Out
                 of the large body of Earth system modeling
                 publications, few thoroughly describe the whole
                 original simulation setting. As a result, the
                 reproduction of a particular simulation experiment by
                 fellow scientists heavily depends on the interaction
                 with the original authors, which is often inconvenient
                 or even impossible. We anticipate bitwise identical
                 reproducibility to be promoted as a worldwide standard,
                 to guarantee the independent reproduction of simulation
                 results and to further improve model development and
                 scientific research.",
  acknowledgement = ack-nhfb,
  journal-URL =  "https://www.geosci-model-dev.net/volumes.html",
}

@Article{Liu:2015:SSS,
  author =       "Weifeng Liu and Brian Vinter",
  title =        "Speculative segmented sum for sparse matrix-vector
                 multiplication on heterogeneous processors",
  journal =      j-PARALLEL-COMPUTING,
  volume =       "49",
  number =       "??",
  pages =        "179--193",
  month =        nov,
  year =         "2015",
  CODEN =        "PACOEJ",
  DOI =          "https://doi.org/10.1016/j.parco.2015.04.004",
  ISSN =         "0167-8191 (print), 1872-7336 (electronic)",
  ISSN-L =       "0167-8191",
  bibdate =      "Thu Oct 29 17:53:44 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/parallelcomputing.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167819115000770",
  acknowledgement = ack-nhfb,
  fjournal =     "Parallel Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01678191/",
}

@Article{Lu:2015:REP,
  author =       "Xin Lu and Shufang Xu",
  title =        "Rounding errors of partial derivatives of simple
                 eigenvalues of the quadratic eigenvalue problem",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "282",
  number =       "??",
  pages =        "268--277",
  month =        jul,
  year =         "2015",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:34:50 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2015.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042715000151",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{Lutz:2015:OLZ,
  author =       "David Raymond Lutz",
  title =        "Optimized leading zero anticipators for faster fused
                 multiply-adds",
  crossref =     "Matthews:2017:CRF",
  pages =        "741--744",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ACSSC.2017.8335443",
  bibdate =      "Mon Feb 10 08:39:02 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/document/8335443/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mack:2015:FPC,
  author =       "Joshua Mack and Sam Bellestri and Daniel Llamocca",
  booktitle =    "{2015 International Conference on ReConFigurable
                 Computing and FPGAs (ReConFig)}",
  title =        "Floating point {CORDIC}-based architecture for
                 powering computation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--6",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ReConFig.2015.7393311",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithm design and analysis; Computer architecture;
                 computer arithmetic; Convergence; CORDIC; Engines;
                 floating point arithmetic; Floating-point arithmetic;
                 Hardware; powering; Signal processing algorithms",
}

@Article{Martin-Dorel:2015:FVC,
  author =       "{\'E}rik Martin-Dorel and Guillaume Hanrot and Micaela
                 Mayero and Laurent Th{\'e}ry",
  title =        "Formally Verified Certificate Checkers for
                 Hardest-to-Round Computation",
  journal =      j-J-AUTOM-REASON,
  volume =       "54",
  number =       "1",
  pages =        "1--29",
  month =        jan,
  year =         "2015",
  CODEN =        "JAREEW",
  DOI =          "https://doi.org/10.1007/s10817-014-9312-2",
  ISSN =         "0168-7433 (print), 1573-0670 (electronic)",
  ISSN-L =       "0168-7433",
  bibdate =      "Sat Apr 2 10:51:12 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
  URL =          "http://link.springer.com/article/10.1007/s10817-014-9312-2",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Autom. Reason.",
  fjournal =     "Journal of Automated Reasoning",
  journal-URL =  "http://link.springer.com/journal/10817",
}

@Article{Matula:2015:MDE,
  author =       "D. W. Matula and M. T. Panu and J. Y. Zhang",
  title =        "Multiplicative Division Employing Independent
                 Factors",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "64",
  number =       "7",
  pages =        "2012--2019",
  month =        "????",
  year =         "2015",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2014.2346206",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Aug 1 08:53:41 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{McCleeary:2015:LAA,
  author =       "Ryan McCleeary and Martin Brain and Aaron Stump",
  title =        "A lazy approach to adaptive exact real arithmetic
                 using floating-point operations",
  journal =      j-ACM-COMM-COMP-ALGEBRA,
  volume =       "49",
  number =       "3",
  pages =        "83--86",
  month =        sep,
  year =         "2015",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2850449.2850456",
  ISSN =         "1932-2232 (print), 1932-2240 (electronic)",
  ISSN-L =       "1932-2232",
  bibdate =      "Wed Dec 2 14:16:56 MST 2015",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
  abstract =     "Arithmetic operations with high degrees of precision
                 are needed for an increasing number of applications. We
                 propose an exact real arithmetic system that achieves
                 adaptive precision using lazy infinite lists of
                 floating-point values.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Communications in Computer Algebra",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}

@Article{Meloni:2015:EDB,
  author =       "N. Meloni and M. A. Hasan",
  title =        "Efficient Double Bases for Scalar Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "64",
  number =       "8",
  pages =        "2204--2212",
  month =        aug,
  year =         "2015",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2014.2360539",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Aug 11 08:24:23 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "double-base number system; elliptic curve",
}

@Article{Michelogiannakis:2015:ESP,
  author =       "George Michelogiannakis and Xiaoye S. Li",
  title =        "Extending Summation Precision for Network Reduction
                 Operations",
  journal =      j-INT-J-PARALLEL-PROG,
  volume =       "43",
  number =       "6",
  pages =        "1218--1243",
  month =        dec,
  year =         "2015",
  CODEN =        "IJPPE5",
  DOI =          "https://doi.org/10.1007/s10766-014-0326-5",
  ISSN =         "0885-7458 (print), 1573-7640 (electronic)",
  ISSN-L =       "0885-7458",
  bibdate =      "Tue Sep 29 10:13:48 MDT 2015",
  bibsource =    "http://link.springer.com/journal/10766/43/6;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/intjparallelprogram.bib",
  URL =          "http://link.springer.com/article/10.1007/s10766-014-0326-5",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Parallel Programming",
  journal-URL =  "http://link.springer.com/journal/10766",
  keywords =     "accurate floating-point summation",
}

@Article{Momeni:2015:DAA,
  author =       "A. Momeni and Jie Han and P. Montuschi and F.
                 Lombardi",
  title =        "Design and Analysis of Approximate Compressors for
                 Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "64",
  number =       "4",
  pages =        "984--994",
  month =        apr,
  year =         "2015",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2014.2308214",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jun 4 19:46:38 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Morar:2015:RMT,
  author =       "Florin-Stefan Morar",
  title =        "Reinventing machines: the transmission history of the
                 {Leibniz} calculator",
  journal =      j-BRITISH-J-HIST-SCI,
  volume =       "48",
  number =       "1",
  pages =        "123--146",
  month =        mar,
  year =         "2015",
  CODEN =        "BJHSAT",
  DOI =          "https://doi.org/10.1017/S0007087414000429",
  ISSN =         "0007-0874 (print), 1474-001X (electronic)",
  ISSN-L =       "0007-0874",
  bibdate =      "Wed Feb 4 10:40:51 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/bjhs2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "British J. Hist. Sci.",
  fjournal =     "British Journal for the History of Science",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=BJH",
  onlinedate =   "Mon Jul 14 00:00:00 BST 2014",
}

@Article{Muller:2015:ECC,
  author =       "Jean-Michel Muller",
  title =        "On the Error of Computing $ a b + c d $ using
                 {Cornea}, {Harrison} and {Tang}'s Method",
  journal =      j-TOMS,
  volume =       "41",
  number =       "2",
  pages =        "7:1--7:8",
  month =        jan,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2629615",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 4 17:49:11 MST 2015",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In their book, \booktitle{Scientific Computing on the
                 Itanium}, Cornea et al. [2002] introduce an accurate
                 algorithm for evaluating expressions of the form $ a b
                 + c d $ in binary floating-point arithmetic, assuming
                 an FMA instruction is available. They show that if $p$
                 is the precision of the floating-point format and if $
                 u = 2^{-p} $, the relative error of the result is of
                 order $u$. We improve their proof to show that the
                 relative error is bounded by $ 2 u + 7 u^2 + 6 u^3 $.
                 Furthermore, by building an example for which the
                 relative error is asymptotically (as $ p \to \infty $
                 or, equivalently, as $ u \to 0 $) equivalent to $ 2 u
                 $, we show that our error bound is asymptotically
                 optimal.",
  acknowledgement = ack-nhfb,
  articleno =    "7",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  remark =       "This article compares two algorithms (Kahan's and
                 Cornea / Harrison / Tang's) for computing $ a b + c d
                 $. It shows that the worst-case error with FMA and
                 round-to-nearest arithmetic is $ 2 u $ for the first,
                 and $ 2 u + 7 u^2 + 6 u^3 $ for the second, suggesting
                 that Kahan's is preferred. However, the second
                 guarantees that $ a b + c d = = c d + a b $, whereas
                 the first does not, so it may be preferred for
                 applications like complex multiplication and division,
                 in order to guarantee commutative arithmetic",
}

@InProceedings{Munoz:2015:IFP,
  author =       "Sergio D. Mu{\~n}oz and Javier Hormigo",
  booktitle =    "{2015 International Symposium on Consumer Electronics
                 (ISCE)}",
  title =        "Improving fixed-point implementation of {$ Q R $}
                 decomposition by rounding-to-nearest",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--2",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ISCE.2015.7177822",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "adaptive filters; Computer architecture; Consumer
                 communication; Consumer electronics; CORDIC; Delays;
                 Field programmable gate arrays; fixed-point
                 optimization; Hardware; Matrix decomposition; MIMO;
                 QRD; watermarking; Watermarking",
}

@TechReport{Neal:2015:FESa,
  author =       "Radford M. Neal",
  title =        "Fast exact summation using small and large
                 superaccumulators",
  type =         "Report",
  institution =  "Department of Statistical Sciences and Department of
                 Computer Science, University of Toronto",
  address =      "Toronto, ON, Canada",
  pages =        "22",
  year =         "2015",
  bibdate =      "Sat Oct 31 07:19:27 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  URL =          "http://www.cs.toronto.edu/~radford/ftp/xsum.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Neal:2015:FESb,
  author =       "Radford M. Neal",
  title =        "Fast exact summation using small and large
                 superaccumulators",
  journal =      "arxiv.org",
  pages =        "22",
  year =         "2015",
  bibdate =      "Sat Oct 31 07:19:27 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  URL =          "https://arxiv.org/pdf/1505.05571v1.pdf",
  abstract =     "I present two new methods for exactly summing a set of
                 floating-point numbers, and then correctly rounding to
                 the nearest floating-point number. Higher accuracy than
                 simple summation (rounding after each addition) is
                 important in many applications, such as finding the
                 sample mean of data. Exact summation also guarantees
                 identical results with parallel and serial
                 implementations, since the exact sum is independent of
                 order. The new methods use variations on the concept of
                 a ``superaccumulator'' --- a large fixed-point number
                 that can exactly represent the sum of any reasonable
                 number of floating-point values. One method uses a
                 ``small'' superaccumulator with sixty-seven 64-bit
                 chunks, each with 32-bit overlap with the next chunk,
                 allowing carry propagation to be done infrequently. The
                 small superaccumulator is used alone when summing a
                 small number of terms. For big summations, a ``large''
                 superaccumulator is used as well. It consists of 4096
                 64-bit chunks, one for every possible combination of
                 exponent bits and sign bit, plus counts of when each
                 chunk needs to be transferred to the small
                 superaccumulator. To add a term to the large
                 superaccumulator, only a single chunk and its
                 associated count need to be updated, which takes very
                 few instructions if carefully implemented. On modern
                 64-bit processors, exactly summing a large array using
                 this combination of large and small superaccumulators
                 takes less than twice the time of simple, inexact,
                 ordered summation, with a serial implementation. A
                 parallel implementation using a small number of
                 processor cores can be expected to perform exact
                 summation of large arrays at a speed that reaches the
                 limit imposed by memory bandwidth. Some common methods
                 that attempt to improve accuracy without being exact
                 may therefore be pointless, at least for large
                 summations, since they are slower than computing the
                 sum exactly.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Negre:2015:EME,
  author =       "Christophe Negre and Thomas Plantard and Jean-Marc
                 Robert",
  title =        "Efficient Modular Exponentiation Based on Multiple
                 Multiplications by a Common Operand",
  crossref =     "Muller:2015:ISC",
  pages =        "144--151",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.24",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2015; ARITH-22",
}

@InProceedings{Nguyen:2015:RTS,
  author =       "Hong Diep Nguyen and James Demmel",
  title =        "Reproducible Tall-Skinny {QR}",
  crossref =     "Muller:2015:ISC",
  pages =        "152--159",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.28",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://bebop.cs.berkeley.edu/reproblas/docs/papers/RepTSQR.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2015; ARITH-22",
}

@Article{Ozaki:2015:IEF,
  author =       "Katsuhisa Ozaki and Takeshi Ogita and Shin'ichi
                 Oishi",
  title =        "Improvement of error-free splitting for accurate
                 matrix multiplication",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "288",
  number =       "??",
  pages =        "127--140",
  month =        nov,
  year =         "2015",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 13:34:52 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2015.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042715002289",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Palmer:2015:MBI,
  author =       "Tim Palmer",
  title =        "Modelling: Build imprecise supercomputers",
  journal =      j-NATURE,
  volume =       "526",
  number =       "7571",
  pages =        "32--33",
  day =          "29",
  month =        sep,
  year =         "2015",
  CODEN =        "NATUAS",
  DOI =          "https://doi.org/10.1038/526032a",
  ISSN =         "0028-0836 (print), 1476-4687 (electronic)",
  ISSN-L =       "0028-0836",
  bibdate =      "Sat Mar 25 18:29:10 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/super.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Nature",
  journal-URL =  "http://www.nature.com/nature/archive/",
  remark =       "This provocative paper argues that future
                 supercomputers should be built with a small number of
                 processors that can do accurate high-precision
                 floating-point arithmetic, with the bulk of
                 computations carried out, to save energy, at lower
                 precision, and possibly with occasional arithmetic
                 errors. I [NHFB] find that a perilous approach that
                 would likely lead to entirely unrepeatable, and thus,
                 almost certainly useless, computations to which it is
                 impossible to apply sensible numerical analysis.!",
}

@Article{Panchekha:2015:AIA,
  author =       "Pavel Panchekha and Alex Sanchez-Stern and James R.
                 Wilcox and Zachary Tatlock",
  title =        "Automatically improving accuracy for floating point
                 expressions",
  journal =      j-SIGPLAN,
  volume =       "50",
  number =       "6",
  pages =        "1--11",
  month =        jun,
  year =         "2015",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/2813885.2737959",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Tue Feb 16 12:01:41 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
  abstract =     "Scientific and engineering applications depend on
                 floating point arithmetic to approximate real
                 arithmetic. This approximation introduces rounding
                 error, which can accumulate to produce unacceptable
                 results. While the numerical methods literature
                 provides techniques to mitigate rounding error,
                 applying these techniques requires manually rearranging
                 expressions and understanding the finer details of
                 floating point arithmetic. We introduce Herbie, a tool
                 which automatically discovers the rewrites experts
                 perform to improve accuracy. Herbie's heuristic search
                 estimates and localizes rounding error using sampled
                 points (rather than static error analysis), applies a
                 database of rules to generate improvements, takes
                 series expansions, and combines improvements for
                 different input regions. We evaluated Herbie on
                 examples from a classic numerical methods textbook, and
                 found that Herbie was able to improve accuracy on each
                 example, some by up to 60 bits, while imposing a median
                 performance overhead of 40\%. Colleagues in machine
                 learning have used Herbie to significantly improve the
                 results of a clustering algorithm, and a mathematical
                 library has accepted two patches generated using
                 Herbie.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  remark =       "PLDI '15 conference proceedings.",
}

@Article{Parhami:2015:DAN,
  author =       "Behrooz Parhami",
  title =        "Digital Arithmetic in Nature: Continuous-Digit {RNS}",
  journal =      j-COMP-J,
  volume =       "58",
  number =       "5",
  pages =        "1214--1223",
  month =        may,
  year =         "2015",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/bxu060",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Sat May 2 08:05:35 MDT 2015",
  bibsource =    "http://comjnl.oxfordjournals.org/content/58/5.toc;
                 https://www.math.utah.edu/pub/tex/bib/compj2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://comjnl.oxfordjournals.org/content/58/5/1214",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "Residue Number System (RNS)",
  onlinedate =   "July 17, 2014",
}

@InProceedings{Patil:2015:OFP,
  author =       "Vinayak Patil and Aneesh Raveendran and P. M. Sobha
                 and A. David Selvakumar and D. Vivian",
  editor =       "{IEEE}",
  booktitle =    "{2015 19th International Symposium on VLSI Design and
                 Test}",
  title =        "Out of order floating point coprocessor for {RISC V
                 ISA}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--7",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ISVDAT.2015.7208116",
  bibdate =      "Sat Dec 16 15:51:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
}

@Article{Peeper:2015:DDP,
  author =       "D. Peeper",
  title =        "Deep-dish peeper [The Big Picture]",
  journal =      j-IEEE-SPECTRUM,
  volume =       "52",
  number =       "11",
  pages =        "16--17",
  month =        nov,
  year =         "2015",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.2015.7335888",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Sat Jan 18 07:02:09 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum2010.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "FAST; five-hundred-meter aperture spherical radio
                 telescope; floating point operations; Puerto Rico;
                 radiotelescopes",
}

@Article{Petrovsky:2015:CLF,
  author =       "Nick Petrovsky and Andrew Stankevich and Alexander
                 Petrovsky",
  title =        "{CORDIC}-lifting factorization of paraunitary filter
                 banks based on the quaternionic multipliers for
                 lossless image coding",
  journal =      "Multidimensional Systems and Signal Processing",
  volume =       "27",
  number =       "3",
  pages =        "667--695",
  month =        mar,
  year =         "2015",
  DOI =          "https://doi.org/10.1007/s11045-015-0323-x",
  ISSN =         "1573-0824",
  bibdate =      "Tue Oct 28 07:04:09 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Proust:2015:KTC,
  author =       "Christine Proust",
  title =        "Keynote Talk: Calculating in Floating Sexagesimal
                 Place Value Notation, 4000 years ago",
  crossref =     "Muller:2015:ISC",
  pages =        "1--1",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.33",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Abstract only.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2015; ARITH-22",
}

@InProceedings{Renardy:2015:HIM,
  author =       "Antonius P. Renardy and Nur Ahmadi and Ashbir A.
                 Fadila and Naufal Shidqi and Trio Adiono",
  editor =       "{IEEE}",
  booktitle =    "2015 International Seminar on Intelligent Technology
                 and Its Applications ({ISITIA}): proceeding: {Surabaya,
                 Indonesia, 20--21 May 2015}",
  title =        "Hardware Implementation of {Montgomery} Modular
                 Multiplication Algorithm Using Iterative Architecture",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  bookpages =    "453",
  pages =        "99--102",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ISITIA.2015.7219961",
  ISBN =         "1-4799-7711-X",
  ISBN-13 =      "978-1-4799-7711-6",
  LCCN =         "TA347.A78",
  bibdate =      "Tue Jul 06 18:27:11 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Modular multiplication is an integral part of RSA
                 cryptosystems and its performance heavily determines
                 the performance of the encryption hardware. This paper
                 provides a hardware implementation of Montgomery's
                 modular multiplication algorithm using iterative
                 architecture. The proposed design is implemented in
                 Verilog HDL and simulated functionally using ModelSim
                 Altera 10.1E. The synthesis is performed using Altera
                 Quartus II 9.1 with target FPGA board Altera DE2-70.
                 The proposed design consumes 17540 logic elements with
                 15480 LUT and takes 2048 clock cycles to perform
                 multiplication process. Based on trade-off parameter
                 AT$^2$ measure, the proposed design offers the best
                 performance among other designs.",
  acknowledgement = ack-nhfb,
  keywords =     "FPGA; Iterative Architecture; Modular Multiplication;
                 Montgomery's Algorithm; RSA Cryptosystem",
}

@Article{Roegel:2015:MCA,
  author =       "Denis Roegel",
  title =        "A Mechanical Calculator for Arithmetic Sequences
                 (1844--1852): Part 1, Historical Context and
                 Structure",
  journal =      j-IEEE-ANN-HIST-COMPUT,
  volume =       "37",
  number =       "4",
  pages =        "90--96",
  month =        "????",
  year =         "2015",
  CODEN =        "IAHCEX",
  DOI =          "https://doi.org/10.1109/MAHC.2015.79",
  ISSN =         "1058-6180 (print), 1934-1547 (electronic)",
  ISSN-L =       "1058-6180",
  bibdate =      "Tue Dec 8 07:02:44 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeeannhistcomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Annals of the History of Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85",
}

@Book{Ruckert:2015:MSS,
  author =       "Martin Ruckert",
  title =        "The {MMIX} supplement: supplement to {{\booktitle{The
                 Art of Computer Programming, volumes 1, 2, 3}} by
                 Donald E. Knuth}",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "xxi + 193",
  year =         "2015",
  ISBN =         "0-13-399231-4 (paperback), 0-13-399289-6",
  ISBN-13 =      "978-0-13-399231-1 (paperback), 978-0-13-399289-2",
  LCCN =         "QA76.6 .K64 2005 Suppl. 1",
  bibdate =      "Wed Feb 4 10:19:23 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/hash.bib;
                 https://www.math.utah.edu/pub/tex/bib/litprog.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/string-matching.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://mmix.cs.hm.edu/",
  abstract =     "In the first edition of Volume 1 of The Art of
                 Computer Programming, Donald E. Knuth introduced the
                 MIX computer and its machine language: a teaching tool
                 that powerfully illuminated the inner workings of the
                 algorithms he documents. Later, with the publication of
                 his Fascicle 1, Knuth introduced MMIX: a modern, 64-bit
                 RISC replacement to the now-obsolete MIX. Now, with
                 Knuth's guidance and approval, Martin Ruckert has
                 rewritten all MIX example programs from Knuth's Volumes
                 1--3 for MMIX, thus completing this MMIX update to the
                 original classic.\par

                 From Donald E. Knuth's Foreword:\par

                 ``I am thrilled to see the present book by Martin
                 Ruckert: It is jam-packed with goodies from which an
                 extraordinary amount can be learned. Martin has not
                 merely transcribed my early programs for MIX and recast
                 them in a modern idiom. He has penetrated to their
                 essence and rendered them anew with elegance and good
                 taste. His carefully checked code represents a
                 significant contribution to the art of pedagogy as well
                 as to the art of programming.''",
  acknowledgement = ack-nhfb,
  libnote =      "Not yet in my library.",
  subject =      "MMIX (Computer architecture); Assembly languages
                 (Electronic computers); Microcomputers; Programming",
  tableofcontents = "Foreword / iii \\
                 Preface / v \\
                 Style Guide / viii \\
                 Programming Techniques / xii \\
                 Basic Concepts / 1 \\
                 Applications to Permutations / 1 \\
                 Input and Output / 8 \\
                 Information Structures / 15 \\
                 Introduction / 15 \\
                 Sequential Allocation / 17 \\
                 Linked Allocation / 18 \\
                 Circular Lists / 25 \\
                 Doubly Linked Lists / 27 \\
                 Arrays and Orthogonal Lists / 36 \\
                 Traversing Binary Trees / 37 \\
                 Binary Tree Representation of Trees / 39 \\
                 Other Representations of Trees / 43 \\
                 Lists and Garbage Collection / 44 \\
                 Dynamic Storage Allocation / 45 \\
                 Random Numbers / 48 \\
                 Choice of modulus / 48 \\
                 Potency / 49 \\
                 Other Methods / 50 \\
                 Numerical Distributions / 51 \\
                 Summary / 52 \\
                 Arithmetic / 53 \\
                 Positional Number Systems / 53 \\
                 Single-Precision Calculations / 53 \\
                 Accuracy of Floating Point Arithmetic / 58 \\
                 Double-Precision Calculations / 58 \\
                 The Classical Algorithms / 62 \\
                 Radix Conversion / 68 \\
                 The Greatest Common Divisor / 70 \\
                 Analysis of Euclid's Algorithm / 71 \\
                 Factoring into Primes / 72 \\
                 Evaluation of Powers / 72 \\
                 Evaluation of Polynomials / 73 \\
                 Sorting / 74 \\
                 Internal Sorting / 74 \\
                 Sorting by Insertion / 76 \\
                 Sorting by Exchanging / 81 \\
                 Sorting by Selection / 87 \\
                 Sorting by Merging / 89 \\
                 Sorting by Distribution / 93 \\
                 Minimum-Comparison Sorting / 94 \\
                 Summary, History and Bibliography / 95 \\
                 Searching / 97 \\
                 Sequential Searching / 97 \\
                 Searching an Ordered Table / 99 \\
                 Binary Tree Searching / 102 \\
                 Balanced Trees / 103 \\
                 Digital Searching / 106 \\
                 Hashing / 108 \\
                 Answers to Exercises / 117 \\
                 The MMIX Assembly Language / 117 \\
                 Applications to Permutations / 120 \\
                 Input and Output / 120 \\
                 Introduction / 122 \\
                 Sequential Allocation / 123 \\
                 Linked Allocation / 124 \\
                 Circular Lists / 128 \\
                 Doubly Linked Lists / 130 \\
                 Arrays and Orthogonal Lists / 132 \\
                 Traversing Binary Trees / 134 \\
                 Binary Tree Representation of Trees / 136 \\
                 Lists and Garbage Collection / 139 \\
                 Dynamic Storage Allocation / 140 \\
                 Choice of modulus / 147 \\
                 Potency / 148 \\
                 Other Methods / 148 \\
                 Numerical Distributions / 149 \\
                 Summary / 150 \\
                 Positional Number Systems / 150 \\
                 Single-Precision Calculations / 151 \\
                 Accuracy of Floating Point Arithmetic / 152 \\
                 Double-Precision Calculations / 153 \\
                 The Classical Algorithms / 156 \\
                 Radix Conversion / 158 \\
                 The Greatest Common Divisor / 160 \\
                 Analysis of Euclid's Algorithm / 160 \\
                 Evaluation of Powers / 161 \\
                 Evaluation of Polynomials / 161 \\
                 Sorting / 162 \\
                 Internal Sorting / 162 \\
                 Sorting by Insertion / 165 \\
                 Sorting by Exchanging / 169 \\
                 Sorting by Selection / 174 \\
                 Sorting by Distribution / 179 \\
                 Minimum-Comparison Sorting / 180 \\
                 Summary, History, and Bibliography / 183 \\
                 Sequential Searching / 183 \\
                 Searching an Ordered Table / 184 \\
                 Binary Tree Searching / 185 \\
                 Balanced Trees / 185 \\
                 Digital Searching / 186 \\
                 Hashing / 186 \\
                 Acknowledgements / 188 \\
                 Index / 189",
}

@Article{Seo:2015:MMS,
  author =       "Hwajeong Seo and Zhe Liu and Yasuyuki Nogami and
                 Jongseok Choi and Howon Kim",
  title =        "{Montgomery} multiplication and squaring for Optimal
                 Prime Fields",
  journal =      j-COMPUT-SECUR,
  volume =       "52",
  number =       "??",
  pages =        "276--291",
  month =        jul,
  year =         "2015",
  CODEN =        "CPSEDU",
  ISSN =         "0167-4048 (print), 1872-6208 (electronic)",
  ISSN-L =       "0167-4048",
  bibdate =      "Mon Sep 23 09:46:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computsecur2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/S0167404815000371",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers \& Security",
  journal-URL =  "https://www.sciencedirect.com/science/journal/01674048",
}

@InProceedings{Singh:2015:DIQ,
  author =       "Arun Kumar Singh and Madhav Kumar Singh and Kailash
                 Chandra Ray",
  booktitle =    "{2015 IEEE International Symposium on Nanoelectronic
                 and Information Systems}",
  title =        "Design and Implementation of Quadruple Floating-Point
                 {CORDIC}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "286--290",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/iNIS.2015.23",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer architecture; CORDIC; Dynamic range; FPGA
                 Implementation; Hardware design languages; Heuristic
                 algorithms; Mathematical model; Quadruple
                 Floating-Point; Signal processing algorithms;
                 Standards; VLSI Architecture",
}

@TechReport{Solovyev:2015:REFa,
  author =       "Alexey Solovyev and Charles Jacobsen and Zvonimir
                 Rakamari{\'c} and Ganesh Gopalakrishnan",
  title =        "Rigorous Estimation of Floating-Point Round-off Errors
                 with Symbolic {Taylor} Expansions",
  type =         "Technical Report",
  number =       "UUCS-15-001",
  institution =  "School of Computing, University of Utah",
  address =      "Salt Lake City, UT 84112 USA",
  pages =        "31",
  day =          "6",
  month =        apr,
  year =         "2015",
  bibdate =      "Fri Apr 17 18:02:17 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://formalverification.cs.utah.edu/papers/fptaylor_report.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Solovyev:2015:REFb,
  author =       "Alexey Solovyev and Charles Jacobsen and Zvonimir
                 Rakamari{\'c} and Ganesh Gopalakrishnan",
  booktitle =    "{20th International Symposium on Formal Methods (FM
                 2015), Oslo, Norway}",
  title =        "Rigorous Estimation of Floating-Point Round-off Errors
                 with Symbolic {Taylor} Expansions",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "532--550",
  day =          "6",
  month =        jun,
  year =         "2015",
  bibdate =      "Fri Apr 17 18:02:17 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Extended version available in
                 \cite{Solovyev:2015:REFa}.",
  URL =          "http://formalverification.cs.utah.edu/papers/fptaylor_report.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sullivan:2015:LCD,
  author =       "Michael B. Sullivan and Earl E. Swartzlander",
  title =        "Low-Cost Duplicate Multiplication",
  crossref =     "Muller:2015:ISC",
  pages =        "2--9",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.29",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2015; ARITH-22",
}

@InProceedings{Thomas:2015:GPM,
  author =       "David B. Thomas",
  title =        "A General-Purpose Method for Faithfully Rounded
                 Floating-Point Function Approximation in {FPGAs}",
  crossref =     "Muller:2015:ISC",
  pages =        "42--49",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.27",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2015; ARITH-22",
}

@Article{Trefethen:2015:CNF,
  author =       "Lloyd N. Trefethen",
  title =        "Computing numerically with functions instead of
                 numbers",
  journal =      j-CACM,
  volume =       "58",
  number =       "10",
  pages =        "91--97",
  month =        oct,
  year =         "2015",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/2814847",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Wed Sep 30 07:29:42 MDT 2015",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  URL =          "http://cacm.acm.org/magazines/2015/10/192390/fulltext",
  abstract =     "Science and engineering depend upon computation of
                 functions such as flow fields, charge distributions,
                 and quantum states. Ultimately, such computations
                 require some kind of discretization, but in recent
                 years, it has become possible in many cases to hide the
                 discretizations from the user. We present the Chebfun
                 system for numerical computation with functions, which
                 is based on a key idea: an analogy of floating-point
                 arithmetic for functions rather than numbers.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Chebfun; Chebyshev approximation; floating-point
                 arithmetic; Matlab; rational arithmetic; symbolic
                 algebra",
}

@InProceedings{vanderHoeven:2015:FFM,
  author =       "Joris van der Hoeven and Gr{\'e}goire Lecerf",
  title =        "Faster {FFTs} in Medium Precision",
  crossref =     "Muller:2015:ISC",
  pages =        "75--82",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.10",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2015; ARITH-22",
}

@InProceedings{Volkova:2015:REW,
  author =       "Anastasia Volkova and Thibault Hilaire and Christoph
                 Lauter",
  title =        "Reliable Evaluation of the Worst-Case Peak Gain Matrix
                 in Multiple Precision",
  crossref =     "Muller:2015:ISC",
  pages =        "96--103",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ARITH.2015.14",
  bibdate =      "Sat Aug 01 08:05:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2015; ARITH-22",
}

@Misc{Wilczak:2015:CAP,
  author =       "Daniel Wilczak and others",
  title =        "Computer Assisted Proofs in Dynamics",
  howpublished = "Web site and software.",
  month =        jun,
  year =         "2015",
  bibdate =      "Wed Jun 17 11:30:51 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://sourceforge.net/projects/capd/",
  acknowledgement = ack-nhfb,
  remark =       "From the Web site: ``The CAPD library is a collection
                 of flexible C++ modules which are mainly designed to
                 computation of homology of sets and maps and
                 nonrigorous and validated numerics for dynamical
                 systems.'' From the announcement on the Reliable
                 Computing mailing list on 14-Jun-2015: ``In 2015, the
                 library has over 100,000 lines of code. It provides
                 rigorous solvers for ODEs, variational equations for
                 ODEs, differential inclusions, automatic computation of
                 Poincare maps and their derivatives, computation of
                 homology of spaces, maps and many other features. Its
                 efficiency is confirmed by several nontrivial results
                 in dynamics, including proving of chaos, presence of
                 local and global bifurcations for ODEs, existence of
                 attractors for ODEs, periodic orbits for PDEs, and many
                 other results.\par

                 The library comes with a comprehensive tutorial with
                 many examples illustrating very basic usage of CAPD as
                 well as quite advanced, like a complete computer
                 assisted proof of the existence of attractor in the
                 Rossler system with uniformly hyperbolic and chaotic
                 invariant set.''",
}

@Article{Wittmann:2015:SNC,
  author =       "Markus Wittmann and Thomas Zeiser and Georg Hager and
                 Gerhard Wellein",
  title =        "Short Note on Costs of Floating Point Operations on
                 current x86-64 Architectures: Denormals, Overflow,
                 Underflow, and Division by Zero",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "12",
  month =        jun,
  year =         "2015",
  CODEN =        "????",
  ISSN =         "????",
  ISSN-L =       "????",
  bibdate =      "Wed Sep 30 12:43:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/1506.03997",
  abstract =     "Simple floating point operations like addition or
                 multiplication on normalized floating point values can
                 be computed by current AMD and Intel processors in
                 three to five cycles. This is different for
                 denormalized numbers, which appear when an underflow
                 occurs and the value can no longer be represented as a
                 normalized floating-point value. Here the costs are
                 about two magnitudes higher.",
  acknowledgement = ack-nhfb,
  subject =      "Performance (cs.PF)",
}

@Article{Yamazaki:2015:MPC,
  author =       "Ichitaro Yamazaki and Stanimire Tomov and Jack
                 Dongarra",
  title =        "Mixed-Precision {Cholesky} {$ Q R $} Factorization and
                 Its Case Studies on Multicore {CPU} with Multiple
                 {GPUs}",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "37",
  number =       "3",
  pages =        "C307--C330",
  month =        "????",
  year =         "2015",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/14M0973773",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Sat Aug 8 06:48:44 MDT 2015",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/37/3;
                 https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  onlinedate =   "January 2015",
}

@InProceedings{Yin:2015:NRT,
  author =       "Hongxu Yin and Bah Hwee Gwee and Zhiping Lin and Anil
                 Kumar and Sirajudeen Gulam Razul and Chong Meng Samson
                 See",
  booktitle =    "{2015 IEEE International Symposium on Circuits and
                 Systems (ISCAS)}",
  title =        "Novel real-time system design for floating-point
                 sub-Nyquist multi-coset signal blind reconstruction",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "954--957",
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ISCAS.2015.7168793",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "CORDIC; Field programmable gate arrays; FPGA; Jacobi;
                 Jacobian matrices; Mathematical model; multi-coset
                 sampling; Multiband; Multiple signal classification;
                 MUSIC; Real-time systems; Reconstruction; Signal to
                 noise ratio; sub-Nyquist",
}

@InProceedings{Ahmed:2016:ILM,
  author =       "Syed Ershad Ahmed and Sanket Kadam and M. B.
                 Srinivas",
  title =        "An Iterative Logarithmic Multiplier with Improved
                 Precision",
  crossref =     "Montuschi:2016:ISC",
  pages =        "104--111",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ARITH.2016.25",
  bibdate =      "Fri Dec 16 15:17:20 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2016; ARITH-23",
}

@TechReport{Ahrens:2016:ERF,
  author =       "Peter Ahrens and Hong Diep Nguyen and James Demmel",
  title =        "Efficient Reproducible Floating Point Summation and
                 {BLAS}",
  type =         "Report",
  number =       "UCB/EECS-2016-121",
  institution =  "EECS Department, UC Berkeley",
  address =      "Berkeley, CA, USA",
  day =          "18",
  month =        jun,
  year =         "2016",
  bibdate =      "Wed Oct 12 18:31:23 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.eecs.berkeley.edu/Pubs/TechRpts/2016/EECS-2016-121.html",
  acknowledgement = ack-nhfb,
  keywords =     "accurate dot product; accurate summation",
}

@InProceedings{Almeida:2016:VCT,
  author =       "Jos{\'e} Bacelar Almeida and Manuel Barbosa and Gilles
                 Barthe and Fran{\c{c}}ois Dupressoir and Michael Emmi",
  editor =       "T. Holz and S. Savage",
  booktitle =    "Proceedings of the {25th USENIX Security 2016, August
                 10--12, 2016, Austin, TX}",
  title =        "Verifying Constant-Time Implementations",
  publisher =    pub-USENIX,
  address =      pub-USENIX:adr,
  pages =        "53--70",
  year =         "2016",
  bibdate =      "Tue Aug 27 06:44:12 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://github.com/kmowery/libfixedtimefixedpoint;
                 https://www.usenix.org/system/files/conference/usenixsecurity16/sec16_paper_almeida.pdf",
  abstract =     "The constant-time programming discipline is an
                 effective countermeasure against timing attacks, which
                 can lead to complete breaks of otherwise secure
                 systems. However, adhering to constant-time programming
                 is hard on its own, and extremely hard under additional
                 efficiency and legacy constraints. This makes automated
                 verification of constant-time code an essential
                 component for building secure software.\par

                 We propose a novel approach for verifying constant-time
                 security of real-world code. Our approach is able to
                 validate implementations that locally and intentionally
                 violate the constant-time policy, when such violations
                 are benign and leak no more information than the public
                 outputs of the computation. Such implementations, which
                 are used in cryptographic libraries to obtain important
                 speedups or to comply with legacy APIs, would be
                 declared insecure by all prior solutions.\par

                 We implement our approach in a publicly available,
                 cross-platform, and fully automated prototype,
                 ct-verif, that leverages the SMACK and Boogie tools and
                 verifies optimized LLVM implementations. We present
                 verification results obtained over a wide range of
                 constant-time components from the NaCl, OpenSSL, FourQ
                 and other off-the-shelf libraries. The diversity and
                 scale of our examples, as well as the fact that we deal
                 with top-level APIs rather than being limited to
                 low-level leaf functions, distinguishes ct-verif from
                 prior tools.\par

                 Our approach is based on a simple reduction of
                 constant-time security of a program $P$ to safety of a
                 product program $Q$ that simulates two executions of
                 $P$. We formalize and verify the reduction for a core
                 high-level language using the Coq proof assistant.",
  acknowledgement = ack-nhfb,
  keywords =     "elliptic curve arithmetic; fixed-point arithmetic;
                 libfixedtimefixedpoint",
}

@Article{Andrysco:2016:PFP,
  author =       "Marc Andrysco and Ranjit Jhala and Sorin Lerner",
  title =        "Printing floating-point numbers: a faster, always
                 correct method",
  journal =      j-SIGPLAN,
  volume =       "51",
  number =       "1",
  pages =        "555--567",
  month =        jan,
  year =         "2016",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/2914770.2837654",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Thu Jun 9 17:13:57 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
  abstract =     "Floating-point numbers are an essential part of modern
                 software, recently gaining particular prominence on the
                 web as the exclusive numeric format of Javascript. To
                 use floating-point numbers, we require a way to convert
                 binary machine representations into human readable
                 decimal outputs. Existing conversion algorithms make
                 trade-offs between completeness and performance. The
                 classic Dragon4 algorithm by Steele and White and its
                 later refinements achieve completeness --- i.e. produce
                 correct and optimal outputs on all inputs --- by using
                 arbitrary precision integer (bignum) arithmetic which
                 leads to a high performance cost. On the other hand,
                 the recent Grisu3 algorithm by Loitsch shows how to
                 recover performance by using native integer arithmetic
                 but sacrifices optimality for 0.5\% of all inputs. We
                 present Errol, a new complete algorithm that is
                 guaranteed to produce correct and optimal results for
                 all inputs while simultaneously being 2x faster than
                 the incomplete Grisu3 and 4x faster than previous
                 complete methods.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  remark =       "POPL '16 conference proceedings.",
}

@InProceedings{Anonymous:2016:KTS,
  author =       "Anonymous",
  title =        "{Keynote} talks and special sessions",
  crossref =     "Montuschi:2016:ISC",
  pages =        "xv--xxi",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ARITH.2016.33",
  bibdate =      "Fri Dec 16 15:17:20 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2016; ARITH-23",
}

@Article{Area:2016:ACS,
  author =       "Iv{\'a}n Area and Dimitar K. Dimitrov and Eduardo
                 Godoy and Vanessa G. Paschoa",
  title =        "Approximate Calculation of Sums {II}: {Gaussian} Type
                 Quadrature",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "54",
  number =       "4",
  pages =        "2210--2227",
  month =        "????",
  year =         "2016",
  CODEN =        "SJNAAM",
  DOI =          "https://doi.org/10.1137/140993752",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  bibdate =      "Fri Sep 23 11:00:53 MDT 2016",
  bibsource =    "http://epubs.siam.org/http://epubs.siam.org/toc/sjnaam/54/4;
                 https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjnumeranal2010.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
  keywords =     "Chebfun",
  onlinedate =   "January 2016",
}

@Article{Avenel:2016:STM,
  author =       "Christophe Avenel and Pierre Fortin and Mourad Gouicem
                 and Samia Zaidi",
  title =        "Solving the {Table Maker}'s Dilemma on Current {SIMD}
                 Architectures",
  journal =      j-SCPE,
  volume =       "17",
  number =       "3",
  pages =        "237--250",
  month =        "????",
  year =         "2016",
  CODEN =        "????",
  ISSN =         "1895-1767",
  ISSN-L =       "1895-1767",
  bibdate =      "Mon Jan 7 06:46:48 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/scpe.bib",
  URL =          "https://www.scpe.org/index.php/scpe/article/view/1183",
  acknowledgement = ack-nhfb,
  fjournal =     "Scalable Computing: Practice and Experience",
  journal-URL =  "http://www.scpe.org/",
}

@Article{Bagnara:2016:EBF,
  author =       "Roberto Bagnara and Matthieu Carlier and Roberta Gori
                 and Arnaud Gotlieb",
  title =        "Exploiting binary floating-point representations for
                 constraint propagation",
  journal =      j-INFORMS-J-COMPUT,
  volume =       "28",
  number =       "1",
  pages =        "31--46",
  month =        "Winter",
  year =         "2016",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1287/ijoc.2015.0663",
  ISSN =         "1091-9856 (print), 1526-5528 (electronic)",
  ISSN-L =       "1091-9856",
  MRclass =      "68M07 (65Y04 68W40)",
  MRnumber =     "3461544",
  bibdate =      "Mon Apr 9 08:22:11 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/informs-j-comput.bib",
  URL =          "https://pubsonline.informs.org/doi/abs/10.1287/ijoc.2015.0663",
  acknowledgement = ack-nhfb,
  ajournal =     "INFORMS J. Comput.",
  fjournal =     "INFORMS Journal on Computing",
  journal-URL =  "https://pubsonline.informs.org/journal/ijoc",
  onlinedate =   "January 21, 2016",
}

@InCollection{Bailey:2016:FRS,
  author =       "David H. Bailey and Jonathan M. Borwein and Victoria
                 Stodden",
  editor =       "Harald Atmanspacher and Sabine Maasen",
  booktitle =    "Reproducibility: Principles, Problems, Practices, and
                 Prospects",
  title =        "Facilitating Reproducibility in Scientific Computing:
                 Principles and Practice",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "205--231",
  year =         "2016",
  DOI =          "https://doi.org/10.1002/9781118865064.ch9",
  ISBN =         "1-118-86506-5",
  ISBN-13 =      "978-1-118-86506-4",
  bibdate =      "Thu Aug 11 11:01:49 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This chapter discusses the roots of the
                 reproducibility problem in scientific computing, and
                 summarizes some possible solutions that have been
                 suggested in the community. Statistical overfitting can
                 be thought of as an instance of ``selection bias'',
                 wherein one presents the results of only those tests
                 that support well one's hypothesis. The problem of
                 statistical overfitting in computational science is
                 perhaps best illustrated in the field of mathematical
                 finance. Present-day researchers are not as fully aware
                 of the potential pitfalls of performance reporting. In
                 any event, various high-performance computing
                 researchers have noted a resurrection of some of these
                 questionable practices. Using high-precision arithmetic
                 (higher than the standard IEEE 64-bit arithmetic) is
                 often quite useful in ameliorating numerical
                 difficulties and enhancing reproducibility. Very
                 high-precision floating-point arithmetic is essential
                 to obtain reproducible results in experimental
                 mathematics and in related mathematical physics
                 applications. The chapter also discusses
                 reproducibility in symbolic computing.",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  keywords =     "high-performance computing; high-precision arithmetic;
                 mathematical physics; numerical reproducibility;
                 performance reporting; scientific computing;
                 statistical overfitting; symbolic computing",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  xxnote =       "This book was awarded the 2017 Prose Award
                 (``Honorable Mention'') in the category ``Textbook /
                 Best in Physical Sciences and Mathematics''; see
                 \url{https://proseawards.com/winners/2017-award-winners/}
                 and
                 \url{http://experimentalmath.org/2017/02/reproducibility-principles-problems-practices-and-prospects/}.",
}

@InProceedings{Bajard:2016:MFA,
  author =       "Jean-Claude Bajard and Julien Eynard and Nabil
                 Merkiche",
  title =        "Multi-fault Attack Detection for {RNS} Cryptographic
                 Architecture",
  crossref =     "Montuschi:2016:ISC",
  pages =        "16--23",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ARITH.2016.16",
  bibdate =      "Fri Dec 16 15:17:20 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2016; ARITH-23",
}

@Article{Ballard:2016:INS,
  author =       "Grey Ballard and Austin R. Benson and Alex Druinsky
                 and Benjamin Lipshitz and Oded Schwartz",
  title =        "Improving the Numerical Stability of Fast Matrix
                 Multiplication",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "37",
  number =       "4",
  pages =        "1382--1418",
  month =        "????",
  year =         "2016",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/15M1032168",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Fri Aug 25 09:01:43 MDT 2017",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/37/4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
  onlinedate =   "January 2016",
}

@Misc{BEBOP:2016:RRB,
  author =       "{Berkeley Benchmarking and OPtimization Group
                 (BEBOP)}",
  title =        "{ReproBLAS: Reproducible BLAS}",
  howpublished = "Web site with software downloads.",
  month =        jan,
  year =         "2016",
  bibdate =      "Sat Jan 02 18:46:46 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://bebop.cs.berkeley.edu/reproblas/",
  acknowledgement = ack-nhfb,
}

@Article{Bigou:2016:BTP,
  author =       "Karim Bigou and Arnaud Tisserand",
  title =        "Binary-Ternary Plus-Minus Modular Inversion in {RNS}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "65",
  number =       "11",
  pages =        "3495--3501",
  month =        nov,
  year =         "2016",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2016.2529625",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Oct 11 05:14:24 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Bigou:2016:HPR,
  author =       "Karim Bigou and Arnaud Tisserand",
  title =        "Hybrid Position-Residues Number System",
  crossref =     "Montuschi:2016:ISC",
  pages =        "126--133",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ARITH.2016.15",
  bibdate =      "Fri Dec 16 15:17:20 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2016; ARITH-23",
}

@Article{Biham:2016:BA,
  author =       "Eli Biham and Yaniv Carmeli and Adi Shamir",
  title =        "Bug Attacks",
  journal =      j-J-CRYPTOLOGY,
  volume =       "29",
  number =       "4",
  pages =        "775--805",
  month =        oct,
  year =         "2016",
  CODEN =        "JOCREQ",
  DOI =          "https://doi.org/10.1007/s00145-015-9209-1",
  ISSN =         "0933-2790 (print), 1432-1378 (electronic)",
  ISSN-L =       "0933-2790",
  bibdate =      "Mon Sep 12 07:07:07 MDT 2016",
  bibsource =    "http://link.springer.com/journal/145/29/4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcryptology.bib",
  URL =          "http://link.springer.com/accesspage/article/10.1007/s00145-015-9209-1;
                 http://link.springer.com/article/10.1007/s00145-015-9209-1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Cryptology",
  journal-URL =  "http://link.springer.com/journal/145",
  keywords =     "Bug attack; ElGamal encryption; Fault attack; Pohlig
                 Hellman; RSA",
  remark =       "From the abstract: ``The best-known example of such a
                 bug is the Intel division bug, which resulted in
                 slightly inaccurate results for extremely rare inputs.
                 \ldots{} such bugs can be a security disaster:
                 decrypting ciphertexts on any computer which [sic]
                 multiplies even one pair of numbers incorrectly can
                 lead to full leakage of the secret key, sometimes with
                 a single well-chosen ciphertext.",
}

@TechReport{Boldo:2016:RFA,
  author =       "Sylvie Boldo and Stef Graillat and Jean-Michel
                 Muller",
  title =        "On the robustness of the {2Sum} and {Fast2Sum}
                 algorithms",
  type =         "Report",
  number =       "ensl-01310023",
  institution =  "Inria, LRI, CNRS \& Universit{\'e} Paris-Sud,
                 Universit{\'e} Paris-Saclay, France",
  pages =        "1 + 17",
  day =          "1",
  month =        may,
  year =         "2016",
  bibdate =      "Thu May 19 10:09:03 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://hal-ens-lyon.archives-ouvertes.fr/ensl-01310023",
  abstract =     "The 2Sum and Fast2Sum algorithms are important
                 building blocks in numerical computing. They are used
                 (implicitly or explicitly) in many compensated
                 algorithms (such as compensated summation or
                 compensated polynomial evaluation). They are also used
                 for manipulating floating-point expansions. We show
                 that these algorithms are much more robust than it is
                 usually believed: the returned result makes sense even
                 when the rounding function is not round-to-nearest, and
                 they are almost immune to overflow.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}

@Article{Brisebarre:2016:CBB,
  author =       "Nicolas Brisebarre and Christoph Lauter and Marc
                 Mezzarobba and Jean-Michel Muller",
  title =        "Comparison between Binary and Decimal Floating-Point
                 Numbers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "65",
  number =       "7",
  pages =        "2032--2044",
  month =        "????",
  year =         "2016",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2015.2479602",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jun 15 06:49:34 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers -",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  remark =       "Longer report in \cite{Brisebarre:2013:CBB}.",
}

@InProceedings{Brzicova:2016:LMD,
  author =       "Marta Brzicov{\'a} and Christiane Frougny and Edita
                 Pelantov{\'a} and Milena Svobodov{\'a}",
  title =        "On-line Multiplication and Division in Real and
                 Complex Bases",
  crossref =     "Montuschi:2016:ISC",
  pages =        "134--141",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ARITH.2016.13",
  bibdate =      "Fri Dec 16 15:17:20 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2016; ARITH-23",
}

@InProceedings{Cervantes:2016:IOC,
  author =       "Adrian Cervantes and Francis Lopez and Jeffry Quiros
                 and Diego Rodriguez and Carlos Salazar-Garcia and
                 Carlos Meza and Alfonso Chacon-Rodriguez",
  booktitle =    "{2016 IEEE 36th Central American and Panama Convention
                 (CONCAPAN XXXVI)}",
  title =        "Implementation of an open core {IEEE 754}-based {FPU}
                 with non-linear arithmetic support",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--6",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/CONCAPAN.2016.7942354",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; CORDIC; Field programmable gate arrays;
                 floating point arithmetic; FPGA; Hardware; IEEE 754
                 floating point representation; Mathematical model;
                 Process control; Signal processing algorithms;
                 Standards; Verilog",
}

@Article{Chen:2016:CFP,
  author =       "Jiyang Chen and Yuanwu Lei and Yuanxi Peng and
                 Tingting He and Ziye Deng",
  title =        "Configurable Floating-Point {FFT} Accelerator on
                 {FPGA} Based Multiple-Rotation {CORDIC}",
  journal =      "Chinese Journal of Electronics",
  volume =       "25",
  number =       "6",
  pages =        "1063--1070",
  year =         "2016",
  DOI =          "https://doi.org/10.1049/cje.2016.08.002",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://onlinelibrary.wiley.com/doi/abs/10.1049/cje.2016.08.002",
  acknowledgement = ack-nhfb,
  eprint =       "https://onlinelibrary.wiley.com/doi/pdf/10.1049/cje.2016.08.002",
  keywords =     "clock frequency; configurable floating-point FFT
                 accelerator; coordinate rotation digital computer;
                 Coordinate rotation digital computer (CORDIC); CORDIC
                 algorithm; CORDIC rotation; Costs; Digital computers;
                 Fast Fourier transform (FFT); fast Fourier transform
                 accelerator; fast Fourier transforms; Fast Fourier
                 transforms; Field programmable gate arrays; floating
                 point arithmetic; Floating-point; FPGA; FPGA based
                 multiple-rotation CORDIC; hardware cost; Prediction
                 algorithms; Random access memory; Real-time systems;
                 redundant CORDIC; redundant number systems;
                 segmented-parallel iteration; signal processing; Signal
                 processing; Signal processing algorithms; Table lookup;
                 twiddle angles; twiddle direction prediction",
}

@Article{Chen:2016:DAR,
  author =       "Linbin Chen and Jie Han and Weiqiang Liu and Fabrizio
                 Lombardi",
  title =        "On the Design of Approximate Restoring Dividers for
                 Error-Tolerant Applications",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "65",
  number =       "8",
  pages =        "2522--2533",
  month =        aug,
  year =         "2016",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2015.2494005",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 18:58:52 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Chen:2016:PSA,
  author =       "D. D. Chen and G. X. Yao and R. C. Cheung and D. Pao
                 and C. K. Koc",
  title =        "Parameter Space for the Architecture of {FFT}-Based
                 {Montgomery} Modular Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "65",
  number =       "1",
  pages =        "147--160",
  month =        "????",
  year =         "2016",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2015.2417553",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Dec 15 09:36:24 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Coleman:2016:LCT,
  author =       "J. N. Coleman and R. Che Ismail",
  title =        "{LNS} with Co-Transformation Competes with
                 Floating-Point",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "65",
  number =       "1",
  pages =        "136--146",
  month =        "????",
  year =         "2016",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Dec 15 09:36:24 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Collange:2016:PFP,
  author =       "Caroline Collange and Mioara Joldes and Jean-Michel
                 Muller and Valentina Popescu",
  editor =       "{IEEE}",
  booktitle =    "{2016 IEEE 27th International Conference on
                 Application-Specific Systems, Architectures and
                 Processors (ASAP). July 6--8, 2016. Imperial College
                 London}",
  title =        "Parallel floating-point expansions for
                 extended-precision {GPU} computations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "139--146",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ASAP.2016.7760783",
  ISBN =         "1-5090-1503-5",
  ISBN-13 =      "978-1-5090-1503-0",
  ISSN =         "2160-0511 (print), 2160-052X (electronic)",
  ISSN-L =       "2160-0511",
  bibdate =      "Fri Sep 29 10:56:29 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cui:2016:PDM,
  author =       "Xiaoping Cui and Weiqiang Liu and Dong Wenwen and
                 Fabrizio Lombardi",
  title =        "A Parallel Decimal Multiplier Using Hybrid Binary
                 Coded Decimal ({BCD}) Codes",
  crossref =     "Montuschi:2016:ISC",
  pages =        "150--155",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ARITH.2016.8",
  bibdate =      "Fri Dec 16 15:17:20 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2016; ARITH-23",
}

@TechReport{Damouche:2016:TSB,
  author =       "Nasrine Damouche and Matthieu Martel and Pavel
                 Panchekha and Jason Qiu and Alex Sanchez-Stern and
                 Zachary Tatlock",
  title =        "Toward a Standard Benchmark Format and Suite for
                 Floating-Point Analysis",
  type =         "Report",
  number =       "??",
  institution =  "Universit{\'e} de Perpignan Via Domitia and University
                 of Washington",
  address =      "Perpignan, France and Seattle, WA, USA",
  pages =        "15",
  month =        jul,
  year =         "2016",
  bibdate =      "Thu Oct 17 05:26:46 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://fpbench.org/;
                 https://homes.cs.washington.edu/~ztatlock/pubs/fpbench-damouche-nsv16.pdf",
  abstract =     "We introduce FPBench, a standard benchmark format for
                 validation and optimization of numerical accuracy in
                 floating-point computations. FPBench is a first step
                 toward addressing an increasing need in our community
                 for comparisons and combinations of tools from
                 different application domains. To this end, FPBench
                 provides a basic floating-point benchmark format and
                 accuracy measures for comparing different tools. The
                 FPBench format and measures allow comparing and
                 composing different floating-point tools. We describe
                 the FPBench format and measures and show that FPBench
                 expresses benchmarks from recent papers in the
                 literature, by building an initial benchmark suite
                 drawn from these papers. We intend for FPBench to grow
                 into a standard benchmark suite for the members of the
                 floating-point tools research community",
  acknowledgement = ack-nhfb,
}

@Article{DelBarrio:2016:PCS,
  author =       "Alberto A. {Del Barrio} and Rom{\'a}n Hermida and Seda
                 Ogrenci Memik",
  title =        "A Partial Carry-Save On-the-Fly Correction
                 Multispeculative Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "65",
  number =       "11",
  pages =        "3251--3264",
  month =        nov,
  year =         "2016",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2016.2529626",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Oct 11 05:14:24 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Adders; Benchmark testing; Computer science; Delays;
                 Encoding; Mathematical model; Proposals",
}

@TechReport{Demmel:2016:ERF,
  author =       "James Demmel and Peter Ahrens and Hong Diep Nguyen",
  title =        "Efficient reproducible floating point summation and
                 {BLAS}",
  type =         "Technical Report",
  number =       "UCB/EECS-2016-121",
  institution =  "EECS Department, University of California, Berkeley",
  address =      "Berkeley, CA, USA",
  year =         "2016",
  bibdate =      "Mon Feb 10 17:49:15 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www2.eecs.berkeley.edu/Pubs/TechRpts/2016/EECS-2016-121.html",
  abstract =     "We define reproducibility to mean getting bitwise
                 identical results from multiple runs of the same
                 program, perhaps with different hardware resources or
                 other changes that should ideally not change the
                 answer. Many users depend on reproducibility for
                 debugging or correctness. However, dynamic scheduling
                 of parallel computing resources, combined with
                 nonassociativity of floating point addition, makes
                 attaining reproducibility a challenge even for simple
                 operations like summing a vector of numbers, or more
                 complicated operations like the Basic Linear Algebra
                 Subprograms (BLAS). We describe an algorithm that
                 computes a reproducible sum of floating point numbers,
                 independent of the order of summation. The algorithm
                 depends only on a subset of the IEEE Floating Point
                 Standard 754-2008. It is communication-optimal, in the
                 sense that it does just one pass over the data in the
                 sequential case, or one reduction operation in the
                 parallel case, requiring an ``accumulator'' represented
                 by just 6 floating point words (more can be used if
                 higher precision is desired). The arithmetic cost with
                 a 6-word accumulator is $ 7 n $ floating point
                 additions to sum $n$ words, and (in IEEE double
                 precision) the final error bound can be up to $ 10^( -
                 8)$ times smaller than the error bound for conventional
                 summation. We describe the basic summation algorithm,
                 the software infrastructure used to build reproducible
                 BLAS (ReproBLAS), and performance results. For example,
                 when computing the dot product of 4096 double precision
                 floating point numbers, we get a $ 4 \times $ slowdown
                 compared to Intel Math Kernel Library (MKL) running on
                 an Intel Core i7-2600 CPU operating at 3.4 GHz and 256
                 KB L2 Cache.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation; reproducible
                 floating point summation",
}

@InProceedings{Denis:2016:VCF,
  author =       "Christophe Denis and Pablo de Oliveira Castro and Eric
                 Petit",
  title =        "{Verificarlo}: Checking Floating Point Accuracy
                 through {Monte Carlo} Arithmetic",
  crossref =     "Montuschi:2016:ISC",
  pages =        "55--62",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ARITH.2016.31",
  bibdate =      "Fri Dec 16 15:17:20 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2016; ARITH-23",
}

@Article{DHollander:2016:HLS,
  author =       "Erik H. D'Hollander",
  title =        "High-Level Synthesis Optimization for Blocked
                 Floating-Point Matrix Multiplication",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "44",
  number =       "4",
  pages =        "74--79",
  month =        sep,
  year =         "2016",
  CODEN =        "CANED2",
  DOI =          "https://doi.org/10.1145/3039902.3039916",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Mon Jun 5 18:01:57 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
  abstract =     "In the last decade floating-point matrix
                 multiplication on FPGAs has been studied extensively
                 and efficient architectures as well as detailed
                 performance models have been developed. By design these
                 IP cores take a fixed footprint which not necessarily
                 optimizes the use of all available resources. Moreover,
                 the low-level architectures are not easily amenable to
                 a parameterized synthesis. In this paper high-level
                 synthesis is used to fine-tune the configuration
                 parameters in order to achieve the highest performance
                 with maximal resource utilization. An\ exploration
                 strategy is presented to optimize the use of critical
                 resources (DSPs, memory) for any given FPGA. To account
                 for the limited memory size on the FPGA, a
                 block-oriented matrix multiplication is organized such
                 that the block summation is done on the CPU while the
                 block multiplication occurs on the logic fabric
                 simultaneously. The communication overhead between the
                 CPU and the FPGA is minimized by streaming the blocks
                 in a Gray code ordering scheme which maximizes the data
                 reuse for consecutive block matrix product
                 calculations. Using highlevel synthesis optimization,
                 the programmable logic operates at 93\% of the
                 theoretical peak performance and the combined CPU-FPGA
                 design achieves 76\% of the available hardware
                 processing speed for the floating-point multiplication
                 of 2K by 2K matrices.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
  remark =       "HEART '16 conference proceedings.",
}

@InProceedings{Du:2016:AEB,
  author =       "Peibing Du and Hao Jiang and Housen Li and Lizhi Cheng
                 and Canqun Yang",
  editor =       "Hong Shen and Yingpeng Sang and Hui Tian",
  booktitle =    "Proceedings of the {Seventeenth International
                 Conference on Parallel and Distributed Computing,
                 Applications and Technologies, PDCAT 2016, Guangzhou,
                 China, December 16--18, 2016}",
  title =        "Accurate evaluation of bivariate polynomials",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "51--56",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/PDCAT.2016.026",
  ISBN =         "1-5090-5081-7, 1-5090-5082-5 (print)",
  ISBN-13 =      "978-1-5090-5081-9, 978-1-5090-5082-6 (print)",
  bibdate =      "Mon Mar 19 14:28:19 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/document/7943331/",
  acknowledgement = ack-nhfb,
  remark =       "IEEE Computer Society Order Number E5982.",
}

@InProceedings{Dukhan:2016:WFP,
  author =       "M. Dukhan and R. Vuduc and J. Riedy",
  editor =       "????",
  booktitle =    "Proceedings of the {2nd International Workshop on
                 Performance Modeling: Methods and Applications (PMMA16)
                 at ISC High Performance, Frankfurt, Germany, [June or]
                 July 2016}",
  title =        "Wanted: Floating-Point Add Round-off Error
                 instruction",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2016",
  LCCN =         "",
  bibdate =      "Wed Oct 12 18:36:50 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/1603.00491",
  acknowledgement = ack-nhfb,
}

@Article{El-Razouk:2016:NAD,
  author =       "Hayssam El-Razouk and Arash Reyhani-Masoleh",
  title =        "New Architectures for Digit-Level Single,
                 Hybrid-Double, Hybrid-Triple Field Multiplications and
                 Exponentiation Using {Gaussian} Normal Bases",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "65",
  number =       "8",
  pages =        "2495--2509",
  month =        aug,
  year =         "2016",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2015.2481408",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 18:58:52 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Emmart:2016:OMM,
  author =       "Niall Emmart and Justin Luitjens and Charles Weems and
                 Cliff Woolley",
  title =        "Optimizing Modular Multiplication for {NVIDIA}'s
                 {Maxwell} {GPUs}",
  crossref =     "Montuschi:2016:ISC",
  pages =        "47--54",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ARITH.2016.21",
  bibdate =      "Fri Dec 16 15:17:20 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2016; ARITH-23",
}

@Article{Fang:2016:OSV,
  author =       "Xin Fang and Miriam Leeser",
  title =        "Open-Source Variable-Precision Floating-Point Library
                 for Major Commercial {FPGAs}",
  journal =      j-TRETS,
  volume =       "9",
  number =       "3",
  pages =        "1--17",
  month =        jul,
  year =         "2016",
  DOI =          "https://doi.org/10.1145/2851507",
  ISSN =         "1936-7406 (print), 1936-7414 (electronic)",
  ISSN-L =       "1936-7406",
  bibdate =      "Sat Feb 8 10:53:20 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/gnu.bib;
                 https://www.math.utah.edu/pub/tex/bib/trets.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/2851507",
  abstract =     "There is increased interest in implementing
                 floating-point designs for different precisions that
                 take advantage of the flexibility offered by
                 Field-Programmable Gate Arrays (FPGAs). In this
                 article, we present updates to the Variable-precision
                 FLOATing Point Library (VFLOAT) developed at
                 Northeastern University and highlight recent
                 improvements in implementations for implementing
                 reciprocal, division, and square root components that
                 scale to double precision for FPGAs from the two major
                 vendors: Altera and Xilinx. Our library is open source
                 and flexible and provides the user with many options. A
                 designer has many tradeoffs to consider including clock
                 frequency, total latency, and resource usage as well as
                 target architecture. We compare the generated cores to
                 those produced by each vendor and to another popular
                 open-source tool: FloPoCo. VFLOAT has the advantage of
                 not tying the user's design to a specific target
                 architecture and of providing the maximum flexibility
                 for all options including clock frequency and latency
                 compared to other alternatives. Our results show that
                 variable-precision as well as double-precision designs
                 can easily be accommodated and the resulting components
                 are competitive and in many cases superior to the
                 alternatives.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Reconfigurable Technology and
                 Systems (TRETS)",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J1151",
}

@TechReport{Fevotte:2016:VAF,
  author =       "Fran{\c{c}}ois F{\'e}votte and Bruno Lathuili{\`e}re",
  title =        "{VERROU}: Assessing Floating-Point Accuracy Without
                 Recompiling",
  type =         "Working paper",
  number =       "??",
  institution =  "????",
  address =      "????",
  month =        oct,
  year =         "2016",
  bibdate =      "Thu Oct 17 05:30:32 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://hal.archives-ouvertes.fr/hal-01383417",
  acknowledgement = ack-nhfb,
}

@Article{Fritz:2016:IPM,
  author =       "Christopher Fritz and Adly T. Fam",
  title =        "Interlaced Partition Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "65",
  number =       "8",
  pages =        "2672--2677",
  month =        aug,
  year =         "2016",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2015.2481379",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 18:58:52 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Garcia-Vega:2016:DMO,
  author =       "Carlos Garcia-Vega and Sonia Gonzalez-Navarro and
                 Pedro Balboa-La Chica and Julio Villalba-Moreno",
  title =        "Decimal Multiformat Online Addition",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "65",
  number =       "10",
  pages =        "3203--3209",
  month =        "????",
  year =         "2016",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2016.2516009",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Sep 13 06:19:58 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Garrido:2016:CIN,
  author =       "Mario Garrido and Petter K{\"a}llstr{\"o}m and Martin
                 Kumm and Oscar Gustafsson",
  title =        "{CORDIC II}: A New Improved {CORDIC} Algorithm",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
  volume =       "63",
  number =       "2",
  pages =        "186--190",
  month =        feb,
  year =         "2016",
  DOI =          "https://doi.org/10.1109/TCSII.2015.2483422",
  ISSN =         "1549-7747 (print), 1558-3791 (electronic)",
  ISSN-L =       "1549-7747",
  bibdate =      "Sat Feb 8 10:11:25 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems II: Express
                 Briefs",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
  keywords =     "Adders; Convergence; CORDIC; CORDIC II; digital
                 arithmetic; friend angles; Hardware; Kernel;
                 Multiplexing; nano-rotation; nanorotation; rotation;
                 rotation angle; Signal processing algorithms; uniformly
                 scaled redundant (USR) CORDIC; USR",
}

@Article{Garrido:2016:MUG,
  author =       "Mario Garrido and Rikard Andersson and Fahad Qureshi
                 and Oscar Gustafsson",
  title =        "Multiplierless Unity-Gain {SDF} {FFTs}",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "24",
  number =       "9",
  pages =        "3003--3007",
  year =         "2016",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/TVLSI.2016.2542583",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
  keywords =     "Adders; Algorithm design and analysis; Combined
                 coefficient selection and shift-and-add implementation
                 (CCSSI); Computer architecture; coordinate rotation
                 digital computer (CORDIC); fast Fourier transform
                 (FFT); Fast Fourier transforms; Hardware;
                 multiplierless; pipelined architecture; single-delay
                 feedback (SDF); Throughput; unity gain; Very large
                 scale integration",
}

@InProceedings{Geran:2016:CBC,
  author =       "Amir Ali Kouzeh Geran and Arash Reyhani-Masoleh",
  title =        "A {CRC}-Based Concurrent Fault Detection Architecture
                 for {Galois\slash Counter Mode (GCM)}",
  crossref =     "Montuschi:2016:ISC",
  pages =        "24--31",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ARITH.2016.19",
  bibdate =      "Fri Dec 16 15:17:20 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2016; ARITH-23",
}

@InProceedings{Gueron:2016:ABI,
  author =       "Shay Gueron and Vlad Krasnov",
  title =        "Accelerating Big Integer Arithmetic Using {Intel}
                 {IFMA} Extensions",
  crossref =     "Montuschi:2016:ISC",
  pages =        "32--38",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ARITH.2016.22",
  bibdate =      "Fri Dec 16 15:17:20 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2016; ARITH-23; integer fused multiply-add
                 (IFMA)",
}

@InProceedings{Gueron:2016:HIA,
  author =       "Shay Gueron and Sanu Mathew",
  title =        "Hardware Implementation of {AES} Using Area-Optimal
                 Polynomials for Composite-Field Representation {$
                 \mathrm {GF}(2^4)^2 $} of {$ \mathrm {GF}(2^8) $}",
  crossref =     "Montuschi:2016:ISC",
  pages =        "112--117",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ARITH.2016.32",
  bibdate =      "Fri Dec 16 15:17:20 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2016; ARITH-23",
}

@Misc{Gustafson:2016:BFP,
  author =       "John L. Gustafson",
  title =        "Beyond Floating Point: Next Generation Computer
                 Arithmetic",
  howpublished = "Stanford seminar video.",
  year =         "2016",
  bibdate =      "Thu Dec 14 16:05:07 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.johngustafson.net/pdfs/DebateTranscription.pdf;
                 https://www.youtube.com/watch?v=aP0Y1uAA-2Y",
  acknowledgement = ack-nhfb,
}

@Article{Gustafson:2016:RAC,
  author =       "John L. Gustafson",
  title =        "A Radical Approach to Computation with Real Numbers",
  journal =      j-SUPERFRI,
  volume =       "3",
  number =       "2",
  pages =        "38--53",
  month =        "????",
  year =         "2016",
  CODEN =        "????",
  DOI =          "https://doi.org/10.14529/jsfi160203",
  ISSN =         "2409-6008 (print), 2313-8734 (electronic)",
  ISSN-L =       "2313-8734",
  bibdate =      "Sat Nov 11 07:15:27 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/superfri.bib",
  URL =          "http://superfri.org/superfri/article/view/94",
  acknowledgement = ack-nhfb,
  fjournal =     "Supercomputing Frontiers and Innovations",
  journal-URL =  "http://superfri.org/superfri/issue/archive",
}

@Misc{Gustafson:2016:TGD,
  author =       "John Gustafson and William Kahan",
  title =        "Transcription of {``The} Great Debate'': {John
                 Gustafson} vs. {William Kahan} on Unum Arithmetic",
  howpublished = "Web document.",
  pages =        "50",
  day =          "12",
  month =        jul,
  year =         "2016",
  bibdate =      "Thu Jan 18 06:36:55 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.johngustafson.net/pdfs/DebateTranscription.pdf;
                 https://www.youtube.com/watch?v=KEAKYDyUua4",
  acknowledgement = ack-nhfb,
}

@Article{Hopkins:2016:WMN,
  author =       "David Hopkins",
  title =        "Will my numbers add up correctly if {I} round them?",
  journal =      j-MATH-GAZ,
  volume =       "100",
  number =       "549",
  pages =        "396--409",
  month =        nov,
  year =         "2016",
  CODEN =        "MAGAAS",
  DOI =          "https://doi.org/10.1017/mag.2016.104",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  ISSN-L =       "0025-5572",
  bibdate =      "Thu Nov 17 10:32:54 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib",
  note =         "The probability that rounding after fixed-point
                 summation of $n$ terms gives the same result as
                 summation of rounded terms is given by $ p(n) = (2 /
                 \pi) \int_0^\infty (\sin (x) / x)^{n + 1} \, d x$, and
                 that function is always a rational number. Its values
                 are $ p(n) = 1, 3 / 4, 2 / 3, 115 / 192, 11 / 20, 5887
                 / 11520, 151 / 315, 259723 / 573440, \ldots {}$ for $ n
                 = 1$ to $8$.",
  URL =          "https://www.cambridge.org/core/product/88F5753DFE9F0DDDEAD1F2552B0F8B22",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Gaz.",
  fjournal =     "The Mathematical Gazette",
  journal-URL =  "http://journals.cambridge.org/action/displayIssue?jid=MAG;
                 http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
  keywords =     "correct rounding; floating-point arithmetic; rounding
                 in fixed-point addition",
  onlinedate =   "17 October 2016",
  remark-1 =     "See also \cite{Nelsen:1987:PSR} for an earlier
                 independent derivation of part of this work.",
  remark-2 =     "From a Maple computer-algebra session: \\
                 p := proc(n) return (2/Pi) * int((sin(x)/x)^(n+1), x =
                 0 .. infinity); end proc; \\
                 for k from 1 to 20 do printf({"}%2d\t%a\n{"}, k, p(k))
                 end do; \\
                 1 1 \\
                 2 3/4 \\
                 3 2/3 \\
                 4 115/192 \\
                 5 11/20 \\
                 6 5887/11520 \\
                 7 151/315 \\
                 8 259723/573440 \\
                 9 15619/36288 \\
                 10 381773117/928972800 \\
                 11 655177/1663200 \\
                 12 20646903199/54499737600 \\
                 13 27085381/74131200 \\
                 14 467168310097/1322526965760 \\
                 15 2330931341/6810804000 \\
                 16 75920439315929441/228532659683328000 \\
                 17 12157712239/37638881280 \\
                 18 5278968781483042969/16783438527143608320 \\
                 19 37307713155613/121645100408832 \\
                 20 9093099984535515162569/30370031620545576960000 \\
                 for k from 10 to 100 by 10 do printf({"}%2d\t%.4f\n{"},
                 k, evalf(p(k),20)) end do; \\
                 10 0.4110 \\
                 20 0.2994 \\
                 30 0.2470 \\
                 40 0.2150 \\
                 50 0.1929 \\
                 60 0.1765 \\
                 70 0.1637 \\
                 80 0.1533 \\
                 90 0.1446 \\
                 100 NaN \\
                 Maple evaluates p(100) as undefined / Pi.",
  remark-3 =     "Equivalent code in the Mathematica computer-algebra
                 system is \\
                 p = Function[n, (2 / Pi) * Integrate[(Sin[x] / x)^(n +
                 1), {x, 0, Infinity}]]; \\
                 For[k = 1, k <= 20, ++k, Print[k, {"} {"}, p[k]]]\\
                 \ldots{} \\
                 Mathematica finds p[100] = 0.137307\ldots{}",
  remark-4 =     "The Maxima computer-algebra system is unable to
                 evaluate p(n) := (2 / %pi) * int((sin(x) / x)^(n + 1),
                 x, 0, inf);.",
}

@Article{Hormigo:2016:MIW,
  author =       "Javier Hormigo and Julio Villalba-Moreno",
  title =        "Measuring Improvement When Using {HUB} Formats to
                 Implement Floating-Point Systems under
                 Round-to-Nearest",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "24",
  number =       "6",
  pages =        "2369--2377",
  month =        jun,
  year =         "2016",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/TVLSI.2015.2502318",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Mon Feb 10 08:19:41 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/document/7349231",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
  keywords =     "HUB (Half-Unit-Biased) floating-point format",
}

@Article{Hormigo:2016:NFC,
  author =       "Javier Hormigo and Julio Villalba",
  title =        "New Formats for Computing with Real-Numbers under
                 Round-to-Nearest",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "65",
  number =       "7",
  pages =        "2158--2168",
  month =        "????",
  year =         "2016",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2015.2479623",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jun 15 06:49:34 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers -",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Hsu:2016:TPE,
  author =       "J. Hsu",
  title =        "Three paths to exascale supercomputing",
  journal =      j-IEEE-SPECTRUM,
  volume =       "53",
  number =       "1",
  pages =        "14--15",
  month =        jan,
  year =         "2016",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.2016.7367447",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Sat Jan 18 07:02:09 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/super.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "exascale computers; exascale supercomputing; floating
                 point arithmetic; floating-point operations;
                 high-performance computing; parallel machines",
}

@MastersThesis{Hunhold:2016:UNF,
  author =       "Laslo Hunhold",
  title =        "The {Unum} Number Format: Mathematical Foundations,
                 Implementation and Comparison to {IEEE 754}
                 Floating-Point Numbers",
  type =         "{Bachelorarbeit}",
  school =       "Universit{\"a}t zu K{\"o}ln",
  address =      "K{\"o}ln, Germany",
  pages =        "iv + 91",
  day =          "8",
  month =        nov,
  year =         "2016",
  bibdate =      "Fri Jan 06 19:16:38 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://frign.de/publications/2016-11-08-the_unum_number_format.pdf",
  abstract =     "This thesis examines a modern concept for machine
                 numbers based on interval arithmetic called `Unums' and
                 compares it to IEEE 754 floating-point arithmetic,
                 evaluating possible uses of this format where
                 floating-point numbers are inadequate. In the course of
                 this examination, this thesis builds theoretical
                 foundations for IEEE 754 floating-point numbers,
                 interval arithmetic based on the projectively extended
                 real numbers and Unums.",
  acknowledgement = ack-nhfb,
  advisor =      "Angela Kunoth and Samuel Leweke",
  keywords =     "interval arithmetic; Unum",
}

@Article{Isupov:2016:AMC,
  author =       "Konstantin Isupov",
  title =        "An Algorithm for Magnitude Comparison in {RNS} based
                 on Mixed-Radix Conversion {II}",
  journal =      j-INT-J-COMP-APPL,
  volume =       "141",
  number =       "??",
  pages =        "1--4",
  month =        may,
  year =         "2016",
  CODEN =        "????",
  DOI =          "https://doi.org/10.5120/ijca2016909626",
  ISSN =         "0975-8887",
  ISSN-L =       "0975-8887",
  bibdate =      "Fri Jan 24 09:27:51 MST 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/intjcompappl.bib",
  URL =          "https://www.ijcaonline.org/archives/volume141/number5/24777-2016909626/",
  acknowledgement = ack-nhfb,
  ajournal =     "Intern. J. of Computer Applications",
  articleno =    "5",
  fjournal =     "International Journal of Computer Applications",
  journal-URL =  "https://www.ijcaonline.org/",
}

@InProceedings{Jaberipur:2016:FFC,
  author =       "Ghassem Jaberipur and Behrooz Parhami and Dariush
                 Abedi",
  title =        "A Formulation of Fast Carry Chains Suitable for
                 Efficient Implementation with Majority Elements",
  crossref =     "Montuschi:2016:ISC",
  pages =        "8--15",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ARITH.2016.14",
  bibdate =      "Fri Dec 16 15:17:20 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2016; ARITH-23",
}

@Misc{Jaeger:2016:OHQ,
  author =       "Andreas Jaeger",
  title =        "{OpenLibm}: A high quality system independent,
                 portable, open source libm implementation",
  howpublished = "Web site",
  year =         "2016",
  bibdate =      "Thu Oct 17 05:37:38 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://openlibm.org/",
  abstract =     "OpenLibm is an effort to have a high quality,
                 portable, standalone C mathematical library (libm). It
                 can be used standalone in applications and programming
                 language implementations. The project was born out of a
                 need to have a good libm for the Julia programming
                 langage that worked consistently across compilers and
                 operating systems, and in 32-bit and 64-bit
                 environments.",
  acknowledgement = ack-nhfb,
}

@Article{Jeannerod:2016:RIE,
  author =       "Claude-Pierre Jeannerod",
  title =        "A Radix-Independent Error Analysis of the
                 {Cornea--Harrison--Tang} Method",
  journal =      j-TOMS,
  volume =       "42",
  number =       "3",
  pages =        "19:1--19:20",
  month =        may,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2824252",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 23 16:40:02 MDT 2016",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Assuming floating-point arithmetic with a fused
                 multiply-add operation and rounding to nearest, the
                 Cornea--Harrison--Tang method aims to evaluate
                 expressions of the form $ a b + c d $ with high
                 relative accuracy. In this article, we provide a
                 rounding error analysis of this method, which unlike
                 previous studies is not restricted to binary
                 floating-point arithmetic but holds for any radix $
                 \beta $. We show first that an asymptotically optimal
                 bound on the relative error of this method is $ 2 \beta
                 u + 2 u^2 / \beta - 2 u^2 = 2 u + 2 / \beta u^2 + O
                 (u^3) $, where $ u = 1 / 2 \beta^{1 - p} $ is the unit
                 roundoff in radix $ \beta $ and precision $p$. Then we
                 show that the possibility of removing the $ O (u^2)$
                 term from this bound is governed by the radix parity
                 and the tie-breaking strategy used for rounding: if $
                 \beta $ is odd or rounding is to nearest even, then the
                 simpler bound $ 2 u$ is obtained, while if $ \beta $ is
                 even and rounding is to nearest away, then there exist
                 floating-point inputs $a$, $b$, $c$, $d$ that lead to a
                 relative error larger than $ 2 u + 2 / \beta u^2 - 4
                 u^3$. All these results hold provided underflows and
                 overflows do not occur and under some mild assumptions
                 on $p$ satisfied by IEEE 754-2008 formats.",
  acknowledgement = ack-nhfb,
  articleno =    "19",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Jeannerod:2016:SEB,
  author =       "Claude-Pierre Jeannerod and Nicolas Louvet and
                 Jean-Michel Muller and Antoine Plet",
  title =        "Sharp error bounds for complex floating-point
                 inversion",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "73",
  number =       "3",
  pages =        "735--760",
  month =        nov,
  year =         "2016",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-016-0115-x",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Wed Mar 1 09:12:13 MST 2017",
  bibsource =    "http://link.springer.com/journal/11075/73/3;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "http://link.springer.com/article/10.1007/s11075-016-0115-x",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Article{Jiang:2016:ARB,
  author =       "Honglan Jiang and Jie Han and Fei Qiao and Fabrizio
                 Lombardi",
  title =        "Approximate Radix-8 {Booth} Multipliers for Low-Power
                 and High-Performance Operation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "65",
  number =       "8",
  pages =        "2638--2644",
  month =        aug,
  year =         "2016",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2015.2493547",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Jul 11 18:58:52 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Joldes:2016:AAE,
  author =       "Mioara Joldes and Olivier Marty and Jean-Michel Muller
                 and Valentina Popescu",
  title =        "Arithmetic Algorithms for Extended Precision Using
                 Floating-Point Expansions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "65",
  number =       "4",
  pages =        "1197--1210",
  month =        "????",
  year =         "2016",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2015.2441714",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Mar 19 07:47:06 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers -",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Kadric:2016:APF,
  author =       "Edin Kadric and Paul Gurniak and Andr{\'e} DeHon",
  title =        "Accurate Parallel Floating-Point Accumulation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "65",
  number =       "11",
  pages =        "3224--3238",
  month =        nov,
  year =         "2016",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2016.2532874",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Oct 11 05:14:24 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "accurate floating-point summation; floating-point
                 arithmetic; rounding errors",
}

@Book{Kneusel:2016:NC,
  author =       "Ronald T. Kneusel",
  title =        "Numbers and Computers",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xi + 231",
  year =         "2016",
  ISBN =         "3-319-35940-1 (softcover), 3-319-17260-3 (e-book)",
  ISBN-13 =      "978-3-319-35940-3 (softcover), 978-3-319-17260-6
                 (e-book)",
  LCCN =         "QA241 .K54 2016",
  bibdate =      "Tue Aug 22 05:53:26 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This is a book about numbers and how those numbers are
                 represented in and operated on by computers. It is
                 crucial that developers understand this area because
                 the numerical operations allowed by computers, and the
                 limitations of those operations, especially in the area
                 of floating point math, affect virtually everything
                 people try to do with computers. This book aims to fill
                 this gap by exploring, in sufficient but not
                 overwhelming detail, just what it is that computers do
                 with numbers. Divided into two parts, the first deals
                 with standard representations of integers and floating
                 point numbers, while the second details several other
                 number representations. Each chapter ends with
                 exercises to review the key points. Topics covered
                 include interval arithmetic, fixed-point numbers,
                 floating point numbers, big integers and rational
                 arithmetic. This book is for anyone who develops
                 software including software engineering, scientists,
                 computer science students, engineering students and
                 anyone who programs for fun.",
  acknowledgement = ack-nhfb,
  subject =      "Number theory; Numerals; Numeration; Computer science;
                 Mathematics",
  tableofcontents = "Number Systems \\
                 Integers \\
                 Floating Point \\
                 Big Integers and Rational Arithmetic \\
                 Fixed-Point Numbers \\
                 Decimal Floating Point \\
                 Interval Arithmetic",
}

@Book{Kumm:2016:MCM,
  author =       "Martin Kumm",
  title =        "Multiple Constant Multiplication Optimizations for
                 Field Programmable Gate Arrays",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xxxiii + 206 + 47",
  year =         "2016",
  DOI =          "https://doi.org/10.1007/978-3-658-13323-8",
  ISBN =         "3-658-13322-8 (print), 3-658-13323-6 (e-book)",
  ISBN-13 =      "978-3-658-13322-1 (print), 978-3-658-13323-8
                 (e-book)",
  LCCN =         "TK7895.G36",
  bibdate =      "Fri Dec 8 13:11:57 MST 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://link.springer.com/book/10.1007/978-3-658-13323-8",
  abstract =     "This work covers field programmable gate array
                 (FPGA)-specific optimizations of circuits computing the
                 multiplication of a variable by several constants,
                 commonly denoted as multiple constant multiplication
                 (MCM). These optimizations focus on low resource usage
                 but high performance. They comprise the use of fast
                 carry-chains in adder-based constant multiplications
                 including ternary (3-input) adders as well as the
                 integration of look-up table-based constant multipliers
                 and embedded multipliers to get the optimal mapping to
                 modern FPGAs. The proposed methods can be used for the
                 efficient implementation of digital filters, discrete
                 transforms and many other circuits in the domain of
                 digital signal processing, communication and image
                 processing.",
  acknowledgement = ack-nhfb,
  subject =      "Engineering; Computer hardware; Applied mathematics;
                 Engineering mathematics; Electrical engineering;
                 Ing{\'e}nierie; Math{\'e}matiques de l'ing{\'e}nieur;
                 G{\'e}nie {\'e}lectrique; engineering.; electrical
                 engineering.; Electrical engineering.; Engineering.;
                 Engineering mathematics.",
  tableofcontents = "Front Matter / i--xxxiii \\
                 Introduction / 1--7 \\
                 Background / 9--35 \\
                 The Pipelined Multiple Constant Multiplication Problem
                 \\
                 Front Matter / 37--37 \\
                 Optimal Pipelining of Precomputed Adder Graphs / 39--51
                 \\
                 The Reduced Pipelined Adder Graph Algorithm / 53--85
                 \\
                 Optimally Solving MCM Related Problems Using Integer
                 Linear Programming / 87--111 \\
                 A Heuristic for the Constant Matrix Multiplication
                 Problem / 113--124 \\
                 FPGA Specific MCM Optimizations \\
                 Front Matter / 125--125 \\
                 Combining Adder Graphs with LUT-Based Constant
                 Multipliers / 127--137 \\
                 Optimization of Hybrid Adder Graphs Containing Embedded
                 Multipliers / 139--152 \\
                 Floating Point Multiple Constant Multiplication /
                 153--162 \\
                 Optimization of Adder Graphs with Ternary (3-Input)
                 Adders / 163--175 \\
                 Conclusion and Future Work / 177--179 \\
                 Back Matter / 181--206",
}

@InProceedings{Langhammer:2016:SPN,
  author =       "Martin Langhammer and Bogdan Pasca",
  title =        "Single Precision Natural Logarithm Architecture for
                 Hard Floating-Point and {DSP}-Enabled {FPGAs}",
  crossref =     "Montuschi:2016:ISC",
  pages =        "164--171",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ARITH.2016.20",
  bibdate =      "Fri Dec 16 15:17:20 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2016; ARITH-23",
}

@InProceedings{Langlois:2016:RNR,
  author =       "Philippe Langlois and Rafife Nheili and Christophe
                 Denis",
  title =        "Recovering Numerical Reproducibility in Hydrodynamic
                 Simulations",
  crossref =     "Montuschi:2016:ISC",
  pages =        "63--70",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ARITH.2016.27",
  bibdate =      "Fri Dec 16 15:17:20 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2016; ARITH-23",
}

@InProceedings{Lauter:2016:NOS,
  author =       "Christoph Lauter",
  editor =       "Michael B. Matthews",
  booktitle =    "Conference Record of the {Fiftieth Asilomar Conference
                 on Signals, Systems and Computers, November 6--9, 2016
                 Pacific Grove, California}",
  title =        "A new open-source {SIMD} vector {\tt libm} fully
                 implemented with high-level scalar {C}",
  volume =       "11",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "407--411",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ACSSC.2016.7869070",
  bibdate =      "Fri Nov 14 15:21:14 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/document/7869070",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1109/IEEECONF38270.2016",
  remark =       "From the abstract: ``We present an Open-Source vector
                 libm implemented with high-level scalar C that a modern
                 compiler can translate to SIMD code. The error of all
                 functions does not exceed 8ulp, while a performance
                 gain of up to 278.5\% is obtained. Our library is fully
                 free-standing, i.e. it does not depend on any other
                 system library.''",
}

@TechReport{Lee:2016:VBM,
  author =       "Wonyeol Lee and Rahul Sharma and Alex Aiken",
  title =        "Verifying Bit-Manipulations of Floating-Point",
  type =         "Report",
  institution =  "Stanford University",
  address =      "Stanford, CA, USA",
  pages =        "15",
  day =          "15",
  month =        apr,
  year =         "2016",
  bibdate =      "Mon May 23 16:07:51 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://theory.stanford.edu/~aiken/publications/papers/pldi16b.pdf",
  acknowledgement = ack-nhfb,
  remark =       "To appear in ACM PLDI'2016 conference proceedings,
                 usually published as an issue of \booktitle{ACM SIGPLAN
                 Notices}.",
}

@InProceedings{Lefevre:2016:CRA,
  author =       "Vincent Lef{\`e}vre",
  title =        "Correctly Rounded Arbitrary-Precision Floating-Point
                 Summation",
  crossref =     "Montuschi:2016:ISC",
  pages =        "71--78",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ARITH.2016.9",
  bibdate =      "Fri Dec 16 15:17:20 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate summation; ARITH 2016; ARITH-23; correct
                 rounding; floating-point arithmetic",
}

@TechReport{Lefevre:2016:OBB,
  author =       "Vincent Lef{\`e}vre and Paul Zimmermann",
  title =        "Optimized {Binary64} and {Binary128} Arithmetic with
                 {GNU MPFR}",
  type =         "Report",
  number =       "hal-01502326",
  institution =  "Inria Grenoble --- Rh{\^o}ne-Alpes, LIP ---
                 Laboratoire de l'Informatique du Parall{\'e}lisme and
                 Inria Nancy --- Grand Est, LORIA --- ALGO ---
                 Department of Algorithms, Computation, Image and
                 Geometry",
  pages =        "10",
  month =        apr,
  year =         "2016",
  bibdate =      "Wed Apr 05 06:51:37 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/gnu.bib",
  note =         "To appear in IEEE ARITH'2016 proceedings London, UK
                 (24--26 July, 2016).",
  URL =          "https://hal.inria.fr/hal-01502326",
  abstract =     "We describe algorithms used to optimize the GNU MPFR
                 library when the operands fit into one or two words. On
                 modern processors, a correctly rounded addition of two
                 quadruple precision numbers is now performed in 22
                 cycles, a subtraction in 24 cycles, a multiplication in
                 32 cycles, a division in 64 cycles, and a square root
                 in 69 cycles. We also introduce a new faithful rounding
                 mode, which enables even faster computations. Those
                 optimizations will be available in version 4 of MPFR.",
  acknowledgement = ack-nhfb,
}

@InProceedings{LeMaire:2016:CFP,
  author =       "Julien {Le Maire} and Nicolas Brunie and Florent de
                 Dinechin and Jean-Michel Muller",
  title =        "Computing floating-point logarithms with fixed-point
                 operations",
  crossref =     "Montuschi:2016:ISC",
  pages =        "156--163",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ARITH.2016.24",
  bibdate =      "Fri Dec 16 15:17:20 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2016; ARITH-23",
}

@InProceedings{Li:2016:SDT,
  author =       "Ang Li and Shuaiwen Leon Song and Mark Wijtvliet and
                 Akash Kumar and Henk Corporaal",
  booktitle =    "{ICS'16}: Proceedings of the {2016 International
                 Conference on Supercomputing, Istanbul Turkey, June
                 1--3, 2016}",
  title =        "{SFU}-Driven Transparent Approximation Acceleration on
                 {GPUs}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "1--14",
  month =        jun,
  year =         "2016",
  DOI =          "https://doi.org/10.1145/2925426.2926255",
  ISBN =         "1-4503-4361-9",
  ISBN-13 =      "978-1-4503-4361-9",
  LCCN =         "QA76.88",
  bibdate =      "Mon Sep 11 07:17:26 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Approximate computing, the technique that sacrifices
                 certain amount of accuracy in exchange for substantial
                 performance boost or power reduction, is one of the
                 most promising solutions to enable power control and
                 performance scaling towards exascale. Although most
                 existing approximation designs target the emerging
                 data-intensive applications that are comparatively more
                 error-tolerable, there is still high demand for the
                 acceleration of traditional scientific applications
                 (e.g., weather and nuclear simulation), which often
                 comprise intensive transcendental function calls and
                 are very sensitive to accuracy loss. To address this
                 challenge, we focus on a very important but long
                 ignored approximation unit on today's commercial GPUs
                 the special-function unit (SFU), and clarify its unique
                 role in performance acceleration of accuracy-sensitive
                 applications in the context of approximate computing.
                 To better understand its features, we conduct a
                 thorough empirical analysis on three generations of
                 NVIDIA GPU architectures to evaluate all the
                 single-precision and double-precision numeric
                 transcendental functions that can be accelerated by
                 SFUs, in terms of their performance, accuracy and power
                 consumption. Based on the insights from the evaluation,
                 we propose a transparent, tractable and portable design
                 framework for SFU-driven approximate acceleration on
                 GPUs. Our design is software-based and requires no
                 hardware or application modifications. Experimental
                 results on three NVIDIA GPU platforms demonstrate that
                 our proposed framework can provide fine-grained tuning
                 for performance and accuracy trade-offs, thus
                 facilitating applications to achieve the maximum
                 performance under certain accuracy constraints.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lichtenau:2016:QPF,
  author =       "Cedric Lichtenau and Steven Carlough and Silvia
                 Melitta Mueller",
  title =        "Quad Precision Floating Point on the {IBM z13}",
  crossref =     "Montuschi:2016:ISC",
  pages =        "87--94",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ARITH.2016.26",
  bibdate =      "Fri Dec 16 15:17:20 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2016; ARITH-23",
}

@Article{Liu:2016:DAI,
  author =       "W. Liu and L. Chen and C. Wang and M. O'Neill and F.
                 Lombardi",
  title =        "Design and Analysis of Inexact Floating-Point Adders",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "65",
  number =       "1",
  pages =        "308--314",
  month =        "????",
  year =         "2016",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2015.2417549",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Dec 15 09:36:24 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Martin-Dorel:2016:PTB,
  author =       "{\'E}rik Martin-Dorel and Guillaume Melquiond",
  title =        "Proving Tight Bounds on Univariate Expressions with
                 Elementary Functions in {Coq}",
  journal =      j-J-AUTOM-REASON,
  volume =       "57",
  number =       "3",
  pages =        "187--217",
  month =        oct,
  year =         "2016",
  CODEN =        "JAREEW",
  DOI =          "https://doi.org/10.1007/s10817-015-9350-4",
  ISSN =         "0168-7433 (print), 1573-0670 (electronic)",
  ISSN-L =       "0168-7433",
  bibdate =      "Fri Sep 2 06:39:36 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
  URL =          "http://link.springer.com/accesspage/article/10.1007/s10817-015-9350-4",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Autom. Reason.",
  fjournal =     "Journal of Automated Reasoning",
  journal-URL =  "http://link.springer.com/journal/10817",
}

@Article{Mascarenhas:2016:FPN,
  author =       "W. F. Mascarenhas",
  title =        "Floating point numbers are real numbers",
  journal =      "arxiv.org",
  pages =        "57",
  month =        may,
  year =         "2016",
  bibdate =      "Tue May 31 07:07:46 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/1605.09202",
  abstract =     "Floating-point arithmetic allows us to use a finite
                 machine, the digital computer, to reach conclusions
                 about models based on continuous mathematics. In this
                 article we work in the other direction, that is, we
                 present examples in which continuous mathematics leads
                 to sharp, simple and new results about the evaluation
                 of sums, square roots and dot products in floating
                 point arithmetic.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "1605.09202",
  keywords =     "Mathematics - Numerical Analysis",
  primaryclass = "math.NA",
}

@InProceedings{Meloni:2016:RDR,
  author =       "Nicolas M{\'e}loni and M. Anwar Hasan",
  title =        "Random Digit Representation of Integers",
  crossref =     "Montuschi:2016:ISC",
  pages =        "118--125",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ARITH.2016.11",
  bibdate =      "Fri Dec 16 15:17:20 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2016; ARITH-23; modular exponentiation",
}

@Article{Montuschi:2016:MCA,
  author =       "Paolo Montuschi and Jean-Michel Muller",
  title =        "Modern Computer Arithmetic",
  journal =      j-IEEE-CGA,
  volume =       "49",
  number =       "9",
  pages =        "12--12",
  month =        sep,
  year =         "2016",
  CODEN =        "ICGADZ",
  DOI =          "https://doi.org/10.1109/MC.2016.277",
  ISSN =         "0272-1716 (print), 1558-1756 (electronic)",
  ISSN-L =       "0272-1716",
  bibdate =      "Tue Oct 25 06:11:19 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeecga.bib",
  URL =          "https://www.computer.org/csdl/mags/co/2016/09/mco2016090012.html",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Computer Graphics and Applications",
  journal-URL =  "http://www.computer.org/portal/web/csdl/magazines/cga",
  remark =       "This one-page editorial draws attention to three
                 papers on computer arithmetic in \booktitle{IEEE
                 Transactions on Computers}
                 \cite{Demmel:2015:PRS,Joldes:2016:AAE,Chen:2016:DAR}..",
}

@InProceedings{Morancho:2016:UAF,
  author =       "Enric Morancho",
  booktitle =    "{2016 Euromicro Conference on Digital System Design
                 (DSD)}",
  title =        "Unum: Adaptive Floating-Point Arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "651--656",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/DSD.2016.39",
  bibdate =      "Fri Dec 15 07:38:18 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Moroz:2016:FCI,
  author =       "Leonid V. Moroz and Cezary J. Walczyk and Andriy
                 Hrynchyshyn and Vijay Holimath and Jan L.
                 Cie{\'s}li{\'n}ski",
  title =        "Fast calculation of inverse square root with the use
                 of magic constant --- analytical approach",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--23",
  day =          "14",
  month =        mar,
  year =         "2016",
  DOI =          "https://doi.org/10.48550/arXiv.1603.04483",
  bibdate =      "Wed Dec 20 07:34:12 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/pdf/1603.04483.pdf",
  abstract =     "We present a mathematical analysis of transformations
                 used in fast calculation of inverse square root for
                 single-precision floating-point numbers. Optimal values
                 of the so called magic constants are derived in a
                 systematic way, minimizing either absolute or relative
                 errors at subsequent stages of the discussed
                 algorithm.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mukunoki:2016:RPF,
  author =       "Daichi Mukunoki and Toshiyuki Imamura",
  booktitle =    "{2016 IEEE International Conference on Cluster
                 Computing (CLUSTER)}",
  title =        "Reduced-Precision Floating-Point Formats on {GPUs} for
                 High Performance and Energy Efficient Computation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "144--145",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/CLUSTER.2016.77",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computers; Conferences; Containers; Graphics
                 processing units; Kernel; Linear algebra; Sparse
                 matrices",
}

@InProceedings{Muller:2016:NMA,
  author =       "Jean-Michel Muller and Valentina Popescu and Ping Tak
                 Peter Tang",
  title =        "A New Multiplication Algorithm for Extended Precision
                 Using Floating-Point Expansions",
  crossref =     "Montuschi:2016:ISC",
  pages =        "39--46",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ARITH.2016.18",
  bibdate =      "Fri Dec 16 15:17:20 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2016; ARITH-23",
}

@Misc{Munshi:2016:OCS,
  author =       "Aaftab Munshi and Lee Howes and Bartosz Sochacki and
                 {Khronos OpenCL Working Group}",
  title =        "The {OpenCL} {C} Specification Version: 2.0 Document
                 Revision: 33",
  howpublished = "Web document.",
  pages =        "205",
  day =          "13",
  month =        apr,
  year =         "2016",
  bibdate =      "Mon Apr 16 14:05:49 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/pvm.bib",
  URL =          "https://www.khronos.org/registry/OpenCL/specs/opencl-2.0-openclc.pdf",
  acknowledgement = ack-nhfb,
  remark =       "Section 6.1.3.2 Math Functions, pages 74ff, defines a
                 function repertoire extended beyond that of ISO C,
                 including {\tt acospi}, {\tt asinpi}, {\tt atanpi},
                 {\tt atan2pi}, {\tt cospi}, {\tt sinpi}, {\tt tanpi},
                 {\tt cospi}, {\tt fract}, {\tt lgamma\_r}, {\tt mad}
                 (approximation to {\tt a * b + c}), {\tt minmag}, {\tt
                 pown}, {\tt rootn}, {\tt sincos}, {\tt sinpi}, and {\tt
                 tanpi}.",
}

@Article{Nannarelli:2016:PPS,
  author =       "Alberto Nannarelli",
  title =        "Performance\slash Power Space Exploration for
                 {Binary64} Division Units",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "65",
  number =       "5",
  pages =        "1671--1677",
  month =        may,
  year =         "2016",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2015.2448097",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue May 31 08:56:47 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers -",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Notzli:2016:LVP,
  author =       "Andres N{\"o}tzli and Fraser Brown",
  title =        "{LifeJacket}: Verifying precise floating-point
                 optimizations in {LLVM}",
  journal =      "arxiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "30",
  month =        mar,
  year =         "2016",
  bibdate =      "Sat Apr 2 06:26:03 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/1603.09290",
  abstract =     "Optimizing floating-point arithmetic is vital because
                 it is ubiquitous, costly, and used in compute-heavy
                 workloads. Implementing precise optimizations
                 correctly, however, is difficult, since developers must
                 account for all the esoteric properties of
                 floating-point arithmetic to ensure that their
                 transformations do not alter the output of a program.
                 Manual reasoning is error prone and stifles
                 incorporation of new optimizations. We present an
                 approach to automate reasoning about floating-point
                 optimizations using satisfiability modulo theories
                 (SMT) solvers. We implement the approach in LifeJacket,
                 a system for automatically verifying precise
                 floating-point optimizations for the LLVM assembly
                 language. We have used LifeJacket to verify 43 LLVM
                 optimizations and to discover eight incorrect ones,
                 including three previously unreported problems.
                 LifeJacket is an open source extension of the Alive
                 system for optimization verification.",
  acknowledgement = ack-nhfb,
}

@Article{Ozaki:2016:EFT,
  author =       "Katsuhisa Ozaki and Takeshi Ogita and Shin'ichi
                 Oishi",
  title =        "Error-free transformation of matrix multiplication
                 with a posteriori validation",
  journal =      j-NUM-LIN-ALG-APPL,
  volume =       "23",
  number =       "5",
  pages =        "931--946",
  month =        oct,
  year =         "2016",
  CODEN =        "NLAAEM",
  DOI =          "https://doi.org/10.1002/nla.2061",
  ISSN =         "1070-5325 (print), 1099-1506 (electronic)",
  ISSN-L =       "1070-5325",
  bibdate =      "Thu Sep 29 08:59:10 MDT 2016",
  bibsource =    "http://www.interscience.wiley.com/jpages/1070-5325;
                 http://www3.interscience.wiley.com/journalfinder.html;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/numlinaa.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Linear Algebra with Applications",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-1506",
  keywords =     "accurate computing; accurate floating-point summation;
                 floating-point arithmetic; interval arithmetic; matrix
                 multiplication",
}

@Article{Ozaki:2016:SFP,
  author =       "Katsuhisa Ozaki and Florian B{\"u}nger and Takeshi
                 Ogita",
  title =        "Simple floating-point filters for the two-dimensional
                 orientation problem",
  journal =      j-BIT-NUM-MATH,
  volume =       "56",
  number =       "2",
  pages =        "729--749",
  month =        jun,
  year =         "2016",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/s10543-015-0574-9",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Mon May 30 06:11:11 MDT 2016",
  bibsource =    "http://link.springer.com/journal/10543/56/2;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer.com/article/10.1007/s10543-015-0574-9",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT Numerical Mathematics",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@InProceedings{Parfieniuk:2016:VQM,
  author =       "Marek Parfieniuk and Sang Yoon Park",
  booktitle =    "{2016 14th IEEE International New Circuits and Systems
                 Conference (NEWCAS)}",
  title =        "A versatile quaternion multiplier based on
                 sparse-iteration {4D} {CORDIC}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--4",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/NEWCAS.2016.7604788",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Hardware; Logic gates; Quaternions; Switches; Table
                 lookup; Transforms; Two dimensional displays",
}

@Article{Paulk:2016:IFP,
  author =       "Mark Paulk and Lori Cameron",
  title =        "{IEEE} Floating Point Standard",
  journal =      j-COMPUTER,
  volume =       "49",
  number =       "6",
  pages =        "10--10",
  month =        jun,
  year =         "2016",
  CODEN =        "CPTRB4",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Tue Jun 21 15:00:51 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computer2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://csdl.computer.org/csdl/mags/co/2016/06/mco2016060010.html",
  abstract-URL = "http://csdl.computer.org/csdl/mags/co/2016/06/mco2016060010-abs.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}

@Article{Petrovsky:2016:CLF,
  author =       "Nick Petrovsky and Andrew Stankevich and Alexander
                 Petrovsky",
  title =        "{CORDIC}-lifting factorization of paraunitary filter
                 banks based on the quaternionic multipliers for
                 lossless image coding",
  journal =      "Multidimensional Syst. Signal Process.",
  volume =       "27",
  number =       "3",
  pages =        "667--695",
  year =         "2016",
  DOI =          "https://doi.org/10.1007/s11045-015-0323-x",
  ISSN =         "0923-6082",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  ZMnumber =     "1441.94022",
  acknowledgement = ack-nhfb,
  fjournal =     "Multidimensional Systems and Signal Processing",
  keywords =     "94A08,94A12",
  ZBmath =       "6758814",
}

@Article{Phatak:2016:NDA,
  author =       "Dhananjay S. Phatak and Steven D. Houston",
  title =        "New distributed algorithms for fast sign detection in
                 residue number systems ({RNS})",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "97",
  number =       "??",
  pages =        "78--95",
  month =        nov,
  year =         "2016",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Thu Aug 25 18:20:29 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jpardistcomp.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0743731516300703",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315/",
}

@InProceedings{Rane:2016:SPF,
  author =       "Ashey Rane and Calvin Lin and Mohit Tiwari",
  editor =       "T. Holz and S. Savage",
  booktitle =    "Proceedings of the {25th USENIX Security 2016, August
                 10--12, 2016, Austin, TX}",
  title =        "Secure, precise, and fast floating-point operations on
                 x86 processors",
  publisher =    pub-USENIX,
  address =      pub-USENIX:adr,
  pages =        "71--86",
  year =         "2016",
  bibdate =      "Mon Aug 26 17:02:50 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.usenix.org/conference/usenixsecurity16/technical-sessions/presentation/rane",
  abstract =     "Floating-point computations introduce several side
                 channels. This paper describes the first solution that
                 closes these side channels while preserving the
                 precision of non-secure executions. Our solution
                 exploits microarchitectural features of the x86
                 architecture along with novel compilation techniques to
                 provide low overhead.\par

                 Because of the details of x86 execution, the evaluation
                 of floating-point side channel defenses is quite
                 involved, but we show that our solution is secure,
                 precise, and fast. Our solution closes more side
                 channels than any prior solution. Despite the added
                 security, our solution does not compromise on the
                 precision of the floating-point operations. Finally,
                 for a set of microkernels, our solution is an order of
                 magnitude more efficient than the previous solution.",
  acknowledgement = ack-nhfb,
  remark =       "ISBN-13 978-1-931971-32-4 from publisher Web site
                 BibTeX entry is incorrect: it is for an unrelated 2005
                 conference paper. Library catalog searches fail to find
                 this proceedings volume.",
  xxISBN =       "1-931971-32-3",
  xxISBN-13 =    "978-1-931971-32-4",
}

@Article{Rashidi:2016:HSH,
  author =       "Bahram Rashidi and Sayed Masoud Sayedi and Reza
                 Rezaeian Farashahi",
  title =        "High-speed hardware architecture of scalar
                 multiplication for binary elliptic curve
                 cryptosystems",
  journal =      j-MICROELECT-J,
  volume =       "52",
  pages =        "49--65",
  month =        jun,
  year =         "2016",
  CODEN =        "MICEB9",
  DOI =          "https://doi.org/10.1016/j.mejo.2016.03.006",
  ISSN =         "0026-2692 (print), 1879-2391 (electronic)",
  ISSN-L =       "0026-2692",
  bibdate =      "Fri Jun 24 16:29:16 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Microelectronics Journal",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00262692",
}

@InProceedings{Revy:2016:ADF,
  author =       "Guillaume Revy",
  title =        "Automated Design of Floating-Point Logarithm Functions
                 on Integer Processors",
  crossref =     "Montuschi:2016:ISC",
  pages =        "172--180",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ARITH.2016.28",
  bibdate =      "Fri Dec 16 15:17:20 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2016; ARITH-23",
}

@Article{Roux:2016:FPR,
  author =       "Pierre Roux",
  title =        "Formal Proofs of Rounding Error Bounds: With
                 Application to an Automatic Positive Definiteness
                 Check",
  journal =      j-J-AUTOM-REASON,
  volume =       "57",
  number =       "2",
  pages =        "135--156",
  month =        aug,
  year =         "2016",
  CODEN =        "JAREEW",
  DOI =          "https://doi.org/10.1007/s10817-015-9339-z",
  ISSN =         "0168-7433 (print), 1573-0670 (electronic)",
  ISSN-L =       "0168-7433",
  bibdate =      "Fri Sep 2 06:39:36 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
  URL =          "http://link.springer.com/accesspage/article/10.1007/s10817-015-9339-z",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Automated Reasoning",
  journal-URL =  "http://link.springer.com/journal/10817",
  keywords =     "floating-point arithmetic; rounding error",
}

@InProceedings{Rubio-Gonzalez:2016:FPP,
  author =       "Cindy Rubio-Gonz{\'a}lez and Cuong Nguyen and Benjamin
                 Mehne and Koushik Sen and James Demmel and William
                 Kahan and Costin Iancu and Wim Lavrijsen and David H.
                 Bailey and David Hough",
  booktitle =    "Proceedings of the 38th International Conference on
                 Software Engineering",
  title =        "Floating-point precision tuning using blame analysis",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "1074--1085",
  year =         "2016",
  bibdate =      "Sat Jun 04 17:19:46 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Rump:2016:DUR,
  author =       "Siegfried M. Rump and Marko Lange",
  title =        "On the definition of unit roundoff",
  journal =      j-BIT-NUM-MATH,
  volume =       "56",
  number =       "1",
  pages =        "309--317",
  month =        mar,
  year =         "2016",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/s10543-015-0554-0",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Mon May 30 06:11:10 MDT 2016",
  bibsource =    "http://link.springer.com/journal/10543/56/1;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer.com/article/10.1007/s10543-015-0554-0",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT Numerical Mathematics",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Rump:2016:IAF,
  author =       "Siegfried M. Rump and Takeshi Ogita and Yusuke
                 Morikura and Shin'ichi Oishi",
  title =        "Interval arithmetic with fixed rounding mode",
  journal =      j-NONLINEAR-THEORY-APPL,
  volume =       "7",
  number =       "3",
  pages =        "362--373",
  year =         "2016",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1587/nolta.7.362",
  ISSN =         "2185-4106",
  ISSN-L =       "2185-4106",
  bibdate =      "Wed Jan 19 10:32:15 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We discuss several methods to simulate interval
                 arithmetic operations using floating-point operations
                 with fixed rounding mode. In particular we present
                 formulas using only rounding to nearest and using only
                 chop rounding (towards zero). The latter was the
                 default and only rounding on GPU (Graphics Processing
                 Unit) and cell processors, which in turn are very fast
                 and therefore attractive in scientific computations.",
  acknowledgement = ack-nhfb,
  fjournal =     "Nonlinear Theory and Its Applications, {IEICE}",
  journal-URL =  "https://www.jstage.jst.go.jp/browse/nolta/",
}

@Article{Rump:2016:IEB,
  author =       "Siegfried M. Rump and Florian B{\"u}nger and
                 Claude-Pierre Jeannerod",
  title =        "Improved error bounds for floating-point products and
                 {Horner}'s scheme",
  journal =      j-BIT-NUM-MATH,
  volume =       "56",
  number =       "1",
  pages =        "293--307",
  month =        mar,
  year =         "2016",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/s10543-015-0555-z",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Mon May 30 06:11:10 MDT 2016",
  bibsource =    "http://link.springer.com/journal/10543/56/1;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer.com/article/10.1007/s10543-015-0555-z",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT Numerical Mathematics",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Sayed:2016:WCR,
  author =       "Wafaa S. Sayed and Hossam A. H. Fahmy",
  title =        "What are the Correct Results for the Special Values of
                 the Operands of the Power Operation?",
  journal =      j-TOMS,
  volume =       "42",
  number =       "2",
  pages =        "14:1--14:17",
  month =        jun,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2809783",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jun 3 18:52:21 MDT 2016",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Language standards such as C99 and C11, as well as the
                 IEEE Standard for Floating-Point Arithmetic 754 (IEEE
                 Std 754-2008) specify the expected behavior of binary
                 and decimal floating-point arithmetic in
                 computer-programming environments and the handling of
                 special values and exception conditions. Many
                 researchers focus on verifying the compliance of
                 implementations for binary and decimal floating-point
                 operations with these standards. In this article, we
                 are concerned with the special values of the operands
                 of the power function Z = X$^Y$. We study how the
                 standards define the correct results for this
                 operation, propose a mathematically justified
                 definition for the correct results of the power
                 function on the occurrence of these special values as
                 its operands, test how different software
                 implementations for the power function deal with these
                 special values, and classify the behavior of different
                 programming languages from the viewpoint of how much
                 they conform to the standards and our proposed
                 mathematical definition. We present inconsistencies
                 between the implementations and the standards, and
                 discuss incompatibilities between different versions of
                 the same software.",
  acknowledgement = ack-nhfb,
  articleno =    "14",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@InProceedings{Schaffner:2016:APT,
  author =       "Michael Schaffner and Michael Gautschi and Frank K.
                 G{\"u}rkaynak and Luca Benini",
  title =        "Accuracy and Performance Trade-Offs of Logarithmic
                 Number Units in Multi-Core Clusters",
  crossref =     "Montuschi:2016:ISC",
  pages =        "95--103",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ARITH.2016.10",
  bibdate =      "Fri Dec 16 15:17:20 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2016; ARITH-23",
}

@Article{Schkufza:2016:SPO,
  author =       "Eric Schkufza and Rahul Sharma and Alex Aiken",
  title =        "Stochastic program optimization",
  journal =      j-CACM,
  volume =       "59",
  number =       "2",
  pages =        "114--122",
  month =        feb,
  year =         "2016",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/2863701",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Tue Feb 16 15:45:15 MST 2016",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://cacm.acm.org/magazines/2016/2/197428/fulltext",
  abstract =     "The optimization of short sequences of loop-free,
                 fixed-point assembly code sequences is an important
                 problem in high-performance computing. However, the
                 competing constraints of transformation correctness and
                 performance improvement often force even special
                 purpose compilers to produce sub-optimal code. We show
                 that by encoding these constraints as terms in a cost
                 function, and using a Markov Chain Monte Carlo sampler
                 to rapidly explore the space of all possible code
                 sequences, we are able to generate aggressively
                 optimized versions of a given target code sequence.
                 Beginning from binaries compiled by 11vm --O0, we are
                 able to produce provably correct code sequences that
                 either match or outperform the code produced by qcc
                 --O3, icc --O3, and in some cases expert handwritten
                 assembly.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Hacker's delight; Henry S. Warren; Montgomery
                 multiplication; SAXPY",
}

@Article{Seo:2016:HMR,
  author =       "Hwajeong Seo and Zhe Liu and Yasuyuki Nogami and
                 Jongseok Choi and Howon Kim",
  title =        "Hybrid {Montgomery} Reduction",
  journal =      j-TECS,
  volume =       "15",
  number =       "3",
  pages =        "58:1--58:??",
  month =        jul,
  year =         "2016",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2890502",
  ISSN =         "1539-9087 (print), 1558-3465 (electronic)",
  ISSN-L =       "1539-9087",
  bibdate =      "Thu Jul 21 17:18:13 MDT 2016",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tecs.bib",
  abstract =     "In this article, we present a hybrid method to improve
                 the performance of the Montgomery reduction by taking
                 advantage of the Karatsuba technique. We divide the
                 Montgomery reduction into two sub-parts, including one
                 for the conventional Montgomery reduction and the other
                 one for Karatsuba-aided multiplication. This approach
                 reduces the multiplication complexity of $n$-limb
                 Montgomery reduction from $ \theta (n^2 + n)$ to
                 asymptotic complexity $ \theta (7 n^2 / 8 + n)$. Our
                 practical implementation results over an 8-bit
                 microcontroller also show performance enhancements by
                 11\%.",
  acknowledgement = ack-nhfb,
  articleno =    "58",
  fjournal =     "ACM Transactions on Embedded Computing Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J840",
}

@Article{Sohn:2016:FFP,
  author =       "Jongwook Sohn and Earl E. {Swartzlander, Jr.}",
  title =        "A Fused Floating-Point Four-Term Dot Product Unit",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-1,
  volume =       "63",
  number =       "3",
  pages =        "370--378",
  month =        mar,
  year =         "2016",
  DOI =          "https://doi.org/10.1109/TCSI.2016.2525042",
  ISSN =         "1549-8328 (print), 1558-0806 (electronic)",
  ISSN-L =       "1549-8328",
  bibdate =      "Mon Feb 10 09:06:33 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/document/7416176",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems I: Regular
                 Papers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8919",
}

@Article{Tada:2016:ESG,
  author =       "Jubee Tada and Maiki Hosokawa and Ryusuke Egawa and
                 Hiroaki Kobayashi",
  title =        "Effects of Stacking Granularity on {$3$-D} Stacked
                 Floating-point Fused Multiply-Add Units",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "44",
  number =       "4",
  pages =        "62--67",
  month =        sep,
  year =         "2016",
  CODEN =        "CANED2",
  DOI =          "https://doi.org/10.1145/3039902.3039914",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Thu Jan 12 18:43:44 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
  abstract =     "Three-dimensional stacked integrated circuits
                 (3D-SICs) have been expected to overcome the
                 limitations of conventional two-dimensional (2-D)
                 implemented circuits. Since a stacking strategy affects
                 the performance and the power consumption of 3D-SICs,
                 this paper examines two stacking strategies for
                 designing the 3-D stacked floating-point fused
                 multiply-add (FP-FMA) module which contains four FP-FMA
                 units. Experimental results show that a coarse-grain
                 stacking strategy is suitable for reducing critical
                 path delay of the 3-D stacked FP-FMA module. On the
                 other hand, a fine-grain stacking strategy is suitable
                 for reducing power consumption. The 3-D stacked FP-FMA
                 module which is designed based on a fine-grain stacking
                 strategy achieves an 8.4\% critical path delay
                 reduction and an 18\% average power reduction compared
                 with the 2-D implementation.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
  remark =       "HEART '16 conference proceedings.",
}

@Article{Tay:2016:NIM,
  author =       "T. Fatt Tay and C. Chang",
  title =        "A Non-Iterative Multiple Residue Digit Error Detection
                 and Correction Algorithm in {RRNS}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "65",
  number =       "2",
  pages =        "396--408",
  month =        "????",
  year =         "2016",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2015.2435773",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Jan 19 07:06:51 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Ugurdag:2016:ECC,
  author =       "H. Fatih Ugurdag and Anil Bayram and Vecdi Emre Levent
                 and Sezer G{\"o}ren",
  title =        "Efficient Combinational Circuits for Division by Small
                 Integer Constants",
  crossref =     "Montuschi:2016:ISC",
  pages =        "1--7",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ARITH.2016.23",
  bibdate =      "Fri Dec 16 15:17:20 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2016; ARITH-23",
}

@InProceedings{vanderHoeven:2016:ESL,
  author =       "Joris van der Hoeven and Gr{\'e}goire Lecerf",
  title =        "Evaluating Straight-Line Programs over Balls",
  crossref =     "Montuschi:2016:ISC",
  pages =        "142--149",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ARITH.2016.12",
  bibdate =      "Fri Dec 16 15:17:20 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2016; ARITH-23; interval arithmetic",
}

@Article{vanderHoeven:2016:MSA,
  author =       "Joris van der Hoeven and Gr{\'e}goire Lecerf and
                 Guillaume Quintin",
  title =        "Modular {SIMD} arithmetic in {Mathemagix}",
  journal =      j-TOMS,
  volume =       "43",
  number =       "1",
  pages =        "5:1--5:37",
  month =        aug,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2876503",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:25 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2876503",
  abstract =     "Modular integer arithmetic occurs in many algorithms
                 for computer algebra, cryptography, and error
                 correcting codes. Although recent microprocessors
                 typically offer a wide range of highly optimized
                 arithmetic functions, modular integer operations still
                 require dedicated implementations. In this article, we
                 survey existing algorithms for modular integer
                 arithmetic and present detailed vectorized
                 counterparts. We also describe several applications,
                 such as fast modular Fourier transforms and
                 multiplication of integer polynomials and matrices. The
                 vectorized algorithms have been implemented in C++
                 inside the free computer algebra and analysis system
                 Mathemagix. The performance of our implementation is
                 illustrated by various benchmarks.",
  acknowledgement = ack-nhfb,
  articleno =    "5",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "http://dl.acm.org/pub.cfm?id=J782",
}

@InProceedings{Villalba-Moreno:2016:DRF,
  author =       "Julio Villalba-Moreno",
  title =        "Digit Recurrence Floating-Point Division under {HUB}
                 Format",
  crossref =     "Montuschi:2016:ISC",
  pages =        "79--86",
  year =         "2016",
  DOI =          "https://doi.org/10.1109/ARITH.2016.17",
  bibdate =      "Fri Dec 16 15:17:20 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2016; ARITH-23; HUB (Half-Unit-Biased)
                 floating-point format",
}

@InProceedings{Wang:2016:DFP,
  author =       "Ran Wang and Daming Zou and Xinrui He and Yingfei
                 Xiong and Lu Zhang and Gang Huang",
  booktitle =    "{Proceedings of the 2016 24th ACM SIGSOFT
                 International Symposium on Foundations of Software
                 Engineering --- FSE 2016}",
  title =        "Detecting and fixing precision-specific operations for
                 measuring floating-point errors",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  year =         "2016",
  DOI =          "https://doi.org/10.1145/2950290.2950355",
  bibdate =      "Thu Oct 17 06:42:14 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The accuracy of the floating-point calculation is
                 critical to many applications and different methods
                 have been proposed around floating-point accuracies,
                 such as detecting the errors in the program, verifying
                 the accuracy of the program, and optimizing the program
                 to produce more accurate results. These approaches need
                 a specification of the program to understand the ideal
                 calculation performed by the program, which is usually
                 approached by interpreting the program in a
                 precision-unspecific way.\par

                 However, many operations programmed in existing code
                 are inherently precision-specific, which cannot be
                 easily interpreted in a precision-unspecific way. In
                 fact, the semantics used in existing approaches usually
                 fail to interpret precision-specific operations
                 correctly.\par

                 In this paper, we present a systematic study on
                 precision-specific operations. First, we propose a
                 detection approach to detect precision-specific
                 operations. Second, we propose a fixing approach to
                 enable the tuning of precisions under the presence of
                 precision-specific operations. Third, we studied the
                 precision-specific operations in the GNU C standard
                 math library based on our detection and fixing
                 approaches. Our results show that (1) a significant
                 number of code fragments in the standard C math library
                 are precision-specific operations, and some large
                 inaccuracies reported in existing studies are false
                 positives or potential false positives due to
                 precision-specific operations; (2) our detection
                 approach has high precision and recall; (3) our fixing
                 approach can lead to overall more accurate result.",
  acknowledgement = ack-nhfb,
}

@Article{Wilson:2016:UAA,
  author =       "David Wilson and Greg Stitt",
  title =        "The Unified Accumulator Architecture: a Configurable,
                 Portable, and Extensible Floating-Point Accumulator",
  journal =      j-TRETS,
  volume =       "9",
  number =       "3",
  pages =        "21:1--21:??",
  month =        jul,
  year =         "2016",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2809432",
  ISSN =         "1936-7406 (print), 1936-7414 (electronic)",
  ISSN-L =       "1936-7406",
  bibdate =      "Thu Jul 14 16:35:43 MDT 2016",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/trets.bib",
  abstract =     "Applications accelerated by field-programmable gate
                 arrays (FPGAs) often require pipelined floating-point
                 accumulators with a variety of different trade-offs.
                 Although previous work has introduced numerous
                 floating-point accumulation architectures, few cores
                 are available for public use, which forces designers to
                 use fixed-point implementations or vendor-provided
                 cores that are not portable and are often not optimized
                 for the desired set of trade-offs. In this article, we
                 combine and extend previous floating-point accumulator
                 architectures into a configurable, open-source core,
                 referred to as the unified accumulator architecture
                 (UAA), which enables designers to choose between
                 different trade-offs for different applications. UAA is
                 portable across FPGAs and allows designers to
                 specialize the underlying adder core to take advantage
                 of device-specific optimizations. By providing an
                 extensible, open-source implementation, we hope for the
                 research community to extend the provided core with new
                 architectures and optimizations.",
  acknowledgement = ack-nhfb,
  articleno =    "21",
  fjournal =     "ACM Transactions on Reconfigurable Technology and
                 Systems (TRETS)",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J1151",
}

@Article{Zhou:2016:PUH,
  author =       "Yuanyuan Zhou",
  title =        "Programming Uncertain {$<$T$>$ hings}",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "44",
  number =       "2",
  pages =        "1--2",
  month =        may,
  year =         "2016",
  CODEN =        "CANED2",
  DOI =          "https://doi.org/10.1145/2980024.2872416",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Thu Jan 12 18:43:42 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
  abstract =     "Innovation flourishes with good abstractions. For
                 instance, codification of the IEEE Floating Point
                 standard in 1985 was critical to the subsequent success
                 of scientific computing. Programming languages
                 currently lack appropriate abstractions for uncertain
                 data. Applications already use estimates from sensors,
                 machine learning, big data, humans, and approximate
                 algorithms, but most programming languages do not help
                 developers address correctness, programmability, and
                 optimization problems due to estimates. To address
                 these problems, we propose a new programming
                 abstraction called Uncertain. We encourage the
                 community to develop and use abstractions for
                 estimates.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "https://dl.acm.org/loi/sigarch",
  remark =       "ASPLOS'16 conference proceedings.",
}

@Article{Aliasgari:2017:SCH,
  author =       "Mehrdad Aliasgari and Marina Blanton and Fattaneh
                 Bayatbabolghani",
  title =        "Secure computation of hidden {Markov} models and
                 secure floating-point arithmetic in the malicious
                 model",
  journal =      j-INT-J-INFO-SEC,
  volume =       "16",
  number =       "6",
  pages =        "577--601",
  month =        nov,
  year =         "2017",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s10207-016-0350-0",
  ISSN =         "1615-5262 (print), 1615-5270 (electronic)",
  ISSN-L =       "1615-5262",
  bibdate =      "Tue Jan 23 16:01:49 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/intjinfosec.bib",
  URL =          "http://link.springer.com/article/10.1007/s10207-016-0350-0",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Information Security",
  journal-URL =  "https://link.springer.com/journal/10207",
  keywords =     "Floating point; Gaussian mixture models; Hidden Markov
                 models; Secure computation",
}

@Article{Anderson:2017:EMF,
  author =       "Andrew Anderson and Servesh Muralidharan and David
                 Gregg",
  title =        "Efficient Multibyte Floating Point Data Formats Using
                 Vectorization",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "66",
  number =       "12",
  pages =        "2081--2096",
  month =        "????",
  year =         "2017",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2017.2716355",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 10 08:32:25 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/document/7950938/",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Angerd:2017:FAC,
  author =       "Alexandra Angerd and Erik Sintorn and Per
                 Stenstr{\"o}m",
  title =        "A Framework for Automated and Controlled
                 Floating-Point Accuracy Reduction in Graphics
                 Applications on {GPUs}",
  journal =      j-TACO,
  volume =       "14",
  number =       "4",
  pages =        "46:1--46:??",
  month =        dec,
  year =         "2017",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3151032",
  ISSN =         "1544-3566 (print), 1544-3973 (electronic)",
  ISSN-L =       "1544-3566",
  bibdate =      "Fri Dec 22 18:25:55 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/taco.bib",
  abstract =     "Reducing the precision of floating-point values can
                 improve performance and/or reduce energy expenditure in
                 computer graphics, among other, applications. However,
                 reducing the precision level of floating-point values
                 in a controlled fashion needs support both at the
                 compiler and at the microarchitecture level. At the
                 compiler level, a method is needed to automate the
                 reduction of precision of each floating-point value. At
                 the microarchitecture level, a lower precision of each
                 floating-point register can allow more floating-point
                 values to be packed into a register file. This,
                 however, calls for new register file organizations.
                 This article proposes an automated precision-selection
                 method and a novel GPU register file organization that
                 can store floating-point register values at arbitrary
                 precisions densely. The automated precision-selection
                 method uses a data-driven approach for setting the
                 precision level of floating-point values, given a
                 quality threshold and a representative set of input
                 data. By allowing a small, but acceptable, degradation
                 in output quality, our method can remove a significant
                 amount of the bits needed to represent floating-point
                 values in the investigated kernels (between 28\% and
                 60\%). Our proposed register file organization exploits
                 these lower-precision floating-point values by packing
                 several of them into the same physical register. This
                 reduces the register pressure per thread by up to 48\%,
                 and by 27\% on average, for a negligible output-quality
                 degradation. This can enable GPUs to keep up to twice
                 as many threads in flight simultaneously.",
  acknowledgement = ack-nhfb,
  articleno =    "46",
  fjournal =     "ACM Transactions on Architecture and Code Optimization
                 (TACO)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J924",
}

@InProceedings{Anonymous:2017:AI,
  author =       "Anonymous",
  title =        "Author index",
  crossref =     "Burgess:2017:ISC",
  pages =        "196--196",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.41",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Presents an index of the authors whose articles are
                 published in the conference proceedings record.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2017; ARITH-24",
}

@InProceedings{Anonymous:2017:C,
  author =       "Anonymous",
  title =        "Committees",
  crossref =     "Burgess:2017:ISC",
  pages =        "x--x",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.5",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Provides a listing of current committee members and
                 society officers.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2017; ARITH-24",
}

@InProceedings{Anonymous:2017:CN,
  author =       "Anonymous",
  title =        "[{Copyright} notice]",
  crossref =     "Burgess:2017:ISC",
  pages =        "iv--iv",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.3",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Presents the copyright information for the conference.
                 May include reprint permission information.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2017; ARITH-24",
}

@InProceedings{Anonymous:2017:F,
  author =       "Anonymous",
  title =        "Foreword",
  crossref =     "Burgess:2017:ISC",
  pages =        "viii--ix",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.4",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Presents the introductory welcome message from the
                 conference proceedings. May include the conference
                 officers' congratulations to all involved with the
                 conference event and publication of the proceedings
                 record.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2017; ARITH-24",
}

@InProceedings{Anonymous:2017:FC,
  author =       "Anonymous",
  title =        "[{Front} cover]",
  crossref =     "Burgess:2017:ISC",
  pages =        "c1--c1",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.43",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Presents the front cover or splash screen of the
                 proceedings record.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2017; ARITH-24",
}

@InProceedings{Anonymous:2017:PCM,
  author =       "Anonymous",
  title =        "Program Committee Members",
  crossref =     "Burgess:2017:ISC",
  pages =        "xi--xi",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.6",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Provides a listing of current committee members and
                 society officers.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2017; ARITH-24",
}

@InProceedings{Anonymous:2017:PI,
  author =       "Anonymous",
  title =        "[{Publisher}'s information]",
  crossref =     "Burgess:2017:ISC",
  pages =        "198--198",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.42",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Provides a listing of current committee members and
                 society officers.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2017; ARITH-24",
}

@InProceedings{Anonymous:2017:SC,
  author =       "Anonymous",
  title =        "Steering Committee",
  crossref =     "Burgess:2017:ISC",
  pages =        "xii--xii",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.7",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Provides a listing of current committee members and
                 society officers.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2017; ARITH-24",
}

@InProceedings{Anonymous:2017:TC,
  author =       "Anonymous",
  title =        "Table of contents",
  crossref =     "Burgess:2017:ISC",
  pages =        "v--vii",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.8",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The following topics are dealt with: multiprecision
                 arithmetic; computer arithmetic; DSP; floating-point
                 error analysis; reproducible arithmetic; FPGA; matrix
                 computations; and cryptography.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2017; ARITH-24; computer arithmetic;
                 cryptography; digital signal processing chips; DSP;
                 error analysis; field programmable gate arrays;
                 floating point arithmetic; floating-point error
                 analysis; FPGA; matrix algebra; matrix computations;
                 multiprecision arithmetic; reproducible arithmetic",
}

@InProceedings{Anonymous:2017:TP,
  author =       "Anonymous",
  title =        "[{Title} page i]",
  crossref =     "Burgess:2017:ISC",
  pages =        "i--i",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.1",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Presents the title page of the proceedings record.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2017; ARITH-24",
}

@InProceedings{Anonymous:2017:TPI,
  author =       "Anonymous",
  title =        "[{Title} page iii]",
  crossref =     "Burgess:2017:ISC",
  pages =        "iii--iii",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.2",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Presents the title page of the proceedings record.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2017; ARITH-24",
}

@Article{Aurentz:2017:CCS,
  author =       "Jared L. Aurentz and Lloyd N. Trefethen",
  title =        "Chopping a {Chebyshev} Series",
  journal =      j-TOMS,
  volume =       "43",
  number =       "4",
  pages =        "33:1--33:21",
  month =        mar,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2998442",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65G50 (65Y04)",
  MRnumber =     "3638570",
  bibdate =      "Fri Mar 24 08:51:05 MDT 2017",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Chebfun and related software projects for numerical
                 computing with functions are based on the idea that at
                 each step of a computation, a function $ f(x) $ defined
                 on an interval $ [a, b] $ is ``rounded'' to a
                 prescribed precision by constructing a Chebyshev series
                 and chopping it at an appropriate point. Designing a
                 chopping algorithm with the right properties proves to
                 be a surprisingly complex and interesting problem. We
                 describe the chopping algorithm introduced in Chebfun
                 Version 5.3 in 2015 after many years of discussion and
                 the considerations that led to this design.",
  acknowledgement = ack-nhfb,
  articleno =    "33",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{B:2017:GML,
  author =       "Sudeepa K. B. and Ganesh Aithal",
  title =        "Generation of maximum length non-binary key sequence
                 and its application for stream cipher based on residue
                 number system",
  journal =      j-J-COMPUT-SCI,
  volume =       "21",
  pages =        "379--386",
  month =        jul,
  year =         "2017",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/j.jocs.2016.10.006",
  ISSN =         "1877-7503 (print), 1877-7511 (electronic)",
  ISSN-L =       "1877-7503",
  MRclass =      "94A60",
  MRnumber =     "3685019",
  bibdate =      "Tue Sep 19 13:54:25 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputsci.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/S1877750316302071",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Comput. Sci.",
  fjournal =     "Journal of Computational Science",
  journal-URL =  "https://www.sciencedirect.com/journal/journal-of-computational-science",
}

@Book{Beebe:2017:MFC,
  author =       "Nelson H. F. Beebe",
  title =        "The Mathematical-Function Computation Handbook:
                 Programming Using the {MathCW} Portable Software
                 Library",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xxxvi + 1114",
  year =         "2017",
  DOI =          "https://doi.org/10.1007/978-3-319-64110-2",
  ISBN =         "3-319-64109-3 (hardcover), 3-319-64110-7 (e-book)",
  ISBN-13 =      "978-3-319-64109-6 (hardcover), 978-3-319-64110-2
                 (e-book)",
  LCCN =         "QA75.5-76.95",
  bibdate =      "Sat Jul 15 19:34:43 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
                 https://www.math.utah.edu/pub/tex/bib/axiom.bib;
                 https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/mupad.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/redbooks.bib;
                 https://www.math.utah.edu/pub/tex/bib/utah-math-dept-books.bib",
  URL =          "http://www.springer.com/us/book/9783319641096",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Beebe, Nelson H. F./0000-0001-7281-4263",
  tableofcontents = "List of figures / xxv \\
                 List of tables / xxxi \\
                 Quick start / xxxv \\
                 1: Introduction / 1 \\
                 1.1: Programming conventions / 2 \\
                 1.2: Naming conventions / 4 \\
                 1.3: Library contributions and coverage / 5 \\
                 1.4: Summary / 6 \\
                 2: Iterative solutions and other tools / 7 \\
                 2.1: Polynomials and Taylor series / 7 \\
                 2.2: First-order Taylor series approximation / 8 \\
                 2.3: Second-order Taylor series approximation / 9 \\
                 2.4: Another second-order Taylor series approximation /
                 9 \\
                 2.5: Convergence of second-order methods / 10 \\
                 2.6: Taylor series for elementary functions / 10 \\
                 2.7: Continued fractions / 12 \\
                 2.8: Summation of continued fractions / 17 \\
                 2.9: Asymptotic expansions / 19 \\
                 2.10: Series inversion / 20 \\
                 2.11: Summary / 22 \\
                 3: Polynomial approximations / 23 \\
                 3.1: Computation of odd series / 23 \\
                 3.2: Computation of even series / 25 \\
                 3.3: Computation of general series / 25 \\
                 3.4: Limitations of Cody\slash Waite polynomials / 28
                 \\
                 3.5: Polynomial fits with Maple / 32 \\
                 3.6: Polynomial fits with Mathematica / 33 \\
                 3.7: Exact polynomial coefficients / 42 \\
                 3.8: Cody\slash Waite rational polynomials / 43 \\
                 3.9: Chebyshev polynomial economization / 43 \\
                 3.10: Evaluating Chebyshev polynomials / 48 \\
                 3.11: Error compensation in Chebyshev fits / 50 \\
                 3.12: Improving Chebyshev fits / 51 \\
                 3.13: Chebyshev fits in rational form / 52 \\
                 3.14: Chebyshev fits with Mathematica / 56 \\
                 3.15: Chebyshev fits for function representation / 57
                 \\
                 3.16: Extending the library / 57 \\
                 3.17: Summary and further reading / 58 \\
                 4: Implementation issues / 61 \\
                 4.1: Error magnification / 61 \\
                 4.2: Machine representation and machine epsilon / 62
                 \\
                 4.3: IEEE 754 arithmetic / 63 \\
                 4.4: Evaluation order in C / 64 \\
                 4.5: The {\tt volatile} type qualifier / 65 \\
                 4.6: Rounding in floating-point arithmetic / 66 \\
                 4.7: Signed zero / 69 \\
                 4.8: Floating-point zero divide / 70 \\
                 4.9: Floating-point overflow / 71 \\
                 4.10: Integer overflow / 72 \\
                 4.11: Floating-point underflow / 77 \\
                 4.12: Subnormal numbers / 78 \\
                 4.13: Floating-point inexact operation / 79 \\
                 4.14: Floating-point invalid operation / 79 \\
                 4.15: Remarks on NaN tests / 80 \\
                 4.16: Ulps --- units in the last place / 81 \\
                 4.17: Fused multiply-add / 85 \\
                 4.18: Fused multiply-add and polynomials / 88 \\
                 4.19: Significance loss / 89 \\
                 4.20: Error handling and reporting / 89 \\
                 4.21: Interpreting error codes / 93 \\
                 4.22: C99 changes to error reporting / 94 \\
                 4.23: Error reporting with threads / 95 \\
                 4.24: Comments on error reporting / 95 \\
                 4.25: Testing function implementations / 96 \\
                 4.26: Extended data types on Hewlett--Packard HP-UX
                 IA-64 / 100 \\
                 4.27: Extensions for decimal arithmetic / 101 \\
                 4.28: Further reading / 103 \\
                 4.29: Summary / 104 \\
                 5: The floating-point environment / 105 \\
                 5.1: IEEE 754 and programming languages / 105 \\
                 5.2: IEEE 754 and the mathcw library / 106 \\
                 5.3: Exceptions and traps / 106 \\
                 5.4: Access to exception flags and rounding control /
                 107 \\
                 5.5: The environment access pragma / 110 \\
                 5.6: Implementation of exception-flag and
                 rounding-control access / 110 \\
                 5.7: Using exception flags: simple cases / 112 \\
                 5.8: Using rounding control / 115 \\
                 5.9: Additional exception flag access / 116 \\
                 5.10: Using exception flags: complex case / 120 \\
                 5.11: Access to precision control / 123 \\
                 5.12: Using precision control / 126 \\
                 5.13: Summary / 127 \\
                 6: Converting floating-point values to integers / 129
                 \\
                 6.1: Integer conversion in programming languages / 129
                 \\
                 6.2: Programming issues for conversions to integers /
                 130 \\
                 6.3: Hardware out-of-range conversions / 131 \\
                 6.4: Rounding modes and integer conversions / 132 \\
                 6.5: Extracting integral and fractional parts / 132 \\
                 6.6: Truncation functions / 135 \\
                 6.7: Ceiling and floor functions / 136 \\
                 6.8: Floating-point rounding functions with fixed
                 rounding / 137 \\
                 6.9: Floating-point rounding functions: current
                 rounding / 138 \\
                 6.10: Floating-point rounding functions without {\em
                 inexact\/} exception / 139 \\
                 6.11: Integer rounding functions with fixed rounding /
                 140 \\
                 6.12: Integer rounding functions with current rounding
                 / 142 \\
                 6.13: Remainder / 143 \\
                 6.14: Why the remainder functions are hard / 144 \\
                 6.15: Computing {\tt fmod} / 146 \\
                 6.16: Computing {\tt remainder} / 148 \\
                 6.17: Computing {\tt remquo} / 150 \\
                 6.18: Computing one remainder from the other / 152 \\
                 6.19: Computing the remainder in nonbinary bases / 155
                 \\
                 6.20: Summary / 156 \\
                 7: Random numbers / 157 \\
                 7.1: Guidelines for random-number software / 157 \\
                 7.2: Creating generator seeds / 158 \\
                 7.3: Random floating-point values / 160 \\
                 7.4: Random integers from floating-point generator /
                 165 \\
                 7.5: Random integers from an integer generator / 166
                 \\
                 7.6: Random integers in ascending order / 168 \\
                 7.7: How random numbers are generated / 169 \\
                 7.8: Removing generator bias / 178 \\
                 7.9: Improving a poor random number generator / 178 \\
                 7.10: Why long periods matter / 179 \\
                 7.11: Inversive congruential generators / 180 \\
                 7.12: Inversive congruential generators, revisited /
                 189 \\
                 7.13: Distributions of random numbers / 189 \\
                 7.14: Other distributions / 195 \\
                 7.15: Testing random-number generators / 196 \\
                 7.16: Applications of random numbers / 202 \\
                 7.17: The \textsf {mathcw} random number routines / 208
                 \\
                 7.18: Summary, advice, and further reading / 214 \\
                 8: Roots / 215 \\
                 8.1: Square root / 215 \\
                 8.2: Hypotenuse and vector norms / 222 \\
                 8.3: Hypotenuse by iteration / 227 \\
                 8.4: Reciprocal square root / 233 \\
                 8.5: Cube root / 237 \\
                 8.6: Roots in hardware / 240 \\
                 8.7: Summary / 242 \\
                 9: Argument reduction / 243 \\
                 9.1: Simple argument reduction / 243 \\
                 9.2: Exact argument reduction / 250 \\
                 9.3: Implementing exact argument reduction / 253 \\
                 9.4: Testing argument reduction / 265 \\
                 9.5: Retrospective on argument reduction / 265 \\
                 10: Exponential and logarithm / 267 \\
                 10.1: Exponential functions / 267 \\
                 10.2: Exponential near zero / 273 \\
                 10.3: Logarithm functions / 282 \\
                 10.4: Logarithm near one / 290 \\
                 10.5: Exponential and logarithm in hardware / 292 \\
                 10.6: Compound interest and annuities / 294 \\
                 10.7: Summary / 298 \\
                 11: Trigonometric functions / 299 \\
                 11.1: Sine and cosine properties / 299 \\
                 11.2: Tangent properties / 302 \\
                 11.3: Argument conventions and units / 304 \\
                 11.4: Computing the cosine and sine / 306 \\
                 11.5: Computing the tangent / 310 \\
                 11.6: Trigonometric functions in degrees / 313 \\
                 11.7: Trigonometric functions in units of $ \pi $ / 315
                 \\
                 11.8: Computing the cosine and sine together / 320 \\
                 11.9: Inverse sine and cosine / 323 \\
                 11.10: Inverse tangent / 331 \\
                 11.11: Inverse tangent, take two / 336 \\
                 11.12: Trigonometric functions in hardware / 338 \\
                 11.13: Testing trigonometric functions / 339 \\
                 11.14: Retrospective on trigonometric functions / 340
                 \\
                 12: Hyperbolic functions / 341 \\
                 12.1: Hyperbolic functions / 341 \\
                 12.2: Improving the hyperbolic functions / 345 \\
                 12.3: Computing the hyperbolic functions together / 348
                 \\
                 12.4: Inverse hyperbolic functions / 348 \\
                 12.5: Hyperbolic functions in hardware / 350 \\
                 12.6: Summary / 352 \\
                 13: Pair-precision arithmetic / 353 \\
                 13.1: Limitations of pair-precision arithmetic / 354
                 \\
                 13.2: Design of the pair-precision software interface /
                 355 \\
                 13.3: Pair-precision initialization / 356 \\
                 13.4: Pair-precision evaluation / 357 \\
                 13.5: Pair-precision high part / 357 \\
                 13.6: Pair-precision low part / 357 \\
                 13.7: Pair-precision copy / 357 \\
                 13.8: Pair-precision negation / 358 \\
                 13.9: Pair-precision absolute value / 358 \\
                 13.10: Pair-precision sum / 358 \\
                 13.11: Splitting numbers into pair sums / 359 \\
                 13.12: Premature overflow in splitting / 362 \\
                 13.13: Pair-precision addition / 365 \\
                 13.14: Pair-precision subtraction / 367 \\
                 13.15: Pair-precision comparison / 368 \\
                 13.16: Pair-precision multiplication / 368 \\
                 13.17: Pair-precision division / 371 \\
                 13.18: Pair-precision square root / 373 \\
                 13.19: Pair-precision cube root / 377 \\
                 13.20: Accuracy of pair-precision arithmetic / 379 \\
                 13.21: Pair-precision vector sum / 384 \\
                 13.22: Exact vector sums / 385 \\
                 13.23: Pair-precision dot product / 385 \\
                 13.24: Pair-precision product sum / 386 \\
                 13.25: Pair-precision decimal arithmetic / 387 \\
                 13.26: Fused multiply-add with pair precision / 388 \\
                 13.27: Higher intermediate precision and the FMA / 393
                 \\
                 13.28: Fused multiply-add without pair precision / 395
                 \\
                 13.29: Fused multiply-add with multiple precision / 401
                 \\
                 13.30: Fused multiply-add, Boldo/\penalty
                 \exhyphenpenalty Melquiond style / 403 \\
                 13.31: Error correction in fused multiply-add / 406 \\
                 13.32: Retrospective on pair-precision arithmetic / 407
                 \\
                 14: Power function / 411 \\
                 14.1: Why the power function is hard to compute / 411
                 \\
                 14.2: Special cases for the power function / 412 \\
                 14.3: Integer powers / 414 \\
                 14.4: Integer powers, revisited / 420 \\
                 14.5: Outline of the power-function algorithm / 421 \\
                 14.6: Finding $a$ and $p$ / 423 \\
                 14.7: Table searching / 424 \\
                 14.8: Computing $\log_n(g/a)$ / 426 \\
                 14.9: Accuracy required for $\log_n(g/a)$ / 429 \\
                 14.10: Exact products / 430 \\
                 14.11: Computing $w$, $w_1$ and $w_2$ / 433 \\
                 14.12: Computing $n^{w_2}$ / 437 \\
                 14.13: The choice of $q$ / 438 \\
                 14.14: Testing the power function / 438 \\
                 14.15: Retrospective on the power function / 440 \\
                 15: Complex arithmetic primitives / 441 \\
                 15.1: Support macros and type definitions / 442 \\
                 15.2: Complex absolute value / 443 \\
                 15.3: Complex addition / 445 \\
                 15.4: Complex argument / 445 \\
                 15.5: Complex conjugate / 446 \\
                 15.6: Complex conjugation symmetry / 446 \\
                 15.7: Complex conversion / 448 \\
                 15.8: Complex copy / 448 \\
                 15.9: Complex division: C99 style / 449 \\
                 15.10: Complex division: Smith style / 451 \\
                 15.11: Complex division: Stewart style / 452 \\
                 15.12: Complex division: Priest style / 453 \\
                 15.13: Complex division: avoiding subtraction loss /
                 455 \\
                 15.14: Complex imaginary part / 456 \\
                 15.15: Complex multiplication / 456 \\
                 15.16: Complex multiplication: error analysis / 458 \\
                 15.17: Complex negation / 459 \\
                 15.18: Complex projection / 460 \\
                 15.19: Complex real part / 460 \\
                 15.20: Complex subtraction / 461 \\
                 15.21: Complex infinity test / 462 \\
                 15.22: Complex NaN test / 462 \\
                 15.23: Summary / 463 \\
                 16: Quadratic equations / 465 \\
                 16.1: Solving quadratic equations / 465 \\
                 16.2: Root sensitivity / 471 \\
                 16.3: Testing a quadratic-equation solver / 472 \\
                 16.4: Summary / 474 \\
                 17: Elementary functions in complex arithmetic / 475
                 \\
                 17.1: Research on complex elementary functions / 475
                 \\
                 17.2: Principal values / 476 \\
                 17.3: Branch cuts / 476 \\
                 17.4: Software problems with negative zeros / 478 \\
                 17.5: Complex elementary function tree / 479 \\
                 17.6: Series for complex functions / 479 \\
                 17.7: Complex square root / 480 \\
                 17.8: Complex cube root / 485 \\
                 17.9: Complex exponential / 487 \\
                 17.10: Complex exponential near zero / 492 \\
                 17.11: Complex logarithm / 495 \\
                 17.12: Complex logarithm near one / 497 \\
                 17.13: Complex power / 500 \\
                 17.14: Complex trigonometric functions / 502 \\
                 17.15: Complex inverse trigonometric functions / 504
                 \\
                 17.16: Complex hyperbolic functions / 509 \\
                 17.17: Complex inverse hyperbolic functions / 514 \\
                 17.18: Summary / 520 \\
                 18: The Greek functions: gamma, psi, and zeta / 521 \\
                 18.1: Gamma and log-gamma functions / 521 \\
                 18.2: The {\tt psi} and {\tt psiln} functions / 536 \\
                 18.3: Polygamma functions / 547 \\
                 18.4: Incomplete gamma functions / 560 \\
                 18.5: A Swiss diversion: Bernoulli and Euler / 568 \\
                 18.6: An Italian excursion: Fibonacci numbers / 575 \\
                 18.7: A German gem: the Riemann zeta function / 579 \\
                 18.8: Further reading / 590 \\
                 18.9: Summary / 591 \\
                 19: Error and probability functions / 593 \\
                 19.1: Error functions / 593 \\
                 19.2: Scaled complementary error function / 598 \\
                 19.3: Inverse error functions / 600 \\
                 19.4: Normal distribution functions and inverses / 610
                 \\
                 19.5: Summary / 617 \\
                 20: Elliptic integral functions / 619 \\
                 20.1: The arithmetic-geometric mean / 619 \\
                 20.2: Elliptic integral functions of the first kind /
                 624 \\
                 20.3: Elliptic integral functions of the second kind /
                 627 \\
                 20.4: Elliptic integral functions of the third kind /
                 630 \\
                 20.5: Computing $K(m)$ and $K'(m)$ / 631 \\
                 20.6: Computing $E(m)$ and $E'(m)$ / 637 \\
                 20.7: Historical algorithms for elliptic integrals /
                 643 \\
                 20.8: Auxiliary functions for elliptic integrals / 645
                 \\
                 20.9: Computing the elliptic auxiliary functions / 648
                 \\
                 20.10: Historical elliptic functions / 650 \\
                 20.11: Elliptic functions in software / 652 \\
                 20.12: Applications of elliptic auxiliary functions /
                 653 \\
                 20.13: Elementary functions from elliptic auxiliary
                 functions / 654 \\
                 20.14: Computing elementary functions via $R_C(x,y)$ /
                 655 \\
                 20.15: Jacobian elliptic functions / 657 \\
                 20.16: Inverses of Jacobian elliptic functions / 664
                 \\
                 20.17: The modulus and the nome / 668 \\
                 20.18: Jacobian theta functions / 673 \\
                 20.19: Logarithmic derivatives of the Jacobian theta
                 functions / 675 \\
                 20.20: Neville theta functions / 678 \\
                 20.21: Jacobian Eta, Theta, and Zeta functions / 679
                 \\
                 20.22: Weierstrass elliptic functions / 682 \\
                 20.23: Weierstrass functions by duplication / 689 \\
                 20.24: Complete elliptic functions, revisited / 690 \\
                 20.25: Summary / 691 \\
                 21: Bessel functions / 693 \\
                 21.1: Cylindrical Bessel functions / 694 \\
                 21.2: Behavior of $J_n(x)$ and $Y_n(x)$ / 695 \\
                 21.3: Properties of $J_n(z)$ and $Y_n(z)$ / 697 \\
                 21.4: Experiments with recurrences for $J_0(x)$ / 705
                 \\
                 21.5: Computing $J_0(x)$ and $J_1(x)$ / 707 \\
                 21.6: Computing $J_n(x)$ / 710 \\
                 21.7: Computing $Y_0(x)$ and $Y_1(x)$ / 713 \\
                 21.8: Computing $Y_n(x)$ / 715 \\
                 21.9: Improving Bessel code near zeros / 716 \\
                 21.10: Properties of $I_n(z)$ and $K_n(z)$ / 718 \\
                 21.11: Computing $I_0(x)$ and $I_1(x)$ / 724 \\
                 21.12: Computing $K_0(x)$ and $K_1(x)$ / 726 \\
                 21.13: Computing $I_n(x)$ and $K_n(x)$ / 728 \\
                 21.14: Properties of spherical Bessel functions / 731
                 \\
                 21.15: Computing $j_n(x)$ and $y_n(x)$ / 735 \\
                 21.16: Improving $j_1(x)$ and $y_1(x)$ / 740 \\
                 21.17: Modified spherical Bessel functions / 743 \\
                 21.18: Software for Bessel-function sequences / 755 \\
                 21.19: Retrospective on Bessel functions / 761 \\
                 22: Testing the library / 763 \\
                 22.1: Testing {\tt tgamma} and {\tt lgamma} / 765 \\
                 22.2: Testing {\tt psi} and {\tt psiln} / 768 \\
                 22.3: Testing {\tt erf} and {\tt erfc} / 768 \\
                 22.4: Testing cylindrical Bessel functions / 769 \\
                 22.5: Testing exponent/\penalty \exhyphenpenalty
                 significand manipulation / 769 \\
                 22.6: Testing inline assembly code / 769 \\
                 22.7: Testing with Maple / 770 \\
                 22.8: Testing floating-point arithmetic / 773 \\
                 22.9: The Berkeley Elementary Functions Test Suite /
                 774 \\
                 22.10: The AT\&T floating-point test package / 775 \\
                 22.11: The Antwerp test suite / 776 \\
                 22.12: Summary / 776 \\
                 23: Pair-precision elementary functions / 777 \\
                 23.1: Pair-precision integer power / 777 \\
                 23.2: Pair-precision machine epsilon / 779 \\
                 23.3: Pair-precision exponential / 780 \\
                 23.4: Pair-precision logarithm / 787 \\
                 23.5: Pair-precision logarithm near one / 793 \\
                 23.6: Pair-precision exponential near zero / 793 \\
                 23.7: Pair-precision base-$n$ exponentials / 795 \\
                 23.8: Pair-precision trigonometric functions / 796 \\
                 23.9: Pair-precision inverse trigonometric functions /
                 801 \\
                 23.10: Pair-precision hyperbolic functions / 804 \\
                 23.11: Pair-precision inverse hyperbolic functions /
                 808 \\
                 23.12: Summary / 808 \\
                 24: Accuracy of the Cody\slash Waite algorithms / 811
                 \\
                 25: Improving upon the Cody\slash Waite algorithms /
                 823 \\
                 25.1: The Bell Labs libraries / 823 \\
                 25.2: The {Cephes} library / 823 \\
                 25.3: The {Sun} libraries / 824 \\
                 25.4: Mathematical functions on EPIC / 824 \\
                 25.5: The GNU libraries / 825 \\
                 25.6: The French libraries / 825 \\
                 25.7: The NIST effort / 826 \\
                 25.8: Commercial mathematical libraries / 826 \\
                 25.9: Mathematical libraries for decimal arithmetic /
                 826 \\
                 25.10: Mathematical library research publications / 826
                 \\
                 25.11: Books on computing mathematical functions / 827
                 \\
                 25.12: Summary / 828 \\
                 26: Floating-point output / 829 \\
                 26.1: Output character string design issues / 830 \\
                 26.2: Exact output conversion / 831 \\
                 26.3: Hexadecimal floating-point output / 832 \\
                 26.4: Octal floating-point output / 850 \\
                 26.5: Binary floating-point output / 851 \\
                 26.6: Decimal floating-point output / 851 \\
                 26.7: Accuracy of output conversion / 865 \\
                 26.8: Output conversion to a general base / 865 \\
                 26.9: Output conversion of Infinity / 866 \\
                 26.10: Output conversion of NaN / 866 \\
                 26.11: Number-to-string conversion / 867 \\
                 26.12: The {\tt printf} family / 867 \\
                 26.13: Summary / 878 \\
                 27: Floating-point input / 879 \\
                 27.1: Binary floating-point input / 879 \\
                 27.2: Octal floating-point input / 894 \\
                 27.3: Hexadecimal floating-point input / 895 \\
                 27.4: Decimal floating-point input / 895 \\
                 27.5: Based-number input / 899 \\
                 27.6: General floating-point input / 900 \\
                 27.7: The {\tt scanf} family / 901 \\
                 27.8: Summary / 910 \\
                 A: Ada interface / 911 \\
                 A.1: Building the Ada interface / 911 \\
                 A.2: Programming the Ada interface / 912 \\
                 A.3: Using the Ada interface / 915 \\
                 B: C\# interface / 917 \\
                 B.1: C\# on the CLI virtual machine / 917 \\
                 B.2: Building the C\# interface / 918 \\
                 B.3: Programming the C\# interface / 920 \\
                 B.4: Using the C\# interface / 922 \\
                 C: C++ interface / 923 \\
                 C.1: Building the C++ interface / 923 \\
                 C.2: Programming the C++ interface / 924 \\
                 C.3: Using the C++ interface / 925 \\
                 D: Decimal arithmetic / 927 \\
                 D.1: Why we need decimal floating-point arithmetic /
                 927 \\
                 D.2: Decimal floating-point arithmetic design issues /
                 928 \\
                 D.3: How decimal and binary arithmetic differ / 931 \\
                 D.4: Initialization of decimal floating-point storage /
                 935 \\
                 D.5: The {\tt <decfloat.h>} header file / 936 \\
                 D.6: Rounding in decimal arithmetic / 936 \\
                 D.7: Exact scaling in decimal arithmetic / 937 \\
                 E: Errata in the Cody\slash Waite book / 939 \\
                 F: Fortran interface / 941 \\
                 F.1: Building the Fortran interface / 943 \\
                 F.2: Programming the Fortran interface / 944 \\
                 F.3: Using the Fortran interface / 945 \\
                 H: Historical floating-point architectures / 947 \\
                 H.1: CDC family / 949 \\
                 H.2: Cray family / 952 \\
                 H.3: DEC PDP-10 / 953 \\
                 H.4: DEC PDP-11 and VAX / 956 \\
                 H.5: General Electric 600 series / 958 \\
                 H.6: IBM family / 959 \\
                 H.7: Lawrence Livermore S-1 Mark IIA / 965 \\
                 H.8: Unusual floating-point systems / 966 \\
                 H.9: Historical retrospective / 967 \\
                 I: Integer arithmetic / 969 \\
                 I.1: Memory addressing and integers / 971 \\
                 I.2: Representations of signed integers / 971 \\
                 I.3: Parity testing / 975 \\
                 I.4: Sign testing / 975 \\
                 I.5: Arithmetic exceptions / 975 \\
                 I.6: Notations for binary numbers / 977 \\
                 I.7: Summary / 978 \\
                 J: Java interface / 979 \\
                 J.1: Building the Java interface / 979 \\
                 J.2: Programming the Java MathCW class / 980 \\
                 J.3: Programming the Java C interface / 982 \\
                 J.4: Using the Java interface / 985 \\
                 L: Letter notation / 987 \\
                 P: Pascal interface / 989 \\
                 P.1: Building the Pascal interface / 989 \\
                 P.2: Programming the Pascal MathCW module / 990 \\
                 P.3: Using the Pascal module interface / 993 \\
                 P.4: Pascal and numeric programming / 994 \\
                 Bibliography / 995 \\
                 Author/editor index / 1039 \\
                 Function and macro index / 1049 \\
                 Subject index / 1065 \\
                 Colophon / 1115",
}

@InProceedings{Bocco:2017:HSU,
  author =       "Andrea Bocco and Yves Durand and Florent de Dinechin",
  booktitle =    "{2017 13th Conference on Ph.D. Research in
                 Microelectronics and Electronics (PRIME)}",
  title =        "Hardware support for {UNUM} floating point
                 arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "93--96",
  year =         "2017",
  DOI =          "https://doi.org/10.1109/PRIME.2017.7974115",
  bibdate =      "Fri Dec 15 07:38:18 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Boehm:2017:SDC,
  author =       "Hans-J. Boehm",
  title =        "Small-data computing: correct calculator arithmetic",
  journal =      j-CACM,
  volume =       "60",
  number =       "8",
  pages =        "44--49",
  month =        aug,
  year =         "2017",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/2911981",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Wed Jul 26 05:35:16 MDT 2017",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Rounding errors are usually avoidable, and sometimes
                 we can afford to avoid them.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Book{Boldo:2017:CAF,
  author =       "Sylvie Boldo and Guillaume Melquiond",
  title =        "Computer arithmetic and formal proofs: verifying
                 floating-point algorithms with the {Coq} system",
  publisher =    "ISTE Press",
  address =      "London, UK",
  year =         "2017",
  ISBN =         "1-78548-112-6, 0-08-101170-9 (e-book)",
  ISBN-13 =      "978-1-78548-112-3, 978-0-08-101170-6 (e-book)",
  LCCN =         "QA76.9.C62",
  bibdate =      "Tue Nov 28 08:55:56 MST 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
  URL =          "http://iste.co.uk/book.php?id=1238",
  abstract =     "Floating-point arithmetic is ubiquitous in modern
                 computing, as it is the tool of choice to approximate
                 real numbers. Due to its limited range and precision,
                 its use can become quite involved and potentially lead
                 to numerous failures. One way to greatly increase
                 confidence in floating-point software is by
                 computer-assisted verification of its correctness
                 proofs. This book provides a comprehensive view of how
                 to formally specify and verify tricky floating-point
                 algorithms with the Coq proof assistant. It describes
                 the Flocq formalization of floating-point arithmetic
                 and some methods to automate theorem proofs. It then
                 presents the specification and verification of various
                 algorithms, from error-free transformations to a
                 numerical scheme for a partial differential equation.
                 The examples cover not only mathematical algorithms but
                 also C programs as well as issues related to
                 compilation. Describes the notions of specification and
                 weakest precondition computation and their practical
                 use. Shows how to tackle algorithms that extend beyond
                 the realm of simple floating-point arithmetic. Includes
                 real analysis and a case study about numerical
                 analysis.",
  acknowledgement = ack-nhfb,
  subject =      "Coq (Electronic resource); Computer arithmetic;
                 Floating-point arithmetic; Computer algorithms;
                 COMPUTERS / Computer Literacy; COMPUTERS / Computer
                 Science; COMPUTERS / Data Processing; COMPUTERS /
                 Hardware / General; COMPUTERS / Information Technology;
                 COMPUTERS / Machine Theory; COMPUTERS / Reference;
                 MATHEMATICS / Discrete Mathematics",
  tableofcontents = "1. Floating-Point Arithmetic \\
                 2. The Coq System \\
                 3. Formalization of Formats and Basic Operators \\
                 4. Automated Methods \\
                 5. Error-Free Computations and Applications \\
                 6. Example Proofs of Advanced Operators \\
                 7. Compilation of FP Programs \\
                 8. Deductive Program Verification \\
                 9. Real and Numerical Analysis",
}

@InProceedings{Boldo:2017:REA,
  author =       "Sylvie Boldo and Florian Faissole and Alexandre
                 Chapoutot",
  title =        "Round-off Error Analysis of Explicit One-Step
                 Numerical Integration Methods",
  crossref =     "Burgess:2017:ISC",
  pages =        "82--89",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.22",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Ordinary differential equations are ubiquitous in
                 scientific computing. Solving exactly these equations
                 is usually not possible, except for special cases,
                 hence the use of numerical schemes to get a discretized
                 solution. We are interested in such numerical
                 integration methods, for instance Euler's method or the
                 Runge-Kutta methods. As they are implemented using
                 floating-point arithmetic, round-off errors occur. In
                 order to guarantee their accuracy, we aim at providing
                 bounds on the round-off errors of explicit one-step
                 numerical integration methods. Our methodology is to
                 apply a fine-grained analysis to these numerical
                 algorithms. Our originality is that our floating-point
                 analysis takes advantage of the linear stability of the
                 scheme, a mathematical property that vouches the scheme
                 is well-behaved.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2017; ARITH-24; differential equations;
                 Differential equations; explicit one-step numerical
                 integration methods; fine-grained analysis; floating
                 point arithmetic; floating-point analysis;
                 floating-point arithmetic; integration; linear
                 stability; Mathematical model; mathematical property;
                 Numerical models; numerical schemes; Numerical
                 simulation; numerical stability; Numerical stability;
                 ordinary differential equations; round-off error
                 analysis; roundoff errors; scientific computing;
                 Stability analysis; Tools",
}

@Article{Boldo:2017:RFA,
  author =       "Sylvie Boldo and Stef Graillat and Jean-Michel
                 Muller",
  title =        "On the Robustness of the {2Sum} and {Fast2Sum}
                 Algorithms",
  journal =      j-TOMS,
  volume =       "44",
  number =       "1",
  pages =        "4:1--4:14",
  month =        jul,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3054947",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jul 14 16:39:28 MDT 2017",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The 2Sum and Fast2Sum algorithms are important
                 building blocks in numerical computing. They are used
                 (implicitly or explicitly) in many compensated
                 algorithms (such as compensated summation or
                 compensated polynomial evaluation). They are also used
                 for manipulating floating-point expansions. We show
                 that these algorithms are much more robust than it is
                 usually believed: The returned result makes sense even
                 when the rounding function is not round-to-nearest, and
                 they are almost immune to overflow.",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "accurate floating-point summation",
}

@InProceedings{Bos:2017:FAM,
  author =       "Joppe W. Bos and Simon Friedberger",
  title =        "Fast Arithmetic Modulo $ 2^x p^y \pm 1 $",
  crossref =     "Burgess:2017:ISC",
  pages =        "148--155",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.15",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We give a systematic overview of techniques to compute
                 arithmetic modulo $ 2^x p^y \pm 1 $ and propose
                 improvements. This is useful for computations in the
                 supersingular isogeny Diffie-Hellman (SIDH)
                 key-exchange protocol which is one of the more recent
                 contenders in the post-quantum public-key arena. One of
                 the main computational bottlenecks in this
                 cryptographic key-exchange protocol is computing
                 modular arithmetic in a finite field defined by a prime
                 of this special shape. Recent implementations already
                 use this special prime shape to speed up the
                 cryptographic implementations but it remains unclear if
                 the choices made are optimal or if one can do better.
                 Our overview shows that in the SIDH setting, where
                 arithmetic over a quadratic extension field is
                 required, the approaches based on Montgomery
                 multiplication are to be preferred. Based on our
                 results, we give selection criteria for such moduli and
                 the outcome of our search reveals that there exist
                 moduli which result in even faster implementations.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2017; ARITH-24; Barrett reduction; computational
                 bottlenecks; cryptographic key-exchange protocol;
                 cryptographic protocols; Electronic mail; Elliptic
                 curves; fast arithmetic modulo; finite field; modular
                 arithmetic; Montgomery multiplication; Optimization;
                 post-quantum cryptography; post-quantum public-key
                 arena; Protocols; Public key cryptography; public key
                 cryptography; quadratic extension field; quantum
                 cryptography; selection criteria; Shape; SIDH; SIDH
                 key-exchange protocol; supersingular isogeny
                 Diffie--Hellman key-exchange protocol",
}

@Article{Brisebarre:2017:ESC,
  author =       "Nicolas Brisebarre and Guillaume Hanrot and Olivier
                 Robert",
  title =        "Exponential Sums and Correctly-Rounded Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "66",
  number =       "12",
  pages =        "2044--2057",
  month =        "????",
  year =         "2017",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2017.2690850",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 10 08:32:25 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/document/7891945/",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@PhdThesis{Brisebarre:2017:PTN,
  author =       "Nicolas Brisebarre",
  title =        "Un peu de th{\'e}orie des nombres et de calcul formel
                 au service de l'arithm{\'e}tique des ordinateurs.
                 ({French}) [{A} little number theory and computer
                 algebra in the service of computer arithmetic]",
  type =         "Habilitation {\`a} Diriger des Recherches",
  school =       "LIP --- Laboratoire de l'Informatique du
                 Parall{\'e}lisme",
  address =      "Lyon, France",
  pages =        "125",
  year =         "2017",
  bibdate =      "Fri Dec 08 10:49:49 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://theses.hal.science/tel-01658342v3",
  acknowledgement = ack-nhfb,
}

@InProceedings{Brunie:2017:MFM,
  author =       "Nicolas Brunie",
  title =        "Modified Fused Multiply and Add for Exact Low
                 Precision Product Accumulation",
  crossref =     "Burgess:2017:ISC",
  pages =        "106--113",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.29",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The implementation of the Fused Multiply and Add (FMA)
                 operation has been extensively studied in the
                 literature on standard and large precisions. We suggest
                 re- visiting those studies for 16-bit precision. We
                 introduce a variation of the Mixed precision FMA
                 targeted for applications processing low precision
                 inputs (such as machine learning). We also introduce
                 several versions of a fixed point based floating- point
                 FMA which performs an exact accumulation of binary16
                 numbers. We study the implementation and area footprint
                 of those operators in comparison with standard FMAs.",
  acknowledgement = ack-nhfb,
  keywords =     "adders; Adders; ARITH 2017; ARITH-24; arithmetic;
                 Complexity theory; Computer architecture; exact low
                 precision product accumulation; fixed point arithmetic;
                 fixed point based floating- point FMA; floating-point;
                 FMA; FPU; fused multiply and add operation; half
                 precision; Hardware; Linear algebra; logic design;
                 mixed precision FMA; multiplying circuits; Standards",
}

@Misc{Carter:2017:PAO,
  author =       "John B. Carter and Bruce G. Mealey and Karthick
                 Rajamani and Eric E. Retter and Jeffrey A. Stuecheli",
  title =        "Performing arithmetic operations using both large and
                 small floating point values",
  howpublished = "US Patent 9,665,346",
  day =          "30",
  month =        may,
  year =         "2017",
  bibdate =      "Thu Oct 17 11:38:25 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://patents.google.com/patent/US9665346B2",
  abstract =     "Mechanisms are provided for performing a floating
                 point arithmetic operation in a data processing system.
                 A plurality of floating point operands of the floating
                 point arithmetic operation are received and bits in a
                 mantissa of at least one floating point operand of the
                 plurality of floating point operands are shifted. One
                 or more bits of the mantissa that are shifted outside a
                 range of bits of the mantissa of at least one floating
                 point operand are stored and a vector value is
                 generated based on the stored one or more bits of the
                 mantissa that are shifted outside of the range of bits
                 of the mantissa of the at least one floating point
                 operand. A resultant value is generated for the
                 floating point arithmetic operation based on the vector
                 value and the plurality of floating point operands.",
  acknowledgement = ack-nhfb,
  remark =       "Patent filed 28 October 2014, granted to IBM 30 May
                 2017, expected expiration 22 December 2031 (in 17th
                 year after filing).",
}

@MastersThesis{Chapp:2017:SIN,
  author =       "Dylan Chapp",
  title =        "Study of the impact of non-determinism on numerical
                 reproducibility and debugging at the exascale",
  type =         "Master of Science in Computer Science",
  school =       "University of Delaware",
  address =      "Newark, DE, USA",
  pages =        "69",
  month =        "Spring",
  year =         "2017",
  ISBN =         "0-355-25168-X",
  ISBN-13 =      "978-0-355-25168-5",
  LCCN =         "????",
  bibdate =      "Mon Feb 10 06:07:39 MST 2020",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://udspace.udel.edu/handle/19716/24492;
                 https://search.proquest.com/pqdtglobal/docview/1957944576",
  abstract =     "Non-determinism in high performance scientific
                 applications has severe detrimental impacts for both
                 numerical reproducibility and accuracy, and debugging.
                 As scientific simulations are migrated to extreme-scale
                 platforms, the increase in platform concurrency and the
                 attendant increase in non-determinism is likely to
                 exacerbate both of these problems. In this thesis, we
                 address the dual challenges of non-determinism's impact
                 on numerical reproducibility and on debugging. To
                 address the numerical challenge, our work investigates
                 the power of mathematical methods to mitigate error
                 propagation at the exascale. We focus on floating-point
                 error accumulation over global summations where
                 enforcing any reduction order is expensive or
                 impossible. We model parallel summations with reduction
                 trees and identify those parameters that can be used to
                 estimate the reduction's sensitivity to variability in
                 the reduction tree. We assess the impact of these
                 parameters on the ability of different reduction
                 methods to successfully mitigate errors. Our results
                 illustrate the pressing need for intelligent runtime
                 selection of reduction operators that ensure a given
                 degree of reproducible accuracy. To address the
                 debugging challenge, our work examines the impact of
                 logical clock ticking policies on the Clock-Delta
                 Compression record-and-replay technique. We assess
                 three logical clock ticking policies in terms of the
                 number of out-of-order messages that result during
                 recording executions under these policies. We examine
                 the performance of Clock-Delta Compression when using
                 the three ticking policies in four distinct application
                 scenarios to probe the impact of floating-point
                 workload and communication intensity on recording
                 performance. Our results illustrate the pressing need
                 for fine-grained logical clock ticking policies that
                 reduce the out-of-order message rate of the Clock-Delta
                 Compression record-and-replay technique.",
  acknowledgement = ack-nhfb,
  advisor =      "Michela Taufer",
}

@InProceedings{Chiang:2017:RFP,
  author =       "Wei-Fan Chiang and Mark Baranowski and Ian Briggs and
                 Alexey Solovyev and Ganesh Gopalakrishnan and Zvonimir
                 Rakamari{\'c}",
  booktitle =    "Proceedings of the {ACM SIGPLAN Symposium on
                 Principles of Programming Languages (POPL)}",
  title =        "Rigorous Floating-Point Mixed-Precision Tuning",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "300--315",
  year =         "2017",
  DOI =          "https://doi.org/10.1145/3009837.3009846",
  bibdate =      "Fri Mar 31 10:00:31 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Virtually all real-valued computations are carried out
                 using floating-point data types and operations. The
                 precision of these data types must be set with the
                 goals of reducing the overall round-off error, but also
                 emphasizing performance improvements. Often, a
                 mixed-precision allocation achieves this optimum;
                 unfortunately, there are no techniques available to
                 compute such allocations and conservatively meet a
                 given error target across all program inputs. In this
                 work, we present a rigorous approach to precision
                 allocation based on formal analysis via Symbolic Taylor
                 Expansions, and error analysis based on interval
                 functions. This approach is implemented in an automated
                 tool called FPTuner that generates and solves a
                 quadratically constrained quadratic program to obtain a
                 precision-annotated version of the given expression.
                 FPTuner automatically introduces all the requisite
                 precision up and down casting operations. It also
                 allows users to flexibly control precision allocation
                 using constraints to cap the number of high precision
                 operators as well as group operators to allocate the
                 same precision to facilitate vectorization. We evaluate
                 FPTuner by tuning several benchmarks and measuring the
                 proportion of lower precision operators allocated as we
                 increase the error threshold. We also measure the
                 reduction in energy consumption resulting from
                 executing mixed-precision tuned code on a real hardware
                 platform. We observe significant energy savings in
                 response to mixed-precision tuning, but also observe
                 situations where unexpected compiler behaviors thwart
                 intended optimizations.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chohra:2017:RAR,
  author =       "Chemseddine Chohra and Philippe Langlois and David
                 Parello",
  title =        "Reproducible, accurately rounded and efficient
                 {BLAS}",
  crossref =     "Desprez:2017:EPP",
  pages =        "609--620",
  year =         "2017",
  DOI =          "https://doi.org/10.1007/978-3-319-58943-5_49",
  bibdate =      "Mon Feb 10 06:36:40 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Constantinides:2017:AAC,
  author =       "George Anthony Constantinides",
  title =        "Algorithms and Arithmetic: Choose Wisely",
  crossref =     "Burgess:2017:ISC",
  pages =        "142--143",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.17",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "I will introduce a semi-formalism to allow us to
                 conceptually reason about the differences between
                 customised arithmetic design, as one might see in
                 FPGA-based compute, and general purpose arithmetic, as
                 one might find in microprocessor design. This framework
                 will, I hope, expose to the reader the reason that we
                 should be thinking carefully about appropriate data
                 representations when designing custom hardware for
                 compute, as well as clearly showing the link between
                 these decisions and algorithmic ones. I will then
                 provide a concrete example from the literature on
                 matrix computation where some careful algorithmic
                 tweaking results in the ability to use fixed-point
                 arithmetic and, hence, far higher performance than
                 would otherwise be achieved.",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithm design and analysis; ARITH 2017; ARITH-24;
                 arithmetic design; Automation; data representations;
                 data structures; digital arithmetic; field programmable
                 gate arrays; Field programmable gate arrays;
                 fixed-point arithmetic; FPGA; general purpose
                 arithmetic; Hardware; Kernel; logic design; matrix
                 algebra; matrix computation; microprocessor design;
                 Microprocessors; Signal processing algorithms",
}

@InProceedings{Cornea:2017:URE,
  author =       "Marius Cornea",
  title =        "{ULPs} and Relative Error",
  crossref =     "Burgess:2017:ISC",
  pages =        "90--97",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.30",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The paper establishes several simple, but useful
                 relationships between ulp (unit in the last place)
                 errors and the corresponding relative errors. These can
                 be used when converting between the two types of
                 errors, ensuring that the least amount of information
                 is lost in the process. The properties presented here
                 were already useful in IEEE conformance proofs for
                 iterative division and square root algorithms, and
                 should be so again to numerical analysts both in 'hand'
                 proofs of error bounds for floating-point computations,
                 and in automated tools which carry out, or support
                 deriving such proofs. In most cases, the properties
                 shown herein establish tighter bounds than found in the
                 literature. They also provide 'conversion' rules of
                 finer granularity, at floating-point value level
                 instead of binade level, and take into account the
                 special conditions which occur at binade ends. For this
                 reason, the paper includes a small, but non-negligible
                 element of novelty.",
  acknowledgement = ack-nhfb,
  keywords =     "approximation; ARITH 2017; ARITH-24; correctly
                 rounded; error; floating point arithmetic;
                 floating-point; floating-point computations; IEEE
                 754-2008; IEEE conformance proofs; iterative division;
                 iterative methods; numerical analysis; quantum;
                 relative error; square root algorithms; ULP; ulp; ulp
                 error; unit in the last place",
}

@Article{Cui:2017:HPP,
  author =       "Xiaoping Cui and Wenwen Dong and Weiqiang Liu and Earl
                 E. Swartzlander and Fabrizio Lombardi",
  title =        "High Performance Parallel Decimal Multipliers Using
                 Hybrid {BCD} Codes",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "66",
  number =       "12",
  pages =        "1994--2004",
  month =        "????",
  year =         "2017",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2017.2706262",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 10 08:32:25 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/document/7931610/",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Dai:2017:ATE,
  author =       "Wangchen Dai and Donald Donglong Chen and Ray C. C.
                 Cheung and {\c{C}}etin Kaya Ko{\c{c}}",
  title =        "Area-Time Efficient Architecture of {FFT}-Based
                 {Montgomery} Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "66",
  number =       "3",
  pages =        "375--388",
  month =        "????",
  year =         "2017",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2016.2601334",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Feb 10 09:07:14 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Damouche:2017:INA,
  author =       "Nasrine Damouche and Matthieu Martel and Alexandre
                 Chapoutot",
  title =        "Improving the numerical accuracy of programs by
                 automatic transformation",
  journal =      j-INT-J-SOFTW-TOOLS-TECHNOL-TRANSFER,
  volume =       "19",
  number =       "4",
  pages =        "427--448",
  month =        aug,
  year =         "2017",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s10009-016-0435-0",
  ISSN =         "1433-2779 (print), 1433-2787 (electronic)",
  ISSN-L =       "1433-2779",
  bibdate =      "Thu Nov 23 07:32:25 MST 2017",
  bibsource =    "http://link.springer.com/journal/10009/19/4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sttt.bib",
  URL =          "https://link.springer.com/article/10.1007/s10009-016-0435-0",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal on Software Tools for Technology
                 Transfer (STTT)",
  journal-URL =  "http://link.springer.com/journal/10009",
  keywords =     "Floating-point numbers; IEEE 754 standard; Numerical
                 accuracy; Program transformation; Static analysis",
}

@Article{Darulova:2017:TCR,
  author =       "Eva Darulova and Viktor Kuncak",
  title =        "Towards a Compiler for Reals",
  journal =      j-TOPLAS,
  volume =       "39",
  number =       "2",
  pages =        "8:1--8:??",
  month =        may,
  year =         "2017",
  CODEN =        "ATPSDT",
  DOI =          "https://doi.org/10.1145/3014426",
  ISSN =         "0164-0925 (print), 1558-4593 (electronic)",
  ISSN-L =       "0164-0925",
  bibdate =      "Mon Jul 24 09:44:40 MDT 2017",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toplas/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toplas.bib",
  abstract =     "Numerical software, common in scientific computing or
                 embedded systems, inevitably uses a finite-precision
                 approximation of the real arithmetic in which most
                 algorithms are designed. In many applications, the
                 roundoff errors introduced by finite-precision
                 arithmetic are not the only source of inaccuracy, and
                 measurement and other input errors further increase the
                 uncertainty of the computed results. Adequate tools are
                 needed to help users select suitable data types and
                 evaluate the provided accuracy, especially for
                 safety-critical applications. We present a
                 source-to-source compiler called Rosa that takes as
                 input a real-valued program with error specifications
                 and synthesizes code over an appropriate floating-point
                 or fixed-point data type. The main challenge of such a
                 compiler is a fully automated, sound, and yet
                 accurate-enough numerical error estimation. We
                 introduce a unified technique for bounding roundoff
                 errors from floating-point and fixed-point arithmetic
                 of various precisions. The technique can handle
                 nonlinear arithmetic, determine closed-form symbolic
                 invariants for unbounded loops, and quantify the
                 effects of discontinuities on numerical errors. We
                 evaluate Rosa on a number of benchmarks from scientific
                 computing and embedded systems and, comparing it to the
                 state of the art in automated error estimation, show
                 that it presents an interesting tradeoff between
                 accuracy and performance.",
  acknowledgement = ack-nhfb,
  articleno =    "8",
  fjournal =     "ACM Transactions on Programming Languages and
                 Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J783",
}

@Article{David:2017:LLD,
  author =       "Jean Pierre David",
  title =        "Low latency and division free {Gauss--Jordan} solver
                 in floating point arithmetic",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "106",
  number =       "??",
  pages =        "185--193",
  month =        aug,
  year =         "2017",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Aug 19 13:10:31 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jpardistcomp.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0743731516301897",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
}

@Article{Dawson:2017:RVE,
  author =       "Andrew Dawson and Peter D. D{\"u}ben",
  title =        "{rpe v5}: an emulator for reduced floating-point
                 precision in large numerical simulations",
  journal =      j-GEOSCI-MODEL-DEV,
  volume =       "10",
  number =       "6",
  pages =        "2221--2230",
  month =        jun,
  year =         "2017",
  DOI =          "https://doi.org/10.5194/gmd-10-2221-2017",
  ISSN =         "1991-959X (print), 1991-9603 (electronic)",
  ISSN-L =       "1991-959X",
  bibdate =      "Thu Nov 7 16:40:41 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Geoscientific Model Development",
  journal-URL =  "http://www.geosci-model-dev.net",
}

@InProceedings{Dimitrov:2017:PMC,
  author =       "Vassil Dimitrov and Viduneth Ariyarathna and Diego F.
                 G. Coelho and Logan Rakai and Arjuna Madanayake and
                 Renato J. Cintra",
  title =        "A Parallel Method for the Computation of Matrix
                 Exponential Based on Truncated {Neumann} Series",
  crossref =     "Burgess:2017:ISC",
  pages =        "35--42",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.23",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper introduces a new method for computing
                 matrix exponential based on truncated Neumann series.
                 The efficiency of the method is based on smart
                 factorizations for evaluation of several Neumann series
                 that can be done in parallel and divided across
                 different processors with low communication overhead. A
                 physical realization on FPGA is provided for
                 proof-of-concept. The method is verified to be
                 advantageous over the usual Horner's rule approach for
                 polynomial evaluation. The hardware verification shows
                 a reduction of 62\% in time required for processing for
                 series approximations with 9 terms. Software
                 verification demonstrates a 30\% reduction in time
                 compared to Horner's rule and the trade-offs between
                 using a higher precision approach is illustrated.",
  acknowledgement = ack-nhfb,
  keywords =     "Approximation algorithms; approximation theory; ARITH
                 2017; ARITH-24; Eigenvalues and eigenfunctions; Error
                 analysis; Fast algorithms; field programmable gate
                 arrays; FPGA; Hardware; Horner's rule approach; low
                 communication overhead; matrix algebra; matrix
                 decomposition; matrix exponential; Matrix exponential;
                 Neumann series; parallel method; polynomial evaluation;
                 polynomials; Program processors; series (mathematics);
                 series approximations; smart factorizations; Software
                 algorithms; software verification; truncated Neumann
                 series; VLSI",
}

@Article{Du:2017:AQD,
  author =       "Peibing Du and Roberto Barrio and Hao Jiang and Lizhi
                 Cheng",
  title =        "Accurate quotient-difference algorithm: Error
                 analysis, improvements and applications",
  journal =      j-APPL-MATH-COMP,
  volume =       "309",
  number =       "??",
  pages =        "245--271",
  day =          "15",
  month =        sep,
  year =         "2017",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Sat Aug 12 16:28:39 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300317302394",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Book{Esmay:2017:HNS,
  author =       "Gabriel Esmay",
  title =        "The History of Number Systems",
  publisher =    "Teacher Created Materials",
  address =      "Huntington Beach, CA",
  pages =        "32",
  year =         "2017",
  ISBN =         "0-7439-2834-2 (e-book), 1-0876-2972-1, 1-4807-5794-2
                 (paperback), 1-4807-5858-2 (e-book)",
  ISBN-13 =      "978-0-7439-2834-2 (e-book), 978-1-0876-2972-8,
                 978-1-4807-5794-3 (paperback), 978-1-4807-5858-2
                 (e-book)",
  LCCN =         "QA141.3 .E86 2018",
  bibdate =      "Fri Mar 17 08:27:53 MDT 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Learn the history of number systems with this engaging
                 math reader! This text combines mathematics and
                 literacy skills, and uses practical, real-world
                 examples of problem solving to teach math and language
                 arts content. Students will learn place value while
                 reading about the number systems of the Egyptians and
                 Romans, and also learn important vocabulary terms like
                 cuneiform, binary systems, roman numerals, and more!
                 The full-color images, math charts, and practice
                 problems make learning math easy and fun. The table of
                 contents, glossary, and index will further
                 understanding of math and reading concepts. The Math
                 Talk problems and Explore Math sidebars provide
                 additional learning opportunities while developing
                 students higher-order thinking skills.",
  acknowledgement = ack-nhfb,
  subject =      "Numeration; History; Juvenile literature; Counting;
                 Calcul; Ouvrages pour la jeunesse; Counting.;
                 Numeration.",
  tableofcontents = "Timeless need \\
                 Egypt \\
                 Babylon \\
                 Roman empire \\
                 Americas \\
                 Modern beginnings \\
                 Future of number systems \\
                 Problem solving \\
                 Glossary",
}

@Misc{Fevotte:2017:LLI,
  author =       "Fran{\c{c}}ois F{\'e}votte and Bruno Lathuili{\`e}re",
  title =        "{LibEFT}: a library implementing Error-Free
                 transformations",
  howpublished = "Web site.",
  year =         "2017",
  bibdate =      "Sat Feb 08 10:47:59 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://github.com/ffevotte/libeft",
  acknowledgement = ack-nhfb,
}

@Article{Fu:2017:AHC,
  author =       "Zhoulai Fu and Zhendong Su",
  title =        "Achieving high coverage for floating-point code via
                 unconstrained programming",
  journal =      j-SIGPLAN,
  volume =       "52",
  number =       "6",
  pages =        "306--319",
  month =        jun,
  year =         "2017",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/3140587.3062383",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Sat Sep 16 10:18:17 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
  abstract =     "Achieving high code coverage is essential in testing,
                 which gives us confidence in code quality. Testing
                 floating-point code usually requires painstaking
                 efforts in handling floating-point constraints, e.g.,
                 in symbolic execution. This paper turns the challenge
                 of testing floating-point code into the opportunity of
                 applying unconstrained programming --- the mathematical
                 solution for calculating function minimum points over
                 the entire search space. Our core insight is to derive
                 a representing function from the floating-point
                 program, any of whose minimum points is a test input
                 guaranteed to exercise a new branch of the tested
                 program. This guarantee allows us to achieve high
                 coverage of the floating-point program by repeatedly
                 minimizing the representing function. We have realized
                 this approach in a tool called CoverMe and conducted an
                 extensive evaluation of it on Sun's C math library. Our
                 evaluation results show that CoverMe achieves, on
                 average, 90.8\% branch coverage in 6.9 seconds,
                 drastically outperforming our compared tools: (1)
                 Random testing, (2) AFL, a highly optimized, robust
                 fuzzer released by Google, and (3) Austin, a
                 state-of-the-art coverage-based testing tool designed
                 to support floating-point code.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  remark =       "PLDI '17 conference proceedings.",
}

@Article{Fumex:2017:AVF,
  author =       "Cl{\'e}ment Fumex and Claude March{\'e} and Yannick
                 Moy",
  editor =       "Andrei Paskevich and Thomas Wies",
  booktitle =    "Verified Software. Theories, Tools, and Experiments:
                 {9th International Conference, VSTTE 2017, Heidelberg,
                 Germany, July 22--23, 2017, Revised Selected Papers}",
  title =        "Automating the Verification of Floating-Point
                 Programs",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "10712",
  pages =        "102--119",
  year =         "2017",
  DOI =          "https://doi.org/10.1007/978-3-319-72308-2_7",
  ISBN =         "3-319-72308-1",
  ISBN-13 =      "978-3-319-72308-2",
  ISSN =         "1611-3349",
  bibdate =      "Sat Jun 8 09:04:13 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-319-72308-2",
}

@InProceedings{Gonzalez-Navarro:2017:NNO,
  author =       "Sonia Gonzalez-Navarro and Javier Hormigo",
  title =        "Normalizing or Not Normalizing? {An} Open Question for
                 Floating-Point Arithmetic in Embedded Systems",
  crossref =     "Burgess:2017:ISC",
  pages =        "188--195",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.16",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Emerging embedded applications lack of a specific
                 standard when they require floating-point arithmetic.
                 In this situation they use the IEEE-754 standard or ad
                 hoc variations of it. However, this standard was not
                 designed for this purpose. This paper aims to open a
                 debate to define a new extension of the standard to
                 cover embedded applications. In this work, we only
                 focus on the impact of not performing normalization. We
                 show how eliminating the condition of normalized
                 numbers, implementation costs can be dramatically
                 reduced, at the expense of a moderate loss of accuracy.
                 Several architectures to implement addition and
                 multiplication for non-normalized numbers are proposed
                 and analyzed. We show that a combined architecture
                 (adder-multiplier) can halve the area and power
                 consumption of its counterpart IEEE-754 architecture.
                 This saving comes at the cost of reducing an average of
                 about 10 dBs the Signal-to-Noise Ratio for the tested
                 algorithms. We think these results should encourage
                 researchers to perform further investigation in this
                 issue.",
  acknowledgement = ack-nhfb,
  keywords =     "ad hoc variations; adder-multiplier; adders; Adders;
                 ARITH 2017; ARITH-24; Computer architecture; DSP;
                 embedded applications; embedded systems; Embedded
                 systems; embedded systems; Field programmable gate
                 arrays; floating point arithmetic; floating-point;
                 floating-point arithmetic; Hardware; IEEE standards;
                 IEEE-754 architecture; IEEE-754 standard; Loss
                 measurement; nonnormalized numbers; Normalization;
                 normalized number condition; power consumption;
                 signal-to-noise ratio; standard; Standards",
}

@Article{Gorantla:2017:DAC,
  author =       "Anusha Gorantla and Deepa P.",
  title =        "Design of Approximate Compressors for Multiplication",
  journal =      j-JETC,
  volume =       "13",
  number =       "3",
  pages =        "44:1--44:??",
  month =        may,
  year =         "2017",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3007649",
  ISSN =         "1550-4832 (print), 1550-4840 (electronic)",
  ISSN-L =       "1550-4832",
  bibdate =      "Tue Jul 11 17:10:31 MDT 2017",
  bibsource =    "http://www.acm.org/pubs/contents/journals/jetc/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jetc.bib",
  abstract =     "Approximate computing is a promising technique for
                 energy-efficient Very Large Scale Integration (VLSI)
                 system design. It is best suited for error-resilient
                 applications such as signal processing and multimedia.
                 Approximate computing reduces accuracy but still
                 provides significant and faster results with lower
                 power consumption. This is attractive to arithmetic
                 circuits. In this article, various novel design
                 approaches of approximate 4-2 and 5-2 compressors have
                 been proposed for reduction of the partial product
                 stages in multiplication. Three approximate 8 $ \times
                 $ 8 Dadda multiplier designs using three novel
                 approximate 4-2 compressors and two approximate 8 $
                 \times $ 8 Dadda multiplier designs using two novel
                 approximate 5-2 compressors have proposed. The
                 synthesis results show that the proposed designs
                 achieved significant accuracy improvement together with
                 power and delay reductions compared to the existing
                 approximate designs.",
  acknowledgement = ack-nhfb,
  articleno =    "44",
  fjournal =     "ACM Journal on Emerging Technologies in Computing
                 Systems (JETC)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J967",
}

@TechReport{Graillat:2017:AAE,
  author =       "Stef Graillat",
  title =        "An accurate algorithm for evaluating rational
                 functions",
  type =         "Report",
  number =       "HAL-01578486",
  institution =  "Laboratoire d'Informatique de Paris 6, Universit{\'e}
                 Sorbonne, Campus Pierre et Marie Curie",
  address =      "4, place Jussieu, F-75252 Paris Cedex 05, France",
  day =          "29",
  month =        aug,
  year =         "2017",
  MRclass =      "15-04 65G99 65-04",
  bibdate =      "Mon Mar 19 08:17:18 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://hal.archives-ouvertes.fr/hal-01578486",
  abstract =     "Several different techniques intend to improve the
                 accuracy of results computed in floating-point
                 precision. Here, we focus on a method to improve the
                 accuracy of the evaluation of rational functions. We
                 present a compensated algorithm to evaluate rational
                 functions. This algorithm is accurate and fast. The
                 accuracy of the computed result is similar to the one
                 given by the classical algorithm computed in twice the
                 working precision and then rounded to the current
                 working precision. This algorithm runs much more faster
                 than existing implementation producing the same output
                 accuracy.",
  acknowledgement = ack-nhfb,
  keywords =     "accuracy; error-free transformation; floating-point;
                 Horner scheme; rational function; rounding errors",
}

@InProceedings{Guney:2017:OMM,
  author =       "Murat Efe Guney and Kazushige Goto and Timothy B.
                 Costa and Sarah Knepper and Louise Huot and Arthur
                 Mitrano and Shane Story",
  title =        "Optimizing Matrix Multiplication on {Intel Xeon Phi TH
                 x200} Architecture",
  crossref =     "Burgess:2017:ISC",
  pages =        "144--145",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.19",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Matrix multiplication is ubiquitous in scientific
                 computing. From computational science to machine
                 learning, a large and diverse set of applications rely
                 on the performance of general matrix-matrix
                 multiplication (GEMM) subroutines. The Intel Math
                 Kernel Library(R) provides highly optimized GEMM
                 subroutines that take full advantage of the available
                 parallelism and vectorization in both Intel Xeon and
                 Intel Xeon Phi(TM) processors. In this paper we discuss
                 the optimization of GEMM subroutines for the Intel Xeon
                 PhiTM x200 (code-named Knights Landing).",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithms; ARITH 2017; ARITH-24; Bandwidth; blas;
                 computational science; Computer architecture; general
                 matrix-matrix multiplication; Intel Math Kernel
                 Library; intel xeon phi; Intel Xeon Phi x200
                 architecture; Kernel; Knights Landing; machine
                 learning; matrix multiplication; microprocessor chips;
                 Optimization; performance optimization; Prefetching;
                 processors; scientific computing",
}

@Misc{Gustafson:2017:BFPa,
  author =       "John Gustafson",
  title =        "Beyond Floating Point: Next Generation Computer
                 Arithmetic",
  howpublished = "Web video",
  month =        feb,
  year =         "2017",
  bibdate =      "Mon Feb 06 06:47:46 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://insidehpc.com/2017/02/john-gustafson-presents-beyond-floating-point-next-generation-computer-arithmetic",
  acknowledgement = ack-nhfb,
  keywords =     "unum floating-point format",
}

@TechReport{Gustafson:2017:BFPb,
  author =       "John Gustafson and Isaac Yonemoto",
  title =        "Beating Floating Point at its Own Game: Posit
                 Arithmetic",
  type =         "Report",
  institution =  "A*STAR Computational Resources Centre and National
                 University of Singapore (joint appointment) [JG],
                 Singapore Interplanetary Robot and Electric Brain
                 Company, Saratoga, California USA [IY]",
  pages =        "16",
  day =          "12",
  month =        jun,
  year =         "2017",
  bibdate =      "Mon Sep 26 13:38:16 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.johngustafson.net/pdfs/BeatingFloatingPoint.pdf",
  abstract =     "A new data type called a posit is designed as a direct
                 drop-in replacement for IEEE Standard 754
                 floating-point numbers (floats). Unlike earlier forms
                 of universal number (unum) arithmetic, posits do not
                 require interval arithmetic or variable size operands;
                 like floats, they round if an answer is inexact.
                 However, they provide compelling advantages over
                 floats, including larger dynamic range, higher
                 accuracy, better closure, bitwise identical results
                 across systems, simpler hardware, and simpler exception
                 handling. Posits never overflow to infinity or
                 underflow to zero, and ``Not-a-Number'' (NaN) indicates
                 an action instead of a bit pattern. A posit processing
                 unit takes less circuitry than an IEEE float FPU. With
                 lower power use and smaller silicon footprint, the
                 posit operations per second (POPS) supported by a chip
                 can be significantly higher than the FLOPS using
                 similar hardware resources. GPU accelerators and Deep
                 Learning processors, in particular, can do more per
                 watt and per dollar with posits, yet deliver superior
                 answer quality.\par

                 A comprehensive series of benchmarks compares floats
                 and posits for decimals of accuracy produced for a set
                 precision. Low precision posits provide a better
                 solution than ``approximate computing'' methods that
                 try to tolerate decreased answer quality. High
                 precision posits provide more correct decimals than
                 floats of the same size; in some cases, a 32-bit posit
                 may safely replace a 64-bit float. In other words,
                 posits beat floats at their own game.",
  acknowledgement = ack-nhfb,
  keywords =     "computer arithmetic; energy-efficient computing;
                 floating point; linear algebra; LINPACK; neural
                 networks; posits; unum computing; valid arithmetic",
}

@Article{Gustafson:2017:BFPc,
  author =       "John L. Gustafson and Isaac Yonemoto",
  title =        "Beating Floating Point at Its Own Game: Posit
                 Arithmetic",
  journal =      j-SUPERFRI,
  volume =       "4",
  number =       "2",
  pages =        "71--86",
  year =         "2017",
  CODEN =        "????",
  DOI =          "https://doi.org/10.14529/jsfi170206",
  ISSN =         "2313-8734 (print), 2409-6008 (electronic)",
  ISSN-L =       "2313-8734",
  bibdate =      "Sun Dec 10 14:34:44 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://superfri.org/index.php/superfri/article/view/137/232",
  acknowledgement = ack-nhfb,
  fjournal =     "Supercomputing Frontiers and Innovations: an
                 International Journal",
  journal-doi =  "https://doi.org/10.14529/jsfi",
  journal-URL =  "https://superfri.org/index.php/superfri/",
  remark =       "Published at South Ural State University, Chelyabinsk,
                 Russia, Russia. Not in US Library of Congress or
                 CASSI.",
  xx-journal-url = "https://superfri.org/index.php/superfri/issue/archive",
}

@Misc{Gustafson:2017:PA,
  author =       "John L. Gustafson",
  title =        "Posit Arithmetic",
  howpublished = "Web PDF file.",
  pages =        "1--137",
  day =          "10",
  month =        oct,
  year =         "2017",
  bibdate =      "Tue Jul 09 10:34:12 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://posithub.org/docs/Posits4.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gustafsson:2017:ANS,
  author =       "Oscar Gustafsson and Erik Bertilsson and Johannes
                 Klasson and Carl Ingemarsson",
  title =        "Approximate {Neumann} Series or Exact Matrix Inversion
                 for Massive {MIMO}?",
  crossref =     "Burgess:2017:ISC",
  pages =        "62--63",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.11",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Approximate matrix inversion based on Neumann series
                 has seen a recent increased interest motivated by
                 massive MIMO systems. There, the matrices are in many
                 cases diagonally dominant, and, hence, a reasonable
                 approximation can be obtained within a few iterations
                 of a Neumann series. In this work, we clarify that the
                 complexity of exact methods are about the same as when
                 three terms are used for the Neumann series, so in this
                 case, the complexity is not lower as often claimed. The
                 second common argument for Neumann series
                 approximation, higher parallelism, is indeed correct.
                 However, in most current practical use cases, such a
                 high degree of parallelism is not required to obtain a
                 low latency realization. Hence, we conclude that a
                 careful evaluation, based on accuracy and latency
                 requirements must be performed and that exact matrix
                 inversion is in fact viable in many more cases than the
                 current literature claims.",
  acknowledgement = ack-nhfb,
  keywords =     "approximate matrix inversion; approximate Neumann
                 series; approximation theory; ARITH 2017; ARITH-24;
                 Clocks; Complexity theory; Computer architecture; exact
                 matrix inversion; iterative methods; Large-scale MIMO;
                 Latency; Massive MIMO; massive MIMO systems; matrix
                 algebra; Matrix inversion; MIMO; MIMO communication;
                 Neumann series; Pipeline processing; Symmetric
                 matrices",
}

@InProceedings{Gustafsson:2017:LBF,
  author =       "Oscar Gustafsson",
  title =        "On Lifting-Based Fixed-Point Complex Multiplications
                 and Rotations",
  crossref =     "Burgess:2017:ISC",
  pages =        "43--49",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.10",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Lifting-based complex multiplications and rotations
                 are integer invertible, i.e., an integer input value is
                 mapped to the same integer output value when rotating
                 forward and backward. This is an important aspect for
                 lossless transform based source coding, but since the
                 structure only require three real-valued
                 multiplications and three real-valued additions it is
                 also a potentially attractive way to perform complex
                 multiplications when the coefficient has unity
                 magnitude. In this work, we consider two aspects of
                 these structures. First, we show that both the
                 magnitude and angular error is dependent on the angle
                 of input value and derive both exact and approximated
                 expressions for these. Second, we discuss how to design
                 such structures without the typical separation into
                 three subsequent matrix multiplications. It is shown
                 that the proposed design method allows many more values
                 which are integer invertible, but can not be separated
                 into three subsequent matrix multiplications with
                 fixed-point values. The results show good
                 correspondence between the error approximations and the
                 actual error as well as a significantly increased
                 design space.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2017; ARITH-24; complex multiplication; complex
                 rotation; Design methodology; digital arithmetic;
                 Digital arithmetic; Discrete cosine transforms;
                 Electrical engineering; error analysis; error
                 approximations; fixed-point; lifting; lifting-based
                 fixed-point complex multiplications; lifting-based
                 fixed-point complex rotations; logic design; lossless
                 transform based source coding; Matrix decomposition;
                 real-valued additions; real-valued multiplications;
                 rotation; source coding; Source coding; transform
                 coding",
}

@InProceedings{Haidar:2017:IHP,
  author =       "Azzam Haidar and Panruo Wu and Stanimire Tomov and
                 Jack Dongarra",
  booktitle =    "Proceedings of the {8th Workshop on Latest Advances in
                 Scalable Algorithms for Large-Scale Systems ---
                 ScalA'17}",
  title =        "Investigating half precision arithmetic to accelerate
                 dense linear system solvers",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  year =         "2017",
  DOI =          "https://doi.org/10.1145/3148226.3148237",
  ISBN =         "1-4503-5125-5 (hardcover)",
  ISBN-13 =      "978-1-4503-5125-6 (hardcover)",
  LCCN =         "????",
  bibdate =      "Thu Nov 7 16:51:39 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Dongarra, Jack/0000-0003-3247-1782",
}

@Book{Hennessy:2017:CAQ,
  author =       "John L. Hennessy and David A. Patterson",
  title =        "Computer Architecture: a Quantitative Approach",
  publisher =    pub-MORGAN-KAUFMANN,
  address =      pub-MORGAN-KAUFMANN:adr,
  edition =      "Sixth",
  pages =        "xxix + 617 + 55 + 67 + 78 + 36 + 48",
  year =         "2017",
  ISBN =         "0-12-383873-8, 0-12-811905-5 (paperback),
                 0-12-811906-3 (e-Pub)",
  ISBN-13 =      "978-0-12-383873-5, 978-0-12-811905-1 (paperback),
                 978-0-12-811906-8 (e-Pub)",
  LCCN =         "QA76.9.A73",
  bibdate =      "Sat Jun 14 07:16:37 MDT 2025",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  abstract =     "\booktitle{Computer Architecture: A Quantitative
                 Approach}, Sixth Edition has been considered essential
                 reading by instructors, students and practitioners of
                 computer design for over 20 years. The sixth edition of
                 this classic textbook from Hennessy and Patterson,
                 winners of the 2017 ACM A. M. Turing Award recognizing
                 contributions of lasting and major technical importance
                 to the computing field, is fully revised with the
                 latest developments in processor and system
                 architecture. The text now features examples from the
                 RISC-V (RISC Five) instruction set architecture, a
                 modern RISC instruction set developed and designed to
                 be a free and openly adoptable standard. It also
                 includes a new chapter on domain-specific architectures
                 and an updated chapter on warehouse-scale computing
                 that features the first public information on Google's
                 newest WSC. True to its original mission of
                 demystifying computer architecture, this edition
                 continues the longstanding tradition of focusing on
                 areas where the most exciting computing innovation is
                 happening, while always keeping an emphasis on good
                 engineering design.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Printed Text \\
                 Foreword / ix--xiii \\
                 Preface / xvii--xxiii \\
                 Acknowledgments / xxv--xxix \\
                 1. Fundamentals of Quantitative Design and Analysis /
                 xxx \\
                 2. Memory Hierarchy Design / 76--164 \\
                 3. Instruction-Level Parallelism and Its Exploitation /
                 166--278 \\
                 4. Data-Level Parallelism in Vector, SIMD, and GPU
                 Architectures / 280--365 \\
                 5. Multiprocessors and Thread-Level Parallelism /
                 366--462 \\
                 6. Warehouse-Scale Computers to Exploit Request-Level
                 and Data-Level Parallelism / 464--537 \\
                 7. Domain Specific Architectures / 538--617 \\
                 A. Instruction Set Principles / A-0--A-66 \\
                 B. Review of Memory Hierarchy / B-0--B-67 \\
                 C. Pipelining: Basic and Intermediate Concepts /
                 C-0--C-78 \\
                 References / R-1--R-36 \\
                 Index / I-1--I-48 \\
                 Online \\
                 https://www.elsevier.com/books-and-journals/book-companion/9780128119051
                 \\
                 D. Storage Systems / D-0--D-67 \\
                 E. Embedded Systems / E-0--E-26 \\
                 F. Interconnection Networks / Revised by Timothy M.
                 Pinkston and Jos{\'e} Duato / F-0--F-118 \\
                 G. Vector Processors in More Depth / Revised by Krste
                 Asanovic / G-0--G-34 \\
                 H. Hardware and Software for VLIW and EPIC / H-0--H-44
                 \\
                 I. Large-Scale Multiprocessors and Scientific
                 Applications / I-0--I-47 \\
                 J. Computer Arithmetic / David Goldberg / J-0--J-73 \\
                 K. Survey of Instruction Set Architectures / K-0--K-75
                 \\
                 L. Advanced Concepts on Address Translation / Abhishek
                 Bhattacharjee / L-0--L-69 \\
                 M. Historical Perspectives and References / M-0--M-93",
}

@Article{Hiasat:2017:ERS,
  author =       "Ahmad Hiasat",
  title =        "Efficient {RNS} Scalers for the Extended Three-Moduli
                 Set $ (2^n - 1, 2^{n + p}, 2^n + 1) $",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "66",
  number =       "7",
  pages =        "1253--1260",
  month =        jul,
  year =         "2017",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2017.2652474",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jun 8 10:22:00 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://www.computer.org/csdl/trans/tc/2017/07/07815319-abs.html",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Residue Number System (RNS)",
}

@Book{Higham:2017:MG,
  author =       "Desmond J. Higham and Nicholas J. Higham",
  title =        "{MATLAB} guide",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xxvi + 476",
  year =         "2017",
  ISBN =         "1-61197-465-8",
  ISBN-13 =      "978-1-61197-465-2",
  MRclass =      "65-00 (00A20)",
  MRnumber =     "3601107",
  bibdate =      "Sat Aug 26 17:40:10 2017",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/numana2010.bib",
  abstract =     "MATLAB is an interactive system for numerical
                 computation that is widely used for teaching and
                 research in industry and academia. It provides a modern
                 programming language and problem solving environment,
                 with powerful data structures, customizable graphics,
                 and easy-to-use editing and debugging tools. This third
                 edition of MATLAB Guide completely revises and updates
                 the best-selling second edition and is more than 25
                 percent longer. The book remains a lively, concise
                 introduction to the most popular and important features
                 of MATLAB and the Symbolic Math Toolbox. Key features
                 are a tutorial in Chapter 1 that gives a hands-on
                 overview of MATLAB, a thorough treatment of MATLAB
                 mathematics, including the linear algebra and numerical
                 analysis functions and the differential equation
                 solvers, and a web page that provides a link to example
                 program files, updates, and links to MATLAB resources.
                 The new edition contains color figures throughout,
                 includes pithy discussions of related topics in new
                 `Asides' boxes that augment the text, has new chapters
                 on the Parallel Computing Toolbox, object-oriented
                 programming, graphs, and large data sets, covers
                 important new MATLAB data types such as categorical
                 arrays, string arrays, tall arrays, tables, and
                 timetables, contains more on MATLAB workflow, including
                 the Live Editor and unit tests, and fully reflects
                 major updates to the MATLAB graphics system.",
  acknowledgement = ack-nhfb,
  remark =       "Third edition of
                 \cite{Higham:2000:MG,Higham:2005:MG}.",
  subject =      "MATLAB (logiciel).; Analyse num{\'e}rique; Logiciels.;
                 Numerical analysis; Data processing; Data processing.",
  tableofcontents = "1: A Brief Tutorial \\
                 2: Basics \\
                 3: Distinctive Features of MATLAB \\
                 4: Arithmetic \\
                 5: Matrices \\
                 6: Operators and Flow Control \\
                 7: Program Files \\
                 8: Graphics \\
                 9: Linear Algebra \\
                 10: More on Functions \\
                 11: Numerical Methods: Part I \\
                 12: Numerical Methods: Part II \\
                 13: Input and Output \\
                 14: Troubleshooting \\
                 15: Sparse Matrices \\
                 16: More on Coding \\
                 17: Advanced Graphics \\
                 18: Other Data Types and Multidimensional Arrays \\
                 19: Object-Oriented Programming \\
                 20: The Symbolic Math Toolbox \\
                 21: Graphs \\
                 22: Large Data Sets \\
                 23: Optimizing Codes \\
                 24: Tricks and Tips \\
                 25: The Parallel Computing Toolbox \\
                 26: Case Studies",
}

@Article{Higham:2017:MW,
  author =       "Nicholas J. Higham",
  title =        "A multiprecision world",
  journal =      j-SIAM-NEWS,
  volume =       "50",
  number =       "8",
  pages =        "??--??",
  day =          "2",
  month =        oct,
  year =         "2017",
  ISSN =         "0036-1437",
  bibdate =      "Wed Aug 07 15:18:43 2024",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://sinews.siam.org/Details-Page/a-multiprecision-world",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM News",
  journal-URL =  "https://sinews.siam.org/",
}

@InProceedings{Higham:2017:RMA,
  author =       "Nicholas John Higham",
  title =        "The Rise of Multiprecision Arithmetic",
  crossref =     "Burgess:2017:ISC",
  pages =        "1--1",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.24",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "There is a growing demand for and availability of
                 multiprecision arithmetic: floating point arithmetic
                 supporting multiple, possibly arbitrary, precisions.
                 For an increasing body of applications, including in
                 supernova simulations, electromagnetic scattering
                 theory, and computational number theory, double
                 precision arithmetic is insufficient to provide results
                 of the required accuracy. On the other hand, for
                 climate modelling and deep learning half precision
                 (about four significant decimal digits) has been shown
                 to be sufficient in some studies. We discuss a number
                 of topics involving multiprecision arithmetic,
                 including: The need for, availability of, and ways to
                 exploit, higher precision arithmetic (e.g., quadruple
                 precision arithmetic). How to derive linear algebra
                 algorithms that will run in any precision, as opposed
                 to be being optimized (as some key algorithms are) for
                 double precision. For solving linear systems with the
                 use of iterative refinement, the benefits of suitably
                 combining three different precisions of arithmetic
                 (say, half, single, and double). How a new form of
                 preconditioned iterative refinement can be used to
                 solve very ill conditioned sparse linear systems to
                 high accuracy.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2017; ARITH-24; climate modelling; Computational
                 modeling; deep learning half precision; Digital
                 arithmetic; double precision arithmetic;
                 Electromagnetic scattering; floating point arithmetic;
                 Floating-point arithmetic; iterative methods; iterative
                 refinement; linear algebra; linear algebra algorithms;
                 linear systems; Linear systems; Mathematical model;
                 multiprecision arithmetic; sparse linear systems",
}

@InProceedings{Ho:2017:EHP,
  author =       "Nhut-Minh Ho and Weng-Fai Wong",
  booktitle =    "{2017 IEEE High Performance Extreme Computing
                 Conference (HPEC)}",
  title =        "Exploiting half precision arithmetic in {Nvidia
                 GPUs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--7",
  year =         "2017",
  DOI =          "https://doi.org/10.1109/HPEC.2017.8091072",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Arrays; Graphics processing units; Hardware;
                 Instruction sets; Registers; Tools",
}

@Article{Hormigo:2017:ISI,
  author =       "Javier Hormigo and Jean-Michel Muller and Stuart
                 Oberman and Nathalie Revol and Arnaud Tisserand and
                 Julio Villalba-Moreno",
  title =        "Introduction to the Special Issue on Computer
                 Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "66",
  number =       "12",
  pages =        "1991--1993",
  month =        "????",
  year =         "2017",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2017.2761278",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 10 08:32:25 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Hou:2017:TGF,
  author =       "Junjie Hou and Yongxin Zhu and Yulan Shen and Mengjun
                 Li and Han Wu and Han Song",
  booktitle =    "{2017 IEEE 19th International Conference on High
                 Performance Computing and Communications; IEEE 15th
                 International Conference on Smart City; IEEE 3rd
                 International Conference on Data Science and Systems
                 (HPCC/SmartCity/DSS)}",
  title =        "Tackling Gaps in Floating-Point Arithmetic: Unum
                 Arithmetic Implementation on {FPGA}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "615--616",
  year =         "2017",
  DOI =          "https://doi.org/10.1109/HPCC-SmartCity-DSS.2017.82",
  bibdate =      "Fri Dec 15 07:38:18 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Ishii:2017:FMA,
  author =       "Masahiro Ishii and J{\'e}r{\'e}mie Detrey and Pierrick
                 Gaudry and Atsuo Inomata and Kazutoshi Fujikawa",
  title =        "Fast Modular Arithmetic on the {Kalray MPPA-256}
                 Processor for an Energy-Efficient Implementation of
                 {ECM}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "66",
  number =       "12",
  pages =        "2019--2030",
  month =        "????",
  year =         "2017",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2017.2704082",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 10 08:32:25 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/document/7927487/",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Istoan:2017:FFP,
  author =       "Matei Istoan and Bogdan Pasca",
  title =        "Flexible Fixed-Point Function Generation for {FPGAs}",
  crossref =     "Burgess:2017:ISC",
  pages =        "123--130",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.31",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Efficient fixed-point function implementation is
                 critical in many FPGA application domains including
                 convolutional neural networks, computer vision, and
                 communication systems. In this work we focus on
                 functions of the form $ x^p $, with $ p \in \{ - 1, - 1
                 / 2, 1 / 2 \} $ as part of a function generator
                 targeting FPGAs. The generator implements architectures
                 based on new but also existing algorithms. In this work
                 we present three distinct methods implemented in this
                 generator that outperform state-of-the-art
                 implementations for certain configurations.
                 Traditionally, fixed-point function implementation
                 requires a normalization stage, compute and
                 denormalization (reconstruction) of the result. The
                 first proposed method implements the function
                 holistically, thus saving the logic and latency
                 required during the normalize and reconstruct stages.
                 The second proposed method is based on a novel second
                 order Taylor implementation. The third method is based
                 on the cubic convergence of Halley's method, which is
                 novel in this context. The proposed methods are
                 compared and contrasted against state-of-the art
                 implementations in the context of FPGA targets.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2017; ARITH-24; arithmetic; communication
                 systems; computer vision; convolutional neural
                 networks; cubic convergence; Digital signal processing;
                 Field programmable gate arrays; field programmable gate
                 arrays; fixed point arithmetic; fixed-point; flexible
                 fixed-point function generation; FPGA; FPGAs;
                 generator; Generators; Halley method; Kernel; Memory
                 management; reciprocal; reciprocal sqrt; second order
                 Taylor implementation; Signal generators; sqrt",
}

@Article{Jaiswal:2017:AEA,
  author =       "Manish Kumar Jaiswal and Hayden K.-H. So",
  title =        "Area-efficient Architecture for Dual-mode Double
                 Precision Floating Point Division",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-1,
  volume =       "64",
  number =       "2",
  pages =        "386--398",
  month =        feb,
  year =         "2017",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/TCSI.2016.2607227",
  ISSN =         "1549-8328 (print), 1558-0806 (electronic)",
  ISSN-L =       "1549-8328",
  bibdate =      "Sat Feb 08 10:59:51 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/document/7590039",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems I: Regular
                 Papers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8919",
}

@InProceedings{Jeannerod:2017:CRE,
  author =       "Claude-Pierre Jeannerod and Jean-Michel Muller and
                 Antoine Plet",
  title =        "The Classical Relative Error Bounds for Computing $
                 \sqrt (a^2 + b^2) $ and $ c / \sqrt (a^2 + b^2) $ in
                 Binary Floating-Point Arithmetic are Asymptotically
                 Optimal",
  crossref =     "Burgess:2017:ISC",
  pages =        "66--73",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.40",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We study the accuracy of classical algorithms for
                 evaluating expressions of the form $ (a^2 + b^2) $ and
                 $ c (a^2 + b^2) $ in radix-2, precision-$p$
                 floating-point arithmetic, assuming that the elementary
                 arithmetic operations $ \pm $, $ \times $, $/$, $ \sqrt
                 $ are rounded to nearest, and assuming an unbounded
                 exponent range. Classical analyses show that the
                 relative error is bounded by $ 2 u + O(u^2)$ for $ (a^2
                 + b^2)$, and by $ 3 u + O(u^2)$ for $ c / (a^2 + b^2)$,
                 where $ u = 2^{-p}$ is the unit roundoff. Recently, it
                 was observed that for $ (a^2 + b^2)$ the $ O(u^2)$ term
                 is in fact not needed [1]. We show here that it is not
                 needed either for $ c / (a^2 + b^2)$. Furthermore, we
                 show that these error bounds are asymptotically
                 optimal. Finally, we show that both the bounds and
                 their asymptotic optimality remain valid when an FMA
                 instruction is used to evaluate $ a^2 + b^2$.",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithm design and analysis; ARITH 2017; ARITH-24;
                 asymptotic optimality; binary floating-point
                 arithmetic; classical relative error bounds; Digital
                 arithmetic; Error analysis; floating point arithmetic;
                 Floating-point arithmetic; FMA instruction; Force;
                 hypotenuse function; Lips; precision-p floating-point
                 arithmetic; relative error; rounding error analysis;
                 unbounded exponent range; unit roundoff; Upper bound",
}

@Article{Jeannerod:2017:EBC,
  author =       "Claude-Pierre Jeannerod and Peter Kornerup and Nicolas
                 Louvet and Jean-Michel Muller",
  title =        "Error bounds on complex floating-point multiplication
                 with an {FMA}",
  journal =      j-MATH-COMPUT,
  volume =       "86",
  number =       "304",
  pages =        "881--898",
  month =        "",
  year =         "2017",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/mcom/3123",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Sat Feb 18 08:32:49 MST 2017",
  bibsource =    "http://www.ams.org/mcom/2017-86-304;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  URL =          "http://www.ams.org/journals/mcom/2017-86-304/S0025-5718-2016-03123-3;
                 http://www.ams.org/journals/mcom/2017-86-304/S0025-5718-2016-03123-3/S0025-5718-2016-03123-3.pdf;
                 http://www.ams.org/mathscinet/search/author.html?authorName=Kornerup%2C%20Peter;
                 http://www.ams.org/mathscinet/search/author.html?authorName=Muller%2C%20Jean-Michel;
                 http://www.ams.org/mathscinet/search/author.html?mrauthid=644190;
                 http://www.ams.org/mathscinet/search/author.html?mrauthid=893389",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@InProceedings{Jeannerod:2017:REC,
  author =       "Claude-Pierre Jeannerod and Jean-Michel Muller",
  editor =       "Michael B. Matthews",
  booktitle =    "{2017 51st Asilomar Conference on Signals, Systems,
                 and Computers. October 29--November 1, 2017. Pacific
                 Grove, California}",
  title =        "On the relative error of computing complex square
                 roots in floating-point arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "737--740",
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ACSSC.2017.8335442",
  ISBN =         "1-5386-1823-0",
  ISBN-13 =      "978-1-5386-1823-3",
  bibdate =      "Fri Sep 29 10:59:32 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We study the accuracy of a classical approach to
                 computing complex square-roots in floating-point
                 arithmetic. Our analyses are done in binary
                 floating-point arithmetic in precision p, and we assume
                 that the (real) arithmetic operations $+$, $-$, $
                 \times $, $ \div $, $ \sqrt {} $ are rounded to
                 nearest, so the unit roundoff is $ u = 2^{-p} $. We
                 show that in the absence of underflow and overflow, the
                 componentwise and normwise relative errors of this
                 approach are at most $ 7 / 2 u $ and $ \sqrt {37} / 2 u
                 $, respectively, and this without having to neglect
                 terms of higher order in $u$. We then provide some
                 input examples showing that these bounds are reasonably
                 sharp for the three basic binary interchange formats
                 (binary32, binary64, and binary128) of the IEEE 754
                 standard for floating-point arithmetic.",
  acknowledgement = ack-nhfb,
}

@Article{Johansson:2017:AEA,
  author =       "Fredrik Johansson",
  title =        "{Arb}: Efficient Arbitrary-Precision Midpoint--Radius
                 Interval Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "66",
  number =       "8",
  pages =        "1281--1292",
  month =        "????",
  year =         "2017",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2017.2690633",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 13 14:57:15 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/document/7891956/",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Joldes:2017:IPE,
  author =       "Mioara Joldes and Jean-Michel Muller and Valentina
                 Popescu",
  title =        "Implementation and Performance Evaluation of an
                 Extended Precision Floating-Point Arithmetic Library
                 for High-Accuracy Semidefinite Programming",
  crossref =     "Burgess:2017:ISC",
  pages =        "27--34",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.18",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Semidefinite programming (SDP) is widely used in
                 optimization problems with many applications, however,
                 certain SDP instances are ill-posed and need more
                 precision than the standard double-precision available.
                 Moreover, these problems are large-scale and could
                 benefit from parallelization on specialized
                 architectures such as GPUs. In this article, we
                 implement and evaluate the performance of a
                 floating-point expansion-based arithmetic library
                 (CAMPARY) in the context of such numerically highly
                 accurate SDP solvers. We plugged-in CAMPARY with the
                 state-of-the-art SDPA solver for both CPU and GPU-tuned
                 implementations. We compare and contrast both the
                 numerical accuracy and performance of SDPA-GMP, -QD and
                 -DD, which employ other multiple-precision arithmetic
                 libraries against SDPA-CAMPARY. We show that CAMPARY is
                 a very good trade-off for accuracy and speed when
                 solving ill-conditioned SDP problems.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2017; ARITH-24; CAMPARY; CPU; error-free
                 transform; floating point arithmetic; floating-point
                 arithmetic; floating-point expansion-based arithmetic
                 library; floating-point expansions; GPGPU computing;
                 GPU; graphics processing units; Graphics processing
                 units; ill-posed semidefinite programming; Libraries;
                 mathematical programming; mathematics computing;
                 multiple precision library; multiple-precision
                 arithmetic libraries; Optimization; Programming; SDP;
                 SDPA-DD; SDPA-GMP; SDPA-QD; semidefinite programming;
                 Standards; Symmetric matrices; Transforms",
}

@Article{Joldes:2017:TRE,
  author =       "Mioara Joldes and Jean-Michel Muller and Valentina
                 Popescu",
  title =        "Tight and Rigorous Error Bounds for Basic Building
                 Blocks of Double-Word Arithmetic",
  journal =      j-TOMS,
  volume =       "44",
  number =       "2",
  pages =        "15res:1--15res:27",
  month =        oct,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3121432",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Oct 10 17:52:02 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3121432",
  abstract =     "We analyze several classical basic building blocks of
                 double-word arithmetic (frequently called
                 ``double-double arithmetic'' in the literature): the
                 addition of a double-word number and a floating-point
                 number, the addition of two double-word numbers, the
                 multiplication of a double-word number by a
                 floating-point number, the multiplication of two
                 double-word numbers, the division of a double-word
                 number by a floating-point number, and the division of
                 two double-word numbers. For multiplication and
                 division we get better relative error bounds than the
                 ones previously published. For addition of two
                 double-word numbers, we show that the previously
                 published bound was incorrect, and we provide a new
                 relative error bound. We introduce new algorithms for
                 division. We also give examples that illustrate the
                 tightness of our bounds.",
  acknowledgement = ack-nhfb,
  articleno =    "15res",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  remark =       "This article is erroneously assigned the same article
                 number as the preceding one!",
}

@Misc{Jorgensen:2017:ACR,
  author =       "Alan A. Jorgensen",
  title =        "Apparatus for Calculating and Retaining a Bound on
                 Error During Floating Point Operations and Methods
                 Thereof",
  howpublished = "US Patent 9,817,662.",
  day =          "14",
  month =        nov,
  year =         "2017",
  bibdate =      "Fri Mar 23 19:14:44 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "This patent, filed 23 October 2016, was issued despite
                 substantial prior art that should have resulted in its
                 rejection: see \cite{Trader:2018:ICS}. The inventor
                 does not appear to have published in the area of
                 floating-point arithmetic (apart from this entry, none
                 by him can be found in this bibliography). The only
                 literature references in the patent are
                 \cite{Monniaux:2008:PVF,Goldberg:1991:WEC,Masotti:2012:FPN,Muller:2010:HFP}.",
  URL =          "https://patents.google.com/patent/US9817662B2/;
                 https://tinyurl.com/y7ctbsez",
  abstract =     "The apparatus and method for calculating and retaining
                 a bound on error during floating point operations
                 inserts an additional bounding field into the standard
                 floating-point format that records the retained
                 significant bits of the calculation with notification
                 upon insufficient retention. The bounding field, which
                 accounts for both rounding and cancellation errors, has
                 two parts, the lost bits D Field and the accumulated
                 rounding error R Field. The D Field states the number
                 of bits in the floating point representation that are
                 no longer meaningful. The bounds on the real value
                 represented are determined from the truncated floating
                 point value (first bound) and the addition of the error
                 determined by the number of lost bits (second bound).
                 The true, real value is absolutely contained by the
                 first and second bounds. The allowed loss (optionally
                 programmable) of significant bits provides a fail-safe,
                 real-time notification of loss of significant bits.",
  acknowledgement = ack-nhfb,
}

@Book{Kneusel:2017:NC,
  author =       "Ronald T. Kneusel",
  title =        "Numbers and Computers",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "xiii + 346",
  year =         "2017",
  DOI =          "https://doi.org/10.1007/978-3-319-50508-4",
  ISBN =         "3-319-50507-6, 3-319-50508-4 (e-book)",
  ISBN-13 =      "978-3-319-50507-7, 978-3-319-50508-4 (e-book)",
  LCCN =         "????",
  bibdate =      "Tue Aug 22 05:58:01 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer.com/10.1007/978-3-319-50508-4",
  abstract =     "This is a book about numbers and how those numbers are
                 represented in and operated on by computers. It is
                 crucial that developers understand this area because
                 the numerical operations allowed by computers, and the
                 limitations of those operations, especially in the area
                 of floating point math, affect virtually everything
                 people try to do with computers. This book aims to fill
                 this gap by exploring, in sufficient but not
                 overwhelming detail, just what it is that computers do
                 with numbers. Divided into two parts, the first deals
                 with standard representations of integers and floating
                 point numbers, while the second examines several other
                 number representations. Details are explained
                 thoroughly, with clarity and specificity. Each chapter
                 ends with a summary, recommendations, carefully
                 selected references, and exercises to review the key
                 points. Topics covered include interval arithmetic,
                 fixed-point numbers, big integers and rational
                 arithmetic. This new edition has three new chapters:
                 Pitfalls of Floating-Point Numbers (and How to Avoid
                 Them), Arbitrary Precision Floating Point, and Other
                 Number Systems. This book is for anyone who develops
                 software including software engineers, scientists,
                 computer science students, engineering students and
                 anyone who programs for fun.",
  acknowledgement = ack-nhfb,
  subject =      "Number theory; Numerals; Numeration; Computer science;
                 Mathematics; Mathematics; Number theory; Numerals;
                 Numeration; Arithmetic and Logic Structures; Numeric
                 Computing; Arithmetik; Informatik; Software
                 Engineering.",
  tableofcontents = "Number Systems \\
                 Integers \\
                 Floating Point \\
                 Pitfalls of Floating-Point Numbers (and How to Avoid
                 Them) \\
                 Big Integers and Rational Arithmetic \\
                 Fixed-Point Numbers \\
                 Decimal Floating Point \\
                 Interval Arithmetic \\
                 Arbitrary Precision Floating-Point \\
                 Other Number Systems",
}

@InProceedings{Koenig:2017:HAC,
  author =       "Jack Koenig and David Biancolin and Jonathan Bachrach
                 and Krste Asanovic",
  title =        "A Hardware Accelerator for Computing an Exact Dot
                 Product",
  crossref =     "Burgess:2017:ISC",
  pages =        "114--121",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.38",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We study the implementation of a hardware accelerator
                 that computes a dot product of IEEE-754 floating-point
                 numbers exactly. The accelerator uses a wide (640 or
                 4288 bits for single or double-precision respectively)
                 fixed-point representation into which intermediate
                 floating-point products are accumulated. We designed
                 the accelerator as a generator in Chisel, which can
                 synthesize various configurations of the accelerator
                 that make different area-performance trade-offs. We
                 integrated eight different configurations into an SoC
                 comprised of RISC-V in-order scalar core, split L1
                 instruction and data caches, and unified L2 cache. In a
                 TSMC 45 nm technology, the accelerator area ranges from
                 0.05 mm2 to 0.32 mm2, and all configurations could be
                 clocked at frequencies in excess of 900MHz. The
                 accelerator successfully saturates the SoC's memory
                 system, achieving the same per-element efficiency (1
                 cycle-per-element) as Intel MKL running on an x86
                 machine with a similar cache configuration.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point dot product; accurate
                 floating-point summation; area-performance trade-offs;
                 ARITH 2017; ARITH-24; Bandwidth; cache configuration;
                 cache storage; Chisel; Coprocessors; data caches; exact
                 dot product; fixed point arithmetic; fixed-point
                 representation; floating point arithmetic; Generators;
                 Hardware; hardware accelerator; IEEE-754 floating-point
                 numbers; Intel MKL; intermediate floating-point
                 products; Microarchitecture; Registers; RISC-V in-order
                 scalar core; Rockets; size 45 nm; SoC memory system;
                 split L1 instruction; system-on-chip; TSMC technology;
                 unified L2 cache",
}

@InProceedings{Kohlbrenner:2017:EMA,
  author =       "David Kohlbrenner and Hovav Shacham",
  editor =       "Another",
  booktitle =    "Proceedings of the {26th Usenix Security Symposium,
                 August 16--18, 2017, Vancouver, BC, Canada}",
  title =        "On the effectiveness of mitigations against
                 floating-point timing channels",
  publisher =    pub-USENIX,
  address =      pub-USENIX:adr,
  pages =        "69--81",
  year =         "2017",
  ISBN =         "1-931971-40-4",
  ISBN-13 =      "978-1-931971-40-9",
  LCCN =         "QA76.9.D5 P76 2005",
  bibdate =      "Mon Aug 26 10:26:59 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://github.com/kmowery/libfixedtimefixedpoint;
                 https://www.usenix.org/system/files/conference/usenixsecurity17/sec17-kohlbrenner.pdf",
  abstract =     "The duration of floating-point instructions is a known
                 timing side channel that has been used to break
                 Same-Origin Policy (SOP) privacy on Mozilla Firefox and
                 the Fuzz differentially private database. Several
                 defenses have been proposed to mitigate these
                 attacks.\par

                 We present detailed benchmarking of floating point
                 performance for various operations based on operand
                 values. We identify families of values that induce slow
                 and fast paths beyond the classes (normal, subnormal,
                 etc.) considered in previous work, and note that
                 different processors exhibit different timing
                 behavior.\par

                 We evaluate the efficacy of the defenses deployed (or
                 not) in Web browsers to floating point side channel
                 attacks on SVG filters. We find that Google Chrome,
                 Mozilla Firefox, and Apple's Safari have insufficiently
                 addressed the floating-point side channel, and we
                 present attacks for each that extract pixel data
                 cross-origin on most platforms.\par

                 We evaluate the vector-operation based defensive
                 mechanism proposed at USENIX Security 2016 by Rane, Lin
                 and Tiwari and find that it only reduces, not
                 eliminates, the floating-point side channel signal.
                 Together, these measurements and attacks cause us to
                 conclude that floating point is simply too variable to
                 use in a timing security sensitive context.",
  acknowledgement = ack-nhfb,
  keywords =     "libfixedtimefixedpoint",
  remark-1 =     "This paper contains floating-point instruction timing
                 tables for the Intel i5-44609 CPU and Nvidia GeForce GT
                 430 GPU, with a brief table about the AMD Phenom II
                 X2-550. It demonstrates that timings can depend
                 significantly on operands, with subnormals sometimes
                 causing a slowdown of more than $ 20 \times $. The
                 scope of attacks from timing measurements is
                 surprisingly broad, including recovery of image pixels,
                 browser history, user geolocation, and browser search
                 strings. Several of the 18 references describe other
                 such attacks. One of the vulnerable graphics rendering
                 libraries, Skia, is used by multiple browsers and
                 window systems: see \url{https://skia.org/}.",
  remark-2 =     "From p. 80: ``Processor vendors have resisted calls to
                 document which of their instructions run in constant
                 time regardless of operands, even for operations as
                 basic as integer multiplication.''",
}

@Article{Kumm:2017:OCM,
  author =       "Martin Kumm and Martin Hardieck and Peter Zipf",
  title =        "Optimization of Constant Matrix Multiplication with
                 Low Power and High Throughput",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "66",
  number =       "12",
  pages =        "2072--2080",
  month =        "????",
  year =         "2017",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2017.2701365",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 10 08:32:25 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/document/7919250/",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Kumm:2017:ROD,
  author =       "Martin Kumm and Johannes Kappauf and Matei Istoan and
                 Peter Zipf",
  title =        "Resource Optimal Design of Large Multipliers for
                 {FPGAs}",
  crossref =     "Burgess:2017:ISC",
  pages =        "131--138",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.35",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This work presents a resource optimal approach for the
                 design of large multipliers for FPGAs. These are
                 composed of smaller multipliers which can be DSP blocks
                 or logic-based multipliers. A previously proposed
                 multiplier tiling methodology is used to describe
                 feasible solutions of the problem. The problem is then
                 formulated as an integer linear programming (ILP)
                 problem which can be solved by standard ILP solvers. It
                 can be used to minimize the total implementation cost
                 or to trade the LUT cost against the DSP cost. It is
                 demonstrated that although the problem is NP-complete,
                 optimal solutions can be found for most practical
                 multiplier sizes up to 64x64. Synthesis experiments on
                 relevant multiplier sizes show slice reductions of up
                 to 47.5\% compared to state-of-the-art heuristic
                 approaches.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2017; ARITH-24; Complexity theory; computational
                 complexity; Digital arithmetic; Digital signal
                 processing; DSP blocks; field programmable gate arrays;
                 Field programmable gate arrays; FPGA; ILP; ILP problem;
                 ILP solvers; integer linear programming problem;
                 integer programming; linear programming; logic design;
                 logic-based multipliers; LUT; multiplier; multiplier
                 design; multiplier tiling methodology; multiplying
                 circuits; NP-complete problem; Optimization;
                 optimization; Shape; table lookup; Table lookup",
}

@Article{Lai:2017:DCN,
  author =       "Liangzhen Lai and Naveen Suda and Vikas Chandra",
  title =        "Deep Convolutional Neural Network Inference with
                 Floating-point Weights and Fixed-point Activations",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--10",
  day =          "8",
  month =        mar,
  year =         "2017",
  bibdate =      "Fri Sep 28 06:16:02 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/pdf/1703.03073.pdf",
  abstract =     "Deep convolutional neural network (CNN) inference
                 requires significant amount of memory and computation,
                 which limits its deployment on embedded devices. To
                 alleviate these problems to some extent, prior research
                 utilize low precision fixed-point numbers to represent
                 the CNN weights and activations. However, the minimum
                 required data precision of fixed-point weights varies
                 across different networks and also across different
                 layers of the same network. In this work, we propose
                 using floating-point numbers for representing the
                 weights and fixed-point numbers for representing the
                 activations. We show that using floating-point
                 representation for weights is more efficient than
                 fixed-point representation for the same bit-width and
                 demonstrate it on popular large-scale CNNs such as
                 AlexNet, SqueezeNet, GoogLeNet and VGG-16. We also show
                 that such a representation scheme enables compact
                 hardware multiply-and-accumulate (MAC) unit design.
                 Experimental results show that the proposed scheme
                 reduces the weight storage by up to 36\% and power
                 consumption of the hardware multiplier by up to 50\%.",
  acknowledgement = ack-nhfb,
}

@Misc{Lam:2017:FPA,
  author =       "Mike Lam",
  title =        "Floating-Point Analysis Research",
  howpublished = "Web site",
  year =         "2017",
  bibdate =      "Thu May 02 17:01:37 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://w3.cs.jmu.edu/lam2mo/fpanalysis.html",
  abstract =     "This page is a compilation of research efforts and
                 software tools devoted to program analysis of
                 floating-point code. This research area is a community
                 of people from many different backgrounds: traditional
                 PL, high performance computing, numerical analysis, and
                 systems software. With this page, I am hoping to help
                 form connections between people and projects that might
                 previously have never encountered each other.",
  acknowledgement = ack-nhfb,
}

@Article{Landy:2017:SAS,
  author =       "Aaron Landy and Greg Stitt",
  title =        "Serial Arithmetic Strategies for Improving {FPGA}
                 Throughput",
  journal =      j-TECS,
  volume =       "16",
  number =       "3",
  pages =        "84:1--84:??",
  month =        jul,
  year =         "2017",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2996459",
  ISSN =         "1539-9087 (print), 1558-3465 (electronic)",
  ISSN-L =       "1539-9087",
  bibdate =      "Mon Jul 24 09:51:12 MDT 2017",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tecs.bib",
  abstract =     "Serial arithmetic has been shown to offer attractive
                 advantages in area for field-programmable gate array
                 (FPGA) datapaths but suffers from a significant
                 reduction in throughput compared to traditional
                 bit-parallel designs. In this work, we perform a
                 performance and trade-off analysis that
                 counterintuitively shows that, despite the decreased
                 throughput of individual serial operators, replication
                 of serial arithmetic can provide a 2.1 $ \times $
                 average increase in throughput compared to bit-parallel
                 pipelines for common FPGA applications. We complement
                 this analysis with a novel SerDes architecture that
                 enables existing FPGA pipelines to be replaced with
                 serial logic with potentially higher throughput. We
                 also present a serialized sliding-window architecture
                 that improves average throughput 2.4 $ \times $
                 compared to existing bit-parallel work.",
  acknowledgement = ack-nhfb,
  articleno =    "84",
  fjournal =     "ACM Transactions on Embedded Computing Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J840",
}

@Article{Lange:2017:EES,
  author =       "Marko Lange and Siegfried M. Rump",
  title =        "Error estimates for the summation of real numbers with
                 application to floating-point summation",
  journal =      j-BIT-NUM-MATH,
  volume =       "57",
  number =       "3",
  pages =        "927--941",
  month =        sep,
  year =         "2017",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/s10543-017-0658-9",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Mon Oct 2 11:20:22 MDT 2017",
  bibsource =    "http://link.springer.com/journal/10543/57/3;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://link.springer.com/article/10.1007/s10543-017-0658-9",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT Numerical Mathematics",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@InProceedings{Langhammer:2017:FPT,
  author =       "Martin Langhammer and Bogdan Pasca",
  title =        "Floating Point Tangent Implementation for {FPGAs}",
  crossref =     "Burgess:2017:ISC",
  pages =        "64--65",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.25",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper presents an implementation of the
                 floating-point (FP) tangent function, optimized for an
                 FPGA containing hard floating point (HFP) DSP Blocks.
                 This function inputs values in the interval [- /2, /2],
                 uses the IEEE-754 single-precision (SP) format, and has
                 an accuracy conforming to OpenCL requirements. The
                 presented architecture is based on a combination of
                 mathematical identities and properties of the tangent
                 function in FP. The resultant design outperforms
                 generic polynomial approximation methods targeting the
                 same resource utilization spectrum, and provides better
                 resource trade-offs than classical CORDIC-based
                 implementations. The presented work is widely available
                 as part of the Intel DSP Builder Advanced Blockset.",
  acknowledgement = ack-nhfb,
  keywords =     "Approximation methods; ARITH 2017; ARITH-24; classical
                 CORDIC-based implementations; Digital arithmetic;
                 Digital signal processing; digital signal processing
                 chips; field programmable gate arrays; Field
                 programmable gate arrays; fixed point arithmetic;
                 floating point arithmetic; floating point tangent
                 function; FPGAs; generic polynomial approximation
                 methods; hard floating point DSP blocks; HFP DSP;
                 IEEE-754 single-precision format; Intel DSP Builder
                 Advanced Blockset; OpenCL; reconfigurable
                 architectures; Resource management; resource
                 utilization spectrum; Table lookup",
}

@InProceedings{Langhammer:2017:QPA,
  author =       "Martin Langhammer",
  title =        "{QRD} for Parallel Arithmetic Structures",
  crossref =     "Burgess:2017:ISC",
  pages =        "146--147",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.26",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present a new organization of the QR decomposition
                 (QRD), which is optimized for implementation on
                 parallel arithmetic structures, such as found in
                 current FPGAs. Data dependencies are hidden in the
                 pipeline depths of the datapaths, allowing
                 implementations to approach 100\% sustained to peak
                 throughput. The algorithm presented here is based on
                 the Modified Gram-Schmidt (MGS) method, and is designed
                 for floating point (FP) arithmetic, with a combination
                 of separate dot product and multiply-add datapaths. In
                 this short paper, we concentrate on the description of
                 the algorithm and architecture, rather than the
                 implementation, of the QRD.",
  acknowledgement = ack-nhfb,
  keywords =     "adders; Algorithm design and analysis; ARITH 2017;
                 ARITH-24; Computer architecture; data dependencies;
                 field programmable gate arrays; Field programmable gate
                 arrays; floating point arithmetic; FP arithmetic; FPGA;
                 MGS method; modified Gram-Schmidt method; multiply-add
                 datapaths; multiplying circuits; Organizations;
                 parallel arithmetic structures; Pipelines; QR
                 decomposition; QRD; Radar antennas; separate dot
                 product; Throughput",
}

@Article{Langhammer:2017:SPL,
  author =       "Martin Langhammer and Bogdan Pasca",
  title =        "Single Precision Logarithm and Exponential
                 Architectures for Hard Floating-Point Enabled {FPGAs}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "66",
  number =       "12",
  pages =        "2031--2043",
  month =        "????",
  year =         "2017",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2017.2703923",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 10 08:32:25 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/document/7927449/",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Lauter:2017:ESI,
  author =       "Christoph Lauter",
  title =        "An Efficient Software Implementation of Correctly
                 Rounded Operations Extending {FMA}: $ a + b + c $ and $
                 a \times b + c \times d $",
  crossref =     "Matthews:2017:CRF",
  pages =        "452--456",
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ACSSC.2017.8335379",
  bibdate =      "Fri Feb 16 08:24:29 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation; complex multiply;
                 fused multiply-add; fused-add-add;
                 fused-multiply-twice-and-add; three-sum",
}

@Article{Lee:2017:APC,
  author =       "Wonyeol Lee and Rahul Sharma and Alex Aiken",
  title =        "On automatically proving the correctness of {\tt
                 math.h} implementations",
  journal =      j-PACMPL,
  volume =       "2",
  number =       "{POPL}",
  pages =        "1--32",
  month =        dec,
  year =         "2017",
  DOI =          "https://doi.org/10.1145/3158135",
  ISSN =         "2475-1421",
  bibdate =      "Thu May 2 17:03:44 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Industry standard implementations of {\tt math.h}
                 claim (often without formal proof) tight bounds on
                 floating-point errors. We demonstrate a novel static
                 analysis that proves these bounds and verifies the
                 correctness of these implementations. Our key insight
                 is a reduction of this verification task to a set of
                 mathematical optimization problems that can be solved
                 by off-the-shelf computer algebra systems. We use this
                 analysis to prove the correctness of implementations in
                 Intel's math library automatically. Prior to this work,
                 these implementations could only be verified with
                 significant manual effort",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the ACM on Programming Languages
                 (PACMPL)",
  journal-URL =  "http://pacmpl.acm.org/",
}

@Article{Lefevre:2017:CRA,
  author =       "Vincent Lef{\`e}vre",
  title =        "Correctly Rounded Arbitrary-Precision Floating-Point
                 Summation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "66",
  number =       "12",
  pages =        "2111--2124",
  month =        "????",
  year =         "2017",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2017.2690632",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 10 08:32:25 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/document/7891894/;
                 https://inria.hal.science/hal-01394289",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Lefevre:2017:OBB,
  author =       "Vincent Lef{\`e}vre and Paul Zimmermann",
  title =        "Optimized {Binary64} and {Binary128} Arithmetic with
                 {GNU MPFR}",
  crossref =     "Burgess:2017:ISC",
  pages =        "18--26",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.28",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/gnu.bib",
  abstract =     "We describe algorithms used to optimize the GNU MPFR
                 library when the operands fit into one or two words. On
                 modern processors, this gives a speedup for a correctly
                 rounded addition, subtraction, multiplication, division
                 or square root in the standard binary64 format (resp.
                 binary128) between 1.8 and 3.5 (resp. between 1.6 and
                 3.2). We also introduce a new faithful rounding mode,
                 which enables even faster computations. Those
                 optimizations will be available in version 4 of MPFR.",
  acknowledgement = ack-nhfb,
  keywords =     "Approximation algorithms; ARITH 2017; ARITH-24; binary
                 floating-point formats; binary128; binary64; correct
                 rounding; faithful rounding; floating point arithmetic;
                 floating-point arithmetic; GNU MPFR; GNU MPFR library;
                 Libraries; Optimization; optimizations; Program
                 processors; Standards; Timing",
}

@InProceedings{Lesavourey:2017:ELR,
  author =       "Andrea Lesavourey and Christophe Negre and Thomas
                 Plantard",
  title =        "Efficient Leak Resistant Modular Exponentiation in
                 {RNS}",
  crossref =     "Burgess:2017:ISC",
  pages =        "156--163",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.39",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The leak resistant arithmetic in RNS was introduced in
                 2004 to randomize RSA modular exponentiation. This
                 randomization is meant to protect implementations on
                 embedded device from side channel analysis. We propose
                 in this paper a faster version of the approach of
                 Bajard et al. in the case of right-to-left
                 square-and-multiply exponentiation. We show that this
                 saves roughly 30\% of the computation when the
                 randomization is done at each loop iteration. We also
                 show that the level of randomization of the proposed
                 approach is better than the one of Bajard et al. after
                 a few number of loop iterations.",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithm design and analysis; ARITH 2017; ARITH-24;
                 Correlation; efficient leak resistant modular
                 exponentiation; embedded device; iterative methods;
                 leak resistant arithmetic; loop iteration; modular
                 exponentiation; Monitoring; Public key cryptography;
                 public key cryptography; public key cryptosystem;
                 randomization; residue number system; residue number
                 systems; Resistance; right-to-left square-and-multiply
                 exponentiation; RNS; RSA; RSA cryptosystem; RSA modular
                 exponentiation randomization; side channel analysis;
                 Xenon",
}

@Article{Li:2017:MFN,
  author =       "Yin Li and Xingpo Ma and Yu Zhang and Chuanda Qi",
  title =        "{Mastrovito} Form of Non-Recursive {Karatsuba}
                 Multiplier for All Trinomials",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "66",
  number =       "9",
  pages =        "1573--1584",
  month =        sep,
  year =         "2017",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2017.2677913",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Aug 17 10:06:38 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/document/7870679/",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Li:2017:URF,
  author =       "Bingyi Li and Linlin Fang and Yizhuang Xie and He Chen
                 and Liang Chen",
  booktitle =    "{2017 International Conference on Field Programmable
                 Technology (ICFPT)}",
  title =        "A unified reconfigurable floating-point arithmetic
                 architecture based on {CORDIC} algorithm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "301--302",
  year =         "2017",
  DOI =          "https://doi.org/10.1109/FPT.2017.8280166",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithm design and analysis; Computer architecture;
                 CORDIC; Field programmable gate arrays; floating-point;
                 FPGA; Hardware; IP networks; reconfigurable; Registers;
                 Signal processing algorithms",
}

@Article{Liu:2017:DAR,
  author =       "Weiqiang Liu and Liangyu Qian and Chenghua Wang and
                 Honglan Jiang and Jie Han and Fabrizio Lombardi",
  title =        "Design of Approximate Radix-4 {Booth} Multipliers for
                 Error-Tolerant Computing",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "66",
  number =       "8",
  pages =        "1435--1441",
  month =        "????",
  year =         "2017",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2017.2672976",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 13 14:57:15 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/document/7862783/",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Liu:2017:MMA,
  author =       "Zhe Liu and Kimmo J{\"a}rvinen and Weiqiang Liu and
                 Hwajeong Seo",
  title =        "Multiprecision Multiplication on {ARMv8}",
  crossref =     "Burgess:2017:ISC",
  pages =        "10--17",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.27",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Multiplication of large integers is a fundamental
                 operation for public key cryptography. In contemporary
                 public key cryptography, the sizes of integers are
                 typically from more than one hundred bits to even
                 several thousands of bits. Because these sizes exceed
                 the bit widths of all general-purpose processors, these
                 multiplications must be performed with a multiprecision
                 multiplication algorithm which splits the operation
                 into multiple partial products and accumulation steps.
                 To ensure efficiency, multiprecision multiplication
                 algorithms must be designed with special care and
                 optimized for the instruction sets of specific
                 processors. Consequently, developing efficient
                 multiprecision multiplication algorithms and optimizing
                 them for specific platforms has been an active research
                 topic. In this paper, we optimize multiprecision
                 multiplication and squaring specifically for the 64-bit
                 ARMv8 processors which are widely used, for example, in
                 modern smart phones and tablets. We combine the
                 subtractive Karatsuba algorithm, operand-scanning
                 techniques (for multiplication) and
                 sliding-block-doubling methods (for squaring) to
                 accelerate the performance of the 256-bit
                 multiprecision multiplication and squaring by 7.6\% and
                 7.0\% compared to the OpenSSL implementations. We focus
                 particularly on the multiprecision multiplications that
                 are required in elliptic curve cryptography. Our
                 implementation supports general elliptic curves of
                 various sizes and all source codes are available in
                 public domain.",
  acknowledgement = ack-nhfb,
  keywords =     "64-bit processor; ARITH 2017; ARITH-24; ARMv8; ARMv8
                 processors; elliptic curve cryptography; Elliptic curve
                 cryptography; elliptic curve cryptography; Instruction
                 sets; Karatsuba algorithm; microprocessor chips;
                 Multiprecision multiplication; multiprecision
                 multiplication algorithm; OpenSSL; operand-scanning
                 techniques; Optimization; public key cryptography;
                 Registers; sliding-block-doubling methods",
}

@Article{Liu:2017:UMF,
  author =       "S. Liu and G. Mingas and C. S. Bouganis",
  title =        "An Unbiased {MCMC} {FPGA}-Based Accelerator in the
                 Land of Custom Precision Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "66",
  number =       "5",
  pages =        "745--758",
  month =        may,
  year =         "2017",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2016.2630682",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Apr 6 07:46:06 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Approximation algorithms; Bayes methods; Computational
                 modeling; custom arithmetic precision; Field
                 programmable gate array; Field programmable gate
                 arrays; logistic regression; Markov chain Monte Carlo;
                 Markov processes; MNIST database; Monte Carlo methods;
                 Probability distribution",
}

@Book{Lockhart:2017:A,
  author =       "Paul Lockhart",
  title =        "Arithmetic",
  publisher =    "The Belknap Press of Harvard University Press",
  address =      "Cambridge, MA, USA",
  pages =        "223",
  year =         "2017",
  ISBN =         "0-674-97223-6",
  ISBN-13 =      "978-0-674-97223-0",
  LCCN =         "QA115 .L713 2017",
  bibdate =      "Sat Dec 22 16:04:02 MST 2018",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  abstract =     "Educator Paul Lockhart's goal is to demystify
                 arithmetic: to bring the subject to life in a fun and
                 accessible way, and to reveal its profound and simple
                 beauty, as seen through the eyes of a modern research
                 mathematician. The craft of arithmetic arises from our
                 natural desire to count, arrange, and compare
                 quantities. Over the centuries, humans have devised a
                 wide variety of strategies for representing and
                 manipulating numerical information: tally marks, rocks
                 and beads, marked-value and place-value systems, as
                 well as mechanical and electronic calculators.
                 \booktitle{Arithmetic} traces the history and
                 development of these various number languages and
                 calculating devices and examines their comparative
                 advantages and disadvantages, providing readers with an
                 opportunity to develop not only their computational
                 skills but also their own personal tastes and
                 preferences. The book is neither a training manual nor
                 an authoritative history, but rather an entertaining
                 survey of ideas and methods for the reader to enjoy and
                 appreciate. Written in a lively conversational style,
                 \booktitle{Arithmetic} is a fun and engaging
                 introduction to both practical techniques as well as
                 the more abstract mathematical aspects of the
                 subject.",
  acknowledgement = ack-nhfb,
  subject =      "Talteori; Arithmetic; History",
  tableofcontents = "Dear Reader / vii \\
                 Things / 1 \\
                 Language / 5 \\
                 Repetition / 10 \\
                 Tribes / 15 \\
                 Egypt / 25 \\
                 Rome / 32 \\
                 China and Japan / 41 \\
                 India / 48 \\
                 Europe / 75 \\
                 Multiplication / 87 \\
                 Division / 117 \\
                 Machines / 136 \\
                 Fractions / 151 \\
                 Negative numbers / 180 \\
                 The art of counting / 197 \\
                 Afterword / 215 \\
                 Index / 217",
}

@InProceedings{Lutz:2017:HPA,
  author =       "David Raymond Lutz and Christopher Neal Hinds",
  title =        "High-Precision Anchored Accumulators for Reproducible
                 Floating-Point Summation",
  crossref =     "Burgess:2017:ISC",
  pages =        "98--105",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.20",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper introduces a new datatype that allows
                 reproducible accumulation of floating-point (FP)
                 numbers in a programmer-selectable range. The new
                 datatype has a larger significand and a smaller range
                 than existing FP formats and has much better arithmetic
                 and computational properties. In particular, it is
                 associative, parallelizable, reproducible and correct.
                 For the modest ranges that will accommodate most
                 problems, it is also much faster: 3 to 12 times faster
                 on a single 256-bit SIMD implementation. The paper also
                 describes a new instruction and associated datapath
                 that support the proposed datatype, and discusses how a
                 recently published software algorithm for reproducible
                 FP summation could be implemented using the proposed
                 approach.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation; ARITH 2017;
                 ARITH-24; arithmetic properties; computational
                 properties; Digital arithmetic; floating point
                 arithmetic; Floating-point; floating-point summation;
                 Hardware; high-precision; high-precision anchored
                 accumulators; Indexes; Limiting; Metadata; parallel
                 processing; programmer-selectable range; Redundancy;
                 Registers; reproducibility; SIMD; software algorithm",
}

@Article{Magron:2017:CRE,
  author =       "Victor Magron and George Constantinides and Alastair
                 Donaldson",
  title =        "Certified Roundoff Error Bounds Using Semidefinite
                 Programming",
  journal =      j-TOMS,
  volume =       "43",
  number =       "4",
  pages =        "34:1--34:31",
  month =        mar,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3015465",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 24 08:51:05 MDT 2017",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Roundoff errors cannot be avoided when implementing
                 numerical programs with finite precision. The ability
                 to reason about rounding is especially important if one
                 wants to explore a range of potential representations,
                 for instance, for FPGAs or custom hardware
                 implementations. This problem becomes challenging when
                 the program does not employ solely linear operations as
                 non-linearities are inherent to many interesting
                 computational problems in real-world applications.
                 Existing solutions to reasoning possibly lead to either
                 inaccurate bounds or high analysis time in the presence
                 of nonlinear correlations between variables.
                 Furthermore, while it is easy to implement a
                 straightforward method such as interval arithmetic,
                 sophisticated techniques are less straightforward to
                 implement in a formal setting. Thus there is a need for
                 methods that output certificates that can be formally
                 validated inside a proof assistant. We present a
                 framework to provide upper bounds on absolute roundoff
                 errors of floating-point nonlinear programs. This
                 framework is based on optimization techniques employing
                 semidefinite programming and sums of squares
                 certificates, which can be checked inside the Coq
                 theorem prover to provide formal roundoff error bounds
                 for polynomial programs. Our tool covers a wide range
                 of nonlinear programs, including polynomials and
                 transcendental operations as well as conditional
                 statements. We illustrate the efficiency and precision
                 of this tool on non-trivial programs coming from
                 biology, optimization, and space control. Our tool
                 produces more accurate error bounds for 23\% of all
                 programs and yields better performance in 66\% of all
                 programs.",
  acknowledgement = ack-nhfb,
  articleno =    "34",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@InProceedings{Malaya:2017:AMP,
  author =       "Nicholas Malaya and Shuai Che and Joseph L. Greathouse
                 and Rene van Oostrum and Michael J. Schulte",
  title =        "Accelerating Matrix Processing with {GPUs}",
  crossref =     "Burgess:2017:ISC",
  pages =        "139--141",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.14",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Matrix operations are common and expensive
                 computations in a variety of applications. They occur
                 frequently in high-performance computing, graphics,
                 graph processing, and machine learning applications.
                 This paper discusses how to map a variety of important
                 matrix computations, including sparse matrix-vector
                 multiplication (SpMV), sparse triangle solve (SpTS),
                 graph processing, and dense matrix-matrix
                 multiplication, to GPUs. Since many emerging systems
                 will use heterogeneous architectures (e.g. CPUs and
                 GPUs) to attain the desired performance targets under
                 strict power constraints, this paper discusses
                 implications and future research for matrix processing
                 with heterogeneous designs. Conclusions common to the
                 matrix operations discussed in this paper are: (1)
                 Future algorithms should be written to ensure that the
                 essential computations fit into local memory, which may
                 require direct programmer management. (2) Algorithms
                 are needed that expose high levels of parallelism. (3)
                 While the scale of computation is often sufficient to
                 support algorithms with superior asymptotic order,
                 additional considerations, such as memory capacity and
                 bandwidth, must also be carefully managed. (4)
                 Libraries should be used to provide portable
                 performance.",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithm design and analysis; ARITH 2017; ARITH-24;
                 dense matrix-matrix multiplication; exascale; GPGPU;
                 GPU; Graph Algorithms; graph processing; graphics
                 processing units; Graphics processing units; Libraries;
                 Linear algebra; matrix computations; matrix
                 multiplication; matrix processing; Matrix-matrix
                 multiplication; Memory management; Parallel processing;
                 Sparse matrices; sparse matrices; sparse matrix-vector
                 multiplication; sparse triangle solve; SpMV; SpTS",
}

@Article{Martins:2017:AIR,
  author =       "Paulo Martins and Julien Eynard and Jean-Claude Bajard
                 and Leonel Sousa",
  title =        "Arithmetical Improvement of the Round-Off for
                 Cryptosystems in High-Dimensional Lattices",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "66",
  number =       "12",
  pages =        "2005--2018",
  month =        "????",
  year =         "2017",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2017.2690420",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 10 08:32:25 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/document/7891511/",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Mascarenhas:2017:ERE,
  author =       "Walter F. Mascarenhas and Andr{\'e} Pierro de
                 Camargo",
  title =        "The effects of rounding errors in the nodes on
                 barycentric interpolation",
  journal =      j-NUM-MATH,
  volume =       "135",
  number =       "1",
  pages =        "113--141",
  month =        jan,
  year =         "2017",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/s00211-016-0798-x",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sat Feb 18 08:20:07 MST 2017",
  bibsource =    "http://link.springer.com/journal/211/135/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath2010.bib",
  URL =          "http://link.springer.com/accesspage/article/10.1007/s00211-016-0798-x;
                 http://link.springer.com/article/10.1007/s00211-016-0798-x",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@Article{Mazahir:2017:PEA,
  author =       "Sana Mazahir and Osman Hasan and Rehan Hafiz and
                 Muhammad Shafique",
  title =        "Probabilistic Error Analysis of Approximate Recursive
                 Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "66",
  number =       "11",
  pages =        "1982--1990",
  month =        "????",
  year =         "2017",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2017.2709542",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Oct 12 06:36:58 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/document/7935435/",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Medhat:2017:MPE,
  author =       "Ramy Medhat and Michael O. Lam and Barry L. Rountree
                 and Borzoo Bonakdarpour and Sebastian Fischmeister",
  title =        "Managing the Performance\slash Error Tradeoff of
                 Floating-point Intensive Applications",
  journal =      j-TECS,
  volume =       "16",
  number =       "5s",
  pages =        "184:1--184:??",
  month =        oct,
  year =         "2017",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3126519",
  ISSN =         "1539-9087 (print), 1558-3465 (electronic)",
  ISSN-L =       "1539-9087",
  bibdate =      "Thu Oct 17 18:16:33 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tecs.bib",
  abstract =     "Modern embedded systems are becoming more reliant on
                 real-valued arithmetic as they employ mathematically
                 complex vision algorithms and sensor signal processing.
                 Double-precision floating point is the most commonly
                 used precision in computer vision algorithm
                 implementations. A single-precision floating point can
                 provide a performance boost due to less memory
                 transfers, less cache occupancy, and relatively faster
                 mathematical operations on some architectures. However,
                 adopting it can result in loss of accuracy. Identifying
                 which parts of the program can run in single-precision
                 floating point with low impact on error is a manual and
                 tedious process. In this paper, we propose an automatic
                 approach to identify parts of the program that have a
                 low impact on error using shadow-value analysis. Our
                 approach provides the user with a performance/error
                 tradeoff, using which the user can decide how much
                 accuracy can be sacrificed in return for performance
                 improvement. We illustrate the impact of the approach
                 using a well known implementation of Apriltag detection
                 used in robotics vision. We demonstrate that an average
                 1.3x speedup can be achieved with no impact on tag
                 detection, and a 1.7x speedup with only 4\% false
                 negatives.",
  acknowledgement = ack-nhfb,
  articleno =    "184",
  fjournal =     "ACM Transactions on Embedded Computing Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J840",
}

@Article{Merchant:2017:ABL,
  author =       "Farhad Merchant and Anupam Chattopadhyay and Soumyendu
                 Raha and S. K. Nandy and Ranjani Narayan",
  title =        "Accelerating {BLAS} and {LAPACK} via Efficient
                 Floating Point Architecture Design",
  journal =      j-PARALLEL-PROCESS-LETT,
  volume =       "27",
  number =       "3--4",
  pages =        "1750006",
  year =         "2017",
  CODEN =        "PPLTEE",
  DOI =          "https://doi.org/10.1142/S0129626417500062",
  ISSN =         "0129-6264 (print), 1793-642X (electronic)",
  ISSN-L =       "0129-6264",
  bibdate =      "Tue May 29 09:05:31 MDT 2018",
  bibsource =    "http://ejournals.wspc.com.sg/ppl/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/parallelprocesslett.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Parallel Processing Letters",
  journal-URL =  "http://www.worldscientific.com/loi/ppl",
}

@MastersThesis{Mian:2017:HPC,
  author =       "Riaz-ul-Haque Mian",
  title =        "High precision computation of decimal logarithm",
  type =         "Master of Engineering in Information and Communication
                 Technology",
  school =       "Institute of Information and Communication Technology,
                 Bangladesh University of Engineering and Technology",
  pages =        "52",
  month =        jan,
  year =         "2017",
  DOI =          "https://doi.org/10.13140/RG.2.2.11851.69924",
  bibdate =      "Tue Jul 06 18:24:02 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.researchgate.net/publication/323265326_High_precision_computation_of_decimal_logarithm",
  abstract =     "his report presents the design of an efficient low
                 power decimal logarithmic converter. The technique is
                 based on shift operation along with a precision unit
                 which is used to prevent unnecessary scan of full
                 memory table. Precision level is user programmable. It
                 does not require multiplication or division circuitry
                 which in turn makes it low power. Proposed decimal
                 logarithmic converter has been designed using Verilog
                 HDL and then compiled and simulated using Altera
                 provided Quartus II compiler and ModelSim simulator.
                 The synthesis results show that the proposed design
                 outperforms all the existing proposed decimal
                 logarithmic converters by other researchers. The
                 calculation is based on memory. Some predefined value
                 and their log value are stored in memory and by using
                 that value we calculate the logarithm of any value.
                 Another feature which is called precision unit is used
                 for controlling unnecessary scan of memory table.
                 According to input of precision value the algorithm
                 calculates logarithm value. Thus by increasing of
                 precision value we can increase accuracy of the result.
                 This algorithm does not need multiplication circuitry
                 and required very low memory thus it makes the
                 algorithm very low power.",
  acknowledgement = ack-nhfb,
}

@Article{Micikevicius:2017:MPT,
  author =       "Paulius Micikevicius and Sharan Narang and Jonah Alben
                 and Gregory Diamos and Erich Elsen and David Garcia and
                 Boris Ginsburg and Michael Houston and Oleksii Kuchaiev
                 and Ganesh Venkatesh and Hao Wu",
  title =        "Mixed Precision Training",
  journal =      "arXiv.org",
  day =          "10",
  month =        oct,
  year =         "2017",
  bibdate =      "Mon Feb 10 09:21:08 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/abs/1710.03740",
  abstract =     "Deep neural networks have enabled progress in a wide
                 variety of applications. Growing the size of the neural
                 network typically results in improved accuracy. As
                 model sizes grow, the memory and compute requirements
                 for training these models also increases. We introduce
                 a technique to train deep neural networks using half
                 precision floating point numbers. In our technique,
                 weights, activations and gradients are stored in IEEE
                 half-precision format. Half-precision floating numbers
                 have limited numerical range compared to
                 single-precision numbers. We propose two techniques to
                 handle this loss of information. Firstly, we recommend
                 maintaining a single-precision copy of the weights that
                 accumulates the gradients after each optimizer step.
                 This single-precision copy is rounded to half-precision
                 format during training. Secondly, we propose scaling
                 the loss appropriately to handle the loss of
                 information with half-precision gradients. We
                 demonstrate that this approach works for a wide variety
                 of models including convolution neural networks,
                 recurrent neural networks and generative adversarial
                 networks. This technique works for large scale models
                 with more than 100 million parameters trained on large
                 datasets. Using this approach, we can reduce the memory
                 consumption of deep learning models by nearly $ 2
                 \times $. In future processors, we can also expect a
                 significant computation speedup using half-precision
                 hardware units.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  primaryclass = "cs.AI",
}

@Misc{Moler:2017:CCB,
  author =       "Cleve Moler",
  title =        "{Cleve}'s Corner: Bug in Half-Precision Floating Point
                 Object",
  howpublished = "MathWorks Web site.",
  day =          "20",
  month =        dec,
  year =         "2017",
  bibdate =      "Sat Jan 19 18:38:12 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Moler:2017:CCH}.",
  URL =          "https://blogs.mathworks.com/cleve/2017/12/20/bug-in-half-precision-floating-point-object/",
  acknowledgement = ack-nhfb,
}

@Misc{Moler:2017:CCH,
  author =       "Cleve Moler",
  title =        "{Cleve}'s Corner: {``Half} Precision'' 16-bit Floating
                 Point Arithmetic",
  howpublished = "MathWorks Web site.",
  day =          "8",
  month =        may,
  year =         "2017",
  bibdate =      "Sat Jan 19 18:38:12 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See bug fix \cite{Moler:2017:CCB}.",
  URL =          "https://blogs.mathworks.com/cleve/2017/05/08/half-precision-16-bit-floating-point-arithmetic/",
  acknowledgement = ack-nhfb,
}

@Misc{Moler:2017:CCQ,
  author =       "Cleve Moler",
  title =        "{Cleve}'s Corner: Quadruple Precision, 128-bit
                 Floating Point Arithmetic",
  howpublished = "MathWorks Web site.",
  day =          "22",
  month =        may,
  year =         "2017",
  bibdate =      "Fri Feb 01 05:12:18 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  URL =          "https://blogs.mathworks.com/cleve/2017/05/22/quadruple-precision-128-bit-floating-point-arithmetic/",
  abstract =     "The floating point arithmetic format that occupies 128
                 bits of storage is known as binary128 or quadruple
                 precision. This blog post describes an implementation
                 of quadruple precision programmed entirely in the
                 MATLAB language.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Monfared:2017:NMI,
  author =       "Amin Monfared and Hayssam El-Razouk and Arash
                 Reyhani-Masoleh",
  title =        "A New Multiplicative Inverse Architecture in Normal
                 Basis Using Novel Concurrent Serial Squaring and
                 Multiplication",
  crossref =     "Burgess:2017:ISC",
  pages =        "164--171",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.37",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Itoh and Tsujii proposed a fast algorithm for
                 computing multiplicative inverses (inversions) over
                 GF(2m) using normal bases by iterating single
                 multiplications and cyclic shifts. Recently, the
                 Itoh--Tsujii algorithm (ITA) has been modified to use
                 two digit-level single multiplications. The
                 improvements of the modified Itoh--Tsujii and its
                 variant algorithms are based on reducing the
                 computational latency at the expense of more area
                 requirements. In this paper, we propose a new inversion
                 architecture based on the classical IT algorithm (or
                 improved one) utilizing a novel interleaved
                 computations of two single multiplications and
                 squarings at the digit-level. The new inverter
                 outperforms previous modified Itoh--Tsujii algorithms
                 (such as the Ternary Itoh--Tsujii and optimal 3-chain
                 algorithms) in terms of its lower latency, higher
                 throughput, and improved hardware efficiency. The
                 efficiency of the proposed field inverter is
                 demonstrated by comparisons based on application
                 specific integrated circuits (ASIC) implementations
                 results using the standard 65nm CMOS technology
                 libraries.",
  acknowledgement = ack-nhfb,
  keywords =     "application specific integrated circuits; ARITH 2017;
                 ARITH-24; ASIC; CMOS technology; Computer architecture;
                 concurrent serial squaring; cyclic shifts; Digit-level
                 multiplier; field inversion; field inverter; finite
                 field; Gaussian processes; High definition video;
                 hybrid-double multiplication; Inverters; invertors;
                 Itoh--Tsujii algorithm; logic design; multiplicative
                 inverse architecture; multiplying circuits; Niobium;
                 Standards; two digit-level single multiplications; Two
                 dimensional displays",
}

@Article{Mopuri:2017:LCM,
  author =       "Suresh Mopuri and Amit Acharyya",
  title =        "Low-Complexity Methodology for Complex Square-Root
                 Computation",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "25",
  number =       "11",
  pages =        "3255--3259",
  year =         "2017",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/TVLSI.2017.2740343",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
  keywords =     "Complex square root; Complexity theory; Computer
                 architecture; coordinate rotation digital computer
                 (CORDIC); Field programmable gate arrays; Hardware;
                 Logic gates; square root; Transistors; Very large scale
                 integration",
}

@Article{Mustapha:2017:RSA,
  author =       "Khalid Shahabdeen Mustapha and Edem Kwedzo Bankas",
  title =        "{RNS} Scaling Algorithm for a New Moduli Set $ \{
                 2^{(2n + 1)} + 1, 2^{(2n + 1)}, 2^{(2n + 1)} - 1 \} $",
  journal =      j-INT-J-COMP-APPL,
  volume =       "165",
  number =       "??",
  pages =        "21--28",
  month =        may,
  year =         "2017",
  CODEN =        "????",
  DOI =          "https://doi.org/10.5120/ijca2017913974",
  ISSN =         "0975-8887",
  ISSN-L =       "0975-8887",
  bibdate =      "Fri Jan 24 09:34:34 MST 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/intjcompappl.bib",
  URL =          "https://www.ijcaonline.org/archives/volume165/number10/27609-2017913974/",
  acknowledgement = ack-nhfb,
  ajournal =     "Intern. J. of Computer Applications",
  articleno =    "10",
  fjournal =     "International Journal of Computer Applications",
  journal-URL =  "https://www.ijcaonline.org/",
}

@Article{Numahata:2017:ASN,
  author =       "Dai Numahata and Hiroshi Sekigawa",
  title =        "An algorithm for symbolic--numeric sparse
                 interpolation of multivariate polynomials whose degree
                 bounds are unknown",
  journal =      j-ACM-COMM-COMP-ALGEBRA,
  volume =       "51",
  number =       "1",
  pages =        "18--20",
  month =        mar,
  year =         "2017",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3096730.3096734",
  ISSN =         "1932-2232 (print), 1932-2240 (electronic)",
  ISSN-L =       "1932-2232",
  bibdate =      "Tue Oct 10 16:29:29 MDT 2017",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
  abstract =     "We consider the problem of sparse interpolation of a
                 multivariate black-box polynomial in floating-point
                 arithmetic. More specifically, we assume that we are
                 given a black-box polynomial $ f(x_1, \ldots {}, x_n) =
                 \sum^t_{j = 1} c_j x_1^{d_j, 1} \ldots {} x_n^{d_j, n}
                 \in C[x_1, \ldots {}, x_n] (c_j \neq 0) $ and the
                 number of terms $t$, and that we can evaluate the value
                 of $ f(x^1, \ldots {}, x_n)$ at any point in $ C^n$ in
                 floating-point arithmetic. The problem is to find the
                 coefficients $ c_1, \ldots {}, c_t$ and the exponents $
                 d_{1, 1}, \ldots {}, d_{t, n}$. We propose an efficient
                 algorithm to solve the problem.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Communications in Computer Algebra",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}

@Book{Patterson:2017:COD,
  author =       "David A. Patterson and John L. Hennessy",
  title =        "Computer Organization and Design: the Hardware\slash
                 Software Interface",
  publisher =    pub-MORGAN-KAUFMANN,
  address =      pub-MORGAN-KAUFMANN:adr,
  edition =      "{RISC-V}",
  pages =        "xxiv + 565 + a-86 + i + 22",
  year =         "2017",
  ISBN =         "0-12-812275-7 (paperback), 0-12-812276-5 (e-book)",
  ISBN-13 =      "978-0-12-812275-4 (paperback), 978-0-12-812276-1
                 (e-book)",
  LCCN =         "QA76.9.C643",
  bibdate =      "Wed Sep 25 15:00:48 MDT 2024",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  series =       "Morgan Kaufmann series in computer architecture and
                 design",
  URL =          "https://www.elsevier.com/books-and-journals/book-companion/9780128119051;
                 https://www.elsevier.com/books/computer-architecture/hennessy/978-0-12-811905-1",
  abstract =     "The new RISC-V Edition of Computer Organization and
                 Design features the RISC-V open source instruction set
                 architecture, the first open source architecture
                 designed to be used in modern computing environments
                 such as cloud computing, mobile devices, and other
                 embedded systems. With the post-PC era now upon us,
                 Computer Organization and Design moves forward to
                 explore this generational change with examples,
                 exercises, and material highlighting the emergence of
                 mobile computing and the Cloud. Updated content
                 featuring tablet computers, Cloud infrastructure, and
                 the x86 (cloud computing) and ARM (mobile computing
                 devices) architectures is included.",
  acknowledgement = ack-nhfb,
  subject =      "Computer organization; Computer engineering; Computer
                 interfaces; Ordinateurs; Conception et construction;
                 Interfaces (Informatique); Computer engineering.;
                 Computer interfaces.; Computer organization.",
  tableofcontents = "1. Computer Abstractions and Technology \\
                 2. Instructions: Language of the Computer \\
                 3. Arithmetic for Computers \\
                 4. The RISC-V Processor \\
                 5. Large and Fast: Exploiting Memory Hierarchy \\
                 6. Parallel Processors from Client to Cloud \\
                 A. The Basics of Logic Design \\
                 B. Graphics and Computing GPUs \\
                 C. Mapping Control to Hardware \\
                 D. A Survey of RISC Architectures",
}

@Article{Rafferty:2017:ELI,
  author =       "Ciara Rafferty and M{\'a}ire O'Neill and Neil Hanley",
  title =        "Evaluation of Large Integer Multiplication Methods on
                 Hardware",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "66",
  number =       "8",
  pages =        "1369--1382",
  month =        "????",
  year =         "2017",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2017.2677426",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 13 14:57:15 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/document/7869256/",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Comba multiplication; Karatsuba multiplication;
                 Karatsuba--Comba multiplier; NTT--Karatsuba--Schoolbook
                 multiplier",
}

@InProceedings{Rieu-Helft:2017:HGE,
  author =       "Rapha{\"e}l Rieu-Helft and Claude March{\'e} and
                 Guillaume Melquiond",
  editor =       "Andrei Paskevich and Thomas Wies",
  booktitle =    "Verified Software. Theories, Tools, and Experiments:
                 {9th International Conference, VSTTE 2017, Heidelberg,
                 Germany, July 22--23, 2017}, Revised Selected Papers",
  title =        "How to get an efficient yet verified
                 arbitrary-precision integer library",
  volume =       "10712",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "xiii + 211 + 69",
  pages =        "84--101",
  year =         "2017",
  DOI =          "https://doi.org/10.1007/978-3-319-72308-2_6",
  ISBN =         "3-319-72308-1",
  ISBN-13 =      "978-3-319-72308-2",
  LCCN =         "QA76.758",
  bibdate =      "Sat Feb 08 09:03:15 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-LNCS,
  URL =          "https://link.springer.com/chapter/10.1007/978-3-319-72308-2_6",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-319-72308-2",
}

@InProceedings{Rioual:2017:LSN,
  author =       "Jean-Christophe Rioual",
  title =        "Large Scale Numerical Simulations of the Climate",
  crossref =     "Burgess:2017:ISC",
  pages =        "122--122",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.21",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Met Office Hadley Centre for Climate Science and
                 Services, based at the Met Office's Exeter HQ, provides
                 world-class guidance on the science of climate change
                 and is the primary focus in the UK for climate science.
                 The Hadley Centre makes significant contributions to
                 scientific literature and to a variety of climate
                 science reports, including the International Panel on
                 Climate Change (IPCC). In October 2014 the Government
                 confirmed its investment of \pounds 97 million in a new
                 high performance computing facility for the Met Office.
                 The new Cray XC40 located at Exeter Science Park is the
                 largest HPC system in the world dedicated to weather
                 and climate research. I will first give an overview of
                 how climate numerical experiments are organised
                 worldwide through the coupled model intercomparison
                 project (CMIP) under the auspices of the world climate
                 research program (WCRP). The numerical results of these
                 simulation campaigns are submitted to intense scrutiny
                 by the scientific community and policy makers.
                 Numerical reproducibility is therefore of paramount
                 importance. I will explain the parameters of what
                 numerical reproducibility means to our community and
                 how we aim to achieve it. I will present the use of
                 different types of floating point arithmetic in the
                 models. Two examples are the use double--double
                 precision for reproducible global sums and research on
                 single precision algorithms for computational
                 efficiency. Finally, I will look at some of the
                 challenges to maintain numerical reproducibility in the
                 exascale era.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2017; ARITH-24; climate change; Computational
                 modeling; coupled model intercomparison project; Cray
                 XC40; Digital arithmetic; floating point arithmetic;
                 geophysics computing; Government; Investment; large
                 scale numerical simulations; largest HPC system;
                 Meteorology; Numerical models; Numerical simulation;
                 parallel processing; world climate research program",
}

@InProceedings{Risse:2017:BEG,
  author =       "Thomas Risse",
  booktitle =    "{2017 8th International Conference on Information
                 Technology (ICIT)}",
  title =        "Better is the enemy of good: Unums: An alternative to
                 {IEEE 754} floats and doubles",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "200--204",
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ICITECH.2017.8080000",
  bibdate =      "Fri Dec 15 07:38:18 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Rocca:2017:CRE,
  author =       "Alexandre Rocca and Victor Magron and Thao Dang",
  title =        "Certified Roundoff Error Bounds Using {Bernstein}
                 Expansions and Sparse {Krivine--Stengle}
                 Representations",
  crossref =     "Burgess:2017:ISC",
  pages =        "74--81",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.36",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Floating point error is a notable drawback of embedded
                 systems implementation. Computing rigorous upper bounds
                 of roundoff errors is absolutely necessary for the
                 validation of critical software. This problem of
                 computing rigorous upper bounds is even more
                 challenging when addressing non-linear programs. In
                 this paper, we propose and compare two new methods
                 based on Bernstein expansions and sparse
                 Krivine--Stengle representations, adapted from the
                 field of the global optimization, to compute upper
                 bounds of roundoff errors for programs implementing
                 polynomial functions. We release two related software
                 package FPBern and FPKriSten, and compare them with
                 state of the art tools. We show that these two methods
                 achieve competitive performance, while computing
                 accurate upper bounds by comparison with other tools.",
  acknowledgement = ack-nhfb,
  keywords =     "Algebra; ARITH 2017; ARITH-24; Bernstein expansions;
                 Bernstein Expansions; certified roundoff error bounds;
                 Computational modeling; floating point arithmetic;
                 Floating Point Arithmetic; floating point error;
                 FPBern; FPKriSten; global optimization; Krivine-Stengle
                 Representations; Linear Programming Relaxations;
                 non-linear programs; nonlinear programming;
                 Optimization; Polynomial Optimization; Roundoff Error
                 Bounds; Roundoff errors; sparse Krivine-Stengle
                 representations; Standards; Tools; Upper bound",
}

@InProceedings{Rovers:2017:IPP,
  author =       "Kenneth C. Rovers and Sam Elliott",
  title =        "On Improving the Performance Per Area of {ASTC} with a
                 Multi-output Decoder",
  crossref =     "Burgess:2017:ISC",
  pages =        "58--59",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.32",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "ASTC is an efficient and flexible texture compression
                 format but it is relatively costly to implement in
                 hardware. By outputting multiple texels from a single
                 encoded ASTC block, we will show an performance per
                 area improvement of 25\%.",
  acknowledgement = ack-nhfb,
  keywords =     "adaptive scalable texture compression; ARITH 2017;
                 ARITH-24; computer graphics; data compression;
                 Decoding; flexible texture compression format;
                 Graphics; Hardware; Image color analysis; image
                 texture; Indexes; Interpolation; multioutput decoder;
                 Performance evaluation; performance per area; single
                 encoded ASTC block; texture decompression",
}

@Article{Rump:2017:IPK,
  author =       "Siegfried M. Rump",
  title =        "{IEEE754} Precision-$k$ base-$ \beta $ Arithmetic
                 Inherited by Precision-$m$ Base-$ \beta $ Arithmetic
                 for $ k < m$",
  journal =      j-TOMS,
  volume =       "43",
  number =       "3",
  pages =        "20:1--20:15",
  month =        jan,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2785965",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 4 10:55:07 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=2785965",
  abstract =     "Suppose an $m$-digit floating-point arithmetic in base
                 $ \beta \geq 2$ following the IEEE754 arithmetic
                 standard is available. We show how a $k$-digit
                 arithmetic with $ k < m$ can be inherited solely using
                 $m$-digit operations. This includes the rounding into
                 $k$ digits, the four basic operations and the square
                 root, all for even or odd base $ \beta $. In
                 particular, we characterize the relation between $k$
                 and $m$ so that no double rounding occurs when
                 computing in $m$ digits and rounding the result into
                 $k$ digits. We discuss rounding to nearest as well as
                 directed rounding, and our approach covers exceptional
                 values including signed zero. For binary arithmetic, a
                 Matlab toolbox based on binary64 including $k$-bit
                 scalar, vector and matrix operations as well as $k$-bit
                 interval arithmetic is part of Version 8 of INTLAB, the
                 Matlab toolbox for reliable computing.",
  acknowledgement = ack-nhfb,
  articleno =    "20",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "double rounding",
}

@Article{Russell:2017:LBR,
  author =       "Brian M. Russell",
  title =        "Lost Bits Regained?",
  journal =      "Resurrection: The Journal of the Computer Conservation
                 Society",
  volume =       "??",
  number =       "79",
  pages =        "??--??",
  month =        "Autumn",
  year =         "2017",
  ISSN =         "0958-7403",
  ISSN-L =       "0958-7403",
  bibdate =      "Mon Jul 27 18:14:57 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://computerconservationsociety.org/resurrection/res79.htm#d",
  acknowledgement = ack-nhfb,
  remark =       "Answers the question: ``Did the Ferranti Atlas
                 floating point arithmetic unit standardise its operands
                 before applying the requested arithmetic function or
                 did it risk losing accuracy if the numbers were not
                 standardised?''",
}

@Article{Saint-Genies:2017:ELT,
  author =       "Hugues de Lassus Saint-Geni{\`e}s and David Defour and
                 Guillaume Revy",
  title =        "Exact Lookup Tables for the Evaluation of
                 Trigonometric and Hyperbolic Functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "66",
  number =       "12",
  pages =        "2058--2071",
  month =        "????",
  year =         "2017",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2017.2703870",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 10 08:32:25 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/document/7927421/",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Sanchez-Stern:2017:FRC,
  author =       "Alex Sanchez-Stern and Pavel Panchekha and Sorin
                 Lerner and Zachary Tatlock",
  title =        "Finding Root Causes of Floating Point Error with
                 {Herbgrind}",
  journal =      "arXiv.org",
  pages =        "15",
  year =         "2017",
  bibdate =      "Sat Feb 8 10:38:13 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/1705.10416",
  abstract =     "Floating-point arithmetic plays a central role in
                 science, engineering, and finance by enabling
                 developers to approximate real arithmetic. To address
                 numerical issues in large floating-point applications,
                 developers must identify root causes, which is
                 difficult because floating-point errors are generally
                 non-local, non-compositional, and non-uniform. This
                 paper presents Herbgrind, a tool to help developers
                 identify and address root causes in numerical code
                 written in low-level C/C++ and Fortran. Herbgrind
                 dynamically tracks dependencies between operations and
                 program outputs to avoid false positives and abstracts
                 erroneous computations to a simplified program fragment
                 whose improvement can reduce output error. We perform
                 several case studies applying Herbgrind to large,
                 expert-crafted numerical programs and show that it
                 scales to applications spanning hundreds of thousands
                 of lines, correctly handling the low-level details of
                 modern floating point hardware and mathematical
                 libraries, and tracking error across function
                 boundaries and through the heap.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  biburl =       "https://dblp.org/rec/bib/journals/corr/Sanchez-SternPL17",
  remark =       "Published in PLDI 18.",
}

@Article{Sano:2017:FBS,
  author =       "Kentaro Sano and Satoru Yamamoto",
  title =        "{FPGA}-Based Scalable and Power-Efficient Fluid
                 Simulation using Floating-Point {DSP} Blocks",
  journal =      j-IEEE-TRANS-PAR-DIST-SYS,
  volume =       "28",
  number =       "10",
  pages =        "2823--2837",
  month =        oct,
  year =         "2017",
  CODEN =        "ITDSEO",
  DOI =          "https://doi.org/10.1109/TPDS.2017.2691770",
  ISSN =         "1045-9219 (print), 1558-2183 (electronic)",
  ISSN-L =       "1045-9219",
  bibdate =      "Thu Oct 12 06:58:12 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranspardistsys.bib",
  URL =          "https://www.computer.org/csdl/trans/td/2017/10/07893769-abs.html",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Parallel Distrib. Syst.",
  fjournal =     "IEEE Transactions on Parallel and Distributed
                 Systems",
  journal-URL =  "http://www.computer.org/tpds/archives.htm",
}

@Article{Schleicher:2017:NMP,
  author =       "Dierk Schleicher and Robin Stoll",
  title =        "{Newton}'s method in practice: Finding all roots of
                 polynomials of degree one million efficiently",
  journal =      j-THEOR-COMP-SCI,
  volume =       "681",
  number =       "??",
  pages =        "146--166",
  day =          "12",
  month =        jun,
  year =         "2017",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Aug 9 15:42:32 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tcs2015.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0304397517302475",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}

@InProceedings{Serre:2017:OSL,
  author =       "Fran{\c{c}}ois Serre and Markus Puschel",
  title =        "Optimal Streamed Linear Permutations",
  crossref =     "Burgess:2017:ISC",
  pages =        "60--61",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.13",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We give an overview on optimal circuits to implement
                 linear permutations on FPGAs using only RAM banks and
                 switches. Linear means that the permutation maps
                 linearly the bit representation of the indices, as it
                 is the case with most permutations arising in digital
                 signal processing algorithms including those in fast
                 Fourier transforms, Viterbi decoders, and sorting
                 networks. Additionally, we assume that the data to be
                 permuted is streamed, i.e., input in chunks over
                 several cycles. The circuits are obtained from a
                 suitable factorization of the bit matrix representing
                 the permutation and achieve the minimal number of
                 switches possible.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2017; ARITH-24; bit representation;
                 Bit-reversal; Complexity; Computer science; Connection
                 network; Data reordering; digital signal processing
                 algorithms; fast Fourier transforms; field programmable
                 gate arrays; Field programmable gate arrays; field
                 programmable gate arrays; FPGA; Matrix factorization;
                 optimal circuits; optimal streamed linear permutations;
                 Parallel processing; Ports (Computers); Program
                 processors; RAM banks; Random access memory;
                 random-access storage; signal processing; Sorting;
                 sorting networks; Streaming datapath; Stride
                 permutation; Viterbi decoders; Viterbi decoding",
}

@Article{Stoutemyer:2017:APC,
  author =       "David R. Stoutemyer",
  title =        "{AskConstants} proposes concise non-floats close to
                 floats",
  journal =      j-ACM-COMM-COMP-ALGEBRA,
  volume =       "51",
  number =       "1",
  pages =        "32--34",
  month =        mar,
  year =         "2017",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3096730.3096739",
  ISSN =         "1932-2232 (print), 1932-2240 (electronic)",
  ISSN-L =       "1932-2232",
  bibdate =      "Tue Oct 10 16:29:29 MDT 2017",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
  abstract =     "This poster presentation is an opportunity to try the
                 downloadable AskConstants program. This copy of some
                 posters is a sequence of images of the program in
                 operation.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Communications in Computer Algebra",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}

@Article{Thevenoux:2017:ASS,
  author =       "Laurent Th{\'e}venoux and Philippe Langlois and
                 Matthieu Martel",
  title =        "Automatic source-to-source error compensation of
                 floating-point programs: code synthesis to optimize
                 accuracy and time",
  journal =      j-CCPE,
  volume =       "29",
  number =       "7",
  pages =        "??--??",
  day =          "10",
  month =        apr,
  year =         "2017",
  CODEN =        "CCPEBO",
  DOI =          "https://doi.org/10.1002/cpe.3953",
  ISSN =         "1532-0626 (print), 1532-0634 (electronic)",
  ISSN-L =       "1532-0626",
  bibdate =      "Fri Mar 31 19:12:52 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/ccpe.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Concurrency and Computation: Practice and Experience",
  journal-URL =  "http://www.interscience.wiley.com/jpages/1532-0626",
}

@Article{Thornes:2017:USD,
  author =       "Tobias Thornes and Peter D{\"u}ben and Tim Palmer",
  title =        "On the use of scale-dependent precision in {Earth
                 System} modelling",
  journal =      j-QUART-J-ROY-METEOROL-SOC,
  volume =       "143",
  number =       "703",
  pages =        "897--908",
  month =        jan,
  year =         "2017",
  CODEN =        "QJRMAM",
  DOI =          "https://doi.org/10.1002/qj.2974",
  ISSN =         "0035-9009 (print), 1477-870X (electronic)",
  ISSN-L =       "0035-9009",
  bibdate =      "Thu Nov 7 17:05:05 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Quarterly journal of the Royal Meteorological
                 Society",
  journal-URL =  "http://rmets.onlinelibrary.wiley.com/hub/journal/10.1002/(ISSN)1477-870X/issues/",
  keywords =     "half-precision floating-point arithmetic; stochastic
                 rounding; variable precision floating-point
                 arithmetic",
}

@InCollection{Titolo:2017:AIF,
  author =       "Laura Titolo and Marco A. Feli{\'u} and Mariano
                 Moscato and C{\'e}sar A. Mu{\~n}oz",
  editor =       "Isil Dillig and Jens Palsberg",
  booktitle =    "Verification, Model Checking, and Abstract
                 Interpretation, {19th International Conference, VMCAI
                 2018, Los Angeles, CA, USA, January 7--9, 2018,
                 Proceedings}",
  title =        "An Abstract Interpretation Framework for the Round-Off
                 Error Analysis of Floating-Point Programs",
  volume =       "10747",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "516--537",
  month =        dec,
  year =         "2017",
  DOI =          "https://doi.org/10.1007/978-3-319-73721-8_24",
  ISBN =         "3-319-73720-1 (print), 3-319-73721-X (e-book)",
  ISBN-13 =      "978-3-319-73720-1 (print), 978-3-319-73721-8
                 (e-book)",
  bibdate =      "Mon Sep 11 07:21:11 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-LNCS,
  abstract =     "This paper presents an abstract interpretation
                 framework for the round-off error analysis of
                 floating-point programs. This framework defines a
                 parametric abstract analysis that computes, for each
                 combination of ideal and floating-point execution path
                 of the program, a sound over-approximation of the
                 accumulated floating-point round-off error that may
                 occur. In addition, a Boolean expression that
                 characterizes the input values leading to the computed
                 error approximation is also computed. An abstraction on
                 the control flow of the program is proposed to mitigate
                 the explosion of the number of elements generated by
                 the analysis. Additionally, a widening operator is
                 defined to ensure the convergence of recursive
                 functions and loops. An instantiation of this framework
                 is implemented in the prototype tool PRECiSA that
                 generates formal proof certificates stating the
                 correctness of the computed round-off errors.",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-319-73721-8",
}

@Article{Ueno:2017:BCF,
  author =       "Tomohiro Ueno and Kentaro Sano and Satoru Yamamoto",
  title =        "Bandwidth Compression of Floating-Point Numerical Data
                 Streams for {FPGA}-Based High-Performance Computing",
  journal =      j-TRETS,
  volume =       "10",
  number =       "3",
  pages =        "18:1--18:??",
  month =        jul,
  year =         "2017",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3053688",
  ISSN =         "1936-7406 (print), 1936-7414 (electronic)",
  ISSN-L =       "1936-7406",
  bibdate =      "Sat Dec 23 10:23:02 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/trets.bib",
  abstract =     "Although computational performance is often limited by
                 insufficient bandwidth to/from an external memory, it
                 is not easy to physically increase off-chip memory
                 bandwidth. In this study, we propose a hardware-based
                 bandwidth compression technique that can be applied to
                 field-programmable gate array-- (FPGA) based
                 high-performance computation with a logically wider
                 effective memory bandwidth. Our proposed hardware
                 approach can boost the performance of FPGA-based stream
                 computations by applying a data compression technique
                 to effectively transfer more data streams. To apply
                 this data compression technique to bandwidth
                 compression via hardware, several requirements must
                 first be satisfied, including an acceptable level of
                 compression performance and a sufficiently small
                 hardware footprint. Our proposed hardware-based
                 bandwidth compressor utilizes an efficient
                 prediction-based data compression algorithm. Moreover,
                 we propose a multichannel serializer and deserializer
                 that enable applications to use multiple channels of
                 computational data with the bandwidth compression. The
                 serializer encodes compressed data blocks of multiple
                 channels into a data stream, which is efficiently
                 written to an external memory. Based on preliminary
                 evaluation, we define an encoding format considering
                 both high compression ratio and small hardware area. As
                 a result, we demonstrate that our area saving bandwidth
                 compressor increases performance of an FPGA-based fluid
                 dynamics simulation by deploying more processing
                 elements to exploit spatial parallelism with the
                 enhanced memory bandwidth.",
  acknowledgement = ack-nhfb,
  articleno =    "18",
  fjournal =     "ACM Transactions on Reconfigurable Technology and
                 Systems (TRETS)",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J1151",
}

@InProceedings{Uguen:2017:BHL,
  author =       "Yohann Uguen and Florent de Dinechin and Steven
                 Derrien",
  booktitle =    "{2017 27th International Conference on Field
                 Programmable Logic and Applications (FPL)}",
  title =        "Bridging high-level synthesis and application-specific
                 arithmetic: The case study of floating-point
                 summations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--8",
  month =        sep,
  year =         "2017",
  DOI =          "https://doi.org/10.23919/FPL.2017.8056792",
  ISSN =         "1946-147X (print), 1946-1488 (electronic)",
  ISSN-L =       "1946-147X",
  bibdate =      "Sat Feb 8 10:26:34 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; application-specific arithmetic; C language;
                 C-C++ dialects; C11 standards; Field programmable gate
                 arrays; field programmable gate arrays; floating point
                 arithmetic; floating-point additions; floating-point
                 summations; FPGA application-specific efficiency; FPGA
                 programming; handcrafted HDL; Hardware; high level
                 synthesis; high-level C description; high-level C
                 language; high-level specification; high-level
                 synthesis; highly-customizable application-specific IP;
                 HLS; IEEE-754 standards; logic design; microprocessor
                 programming; nonstandard arithmetic formats;
                 nonstandard computations; Open area test sites;
                 Optimization; program compilers; Program processors;
                 source-to-source compiler; Tools; ubiquitous
                 floating-point summation-reduction pattern",
}

@Article{Ugurdag:2017:HDS,
  author =       "H. Fatih Ugurdag and Florent de Dinechin and Y. Serhan
                 Gener and Sezer G{\"o}ren and Laurent-St{\'e}phane
                 Didier",
  title =        "Hardware Division by Small Integer Constants",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "66",
  number =       "12",
  pages =        "2097--2110",
  month =        dec,
  year =         "2017",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2017.2707488",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Nov 10 08:32:25 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/document/7933010/",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{vanderHoeven:2017:MPF,
  author =       "Joris van der Hoeven",
  title =        "Multiple Precision Floating-Point Arithmetic on {SIMD}
                 Processors",
  crossref =     "Burgess:2017:ISC",
  pages =        "2--9",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.12",
  ISSN =         "1063-6889",
  MRclass =      "65Y04, 65T50, 68W30",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Current general purpose libraries for multiple
                 precision floating-point arithmetic such as MPFR suffer
                 from a large performance penalty with respect to
                 hard-wired instructions. The performance gap tends to
                 become even larger with the advent of wider SIMD
                 arithmetic in both CPUs and GPUs. In this paper, we
                 present efficient algorithms for multiple precision
                 floating-point arithmetic that are suitable for
                 implementations on SIMD processors. A.C.M. subject
                 classification: G.1.0 Computer-arithmetic A.M.S.
                 subject classification: 65Y04, 65T50, 68W30.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2017; ARITH-24; floating point arithmetic;
                 floating-point arithmetic; Frequency modulation;
                 Hardware; Indexes; Libraries; multiple precision;
                 multiple precision floating-point arithmetic; Numerical
                 analysis; parallel processing; Program processors;
                 SIMD; SIMD processors; Standards",
}

@Article{VanZee:2017:IHP,
  author =       "Field G. {Van Zee} and Tyler M. Smith",
  title =        "Implementing High-performance Complex Matrix
                 Multiplication via the 3m and 4m Methods",
  journal =      j-TOMS,
  volume =       "44",
  number =       "1",
  pages =        "7:1--7:36",
  month =        jul,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3086466",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 4 10:55:07 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3086466",
  abstract =     "In this article, we explore the implementation of
                 complex matrix multiplication. We begin by briefly
                 identifying various challenges associated with the
                 conventional approach, which calls for a carefully
                 written kernel that implements complex arithmetic at
                 the lowest possible level (i.e., assembly language). We
                 then set out to develop a method of complex matrix
                 multiplication that avoids the need for complex kernels
                 altogether. This constraint promotes code reuse and
                 portability within libraries such as Basic Linear
                 Algebra Subprograms and BLAS-Like Library Instantiation
                 Software (BLIS) and allows kernel developers to focus
                 their efforts on fewer and simpler kernels. We develop
                 two alternative approaches --- one based on the 3m
                 method and one that reflects the classic 4m formulation
                 --- each with multiple variants, all of which rely only
                 on real matrix multiplication kernels. We discuss the
                 performance characteristics of these ``induced''
                 methods and observe that the assembly-level method
                 actually resides along the 4m spectrum of algorithmic
                 variants. Implementations are developed within the BLIS
                 framework, and testing on modern hardware confirms that
                 while the less numerically stable 3m method yields the
                 fastest runtimes, the more stable (and thus widely
                 applicable) 4m method's performance is somewhat limited
                 due to implementation challenges that appear inherent
                 in nature.",
  acknowledgement = ack-nhfb,
  articleno =    "7",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@InProceedings{Vazquez:2017:SED,
  author =       "Alvaro V{\'a}zquez and Elisardo Antelo",
  title =        "A Sum Error Detection Scheme for Decimal Arithmetic",
  crossref =     "Burgess:2017:ISC",
  pages =        "172--179",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.34",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Users of financial and e-commerce services demand a
                 high degree of reliability and at the same time an
                 increasing demand of speed of processing. On the other
                 hand, soft errors are becoming more significant due to
                 the higher densities and reduced CMOS integration
                 technology sizes. Among the basic arithmetic
                 operations, addition/subtraction is the most demanded.
                 Although in the past, binary implementations were only
                 considered, today decimal implementations are becoming
                 important. In this context, we introduce a modular
                 design for fast error checking of binary and decimal
                 (BCD) addition/subtraction operations that avoids the
                 whole replication of the arithmetic units. Unlike other
                 error checkers based on parity prediction or residue
                 checking, this is a separable design that lies
                 completely off of the critical path of the protected
                 adder without incurring in important penalties in area
                 or performance.",
  acknowledgement = ack-nhfb,
  keywords =     "adders; Adders; ARITH 2017; ARITH-24; arithmetic
                 units; CMOS; CMOS integrated circuits; CMOS logic
                 circuits; Combined decimal/binary Adders; Computer
                 architecture; decimal arithmetic; Decimal arithmetic;
                 Detectors; digital arithmetic; error checking; logic
                 design; Microprocessors; parity prediction; radiation
                 hardening (electronics); Reliability; residue checking;
                 Residue Checking; Silicon; soft errors; sum error
                 detection scheme; Transient analysis",
}

@InProceedings{Vo-Thi:2017:FPF,
  author =       "Phuong-Thao Vo-Thi and Trong-Thuc Hoang and Cong-Kha
                 Pham and Duc-Hung Le",
  booktitle =    "{2017 International Conference on Recent Advances in
                 Signal Processing, Telecommunications \& Computing
                 (SigTelCom)}",
  title =        "A floating-point {FFT} Twiddle factor implementation
                 based on adaptive angle recoding {CORDIC}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "21--26",
  year =         "2017",
  DOI =          "https://doi.org/10.1109/SIGTELCOM.2017.7849789",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithm design and analysis; Computer architecture;
                 Field programmable gate arrays; OFDM; Signal
                 processing; Signal processing algorithms;
                 Telecommunications",
}

@InProceedings{Volkova:2017:RVD,
  author =       "Anastasia Volkova and Christoph Lauter and Thibault
                 Hilaire",
  title =        "Reliable Verification of Digital Implemented Filters
                 Against Frequency Specifications",
  crossref =     "Burgess:2017:ISC",
  pages =        "180--187",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.9",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Reliable implementation of digital filters in finite
                 precision is based on accurate error analysis. However,
                 a small error in the time domain does not guarantee
                 that the implemented filter verifies the initial band
                 specifications in the frequency domain. We propose a
                 novel certified algorithm for the verification of a
                 filter's transfer function, or of an existing
                 finite-precision implementation. We show that this
                 problem boils down to the verification of bounds on a
                 rational function, and further to the positivity of a
                 polynomial. Our algorithm has reasonable runtime
                 efficiency to be used as a criterion in large
                 implementation space explorations. We ensure that there
                 are no false positives but false negative answers may
                 occur. For negative answers we give a tight bound on
                 the margin of acceptable specifications. We demonstrate
                 application of our algorithm to the comparison of
                 various finite-precision implementations of filters
                 already fully designed.",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithm design and analysis; ARITH 2017; ARITH-24;
                 digital filters; digital implemented filters;
                 eigendecomposition; filters; finite-precision
                 implementation; fixed-point arithmetic; floating-point
                 arithmetic; frequency specifications; Frequency-domain
                 analysis; interval arithmetic; polynomials;
                 Positivstellensatz; reliability; Reliability; rigorous
                 computation; Signal processing algorithms; Software
                 algorithms; transfer function; transfer functions;
                 Transfer functions; Transforms",
}

@InProceedings{Vzquez:2017:NSA,
  author =       "Alvaro V{\'a}zquez and Elisardo Antelo",
  title =        "A Number System Approach for Adder Topologies",
  crossref =     "Burgess:2017:ISC",
  pages =        "50--57",
  month =        jul,
  year =         "2017",
  DOI =          "https://doi.org/10.1109/ARITH.2017.33",
  ISSN =         "1063-6889",
  bibdate =      "Fri Nov 17 09:10:14 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The design space exploration for fast and power
                 efficient adders is of increasing interest for
                 microprocessors and graphic and digital signal
                 processors. Recently, several methods have been
                 proposed to explore the design space of adders, where
                 well known designs appear as possible instances. These
                 methods are based on the identification of parameters
                 that lead to different hardware structures. In this
                 work, we go a step further by exploring the
                 mathematical foundation behind the trees for carry
                 computation. We propose an algorithm that allows to
                 obtain any adder topology based on design decisions.
                 The method is based on finding representations of
                 integers in a given number system. This leads to an
                 adder model that allows the design of any adder
                 structure in a compact a formal way. The proposed
                 formal model might be useful for a formal design
                 description of adders and it can be incorporated to CAD
                 tools.",
  acknowledgement = ack-nhfb,
  keywords =     "Adder Topologies; adder topology; Adders; adders;
                 ARITH 2017; ARITH-24; carry computation; carry logic;
                 Computational modeling; design space exploration; logic
                 design; Mathematical model; Number Systems; Prefix
                 Adders; Solid modeling; Space exploration; Sparse
                 Trees; Tools; Topology",
}

@Article{Wahba:2017:AEF,
  author =       "Ahmed A. Wahba and Hossam A. H. Fahmy",
  title =        "Area Efficient and Fast Combined Binary\slash Decimal
                 Floating Point Fused Multiply Add Unit",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "66",
  number =       "2",
  pages =        "226--239",
  month =        "????",
  year =         "2017",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2016.2584067",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jan 19 06:52:50 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Zhu:2017:LLL,
  author =       "Baozhou Zhu and Yuanwu Lei and Yuanxi Peng and
                 Tingting He",
  title =        "Low Latency and Low Error Floating-Point Sine\slash
                 Cosine Function Based {TCORDIC} Algorithm",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-1,
  volume =       "64",
  number =       "4",
  pages =        "892--905",
  year =         "2017",
  DOI =          "https://doi.org/10.1109/TCSI.2016.2631588",
  ISSN =         "1549-8328 (print), 1558-0806 (electronic)",
  ISSN-L =       "1549-8328",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems I: Regular
                 Papers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8919",
  keywords =     "Adders; Algorithm design and analysis; Convergence;
                 CORDIC; Delays; floating-point sine/cosine; low
                 latency; Prediction algorithms; Signal processing
                 algorithms; Table lookup; Taylor",
}

@Article{Adams:2018:RFF,
  author =       "Ulf Adams",
  title =        "{Ry{\=u}}: fast float-to-string conversion",
  journal =      j-SIGPLAN,
  volume =       "53",
  number =       "4",
  pages =        "270--282",
  month =        apr,
  year =         "2018",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/3296979.3192369",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Wed Oct 16 14:12:57 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
  abstract =     "We present Ry{\=u}, a new routine to convert binary
                 floating point numbers to their decimal representations
                 using only fixed-size integer operations, and prove its
                 correctness. Ry{\=u} is simpler and approximately three
                 times faster than the previously fastest
                 implementation.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "base conversion; correct rounding; floating-point
                 arithmetic; input-output conversion; radix conversion;
                 round-trip base conversion",
  remark =       "PLDI '18 proceedings.",
}

@Article{Afriyie:2018:MBE,
  author =       "Yaw Afriyie and M. I. Daabo",
  title =        "Multiple Bits Error Detection and Correction in {RRNS}
                 Architecture using the {MRC} and {HD} Techniques",
  journal =      j-INT-J-COMP-APPL,
  volume =       "180",
  number =       "??",
  pages =        "18--23",
  month =        may,
  year =         "2018",
  CODEN =        "????",
  DOI =          "https://doi.org/10.5120/ijca2018917030",
  ISSN =         "0975-8887",
  ISSN-L =       "0975-8887",
  bibdate =      "Fri Jan 24 09:43:10 MST 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/intjcompappl.bib",
  URL =          "https://www.ijcaonline.org/archives/volume180/number39/29387-2018917030/",
  acknowledgement = ack-nhfb,
  ajournal =     "Intern. J. of Computer Applications",
  articleno =    "39",
  fjournal =     "International Journal of Computer Applications",
  journal-URL =  "https://www.ijcaonline.org/",
  keywords =     "Redundant Residue Number System (RRNS)",
}

@Article{Alaghi:2018:CR,
  author =       "A. Alaghi and J. P. Hayes",
  title =        "Computing with Randomness",
  journal =      j-IEEE-SPECTRUM,
  volume =       "55",
  number =       "3",
  pages =        "46--51",
  month =        mar,
  year =         "2018",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.2018.8302387",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Sat Jan 18 07:02:09 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum2010.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "analog numbers; analog signal; arithmetic operations;
                 brains-process; computer process; Computers; digital
                 arithmetic; Digital circuits; human hearing; human
                 nervous system; human vision; Image restoration;
                 Implants; logic circuits; Logic gates; neural impulse
                 sequence; Parity check codes; random binary digit
                 stream; Retina; stochastic bitstreams; stochastic
                 computing; stochastic processes; time 50 year",
}

@Article{Amanollahi:2018:ERD,
  author =       "Saba Amanollahi and Ghassem Jaberipur",
  title =        "Extended Redundant-Digit Instruction Set for
                 Energy-Efficient Processors",
  journal =      j-TECS,
  volume =       "17",
  number =       "3",
  pages =        "70:1--70:??",
  month =        jun,
  year =         "2018",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3202664",
  ISSN =         "1539-9087 (print), 1558-3465 (electronic)",
  ISSN-L =       "1539-9087",
  bibdate =      "Thu Oct 17 18:16:35 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tecs.bib",
  abstract =     "The impact of extending the instruction set
                 architecture (ISA) of a conventional binary processor
                 by a set of redundant-digit arithmetic instructions is
                 studied. Selected binary arithmetic instructions within
                 a given code sequence are replaced with appropriate
                 redundant-digit ones. The selection criteria is so
                 enforced to lead to overall reduction of execution
                 energy and energy-delay product (EDP). A special branch
                 and bound algorithm is devised to modify the dataflow
                 graph (DFG) to a new one that takes advantage of the
                 extended redundant-digit instruction set. The DFG is
                 obtained, via an in-house tool, from the intermediate
                 code representation that is normally produced by the
                 utilized compiler. The required redundant-digit
                 arithmetic operations (including a multiplier, a
                 multiply accumulator, and three- to four-operand
                 redundant-digit adders specially designed for this
                 work) have been synthesized on 45nm NanGate technology
                 by a Synopsys Design Compiler. To evaluate the impact
                 of the proposed ISA augmentation on actual code
                 execution, the simulation and evaluation platform of
                 our choice is an MIPS processor whose ISA is extended
                 by the proposed redundant-digit instructions. Several
                 digital signal processing benchmarks are utilized as
                 the source of the baseline MIPS codes, which are
                 converted (via the aforementioned algorithm) to the
                 equivalent mixed binary/redundant-digit codes. Our
                 experiments, as such, show up to 26\% energy and 44\%
                 EDP savings.",
  acknowledgement = ack-nhfb,
  articleno =    "70",
  fjournal =     "ACM Transactions on Embedded Computing Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J840",
}

@InProceedings{Anders:2018:WRD,
  author =       "Mark Anders and Himanshu Kaul and Sanu Mathew and
                 Vikram Suresh and Sudhir Satpathy and Amit Agarwal and
                 Steven Hsu and Ram Krishnamurthy",
  booktitle =    "{2018 IEEE Symposium on VLSI Circuits}",
  title =        "{2.9TOPS/W} Reconfigurable Dense\slash Sparse
                 Matrix-Multiply Accelerator with Unified {INT8\slash
                 INTI6\slash FP16} Datapath in 14nm Tri-Gate {CMOS}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "39--40",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/VLSIC.2018.8502333",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; Energy efficiency; Pipelines; Routing; Sparse
                 matrices; Throughput; Voltage measurement",
}

@InProceedings{Anderson:2018:EVM,
  author =       "Cristina S. Anderson and Jingwei Zhang and Marius
                 Cornea",
  title =        "Enhanced Vector Math Support on the {Intel AVX-512}
                 Architecture",
  crossref =     "Tenca:2018:PIS",
  pages =        "120--124",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ARITH.2018.8464794",
  bibdate =      "Fri Jan 31 08:05:31 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Intel AVX-512 architecture adds new capabilities
                 such as masked execution, floating-point exception
                 suppression and static rounding modes, as well as a
                 small set of new instructions for mathematical library
                 support. These new features allow for better compliance
                 with floating-point or language standards (e.g. no
                 spurious floating-point exceptions, and faster or more
                 accurate code for directed rounding modes), as well as
                 simpler, smaller footprint implementations that
                 eliminate branches and special case paths. Performance
                 is also improved, in particular for vector mathematical
                 functions (which benefit from easier processing in the
                 main path, and fast access to small lookup tables). In
                 this paper, we describe the relevant new features and
                 their possible applications to floating-point
                 computation. The code examples include a few compact
                 implementation sequences for some common vector
                 mathematical functions.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2018; ARITH-25; common vector mathematical
                 functions; directed rounding modes; enhanced vector
                 math support; floating-point; floating-point
                 computation; floating-point exception suppression;
                 floating-point exceptions; Instruction sets; Intel
                 AVX-512 architecture; Libraries; masked execution;
                 mathematical library support; mathematics computing;
                 Registers; SIMD; Standards; static rounding modes;
                 Support vector machines; Table lookup; table lookup;
                 vector mathematical function; vectors",
}

@Misc{Anonymous:2018:DRD,
  author =       "Anonymous",
  title =        "Driverless racecar drives straight into a wall",
  howpublished = "Web site",
  year =         "2018",
  bibdate =      "Mon Aug 26 12:09:20 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "The report describes how an unanticipated
                 floating-point NaN caused the steering wheel to lock to
                 its maximum right. From the report: ``the [controller]
                 output values are transferred via control area network
                 (CAN) to the actuators, but there is no definition for
                 a NaN in the CAN specs, so it just transformed it into
                 a normal number, albeit a very large one.''",
  URL =          "https://www.reddit.com/r/formula1/comments/jk9jrg/comment/gai295l/",
  acknowledgement = ack-nhfb,
}

@Misc{Anonymous:2018:FVF,
  author =       "Anonymous",
  title =        "Formal Verification of Floating-Point Hardware with
                 Assertion-Based {VIP}",
  howpublished = "Web site.",
  year =         "2018",
  bibdate =      "Fri Sep 28 06:31:32 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.onespin.com/fpu/",
  acknowledgement = ack-nhfb,
  remark =       "Sections labeled ``Nicolae Tusinschi about
                 Verification of Floating-Point Hardware Designs'' and
                 ``Xilinx verifies Floating-Point Hardware IP with
                 OneSpin FPU App''.",
}

@Misc{Anonymous:2018:HFF,
  author =       "Anonymous",
  title =        "{Herbie}: Find and fix floating-point problems",
  howpublished = "Web site and software source.",
  year =         "2018",
  bibdate =      "Thu May 02 16:59:16 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://herbie.uwplse.org/",
  abstract =     "Herbie detects inaccurate expressions and finds more
                 accurate replacements.",
  acknowledgement = ack-nhfb,
}

@Misc{Anonymous:2018:OLA,
  author =       "Anonymous",
  title =        "{OneSpin} Launches {``App''} for Formal Verification
                 of Floating-Point Hardware Critical for Machine
                 Learning and Deep Learning Chips: Offers Exhaustive
                 Coverage of Floating-Point Arithmetic Operations
                 Compliant with {IEEE 754 Standard}",
  howpublished = "Web site",
  day =          "27",
  month =        nov,
  year =         "2018",
  bibdate =      "Wed Nov 28 10:06:08 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://globenewswire.com/news-release/2018/11/27/1657662/0/en/OneSpin-Launches-App-for-Formal-Verification-of-Floating-Point-Hardware-Critical-for-Machine-Learning-and-Deep-Learning-Chips.html",
  acknowledgement = ack-nhfb,
}

@Article{Babuska:2018:REG,
  author =       "Ivo Babuska and Gustaf S{\"o}derlind",
  title =        "On Roundoff Error Growth in Elliptic Problems",
  journal =      j-TOMS,
  volume =       "44",
  number =       "3",
  pages =        "33:1--33:22",
  month =        apr,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3134444",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Oct 5 11:23:12 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3134444",
  abstract =     "Large-scale linear systems arise in finite-difference
                 and finite-element discretizations of elliptic
                 problems. With increasing computer performance, ever
                 larger systems are solved using direct methods. How
                 large can such systems be without roundoff compromising
                 accuracy? Here we model roundoff dynamics in standard $
                 L U $ and $ L D L^T $ decompositions with respect to
                 problem size $N$. For the one-dimensional (1D) Poisson
                 equation with Dirichlet boundary conditions on an
                 equidistant grid, we show that the relative error in
                 the factorized matrix grows like $ O(\epsilon \sqrt N)$
                 if roundoffs are modeled as independent, expectation
                 zero random variables. With bias, the growth rate
                 changes to $ O(\epsilon N)$. Subsequent back
                 substitution results in typical error growths of $
                 O(\epsilon > N \sqrt {N})$ and $ O(\epsilon N^2)$,
                 respectively. Error growth is governed by the dynamics
                 of the computational process and by the structure of
                 the boundary conditions rather than by the condition
                 number. Computational results are demonstrated in
                 several examples, including a few fourth-order 1D
                 problems and second-order 2D problems, showing that
                 error accumulation depends strongly on the solution
                 method. Thus, the same $ L U$ solver may exhibit
                 different growth rates for the same 2D Poisson problem,
                 depending on whether the five-point or nine-point FDM
                 operator is used.",
  acknowledgement = ack-nhfb,
  articleno =    "33",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bajard:2018:MRW,
  author =       "Jean-Claude Bajard and Julien Eynard and Nabil
                 Merkiche",
  title =        "{Montgomery} reduction within the context of residue
                 number system arithmetic",
  journal =      j-J-CRYPTO-ENG,
  volume =       "8",
  number =       "3",
  pages =        "189--200",
  month =        sep,
  year =         "2018",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s13389-017-0154-9",
  ISSN =         "2190-8508 (print), 2190-8516 (electronic)",
  ISSN-L =       "2190-8508",
  bibdate =      "Wed Oct 2 11:24:50 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcryptoeng.bib",
  URL =          "http://link.springer.com/article/10.1007/s13389-017-0154-9",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Cryptographic Engineering",
  journal-URL =  "http://link.springer.com/journal/13389",
}

@InProceedings{Barthel:2018:HIB,
  author =       "Moritz B{\"a}rthel and Jochen Rust and Steffen Paul",
  booktitle =    "{2018 52nd Asilomar Conference on Signals, Systems,
                 and Computers}",
  title =        "Hardware Implementation of Basic Arithmetics and
                 Elementary Functions for Unum Computing",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "125--129",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ACSSC.2018.8645453",
  bibdate =      "Fri Dec 15 07:38:18 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InBook{Baruah:2018:EVI,
  author =       "Rashmita Baruah and Preetisudha Meher and Ashwini
                 Kumar Pradhan",
  booktitle =    "Information Systems Design and Intelligent
                 Applications",
  title =        "Efficient {VLSI} Implementation of {CORDIC}-Based
                 Multiplier Architecture",
  publisher =    "Springer Singapore",
  pages =        "441--450",
  month =        dec,
  year =         "2018",
  DOI =          "https://doi.org/10.1007/978-981-13-3329-3_41",
  ISBN =         "981-13-3329-7",
  ISBN-13 =      "978-981-13-3329-3",
  ISSN =         "2194-5365",
  bibdate =      "Tue Oct 28 07:04:09 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Becker:2018:NOS,
  author =       "Ruben Becker and Michael Sagraloff and Vikram Sharma
                 and Chee Yap",
  title =        "A near-optimal subdivision algorithm for complex root
                 isolation based on the {Pellet} test and {Newton}
                 iteration",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "86",
  number =       "??",
  pages =        "51--96",
  month =        may # "\slash " # jun,
  year =         "2018",
  CODEN =        "JSYCEH",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  bibdate =      "Wed Nov 22 16:17:19 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0747717117300378",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171",
}

@InProceedings{Boldo:2018:FPA,
  author =       "Sylvie Boldo and Florian Faissole and Vincent
                 Tourneur",
  title =        "A Formally-Proved Algorithm to Compute the Correct
                 Average of Decimal Floating-Point Numbers",
  crossref =     "Tenca:2018:PIS",
  pages =        "69--75",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ARITH.2018.8464761",
  bibdate =      "Fri Jan 31 08:05:31 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Some modern processors include decimal floating-point
                 units, with a conforming implementation of the IEEE-754
                 2008 standard. Unfortunately, many algorithms from the
                 computer arithmetic literature are not correct anymore
                 when computations are done in radix 10. This is in
                 particular the case for the computation of the average
                 of two floating-point numbers. Several radix-2
                 algorithms are available, including one that provides
                 the correct rounding, but none hold in radix 10. This
                 paper presents a new radix-10 algorithm that computes
                 the correctly-rounded average. To guarantee a higher
                 level of confidence, we also provide a Coq formal proof
                 of our theorems, that takes gradual underflow into
                 account. Note that our formal proof was generalized to
                 ensure this algorithm is correct when computations are
                 done with any even radix.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2018; ARITH-25; Coq formal proof; correct
                 rounding; correctly-rounded average; decimal
                 floating-point numbers; decimal floating-point units;
                 Digital arithmetic; floating point arithmetic;
                 formally-proved algorithm; Hardware; IEEE standards;
                 IEEE-754 2008 standard; Libraries; Program processors;
                 radix-10 algorithm; radix-2 algorithms; Software
                 algorithms; Standards; theorem proving",
}

@Misc{Bradbury:2018:RSR,
  author =       "Jonathan D. Bradbury and Steven R. Carlough and Brian
                 R. Prasky and Eric M. Schwarz",
  title =        "Reproducible stochastic rounding for out of order
                 processors",
  howpublished = "U.S. Patent US10209958B2",
  day =          "23",
  month =        jul,
  year =         "2018",
  bibdate =      "Fri Sep 22 17:33:27 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  note =         "Patent granted 19 February 2019; expired (fee
                 related)",
  abstract =     "A method for generating a random number for use in a
                 stochastic rounding operation is provided. The method
                 includes executing an instruction that causes at least
                 two operands to produce an intermediate result and
                 incrementing a state of a random number generator. The
                 method further includes causing the random number
                 generator to generate a random number in accordance
                 with the state and producing a final result by
                 utilizing the random number to determine a rounding of
                 the intermediate result.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Brisebarre:2018:HTP,
  author =       "Nicolas Brisebarre and George Constantinides and
                 Milo{\v{s}} Ercezovac and Silviu-Ioan Filip and Matei
                 Istoan and Jean-Michel Muller",
  title =        "A High Throughput Polynomial and Rational Function
                 Approximations Evaluator",
  crossref =     "Tenca:2018:PIS",
  pages =        "99--106",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ARITH.2018.8464778",
  bibdate =      "Fri Jan 31 08:05:31 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present an automatic method for the evaluation of
                 functions via polynomial or rational approximations and
                 its hardware implementation, on FPGAs. These
                 approximations are evaluated using Ercegovac's
                 iterative E-method adapted for FPGA implementation. The
                 polynomial and rational function coefficients are
                 optimized such that they satisfy the constraints of the
                 E-method. We present several examples of practical
                 interest; in each case a resource-efficient
                 approximation is proposed and comparisons are made with
                 alternative approaches.",
  acknowledgement = ack-nhfb,
  keywords =     "Approximation algorithms; approximation theory; ARITH
                 2018; ARITH-25; Convergence; Electronic mail; Ercegovac
                 iterative E-method; field programmable gate arrays;
                 Field programmable gate arrays; FPGA implementation;
                 function approximation; Hardware; hardware
                 implementation; Lattices; Linear systems; polynomial
                 function approximations evaluator; polynomials;
                 rational function approximations evaluator; rational
                 functions; resource-efficient approximation",
}

@InProceedings{Bruguera:2018:PII,
  author =       "J. D. Bruguera",
  booktitle =    "Proceedings of the {25th IEEE International Symposium
                 on Computer Arithmetic}",
  title =        "Radix-64 floating-point divider",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "87--94",
  year =         "2018",
  bibdate =      "Thu Jan 30 16:14:30 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bruguera:2018:RFP,
  author =       "Javier D. Bruguera",
  title =        "Radix-64 Floating-Point Divider",
  crossref =     "Tenca:2018:PIS",
  pages =        "84--91",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ARITH.2018.8464815",
  bibdate =      "Fri Jan 31 08:05:31 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The following topics are dealt with: floating point
                 arithmetic; digital arithmetic; IEEE standards; field
                 programmable gate arrays; learning (artificial
                 intelligence); cryptography; parallel processing; table
                 lookup; multiplying circuits; mathematics computing.",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; ARITH 2018; ARITH-25; artificial intelligence;
                 Convergence; cryptography; digital arithmetic; Digital
                 arithmetic; field programmable gate arrays; floating
                 point arithmetic; IEEE standards; learning; learning
                 (artificial intelligence); Mathematical model;
                 mathematics computing; multiplying circuits; parallel
                 processing; Program processors; table lookup; Timing;
                 Two dimensional displays",
}

@Article{Cannizzo:2018:FVA,
  author =       "Fabio Cannizzo",
  title =        "A fast and vectorizable alternative to binary search
                 in {$ O(1) $} with wide applicability to arrays of
                 floating point numbers",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "113",
  number =       "??",
  pages =        "37--54",
  month =        mar,
  year =         "2018",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Sat Jan 13 12:26:41 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jpardistcomp.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0743731517302836",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
}

@Article{Canto-Navarro:2018:FPA,
  author =       "E. Cant{\'o}-Navarro and M. L{\'o}pez-Garc{\'\i}a and
                 R. Ramos-Lara",
  title =        "Floating-point accelerator for biometric recognition
                 on {FPGA} embedded systems",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "112 (part 1)",
  number =       "??",
  pages =        "20--34",
  month =        feb,
  year =         "2018",
  CODEN =        "JPDCER",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Fri Nov 24 17:01:13 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jpardistcomp.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0743731517302642",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
}

@InProceedings{Chatelain:2018:VCE,
  author =       "Yohan Chatelain and Pablo {De Oliveira Castro} and
                 Eric Petit and David Defour and Jordan Bieder and Marc
                 Torrent",
  title =        "{VeriTracer}: Context-enriched tracer for
                 floating-point arithmetic analysis",
  crossref =     "Tenca:2018:PIS",
  pages =        "61--68",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ARITH.2018.8464687",
  bibdate =      "Fri Jan 31 08:05:31 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "VeriTracer automatically instruments a code and traces
                 the accuracy of floating-point variables over time.
                 VeriTracer enriches the visual traces with contextual
                 information such as the call site path in which a value
                 was modified. Contextual information is important to
                 understand how the floating-point errors propagate in
                 complex codes. VeriTracer is implemented as an LLVM
                 compiler tool on top of Verificarlo. We demonstrate how
                 VeriTracer can detect accuracy loss and quantify the
                 impact of using a compensated algorithm on ABINIT, an
                 industrial HPC application for Ab Initio quantum
                 computation.",
  acknowledgement = ack-nhfb,
  keywords =     "ab initio calculations; Ab Initio quantum computation;
                 ABINIT; ARITH 2018; ARITH-25; complex codes;
                 Computational modeling; Computer bugs; Context-enriched
                 tracer; contextual information; floating point
                 arithmetic; floating-point arithmetic analysis;
                 floating-point errors; floating-point variables;
                 industrial HPC application; LLVM compiler; Numerical
                 models; parallel processing; Probes; program compilers;
                 quantum computing; Tools; Verificarlo; VeriTracer;
                 visual traces; Visualization",
}

@InProceedings{Chaurasiya:2018:PPA,
  author =       "Rohit Chaurasiya and John Gustafson and Rahul Shrestha
                 and Jonathan Neudorfer and Sangeeth Nambiar and Kaustav
                 Niyogi and Farhad Merchant and Rainer Leupers",
  editor =       "{IEEE}",
  booktitle =    "{2018 IEEE 36th International Conference on Computer
                 Design (ICCD)}",
  title =        "Parameterized Posit Arithmetic Hardware Generator",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "334--341",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ICCD.2018.00057",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chen:2018:MMU,
  author =       "Jianyu Chen and Zaid Al-Ars",
  title =        "A Matrix-Multiply Unit for Posits in Reconfigurable
                 Logic Using {(OPEN)CAPI}",
  crossref =     "ACM:2018:CNG",
  pages =        "1--5",
  year =         "2018",
  DOI =          "https://doi.org/10.1145/3190339.3190340",
  bibdate =      "Mon Dec 11 08:58:21 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  articleno =    "1",
  keywords =     "posit arithmetic; universal number (unum) arithmetic",
}

@Misc{Cherkaev:2018:SLN,
  author =       "Annie Cherkaev",
  title =        "The secret life of {NaN}",
  howpublished = "Web site",
  month =        mar,
  year =         "2018",
  bibdate =      "Fri Dec 01 14:21:50 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://anniecherkaev.com/the-secret-life-of-nan",
  acknowledgement = ack-nhfb,
  remark =       "The site discusses IEEE 754 number encoding, and how
                 NaN payloads can be used to hold other things, like
                 data type codes, integers, and pointers, hidden inside
                 binary64 values.",
}

@InProceedings{Chung:2018:PCP,
  author =       "Shin Yee Chung",
  title =        "Provably Correct Posit Arithmetic with Fixed-Point Big
                 Integer",
  crossref =     "ACM:2018:CNG",
  pages =        "1--5",
  year =         "2018",
  DOI =          "https://doi.org/10.1145/3190339.3190341",
  bibdate =      "Mon Dec 11 09:00:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  articleno =    "2",
  keywords =     "posit arithmetic; universal number (unum) arithmetic",
}

@InProceedings{Cococcioni:2018:EPA,
  author =       "Marco Cococcioni and Emanuele Ruffaldi and Sergio
                 Saponara",
  editor =       "{IEEE}",
  booktitle =    "{2018 International Conference of Electrical and
                 Electronic Technologies for Automotive}",
  title =        "Exploiting Posit Arithmetic for Deep Neural Networks
                 in Autonomous Driving Applications",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--6",
  year =         "2018",
  DOI =          "https://doi.org/10.23919/EETA.2018.8493233",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Costello:2018:MCT,
  author =       "Craig Costello and Benjamin Smith",
  title =        "{Montgomery} curves and their arithmetic",
  journal =      j-J-CRYPTO-ENG,
  volume =       "8",
  number =       "3",
  pages =        "227--240",
  month =        sep,
  year =         "2018",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s13389-017-0157-6",
  ISSN =         "2190-8508 (print), 2190-8516 (electronic)",
  ISSN-L =       "2190-8508",
  bibdate =      "Wed Oct 2 11:24:50 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcryptoeng.bib",
  URL =          "http://link.springer.com/article/10.1007/s13389-017-0157-6",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Cryptographic Engineering",
  journal-URL =  "http://link.springer.com/journal/13389",
}

@Article{Dai:2018:FBM,
  author =       "Wangchen Dai and Donglong Chen and Ray C. C. Cheung
                 and {\c{C}}etin Kaya Ko{\c{c}}",
  title =        "{FFT}-Based {McLaughlin}'s {Montgomery} Exponentiation
                 without Conditional Selections",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "67",
  number =       "9",
  pages =        "1301--1314",
  month =        sep,
  year =         "2018",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2018.2811466",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Mar 15 08:10:13 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/document/8307235/",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Dai:2018:SAM,
  author =       "Wangchen Dai and Ray C. C. Cheung",
  title =        "Spectral arithmetic in {Montgomery} modular
                 multiplication",
  journal =      j-J-CRYPTO-ENG,
  volume =       "8",
  number =       "3",
  pages =        "211--226",
  month =        sep,
  year =         "2018",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s13389-017-0151-z",
  ISSN =         "2190-8508 (print), 2190-8516 (electronic)",
  ISSN-L =       "2190-8508",
  bibdate =      "Wed Oct 2 11:24:50 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcryptoeng.bib",
  URL =          "http://link.springer.com/article/10.1007/s13389-017-0151-z",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Cryptographic Engineering",
  journal-URL =  "http://link.springer.com/journal/13389",
}

@Article{Das:2018:MPT,
  author =       "Dipankar Das and Naveen Mellempudi and Dheevatsa
                 Mudigere and Dhiraj Kalamkar and Sasikanth Avancha and
                 Kunal Banerjee and Srinivas Sridharan and Karthik
                 Vaidyanathan and Bharat Kaul and Evangelos Georganas
                 and Alexander Heinecke and Pradeep Dubey and Jesus
                 Corbal and Nikita Shustrov and Roma Dubtsov and Evarist
                 Fomenko and Vadim Pirogov",
  title =        "Mixed Precision Training of Convolutional Neural
                 Networks using Integer Operations",
  journal =      "arXiv.org",
  pages =        "11",
  day =          "3",
  month =        feb,
  year =         "2018",
  bibdate =      "Mon Feb 10 09:24:48 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/abs/1802.00930",
  abstract =     "The state-of-the-art (SOTA) for mixed precision
                 training is dominated by variants of low precision
                 floating point operations, and in particular, FP16
                 accumulating into FP32 Micikevicius et al. (2017). On
                 the other hand, while a lot of research has also
                 happened in the domain of low and mixed-precision
                 Integer training, these works either present results
                 for non-SOTA networks (for instance only AlexNet for
                 ImageNet-1K), or relatively small datasets (like
                 CIFAR-10). In this work, we train state-of-the-art
                 visual understanding neural networks on the ImageNet-1K
                 dataset, with Integer operations on General Purpose
                 (GP) hardware. In particular, we focus on Integer
                 Fused-Multiply-and-Accumulate (FMA) operations which
                 take two pairs of INT16 operands and accumulate results
                 into an INT32 output.We propose a shared exponent
                 representation of tensors and develop a Dynamic Fixed
                 Point (DFP) scheme suitable for common neural network
                 operations. The nuances of developing an efficient
                 integer convolution kernel is examined, including
                 methods to handle overflow of the INT32 accumulator. We
                 implement CNN training for ResNet-50, GoogLeNet-v1,
                 VGG-16 and AlexNet; and these networks achieve or
                 exceed SOTA accuracy within the same number of
                 iterations as their FP32 counterparts without any
                 change in hyper-parameters and with a 1.8X improvement
                 in end-to-end training throughput. To the best of our
                 knowledge these results represent the first INT16
                 training results on GP hardware for ImageNet-1K dataset
                 using SOTA CNNs and achieve highest reported accuracy
                 using half-precision",
  acknowledgement = ack-nhfb,
  primaryclass = "cs.NE",
}

@InProceedings{De:2018:MLH,
  author =       "Debaprasad De and Archisman Ghosh and K. Gaurav Kumar
                 and Anurup Saha and Mrinal Kanti Naskar",
  booktitle =    "{2018 IEEE Applied Signal Processing Conference
                 (ASPCON)}",
  title =        "Multiplier-less Hardware Realization of Trigonometric
                 Functions for High Speed Applications",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "149--152",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ASPCON.2018.8748709",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Conferences; CORDIC; Field programmable gate arrays;
                 FPGA; Hardware; Signal processing; Signal processing
                 algorithms; Table lookup; Trigonometric functions;
                 Unified architecture",
}

@InProceedings{Defour:2018:FAR,
  author =       "David Defour",
  title =        "{FP-ANR}: A representation format to handle
                 floating-point cancellation at run-time",
  crossref =     "Tenca:2018:PIS",
  pages =        "76--83",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ARITH.2018.8464784",
  bibdate =      "Fri Jan 31 08:05:31 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "When dealing with floating-point numbers, there are
                 several sources of error which can drastically reduce
                 the numerical quality of computed results. One of those
                 error sources is the loss of significance or
                 cancellation, which occurs during for example, the
                 subtraction of two nearly equal numbers. In this
                 article, we propose a representation format named
                 Floating-Point Adaptive Noise Reduction (FP-ANR). This
                 format embeds cancellation information directly into
                 the floating-point representation format thanks to a
                 dedicated pattern. With this format, insignificant
                 trailing bits lost during cancellation are removed from
                 every manipulated floating-point number. The immediate
                 consequence is that it increases the numerical
                 confidence of computed values. The proposed
                 representation format corresponds to a simple and
                 efficient implementation of significance arithmetic
                 based and compatible with the IEEE Standard 754
                 standard.",
  acknowledgement = ack-nhfb,
  keywords =     "adaptive signal processing; ARITH 2018; ARITH-25;
                 cancellation information; Computers; Encoding; floating
                 point arithmetic; Floating-Point Adaptive Noise
                 Reduction; floating-point cancellation; floating-point
                 numbers; floating-point representation format; FP-ANR;
                 IEEE Standard 754 standard; IEEE standards; IEEE
                 Standards; interference suppression; Noise reduction;
                 numerical quality; signal denoising; Software;
                 Uncertainty",
}

@Article{Demmel:2018:RBM,
  author =       "James Demmel and Jason Riedy and Peter Ahrens",
  title =        "{Reproducible BLAS}: Make Addition Associative
                 Again!",
  journal =      j-SIAM-NEWS,
  volume =       "51",
  number =       "8",
  pages =        "??--??",
  month =        oct,
  year =         "2018",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibdate =      "Sat Oct 06 08:42:06 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://sinews.siam.org/Details-Page/reproducible-blas-make-addition-associative-again",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
}

@Article{Dolbeau:2018:TPF,
  author =       "Romain Dolbeau",
  title =        "Theoretical peak {FLOPS} per instruction set: a
                 tutorial",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "74",
  number =       "3",
  pages =        "1341--1377",
  month =        mar,
  year =         "2018",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1007/s11227-017-2177-5",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Fri Mar 2 12:22:02 MST 2018",
  bibsource =    "http://link.springer.com/journal/11227/74/3;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsuper2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsuper2020.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
}

@Article{Doliskani:2018:SCR,
  author =       "Javad Doliskani and Pascal Giorgi and Romain Lebreton
                 and Eric Schost",
  title =        "Simultaneous Conversions with the Residue Number
                 System Using Linear Algebra",
  journal =      j-TOMS,
  volume =       "44",
  number =       "3",
  pages =        "27:1--27:21",
  month =        apr,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3145573",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Jan 22 17:49:32 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3145573",
  abstract =     "We present an algorithm for simultaneous conversions
                 between a given set of integers and their Residue
                 Number System representations based on linear algebra.
                 We provide a highly optimized implementation of the
                 algorithm that exploits the computational features of
                 modern processors. The main application of our
                 algorithm is matrix multiplication over integers. Our
                 speed-up of the conversions to and from the Residue
                 Number System significantly improves the overall
                 running time of matrix multiplication.",
  acknowledgement = ack-nhfb,
  articleno =    "27",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Dosso:2018:EAC,
  author =       "Yssouf Dosso and Fabien Herbaut and Nicolas M{\'e}loni
                 and Pascal V{\'e}ron",
  title =        "{Euclidean} addition chains scalar multiplication on
                 curves with efficient endomorphism",
  journal =      j-J-CRYPTO-ENG,
  volume =       "8",
  number =       "4",
  pages =        "351--367",
  month =        nov,
  year =         "2018",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s13389-018-0190-0",
  ISSN =         "2190-8508 (print), 2190-8516 (electronic)",
  ISSN-L =       "2190-8508",
  bibdate =      "Wed Oct 2 11:24:50 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcryptoeng.bib",
  URL =          "http://link.springer.com/article/10.1007/s13389-018-0190-0",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Cryptographic Engineering",
  journal-URL =  "http://link.springer.com/journal/13389",
}

@InProceedings{Drucker:2018:CRS,
  author =       "Nir Drucker and Shay Gueron and Vlad Krasnov",
  title =        "The Comeback of {Reed--Solomon} Codes",
  crossref =     "Tenca:2018:PIS",
  pages =        "125--129",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ARITH.2018.8464690",
  bibdate =      "Fri Jan 31 08:05:31 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Distributed storage systems utilize erasure codes to
                 reduce their storage costs while efficiently handling
                 failures. Many of these codes (e.g., Reed-Solomon (RS)
                 codes) rely on Galois Field (GF) arithmetic, which is
                 considered to be fast when the field characteristic is
                 2. Nevertheless, some developments in the field of
                 erasure codes offer new efficient techniques that
                 require mostly XOR operations, and are thus faster than
                 GF operations. Recently, Intel announced [1] that its
                 future architecture (codename Ice Lake) will introduce
                 new set of instructions called Galois Field New
                 Instruction (GF-NI). These instructions allow software
                 flows to perform vector and matrix multiplications over
                 GF ($ 2^8$) on the wide registers that are available on
                 the AVX512 architectures. In this paper, we explain the
                 functionality of these instructions, and demonstrate
                 their usage for some fast computations in GF($ 2^8$).
                 We also use the Intel Intelligent Storage Acceleration
                 Library (ISA-L) in order to estimate potential future
                 improvement for erasure codes that are based on RS
                 codes. Our results predict $ 1.4 \times $ speedup for
                 vectorized multiplication, and $ 1.83 \times $ speedup
                 for the actual encoding.",
  acknowledgement = ack-nhfb,
  keywords =     "Acceleration; ARITH 2018; ARITH-25; AVX512
                 architectures; codename Ice Lake; Computer
                 architecture; distributed storage systems; Encoding;
                 erasure codes; field characteristic; Galois Field
                 arithmetic; Galois fields; GF operations; GF-NI; Intel;
                 Intelligent Storage Acceleration Library; matrix
                 multiplication; matrix multiplications; Reed-Solomon
                 codes; Registers; RS codes; storage costs; vector;
                 vectors; Web services; XOR operations",
}

@InProceedings{Drucker:2018:FMB,
  author =       "Nir Drucker and Shay Gueron and Vlad Krasnov",
  title =        "Fast multiplication of binary polynomials with the
                 forthcoming vectorized {VPCLMULQDQ} instruction",
  crossref =     "Tenca:2018:PIS",
  pages =        "115--119",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ARITH.2018.8464777",
  bibdate =      "Fri Jan 31 08:05:31 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Polynomial multiplication over binary fields $ \mathbb
                 {F}_{2^n} $ is a common primitive, used for example by
                 current cryptosystems such as AES-GCM (with $ n =
                 128$). It also turns out to be a primitive for other
                 cryptosystems, that are being designed for the Post
                 Quantum era, with values n 128. Examples from the
                 recent submissions to the NIST Post-Quantum
                 Cryptography project, are BIKE, LEDAKem, and GeMSS,
                 where the performance of the polynomial
                 multiplications, is significant. Therefore, efficient
                 polynomial multiplication over $ \mathbb {F}_{2^n}$,
                 with large $n$, is a significant emerging optimization
                 target. Anticipating future applications, Intel has
                 recently announced that its future architecture
                 (codename Ice Lake) will introduce a new vectorized way
                 to use the current VPCLMULQDQ instruction. In this
                 paper, we demonstrate how to use this instruction for
                 accelerating polynomial multiplication. Our analysis
                 shows a prediction for at least $ 2 \times $ speedup
                 for multiplications with polynomials of degree 512 or
                 more.",
  acknowledgement = ack-nhfb,
  keywords =     "Acceleration; AES-GCM; ARITH 2018; ARITH-25; BIKE;
                 binary field-mathbbF2n; Computer architecture;
                 Cryptography; cryptosystems; fast binary polynomial
                 multiplication; fast multiplication; GeMSS; ice lake;
                 LEDAKem; NIST; NIST Post-Quantum Cryptography project;
                 optimisation; Optimization; optimization target;
                 polynomials; post quantum cryptography; quantum
                 cryptography; Registers; vectorized VPCLMULQDQ
                 instruction; Web services",
}

@Article{Dutt:2018:ADA,
  author =       "Sunil Dutt and Sukumar Nandi and Gaurav Trivedi",
  title =        "Analysis and Design of Adders for Approximate
                 Computing",
  journal =      j-TECS,
  volume =       "17",
  number =       "2",
  pages =        "40:1--40:??",
  month =        apr,
  year =         "2018",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3131274",
  ISSN =         "1539-9087 (print), 1558-3465 (electronic)",
  ISSN-L =       "1539-9087",
  bibdate =      "Thu Oct 17 18:16:34 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tecs.bib",
  abstract =     "The concept of approximate computing, that is, to
                 sacrifice computation quality for computation efforts,
                 has recently emerged as a promising design approach.
                 Over the past decade, several research works have
                 explored approximate computing at both the software
                 level and hardware level of abstraction with
                 encouraging results. At the hardware level of
                 abstraction, adders (being the fundamental and most
                 widely used data operators in digital systems) have
                 attracted a significant attention for approximation. In
                 this article, we first explain briefly the
                 need/significance of approximate adders. We then
                 propose four Approximate Full Adders (AFAs) for
                 high-performance energy-efficient approximate
                 computing. The key design objective behind the proposed
                 AFAs is to curtail the length of carry propagation
                 subjected to minimal error rate. Next, we exploit one
                 of the proposed AFAs (optimal one) to construct an
                 N-bit approximate adder that hereinafter is referred as
                 ``ApproxADD.'' An emergent property of ApproxADD is
                 that carries do not propagate in it, and, consequently,
                 it provides bit-width-aware constant delay (O(1)).
                 ApproxADD also provides improvement in dynamic power
                 consumption by 46.31\% and in area by 28.57\% w.r.t.
                 Ripple Carry Adder (RCA), which exhibits the lowest
                 power and area. Although ApproxADD provides a
                 significant improvement in delay, power, and area, it
                 may not be preferred for some of the error-resilient
                 applications because its: (i) Error Distance (ED) is
                 too high; and (ii) Error Rate (ER) increases rapidly
                 with bit-width ($N$). To improve ED and ER, we exploit
                 the concept of carry-lifetime and Error Detection and
                 Correction logic, respectively. In this way, we
                 introduce two more (improved) versions of
                 ApproxADD--ApproxADD $ \upsilon $ 1 and ApproxADD. We
                 call these as ApproxADD $ \upsilon $ 1 and ApproxADD $
                 \upsilon $ 2 with existing approximate adders based on
                 conventional design metrics and approximate computing
                 design metrics. Furthermore, to inspect effectiveness
                 of the proposed approach in real-life applications, we
                 demonstrate image compression and decompression by
                 replacing the conventional addition operations in
                 Discrete Cosine Transform (DCT) and Inverse Discrete
                 Cosine Transform (IDCT) modules with ApproxADD $
                 \upsilon $ 2.",
  acknowledgement = ack-nhfb,
  articleno =    "40",
  fjournal =     "ACM Transactions on Embedded Computing Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J840",
}

@InProceedings{Emmart:2018:FME,
  author =       "Niall Emmart and Fangyu Zhengt and Charles Weems",
  title =        "Faster Modular Exponentiation Using Double Precision
                 Floating Point Arithmetic on the {GPU}",
  crossref =     "Tenca:2018:PIS",
  pages =        "130--137",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ARITH.2018.8464792",
  bibdate =      "Fri Jan 31 08:05:31 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper presents a new approach to integer multiple
                 precision (MP) modular exponentiation, using
                 double-precision floating point (DPF) operations, that
                 is suitable for GPU implementation. We show speedups
                 ranging from 20\% to 34\% over the best prior GPU times
                 for sizes corresponding to common RSA cryptographic
                 operations (2048 to 4096 bits). Three techniques are
                 described. First, by adding $ 2^{104} $ to the high
                 half of the product, and $ 2^{52} $ to the low half, we
                 set the implicit leading 1 in the DPF mantissa so that
                 the full 52 explicit bits are available for each half
                 of the 104-bit products of samples. Second, the DPF
                 values are cast bitwise to 64-bit integers for adding
                 the column sums to get the MP result. Normally the cast
                 would require masking off the exponents, but because
                 they are constant, we can include them in the column
                 sums and correct just once for their total. Third, by
                 initializing the column sums with the appropriate
                 negative value to compensate for the exponent sums, no
                 corrective subtraction is needed. Our implementation on
                 an NVIDIA GTX Titan Black GPU achieves between 132.5K
                 and 161.9K modular exponentiations per second of size
                 1024 bits, with latencies ranging from 21.7 ms to 17.8
                 ms, making it practical for online RSA applications.
                 Proportional results are shown for 1536 and 2048 bits.
                 The implementation is so efficient that its maximum
                 sustained performance is actually bounded by the
                 thermal limit of the GPU.",
  acknowledgement = ack-nhfb,
  keywords =     "appropriate negative value; ARITH 2018; ARITH-25;
                 column sums; common RSA cryptographic operations;
                 Computer architecture; cryptography; Cryptography;
                 double precision floating point arithmetic; DPF
                 mantissa; exponent sum compensation; faster modular
                 exponentiation; floating point arithmetic;
                 Floating-point arithmetic; Graphics processing units;
                 graphics processing units; Hardware; integer multiple
                 precision modular exponentiation; multiple precision
                 modular exponentiation; NVIDIA GTX Titan Black GPU;
                 online RSA applications; parallel architectures; time
                 17.8 ms to 21.7 ms; word length 1024.0 bit; word length
                 104 bit; word length 1536.0 bit; word length 2048 bit
                 to 4096 bit; word length 64 bit",
}

@InProceedings{Emmart:2018:NVB,
  author =       "Niall Emmart and Fangyu Zheng and Charles Weems",
  title =        "A New Variant of the {Barrett} Algorithm Applied to
                 Quotient Selection",
  crossref =     "Tenca:2018:PIS",
  pages =        "138--144",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ARITH.2018.8464771",
  bibdate =      "Fri Jan 31 08:05:31 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Quotient Selection (QS) is a key step in the classic $
                 O(n^2) $ multiple precision division algorithm. On
                 processors with fast hardware division, it is a trivial
                 problem, but on GPUs, division is quite slow. In this
                 paper we investigate the effectiveness of Brent and
                 Zimmermann's variant as well as our own novel variant
                 of Barrett's algorithm. Our new approach is shown to be
                 suitable for low radix (single precision) QS. Three
                 highly optimized implementations, two of the Brent and
                 Zimmerman variant and one based on our new approach,
                 have been developed and we show that each is many times
                 faster than using the division operation built in to
                 the compiler. In addition, our variant is on average
                 22\% faster than the other two implementations. We also
                 sketch proofs of correctness for all of the
                 implementations and our new algorithm.",
  acknowledgement = ack-nhfb,
  keywords =     "Approximation algorithms; ARITH 2018; ARITH-25;
                 Barrett algorithm; Barrett reduction; classic $O(n^2)$
                 multiple precision division algorithm; Computer
                 security; digital arithmetic; Digital arithmetic;
                 division operation; fast hardware division; GPU;
                 graphics processing units; Hardware; low radix QS;
                 multiple precision division; Newton method; O;
                 processors; Program processors; quotient selection;
                 Zimmermann variant",
}

@Article{Ferguson:2018:DSM,
  author =       "Warren E. Ferguson and Jesse Bingham and Levent
                 Erk{\"o}k and John R. Harrison and Joe Leslie-Hurd",
  title =        "Digit Serial Methods with Applications to Division and
                 Square Root",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "67",
  number =       "3",
  pages =        "449--456",
  month =        mar,
  year =         "2018",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2017.2759764",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Feb 15 05:53:34 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/document/8060979/",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Garland:2018:LCM,
  author =       "James Garland and David Gregg",
  title =        "Low Complexity Multiply-Accumulate Units for
                 Convolutional Neural Networks with Weight-Sharing",
  journal =      j-TACO,
  volume =       "15",
  number =       "3",
  pages =        "31:1--31:??",
  month =        oct,
  year =         "2018",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3233300",
  ISSN =         "1544-3566 (print), 1544-3973 (electronic)",
  ISSN-L =       "1544-3566",
  bibdate =      "Tue Jan 8 17:19:59 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/taco.bib",
  abstract =     "Convolutional neural networks (CNNs) are one of the
                 most successful machine-learning techniques for image,
                 voice, and video processing. CNNs require large amounts
                 of processing capacity and memory bandwidth. Hardware
                 accelerators have been proposed for CNNs that typically
                 contain large numbers of multiply-accumulate (MAC)
                 units, the multipliers of which are large in integrated
                 circuit (IC) gate count and power consumption.
                 ``Weight-sharing'' accelerators have been proposed
                 where the full range of weight values in a trained CNN
                 are compressed and put into bins, and the bin index is
                 used to access the weight-shared value. We reduce power
                 and area of the CNN by implementing parallel accumulate
                 shared MAC (PASM) in a weight-shared CNN. PASM
                 re-architects the MAC to instead count the frequency of
                 each weight and place it in a bin. The accumulated
                 value is computed in a subsequent multiply phase,
                 significantly reducing gate count and power consumption
                 of the CNN. In this article, we implement PASM in a
                 weight-shared CNN convolution hardware accelerator and
                 analyze its effectiveness. Experiments show that for a
                 clock speed 1GHz implemented on a 45nm ASIC process our
                 approach results in fewer gates, smaller logic, and
                 reduced power with only a slight increase in latency.
                 We also show that the same weight-shared-with-PASM CNN
                 accelerator can be implemented in resource-constrained
                 FPGAs, where the FPGA has limited numbers of digital
                 signal processor (DSP) units to accelerate the MAC
                 operations.",
  acknowledgement = ack-nhfb,
  articleno =    "31",
  fjournal =     "ACM Transactions on Architecture and Code Optimization
                 (TACO)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J924",
}

@InProceedings{Glaser:2018:MMU,
  author =       "Florian Glaser and Stefan Mach and Abbas Rahimi and
                 Frank K. G{\"u}rkaynak and Qiuting Huang and Luca
                 Benini",
  booktitle =    "{2018 IEEE International Symposium on Circuits and
                 Systems (ISCAS)}",
  title =        "An {826 MOPS}, {210uW\slash MHz} Unum {ALU} in 65nm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--5",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ISCAS.2018.8351546",
  bibdate =      "Fri Dec 15 07:38:18 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Graillat:2018:NVC,
  author =       "Stef Graillat and Fabienne J{\'e}z{\'e}quel and Romain
                 Picot",
  title =        "Numerical validation of compensated algorithms with
                 stochastic arithmetic",
  journal =      j-APPL-MATH-COMP,
  volume =       "329",
  number =       "??",
  pages =        "339--363",
  day =          "15",
  month =        jul,
  year =         "2018",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2018.02.004",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Sat Mar 17 16:59:00 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300318300985",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  keywords =     "accurate floating-point dot product; accurate
                 floating-point summation; CADNA; compensated
                 algorithms; discrete stochastic arithmetic; error-free
                 transformations; floating-point arithmetic; numerical
                 validation; rounding errors",
}

@InCollection{Haidar:2018:DFE,
  author =       "Azzam Haidar and Ahmad Abdelfattah and Mawussi Zounon
                 and Panruo Wu and Srikara Pranesh and Stanimire Tomov
                 and Jack Dongarra",
  booktitle =    "Computational science---{ICCS 2018}. {Part I}",
  title =        "The design of fast and energy-efficient linear
                 solvers: on the potential of half-precision arithmetic
                 and iterative refinement techniques",
  volume =       "10860",
  publisher =    "Springer",
  address =      "Cham, Switzerland",
  pages =        "586--600",
  year =         "2018",
  MRclass =      "65Fxx (65Y10)",
  MRnumber =     "3815810",
  bibdate =      "Tue Jan 8 09:18:00 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Dongarra, Jack/0000-0003-3247-1782",
}

@InProceedings{Haidar:2018:HGT,
  author =       "Azzam Haidar and Stanimire Tomov and Jack Dongarra and
                 Nicholas J. Higham",
  editor =       "{IEEE}",
  booktitle =    "{SC '18 Proceedings of the International Conference
                 for High Performance Computing, Networking, Storage,
                 and Analysis, Dallas, Texas, November 11--16, 2018}",
  title =        "Harnessing {GPU} {Tensor Cores} for Fast {FP16}
                 Arithmetic to Speed up Mixed-Precision Iterative
                 Refinement Solvers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "603--613",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/SC.2018.00050",
  ISBN =         "1-5386-8384-9",
  ISBN-13 =      "978-1-5386-8384-2",
  LCCN =         "????",
  bibdate =      "Sat Jan 19 18:51:19 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3291656.3291719",
  abstract =     "Low-precision floating-point arithmetic is a powerful
                 tool for accelerating scientific computing
                 applications, especially those in artificial
                 intelligence. Here, we present an investigation showing
                 that other high-performance computing (HPC)
                 applications can also harness this power. Specifically,
                 we use the general HPC problem, Ax = b, where A is a
                 large dense matrix, and a double precision (FP64)
                 solution is needed for accuracy. Our approach is based
                 on mixed-precision (FP16 $ \to $ FP64) iterative
                 refinement, and we generalize and extend prior advances
                 into a framework, for which we develop
                 architecture-specific algorithms and highly tuned
                 implementations. These new methods show how using
                 half-precision Tensor Cores (FP16-TC) for the
                 arithmetic can provide up to 4X speedup. This is due to
                 the performance boost that the FP16-TC provide as well
                 as to the improved accuracy over the classical FP16
                 arithmetic that is obtained because the GEMM
                 accumulation occurs in FP32 arithmetic.",
  acknowledgement = ack-nhfb,
  keywords =     "Acceleration; FP16 Arithmetic; GPU Computing; Graphics
                 processing units; Half Precision; Iterative algorithms;
                 Iterative Refinement Computation; Linear Algebra;
                 Matrices; Mixed Precision Solvers",
  xxpages =      "47:1--47:11",
}

@Article{Hanson:2018:RAM,
  author =       "Richard J. Hanson and Tim Hopkins",
  title =        "Remark on {Algorithm 539: A Modern Fortran Reference
                 Implementation for Carefully Computing the Euclidean
                 Norm}",
  journal =      j-TOMS,
  volume =       "44",
  number =       "3",
  pages =        "24:1--24:23",
  month =        apr,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3134441",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Jan 22 17:49:32 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3134441",
  abstract =     "We propose a set of new Fortran reference
                 implementations, based on an algorithm proposed by
                 Kahan, for the Level 1 BLAS routines *NRM2 that compute
                 the Euclidean norm of a real or complex input vector.
                 The principal advantage of these routines over the
                 current offerings is that, rather than losing accuracy
                 as the length of the vector increases, they generate
                 results that are accurate to almost machine precision
                 for vectors of length $ N < N_{\rm max} $ where $
                 N_{\rm max} $ depends upon the precision of the
                 floating point arithmetic being used. In addition, we
                 make use of intrinsic modules, introduced in the latest
                 Fortran standards, to detect occurrences of non-finite
                 numbers in the input data and return suitable values as
                 well as setting IEEE floating point status flags as
                 appropriate. A set of C interface routines is also
                 provided to allow simple, portable access to the new
                 routines. To improve execution speed, we advocate a
                 hybrid algorithm; a simple loop is used first and, only
                 if IEEE floating point exception flags signal, do we
                 fall back on Kahan's algorithm. Since most input
                 vectors are ``easy,'' i.e., they do not require the
                 sophistication of Kahan's algorithm, the simple loop
                 improves performance while the use of compensated
                 summation ensures high accuracy. We also report on a
                 comprehensive suite of test problems that has been
                 developed to test both our new implementation and
                 existing codes for both accuracy and the appropriate
                 settings of the IEEE arithmetic status flags.",
  acknowledgement = ack-nhfb,
  articleno =    "24",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  xxnote =       "See \cite{Lawson:1979:ABL}.",
}

@Article{Hasanikhah:2018:EIS,
  author =       "Narjes Hasanikhah and Siavash Amin-Nejad and Ghafar
                 Darvish and M. R. Moniri",
  title =        "Efficient implementation of space-time adaptive
                 processing for adaptive weights calculation based on
                 floating point {FPGAs}",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "74",
  number =       "7",
  pages =        "3193--3210",
  month =        jul,
  year =         "2018",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1007/s11227-018-2369-7",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Thu Oct 10 15:31:13 MDT 2019",
  bibsource =    "http://link.springer.com/journal/11227/74/7;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsuper.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
}

@Misc{Higham:2018:HPA,
  author =       "Nicholas J. Higham",
  title =        "Half Precision Arithmetic: fp16 Versus bfloat16",
  howpublished = "Web site.",
  day =          "3",
  month =        dec,
  year =         "2018",
  bibdate =      "Sat Jan 19 18:43:15 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://nickhigham.wordpress.com/2018/12/03/half-precision-arithmetic-fp16-versus-bfloat16/",
  abstract =     "The 2008 revision of the IEEE Standard for
                 Floating-Point Arithmetic introduced a half precision
                 16-bit floating point format, known as fp16, as a
                 storage format. Various manufacturers have adopted fp16
                 for computation, using the obvious extension of the
                 rules for the fp32 (single precision) and fp64 (double
                 precision) formats. For example, fp16 is supported by
                 the NVIDIA P100 and V100 GPUs and the AMD Radeon
                 Instinct MI25 GPU, as well as the A64FX Arm processor
                 that will power the Fujitsu Post-K exascale computer.",
  acknowledgement = ack-nhfb,
}

@Article{Higham:2018:UN,
  author =       "Nicholas J. Higham",
  title =        "The Unwinding Number",
  journal =      j-SIAM-NEWS,
  volume =       "51",
  number =       "8",
  pages =        "??--??",
  month =        oct,
  year =         "2018",
  ISSN =         "0036-1437",
  ISSN-L =       "0036-1437",
  bibdate =      "Sat Oct 06 08:46:15 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://sinews.siam.org/Details-Page/the-unwinding-number",
  abstract =     "While Fortran 66 had a complex data type, this was not
                 true of most other early programming languages, such as
                 Algol 60. As a result, programmers had to write their
                 own procedures to implement complex arithmetic and
                 transcendental functions in terms of separately stored
                 real and imaginary parts. They quickly realized that
                 this is not a trivial task; in the early 1960s, it took
                 five published attempts over three years to obtain a
                 correct implementation of the complex logarithm in
                 Algol 60.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM News",
  journal-URL =  "https://sinews.siam.org/",
}

@Article{Hines:2018:MPS,
  author =       "Jonathan Hines",
  title =        "Mixed Precision: A Strategy for New Science
                 Opportunities",
  journal =      j-COMPUT-SCI-ENG,
  volume =       "20",
  number =       "6",
  pages =        "67--71",
  month =        nov # "\slash " # dec,
  year =         "2018",
  CODEN =        "CSENFA",
  DOI =          "https://doi.org/10.1109/MCSE.2018.2874161",
  ISSN =         "1521-9615 (print), 1558-366X (electronic)",
  ISSN-L =       "1521-9615",
  bibdate =      "Wed Jan 30 17:58:50 MST 2019",
  bibsource =    "http://csdl.computer.org/comp/mags/cs/2018/06/c6toc.htm;
                 https://www.math.utah.edu/pub/tex/bib/computscieng.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.computer.org/csdl/mags/cs/2018/06/08625902-abs.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing in Science and Engineering",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5992",
}

@InProceedings{Hoang:2018:VDF,
  author =       "Trong-Thuc Hoang and Duc-Hung Le and Cong-Kha Pham",
  booktitle =    "{2018 IEEE 12th International Symposium on Embedded
                 Multicore/Many-core Systems-on-Chip (MCSoC)}",
  title =        "{VLSI} Design of Floating-Point Twiddle Factor Using
                 Adaptive {CORDIC} on Various Iteration Limitations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "225--232",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/MCSoC2018.2018.00044",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "CORDIC; Fast Fourier transforms; Field programmable
                 gate arrays; Floating point; Synthetic aperture radar;
                 Table lookup; Throughput; Timing; Twiddle Factor;
                 VLSI",
}

@Article{Hou:2018:EAD,
  author =       "Junjie Hou and Yongxin Zhu and Sen Du and Shijin
                 Song",
  title =        "Enhancing Accuracy and Dynamic Range of Scientific
                 Data Analytics by Implementing Posit Arithmetic on
                 {FPGA}",
  journal =      "Journal of Signal Processing Systems",
  volume =       "91",
  number =       "10",
  pages =        "1137--1148",
  month =        nov,
  year =         "2018",
  DOI =          "https://doi.org/10.1007/s11265-018-1420-5",
  ISSN =         "1939-8018 (print), 1939-8115 (electronic)",
  ISSN-L =       "1939-8115",
  bibdate =      "Fri Dec 15 11:31:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@Article{Hrycak:2018:ECP,
  author =       "Tomasz Hrycak and Sebastian Schmutzhard",
  title =        "Evaluation of {Chebyshev} polynomials by a three-term
                 recurrence in floating-point arithmetic",
  journal =      j-BIT-NUM-MATH,
  volume =       "58",
  number =       "2",
  pages =        "317--330",
  month =        jun,
  year =         "2018",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/s10543-017-0683-8",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Sep 26 07:36:57 MDT 2018",
  bibsource =    "http://link.springer.com/journal/10543/58/2;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://link.springer.com/article/10.1007/s10543-017-0683-8",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT Numerical Mathematics",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Hutter:2018:FMP,
  author =       "Michael Hutter and Erich Wenger",
  title =        "Fast Multi-precision Multiplication for Public-Key
                 Cryptography on Embedded Microprocessors",
  journal =      j-J-CRYPTOLOGY,
  volume =       "31",
  number =       "4",
  pages =        "1164--1182",
  month =        oct,
  year =         "2018",
  CODEN =        "JOCREQ",
  DOI =          "https://doi.org/10.1007/s00145-018-9298-8",
  ISSN =         "0933-2790 (print), 1432-1378 (electronic)",
  ISSN-L =       "0933-2790",
  bibdate =      "Wed Sep 26 09:58:08 MDT 2018",
  bibsource =    "http://link.springer.com/journal/145/31/4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcryptology.bib",
  URL =          "https://link.springer.com/article/10.1007/s00145-018-9298-8",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Cryptology",
  journal-URL =  "http://link.springer.com/journal/145",
}

@InProceedings{Ichimura:2018:FSI,
  author =       "Tsuyoshi Ichimura and Kohei Fujita and Takuma
                 Yamaguchi and Akira Naruse and Jack C. Wells and Thomas
                 C. Schulthess and Tjerk P. Straatsma and Christopher J.
                 Zimmer and Maxime Martinasso and Kengo Nakajima and
                 Muneo Hori and Lalith Maddegedara",
  booktitle =    "{SC18: International Conference for High Performance
                 Computing, Networking, Storage and Analysis}",
  title =        "A Fast Scalable Implicit Solver for Nonlinear
                 Time-Evolution Earthquake City Problem on Low-Ordered
                 Unstructured Finite Elements with Artificial
                 Intelligence and Transprecision Computing",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "627--637",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/SC.2018.00052",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Analytical models; Artificial intelligence;
                 Computational modeling; Earthquakes; Finite element
                 analysis; Mathematical model; Urban areas",
}

@TechReport{Intel:2018:BHN,
  author =       "{Intel Corporation}",
  title =        "{BFLOAT16} --- Hardware Numerics Definition",
  type =         "White paper",
  number =       "338302-001US",
  institution =  pub-INTEL,
  address =      pub-INTEL:adr,
  pages =        "7",
  month =        nov,
  year =         "2018",
  bibdate =      "Sat Jan 19 18:48:10 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://software.intel.com/en-us/download/bfloat16-hardware-numerics-definition",
  acknowledgement = ack-nhfb,
  remark =       "The BFLOAT16 (BF16) format has a 1-bit sign, 8-bit
                 exponent, and 7-bit stored significand, corresponding
                 to the top 16 bits of IEEE 754 Binary32. However,
                 Intel's implementation does not provide subnormal
                 numbers, or floating-point exceptions, and it only
                 supports the IEEE 754 round-to-nearest ties-to-even
                 rounding mode. Subnormal inputs are reduced to zero.",
}

@InProceedings{Jaiswal:2018:AGT,
  author =       "Manish Kumar Jaiswal and Hayden K.-H So",
  editor =       "{IEEE}",
  booktitle =    "{2018 IEEE International Symposium on Circuits and
                 Systems (ISCAS)}",
  title =        "Architecture Generator for {Type-3} Unum Posit
                 Adder\slash Subtractor",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--5",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ISCAS.2018.8351142",
  bibdate =      "Fri Dec 15 07:38:18 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Jaiswal:2018:UNP,
  author =       "Manish Kumar Jaiswal and Hayden K.-H So",
  editor =       "{IEEE}",
  booktitle =    "{2018 Design, Automation \& Test in Europe Conference
                 \& Exhibition (DATE)}",
  title =        "Universal number posit arithmetic generator on
                 {FPGA}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1159--1162",
  year =         "2018",
  DOI =          "https://doi.org/10.23919/DATE.2018.8342187",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Jeangoudoux:2018:CRM,
  author =       "Clothilde Jeangoudoux and Christoph Lauter",
  title =        "A Correctly Rounded Mixed-Radix Fused-Multiply-Add",
  crossref =     "Tenca:2018:PIS",
  pages =        "21--28",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ARITH.2018.8464818",
  bibdate =      "Fri Jan 31 08:05:31 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The IEEE 754-2008 Standard governs Floating-Point
                 Arithmetic in all types of Computer Systems. The
                 Standard provides for two radices, 2 and 10. It
                 specifies conversion operations between these radices,
                 but does not allow floating-point formats of different
                 radices to be mixed in computational operations. In
                 contrast, the Standard does provide for mixing formats
                 of one radix in one operation. In order to enhance the
                 Standard and make it closed under all basic
                 computational operations, we propose an algorithm for a
                 correctly rounded mixed-radix Fused-Multiply-and-Add
                 (FMA). Our algorithm takes any combination of IEEE754
                 binary64 and decimal64 numbers in argument and provides
                 a result in IEEE754 binary64 and decimal64, rounded
                 according to any for the five IEEE754 rounding modes.
                 Our implementation does not require any dynamic memory
                 allocation; its runtime can be bounded statically. We
                 compare our implementation to a basic mixed-radix FMA
                 implementation based on the GMP Multiple Precision
                 library.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2018; ARITH-25; basic computational operations;
                 computer systems; conversion operations; correctly
                 rounded mixed-radix Fused; decimal64 numbers;
                 Electronic mail; floating point arithmetic;
                 floating-point arithmetic; Floating-point arithmetic;
                 floating-point formats; Heuristic algorithms; IEEE
                 754-2008 Standard; IEEE standards; IEEE754 rounding
                 modes; Libraries; mixed-radix FMA implementation;
                 Software; Standards; Systematics",
}

@Article{Jeannerod:2018:REF,
  author =       "Claude-Pierre Jeannerod and Siegfried M. Rump",
  title =        "On relative errors of floating-point operations:
                 {Optimal} bounds and applications",
  journal =      j-MATH-COMPUT,
  volume =       "87",
  number =       "310",
  pages =        "803--819",
  month =        "",
  year =         "2018",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Sat Jan 13 15:49:09 MST 2018",
  bibsource =    "http://www.ams.org/mcom/2018-87-310;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  URL =          "http://www.ams.org/journals/mcom/2018-87-310/S0025-5718-2017-03234-8;
                 http://www.ams.org/journals/mcom/2018-87-310/S0025-5718-2017-03234-8/S0025-5718-2017-03234-8.pdf;
                 https://www.ams.org/mathscinet/search/authors.html?authorName=Rump%2C%20Siegfried%20M.;
                 https://www.ams.org/mathscinet/search/authors.html?mrauthid=644190",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@InProceedings{Jeannerod:2018:VWS,
  author =       "Claude-Pierre Jeannerod and Jean-Michel Muller and
                 Paul Zimmermann",
  title =        "On Various Ways to Split a Floating-Point Number",
  crossref =     "Tenca:2018:PIS",
  pages =        "53--60",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ARITH.2018.8464793",
  bibdate =      "Fri Jan 31 08:05:31 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We review several ways to split a floating-point
                 number, that is, to decompose it into the exact sum of
                 two floating-point numbers of smaller precision. All
                 the methods considered here involve only a few IEEE
                 floating-point operations, with rounding to nearest and
                 including possibly the fused multiply-add (FMA).
                 Applications range from the implementation of integer
                 functions such as round and floor to the computation of
                 suitable scaling factors aimed, for example, at
                 avoiding spurious underflows and overflows when
                 implementing functions such as the hypotenuse.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2018; ARITH-25; Computer architecture;
                 Containers; Digital arithmetic; floating point
                 arithmetic; floating-point number; Floors; IEEE
                 floating-point operations; integer functions; Lips;
                 Matlab; Optimization",
}

@Article{Jeon:2018:HMP,
  author =       "Dong-Ik Jeon and Kyeong-Bin Park and Ki-Seok Chung",
  title =        "{HMC-MAC}: Processing-in Memory Architecture for
                 Multiply--Accumulate Operations with Hybrid Memory
                 Cube",
  journal =      j-IEEE-COMPUT-ARCHIT-LETT,
  volume =       "17",
  number =       "1",
  pages =        "5--8",
  month =        jan # "\slash " # jun,
  year =         "2018",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/LCA.2017.2700298",
  ISSN =         "1556-6056 (print), 1556-6064 (electronic)",
  ISSN-L =       "1556-6056",
  bibdate =      "Tue Jun 25 07:41:05 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeecomputarchitlett.bib",
  abstract =     "Many studies focus on implementing processing-in
                 memory (PIM) on the logic die of the hybrid memory cube
                 (HMC) architecture. The multiply-accumulate (MAC)
                 operation is heavily used in digital signal processing
                 (DSP) systems. In this paper, a novel PIM architecture
                 called HMC-MAC that implements the MAC operation in the
                 HMC is proposed. The vault controllers of the
                 conventional HMC are working independently to maximize
                 the parallelism, and HMC-MAC is based on the
                 conventional HMC without modifying the architecture
                 much. Therefore, a large number of MAC operations can
                 be processed in parallel. In HMC-MAC, the MAC operation
                 can be carried out simultaneously with as much as 128
                 KB data. The correctness on HMC-MAC is verified by
                 simulations, and its performance is better than the
                 conventional CPU-based MAC operation when the MAC
                 operation is consecutively executed at least six
                 times",
  acknowledgement = ack-nhfb,
  affiliation =  "Chung, KS (Reprint Author), Hanyang Univ, Dept Elect
                 \& Comp Engn, Seoul 04763, South Korea. Jeon, Dong-Ik;
                 Park, Kyeong-Bin; Chung, Ki-Seok, Hanyang Univ, Dept
                 Elect \& Comp Engn, Seoul 04763, South Korea.",
  author-email = "estwingz@naver.com lay1523@naver.com
                 kchung@hanyang.ac.kr",
  da =           "2019-06-20",
  doc-delivery-number = "FZ6EO",
  eissn =        "1556-6064",
  fjournal =     "IEEE Computer Architecture Letters",
  funding-acknowledgement = "Basic Science Research Program through the
                 National Research Foundation of Korea(NRF) --- Ministry
                 of Education [NRF-2015R1D1A1A09061079]",
  funding-text = "This research was supported by Basic Science Research
                 Program through the National Research Foundation of
                 Korea(NRF) funded by the Ministry of Education
                 (NRF-2015R1D1A1A09061079).",
  journal-iso =  "IEEE Comput. Archit. Lett.",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=10208",
  keywords =     "Computers; CPU-based MAC operation; digital signal
                 processing; digital signal processing systems; DRAM
                 chips; DSP systems; Electronic mail; HMC-MAC; hybrid
                 memory cube architecture; logic circuits; logic die;
                 memory architecture; Memory architecture; Memory
                 management; memory size 128.0 KByte; Memory structures;
                 memory used as logic; multiple data stream
                 architectures; multiply-accumulate operation; parallel
                 processing; processing-in memory architecture; Random
                 access memory; Registers; vault controllers",
  number-of-cited-references = "11",
  ORCID-numbers = "Jeon, Dong-Ik/0000-0002-8572-4184",
  research-areas = "Computer Science",
  times-cited =  "0",
  unique-id =    "Jeon:2018:HMP",
  web-of-science-categories = "Computer Science, Hardware \&
                 Architecture",
}

@Article{Jiang:2018:EFD,
  author =       "Xiaoyu Jiang and Kicheon Hong",
  title =        "Explicit form of determinants and inverse matrices of
                 {Tribonacci} $r$-circulant type matrices",
  journal =      j-J-MATH-CHEM,
  volume =       "56",
  number =       "4",
  pages =        "1234--1249",
  month =        apr,
  year =         "2018",
  CODEN =        "JMCHEG",
  DOI =          "https://doi.org/10.1007/s10910-017-0843-8",
  ISSN =         "0259-9791 (print), 1572-8897 (electronic)",
  ISSN-L =       "0259-9791",
  bibdate =      "Tue Mar 6 07:08:26 MST 2018",
  bibsource =    "http://link.springer.com/journal/10910/56/4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathchem.bib",
  URL =          "https://link.springer.com/article/10.1007/s10910-017-0843-8",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Chemistry",
  journal-URL =  "http://link.springer.com/journal/10910",
  journalabr =   "J. Math. Chem.",
}

@Article{Johnson:2018:RFP,
  author =       "Jeff Johnson",
  title =        "Rethinking floating point for deep learning",
  journal =      "arXiv.org",
  pages =        "8",
  day =          "1",
  month =        nov,
  year =         "2018",
  bibdate =      "Mon Feb 10 09:27:01 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/abs/1811.01721",
  abstract =     "Reducing hardware overhead of neural networks for
                 faster or lower power inference and training is an
                 active area of research. Uniform quantization using
                 integer multiply-add has been thoroughly investigated,
                 which requires learning many quantization parameters,
                 fine-tuning training or other prerequisites. Little
                 effort is made to improve floating point relative to
                 this baseline; it remains energy inefficient, and word
                 size reduction yields drastic loss in needed dynamic
                 range. We improve floating point to be more energy
                 efficient than equivalent bit width integer hardware on
                 a 28 nm ASIC process while retaining accuracy in 8 bits
                 with a novel hybrid log multiply\slash linear add,
                 Kulisch accumulation and tapered encodings from
                 Gustafson's posit format. With no network retraining,
                 and drop-in replacement of all math and float32
                 parameters via round-to-nearest-even only, this
                 open-sourced 8-bit log float is within 0.9\% top-1 and
                 0.2\% top-5 accuracy of the original float32 ResNet-50
                 CNN model on ImageNet. Unlike int8 quantization, it is
                 still a general purpose floating point arithmetic,
                 interpretable out-of-the-box. Our 8/38-bit log float
                 multiply-add is synthesized and power profiled at 28 nm
                 at $ 0.96 \times $ the power and $ 1.12 \times $ the
                 area of 8/32-bit integer multiply-add. In 16 bits, our
                 log float multiply-add is $ 0.59 \times $ the power and
                 $ 0.68 \times $ the area of IEEE 754 float16 fused
                 multiply-add, maintaining the same significand
                 precision and dynamic range, proving useful for
                 training ASICs as well.",
  acknowledgement = ack-nhfb,
  primaryclass = "cs.NA",
}

@InProceedings{Kohlbecker:2018:SNF,
  author =       "Ignaz Kohlbecker",
  title =        "The Slide Number Format",
  crossref =     "ACM:2018:CNG",
  pages =        "1--6",
  year =         "2018",
  DOI =          "https://doi.org/10.1145/3190339.3190342",
  bibdate =      "Mon Dec 11 09:01:38 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Slide number format divides the real number line
                 into connected sets. Compared to the unum format [3],
                 there is no ubit, no infinity, and values are placed on
                 a logarithmic scale with base 10. Formal definitions
                 for Slides and intervals composed of Slide pairs are
                 provided. The relative error is compared with that of
                 single precision floats. The performance of conversions
                 to and from human readable form is measured.",
  acknowledgement = ack-nhfb,
  articleno =    "3",
  keywords =     "posit arithmetic; slide number format; universal
                 number (unum) arithmetic",
}

@Article{Kromer:2018:AQO,
  author =       "Pavel Kr{\"o}mer and Jan Plato{\v{s}} and Jana
                 Nowakov{\'a} and V{\'a}clav Sn{\'a}{\v{s}}el",
  title =        "An acceleration of quasigroup operations by residue
                 arithmetic",
  journal =      j-CCPE,
  volume =       "30",
  number =       "2",
  pages =        "??--??",
  day =          "25",
  month =        jan,
  year =         "2018",
  CODEN =        "CCPEBO",
  DOI =          "https://doi.org/10.1002/cpe.4239",
  ISSN =         "1532-0626 (print), 1532-0634 (electronic)",
  ISSN-L =       "1532-0626",
  bibdate =      "Sat Dec 30 09:12:00 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/ccpe.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Concurrency and Computation: Practice and Experience",
  journal-URL =  "http://www.interscience.wiley.com/jpages/1532-0626",
}

@InBook{Kumari:2018:RLS,
  author =       "Aishwarya Kumari and D. P. Acharya",
  booktitle =    "Recent Findings in Intelligent Computing Techniques",
  title =        "Reduced Latency Square-Root Calculation for Signal
                 Processing Using Radix-4 Hyperbolic {CORDIC}",
  publisher =    "Springer Singapore",
  pages =        "219--225",
  year =         "2018",
  DOI =          "https://doi.org/10.1007/978-981-10-8636-6_23",
  ISBN =         "981-10-8636-2",
  ISBN-13 =      "978-981-10-8636-6",
  ISSN =         "2194-5365",
  bibdate =      "Tue Oct 28 07:04:09 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kumm:2018:KRM,
  author =       "Martin Kumm and Oscar Gustafsson and Florent de
                 Dinechin and Johannes Kappauf and Peter Zipf",
  title =        "{Karatsuba} with Rectangular Multipliers for {FPGAs}",
  crossref =     "Tenca:2018:PIS",
  pages =        "13--20",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ARITH.2018.8464809",
  bibdate =      "Fri Jan 31 08:05:31 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This work presents an extension of Karatsuba's method
                 to efficiently use rectangular multipliers as a base
                 for larger multipliers. The rectangular multipliers
                 that motivate this work are the embedded $ 18 \times
                 25$-bit signed multipliers found in the DSP blocks of
                 recent Xilinx FPGAs: The traditional Karatsuba approach
                 must under-use them as square $ 18 \times 18 $ ones.
                 This work shows that rectangular multipliers can be
                 efficiently exploited in a modified Karatsuba method if
                 their input word sizes have a large greatest common
                 divider. In the Xilinx FPG A case, this can be obtained
                 by using the embedded multipliers as $ 16 \times 24 $
                 unsigned and as $ 17 \times 25$ signed ones. The
                 obtained architectures are implemented with due detail
                 to architectural features such as the pre-adders and
                 post-adders available in Xilinx DSP blocks. They are
                 synthesized and compared with traditional Karatsuba,
                 but also with (non-Karatsuba) state-of-the-art tiling
                 techniques that make use of the full rectangular
                 multipliers. The proposed technique improves resource
                 consumption and performance for multipliers of numbers
                 larger than 64 bits.",
  acknowledgement = ack-nhfb,
  keywords =     "25-bit signed multipliers; adders; ARITH 2018;
                 ARITH-25; Computer architecture; Delays; Digital
                 arithmetic; digital arithmetic; Electrical engineering;
                 embedded multipliers; field programmable gate arrays;
                 Field programmable gate arrays; Hardware; larger
                 multipliers; modified Karatsuba method; multiplying
                 circuits; rectangular multipliers; word length 64.0
                 bit",
}

@Article{Kumm:2018:OSC,
  author =       "Martin Kumm and Oscar Gustafsson and Mario Garrido and
                 Peter Zipf",
  title =        "Optimal Single Constant Multiplication Using Ternary
                 Adders",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
  volume =       "65",
  number =       "7",
  pages =        "928--932",
  month =        jul,
  year =         "2018",
  DOI =          "https://doi.org/10.1109/TCSII.2016.2631630",
  ISSN =         "1549-7747 (print), 1558-3791 (electronic)",
  ISSN-L =       "1549-7747",
  bibdate =      "Sat Feb 8 09:52:23 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE trans. circuits syst., II Express briefs",
  fjournal =     "IEEE Transactions on Circuits and Systems II: Express
                 Briefs",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
  keywords =     "adders; Adders; Arithmetic; average adder reductions;
                 bit shifts; circuit optimization; circuits; coefficient
                 word sizes; Complexity theory; digital arithmetic;
                 field programmable gate arrays; Field programmable gate
                 arrays; field-programmable gate arrays;
                 field-programmable gate arrays (FPGAs); fixed-point
                 arithmetic optimization; FPGA; mathematics; multiplying
                 circuits; numeric algorithms; optimal constant
                 multiplication circuits; optimal single constant
                 multiplication; Optimization; optimization methods;
                 Signal processing algorithms; single constant
                 coefficient multiplication; support efficient ternary
                 adders; Topology; two-input adders; word length 22.0
                 bit; word length 5.0 bit",
}

@Article{Kwon:2018:IJX,
  author =       "Oh-Jin Kwon and Seungcheol Choi and Dongkyoo Shin",
  title =        "Improvement of {JPEG XT} Floating-Point {HDR} Image
                 Coding Using Region Adaptive Prediction",
  journal =      j-IEEE-ACCESS,
  volume =       "6",
  pages =        "3321--3335",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ACCESS.2018.2793228",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Tue Sep 30 17:30:28 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "Decoding; Encoding; HDR from LDR predictor (HLP);
                 high-dynamic range image; Image coding; image coding;
                 Image reconstruction; Imaging; JPEG XT; Standards;
                 Transform coding",
}

@Article{Lam:2018:FGF,
  author =       "Michael O. Lam and Jeffrey K. Hollingsworth",
  title =        "Fine-grained floating-point precision analysis",
  journal =      j-IJHPCA,
  volume =       "32",
  number =       "2",
  pages =        "231--245",
  year =         "2018",
  CODEN =        "IHPCFL",
  DOI =          "https://doi.org/10.1177/1094342016652462",
  ISSN =         "1094-3420 (print), 1741-2846 (electronic)",
  ISSN-L =       "1094-3420",
  bibdate =      "Mon Nov 5 17:34:16 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijsa.bib",
  URL =          "http://journals.sagepub.com/doi/full/10.1177/1094342016652462",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of High Performance Computing
                 Applications",
  journal-URL =  "http://hpc.sagepub.com/content/by/year",
  keywords =     "interval arithmetic; truncating arithmetic;
                 variable-precision arithmetic",
  xxmonth =      mar,
}

@InProceedings{Langhammer:2018:HDP,
  author =       "Martin Langhammer and Gregg Baeckler",
  title =        "High Density and Performance Multiplication for
                 {FPGA}",
  crossref =     "Tenca:2018:PIS",
  pages =        "5--12",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ARITH.2018.8464695",
  bibdate =      "Fri Jan 31 08:05:31 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Arithmetic based applications are one of the most
                 common use cases for modern FPGAs. Currently, machine
                 learning is emerging as the fastest growth area for FPG
                 As, renewing an interest in low precision
                 multiplication. There is now a new focus on
                 multiplication in the soft fabric --- very high-density
                 systems, consisting of many thousands of operations,
                 are the current norm. In this paper we introduce
                 multiplier regularization, which restructures common
                 multiplier algorithms into smaller, and more efficient
                 architectures. The multiplier structure is
                 parameterizable, and results are given for a continuous
                 range of input sizes, although the algorithm is most
                 efficient for small input precisions. The multiplier is
                 particularly effective for typical machine learning
                 inferencing uses, and the presented cores can be used
                 for dot products required for these applications.
                 Although the examples presented here are optimized for
                 Intel Stratix 10 devices, the concept of regularized
                 arithmetic structures are applicable to generic FPGA
                 LUT architectures. Results are compared to Intel
                 Megafunction IP as well as contrasted with normalized
                 representations of recently published results for
                 Xilinx devices. We report a 10\% to 35\% smaller area,
                 and a more significant latency reduction, in the range
                 of 25\% to 50\%, for typical inferencing use cases.",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; ARITH 2018; ARITH-25; arithmetic based
                 applications; common multiplier algorithms; digital
                 arithmetic; dot products; Field programmable gate
                 arrays; field programmable gate arrays; generic FPGA
                 LUT architectures; high-density systems; Intel
                 Megafunction IP; Intel Stratix devices; IP networks;
                 latency reduction; logic design; low precision
                 multiplication; Machine learning; machine learning;
                 multiplier regularization; multiplier structure;
                 Performance evaluation; performance multiplication;
                 regularized arithmetic structures; Routing; soft
                 fabric-very high-density systems; table lookup; Table
                 lookup",
}

@InProceedings{Langroudi:2018:DLI,
  author =       "Seyed Hamed Fatemi Langroudi and Tej Pandit and
                 Dhireesha Kudithipudi",
  editor =       "{IEEE}",
  booktitle =    "{2018 1st Workshop on Energy Efficient Machine
                 Learning and Cognitive Computing for Embedded
                 Applications (EMC2)}",
  title =        "Deep Learning Inference on Embedded Devices:
                 Fixed-Point vs Posit",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "19--23",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/EMC2.2018.00012",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Lee:2018:APC,
  author =       "Wonyeol Lee and Rahul Sharma and Alex Aiken",
  title =        "On automatically proving the correctness of {\tt
                 math.h} implementations",
  journal =      j-PACMPL,
  volume =       "2",
  number =       "POPL",
  pages =        "47:1--47:??",
  month =        jan,
  year =         "2018",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3158135",
  ISSN =         "2475-1421",
  bibdate =      "Wed Jan 10 09:45:26 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/pacmpl.bib",
  abstract =     "Industry standard implementations of {\tt math.h}
                 claim (often without formal proof) tight bounds on
                 floating-point errors. We demonstrate a novel static
                 analysis that proves these bounds and verifies the
                 correctness of these implementations. Our key insight
                 is a reduction of this verification task to a set of
                 mathematical optimization problems that can be solved
                 by off-the-shelf computer algebra systems. We use this
                 analysis to prove the correctness of implementations in
                 Intel's math library automatically. Prior to this work,
                 these implementations could only be verified with
                 significant manual effort.",
  acknowledgement = ack-nhfb,
  articleno =    "47",
  fjournal =     "Proceedings of the ACM on Programming Languages",
  journal-URL =  "https://pacmpl.acm.org/",
}

@InProceedings{Lehoczky:2018:HLN,
  author =       "Zolt{\'a}n Leh{\'o}czky and Andr{\'a}s Retzler and
                 Rich{\'a}rd T{\'o}th and {\'A}lmos Szab{\'o} and
                 Benedek Farkas and Kriszti{\'a}n Somogyi",
  title =        "High-level {.NET} Software Implementations of Unum
                 {Type I} and Posit with Simultaneous {FPGA}
                 Implementation Using {Hastlayer}",
  crossref =     "ACM:2018:CNG",
  pages =        "1--7",
  year =         "2018",
  DOI =          "https://doi.org/10.1145/3190339.3190343",
  bibdate =      "Mon Dec 11 09:02:49 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The unum arithmetic framework has been proposed by
                 Gustafson, D. J. to address the short-comings of the
                 IEEE 754 Standard's floating-point. In this paper, we
                 present our software and hardware implementations of
                 Type I and posit unums. The software implementation is
                 built on the .NET platform as an open source library
                 written in the C\# programming language. We
                 automatically create hardware implementations using our
                 .NET to FPGA converter tool called Hastlayer. The
                 amount of hardware resources needed for addition
                 operations are quantified, and the performance of
                 software and prototype hardware for posits are
                 compared. We show that posits are significantly more
                 hardware friendly than Type I unums. Furthermore, our
                 posit FPGA implementation is about 2.04 times more
                 efficient per clock cycle than its software
                 implementation.",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  keywords =     "posit arithmetic; universal number arithmetic",
}

@Misc{Leong:2018:SV,
  author =       "Cerlane Leong",
  title =        "{SoftPosit} Version 0.4.1rc",
  howpublished = "Web source code.",
  year =         "2018",
  bibdate =      "Sat Dec 16 15:18:01 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://gitlab.com/cerlane/SoftPosit",
  acknowledgement = ack-nhfb,
}

@InProceedings{Li:2018:DEA,
  author =       "He Li and James J. Davis and John Wickerson and George
                 A. Constantinides",
  title =        "Digit Elision for Arbitrary-accuracy Iterative
                 Computation",
  crossref =     "Tenca:2018:PIS",
  pages =        "107--114",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ARITH.2018.8464691",
  bibdate =      "Fri Jan 31 08:05:31 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We recently proposed the first hardware architecture
                 enabling the iterative solution of systems of linear
                 equations to accuracies limited only by the amount of
                 available memory. This technique, named ARCHITECT,
                 achieves exact numeric computation by using online
                 arithmetic to allow the refinement of results from
                 earlier iterations over time, eschewing rounding error.
                 ARCHITECT has a key drawback, however: often, many more
                 digits than strictly necessary are generated, with this
                 problem exacerbating the more accurate a solution is
                 sought. In this paper, we infer the locations of these
                 superfluous digits within stationary iterative
                 calculations by exploiting online arithmetic's digit
                 dependencies and using forward error analysis. We
                 demonstrate that their lack of computation is
                 guaranteed not to affect the ability to reach a
                 solution of any accuracy. Versus ARCHITECT, our
                 illustrative hardware implementation achieves a
                 geometric mean $ 20.1 \times $ speedup in the solution
                 of a set of representative linear systems through the
                 avoidance of redundant digit calculation. For the
                 computation of high-precision results, we also obtain
                 an up-to $ 22.4 \times $ memory requirement reduction
                 over the same baseline. Finally, we demonstrate that
                 solvers implemented following our proposals can show
                 superiority over conventional arithmetic
                 implementations by virtue of their runtime-tunable
                 precisions.",
  acknowledgement = ack-nhfb,
  keywords =     "arbitrary-accuracy iterative computation; ARCHITECT;
                 ARITH 2018; ARITH-25; arithmetic implementations;
                 Delays; digit dependencies; digit elision; digital
                 arithmetic; error analysis; exact numeric computation;
                 forward error analysis; Hardware; hardware
                 architecture; iterative methods; Iterative methods;
                 iterative solution; Jacobian matrices; linear
                 equations; Linear systems; linear systems; memory
                 requirement reduction; online arithmetic; Proposals;
                 redundant digit calculation; rounding error; Runtime;
                 stationary iterative calculations; superfluous digits",
}

@Misc{Lie:2018:FPU,
  author =       "Sean Lie and Michael Edwin James and Michael Morrison
                 and Gary R. Lauterbach and Srikanth Arekapudi",
  title =        "Floating-point unit stochastic rounding for
                 accelerated deep learning",
  howpublished = "U.S. Patent US11449574B2",
  day =          "13",
  month =        apr,
  year =         "2018",
  bibdate =      "Fri Sep 22 17:25:05 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Patent granted 20 September 2022; expires 29 November
                 2038.",
  abstract =     "Techniques in advanced deep learning provide
                 improvements in one or more of accuracy, performance,
                 and energy efficiency. An array of processing elements
                 comprising a portion of a neural network accelerator
                 performs flow-based computations on wavelets of data.
                 Each processing element has a respective compute
                 element and a respective routing element. Each compute
                 element has a respective floating-point unit enabled to
                 perform stochastic rounding, thus in some circumstances
                 enabling reducing systematic bias in long dependency
                 chains of floating-point computations. The long
                 dependency chains of floating-point computations are
                 performed, e.g., to train a neural network or to
                 perform inference with respect to a trained neural
                 network.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lindstrom:2018:UCR,
  author =       "Peter Lindstrom and Scott Lloyd and Jeffrey
                 Hittinger",
  title =        "Universal Coding of the Reals: Alternatives to {IEEE}
                 Floating Point",
  crossref =     "ACM:2018:CNG",
  pages =        "1--14",
  year =         "2018",
  DOI =          "https://doi.org/10.1145/3190339.3190344",
  bibdate =      "Sun Dec 10 14:24:09 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We propose a modular framework for representing the
                 real numbers that generalizes IEEE, posits, and related
                 floating-point number systems, and which has its roots
                 in universal codes for the positive integers such as
                 the Elias codes. This framework unifies several known
                 but seemingly unrelated representations within a single
                 schema while also introducing new representations. We
                 particularly focus on variable-length encoding of the
                 binary exponent and on the manner in which fraction
                 bits are mapped to values. Our framework builds upon
                 and shares many of the attractive properties of posits
                 but allows for independent experimentation with
                 exponent codes, fraction mappings, reciprocal closure,
                 rounding modes, handling of under- and overflow, and
                 underlying precision.",
  acknowledgement = ack-nhfb,
  articleno =    "5",
}

@InProceedings{Liu:2018:CRA,
  author =       "Weiqiang Liu and Jing Li and Tao Xu and Chenghua Wang
                 and Paolo Montuschi and Fabrizio Lombardi",
  title =        "Combining Restoring Array and Logarithmic Dividers
                 into an Approximate Hybrid Design",
  crossref =     "Tenca:2018:PIS",
  pages =        "92--98",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ARITH.2018.8464807",
  bibdate =      "Fri Jan 31 08:05:31 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper proposes a new design of an approximate
                 hybrid divider (AXHD), which combines the restoring
                 array and the logarithmic dividers to achieve an
                 excellent tradeoff between accuracy and hardware
                 performance. Exact restoring divider cells (EXDCrs) are
                 used to generate the MSBs of the quotient for attaining
                 a high accuracy; the other quotient digits are
                 processed by a logarithmic divider as inexact scheme to
                 improve figures of merit such as power consumption,
                 area and delay. The proposed AXHD is evaluated and
                 analyzed using error and hardware metrics. The proposed
                 design is also compared with the exact restoring
                 divider (EXDr) and previous approximate restoring
                 dividers (AXDrs). The results show that the proposed
                 design achieves very good performance in terms of
                 accuracy and hardware; case studies for image
                 processing also show the validity of the proposed
                 designs.",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; Approximate Computing; approximate hybrid
                 divider design; approximate restoring dividers; ARITH
                 2018; ARITH-25; AXDrs; AXHD; circuit stability;
                 dividing circuits; Electronic mail; Error analysis;
                 exact restoring divider cells; EXDCrs; Hardware;
                 hardware metrics; hardware performance; image
                 processing; Image restoration; logarithmic divider;
                 Logarithmic Divider; logic design; Low Power; MSBs;
                 Power demand; quotient digit processing; restoring
                 array; Restoring Array Divider",
}

@Article{Loeffler:2018:WBP,
  author =       "John Loeffler",
  title =        "When Bad Programming Turns Deadly: A look at
                 programming disasters and how bad programming can be
                 deadly",
  journal =      "Interesting Engineering",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "22",
  month =        nov,
  year =         "2018",
  bibdate =      "Fri Nov 23 11:32:14 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://interestingengineering.com/when-bad-programming-turns-deadly",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; Patriot missile;
                 radiological equipment software malfunction",
}

@Misc{Marchese:2018:ACM,
  author =       "Sergio Marchese",
  title =        "{AI} Chips Must Get The Floating-Point Math Right:
                 Formal verification of {FPUs} is no longer a
                 prerogative of big companies spending big bucks",
  howpublished = "Web site.",
  day =          "27",
  month =        sep,
  year =         "2018",
  bibdate =      "Fri Sep 28 06:12:07 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Markidis:2018:NTC,
  author =       "Stefano Markidis and Steven Wei Der Chien and Erwin
                 Laure and Ivy Bo Peng and Jeffrey S. Vetter",
  booktitle =    "2018 {IEEE} International Parallel and Distributed
                 Processing Symposium Workshops ({IPDPSW})",
  title =        "{NVIDIA} Tensor Core Programmability, Performance \&
                 Precision",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "522--531",
  month =        may,
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ipdpsw.2018.00091",
  bibdate =      "Tue Jan 28 06:32:08 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}

@InProceedings{Mikaitis:2018:AFP,
  author =       "Mantas Mikaitis and David R. Lester and Delong Shang
                 and Steve Furber and Gengting Liu and Jim Garside and
                 Stefan Scholze and Sebastian H{\"o}ppner and Andreas
                 Dixius",
  title =        "Approximate Fixed-Point Elementary Function
                 Accelerator for the {SpiNNaker-2} Neuromorphic Chip",
  crossref =     "Tenca:2018:PIS",
  pages =        "37--44",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ARITH.2018.8464785",
  bibdate =      "Fri Jan 31 08:05:31 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Neuromorphic chips are used to model biologically
                 inspired Spiking-Neural-Networks (SNNs) where most
                 models are based on differential equations. Equations
                 for most SNN algorithms usually contain variables with
                 one or more ex components. SpiNNaker is a digital
                 neuromorphic chip that has so far been using
                 pre-calculated look-up tables for exponential function.
                 However this approach is limited because the memory
                 requirements grow as more complex neural models are
                 developed. To save already limited memory resources in
                 the next generation SpiNNaker chip, we are including a
                 fast exponential function in the silicon. In this paper
                 we analyse iterative algorithms for elementary
                 functions and show how to build a single hardware
                 accelerator for exp and natural log, for a neuromorphic
                 chip prototype, to be manufactured in a 22 nm FDSOI
                 process. We present the accelerator that has
                 algorithmic level approximation control, allowing it to
                 trade precision for latency and energy efficiency. As
                 an addition to neuromorphic chip application, we
                 provide analysis of a parameterized elementary function
                 unit that can be tailored for other systems with
                 different power, area, accuracy and latency
                 constraints.",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; algorithmic level approximation control;
                 approximate arithmetic; approximate fixed-point
                 elementary function accelerator; ARITH 2018; ARITH-25;
                 Biological system modeling; biologically inspired
                 spiking-neural-networks; complex neural models;
                 Computational modeling; Convergence; differential
                 equations; digital neuromorphic chip; energy
                 efficiency; exponential function; fast exponential
                 function; FDSOI process; fixed-point arithmetic;
                 hardware accelerators; iterative algorithms; iterative
                 methods; logarithm function; Mathematical model; memory
                 requirements; memory resources; MPSoC; neural chips;
                 neuromorphic chip prototype; neuromorphic computing;
                 Neuromorphics; next generation SpiNNaker chip;
                 parameterized elementary function unit; pre-calculated
                 look-up tables; single hardware accelerator; size 22.0
                 nm; SNN algorithms; SpiNNaker-2 neuromorphic chip;
                 SpiNNaker2; table lookup; Table lookup",
}

@InProceedings{Mokhtar:2018:ITF,
  author =       "A. S. N. Mokhtar and M. I. Ayub and N. Ismail and N.
                 G. Nik Daud",
  booktitle =    "{AIP} Conference Proceedings",
  title =        "Implementation of trigonometric function using
                 {CORDIC} algorithms",
  volume =       "1930",
  publisher =    pub-AIP,
  address =      pub-AIP:adr,
  pages =        "020040",
  year =         "2018",
  DOI =          "https://doi.org/10.1063/1.5022934",
  ISSN =         "0094-243X",
  bibdate =      "Sat Oct 18 15:41:08 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Moroz:2018:FCI,
  author =       "Leonid V. Moroz and Cezary J. Walczyk and Andriy
                 Hrynchyshyn and Vijay Holimath and Jan L.
                 Cie{\'s}li{\'n}ski",
  title =        "Fast calculation of inverse square root with the use
                 of magic constant --- analytical approach",
  journal =      j-APPL-MATH-COMP,
  volume =       "316",
  number =       "??",
  pages =        "245--255",
  day =          "1",
  month =        jan,
  year =         "2018",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2017.08.025",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Oct 10 15:56:03 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300317305763",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  keywords =     "single-precision 32-bit IEEE 754 binary arithmetic",
}

@Book{Muller:2018:HFP,
  author =       "Jean-Michel Muller and Nicolas Brunie and Florent de
                 Dinechin and Claude-Pierre Jeannerod and Mioara Joldes
                 and Vincent Lef{\`e}vre and Guillaume Melquiond and
                 Nathalie Revol and Serge Torres",
  title =        "Handbook of Floating-Point Arithmetic",
  publisher =    pub-BIRKHAUSER,
  address =      pub-BIRKHAUSER:adr,
  edition =      "Second",
  pages =        "xxv + 627",
  year =         "2018",
  DOI =          "https://doi.org/10.1007/978-3-319-76526-6",
  ISBN =         "3-319-76525-6, 3-319-76526-4 (e-book)",
  ISBN-13 =      "978-3-319-76525-9, 978-3-319-76526-6 (e-book)",
  LCCN =         "QA76.9.C62",
  bibdate =      "Fri Jun 1 06:59:01 MDT 2018",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  abstract =     "This handbook aims to provide a complete overview of
                 modern floating-point arithmetic. This includes a
                 detailed treatment of the current (IEEE-754) and next
                 (preliminarily called IEEE-754R) standards for
                 floating-point arithmetic.",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "Introduction / 3--14 \\
                 Definitions and Basic Notions / 15--45 \\
                 Floating-Point Formats and Environment / 47--93 \\
                 Basic Properties and Algorithms / 97--162 \\
                 Enhanced Floating-Point Sums, Dot Products, and
                 Polynomial Values / 163--192 \\
                 Languages and Compilers / 193--230 \\
                 Algorithms for the Basic Operations / 233--266 \\
                 Hardware Implementation of Floating-Point Arithmetic /
                 267--320 \\
                 Software Implementation of Floating-Point Arithmetic /
                 321--374 \\
                 Evaluating Floating-Point Elementary Functions /
                 375--433 \\
                 Complex Numbers / 437--452 \\
                 Interval Arithmetic / 453--477 \\
                 Verifying Floating-Point Algorithms / 479--511 \\
                 Extending the Precision / 513--552",
  subject =      "Floating-point arithmetic; Handbooks, manuals, etc;
                 Computer arithmetic; COMPUTERS / Computer Literacy;
                 COMPUTERS / Computer Science; COMPUTERS / Data
                 Processing; COMPUTERS / Hardware / General; COMPUTERS /
                 Information Technology; COMPUTERS / Machine Theory;
                 COMPUTERS / Reference.",
  tableofcontents = "Intro \\
                 Contents \\
                 List of Figures \\
                 List of Tables \\
                 Preface \\
                 I Introduction, Basic Definitions, and Standards \\
                 1 Introduction \\
                 1.1 Some History \\
                 1.2 Desirable Properties \\
                 1.3 Some Strange Behaviors \\
                 1.3.1 Some famous bugs \\
                 1.3.2 Difficult problems \\
                 1.3.2.1 A sequence that seems to converge to a wrong
                 limit \\
                 1.3.2.2 The Chaotic Bank Society \\
                 1.3.2.3 Rump's example \\
                 2 Definitions and Basic Notions \\
                 2.1 Floating-Point Numbers \\
                 2.1.1 Main definitions \\
                 2.1.2 Normalized representations, normal and subnormal
                 numbers \\
                 2.1.3 A note on underflow \\
                 2.1.4 Special floating-point data \\
                 2.2 Rounding \\
                 2.2.1 Rounding functions \\
                 2.2.2 Useful properties \\
                 2.3 Tools for Manipulating Floating-Point Errors \\
                 2.3.1 Relative error due to rounding \\
                 2.3.2 The ulp function \\
                 2.3.3 Link between errors in ulps and relative errors
                 \\
                 2.3.3.1 Converting from errors in ulps to relative
                 errors \\
                 2.3.3.2 Converting from relative errors to errors in
                 ulps \\
                 2.3.3.3 Loss of information during these conversions
                 \\
                 2.3.4 An example: iterated products \\
                 2.4 The Fused Multiply-Add (FMA) Instruction \\
                 2.5 Exceptions \\
                 2.6 Lost and Preserved Properties of Real Arithmetic
                 \\
                 2.7 Note on the Choice of the Radix \\
                 2.7.1 Representation errors \\
                 2.7.2 A case for radix 10 \\
                 2.8 Reproducibility \\
                 3 Floating-Point Formats and Environment \\
                 3.1 The IEEE 754-2008 Standard \\
                 3.1.1 Formats \\
                 3.1.1.1 Binary interchange format encodings \\
                 3.1.1.2 Decimal interchange format encodings \\
                 3.1.1.3 Larger formats \\
                 3.1.1.4 Extended and extendable precisions \\
                 3.1.1.5 Little-endian, big-endian \\
                 3.1.2 Attributes and rounding \\
                 3.1.2.1 Rounding direction attributes \\
                 3.1.2.2 Alternate exception-handling attributes \\
                 3.1.2.3 Preferred width attributes \\
                 3.1.2.4 Value-changing optimization attributes \\
                 3.1.2.5 Reproducibility attributes \\
                 3.1.3 Operations specified by the standard \\
                 3.1.3.1 Arithmetic operations and square root \\
                 3.1.3.2 Remainders \\
                 3.1.3.3 Preferred exponent for arithmetic operations in
                 the decimal format \\
                 3.1.3.4 scaleB and logB \\
                 3.1.3.5 Miscellaneous \\
                 3.1.4 Comparisons \\
                 3.1.5 Conversions to/from string representations \\
                 3.1.6 Default exception handling \\
                 3.1.6.1 Invalid operation \\
                 3.1.6.2 Division by zero \\
                 3.1.6.3 Overflow \\
                 3.1.6.4 Underflow \\
                 3.1.6.5 Inexact \\
                 3.1.7 Special values \\
                 3.1.7.1 NaN: Not a Number \\
                 3.1.7.2 Arithmetic of infinities and zeros \\
                 3.1.8 Recommended functions \\
                 3.2 On the Possible Hidden Use of a Higher Internal
                 Precision \\
                 3.3 Revision of the IEEE 754-2008 Standard \\
                 3.4 Floating-Point Hardware in Current Processors \\
                 3.4.1 The common hardware denominator \\
                 3.4.2 Fused multiply-add \\
                 3.4.3 Extended precision and 128-bit formats \\
                 3.4.4 Rounding and precision control \\
                 3.4.5 SIMD instructions \\
                 3.4.6 Binary16 (half-precision) support \\
                 3.4.7 Decimal arithmetic \\
                 3.4.8 The legacy x87 processor \\
                 3.5 Floating-Point Hardware in Recent Graphics
                 Processing Units \\
                 3.6 IEEE Support in Programming Languages \\
                 3.7 Checking the Environment \\
                 3.7.1 MACHAR \\
                 3.7.2 Paranoia \\
                 \ldots{} \\
                 Basic Properties and Algorithms \\
                 Enhanced Floating-Point Sums, Dot Products, and
                 Polynomial Values \\
                 Languages and Compilers \\
                 Algorithms for the Basic Operations \\
                 Hardware Implementation of Floating-Point Arithmetic
                 \\
                 Software Implementation of Floating-Point Arithmetic
                 \\
                 Evaluating Floating-Point Elementary Functions \\
                 Complex Numbers \\
                 Interval Arithmetic \\
                 Verifying Floating-Point Algorithms \\
                 Extending the Precision",
}

@Article{Munoz-Coreas:2018:CQO,
  author =       "Edgard Mu{\~n}oz-Coreas and Himanshu Thapliyal",
  title =        "{T}-count and Qubit Optimized Quantum Circuit Design
                 of the Non-Restoring Square Root Algorithm",
  journal =      j-JETC,
  volume =       "14",
  number =       "3",
  pages =        "36:1--36:15",
  month =        oct,
  year =         "2018",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3264816",
  ISSN =         "1550-4832 (print), 1550-4840 (electronic)",
  ISSN-L =       "1550-4832",
  bibdate =      "Thu Nov 1 16:44:41 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jetc.bib",
  abstract =     "Quantum circuits for basic mathematical functions such
                 as the square root are required to implement scientific
                 computing algorithms on quantum computers. Quantum
                 circuits that are based on Clifford+T gates can easily
                 be made fault tolerant, but the T gate is very costly
                 to implement. As a result, reducing T-count has become
                 an important optimization goal. Further, quantum
                 circuits with many qubits are difficult to realize,
                 making designs that save qubits and produce no garbage
                 outputs desirable. In this work, we present a T-count
                 optimized quantum square root circuit with only $ 2 s n
                 + 1 $ qubits and no garbage output. To make a fair
                 comparison against existing work, the Bennett's garbage
                 removal scheme is used to remove garbage output from
                 existing works. We determined that our proposed design
                 achieves an average T-count savings of 43.44\%,
                 98.95\%, 41.06\%, and 20.28\% as well as qubit savings
                 of 85.46\%, 95.16\%, 90.59\%, and 86.77\% compared to
                 existing works.",
  acknowledgement = ack-nhfb,
  articleno =    "36",
  fjournal =     "ACM Journal on Emerging Technologies in Computing
                 Systems (JETC)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J967",
}

@InProceedings{Nannarelli:2018:TFP,
  author =       "Alberto Nannarelli",
  title =        "Tunable Floating-Point for Energy Efficient
                 Accelerators",
  crossref =     "Tenca:2018:PIS",
  pages =        "29--36",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ARITH.2018.8464797",
  bibdate =      "Fri Jan 31 08:05:31 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this work, we address the design of an on-chip
                 accelerator for Machine Learning and other
                 computation-demanding applications with a Tunable
                 Floating-Point (TFP) precision. The precision can be
                 chosen for a single operation by selecting a specific
                 number of bits for significand and exponent in the
                 floating-point representation. By tuning the precision
                 of a given algorithm to the minimum precision achieving
                 an acceptable target error, we can make the computation
                 more power efficient. We focus on floating-point
                 multiplication, which is the most power demanding
                 arithmetic operation.",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; ARITH 2018; ARITH-25; computation-demanding
                 applications; Decoding; Dynamic range; electronic
                 engineering computing; energy efficient accelerators;
                 floating point arithmetic; floating-point
                 multiplication; floating-point representation;
                 Hardware; learning (artificial intelligence); Machine
                 Learning; Machine learning; on-chip accelerator;
                 Standards; System-on-chip; TFP precision; Tunable
                 Floating-Point precision",
}

@InProceedings{Nguyen:2018:EFP,
  author =       "Hong-Thu Nguyen and Xuan-Thuan Nguyen and Cong-Kha
                 Pham",
  booktitle =    "{2018 23rd Asia and South Pacific Design Automation
                 Conference (ASP-DAC)}",
  title =        "An efficient fixed-point arithmetic processor using a
                 hybrid {CORDIC} algorithm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "327--328",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ASPDAC.2018.8297343",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; Approximation algorithms; CMOS technology;
                 Complexity theory; Hardware; Logic gates; Power
                 demand",
}

@Article{Numahata:2018:RAS,
  author =       "Dai Numahata and Hiroshi Sekigawa",
  title =        "Robust algorithms for sparse interpolation of
                 multivariate polynomials",
  journal =      j-ACM-COMM-COMP-ALGEBRA,
  volume =       "52",
  number =       "4",
  pages =        "145--147",
  month =        dec,
  year =         "2018",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3338637.3338648",
  ISSN =         "1932-2232 (print), 1932-2240 (electronic)",
  ISSN-L =       "1932-2232",
  bibdate =      "Wed Oct 23 07:34:18 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
  abstract =     "We consider the problem of symbolic-numeric sparse
                 interpolation of multivariate polynomials. The problem
                 is to find the coefficients and the exponents of a
                 given black-box polynomial $ f(x_1, \ldots, x_n) =
                 \sum_{j = 1}^t c_j x_1^{d_{j, 1}} \ldots {} x_n^{d_{j,
                 n}} \in \mathbb {C}[x_1, \ldots, x_n] (c_j \neq 0) $ by
                 evaluating the value of $ f(x_1, \ldots, x_n) $ at any
                 point in $ \mathbb {C}^n $ in floating-point arithmetic
                 and by using the conditions of the input.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Communications in Computer Algebra",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}

@Article{Oliveira:2018:MLB,
  author =       "Thomaz Oliveira and Julio L{\'o}pez and Francisco
                 Rodr{\'{\i}}guez-Henr{\'{\i}}quez",
  title =        "The {Montgomery} ladder on binary elliptic curves",
  journal =      j-J-CRYPTO-ENG,
  volume =       "8",
  number =       "3",
  pages =        "241--258",
  month =        sep,
  year =         "2018",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s13389-017-0163-8",
  ISSN =         "2190-8508 (print), 2190-8516 (electronic)",
  ISSN-L =       "2190-8508",
  bibdate =      "Wed Oct 2 11:24:50 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcryptoeng.bib",
  URL =          "http://link.springer.com/article/10.1007/s13389-017-0163-8",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Cryptographic Engineering",
  journal-URL =  "http://link.springer.com/journal/13389",
}

@Article{Omari:2018:ICB,
  author =       "Mohammed Omari and Salah Yaichi",
  title =        "Image Compression Based on Mapping Image Fractals to
                 Rational Numbers",
  journal =      j-IEEE-ACCESS,
  volume =       "6",
  pages =        "47062--47074",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ACCESS.2018.2865784",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Wed Oct 1 06:08:36 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "Discrete transforms; Fractal image; Fractals; Genetic
                 algorithms; genetic algorithms; Image coding; lossy
                 compression; Mersenne numbers; rational numbers;
                 Sociology; Statistics",
}

@InProceedings{Pendem:2018:ECA,
  author =       "Suganda Pendem and Rajshekar B. Shettar",
  booktitle =    "{2018 International Conference on Networking, Embedded
                 and Wireless Systems (ICNEWS)}",
  title =        "Enhancing Computational Accuracy and Performance of
                 Interval Arithmetic Double Rotation {CORDIC}
                 algorithm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--4",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ICNEWS.2018.8903935",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Arithmetic; Computer architecture; Cordic;
                 Digital signal processing; DSP; Interval arithmetic;
                 MATLAB; MATLAB and INTLAB; Monitoring; Real-time
                 systems; Signal processing algorithms; Very large scale
                 integration; Wireless communication",
}

@InProceedings{Peou:2018:CSO,
  author =       "Kenny Peou and Alan Kelly and Joel Falcou and Cecile
                 Germain",
  editor =       "{IEEE}",
  booktitle =    "{2018 30th International Symposium on Computer
                 Architecture and High Performance Computing (SBAC-PAD):
                 Lyon, France, 24--27 September 2018}",
  title =        "A Case Study on Optimizing Accurate Half Precision
                 Average",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "356--363",
  month =        sep,
  year =         "2018",
  DOI =          "https://doi.org/10.1109/cahpc.2018.8645923",
  ISBN =         "1-5386-7769-5",
  ISBN-13 =      "978-1-5386-7769-8",
  bibdate =      "Fri Apr 11 08:36:46 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this work, we study the numerical performance of
                 various common algorithms used to calculate the average
                 of an array of half precision (FP16) floating point
                 values. While the current generation of CPUs does not
                 support native FP16 arithmetic, it is a planned feature
                 in a number of next-generation CPUs. FP16 arithmetic
                 was emulated via the half software library. Due to the
                 limitations of the FP16 data type, some algorithms
                 proved insufficient for arrays as small as 100
                 elements. We propose an algorithm that allows
                 numerically stable FP16 computation of the average and
                 compare it to the naive floating point (FP32) algorithm
                 in terms of both numerical precision and runtime
                 performance. We find that our algorithm offers
                 comparable robustness, numerical precision, and SIMD
                 performance to the higher precision computation.",
  acknowledgement = ack-nhfb,
  keywords =     "Clustering algorithms; Half-Precision; Machine
                 learning algorithms; Memory management; Numerical
                 Precision; Program processors; Random access memory;
                 Registers; SIMD; Software algorithms",
}

@InProceedings{Podobas:2018:HIP,
  author =       "Artur Podobas and Satoshi Matsuoka",
  editor =       "{IEEE}",
  booktitle =    "{2018 IEEE International Parallel and Distributed
                 Processing Symposium Workshops (IPDPSW)}",
  title =        "Hardware Implementation of {POSITs} and Their
                 Application in {FPGAs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "138--145",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/IPDPSW.2018.00029",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Popescu:2018:FPN,
  author =       "Valentina Popescu and Marcel Nassar and Xin Wang and
                 Evren Tumer and Tristania Webb",
  title =        "{Flexpoint}: Predictive Numerics for Deep Learning",
  crossref =     "Tenca:2018:PIS",
  pages =        "1--4",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ARITH.2018.8464801",
  bibdate =      "Fri Jan 31 08:05:31 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Deep learning has been undergoing rapid growth in
                 recent years thanks to its state-of-the-art performance
                 across a wide range of real-world applications.
                 Traditionally neural networks were trained in IEEE-754
                 binary64 or binary32 format, a common practice in
                 general scientific computing. However, the unique
                 computational requirements of deep neural network
                 training workloads allow for much more efficient and
                 inexpensive alternatives, unleashing a new wave of
                 numerical innovations powering specialized computing
                 hardware. We previously presented Flexpoint, a blocked
                 fixed-point data type combined with a novel predictive
                 exponent management algorithm designed to support
                 training of deep networks without modifications, aiming
                 at a seamless replacement of the binary32 widely in
                 practice today. We showed that Flexpoint with 16-bit
                 mantissa and 5-bit shared exponent (flex16+S) achieved
                 numerical parity to binary32 in training a number of
                 convolutional neural networks. In the current paper we
                 review the continuing trend of predictive numerics
                 enhancing deep neural network training in specialized
                 computing devices such as the Intel Nervana Neural
                 Network Processor.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2018; ARITH-25; blocked fixed-point data type;
                 convolution; convolutional neural networks; deep
                 learning; Deep Learning; deep neural network training;
                 feedforward neural nets; Flexpoint; floating point
                 arithmetic; general scientific computing; Hardware;
                 learning (artificial intelligence); Machine learning;
                 Market research; Neural networks; Neural Networks;
                 Prediction algorithms; predictive exponent management
                 algorithm; Tensile stress; Training",
}

@Article{Radford:2018:FIF,
  author =       "Peter Radford",
  title =        "A {``Feature''} of {IBM 360} Floating Point",
  journal =      "Resurrection: The Journal of the Computer Conservation
                 Society",
  volume =       "??",
  number =       "82",
  pages =        "??--??",
  month =        "Summer",
  year =         "2018",
  ISSN =         "0958-7403",
  ISSN-L =       "0958-7403",
  bibdate =      "Mon Jul 27 18:19:06 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://computerconservationsociety.org/resurrection/res82.htm#f",
  acknowledgement = ack-nhfb,
  remark =       "The short article discusses the impact of hexadecimal
                 normalization on representation of decimal input
                 values, and ends with the statement: ``32-bit floating
                 point remains an elephant trap for programmers to this
                 day.''.",
}

@InProceedings{Ram:2018:FVF,
  author =       "Ravi Ram and Adam Elkins and Adnan Pratama and Sasa
                 Stamenkovic and Sven Beyer and Sergio Marchese",
  editor =       "????",
  booktitle =    "Proceedings of {DVCon US 2018}",
  title =        "Formal Verification of Floating-Point Hardware with
                 Assertion-Based {VIP}",
  publisher =    "????",
  address =      "????",
  pages =        "1--9",
  day =          "5",
  month =        jun,
  year =         "2018",
  bibdate =      "Fri Sep 28 06:20:43 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.onespin.com/fileadmin/user_upload/pdf/whitepapers/Formal_Verification_of_Floating_Point_Hardware.pdf",
  abstract =     "Hardware for integer or fixed-point arithmetic is
                 relatively simple to design, at least at the
                 register-transfer level. If the range of values and
                 precision that can be represented with these formats is
                 not sufficient for the target application,
                 floating-point hardware might be required.
                 Unfortunately, floating-point units are complex to
                 design, and notoriously challenging to verify. Since
                 the famous 1994 Intel Pentium bug, many companies have
                 investigated and successfully applied formal methods to
                 this task. However, solutions often rely on a mix of
                 the following: hard-to-use formal tools; highly
                 specialized engineering skills; availability of a
                 suitable executable model of the hardware; and
                 significant, design-specific engineering effort. In
                 this paper, we present an alternative floating-point
                 hardware verification approach based on a reusable,
                 IEEE 754 compliant SystemVerilog arithmetic library.
                 While not addressing all verification challenges, this
                 method enables engineers to set up a formal testbench
                 and uncover deep corner-case bugs with minimal effort.
                 Results from industrial applications are reported.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Reddy:2018:DAD,
  author =       "K. Manikantta Reddy and M. H. Vasantha and Y. B.
                 Nithin Kumar and Devesh Dwivedi",
  booktitle =    "{2018 IEEE 61st International Midwest Symposium on
                 Circuits and Systems (MWSCAS)}",
  title =        "Design of Approximate Dividers for Error Tolerant
                 Applications",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  month =        aug,
  year =         "2018",
  DOI =          "https://doi.org/10.1109/mwscas.2018.8623909",
  bibdate =      "Wed Dec 20 07:39:14 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Reyhani-Masoleh:2018:NAR,
  author =       "Arash Reyhani-Masoleh and Mostafa Taha and Doaa
                 Ashmawy",
  title =        "New Area Record for the {AES} Combined {S}-Box\slash
                 Inverse {S}-Box",
  crossref =     "Tenca:2018:PIS",
  pages =        "145--152",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ARITH.2018.8464780",
  bibdate =      "Fri Jan 31 08:05:31 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The AES combined S-box/inverse S-box is a single
                 construction that is shared between the encryption and
                 decryption data paths of the AES. The currently most
                 compact implementation of the AES combined
                 S-box/inverse S-box is Canright's design, introduced
                 back in 2005. Since then, the research community has
                 introduced several optimizations over the S-box only,
                 however the combined S-boxlinverse S-box received
                 little attention. In this paper, we propose a new AES
                 combined S-boxlinverse S-box design that is both
                 smaller and faster than Canright's design. We achieve
                 this goal by proposing to use new tower field and
                 optimizing each and every block inside the combined
                 architecture for this field. Our complexity analysis
                 and ASIC implementation results in the CMOS STM 65nm
                 and NanGate 15nm technologies show that our design
                 outperforms the counterparts in terms of area and
                 speed.",
  acknowledgement = ack-nhfb,
  keywords =     "AES combined S-box-inverse S-box; application specific
                 integrated circuits; ARITH 2018; ARITH-25; Canright
                 design; circuit optimisation; CMOS STM; Complexity
                 theory; Computer architecture; cryptography; decryption
                 data paths; Encryption; encryption data paths;
                 Generators; Logic gates; Multiplexing; NanGate; Poles
                 and towers; size 15.0 nm; size 65.0 nm",
}

@InProceedings{Riedy:2018:AAO,
  author =       "Jason Riedy and James Demmel",
  title =        "Augmented Arithmetic Operations Proposed for {IEEE-754
                 2018}",
  crossref =     "Tenca:2018:PIS",
  pages =        "45--52",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ARITH.2018.8464813",
  bibdate =      "Fri Jan 31 08:05:31 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Algorithms for extending arithmetic precision through
                 compensated summation or arithmetics like double-double
                 rely on operations commonly called twoSum and
                 twoProduct. The current draft of the IEEE 754 standard
                 specifies these operations under the names
                 augmentedAddition and augmentedMultiplication. These
                 operations were included after three decades of
                 experience because of a motivating new use: bitwise
                 reproducible arithmetic. Standardizing the operations
                 provides a hardware acceleration target that can
                 provide at least a 33\% speed improvements in
                 reproducible dot product, placing reproducible dot
                 product almost within a factor of two of common dot
                 product. This paper provides history and motivation for
                 standardizing these operations. We also define the
                 operations, explain the rationale for all the specific
                 choices, and provide parameterized test cases for new
                 boundary behaviors.",
  acknowledgement = ack-nhfb,
  keywords =     "Acceleration; ARITH 2018; ARITH-25; arithmetic
                 precision; augmented arithmetic operations; bitwise
                 reproducible arithmetic; common dot product; floating
                 point arithmetic; Hardware; hardware acceleration
                 target; History; IEEE 754 standard; IEEE standards;
                 IEEE-754 2018; Libraries; Magnetic heads; reproducible
                 dot product; Software; Standards",
}

@Article{Rodriguez-Henriquez:2018:SIH,
  author =       "Francisco Rodr{\'\i}guez-Henr{\'\i}quez and Erkay
                 Savas",
  title =        "Special issue in honor of {Peter Lawrence
                 Montgomery}",
  journal =      j-J-CRYPTO-ENG,
  volume =       "8",
  number =       "3",
  pages =        "185--187",
  month =        sep,
  year =         "2018",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s13389-017-0168-3",
  ISSN =         "2190-8508 (print), 2190-8516 (electronic)",
  ISSN-L =       "2190-8508",
  bibdate =      "Wed Oct 2 11:24:50 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcryptoeng.bib",
  URL =          "http://link.springer.com/article/10.1007/s13389-017-0168-3;
                 https://link.springer.com/content/pdf/10.1007/s13389-017-0168-3.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Cryptographic Engineering",
  journal-URL =  "http://link.springer.com/journal/13389",
}

@Article{Saadat:2018:MBM,
  author =       "Hassaan Saadat and Haseeb Bokhari and Sri
                 Parameswaran",
  title =        "Minimally Biased Multipliers for Approximate Integer
                 and Floating-Point Multiplication",
  journal =      j-IEEE-TRANS-CAD-ICS,
  volume =       "37",
  number =       "11",
  pages =        "2623--2635",
  month =        nov,
  year =         "2018",
  CODEN =        "ITCSDI",
  DOI =          "https://doi.org/10.1109/tcad.2018.2857262",
  ISSN =         "0278-0070 (print), 1937-4151 (electronic)",
  ISSN-L =       "0278-0070",
  bibdate =      "Wed Dec 20 07:46:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computer-Aided Design of
                 Integrated Circuits and Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=43",
}

@Article{Sanchez-Stern:2018:FRC,
  author =       "Alex Sanchez-Stern and Pavel Panchekha and Sorin
                 Lerner and Zachary Tatlock",
  title =        "Finding root causes of floating point error",
  journal =      j-SIGPLAN,
  volume =       "53",
  number =       "4",
  pages =        "256--269",
  month =        apr,
  year =         "2018",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/3296979.3192411",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Wed Oct 16 14:12:57 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
  abstract =     "Floating-point arithmetic plays a central role in
                 science, engineering, and finance by enabling
                 developers to approximate real arithmetic. To address
                 numerical issues in large floating-point applications,
                 developers must identify root causes, which is
                 difficult because floating-point errors are generally
                 non-local, non-compositional, and non-uniform. This
                 paper presents Herbgrind, a tool to help developers
                 identify and address root causes in numerical code
                 written in low-level languages like C/C++ and Fortran.
                 Herbgrind dynamically tracks dependencies between
                 operations and program outputs to avoid false positives
                 and abstracts erroneous computations to simplified
                 program fragments whose improvement can reduce output
                 error. We perform several case studies applying
                 Herbgrind to large, expert-crafted numerical programs
                 and show that it scales to applications spanning
                 hundreds of thousands of lines, correctly handling the
                 low-level details of modern floating point hardware and
                 mathematical libraries and tracking error across
                 function boundaries and through the heap.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  remark =       "PLDI '18 proceedings.",
}

@Article{Savas:2018:MI,
  author =       "Erkay Savas and {\c{C}}etin Kaya Ko{\c{c}}",
  title =        "{Montgomery} inversion",
  journal =      j-J-CRYPTO-ENG,
  volume =       "8",
  number =       "3",
  pages =        "201--210",
  month =        sep,
  year =         "2018",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s13389-017-0161-x",
  ISSN =         "2190-8508 (print), 2190-8516 (electronic)",
  ISSN-L =       "2190-8508",
  bibdate =      "Wed Oct 2 11:24:50 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcryptoeng.bib",
  URL =          "http://link.springer.com/article/10.1007/s13389-017-0161-x",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Cryptographic Engineering",
  journal-URL =  "http://link.springer.com/journal/13389",
}

@Article{Schneider:2018:USS,
  author =       "D. Schneider",
  title =        "{U.S.} supercomputing strikes back",
  journal =      j-IEEE-SPECTRUM,
  volume =       "55",
  number =       "1",
  pages =        "52--53",
  month =        jan,
  year =         "2018",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.2018.8241739",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Sat Jan 18 07:02:09 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/super.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "Companies; Computational modeling; floating-point
                 operations; Games; Hardware; parallel machines;
                 Payloads; petaflops; Rockets; Supercomputers; Titan
                 machine; U.S. high-performance computing community;
                 U.S. supercomputing",
}

@Article{Seo:2018:FBM,
  author =       "Jungjoo Seo and Kunsoo Park",
  title =        "Fast batch modular exponentiation with
                 common-multiplicand multiplication",
  journal =      j-INFO-PROC-LETT,
  volume =       "129",
  number =       "??",
  pages =        "5--10",
  month =        jan,
  year =         "2018",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Mon Oct 30 08:48:26 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/infoproc2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0020019017301527",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}

@Misc{Shirriff:2018:TBP,
  author =       "Ken Shirriff",
  title =        "Two bits per transistor: high-density {ROM} in
                 {Intel}'s 8087 floating point chip",
  howpublished = "Blog posting",
  pages =        "16",
  month =        sep,
  year =         "2018",
  bibdate =      "Sat Aug 23 07:23:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Analysis of the transistors invented by the 8087 team
                 in order to reduce the footprint of the microcode ROM
                 on the die. See patent \cite{Stark:1981:MBR}.",
  URL =          "https://ieeemilestones.ethw.org/w/images/6/66/Shirriff_8087_two_bit_transistors.pdf;
                 https://www.righto.com/2018/09/two-bits-per-transistor-high-density.html",
  acknowledgement = ack-nhfb,
}

@Misc{Trader:2018:ICS,
  author =       "Tiffany Trader",
  title =        "Inventor Claims to Have Solved Floating Point Error
                 Problem",
  howpublished = "HPC Web site.",
  day =          "17",
  month =        jan,
  year =         "2018",
  bibdate =      "Fri Mar 23 19:13:03 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "From the HPC editor: ``After this article was
                 published, a number of readers raised concerns about
                 the originality of Jorgensen's techniques, noting the
                 existence of prior art going back years. Specifically,
                 there is precedent in John Gustafson's work on unums
                 and interval arithmetic both at Sun and in his 2015
                 book, \booktitle{The End of Error}, which was published
                 19 months before Jorgensen's patent application was
                 filed. ''",
  URL =          "https://www.hpcwire.com/2018/01/17/inventor-claims-solved-floating-point-error-problem/",
  acknowledgement = ack-nhfb,
}

@Article{Villalba-Moreno:2018:FHF,
  author =       "Julio Villalba-Moreno and Javier Hormigo and Sonia
                 Gonz{\'a}lez-Navarro",
  title =        "Fast {HUB} Floating-point Adder for {FPGA}",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
  volume =       "66",
  number =       "6",
  pages =        "1028--1032",
  month =        jun,
  year =         "2018",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1109/TCSII.2018.2873194",
  ISSN =         "1549-7747 (print), 1558-3791 (electronic)",
  ISSN-L =       "1549-7747",
  bibdate =      "Mon Feb 10 08:25:14 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/document/8477084",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Circuits Syst., II Express Briefs",
  fjournal =     "IEEE Transactions on Circuits and Systems II: Express
                 Briefs",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
  keywords =     "HUB (Half-Unit-Biased) floating-point format",
}

@Article{Villalba-Moreno:2018:URH,
  author =       "Julio Villalba-Moreno and Javier Hormigo and Sonia
                 Gonz{\'a}lez-Navarro",
  title =        "Unbiased Rounding for {HUB} Floating-Point Addition",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "67",
  number =       "9",
  pages =        "1359--1365",
  month =        sep,
  year =         "2018",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2018.2807429",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Mar 15 08:10:13 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/document/8300633/",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "HUB (Half-Unit-Biased) floating-point format",
}

@Article{Walczyk:2018:IAF,
  author =       "Cezary J. Walczyk and Leonid V. Moroz and Jan L.
                 Cie{\'s}li{\'n}ski",
  title =        "Improving the accuracy of the fast inverse square root
                 algorithm",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--21",
  day =          "17",
  month =        feb,
  year =         "2018",
  DOI =          "https://doi.org/10.48550/arXiv.1802.06302",
  bibdate =      "Wed Dec 20 07:55:45 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/abs/1802.06302",
  abstract =     "We present improved algorithms for fast calculation of
                 the inverse square root for single-precision
                 floating-point numbers. The algorithms are much more
                 accurate than the famous fast inverse square root
                 algorithm and have the same or similar computational
                 cost. The main idea of our work consists in modifying
                 the Newton-Raphson method and demanding that the
                 maximal error is as small as possible. Such
                 modification is possible when the distribution of
                 Newton-Raphson corrections is not symmetric (e.g., if
                 they are non-positive functions).",
  acknowledgement = ack-nhfb,
}

@InProceedings{Wang:2018:TDN,
  author =       "Naigang Wang and Jungwook Choi and Daniel Brand and
                 Chia-Yu Chen and Kailash Gopalakrishnan",
  editor =       "S. Bengio and others",
  booktitle =    "{Proceedings of the 32nd Conference on Neural
                 Information Processing Systems (NeurIPS 2018),
                 Montr{\'e}al, Canada}",
  title =        "Training {Deep Neural Networks} with 8-bit Floating
                 Point Numbers",
  publisher =    "Curran Associates, Inc.",
  address =      "????",
  pages =        "7675--7684",
  year =         "2018",
  bibdate =      "Wed Dec 19 19:17:48 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/abs/1812.08011;
                 https://papers.nips.cc/paper/7994-training-deep-neural-networks-with-8-bit-floating-point-numbers.pdf",
  abstract =     "The state-of-the-art hardware platforms for training
                 Deep Neural Networks (DNNs) are moving from traditional
                 single precision (32-bit) computations towards 16 bits
                 of precision in large part due to the high energy
                 efficiency and smaller bit storage associated with
                 using reduced-precision representations. However,
                 unlike inference, training with numbers represented
                 with less than 16 bits has been challenging due to the
                 need to maintain fidelity of the gradient computations
                 during back-propagation. Here we demonstrate, for the
                 first time, the successful training of DNNs using 8-bit
                 floating point numbers while fully maintaining the
                 accuracy on a spectrum of Deep Learning models and
                 datasets. In addition to reducing the data and
                 computation precision to 8 bits, we also successfully
                 reduce the arithmetic precision for additions (used in
                 partial product accumulation and weight updates) from
                 32 bits to 16 bits through the introduction of a number
                 of key ideas including chunk-based accumulation and
                 floating point stochastic rounding. The use of these
                 novel techniques lays the foundation for a new
                 generation of hardware training platforms with the
                 potential for 2--4 $ \times $ improved throughput over
                 today's systems.",
  acknowledgement = ack-nhfb,
  remark =       "The 8-bit floating-point format, FP8, has 1 sign bit,
                 5 exponent bits, and 2 significand bits (1,5,2); the
                 16-bit format, FP16, has 1 sign bit, 6 exponent bits,
                 and 9 significand bits (1,6,9). There is no mention of
                 Infinity, NaN, signed zeros, or FMA operations",
  xxpages =      "1--10",
}

@InProceedings{Yang:2018:OMP,
  author =       "Xiong Yang and Hongbin Zhang and Tianyou Cheng and
                 Xuebin Ni and Chenhao Wu and Huaizhi Zong and Haojian
                 Lu and Zhiguo Lu and Yajing Shen",
  editor =       "{IEEE}",
  booktitle =    "{2018 IEEE International Conference on Intelligence
                 and Safety for Robotics (ISR)}",
  title =        "An Omnidirectional and Movable Palletizing Robot based
                 on Computer Vision Positing",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "423--428",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/IISR.2018.8535688",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Yeshwanth:2018:HSS,
  author =       "Balaji Yeshwanth and Vutukuri Venkatesh and Repala
                 Akhil",
  booktitle =    "{2018 International Conference on Electrical,
                 Electronics, Communication, Computer, and Optimization
                 Techniques (ICEECCOT)}",
  title =        "High-Speed Single Precision Floating Point Multiplier
                 using {CORDIC} Algorithm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "135--141",
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ICEECCOT43722.2018.9001506",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; Clocks; Computer architecture; CORDIC
                 algorithm; Delays; Kogge-Stone adder; Parallel
                 Prefixadder; Pipelines; Routing; Signal processing
                 algorithms; Single precision floating point multiplier;
                 Vedic multiplier",
}

@Article{Zhang:2018:HSA,
  author =       "Yunxiang Zhang and Xiaokun Yang and Lei Wu and Archit
                 Gajjar and Han He",
  title =        "Hierarchical Synthesis of Approximate Multiplier
                 Design for Field-programmable Gate Arrays
                 {(FPGA)-CSRmesh} System",
  journal =      j-INT-J-COMP-APPL,
  volume =       "180",
  number =       "??",
  pages =        "1--7",
  month =        feb,
  year =         "2018",
  CODEN =        "????",
  DOI =          "https://doi.org/10.5120/ijca2018916380",
  ISSN =         "0975-8887",
  ISSN-L =       "0975-8887",
  bibdate =      "Fri Jan 24 09:43:10 MST 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/intjcompappl.bib",
  URL =          "https://www.ijcaonline.org/archives/volume180/number17/29021-2018916380/",
  acknowledgement = ack-nhfb,
  ajournal =     "Intern. J. of Computer Applications",
  articleno =    "17",
  fjournal =     "International Journal of Computer Applications",
  journal-URL =  "https://www.ijcaonline.org/",
}

@InProceedings{Abdelfattah:2019:THP,
  author =       "Ahmad Abdelfattah and Stanimire Tomov and Jack
                 Dongarra",
  booktitle =    "{2019 IEEE/ACM 10th Workshop on Latest Advances in
                 Scalable Algorithms for Large-Scale Systems (ScalA)}",
  title =        "Towards Half-Precision Computation for Complex
                 Matrices: a Case Study for Mixed Precision Solvers on
                 {GPUs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "17--24",
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ScalA49573.2019.00008",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Acceleration; Computer architecture; Graphics
                 processing units; Half precision; Kernel; Libraries;
                 mixed-precision solvers; Standards; Tensor cores FP16
                 arithmetic; Tensors",
}

@Article{Adams:2019:RRP,
  author =       "Ulf Adams",
  title =        "{Ry{\=u}} revisited: {\tt printf} floating point
                 conversion",
  journal =      j-PACMPL,
  volume =       "3",
  number =       "OOPSLA",
  pages =        "169:1--169:23",
  month =        oct,
  year =         "2019",
  DOI =          "https://doi.org/10.1145/3360595",
  ISSN =         "2475-1421",
  bibdate =      "Fri Aug 7 19:22:30 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/pacmpl.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3360595",
  abstract =     "Ry{\=u} Printf is a new algorithm to convert
                 floating-point numbers to decimal strings according to
                 the {\tt printf} {\tt \%f}, {\tt \%e}, and {\tt \%g}
                 formats: {\tt \%f} generates `full' output (integer
                 part of the input, dot, configurable number of digits),
                 {\tt \%e} generates scientific output (one leading
                 digit, dot, configurable number of digits, exponent),
                 and {\tt \%g} generates the shorter of the two.
                 Ry{\=u}'s Printf is based on the Ry{\=u} algorithm,
                 which converts binary floating-point numbers to the
                 shortest equivalent decimal floating-point
                 representation. We provide quantitative evidence that
                 Ry{\=u} Printf is between 3.8 and 55 times faster than
                 existing {\tt printf} implementations.\par

                 Furthermore, we show that both Ry{\=u} and Ry{\=u}
                 Printf generalize to arbitrary number bases. This
                 finding implies the existence of a fast algorithm to
                 convert from base-10 to base-2, as long as the maximum
                 precision of the input is known a priori.",
  acknowledgement = ack-nhfb,
  articleno =    "169",
  fjournal =     "Proceedings of the ACM on Programming Languages",
  journal-URL =  "https://pacmpl.acm.org/",
  keywords =     "base conversion",
}

@Misc{Adams:2019:URP,
  author =       "Ulf Adams and Stephan T. Lavavej and Alexander Bolz
                 and Vinnie Falco and David Tolnay and Mitchell {Blank,
                 Jr.} and Mara Bos and Caleb Spare and Alexander Iljin",
  title =        "{ulfjack\slash ryu}: Printf Support",
  howpublished = "Web site",
  day =          "12",
  month =        aug,
  year =         "2019",
  DOI =          "https://doi.org/10.5281/zenodo.3366212",
  bibdate =      "Sun Aug 16 18:37:00 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/java2010.bib",
  URL =          "https://github.com/ulfjack/ryu/tree/v2.0;
                 https://zenodo.org/record/3366212",
  abstract =     "This project contains C and Java implementation of
                 Ryu, as well as a C implementation of Ryu Printf. Ryu
                 converts a floating point number to its shortest
                 decimal representation, whereas Ryu Printf converts a
                 floating point number according to the printf \%f or
                 \%e format. At the time of this writing, these are the
                 fastest known float-to-string conversion algorithms. We
                 have tested the code on Ubuntu 19.04, MacOS Mojave, and
                 Windows 10.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Agrawal:2019:DBF,
  author =       "Ankur Agrawal and Silvia M. Mueller and Bruce M.
                 Fleischer and Xiao Sun and Naigang Wang and Jungwook
                 Choi and Kailash Gopalakrishnan",
  title =        "{DLFloat}: A 16-b Floating Point Format Designed for
                 Deep Learning Training and Inference",
  crossref =     "Takagi:2019:ISC",
  pages =        "92--95",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00023",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The resilience of Deep Learning (DL) training and
                 inference workloads to low-precision computations,
                 coupled with the demand for power-and area-efficient
                 hardware accelerators for these workloads, has led to
                 the emergence of 16-bit floating point formats as the
                 precision of choice for DL hardware accelerators. This
                 paper describes our optimized 16-bit format that has 6
                 exponent bits and 9 fraction bits, derived from a study
                 of the range of values encountered in DL applications.
                 We demonstrate that our format preserves the accuracy
                 of DL networks, and we compare its ease-of-use for DL
                 against IEEE-754 half-precision (5 exponent bits and 10
                 fraction bits) and bfloat16 (8 exponent bits and 7
                 fraction bits). Further, our format eliminated
                 sub-normals and simplifies rounding modes and handling
                 of corner cases. This streamlines floating-point unit
                 logic and enables realization of a compact
                 power-efficient computation engine.",
  acknowledgement = ack-nhfb,
  keywords =     "16-b floating point format; 16-bit floating point
                 formats; Adders; ARITH-26; compact power-efficient
                 computation engine; Deep learning; deep learning
                 training; DL hardware accelerators; Dynamic range;
                 Engines; floating point arithmetic; floating-point unit
                 logic; Hardware; IEEE-754 half-precision; Image
                 recognition; learning (artificial intelligence);
                 low-precision computations; neural nets; power-and
                 area-efficient hardware accelerators; reduced precision
                 computation, floating point, machine learning, deep
                 learning; streamlines floating-point unit logic;
                 Training",
  remark =       "The DLFloat format has a 1-bit sign, 6-bit exponent,
                 and 10-bit normalized significand including the hidden
                 leading one-bit. Subnormals are not supported, and
                 underflows flush to zero. Infinity and NaN are fused
                 into a single value with the largest exponent and
                 significand; other significands with that exponent are
                 normal numbers. Zero and Inf-NaN are considered to be
                 unsigned. There is only one rounding mode:
                 round-nearest-up. Fused multiply-add (FMA) is
                 supported.",
}

@InProceedings{Anderson:2019:SAM,
  author =       "Andrew Anderson and Michael Doyle and David Gregg",
  title =        "Scalar Arithmetic Multiple Data: Customizable
                 Precision for Deep Neural Networks",
  crossref =     "Takagi:2019:ISC",
  pages =        "61--68",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00018",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Quantization of weights and activations in Deep Neural
                 Networks (DNNs) is a powerful technique for network
                 compression, and has enjoyed significant attention and
                 success. However, much of the inference-time benefit of
                 quantization is accessible only through customized
                 hardware accelerators or with an FPGA implementation of
                 quantized arithmetic. Building on prior work, we show
                 how to construct very fast implementations of arbitrary
                 bit-precise signed and unsigned integer operations
                 using a software technique which logically embeds a
                 vector architecture with custom bit-width lanes in
                 fixed-width scalar arithmetic. At the strongest level
                 of quantization, our approach yields a maximum speedup
                 of $ \approx 6 \% $ on an x86 platform, and $ \approx
                 10 \% $ on an ARM platform versus quantization to
                 native 8-bit integers.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-26; bit-width lanes; Computer architecture;
                 Custom Arithmetic; Deep Neural Networks; digital
                 arithmetic; Field programmable gate arrays; field
                 programmable gate arrays; fixed-width scalar
                 arithmetic; FPGA implementation; Hardware; hardware
                 accelerators; Machine Learning; network compression;
                 neural nets; Program processors; quantisation (signal);
                 quantization; Quantization (signal); quantized
                 arithmetic; Registers; scalar arithmetic multiple data;
                 Software Performance; software technique; vectors",
}

@InProceedings{Andrlon:2019:OBF,
  author =       "Mak Andrlon and Peter Schachte and Harald
                 S{\o}ndergaard and Peter J. Stuckey",
  title =        "Optimal Bounds for Floating-Point Addition in Constant
                 Time",
  crossref =     "Takagi:2019:ISC",
  pages =        "159--166",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00038",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Reasoning about floating-point numbers is notoriously
                 difficult, owing to the lack of convenient algebraic
                 properties such as associativity. This poses a
                 substantial challenge for program analysis and
                 verification tools which rely on precise floating-point
                 constraint solving. Currently, interval methods in this
                 domain often exhibit slow convergence even on simple
                 examples. We present a new theorem supporting efficient
                 computation of exact bounds of the intersection of a
                 rectangle with the preimage of an interval under
                 floating-point addition, in any radix or rounding mode.
                 We thus give an efficient method of deducing optimal
                 bounds on the components of an addition, solving the
                 convergence problem.",
  acknowledgement = ack-nhfb,
  keywords =     "addition; arbitrary radix; ARITH-26; Australia; bound
                 analysis; constant time; constraint handling;
                 convenient algebraic properties; Convergence; Digital
                 arithmetic; exact bounds; floating point arithmetic;
                 floating-point addition; Floating-point arithmetic;
                 floating-point numbers; Information systems; interval
                 methods; optimal bounds; precise floating-point
                 constraint solving; program analysis; radix mode;
                 rounding mode; Software; Standards",
}

@Article{Anonymous:2019:CPC,
  author =       "Anonymous",
  title =        "Computational `pathology' could hamper climate and
                 fusion simulations",
  journal =      j-PHYS-WORLD,
  day =          "26",
  month =        sep,
  year =         "2019",
  CODEN =        "PHWOEW",
  ISSN =         "0953-8585 (print), 2058-7058 (electronic)",
  bibdate =      "Mon Sep 30 11:21:38 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Boghosian:2019:NPS}.",
  URL =          "https://physicsworld.com/a/computational-pathology-could-hamper-climate-and-fusion-simulations/",
  acknowledgement = ack-nhfb,
  fjournal =     "Physics World",
  journal-URL =  "http://physicsworldarchive.iop.org/",
}

@Misc{Anonymous:2019:MCT,
  author =       "Anonymous",
  title =        "Multiprecision Computing Toolbox for {MATLAB}",
  howpublished = "Web site",
  day =          "26",
  month =        sep,
  year =         "2019",
  bibdate =      "Tue Nov 05 15:46:16 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  URL =          "https://www.advanpix.com/",
  acknowledgement = ack-nhfb,
}

@Misc{Anonymous:2019:RMV,
  author =       "Anonymous",
  title =        "{Realtime Math v1.0} Open Sourced",
  howpublished = "Web site",
  day =          "19",
  month =        jan,
  year =         "2019",
  bibdate =      "Tue Jan 22 16:00:13 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.gamedev.net/news/realtime-math-v10-open-sourced-r740/",
  acknowledgement = ack-nhfb,
  remark =       "From the Web site: ``Realtime Math \ldots{} consists
                 entirely of C++11 headers, it runs almost everywhere,
                 it supports 64 bit floating point arithmetic, and it
                 sports a very permissive MIT license.''",
}

@Misc{Anonymous:2019:SOL,
  author =       "Anonymous",
  title =        "{SiSoftware} Official Live Ranker: Top Processor
                 Arithmetic Ranks",
  howpublished = "Web site",
  year =         "2019",
  bibdate =      "Fri May 24 07:49:33 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Floating-point performance ranking of more than 94,500
                 CPU models.",
  acknowledgement = ack-nhfb,
  remark =       "In May 2019, the top 15 entries were Intel Xeon
                 X-3175X and AMD Ryzen Threadripper CPUs.",
}

@Misc{Anonymous:2019:UFP,
  author =       "Anonymous",
  title =        "Universal floating-point instruction set architecture,
                 method, and language for computing directly with
                 decimal character sequences and binary formats in any
                 combination",
  howpublished = "Attorney Docket No. 6324-5986",
  pages =        "136",
  day =          "14",
  month =        aug,
  year =         "2019",
  bibdate =      "Fri Aug 30 07:24:55 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://drive.google.com/file/d/1-gx_P5vBRppa6T3rdv8h6RNXz2Q_ILwg/view;
                 https://drive.google.com/file/d/1fOhVAwdhiebumKkgljKfLqyOaFpUDhQL/view",
  abstract =     "A universal floating-point Instruction Set
                 Architecture (ISA) and associated method and language.
                 Using a single instruction, the universal
                 floating-point ISA has the ability, in hardware, to
                 compute directly with dual decimal character sequences
                 up to IEEE 754-2008 ``H'' in length, without first
                 having to explicitly perform a
                 conversion-to-binary-format process in software before
                 computing with these human-readable floating-point or
                 integer representations. The ISA does not employ
                 opcodes, but rather pushes and pulls ``gobs'' of data
                 without the encumbering opcode fetch, decode, and
                 execute bottleneck. Instead, the ISA employs
                 stand-alone, memory-mapped operators, complete with
                 their own pipeline that is completely decoupled from
                 the processor's primary push-pull pipeline. The ISA
                 employs special three-port, 1024-bit wide SRAMS; a
                 special dual asymmetric system stack; memory-mapped
                 stand-alone hardware operators with private result
                 buffers having simultaneously readable side-A and
                 side-B read ports; and dual hardware
                 HconvertFromDecimalCharacter conversion operators.",
  acknowledgement = ack-nhfb,
}

@Misc{Anonymous:2019:YAF,
  author =       "Anonymous",
  title =        "Yet another floating point tutorial",
  howpublished = "Web site",
  year =         "2019",
  bibdate =      "Fri May 17 07:24:35 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://wordsandbuttons.online/yet_another_floating_point_tutorial.html",
  acknowledgement = ack-nhfb,
}

@InProceedings{Arnold:2019:UOD,
  author =       "Mark G. Arnold and Ioannis Kouretas and Vassilis
                 Paliouras and John R. Cowles",
  title =        "Under- and Overflow Detection in the Residue
                 Logarithmic Number System",
  crossref =     "Takagi:2019:ISC",
  pages =        "112--115",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00030",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Residue Number System (RNS) offers fast and cheap
                 carry-free integer arithmetic but has slow and
                 expensive overflow detection. The Logarithmic Number
                 System (LNS) offers fast real multiplication, division
                 and powers with floating-point-like relative precision.
                 The Residue Logarithmic Number System (RLNS) is a
                 combination of the two systems that offers advantages
                 for moderate-precision real applications where a-priori
                 analysis allows under-and overflow to be ignored. An
                 arithmetic hardware generator is essential because of
                 the mathematical obscurity of combining RNS and LNS.
                 Unfortunately, real applications often underflow. We
                 consider options to deal with under-and overflow using
                 the RLNSTool generator as a foundation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-26; Arithmetic Generator; carry-free integer
                 arithmetic; Computational modeling; Delays; Digital
                 arithmetic; dividing circuits; expensive overflow
                 detection; fast carry-free integer arithmetic; floating
                 point arithmetic; floating-point-like relative
                 precision; Generators; Hardware; Hardware design
                 languages; LNS; moderate-precision real applications;
                 multiplying circuits; number theory; Overflow; Residue
                 Logarithmic Number System; residue number systems; RNS;
                 Wires",
}

@InProceedings{Arzelier:2019:EAE,
  author =       "Denis Arzelier and Florent Br{\'e}hard and Mioara
                 Joldes",
  title =        "Exchange Algorithm for Evaluation and Approximation
                 Error-Optimized Polynomials",
  crossref =     "Takagi:2019:ISC",
  pages =        "30--37",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00014",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Machine implementation of mathematical functions often
                 relies on polynomial approximations. The particularity
                 is that rounding errors occur both when representing
                 the polynomial coefficients on a finite number of bits,
                 and when evaluating it in finite precision. Hence, for
                 finding the best polynomial (for a given fixed degree,
                 norm and interval), one has to consider both types of
                 errors: approximation and evaluation. While efficient
                 algorithms were already developed for taking into
                 account the approximation error, the evaluation part is
                 usually a posteriori handled, in an ad-hoc manner.
                 Here, we formulate a semi-infinite linear optimization
                 problem whose solution is the best polynomial with
                 respect to the supremum norm of the sum of both errors.
                 This problem is then solved with an iterative exchange
                 algorithm, which can be seen as an extension of the
                 well-known Remez algorithm. A discussion and comparison
                 of the obtained results on different examples are
                 finally presented.",
  acknowledgement = ack-nhfb,
  keywords =     "Approximation algorithms; Approximation error;
                 approximation error; approximation error-optimized
                 polynomials; ARITH-26; Digital arithmetic; evaluation
                 error; exchange algorithm; function approximation;
                 Indexes; Input variables; iterative exchange algorithm;
                 iterative methods; learning (artificial intelligence);
                 libm; linear programming; machine implementation;
                 mathematical functions; mathematics computing;
                 optimisation; Optimization; polynomial approximation;
                 polynomial approximations; polynomial coefficients;
                 Programming; remez algorithm; Remez algorithm;
                 semi-infinite programming; semiinfinite linear
                 optimization problem",
}

@Misc{Bailey:2019:AM,
  author =       "David H. Bailey",
  title =        "An $ n \log (n) $ algorithm for multiplication",
  howpublished = "Math Scholar blog",
  day =          "12",
  month =        apr,
  year =         "2019",
  bibdate =      "Fri Apr 12 14:14:40 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://mathscholar.org/2019/04/an-n-log-n-algorithm-for-multiplication/",
  acknowledgement = ack-nhfb,
  remark =       "Description of research in \cite{Harvey:2019:IMT}.",
}

@InProceedings{Barthel:2019:SAM,
  author =       "Moritz B{\"a}rthel and Pascal Seidel and Jochen Rust
                 and Steffen Paul",
  booktitle =    "{2019 17th IEEE International New Circuits and Systems
                 Conference (NEWCAS)}",
  title =        "{SORN} Arithmetic for {MIMO} Symbol Detection ---
                 Exploration of the {Type-2} Unum Format",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--4",
  year =         "2019",
  DOI =          "https://doi.org/10.1109/NEWCAS44328.2019.8961226",
  bibdate =      "Fri Dec 15 07:38:18 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Beame:2019:TVN,
  author =       "Paul Beame and Vincent Liew",
  title =        "Toward Verifying Nonlinear Integer Arithmetic",
  journal =      j-J-ACM,
  volume =       "66",
  number =       "3",
  pages =        "22:1--22:??",
  month =        jun,
  year =         "2019",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/3319396",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Wed Oct 23 06:51:06 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jacm.bib",
  URL =          "https://dl.acm.org/ft_gateway.cfm?id=3319396",
  abstract =     "We eliminate a key roadblock to efficient verification
                 of nonlinear integer arithmetic using CDCL SAT solvers,
                 by showing how to construct short resolution proofs for
                 many properties of the most widely used multiplier
                 circuits. Such short proofs were conjectured not to
                 exist. More precisely, we give $ n^{O (1)} $ size
                 regular resolution proofs for arbitrary degree $2$
                 identities on array, diagonal, and Booth multipliers
                 and $ n^{O(\log n)}$ size proofs for these identities
                 on Wallace tree multipliers.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  articleno =    "22",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}

@Article{Bellal:2019:IAA,
  author =       "R. Bellal and E. Lamini and H. Belbachir and S.
                 Tagzout and A. Belouchrani",
  title =        "Improved Affine Arithmetic-Based Precision Analysis
                 for Polynomial Function Evaluation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "68",
  number =       "5",
  pages =        "702--712",
  month =        may,
  year =         "2019",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2018.2882537",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 11 09:46:20 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "affine arithmetic; affine arithmetic-based precision
                 analysis; Compounds; degree-n polynomial Horner's rule;
                 design phase; enhanced precision analysis; error
                 propagating formula; fixed point arithmetic;
                 Fixed-point arithmetic; fixed-point numbers; Hardware;
                 hardware function evaluation; hardware implementations;
                 hardware resources; Interpolation; iterative methods;
                 optimisation; Optimization; polynomial approximation;
                 polynomial function evaluation; polynomials; precision
                 analysis; quantisation (signal); Quantization (signal);
                 quantization error; Resource management; table lookup;
                 tighter upper bound error; Upper bound; VLSI systems;
                 word-length allocation; word-length optimization",
}

@TechReport{Blanchard:2019:MPB,
  author =       "Pierre Blanchard and Nicholas J. Higham and Florent
                 Lopez and Theo Mary and Srikara Pranesh",
  title =        "Mixed Precision Block Fused Multiply-Add: Error
                 Analysis and Application to {GPU} Tensor Cores",
  type =         "MIMS EPrint",
  number =       "2019.18",
  institution =  "Manchester Institute for Mathematical Sciences, School
                 of Mathematics, The University of Manchester",
  address =      "Manchester, UK",
  day =          "24",
  month =        sep,
  year =         "2019",
  ISSN =         "1749-9097",
  bibdate =      "Thu Dec 05 10:14:37 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://eprints.maths.manchester.ac.uk/2733/;
                 https://en.wikipedia.org/wiki/Bfloat16_floating-point_format",
  abstract =     "Computing units that carry out a fused multiply-add
                 (FMA) operation with matrix arguments, referred to as
                 tensor units by some vendors, have great potential for
                 use in scientific computing. However, these units are
                 inherently mixed precision and existing rounding error
                 analyses do not support them. We consider a mixed
                 precision block FMA that generalizes both the usual
                 scalar FMA and existing tensor units. We describe how
                 to exploit such a block FMA in the numerical linear
                 algebra kernels of matrix multiplication and LU
                 factorization and give rounding error analyses of both
                 kernels. An important application is to GMRES-based
                 iterative refinement with block FMAs, for which our
                 analysis provides new insight. Our framework is
                 applicable to the tensor core units in the NVIDIA Volta
                 and Turing GPUs. For these we compare matrix
                 multiplication and LU factorization with TC16 and TC32
                 forms of FMA, which differ in the precision used for
                 the output of the tensor cores. Our experiments on an
                 NVDIA V100 GPU confirm the predictions of the analysis
                 that the TC32 variant is much more accurate than the
                 TC16 one, while achieving almost the same
                 performance.",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; fused multiply-add; LU
                 factorization; matrix multiplication; rounding error
                 analysis, NVIDIA GPU; tensor cores",
}

@InProceedings{Bocco:2019:BAF,
  author =       "Andrea Bocco and Tiago T. Jost and Albert Cohen and
                 Florent de Dinechin and Yves Durand and Christian
                 Fabre",
  booktitle =    "{2019 IFIP/IEEE 27th International Conference on Very
                 Large Scale Integration (VLSI-SoC)}",
  title =        "Byte-Aware Floating-point Operations through a {UNUM}
                 Computing Unit",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "323--328",
  year =         "2019",
  DOI =          "https://doi.org/10.1109/VLSI-SoC.2019.8920387",
  bibdate =      "Fri Dec 15 07:38:18 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bocco:2019:DPN,
  author =       "Andrea Bocco and Yves Durand and Florent de Dinechin",
  title =        "Dynamic Precision Numerics Using a Variable-Precision
                 {UNUM Type I HW} Coprocessor",
  crossref =     "Takagi:2019:ISC",
  pages =        "104--107",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00028",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A very large internal accumulation register has been
                 proposed to increase the accuracy of scientific code.
                 However, there is a general class of iterative kernels
                 where a vector of high-precision data must be saved
                 from one iteration to the next. Saving the large
                 internal accumulator to memory is impractical in such
                 cases. This work proposes a Variable Precision (VP)
                 Floating Point (FP) arithmetic co-processor
                 architecture based on RISC-V, which 1/ supports legacy
                 IEEE formats for input and output variables, 2/ uses
                 variable length internal registers (up to 512 bits of
                 mantissa) for inner loop multiply-add and 3/ supports
                 loads and stores of intermediate results to cache
                 memory with a dynamically adjustable precision (up to
                 256 bits of mantissa). It exploits the UNUM type I
                 floating point format, proposing solutions to address
                 some of its pitfalls such as the variable latency of
                 the internal operation, and the variable memory
                 footprint of the intermediate variables. This work is
                 integrated on FPGA and demonstrated on a representative
                 example.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-26; Arrays; cache storage; Computational
                 modeling; coprocessors; Coprocessors; dynamic Precision
                 numerics; field programmable gate arrays; floating
                 point arithmetic; floating point arithmetic
                 co-processor architecture; FPGA; internal accumulation
                 register; iterative kernels; iterative methods; Kernel;
                 Programming; reduced instruction set computing;
                 Registers; RISC-V; Variable Precision; Variable
                 precision, Floating-point, UNUM, Scientific computing,
                 Instruction set design, Hardware architecture, RISC-V,
                 Coprocessor, Multiple precision, FPGA, ASIC;
                 variable-precision UNUM Type I HW coprocessor",
}

@InProceedings{Bocco:2019:SSM,
  author =       "Andrea Bocco and Yves Durand and Florent de Dinechin",
  title =        "{SMURF}: {Scalar Multiple-precision Unum RISC-V
                 Floating-point} Accelerator for Scientific Computing",
  crossref =     "Gustafson:2019:CPC",
  pages =        "1:1--1:8",
  year =         "2019",
  DOI =          "https://doi.org/10.1145/3316279.3316280",
  bibdate =      "Mon Feb 10 09:31:49 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  URL =          "https://hal.inria.fr/hal-02087098",
  abstract =     "This paper proposes an innovative Floating Point (FP)
                 architecture for Variable Precision (VP) computation
                 suitable for high precision FP computing, based on a
                 refined version of the UNUM type I format. This
                 architecture supports VP FP intervals where each
                 interval endpoint can have up to 512 bits of mantissa.
                 The proposed hardware architecture is pipelined and has
                 an internal word-size of 64 bits. Computations on
                 longer mantissas are performed iteratively on the
                 existing hardware. The prototype is integrated in a
                 RISC-V environment, it is exposed to the user through
                 an instruction set extension. The paper we provide an
                 example of software usage. The system has been
                 prototyped on a FPGA (Field-Programmable Gate Array)
                 platform and also synthesized for a 28nm FDSOI process
                 technology. The respective working frequency of FPGA
                 and ASIC implementations are 50MHz and 600MHz. The
                 estimated chip area is 1.5mm 2 and the estimated power
                 consumption is 95mW. The flops performance of this
                 architecture remains within the range of a regular
                 fixed-precision IEEE FPU while enabling arbitrary
                 precision computation at reasonable cost.",
  acknowledgement = ack-nhfb,
  articleno =    "1",
  keywords =     "ASIC, UNUM, Floating-point, RISC-V, Coprocessor,
                 Instruction set design, Variable precision, Scientific
                 computing, Hardware architecture, Multiple precision,
                 FPGA",
}

@Article{Boghosian:2019:NPS,
  author =       "Bruce M. Boghosian and Peter V. Coveney and Hongyan
                 Wang",
  title =        "A New Pathology in the Simulation of Chaotic Dynamical
                 Systems on Digital Computers",
  journal =      j-ADV-THEORY-SIMUL,
  pages =        "1900125",
  month =        sep,
  year =         "2019",
  CODEN =        "ATSDCW",
  DOI =          "https://doi.org/10.1002/adts.201900125",
  ISSN =         "2513-0390",
  bibdate =      "Tue Sep 24 05:31:42 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also news releases
                 \cite{Caygill:2019:NLH,Caygill:2019:DCF,Silver:2019:CCN,Anonymous:2019:CPC,Dockrill:2019:CMH,Grossman:2019:CSC}.",
  URL =          "https://onlinelibrary.wiley.com/journal/25130390",
  abstract =     "Systematic distortions are uncovered in the
                 statistical properties of chaotic dynamical systems
                 when represented and simulated on digital computers
                 using standard IEEE floating-point numbers. This is
                 done by studying a model chaotic dynamical system with
                 a single free parameter $ \beta $, known as the
                 generalized Bernoulli map, many of whose exact
                 properties are known. Much of the structure of the
                 dynamical system is lost in the floating-point
                 representation. For even integer values of the
                 parameter, the long time behaviour is completely wrong,
                 subsuming the known anomalous behaviour for $ \beta = 2
                 $. For non-integer $ \beta $, relative errors in
                 observables can reach 14\%. For odd integer values of $
                 \beta $, floating-point results are more accurate, but
                 still produce relative errors two orders of magnitude
                 larger than those attributable to roundoff. The
                 analysis indicates that the pathology described, which
                 cannot be mitigated by increasing the precision of the
                 floating point numbers, is a representative example of
                 a deeper problem in the computation of expectation
                 values for chaotic systems. The findings sound a
                 warning about the uncritical application of numerical
                 methods in studies of the statistical properties of
                 chaotic dynamical systems, such as are routinely
                 performed throughout computational science, including
                 turbulence and molecular dynamics.",
  acknowledgement = ack-nhfb,
  ajournal =     "Adv. Theory Simul.",
  fjournal =     "Advanced Theory and Simulations",
  journal-URL =  "https://onlinelibrary.wiley.com/journal/25130390",
  remark =       "This study demonstrates the perils of computing with
                 too few significant digits in the floating-point
                 representation. However, the authors report: ``Though
                 the root of this problem resides in the use of
                 finite-precision floating-point arithmetic, it cannot
                 be mitigated by increasing the precision of the
                 floating-point representation. Our analysis strongly
                 suggests that the pathology we describe will exhibit
                 for mantissa and exponent fields of any finite length
                 whatsoever, and for floating-point numbers encoded in
                 any radix whatsoever. Indeed, there is every reason to
                 anticipate that this anomalous behaviour is generic in
                 dissipative chaotic systems of the kind encountered in
                 turbulence and molecular dynamics, and that it is
                 entirely possible that many published results of
                 numerical simulation are substantially inaccurate for
                 this reason.''",
}

@Article{Borges:2019:IAH,
  author =       "Carlos F. Borges",
  title =        "An Improved Algorithm for {\tt hypot(a,b)}",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--15",
  day =          "14",
  month =        jun,
  year =         "2019",
  bibdate =      "Fri Apr 19 05:40:55 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/abs/1904.09481",
  abstract =     "We develop a fast and accurate algorithm for
                 evaluating $ \sqrt {x^2 + y^2} $ for two floating point
                 numbers $a$ and $b$. Library functions that perform
                 this computation are generally named {\tt hypot(a,b)}.
                 We will compare four approaches that we will develop in
                 this paper to the current resident library function
                 that is delivered with Julia 1.1 and to the code that
                 has been distributed with the C math library for
                 decades. We will demonstrate the performance of our
                 algorithms by simulation.",
  acknowledgement = ack-nhfb,
}

@Article{Bos:2019:ACI,
  author =       "J. W. Bos and S. J. Friedberger",
  title =        "Arithmetic Considerations for Isogeny-Based
                 Cryptography",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "68",
  number =       "7",
  pages =        "979--990",
  month =        jul,
  year =         "2019",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2018.2851238",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 11 09:46:20 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "arithmetic; arithmetic considerations; arithmetic
                 techniques; Computer architecture; cryptographic
                 protocols; curve models; digital arithmetic; efficient
                 addition-subtraction chains; efficient arithmetic
                 modulo; efficient chains; elliptic curve scalar
                 multiplication; Elliptic curves; isogeny-based
                 cryptography; Montgomery curves; Montgomery reduction;
                 NIST; Optimization; post-quantum public-key arena;
                 Protocols; Public key cryptography; quadratic extension
                 field; scalar multiplication arithmetic; SIDH setting;
                 special shape; supersingular isogeny Diffie-Hellman
                 key-exchange protocol; systematic overview; twisted
                 Edwards curves",
}

@Misc{Bright:2019:CEN,
  author =       "Peter Bright",
  title =        "{\tt calc.exe} is now open source; there's surprising
                 depth in its ancient code. {The} actual calculation
                 engine is more than 20 years old",
  howpublished = "Web site",
  day =          "7",
  month =        mar,
  year =         "2019",
  bibdate =      "Fri Mar 08 07:46:06 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arstechnica.com/gadgets/2019/03/calc-exe-is-now-open-source-theres-surprising-depth-in-its-ancient-code/;
                 https://github.com/Microsoft/calculator",
  abstract =     "Microsoft's embrace and adoption of open source
                 software has continued with the surprising decision to
                 publish the code for Windows Calculator and release it
                 on GitHub under the permissive MIT license.",
  acknowledgement = ack-nhfb,
}

@Misc{Brown:2019:RCF,
  author =       "Erin Clare Brown",
  title =        "{Rust} and {C++} on Floating-point Intensive Code",
  howpublished = "Web site.",
  day =          "19",
  month =        oct,
  year =         "2019",
  bibdate =      "Fri Oct 25 06:25:15 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://upshed.com/2019/10/24/rust-and-c-on-floating-point-intensive-code/",
  acknowledgement = ack-nhfb,
}

@Article{Bruguera:2019:GEI,
  author =       "J. D. Bruguera and F. de Dinechin",
  title =        "{Guest Editors} Introduction: Special Section on
                 Computer Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "68",
  number =       "7",
  pages =        "951--952",
  month =        jul,
  year =         "2019",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2019.2918447",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 11 09:46:20 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Cryptography; Digital arithmetic; Mathematics;
                 Software algorithms; Special issues and sections",
}

@InProceedings{Bui:2019:VMS,
  author =       "Ngoc-Tu Bui and Trong-Thuc Hoang and Duc-Hung Le and
                 Cong-Kha Pham",
  booktitle =    "{2019 IEEE International Conference on Industrial
                 Technology (ICIT)}",
  title =        "A 0.75-V {32-MHz 181-$ \mu $W} {SOTB-65nm}
                 Floating-point Twiddle Factor Using Adaptive {CORDIC}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "835--840",
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ICIT.2019.8754955",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Decision making; Frequency measurement; Registers;
                 Semiconductor device measurement; Silicon; Table
                 lookup",
}

@InProceedings{Burgess:2019:BPN,
  author =       "Neil Burgess and Jelena Milanovic and Nigel Stephens
                 and Konstantinos Monachopoulos and David Mansell",
  title =        "{Bfloat16} Processing for Neural Networks",
  crossref =     "Takagi:2019:ISC",
  pages =        "88--91",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00022",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Bfloat16 (``BF16'') is a new floating-point format
                 tailored specifically for high-performance processing
                 of Neural Networks and will be supported by major CPU
                 and GPU architectures as well as Neural Network
                 accelerators. This paper proposes a possible
                 implementation of a BF16 multiply-accumulation
                 operation that relaxes several IEEE Floating-Point
                 Standard features to afford low-cost hardware
                 implementations. Specifically, subnorms are flushed to
                 zero; only one non-standard rounding mode (Round-Odd)
                 is supported; NaNs are not propagated; and IEEE
                 exception flags are not provided. The paper shows that
                 this approach achieves the same network-level accuracy
                 as using IEEE single-precision arithmetic (``FP32'')
                 for less than half the datapath area cost and with
                 greater throughput.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-26; Artificial neural networks; BF16
                 multiply-accumulation operation; bfloat16 processing;
                 Computer architecture; CPU architectures; Digital
                 arithmetic; Error analysis; floating point arithmetic;
                 floating-point, rounding mode, neural networks; FP32;
                 GPU architectures; high-performance processing; IEEE
                 exception flags; IEEE floating-point standard features;
                 IEEE single-precision arithmetic; low-cost hardware
                 implementations; network-level accuracy; neural nets;
                 Neural Network accelerators; neural networks;
                 nonstandard rounding mode; Standards; Training",
}

@Article{Burgess:2019:HPA,
  author =       "Neil Burgess and Chris Goodyer and Christopher N.
                 Hinds and David R. Lutz",
  title =        "High-Precision Anchored Accumulators for Reproducible
                 Floating-Point Summation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "68",
  number =       "7",
  pages =        "967--978",
  month =        jul,
  year =         "2019",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2018.2855729",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 11 09:46:20 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "2-lane HPA accumulation; 3-lane reproducible FP
                 summation; accurate floating-point summation;
                 computational properties; Computer architecture;
                 datatype; double double accumulation; Electronic mail;
                 Encoding; existing FP formats; floating point
                 arithmetic; Floating-point addition; floating-point
                 numbers; floating-point summation; FP arithmetic; FP16
                 summations; FP32 summations; FP64 accumulations; FP64
                 operands; Hardware; high-precision anchored
                 accumulators; high-precision anchored number;
                 high-precision computing; HPA processing; Instruction
                 sets; modest ranges; programmer-selectable range;
                 Proposals; Registers; reproducibility; reproducible
                 accumulation; reproducible floating-point summation;
                 scalable vector extension; SVE; vector architecture;
                 vector processing",
}

@Article{Cappello:2019:UCL,
  author =       "Franck Cappello and Sheng Di and Sihuan Li and Xin
                 Liang and Ali Murat Gok and Dingwen Tao and Chun Hong
                 Yoon and Xin-Chuan Wu and Yuri Alexeev and Frederic T.
                 Chong",
  title =        "Use cases of lossy compression for floating-point data
                 in scientific data sets",
  journal =      j-IJHPCA,
  volume =       "33",
  number =       "6",
  pages =        "1201--1220",
  day =          "1",
  month =        nov,
  year =         "2019",
  CODEN =        "IHPCFL",
  DOI =          "https://doi.org/10.1177/1094342019853336",
  ISSN =         "1094-3420 (print), 1741-2846 (electronic)",
  ISSN-L =       "1094-3420",
  bibdate =      "Wed Oct 9 14:35:54 MDT 2019",
  bibsource =    "http://hpc.sagepub.com/;
                 https://www.math.utah.edu/pub/tex/bib/datacompression.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijsa.bib",
  URL =          "https://journals.sagepub.com/doi/full/10.1177/1094342019853336",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of High Performance Computing
                 Applications",
  journal-URL =  "https://journals.sagepub.com/home/hpc",
}

@Misc{Carlough:2019:DBF,
  author =       "Steven R. Carlough and Juergen Haess and Michael Klein
                 and Klaus M. Kroener and Petra Leber and Silvia M.
                 Mueller and Kerstin Schelm",
  title =        "Decimal and binary floating point arithmetic
                 calculations",
  howpublished = "US Patent 10,416,962",
  day =          "17",
  month =        sep,
  year =         "2019",
  bibdate =      "Thu Oct 17 11:29:24 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://patents.google.com/patent/US10416962B2",
  abstract =     "Logic is provided for performing decimal and binary
                 floating point arithmetic calculations on first and
                 second operands. The method includes: receiving the
                 first and second operands in packed format; unpacking
                 the first and second operands; swapping the first
                 operand to a fourth operand and the second operand to a
                 third operand, if an exponent of the first operand is
                 less than an exponent of the second operand, otherwise
                 storing the first operand to the third operand and the
                 second operand to the fourth operand; aligning the
                 third operand and the fourth operands based on the
                 exponent difference of the third and fourth operand and
                 a number of leading zeroes of the third operand;
                 performing an add/subtract operation on the aligned
                 third and fourth operands with normalizing and rounding
                 between the operands; and packing the result obtained
                 from the add/subtract.",
  acknowledgement = ack-nhfb,
  remark =       "Patent filed 2 October 2015 based on British patent
                 GB1417582.2 of 6 October 2014, granted 17 September
                 2019 to IBM, expected expiration 11 January 2036 (in
                 17th year after grant).",
}

@InProceedings{Carmichael:2019:DPD,
  author =       "Zachariah Carmichael and Hamed F. Langroudi and Char
                 Khazanov and Jeffrey Lillie and John L. Gustafson and
                 Dhireesha Kudithipudi",
  editor =       "{IEEE}",
  booktitle =    "{2019 Design, Automation \& Test in Europe Conference
                 \& Exhibition (DATE)}",
  title =        "{Deep Positron}: a Deep Neural Network Using the Posit
                 Number System",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1421--1426",
  year =         "2019",
  DOI =          "https://doi.org/10.23919/DATE.2019.8715262",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Carmichael:2019:PET,
  author =       "Zachariah Carmichael and Hamed F. Langroudi and Char
                 Khazanov and Jeffrey Lillie and John L. Gustafson and
                 Dhireesha Kudithipudi",
  title =        "Performance-Efficiency Trade-off of Low-Precision
                 Numerical Formats in Deep Neural Networks",
  crossref =     "Gustafson:2019:CPC",
  pages =        "3:1--3:9",
  year =         "2019",
  DOI =          "https://doi.org/10.1145/3316279.3316282",
  bibdate =      "Mon Feb 10 12:11:16 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  articleno =    "3",
  keywords =     "machine learning, deep neural networks, floating
                 point, posit numerical format, DNN accelerators,
                 tapered precision, low-precision",
  location =     "Singapore, Singapore",
  numpages =     "9",
}

@Misc{Caygill:2019:DCF,
  author =       "Rebecca Caygill",
  title =        "Digital Computers Fail to Accurately Model Chaos
                 Because of Fundamental Numbers Limit",
  howpublished = "University College London news release.",
  day =          "23",
  month =        sep,
  year =         "2019",
  bibdate =      "Tue Sep 24 05:29:26 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Boghosian:2019:NPS}.",
  URL =          "https://scitechdaily.com/digital-computers-fail-to-accurately-model-chaos-because-of-fundamental-numbers-limit/",
  acknowledgement = ack-nhfb,
}

@Misc{Caygill:2019:NLH,
  author =       "Rebecca Caygill",
  title =        "Numbers limit how accurately digital computers model
                 chaos",
  howpublished = "University College London news release.",
  day =          "23",
  month =        sep,
  year =         "2019",
  bibdate =      "Tue Sep 24 05:29:26 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Boghosian:2019:NPS}.",
  URL =          "https://www.eurekalert.org/pub_releases/2019-09/ucl-nlh092019.php",
  acknowledgement = ack-nhfb,
}

@Article{Chen:2019:EIR,
  author =       "K. Chen and L. Chen and P. Reviriego and F. Lombardi",
  title =        "Efficient Implementations of Reduced Precision
                 Redundancy ({RPR}) Multiply and Accumulate ({MAC})",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "68",
  number =       "5",
  pages =        "784--790",
  month =        may,
  year =         "2019",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2018.2885044",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 11 09:46:20 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Adders; arithmetic circuits; circuit overhead;
                 computational environments; critical systems; deep
                 machine learning; digital arithmetic; Discrete cosine
                 transforms; error correction; error correction
                 capabilities; error correction codes; implementation
                 overhead; learning (artificial intelligence); MAC
                 implementations; MAC operation; Machine learning;
                 matrix multiplication; Mean Square Error; mean square
                 error methods; modern computing systems; multiply and
                 accumulate; neural networks; Neural networks; object
                 recognition; precision copies; reduced precision
                 redundancy; redundancy; Redundancy; RPR
                 implementations; signed integer multiplication; soft
                 error; Soft errors; Tunneling magnetoresistance",
}

@Article{Cheng:2019:TCI,
  author =       "Xi Cheng and Min Zhou and Xiaoyu Song and Ming Gu and
                 Jiaguang Sun",
  title =        "Tolerating {C} Integer Error via Precision Elevation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "68",
  number =       "2",
  pages =        "270--286",
  month =        feb,
  year =         "2019",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2018.2866388",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Feb 4 19:28:55 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://ieeexplore.ieee.org/document/8443077/",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Cornea:2019:NTI,
  author =       "Marius Cornea",
  title =        "New Technologies for Improved Computing",
  crossref =     "Takagi:2019:ISC",
  pages =        "96--96",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00024",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In recent years, we learned to live with a slow-down
                 in the growth rates predicted so far with remarkable
                 accuracy by Moore's law. However, this does not
                 necessarily mean that advancements in performance and
                 reduced power consumption are not possible anymore.
                 There will be more innovations and improvements in
                 processor and system architecture and microarchitecture
                 than before, which will enable continued growth - at
                 Intel, and in the industry. Intel has identified
                 several areas which deserve focused efforts and
                 investment, with the promise of providing in return
                 growth and results we came to expect. Manufacturing
                 processes constitute the first such area. Besides using
                 more advanced technologies to achieve smaller features
                 on our ICs, Intel is also introducing advanced
                 packaging solutions, which will enable exponential
                 scaling in computing density by extending transistor
                 placement in a third dimension. The second area is that
                 of processor and system architecture. Computing
                 architectures from Intel span most of the existing
                 compute spectrum, with scalar, vector, matrix, and
                 spatial architectures. These map roughly to our CPUs,
                 GPUs, accelerators, and FPGAs. Memory is at the center
                 of the third focus area. The memory hierarchy is
                 optimized by capacity, latency, bandwidth, cost, and
                 other features. Persistent memory and high-bandwidth
                 memory have been introduced relatively recently in
                 Intel systems, and will continue to influence the way
                 the memory system is structured. The interconnect is
                 the next important component, in a vastly heterogeneous
                 computing environment for almost all compute devices.
                 Communication has to keep up with computation capacity,
                 a true challenge when trillions of operations per
                 second are possible in many commonly used systems.
                 Security is the fifth focus area, where Intel has the
                 components to improve safety in computation and data
                 preservation in a world where threats increase in
                 number and sophistication, as seen too often recently.
                 Last but not least, software has a significant
                 potential in increasing computing capabilities. Intel
                 is aiming to offer a common set of tools that can
                 address the needs of developers for all the devices we
                 offer, from CPUs and GPUs, to accelerators and FPGAs.
                 Computer arithmetic is central to several of the areas
                 highlighted above. Advancements in this field will play
                 an important role in present as well as future
                 processor architectures and implementations. In
                 conclusion, we will also look at developments in this
                 area for future Intel processors.",
  acknowledgement = ack-nhfb,
  keywords =     "accelerator; ARITH-26; Computer architecture; computer
                 arithmetic; computing architectures; Cornea; CPU; data
                 preservation; data security; Digital arithmetic;
                 digital arithmetic; Field programmable gate arrays;
                 field programmable gate arrays; FPGA; GPU; hardware
                 accelerators; heterogeneous computing environment;
                 improved computing; industrial economics; integrated
                 circuit manufacture; integrated circuit packaging;
                 manufacturing processes; memory hierarchy;
                 microprocessor chips; packaging solutions; Power
                 demand; security of data; semiconductor storage;
                 semiconductor technology; Systems architecture;
                 Technological innovation; three-dimensional integrated
                 circuits; transistor placement",
}

@Article{Courtois:2019:RRR,
  author =       "J. Courtois and L. Abbas-Turki and J. Bajard",
  title =        "Resilience of Randomized {RNS} Arithmetic with Respect
                 to Side-Channel Leaks of Cryptographic Computation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "68",
  number =       "12",
  pages =        "1720--1730",
  month =        dec,
  year =         "2019",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2019.2924630",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Nov 7 11:20:24 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "CPA; DPA; ECC; Elliptic curve cryptography; Elliptic
                 curves; Hamming distance; Hamming weight; information
                 leakage; Maximum likelihood estimation; maximum
                 likelihood estimator; moduli randomization; Monte
                 Carlo; Multiprotocol label switching; Resilience; RNS;
                 side channel",
}

@Article{Covanov:2019:FIM,
  author =       "Svyatoslav Covanov and Emmanuel Thom{\'e}",
  title =        "Fast integer multiplication using generalized {Fermat}
                 primes",
  journal =      j-MATH-COMPUT,
  volume =       "88",
  number =       "317",
  pages =        "1449--1477",
  month =        jan,
  year =         "2019",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/mcom/3367",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Jul 14 06:45:38 MDT 2020",
  bibsource =    "http://www.ams.org/mcom/2019-88-317;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  URL =          "https://www.ams.org/journals/mcom/2019-88-317/S0025-5718-2018-03367-1;
                 https://www.ams.org/journals/mcom/2019-88-317/S0025-5718-2018-03367-1/S0025-5718-2018-03367-1.pdf;
                 https://www.ams.org/mathscinet/search/authors.html?authorName=Thome%2C%20Emmanuel;
                 https://www.ams.org/mathscinet/search/authors.html?mrauthid=1105937",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Misc{Cowlishaw:2019:AIS,
  author =       "Mike Cowlishaw and David Hough",
  title =        "{ANSI\slash IEEE Std 754-2019}",
  howpublished = "Web site",
  day =          "13",
  month =        jun,
  year =         "2019",
  bibdate =      "Fri Aug 30 07:30:45 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://754r.ucbtest.org/remote/background/",
  abstract =     "The IEEE 754-2008 standard expired in 2019, so a minor
                 revision was undertaken, to determine a set of
                 relatively non-controversial upward-compatible
                 editorial corrections and clarifications and minor
                 enhancements to the 2008 standard. 754-2019 was
                 approved by IEEE Standards Board on 13 June 2019 and
                 published in July 2019. David Hough was chair, Mike
                 Cowlishaw was editor. The base document was the
                 technical content of ANSI/IEEE Std 754-2008.

                 Some new operations have been recommended in 2019. In
                 particular, new min/max operations better match
                 application requirements, augmented addition,
                 subtraction, and multiplication operations support
                 building higher precision in software and support
                 reproducible reductions on arrays, and new operations
                 get and set NaN payloads. These recommended operations
                 might be required in a future edition of this
                 standard.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Das:2019:FSA,
  author =       "Sambit Das and Phani Motamarri and Vikram Gavini and
                 Bruno Turcksin and Ying Wai Li and Brent Leback",
  booktitle =    "{SC19: International Conference for High Performance
                 Computing, Networking, Storage and Analysis}",
  title =        "Fast, Scalable and Accurate Finite-Element Based Ab
                 Initio Calculations Using Mixed Precision Computing: 46
                 {PFLOPS} Simulation of a Metallic Dislocation System",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--11",
  year =         "2019",
  DOI =          "https://doi.org/10.1145/3295500.3357157",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Codes; Computational efficiency; Density
                 functional theory; Discrete Fourier transforms;
                 Electrons; Finite element analysis; Finite-elements;
                 Graphics processing units; Heterogeneous architectures;
                 High performance computing; Light-weight alloys;
                 Magnesium; Mixed precision; Scalability",
}

@InProceedings{deDinechin:2019:PGB,
  author =       "Florent de Dinechin and Luc Forget and Jean-Michel
                 Muller and Yohann Uguen",
  title =        "Posits: The Good, the Bad and the Ugly",
  crossref =     "Gustafson:2019:CPC",
  pages =        "6:1--6:10",
  year =         "2019",
  DOI =          "https://doi.org/10.1145/3316279.3316285",
  bibdate =      "Mon Feb 10 12:11:16 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  articleno =    "6",
  keywords =     "numerical analysis, Posits, floating-point",
  location =     "Singapore, Singapore",
  numpages =     "10",
}

@InProceedings{deDinechin:2019:RYF,
  author =       "Florent de Dinechin",
  title =        "Reflections on 10 Years of {FloPoCo}",
  crossref =     "Takagi:2019:ISC",
  pages =        "187--189",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00042",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The FloPoCo open-source arithmetic core generator
                 project started modestly in 2008 with a few parametric
                 floating point cores. It has since then evolved to
                 become a framework for research on hardware arithmetic
                 cores at large. This article reviews some of the
                 choices made in this past decade, and some of the
                 challenges ahead for the next.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-26; arithmetic core generation; Computer
                 architecture; Digital arithmetic; Field programmable
                 gate arrays; floating point arithmetic; flopoco;
                 FloPoCo open-source arithmetic core generator project;
                 Generators; Hardware; hardware arithmetic cores;
                 parametric floating point cores; Tools; VHDL",
}

@InProceedings{deDinechin:2019:TBV,
  author =       "Florent de Dinechin and Silviu-Ioan Filip and Martin
                 Kumm and Luc Forget",
  title =        "Table-Based versus Shift-And-Add Constant Multipliers
                 for {FPGAs}",
  crossref =     "Takagi:2019:ISC",
  pages =        "151--158",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00037",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The multiplication by a constant is a frequently used
                 operation. To implement it on Field Programmable Gate
                 Arrays (FPGAs), the state of the art offers two
                 completely different methods: one relying on bit shifts
                 and additions/subtractions, and another one using
                 look-up tables and additions. So far, it was unclear
                 which method performs best for a given constant and
                 input/output data types. The main contribution of this
                 work is a thorough comparison of both methods in the
                 main application contexts of constant multiplication:
                 filters, signal-processing transforms, and elementary
                 functions. Most of the previous state of the art
                 addresses multiplication by an integer constant. This
                 work shows that, in most of these application contexts,
                 a formulation of the problem as the multiplication by a
                 real constant allows for more efficient architectures.
                 Another contribution is a novel extension of the
                 shift-and-add method to real constants. For that, an
                 integer linear programming (ILP) formulation is
                 proposed, which truncates each component in the
                 shift-and-add network to a minimum necessary word size
                 that is aligned with the approximation error of the
                 coefficient. All methods are implemented within the
                 open-source FloPoCo framework.",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; approximation theory; ARITH-26; Complexity
                 theory; constant multiplier, FPGA, optimization, ILP;
                 Field programmable gate arrays; Field Programmable Gate
                 Arrays; field programmable gate arrays; FPGAs;
                 Hardware; integer linear programming; integer
                 programming; linear programming; look-up tables;
                 multiplying circuits; shift-and-add network;
                 signal-processing transforms; Table lookup; table
                 lookup; table-based versus shift-and-add constant
                 multipliers; Throughput",
}

@InProceedings{Didier:2019:RAP,
  author =       "Laurent-Stephane Didier and Fangan-Yssouf Dosso and
                 Nadia {El Mrabet} and Jeremy Marrez and Pascal
                 V{\'e}ron",
  title =        "Randomization of Arithmetic Over Polynomial Modular
                 Number System",
  crossref =     "Takagi:2019:ISC",
  pages =        "199--206",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00048",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Polynomial Modular Number System (PMNS) is an
                 integer number system designed to speed up arithmetic
                 operations modulo a prime p. Such a system is defined
                 by a tuple B = (p, n, E) where E Z[X] and E() = 0 mod
                 p. In a PMNS, an element a of Z/pZ is represented by a
                 polynomial A such that: A() = a mod p, deg A <; n ||A||
                 <; p. In [6], the authors mentioned that PMNS can be
                 highly redundant but they didn't really take advantage
                 of this possibility. In this paper we use, for the
                 first time, the redundancy of PMNS to protect
                 algorithms against Side Channel Attacks (SCA). More
                 precisely, we focus on elliptic curve cryptography. We
                 show how to randomize the modular multiplication in
                 order to be safe against existing SCA and we
                 demonstrate the resistance of our construction. We
                 describe the generation of a PMNS while guaranteeing,
                 for all elements of Z/pZ, the minimum number of
                 distinct representations we want. We also show how to
                 reach all these representations.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-26; arithmetic operations; digital arithmetic;
                 elliptic curve cryptography; Elliptic curve
                 cryptography; Elliptic curves; integer number system;
                 Lattices; Manganese; modular multiplication; PMNS;
                 polynomial modular number system; Polynomial Modular
                 Number System, Side Channel Countermeasure, Modular
                 Arithmetic; polynomials; Protocols; public key
                 cryptography; Resistance; side channel attacks;
                 Side-channel attacks",
}

@Article{Diffenderfer:2019:EAZ,
  author =       "James Diffenderfer and Alyson L. Fox and Jeffrey A.
                 Hittinger and Geoffrey Sanders and Peter G. Lindstrom",
  title =        "Error Analysis of {ZFP} Compression for Floating-Point
                 Data",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "41",
  number =       "3",
  pages =        "A1867--A1898",
  month =        "????",
  year =         "2019",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/18M1168832",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Thu Oct 10 06:58:05 MDT 2019",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/41/3;
                 https://www.math.utah.edu/pub/tex/bib/datacompression.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  onlinedate =   "January 2019",
}

@InProceedings{Djath:2019:HAR,
  author =       "Libey Djath and Karim Bigou and Arnaud Tisserand",
  title =        "Hierarchical Approach in {RNS} Base Extension for
                 Asymmetric Cryptography",
  crossref =     "Takagi:2019:ISC",
  pages =        "46--53",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00016",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Base extension is a critical operation in RNS
                 implementations of asymmetric cryptosystems. In this
                 paper, we propose a new way to perform base extensions
                 using a hierarchical approach for computing the Chinese
                 remainder theorem. For well chosen parameters, it
                 significantly reduces the computational cost and still
                 ensures a high level of internal parallelism. We
                 illustrate the interest of the proposed approach on the
                 cost of typical arithmetic primitives used in
                 asymmetric cryptography. We also demonstrate
                 improvements in FPGA implementations of base extensions
                 on typical elliptic curve cryptography field sizes
                 using high-level synthesis tools.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-26; asymmetric cryptosystems; Cathode ray tubes;
                 Chinese remainder theorem; Computer architecture;
                 computer arithmetic; cryptography; Elliptic curve
                 cryptography; elliptic curve cryptography field sizes;
                 field programmable gate arrays; FPGA implementations;
                 hardware implementation; high level synthesis;
                 high-level synthesis tools; modular reduction; Parallel
                 processing; residue number system; residue number
                 systems; RNS base extension; RNS implementations;
                 Signal processing algorithms; Standards",
}

@Misc{Dockrill:2019:CMH,
  author =       "Peter Dockrill",
  title =        "Computers Are Making Huge Mistakes Because They Can't
                 Understand Chaos, Scientists Warn",
  howpublished = "ScienceAlert Web site",
  day =          "27",
  month =        sep,
  year =         "2019",
  bibdate =      "Mon Sep 30 11:25:59 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Boghosian:2019:NPS}.",
  URL =          "https://www.sciencealert.com/computers-are-making-huge-mistakes-because-they-can-t-understand-chaos-scientists-warn",
  acknowledgement = ack-nhfb,
}

@InProceedings{Ensor:2019:BNB,
  author =       "Andrew Ensor",
  title =        "Big Numbers for a Big Universe",
  crossref =     "Takagi:2019:ISC",
  pages =        "99--99",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00026",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Square Kilometre Array is the world's largest
                 mega-Science project of the next decade aiming to build
                 enormous radio telescope arrays across Western
                 Australia and Southern Africa. With 160 TeraByte/sec
                 data generated in just stage one of the 50 year project
                 and over 260 PetaFLOPS compute requirements it presents
                 unprecedented data movement and processing challenges
                 in its correlators, the detection and timing of
                 pulsars, supercomputing pipelines for generating
                 images, and scalable middleware. This talk will outline
                 the project and its scientific goals, some of the key
                 data processing pipelines, and will discuss the
                 progress made by the design teams toward overcoming its
                 computing challenges.",
  acknowledgement = ack-nhfb,
  keywords =     "Africa; ARITH-26; Arrays; Australia; big numbers; big
                 universe; computing challenges; design teams; Digital
                 arithmetic; generating images; High performance
                 computing; key data processing pipelines; mega-Science
                 project; middleware; parallel machines; PetaFLOPS
                 compute requirements; Pipelines; processing challenges;
                 Radio astronomy; radio telescope arrays;
                 radiotelescopes; scalable middleware; scientific goals;
                 Southern Africa; Square Kilometre Array; supercomputing
                 pipelines; time 50.0 year; unprecedented data movement;
                 Western Australia",
}

@Article{Fabiano:2019:ATW,
  author =       "Nicolas Fabiano and Jean-Michel Muller and Joris
                 Picot",
  title =        "Algorithms for Triple-Word Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "68",
  number =       "11",
  pages =        "1573--1583",
  month =        nov,
  year =         "2019",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2019.2918451",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Oct 29 11:08:44 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  URL =          "https://hal.archives-ouvertes.fr/hal-01869009v2",
  abstract =     "Triple-word arithmetic consists in representing
                 high-precision numbers as the unevaluated sum of three
                 floating-point numbers (with nonoverlapping constraints
                 that are explicited in the paper). We introduce and
                 analyze various algorithms for manipulating triple-word
                 numbers: rounding a triple-word number to a
                 floating-point number, adding, multiplying, dividing,
                 and computing square-roots of triple-word numbers, etc.
                 We compare our algorithms, implemented in the Campary
                 library, with other solutions of comparable accuracy.
                 It turns out that our new algorithms are significantly
                 faster than what one would obtain by just using the
                 usual floating-point expansion algorithms in the
                 special case of expansions of length 3.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Computer arithmetic, floating-point arithmetic,
                 triple-word arithmetic; Floating-point arithmetic;
                 Libraries; Lips; Memory management; Physics;
                 Programming; Standards",
}

@Article{Fang:2019:GSC,
  author =       "Linlin Fang and Yizhuang Xie and Bingyi Li and He
                 Chen",
  title =        "Generation scheme of chirp scaling phase functions
                 based on floating-point {CORDIC} processor",
  journal =      "The Journal of Engineering",
  volume =       "2019",
  number =       "21",
  pages =        "7436--7439",
  year =         "2019",
  DOI =          "https://doi.org/10.1049/joe.2019.0623",
  bibdate =      "Wed Oct 29 15:08:31 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://onlinelibrary.wiley.com/doi/abs/10.1049/joe.2019.0623",
  acknowledgement = ack-nhfb,
  eprint =       "https://onlinelibrary.wiley.com/doi/pdf/10.1049/joe.2019.0623",
  keywords =     "synthetic aperture radar, floating point arithmetic,
                 field programmable gate arrays, radar imaging, logic
                 design, function generators, chirp scaling phase
                 functions, chirp scaling phase function generation
                 scheme, CORDIC algorithm, single precision
                 floating-point CORDIC processor, nonlinear operations,
                 hardware resource reduction scheme, unified CORDIC
                 processor, division operation, Xilinx XC7VX690T FPGA
                 platform, SAR imaging system, CS synthetic aperture
                 radar imaging algorithm, multiplication operation,
                 square root operation",
}

@Misc{Feldman:2019:NAC,
  author =       "Michael Feldman",
  title =        "New Approach Could Sink Floating Point Computation",
  howpublished = "Web site",
  day =          "8",
  month =        jul,
  year =         "2019",
  bibdate =      "Tue Jul 09 10:28:21 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.nextplatform.com/2019/07/08/new-approach-could-sink-floating-point-computation/",
  acknowledgement = ack-nhfb,
  remark =       "Interview with John L. Gustafson on Posits (universal
                 numbers).",
}

@Article{Flegar:2019:FCL,
  author =       "Goran Flegar and Florian Scheidegger and Vedran
                 Novakovi{\'c} and Giovani Mariani and Andr{\'e}s E.
                 Tom{\'a}s and A. Cristiano I. Malossi and Enrique S.
                 Quintana-Ort{\'\i}",
  title =        "{FloatX}: A {C++} Library for Customized
                 Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "45",
  number =       "4",
  pages =        "40:1--40:??",
  month =        dec,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3368086",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Dec 27 14:56:25 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3368086",
  abstract =     "We present FloatX (Float eXtended), a C ++ framework
                 to investigate the effect of leveraging customized
                 floating-point formats in numerical applications.
                 FloatX formats are based on binary IEEE 754 with
                 smaller significand and exponent bit counts specified
                 by the user. Among other properties, FloatX facilitates
                 an incremental transformation of the code, relies on
                 hardware-supported floating-point types as back-end to
                 preserve efficiency, and incurs no storage overhead.
                 The article discusses in detail the design principles,
                 programming interface, and datatype casting rules
                 behind FloatX. Furthermore, it demonstrates FloatX's
                 usage and benefits via several case studies from
                 well-known numerical dense linear algebra libraries,
                 such as BLAS and LAPACK; the Ginkgo library for sparse
                 linear systems; and two neural network applications
                 related with image processing and text recognition.",
  acknowledgement = ack-nhfb,
  articleno =    "40",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Manual{Fog:2019:ITL,
  author =       "Agner Fog",
  title =        "4. {Instruction} tables: Lists of instruction
                 latencies, throughputs and micro-operation breakdowns
                 for {Intel}, {AMD}, and {VIA CPUs}",
  organization = "Technical University of Denmark",
  address =      "Lyngby, Denmark",
  pages =        "367",
  day =          "15",
  month =        aug,
  year =         "2019",
  bibdate =      "Thu Jan 30 16:18:42 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.agner.org/optimize/instruction_tables.pdf",
  acknowledgement = ack-nhfb,
  remark =       "This is the fourth in a series of five manuals: 1.
                 Optimizing software in C++: An optimization guide for
                 Windows, Linux and Mac platforms. 2. Optimizing
                 subroutines in assembly language: An optimization guide
                 for x86 platforms. 3. The microarchitecture of Intel,
                 AMD and VIA CPUs: An optimization guide for assembly
                 programmers and compiler makers. 4. Instruction tables:
                 Lists of instruction latencies, throughputs and
                 micro-operation breakdowns for Intel, AMD and VIA CPUs.
                 5. Calling conventions for different C++ compilers and
                 operating systems. The manuals are copyrighted from
                 1996 to 2019.",
}

@Article{Gallin:2019:GFP,
  author =       "G. Gallin and A. Tisserand",
  title =        "Generation of Finely-Pipelined {GF($P$P)} Multipliers
                 for Flexible Curve Based Cryptography on {FPGAs}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "68",
  number =       "11",
  pages =        "1612--1622",
  month =        nov,
  year =         "2019",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2019.2920352",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Oct 29 11:08:44 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "arithmetic operator generation; Clocks; Computer
                 architecture; Cryptography; elliptic curve
                 cryptography; Field programmable gate arrays; Hardware;
                 Modular arithmetic; Montgomery multiplication;
                 Pipelines; Tools",
}

@InProceedings{Gorodecky:2019:EIM,
  author =       "Danila Gorodecky and Tiziano Villa",
  title =        "Efficient Implementation of Modular Division by Input
                 Bit Splitting",
  crossref =     "Takagi:2019:ISC",
  pages =        "54--60",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00017",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Arithmetic operations, such as addition,
                 multiplication, division and modular division, impact
                 on the quality of arithmetic logic units and of the
                 whole processor, with respect to area and delay of the
                 circuit, power consumption, testability. In this
                 article we propose an algorithm to implement
                 efficiently the operation of modular division (X (mod
                 P)), where P is pre-selected. The proposed approach is
                 based on splitting the input operands into smaller
                 binary tuples and then minimizing in parallel the
                 two-level form of each suboperation on the tuples of
                 the decomposition. The experiments show gains in
                 performance and area of our approach vs. to circuits
                 synthesized by state-of-art EDA tools with an advantage
                 in delay and area up to 30 times.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-26; arithmetic logic units; Boolean functions;
                 Complexity theory; computer arithmetic, multiplication,
                 modular division, logic minimization; Delays; digital
                 arithmetic; dividing circuits; EDA tools; input bit
                 splitting; input operands; logic design; Minimization;
                 modular division; Partitioning algorithms; Power
                 demand; smaller binary tuples; Tools",
}

@Article{Graillat:2019:ATF,
  author =       "Stef Graillat and Fabienne J{\'e}z{\'e}quel and Romain
                 Picot and Fran{\c{c}}ois F{\'e}votte and Bruno
                 Lathuili{\`e}re",
  title =        "Auto-tuning for floating-point precision with
                 {Discrete Stochastic Arithmetic}",
  journal =      j-J-COMPUT-SCI,
  volume =       "36",
  pages =        "??--??",
  month =        sep,
  year =         "2019",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/j.jocs.2019.07.004",
  ISSN =         "1877-7503 (print), 1877-7511 (electronic)",
  ISSN-L =       "1877-7503",
  MRclass =      "65Y20 (65C50)",
  MRnumber =     "4007597",
  bibdate =      "Tue Sep 19 13:55:19 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputsci.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/S1877750318309475",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Comput. Sci.",
  articleno =    "101017",
  fjournal =     "Journal of Computational Science",
  journal-URL =  "https://www.sciencedirect.com/journal/journal-of-computational-science",
  pagecount =    "11",
}

@Misc{Grossman:2019:CSC,
  author =       "David Grossman",
  title =        "Computers Suck at Creating Chaos",
  howpublished = "Popular Mechanics Web site",
  day =          "30",
  month =        sep,
  year =         "2019",
  bibdate =      "Tue Oct 01 08:57:55 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Boghosian:2019:NPS}.",
  URL =          "https://www.popularmechanics.com/science/a29271351/computers-chaotic-systems/",
  acknowledgement = ack-nhfb,
}

@Article{Gu:2019:GRM,
  author =       "Z. Gu and S. Li",
  title =        "A Generalized {RNS} {Mclaughlin} Modular
                 Multiplication with Non-Coprime Moduli Sets",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "68",
  number =       "11",
  pages =        "1689--1696",
  month =        nov,
  year =         "2019",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2019.2917433",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Oct 29 11:08:44 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Digital arithmetic; Elliptic curve cryptography;
                 Indexes; McLaughlin modular multiplication;
                 Microelectronics; Montgomery modular multiplication;
                 Performance evaluation; Residue number systems",
}

@Article{Guerreiro:2019:MDG,
  author =       "Jo{\~a}o Guerreiro and Aleksandar Ilic and Nuno Roma
                 and Pedro Tom{\'a}s",
  title =        "Modeling and Decoupling the {GPU} Power Consumption
                 for Cross-Domain {DVFS}",
  journal =      j-IEEE-TRANS-PAR-DIST-SYS,
  volume =       "30",
  number =       "11",
  pages =        "2494--2506",
  year =         "2019",
  CODEN =        "ITDSEO",
  DOI =          "https://doi.org/10.1109/TPDS.2019.2917181",
  ISSN =         "1045-9219 (print), 1558-2183 (electronic)",
  ISSN-L =       "1045-9219",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Parallel Distrib. Syst.",
  fjournal =     "IEEE Transactions on Parallel and Distributed
                 Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=71",
  keywords =     "Benchmark testing; Computational modeling; DVFS;
                 Frequency-domain analysis; GPGPU; Graphics processing
                 units; Memory management; Power demand; power modeling;
                 Predictive models; scaling-factors",
}

@Article{Han:2019:FFE,
  author =       "Dong Han and Shengyuan Zhou and Tian Zhi and Yibo Wang
                 and Shaoli Liu",
  title =        "{Float-Fix}: An Efficient and Hardware-Friendly Data
                 Type for Deep Neural Network",
  journal =      j-INT-J-PARALLEL-PROG,
  volume =       "47",
  number =       "3",
  pages =        "345--359",
  month =        jun,
  year =         "2019",
  CODEN =        "IJPPE5",
  DOI =          "https://doi.org/10.1007/s10766-018-00626-7",
  ISSN =         "0885-7458 (print), 1573-7640 (electronic)",
  ISSN-L =       "0885-7458",
  bibdate =      "Fri Oct 11 08:37:52 MDT 2019",
  bibsource =    "http://link.springer.com/journal/10766/47/3;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/intjparallelprogram.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Parallel Programming",
  journal-URL =  "http://link.springer.com/journal/10766",
}

@Article{Hanuman:2019:IMP,
  author =       "C. R. S. Hanuman and J. Kamala and A. R. Aruna",
  title =        "Implementation of multi-precision floating point
                 divider for high speed signal processing applications",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "75",
  number =       "9",
  pages =        "6038--6054",
  month =        sep,
  year =         "2019",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1007/s11227-019-02902-w",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Thu Oct 10 15:31:22 MDT 2019",
  bibsource =    "http://link.springer.com/journal/11227/75/9;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsuper.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
}

@InProceedings{Hao:2019:VID,
  author =       "Liu Hao and Wang Ming-Jiang and Chen Mo-Ran and Liu
                 Ming",
  booktitle =    "{2019 IEEE 4th International Conference on Signal and
                 Image Processing (ICSIP)}",
  title =        "A {VLSI} Implementation of Double Precision
                 Floating-Point Logarithmic Function",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "345--349",
  year =         "2019",
  DOI =          "https://doi.org/10.1109/SIPROCESS.2019.8868367",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Clocks; Convergence; CORDIC algorithm; Delays; double
                 precision; floating-point number; Hardware; logarithmic
                 function; Parallel processing; Prediction algorithms;
                 Very large scale integration; VLSI",
}

@Article{Harase:2019:CMT,
  author =       "Shin Harase",
  title =        "Conversion of {Mersenne Twister} to double-precision
                 floating-point numbers",
  journal =      j-MATH-COMPUT-SIMUL,
  volume =       "161",
  pages =        "76--83",
  month =        jul,
  year =         "2019",
  CODEN =        "MCSIDR",
  DOI =          "https://doi.org/10.1016/j.matcom.2018.08.006",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  bibdate =      "Sat Aug 16 06:05:54 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomputsimul2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/S0378475418302040",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput. Simul.",
  fjournal =     "Mathematics and Computers in Simulation",
  journal-URL =  "https://www.sciencedirect.com/science/journal/03784754",
}

@Misc{Harthcock:2019:BUF,
  author =       "Jerry D. Harthcock",
  title =        "{64-bit-Universal-Floating-Point-ISA-Compute-Engine}",
  howpublished = "Github Web site.",
  day =          "8",
  month =        oct,
  year =         "2019",
  bibdate =      "Wed Oct 09 05:34:48 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://github.com/jerry-D/64-bit-Universal-Floating-Point-ISA-Compute-Engine",
  abstract =     "New 64-bit Universal Floating-Point ISA Compute Engine
                 computes directly with human-readable decimal character
                 sequences, binary64, 32, 16 or bfloat16 formatted
                 numbers in any combination.",
  acknowledgement = ack-nhfb,
}

@Article{Harvey:2019:FIM,
  author =       "David Harvey and Joris van der Hoeven",
  title =        "Faster integer multiplication using plain vanilla
                 {FFT} primes",
  journal =      j-MATH-COMPUT,
  volume =       "88",
  number =       "315",
  pages =        "501--514",
  month =        jul,
  year =         "2019",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/mcom/3328",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Jul 14 06:45:34 MDT 2020",
  bibsource =    "http://www.ams.org/mcom/2019-88-315;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  URL =          "https://www.ams.org/journals/mcom/2019-88-315/S0025-5718-2018-03328-2;
                 https://www.ams.org/journals/mcom/2019-88-315/S0025-5718-2018-03328-2/S0025-5718-2018-03328-2.pdf;
                 https://www.ams.org/mathscinet/search/authors.html?mrauthid=621578;
                 https://www.ams.org/mathscinet/search/authors.html?mrauthid=734771",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@TechReport{Harvey:2019:IMT,
  author =       "David Harvey and Joris {Van Der Hoeven}",
  title =        "Integer multiplication in time {$ O(n \log n) $}",
  type =         "Report",
  number =       "hal-02070778",
  institution =  "School of Mathematics and Statistics, University of
                 New South Wales, and CNRS, Laboratoire d'informatique,
                 {\'E}cole polytechnique",
  address =      "Sydney, NSW 2052, Australia and 91128 Palaiseau,
                 France",
  day =          "18",
  month =        mar,
  year =         "2019",
  bibdate =      "Fri Apr 12 14:09:18 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://hal.archives-ouvertes.fr/hal-02070778/document",
  abstract =     "We present an algorithm that computes the product of
                 two $n$-bit integers in $ O(n \log n)$ bit
                 operations.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hayes:2019:DCB,
  author =       "Ari B. Hayes and Fei Hua and Jin Huang and Yanhao Chen
                 and Eddy Z. Zhang",
  editor =       "Mahmut Taylan Kandemir and Alexandra Jimborean and
                 Tipp Moseley",
  booktitle =    "{CGO'19: Proceedings of the 2019 IEEE\slash ACM
                 International Symposium on Code Generation and
                 Optimization, 16--20 February 2019, Washington, DC,
                 USA}",
  title =        "Decoding {CUDA} Binary",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  bookpages =    "xv + 287",
  pages =        "229--241",
  year =         "2019",
  DOI =          "https://doi.org/10.1109/cgo.2019.8661186",
  ISBN =         "1-72811-436-5, 1-72811-437-3",
  ISBN-13 =      "978-1-72811-436-1, 978-1-72811-437-8",
  LCCN =         "QA76.76.G46 I57 2019",
  bibdate =      "Mon Sep 11 06:57:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE Catalog Number CFP19CGO-ART.",
  URL =          "https://ieeexplore.ieee.org/document/8661186",
  abstract =     "NVIDIA's software does not offer translation of
                 assembly code to binary for their GPUs, since the
                 specifications are closed-source. This work fills that
                 gap. We develop a systematic method of decoding the
                 Instruction Set Architectures (ISAs) of NVIDIA's GPUs,
                 and generating assemblers for different generations of
                 GPUs. Our framework enables cross-architecture binary
                 analysis and transformation. Making the ISA accessible
                 in this manner opens up a world of opportunities for
                 developers and researchers, enabling numerous
                 optimizations and explorations that are unachievable at
                 the source-code level. Our infrastructure has already
                 benefited and been adopted in important applications
                 including performance tuning, binary instrumentation,
                 resource allocation, and memory protection.",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1109/CGO46174.2019",
}

@InProceedings{Henry:2019:LBA,
  author =       "Greg Henry and Ping Tak Peter Tang and Alexander
                 Heinecke",
  title =        "Leveraging the bfloat16 Artificial Intelligence
                 Datatype For Higher-Precision Computations",
  crossref =     "Takagi:2019:ISC",
  pages =        "69--76",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00019",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In recent years fused-multiply-add (FMA) units with
                 lower-precision multiplications and higher-precision
                 accumulation have proven useful in machine
                 learning/artificial intelligence applications, most
                 notably in training deep neural networks due to their
                 extreme computational intensity. Compared to classical
                 IEEE-754 32 bit (FP32) and 64 bit (FP64) arithmetic,
                 these reduced precision arithmetic can naturally be
                 sped up disproportional to their shortened width. The
                 common strategy of all major hardware vendors is to
                 aggressively further enhance their performance
                 disproportionately. One particular FMA operation that
                 multiplies two BF16 numbers while accumulating in FP32
                 has been found useful in deep learning, where BF16 is
                 the 16-bit floating point datatype with IEEE FP32
                 numerical range but 8 significant bits of precision. In
                 this paper, we examine the use this FMA unit to
                 implement higher-precision matrix routines in terms of
                 potential performance gain and implications on
                 accuracy. We demonstrate how a decomposition into
                 multiple smaller datatypes can be used to assemble a
                 high-precision result, leveraging the higher precision
                 accumulation of the FMA unit. We first demonstrate that
                 computations of vector inner products and by natural
                 extension, matrix-matrix products can be achieved by
                 decomposing FP32 numbers in several BF16 numbers
                 followed by appropriate computations that can
                 accommodate the dynamic range and preserve accuracy
                 compared to standard FP32 computations, while
                 projecting up to 5.2x speed-up. Furthermore, we examine
                 solution of linear equations formulated in the residual
                 form that allows for iterative refinement. We
                 demonstrate that the solution obtained to be comparable
                 to those offered by FP64 under a large range of linear
                 system condition numbers.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-26; artificial intelligence datatype; bfloat16,
                 float16, mixed precision, combined datatypes; Deep
                 learning; deep learning; deep neural networks; floating
                 point arithmetic; floating point datatype; FMA unit;
                 FP32 computations; fused-multiply-add units; Hardware;
                 higher-precision matrix routines; IEEE-754 32 bit
                 arithmetic; IEEE-754 FP32 arithmetic; IEEE-754 FP64
                 arithmetic; iterative methods; learning (artificial
                 intelligence); matrix algebra; Matrix decomposition;
                 matrix-matrix products; neural nets; Neural networks;
                 Standards; Task analysis; Training",
}

@Article{Hiasat:2019:DRI,
  author =       "Ahmad Hiasat and Leonel Sousa",
  title =        "On the Design of {RNS} Inter-Modulo Processing Units
                 for the Arithmetic-Friendly Moduli Sets $ 2^{n + k} $,
                 $ 2^n - 1 $, $ 2^{n + 1} - 1 $",
  journal =      j-COMP-J,
  volume =       "62",
  number =       "2",
  pages =        "292--300",
  day =          "1",
  month =        feb,
  year =         "2019",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/bxy119",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Mon Feb 11 10:50:41 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compj2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://academic.oup.com/comjnl/article/62/2/292/5224762",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "Residue Number System (RNS)",
}

@InProceedings{Hickmann:2019:EAM,
  author =       "Brian Hickmann and Dennis Bradford",
  title =        "Experimental Analysis of Matrix Multiplication
                 Functional Units",
  crossref =     "Takagi:2019:ISC",
  pages =        "116--119",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00031",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The rapid growth of AI has led to the introduction of
                 several new hardware designs to accelerate the matrix
                 multiplication operation at the heart of AI
                 applications. Examples include NVIDIA's Tensor Core*,
                 Google's TPU*, and Intel's Neural Compute Stick*.
                 However, the IEEE 754 standard gives significant
                 implementation-specific flexibility in the definition
                 of the matrix multiplication operation and the
                 precision and compatibility of these new accelerators
                 is not well documented. This paper describes a method
                 exploiting the rounding modes and other features of the
                 IEEE 754 standard in order to gain deeper insight into
                 the design and functionality of matrix multiplication
                 units. We apply this method to the NVIDIA V100 GPU
                 Tensor Core* units and report our findings on the
                 design properties and micro-architecture.",
  acknowledgement = ack-nhfb,
  keywords =     "AI applications; ARITH-26; Deep learning; Google TPU;
                 Graphics processing units; Hardware; hardware designs;
                 IEEE 754 standard; IEEE standards;
                 implementation-specific flexibility; Intel Neural
                 Compute Stick; learning (artificial intelligence);
                 Machine learning, deep learning, tensor, half
                 precision, single precision, Volta, matrix
                 multiplication; mathematics computing; matrix
                 multiplication; matrix multiplication functional units;
                 matrix multiplication units; Microarchitecture; neural
                 nets; NVIDIA Tensor Core; NVIDIA V100 GPU Tensor Core
                 units; Standards; Testing",
}

@Article{Higham:2019:NAP,
  author =       "Nicholas J. Higham and Theo Mary",
  title =        "A New Approach to Probabilistic Rounding Error
                 Analysis",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "41",
  number =       "5",
  pages =        "A2815--A2835",
  month =        "????",
  year =         "2019",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/18M1226312",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Tue Nov 5 05:24:19 MST 2019",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/41/5;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  keywords =     "floating-point arithmetic; MATLAB; numerical linear
                 algebra; rounding error analysis",
  onlinedate =   "January 2019",
}

@Article{Higham:2019:SLP,
  author =       "Nicholas J. Higham and Srikara Pranesh",
  title =        "Simulating Low Precision Floating-Point Arithmetic",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "41",
  number =       "5",
  pages =        "C585--C602",
  month =        "????",
  year =         "2019",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/19M1251308",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Tue Nov 5 05:24:19 MST 2019",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/41/5;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  keywords =     "bfloat16; bit flips; directed rounding; floating-point
                 arithmetic; fp16; half precision; IEEE arithmetic; low
                 precision; MATLAB; mixed precision; round to nearest;
                 rounding error analysis; simulation; stochastic
                 rounding; subnormal numbers",
  onlinedate =   "January 2019",
}

@Article{Higham:2019:SMH,
  author =       "Nicholas J. Higham and Srikara Pranesh and Mawussi
                 Zounon",
  title =        "Squeezing a Matrix into Half Precision, with an
                 Application to Solving Linear Systems",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "41",
  number =       "4",
  pages =        "A2536--A2551",
  month =        "????",
  year =         "2019",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/18M1229511",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Thu Oct 10 06:58:08 MDT 2019",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/41/4;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  keywords =     "diagonal scaling; fp16; GMRES; half precision
                 arithmetic; iterative refinement; linear system;
                 MATLAB; mixed precision; overflow; preconditioning;
                 subnormal numbers; underflow",
  onlinedate =   "January 2019",
}

@Article{Hoang:2019:LPF,
  author =       "Trong-Thuc Hoang and Xuan-Thuan Nguyen and Duc-Hung Le
                 and Cong-Kha Pham",
  title =        "Low-Power Floating-Point Adaptive-{CORDIC}-based {FFT}
                 Twiddle Factor on 65-nm {Silicon-on-Thin-BOX} ({SOTB})
                 With Back-Gate Bias",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
  volume =       "66",
  number =       "10",
  pages =        "1723--1727",
  year =         "2019",
  DOI =          "https://doi.org/10.1109/TCSII.2019.2928138",
  ISSN =         "1549-7747 (print), 1558-3791 (electronic)",
  ISSN-L =       "1549-7747",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems II: Express
                 Briefs",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
  keywords =     "Back-gate bias; Circuits and systems; CORDIC; Delays;
                 Energy consumption; floating-point; Frequency
                 measurement; low-power; Memory management; SOTB; Table
                 lookup; twiddle factor",
}

@Article{Horyachyy:2019:SEF,
  author =       "Oleh Horyachyy and Leonid Moroz and Viktor Otenko",
  title =        "Simple Effective Fast Inverse Square Root Algorithm
                 with Two Magic Constants",
  journal =      "International Journal of Computing",
  volume =       "18",
  number =       "4",
  pages =        "461--470",
  month =        dec,
  year =         "2019",
  ISSN =         "1727-6209 (print), 2312-5381 (electronic)",
  ISSN-L =       "1727-6209",
  bibdate =      "Thu Feb 11 11:01:47 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.computingonline.net/computing/article/view/1616;
                 https://www.researchgate.net/publication/349173096_SIMPLE_EFFECTIVE_FAST_INVERSE_SQUARE_ROOT_ALGORITHM_WITH_TWO_MAGIC_CONSTANTS",
  acknowledgement = ack-nhfb,
  keywords =     "FISR algorithm; floating-point arithmetic; FMA
                 function; Householder.; IEEE 754 standard; initial
                 approximation; inverse square root; magic constant;
                 maximum relative error; Newton-Raphson",
}

@InProceedings{Hou:2019:LLF,
  author =       "Nanxin Hou and Mingjiang Wang and Xiafeng Zou and Ming
                 Liu",
  booktitle =    "{2019 IEEE 4th International Conference on Signal and
                 Image Processing (ICSIP)}",
  title =        "A Low Latency Floating Point {CORDIC} Algorithm for
                 Sin\slash Cosine Function",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "751--755",
  year =         "2019",
  DOI =          "https://doi.org/10.1109/SIPROCESS.2019.8868623",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Circuits and systems; Conferences; CORDIC; Digital
                 arithmetic; Digital signal processing;
                 double-precision; floating-point; IEEE transactions;
                 Image processing; low latency; Manganese; sin/cosine",
}

@Article{Hough:2019:ISO,
  author =       "David G. Hough",
  title =        "The {IEEE Standard 754}: One for the History Books",
  journal =      j-COMPUTER,
  volume =       "52",
  number =       "12",
  pages =        "109--112",
  month =        dec,
  year =         "2019",
  CODEN =        "CPTRB4",
  DOI =          "https://doi.org/10.1109/MC.2019.2926614",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Fri Nov 29 06:16:06 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computer2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://grouper.ieee.org/groups/msc/ANSI_IEEE-Std-754-2019/background/ieee-computer.pdf;
                 https://www.computer.org/csdl/magazine/co/2019/12/08909942/1f8KFWxbTCU",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
  keywords =     "Floating-point arithmetic; Hardware; History; IEEE
                 Standards; Microprocessors; Software",
}

@Article{Hrycak:2019:AEC,
  author =       "Tomasz Hrycak and Sebastian Schmutzhard",
  title =        "Accurate evaluation of {Chebyshev} polynomials in
                 floating-point arithmetic",
  journal =      j-BIT-NUM-MATH,
  volume =       "59",
  number =       "2",
  pages =        "403--416",
  month =        jun,
  year =         "2019",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/s10543-018-0738-5",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Fri Sep 6 09:16:11 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer.com/article/10.1007/s10543-018-0738-5",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT Numerical Mathematics",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Book{IEEE-754:2019:ISF,
  author =       "{IEEE-754}",
  title =        "{IEEE 754-2019, Standard for Floating-Point
                 Arithmetic}",
  publisher =    pub-IEEE-STD,
  address =      pub-IEEE-STD:adr,
  pages =        "82",
  day =          "13",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/IEEESTD.2019.876622",
  ISBN =         "1-5044-5925-3 (print), 1-5044-5924-5 (e-PDF)",
  ISBN-13 =      "978-1-5044-5925-9 (print), 978-1-5044-5924-2 (e-PDF)",
  bibdate =      "Tue Nov 05 08:49:56 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeestd.bib",
  abstract =     "This standard specifies interchange and arithmetic
                 formats and methods for binary and decimal
                 floating-point arithmetic in computer programming
                 environments. This standard specifies exception
                 conditions and their default handling. An
                 implementation of a floating-point system conforming to
                 this standard may be realized entirely in software,
                 entirely in hardware, or in any combination of software
                 and hardware. For operations specified in the normative
                 part of this standard, numerical results and exceptions
                 are uniquely determined by the values of the input
                 data, sequence of operations, and destination formats,
                 all under user control.",
  acknowledgement = ack-nhfb,
}

@Misc{IEEE:2019:PDA,
  author =       "{IEEE}",
  title =        "{P754\slash D2.50, Apr 2019 --- IEEE Approved Draft
                 Standard for Floating-Point Arithmetic: Revision of
                 IEEE Std 754-2008}",
  howpublished = "Web site",
  month =        apr,
  year =         "2019",
  bibdate =      "Thu Jun 20 15:39:16 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/document/8739150",
  abstract =     "This standard specifies interchange and arithmetic
                 formats and methods for binary and decimal
                 floating-point arithmetic in computer programming
                 environments. This standard specifies exception
                 conditions and their default handling. An
                 implementation of a floating-point system conforming to
                 this standard may be realized entirely in software,
                 entirely in hardware, or in any combination of software
                 and hardware. For operations specified in the normative
                 part of this standard, numerical results and exceptions
                 are uniquely determined by the values of the input
                 data, sequence of operations, and destination formats,
                 all under user control.",
  acknowledgement = ack-nhfb,
}

@Article{Issa:2019:FIF,
  author =       "Hanady Hussein Issa and Saleh Mohamed Eisa Ahmed",
  title =        "{FPGA} Implementation of Floating Point Based Cuckoo
                 Search Algorithm",
  journal =      j-IEEE-ACCESS,
  volume =       "7",
  pages =        "134434--134447",
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ACCESS.2019.2942205",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Tue Sep 30 17:30:28 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "Birds; Cuckoo search algorithm (CSA); field
                 programmable gate array (FPGA); Field programmable gate
                 arrays; finite state machine (FSM); Hardware; IEEE
                 floating point format; Optimization; Search problems;
                 Signal processing algorithms; Wireless sensor
                 networks",
}

@InProceedings{Jaberipur:2019:MPP,
  author =       "Ghassem Jaberipur and Sahar {Moradi Cherati}",
  title =        "Modulo-$ (2 n + 3) $ Parallel Prefix Addition via
                 Diminished-3 Representation of Residues",
  crossref =     "Takagi:2019:ISC",
  pages =        "135--142",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00035",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Diminished-1 (D1) representation of modulo-(2n + 1)
                 residues in [1, 2n] uses the n-bit codes [0, 2n - 1]
                 and maintains a zero-indicator bit. Such D1 encoding
                 has led to efficient parallel prefix modulo-(2n + 1)
                 adders that perform as fast as the companion modulo-(2n
                 - 1) and -2n adders with (3 + 2 log n) delay, where
                 denotes the delay of a simple 2-input gate. Also
                 similar, but slower (i.e., with one more delay) and
                 slightly more complex, parallel prefix architectures
                 have been offered for modulo-(2n - 3) adders. On the
                 other hand, reverse conversion schemes for 4and
                 5-moduli sets that include conjugate moduli pairs 2n
                 \pm 1 and 2n \pm 3 are already available, while we have
                 not encountered any efficient modulo(2n + 3) adder.
                 Therefore, in this paper, we offer the diminished-3
                 (D3) representation of modulo-(2n + 3) residues that
                 maps the residue interval [3, 2n + 2] to [0, 2n - 1]
                 and maintains a 2-bit {0,1, 2}-indicator. The
                 corresponding parallel prefix adder, which performs as
                 fast as the fastest previous modulo-(2n - 3) adder is
                 designed, where a 3-way compound architecture is
                 devised as the bulk of modular addition that yields
                 sum, sum+1, and sum+2. The proposed architecture is
                 fully synthesized via Synopsis Design Compiler and
                 tested for correctness, and its figures of merit
                 compared with modulo(2n - 3) and -(2n + 1) adders.",
  acknowledgement = ack-nhfb,
  keywords =     "3-way compound architecture; adders; Adders; ARITH-26;
                 complex prefix architectures; Compounds; Computer
                 architecture; Computer science; D1 representation; D3
                 representation; Delays; Digital arithmetic;
                 Diminished-1 representation; diminished-3
                 representation; Encoding; logic design; Modulo-(2n+3)
                 parallel prefix addition; modulo-(2n-3) adders;
                 parallel prefix adder; Residue Number System, Parallel
                 Prefix Adder, Diminished-1, Diminished 3, 3-way
                 compound adder; residue number systems; simple 2-input
                 gate; Synopsis Design Compiler; zero-indicator bit",
}

@Article{Jaiswal:2019:PHP,
  author =       "Manish Kumar Jaiswal and Hayden K.-H. So",
  title =        "{PACoGen}: a Hardware Posit Arithmetic Core
                 Generator",
  journal =      j-IEEE-ACCESS,
  volume =       "7",
  pages =        "74586--74601",
  year =         "2019",
  DOI =          "https://doi.org/10.1109/access.2019.2920936",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Thu Dec 14 18:07:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "Adder; Adders; ASIC; digital arithmetic; division;
                 Dynamic range; Field programmable gate arrays; floating
                 point arithmetic; FPGA; Generators; Hardware; Hardware
                 design languages; multiplier; posit arithmetic;
                 Standards; subtractor; universal number system",
}

@Article{Jia:2019:DNT,
  author =       "Zhe Jia and Marco Maggioni and Jeffrey Smith and
                 Daniele Paolo Scarpazza",
  title =        "Dissecting the {NVidia Turing T4 GPU} via
                 Microbenchmarking",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "65",
  day =          "18",
  month =        mar,
  year =         "2019",
  DOI =          "https://doi.org/10.48550/ARXIV.1903.07486",
  bibdate =      "Mon Sep 11 07:00:16 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/abs/1903.07486",
  abstract =     "In 2019, the rapid rate at which GPU manufacturers
                 refresh their designs, coupled with their reluctance to
                 disclose microarchitectural details, is still a hurdle
                 for those software designers who want to extract the
                 highest possible performance. Last year, these very
                 reasons motivated us to dissect the Volta GPU
                 architecture using microbenchmarks.\par

                 The introduction in August 2018 of Turing, NVidia's
                 latest architecture, pressed us to update our study. In
                 this report, we examine Turing and compare it
                 quantitatively against previous NVidia GPU generations.
                 Specifically, we study the T4 GPU: a low-power board
                 aiming at inference applications. We describe its
                 improvements against its inference-oriented
                 predecessor: the P4 GPU based on the Pascal
                 architecture. Both T4 and P4 GPUs achieve significantly
                 higher frequency-per-Watt figures than their full-size
                 counterparts.\par

                 We study the performance of the T4's TensorCores,
                 finding a much higher throughput on low-precision
                 operands than on the P4 GPU. We reveal that Turing
                 introduces new instructions that express matrix math
                 more succinctly. We map Turing's instruction space,
                 finding the same encoding as Volta, and additional
                 instructions. We reveal that the Turing TU104 chip has
                 the same memory hierarchy depth as the Volta GV100;
                 cache levels sizes on the TU104 are frequently twice as
                 large as those found on the Pascal GP104. We benchmark
                 each constituent of the T4 memory hierarchy and find
                 substantial overall performance improvements over its
                 P4 predecessor. We studied how clock throttling affects
                 compute-intensive workloads that hit power or thermal
                 limits.\par

                 Many of our findings are novel, published here for the
                 first time. All of them can guide high-performance
                 software developers get closer to the GPU's peak
                 performance.",
  acknowledgement = ack-nhfb,
}

@Article{Jiang:2019:LPU,
  author =       "H. Jiang and L. Liu and F. Lombardi and J. Han",
  title =        "Low-Power Unsigned Divider and Square Root Circuit
                 Designs Using Adaptive Approximation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "68",
  number =       "11",
  pages =        "1635--1646",
  month =        nov,
  year =         "2019",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2019.2916817",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Oct 29 11:08:44 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Adaptive approximation; Circuit synthesis; Delays;
                 divider; Error correction; Hardware; image processing;
                 Image reconstruction; low-power; overflow; Power
                 dissipation; SQR circuit",
}

@InProceedings{Johansson:2019:FAP,
  author =       "Fredrik Johansson",
  title =        "Faster Arbitrary-Precision Dot Product and Matrix
                 Multiplication",
  crossref =     "Takagi:2019:ISC",
  pages =        "15--22",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00012",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present algorithms for real and complex dot product
                 and matrix multiplication in arbitrary-precision
                 floating-point and ball arithmetic. A low-overhead dot
                 product is implemented on the level of GMP limb arrays;
                 it is about twice as fast as previous code in MPFR and
                 Arb at precision up to several hundred bits. Up to 128
                 bits, it is 3-4 times as fast, costing 20-30 cycles per
                 term for floating-point evaluation and 40-50 cycles per
                 term for balls. We handle large matrix multiplications
                 even more efficiently via blocks of scaled integer
                 matrices. The new methods are implemented in Arb and
                 significantly speed up polynomial operations and linear
                 algebra.",
  acknowledgement = ack-nhfb,
  keywords =     "arbitrary-precision arithmetic, ball arithmetic, dot
                 product, matrix multiplication; arbitrary-precision dot
                 product; arbitrary-precision floating-point; ARITH-26;
                 ball arithmetic; complex dot product; Costing; Digital
                 arithmetic; floating point arithmetic; floating-point
                 evaluation; GMP limb arrays; Indexes; Libraries; Linear
                 algebra; linear algebra; low-overhead dot product;
                 mathematics computing; matrix multiplication;
                 polynomial operations; polynomials; real dot product;
                 scaled integer matrices; Software; Upper bound; word
                 length 128.0 bit",
}

@InProceedings{Jugade:2019:MEE,
  author =       "Chaitanya Jugade and Deepak Ingole and Dayaram
                 Sonawane and Michal Kvasnica and John Gustafson",
  editor =       "{IEEE}",
  booktitle =    "{2019 Sixth Indian Control Conference (ICC)}",
  title =        "A Memory-Efficient Explicit Model Predictive Control
                 using Posits",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "188--193",
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ICC47138.2019.9123179",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Kalamkar:2019:SBD,
  author =       "Dhiraj D. Kalamkar and Dheevatsa Mudigere and Naveen
                 Mellempudi and Dipankar Das and Kunal Banerjee and
                 Sasikanth Avancha and Dharma Teja Vooturi and Nataraj
                 Jammalamadaka and Jianyu Huang and Hector Yuen and
                 Jiyan Yang and Jongsoo Park and Alexander Heinecke and
                 Evangelos Georganas and Sudarshan Srinivasan and
                 Abhisek Kundu and Misha Smelyanskiy and Bharat Kaul and
                 Pradeep Dubey",
  title =        "A Study of {BFLOAT16} for Deep Learning Training",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--10",
  day =          "29",
  month =        may,
  year =         "2019",
  bibdate =      "Fri Aug 30 17:25:53 2019",
  bibsource =    "DBLP archive;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://arxiv.org/abs/1905.12322",
  abstract =     "This paper presents the first comprehensive empirical
                 study demonstrating the efficacy of the Brain Floating
                 Point (BFLOAT16) half-precision format for Deep
                 Learning training across image classification, speech
                 recognition, language modeling, generative networks and
                 industrial recommendation systems. BFLOAT16 is
                 attractive for Deep Learning training for two reasons:
                 the range of values it can represent is the same as
                 that of IEEE 754 floating-point format (FP32) and
                 conversion to/from FP32 is simple. Maintaining the same
                 range as FP32 is important to ensure that no
                 hyper-parameter tuning is required for convergence;
                 e.g., IEEE 754 compliant half-precision floating point
                 (FP16) requires hyper-parameter tuning. In this paper,
                 we discuss the flow of tensors and various key
                 operations in mixed precision training, and delve into
                 details of operations, such as the rounding modes for
                 converting FP32 tensors to BFLOAT16. We have
                 implemented a method to emulate BFLOAT16 operations in
                 Tensorflow, Caffe2, IntelCaffe, and Neon for our
                 experiments. Our results show that deep learning
                 training using BFLOAT16 tensors achieves the same
                 state-of-the-art (SOTA) results across domains as FP32
                 tensors in the same number of iterations and with no
                 changes to hyper-parameters.",
  acknowledgement = ack-nhfb,
  biburl =       "https://dblp.org/rec/bib/journals/corr/abs-1905-12322",
  eprint =       "1905.12322",
  timestamp =    "Wed Jan 3 07:58:16 2024",
}

@InProceedings{Katajainen:2019:HMP,
  author =       "Jyrki Katajainen",
  editor =       "I. Kotsireas and P. Pardalos and K. Parsopoulos and D.
                 Souravlias and A. Tsokas",
  booktitle =    "Analysis of Experimental Algorithms. {SEA 2019}",
  title =        "Hacker's Multiple-Precision Integer-Division Program
                 in Close Scrutiny",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "376--391",
  year =         "2019",
  DOI =          "https://doi.org/10.1007/978-3-030-34029-2_25",
  bibdate =      "Thu Jan 28 19:43:12 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-LNCS,
  URL =          "http://www.cphstl.dk/Paper/Division/division.pdf",
  abstract =     "Before the era of ubiquitous computers, the
                 long-division method was presented in primary schools
                 as a paper-and-pencil technique to do whole-number
                 division. In the book \booktitle{Hacker's Delight} by
                 Warren [2nd edition, 2013], an implementation of this
                 algorithm was given using the C programming language.
                 In this paper we will report our experiences when
                 converting this program to a generic program-library
                 routine.\par

                 The highlights of the paper are as follows: (1) We
                 describe the long-division algorithm this is done for
                 educational purposes. (2) We outline its implementation
                 the goal is to show how to use modern C++ to achieve
                 flexibility, portability, and efficiency. (3) We
                 analyse its computational complexity by paying
                 attention to how the digit width affects the running
                 time. (4) We compare the practical performance of the
                 library routine against Warren's original. It is
                 pleasure to announce that the library routine is
                 faster. (5) We release the developed routine as part of
                 a software package that provides fixed-width integers
                 of arbitrary length, e.g. a number of type Open image
                 in new window has 2019 bits and it supports the same
                 operations with the same semantics as a number of type
                 {\tt unsigned int}",
  acknowledgement = ack-nhfb,
  keywords =     "Algorithm; Description; Experimentation;
                 Implementation; Long division; Meticulous analysis;
                 Multiple-precision arithmetic; Software library",
  ORCID-numbers = "Katajainen, Jyrki/0000-0002-7714-5588",
}

@InProceedings{Kaul:2019:OFF,
  author =       "Himanshu Kaul and Mark Anders and Sanu Mathew and
                 Seongjong Kim and Ram Krishnamurthy",
  title =        "Optimized Fused Floating-Point Many-Term Dot-Product
                 Hardware for Machine Learning Accelerators",
  crossref =     "Takagi:2019:ISC",
  pages =        "84--87",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00021",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper describes optimizations for the critical
                 maximum exponent and alignment operations, with
                 scalability for many-term fused floating-point
                 dot-product units. The impact of these optimizations is
                 quantified for up to 32-term BFloat16 weight/activation
                 inputs with single-precision dot-product output,
                 targeted for machine learning accelerators. Area and
                 energy efficiency results are compared across
                 performance targets, design parameters, and data
                 statistics.",
  acknowledgement = ack-nhfb,
  keywords =     "32-term BFloat16 weight inputs; Adders; alignment
                 operation; ARITH-26; Computer architecture; critical
                 maximum exponent operation; deep neural networks;
                 dot-product; Energy efficiency; floating point
                 arithmetic; floating-point; Hardware; learning
                 (artificial intelligence); Machine learning; machine
                 learning; machine learning accelerators; neural nets;
                 Optimization; optimized fused floating-point many-term
                 dot-product hardware; single-precision dot-product
                 output; Throughput",
}

@InProceedings{Kim:2019:CEI,
  author =       "HyunJin Kim and Min Soo Kim and Alberto A. {Del
                 Barrio} and Nader Bagherzadeh",
  title =        "A Cost-Efficient Iterative Truncated Logarithmic
                 Multiplication for Convolutional Neural Networks",
  crossref =     "Takagi:2019:ISC",
  pages =        "108--111",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00029",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper proposes a cost-efficient approximate
                 logarithmic multiplication for convolutional neural
                 networks (CNNs), where two truncated logarithmic
                 multipliers are connected for error correction. The
                 proposed iterative logarithmic multiplication achieves
                 low and unbiased average error while the hardware cost
                 is significantly reduced by utilizing the truncated
                 Mitchell multiplier and approximating error terms from
                 the first stage. The proposed design has error
                 characteristics that are suitable for neural network
                 inferences, and the experiments on contemporary CNNs
                 show that the proposed multiplier does not cause
                 significant degradation on accuracy compared to exact
                 multiplication.",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; approximate multiplier; ARITH-26;
                 convolutional neural nets; convolutional neural
                 network; convolutional neural networks; Convolutional
                 neural networks; cost-efficient approximate logarithmic
                 multiplication; Delays; Detectors; Digital arithmetic;
                 error correction; Hardware; iterative methods;
                 iterative truncated logarithmic multiplication;
                 logarithmic multiplication; Mitchell multiplier; neural
                 network inferences; truncated logarithmic multipliers;
                 truncated Mitchell multiplier",
}

@Article{Kim:2019:EMA,
  author =       "M. S. Kim and A. A. D. Barrio and L. T. Oliveira and
                 R. Hermida and N. Bagherzadeh",
  title =        "Efficient {Mitchell}'s Approximate Log Multipliers for
                 Convolutional Neural Networks",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "68",
  number =       "5",
  pages =        "660--675",
  month =        may,
  year =         "2019",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2018.2880742",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 11 09:46:20 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "approximate log multipliers; Approximation algorithms;
                 approximation theory; Arithmetic and logic units; CNN;
                 computer vision; convolutional neural nets;
                 convolutional neural networks; Convolutional neural
                 networks; customizable design; customizable log
                 multiplier; Degradation; design techniques; efficient
                 shift amount calculation; Energy consumption; energy
                 consumption reduction; energy-efficient approximate
                 multipliers; exact zero computation; floating point
                 arithmetic; fully-parallel LOD; ImageNet ILSVRC2012
                 dataset; Logic gates; low-power design; machine
                 learning; multiplying circuits; object recognition;
                 power aware computing; probability; Training",
}

@InProceedings{Klower:2019:PAF,
  author =       "Milan Kl{\"o}wer and Peter D. D{\"u}ben and Tim N.
                 Palmer",
  title =        "Posits as an Alternative to Floats for Weather and
                 Climate Models",
  crossref =     "Gustafson:2019:CPC",
  pages =        "1:1--1:8",
  year =         "2019",
  DOI =          "https://doi.org/10.1145/3316279.3316281",
  bibdate =      "Mon Feb 10 12:11:16 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  articleno =    "2",
  keywords =     "Computational fluid dynamics, floating point, computer
                 arithmetic, posits, reduced precision, climate
                 projections, weather forecast",
  location =     "Singapore, Singapore",
  numpages =     "8",
}

@InProceedings{Kostic:2019:UNV,
  author =       "Dusan Kostic and Shay Gueron",
  title =        "Using the New {VPMADD} Instructions for the New Post
                 Quantum Key Encapsulation Mechanism {SIKE}",
  crossref =     "Takagi:2019:ISC",
  pages =        "215--218",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00050",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper demonstrates the use of new processor
                 instructions VPMADD, intended to appear in the coming
                 generation of Intel processors (codename ``Cannon
                 Lake''), in order to accelerate the newly proposed key
                 encapsulation mechanism (KEM) named SIKE. SIKE is one
                 of the submissions to the NIST standardization process
                 on post-quantum cryptography, and is based on
                 pseudo-random walks in supersingular isogeny graphs.
                 While very small keys are the main advantage of SIKE,
                 its extreme computational intensiveness makes it one of
                 the slowest KEM proposals. Performance optimizations
                 are needed. We address here the ``Level 1'' parameters
                 that target 64-bit quantum security, and deemed
                 sufficient for the NIST standardization effort. Thus,
                 we focus on SIKE503 that operates over Fp2 with a
                 503-bit prime p. These short operands pose a
                 significant challenge on using VPMADD effectively. We
                 demonstrate several optimization methods to accelerate
                 Fp, Fp2, and the elliptic curve arithmetic, and predict
                 a potential speedup by a factor of 1.72x.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-26; codename CannonLake; Computer architecture;
                 Encapsulation; extreme computational intensiveness;
                 Intel processors; KEM proposals; key encapsulation
                 mechanism; NIST; NIST standardization effort; NIST
                 standardization process; Optimization; post quantum key
                 encapsulation mechanism SIKE; post-quantum
                 cryptography; processor instructions VPMADD; Proposals;
                 pseudorandom walks; Quantum computing; quantum
                 cryptography; quantum security; Registers; SIKE503;
                 supersingular isogeny graphs; VPMADD instructions;
                 VPMADD processor instructions, software optimization,
                 post quantum cryptography, supersingular isogeny",
}

@InProceedings{Kouya:2019:PEE,
  author =       "Tomonori Kouya",
  title =        "Performance Evaluation of an Efficient Double-Double
                 {BLAS1} Function With Error-Free Transformation and its
                 Application to Explicit Extrapolation Methods",
  crossref =     "Takagi:2019:ISC",
  pages =        "120--123",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00032",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Error-free transformation (EFT) has been recently
                 applied to solve ill-conditioned problems. This
                 transformation can reduce the number of arithmetic
                 operations required compared to multiple precision
                 arithmetic. In this study, we implement double-double
                 (DD) BLAS1 functions with EFT and propose the
                 application of the approach to explicit extrapolation
                 methods for solving initial value problems of ordinary
                 differential equations (ODEs). The presented routines
                 can be effective for a large system of linear ODEs,
                 especially when a harmonic sequence is used.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-26; arithmetic operations; BLAS1 functions;
                 Convergence; differential equations; efficient
                 double-double BLAS1 function; EFT; error-free
                 transformation; error-free transformation,
                 extrapolation, ordinary differential equation; explicit
                 extrapolation methods; extrapolation; Extrapolation;
                 floating point arithmetic; Harmonic analysis; harmonic
                 sequence; ill-conditioned problems; initial value
                 problems; Libraries; mathematics computing; multiple
                 precision arithmetic; ordinary differential equations;
                 performance evaluation; Silicon; Standards",
}

@Article{Kulisch:2019:MSI,
  author =       "Ulrich Kulisch",
  title =        "Mathematics and Speed for Interval Arithmetic: A
                 Complement to {IEEE 1788}",
  journal =      j-TOMS,
  volume =       "45",
  number =       "1",
  pages =        "5:1--5:22",
  month =        mar,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3264448",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3264448",
  abstract =     "After a short introduction, the article begins with an
                 axiomatic definition of rounded arithmetic. The
                 concepts of rounding and of rounded arithmetic
                 operations are defined in an axiomatic manner fully
                 independent of special data formats and encodings.
                 Basic properties of floating-point and interval
                 arithmetic can directly be derived from this abstract
                 mathematical model. Interval operations are defined as
                 set operations for elements of the set {\=I}R of closed
                 and connected sets of real numbers. As such, they form
                 an algebraically closed subset of the powerset of the
                 real numbers. This property leads to explicit formulas
                 for the arithmetic operations of floating-point
                 intervals of {\=I}F, which are executable on the
                 computer. Arithmetic for intervals of {\=I}F forms an
                 exception free calculus, i.e., arithmetic operations
                 for intervals of {\=I}F always lead to intervals of
                 {\=I}F again. Later sections are concerned with
                 programming support and hardware for interval
                 arithmetic. Both are a must and absolutely necessary to
                 move interval arithmetic more into the center of
                 scientific computing. With some minor hardware
                 additions, interval operations can be made as fast as
                 simple floating-point operations. In vector and matrix
                 spaces for real, complex, and interval data, the dot
                 product is a fundamental arithmetic operation.
                 Computing the dot product of two vectors with
                 floating-point components exactly substantially speeds
                 up floating-point and interval arithmetic as well as
                 the accuracy of the computed result. Hardware needed
                 for the exact dot product is very modest. The exact dot
                 product is essential for long real and long interval
                 arithmetic. Section 9 illustrates that interval
                 arithmetic as developed in this article already has a
                 long tradition. Products based on these ideas have been
                 available since 1980. Implementing what the article
                 advocates would have a profound effect on mathematical
                 software. Modern processor architecture from Intel, for
                 example, comes quite close to what is requested in this
                 article.",
  acknowledgement = ack-nhfb,
  articleno =    "5",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@InProceedings{Laguna:2019:FDF,
  author =       "Ignacio Laguna",
  editor =       "IEEE\slash ACM",
  booktitle =    "{ASE'19: 34th IEEE\slash ACM International Conference
                 on Automated Software Engineering, San Diego,
                 California, November 10--15, 2019}",
  title =        "{FPChecker}: Detecting Floating-Point Exceptions in
                 {GPU} Applications",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  bookpages =    "xxxv + 1296",
  pages =        "1126--1129",
  month =        nov,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ase.2019.00118",
  ISBN =         "1-72812-508-1",
  ISBN-13 =      "978-1-72812-508-4",
  LCCN =         "QA76.758 .Z566 2019",
  bibdate =      "Mon Sep 11 07:07:01 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Floating-point arithmetic is widely used in
                 applications from several fields including scientific
                 computing, machine learning, graphics, and finance.
                 Many of these applications are rapidly adopting the use
                 of GPUs to speedup computations. GPUs, however, have
                 limited support to detect floating-point exceptions,
                 which hinders the development of reliable applications
                 in GPU-based systems. We present FPCHECKER, the first
                 tool to automatically detect floating-point exceptions
                 in GPU applications. FPCHECKER uses the clang\slash
                 LLVM compiler to instrument GPU kernels and to detect
                 exceptions at runtime. Once an exception is detected,
                 it reports to the programmer the code location of the
                 exception as well as other useful information. The
                 programmer can then use this report to avoid the
                 exception, e.g., by modifying the application algorithm
                 or changing the input. We present the design of
                 FPCHECKER, an evaluation of the overhead of the tool,
                 and a real-world case scenario on which the tool is
                 used to identify a hidden exception. The slowdown of
                 FPCHECKER is moderate and the code is publicly
                 available as open source.",
  acknowledgement = ack-nhfb,
}

@TechReport{Laguna:2019:GPD,
  author =       "Ignacio Laguna and Paul C. Wood and Ranvijay Singh and
                 Saurabh Bagchi",
  title =        "{GPUMixer}: Performance-Driven Floating-Point Tuning
                 for {GPU} Scientific Applications",
  type =         "Report",
  institution =  "Lawrence Livermore National Laboratory",
  address =      "Livermore CA 94550, USA",
  year =         "2019",
  bibdate =      "Tue Aug 06 05:54:23 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/multithreading.bib;
                 https://www.math.utah.edu/pub/tex/bib/pvm.bib",
  URL =          "http://lagunaresearch.org/docs/isc-2019.pdf;
                 https://www.hpcwire.com/2019/08/05/llnl-purdue-researchers-harness-gpu-mixed-precision-for-accuracy-performance-tradeoff/",
  abstract =     "We present GPUMixer, a tool to perform mixed-precision
                 floating-point tuning on scientific GPU applications.
                 While precision tuning techniques are available, they
                 are designed for serial programs and are
                 accuracy-driven, i.e., they consider configurations
                 that satisfy accuracy constraints, but these
                 configurations may degrade performance. GPUMixer, in
                 contrast, presents a performance-driven approach for
                 tuning. We introduce a novel static analysis that finds
                 Fast Imprecise Sets (FISets), sets of operations on low
                 precision that minimize type conversions, which often
                 yield performance speedups. To estimate the relative
                 error introduced by GPU mixed-precision, we propose
                 shadow computations analysis for GPUs, the first of
                 this class for multi-threaded applications. GPUMixer
                 obtains performance improvements of up to 46.4\% of the
                 ideal speedup in comparison to only 20.7\% found by
                 state-of-the-art methods.",
  acknowledgement = ack-nhfb,
  remark =       "Best paper award at the 33rd ISC High Performance
                 conference held June 16--20, 2019.",
}

@Article{Lange:2019:SEP,
  author =       "Marko Lange and Siegfried M. Rump",
  title =        "Sharp estimates for perturbation errors in
                 summations",
  journal =      j-MATH-COMPUT,
  volume =       "88",
  number =       "315",
  pages =        "349--368",
  month =        jul,
  year =         "2019",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/mcom/3355",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Jul 14 06:45:34 MDT 2020",
  bibsource =    "http://www.ams.org/mcom/2019-88-315;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  URL =          "https://www.ams.org/journals/mcom/2019-88-315/S0025-5718-2018-03355-5;
                 https://www.ams.org/journals/mcom/2019-88-315/S0025-5718-2018-03355-5/S0025-5718-2018-03355-5.pdf;
                 https://www.ams.org/mathscinet/search/authors.html?mrauthid=1082372;
                 https://www.ams.org/mathscinet/search/authors.html?mrauthid=151815",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "accurate floating-point summation",
}

@Article{Lee:2019:EES,
  author =       "Jinsu Lee and Juhyoung Lee and Donghyeon Han and
                 Jinmook Lee and Gwangtae Park and Hoi-Jun Yoo",
  title =        "An Energy-Efficient Sparse Deep-Neural-Network
                 Learning Accelerator With Fine-Grained Mixed Precision
                 of {FP8--FP16}",
  journal =      "IEEE Solid-State Circuits Letters",
  volume =       "2",
  number =       "11",
  pages =        "232--235",
  year =         "2019",
  DOI =          "https://doi.org/10.1109/LSSC.2019.2937440",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accelerators; Arrays; deep learning (DL); deep-neural
                 network (DNN); Energy efficiency; energy efficient;
                 Hardware; Memory management; Solid state circuits;
                 Throughput; Training; training",
}

@InProceedings{Lee:2019:LWS,
  author =       "Jinsu Lee and Juhyoung Lee and Donghyeon Han and
                 Jinmook Lee and Gwangtae Park and Hoi-Jun Yoo",
  booktitle =    "{2019 IEEE International Solid-State Circuits
                 Conference --- (ISSCC)}",
  title =        "7.7 {LNPU}: a {25.3TFLOPS/W} Sparse
                 Deep-Neural-Network Learning Processor with
                 Fine-Grained Mixed Precision of {FP8--FP16}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "142--144",
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ISSCC.2019.8662302",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Acceleration; Deep learning; Neural networks;
                 Registers; Throughput; Training",
}

@InProceedings{Lefevre:2019:ACM,
  author =       "Vincent Lef{\`e}vre and Jean-Michel Muller",
  title =        "Accurate Complex Multiplication in Floating-Point
                 Arithmetic",
  crossref =     "Takagi:2019:ISC",
  pages =        "23--29",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00013",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We deal with accurate complex multiplication in binary
                 floating-point arithmetic, with an emphasis on the case
                 where one of the operands is a ``double-word'' number.
                 We provide an algorithm that returns a complex product
                 with normwise relative error bound close to the best
                 possible one, i.e., the rounding unit u.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate complex multiplication; Approximation
                 algorithms; ARITH-26; binary floating-point arithmetic;
                 complex product; Digital arithmetic; double-word
                 number; floating point arithmetic; Floating-point
                 arithmetic; Floating-point arithmetic, Complex
                 multiplication, Rounding error analysis; Lips; Parallel
                 processing; Standards; Zirconium",
}

@Article{Lemire:2019:FRD,
  author =       "Daniel Lemire and Owen Kaser and Nathan Kurz",
  title =        "Faster remainder by direct computation: Applications
                 to compilers and software libraries",
  journal =      j-SPE,
  volume =       "49",
  number =       "6",
  pages =        "953--970",
  month =        jun,
  year =         "2019",
  CODEN =        "SPEXBL",
  DOI =          "https://doi.org/10.1002/spe.2689",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Sat Oct 12 09:43:47 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/spe.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Software --- Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  keywords =     "integer division; integer remainder",
  onlinedate =   "27 February 2019",
  remark =       "Paul Zimmermann reported on the gmp-devel mailing list
                 on Tue, 15 Oct 2019 10:40:48 +0200 that the remainder
                 algorithm in this report was described earlier in
                 unpublished work in \cite{Bernstein:2004:SRT}.",
}

@InProceedings{Lindstrom:2019:UCR,
  author =       "Peter Lindstrom",
  title =        "Universal Coding of the Reals Using Bisection",
  crossref =     "Gustafson:2019:CPC",
  pages =        "7:1--7:10",
  year =         "2019",
  DOI =          "https://doi.org/10.1145/3316279.3316286",
  bibdate =      "Mon Feb 10 12:11:16 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  articleno =    "7",
  keywords =     "wobbling accuracy, floating point, bracketing, binary
                 search, bisection, Universal coding, posits, unbounded
                 search",
  location =     "Singapore, Singapore",
  numpages =     "10",
}

@Article{Liu:2019:DAA,
  author =       "W. Liu and T. Cao and P. Yin and Y. Zhu and C. Wang
                 and E. E. Swartzlander and F. Lombardi",
  title =        "Design and Analysis of Approximate Redundant Binary
                 Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "68",
  number =       "6",
  pages =        "804--819",
  month =        jun,
  year =         "2019",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2018.2890222",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 11 09:46:20 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "adders; Adders; approximate arithmetic designs;
                 approximate Booth encoders; approximate circuits;
                 approximate computing; Approximate computing;
                 approximate NB Booth multipliers; approximate product
                 arrays; approximate RB multipliers; approximate
                 redundant binary multiplier design; Compressors;
                 Delays; Error analysis; error analysis; error
                 characteristics; error-resilient applications;
                 error-tolerant applications; exact regular partial
                 product arrays; Hardware; hardware simulation; logic
                 design; low power; low power circuits; modified Booth
                 encoder; multiplying circuits; partial product array;
                 Power demand; RB 4:2 compressors; RB adders; RB
                 compressor; RB compressors; RB-NB converter; RB-normal
                 binary converter; redundant binary (RB) multiplier",
}

@Article{Lourenco:2019:ESS,
  author =       "Christopher Lourenco and Adolfo R. Escobedo and Erick
                 Moreno-Centeno and Timothy A. Davis",
  title =        "Exact Solution of Sparse Linear Systems via
                 Left-Looking Roundoff-Error-Free {$ L U $}
                 Factorization in Time Proportional to Arithmetic Work",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "40",
  number =       "2",
  pages =        "609--638",
  month =        "????",
  year =         "2019",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/18M1202499",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Thu Oct 10 08:00:32 MDT 2019",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/40/2;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
  keywords =     "exact rational arithmetic; Sparse Left-looking
                 Integer-Preserving (SLIP) LU factorization",
  onlinedate =   "January 2019",
}

@InProceedings{Lu:2019:TDN,
  author =       "Jinming Lu and Siyuan Lu and Zhisheng Wang and Chao
                 Fang and Jun Lin and Zhongfeng Wang and Li Du",
  editor =       "{IEEE}",
  booktitle =    "{2019 32nd IEEE International System-on-Chip
                 Conference (SOCC)}",
  title =        "Training Deep Neural Networks Using Posit Number
                 System",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "62--67",
  year =         "2019",
  DOI =          "https://doi.org/10.1109/SOCC46988.2019.1570558530",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lutz:2019:AFP,
  author =       "David Lutz",
  title =        "{ARM} Floating Point 2019: Latency, Area, Power",
  crossref =     "Takagi:2019:ISC",
  pages =        "97--98",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00025",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We have had little or no speed increase from process
                 in the past few years, but latency continues to
                 decrease due to algorithmic improvements [1] and a
                 decision to spend more area on CPU datapaths [2]. A
                 binary64 floating-point (FP) add now takes two cycles
                 when done as part of a 2+2-cycle FMA, and even one
                 cycle when done as part of an in-order vector
                 reduction. Smaller and more specialized FP operations
                 (bfloat16) are even faster. Finally, the decision to
                 spend more area on datapath logic took a new twist this
                 year when we applied it to GPUs, cutting dynamic power
                 there by a third.",
  acknowledgement = ack-nhfb,
  keywords =     "2+2-cycle FMA; adders; Adders; ARITH-26; ARM floating
                 point 2019; bfloat16; binary64 floating-point; Clocks;
                 CPU datapaths; datapath logic; Digital arithmetic;
                 floating point arithmetic; in-order vector reduction;
                 Microarchitecture; Pipelines; random number generation;
                 Security; Standards; vectors",
}

@Misc{Lutz:2019:AMP,
  author =       "David Raymond Lutz and Neil Burgess and Christopher
                 Neal Hinds and Andreas Due Engh-Halstvedt",
  title =        "Apparatus and method for performing arithmetic
                 operations to accumulate floating-point numbers",
  howpublished = "US Patent 10,216,479",
  day =          "26",
  month =        feb,
  year =         "2019",
  bibdate =      "Thu Oct 17 11:34:51 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://patents.google.com/patent/US10216479B2",
  abstract =     "An apparatus and method are provided for performing
                 arithmetic operations to accumulate floating-point
                 numbers. The apparatus comprises execution circuitry to
                 perform arithmetic operations, and decoder circuitry to
                 decode a sequence of instructions. A convert and
                 accumulate instruction is provided, and the decoder
                 circuitry is responsive to decoding the convert and
                 accumulate instruction to generate one or more control
                 signals to control the execution circuitry to convert
                 at least one floating-point operand identified by the
                 convert and accumulate instruction into a corresponding
                 N-bit fixed-point operand having M fraction bits, where
                 M is less than N and M is dependent on a format of the
                 floating-point operand. The execution circuitry
                 accumulates each corresponding N bit fixed-point
                 operand and a P bit fixed-point operand identified by
                 the convert and accumulate instruction in order to
                 generate a P bit fixed-point result value, where P is
                 greater than N and also has M fraction bits.",
  acknowledgement = ack-nhfb,
  remark =       "Patent filed 6 December 2016, granted to Arm Ltd. on
                 26 February 2019, expected expiration 2 February 2037
                 (in 17th year of grant).",
}

@InProceedings{Mach:2019:FSB,
  author =       "Stefan Mach and Fabian Schuiki and Florian Zaruba and
                 Luca Benini",
  editor =       "{IEEE}",
  booktitle =    "{2019 IFIP\slash IEEE 27th International Conference on
                 Very Large Scale Integration (VLSI-SoC)}",
  title =        "A {0.80pJ\slash flop, 1.24Tflop\slash sW} 8-to-64 bit
                 Transprecision Floating-Point Unit for a 64 bit
                 {RISC-V} Processor in 22nm {FD-SOI}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "95--98",
  year =         "2019",
  DOI =          "https://doi.org/10.1109/VLSI-SoC.2019.8920307",
  bibdate =      "Sat Dec 16 15:51:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
}

@Article{Magron:2019:CRE,
  author =       "V. Magron and A. Rocca and T. Dang",
  title =        "Certified Roundoff Error Bounds Using {Bernstein}
                 Expansions and Sparse {Krivine--Stengle}
                 Representations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "68",
  number =       "7",
  pages =        "953--966",
  month =        jul,
  year =         "2019",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2018.2851235",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 11 09:46:20 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Algebra; Bernstein expansions; Convergence; embedded
                 systems; embedded systems implementation; error
                 analysis; floating point arithmetic; FPBern software
                 package; FPKriSten software package; Krivine-Stengle
                 representations; linear programming; linear programming
                 relaxations; nonlinear programs; Optimization;
                 Polynomial optimization; polynomials; rational
                 functions; rigorous upper bounds; roundoff error
                 bounds; roundoff errors; Roundoff errors; Software
                 algorithms; Tools; Upper bound",
}

@InProceedings{Martins:2019:HHR,
  author =       "Paulo Martins and Jeremy Marrez and Jean-Claude Bajard
                 and Leonel Sousa",
  title =        "{HyPoRes}: An Hybrid Representation System for {ECC}",
  crossref =     "Takagi:2019:ISC",
  pages =        "207--214",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00049",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Residue Number System (RNS) is a numeral
                 representation enabling for more efficient addition and
                 multiplication implementations. However, due its
                 non-positional nature, modular reductions, required for
                 example by Elliptic Curve (EC) Cryptography (ECC),
                 become costlier. Traditional approaches to RNS modular
                 reduction resort to the Montgomery algorithm,
                 underpinned by large basis extensions. Recently,
                 Hybrid-Positional Residue Number Systems (HPRs) have
                 been proposed, providing a trade-off between the
                 efficiency of RNS and the flexibility of positional
                 number representations. Numbers are represented in a
                 positional representation with the coefficients
                 represented in RNS. By crafting primes of a special
                 form, the complexity of reductions modulo those primes
                 is mitigated, relying on extensions of smaller bases.
                 Due to the need of crafting special primes, this
                 approach is not directly extensible to group operations
                 over currently standardised elliptic curves. In this
                 paper, the Hybrid-Polynomial Residue Number System
                 (HyPoRes) is proposed, enabling for improved modular
                 reductions for any prime. Experimental results show
                 that the modular reduction of HyPoRes, although at most
                 1.4 times slower than HPR for HPR-crafted primes, is up
                 to 1.4 times faster than a generic RNS approach for
                 primes of ECC standards.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-26; Art; Complexity theory; Dynamic range; ECC
                 standards; Elliptic Curve Cryp-tography; Elliptic curve
                 cryptography; elliptic curve cryptography; Elliptic
                 curves; generic RNS approach; HPR-crafted primes;
                 hybrid representation system; hybrid-polynomial residue
                 number system; hybrid-positional residue number
                 systems; HyPoRes; improved modular reductions;
                 Lattices; Modular Arithmetic; Montgomery algorithm;
                 multiplication implementations; polynomials; positional
                 number representations; public key cryptography;
                 Residue Number System; residue number systems; RNS
                 modular reduction",
}

@InProceedings{Matula:2019:PCG,
  author =       "David W. Matula and Zizhen Chen",
  title =        "Precise and Concise Graphical Representation of the
                 Natural Numbers",
  crossref =     "Takagi:2019:ISC",
  pages =        "100--103",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00027",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A graphical number representation system based on the
                 formal logic foundation of a recursively defined
                 function is presented. The function exposes a
                 one-to-one correspondence between the natural numbers
                 and the set of rooted trees. Secondly, a relation
                 between pairs of natural numbers is shown to partition
                 the integers into disjoint finite sets each visualized
                 as a tree in the forest of all finite trees. This
                 relation encapsulates in visual form the natural
                 structure and distribution of primes in a manner not
                 previously investigated. These representations allow
                 arithmeticians to visually experience natural numbers
                 in a 2D graphical layout. This form is free of cultural
                 choices such as the number of symbols in an alphabet
                 and/or one-dimensional symbol strings. The fundamental
                 nature of these mappings is argued to be accessible to
                 a creative mind independent of formal schooling. This
                 short note includes examples illustrating the
                 simplicity of the constructions.",
  acknowledgement = ack-nhfb,
  keywords =     "2D graphical layout; ARITH-26; Computer science;
                 disjoint finite sets; finite trees; Forestry; formal
                 logic foundation; graphical number representation
                 system; graphical representation; Labeling; natural
                 numbers; natural structure; number fonts;
                 one-dimensional symbol strings; one-to-one
                 correspondence; prime factorization; prime number
                 function; recursive function; recursive functions;
                 recursively defined function; rooted trees; trees
                 (mathematics); Two dimensional displays; Vegetation;
                 Visualization",
}

@Article{Maynard:2019:MPA,
  author =       "C. M. Maynard and D. N. Walters",
  title =        "Mixed-precision arithmetic in the {ENDGame} dynamical
                 core of the {Unified Model}, a numerical weather
                 prediction and climate model code",
  journal =      j-COMP-PHYS-COMM,
  volume =       "244",
  number =       "??",
  pages =        "69--75",
  month =        nov,
  year =         "2019",
  CODEN =        "CPHCBZ",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Fri Sep 6 11:03:48 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/S0010465519302127",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{McCullough:2019:WTS,
  author =       "B. D. McCullough and Taha Mokfi and Mahsa Almaeenjad",
  title =        "{Wilkinson}'s Tests and {SQL} Packages",
  journal =      j-SIGMOD,
  volume =       "48",
  number =       "3",
  pages =        "17--22",
  month =        sep,
  year =         "2019",
  CODEN =        "SRECD8",
  DOI =          "https://doi.org/10.1145/3377391.3377395",
  ISSN =         "0163-5808 (print), 1943-5835 (electronic)",
  ISSN-L =       "0163-5808",
  bibdate =      "Sat Dec 21 07:26:01 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigmod.bib",
  abstract =     "Wilkinson's Tests are used to benchmark the accuracy
                 of some statistical functions in six SQL packages:
                 Apache Hive, Microsoft Access, Microsoft SQL Server,
                 MySQL, Oracle 11g SQL, and SAP Hana. Using the best
                 choice of data type, we find that different packages
                 use different rounding schemes, two packages use
                 unreliable algorithms to compute the sample variance,
                 one package returns the population standard deviation
                 when the sample standard deviation is called, and one
                 package has an unstable algorithm for computing the
                 correlation coefficient. Using the wrong data type all
                 but guarantees inaccurate results.",
  acknowledgement = ack-nhfb,
  fjournal =     "SIGMOD Record (ACM Special Interest Group on
                 Management of Data)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J689",
  remark =       "This paper looks at statistical software inside six
                 widely-used SQL databases, and find serious errors in
                 most of them, and poor numerical implementations for
                 standard deviations and other well-understood
                 computational algorithms. See also earlier work
                 recorded in fparith.bib
                 \cite{McCullough:1998:ARS,McCullough:1999:ARS,McCullough:1999:NRE}.",
}

@InProceedings{McKinstry:2019:DLP,
  author =       "Jeffrey L. McKinstry and Steven K. Esser and
                 Rathinakumar Appuswamy and Deepika Bablani and John V.
                 Arthur and Izzet B. Yildiz and Dharmendra S. Modha",
  booktitle =    "{2019 Fifth Workshop on Energy Efficient Machine
                 Learning and Cognitive Computing --- NeurIPS Edition
                 (EMC2-NIPS)}",
  title =        "Discovering Low-Precision Networks Close to
                 Full-Precision Networks for Efficient Inference",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "6--9",
  year =         "2019",
  DOI =          "https://doi.org/10.1109/EMC2-NIPS53020.2019.00009",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benchmark testing; computer vision; Conferences; deep
                 learning; Energy efficiency; fp32; low precision;
                 Machine learning; Quantization (signal); Sensitivity
                 analysis; Training",
}

@InProceedings{Melquiond:2019:FVS,
  author =       "Guillaume Melquiond and Raphael Rieu-Helft",
  title =        "Formal Verification of a State-of-the-Art Integer
                 Square Root",
  crossref =     "Takagi:2019:ISC",
  pages =        "183--186",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00041",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present the automatic formal verification of a
                 state-of-the-art algorithm from the GMP library that
                 computes the square root of a 64-bit integer. Although
                 it uses only integer operations, the best way to
                 understand the program is to view it as a fixed-point
                 arithmetic algorithm that implements Newton's method.
                 The C code is short but intricate, involving magic
                 constants and intentional arithmetic overflows. We have
                 verified the algorithm using the Why3 tool and
                 automated solvers such as Gappa.",
  acknowledgement = ack-nhfb,
  keywords =     "64-bit integer; Approximation algorithms; ARITH-26;
                 automatic formal verification; C code; C language;
                 Convergence; Digital arithmetic; electronic engineering
                 computing; fixed point arithmetic; Fixed-point
                 arithmetic; fixed-point arithmetic algorithm; floating
                 point arithmetic; Floors; Formal verification; GMP
                 library; integer operations; integer square root;
                 intentional arithmetic overflows; Libraries; Newton
                 method; program verification; programming; Tools; Why3
                 tool",
}

@PhdThesis{Melquiond:2019:NVN,
  author =       "Guillaume Melquiond",
  title =        "Normal Verification for Numerical Computations, and
                 the Other Way Around",
  type =         "{Habilitation {\`a} Diriger des Recherches}",
  school =       "Universit{\'e} Paris Sud, 2",
  address =      "Paris, France",
  pages =        "x + 163",
  day =          "25",
  month =        jul,
  year =         "2019",
  bibdate =      "Fri Sep 22 16:46:42 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://theses.hal.science/tel-02194683/document",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mian:2019:CAE,
  author =       "Riaz-ul-haque Mian and Michihiro Shintani and Michiko
                 Inoue",
  editor =       "{IEEE}",
  booktitle =    "{2019 32nd IEEE International System-on-Chip
                 Conference (SOCC)}",
  title =        "Cycle-Accurate Evaluation of Software-Hardware
                 Co-Design of Decimal Computation in {RISC-V}
                 Ecosystem",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "412--417",
  year =         "2019",
  DOI =          "https://doi.org/10.1109/SOCC46988.2019.1570559752",
  bibdate =      "Sat Dec 16 15:51:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Decimal arithmetic; Decimal multiplication; Evaluation
                 framework; Hardware accelerator; RISC-V; RoCC; Rocket
                 chip",
}

@Misc{Moler:2019:CCF,
  author =       "Cleve Moler",
  title =        "{Cleve}'s Corner: Floating Point Arithmetic Before
                 {IEEE 754}",
  howpublished = "MathWorks Web site.",
  day =          "18",
  month =        jan,
  year =         "2019",
  bibdate =      "Sat Jan 19 15:18:17 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://blogs.mathworks.com/cleve/2019/01/18/floating-point-arithmetic-before-ieee-754/",
  abstract =     "In a comment following my post about half-precision
                 arithmetic, ``Raj C'' asked how the parameters for IEEE
                 Standard 754 floating point arithmetic were chosen. I
                 replied that I didn't know but would try to find out. I
                 called emeritus U. C. Berkeley Professor W. (Velvel)
                 Kahan, who was the principle architect of 754. Here is
                 what I learned.",
  acknowledgement = ack-nhfb,
}

@Misc{Moler:2019:CCV,
  author =       "Cleve Moler",
  title =        "{Cleve}'s Corner: Variable Format Half Precision
                 Floating Point Arithmetic",
  howpublished = "MathWorks Web site.",
  day =          "16",
  month =        jan,
  year =         "2019",
  bibdate =      "Sat Jan 19 15:14:03 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://blogs.mathworks.com/cleve/2019/01/16/variable-format-half-precision-floating-point-arithmetic/",
  abstract =     "A year and a half ago I wrote a post about ``half
                 precision'' 16-bit floating point arithmetic, Moler on
                 fp16. I followed this with a bug fix, bug in fp16. Both
                 posts were about fp16, defined in IEEE standard 754.
                 This is only one of 15 possible 16-bit formats. In this
                 post I am going to consider all 15.",
  acknowledgement = ack-nhfb,
}

@Article{Mopuri:2019:CRB,
  author =       "Suresh Mopuri and Swati Bhardwaj and Amit Acharyya",
  title =        "Coordinate Rotation-Based Design Methodology for
                 Square Root and Division Computation",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
  volume =       "66",
  number =       "7",
  pages =        "1227--1231",
  year =         "2019",
  DOI =          "https://doi.org/10.1109/TCSII.2018.2878599",
  ISSN =         "1549-7747 (print), 1558-3791 (electronic)",
  ISSN-L =       "1549-7747",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems II: Express
                 Briefs",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
  keywords =     "Circuits and systems; Computer architecture; CORDIC;
                 Covariance matrices; Design methodology; division;
                 Hardware; Matrix decomposition; Monitoring; Square
                 root",
}

@InProceedings{Moriai:2019:PPD,
  author =       "Shiho Moriai",
  title =        "Privacy-Preserving Deep Learning via Additively
                 Homomorphic Encryption",
  crossref =     "Takagi:2019:ISC",
  pages =        "198--198",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00047",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We aim at creating a society where we can resolve
                 various social challenges by incorporating the
                 innovations of the fourth industrial revolution (e.g.
                 IoT, big data, AI, robot, and the sharing economy) into
                 every industry and social life. By doing so the society
                 of the future will be one in which new values and
                 services are created continuously, making people's
                 lives more conformable and sustainable. This is Society
                 5.0, a super-smart society. Security and privacy are
                 key issues to be addressed to realize Society 5.0.
                 Privacy-preserving data analytics will play an
                 important role. In this talk we show our recent works
                 on privacy-preserving data analytics such as
                 privacy-preserving logistic regression and
                 privacy-preserving deep learning. Finally, we show our
                 ongoing research project under JST CREST AI. In this
                 project we are developing privacy-preserving financial
                 data analytics systems that can detect fraud with high
                 security and accuracy. To validate the systems, we will
                 perform demonstration tests with several financial
                 institutions and solve the problems necessary for their
                 implementation in the real world.",
  acknowledgement = ack-nhfb,
  keywords =     "additively homomorphic encryption; ARITH-26; Big Data;
                 data analysis; Data analysis; data privacy; Deep
                 learning; Digital arithmetic; Encryption; financial
                 data processing; financial institutions; fourth
                 industrial revolution; fraud; Information and
                 communication technology; IoT; JST CREST AI; neural
                 nets; privacy issues; privacy-preserving deep learning;
                 privacy-preserving financial data analytics systems;
                 privacy-preserving logistic regression; regression
                 analysis; social challenges; social life; social
                 sciences computing; Society 5.0; super-smart society",
}

@Article{Moroz:2019:EFP,
  author =       "Leonid Moroz and Volodymyr Samotyy",
  title =        "Efficient Floating-Point Division for Digital Signal
                 Processing Application [Tips \& Tricks]",
  journal =      j-IEEE-SIGNAL-PROCESS-MAG,
  volume =       "36",
  number =       "1",
  pages =        "159--163",
  month =        jan,
  year =         "2019",
  CODEN =        "ISPRE6",
  DOI =          "https://doi.org/10.1109/msp.2018.2875977",
  ISSN =         "1053-5888 (print), 1558-0792 (electronic)",
  ISSN-L =       "1053-5888",
  bibdate =      "Thu Apr 10 15:04:29 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Signal Processing Magazine",
}

@Article{Munoz-Coreas:2019:QCD,
  author =       "E. Mu{\~n}oz-Coreas and H. Thapliyal",
  title =        "Quantum Circuit Design of a {$T$}-count Optimized
                 Integer Multiplier",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "68",
  number =       "5",
  pages =        "729--739",
  month =        may,
  year =         "2019",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2018.2882774",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 11 09:46:20 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "adders; Adders; Clifford+T gates; conditional adder;
                 fault tolerance; Fault tolerance; fault tolerant
                 implementations; Fault tolerant systems; integer
                 multiplication; logic design; Logic gates; quantum
                 arithmetic; quantum circuit design; quantum circuits;
                 Quantum computing; quantum conditional adder circuit;
                 quantum gates; quantum hardware resources; quantum
                 multiplier design; qubits; Registers; reliable quantum
                 circuits; scalable quantum circuits; T-count optimized
                 quantum circuit; T-count savings; Toffoli gate array",
}

@Article{Nabavinejad:2019:CDP,
  author =       "Seyed Morteza Nabavinejad and Hassan Hafez-Kolahi and
                 Sherief Reda",
  title =        "Coordinated {DVFS} and Precision Control for Deep
                 Neural Networks",
  journal =      j-IEEE-COMPUT-ARCHIT-LETT,
  volume =       "18",
  number =       "2",
  pages =        "136--140",
  year =         "2019",
  DOI =          "https://doi.org/10.1109/LCA.2019.2942020",
  ISSN =         "1556-6056 (print), 1556-6064 (electronic)",
  ISSN-L =       "1556-6056",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Computer Architecture Letters",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=10208",
  keywords =     "accuracy; Deep neural network; Graphics processing
                 units; hardware accelerator; Neural networks; power;
                 Power demand; response time; Runtime; Servers; Time
                 factors; Time-frequency analysis",
}

@Article{Nannarelli:2019:TFP,
  author =       "A. Nannarelli",
  title =        "Tunable Floating-Point Adder",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "68",
  number =       "10",
  pages =        "1553--1560",
  month =        oct,
  year =         "2019",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2019.2906907",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 12 13:33:25 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Adders; addition; Computer architecture; energy
                 efficiency; Floating-point; Google; Hardware; IEEE
                 rounding; Indexes; Standards; Tuning",
  remark =       "From the abstract: ``TFP is a variable precision
                 format in which a given precision can be chosen for a
                 single operation by selecting a specific number of bits
                 for significand and exponent in the floating-point
                 representation. By tuning the precision of an algorithm
                 to the minimum precision achieving an acceptable target
                 error, we can make the computation more power
                 efficient.''",
}

@InProceedings{Nogami:2019:OWV,
  author =       "Wakana Nogami and Tsutomu Ikegami and Shin-ichi O'uchi
                 and Ryousei Takano and Tomohiro Kudoh",
  booktitle =    "{2019 International Joint Conference on Neural
                 Networks (IJCNN)}",
  title =        "Optimizing Weight Value Quantization for {CNN}
                 Inference",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--8",
  year =         "2019",
  DOI =          "https://doi.org/10.1109/IJCNN.2019.8852331",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computational modeling; Convolutional Neural Network;
                 Genetic Algorithm; Genetic algorithms; Genomics;
                 Mathematical model; Neural networks; Optimization;
                 Quantization; Quantization (signal); Simulated
                 Annealing; Training",
}

@InProceedings{Nurvitadhi:2019:WCW,
  author =       "Eriko Nurvitadhi and Dongup Kwon and Ali Jafari and
                 Andrew Boutros and Jaewoong Sim and Phillip Tomson and
                 Huseyin Sumbul and Gregory Chen and Phil Knag and
                 Raghavan Kumar and Ram Krishnamurthy and Sergey Gribok
                 and Bogdan Pasca and Martin Langhammer and Debbie Marr
                 and Aravind Dasu",
  booktitle =    "{2019 IEEE 27th Annual International Symposium on
                 Field-Programmable Custom Computing Machines (FCCM)}",
  title =        "Why Compete When You Can Work Together: {FPGA-ASIC}
                 Integration for Persistent {RNNs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "199--207",
  year =         "2019",
  DOI =          "https://doi.org/10.1109/FCCM.2019.00035",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "chiplet; Computational modeling; Deep learning; Field
                 programmable gate arrays; fpga; Graphics processing
                 units; Hazards; persistent AI; Real-time systems;
                 system in package; System-on-chip; Throughput",
}

@InProceedings{Pandey:2019:UFP,
  author =       "Kumar Sambhav Pandey and Dinesh Kumar B and Neeraj
                 Goel and Hitesh Shrimali",
  title =        "An Ultra-Fast Parallel Prefix Adder",
  crossref =     "Takagi:2019:ISC",
  pages =        "125--134",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00034",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Parallel Prefix adders are arguably the most commonly
                 used arithmetic units. They have been extensively
                 investigated at architecture level, register transfer
                 level (RTL), gate level, circuit level as well as
                 layout level giving rise to a plethora of mathematical
                 formulations, topologies and implementations. This
                 paper contributes significantly to the understanding of
                 these parallel prefix adders in a couple of ways.
                 Firstly, it attempts to describe various such parallel
                 prefix adders in elegant and consistent formulations.
                 Secondly, a new family of parallel prefix adders is
                 proposed at architecture level. The estimates of the
                 area-throughput characteristics for an instance of this
                 family are also presented. While the speeds achieved by
                 this instance match those achieved by the state of the
                 art adders, their area characteristics exhibit upto
                 26\% improvement.",
  acknowledgement = ack-nhfb,
  keywords =     "adder recurrence relations; Adders; adders;
                 architecture level; area-throughput characteristics;
                 ARITH-26; arithmetic units; Computer architecture;
                 Digital arithmetic; digital arithmetic; integrated
                 circuit layout; integrated logic circuits; logic
                 design; Logic gates; Microprocessors; Parallel prefix
                 adders; Terminology; Topology; ultrafast parallel
                 prefix adder",
}

@Article{Parhi:2019:CAF,
  author =       "Keshab K. Parhi and Yin Liu",
  title =        "Computing Arithmetic Functions Using Stochastic Logic
                 by Series Expansion",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "7",
  number =       "1",
  pages =        "44--59",
  month =        jan # "\slash " # mar,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/TETC.2016.2618750",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  abstract =     "Stochastic logic implementations of complex arithmetic
                 functions, such as trigonometric, exponential, and
                 sigmoid, are derived based on truncated versions of
                 their Maclaurin series expansions. This paper makes
                 three contributions. First, it is shown that a
                 polynomial can be implemented using multiple levels of
                 NAND gates based on Horner's rule, if the coefficients
                 are alternately positive and negative and their
                 magnitudes are monotonically decreasing. Truncated
                 Maclaurin series expansions of arithmetic functions are
                 used to generate polynomials which satisfy these
                 constraints. The input and output in these functions
                 are represented by unipolar representation. Functions
                 including sine, cosine, tangent hyperbolic, logarithm
                 and exponential can be implemented using this method.
                 Second, for a polynomial that does not satisfy these
                 constraints, it still can be implemented based on
                 Horner's rule if each factor of the polynomial
                 satisfies these constraints. It is shown that functions
                 such as $ \sin \pi x / \pi $, $ e^{-a x} $, $ \tanh a x
                 $ and $ \sigmoid (a x^3) $ (for values of $ a > 1$) can
                 be implemented using stochastic logic using
                 factorization in combination with Horner's rule. Third,
                 format conversion is proposed for arithmetic functions
                 with input and output represented in different formats,
                 such as $ \cos \pi x$ given $ x \in [0, 1]$ and $
                 \sigmoid (x)$ given $ x \in [ - 1, 1]$. Polynomials are
                 transformed to equivalent forms that naturally exploit
                 format conversions. The proposed stochastic logic
                 circuits outperform the well-known Bernstein polynomial
                 based and finite-state-machine (FSM) based
                 implementations. Furthermore, the hardware complexity
                 and the critical path of the proposed implementations
                 are less than the well-known Bernstein polynomial based
                 and FSM based implementations for most cases",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}

@InProceedings{Parry:2019:PSO,
  author =       "Katherine Parry",
  title =        "A Perspective into Squarer Optimization",
  crossref =     "Takagi:2019:ISC",
  pages =        "124--124",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00033",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Artificial Intelligence applications do millions of
                 square calculations, such as within Gradient Descent or
                 Principle Component Analysis (PCA). Any time measured
                 or observed data is analyzed; the error, residual, or a
                 comparison against a norm, it is evaluated using a
                 square operation. Squarers are special purpose
                 multipliers that can be employed when the operands are
                 identical. Most calculations use slower multipliers,
                 even though squarers calculate faster, use less power,
                 and occupy less area. Multiplication is composed of a
                 series of partial products that are accumulated to
                 result in the multiplied product. Multiplier and
                 squarer propagation delay is assessed using the number
                 of partial products, or more their addition. The
                 calculation of partial products can occur in parallel,
                 thus does not significantly tax the propagation delay,
                 but carries from their addition create computational
                 dependencies. A standard 8-bit multiplier requires 56
                 partial product additions and previous work has reduced
                 a squarer to 22 partial products sums. This paper
                 reviews the previous technology and illustrates further
                 Boolean optimizations that minimize the number of
                 additions to 15 partial products.",
  acknowledgement = ack-nhfb,
  keywords =     "8-bit multiplier; ARITH-26; Artificial intelligence;
                 artificial intelligence applications; Boolean
                 functions; Boolean optimizations; Digital arithmetic;
                 digital arithmetic; gradient descent; Measurement
                 uncertainty; multiplied product; multiplying circuits;
                 optimisation; Optimization; partial product additions;
                 partial products sums; Principal component analysis;
                 principle component analysis; Propagation delay;
                 special purpose multipliers; square calculations;
                 square operation; squarer optimization; squarer
                 propagation delay; Urban areas",
}

@InProceedings{Pasca:2019:HDP,
  author =       "Bogdan Pasca",
  title =        "Hybrid Dot-Product Design for {FP}-Enabled {FPGAs}",
  crossref =     "Takagi:2019:ISC",
  pages =        "194--196",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00045",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "FPGAs are becoming interesting solutions for neural
                 network training acceleration. Efficient implementation
                 of dot-products, as part of matrix-matrix multiply
                 engines, plays a key role towards this. The now de
                 facto standard involves the matrix multiplication on
                 bfloat16 inputs, with all reductions be performed in
                 single-precision arithmetic. We present here a generic
                 hybrid dot-product implementation that: (1) has a
                 user-defined accuracy knob and (2) targets a
                 user-defined logic/DSP ratio. Since our architecture is
                 very specialized to a given target device, we discuss
                 the challenges in generating this architecture
                 automatically.",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; ARITH-26; arithmetic; Bandwidth; bfloat16; dot
                 product; dot-products; Field programmable gate arrays;
                 field programmable gate arrays; floating point;
                 floating point arithmetic; FP-enabled FPGA; FPGA;
                 generator; hybrid; hybrid dot-product design; hybrid
                 dot-product implementation; Lead; logic design; matrix
                 multiplication; matrix-matrix multiply engines;
                 multiplying circuits; neural nets; neural network
                 training; Neural networks; single precision;
                 single-precision arithmetic; Tools; Training",
}

@Article{Pranesh:2019:LPF,
  author =       "Srikara Pranesh",
  title =        "Low Precision Floating-Point Formats: The {Wild West}
                 of Computer Arithmetic",
  journal =      j-SIAM-NEWS,
  volume =       "52",
  number =       "9",
  pages =        "12--12",
  month =        nov,
  year =         "2019",
  DOI =          "",
  ISSN =         "0036-1437",
  bibdate =      "Mon Nov 04 14:49:07 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://sinews.siam.org/Details-Page/low-precision-floating-point-formats-the-wild-west-of-computer-arithmetic",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
}

@Article{Qi:2019:GGI,
  author =       "Meng Qi and Ke Yan and Yuanjie Zheng",
  title =        "{GPredicates}: {GPU} Implementation of Robust and
                 Adaptive Floating-Point Predicates for Computational
                 Geometry",
  journal =      j-IEEE-ACCESS,
  volume =       "7",
  pages =        "60868--60876",
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ACCESS.2019.2911641",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Tue Sep 30 17:30:28 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "Arbitrary precision floating-point arithmetic;
                 Computational geometry; computational geometry;
                 geometric robustness; GPGPU; Graphics processing units;
                 incircle test; Instruction sets; Memory management;
                 orientation test; Parallel processing;
                 Three-dimensional displays; Two dimensional displays",
}

@Article{Reyhani-Masoleh:2019:NMI,
  author =       "A. Reyhani-Masoleh and H. El-Razouk and A. Monfared",
  title =        "New Multiplicative Inverse Architectures Using
                 {Gaussian} Normal Basis",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "68",
  number =       "7",
  pages =        "991--1006",
  month =        jul,
  year =         "2019",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2018.2859941",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 11 09:46:20 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "application specific integrated circuits; arithmetic
                 operations; binary fields; classic inversion scheme;
                 classic-based addition chains; classical-interleaved
                 architecture; classical-interleaved inverter; CMOS
                 integrated circuits; Computer architecture;
                 cryptography; Digit-level multiplier; digital
                 arithmetic; field inversion; field programmable gate
                 arrays; finite field; FSISM; FSISM processor;
                 fully-serial-in square-multiply processor; Galois
                 fields; Gaussian normal basis; Gaussian processes;
                 hybrid-double multiplication; input registers;
                 inversion architecture; inversion architectures;
                 Inverters; invertors; Itoh-Tsujii algorithm; latency;
                 Logic gates; multiplication cycle; multiplicative
                 inverse architectures; multiplying circuits; NIST;
                 Propagation delay; size 65.0 nm; ternary Itoh-Tsujii
                 algorithm",
}

@InProceedings{Rohloff:2019:CAR,
  author =       "Kurt Rohloff",
  title =        "Computer Arithmetic Research to Accelerate
                 Privacy-Protecting Encrypted Computing Such as
                 Homomorphic Encryption",
  crossref =     "Takagi:2019:ISC",
  pages =        "197--197",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00046",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "One of the first major breakthroughs of computer
                 science in the 21st century has been the discovery and
                 practical demonstration of encrypted computing
                 technologies such as Fully Homomorphic Encryption
                 (FHE). Encrypted computing technologies allow sensitive
                 data to be encrypted such that arbitrary programs can
                 be securely run over the encrypted data where the
                 output, when decrypted, is equivalent to the result of
                 running the original algorithm on the unencrypted data.
                 In this talk we focus on the use of and potential for
                 computer arithmetic research to enable more practical
                 encrypted computing, such as to accelerate advanced
                 encryption implementations on custom hardware. These
                 technologies are ground-breaking in their ability for
                 privacy-preserving data science on sensitive data sets
                 with minimal costs in terms of engineering effort,
                 power, compute resources, etc. \ldots{}. We discuss
                 theory, design, algorithmic, hardware, software
                 engineering and systems research that is enabling
                 applications of encrypted computing in regulated data
                 industries, such as in medical and financial domains.
                 We use our work using accelerating the PALISADE
                 open-source homomorphic encryption software library for
                 practical applications in case studies.",
  acknowledgement = ack-nhfb,
  keywords =     "Acceleration; advanced encryption implementations;
                 ARITH-26; computer arithmetic research; computer
                 science; Computer science; Computers; cryptography;
                 data privacy; Digital arithmetic; encrypted computing
                 technologies; encrypted data; Encryption; fully
                 homomorphic encryption; Hardware; PALISADE open-source
                 homomorphic encryption software library;
                 privacy-preserving data science; privacy-protecting
                 encrypted computing; public domain software; regulated
                 data industries; sensitive data sets; software
                 engineering; software libraries; unencrypted data",
}

@Article{Roughan:2019:PSS,
  author =       "Matthew Roughan",
  title =        "Practically surreal: {Surreal} arithmetic in {Julia}",
  journal =      j-SOFTWAREX,
  volume =       "9",
  number =       "??",
  pages =        "293--298",
  month =        jan # "\slash " # jun,
  year =         "2019",
  CODEN =        "????",
  ISSN =         "2352-7110",
  ISSN-L =       "2352-7110",
  bibdate =      "Mon Oct 14 09:45:43 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/softwarex.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S2352711018302152",
  acknowledgement = ack-nhfb,
  fjournal =     "SoftwareX",
  journal-URL =  "https://www.sciencedirect.com/journal/softwarex/issues",
  keywords =     "Conway's surreal numbers",
}

@InProceedings{Rump:2019:EBC,
  author =       "Siegfried M. Rump",
  title =        "Error Bounds for Computer Arithmetics",
  crossref =     "Takagi:2019:ISC",
  pages =        "1--14",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00011",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This note summarizes recent progress in error bounds
                 for compound operations performed in some computer
                 arithmetic. Given a general set of real numbers
                 together with some operations satisfying the first
                 standard model, we identify three types A, B, and C of
                 weak sufficient assumptions implying new results and
                 sharper error estimates. Those include linearized error
                 estimates in the number of operations, faithfully
                 rounded and reproducible results. All types of
                 assumptions are satisfied for an IEEE-754 p-digit base-
                 floating-point arithmetic.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-26; Compounds; Computational modeling; computer
                 arithmetic; CREST; Digital arithmetic; error analysis;
                 error bounds; floating point arithmetic; IEEE-754
                 p-digit base- floating-point arithmetic; Japan Science
                 and Technology Agency; Kernel; Standards; Switches;
                 Vegetation",
}

@Article{Salamati:2019:MEM,
  author =       "Mahmoud Salamati and Rocco Salvia and Eva Darulova and
                 Sadegh Soudjani and Rupak Majumdar",
  title =        "Memory-Efficient Mixed-Precision Implementations for
                 Robust Explicit Model Predictive Control",
  journal =      j-TECS,
  volume =       "18",
  number =       "5s",
  pages =        "100:1--100:??",
  month =        oct,
  year =         "2019",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3358223",
  ISSN =         "1539-9087 (print), 1558-3465 (electronic)",
  ISSN-L =       "1539-9087",
  bibdate =      "Thu Oct 17 18:16:44 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tecs.bib",
  URL =          "https://dl.acm.org/ft_gateway.cfm?id=3358223",
  abstract =     "We propose an optimization for space-efficient
                 implementations of explicit model-predictive
                 controllers (MPC) for robust control of linear
                 time-invariant (LTI) systems on embedded platforms. We
                 obtain an explicit-form robust model-predictive
                 controller as a solution to a multi-parametric linear
                 programming problem. The structure of the controller is
                 a polyhedral decomposition of the control domain, with
                 an affine map for each domain. While explicit MPC is
                 suited for embedded devices with low computational
                 power, the memory requirements for such controllers can
                 be high. We provide an optimization algorithm for a
                 mixed-precision implementation of the controller, where
                 the deviation of the implemented controller from the
                 original one is within the robustness margin of the
                 robust control problem. The core of the mixed-precision
                 optimization is an iterative static analysis that
                 co-designs a robust controller and a low-bitwidth
                 approximation that is statically guaranteed to always
                 be within the robustness margin of the original
                 controller. We have implemented our algorithm and show
                 on a set of benchmarks that our optimization can reduce
                 space requirements by up to 20.9\% and on average by
                 12.6\% compared to a minimal uniform precision
                 implementation of the original controller.",
  acknowledgement = ack-nhfb,
  articleno =    "100",
  fjournal =     "ACM Transactions on Embedded Computing Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J840",
}

@InProceedings{Sarkar:2019:RAP,
  author =       "Souradip Sarkar and Purushotham Murugappa Velayuthan
                 and Manil Dev Gomony",
  editor =       "{IEEE}",
  booktitle =    "{2019 22nd Euromicro Conference on Digital System
                 Design (DSD)}",
  title =        "A Reconfigurable Architecture for Posit Arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "82--87",
  year =         "2019",
  DOI =          "https://doi.org/10.1109/DSD.2019.00022",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Seo:2019:HTM,
  author =       "Jihee Seo and Dae Hyun Kim",
  title =        "High-Throughput Multiplier Architectures Enabled by
                 Intra-Unit Fast Forwarding",
  crossref =     "Takagi:2019:ISC",
  pages =        "143--150",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00036",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this paper, we propose a pipelined multiplier
                 architecture that can resolve data dependencies. The
                 proposed architecture generates partial results in the
                 pipeline stages of the multiplier and forwards the
                 partial results back to the pipeline stages through
                 so-called fast-forwarding paths, thereby enabling an
                 execution of dependent multiplications with a minimum
                 delay penalty. We apply the architecture to a normal
                 binary multiplier (NBBE-2) and two redundant binary
                 multipliers (RBBE-4 and CRBBE-4) and compare the
                 execution time, clock period, area, and power
                 consumption of the multipliers. The simulation results
                 show that the proposed architecture achieves up to 30\%
                 execution time reduction.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-26; Clocks; Computer architecture; data
                 dependencies; Delays; dependent multiplications;
                 digital arithmetic; execution time reduction; Fast
                 Forwarding; fast-forwarding paths; high-throughput
                 multiplier architectures; intra-unit fast forwarding;
                 minimum delay penalty; Multiplexing; Multiplication;
                 Multiplier; multiplying circuits; normal binary
                 multiplier; pipeline processing; Pipeline processing;
                 pipeline stages; pipelined multiplier architecture;
                 Pipelines; redundant binary multipliers; Throughput",
}

@InProceedings{Serre:2019:DBM,
  author =       "Fran{\c{c}}ois Serre and Markus P{\"u}schel",
  title =        "{DSL}-Based Modular {IP} Core Generators: Example
                 {FFT} and Related Structures",
  crossref =     "Takagi:2019:ISC",
  pages =        "190--191",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00043",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present a hardware generator for signal processing
                 algorithms that consist of a network of small
                 processing elements, including the fast Fourier
                 transform and sorting networks. The generator is
                 implemented in Scala and uses a principled design that
                 leverages modern language features to generate an
                 entire design space of hardware implementations.
                 Examples include the use of embedded domain-specific
                 languages and staging to represent and optimize the
                 designs at different levels of abstraction, and the use
                 of Scala's type system to efficiently encode different
                 degrees of hardware reuse and arithmetic formats.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-26; arithmetic formats; Design automation;
                 design space; digital arithmetic; Domain specific
                 language; DSL; DSL-based modular IP core generators;
                 electronic engineering computing; embedded
                 domain-specific languages; embedded systems; fast
                 Fourier transform; fast Fourier transforms; FFT;
                 Generators; Hardware; hardware generator; Hardware
                 generator; hardware implementations; hardware reuse;
                 microprocessor chips; object-oriented programming;
                 Optimization; processing elements; Random access
                 memory; Scala type system; signal processing; signal
                 processing algorithms; Sorting; sorting; sorting
                 networks; specification languages; Staging; Streaming
                 hardware",
}

@Article{Sherman:2019:SRS,
  author =       "Benjamin Sherman and Jesse Michel and Michael Carbin",
  title =        "Sound and robust solid modeling via exact real
                 arithmetic and continuity",
  journal =      j-PACMPL,
  volume =       "3",
  number =       "ICFP",
  pages =        "99:1--99:29",
  month =        jul,
  year =         "2019",
  DOI =          "https://doi.org/10.1145/3341703",
  ISSN =         "2475-1421",
  bibdate =      "Fri Aug 7 19:22:28 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/pacmpl.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3341703",
  abstract =     "Algorithms for solid modeling, i.e., Computer-Aided
                 Design (CAD) and computer graphics, are often specified
                 on real numbers and then implemented with
                 finite-precision arithmetic, such as floating-point.
                 The result is that these implementations do not soundly
                 compute the results that are expected from their
                 specifications.\par

                 We present a new library, StoneWorks, that provides
                 sound and robust solid modeling primitives. We
                 implement StoneWorks in MarshallB, a pure functional
                 programming language for exact real arithmetic in which
                 types denote topological spaces and functions denote
                 continuous maps, ensuring that all programs are sound
                 and robust. We developed MarshallB as an extension of
                 the Marshall language.\par

                 We also define a new shape representation, compact
                 representation (K-rep), that enables constructions such
                 as Minkowski sum and analyses such as Hausdorff
                 distance that are not possible with traditional
                 representations. K-rep is a nondeterminism monad for
                 describing all the points in a shape.\par

                 With our library, language, and representation
                 together, we show that short StoneWorks programs can
                 specify and execute sound and robust solid modeling
                 algorithms and tasks.",
  acknowledgement = ack-nhfb,
  articleno =    "99",
  fjournal =     "Proceedings of the ACM on Programming Languages",
  journal-URL =  "https://pacmpl.acm.org/",
}

@Misc{Silver:2019:CCN,
  author =       "Mike Silver and Kalimah Redd Knight",
  title =        "Cutting Corners on Numbers",
  howpublished = "TuftsNow Web site.",
  day =          "24",
  month =        sep,
  year =         "2019",
  bibdate =      "Wed Sep 25 10:47:09 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Boghosian:2019:NPS}.",
  URL =          "https://now.tufts.edu/articles/cutting-corners-numbers-computation",
  abstract =     "Tufts mathematicians find the way we represent numbers
                 in computers can lead to large computational errors,
                 especially for modeling dynamical systems.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Singh:2019:LPP,
  author =       "Gagandeep Singh and Dionysios Diamantopoulos and
                 Sander Stuijk and Christoph Hagleitner and Henk
                 Corporaal",
  booktitle =    "Embedded Computer Systems: Architectures, Modeling,
                 and Simulation",
  title =        "Low Precision Processing for High Order Stencil
                 Computations",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "403--415",
  year =         "2019",
  DOI =          "https://doi.org/10.1007/978-3-030-27562-4_29",
  ISBN =         "3-030-27562-0",
  ISBN-13 =      "978-3-030-27562-4",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Fri Dec 15 11:31:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@Article{Solovyev:2019:REF,
  author =       "Alexey Solovyev and Marek S. Baranowski and Ian Briggs
                 and Charles Jacobsen and Zvonimir Rakamari{\'c} and
                 Ganesh Gopalakrishnan",
  title =        "Rigorous Estimation of Floating-Point Round-Off Errors
                 with Symbolic {Taylor} Expansions",
  journal =      j-TOPLAS,
  volume =       "41",
  number =       "1",
  pages =        "2:1--2:??",
  month =        mar,
  year =         "2019",
  CODEN =        "ATPSDT",
  DOI =          "https://doi.org/10.1145/3230733",
  ISSN =         "0164-0925 (print), 1558-4593 (electronic)",
  ISSN-L =       "0164-0925",
  bibdate =      "Mon Mar 4 08:35:09 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toplas.bib",
  URL =          "https://dl.acm.org/ft_gateway.cfm?id=3230733",
  abstract =     "Rigorous estimation of maximum floating-point
                 round-off errors is an important capability central to
                 many formal verification tools. Unfortunately,
                 available techniques for this task often provide very
                 pessimistic overestimates, causing unnecessary
                 verification failure. We have developed a new approach
                 called Symbolic Taylor Expansions that avoids these
                 problems, and implemented a new tool called FPTaylor
                 embodying this approach. Key to our approach is the use
                 of rigorous global optimization, instead of the more
                 familiar interval arithmetic, affine arithmetic, and/or
                 SMT solvers. FPTaylor emits per-instance analysis
                 certificates in the form of HOL Light proofs that can
                 be machine checked. In this article, we present the
                 basic ideas behind Symbolic Taylor Expansions in
                 detail. We also survey as well as thoroughly evaluate
                 six tool families, namely, Gappa (two tool options
                 studied), Fluctuat, PRECiSA, Real2Float, Rosa, and
                 FPTaylor (two tool options studied) on 24 examples,
                 running on the same machine, and taking care to find
                 the best options for running each of these tools. This
                 study demonstrates that FPTaylor estimates round-off
                 errors within much tighter bounds compared to other
                 tools on a significant number of case studies. We also
                 release FPTaylor along with our benchmarks, thus
                 contributing to future studies and tool development in
                 this area.",
  acknowledgement = ack-nhfb,
  articleno =    "2",
  fjournal =     "ACM Transactions on Programming Languages and
                 Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J783",
}

@Misc{Stephens:2019:BPN,
  author =       "Nigel Stephens",
  title =        "{BFloat16} processing for Neural Networks on
                 {Armv8-A}",
  howpublished = "Web site.",
  day =          "29",
  month =        aug,
  year =         "2019",
  bibdate =      "Mon Sep 23 07:25:21 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://community.arm.com/developer/ip-products/processors/b/ml-ip-blog/posts/bfloat16-processing-for-neural-networks-on-armv8_2d00_a",
  acknowledgement = ack-nhfb,
  remark =       "From the article: ``The next revision of the Armv8-A
                 architecture will introduce Neon and SVE vector
                 instructions designed to accelerate certain
                 computations using the BFloat16 (BF16) floating-point
                 number format. BF16 has recently emerged as a format
                 tailored specifically to high-performance processing of
                 Neural Networks (NNs). BF16 is a truncated form of the
                 IEEE 754 [ieee754-2008] single-precision representation
                 (IEEE-FP32), which has only 7 fraction bits, instead of
                 23.'' IEEE FP16 has 1-bit sign, 5-bit exponent, and
                 10-bit significand. BF16 has 1-bit sign, 8-bit
                 exponent, and 7-bit significand. [This disagrees with
                 \cite{Verheyde:2019:BDD}, which says 5-bit exponent,
                 and 10-bit significand.] The article also says that two
                 instructions, BFDOT and BFMMLA have only one rounding
                 mode: Round to Odd, one type of NaN, and flush-to-zero
                 on underflow.",
}

@InProceedings{Takagi:2019:AI,
  author =       "Naofumi Takagi and Sylvie Boldo and Martin
                 Langhammer",
  title =        "Author Index",
  crossref =     "Takagi:2019:ISC",
  pages =        "219--220",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00051",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Presents an index of the authors whose articles are
                 published in the conference proceedings record.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2019; ARITH-26",
}

@InProceedings{Takagi:2019:CN,
  author =       "Naofumi Takagi and Sylvie Boldo and Martin
                 Langhammer",
  title =        "[{Copyright} notice]",
  crossref =     "Takagi:2019:ISC",
  pages =        "4--4",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00003",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Presents the copyright information for the conference.
                 May include reprint permission information.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2019; ARITH-26",
}

@InProceedings{Takagi:2019:CO,
  author =       "Naofumi Takagi and Sylvie Boldo and Martin
                 Langhammer",
  title =        "Conference Organization",
  crossref =     "Takagi:2019:ISC",
  pages =        "11--11",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00006",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Provides a listing of current committee members and
                 society officers.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2019; ARITH-26",
}

@InProceedings{Takagi:2019:F,
  author =       "Naofumi Takagi and Sylvie Boldo and Martin
                 Langhammer",
  title =        "Foreword",
  crossref =     "Takagi:2019:ISC",
  pages =        "10--10",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00005",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Presents the introductory welcome message from the
                 conference proceedings. May include the conference
                 officers' congratulations to all involved with the
                 conference event and publication of the proceedings
                 record.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2019; ARITH-26",
}

@InProceedings{Takagi:2019:PC,
  author =       "Naofumi Takagi and Sylvie Boldo and Martin
                 Langhammer",
  title =        "Program Committee",
  crossref =     "Takagi:2019:ISC",
  pages =        "12--12",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00007",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Provides a listing of current committee members and
                 society officers.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2019; ARITH-26",
}

@InProceedings{Takagi:2019:Sa,
  author =       "Naofumi Takagi and Sylvie Boldo and Martin
                 Langhammer",
  title =        "Sponsors",
  crossref =     "Takagi:2019:ISC",
  pages =        "14--14",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00009",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The conference organizers greatly appreciate the
                 support of the various corporate sponsors listed.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2019; ARITH-26",
}

@InProceedings{Takagi:2019:Sb,
  author =       "Naofumi Takagi and Sylvie Boldo and Martin
                 Langhammer",
  title =        "Supporters",
  crossref =     "Takagi:2019:ISC",
  pages =        "15--15",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00010",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The conference organizers greatly appreciate the
                 support of the various corporate sponsors listed.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2019; ARITH-26",
}

@InProceedings{Takagi:2019:SC,
  author =       "Naofumi Takagi and Sylvie Boldo and Martin
                 Langhammer",
  title =        "Steering Committee",
  crossref =     "Takagi:2019:ISC",
  pages =        "13--13",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00008",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Provides a listing of current committee members and
                 society officers.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2019; ARITH-26",
}

@InProceedings{Takagi:2019:TC,
  author =       "Naofumi Takagi and Sylvie Boldo and Martin
                 Langhammer",
  title =        "Table of contents",
  crossref =     "Takagi:2019:ISC",
  pages =        "5--9",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00004",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Presents the table of contents/splash page of the
                 proceedings record.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2019; ARITH-26",
}

@InProceedings{Takagi:2019:TPI,
  author =       "Naofumi Takagi and Sylvie Boldo and Martin
                 Langhammer",
  title =        "[{Title} page iii]",
  crossref =     "Takagi:2019:ISC",
  pages =        "3--3",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00002",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Presents the title page of the proceedings record.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2019; ARITH-26",
}

@InProceedings{Thibault:2019:OWL,
  author =       "Hilaire Thibault and Hacene Ouzia and Benoit Lopez",
  title =        "Optimal Word-Length Allocation for the Fixed-Point
                 Implementation of Linear Filters and Controllers",
  crossref =     "Takagi:2019:ISC",
  pages =        "175--182",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00040",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This article presents a word-length optimization
                 problem under accuracy constraints for the hardware
                 implementation of linear signal processing systems with
                 fixed-point arithmetic. For State-Space systems
                 (describing a linear filter or a controller), a
                 complete error analysis is exhibited, where the final
                 output error bound depends on the word-lengths and the
                 fixed-point formats chosen for each variable. The Most
                 Significant Bit of each one can be determined in order
                 to guarantee that no overflow occurs. Thus, it is
                 possible to obtain a hardware implementation minimizing
                 resource use. This leads to a convex nonlinear integer
                 optimization problem where the resources to minimize
                 and the accuracy constraints depend on the internal
                 word-lengths. This problem can then be solved with
                 appropriate heuristics. Finally, a global approach is
                 proposed and illustrated by some examples.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-26; convex nonlinear integer optimization
                 problem; convex programming; error analysis; filters;
                 fixed point arithmetic; fixed-point arithmetic;
                 Hardware; hardware implementation; integer programming;
                 linear filter; linear signal processing systems;
                 nonlinear programming; optimal word-length allocation;
                 Optimization; Quantization (signal); Roundoff errors;
                 signal processing; Signal processing algorithms;
                 state-space methods; state-space systems; word length
                 optimization; word-length optimization problem; worst
                 case MSB",
}

@InProceedings{Thomas:2019:CTG,
  author =       "David B. Thomas",
  title =        "Compile-Time Generation of Custom-Precision
                 Floating-Point {IP} using {HLS} Tools",
  crossref =     "Takagi:2019:ISC",
  pages =        "192--193",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00044",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "High-Level Synthesis (HLS) tools usually treat
                 floating-point operators as black-box IP cores, and
                 then schedule them as primitives when synthesising code
                 to circuits. This approach relies on a library of IP
                 blocks for chosen floating-point formats, which are
                 pre-characterised to determine latency and area
                 properties needed at compilation time. Two weaknesses
                 of this approach are that it limits the number of
                 floating-point formats - typically to half, single, and
                 double - and that it requires conservative per-cycle
                 scheduling of operators. Modern HLS tools have
                 sophisticated intra-cycle scheduling of integer
                 primitives, as well as C++ front-ends that can execute
                 substantial algorithms at compile-time. This has
                 enabled the creation of platform-independent C++
                 floating-point libraries which generate
                 custom-precision operators at compile-time, while
                 providing similar or better results as vendor-supplied
                 IP blocks. However, certain problems and questions
                 related to compilation performance and verification
                 remain, so it is not yet clear how widely applicable
                 this technique is.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-26; black-box IP cores; C++; C++ languages;
                 chosen floating-point formats; compilation performance;
                 compilation time; Compile time IP; compile-time
                 generation; custom-precision floating-point IP;
                 custom-precision operators; field programmable gate
                 arrays; Field programmable gate arrays; Floating point;
                 floating point arithmetic; floating-point libraries;
                 floating-point operators; FPGA; High Level Synthesis;
                 high level synthesis; High-Level Synthesis tools; HLS;
                 intra-cycle scheduling; IP networks; Libraries; Meta
                 programming; modern HLS tools; Pipelines; Schedules;
                 Templates; Tools; vendor-supplied IP blocks",
}

@Article{Tiwari:2019:PPE,
  author =       "Sugandha Tiwari and Neel Gala and Chester Rebeiro and
                 V. Kamakoti",
  title =        "{PERI}: A Posit Enabled {RISC-V} Core",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--14",
  month =        nov,
  year =         "2019",
  bibdate =      "Thu Apr 09 15:06:39 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/pdf/1908.01466.pdf",
  abstract =     "Owing to the failure of Dennard's scaling the last
                 decade has seen a steep growth of prominent new
                 paradigms leveraging opportunities in computer
                 architecture. Two technologies of interest are Posit
                 and RISC-V. Posit was introduced in mid-2017 as a
                 viable alternative to IEEE 754-2008. Posit promises
                 more accuracy, higher dynamic range and fewer unused
                 states along with simpler hardware designs as compared
                 to IEEE 754- 2008. RISC-V, on the other hand, provides
                 a commercial-grade open-source ISA. It is not only
                 elegant and simple but also highly extensible and
                 customizable, thereby facilitating novel
                 micro-architectural research and exploration. In this
                 paper, we bring these two technologies together and
                 propose the first Posit Enabled RISC-V core. The paper
                 provides insights on how the current 'F' extension and
                 the custom op-code space of RISCV can be
                 leveraged/modified to support Posit arithmetic. We also
                 present implementation details of a parameterized and
                 feature-complete Posit FPU which is integrated with the
                 RISC-V compliant SHAKTI C-class core either as an
                 execution unit or as an accelerator. To fully leverage
                 the potential of Posit, we further enhance our Posit
                 FPU, with minimal overheads, to support two different
                 exponent sizes (with posit-size being 32-bits). This
                 allows applications to switch from high-accuracy
                 computation mode to a mode with higher dynamic-range at
                 run-time. In the absence of viable software tool-chain
                 to enable porting of applications in the Posit domain,
                 we present a workaround on how certain applications can
                 be modified minimally to exploit the existing RISC-V
                 tool-chain. We also provide examples of applications
                 which can perform better with Posit as compared to IEEE
                 754-2008. The proposed Posit FPU consumes 3507 slice
                 LUTs and 1294 slice registers on an Artix-7-100T Xilinx
                 FPGA while capable of operating at 100 MHz.",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point; IEEE-754; Posit; processor; RISC-V",
}

@InProceedings{Uguen:2019:EHC,
  author =       "Yohann Uguen and Luc Forget and Florent de Dinechin",
  editor =       "{IEEE}",
  booktitle =    "{2019 29th International Conference on Field
                 Programmable Logic and Applications (FPL)}",
  title =        "Evaluating the Hardware Cost of the Posit Number
                 System",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "106--113",
  year =         "2019",
  DOI =          "https://doi.org/10.1109/FPL.2019.00026",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{vanDam:2019:APA,
  author =       "Laurens van Dam and Johan Peltenburg and Zaid Al-Ars
                 and H. Peter Hofstee",
  title =        "An Accelerator for Posit Arithmetic Targeting Posit
                 Level 1 {BLAS} Routines and {Pair-HMM}",
  crossref =     "Gustafson:2019:CPC",
  pages =        "5:1--5:10",
  year =         "2019",
  DOI =          "https://doi.org/10.1145/3316279.3316284",
  bibdate =      "Mon Feb 10 12:11:16 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  articleno =    "5",
  keywords =     "pair-HMM, BLAS, decimal accuracy, arithmetic,
                 unum-III, accelerator, posit, unum, FPGA",
  location =     "Singapore, Singapore",
  numpages =     "10",
}

@Article{vanWyk:2019:RVT,
  author =       "Leonard van Wyk",
  title =        "Rounding versus truncation estimates in difference
                 calculations",
  journal =      j-MATH-GAZ,
  volume =       "103",
  number =       "557",
  pages =        "285--292",
  month =        jul,
  year =         "2019",
  CODEN =        "MAGAAS",
  DOI =          "https://doi.org/10.1017/mag.2019.60",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  ISSN-L =       "0025-5572",
  bibdate =      "Mon Jul 22 08:44:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib",
  URL =          "https://www.cambridge.org/core/journals/mathematical-gazette/article/rounding-versus-truncation-estimates-in-difference-calculations/57BD92568C03F0FCDE63BBBDB5E6FF6D",
  abstract =     "Two common methods of approximating difference
                 problems are by rounding or truncating the minuend and
                 the subtrahend before calculating the difference. Since
                 rounding generally gives a better approximation of a
                 number than truncation, one might expect that rounding
                 also generally gives a better approximation in
                 difference problems. We show that intuition to be
                 false.",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Gaz.",
  fjournal =     "The Mathematical Gazette",
  journal-URL =  "http://journals.cambridge.org/action/displayIssue?jid=MAG;
                 http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
  onlinedate =   "06 June 2019",
}

@InProceedings{Vazquez:2019:NPT,
  author =       "Alvaro V{\'a}zquez and Elisardo Antelo",
  title =        "New {$3$D} Projection Transformation for Point
                 Clouds",
  crossref =     "Takagi:2019:ISC",
  pages =        "77--83",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00020",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "3D Computer Graphics based on clouds of points is an
                 alternative of interest for high quality rendering of
                 complex scenes. For high quality graphics, the
                 computational requirements are significantly higher
                 than in the case of conventional front-end vertex
                 processing. One of the key computations in the graphics
                 pipeline is the projection transformation. Conventional
                 computation of the point-based projection using current
                 vertex processors might not be the best option for
                 scalable, high quality 3D graphics based on point
                 clouds. In this work we propose a new scalable method
                 that takes advantage of the special characteristics of
                 the point rendering model. The number of
                 reciprocal/division computations for perspective
                 correction is reduced, using instead more effective
                 multiply-accumulate operations. This is done by
                 performing a linear approximation of the reciprocal at
                 the cost of introducing an error in the pixel value.
                 There is a trade-off in the error introduced and the
                 exactness of the computation (linear approximation
                 instead of reciprocal).",
  acknowledgement = ack-nhfb,
  keywords =     "3D computer graphics; 3D projection transformation;
                 ARITH-26; Cameras; complex geometry; computational
                 geometry; graphics processor; high quality 3D graphics;
                 Linear approximation; Point based rendering; point
                 clouds; point rendering model; point-based projection;
                 projection transform; Rendering (computer graphics);
                 rendering (computer graphics); rendering quality;
                 Three-dimensional displays; Upper bound; vertex
                 processing; VLSI graphis hardware; Zirconium",
}

@Article{Venkatachalam:2019:DAA,
  author =       "S. Venkatachalam and E. Adams and H. J. Lee and S.
                 Ko",
  title =        "Design and Analysis of Area and Power Efficient
                 Approximate {Booth} Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "68",
  number =       "11",
  pages =        "1697--1703",
  month =        nov,
  year =         "2019",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2019.2926275",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Oct 29 11:08:44 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Adders; Approximate Booth arithmetic; Complexity
                 theory; Computational modeling; Digital signal
                 processing; Encoding; Generators; inexact computing;
                 Integrated circuit modeling; radix-4 partial product
                 generators",
}

@Misc{Verheyde:2019:BDD,
  author =       "Arne Verheyde",
  title =        "{BFloat16} Deep Dive: {ARM} Brings {BF16} Deep
                 Learning Data Format to {ARMv8-A}",
  howpublished = "Tom's Hardware Web site.",
  day =          "21",
  month =        sep,
  year =         "2019",
  bibdate =      "Mon Sep 23 07:15:36 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.tomshardware.com/news/bfloat16-deep-dive-arm-bf16-support-armv8-a,40305.html",
  abstract =     "RM will be adding BFloat16 support in the next
                 revision of the ARMv8-A architecture under its Project
                 Trillium ML platform. It marks a new major milestone in
                 the widespread adoption of the young data format that
                 is taking the deep learning community by storm. In this
                 article, we'll dive into the origins and benefits of
                 the format.",
  acknowledgement = ack-nhfb,
  remark =       "The BFloat16 format has 1-bit sign, 5-bit exponent,
                 and 10-bit significand. From the article: ``\ldots{}
                 hardware area (number of transistors) scales roughly
                 with the square of the mantissa width. So having just
                 three fewer mantissa bits (7 instead of 10) means that
                 a bfloat16 multiplier takes up about half the area of a
                 conventional FP16 unit. Compared to an FP32 multiplier,
                 its size is eight times smaller, with an equivalent
                 reduction in power consumption as well. Or conversely,
                 within the same silicon area more useful hardware can
                 be put to achieve higher performance. \ldots{} Bfloat16
                 is called Brain Floating Point Format in full (or BF16
                 in short), as it is named after the Google Brain
                 research group where it was conceived. As Jeff Dean,
                 Senior Fellow of Google AI, explained in a series of
                 Twitter posts, Google started using the format since
                 the early days of TensorFlow. More specifically, it was
                 supported in hardware since the second version of its
                 Tensor Processing Units (TPUs), the TPU v2 in 2017.
                 \ldots{} Intel showed that an integer multiplier costs
                 less than half the area of a floating point multiplier
                 of the same number of bits. Though less relevant, the
                 difference is even larger for addition: while an
                 integer adder scales linearly with the number of bits,
                 a floating point adder scales quadratically,
                 \ldots{}''",
}

@InProceedings{Villa:2019:NDB,
  author =       "Oreste Villa and Mark Stephenson and David Nellans and
                 Stephen W. Keckler",
  editor =       "{IEEE\slash ACM}",
  booktitle =    "{MICRO '52: Proceedings of the 52nd Annual IEEE\slash
                 ACM International Symposium on Microarchitecture,
                 Columbus OH, USA, October 12--16, 2019}",
  title =        "{Nvbit}: A dynamic binary instrumentation framework
                 for {NVIDIA GPUs}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  bookpages =    "1104",
  pages =        "372--383",
  year =         "2019",
  ISBN =         "1-4503-6938-3",
  ISBN-13 =      "978-1-4503-6938-1",
  LCCN =         "QA76.6 .A568",
  bibdate =      "Mon Sep 11 07:23:59 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1145/3352460",
}

@InProceedings{Villalba-Moreno:2019:RSU,
  author =       "Julio Villalba-Moreno and Javier Hormigo and Francisco
                 Jaime",
  title =        "Reproducible Summation Under {HUB} Format",
  crossref =     "Takagi:2019:ISC",
  pages =        "38--45",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00015",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Floating point reproducibility is a property claimed
                 by programmers and end users. Half-Unit-Biased (HUB) is
                 a new representation format in which the round to
                 nearest is carried out by truncation, preventing any
                 carry propagation and saving time and area. In this
                 paper we study the reproducible summation of HUB
                 numbers by using a error-free vector transformation
                 technique, providing both a specific architecture and
                 the usage of combined HUB/Standard floating point
                 adders to achieve a reproducible result.",
  acknowledgement = ack-nhfb,
  keywords =     "adders; Adders; ARITH-26; carry propagation; Computer
                 architecture; Computer science; Delays; Digital
                 arithmetic; end users; error-free vector transformation
                 technique; floating point arithmetic; Half-Unit-Biased;
                 HUB (Half-Unit-Biased) floating-point format; HUB
                 format; HUB numbers; point adders; point
                 reproducibility; representation format; reproducible
                 summation; Reproducible summation, HUB format;
                 Standards; Terminology",
}

@InProceedings{Volkova:2019:SAI,
  author =       "Anastasia Volkova and Jean-Michel Muller",
  title =        "Semi-Automatic Implementation of the Complementary
                 Error Function",
  crossref =     "Takagi:2019:ISC",
  pages =        "167--174",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00039",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The normal and complementary error functions are
                 ubiquitous special functions for any mathematical
                 library. They have a wide range of applications.
                 Practical applications call for customized
                 implementations that have strict accuracy requirements.
                 Accurate numerical implementation of these functions
                 is, however, non-trivial. In particular, the
                 complementary error function erfc for large positive
                 arguments heavily suffers from cancellation, which is
                 largely due to its asymptotic behavior. We provide a
                 semi-automatic code generator for the erfc function
                 which is parameterized by the user-given bound on the
                 relative error. Our solution exploits the asymptotic
                 expression of erfc and leverages the automatic code
                 generator Metalibm that provides accurate polynomial
                 approximations. A fine-grained a priori error analysis
                 provides a libm developer with the required accuracy
                 for each step of the evaluation. In critical parts, we
                 exploit double-word arithmetic to achieve
                 implementations that are fast, yet accurate up to 50
                 bits, even for large input arguments. We demonstrate
                 that for high required accuracies the automatically
                 generated code has performance comparable to that of
                 the standard libm and for lower ones our code
                 demonstrated roughly 25\% speedup.",
  acknowledgement = ack-nhfb,
  keywords =     "a priori error analysis; ARITH-26; asymptotic
                 behavior; asymptotic expression; complementary error
                 functions; Digital arithmetic; Error analysis; error
                 analysis; error function; floating-point arithmetic;
                 Generators; Libraries; Lips; mathematical library;
                 Metalibm; normal error functions; polynomial
                 approximation; polynomial approximations; program
                 compilers; semi-automated code generation;
                 semiautomatic code generator; semiautomatic
                 implementation; Standards; Tools; ubiquitous special
                 functions",
}

@Article{Walczyk:2019:MFI,
  author =       "Cezary J. Walczyk and Leonid V. Moroz and Jan L.
                 Cie{\'s}li{\'n}ski",
  title =        "A Modification of the Fast Inverse Square Root
                 Algorithm",
  journal =      "Computation",
  volume =       "7",
  number =       "3",
  pages =        "41",
  month =        aug,
  year =         "2019",
  DOI =          "https://doi.org/10.3390/computation7030041",
  ISSN =         "2079-3197",
  ISSN-L =       "2079-3197",
  bibdate =      "Thu Apr 10 15:20:23 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Walther:2019:VNR,
  author =       "Christoph Walther",
  title =        "Verified {Newton--Raphson} Iteration for
                 Multiplicative Inverses Modulo Powers of Any Base",
  journal =      j-TOMS,
  volume =       "45",
  number =       "1",
  pages =        "9:1--9:7",
  month =        mar,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3301317",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Dumas:2014:NRI}.",
  URL =          "https://dl.acm.org/citation.cfm?id=3301317",
  abstract =     "We identify two faults in a published algorithm for
                 fast computation of multiplicative inverses modulo
                 prime powers. We patch the algorithm and present
                 machine-assisted proofs of correctness of the repair.
                 Our formal proofs also reveal that being prime is an
                 unnecessary demand for the power base, thus attributing
                 a wider scope of applications to the repaired
                 algorithm.",
  acknowledgement = ack-nhfb,
  articleno =    "9",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Misc{Wang:2019:BSH,
  author =       "Shibo Wang and Pankaj Kanwar",
  title =        "{BFloat16}: The secret to high performance on Cloud
                 {TPUs}",
  howpublished = "Web site",
  day =          "23",
  month =        aug,
  year =         "2019",
  bibdate =      "Fri Apr 03 09:12:39 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://cloud.google.com/blog/products/ai-machine-learning/bfloat16-the-secret-to-high-performance-on-cloud-tpus",
  acknowledgement = ack-nhfb,
}

@Article{Wang:2019:PAA,
  author =       "Shouxiang Wang and Kai Wang and Lei Wu and Chengshan
                 Wang",
  title =        "Polar Affine Arithmetic: Optimal Affine Approximation
                 and Operation Development for Computation in Polar Form
                 Under Uncertainty",
  journal =      j-TOMS,
  volume =       "45",
  number =       "1",
  pages =        "6:1--6:29",
  month =        mar,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3274659",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3274659",
  abstract =     "Uncertainties practically arise from numerous factors,
                 such as ambiguous information, inaccurate model, and
                 environment disturbance. Interval arithmetic has
                 emerged to solve problems with uncertain parameters,
                 especially in the computational process where only the
                 upper and lower bounds of parameters can be
                 ascertained. In rectangular coordinate systems, the
                 basic interval operations and improved interval
                 algorithms have been developed in the numerical
                 analysis. However, in polar coordinate systems,
                 interval arithmetic still suffers from issues of
                 complex computation and overestimation. This article
                 defines a polar affine variable and develops a polar
                 affine arithmetic (PAA) that extends affine arithmetic
                 to the polar coordinate systems, which performs better
                 in many aspects than the corresponding polar interval
                 arithmetic (PIA). Basic arithmetic operations are
                 developed based on the complex affine arithmetic. The
                 Chebyshev approximation theory and the min-range
                 approximation theory are used to identify the best
                 affine approximation. PAA can accurately keep track of
                 the interdependency among multiple variables throughout
                 the calculation procedure, which prominently reduces
                 the solution conservativeness. Numerical examples
                 implemented in MATLAB programs show that, compared with
                 benchmark results from the Monte Carlo method, the
                 proposed PAA ensures completeness of the exact solution
                 and presents a more compact solution region than PIA
                 when dependency exists in the calculation process.
                 Meanwhile, a comparison of affine arithmetic in polar
                 and rectangular coordinates is presented. An
                 application of PAA in circuit analysis is
                 quantitatively presented and potential applications in
                 other research fields involving complex variables in
                 polar form will be gradually developed.",
  acknowledgement = ack-nhfb,
  articleno =    "6",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ye:2019:NCA,
  author =       "T. Ye and Y. Wei and W. Meier",
  title =        "A New Cube Attack on {MORUS} by Using Division
                 Property",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "68",
  number =       "12",
  pages =        "1731--1740",
  month =        dec,
  year =         "2019",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2019.2929137",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Nov 7 11:20:24 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Authenticated encryption algorithm; Boolean functions;
                 cube attack; division property; Encryption; mixed
                 integer linear programming; MORUS; Software algorithms;
                 Time complexity; time complexity",
}

@Article{Zhang:2019:EMP,
  author =       "H. Zhang and D. Chen and S. Ko",
  title =        "Efficient Multiple-Precision Floating-Point Fused
                 Multiply-Add with Mixed-Precision Support",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "68",
  number =       "7",
  pages =        "1035--1048",
  month =        jul,
  year =         "2019",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2019.2895031",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 11 09:46:20 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Adders; Clocks; Computer architecture; Deep learning;
                 double-precision operations; efficiency 10.6 percent;
                 efficiency 6.5 percent; floating point arithmetic;
                 floating-point arithmetics; floating-point operations;
                 FMA architecture; Fused multiply-add; half-precision
                 FMA operations; Hardware; logic design; mixed-precision
                 arithmetics; mixed-precision dot-product operations;
                 mixed-precision FMA operations; mixed-precision
                 operations; mixed-precision support; multiple-precision
                 arithmetics; multiple-precision floating-point;
                 multiple-precision FMA design; multiple-precision FMA
                 unit; multiplying circuits; normal FMA operations;
                 parallel half-precision operations; Pipelines;
                 quadruple-precision operation; single-precision
                 operations; Standards",
}

@InProceedings{Zhang:2019:EPM,
  author =       "Hao Zhang and Jiongrui He and Seok-Bum Ko",
  editor =       "IEEE",
  booktitle =    "{2019 IEEE International Symposium on Circuits and
                 Systems (ISCAS)}",
  title =        "Efficient Posit Multiply-Accumulate Unit Generator for
                 Deep Learning Applications",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--5",
  month =        may,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/iscas.2019.8702349",
  bibdate =      "Thu Dec 14 18:03:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Zhu:2019:DPS,
  author =       "Weibin Zhu and Shengjin Ye and Yao Huang and Zi Xue",
  title =        "Design of a precise subdivision system for gratings
                 using a modified {CORDIC} algorithm",
  journal =      "IET Circuits, Devices \& Systems",
  volume =       "13",
  number =       "8",
  pages =        "1284--1291",
  year =         "2019",
  DOI =          "https://doi.org/10.1049/iet-cds.2019.0150",
  bibdate =      "Wed Oct 29 15:08:31 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://onlinelibrary.wiley.com/doi/abs/10.1049/iet-cds.2019.0150",
  acknowledgement = ack-nhfb,
  eprint =       "https://onlinelibrary.wiley.com/doi/pdf/10.1049/iet-cds.2019.0150",
  keywords =     "amplitude deviation; angle-measurement accuracy;
                 angle-measuring device; angular measurement; arccosine
                 functions; circular grating; digital arithmetic;
                 digital subdivision; direct current offset deviation;
                 double-rotation iteration; dynamic response; error
                 compensation; field programmable gate arrays;
                 field-programmable gate array chip; function generator;
                 function generators; grating lines; grating Moircg{\'e}
                 signal; ideal subdivision effect; light
                 interferometers; measurement error; measurement errors;
                 MicroE system; modified CORDIC algorithm; Moir{\'e}
                 signals; nonlinear subdivision; precise subdivision
                 system design; robust linearisation method; rotation
                 digital computer algorithm; sinusoidal signal; stable
                 signals",
}

@InProceedings{Zorn:2019:SPD,
  author =       "Bill Zorn and Dan Grossman and Zach Tatlock",
  title =        "Sinking Point: Dynamic Precision Tracking for
                 Floating-Point",
  crossref =     "Gustafson:2019:CPC",
  pages =        "4:1--4:8",
  year =         "2019",
  DOI =          "https://doi.org/10.1145/3316279.3316283",
  bibdate =      "Mon Feb 10 12:11:16 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  keywords =     "Floating point, numerical analysis",
  location =     "Singapore, Singapore",
  numpages =     "8",
}

@InProceedings{Abdelfattah:2020:IBF,
  author =       "Ahmad Abdelfattah and Stan Tomov and Jack Dongarra",
  title =        "Investigating the Benefit of {FP16}-Enabled
                 Mixed-Precision Solvers for Symmetric Positive Definite
                 Matrices Using {GPUs}",
  crossref =     "Krzhizhanovskaya:2020:CSI",
  pages =        "237--250",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-50417-5_18",
  bibdate =      "Thu Jun 25 08:49:09 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Abdelfattah:2020:MMB,
  author =       "Ahmad Abdelfattah and Stanimire Tomov and Jack
                 Dongarra",
  title =        "Matrix multiplication on batches of small matrices in
                 half and half-complex precisions",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "145",
  number =       "??",
  pages =        "188--201",
  month =        nov,
  year =         "2020",
  CODEN =        "JPDCER",
  DOI =          "https://doi.org/10.1016/j.jpdc.2020.07.001",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Wed May 26 16:11:03 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jpardistcomp.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0743731520303300",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
}

@Article{Adams:2020:ARD,
  author =       "E. Adams and S. Venkatachalam and S. Ko",
  title =        "Approximate Restoring Dividers Using Inexact Cells and
                 Estimation From Partial Remainders",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "69",
  number =       "4",
  pages =        "468--474",
  month =        apr,
  year =         "2020",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2019.2953751",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Mar 12 16:58:27 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Approximate computing; error analysis; image
                 processing applications; low-power; restoring
                 division",
}

@InProceedings{Agrawal:2020:FAH,
  author =       "Rashmi Agrawal and Lake Bu and Michel A. Kinsy",
  booktitle =    "{2020 IEEE 28th Annual International Symposium on
                 Field-Programmable Custom Computing Machines (FCCM)}",
  title =        "Fast Arithmetic Hardware Library For {RLWE-Based}
                 Homomorphic Encryption",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "206--206",
  year =         "2020",
  DOI =          "https://doi.org/10.1109/FCCM48280.2020.00037",
  bibdate =      "Fri Sep 22 08:05:37 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Ahrens:2020:AER,
  author =       "Peter Ahrens and James Demmel and Hong Diep Nguyen",
  title =        "Algorithms for Efficient Reproducible Floating Point
                 Summation",
  journal =      j-TOMS,
  volume =       "46",
  number =       "3",
  pages =        "22:1--22:49",
  month =        sep,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3389360",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Sep 26 07:28:19 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3389360",
  abstract =     "We define ``reproducibility'' as getting bitwise
                 identical results from multiple runs of the same
                 program, perhaps with different hardware resources or
                 other changes that should not affect the answer. Many
                 users depend on reproducibility for debugging or
                 correctness. However, dynamic scheduling of parallel
                 computing resources, combined with nonassociative
                 floating point addition, makes reproducibility
                 challenging even for summation, or operations like the
                 BLAS. We describe a ``reproducible accumulator'' data
                 structure (the ``binned number'') and associated
                 algorithms to reproducibly sum binary floating point
                 numbers, independent of summation order. We use a
                 subset of the IEEE Floating Point Standard 754-2008 and
                 bitwise operations on the standard representations in
                 memory. Our approach requires only one read-only pass
                 over the data, and one reduction in parallel, using a
                 6-word reproducible accumulator (more words can be used
                 for higher accuracy), enabling standard tiling
                 optimization techniques. Summing $n$ words with a
                 6-word reproducible accumulator requires approximately
                 $ 9 n$ floating point operations (arithmetic,
                 comparison, and absolute value) and approximately $ 3
                 n$ bitwise operations. The final error bound with a
                 6-word reproducible accumulator and our default
                 settings can be up to 229 times smaller than the error
                 bound for conventional (recursive) summation on
                 ill-conditioned double-precision inputs",
  acknowledgement = ack-nhfb,
  articleno =    "22",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "accurate floating-point summation",
}

@InProceedings{Anonymous:2020:ACa,
  author =       "Anonymous",
  title =        "{ARITH 2020} Committees",
  crossref =     "Cornea:2020:ISC",
  pages =        "i--i",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00006",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Provides a listing of current committee members and
                 society officers.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2020; ARITH-27",
}

@InProceedings{Anonymous:2020:ACb,
  author =       "Anonymous",
  title =        "{ARITH 2020} Committees",
  crossref =     "Cornea:2020:ISC",
  pages =        "i--i",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00007",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Provides a listing of current committee members and
                 society officers.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2020; ARITH-27",
}

@InProceedings{Anonymous:2020:ACN,
  author =       "Anonymous",
  title =        "[{ARITH 2020} Copyright notice]",
  crossref =     "Cornea:2020:ISC",
  pages =        "i--i",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00003",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Presents the copyright information for the conference.
                 May include reprint permission information.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2020; ARITH-27",
}

@InProceedings{Anonymous:2020:AI,
  author =       "Anonymous",
  title =        "{ARITH 2020} Index",
  crossref =     "Cornea:2020:ISC",
  pages =        "i--i",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00030",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Presents an index of the authors whose articles are
                 published in the conference proceedings record.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2020; ARITH-27",
}

@InProceedings{Anonymous:2020:ALR,
  author =       "Anonymous",
  title =        "{ARITH 2020} List Reviewer Page",
  crossref =     "Cornea:2020:ISC",
  pages =        "i--i",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00008",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The conference offers a note of thanks and lists its
                 reviewers.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2020; ARITH-27",
}

@Misc{Anonymous:2020:RVE,
  author =       "Anonymous",
  title =        "{RISC-V} embedded variant {RV32E} now fully supported
                 by {SEGGER}'s Floating-Point library",
  howpublished = "Web site",
  day =          "21",
  month =        sep,
  year =         "2020",
  bibdate =      "Thu Jan 28 18:02:53 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.design-reuse.com/news/48672/segger-s-floating-point-library-risc-v-rv32e.html",
  acknowledgement = ack-nhfb,
  remark =       "The story reports a significant code size reduction,
                 and speedup, over the GNU floating-point library.",
}

@InProceedings{Anonymous:2020:SA,
  author =       "Anonymous",
  title =        "Sponsors {ARITH 2020}",
  crossref =     "Cornea:2020:ISC",
  pages =        "i--i",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00009",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The conference organizers greatly appreciate the
                 support of the various corporate sponsors listed.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2020; ARITH-27",
}

@InProceedings{Anonymous:2020:TC,
  author =       "Anonymous",
  title =        "Table of Contents",
  crossref =     "Cornea:2020:ISC",
  pages =        "i--iii",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00004",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Presents the table of contents/splash page of the
                 proceedings record.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2020; ARITH-27",
}

@InProceedings{Anonymous:2020:TPa,
  author =       "Anonymous",
  title =        "[{Title} page]",
  crossref =     "Cornea:2020:ISC",
  pages =        "i--i",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00001",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Presents the title page of the proceedings record.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2020; ARITH-27",
}

@InProceedings{Anonymous:2020:TPb,
  author =       "Anonymous",
  title =        "[{Title} page]",
  crossref =     "Cornea:2020:ISC",
  pages =        "i--i",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00002",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Presents the title page of the proceedings record.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2020; ARITH-27",
}

@Article{Arnold:2020:IRL,
  author =       "M. G. Arnold and V. Paliouras and I. Kouretas",
  title =        "Implementing the Residue Logarithmic Number System
                 Using Interpolation and Cotransformation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "69",
  number =       "12",
  pages =        "1719--1732",
  month =        dec,
  year =         "2020",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2019.2930514",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Nov 24 09:42:22 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Bajard:2020:AFV,
  author =       "Jean-Claude Bajard and Julien Eynard and Paulo Martins
                 and Leonel Sousa and Vincent Zucca",
  title =        "An asymptotically faster version of {FV} supported on
                 {HPR}",
  crossref =     "Cornea:2020:ISC",
  pages =        "80--87",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00020",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "State-of-the-art implementations of homomorphic
                 encryption exploit the Fan and Vercauteren (FV) scheme
                 and the Residue Number System (RNS). While the RNS
                 breaks down large integer arithmetic into smaller
                 independent channels, its non-positional nature makes
                 operations such as division and rounding hard to
                 implement, and makes the representation of small values
                 inefficient. In this work, we propose the application
                 of the Hybrid Position-Residues Number System
                 representation to the FV scheme. This is a positional
                 representation of large radix where the digits are
                 represented in RNS. It inherits the benefits from RNS
                 and allows to accelerate the critical division and
                 rounding operations while also making the
                 representation of smaller values more compact. This
                 directly benefits the decryption and the homomorphic
                 multiplication procedures, reducing their asymptotic
                 complexity, in dimension n, from O(n2 log n) to O(n log
                 n) and from O(n3 log n) to O(n3), respectively and has
                 resulted in noticeable speedups when experimentally
                 compared to related art RNS implementations.",
  acknowledgement = ack-nhfb,
  keywords =     "Acceleration; ARITH 2020; ARITH-27; Art; Complexity
                 theory; Encryption; Fan-Vercauteren scheme; Fans;
                 Homomorphic Encryption; Indexes; Residue Number
                 System",
}

@InProceedings{Barthel:2020:ASA,
  author =       "Moritz B{\"a}rthel and Jochen Rust and Steffen Paul",
  booktitle =    "{2020 IEEE International Symposium on Circuits and
                 Systems (ISCAS)}",
  title =        "Application-Specific Analysis of Different {SORN}
                 Datatypes for Unum Type-2-Based Arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--5",
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ISCAS45731.2020.9181182",
  bibdate =      "Fri Dec 15 07:38:18 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Boldo:2020:CRF,
  author =       "Sylvie Boldo and Diane Gallois-Wong and Thibault
                 Hilaire",
  title =        "A Correctly-Rounded Fixed-Point-Arithmetic Dot-Product
                 Algorithm",
  crossref =     "Cornea:2020:ISC",
  pages =        "9--16",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00011",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Dot products (also called sums of products) are
                 ubiquitous in matrix computations, for instance in
                 signal processing. We are especially interested in
                 digital filters, where they are the core operation. We
                 therefore focus on fixed-point arithmetic, used in
                 embedded systems for time and energy efficiency. Common
                 dot product algorithms ensure faithful rounding. For
                 the sake of accuracy and reproducibility, we want to
                 ensure correct rounding. This article describes an
                 algorithm that computes a correctly-rounded sum of
                 products from inputs whose format is known in advance.
                 This algorithm relies on odd rounding (that is easily
                 implemented in hardware) and comes with a careful proof
                 and some cost analysis.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2020; ARITH-27; Correct Rounding; Dot Product;
                 Embedded systems; Fixed-point arithmetic; Fixed-Point
                 Arithmetic; floating-point arithmetic; Hardware; Odd
                 Rounding; Runtime; Signal processing; Signal processing
                 algorithms; Sorting; Sum-of-Products",
}

@InProceedings{Bottcher:2020:HDL,
  author =       "Andreas B{\"o}ttcher and Keanu Kullmann and Martin
                 Kumm",
  title =        "Heuristics for the Design of Large Multipliers for
                 {FPGAs}",
  crossref =     "Cornea:2020:ISC",
  pages =        "17--24",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00012",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The following topics are dealt with: floating point
                 arithmetic; cryptography; field programmable gate
                 arrays; computational complexity; embedded systems;
                 public key cryptography; optimisation; probability;
                 fixed point arithmetic; and digital signal processing
                 chips.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2020; ARITH-27; Complexity theory; computer
                 arithmetic; Digital arithmetic; Field programmable gate
                 arrays; heuristics; Integer linear programming;
                 Karatsuba multiplier; large multiplier; Optimization;
                 post quantum cryptography; Shape; Table lookup;
                 tiling",
}

@Article{Boyvalenkov:2020:CMS,
  author =       "Peter Boyvalenkov and Nikolay I. Chervyakov and Pavel
                 Lyakhov and Nataliya Semyonova and Anton Nazarov and
                 Maria Valueva and Georgi Boyvalenkov and Danil
                 Bogaevskiy and Dmitrii Kaplun",
  title =        "Classification of Moduli Sets for Residue Number
                 System With Special Diagonal Functions",
  journal =      j-IEEE-ACCESS,
  volume =       "8",
  pages =        "156104--156116",
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ACCESS.2020.3019452",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Wed Oct 1 06:08:36 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "average bit-width; Current measurement; diagonal
                 function; FPGA; Hardware; hardware implementation;
                 Heuristic algorithms; non-modular operations; Object
                 recognition; Parallel processing; quadruples; Residue
                 number system; RNS balance; triples",
}

@Article{Brisebarre:2020:EAS,
  author =       "Nicolas Brisebarre and Mioara Joldes and Jean-Michel
                 Muller and Ana-Maria Nanes and Joris Picot",
  title =        "Error Analysis of Some Operations Involved in the
                 {Cooley--Tukey Fast Fourier Transform}",
  journal =      j-TOMS,
  volume =       "46",
  number =       "2",
  pages =        "11:1--11:27",
  month =        jun,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3368619",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jun 12 07:37:53 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3368619",
  abstract =     "We are interested in obtaining error bounds for the
                 classical Cooley--Tukey fast Fourier transform
                 algorithm in floating-point arithmetic, for the 2-norm
                 as well as for the infinity norm. For that purpose, we
                 also give some results on the relative error of the
                 complex multiplication by a root of unity, and on the
                 largest value that can take the real or imaginary part
                 of one term of the fast Fourier transform of a vector
                 $x$, assuming that all terms of $x$ have real and
                 imaginary parts less than some value $b$.",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bruguera:2020:LLF,
  author =       "J. D. Bruguera",
  title =        "Low Latency Floating-Point Division and Square Root
                 Unit",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "69",
  number =       "2",
  pages =        "274--287",
  month =        feb,
  year =         "2020",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2019.2947899",
  ISSN =         "2326-3814",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jan 22 06:44:09 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Computer architecture; Convergence; Digit-recurrence
                 algorithms; Estimation; floating-point division, and
                 square root; Iterative methods; Organizations;
                 Registers; Timing",
}

@InProceedings{Brunie:2020:TFP,
  author =       "Hugo Brunie and Costin Iancu and Khaled Z. Ibrahim and
                 Philip Brisk and Brandon Cook",
  title =        "Tuning floating-point precision using dynamic program
                 information and temporal locality",
  crossref =     "IEEE:2020:SPI",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--14",
  year =         "2020",
  bibdate =      "Mon Sep 11 08:19:28 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We present a methodology for precision tuning of full
                 applications. These techniques must select a search
                 space composed of either variables or instructions and
                 provide a scalable search strategy. In full application
                 settings one cannot assume compiler support for
                 practical reasons. Thus, an additional important
                 challenge is enabling code refactoring. We argue for an
                 instruction-based search space and we show: (1) how to
                 exploit dynamic program information based on call
                 stacks; and (2) how to exploit the iterative nature of
                 scientific codes, combined with temporal locality. We
                 applied the methodology to tune the implementation of
                 scientific codes written in a combination of Python,
                 CUDA, C++ and Fortran, tuning calls to math exp library
                 functions. The iterative search refinement always
                 reduces the search complexity and the number of steps
                 to solution. Dynamic program information increases
                 search efficacy. Using this approach, we obtain
                 application runtime performance improvements up to
                 27\%.",
  acknowledgement = ack-nhfb,
  articleno =    "50",
}

@InProceedings{Buoncristiani:2020:ENS,
  author =       "Nicholas Buoncristiani and Sanjana Shah and David
                 Donofrio and John Shalf",
  editor =       "{IEEE}",
  booktitle =    "{2020 IEEE International Parallel and Distributed
                 Processing Symposium (IPDPS)}",
  title =        "Evaluating the Numerical Stability of Posit
                 Arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "612--621",
  year =         "2020",
  DOI =          "https://doi.org/10.1109/IPDPS47924.2020.00069",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Misc{Calligo:2020:PNU,
  author =       "{Calligo Technologies}",
  title =        "Posit Numeric Unit ({PNU-IP})",
  howpublished = "Web software.",
  year =         "2020",
  bibdate =      "Sat Dec 16 15:24:16 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://calligotech.com/posit-numeric-unit-pnu-ip",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@Article{Cavalcante:2020:AGS,
  author =       "Matheus Cavalcante and Fabian Schuiki and Florian
                 Zaruba and Michael Schaffner and Luca Benini",
  title =        "{Ara}: a {1-GHz+} Scalable and Energy-Efficient
                 {RISC-V} Vector Processor With Multiprecision
                 Floating-Point Support in 22-nm {FD-SOI}",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "28",
  number =       "2",
  pages =        "530--543",
  year =         "2020",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/TVLSI.2019.2950087",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Sat Dec 16 15:51:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
}

@Article{Cherubin:2020:TRP,
  author =       "Stefano Cherubin and Giovanni Agosta",
  title =        "Tools for Reduced Precision Computation: a Survey",
  journal =      j-COMP-SURV,
  volume =       "53",
  number =       "2",
  pages =        "33:1--33:35",
  month =        jul,
  year =         "2020",
  CODEN =        "CMSVAN",
  DOI =          "https://doi.org/10.1145/3381039",
  ISSN =         "0360-0300 (print), 1557-7341 (electronic)",
  ISSN-L =       "0360-0300",
  bibdate =      "Wed Jul 8 17:24:43 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compsurv.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3381039",
  abstract =     "The use of reduced precision to improve performance
                 metrics such as computation latency and power
                 consumption is a common practice in the embedded
                 systems field. This practice is emerging as a new trend
                 in High Performance Computing (HPC), especially when
                 new error-tolerant applications are considered.
                 However, standard compiler frameworks do not support
                 automated precision customization, and manual tuning
                 and code transformation is the approach usually adopted
                 in most domains. In recent years, research have been
                 studying ways to improve the automation of this
                 process. This article surveys this body of work,
                 identifying the critical steps of this process, the
                 most advanced tools available, and the open challenges
                 in this research area. We conclude that, while several
                 mature tools exist, there is still a gap to close,
                 especially for tools based on static analysis rather
                 than profiling, as well as for integration within
                 mainstream, industry-strength compiler frameworks.",
  acknowledgement = ack-nhfb,
  articleno =    "33",
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "https://dl.acm.org/loi/csur",
}

@InProceedings{Chien:2020:PNA,
  author =       "Steven W. D. Chien and Ivy B. Peng and Stefano
                 Markidis",
  title =        "Posit {NPB}: Assessing the Precision Improvement in
                 {HPC} Scientific Applications",
  crossref =     "Wyrzykowski:2020:PPA",
  pages =        "301--310",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-43229-4_26",
  bibdate =      "Fri Dec 15 11:31:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@InProceedings{Chowdhary:2020:DDN,
  author =       "Sangeeta Chowdhary and Jay P. Lim and Santosh
                 Nagarakatte",
  booktitle =    "{PLDI 2020: Proceedings of the 41st ACM SIGPLAN
                 Conference on Programming Language Design and
                 Implementation}",
  title =        "Debugging and detecting numerical errors in
                 computation with posits",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "731--746",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1145/3385412.3386004",
  bibdate =      "Sat Dec 9 08:43:53 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@InProceedings{Cococcioni:2020:FAH,
  author =       "Marco Cococcioni and Federico Rossi and Emanuele
                 Ruffaldi and Sergio Saponara",
  booktitle =    "Applications in Electronics Pervading Industry,
                 Environment and Society",
  title =        "A Fast Approximation of the Hyperbolic Tangent When
                 Using Posit Numbers and Its Application to Deep Neural
                 Networks",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "213--221",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-37277-4_25",
  ISBN =         "3-030-37277-4",
  ISBN-13 =      "978-3-030-37277-4",
  ISSN =         "1876-1119",
  ISSN-L =       "1876-1100",
  bibdate =      "Fri Dec 15 11:31:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@Article{Cococcioni:2020:FDN,
  author =       "Marco Cococcioni and Federico Rossi and Emanuele
                 Ruffaldi and Sergio Saponara",
  title =        "Fast deep neural networks for image processing using
                 posits and {ARM} scalable vector extension",
  journal =      "Journal of Real-Time Image Processing",
  volume =       "17",
  number =       "3",
  pages =        "759--771",
  month =        may,
  year =         "2020",
  DOI =          "https://doi.org/10.1007/s11554-020-00984-x",
  ISSN =         "1861-8219",
  ISSN-L =       "1861-8200",
  bibdate =      "Fri Dec 15 11:31:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@InProceedings{Cococcioni:2020:NPB,
  author =       "Marco Cococcioni and Federico Rossi and Emanuele
                 Ruffaldi and Sergio Saponara",
  editor =       "{IEEE}",
  booktitle =    "{2020 IEEE International Conference on Smart Computing
                 (SMARTCOMP)}",
  title =        "A Novel Posit-based Fast Approximation of {ELU}
                 Activation Function for Deep Neural Networks",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "244--246",
  year =         "2020",
  DOI =          "https://doi.org/10.1109/SMARTCOMP50058.2020.00053",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Cornea:2020:FA,
  author =       "Marius Cornea and Weiqiang Liu and Arnaud Tisserand",
  title =        "Foreword {ARITH 2020}",
  crossref =     "Cornea:2020:ISC",
  pages =        "i--i",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00005",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The 27th IEEE Symposium on Computer Arithmetic,
                 ARITH-2020, was initially planned to be held in
                 Portland, Oregon, USA on Jun 7-10, 2020. Due to the
                 COVID-19 crisis all around the world in 2020, the
                 face-to-face meeting has been canceled. The paper
                 selection process was completed, and the accepted
                 papers have been included in the ARITH-2020
                 proceedings. For ARITH-2020, 73 anonymous submissions
                 have been submitted at the beginning of February.
                 Following the peer-review practice of this symposium,
                 each paper was blind-reviewed by at least three, and up
                 to five, Program Committee members, and a final
                 decision was made by the committee in mid-April. 40 PC
                 members and some external reviewers were involved in
                 this process. The technical program of ARITH- 2020
                 includes 16 regular papers (8 pages) and 4 short papers
                 (4 pages).",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2020; ARITH-27",
}

@InProceedings{Coward:2020:ADS,
  author =       "Samuel Coward and Theo Drane and Yoav Harel",
  title =        "Automatic Design Space Exploration for an Error
                 Tolerant Application",
  crossref =     "Cornea:2020:ISC",
  pages =        "117--120",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00025",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Creating optimized hardware for error tolerant
                 applications presents significant challenges as well as
                 opportunities. Many algorithms in computer graphics &
                 vision are error tolerant, as their application level
                 correctness ultimately rests on human perception. This
                 error tolerance can be exploited in reducing hardware
                 implementation cost. The challenge is how to explore
                 the space of application level correct designs to
                 determine the optimized hardware architecture. This
                 paper puts forward an approach to automatically explore
                 the space which maximally exploits the acceptable error
                 to minimize hardware cost for a particular graphics
                 algorithm --- Level-Of-Detail. Results, so far, have
                 shown a 26\% hardware area improvement.",
  acknowledgement = ack-nhfb,
  keywords =     "accuracy hardware tradeoffs; approximate computing;
                 ARITH 2020; ARITH-27; computer graphics; Computer
                 graphics; Delays; design automation; floating-point;
                 Hardware; Logic gates; Minimization;
                 multiple-precision; numerical analysis;
                 power-efficient; Space exploration",
}

@InProceedings{Das:2020:SYR,
  author =       "Arnab Das and Ian Briggs and Ganesh Gopalakrishnan and
                 Sriram Krishnamoorthy and Pavel Panchekha",
  title =        "Scalable yet Rigorous Floating-Point Error Analysis",
  crossref =     "IEEE:2020:SPI",
  pages =        "1--14",
  year =         "2020",
  bibdate =      "Mon Sep 11 06:40:11 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Automated techniques for rigorous floating-point
                 round-off error analysis are a prerequisite to placing
                 important activities in HPC such as precision
                 allocation, verification, and code optimization on a
                 formal footing. Yet existing techniques cannot provide
                 tight bounds for expressions beyond a few dozen
                 operators --- barely enough for HPC. In this work, we
                 offer an approach embedded in a new tool called Satire
                 that scales error analysis by four orders of magnitude
                 compared to today's best-of-class tools. We explain how
                 three key ideas underlying Satire helps it attain such
                 scale: path strength reduction, bound optimization, and
                 abstraction. Satire provides tight bounds and rigorous
                 guarantees on significantly larger expressions with
                 well over a hundred thousand operators, covering
                 important examples including FFT, matrix
                 multiplication, and PDE stencils.",
  acknowledgement = ack-nhfb,
  articleno =    "51",
}

@Article{deCamargo:2020:REA,
  author =       "Andr{\'e} Pierro de Camargo",
  title =        "Rounding error analysis of divided differences
                 schemes: {Newton}'s divided differences; {Neville}'s
                 algorithm; {Richardson} extrapolation; {Romberg}
                 quadrature; etc.",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "85",
  number =       "2",
  pages =        "591--606",
  month =        oct,
  year =         "2020",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-019-00828-1",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Thu Sep 10 11:29:47 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "http://link.springer.com/article/10.1007/s11075-019-00828-1",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@InProceedings{Defour:2020:CPM,
  author =       "David Defour and Pablo de Oliveira Castro and Matei
                 I{\c{s}}toan and Eric Petit",
  title =        "Custom-Precision Mathematical Library Explorations for
                 Code Profiling and Optimization",
  crossref =     "Cornea:2020:ISC",
  pages =        "121--124",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00026",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The typical processors used for scientific computing
                 have fixed-width data-paths. This implies that
                 mathematical libraries were specifically developed to
                 target each of these fixed precisions (binary16,
                 binary32, binary64). However, to address the increasing
                 energy consumption and throughput requirements of
                 scientific applications, library and hardware designers
                 are moving beyond this one-size-fits-all approach. In
                 this article we propose to study the effects and
                 benefits of using user-defined floating-point formats
                 and target accuracies in calculations involving
                 mathematical functions. Our tool collects input-data
                 profiles and iteratively explores lower precisions for
                 each call-site of a mathematical function in user
                 applications. This profiling data will be a valuable
                 asset for specializing and fine-tuning mathematical
                 function implementations for a given application. We
                 demonstrate the tool's capabilities on SGP4, a
                 satellite tracking application. The profile data shows
                 the potential for specialization and provides insight
                 into answering where it is useful to provide
                 variable-precision designs for elementary function
                 evaluation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2020; ARITH-27; custom-precision;
                 floating-point; Hardware; HPC; libm; Libraries;
                 Mathematical model; Optimization; optimization;
                 Satellites; specialization; Standards; Tools",
}

@InProceedings{Dinda:2020:SFP,
  author =       "Peter Dinda and Alex Bernat and Conor Hetland",
  editor =       "????",
  booktitle =    "Proceedings of the 29th International Symposium on
                 High-Performance Parallel and Distributed Computing",
  title =        "Spying on the floating point behavior of existing,
                 unmodified scientific applications",
  publisher =    "????",
  address =      "????",
  pages =        "5--16",
  year =         "2020",
  bibdate =      "Mon Sep 11 06:53:07 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Dolgov:2020:PCI,
  author =       "Sergey Dolgov and Dmitry Savostyanov",
  title =        "Parallel cross interpolation for high-precision
                 calculation of high-dimensional integrals",
  journal =      j-COMP-PHYS-COMM,
  volume =       "246",
  number =       "??",
  pages =        "Article 106869",
  month =        jan,
  year =         "2020",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2019.106869",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Tue Oct 29 14:07:57 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465519302565",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  keywords =     "Cross interpolation; High precision; High-dimensional
                 integration; Ising integrals; Ising model; Monte Carlo
                 integration; Parallel algorithms; quasi Monte Carlo
                 integration; Tensor train format",
  ORCID-numbers = "Bailey, David H./0000-0002-7574-8342; Borwein,
                 Jonathan/0000-0002-1263-0646",
  remark =       "See \cite{Bailey:2006:IIC,Bailey:2015:HPA}.",
}

@InProceedings{Dutt:2020:HSL,
  author =       "Rashi Dutt and Amit Acharyya",
  booktitle =    "{2020 European Conference on Circuit Theory and Design
                 (ECCTD)}",
  title =        "A High Speed and Low Complexity Architecture Design
                 Methodology for Square Root Unscented {Kalman} Filter
                 based {SLAM}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--4",
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ECCTD49232.2020.9218287",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Complexity theory; Computational modeling; Computer
                 architecture; Covariance matrices; Householder CORDIC;
                 Kalman filters; Low Complexity Architecture;
                 Simultaneous localization and mapping; Simultaneous
                 Localization and Mapping; Square Root Unscented Kalman
                 Filter",
}

@InProceedings{Elkhatib:2020:HOM,
  author =       "Rami Elkhatib and Reza Azarderakhsh and Mehran
                 Mozaffari-Kermani",
  title =        "Highly Optimized {Montgomery} Multiplier for {SIKE}
                 Primes on {FPGA}",
  crossref =     "Cornea:2020:ISC",
  pages =        "64--71",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00018",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "New primes were proposed for Supersingular Isogeny Key
                 Encapsulation (SIKE) in NIST standardization process of
                 Round 2 after further cryptanalysis research showed
                 that the security levels of the initial primes chosen
                 were overestimated [1], [2]. In this paper, we develop
                 a highly optimized Ep Montgomery multiplication
                 algorithm and architecture that further utilizes the
                 special form of SIKE prime compared to previous
                 implementations available in the literature. We then
                 implement SIKE for all Round 2 NIST security levels
                 (SIKEp434 for NIST security level 1, SIKEp503 for NIST
                 security level 2, SIKEp610 for NIST security level 3,
                 and SIKEp751 for NIST security level 5) on Xilinx
                 Virtex 7 using the proposed multiplier. Our best
                 implementation (NIST security level 1) runs 29\% faster
                 and occupies 30\% less hardware resources in comparison
                 to the leading counterpart available in the literature
                 [3] and implementations for other security levels
                 achieved similar improvement.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2020; ARITH-27; Computer architecture; Elliptic
                 curve cryptography; Hardware; hardware architectures;
                 isogeny-based cryptography; Montgomery multiplication;
                 NIST; post-quantum cryptography; SIKE",
}

@Misc{Erickson:2020:GNF,
  author =       "Jack Erickson",
  title =        "Generate Native Floating-Point {FPGA} Implementations
                 for Field-Oriented Control of Motors",
  howpublished = "MathWorks Web site.",
  day =          "17",
  month =        feb,
  year =         "2020",
  bibdate =      "Mon Feb 17 10:32:39 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.mathworks.com/videos/generate-native-floating-point-fpga-implementations-for-field-oriented-control-of-motors.html",
  abstract =     "HDL Coder now supports native floating-point code
                 generation, where you can implement your high-dynamic
                 range operations in single-precision floating point,
                 and generate VHDL or Verilog code directly without
                 converting to fixed-point types and operations.",
  acknowledgement = ack-nhfb,
}

@Article{Fang:2020:URC,
  author =       "Linlin Fang and Bingyi Li and Yizhuang Xie and He Chen
                 and Long Pang",
  title =        "A unified reconfigurable {CORDIC} processor for
                 floating-point arithmetic",
  journal =      j-INT-J-ELECTRON,
  volume =       "107",
  number =       "9",
  pages =        "1436--1450",
  month =        feb,
  year =         "2020",
  CODEN =        "IJELA2",
  DOI =          "https://doi.org/10.1080/00207217.2020.1726497",
  ISSN =         "1362-3060",
  ISSN-L =       "0020-7217",
  bibdate =      "Tue Nov 11 14:27:07 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Electronics Theoretical \&
                 Experimental",
}

@TechReport{Fasi:2020:CCL,
  author =       "Massimiliano Fasi and Mantas Mikaitis",
  title =        "{CPFloat}: a {C} library for emulating low-precision
                 arithmetic",
  type =         "MIMS EPrint",
  number =       "2020.22",
  institution =  "Manchester Institute for Mathematical Sciences, The
                 University of Manchester",
  address =      "Manchester, UK",
  month =        oct,
  year =         "2020",
  bibdate =      "Sat Nov 15 06:52:11 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Fog:2020:FPE,
  author =       "Agner Fog",
  title =        "Floating point exception tracking and {NAN}
                 propagation",
  type =         "Report",
  institution =  "Technical University of Denmark",
  address =      "Lyngby, Denmark",
  pages =        "10",
  day =          "27",
  month =        apr,
  year =         "2020",
  bibdate =      "Wed May 17 11:52:28 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.agner.org/optimize/nan_propagation.pdf",
  abstract =     "The most common methods for detecting floating point
                 errors are based on exception trapping or a global
                 status register. These methods are inefficient in
                 modern systems that use out-of-order parallelism and
                 single-instruction-multiple-data (SIMD) parallelism for
                 improving performance. It is argued that a method based
                 on NAN propagation is more efficient and deterministic.
                 Problems with NAN propagation in current systems are
                 discussed. Examples of implementation in the C++ vector
                 class library and in an experimental instruction set
                 named ForwardCom are presented. The IEEE-754 standard
                 for floating point arithmetic may need adjustment to
                 accommodate the needs of modern forms of parallelism.",
  acknowledgement = ack-nhfb,
  remark =       "See also later revisions \cite{Fog:2023:FPE} and
                 \cite{Fog:2024:FPE}.",
}

@Article{Gallois-Wong:2020:OIP,
  author =       "Diane Gallois-Wong and Sylvie Boldo and Pascal Cuoq",
  title =        "Optimal inverse projection of floating-point
                 addition",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "83",
  number =       "3",
  pages =        "957--986",
  month =        mar,
  year =         "2020",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-019-00711-z",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Tue Feb 18 08:09:21 MST 2020",
  bibsource =    "http://link.springer.com/journal/11075/83/3;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "floating-point arithmetic; interval arithmetic",
}

@Article{Godunov:2020:ACC,
  author =       "A. Godunov",
  title =        "Algorithms for Calculating Correctly Rounded
                 Exponential Function in Double-Precision Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "69",
  number =       "9",
  pages =        "1388--1400",
  month =        sep,
  year =         "2020",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2020.2972901",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Aug 12 14:58:16 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  abstract =     "Correct rounding provides the best approximation of
                 the exponential function by double-precision numbers.
                 To obtain the correctly rounded exponential of some
                 arguments, the exponential should be calculated with
                 high accuracy. For small arguments, even higher
                 accuracy is required. This article presents simple and
                 very fast algorithms for small arguments. Yet another
                 algorithm presented here demonstrates a good maximum
                 execution time, which may be important for critical
                 applications. This algorithm can be combined with some
                 other already existing algorithms to achieve the best
                 maximum and average execution times. All proposed
                 algorithms calculate the correctly rounded exponential
                 function for all rounding modes and use only
                 double-precision arithmetic for computation. In the
                 argument reduction step, precalculated tables are used.
                 Test implementations of these algorithms were developed
                 in C language and are portable. Full proofs are
                 presented either in this article itself or in its
                 appendices.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Gonzalez-Navarro:2020:NRN,
  author =       "S. Gonz{\'a}lez-Navarro and J. Hormigo",
  title =        "New Results on Non-Normalized Floating-Point Formats",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "69",
  number =       "12",
  pages =        "1733--1744",
  month =        dec,
  year =         "2020",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2019.2929039",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Nov 24 09:42:22 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Goualard:2020:GRF,
  author =       "Fr{\'e}d{\'e}ric Goualard",
  title =        "Generating Random Floating-Point Numbers by Dividing
                 Integers: a Case Study",
  crossref =     "Krzhizhanovskaya:2020:CSI",
  pages =        "15--28",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-50417-5_2",
  bibdate =      "Thu Jun 25 07:31:47 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/julia.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  acknowledgement = ack-nhfb,
  keywords =     "error analysis; floating-point number; GMP; Julia;
                 Matlab; Mersenne Twister; PRNG; pseudo-random numbers;
                 random number",
}

@InProceedings{Graillat:2020:ASF,
  author =       "Stef Graillat and Vincent Lef{\`e}vre and Jean-Michel
                 Muller",
  title =        "Alternative Split Functions and {Dekker}'s Product",
  crossref =     "Cornea:2020:ISC",
  pages =        "41--47",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00015",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We introduce algorithms for splitting a positive
                 binary floating-point number into two numbers of around
                 half the system precision, using arithmetic operations
                 all rounded either toward $-$ or toward $+$. We use
                 these algorithms to compute exact products (i.e., to
                 express the product of two floating-point numbers as
                 the unevaluated sum of two floating-point numbers, the
                 rounded product and an error term). This is similar to
                 the classical Dekker product, adapted here to directed
                 roundings.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate products; Approximation algorithms; ARITH
                 2020; ARITH-27; Cognition; Digital arithmetic;
                 Floating-point arithmetic; Indexes; Lips; split
                 functions; Standards; Switches",
}

@Article{Grutzmacher:2020:APC,
  author =       "Thomas Gr{\"u}tzmacher and Terry Cojean and Goran
                 Flegar and Hartwig Anzt and Enrique S.
                 Quintana-Ort{\'\i}",
  title =        "Acceleration of {PageRank} with Customized Precision
                 Based on Mantissa Segmentation",
  journal =      j-TOPC,
  volume =       "7",
  number =       "1",
  pages =        "4:1--4:19",
  month =        apr,
  year =         "2020",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3380934",
  ISSN =         "2329-4949 (print), 2329-4957 (electronic)",
  ISSN-L =       "2329-4949",
  bibdate =      "Mon Apr 6 08:56:55 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/pagerank.bib;
                 https://www.math.utah.edu/pub/tex/bib/topc.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3380934",
  abstract =     "We describe the application of a
                 communication-reduction technique for the PageRank
                 algorithm that dynamically adapts the precision of the
                 data access to the numerical requirements of the
                 algorithm as the iteration converges. Our
                 variable-precision strategy, using a customized
                 precision format based on mantissa segmentation (CPMS),
                 abandons the IEEE 754 single- and double-precision
                 number representation formats employed in the standard
                 implementation of PageRank, and instead handles the
                 data in memory using a customized floating-point
                 format. The customized format enables fast data access
                 in different accuracy, prevents overflow/underflow by
                 preserving the IEEE 754 double-precision exponent, and
                 efficiently avoids data duplication, since all bits of
                 the original IEEE 754 double-precision mantissa are
                 preserved in memory, but re-organized for efficient
                 reduced precision access. With this approach, the
                 truncated values (omitting significand bits), as well
                 as the original IEEE double-precision values, can be
                 retrieved without duplicating the data in different
                 formats.\par

                 Our numerical experiments on an NVIDIA V100 GPU (Volta
                 architecture) and a server equipped with two Intel Xeon
                 Platinum 8168 CPUs (48 cores in total) expose that,
                 compared with a standard IEEE double-precision
                 implementation, the CPMS-based PageRank completes about
                 10\% faster if high-accuracy output is needed, and
                 about 30\% faster if reduced output accuracy is
                 acceptable.",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  fjournal =     "ACM Transactions on Parallel Computing",
  journal-URL =  "https://dl.acm.org/loi/topc",
}

@InProceedings{Gu:2020:NMM,
  author =       "Zhen Gu and Shuguo Li",
  title =        "A Novel Method of Modular Multiplication Based on
                 {Karatsuba}-like Multiplication",
  crossref =     "Cornea:2020:ISC",
  pages =        "33--40",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00014",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this paper, we propose a novel method of modular
                 multiplication which embeds the modular reduction in
                 the evaluation and interpolation parts of the
                 Karatsuba-like multiplication. Before, the modular
                 reduction can only be performed independently between
                 multiplication. However, applying our method, the
                 interpolation of the previous multiplication, modular
                 reduction and evaluation of the next multiplication are
                 merged as a whole step, which leads to the
                 simplification of computations and improvement of
                 parallelism. This method can be applied to the modular
                 multiplication with simple moduli like NIST primes, and
                 for general moduli, we can apply this method by using
                 Montgomery modular multiplication instead.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2020; ARITH-27; Digital arithmetic;
                 Interpolation; Karatsuba-like multiplication;
                 Microelectronics; Modular multiplication; Montgomery
                 modular multiplication; NIST; Public key cryptography;
                 Transforms",
}

@InProceedings{Guo:2020:EGE,
  author =       "Hui Guo and Cindy Rubio-Gonz{\'a}lez",
  booktitle =    "Proceedings of the {ACM/IEEE 42nd International
                 Conference on Software Engineering}",
  title =        "Efficient generation of error-inducing floating-point
                 inputs via symbolic execution",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1145/3377811.3380359",
  bibdate =      "Sat Dec 9 08:57:26 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Floating point is widely used in software to emulate
                 arithmetic over reals. Unfortunately, floating point
                 leads to rounding errors that propagate and accumulate
                 during execution. Generating inputs to maximize the
                 numerical error is critical when evaluating the
                 accuracy of floating-point code. In this paper, we
                 formulate the problem of generating high error-inducing
                 floating-point inputs as a code coverage maximization
                 problem solved using symbolic execution. Specifically,
                 we define inaccuracy checks to detect large precision
                 loss and cancellation. We inject these checks at
                 strategic program locations to construct specialized
                 branches that, when covered by a given input, are
                 likely to lead to large errors in the result. We apply
                 symbolic execution to generate inputs that exercise
                 these specialized branches, and describe optimizations
                 that make our approach practical. We implement a tool
                 named FPGen and present an evaluation on 21 numerical
                 programs including matrix computation and statistics
                 libraries. We show that FPGen exposes errors for 20 of
                 these programs and triggers errors that are, on
                 average, over 2 orders of magnitude larger than the
                 state of the art.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Guo:2020:PIL,
  author =       "Hui Guo and Ignacio Laguna and Cindy
                 Rubio-Gonz{\'a}lez",
  title =        "{pLiner}: isolating lines of floating-point code for
                 compiler-induced variability",
  crossref =     "IEEE:2020:SPI",
  pages =        "1--14",
  year =         "2020",
  bibdate =      "Mon Sep 11 08:22:13 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Scientific applications are often impacted by
                 numerical inconsistencies when using different
                 compilers or when a compiler is used with different
                 optimization levels; such inconsistencies hinder
                 reproducibility and can be hard to diagnose. We present
                 pLiner, a tool to automatically pinpoint code lines
                 that trigger compiler-induced variability. pLiner uses
                 a novel approach to enhance floating-point precision at
                 different levels of code granularity, and performs a
                 guided search to identify locations affected by
                 numerical inconsistencies. We demonstrate pLiner on a
                 real-world numerical inconsistency that required weeks
                 to diagnose, which pLiner isolates in minutes. We also
                 evaluate pLiner on 100 synthetic programs, and the NAS
                 Parallel Benchmarks (NPB). On the synthetic programs,
                 pLiner detects the affected lines of code 87\% of the
                 time while the state-of-the-art approach only detects
                 the affected lines 6\% of the time. Furthermore, pLiner
                 successfully isolates all numerical inconsistencies
                 found in the NPB.",
  acknowledgement = ack-nhfb,
  articleno =    "49",
}

@Article{Harris:2020:APN,
  author =       "Charles R. Harris and K. Jarrod Millman and St{\'e}fan
                 J. van der Walt and Ralf Gommers and Pauli Virtanen and
                 David Cournapeau and Eric Wieser and Julian Taylor and
                 Sebastian Berg and Nathaniel J. Smith and Robert Kern
                 and Matti Picus and Stephan Hoyer and Marten H. van
                 Kerkwijk and Matthew Brett and Allan Haldane and Jaime
                 Fern{\'a}ndez del R{\'\i}o and Mark Wiebe and Pearu
                 Peterson and Pierre G{\'e}rard-Marchant and Kevin
                 Sheppard and Tyler Reddy and Warren Weckesser and
                 Hameer Abbasi and Christoph Gohlke and Travis E.
                 Oliphant",
  title =        "Array programming with {NumPy}",
  journal =      j-NATURE,
  volume =       "585",
  number =       "7825",
  pages =        "357--362",
  month =        sep,
  year =         "2020",
  CODEN =        "NATUAS",
  DOI =          "https://doi.org/10.1038/s41586-020-2649-2",
  ISSN =         "0028-0836 (print), 1476-4687 (electronic)",
  ISSN-L =       "0028-0836",
  bibdate =      "Tue Jan 28 06:28:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Nature",
  journal-URL =  "http://www.nature.com/nature/archive/",
  keywords =     "accurate floating-point summation",
}

@TechReport{Harvey:2020:IMT,
  author =       "David Harvey and Joris van der Hoeven",
  title =        "Integer multiplication in time {$ O(n \log n) $}",
  type =         "Report",
  number =       "hal-02070778",
  institution =  "School of Mathematics and Statistics, University of
                 New South Wales",
  address =      "Sydney NSW 2052, Australia",
  pages =        "45",
  day =          "28",
  month =        nov,
  year =         "2020",
  bibdate =      "Thu May 16 15:51:09 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://hal.science/hal-02070778v2",
  abstract =     "We present an algorithm that computes the product of
                 two $n$-bit integers in $ O(n \log n)$ bit operations,
                 thus confirming a conjecture of Sch{\"o}nhage and
                 Strassen from 1971. Our complexity analysis takes place
                 in the multitape Turing machine model, with integers
                 encoded in the usual binary representation. Central to
                 the new algorithm is a novel Gaussian resampling
                 technique that enables us to reduce the integer
                 multiplication problem to a collection of
                 multidimensional discrete Fourier transforms over the
                 complex numbers, whose dimensions are all powers of
                 two. These transforms may then be evaluated rapidly by
                 means of Nussbaumer's fast polynomial transforms.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hickmann:2020:INN,
  author =       "Brian Hickmann and Jieasheng Chen and Michael Rotzin
                 and Andrew Yang and Maciej Urbanski and Sasikanth
                 Avancha",
  title =        "{Intel Nervana Neural Network Processor-T (NNP-T)}
                 Fused Floating Point Many-Term Dot Product",
  crossref =     "Cornea:2020:ISC",
  pages =        "133--136",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00029",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Intel's Nervana Neural Network Processor for Training
                 (NNP-T) contains at its core an advanced floating point
                 dot product design to accelerate the matrix
                 multiplication operations found in many AI
                 applications. Each Matrix Processing Unit (MPU) on the
                 Intel NNP-T can process a 32x32 BFloat16 matrix
                 multiplication every 32 cycles, accumulating the result
                 in single precision (FP32). To reduce hardware costs,
                 the MPU uses a fused many-term floating point dot
                 product design with block alignment of the many input
                 terms during addition, resulting in a unique datapath
                 with several interesting design trade-offs. In this
                 paper, we describe the details of the MPU pipeline,
                 discuss the trade-offs made in the design, and present
                 information on the accuracy of the computation as
                 compared to traditional FMA implementations.",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; ARITH 2020; ARITH-27; Artificial neural
                 networks; deep learning; floating point dot product;
                 Hardware; Machine learning; matrix multiplication;
                 Tensile stress; tensor; Training",
}

@Misc{Higham:2020:NLM,
  author =       "Nicholas J. Higham",
  title =        "{2020 Naylor Lecture}: Mathematics of today's
                 floating-point arithmetic",
  howpublished = "Video recording (47m)",
  day =          "20",
  month =        nov,
  year =         "2020",
  bibdate =      "Sat Nov 15 11:51:27 2025",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.youtube.com/watch?v=aAGJ00OSI7I",
  acknowledgement = ack-nhfb,
  remark =       "The {\tt bit.ly} link to the slides in the first and
                 last slides has been deleted.",
}

@Article{Hopkins:2020:SRR,
  author =       "Michael Hopkins and Mantas Mikaitis and Dave R. Lester
                 and Steve Furber",
  title =        "Stochastic rounding and reduced-precision fixed-point
                 arithmetic for solving neural ordinary differential
                 equations",
  journal =      j-PHILOS-TRANS-R-SOC-LOND-SER-A,
  volume =       "378",
  number =       "2166",
  pages =        "20190052",
  month =        jan,
  year =         "2020",
  CODEN =        "PTRMAD, PTMSFB",
  DOI =          "https://doi.org/10.1098/rsta.2019.0052",
  ISSN =         "1364-503X (print), 1471-2962 (electronic)",
  ISSN-L =       "1364-503X",
  bibdate =      "Fri Sep 22 17:51:44 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Philosophical Transactions of the Royal Society A:
                 Mathematical, Physical, and Engineering Sciences",
  journal-URL =  "http://rsta.royalsocietypublishing.org/",
}

@InProceedings{Hormigo:2020:FPF,
  author =       "Javier Hormigo and Julio Villalba-Moreno and Sonia
                 Gonzalez-Navarro",
  title =        "Floating Point Fused Multiply Add under {HUB} Format",
  crossref =     "Cornea:2020:ISC",
  pages =        "1--8",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00010",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The Half-Unit-Biased (HUB) format has interesting
                 advantages for implementing floating-point arithmetic
                 which has been proved for the four basic arithmetic
                 operations as well as square root. Nevertheless,
                 although Floating-point Fused Multiply-add (FMA)
                 operation ($ A \times B + C$) is one of the most
                 important and complex arithmetic instructions in modern
                 processors, FMA operation for HUB numbers has not been
                 confronted yet. In this paper, we present a design to
                 deal with this operation under HUB format. The key
                 points to turn the conventional FMA architecture into a
                 HUB unit are explained. Comparing the ASIC
                 implementation of a HUB FMA unit with the conventional
                 one, the former reduces the required area and power up
                 to 38\% and 35\%, respectively, for single-precision.
                 For BFloat16, the HUB FMA increases the speed a 15\%,
                 and even then, reduces the area and power by 26\% and
                 12\%, respectively.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2020; ARITH-27; Computer architecture;
                 Deep-learning; Delays; Digital arithmetic; DSP
                 applications; Fused multiplication-addition; Hardware;
                 HUB format; Inverters; Program processors; Standards",
}

@Article{Hrycak:2020:ELP,
  author =       "Tomasz Hrycak and Sebastian Schmutzhard",
  title =        "Evaluation of {Legendre} polynomials by a three-term
                 recurrence in floating-point arithmetic",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "40",
  number =       "1",
  pages =        "587--605",
  month =        jan,
  year =         "2020",
  CODEN =        "IJNADH",
  DOI =          "https://doi.org/10.1093/imanum/dry079",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  bibdate =      "Sat Feb 29 14:22:43 MST 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib",
  URL =          "http://academic.oup.com/imajna/article/40/1/587/5162990",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
}

@Article{Ipsen:2020:PEA,
  author =       "Ilse C. F. Ipsen and Hua Zhou",
  title =        "Probabilistic Error Analysis for Inner Products",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "41",
  number =       "4",
  pages =        "1726--1741",
  month =        "????",
  year =         "2020",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/19M1270434",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Fri Mar 12 10:18:05 MST 2021",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/41/4;
                 https://www.math.utah.edu/pub/bibnet/authors/i/ipsen-ilse-c-f.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
  onlinedate =   "January 2020",
}

@Book{ISO:2020:III,
  author =       "{ISO}",
  title =        "{ISO\slash IEC 60559:2020} Information technology ---
                 Microprocessor Systems --- Floating-Point arithmetic",
  publisher =    pub-ISO,
  address =      pub-ISO:adr,
  pages =        "74",
  year =         "2020",
  bibdate =      "Thu Jan 28 07:09:28 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/isostd.bib",
  URL =          "https://www.iso.org/standard/80985.html",
  abstract =     "This standard specifies interchange and arithmetic
                 formats and methods for binary and decimal
                 floating-point arithmetic in computer programming
                 environments. This standard specifies exception
                 conditions and their default handling. An
                 implementation of a floating-point system conforming to
                 this standard may be realized entirely in software,
                 entirely in hardware, or in any combination of software
                 and hardware. For operations specified in the normative
                 part of this standard, numerical results and exceptions
                 are uniquely determined by the values of the input
                 data, sequence of operations, and destination formats,
                 all under user control.",
  acknowledgement = ack-nhfb,
  remark =       "This is the international version of IEEE 754-2019. It
                 replaces ISO/IEC/IEEE 60559:2011.",
}

@InProceedings{Isono:2020:TWM,
  author =       "Takanori Isono and Makoto Yamakura and Satoshi Shimaya
                 and Isao Kawamoto and Nobuhiro Tsuboi and Masaaki Mineo
                 and Wataru Nakajima and Kenichi Ishida and Shin Sasaki
                 and Toshio Higuchi and Masahiro Hoshaku and Daisuke
                 Murakami and Toshifumi Iwasaki and Hiroshi Hirai",
  booktitle =    "{2020 IEEE Asian Solid-State Circuits Conference
                 (A-SSCC)}",
  title =        "A 12.1 {TOPS/W} Mixed-precision Quantized Deep
                 Convolutional Neural Network Accelerator for Low Power
                 on Edge\slash Endpoint Device",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--4",
  year =         "2020",
  DOI =          "https://doi.org/10.1109/A-SSCC48613.2020.9336137",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Bandwidth; Binary; Convolutional neural networks; deep
                 Neural network; Memory management; Mixed-precision;
                 NPU; Power demand; Quantized; Redundancy; Solid state
                 circuits; System-on-chip; Ternary",
}

@Article{Isupov:2020:DIM,
  author =       "Konstantin Isupov and Vladimir Knyazkov and Alexander
                 Kuvaev",
  title =        "Design and implementation of multiple-precision {BLAS
                 Level 1} functions for graphics processing units",
  journal =      j-J-PAR-DIST-COMP,
  volume =       "140",
  number =       "??",
  pages =        "25--36",
  month =        jun,
  year =         "2020",
  CODEN =        "JPDCER",
  DOI =          "https://doi.org/10.1016/j.jpdc.2020.02.006",
  ISSN =         "0743-7315 (print), 1096-0848 (electronic)",
  ISSN-L =       "0743-7315",
  bibdate =      "Wed May 26 16:11:01 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jpardistcomp.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0743731519303302",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Parallel and Distributed Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07437315",
}

@Misc{Isupov:2020:MPB,
  author =       "Konstantin Isupov and Vladimir Knyazkov",
  title =        "Multiple-Precision {BLAS} Library for Graphics
                 Processing Units",
  howpublished = "TechRxiv preprint.",
  day =          "30",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.36227/techrxiv.12580301.v1",
  bibdate =      "Fri Sep 29 14:30:54 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The binary32 and binary64 floating-point formats
                 provide good performance on current hardware, but also
                 introduce a rounding error in almost every arithmetic
                 operation. Consequently, the accumulation of rounding
                 errors in large computations can cause accuracy issues.
                 One way to prevent these issues is to use
                 multiple-precision floating-point arithmetic. This
                 preprint, submitted to Russian Supercomputing Days
                 2020, presents a new library of basic linear algebra
                 operations with multiple precision for graphics
                 processing units. The library is written in CUDA C/C++
                 and uses the residue number system to represent
                 multiple-precision significands of floating-point
                 numbers. The supported data types, memory layout, and
                 main features of the library are considered.
                 Experimental results are presented showing the
                 performance of the library.",
  acknowledgement = ack-nhfb,
  remark =       "Preprint submitted to Russian Supercomputing Days
                 2020.",
}

@Article{Isupov:2020:UFP,
  author =       "Konstantin Isupov",
  title =        "Using Floating-Point Intervals for Non-Modular
                 Computations in Residue Number System",
  journal =      j-IEEE-ACCESS,
  volume =       "8",
  pages =        "58603--58619",
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ACCESS.2020.2982365",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Wed Oct 1 06:08:36 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "Cathode ray tubes; Cryptography; CUDA; division;
                 Dynamic range; floating-point arithmetic; graphics
                 processing unit; Graphics processing units; Heuristic
                 algorithms; high performance; magnitude comparison;
                 Memory management; non-modular operations; parallel
                 algorithms; Residue number system; Signal processing
                 algorithms",
}

@Article{Jeannerod:2020:RAX,
  author =       "Claude-Pierre Jeannerod",
  title =        "The relative accuracy of $ (x + y) * (x - y) $",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "369",
  number =       "??",
  pages =        "Article 112613",
  day =          "1",
  month =        may,
  year =         "2020",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/j.cam.2019.112613",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Wed May 13 06:58:31 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2020.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042719306181",
  acknowledgement = ack-nhfb,
  articleno =    "112613",
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@Article{Johnson:2020:EAHa,
  author =       "Jeff Johnson",
  title =        "Efficient, arbitrarily high precision hardware
                 logarithmic arithmetic for linear algebra",
  journal =      "arxiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--8",
  day =          "14",
  month =        may,
  year =         "2020",
  bibdate =      "Tue Jul 06 18:17:13 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/pdf/2004.09313.pdf",
  abstract =     "The logarithmic number system (LNS) is arguably not
                 broadly used due to exponential circuit overheads for
                 summation tables relative to arithmetic precision.
                 Methods to reduce this overhead have been proposed, yet
                 still yield designs with high chip area and power
                 requirements. Use remains limited to lower precision or
                 high multiply/add ratio cases, while much of linear
                 algebra (near 1:1 multiply/add ratio) does not
                 qualify.\par

                 We present a dual-base approximate logarithmic
                 arithmetic comparable to floating point in use, yet
                 unlike LNS it is easily fully pipelined, extendable to
                 arbitrary precision with $ O(n^2) $ overhead, and
                 energy efficient at a 1:1 multiply/add ratio.Compared
                 to float32 or float64 vector inner product with FMA,
                 our design is respectively $ 2.3 \times $ and $ 4.6
                 \times $ more energy efficient in 7 nm CMOS. It depends
                 on exp and log evaluation $ 5.4 \times $ and $ 3.2
                 \times $ more energy efficient, at $ 0.23 \times $ and
                 $ 0.37 \times $ the chip area for equivalent accuracy
                 versus standard hyperbolic CORDIC using shift-and-add
                 and approximated ODE integration in the style of Revol
                 and Yakoubsohn. This technique is a novel alternative
                 for low power, high precision hardened linear algebra
                 in computer vision, graphics and machine learning
                 applications.",
  acknowledgement = ack-nhfb,
  keywords =     "approximate arithmetic; elementary function
                 evaluation; hardware linear algebra; logarithmic
                 arithmetic",
  remark =       "Published in \cite{Johnson:2020:EAHb}.",
}

@InProceedings{Johnson:2020:EAHb,
  author =       "Jeff Johnson",
  title =        "Efficient, arbitrarily high precision hardware
                 logarithmic arithmetic for linear algebra",
  crossref =     "Cornea:2020:ISC",
  pages =        "25--32",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00013",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The logarithmic number system (LNS) is arguably not
                 broadly used due to exponential circuit overheads for
                 summation tables relative to arithmetic precision.
                 Methods to reduce this overhead have been proposed, yet
                 still yield designs with high chip area and power
                 requirements. Use remains limited to lower precision or
                 high multiply/add ratio cases, while much of linear
                 algebra (near 1:1 multiply/add ratio) does not qualify.
                 We present a dual-base approximate logarithmic
                 arithmetic comparable to floating point in use, yet
                 unlike LNS it is easily fully pipelined, extendable to
                 arbitrary precision with $ O(n^2) $ overhead, and
                 energy efficient at a 1:1 multiply/add ratio. Compared
                 to float32 or float64 vector inner product with FMA,
                 our design is respectively $ 2.3 \times $ and $ 4.6
                 \times $ more energy efficient in 7 nm CMOS. It depends
                 on exp and log evaluation 5.4 and $ 3.2 \times $ more
                 energy efficient, at $ 0.23 \times $ and $ 0.37 \times
                 $ the chip area for equivalent accuracy versus standard
                 hyperbolic CORDIC using shift-and-add and approximated
                 ODE integration in the style of Revol and Yakoubsohn.
                 This technique is a novel alternative for low power,
                 high precision hardened linear algebra in computer
                 vision, graphics and machine learning applications.",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; approximate arithmetic; ARITH 2020; ARITH-27;
                 Clocks; elementary function evaluation; Hardware;
                 hardware linear algebra; Linear algebra; logarithmic
                 arithmetic; Pipeline processing; Read only memory;
                 Switches",
}

@InProceedings{Joldes:2020:AMQ,
  author =       "Mioara Jolde{\c{s}} and Jean-Michel Muller",
  title =        "Algorithms for Manipulating Quaternions in
                 Floating-Point Arithmetic",
  crossref =     "Cornea:2020:ISC",
  pages =        "48--55",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00016",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Quaternions form a set of four global but not unique
                 parameters, which can represent three-dimensional
                 rotations in a non-singular way. They are frequently
                 used in computer graphics, drone and aerospace vehicle
                 control. Floating-point quaternion operations
                 (addition, multiplication, reciprocal, norm) are often
                 implemented by the book. Although all usual
                 implementations are algebraically equivalent, their
                 numerical behavior can be quite different. For
                 instance, the arithmetic operations on quaternions as
                 well as conversion algorithms to/from rotation matrices
                 are subject to spurious under/overflow (an intermediate
                 calculation underflows or overflows, making the
                 computed final result irrelevant, although the exact
                 result is in the domain of the representable numbers).
                 The goal of this paper is to analyze and then propose
                 workarounds and better accuracy alternatives for such
                 algorithms.",
  acknowledgement = ack-nhfb,
  keywords =     "Aerospace control; Algebra; ARITH 2020; ARITH-27;
                 Computer graphics; Drones; Error analysis;
                 Floating-point arithmetic; Quaternions; quaternions;
                 rounding error analysis; Standards",
}

@InProceedings{Jugade:2020:FEM,
  author =       "Chaitanya Jugade and Deepak Ingole and Dayaram
                 Sonawane and Michal Kvasnica and John Gustafson",
  editor =       "{IEEE}",
  booktitle =    "{2020 59th IEEE Conference on Decision and Control
                 (CDC)}",
  title =        "A Framework for Embedded Model Predictive Control
                 using Posits",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2509--2514",
  year =         "2020",
  DOI =          "https://doi.org/10.1109/CDC42340.2020.9304262",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kim:2020:PPC,
  author =       "Boyeal Kim and Sang Hyun Lee and Hyun Kim and
                 Duy-Thanh Nguyen and Minh-Son Le and Ik Joon Chang and
                 Dohun Kwon and Jin Hyeok Yoo and Jun Won Choi and
                 Hyuk-Jae Lee",
  booktitle =    "{2020 Design, Automation \& Test in Europe Conference
                 \& Exhibition (DATE)}",
  title =        "{PCM}: Precision-Controlled Memory System for Energy
                 Efficient Deep Neural Network Training",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1199--1204",
  year =         "2020",
  DOI =          "https://doi.org/10.23919/DATE48585.2020.9116530",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Approximate Computing; Deep Neural Network; Energy
                 consumption; General Purpose Graphic Processing Unit;
                 Hardware; High Bandwidth Memory; Memory management;
                 Phase change materials; Precision Control; Random
                 access memory; Refresh Period Control; Training",
}

@Article{Klarreich:2020:NMH,
  author =       "Erica Klarreich",
  title =        "News: Multiplication hits the speed limit",
  journal =      j-CACM,
  volume =       "63",
  number =       "1",
  pages =        "11--13",
  month =        jan,
  year =         "2020",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/3371387",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Jan 2 16:41:05 MST 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3371387",
  abstract =     "A problem ``around since antiquity'' may have been
                 resolved by a new algorithm.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@Article{Klower:2020:NFE,
  author =       "Milan Kl{\"o}wer and Peter D. D{\"u}ben and Tim N.
                 Palmer",
  title =        "Number Formats, Error Mitigation, and Scope for 16-Bit
                 Arithmetics in Weather and Climate Modeling Analyzed
                 With a Shallow Water Model",
  journal =      j-J-ADV-MODEL-EARTH-SYST,
  volume =       "12",
  number =       "10",
  pages =        "1--17",
  month =        oct,
  year =         "2020",
  DOI =          "https://doi.org/10.1029/2020MS002246",
  ISSN =         "1942-2466 (print), 1942-2466 (electronic)",
  ISSN-L =       "1942-2466",
  bibdate =      "Fri Dec 15 11:03:12 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Adv. Model. Earth Syst. [JAMES]",
  fjournal =     "Journal of Advances in Modeling Earth Systems",
  journal-URL =  "https://agupubs.onlinelibrary.wiley.com/journal/19422466",
}

@InProceedings{Knobbe:2020:CRS,
  author =       "Simon Knobbe and Moritz B{\"a}rthel and Steffen Paul
                 and Jochen Rust",
  booktitle =    "{2020 9th International Conference on Modern Circuits
                 and Systems Technologies (MOCAST)}",
  title =        "Complexity Reduction for Sphere Decoding using
                 {Unum-Type-II}-Based {SORN}-Arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--4",
  year =         "2020",
  DOI =          "https://doi.org/10.1109/MOCAST49295.2020.9200263",
  bibdate =      "Fri Dec 15 07:38:18 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Koc:2020:AIM,
  author =       "{\c{C}}etin Kaya Ko{\c{c}}",
  title =        "Algorithms for Inversion Mod $ p^k $",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "69",
  number =       "6",
  pages =        "907--913",
  year =         "2020",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2020.2970411",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 23 16:03:24 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  abstract =     "This article describes and analyzes all existing
                 algorithms for computing $ x = a^{-1} (\bmod p^k) $ for
                 a prime $p$, and also introduces a new algorithm based
                 on the exact solution of linear equations using
                 $p$-adic expansions. The algorithm starts with the
                 initial value $ c = a^{-1} (\bmod p)$ and iteratively
                 computes the digits of the inverse $ x = a^{-1} (\bmod
                 p^k)$ in base $p$. The $ \bmod 2$ version of the
                 algorithm is more efficient than all existing
                 algorithms for small values of $k$. Moreover, it stands
                 out as being the only one that works for any $p$, any
                 $k$, and digit-by-digit. While the new algorithm is
                 asymptotically worse off, it requires the minimal
                 number of arithmetic operations (just a single
                 addition) per step, as compared to all existing
                 algorithms.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Kudo:2020:INT,
  author =       "Shuhei Kudo and Keigo Nitadori and Takuya Ina and
                 Toshiyuki Imamura",
  booktitle =    "{2020 IEEE\slash ACM 11TH Workshop on Latest Advances
                 in Scalable Algorithms for Large-Scale Systems
                 (SCALA)}",
  title =        "Implementation and Numerical Techniques for One
                 Eflop/s {HPL-AI} Benchmark on {Fugaku}",
  publisher =    PUB-IEEE,
  address =      PUB-IEEE:ADR,
  pages =        "69--76",
  year =         "2020",
  DOI =          "https://doi.org/10.1109/scala51936.2020.00014",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "artificial intelligence; benchmark testing; computer
                 architecture; exaflop/s; FP16; FP32; Fugaku; HPL-AI;
                 iterative methods; Jacobian matrices; matrix
                 decomposition; mixed-precision; supercomputers",
}

@InProceedings{Kudo:2020:PRE,
  author =       "Shuhei Kudo and Keigo Nitadori and Takuya Ina and
                 Toshiyuki Imamura",
  booktitle =    "{2020 IEEE International Conference on Cluster
                 Computing (CLUSTER)}",
  title =        "Prompt Report on Exa-Scale {HPL-AI} Benchmark",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "418--419",
  year =         "2020",
  DOI =          "https://doi.org/10.1109/CLUSTER49012.2020.00058",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benchmark testing; Conferences; Exa flop/s;
                 Floating-point arithmetic; Fugaku; Guidelines; HPL-AI;
                 mixed-precision; Numerical analysis; Optimization;
                 Supercomputers",
}

@InProceedings{Laguna:2020:VQF,
  author =       "Ignacio Laguna",
  booktitle =    "2020 {IEEE} International Parallel and Distributed
                 Processing Symposium ({IPDPS})",
  title =        "{Varity}: Quantifying Floating-Point Variations in
                 {HPC} Systems Through Randomized Testing",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "622--633",
  month =        may,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ipdps47924.2020.00070",
  bibdate =      "Tue Jan 28 06:34:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}

@Article{Lange:2020:FRF,
  author =       "Marko Lange and Siegfried M. Rump",
  title =        "Faithfully Rounded Floating-point Computations",
  journal =      j-TOMS,
  volume =       "46",
  number =       "3",
  pages =        "21:1--21:20",
  month =        sep,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3290955",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Sep 26 07:28:19 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3290955",
  abstract =     "We present a pair arithmetic for the four basic
                 operations and square root. It can be regarded as a
                 simplified, more-efficient double-double arithmetic.
                 The central assumption on the underlying arithmetic is
                 the first standard model for error analysis for
                 operations on a discrete set of real numbers. Neither
                 do we require a floating-point grid nor a rounding to
                 nearest property. Based on that, we define a relative
                 rounding error unit $u$ and prove rigorous error bounds
                 for the computed result of an arbitrary arithmetic
                 expression depending on $u$, the size of the
                 expression, and possibly a condition measure. In the
                 second part of this note, we extend the error analysis
                 by examining requirements to ensure faithfully rounded
                 outputs and apply our results to IEEE 754 standard
                 conform floating-point systems. For a class of
                 mathematical expressions, using an IEEE 754 standard
                 conform arithmetic with base $ \beta $, the result is
                 proved to be faithfully rounded for up to $ 1 / \sqrt
                 {\beta u - 2}$ operations. Our findings cover a number
                 of previously published algorithms to compute
                 faithfully rounded results, among them Horner's scheme,
                 products, sums, dot products, or Euclidean norm. Beyond
                 that, several other problems can be analyzed, such as
                 polynomial interpolation, orientation problems,
                 Householder transformations, or the smallest singular
                 value of Hilbert matrices of large size.",
  acknowledgement = ack-nhfb,
  articleno =    "21",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Lange:2020:NDF,
  author =       "Marko Lange and Shin'ichi Oishi",
  title =        "A note on {Dekker}'s {FastTwoSum} algorithm",
  journal =      j-NUM-MATH,
  volume =       "145",
  number =       "2",
  pages =        "383--403",
  month =        jun,
  year =         "2020",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/s00211-020-01114-2",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Thu Jun 4 12:18:54 MDT 2020",
  bibsource =    "http://link.springer.com/journal/211/145/2;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath2020.bib",
  note =         "See correction \cite{Lange:2021:CND}.",
  URL =          "https://link.springer.com/article/10.1007/s00211-020-01114-2",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@InProceedings{Langroudi:2020:APP,
  author =       "Hamed F. Langroudi and Vedant Karia and John L.
                 Gustafson and Dhireesha Kudithipudi",
  editor =       "{IEEE}",
  booktitle =    "{2020 IEEE/CVF Conference on Computer Vision and
                 Pattern Recognition Workshops (CVPRW)}",
  title =        "Adaptive Posit: Parameter aware numerical format for
                 deep learning inference on the edge",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "3123--3131",
  year =         "2020",
  DOI =          "https://doi.org/10.1109/CVPRW50498.2020.00371",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Lauter:2020:FSA,
  author =       "Christoph Lauter and Anastasia Volkova",
  title =        "A Framework for Semi-Automatic Precision and Accuracy
                 Analysis for Fast and Rigorous Deep Learning",
  crossref =     "Cornea:2020:ISC",
  pages =        "103--110",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00023",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Deep Neural Networks (DNN) represent a
                 performance-hungry application. Floating-Point (FP) and
                 custom floating-point-like arithmetic satisfies this
                 hunger. While there is need for speed, inference in
                 DNNs does not seem to have any need for precision. Many
                 papers experimentally observe that DNNs can
                 successfully run at almost ridiculously low precision.
                 The aim of this paper is two-fold: first, to shed some
                 theoretical light upon why a DNN's FP accuracy stays
                 high for low FP precision. We observe that the loss of
                 relative accuracy in the convolutional steps is
                 recovered by the activation layers, which are extremely
                 well-conditioned. We give an interpretation for the
                 link between precision and accuracy in DNNs. Second,
                 the paper presents a software framework for
                 semi-automatic FP error analysis for the inference
                 phase of deep-learning. Compatible with common
                 Tensorflow/Keras models, it leverages the frugally-deep
                 Python/C++ library to transform a neural network into
                 C++ code in order to analyze the network's need for
                 precision. This rigorous analysis is based an Interval
                 and Affine arithmetics to compute absolute and relative
                 error bounds for a DNN. We demonstrate our tool with
                 several examples.",
  acknowledgement = ack-nhfb,
  keywords =     "affine arithmetic; Analytical models; ARITH 2020;
                 ARITH-27; Biological neural networks; Computational
                 modeling; deep learning; Digital arithmetic; error
                 analysis; floating-point arithmetic; interval
                 arithmetic; Machine learning; Neurons; Tools",
}

@InProceedings{Lindstrom:2020:VRC,
  author =       "Peter Lindstrom",
  title =        "Variable-Radix Coding of the Reals",
  crossref =     "Cornea:2020:ISC",
  pages =        "111--116",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00024",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Recently proposed real number systems like Posits and
                 Elias codes make use of tapered accuracy resulting from
                 variable-length coding of exponents and significands.
                 Several quite different interpretations of these number
                 systems have been provided, though most often these
                 rely on some combination of fixed- and variable-length
                 codes for exponent and significand. We provide a new
                 perspective on these number systems that unifies known
                 representations while suggesting new ones. Our
                 framework is based on multibit radix representations
                 that encode the exponent in unary, the leading nonzero
                 digit in a variable-length code, and the remaining
                 digits in fixed-length binary code. We show how Posits,
                 the various Elias codes, and IEEE 754 like
                 representations can be expressed in this framework.
                 Moreover, we show that Posits and the Elias and codes
                 represent the leading digit using the canonical Huffman
                 code for a probability distribution given by Benford's
                 law, which governs the probability of leading digits.
                 We further show that Posits correspond to the use of a
                 fixed radix while Elias and codes are based on simple
                 sequences of increasing radix. Our approach provides
                 for an intuitive and uniform framework for representing
                 numbers that reveals a visual mapping between codewords
                 and the binary representation of real numbers obscured
                 by prior frameworks. This new interpretation suggests a
                 generalization of Posits and other number systems and
                 provides simple rules for designing
                 information-theoretically optimal codes.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2020; ARITH-27; Benford's law; Binary codes;
                 Digital arithmetic; Elias codes; Encoding; floating
                 point; Huffman code; Indexes; posits; Probability
                 distribution; Proposals; real number systems; tapered
                 accuracy; Visualization",
}

@Article{Luo:2020:ADN,
  author =       "Y. Luo and S. Yu",
  title =        "Accelerating Deep Neural Network In-Situ Training With
                 Non-Volatile and Volatile Memory Based Hybrid Precision
                 Synapses",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "69",
  number =       "8",
  pages =        "1113--1127",
  year =         "2020",
  CODEN =        "ITCOB4",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jul 23 16:03:24 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Lyakhov:2020:HPD,
  author =       "Pavel Lyakhov and Maria Valueva and Georgii Valuev and
                 Nikolai Nagornov",
  title =        "High-Performance Digital Filtering on Truncated
                 Multiply-Accumulate Units in the Residue Number
                 System",
  journal =      j-IEEE-ACCESS,
  volume =       "8",
  pages =        "209181--209190",
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ACCESS.2020.3038496",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Wed Oct 1 06:08:36 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "Adders; Delays; digital filter; Digital signal
                 processing; Filtering; Finite impulse response filters;
                 Hardware; modular Multiply-Accumulate unit; Performance
                 evaluation; residue number system",
}

@InProceedings{Marquer:2020:HLI,
  author =       "Yoann Marquer and Tania Richmond",
  title =        "A Hole in the Ladder: Interleaved Variables in
                 Iterative Conditional Branching",
  crossref =     "Cornea:2020:ISC",
  pages =        "56--63",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00017",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The modular exponentiation is crucial to the RSA
                 cryptographic protocol, and variants inspired by the
                 Montgomery ladder have been studied to provide more
                 secure algorithms. In this paper, we abstract away the
                 iterative conditional branching used in the Montgomery
                 ladder, and formalize systems of equations necessary to
                 obtain what we call the semi-interleaved and
                 fully-interleaved ladder properties. In particular, we
                 design fault-injection attacks able to obtain bits of
                 the secret against semi-interleaved ladders, including
                 the Montgomery ladder, but not against
                 fully-interleaved ladders that are more secure. We also
                 apply these equations to extend the Montgomery ladder
                 for both the semi- and fully-interleaved cases, thus
                 proposing novel and more secure algorithms to compute
                 the modular exponentiation.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2020; ARITH-27; Countermeasures (computer);
                 Cryptography; Fault detection; Iterative algorithms;
                 Mathematical model; Public-key cryptography; Registers;
                 Security; Side-channel attacks; Space exploration",
}

@TechReport{Meurant:2020:PFM,
  author =       "G{\'e}rard Meurant",
  title =        "\pkg{FLOATP\_toolbox}, {Matlab} software, variable
                 precision floating point arithmetic.",
  type =         "Report",
  number =       "????",
  institution =  "Commissariat a l'{\'E}nergie Atomique (CEA)",
  address =      "????, France",
  year =         "2020",
  bibdate =      "Sat Dec 23 12:13:27 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  URL =          "https://gerard-meurant.pagesperso-orange.fr/soft_meurant_n.html",
  acknowledgement = ack-nhfb,
  remark =       "URL links to almost-empty home page.",
}

@InProceedings{Mikaitis:2020:IRG,
  author =       "Mantas Mikaitis",
  title =        "Issues with rounding in the {GCC} implementation of
                 the {ISO 18037:2008} standard fixed-point arithmetic",
  crossref =     "Cornea:2020:ISC",
  pages =        "129--132",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00028",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/gnu.bib",
  abstract =     "We describe various issues caused by the lack of
                 round-to-nearest mode in the gcc compiler
                 implementation of the fixed-point arithmetic data types
                 and operations. We demonstrate that round-to-nearest is
                 not performed in the conversion of constants,
                 conversion from one numerical type to a less precise
                 type and results of multiplications. Furthermore, we
                 show that mixed-precision operations in fixed-point
                 arithmetic lose precision on arguments, even before
                 carrying out arithmetic operations. The ISO 18037:2008
                 standard was created to standardize C language
                 extensions, including fixed-point arithmetic, for
                 embedded systems. Embedded systems are usually based on
                 ARM processors, of which approximately 100 billion have
                 been manufactured by now. Therefore, the observations
                 about numerical issues that we discuss in this paper
                 can be rather dangerous and are important to address,
                 given the wide ranging type of applications that these
                 embedded systems are running.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2020; ARITH-27; Computer languages; Embedded
                 systems; fixed-point arithmetic; Hardware; ISO
                 18037:2008; ISO Standards; Libraries; Program
                 processors; rounding",
}

@Article{Mikaitis:2020:SRA,
  author =       "Mantas Mikaitis",
  title =        "Stochastic Rounding: Algorithms and Hardware
                 Accelerator",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--6",
  day =          "29",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.48550/arXiv.2001.01501",
  bibdate =      "Wed Aug 07 16:03:40 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "https://arxiv.org/abs/2001.01501#",
  abstract =     "Algorithms and a hardware accelerator for performing
                 stochastic rounding (SR) are presented. The main goal
                 is to augment the ARM M4F based multi-core processor
                 SpiNNaker2 with a more flexible rounding functionality
                 than is available in the ARM processor itself. The
                 motivation of adding such an accelerator in hardware is
                 based on our previous results showing improvements in
                 numerical accuracy of ODE solvers in fixed-point
                 arithmetic with SR, compared to standard round to
                 nearest or bit truncation rounding modes. Furthermore,
                 performing SR purely in software can be expensive, due
                 to requirement of a pseudorandom number generator
                 (PRNG), multiple masking and shifting instructions, and
                 an addition operation. Also, saturation of the rounded
                 values is included, since rounding is usually followed
                 by saturation, which is especially important in
                 fixed-point arithmetic due to a narrow dynamic range of
                 representable values. The main intended use of the
                 accelerator is to round fixed-point multiplier outputs,
                 which are returned unrounded by the ARM processor in a
                 wider fixed-point format than the arguments.",
  acknowledgement = ack-nhfb,
}

@Article{Muller:2020:EFA,
  author =       "Jean-Michel Muller",
  title =        "Elementary Functions and Approximate Computing",
  journal =      j-PROC-IEEE,
  volume =       "108",
  number =       "12",
  pages =        "2136--2149",
  month =        dec,
  year =         "2020",
  CODEN =        "IEEPAD",
  DOI =          "https://doi.org/10.1109/jproc.2020.2991885",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Tue Mar 1 06:07:02 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In this article, we review some of the classical
                 methods used for quickly obtaining low-precision
                 approximations to the elementary functions. Then, for
                 each of the three main classes of elementary function
                 algorithms (shift-and-add algorithms, polynomial or
                 rational approximations, and table-based methods) and
                 for the additional, specific to approximate computing,
                 ``bit-manipulation'' techniques, we examine what can be
                 done for obtaining very fast estimates of a function,
                 at the cost of a (controlled) loss in terms of
                 accuracy.",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
}

@InProceedings{Murillo:2020:CPA,
  author =       "Raul Murillo and Alberto A. {Del Barrio} and Guillermo
                 Botella",
  editor =       "{IEEE}",
  booktitle =    "{IEEE International Symposium on Circuits and Systems
                 (ISCAS): Seville, Spain, October 11--14, 2020}",
  title =        "Customized Posit Adders and Multipliers using the
                 {FloPoCo} Core Generator",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--5",
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ISCAS45731.2020.9180771",
  ISBN =         "1-72813-320-3",
  ISBN-13 =      "978-1-72813-320-1",
  ISSN =         "0271-4302 (print), 2158-1525 (electronic)",
  ISSN-L =       "0271-4302",
  bibdate =      "Thu Dec 14 17:18:33 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1109/ISCAS45731.2020",
}

@Article{Murillo:2020:DPD,
  author =       "R. Murillo and A. A. {Del Barrio} and G. Botella",
  title =        "{Deep PeNSieve}: a deep learning framework based on
                 the posit number system",
  journal =      j-DIGIT-SIGNAL-PROCESS,
  volume =       "102",
  pages =        "1--8",
  month =        jul,
  year =         "2020",
  CODEN =        "DSPREJ",
  DOI =          "https://doi.org/10.1016/j.dsp.2020.102762",
  ISSN =         "1051-2004 (print), 1095-4333 (electronic)",
  ISSN-L =       "1051-2004",
  bibdate =      "Thu Dec 14 17:04:34 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/S105120042030107X",
  acknowledgement = ack-nhfb,
  articleno =    "102762",
  fjournal =     "Digital Signal Processing",
  journal-URL =  "https://www.sciencedirect.com/journal/digital-signal-processing",
}

@InProceedings{Nannarelli:2020:VPB,
  author =       "Alberto Nannarelli",
  title =        "Variable Precision 16-Bit Floating-Point Vector Unit
                 for Embedded Processors",
  crossref =     "Cornea:2020:ISC",
  pages =        "96--102",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00022",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The increasing demand of computation at the edge and
                 the tight power budgets push designers to migrate
                 double and single-precision calculations to formats of
                 reduced precision and dynamic range for applications
                 that can tolerate some inaccuracy.In this context, we
                 introduce a variable format for reduced precision
                 floating-point with storage limited to 16 bits. This
                 format is suitable for applications in signal
                 processing, machine learning and other applications in
                 embedded systems. We present the hardware
                 implementations for multiplication and division units
                 that can sustain a throughput of one result per clock
                 cycle designed for vector processing. We also show some
                 examples of applications that can benefit from the
                 proposed format.",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; ARITH 2020; ARITH-27; customizable bias;
                 Dynamic range; Encoding; Floating-point; Hardware;
                 Program processors; Signal processing; Standards;
                 variable precision",
}

@Misc{Nass:2020:GUL,
  author =       "Rich Nass",
  title =        "{GreenWaves} Ultra-Low Power {GAP9} {IoT} Apps
                 Processor Suits Intelligence at the Edge",
  howpublished = "Web site",
  day =          "21",
  month =        jan,
  year =         "2020",
  bibdate =      "Wed Jan 22 07:07:03 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "GAP9 offers vectorized 2-bit and 4-bit fixed-point
                 arithmetic, and 8-, 16-, and 32-bit floating-point
                 arithmetic.",
  URL =          "https://www.embedded-computing.com/guest-blogs/greenwaves-ultra-low-power-gap9-iot-apps-processor-suits-intelligence-at-the-edge",
  acknowledgement = ack-nhfb,
}

@InProceedings{Neves:2020:DFM,
  author =       "Nuno Neves and Pedro Tom{\'a}s and Nuno Roma",
  editor =       "{IEEE}",
  booktitle =    "{2020 IEEE Workshop on Signal Processing Systems
                 (SiPS)}",
  title =        "Dynamic Fused Multiply-Accumulate Posit Unit with
                 Variable Exponent Size for Low-Precision {DSP}
                 Applications",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--6",
  year =         "2020",
  DOI =          "https://doi.org/10.1109/SiPS50750.2020.9195256",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Neves:2020:RSB,
  author =       "Nuno Neves and Pedro Tom{\'a}s and Nuno Roma",
  editor =       "{IEEE}",
  booktitle =    "{2020 IEEE 31st International Conference on
                 Application-specific Systems, Architectures and
                 Processors (ASAP)}",
  title =        "Reconfigurable Stream-based Tensor Unit with
                 Variable-Precision Posit Arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "149--156",
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ASAP49362.2020.00033",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Niasar:2020:FSA,
  author =       "Mojtaba Bisheh Niasar and Rami {El Khatib} and Reza
                 Azarderakhsh and Mehran Mozaffari-Kermani",
  title =        "Fast, Small, and Area-Time Efficient Architectures for
                 Key-Exchange on {Curve25519}",
  crossref =     "Cornea:2020:ISC",
  pages =        "72--79",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00019",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper demonstrates fast and compact
                 implementations of Elliptic Curve Cryptography (ECC)
                 for efficient key agreement over Curve25519. Curve25519
                 has been recently adopted as a key exchange method for
                 several applications and included in the National
                 Institute of Standards and Technology (NIST)
                 recommendations for public key cryptography. This paper
                 presents three different performance level designs
                 including lightweight, area-time efficient, and
                 high-performance architectures. Lightweight hardware
                 implementations are used for several Internet of Things
                 (IoT) applications due to their resources being at
                 premium. Our lightweight architecture utilizes 90\%
                 less resources compared to the best previous work while
                 it is still more optimized in term of A $ \cdot $ T
                 (area $ \times $ time). For efficient implementation
                 from either time or utilized resources, our area-time
                 efficient architecture can establish almost 7,000 key
                 sessions per second which is 64\% faster than the
                 previous works. The area-time efficient architecture
                 uses well scheduled interleaved multiplication combined
                 with a reduction algorithm. Additionally, we offer a
                 fast architecture for high performance applications
                 based on the 4-level Karatsuba method and Carry-Compact
                 Addition (CCA). Our high-performance architecture also
                 outperforms previous work in terms of A middot; T. The
                 results show 9\% and 29\% improvement in A middot; T
                 and Admiddot; T (DSP\_count $ \times $ time),
                 respectively. All architectures are variable-base-point
                 implemented on the Xilinx Zynq-7020 FPGA family where
                 performance and implementation metrics are reported and
                 compared. Finally, various side-channel attack
                 countermeasures are embedded in the proposed
                 architectures.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2020; ARITH-27; Computer architecture;
                 Curve25519; Elliptic curve cryptography; elliptic curve
                 Diffie-Hellman (ECDH); Elliptic curves; Field
                 programmable gate arrays; field-programmable gate array
                 (FPGA); Hardware; NIST; point multiplication; Random
                 access memory",
}

@InProceedings{Papachatzopoulos:2020:MDM,
  author =       "Kleanthis Papachatzopoulos and Vassilis Paliouras",
  title =        "Maximum Delay Models for Parallel-Prefix Adders in the
                 Presence of Threshold Voltage Variations",
  crossref =     "Cornea:2020:ISC",
  pages =        "88--95",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00021",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper introduces a delay modeling formulation for
                 several Parallel-Prefix Adders in the presence of
                 threshold voltage variability. A path-based model is
                 derived for the delay variability of Kogge-Stone,
                 Knowles, Sklansky, Brent-Kung, Han-Carlson,
                 Ladner-Fischer, and New Adder architectures. The delay
                 model accuracy is evaluated for the specific adders on
                 the basis of SPICE Monte-Carlo Simulations at 45 nm and
                 16 nm nodes. The presented analysis reveals that the
                 proposed path-based model estimates the maximum delay
                 Probability Density Function of the particular adder
                 architectures with sufficient accuracy, assuming 3
                 intra-die threshold voltage variations as high as 10\%
                 of nominal value. Delay yield estimations produced by
                 the proposed model are found to agree with those of
                 Monte-Carlo Simulations for a number of highly probable
                 critical paths, presenting an error less than 2\%. For
                 the particular adders and technology nodes, an
                 approximately 10-fold reduction in simulation time is
                 obtained when exploiting the proposed model. The
                 particular observation indicates that the computational
                 time for delay yield estimation of Parallel-Prefix
                 Adders can be exponentially reduced with negligible
                 accuracy loss when the analysis focuses solely on the
                 Nominal-Maximum Delay critical path. Finally, a
                 quantitative comparison of prefix adders to the
                 Borrow-Save Adder is offered, in terms of complexity
                 and susceptibility to variations.",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; ARITH 2020; ARITH-27; critical path; delay
                 yield; Delays; Gaussian distribution; Monte Carlo
                 methods; parallel-prefix adders; SPICE; Threshold
                 voltage; threshold voltage variations; variability",
}

@InProceedings{Payer:2020:SMF,
  author =       "Stefan Payer and Cedric Lichtenau and Michael Klein
                 and Kerstin Schelm and Petra Leber and Nicol Hofmann
                 and Tina Babinsky",
  title =        "{SIMD} Multi Format Floating-Point Unit on the {IBM
                 z15}",
  crossref =     "Cornea:2020:ISC",
  pages =        "125--128",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00027",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The IBM z Systems(TM) is the backbone of the
                 insurance, banking, and retail industry. Innovation in
                 these markets is driving the demand for new and
                 additional applications to better serve the customers.
                 These workloads like machine learning, data analytics,
                 AI, etc. require a rapidly increasing number of
                 computations in smaller precision formats. With IBM
                 z15(TM) we completely redesigned the binary and
                 hexadecimal floating-point unit to efficiently
                 implement SIMD operations at 5.2GHz while maintaining
                 the industry leading reliability, availability and
                 serviceability standard. This paper describes the new
                 design and special techniques used to achieve these
                 goals like reusing the existing double precision unit
                 pipeline for lower precision parallel SIMD, new
                 approaches to formally verify the design, and improving
                 error detection for the 14nm technology node.",
  acknowledgement = ack-nhfb,
  keywords =     "AI; ARITH 2020; ARITH-27; Binary; Digital arithmetic;
                 Floating Point Unit; Formal Verification; Hafnium;
                 Hexadecimal; IBM z15(TM); Machine Learning; Multi
                 Format; SIMD",
}

@InProceedings{RAos:2020:EMP,
  author =       "John Osorio R{\'\i}os and Adri{\`a} Armejach and
                 Gulrukh Khattak and Eric Petit and Sofia Vallecorsa and
                 Marc Casas",
  booktitle =    "{2020 19th IEEE International Conference on Machine
                 Learning and Applications (ICMLA)}",
  title =        "Evaluating Mixed-Precision Arithmetic for {3D}
                 Generative Adversarial Networks to Simulate High Energy
                 Physics Detectors",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "49--56",
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ICMLA51294.2020.00017",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "3DGAN; Binary Analysis Tool; Brain Float 16 (BF16);
                 Computational modeling; Detectors; Generative
                 adversarial networks; Generative Adversarial Networks;
                 Hardware; High Energy Physics; Mixed Precision (MP);
                 Numerical models; Reduced Precision; Tools; Training",
}

@InProceedings{Raveendran:2020:NPF,
  author =       "Aneesh Raveendran and Sandra Jean and J. Mervin and D.
                 Vivian and David Selvakumar",
  editor =       "{IEEE}",
  booktitle =    "{2020 33rd International Conference on VLSI Design and
                 2020 19th International Conference on Embedded Systems
                 (VLSID), Bengaluru, India, 4--8 January 2020}",
  title =        "A Novel Parametrized Fused Division and Square-Root
                 {POSIT} Arithmetic Architecture",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "207--212",
  month =        jan,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/vlsid49098.2020.00053",
  ISBN =         "1-72815-701-3",
  ISBN-13 =      "978-1-72815-701-6",
  ISSN =         "1063-9667 (print), 2380-6923 (electronic)",
  ISSN-L =       "1063-9667",
  bibdate =      "Fri Dec 15 07:29:26 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Saadat:2020:WWC,
  author =       "Hassaan Saadat and Haris Javaid and Aleksandar
                 Ignjatovic and Sri Parameswaran",
  booktitle =    "{2020 25th Asia and South Pacific Design Automation
                 Conference (ASP-DAC)}",
  title =        "{WEID}: Worst-case Error Improvement in Approximate
                 Dividers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "8D-1--8D-6",
  month =        jan,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/asp-dac47756.2020.9045504",
  bibdate =      "Wed Dec 20 08:02:22 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Approximate integer dividers suffer from unreasonably
                 high worst-case relative errors (such as 50\% or
                 100\%), which can adversely affect the
                 application-level output. In this paper, we propose
                 WEID, which is a novel lightweight method to improve
                 the worst-case relative errors in approximate integer
                 dividers. We first present an in-depth analysis to gain
                 insights into the cause of the high worst-case relative
                 error. Based on our insights, we propose a novel method
                 to detect when an error occurs in an approximate
                 divider, and modify the output to reduce the error.
                 Further, we present the hardware realization of WEID
                 method and demonstrate that it can be generically
                 coupled with several state-of-the-art approximate
                 dividers. Our results show that for 32-by-16 dividers,
                 WEID reduces worst-case relative errors from 100\% to $
                 \approx 20 $ \%, while still achieving $ \approx 80 \%
                 $ and $ \approx 70 \% $ reduction in delay and energy
                 compared to an accurate array divider.",
  acknowledgement = ack-nhfb,
}

@Misc{SEGGER:2020:SFP,
  author =       "{SEGGER Microcontroller}",
  title =        "{SEGGER} Floating-Point Library",
  howpublished = "Web site.",
  month =        jan,
  year =         "2020",
  bibdate =      "Fri Feb 07 06:02:26 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.segger.com/products/development-tools/runtime-library/technology/floating-point-library/",
  abstract =     "The floating-point library contains complete, fully
                 optimized and verified floating point functionality,
                 which is required for devices without an FPU. The
                 floating-point emulator, a crucial part of the
                 floating-point library, of the Arm and RISC-V variants
                 are written in assembly language, optimized either for
                 small code size or increased execution speed. For other
                 processor architectures the library has a portable C
                 implementation. \ldots{} The SEGGER Floating-Point
                 Library is delivered in source code, with optional
                 rights for redistribution in object code form. All
                 source files, a mix of C code and assembly, are fully
                 commented. The floating-point emulator, providing the
                 low-level functions, is entirely written in assembly.
                 Higher level functions are implemented as a mix of
                 primarily C code with some assembly routines. The code
                 can be compiled with any ANSO-compliant C compiler,
                 such as GCC, Clang, or IAR.",
  acknowledgement = ack-nhfb,
}

@Article{Sharma:2020:CRV,
  author =       "Niraj Sharma and Riya Jain and Madhumita Mohan and
                 Sachin Patkar and Rainer Leupers and Nikhil Rishiyur
                 and Farhad Merchant",
  title =        "{CLARINET}: A {RISC-V} Based Framework for Posit
                 Arithmetic Empiricism",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--20",
  day =          "30",
  month =        may,
  year =         "2020",
  DOI =          "https://doi.org/10.48550/arXiv.2006.00364",
  bibdate =      "Sat Dec 16 10:27:27 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  URL =          "https://arxiv.org/abs/2006.00364",
  abstract =     "Many engineering and scientific applications require
                 high precision arithmetic. IEEE 754-2008 compliant
                 (floating-point) arithmetic is the de facto standard
                 for performing these computations. Recently, posit
                 arithmetic has been proposed as a drop-in replacement
                 for floating-point arithmetic. The posit{\TM} data
                 representation and arithmetic claim several absolute
                 advantages over the floating-point format and
                 arithmetic, including higher dynamic range, better
                 accuracy, and superior performance-area trade-offs.
                 However, there does not exist any accessible, holistic
                 framework that facilitates the validation of these
                 claims of posit arithmetic, especially when the claims
                 involve long accumulations (quire).\par

                 In this paper, we present a consolidated
                 general-purpose processor-based framework to support
                 posit arithmetic empiricism. The end-users of the
                 framework have the liberty to seamlessly experiment
                 with their applications using posit and floating-point
                 arithmetic since the framework is designed for the two
                 number systems to coexist. Melodica is a posit
                 arithmetic core that implements parametric fused
                 operations that uniquely involve the quire data type.
                 Clarinet is a Melodica-enabled processor based on the
                 RISC-V ISA. To the best of our knowledge, this is the
                 first-ever integration of quire with a RISC-V core. To
                 show the effectiveness of the Clarinet platform, we
                 perform an extensive application study and benchmark
                 some of the common linear algebra and computer vision
                 kernels. We emulate Clarinet on a Xilinx FPGA and
                 present utilization and timing data. Clarinet and
                 Melodica remain actively under development and are
                 available in open-source for posit arithmetic
                 empiricism.",
  acknowledgement = ack-nhfb,
}

@Article{Shibata:2020:SPV,
  author =       "Naoki Shibata and Francesco Petrogalli",
  title =        "{SLEEF}: a Portable Vectorized Library of {C} Standard
                 Mathematical Functions",
  journal =      j-IEEE-TRANS-PAR-DIST-SYS,
  volume =       "31",
  number =       "6",
  pages =        "1316--1327",
  month =        jun,
  year =         "2020",
  CODEN =        "ITDSEO",
  DOI =          "https://doi.org/10.1109/TPDS.2019.2960333",
  ISSN =         "1045-9219 (print), 1558-2183 (electronic)",
  ISSN-L =       "1045-9219",
  bibdate =      "Thu Feb 20 10:08:58 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranspardistsys2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Parallel Distrib. Syst.",
  fjournal =     "IEEE Transactions on Parallel and Distributed
                 Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=71",
  keywords =     "elementary functions; floating-point arithmetic;
                 Parallel and vector implementations; SIMD processors",
}

@Misc{Shirriff:2020:AMC,
  author =       "Ken Shirriff",
  title =        "Die analysis of the 8087 math coprocessor's fast bit
                 shifter",
  howpublished = "Blog post",
  pages =        "16",
  month =        may,
  year =         "2020",
  bibdate =      "Sat Aug 23 07:23:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Analysis of the barrel shifter at the heart of both
                 the arithmetic operations and the CORDIC-like
                 transcendental functions in the 8087. See patent
                 \cite{Palmer:1985:PBS}.",
  URL =          "https://ieeemilestones.ethw.org/w/images/0/0c/Shirriff_8087_barrel_shifter.pdf;
                 https://www.righto.com/2020/05/die-analysis-of-8087-math-coprocessors.html",
  acknowledgement = ack-nhfb,
}

@Misc{Shirriff:2020:ERC,
  author =       "Ken Shirriff",
  title =        "Extracting {ROM} constants from the 8087 math
                 coprocessor's die",
  howpublished = "Blog posting",
  pages =        "16",
  month =        may,
  year =         "2020",
  bibdate =      "Sat Aug 23 07:21:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeemilestones.ethw.org/w/images/8/87/Shirriff_8087_ROM_constants.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Smith:2020:HMC,
  author =       "Ernie Smith",
  title =        "How a Minor Calculation Error Cost {Intel} Half a
                 Billion Dollars: How one of the most famous computer
                 bugs of all time, the {Intel Pentium} floating-point
                 division glitch, blew out of proportion into a {PR}
                 crisis",
  howpublished = "Web site.",
  day =          "14",
  month =        sep,
  year =         "2020",
  bibdate =      "Thu Jan 28 17:58:10 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.vice.com/en/article/dyzqdj/how-a-minor-calculation-error-cost-intel-half-a-billion-dollars",
  acknowledgement = ack-nhfb,
  remark =       "This is a retrospective on the infamous Pentium divide
                 flaw of the 1990s. Near the end, it remarks about the
                 discoverer of the bug ``[Thomas] Nicely, who died last
                 year and was largely seen as legendary by his peers,
                 spent roughly three decades at the University of
                 Lynchburg before retiring in 2000.''",
}

@InProceedings{Sommer:2020:CAN,
  author =       "Lukas Sommer and Lukas Weber and Martin Kumm and
                 Andreas Koch",
  booktitle =    "{2020 IEEE 28th Annual International Symposium on
                 Field-Programmable Custom Computing Machines (FCCM)}",
  title =        "Comparison of Arithmetic Number Formats for Inference
                 in Sum--Product Networks on {FPGAs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "75--83",
  year =         "2020",
  DOI =          "https://doi.org/10.1109/FCCM48280.2020.00020",
  bibdate =      "Fri Sep 22 08:07:44 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Sousa:2020:TIR,
  author =       "L. Sousa and R. Paludo and P. Martins and H.
                 Pettenghi",
  title =        "Towards the Integration of Reverse Converters into the
                 {RNS} Channels",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "69",
  number =       "3",
  pages =        "342--348",
  month =        mar,
  year =         "2020",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2019.2948335",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Mar 5 13:54:11 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Adders; arithmetic units; Computer architecture;
                 Delays; Logic gates; modular arithmetic; Power demand;
                 Program processors; Proposals; Residue number systems;
                 reverse conversion",
}

@InProceedings{Stine:2020:AIV,
  author =       "James E. Stine and Milo D. Ercegovac and Jean-Michel
                 Muller",
  editor =       "Michael B. Matthews",
  booktitle =    "{2020 54th Asilomar Conference on Signals, Systems,
                 and Computers. November 1--5, 2020. Pacific Grove,
                 California}",
  title =        "An Architecture for Improving Variable Radix Real and
                 Complex Division Using Recurrence Division",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "529--533",
  year =         "2020",
  DOI =          "https://doi.org/10.1109/IEEECONF51394.2020.9443498",
  ISBN =         "0-7381-3126-1",
  ISBN-13 =      "978-0-7381-3126-9",
  bibdate =      "Fri Sep 29 11:01:45 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sun:2020:ULP,
  author =       "Xiao Sun and Naigang Wang and Chia-Yu Chen and Jiamin
                 Ni and Ankur Agrawal and Xiaodong Cui and Swagath
                 Venkataramani and Kaoutar El Maghraoui and
                 Vijayalakshmi (Viji) Srinivasan and Kailash
                 Gopalakrishnan",
  editor =       "H. Larochelle and M. Ranzato and R. Hadsell and M. F.
                 Balcan and H. Lin",
  booktitle =    "Advances in Neural Information Processing Systems
                 ({NeurIPS 2020})",
  title =        "Ultra-low precision 4-bit training of deep neural
                 networks",
  publisher =    "Curran Associates, Inc.",
  address =      "Red Hook, NY, USA",
  pages =        "1796--1807",
  year =         "2020",
  ISBN =         "1-71382-954-1",
  ISBN-13 =      "978-1-71382-954-6",
  LCCN =         "????",
  bibdate =      "Wed Aug 07 16:44:01 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://proceedings.neurips.cc/paper_files/paper/2020/file/13b919438259814cd5be8cb45877d577-Paper.pdf",
  abstract =     "In this paper, we propose a number of novel techniques
                 and numerical representation formats that enable, for
                 the very first time, the precision of training systems
                 to be aggressively scaled from 8-bits to 4-bits. To
                 enable this advance, we explore a novel adaptive
                 Gradient Scaling technique (Gradscale) that addresses
                 the challenges of insufficient range and resolution in
                 quantized gradients as well as explores the impact of
                 quantization errors observed during model training. We
                 theoretically analyze the role of bias in gradient
                 quantization and propose solutions that mitigate the
                 impact of this bias on model convergence. Finally, we
                 examine our techniques on a spectrum of deep learning
                 models in computer vision, speech, and NLP. In
                 combination with previously proposed solutions for
                 4-bit quantization of weight and activation tensors,
                 4-bit training shows a non-significant loss in accuracy
                 across application domains while enabling significant
                 hardware acceleration (> 7X over state-of-the-art FP16
                 systems).",
  acknowledgement = ack-nhfb,
}

@InProceedings{Ternovoy:2020:CAF,
  author =       "E. Ternovoy and Mikhail G. Popov and Dmitrii V. Kaleev
                 and Yurii V. Savchenko and Alexey L. Pereverzev",
  editor =       "{IEEE}",
  booktitle =    "{2020 IEEE Conference of Russian Young Researchers in
                 Electrical and Electronic Engineering (EIConRus)}",
  title =        "Comparative Analysis of Floating-Point Accuracy of
                 {IEEE 754} and Posit Standards",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1883--186",
  year =         "2020",
  DOI =          "https://doi.org/10.1109/EIConRus49466.2020.9039521",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Misc{ThoughtWorks:2020:PER,
  author =       "{ThoughtWorks}",
  title =        "{Posit Enhanced Rocket Chip (PERC)}",
  howpublished = "Web software.",
  year =         "2020",
  bibdate =      "Sat Dec 16 15:25:19 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.thoughtworks.com/engineering-research/perc",
  acknowledgement = ack-nhfb,
}

@Misc{Turley:2020:WBA,
  author =       "Jim Turley",
  title =        "What Is bfloat16, Anyway? {New} Floating-Point Format
                 is Suddenly Popular for Machine Learning",
  howpublished = "Electronic Engineering journal Web site",
  day =          "23",
  month =        mar,
  year =         "2020",
  bibdate =      "Fri Apr 03 09:07:54 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.eejournal.com/article/what-is-bfloat16-anyway/",
  acknowledgement = ack-nhfb,
}

@Article{Uguen:2020:ASA,
  author =       "Yohann Uguen and Florent {De Dinechin} and Victor
                 Lezaud and Steven Derrien",
  title =        "Application-Specific Arithmetic in High-Level
                 Synthesis Tools",
  journal =      j-TACO,
  volume =       "17",
  number =       "1",
  pages =        "5:1--5:23",
  month =        mar,
  year =         "2020",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3377403",
  ISSN =         "1544-3566 (print), 1544-3973 (electronic)",
  ISSN-L =       "1544-3566",
  bibdate =      "Tue Mar 10 08:30:23 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/taco.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3377403",
  abstract =     "This work studies hardware-specific optimization
                 opportunities currently unexploited by high-level
                 synthesis compilers. Some of these optimizations are
                 specializations of floating-point operations that
                 respect the usual semantics of the input program
                 without changing the numerical result. Some other
                 optimizations, locally triggered by the programmer
                 thanks to a pragma, assume a different semantics, where
                 floating-point code is interpreted as the specification
                 of computation with real numbers. The compiler is then
                 in charge to ensure an application-level accuracy
                 constraint expressed in the pragma and has the freedom
                 to use non-standard arithmetic hardware when more
                 efficient. These two classes of optimizations are
                 prototyped in the GeCoS source-to-source compiler and
                 evaluated on the Polybench and EEMBC benchmark suites.
                 Latency is reduced by up to 93\%, and resource usage is
                 reduced by up to 58\%.",
  acknowledgement = ack-nhfb,
  articleno =    "5",
  fjournal =     "ACM Transactions on Architecture and Code Optimization
                 (TACO)",
  journal-URL =  "https://dl.acm.org/loi/taco",
}

@Article{Valueva:2020:ARN,
  author =       "M. V. Valueva and N. N. Nagornov and P. A. Lyakhov and
                 G. V. Valuev and N. I. Chervyakov",
  title =        "Application of the residue number system to reduce
                 hardware costs of the convolutional neural network
                 implementation",
  journal =      j-MATH-COMPUT-SIMUL,
  volume =       "177",
  pages =        "232--243",
  month =        nov,
  year =         "2020",
  CODEN =        "MCSIDR",
  DOI =          "https://doi.org/10.1016/j.matcom.2020.04.031",
  ISSN =         "0378-4754 (print), 1872-7166 (electronic)",
  ISSN-L =       "0378-4754",
  bibdate =      "Fri Aug 15 14:51:15 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomputsimul2020.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/S0378475420301580",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput. Simul.",
  fjournal =     "Mathematics and Computers in Simulation",
  journal-URL =  "https://www.sciencedirect.com/science/journal/03784754",
}

@Article{Volkova:2020:AAR,
  author =       "A. Volkova and T. Hilaire and C. Lauter",
  title =        "Arithmetic Approaches for Rigorous Design of Reliable
                 Fixed-Point {LTI} Filters",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "69",
  number =       "4",
  pages =        "489--504",
  month =        apr,
  year =         "2020",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2019.2950658",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Mar 12 16:58:27 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "digital filters; eigendecomposition; Error analysis;
                 fixed-point arithmetic; Floating-point arithmetic;
                 Gershgorin circles; Heuristic algorithms; interval
                 arithmetic; Linear matrix inequalities; Linear systems;
                 Mathematical model; multiple precision; Reliability;
                 reliable computations; Signal processing algorithms;
                 table maker's dilemma",
}

@Article{Wang:2020:GCB,
  author =       "Yuxuan Wang and Yuanyong Luo and Zhongfeng Wang and
                 Qinghong Shen and Hongbing Pan",
  title =        "{GH} {CORDIC}-based Architecture for Computing
                 {$N$}-th Root of Single-Precision Floating-Point
                 Number",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "28",
  number =       "4",
  pages =        "864--875",
  year =         "2020",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/TVLSI.2019.2959847",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
  keywords =     "Binary floating point (BFP); Computer architecture;
                 COordinate Rotation Digital Computer (CORDIC); Field
                 programmable gate arrays; Graphics; Hardware; high
                 speed; Mathematical model; Nth root; Standards; Very
                 large scale integration",
}

@Article{Ward-Foxton:2020:AIG,
  author =       "Sally Ward-Foxton",
  title =        "Artificial Intelligence Gets Its Own System of
                 Numbers",
  journal =      "EE Times",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "14",
  month =        feb,
  year =         "2020",
  bibdate =      "Wed May 19 11:58:46 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.eetimes.com/artificial-intelligence-gets-its-own-system-of-numbers/",
  acknowledgement = ack-nhfb,
  keywords =     "BF16 (1 + 8 + 7); FP16 (1 + 5 + 10); Nervana
                 Flexpoint",
}

@Article{Xiao:2020:PAH,
  author =       "Feibao Xiao and Feng Liang and Bin Wu and Junzhe Liang
                 and Shuting Cheng and Guohe Zhang",
  title =        "Posit Arithmetic Hardware Implementations with The
                 Minimum Cost Divider and Square Root",
  journal =      j-ELECTRONICS,
  volume =       "9",
  number =       "10",
  pages =        "1622:1--1622:16",
  month =        oct,
  year =         "2020",
  DOI =          "https://doi.org/10.3390/electronics9101622",
  ISSN =         "2079-9292",
  ISSN-L =       "2079-9292",
  bibdate =      "Fri Dec 15 07:25:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics",
  journal-URL =  "https://www.mdpi.com/journal/electronics",
}

@InProceedings{Yin-Di:2020:HMH,
  author =       "Zhang Yin-Di and Liu Ming and Wang Ming-Jiang",
  booktitle =    "{2020 IEEE 5th International Conference on Signal and
                 Image Processing (ICSIP)}",
  title =        "A Hardware Modeling of High Precision Floating Point
                 Arcsine\slash Arccosine Function Based on {CORDIC}
                 Algorithm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1040--1044",
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ICSIP49896.2020.9339409",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "arcsine/arccosine; Clocks; CORDIC; floating point;
                 four-step rotation prediction iteration; Hardware;
                 Hardware design languages; Image processing; Indexes;
                 Prediction algorithms; Standards",
}

@Article{Yun:2020:LEP,
  author =       "Juwon Yun and Jinyoung Lee and Woo-Nam Chung and
                 Cheong Ghil Kim and Woo-Chan Park",
  title =        "A Latency-Effective Pipelined Divider for
                 Double-Precision Floating-Point Numbers",
  journal =      j-IEEE-ACCESS,
  volume =       "8",
  pages =        "165740--165747",
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ACCESS.2020.3022657",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Tue Sep 30 17:30:28 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "Computer arithmetic; division; Error analysis;
                 floating-point; Hardware; lookup table; Pipelines;
                 Signal processing algorithms; Table lookup; Taylor
                 series",
}

@InProceedings{Zaruba:2020:CRV,
  author =       "Florian Zaruba and Fabian Schuiki and Luca Benini",
  editor =       "{IEEE}",
  booktitle =    "{2020 IEEE Hot Chips 32 Symposium (HCS)}",
  title =        "A 4096-core {RISC-V} Chiplet Architecture for
                 Ultra-efficient Floating-point Computing",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--24",
  year =         "2020",
  DOI =          "https://doi.org/10.1109/HCS49909.2020.9220474",
  bibdate =      "Sat Dec 16 15:51:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  remark =       "This article consists only of a collection of slides
                 from the author's conference presentation",
}

@Article{Zhang:2020:DPE,
  author =       "Hao Zhang and Seok-Bum Ko",
  title =        "Design of Power Efficient Posit Multiplier",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
  volume =       "67",
  number =       "5",
  pages =        "861--865",
  year =         "2020",
  DOI =          "https://doi.org/10.1109/TCSII.2020.2980531",
  ISSN =         "1549-7747 (print), 1558-3791 (electronic)",
  ISSN-L =       "1549-7747",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems II: Express
                 Briefs",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
}

@Article{Zhang:2020:NAE,
  author =       "N. Zhang and Q. Qin and H. Yuan and C. Zhou and S. Yin
                 and S. Wei and L. Liu",
  title =        "{NTTU}: An Area-Efficient Low-Power {NTT}-Uncoupled
                 Architecture for {NTT}-Based Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "69",
  number =       "4",
  pages =        "520--533",
  month =        apr,
  year =         "2020",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2019.2958334",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Mar 12 16:58:27 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Clocks; Cloud computing; Complexity theory; Computer
                 architecture; Encryption; Fully homomorphic encryption;
                 large integer multiplication; number theoretical
                 conversion; polynomial multiplication; Random access
                 memory; Transforms",
}

@Article{Zhang:2020:NFM,
  author =       "H. Zhang and D. Chen and S. Ko",
  title =        "New Flexible Multiple-Precision Multiply-Accumulate
                 Unit for Deep Neural Network Training and Inference",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "69",
  number =       "1",
  pages =        "26--38",
  month =        jan,
  year =         "2020",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2019.2936192",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jan 9 07:48:57 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Adders; computer arithmetic; Deep learning; deep
                 neural network computing; flexible precision
                 arithmetic; Hardware; multiple-precision arithmetic;
                 Multiply-accumulate unit; Neural networks; Pipelines;
                 Standards; Training",
}

@Article{Zhang:2020:SAA,
  author =       "Longlong Zhang and Yuanxi Peng and Ahui Huang and Xiao
                 Hu",
  title =        "A Scalable Architecture for Accelerating
                 Multi-Operation and Continuous Floating-Point Matrix
                 Computing on {FPGAs}",
  journal =      j-IEEE-ACCESS,
  volume =       "8",
  pages =        "92469--92478",
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ACCESS.2020.2994657",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Tue Sep 30 17:30:28 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "Acceleration; accelerator; Arrays; Data transfer;
                 Field programmable gate arrays; floating-point; FPGAs;
                 Matrix computing; Registers; scalability",
}

@TechReport{Zimmermann:2020:AMFa,
  author =       "Paul Zimmermann",
  title =        "Accuracy of Mathematical Functions in Single
                 Precision",
  institution =  "????",
  pages =        "2",
  day =          "3",
  month =        feb,
  year =         "2020",
  bibdate =      "Mon Aug 17 15:41:19 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Previous versions dated 4 February 2020, 10 May 2020,
                 26 May 2020, 7 August 2020, 25 August 2020, 28 August
                 2020, 15 September 2020, 17 September 2020.",
  URL =          "https://members.loria.fr/PZimmermann/papers/accuracy.pdf",
  acknowledgement = ack-nhfb,
  remark =       "Tabular comparison of GNU and Intel -lm libraries for
                 correct rounding, versus results from MPFR.",
}

@TechReport{Zimmermann:2020:AMFb,
  author =       "Paul Zimmermann",
  title =        "Accuracy of Mathematical Functions in Single, Double,
                 and Quadruple Precision",
  institution =  "????",
  pages =        "14",
  day =          "4",
  month =        dec,
  year =         "2020",
  bibdate =      "Fri Dec 04 11:52:43 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Revised February 4, May 10, May 26 and August 7
                 [2020].",
  URL =          "https://members.loria.fr/PZimmermann/papers/accuracy.pdf",
  acknowledgement = ack-nhfb,
  remark =       "Tabular comparison of AMD, GNU, Intel, RedHat,
                 OpenLibm, and Musl -lm libraries for correct rounding,
                 versus results from MPFR.",
}

@Article{Zou:2020:DFP,
  author =       "Daming Zou and Muhan Zeng and Yingfei Xiong and
                 Zhoulai Fu and Lu Zhang and Zhendong Su",
  title =        "Detecting floating-point errors via atomic
                 conditions",
  journal =      j-PACMPL,
  volume =       "4",
  number =       "POPL",
  pages =        "60:1--60:27",
  month =        jan,
  year =         "2020",
  DOI =          "https://doi.org/10.1145/3371128",
  ISSN =         "2475-1421",
  bibdate =      "Fri Aug 7 18:46:52 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/pacmpl.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3371128",
  abstract =     "This paper tackles the important, difficult problem of
                 detecting program inputs that trigger large
                 floating-point errors in numerical code. It introduces
                 a novel, principled {\em dynamic analysis\/} that
                 leverages the mathematically rigorously analyzed {\em
                 condition numbers\/} for atomic numerical operations,
                 which we call {\em atomic conditions}, to effectively
                 guide the search for large floating-point errors.
                 Compared with existing approaches, our work based on
                 atomic conditions has several distinctive benefits: (1)
                 it does not rely on high-precision implementations to
                 act as approximate oracles, which are difficult to
                 obtain in general and computationally costly; and (2)
                 atomic conditions provide accurate, modular search
                 guidance. These benefits in combination lead to a
                 highly effective approach that detects more significant
                 errors in real-world code (e.g., widely-used numerical
                 library functions) and achieves several orders of
                 speedups over the state-of-the-art, thus making error
                 analysis significantly more practical. We expect the
                 methodology and principles behind our approach to
                 benefit other floating-point program analysis tasks
                 such as debugging, repair and synthesis. To facilitate
                 the reproduction of our work, we have made our
                 implementation, evaluation data and results publicly
                 available on GitHub at
                 \url{https://github.com/FP-Analysis/atomic-condition}",
  acknowledgement = ack-nhfb,
  articleno =    "60",
  fjournal =     "Proceedings of the ACM on Programming Languages",
  journal-URL =  "https://pacmpl.acm.org/",
}

@InProceedings{Agrawal:2021:CAC,
  author =       "Ankur Agrawal and Sae Kyu Lee and Joel Silberman and
                 Matthew Ziegler and Mingu Kang and Swagath
                 Venkataramani and Nianzheng Cao and Bruce Fleischer and
                 Michael Guillorn and Matthew Cohen and Silvia Mueller
                 and Jinwook Oh and Martin Lutz and Jinwook Jung and
                 Siyu Koswatta and Ching Zhou and Vidhi Zalani and James
                 Bonanno and Robert Casatuta and Chia-Yu Chen and
                 Jungwook Choi and Howard Haynie and Alyssa Herbert and
                 Radhika Jain and Monodeep Kar and Kyu-Hyoun Kim and
                 Yulong Li and Zhibin Ren and Scot Rider and Marcel
                 Schaal and Kerstin Schelm and Michael Scheuermann and
                 Xiao Sun and Hung Tran and Naigang Wang and Wei Wang
                 and Xin Zhang and Vinay Shah and Brian Curran and
                 Vijayalakshmi Srinivasan and Pong-Fei Lu and Sunil
                 Shukla and Leland Chang and Kailash Gopalakrishnan",
  booktitle =    "{2021 IEEE International Solid-State Circuits
                 Conference (ISSCC)}",
  title =        "9.1 A 7nm 4-Core {AI} Chip with {25.6TFLOPS} Hybrid
                 {FP8} Training, {102.4TOPS} {INT4} Inference and
                 Workload-Aware Throttling",
  volume =       "64",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "144--146",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ISSCC42613.2021.9365791",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "AI accelerators; Inference algorithms; Integrated
                 circuit modeling; Optimization; Power system
                 management; Solid state circuits; Training",
}

@Article{Ahn:2021:KSK,
  author =       "Dong H. Ahn and Allison H. Baker and Michael Bentley
                 and Ian Briggs and Ganesh Gopalakrishnan and Dorit M.
                 Hammerling and Ignacio Laguna and Gregory L. Lee and
                 Daniel J. Milroy and Mariana Vertenstein",
  title =        "Keeping science on keel when software moves",
  journal =      j-CACM,
  volume =       "64",
  number =       "2",
  pages =        "66--74",
  month =        feb,
  year =         "2021",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/3382037",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Tue Jan 26 14:34:25 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3382037",
  abstract =     "An approach to reproducibility problems related to
                 porting software across machines and compilers.",
  acknowledgement = ack-nhfb,
  ajournal =     "Commun. ACM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}

@InProceedings{Alouani:2021:IIR,
  author =       "Ihsen Alouani and Anouar {Ben Khalifa} and Farhad
                 Merchant and Rainer Leupers",
  editor =       "{IEEE}",
  booktitle =    "{2021 34th International Conference on VLSI Design and
                 2021 20th International Conference on Embedded Systems
                 (VLSID)}",
  title =        "An Investigation on Inherent Robustness of Posit Data
                 Representation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "276--281",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/VLSID51830.2021.00052",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Andrysco:2021:SFP,
  author =       "Marc Andrysco and David Kohlbrenner and Keaton Mowery
                 and Ranjit Jhala and Sorin Lerner and Hovav Shacham",
  title =        "On Subnormal Floating Point and Abnormal Timing",
  type =         "Report",
  institution =  "Department of Computer Science and Engineering
                 University of California, San Diego",
  address =      "La Jolla, California, USA",
  pages =        "17",
  day =          "2",
  month =        jan,
  year =         "2021",
  bibdate =      "Fri Sep 06 10:04:19 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We identify a timing channel in the floating point
                 instructions of modern x86 processors: the running time
                 of floating point addition and multiplication
                 instructions can vary by two orders of magnitude
                 depending on their operands. We develop a benchmark
                 measuring the timing variability of floating point
                 operations and report on its results. We use floating
                 point data timing variability to demonstrate practical
                 attacks on the security of the Firefox browser
                 (versions 23 through 27) and the Fuzz differentially
                 private database. Finally, we initiate the study of
                 mitigations to floating point data timing channels with
                 libfixedtimefixedpoint, a new fixed-point,
                 constant-time math library.\par

                 Modern floating point standards and implementations are
                 sophisticated, complex, and subtle, a fact that has not
                 been sufficiently recognized by the security community.
                 More work is needed to assess the implications of the
                 use of floating point instructions in security-relevant
                 software.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Anonymous:2021:AI,
  author =       "Anonymous",
  title =        "Author Index",
  crossref =     "IEEE:2021:ISC",
  pages =        "141--141",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00037",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@InProceedings{Anonymous:2021:CN,
  author =       "Anonymous",
  title =        "[{Copyright} notice]",
  crossref =     "IEEE:2021:ISC",
  pages =        "1--1",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00003",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@InProceedings{Anonymous:2021:FC,
  author =       "Anonymous",
  title =        "[{Front} cover]",
  crossref =     "IEEE:2021:ISC",
  pages =        "1--1",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00002",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@InProceedings{Anonymous:2021:IPA,
  author =       "Anonymous",
  title =        "Industry Panel {ARITH 2021}: Processors for the
                 Computing of the 2020s",
  crossref =     "IEEE:2021:ISC",
  pages =        "xv--xv",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00010",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@InProceedings{Anonymous:2021:PCA,
  author =       "Anonymous",
  title =        "Program Committee {ARITH 2021}",
  crossref =     "IEEE:2021:ISC",
  pages =        "xii--xii",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00007",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@InProceedings{Anonymous:2021:SA,
  author =       "Anonymous",
  title =        "Sponsors {ARITH 2021}",
  crossref =     "IEEE:2021:ISC",
  pages =        "xviii--xviii",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00012",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@InProceedings{Anonymous:2021:SCA,
  author =       "Anonymous",
  title =        "Steering Committee {ARITH 2021}",
  crossref =     "IEEE:2021:ISC",
  pages =        "xiii--xiii",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00008",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@InProceedings{Anonymous:2021:TC,
  author =       "Anonymous",
  title =        "Table of Contents",
  crossref =     "IEEE:2021:ISC",
  pages =        "v--viii",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00004",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@InProceedings{Anonymous:2021:TP,
  author =       "Anonymous",
  title =        "[{Title} page]",
  crossref =     "IEEE:2021:ISC",
  pages =        "1--1",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00001",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@InProceedings{Ashmawy:2021:FHI,
  author =       "Doaa Ashmawy and Arash Reyhani-Masoleh",
  title =        "A Faster Hardware Implementation of the {AES}
                 {S}-box",
  crossref =     "IEEE:2021:ISC",
  pages =        "123--130",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00034",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@Article{Bagnara:2021:PAV,
  author =       "Roberto Bagnara and Michele Chiari and Roberta Gori
                 and Abramo Bagnara",
  title =        "A Practical Approach to Verification of Floating-Point
                 {C\slash C++} Programs with {\tt math.h}\slash {\tt
                 cmath} Functions",
  journal =      j-TOSEM,
  volume =       "30",
  number =       "1",
  pages =        "9:1--9:53",
  month =        jan,
  year =         "2021",
  CODEN =        "ATSMER",
  DOI =          "https://doi.org/10.1145/3410875",
  ISSN =         "1049-331X (print), 1557-7392 (electronic)",
  ISSN-L =       "1049-331X",
  bibdate =      "Fri Jan 22 07:02:14 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tosem.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3410875",
  abstract =     "Verification of C/C++ programs has seen considerable
                 progress in several areas, but not for programs that
                 use these languages' mathematical libraries. The reason
                 is that all libraries in widespread use come with no
                 guarantees about the computed results. This would seem
                 to prevent any attempt at formal verification of
                 programs that use them: without a specification for the
                 functions, no conclusion can be drawn statically about
                 the behavior of the program. We propose an alternative
                 to surrender. We introduce a pragmatic approach that
                 leverages the fact that most {\tt math.h}\slash {\tt
                 cmath} functions are almost piecewise monotonic: as we
                 discovered through exhaustive testing, they may have
                 glitches, often of very small size and in small
                 numbers. We develop interval refinement techniques for
                 such functions based on a modified dichotomic search,
                 which enable verification via symbolic execution based
                 model checking, abstract interpretation, and test data
                 generation. To the best of our knowledge, our
                 refinement algorithms are the first in the literature
                 to be able to handle non-correctly rounded function
                 implementations, enabling verification in the presence
                 of the most common implementations. We experimentally
                 evaluate our approach on real-world code, showing its
                 ability to detect or rule out anomalous behaviors.",
  acknowledgement = ack-nhfb,
  articleno =    "9",
  fjournal =     "ACM Transactions on Software Engineering and
                 Methodology",
  journal-URL =  "https://dl.acm.org/loi/tosem",
}

@Misc{Bailey:2021:PMN,
  author =       "David H. Bailey",
  title =        "\pkg{MPFUN2020}: A new thread-safe arbitrary precision
                 package",
  howpublished = "Web document",
  pages =        "54",
  day =          "18",
  month =        may,
  year =         "2021",
  bibdate =      "Mon Dec 05 07:32:16 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.davidhbailey.com/dhbpapers/mpfun2020.pdf",
  abstract =     "Numerous research studies have arisen, particularly in
                 mathematical physics and experimental mathematics, that
                 require extremely high numeric precision. Such
                 precision greatly magnifies computer run times, so
                 software packages to support high-precision computing
                 must be designed for thread-based parallel
                 processing.

                 This paper describes a new arbitrary precision software
                 package (``MPFUN2020'') that features several
                 significant improvements over an earlier package. It
                 comes in two versions: a self-contained all-Fortran
                 version, and a version based on the MPFR package, which
                 is even faster. Both versions feature: (a) a completely
                 thread-safe design, so user codes can be converted for
                 parallel execution at the application level; (b) a
                 full-featured high-level Fortran interface, so that
                 most applications can be converted to multiprecision
                 with relatively minor changes to source code; (c) full
                 support for both real and complex datatypes; (d) a wide
                 variety of transcendental functions and special
                 functions; (e) run-time checking and other facilities
                 to overcome problems with converting double precision
                 constants and data; (f) a medium precision datatype,
                 which improves performance and reduces memory cost on
                 large variable precision applications; and (g)
                 interoperability --- with a simple restriction,
                 application codes written for one version can be run
                 with the other without change.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bajard:2021:GRN,
  author =       "Jean-Claude Bajard and Kazuhide Fukushima and Shinsaku
                 Kiyomoto and Thomas Plantard and Arnaud Sipasseuth and
                 Willy Susilo",
  title =        "Generating Residue Number System Bases",
  crossref =     "IEEE:2021:ISC",
  pages =        "86--93",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00027",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@InProceedings{Bertaccini:2021:TFL,
  author =       "Luca Bertaccini and Matteo Perotti and Stefan Mach and
                 Pasquale Davide Schiavone and Florian Zaruba and Luca
                 Benini",
  editor =       "{IEEE}",
  booktitle =    "{2021 IEEE International Symposium on Circuits and
                 Systems (ISCAS)}",
  title =        "{Tiny-FPU}: Low-Cost Floating-Point Support for Small
                 {RISC-V MCU} Cores",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--5",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ISCAS51556.2021.9401149",
  bibdate =      "Sat Dec 16 15:51:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Bigou:2021:ERA,
  author =       "Karim Bigou and Mojtaba Bisheh Niasar and Lu{\'\i}s
                 Fiolhais and Rogerio Paludo and Hwajeong Seo",
  title =        "External Reviewers {ARITH 2021}",
  crossref =     "IEEE:2021:ISC",
  pages =        "xiv--xiv",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00009",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@InProceedings{Bisheh-Niasar:2021:HSN,
  author =       "Mojtaba Bisheh-Niasar and Reza Azarderakhsh and Mehran
                 Mozaffari-Kermani",
  title =        "High-Speed {NTT}-based Polynomial Multiplication
                 Accelerator for Post-Quantum Cryptography",
  crossref =     "IEEE:2021:ISC",
  pages =        "94--101",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00028",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@Article{Boldo:2021:ERN,
  author =       "Sylvie Boldo and Christoph Quirin Lauter and
                 Jean-Michel Muller",
  title =        "Emulating Round-to-Nearest-Ties-to-Zero ``augmented''
                 Floating-Point Operations Using
                 Round-to-Nearest-Ties-to-Even Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "70",
  number =       "7",
  pages =        "1046--1058",
  month =        jul,
  year =         "2021",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2020.3002702",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jun 10 15:51:57 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Boldo:2021:SFT,
  author =       "Sylvie Boldo and Guillaume Melquiond",
  title =        "Some Formal Tools for Computer Arithmetic: {Flocq} and
                 {Gappa}",
  crossref =     "IEEE:2021:ISC",
  pages =        "111--114",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00031",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@Article{Borges:2021:AIA,
  author =       "Carlos F. Borges",
  title =        "{Algorithm 1014}: an Improved Algorithm for {\tt
                 hypot(x,y)}",
  journal =      j-TOMS,
  volume =       "47",
  number =       "1",
  pages =        "9:1--9:12",
  month =        jan,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3428446",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jan 7 10:31:04 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/julia.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3428446",
  abstract =     "We develop fast and accurate algorithms for evaluating
                 $ \sqrt {x^2 + y^2} $ for two floating-point numbers
                 $x$ and $y$. Library functions that perform this
                 computation are generally named {\tt hypot(x,y)}. We
                 compare five approaches that we will develop in this
                 article to the current resident library function that
                 is delivered with Julia 1.1 and to the code that has
                 been distributed with the C math library for decades.
                 We will investigate the accuracy of our algorithms by
                 simulation.",
  acknowledgement = ack-nhfb,
  articleno =    "9",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Borges:2021:CRN,
  author =       "Carlos F. Borges",
  title =        "A Correctly Rounded {Newton} Step for the Reciprocal
                 Square Root",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--8",
  day =          "28",
  month =        dec,
  year =         "2021",
  bibdate =      "Fri Sep 22 16:08:53 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/abs/2112.14321",
  abstract =     "The reciprocal square root is an important computation
                 for which many sophisticated algorithms exist (see for
                 example \ldots{} and the references therein). A common
                 theme is the use of Newton's method to refine the
                 estimates. In this paper we develop a correctly rounded
                 Newton step that can be used to improve the accuracy of
                 a naive calculation (using methods similar to those
                 developed in \ldots{}) The approach relies on the use
                 of the fused multiply-add (FMA) which is widely
                 available in hardware on a variety of modern computer
                 architectures. We then introduce the notion of {\em
                 weak rounding} and prove that our proposed algorithm
                 meets this standard. We then show how to leverage the
                 exact Newton step to get a Halley's method compensation
                 which requires one additional FMA and one additional
                 multiplication. This method appears to give correctly
                 rounded results experimentally and we show that it can
                 be combined with a square root free method for
                 estimating the reciprocal square root to get a method
                 that is both very fast (in computing environments with
                 a slow square root) and, experimentally, highly
                 accurate.",
  acknowledgement = ack-nhfb,
}

@Article{Borges:2021:FCA,
  author =       "Carlos F. Borges",
  title =        "Fast compensated algorithms for the reciprocal square
                 root, the reciprocal hypotenuse, and {Givens}
                 rotations",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--11",
  day =          "23",
  month =        feb,
  year =         "2021",
  bibdate =      "Fri Sep 22 16:05:47 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/abs/2103.08694",
  abstract =     "The reciprocal square root is an important computation
                 for which many very sophisticated algorithms exist (see
                 for example \ldots{} and the references
                 therein). In this paper we develop a simple
                 differential compensation (much like those developed in
                 \ldots{}) that can be used to improve the accuracy
                 of a naive calculation. The approach relies on the use
                 of the fused multiply-add (FMA) which is widely
                 available in hardware on a variety of modern computer
                 architectures. We then demonstrate how to combine this
                 approach with a somewhat inaccurate but fast square
                 root free method for estimating the reciprocal square
                 root to get a method that is both fast (in computing
                 environments with a slow square root) and,
                 experimentally, highly accurate. Finally, we show how
                 this same approach can be extended to the reciprocal
                 hypotenuse calculation and, most importantly, to the
                 construction of Givens rotations.",
  acknowledgement = ack-nhfb,
}

@Article{Bos:2021:MPM,
  author =       "Joppe W. Bos and Kristin E. Lauter",
  title =        "In Memoriam: {Peter L. Montgomery} (1947--2020)",
  journal =      j-NAMS,
  volume =       "68",
  number =       "4",
  pages =        "538--545",
  month =        apr,
  year =         "2021",
  CODEN =        "AMNOAN",
  DOI =          "https://doi.org/10.1090/noti2258",
  ISSN =         "0002-9920 (print), 1088-9477 (electronic)",
  ISSN-L =       "0002-9920",
  MRclass =      "01A70 (11-03 11Yxx 94A60)",
  MRnumber =     "4228130",
  bibdate =      "Sat May 29 18:37:36 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/nams2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Notices Amer. Math. Soc.",
  fjournal =     "Notices of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/notices/",
}

@InProceedings{Bottcher:2021:ROT,
  author =       "Andreas B{\"o}ttcher and Martin Kumm and Florent de
                 Dinechin",
  title =        "Resource Optimal Truncated Multipliers for {FPGAs}",
  crossref =     "IEEE:2021:ISC",
  pages =        "102--109",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00029",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@Article{Brun:2021:SEBa,
  author =       "Emeric Brun and David Defour and Pablo {de Oliveira
                 Castro} and Matei I{\c{s}}toan and Davide Mancusi and
                 Eric Petit and Alan Vaquet",
  title =        "A Study of the Effects and Benefits of
                 Custom-Precision Mathematical Libraries for {HPC}
                 Codes",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "9",
  number =       "3",
  pages =        "1467--1478",
  month =        jul # "\slash " # sep,
  year =         "2021",
  DOI =          "https://doi.org/10.1109/TETC.2021.3070422",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  note =         "See \cite{Brun:2021:SEBb}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
  keywords =     "ARITH 2021; ARITH-28",
}

@InProceedings{Brun:2021:SEBb,
  author =       "Emeric Brun and David Defour and Pablo {De Oliveira
                 Castro} and Matei Istoan and Davide Mancusi and Eric
                 Petit and Alan Vaquet",
  title =        "A Study of the Effects and Benefits of
                 Custom-Precision Mathematical Libraries for {HPC}
                 Codes",
  crossref =     "IEEE:2021:ISC",
  pages =        "62--62",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00022",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Brun:2021:SEBa}.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
  remark =       "Published in IEEE Transactions on Emerging Topics in
                 Computing, Volume: 9, Issue: 3, July--September 2021,
                 and orally presented at ARITH 2021.",
}

@InProceedings{Brunie:2021:MAE,
  author =       "Nicolas Brunie",
  title =        "Manifest for an Approximation Exchange Format",
  crossref =     "IEEE:2021:ISC",
  pages =        "63--68",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00023",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "We introduce AXF, Approximation eXchange Format, a
                 file format dedicated to the description of basic
                 constructs for function approximation, such as
                 numerical description of piecewise polynomial
                 approximations. AXF is designed as a numerical
                 intermediate representation between approximation
                 generation and approximation implementation tools.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@InProceedings{Chen:2021:QIL,
  author =       "Lin Chen and Kang He and Hao Jiang and Roberto Barrio
                 and Jie Liu and Tiejun Li",
  booktitle =    "{2021 IEEE Intl Conf on Parallel \& Distributed
                 Processing with Applications, Big Data \& Cloud
                 Computing, Sustainable Computing \& Communications,
                 Social Computing \& Networking
                 (ISPA/BDCloud/SocialCom/SustainCom)}",
  title =        "Quantization improvements for {$ L U $} Decomposition
                 to Solve Linear Equations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1075--1082",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ISPA-BDCloud-SocialCom-SustainCom52081.2021.00149",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benchmark testing; Deep learning; GMRES-IR; Gold; LU
                 Factorization; Matrix Multiplication; Mixed-precision;
                 Quantization; Quantization (signal)",
}

@Article{Ciocirlan:2021:AEPa,
  author =       "Stefan Dan Ciocirlan and Dumitrel Loghin and Lavanya
                 Ramapantulu and Nicolae Tapus and Yong Meng Teo",
  title =        "The Accuracy and Efficiency of Posit Arithmetic",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  day =          "16",
  month =        sep,
  year =         "2021",
  bibdate =      "Sat Dec 16 15:13:00 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  abstract =     "Motivated by the increasing interest in the posit
                 numeric format, in this paper we evaluate the accuracy
                 and efficiency of posit arithmetic in contrast to the
                 traditional IEEE 754 32-bit floating-point (FP32)
                 arithmetic. We first design and implement a Posit
                 Arithmetic Unit (PAU), called POSAR, with flexible
                 bit-sized arithmetic suitable for applications that can
                 trade accuracy for savings in chip area. Next, we
                 analyze the accuracy and efficiency of POSAR with a
                 series of benchmarks including mathematical
                 computations, ML kernels, NAS Parallel Benchmarks
                 (NPB), and Cifar-10 CNN. This analysis is done on our
                 implementation of POSAR integrated into a RISC-V Rocket
                 Chip core in comparison with the IEEE 754-based
                 Floating Point Unit (FPU) of Rocket Chip. Our analysis
                 shows that POSAR can outperform the FPU, but the
                 results are not spectacular. For NPB, 32-bit posit
                 achieves better accuracy than FP32 and improves the
                 execution by up to 2\%. However, POSAR with 32-bit
                 posit needs 30\% more FPGA resources compared to the
                 FPU. For classic ML algorithms, we find that 8-bit
                 posits are not suitable to replace FP32 because they
                 exhibit low accuracy leading to wrong results. Instead,
                 16-bit posit offers the best option in terms of
                 accuracy and efficiency. For example, 16-bit posit
                 achieves the same Top-1 accuracy as FP32 on a Cifar-10
                 CNN with a speedup of 18\%.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "2109.08225",
  primaryclass = "cs.AR",
}

@InProceedings{Ciocirlan:2021:AEPb,
  author =       "Stefan Dan Ciocirlan and Dumitrel Loghin and Lavanya
                 Ramapantulu and Nicolae {\c{T}}{\u{a}}pu{\c{s}} and
                 Yong Meng Teo",
  editor =       "{IEEE}",
  booktitle =    "{2021 IEEE 39th International Conference on Computer
                 Design (ICCD)}",
  title =        "The Accuracy and Efficiency of Posit Arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "83--87",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ICCD53106.2021.00024",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accuracy; Benchmark testing; Computational efficiency;
                 Conferences; efficiency; floating-point; IEEE 754;
                 Kernel; Machine learning; posit arithmetic; Resource
                 management; RISC-V; Rockets",
}

@Article{Cococcioni:2021:VPO,
  author =       "Marco Cococcioni and Federico Rossi and Emanuele
                 Ruffaldi and Sergio Saponara",
  title =        "Vectorizing posit operations on {RISC-V} for faster
                 deep neural networks: experiments and comparison with
                 {ARM SVE}",
  journal =      "Neural Computing and Applications",
  volume =       "33",
  number =       "16",
  pages =        "10575--10585",
  month =        feb,
  year =         "2021",
  DOI =          "https://doi.org/10.1007/s00521-021-05814-0",
  ISSN =         "1433-3058",
  ISSN-L =       "0941-0643",
  bibdate =      "Fri Dec 15 11:31:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@InProceedings{Coladon:2021:MFR,
  author =       "Titouan Coladon and Philippe Elbaz-Vincent and Cyril
                 Hugounenq",
  title =        "{MPHELL}: a fast and robust library with unified and
                 versatile arithmetics for elliptic curves
                 cryptography",
  crossref =     "IEEE:2021:ISC",
  pages =        "78--85",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00026",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@Article{Connolly:2021:SRP,
  author =       "Michael P. Connolly and Nicholas J. Higham and Theo
                 Mary",
  title =        "Stochastic Rounding and Its Probabilistic Backward
                 Error Analysis",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "43",
  number =       "1",
  pages =        "A566--A585",
  month =        "????",
  year =         "2021",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/20M1334796",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Fri Mar 12 11:40:06 MST 2021",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/43/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  onlinedate =   "January 2021",
}

@Article{Courbet:2021:NFP,
  author =       "Clement Courbet",
  title =        "{NSan}: a Floating-Point Numerical Sanitizer",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "",
  day =          "25",
  month =        feb,
  year =         "2021",
  DOI =          "https://doi.org/10.48550/arXiv.2102.12782",
  bibdate =      "Sat Jan 24 17:11:41 2026",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/abs/2102.12782",
  abstract =     "Sanitizers are a relatively recent trend in software
                 engineering. They aim at automatically finding bugs in
                 programs, and they are now commonly available to
                 programmers as part of compiler toolchains. For
                 example, the LLVM project includes out-of-the-box
                 sanitizers to detect thread safety (tsan), memory
                 (asan,msan,lsan), or undefined behaviour (ubsan)
                 bugs.\par

                 In this article, we present nsan, a new sanitizer for
                 locating and debugging floating-point numerical issues,
                 implemented inside the LLVM sanitizer framework. nsan
                 puts emphasis on practicality. It aims at providing
                 precise, and actionable feedback, in a timely
                 manner.\par

                 nsan uses compile-time instrumentation to augment each
                 floating-point computation in the program with a
                 higher-precision shadow which is checked for
                 consistency during program execution. This makes nsan
                 between 1 and 4 orders of magnitude faster than
                 existing approaches, which allows running it routinely
                 as part of unit tests, or detecting issues in large
                 production applications.",
  acknowledgement = ack-nhfb,
}

@Article{Czachor:2021:NNM,
  author =       "Marek Czachor",
  title =        "Non-{Newtonian} Mathematics Instead of Non-{Newtonian}
                 Physics: Dark Matter and Dark Energy from a Mismatch of
                 Arithmetics",
  journal =      j-FOUND-SCI,
  volume =       "26",
  number =       "1",
  pages =        "75--95",
  month =        mar,
  year =         "2021",
  CODEN =        "FOSCFI",
  DOI =          "https://doi.org/10.1007/s10699-020-09687-9",
  ISSN =         "1233-1821 (print), 1572-8471 (electronic)",
  ISSN-L =       "1233-1821",
  bibdate =      "Mon Apr 19 10:16:53 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/foundsci.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://link.springer.com/article/10.1007/s10699-020-09687-9",
  acknowledgement = ack-nhfb,
  ajournal =     "Found. Sci.",
  fjournal =     "Foundations of Science",
  journal-URL =  "http://link.springer.com/journal/10699",
  online-date =  "Published: 28 July 2020 Pages: 75 - 95",
}

@Misc{Darcy:2021:FPA,
  author =       "Joseph D. Darcy",
  title =        "Floating-Point Arithmetic: What Every {Java}
                 Programmer Should Know!",
  howpublished = "Web site 29m37s video.",
  year =         "2021",
  bibdate =      "Tue Feb 27 11:53:09 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/java2020.bib",
  URL =          "https://youtu.be/ajaHQ9S4uTA",
  acknowledgement = ack-nhfb,
}

@InProceedings{deDinechin:2021:TAC,
  author =       "Florent de Dinechin and Silviu-Ioan Filip and Martin
                 Kumm and Anastasia Volkova",
  title =        "Towards Arithmetic-Centered Filter Design",
  crossref =     "IEEE:2021:ISC",
  pages =        "115--118",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00032",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@InProceedings{Defour:2021:SCB,
  author =       "David Defour and Pablo de Oliveira Castro and Matei
                 I{\c{s}}toan and Eric Petit",
  title =        "Shadow computation with {BFloat16} to estimate the
                 numerical accuracy of summations",
  crossref =     "IEEE:2021:ISC",
  pages =        "33--36",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00017",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@Article{delaFraga:2021:DEU,
  author =       "Luis Gerardo de la Fraga",
  title =        "Differential Evolution under Fixed Point Arithmetic
                 and {FP16} Numbers",
  journal =      j-MATH-COMPUT-APPL,
  volume =       "26",
  number =       "1",
  pages =        "13--??",
  month =        mar,
  year =         "2021",
  CODEN =        "????",
  DOI =          "https://doi.org/10.3390/mca26010013",
  ISSN =         "2297-8747",
  ISSN-L =       "2297-8747",
  bibdate =      "Sun Feb 18 06:28:40 MST 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/math-comput-appl.bib",
  URL =          "https://www.mdpi.com/2297-8747/26/1/13",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical and Computational Applications",
  journal-URL =  "https://www.mdpi.com/journal/mca",
}

@InProceedings{Demeure:2021:TET,
  author =       "Nestor Demeure and C{\'e}dric Chevalier and Christophe
                 Denis and Pierre Dossantos-Uzarralde",
  title =        "Tagged error: tracing numerical error through
                 computations",
  crossref =     "IEEE:2021:ISC",
  pages =        "9--16",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00014",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@Article{Demmel:2021:NIS,
  author =       "James Demmel and Jason Riedy",
  title =        "A New {IEEE 754} Standard for Floating-Point
                 Arithmetic in an Ever-Changing World",
  journal =      j-SIAM-NEWS,
  volume =       "54",
  number =       "6",
  pages =        "??--??",
  month =        jul # "\slash " # aug,
  year =         "2021",
  ISSN =         "0036-1437",
  bibdate =      "Tue Nov 16 08:21:39 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://sinews.siam.org/Details-Page/a-new-ieee-754-standard-for-floating-point-arithmetic-in-an-ever-changing-world",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM News",
  journal-URL =  "http://www.siam.org/news/",
}

@Article{Dimitrakopoulos:2021:SPAa,
  author =       "Giorgos Dimitrakopoulos and Kleanthis Papachatzopoulos
                 and Vassilis Paliouras",
  title =        "Sum Propagate Adders",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "9",
  number =       "3",
  pages =        "1479--1488",
  month =        jul # "\slash " # sep,
  year =         "2021",
  DOI =          "https://doi.org/10.1109/TETC.2021.3068729",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  note =         "See \cite{Dimitrakopoulos:2021:SPAb}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}

@InProceedings{Dimitrakopoulos:2021:SPAb,
  author =       "Giorgos Dimitrakopoulos and Kleanthis Papachatzopoulos
                 and Vassilis Paliouras",
  title =        "Sum Propagate Adders",
  crossref =     "IEEE:2021:ISC",
  pages =        "110--110",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00030",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Dimitrakopoulos:2021:SPAa}.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
  remark =       "Published in IEEE Transactions on Emerging Topics in
                 Computing, Volume: 9, Issue: 3, July--September 2021,
                 and orally presented at ARITH 2021.",
}

@Misc{Druck:2021:NSB,
  author =       "Philip Druck",
  title =        "A Novel Set of Base-Prime Floating Point Numbers",
  howpublished = "TechRxiv preprint.",
  day =          "16",
  month =        feb,
  year =         "2021",
  DOI =          "https://doi.org/10.36227/techrxiv.13960829.v1",
  bibdate =      "Fri Sep 29 14:28:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "A novel set is presented that generalizes the usual
                 base representations of floating point real numbers. It
                 uses base-prime numbers instead of the usual base 2
                 (binary), base 3 (for the Cantor set), base 10
                 (decimal), base 16 (hexadecimal) and the like. This
                 base-prime set, denoted DS, is essentially an
                 experimental finding, identified in unrelated patented
                 research on nonuniform signal data sampling [1] and
                 self-stabilizing computer arithmetic [2].",
  acknowledgement = ack-nhfb,
}

@Article{Eliahu:2021:MME,
  author =       "Adi Eliahu and Ronny Ronen and Pierre-Emmanuel
                 Gaillardon and Shahar Kvatinsky",
  title =        "{multiPULPly}: a Multiplication Engine for
                 Accelerating Neural Networks on Ultra-low-power
                 Architectures",
  journal =      j-JETC,
  volume =       "17",
  number =       "2",
  pages =        "24:1--24:27",
  month =        apr,
  year =         "2021",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3432815",
  ISSN =         "1550-4832 (print), 1550-4840 (electronic)",
  ISSN-L =       "1550-4832",
  bibdate =      "Fri Apr 30 06:39:29 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jetc.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3432815",
  abstract =     "Computationally intensive neural network applications
                 often need to run on resource-limited low-power
                 devices. Numerous hardware accelerators have been
                 developed to speed up the performance of neural network
                 applications and reduce power consumption; however,
                 most focus on data centers and full-fledged systems.
                 Acceleration in ultra-low-power systems has been only
                 partially addressed. In this article, we present
                 multiPULPly, an accelerator that integrates memristive
                 technologies within standard low-power CMOS technology,
                 to accelerate multiplication in neural network
                 inference on ultra-low-power systems. This accelerator
                 was designated for PULP, an open-source microcontroller
                 system that uses low-power RISC-V processors.
                 Memristors were integrated into the accelerator to
                 enable power consumption only when the memory is
                 active, to continue the task with no context-restoring
                 overhead, and to enable highly parallel analog
                 multiplication. To reduce the energy consumption, we
                 propose novel dataflows that handle common
                 multiplication scenarios and are tailored for our
                 architecture. The accelerator was tested on FPGA and
                 achieved a peak energy efficiency of 19.5 TOPS/W,
                 outperforming state-of-the-art accelerators by $ 1.5
                 \times $ to $ 4.5 \times $.",
  acknowledgement = ack-nhfb,
  articleno =    "24",
  fjournal =     "ACM Journal on Emerging Technologies in Computing
                 Systems (JETC)",
  journal-URL =  "https://dl.acm.org/loi/jetc",
}

@InProceedings{Elkhatib:2021:ARV,
  author =       "Rami Elkhatib and Reza Azarderakhsh and Mehran
                 Mozaffari-Kermani",
  title =        "Accelerated {RISC-V} for {SIKE}",
  crossref =     "IEEE:2021:ISC",
  pages =        "131--138",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00035",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@Article{Fasi:2021:ASRa,
  author =       "Massimiliano Fasi and Mantas Mikaitis",
  title =        "Algorithms for Stochastically Rounded Elementary
                 Arithmetic Operations in {IEEE 754} Floating-Point
                 Arithmetic",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "9",
  number =       "3",
  pages =        "1451--1466",
  month =        jul # "\slash " # sep,
  year =         "2021",
  DOI =          "https://doi.org/10.1109/TETC.2021.3069165",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  note =         "See \cite{Fasi:2021:ASRb}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
  keywords =     "ARITH 2021; ARITH-28",
}

@InProceedings{Fasi:2021:ASRb,
  author =       "Massimiliano Fasi and Mantas Mikaitis",
  title =        "Algorithms for Stochastically Rounded Elementary
                 Arithmetic Operations in {IEEE 754} Floating-Point
                 Arithmetic",
  crossref =     "IEEE:2021:ISC",
  pages =        "69--69",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00024",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Fasi:2021:ASRa}.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
  remark =       "Published in IEEE Transactions on Emerging Topics in
                 Computing, Volume: 9, Issue: 3, July--September 2021,
                 and orally presented at ARITH 2021.",
}

@Article{Fasi:2021:NBN,
  author =       "Massimiliano Fasi and Nicholas J. Higham and Mantas
                 Mikaitis and Srikara Pranesh",
  title =        "Numerical behavior of {NVIDIA} tensor cores",
  journal =      "PeerJ Computer Science",
  volume =       "7",
  pages =        "e330:1--e330:19",
  month =        feb,
  year =         "2021",
  DOI =          "https://doi.org/10.7717/peerj-cs.330",
  ISSN =         "2376-5992",
  bibdate =      "Mon Apr 22 14:18:25 2024",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  journal-URL =  "https://peerj.com/cs/",
}

@Article{Fortin:2021:HPS,
  author =       "Pierre Fortin and Ambroise Fleury and Fran{\c{c}}ois
                 Lemaire and Michael Monagan",
  title =        "High-performance {SIMD} modular arithmetic for
                 polynomial evaluation",
  journal =      j-CCPE,
  volume =       "33",
  number =       "16",
  pages =        "e6270:1--e6270:??",
  day =          "25",
  month =        aug,
  year =         "2021",
  CODEN =        "CCPEBO",
  DOI =          "https://doi.org/10.1002/cpe.6270",
  ISSN =         "1532-0626 (print), 1532-0634 (electronic)",
  ISSN-L =       "1532-0626",
  bibdate =      "Tue Feb 22 09:49:56 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/ccpe.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Concurr. Comput.",
  fjournal =     "Concurrency and Computation: Practice and Experience",
  journal-URL =  "http://www.interscience.wiley.com/jpages/1532-0626",
  onlinedate =   "25 May 2021",
}

@Article{Garofalo:2021:XEEa,
  author =       "Angelo Garofalo and Giuseppe Tagliavini and Francesco
                 Conti and Luca Benini and Davide Rossi",
  title =        "{XpulpNN}: Enabling Energy Efficient and Flexible
                 Inference of Quantized Neural Networks on {RISC-V}
                 Based {IoT} End Nodes",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "9",
  number =       "3",
  pages =        "1489--1505",
  month =        jul # "\slash " # sep,
  year =         "2021",
  DOI =          "https://doi.org/10.1109/TETC.2021.3072337",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  note =         "See \cite{Garofalo:2021:XEEb}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}

@InProceedings{Garofalo:2021:XEEb,
  author =       "Angelo Garofalo and Giuseppe Tagliavini and Francesco
                 Conti and Luca Benini and Davide Rossi",
  title =        "{XpulpNN}: Enabling Energy Efficient and Flexible
                 Inference of Quantized Neural Networks on {RISC-V}
                 based {IoT} End Nodes",
  crossref =     "IEEE:2021:ISC",
  pages =        "53--53",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00020",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Garofalo:2021:XEEa}.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
  remark =       "Published in IEEE Transactions on Emerging Topics in
                 Computing, Volume: 9, Issue: 3, July--September 2021,
                 and orally presented at ARITH 2021.",
}

@Article{Gohil:2021:FPF,
  author =       "Varun Gohil and Sumit Walia and Joycee Mekie and Manu
                 Awasthi",
  title =        "Fixed-Posit: a Floating-Point Representation for
                 Error-Resilient Applications",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
  volume =       "68",
  number =       "10",
  pages =        "3341--3345",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/TCSII.2021.3072217",
  ISSN =         "1549-7747 (print), 1558-3791 (electronic)",
  ISSN-L =       "1549-7747",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems II: Express
                 Briefs",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
}

@InProceedings{Gopalakrishnan:2021:GNA,
  author =       "Ganesh Gopalakrishnan and Ignacio Laguna and Ang Li
                 and Pavel Panchekha and Cindy Rubio-Gonz{\'a}lez and
                 Zachary Tatlock",
  editor =       "????",
  booktitle =    "{Correctness 2021: Fifth International Workshop on
                 Software Correctness for HPC Applications, November 19,
                 2021, America's Center Convention Complex St. Louis,
                 MO, USA}",
  title =        "Guarding Numerics Amidst Rising Heterogeneity",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2021",
  bibdate =      "Mon Sep 11 06:54:23 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://correctness-workshop.github.io/2021/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gustafsson:2021:AFP,
  author =       "Oscar Gustafsson and Noah Hellman",
  title =        "Approximate Floating-Point Operations with Integer
                 Units by Processing in the Logarithmic Domain",
  crossref =     "IEEE:2021:ISC",
  pages =        "45--52",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00019",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@Book{Haigh:2021:NHM,
  author =       "Thomas Haigh and Paul E. Ceruzzi",
  title =        "A New History of Modern Computing",
  publisher =    pub-MIT,
  address =      pub-MIT:adr,
  pages =        "x + 528",
  year =         "2021",
  ISBN =         "0-262-54290-0 (paperback), 0-262-36647-9 (e-book)",
  ISBN-13 =      "978-0-262-54290-6 (paperback), 978-0-262-36647-2
                 (e-book)",
  LCCN =         "QA76.17 .H34 2021",
  bibdate =      "Mon Nov 15 15:00:52 MST 2021",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  series =       "History of computing",
  abstract =     "Bringing the history of modern computing fully up to
                 date, from new applications to scientific computation
                 to video games and the ubiquitous smartphone.",
  acknowledgement = ack-nhfb,
  libnote =      "Not yet in my library.",
  remark =       "See also earlier editions
                 \cite{Ceruzzi:1998:HMC,Ceruzzi:2003:HMC}.",
  subject =      "Computer science; History; Electronic digital
                 computers; Informatique; Histoire; Ordinateurs",
  tableofcontents = "Acknowledgments / ix \\
                 Inventing the computer / 1 \\
                 The computer becomes a scientific supertool / 29 \\
                 The computer becomes a data processing device / 55 \\
                 The computer becomes a real-time control system / 83
                 \\
                 The computer becomes an interactive tool / 109 \\
                 The computer becomes a communications platform / 139
                 \\
                 The computer becomes a personal plaything / 167 \\
                 The computer becomes office equipment / 207 \\
                 The computer becomes a graphical tool / 243 \\
                 The pc becomes a minicomputer / 263 \\
                 The computer becomes a universal media device / 293 \\
                 The computer becomes a publishing platform / 329 \\
                 The computer becomes a network / 359 \\
                 The computer is everywhere and nowhere / 385 \\
                 Epilogue: a Tesla in the Valley / 409 \\
                 Notes / 425 \\
                 Bibliography / 467 \\
                 Index / 495",
}

@InProceedings{Held:2021:KRP,
  author =       "James P. Held and Th{\'e}o Mary",
  title =        "Keynote 1: Realizing the Promise of Quantum
                 Computing",
  crossref =     "IEEE:2021:ISC",
  pages =        "xvi--xvi",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00011",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@MastersThesis{Hellman:2021:MBA,
  author =       "Noah Hellman",
  title =        "{Mitchell}-Based Approximate Operations on
                 Floating-Point Numbers",
  type =         "{Master of Science Thesis in Electrical Engineering}",
  school =       "Department of Electrical Engineering, Link{\"o}ping
                 University",
  address =      "Link{\"o}ping, Sweden",
  pages =        "56",
  day =          "19",
  month =        jun,
  year =         "2021",
  bibdate =      "Wed Dec 20 07:05:10 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://liu.diva-portal.org/smash/get/diva2:1590166/FULLTEXT01.pdf;
                 http://liu.diva-portal.org/smash/record.jsf?pid=diva2%3A1590166&dswid=5128",
  abstract =     "By adapting Mitchell's algorithm for floating-point
                 numbers, one can efficiently perform arithmetic
                 floating-point operations in an approximate logarithmic
                 domain in order to perform approximate computations of
                 functions such as multiplication, division, square root
                 and others. This work examines how this algorithm can
                 be improved in terms of accuracy and hardware
                 complexity by applying a set of various methods that
                 are parametrized and offer a large design space.
                 Optimal coefficients for a large portion of this space
                 is determined and used to synthesize circuits for both
                 ASIC and FPGA circuits using the bfloat16 format.
                 Optimal configurations are then extracted to create an
                 optimal curve where one can select an acceptable error
                 range and obtain a circuit with a minimal hardware
                 cost.",
  acknowledgement = ack-nhfb,
  advisor =      "Oscar Gustafsson",
  remark =       "See \cite{Mitchell:1962:CMD}.",
}

@Article{Higham:2021:MFP,
  author =       "Nicholas J. Higham",
  title =        "The mathematics of floating-point arithmetic",
  journal =      j-LOND-MATH-SOC-NEWSL,
  number =       "493",
  pages =        "35--41",
  month =        mar,
  year =         "2021",
  ISSN =         "2516-3841 (print), 2516-385X (electronic)",
  ISSN-L =       "2516-3841",
  bibdate =      "Fri Nov 14 16:23:21 2025",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.lms.ac.uk/sites/lms.ac.uk/files/files/NLMS_493_for%20web2.pdf",
  acknowledgement = ack-nhfb,
  author-dates = "Nicholas John Higham (25 December 1961--20 January
                 2024)",
  fjournal =     "LMS Newsletter",
  journal-doi =  "https://doi.org/10.1112/NLMS",
  journal-URL =  "https://www.lms.ac.uk/publications/lms-newsletter-back-issues",
}

@Article{Trefethen:2021:NNAe,
  author =       "Nick Trefethen",
  title =        "Notes of a numerical analyst. {Floating} point numbers
                 and physics",
  journal =      j-LOND-MATH-SOC-NEWSL,
  number =       "497",
  pages =        "36--36",
  month =        nov,
  year =         "2021",
  ISSN =         "2516-3841 (print), 2516-385X (electronic)",
  ISSN-L =       "2516-3841",
  MRclass =      "00A30",
  bibdate =      "Tue Nov 18 14:22:27 2025",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.lms.ac.uk/sites/default/files/inline-files/NLMS_497_for%20web_1.pdf",
  ZMnumber =     "7457043; 1480.00036",
  acknowledgement = ack-nhfb,
  fjournal =     "LMS Newsletter",
  journal-DOI =  "https://doi.org/10.1112/NLMS",
  journal-URL =  "https://www.lms.ac.uk/publications/lms-newsletter-back-issues",
}

@Article{Ho:2021:GFD,
  author =       "Nhut-Minh Ho and Himeshi {De Silva} and Weng-Fai
                 Wong",
  title =        "{GRAM}: a Framework for Dynamically Mixing Precisions
                 in {GPU} Applications",
  journal =      j-TACO,
  volume =       "18",
  number =       "2",
  pages =        "19:1--19:24",
  month =        mar,
  year =         "2021",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3441830",
  ISSN =         "1544-3566 (print), 1544-3973 (electronic)",
  ISSN-L =       "1544-3566",
  bibdate =      "Sat Mar 20 17:25:10 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/pvm.bib;
                 https://www.math.utah.edu/pub/tex/bib/taco.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3441830",
  abstract =     "This article presents GRAM (GPU-based Runtime Adaption
                 for Mixed-precision) a framework for the effective use
                 of mixed precision arithmetic for CUDA programs. Our
                 method provides a fine-grain tradeoff between output
                 error and performance. It can create many variants that
                 satisfy different accuracy requirements by assigning
                 different groups of threads to different precision
                 levels adaptively at runtime. To widen the range of
                 applications that can benefit from its approximation,
                 GRAM comes with an optional half-precision approximate
                 math library. Using GRAM, we can trade off precision
                 for any performance improvement of up to 540\%,
                 depending on the application and accuracy
                 requirement.",
  acknowledgement = ack-nhfb,
  articleno =    "19",
  fjournal =     "ACM Transactions on Architecture and Code Optimization
                 (TACO)",
  journal-URL =  "https://dl.acm.org/loi/taco",
}

@InProceedings{Ho:2021:PAT,
  author =       "Nhut-Minh Ho and Duy-Thanh Nguyen and Himeshi {De
                 Silva} and John L. Gustafson and Weng-Fai Wong and Ik
                 Joon Chang",
  editor =       "{IEEE}",
  booktitle =    "{2021 Design, Automation \& Test in Europe Conference
                 \& Exhibition (DATE)}",
  title =        "Posit Arithmetic for the Training and Deployment of
                 Generative Adversarial Networks",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1350--1355",
  year =         "2021",
  DOI =          "https://doi.org/10.23919/DATE51398.2021.9473933",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Hormigo:2021:FAB,
  author =       "Javier Hormigo and Gabriel Caffarena",
  title =        "{FPGA} acceleration of bit-true simulations for
                 word-length optimization",
  crossref =     "IEEE:2021:ISC",
  pages =        "119--122",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00033",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@Article{Hough:2021:ISO,
  author =       "David G. Hough",
  title =        "The {IEEE Standard 754}: One for the History Books",
  journal =      j-COMPUT-EDGE,
  volume =       "??",
  number =       "4",
  pages =        "42--46",
  month =        aug,
  year =         "2021",
  DOI =          "https://doi.org/10.1109/MC.2019.2926614",
  ISSN =         "2469-7087",
  bibdate =      "Thu Aug 19 14:23:25 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://grouper.ieee.org/groups/msc/ANSI_IEEE-Std-754-2019/background/ieee-computer.pdf;
                 https://www.computer.org/csdl/magazine/co/2019/12/08909942/1f8KFWxbTCU",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing Edge",
  journal-URL =  "http://www.computer.org/web/computingedge",
  keywords =     "Floating-point arithmetic; Hardware; History; IEEE
                 Standards; Microprocessors; Software",
  remark =       "Reprint of \cite{Hough:2019:ISO}.",
  xxISSN =       "2376-113X",
}

@InProceedings{Ina:2021:IMM,
  author =       "T. Ina and Y. Idomura and T. Imamura and S. Yamashita
                 and N. Onodera",
  booktitle =    "{2021 12th Workshop on Latest Advances in Scalable
                 Algorithms for Large-Scale Systems (ScalA)}",
  title =        "Iterative methods with mixed-precision preconditioning
                 for ill-conditioned linear systems in multiphase {CFD}
                 simulations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--8",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ScalA54577.2021.00006",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computational modeling; Iterative refinement method;
                 Jacobian matrices; Jupiter; Linear systems;
                 Mixed-precision computing; Multi-phase CFD simulation;
                 Robustness; Roundoff errors; Software",
}

@Misc{Jain:2021:M,
  author =       "Riya Jain and Niraj Nayan Sharma",
  title =        "{Melodica}",
  howpublished = "Web software.",
  year =         "2021",
  bibdate =      "Sat Dec 16 15:21:57 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://github.com/HPC-Lab-IITB/Melodica",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@InProceedings{Jean:2021:PFN,
  author =       "Sandra Jean and Aneesh Raveendran and A. David
                 Selvakumar and Gagandeep Kaur and Shankar G. Dharani
                 and Shashikala Gunderao Pattanshetty and Vivian
                 Desalphine",
  editor =       "{IEEE}",
  booktitle =    "{2021 34th International Conference on VLSI Design and
                 2021 20th International Conference on Embedded Systems
                 (VLSID)}",
  title =        "{P-FMA}: a Novel Parameterized Posit Fused
                 Multiply-Accumulate Arithmetic Processor",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "282--287",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/VLSID51830.2021.00053",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Joldes:2021:FA,
  author =       "Mioara Joldes and Fabrizio Lambert",
  title =        "Foreword {ARITH 2021}",
  crossref =     "IEEE:2021:ISC",
  pages =        "ix--x",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00005",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@Article{Joldes:2021:SSE,
  author =       "Mioara Joldes and Fabrizio Lamberti and Alberto
                 Nannarelli",
  title =        "Special Section on Emerging and Impacting Trends on
                 Computer Arithmetic",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "9",
  number =       "3",
  pages =        "1449--1450",
  month =        jul # "\slash " # sep,
  year =         "2021",
  DOI =          "https://doi.org/10.1109/TETC.2021.3096698",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}

@InProceedings{Kant:2021:IPI,
  author =       "Manash Kant and Rajeev Thakur",
  editor =       "{IEEE}",
  booktitle =    "{2021 Fifth International Conference on I-SMAC (IoT in
                 Social, Mobile, Analytics and Cloud) (I-SMAC)}",
  title =        "Implementation and Performance Improvement of {POSIT}
                 Multiplier for Advance {DSP} Applications",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1730--1736",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/I-SMAC52330.2021.9640999",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Kaplun:2021:TAA,
  author =       "Dmitrii Kaplun and Alexander Voznesensky and Alexander
                 V. Veligosha and Igor A. Kalmykov and Kandarpa Kumar
                 Sarma",
  title =        "Technique to Adjust Adaptive Digital Filter
                 Coefficients in Residue Number System Based Filters",
  journal =      j-IEEE-ACCESS,
  volume =       "9",
  pages =        "82402--82416",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ACCESS.2021.3085704",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Wed Oct 1 06:08:36 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "Adaptive digital filter; Approximation algorithms;
                 computational complexity; denoising quality; Digital
                 filters; Electronic mail; Filtering algorithms; Finite
                 impulse response filters; least mean square algorithm;
                 recursive least square algorithm; residue number
                 system; Signal processing algorithms; Wiener filters",
}

@InProceedings{Kouya:2021:ALD,
  author =       "Tomonori Kouya",
  title =        "Acceleration of {$ L U $} decomposition supporting
                 double--double, triple--double, and quadruple--double
                 precision floating-point arithmetic with {AVX2}",
  crossref =     "IEEE:2021:ISC",
  pages =        "54--61",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00021",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@InProceedings{Kulkarni:2021:PVS,
  author =       "Annarao Kulkarni and Shashikala Pattanshetty and
                 Aneesh Raveendran and David Selvakumar and Sandra Jean
                 and Vivian Desalphine",
  editor =       "{IEEE}",
  booktitle =    "{2021 34th International Conference on VLSI Design and
                 2021 20th International Conference on Embedded Systems
                 (VLSID)}",
  title =        "{PositGen} --- a Verification Suite for Posit
                 Arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "204--209",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/VLSID51830.2021.00040",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Lange:2021:CND,
  author =       "Marko Lange and Shin'ichi Oishi",
  title =        "Correction to: {A note on Dekker's FastTwoSum
                 algorithm}",
  journal =      j-NUM-MATH,
  volume =       "149",
  number =       "1",
  pages =        "227--228",
  month =        sep,
  year =         "2021",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/s00211-021-01213-8",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Wed Sep 15 05:50:42 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath2020.bib",
  note =         "See \cite{Lange:2020:NDF}.",
  URL =          "http://link.springer.com/article/10.1007/s00211-021-01213-8;
                 https://link.springer.com/content/pdf/10.1007/s00211-021-01213-8.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}

@InProceedings{Langroudi:2021:AAQ,
  author =       "Hamed F. Langroudi and Vedant Karia and Zachariah
                 Carmichael and Abdullah Zyarah and Tej Pandit and John
                 L. Gustafson and Dhireesha Kudithipudi",
  editor =       "{IEEE}",
  booktitle =    "{2021 IEEE/CVF Conference on Computer Vision and
                 Pattern Recognition Workshops (CVPRW)}",
  title =        "Alps: Adaptive Quantization of Deep Neural Networks
                 with {GeneraLized} {PositS}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "3094--3103",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/CVPRW53098.2021.00346",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Lemire:2021:NPG,
  author =       "Daniel Lemire",
  title =        "Number parsing at a gigabyte per second",
  journal =      j-SPE,
  volume =       "51",
  number =       "8",
  pages =        "1700--1727",
  month =        aug,
  year =         "2021",
  CODEN =        "SPEXBL",
  DOI =          "https://doi.org/10.1002/spe.2984",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Fri Jul 23 09:04:36 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/go.bib;
                 https://www.math.utah.edu/pub/tex/bib/spe.bib",
  note =         "See improvement \cite{Mushtak:2023:FNP}.",
  abstract =     "With disks and networks providing gigabytes per
                 second, parsing decimal numbers from strings becomes a
                 bottleneck. We consider the problem of parsing decimal
                 numbers to the nearest binary floating-point value. The
                 general problem requires variable-precision arithmetic.
                 However, we need at most 17 digits to represent 64-bit
                 standard floating-point numbers (IEEE 754). Thus, we
                 can represent the decimal significand with a single
                 64-bit word. By combining the significand and
                 precomputed tables, we can compute the nearest
                 floating-point number using as few as one or two 64-bit
                 multiplications. Our implementation can be several
                 times faster than conventional functions present in
                 standard C libraries on modern 64-bit systems (Intel,
                 AMD, ARM, and POWER9). Our work is available as open
                 source software used by major systems such as Apache
                 Arrow and Yandex ClickHouse. The Go standard library
                 has adopted a version of our approach.",
  acknowledgement = ack-nhfb,
  ajournal =     "Softw. Pract. Exp.",
  fjournal =     "Software --- Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  onlinedate =   "11 May 2021",
}

@Article{Leon:2021:IPD,
  author =       "Vasileios Leon and Theodora Paparouni and Evangelos
                 Petrongonas and Dimitrios Soudris and Kiamal
                 Pekmestzi",
  title =        "Improving Power of {DSP} and {CNN} Hardware
                 Accelerators Using Approximate Floating-point
                 Multipliers",
  journal =      j-TECS,
  volume =       "20",
  number =       "5",
  pages =        "39:1--39:21",
  month =        jul,
  year =         "2021",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3448980",
  ISSN =         "1539-9087 (print), 1558-3465 (electronic)",
  ISSN-L =       "1539-9087",
  bibdate =      "Tue Aug 10 13:35:00 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tecs.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3448980",
  abstract =     "Approximate computing has emerged as a promising
                 design alternative for delivering power-efficient
                 systems and circuits by exploiting the inherent error
                 resiliency of numerous applications. The current
                 article aims to tackle the increased hardware cost of
                 floating-point multiplication units, which prohibits
                 their usage in embedded computing. We introduce AFMU
                 (Approximate Floating-point MUltiplier), an
                 area/power-efficient family of multipliers, which apply
                 two approximation techniques in the resource-hungry
                 mantissa multiplication and can be seamlessly extended
                 to support dynamic configuration of the approximation
                 levels via gating signals. AFMU offers large accuracy
                 configuration margins, provides negligible logic
                 overhead for dynamic configuration, and detects
                 unexpected results that may arise due to the
                 approximations. Our evaluation shows that AFMU delivers
                 energy gains in the range 3.6\%--53.5\% for
                 half-precision and 37.2\%--82.4\% for single-precision,
                 in exchange for mean relative error around
                 0.05\%--3.33\% and 0.01\%--2.20\%, respectively. In
                 comparison with state-of-the-art multipliers, AFMU
                 exhibits up to 4--6 $ \times $ smaller error on average
                 while delivering more energy-efficient computing. The
                 evaluation in image processing shows that AFMU provides
                 sufficient quality of service, i.e., more than 50db
                 PSNR and near 1 SSIM values, and up to 57.4\% power
                 reduction. When used in floating-point CNNs, the
                 accuracy loss is small (or zero), i.e., up to 5.4\% for
                 MNIST and CIFAR-10, in exchange for up to 63.8\% power
                 gain.",
  acknowledgement = ack-nhfb,
  articleno =    "39",
  fjournal =     "ACM Transactions on Embedded Computing Systems",
  journal-URL =  "https://dl.acm.org/loi/tecs",
}

@InProceedings{Li:2021:MPF,
  author =       "Kai Li and Wei Mao and Xinang Xie and Quan Cheng and
                 Huan Xie and Zhenjiang Dong and Hao Yu",
  booktitle =    "{2021 IEEE 3rd International Conference on Artificial
                 Intelligence Circuits and Systems (AICAS)}",
  title =        "Multiple-Precision Floating-Point Dot Product Unit for
                 Efficient Convolution Computation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--4",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/AICAS51828.2021.9458534",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Artificial intelligence; Circuits and systems;
                 Computational efficiency; Conferences; Convolution;
                 Convolutional neural networks; CSLA; dot product;
                 floating-point; Hardware; multiple-precision;
                 multiplier; radix-4 booth",
}

@InProceedings{Lim:2021:HPC,
  author =       "Jay P. Lim and Santosh Nagarakatte",
  editor =       "Stephen N. Freund and Eran Yahav",
  booktitle =    "{PLDI '21: Proceedings of the 42nd ACM SIGPLAN
                 International Conference on Programming Language Design
                 and Implementation, June 20--25, 2021 [virtual
                 meeting]}",
  title =        "High performance correctly rounded math libraries for
                 32-bit floating point representations",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "359--374",
  month =        jun,
  year =         "2021",
  DOI =          "https://doi.org/10.1145/3453483.3454049",
  ISBN =         "1-4503-8391-2",
  ISBN-13 =      "978-1-4503-8391-2",
  LCCN =         "QA76.7 G878",
  bibdate =      "Thu Sep 19 15:15:02 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This paper proposes a set of techniques to develop
                 correctly rounded math libraries for 32-bit float and
                 posit types. It enhances our RLibm approach that frames
                 the problem of generating correctly rounded libraries
                 as a linear programming problem in the context of
                 16-bit types to scale to 32-bit types. Specifically,
                 this paper proposes new algorithms to (1) generate
                 polynomials that produce correctly rounded outputs for
                 all inputs using counterexample guided polynomial
                 generation, (2) generate efficient piecewise
                 polynomials with bit-pattern based domain splitting,
                 and (3) deduce the amount of freedom available to
                 produce correct results when range reduction involves
                 multiple elementary functions. The resultant math
                 library for the 32-bit float type is faster than
                 state-of-the-art math libraries while producing the
                 correct output for all inputs. We have also developed a
                 set of correctly rounded elementary functions for
                 32-bit posits.",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1145/3453483",
  keywords =     "posit arithmetic",
}

@Article{Lim:2021:RAN,
  author =       "Jay P. Lim and Santosh Nagarakatte",
  title =        "{RLibm-All}: A Novel Polynomial Approximation Method
                 to Produce Correctly Rounded Results for Multiple
                 Representations and Rounding Modes",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--28",
  day =          "30",
  month =        nov,
  year =         "2021",
  bibdate =      "Thu Sep 04 10:51:23 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Also available as Rutgers Department of Computer
                 Science Technical Report DCS-TR-757.",
  URL =          "https://arxiv.org/pdf/2108.06756",
  abstract =     "Mainstream math libraries for floating point (FP) do
                 not produce correctly rounded results for all inputs.
                 In contrast, CR-LIBM and RLibm provide correctly
                 rounded implementations for a specific FP
                 representation with one rounding mode. Using such
                 libraries for a representation with a new rounding mode
                 or with different precision will result in wrong
                 results due to double rounding. This paper proposes a
                 novel method to generate a single polynomial
                 approximation that produces correctly rounded results
                 for all inputs for multiple rounding modes and multiple
                 precision configurations. To generate a correctly
                 rounded library for $n$-bits, our key idea is to
                 generate a polynomial approximation for a
                 representation with $ n + 2$-bits using the
                 round-to-odd mode. We prove that the resulting
                 polynomial approximation will produce correctly rounded
                 results for all five rounding modes in the standard and
                 for multiple representations with $k$-bits such that $
                 |E| + 1 < k \leq n$, where $ |E|$ is the number of
                 exponent bits in the representation. Similar to our
                 prior work in the RLibm project, we approximate the
                 correctly rounded result when we generate the library
                 with $ n + 2$-bits using the round-to-odd mode. We also
                 generate polynomial approximations by structuring it as
                 a linear programming problem but propose enhancements
                 to polynomial generation to handle the round-to-odd
                 mode. Our prototype is the first 32-bit float library
                 that produces correctly rounded results with all
                 rounding modes in the IEEE standard for all inputs with
                 a single polynomial approximation. It also produces
                 correctly rounded results for any FP configuration
                 ranging from 10-bits to 32-bits while also being faster
                 than mainstream libraries.",
  acknowledgement = ack-nhfb,
  keywords =     "correct rounding; double rounding; Floating-point;
                 floating-point arithmetic; round-to-odd (RO(x))",
}

@Article{Liu:2021:DAM,
  author =       "Weiqiang Liu and Tingting Zhang and Emma McLarnon and
                 Maire O'Neill and Paolo Montuschi and Fabrizio
                 Lombardi",
  title =        "Design and Analysis of Majority Logic-Based
                 Approximate Adders and Multipliers",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "9",
  number =       "3",
  pages =        "1609--1624",
  month =        jul # "\slash " # sep,
  year =         "2021",
  DOI =          "https://doi.org/10.1109/TETC.2019.2929100",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}

@Article{Lu:2021:EDN,
  author =       "Jinming Lu and Chao Fang and Mingyang Xu and Jun Lin
                 and Zhongfeng Wang",
  title =        "Evaluations on Deep Neural Networks Training Using
                 Posit Number System",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "70",
  number =       "2",
  pages =        "174--187",
  year =         "2021",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2020.2985971",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Mach:2021:FOS,
  author =       "Stefan Mach and Fabian Schuiki and Florian Zaruba and
                 Luca Benini",
  title =        "{FPnew}: an Open-Source Multiformat Floating-Point
                 Unit Architecture for Energy-Proportional
                 Transprecision Computing",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "29",
  number =       "4",
  pages =        "774--787",
  year =         "2021",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/TVLSI.2020.3044752",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
  keywords =     "Computer architecture; Energy efficient;
                 floating-point unit; Hardware; multiformat; Open source
                 software; Optimization; Pipeline processing; RISC-V;
                 Silicon; Standards; transprecision computing",
}

@InProceedings{Mao:2021:RMP,
  author =       "Wei Mao and Kai Li and Xinang Xie and Shirui Zhao and
                 He Li and Hao Yu",
  booktitle =    "{2021 Design, Automation \& Test in Europe Conference
                 \& Exhibition (DATE)}",
  title =        "A Reconfigurable Multiple-Precision Floating-Point Dot
                 Product Unit for High-Performance Computing",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1793--1798",
  year =         "2021",
  DOI =          "https://doi.org/10.23919/DATE51398.2021.9473928",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benchmark testing; Computational modeling; Deep
                 learning; dot product unit; floating point;
                 mix-precision; Multiple-precision; multiplier;
                 partitioning; Scientific computing; SIMD; Simulation;
                 Throughput; Training",
}

@InProceedings{Mary:2021:KOM,
  author =       "Th{\'e}o Mary",
  title =        "Keynote 2: Opportunities for Mixed Precision
                 Arithmetic in Numerical Linear Algebra",
  crossref =     "IEEE:2021:ISC",
  pages =        "xvii--xvii",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00011",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@Article{Matos:2021:EFP,
  author =       "Jos{\'e} A. O. Matos and Paulo B. Vasconcelos",
  title =        "Effectiveness of Floating-Point Precision on the
                 Numerical Approximation by Spectral Methods",
  journal =      j-MATH-COMPUT-APPL,
  volume =       "26",
  number =       "2",
  pages =        "42--??",
  month =        jun,
  year =         "2021",
  CODEN =        "????",
  DOI =          "https://doi.org/10.3390/mca26020042",
  ISSN =         "2297-8747",
  ISSN-L =       "2297-8747",
  bibdate =      "Sun Feb 18 06:28:40 MST 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/math-comput-appl.bib",
  URL =          "https://www.mdpi.com/2297-8747/26/2/42",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical and Computational Applications",
  journal-URL =  "https://www.mdpi.com/journal/mca",
}

@TechReport{MPFR:2021:MLA,
  author =       "{The MPFR Team}",
  title =        "The {MPFR} Library: Algorithms and Proofs",
  type =         "Report",
  institution =  "????",
  address =      "????",
  pages =        "69",
  day =          "5",
  month =        nov,
  year =         "2021",
  bibdate =      "Tue Mar 14 13:13:13 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.mpfr.org/algorithms.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Muller:2021:X,
  author =       "Jean-Michel Muller",
  title =        "$ a \cdot (x \cdot \ x) $ or $ (a \cdot x) \cdot x?
                 $",
  crossref =     "IEEE:2021:ISC",
  pages =        "17--24",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00015",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Expressions such as $ a x^2 $, $ a x y $, or $ a x^3
                 $, where $a$ is a constant, are not infrequent in
                 computing. There are several ways of parenthesizing
                 them (and therefore, choosing the order of evaluation).
                 Depending on the value of $a$, is there a more accurate
                 evaluation order? We discuss this point (with a small
                 digression on spurious underflows and overflows).",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@Article{Muntean:2021:IIR,
  author =       "Paul Muntean and Martin Monperrus and Hao Sun and Jens
                 Grossklags and Claudia Eckert",
  title =        "{IntRepair}: Informed Repairing of Integer Overflows",
  journal =      j-IEEE-TRANS-SOFTW-ENG,
  volume =       "47",
  number =       "10",
  pages =        "2225--2241",
  month =        oct,
  year =         "2021",
  CODEN =        "IESEDJ",
  DOI =          "https://doi.org/10.1109/TSE.2019.2946148",
  ISSN =         "0098-5589 (print), 1939-3520 (electronic)",
  ISSN-L =       "0098-5589",
  bibdate =      "Thu Oct 21 10:49:15 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranssoftweng2020.bib",
  abstract =     "Integer overflows have threatened software
                 applications for decades. Thus, in this paper, we
                 propose a novel technique to provide automatic repairs
                 of integer overflows in C source code. Our technique,
                 based on static symbolic execution, fuses detection,
                 repair generation and validation. This technique is
                 implemented in a prototype named IntRepair. We applied
                 IntRepair to 2,052 C programs (approx. 1 million lines
                 of code) contained in SAMATE's Juliet test suite and 50
                 synthesized programs that range up to 20 KLOC. Our
                 experimental results show that IntRepair is able to
                 effectively detect integer overflows and successfully
                 repair them, while only increasing the source code
                 (LOC) and binary (Kb) size by around 1 percent,
                 respectively. Further, we present the results of a user
                 study with 30 participants which shows that IntRepair
                 repairs are more than 10x efficient as compared to
                 manually generated code repairs.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Software Engineering",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=32",
  keywords =     "integer overflow detection and repair",
}

@InProceedings{Murillo:2021:EEM,
  author =       "Raul Murillo and David Mallasen and Alberto A. {Del
                 Barrio} and Guillermo Botella",
  editor =       "{IEEE}",
  booktitle =    "{2021 IEEE 39th International Conference on Computer
                 Design (ICCD): 24--27 October 2021, Storrs, CT, USA}",
  title =        "Energy-Efficient {MAC} Units for Fused Posit
                 Arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "138--145",
  month =        oct,
  year =         "2021",
  DOI =          "https://doi.org/10.1109/iccd53106.2021.00032",
  bibdate =      "Thu Dec 14 18:10:59 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Nambi:2021:EDE,
  author =       "Suresh Nambi and Salim Ullah and Siva Satyendra Sahoo
                 and Aditya Lohana and Farhad Merchant and Akash Kumar",
  title =        "{ExPAN(N)D}: Exploring Posits for Efficient Artificial
                 Neural Network Design in {FPGA}-Based Systems",
  journal =      j-IEEE-ACCESS,
  volume =       "9",
  pages =        "103691--103708",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ACCESS.2021.3098730",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "Computer arithmetic; deep neural networks; Delays;
                 Dynamic range; energy efficient computing; Field
                 programmable gate arrays; FPGA; Hardware; high-level
                 synthesis; Machine learning algorithms; Neural
                 networks; posits; Quantization (signal)",
}

@InProceedings{Nannarelli:2021:OCA,
  author =       "Alberto Nannarelli and Mioara Joldes and Fabrizio
                 Lamberti and Flemming Stassen and Daniele Jahier
                 Pagliari and Alberto Cannav{\`o}",
  title =        "Organizing Committee {ARITH 2021}",
  crossref =     "IEEE:2021:ISC",
  pages =        "xi--xi",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00006",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@Article{Nevarez:2021:ASS,
  author =       "Yarib Nevarez and David Rotermund and Klaus R.
                 Pawelzik and Alberto Garcia-Ortiz",
  title =        "Accelerating Spike-by-Spike Neural Networks on {FPGA}
                 With Hybrid Custom Floating-Point and Logarithmic
                 Dot-Product Approximation",
  journal =      j-IEEE-ACCESS,
  volume =       "9",
  pages =        "80603--80620",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ACCESS.2021.3085216",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Tue Sep 30 17:30:28 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "Approximate computing; approximate computing;
                 Artificial intelligence; Biological neural networks;
                 Computational modeling; Degradation; embedded systems;
                 FPGA; Hardware; hardware accelerator; logarithmic;
                 Neurons; optimization; parameterisable floating-point;
                 Quantization (signal); spiking neural networks",
}

@InProceedings{Norris:2021:AIP,
  author =       "Cameron James Norris and Sunwoong Kim",
  editor =       "{IEEE}",
  booktitle =    "{2021 IEEE International Symposium on Circuits and
                 Systems (ISCAS)}",
  title =        "An Approximate and Iterative Posit Multiplier
                 Architecture for {FPGAs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--5",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ISCAS51556.2021.9401158",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Parrot:2021:POU,
  author =       "R{\'e}mi Parrot and Mika{\"e}l Briday and Olivier H.
                 Roux",
  title =        "Pipeline Optimization using a Cost Extension of Timed
                 Petri Nets",
  crossref =     "IEEE:2021:ISC",
  pages =        "37--44",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00018",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@Article{Patankar:2021:RBC,
  author =       "Udayan S. Patankar and Ants Koel",
  title =        "Review of Basic Classes of Dividers Based on Division
                 Algorithm",
  journal =      j-IEEE-ACCESS,
  volume =       "9",
  pages =        "23035--23069",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/access.2021.3055735",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Thu Apr 10 15:08:12 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
}

@InProceedings{Peric:2021:FPF,
  author =       "Zoran Peric and Milan Savic and Milan Dincic and
                 Nikola Vucic and Danijel Djosic and Srdjan
                 Milosavljevic",
  booktitle =    "{2021 12th International Symposium on Advanced Topics
                 in Electrical Engineering (ATEE)}",
  title =        "Floating Point and Fixed Point 32-bits Quantizers for
                 Quantization of Weights of Neural Networks",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--4",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ATEE52255.2021.9425265",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Artificial neural networks; Electrical engineering;
                 Fixed Floating Point data representation; IEEE
                 Standards; Laplace equations; Quantization (signal);
                 Quantization of weights of Neural networks; Standards;
                 Uniform and Piecewise Uniform Quantization",
}

@InProceedings{Pisha:2021:ANP,
  author =       "Louis Pisha and ukasz Ligowski",
  booktitle =    "{2021 IEEE International Parallel and Distributed
                 Processing Symposium (IPDPS)}",
  title =        "Accelerating non-power-of-2 size {Fourier} transforms
                 with {GPU} {Tensor Cores}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "507--516",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/IPDPS49936.2021.00059",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "accelerated matrix multiply hardware; Discrete Fourier
                 transforms; Distributed processing; emergent
                 floating-point formats; Fast Fourier transforms; fast
                 Fourier transforms; Graphics processing units;
                 Libraries; mixed-precision arithmetic; parallel
                 algorithms; Tensors; Throughput; {Tensor Cores}",
}

@Article{Plantard:2021:EWSa,
  author =       "Thomas Plantard",
  title =        "Efficient Word Size Modular Arithmetic",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "9",
  number =       "3",
  pages =        "1506--1518",
  month =        jul # "\slash " # sep,
  year =         "2021",
  DOI =          "https://doi.org/10.1109/TETC.2021.3073475",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  note =         "See \cite{Plantard:2021:EWSb}.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
  keywords =     "ARITH 2021; ARITH-28",
}

@InProceedings{Plantard:2021:EWSb,
  author =       "Thomas Plantard",
  title =        "Efficient Word Size Modular Arithmetic",
  crossref =     "IEEE:2021:ISC",
  pages =        "139--139",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00036",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Plantard:2021:EWSa}.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
  remark =       "Published in IEEE Transactions on Emerging Topics in
                 Computing, Volume: 9, Issue: 3, July--September 2021,
                 and orally presented at ARITH 2021.",
}

@InProceedings{Rao:2021:PND,
  author =       "Dhage Navaneet Rao and Ganne Sai Charan and Degala
                 Veera Venkata Sairam and Kamatchi S.",
  booktitle =    "{2021 International Conference on Advances in
                 Electrical, Computing, Communication and Sustainable
                 Technologies (ICAECT)}",
  title =        "Posit Number Division using {Newton--Raphson} method",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--6",
  month =        feb,
  year =         "2021",
  DOI =          "https://doi.org/10.1109/icaect49130.2021.9392582",
  bibdate =      "Fri Dec 15 06:57:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{RAos:2021:DAF,
  author =       "John Osorio R{\'\i}os and Adri{\`a} Armejach and Eric
                 Petit and Greg Henry and Marc Casas",
  booktitle =    "{2021 20th IEEE International Conference on Machine
                 Learning and Applications (ICMLA)}",
  title =        "Dynamically Adapting Floating-Point Precision to
                 Accelerate Deep Neural Network Training",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "980--987",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ICMLA52953.2021.00161",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "bfloat16; Binary Analysis Tool; Deep learning; Dynamic
                 Precision.; Mixed Precision (MP); Neural networks;
                 Numerical models; Performance evaluation; Reduced
                 Precision; Registers; Switches; Training",
}

@InProceedings{Raposo:2021:PTD,
  author =       "Gon{\c{c}}alo Raposo and Pedro Tom{\'a}s and Nuno
                 Roma",
  editor =       "{IEEE}",
  booktitle =    "{ICASSP 2021 - 2021 IEEE International Conference on
                 Acoustics, Speech and Signal Processing (ICASSP)}",
  title =        "Positnn: Training Deep Neural Networks with Mixed
                 Low-Precision Posit",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "7908--7912",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ICASSP39728.2021.9413919",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Reichenbach:2021:RVR,
  author =       "Marc Reichenbach and Johannes Kn{\"o}dtel and
                 Sebastian Rachuj and Dietmar Fey",
  title =        "{RISC-V3}: a {RISC-V} Compatible {CPU} With a Data
                 Path Based on Redundant Number Systems",
  journal =      j-IEEE-ACCESS,
  volume =       "9",
  pages =        "43684--43700",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ACCESS.2021.3063238",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Sat Dec 16 15:51:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
}

@InProceedings{Revy:2021:AIF,
  author =       "Guillaume Revy",
  title =        "Analyzing the impact of floating-point precision
                 adaptation in iterative programs",
  crossref =     "IEEE:2021:ISC",
  pages =        "25--32",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00016",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@Book{Rodriguez:2021:DLS,
  author =       "Andres Rodriguez",
  title =        "Deep Learning Systems: Algorithms, Compilers, and
                 Processors for Large-Scale Production",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  year =         "2021",
  DOI =          "https://doi.org/10.1007/978-3-031-01769-8",
  ISBN =         "3-031-01769-2",
  ISBN-13 =      "978-3-031-01769-8",
  ISSN =         "1935-3243",
  ISSN-L =       "1935-3235",
  bibdate =      "Fri Dec 15 11:31:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Synthesis Lectures on Computer Architecture",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@Article{Romanov:2021:APB,
  author =       "Aleksandr Yu. Romanov and Alexander L. Stempkovsky and
                 Ilia V. Lariushkin and Georgy E. Novoselov and Roman A.
                 Solovyev and Vladimir A. Starykh and Irina I. Romanova
                 and Dmitry V. Telpukhov and Ilya A. Mkrtchan",
  title =        "Analysis of Posit and {Bfloat} Arithmetic of Real
                 Numbers for Machine Learning",
  journal =      j-IEEE-ACCESS,
  volume =       "9",
  pages =        "82318--82324",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ACCESS.2021.3086669",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "benchmark; floating point; Hardware; IEEE 754;
                 Libraries; Machine learning; Machine learning
                 algorithms; Memory management; posit; Software;
                 Standards",
}

@Article{Sahu:2021:DFP,
  author =       "Ajay Kumar Sahu and Vishnumurthy Kedlaya K. and
                 Subramanya G. Nayak",
  title =        "Development of Floating-Point {MAC} Engine for {2-D}
                 Convolution of Image",
  journal =      j-IEEE-ACCESS,
  volume =       "9",
  pages =        "138849--138857",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ACCESS.2021.3117335",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Tue Sep 30 17:30:28 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "2-D image convolution; Convolution; convolution
                 accelerator; Engines; Heuristic algorithms; Image
                 processing; increment by one; Kernel; low-power
                 multiplier; Parallel processing; Registers",
}

@InProceedings{Saiki:2021:CPT,
  author =       "Brett Saiki and Oliver Flatt and Chandrakana Nandi and
                 Pavel Panchekha and Zachary Tatlock",
  title =        "Combining Precision Tuning and Rewriting",
  crossref =     "IEEE:2021:ISC",
  pages =        "1--8",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00013",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@InProceedings{Saxena:2021:BOF,
  author =       "Vinay Saxena and Ankitha Reddy and Jonathan Neudorfer
                 and John Gustafson and Sangeeth Nambiar and Rainer
                 Leupers and Farhad Merchant",
  editor =       "{IEEE}",
  booktitle =    "{2021 22nd International Symposium on Quality
                 Electronic Design (ISQED)}",
  title =        "Brightening the Optical Flow through Posit
                 Arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "463--468",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ISQED51717.2021.9424360",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sergiyenko:2021:FIC,
  author =       "Anatoliy Sergiyenko and Leonid Moroz and Lesya Mychuda
                 and Volodymir Samotyj",
  booktitle =    "{2021 11th IEEE International Conference on
                 Intelligent Data Acquisition and Advanced Computing
                 Systems: Technology and Applications (IDAACS)}",
  title =        "{FPGA} Implementation of {CORDIC} Algorithms for Sine
                 and Cosine Floating-Point Calculations",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "383--386",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/IDAACS53288.2021.9660963",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Approximation algorithms; Conferences; CORDIC; Costs;
                 Data acquisition; Delays; floating-point; FPGA;
                 Function approximation; Hardware; sine function",
}

@InProceedings{Shah:2021:PWS,
  author =       "Nimish Shah and Laura Isabel Galindez Olascoaga and
                 Shirui Zhao and Wannes Meert and Marian Verhelst",
  editor =       "{IEEE}",
  booktitle =    "{2021 IEEE International Solid-State Circuits
                 Conference (ISSCC)}",
  title =        "{9.4 PIU}: a {248GOPS/W} Stream-Based Processor for
                 Irregular Probabilistic Inference Networks Using
                 Precision-Scalable Posit Arithmetic in 28nm",
  volume =       "64",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "150--152",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ISSCC42613.2021.9366061",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Shekhawat:2021:HGP,
  author =       "Diksha Shekhawat and Apoorva Jangir and Jai Gopal
                 Pandey",
  editor =       "{IEEE}",
  booktitle =    "{2021 25th International Symposium on VLSI Design and
                 Test (VDAT)}",
  title =        "A Hardware Generator for Posit Arithmetic and its
                 {FPGA} Prototyping",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--6",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/VDAT53777.2021.9601025",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Singha:2021:NAT,
  author =       "Satrughna Singha and Amitabha Sinha",
  title =        "A New Architecture for Transformation of Binary to
                 Double Base Number System ({DBNS}) with Bases 2 and 5
                 using Different Search Algorithms",
  journal =      "{IOP} Conference Series: Materials Science and
                 Engineering",
  volume =       "1084",
  number =       "1",
  pages =        "012057",
  month =        mar,
  year =         "2021",
  DOI =          "https://doi.org/10.1088/1757-899x/1084/1/012057",
  ISSN =         "1757-8981 (print), 1757-899X (electronic)",
  ISSN-L =       "1757-8981",
  bibdate =      "Tue Nov 11 13:50:41 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Misc{SmallPositHDL:2021:CBS,
  author =       "{SmallPositHDL}",
  title =        "Chisel-based {SmallPositHDL}",
  howpublished = "Web software",
  year =         "2021",
  bibdate =      "Sat Dec 16 15:23:17 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://github.com/starbrilliance/SmallPositHDL",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@Article{Sohier:2021:CIS,
  author =       "Devan Sohier and Pablo {De Oliveira Castro} and
                 Fran{\c{c}}ois F{\'e}votte and Bruno Lathuili{\`e}re
                 and Eric Petit and Olivier Jamond",
  title =        "Confidence Intervals for Stochastic Arithmetic",
  journal =      j-TOMS,
  volume =       "47",
  number =       "2",
  pages =        "10:1--10:33",
  month =        apr,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3432184",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 27 08:23:28 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3432184",
  abstract =     "Quantifying errors and losses due to the use of
                 Floating-point (FP) calculations in industrial
                 scientific computing codes is an important part of the
                 Verification, Validation, and Uncertainty
                 Quantification process. Stochastic Arithmetic is one
                 way to model and estimate FP losses of accuracy, which
                 scales well to large, industrial codes. It exists in
                 different flavors, such as CESTAC or MCA, implemented
                 in various tools such as CADNA, Verificarlo, or Verrou.
                 These methodologies and tools are based on the idea
                 that FP losses of accuracy can be modeled via
                 randomness. Therefore, they share the same need to
                 perform a statistical analysis of programs results to
                 estimate the significance of the results.\par

                 In this article, we propose a framework to perform a
                 solid statistical analysis of Stochastic Arithmetic.
                 This framework unifies all existing definitions of the
                 number of significant digits (CESTAC and MCA), and also
                 proposes a new quantity of interest: the number of
                 digits contributing to the accuracy of the results.
                 Sound confidence intervals are provided for all
                 estimators, both in the case of normally distributed
                 results, and in the general case. The use of this
                 framework is demonstrated by two case studies of
                 industrial codes: Europlexus and code\aster.",
  acknowledgement = ack-nhfb,
  articleno =    "10",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Soylu:2021:IAC,
  author =       "G{\"u}ltekin Soylu",
  title =        "Improved Arithmetic of Complex Fans",
  journal =      j-TOMS,
  volume =       "47",
  number =       "2",
  pages =        "11:1--11:10",
  month =        apr,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3434400",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 27 08:23:28 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3434400",
  abstract =     "Complex fans are sets of complex numbers whose
                 magnitudes and angles range in closed intervals. The
                 fact that the sum of two fans is a disordered shape
                 gives rise to the need for computational methods to
                 find the minimal enclosing fan. Cases where the sum of
                 two fans contains the origin of the complex plane as a
                 boundary point are of special interest. The result of
                 the addition is then enclosed by circles in current
                 methods, but under certain circumstances this turns out
                 to be an overestimate. The focus of this article is the
                 diagnosis and treatment of such cases.",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Thapliyal:2021:QCD,
  author =       "Himanshu Thapliyal and Edgard Mu{\~n}oz-Coreas and T.
                 S. S. Varun and Travis S. Humble",
  title =        "Quantum Circuit Designs of Integer Division Optimizing
                 {T}-count and {T}-depth",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "9",
  number =       "2",
  pages =        "1045--1056",
  month =        apr # "\slash " # jun,
  year =         "2021",
  DOI =          "https://doi.org/10.1109/TETC.2019.2910870",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}

@Article{Tiwari:2021:PCP,
  author =       "Sugandha Tiwari and Neel Gala and Chester Rebeiro and
                 V. Kamakoti",
  title =        "{PERI}: a Configurable Posit Enabled {RISC-V} Core",
  journal =      j-TACO,
  volume =       "18",
  number =       "3",
  pages =        "25:1--25:26",
  month =        jun,
  year =         "2021",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3446210",
  ISSN =         "1544-3566 (print), 1544-3973 (electronic)",
  ISSN-L =       "1544-3566",
  bibdate =      "Tue Jun 29 08:21:11 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib;
                 https://www.math.utah.edu/pub/tex/bib/taco.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3446210",
  abstract =     "Owing to the failure of Dennard's scaling, the past
                 decade has seen a steep growth of prominent new
                 paradigms leveraging opportunities in computer
                 architecture. Two technologies of interest are Posit
                 and RISC-V. Posit was introduced in mid-2017 as a
                 \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "25",
  fjournal =     "ACM Transactions on Architecture and Code Optimization
                 (TACO)",
  journal-URL =  "https://dl.acm.org/loi/taco",
}

@Article{Ullah:2021:AOA,
  author =       "S. Ullah and H. Schmidl and S. S. Sahoo and S. Rehman
                 and A. Kumar",
  title =        "Area-Optimized Accurate and Approximate Softcore
                 Signed Multiplier Architectures",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "70",
  number =       "3",
  pages =        "384--392",
  year =         "2021",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2020.2988404",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Feb 23 12:51:19 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Valueva:2021:DFA,
  author =       "Maria Valueva and Pavel Lyakhov and Georgii Valuev and
                 Nikolay Nagornov",
  title =        "Digital Filter Architecture With Calculations in the
                 Residue Number System by {Winograd} Method {$ F(2
                 \times 2, 2 \times 2) $}",
  journal =      j-IEEE-ACCESS,
  volume =       "9",
  pages =        "143331--143340",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ACCESS.2021.3121520",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Wed Oct 1 06:08:36 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "Computer architecture; Digital filters; Field
                 programmable gate arrays; Filtering; Filtering
                 algorithms; Hardware; Performance evaluation; residue
                 number system; Winograd method",
}

@Article{VanZee:2021:SMD,
  author =       "Field G. {Van Zee} and Devangi N. Parikh and Robert A.
                 {Van De Geijn}",
  title =        "Supporting Mixed-domain Mixed-precision Matrix
                 Multiplication within the {BLIS} Framework",
  journal =      j-TOMS,
  volume =       "47",
  number =       "2",
  pages =        "12:1--12:26",
  month =        apr,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3402225",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 27 08:23:28 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3402225",
  abstract =     "We approach the problem of implementing mixed-datatype
                 support within the general matrix multiplication (gemm)
                 operation of the BLAS-like Library Instantiation
                 Software framework, whereby each matrix operand A, B,
                 and C may be stored as single- or double-precision real
                 or complex values. Another factor of complexity,
                 whereby the matrix product and accumulation are allowed
                 to take place in a precision different from the storage
                 precisions of either A or B, is also discussed. We
                 first break the problem into orthogonal dimensions,
                 considering the mixing of domains separately from
                 mixing precisions. Support for all combinations of
                 matrix operands stored in either the real or complex
                 domain is mapped out by enumerating the cases and
                 describing an implementation approach for each.
                 Supporting all combinations of storage and computation
                 precisions is handled by typecasting the matrices at
                 key stages of the computation --- during packing and/or
                 accumulation, as needed. Several optional optimizations
                 are also documented. Performance results gathered on a
                 56-core Marvell ThunderX2 and a 52-core Intel Xeon
                 Platinum demonstrate that high performance is mostly
                 preserved, with modest slowdowns incurred from
                 unavoidable typecast instructions. The mixed-datatype
                 implementation confirms that combinatorial
                 intractability is avoided, with the framework relying
                 on only two assembly microkernels to implement 128
                 datatype combinations.",
  acknowledgement = ack-nhfb,
  articleno =    "12",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@InProceedings{Venkataramani:2021:RAA,
  author =       "Swagath Venkataramani and Vijayalakshmi Srinivasan and
                 Wei Wang and Sanchari Sen and Jintao Zhang and Ankur
                 Agrawal and Monodeep Kar and Shubham Jain and Alberto
                 Mannari and Hoang Tran and Yulong Li and Eri Ogawa and
                 Kazuaki Ishizaki and Hiroshi Inoue and Marcel Schaal
                 and Mauricio Serrano and Jungwook Choi and Xiao Sun and
                 Naigang Wang and Chia-Yu Chen and Allison Allain and
                 James Bonano and Nianzheng Cao and Robert Casatuta and
                 Matthew Cohen and Bruce Fleischer and Michael Guillorn
                 and Howard Haynie and Jinwook Jung and Mingu Kang and
                 Kyu-hyoun Kim and Siyu Koswatta and Saekyu Lee and
                 Martin Lutz and Silvia Mueller and Jinwook Oh and
                 Ashish Ranjan and Zhibin Ren and Scot Rider and Kerstin
                 Schelm and Michael Scheuermann and Joel Silberman and
                 Jie Yang and Vidhi Zalani and Xin Zhang and Ching Zhou
                 and Matt Ziegler and Vinay Shah and Moriyoshi Ohara and
                 Pong-Fei Lu and Brian Curran and Sunil Shukla and
                 Leland Chang and Kailash Gopalakrishnan",
  booktitle =    "{2021 ACM/IEEE 48th Annual International Symposium on
                 Computer Architecture (ISCA)}",
  title =        "{RaPiD}: {AI} Accelerator for Ultra-low Precision
                 Training and Inference",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "153--166",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ISCA52012.2021.00021",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "AI accelerators; Computer architecture; Deep Neural
                 Networks; Hardware Acceleration; Inference algorithms;
                 Reduced Precision; Semiconductor device measurement;
                 Silicon; Training; Transformer cores",
}

@Article{Vestias:2021:DMF,
  author =       "M{\'a}rio P. V{\'e}stias and Hor{\'a}cio C. Neto",
  title =        "Decimal Multiplication in {FPGA} with a Novel Decimal
                 Adder\slash Subtractor",
  journal =      j-ALGORITHMS-BASEL,
  volume =       "14",
  number =       "7",
  month =        jul,
  year =         "2021",
  CODEN =        "ALGOCH",
  DOI =          "https://doi.org/10.3390/a14070198",
  ISSN =         "1999-4893 (electronic)",
  ISSN-L =       "1999-4893",
  bibdate =      "Fri Jul 23 15:05:28 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/algorithms.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.mdpi.com/1999-4893/14/7/198",
  acknowledgement = ack-nhfb,
  articleno =    "198",
  fjournal =     "Algorithms (Basel)",
  journal-URL =  "https://www.mdpi.com/journal/algorithms",
  pagecount =    "??",
}

@Article{Walczyk:2021:IAF,
  author =       "Cezary J. Walczyk and Leonid V. Moroz and Jan L.
                 Cie{\'s}li{\'n}ski",
  title =        "Improving the Accuracy of the Fast Inverse Square Root
                 by Modifying {Newton--Raphson} Corrections",
  journal =      j-ENTROPY,
  volume =       "23",
  number =       "1",
  pages =        "86:1--86:20",
  month =        jan,
  year =         "2021",
  CODEN =        "ENTRFG",
  DOI =          "https://doi.org/10.3390/e23010086",
  ISSN =         "1099-4300",
  ISSN-L =       "1099-4300",
  bibdate =      "Wed Dec 20 07:52:39 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Entropy",
  journal-URL =  "https://www.mdpi.com/journal/entropy/",
}

@InProceedings{Wang:2021:LLP,
  author =       "Yang Wang and Dazheng Deng and Leibo Liu and Shaojun
                 Wei and Shouyi Yin",
  editor =       "{IEEE}",
  booktitle =    "{2021 IEEE 3rd International Conference on Artificial
                 Intelligence Circuits and Systems (AICAS)}",
  title =        "{LPE}: Logarithm Posit Processing Element for
                 Energy-Efficient Edge-Device Training",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--4",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/AICAS51828.2021.9458421",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Misc{Ward-Foxton:2021:BBT,
  author =       "Sally Ward-Foxton",
  title =        "Bringing 8-Bit Training Breakthroughs to {AI}
                 Hardware",
  howpublished = "EET Asia Web site",
  day =          "2",
  month =        mar,
  year =         "2021",
  bibdate =      "Wed May 19 12:05:25 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.eetasia.com/bringing-8-bit-training-breakthroughs-to-ai-hardware/",
  acknowledgement = ack-nhfb,
  keywords =     "FP8",
}

@InProceedings{Wong:2021:LBC,
  author =       "Yuk Wong and Zhenjiang Dong and Wei Zhang",
  booktitle =    "{2021 IEEE Computer Society Annual Symposium on VLSI
                 (ISVLSI)}",
  title =        "Low Bitwidth {CNN} Accelerator on {FPGA} Using
                 {Winograd} and Block Floating Point Arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "218--223",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ISVLSI51109.2021.00048",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Block floating point (BFP); Convolutional neural
                 network (CNN); Convolutional neural networks; Field
                 programmable gate array (FPGA); Filtering algorithms;
                 Hardware Accelerator; Quantization (signal); Registers;
                 Table lookup; Training; Very large scale integration;
                 Winograd",
}

@InProceedings{Wu:2021:DCH,
  author =       "Chai Wah Wu",
  title =        "Dither computing: a hybrid deterministic-stochastic
                 computing framework",
  crossref =     "IEEE:2021:ISC",
  pages =        "70--77",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021.00025",
  bibdate =      "Thu Sep 21 10:36:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
}

@Article{Xia:2021:EDA,
  author =       "Yuanyuan Xia and Shaozhong Guo and Jinchen Xu",
  title =        "Error detection of arithmetic expressions",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "77",
  number =       "6",
  pages =        "5492--5509",
  month =        jun,
  year =         "2021",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1007/s11227-020-03469-7",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Fri May 14 09:20:01 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsuper2020.bib",
  URL =          "https://link.springer.com/article/10.1007/s11227-020-03469-7",
  abstract =     "Inspecting floating-point errors is essential to
                 floating-point operations. In this paper, we present
                 floating-point error detector (FPED), an inspector of
                 floating-point errors for arithmetic expressions. FPED
                 can pick a suitable benchmark generation approach by
                 analyzing the distribution of the expression of a
                 floating-point operation, thereby minimizing the
                 possibilities of underreporting floating-point errors.
                 FPED is also able to determine the significant sources
                 of errors in a floating-point operation according to
                 the frequencies of computation building blocks that
                 contribute most to the floating-point errors,
                 benefiting the follow-up optimizations of computation
                 accuracies. We validate the correctness and
                 functionalities of FPED by conducting experiments on
                 the FPBench benchmark suite. The experimental results
                 demonstrate that FPED can obtain more accurate
                 detection results than the random detecting approach
                 with respect to floating-point error detection. We also
                 compare FPED with the existing dynamic error detection
                 tools. The experimental results show that in most of
                 the 33 test benchmarks, the maximum error results of
                 FPED are greater than Herbgrind and the detection
                 performance is higher than Herbgrind.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Supercomputing",
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
  online-date =  "Published: 09 November 2020 Pages: 5492--5509",
}

@Article{Xiang:2021:MNP,
  author =       "Yiyao Xiang and Lei Li and Shiwei Yuan and Wanting
                 Zhou and Benqing Guo",
  title =        "Metrics, Noise Propagation Models, and Design
                 Framework for Floating-Point Approximate Computing",
  journal =      j-IEEE-ACCESS,
  volume =       "9",
  pages =        "71039--71052",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ACCESS.2021.3053578",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Tue Sep 30 17:30:28 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "Adders; Approximate computing; Approximation
                 algorithms; Computational modeling; efficient bit
                 width; floating-point; Image edge detection; Logic
                 gates; mantissa; Measurement; noise propagation models;
                 truncation",
}

@InProceedings{Xu:2021:LCA,
  author =       "Jin Xu and Lin Jiang and Hui Chen and Yuxiang Fu and
                 Li Li",
  booktitle =    "{2021 18th International SoC Design Conference
                 (ISOCC)}",
  title =        "A Low-Complexity Architecture for Implementing Square
                 to Tenth Root of Complex Numbers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "15--16",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ISOCC53507.2021.9613873",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "complex number Nth root; Complexity theory; Computer
                 architecture; Convergence; CORDIC; Digital computers;
                 Hardware; high efficiency; high precision; low hardware
                 complexity; Power demand; Quantization (signal)",
}

@InProceedings{Yamaguchi:2021:TDN,
  author =       "Hisakatsu Yamaguchi and Makiko Ito and Katsuhiro Yoda
                 and Atsushi Ike",
  booktitle =    "{2021 Design, Automation \& Test in Europe Conference
                 \& Exhibition (DATE)}",
  title =        "Training Deep Neural Networks in 8-bit Fixed Point
                 with Dynamic Shared Exponent Management",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1536--1541",
  year =         "2021",
  DOI =          "https://doi.org/10.23919/DATE51398.2021.9473997",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Degradation; Hardware; Neural networks; Quantization
                 (signal); Tensors; Throughput; Training",
}

@Article{Yang:2021:AAE,
  author =       "Yuheng Yang and Qing Yuan and Jian Liu",
  title =        "An Architecture of Area-Effective High Radix
                 Floating-Point Divider With Low-Power Consumption",
  journal =      j-IEEE-ACCESS,
  volume =       "9",
  pages =        "40039--40048",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ACCESS.2021.3065063",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Tue Sep 30 17:30:28 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "Approximation algorithms; division; Estimation;
                 Heuristic algorithms; High-radix; Power demand;
                 quotient-digits-selection; Registers; SRT; Standards",
}

@Article{Zaruba:2021:MCR,
  author =       "Florian Zaruba and Fabian Schuiki and Luca Benini",
  title =        "{Manticore}: A 4096-Core {RISC-V} Chiplet Architecture
                 for Ultraefficient Floating-Point Computing",
  journal =      j-IEEE-MICRO,
  volume =       "41",
  number =       "2",
  pages =        "36--42",
  month =        mar # "\slash " # apr,
  year =         "2021",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.2020.3045564",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Sat Dec 16 15:51:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/hot-chips.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeemicro.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=40",
}

@Article{Zaruba:2021:STP,
  author =       "Florian Zaruba and Fabian Schuiki and Torsten Hoefler
                 and Luca Benini",
  title =        "{Snitch}: A Tiny Pseudo Dual-Issue Processor for Area
                 and Energy Efficient Execution of Floating-Point
                 Intensive Workloads",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "70",
  number =       "11",
  pages =        "1845--1860",
  month =        nov,
  year =         "2021",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2020.3027900",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Oct 14 10:04:00 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Zhang:2021:EMP,
  author =       "Hao Zhang and Seok-Bum Ko",
  editor =       "{IEEE}",
  booktitle =    "{2021 IEEE International Symposium on Circuits and
                 Systems (ISCAS)}",
  title =        "Efficient Multiple-Precision Posit Multiplier",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--5",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ISCAS51556.2021.9401213",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Zhu:2021:PBP,
  author =       "Yongwen Zhu",
  title =        "The Plum-Blossom Product Method of Large Digit
                 Multiplication and Its Application to Computer
                 Science",
  journal =      j-INT-J-COMP-APPL,
  volume =       "183",
  number =       "??",
  pages =        "17--23",
  month =        dec,
  year =         "2021",
  CODEN =        "????",
  DOI =          "https://doi.org/10.5120/ijca2021921805",
  ISSN =         "0975-8887",
  ISSN-L =       "0975-8887",
  bibdate =      "Fri Jan 24 09:46:40 MST 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/intjcompappl.bib",
  URL =          "https://www.ijcaonline.org/archives/volume183/number41/32202-2021921805/",
  acknowledgement = ack-nhfb,
  ajournal =     "Intern. J. of Computer Applications",
  articleno =    "41",
  fjournal =     "International Journal of Computer Applications",
  journal-URL =  "https://www.ijcaonline.org/",
}

@Article{Ziols:2021:HPB,
  author =       "Ryan Ziols and Kathryn L. Kirchgasler",
  title =        "Health and pathology: a brief history of the
                 biopolitics of {US} mathematics education",
  journal =      j-EDUC-STUD-MATH,
  volume =       "108",
  number =       "1--2",
  pages =        "123--142",
  month =        oct,
  year =         "2021",
  CODEN =        "EDSMAN",
  DOI =          "https://doi.org/10.1007/s10649-021-10110-8",
  ISSN =         "1573-0816",
  ISSN-L =       "0013-1954",
  bibdate =      "Fri Dec 15 11:31:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Educational Studies in Mathematics",
  journal-URL =  "http://link.springer.com/journal/10649",
  keywords =     "posit arithmetic",
}

@Article{Zlatopolski:2021:MES,
  author =       "Dmitry M. Zlatopolski",
  title =        "Method for extracting square and cubic roots in the
                 binary number system. ({Russian})",
  journal =      "Inform. School",
  volume =       "1",
  number =       "??",
  pages =        "42--45",
  month =        "????",
  year =         "2021",
  DOI =          "https://doi.org/10.32517/2221-1993-2021-1-42-45",
  bibdate =      "Fri Mar 17 09:03:18 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
  remark =       "DOI does not resolve; cited as final reference in
                 \cite{Zlatopolski:2023:PAV}.",
}

@Article{Abdulah:2022:AGM,
  author =       "Sameh Abdulah and Qinglei Cao and Yu Pei and George
                 Bosilca and Jack Dongarra and Marc G. Genton and David
                 E. Keyes and Hatem Ltaief and Ying Sun",
  title =        "Accelerating Geostatistical Modeling and Prediction
                 With Mixed-Precision Computations: a High-Productivity
                 Approach With {PaRSEC}",
  journal =      j-IEEE-TRANS-PAR-DIST-SYS,
  volume =       "33",
  number =       "4",
  pages =        "964--976",
  year =         "2022",
  CODEN =        "ITDSEO",
  DOI =          "https://doi.org/10.1109/TPDS.2021.3084071",
  ISSN =         "1045-9219 (print), 1558-2183 (electronic)",
  ISSN-L =       "1045-9219",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Parallel Distrib. Syst.",
  fjournal =     "IEEE Transactions on Parallel and Distributed
                 Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=71",
  keywords =     "Climate/weather prediction; Computational modeling;
                 Covariance matrices; Data models; dynamic runtime
                 systems; geospatial statistics; high performance
                 computing; Maximum likelihood estimation; multiple
                 precisions; Predictive models; Runtime; Task analysis;
                 user-productivity",
}

@Article{Ahmadinejad:2022:EQE,
  author =       "Mohammad Ahmadinejad and Mohammad Hossein Moaiyeri",
  title =        "Energy- and Quality-Efficient Approximate Multipliers
                 for Neural Network and Image Processing Applications",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "10",
  number =       "2",
  pages =        "1105--1116",
  month =        apr # "\slash " # jun,
  year =         "2022",
  DOI =          "https://doi.org/10.1109/TETC.2021.3072666",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  abstract =     "Approximate computing is a new trend that trades off
                 computational accuracy for lower energy dissipation and
                 design complexity in various applications, where high
                 precision is not a critical need. In this paper,
                 energy- and quality- efficient approximate multipliers
                 based on new approximate compressors are proposed. We
                 use NAND gates for generating the complemented partial
                 products, which reduces the number of transistors.
                 Furthermore, new approximate compressors with different
                 accuracy and performance characteristics are designed.
                 Accordingly, three hybrid approximate multipliers
                 offering different trade-offs between accuracy and
                 hardware efficiency are proposed. The proposed designs
                 are simulated using HSPICE with the 7nm FinFET model as
                 a modern technology. Furthermore, the efficacies of the
                 approximate multipliers in the neural network and image
                 processing applications are evaluated using MATLAB.
                 According to the results, the proposed designs provide
                 far better compromises between the quality and energy
                 metrics in comparison with the previous designs and can
                 be considered as efficient alternatives for the exact
                 multipliers in neural network and image processing
                 applications.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}

@Article{Ahmadpour:2022:BMM,
  author =       "Zabihollah Ahmadpour and Ghassem Jaberipur",
  title =        "Up to $ 8 k $-bit Modular {Montgomery} Multiplication
                 in Residue Number Systems With Fast 16-bit Residue
                 Channels",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "71",
  number =       "6",
  pages =        "1399--1410",
  month =        jun,
  year =         "2022",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2021.3086071",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed May 25 09:41:19 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Alder:2022:FPU,
  author =       "Fritz Alder and Jo {Van Bulck} and Jesse Spielman and
                 David Oswald and Frank Piessens",
  title =        "Faulty Point Unit: {ABI} Poisoning Attacks on Trusted
                 Execution Environments",
  journal =      j-DTRAP,
  volume =       "3",
  number =       "2",
  pages =        "13:1--13:26",
  month =        jun,
  year =         "2022",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3491264",
  ISSN =         "2692-1626 (print), 2576-5337 (electronic)",
  ISSN-L =       "2576-5337",
  bibdate =      "Sat Jul 30 07:34:14 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/dtrap.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3491264",
  abstract =     "This article analyzes a previously overlooked attack
                 surface that allows unprivileged adversaries to impact
                 floating-point computations in enclaves through the
                 Application Binary Interface (ABI). In a comprehensive
                 study across 7 industry-standard and esearch enclave
                 shielding runtimes for Intel Software Guard Extensions
                 (SGX), we show that control and state registers of the
                 x87 Floating-Point Unit (FPU) and Intel Streaming SIMD
                 Extensions are not always properly sanitized on enclave
                 entry. We furthermore show that this attack goes beyond
                 the x86 architecture and can also affect RISC-V
                 enclaves. Focusing on SGX, we abuse the adversary's
                 control over precision and rounding modes as an ABI
                 fault injection primitive to corrupt enclaved
                 floating-point operations. Our analysis reveals that
                 this is especially relevant for applications that use
                 the older x87 FPU, which is still under certain
                 conditions used by modern compilers. We exemplify the
                 potential impact of ABI quality-degradation attacks for
                 enclaved machine learning and for the SPEC benchmarks.
                 We then explore the impact on confidentiality, showing
                 that control over exception masks can be abused as a
                 controlled channel to recover enclaved multiplication
                 operands. Our findings, affecting 5 of 7 studied SGX
                 runtimes and one RISC-V runtime, demonstrate the
                 challenges of implementing high-assurance trusted
                 execution across computing architectures.",
  acknowledgement = ack-nhfb,
  articleno =    "13",
  fjournal =     "Digital Threats: Research and Practice (DTRAP)",
  journal-URL =  "https://dl.acm.org/loi/dtrap",
}

@Misc{AMD:2022:AIM,
  author =       "{AMD Corporation}",
  title =        "{``AMD Instinct MI200''} Instruction Set Architecture
                 Reference Guide",
  howpublished = "Web document",
  pages =        "viii + 267",
  day =          "4",
  month =        feb,
  year =         "2022",
  bibdate =      "Fri Dec 01 14:05:58 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.amd.com/content/dam/amd/en/documents/instinct-tech-docs/instruction-set-architectures/instinct-mi200-cdna2-instruction-set-architecture.pdf",
  acknowledgement = ack-nhfb,
  remark =       "This document describes the AMD GPUs in the
                 ``Instinct'' product line, which replaces the earlier
                 FirePro and Radeon products. The new CPUs support 8-,
                 16-, 32-, and 64-bit signed and unsigned integers, the
                 binary32 and binary64 IEEE 754 floating-point formats,
                 and the BF16 (Bfloat16) 16-bit floating-point values.
                 However, it appears that fused multiply-add is only
                 supported in the vector instruction set.",
}

@InProceedings{Anonymous:2022:AI,
  author =       "Anonymous",
  title =        "Author Index",
  crossref =     "IEEE:2022:ISC",
  pages =        "133--134",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00033",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
}

@InProceedings{Anonymous:2022:C,
  author =       "Anonymous",
  title =        "Copyright",
  crossref =     "IEEE:2022:ISC",
  pages =        "1--1",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00003",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
}

@InProceedings{Anonymous:2022:PCA,
  author =       "Anonymous",
  title =        "Program Committee: {ARITH 2022}",
  crossref =     "IEEE:2022:ISC",
  pages =        "ix--ix",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00007",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
}

@InProceedings{Anonymous:2022:SA,
  author =       "Anonymous",
  title =        "Sponsors: {ARITH 2022}",
  crossref =     "IEEE:2022:ISC",
  pages =        "xi--xi",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00009",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
}

@InProceedings{Anonymous:2022:SCA,
  author =       "Anonymous",
  title =        "Steering Committee: {ARITH 2022}",
  crossref =     "IEEE:2022:ISC",
  pages =        "x--x",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00008",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
}

@InProceedings{Anonymous:2022:TC,
  author =       "Anonymous",
  title =        "Table of Contents",
  crossref =     "IEEE:2022:ISC",
  pages =        "iv--vi",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00004",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
}

@InProceedings{Anonymous:2022:TP,
  author =       "Anonymous",
  title =        "Title Page {I}",
  crossref =     "IEEE:2022:ISC",
  pages =        "1--1",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00001",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
}

@InProceedings{Anonymous:2022:TPI,
  author =       "Anonymous",
  title =        "Title Page {III}",
  crossref =     "IEEE:2022:ISC",
  pages =        "1--1",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00002",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
}

@InProceedings{Aoki:2022:EWS,
  author =       "Daichi Aoki and Kazuhiko Minematsu and Toshihiko
                 Okamura and Tsuyoshi Takagi",
  title =        "Efficient Word Size Modular Multiplication over Signed
                 Integers",
  crossref =     "IEEE:2022:ISC",
  pages =        "94--101",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00026",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
}

@InProceedings{Arnold:2022:TQL,
  author =       "Mark G. Arnold",
  title =        "Towards Quantum Logarithm Number Systems",
  crossref =     "IEEE:2022:ISC",
  pages =        "76--83",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00022",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
}

@InProceedings{Bajard:2022:GVL,
  author =       "Jean-Claude Bajard and Kazuhide Fukushima and Thomas
                 Plantard and Arnaud Sipasseuth",
  title =        "Generating Very Large {RNS} Bases",
  crossref =     "IEEE:2022:ISC",
  pages =        "102--102",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00027",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29; Residue Number System (RNS)",
}

@InProceedings{Barthel:2022:TIO,
  author =       "Moritz B{\"a}rthel and Nils H{\"u}lsmeier and Jochen
                 Rust and Steffen Paul",
  title =        "On the Implementation of Edge Detection Algorithms
                 with {SORN} Arithmetic",
  crossref =     "Gustafson:2022:NGA",
  pages =        "1--13",
  year =         "2022",
  DOI =          "https://doi.org/10.1007/978-3-031-09779-9_1",
  bibdate =      "Fri Dec 15 07:04:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic; Sets-Of-Real-Numbers (SORN)
                 arithmetic",
}

@InProceedings{Benmouhoub:2022:ESA,
  author =       "Farah Benmouhoub and Pierre-Loic Garoche and Matthieu
                 Martel",
  booktitle =    "Software Verification: {13th International Conference,
                 VSTTE 2021, New Haven, CT, USA, October 18--19, 2021,
                 and 14th International Workshop, NSV 2021, Los Angeles,
                 CA, USA, July 18--19, 2021}",
  title =        "An Efficient Summation Algorithm for the Accuracy,
                 Convergence and Reproducibility of Parallel Numerical
                 Methods",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "165--181",
  year =         "2022",
  DOI =          "https://doi.org/10.1007/978-3-030-95561-8_10",
  ISBN =         "3-030-95561-3",
  ISBN-13 =      "978-3-030-95561-8",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Dec 9 08:51:02 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Nowadays, parallel computing is ubiquitous in several
                 application fields, both in engineering and science.
                 The computations rely on the floating-point arithmetic
                 specified by the IEEE 754 Standard. In this context, an
                 elementary brick of computation, used everywhere, is
                 the sum of a sequence of numbers. This sum is subject
                 to many numerical errors in floating-point arithmetic.
                 To alleviate this issue, we have introduced a new
                 parallel algorithm for summing a sequence of
                 floating-point numbers. This algorithm which scales up
                 easily with the number of processors, adds numbers of
                 the same exponents first. In this article, our main
                 contribution is an extensive analysis of its efficiency
                 with respect to several properties: accuracy,
                 convergence and reproducibility. In order to show the
                 usefulness of our algorithm, we have chosen a set of
                 representative numerical methods which are Simpson,
                 Jacobi, LU factorization and the Iterated power
                 method.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation; floating-point
                 arithmetic",
}

@InProceedings{BenSalem-Knapp:2022:BRE,
  author =       "Louise {Ben Salem-Knapp} and Sylvie Boldo and William
                 Weens",
  title =        "Bounding the Round-Off Error of the Upwind Scheme for
                 Advection",
  crossref =     "IEEE:2022:ISC",
  pages =        "127--127",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00031",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
}

@InProceedings{Bertaccini:2022:MNE,
  author =       "Luca Bertaccini and Gianna Paulin and Tim Fischer and
                 Stefan Mach and Luca Benini",
  title =        "{MiniFloat-NN} and {ExSdotp}: an {ISA} Extension and a
                 Modular Open Hardware Unit for Low-Precision Training
                 on {RISC-V} Cores",
  crossref =     "IEEE:2022:ISC",
  pages =        "1--8",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00010",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29; Artificial neural networks; Digital
                 arithmetic; Dot Product; FinFETs; Floating Point Unit;
                 Hardware; Instruction sets; Low Precision NN Training;
                 Manycore Architectures; Memory management; RISC V;
                 Training",
}

@InProceedings{Borges:2022:HLA,
  author =       "Carlos F. Borges and Claude-Pierre Jeannerod and
                 Jean-Michel Muller",
  title =        "High-level algorithms for correctly-rounded reciprocal
                 square roots",
  crossref =     "IEEE:2022:ISC",
  pages =        "18--25",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00013",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29; correct rounding; floating-point
                 arithmetic",
}

@InProceedings{Bruguera:2022:LLH,
  author =       "Javier D. Bruguera",
  title =        "Low-Latency and High-Bandwidth Pipelined Radix-64
                 Division and Square Root Unit",
  crossref =     "IEEE:2022:ISC",
  pages =        "10--17",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00012",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
}

@Article{Buhrow:2022:PMM,
  author =       "Benjamin Buhrow and Barry Gilbert and Clifton Haider",
  title =        "Parallel modular multiplication using 512-bit advanced
                 vector instructions",
  journal =      j-J-CRYPTO-ENG,
  volume =       "12",
  number =       "1",
  pages =        "95--105",
  month =        apr,
  year =         "2022",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s13389-021-00256-9",
  ISSN =         "2190-8508 (print), 2190-8516 (electronic)",
  ISSN-L =       "2190-8508",
  bibdate =      "Sat Apr 16 13:18:32 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcryptoeng.bib",
  URL =          "https://link.springer.com/article/10.1007/s13389-021-00256-9",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Crypto. Eng.",
  fjournal =     "Journal of Cryptographic Engineering",
  journal-URL =  "http://link.springer.com/journal/13389",
}

@Article{Cardarilli:2022:DSE,
  author =       "Gian Carlo Cardarilli and Luca {Di Nunzio} and Rocco
                 Fazzolari and Alberto Nannarelli and Massimo Petricca
                 and Marco Re",
  title =        "Design Space Exploration Based Methodology for Residue
                 Number System Digital Filters Implementation",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "10",
  number =       "1",
  pages =        "186--198",
  month =        jan # "\slash " # mar,
  year =         "2022",
  DOI =          "https://doi.org/10.1109/TETC.2020.2997067",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}

@Article{Chen:2022:PPL,
  author =       "Chuangtao Chen and Weikang Qian and Mohsen Imani and
                 Xunzhao Yin and Cheng Zhuo",
  title =        "{PAM}: a Piecewise-Linearly-Approximated
                 Floating-Point Multiplier With Unbiasedness and
                 Configurability",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "71",
  number =       "10",
  pages =        "2473--2486",
  month =        oct,
  year =         "2022",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2021.3131850",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 8 07:59:47 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Choi:2022:HFL,
  author =       "Dahun Choi and Hyun Kim",
  booktitle =    "{2022 IEEE 4th International Conference on Artificial
                 Intelligence Circuits and Systems (AICAS)}",
  title =        "Hardware-Friendly Logarithmic Quantization with
                 Mixed-Precision for {MobileNetV2}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "348--351",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/AICAS54282.2022.9869994",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer vision; Convolutional Neural Network; Deep
                 learning; Degradation; Lightweight structures;
                 logarithmic quantization; MobileNetV2; Performance
                 evaluation; Power demand; Quantization (signal);
                 Training",
}

@InProceedings{Cococcioni:2022:ERO,
  author =       "Marco Cococcioni and Federico Rossi and Emanuele
                 Ruffaldi and Sergio Saponara",
  booktitle =    "Applications in Electronics Pervading Industry,
                 Environment and Society",
  title =        "Experimental Results of Vectorized Posit-Based {DNNs}
                 on a Real {ARM SVE} High Performance Computing
                 Machine",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "61--68",
  year =         "2022",
  DOI =          "https://doi.org/10.1007/978-3-030-95498-7_9",
  ISBN =         "3-030-95498-6",
  ISBN-13 =      "978-3-030-95498-7",
  ISSN =         "1876-1119",
  ISSN-L =       "1876-1100",
  bibdate =      "Fri Dec 15 11:31:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@Article{Cococcioni:2022:LPP,
  author =       "Marco Cococcioni and Federico Rossi and Emanuele
                 Ruffaldi and Sergio Saponara",
  title =        "A Lightweight Posit Processing Unit for {RISC-V}
                 Processors in Deep Neural Network Applications",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "10",
  number =       "4",
  pages =        "1898--1908",
  month =        oct # "\slash " # dec,
  year =         "2022",
  DOI =          "https://doi.org/10.1109/TETC.2021.3120538",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}

@InProceedings{Cococcioni:2022:SRR,
  author =       "Marco Cococcioni and Federico Rossi and Emanuele
                 Ruffaldi and Sergio Saponara",
  title =        "Small Reals Representations for Deep Learning at the
                 Edge: a Comparison",
  crossref =     "Gustafson:2022:NGA",
  pages =        "117--133",
  year =         "2022",
  DOI =          "https://doi.org/10.1007/978-3-031-09779-9_8",
  bibdate =      "Fri Dec 15 07:04:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@InProceedings{Coward:2022:ADO,
  author =       "Samuel Coward and George A. Constantinides and Theo
                 Drane",
  title =        "Automatic Datapath Optimization using E-Graphs",
  crossref =     "IEEE:2022:ISC",
  pages =        "43--50",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00016",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
}

@Misc{Cowlishaw:2022:DAFa,
  author =       "Mike Cowlishaw",
  title =        "Decimal Arithmetic {FAQ}: {Part} 1 --- General
                 Questions",
  howpublished = "Web site.",
  day =          "21",
  month =        apr,
  year =         "2022",
  bibdate =      "Mon Apr 25 17:12:00 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://speleotrove.com/decimal/decifaq1.html",
  acknowledgement = ack-nhfb,
  remark =       "Previous versions 2000, 2007.",
}

@Misc{Cowlishaw:2022:DAFb,
  author =       "Mike Cowlishaw",
  title =        "Decimal Arithmetic {FAQ}: {Part} 2 --- Definitions",
  howpublished = "Web site.",
  day =          "25",
  month =        apr,
  year =         "2022",
  bibdate =      "Mon Apr 25 17:12:00 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://speleotrove.com/decimal/decifaq2.html",
  acknowledgement = ack-nhfb,
  remark =       "Previous versions 2000, 2007.",
}

@Misc{Cowlishaw:2022:DAFc,
  author =       "Mike Cowlishaw",
  title =        "Decimal Arithmetic {FAQ}: {Part} 3 --- Hardware
                 Questions",
  howpublished = "Web site.",
  day =          "25",
  month =        apr,
  year =         "2022",
  bibdate =      "Mon Apr 25 17:12:00 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://speleotrove.com/decimal/decifaq3.html",
  acknowledgement = ack-nhfb,
  remark =       "Previous versions 2000, 2007.",
}

@Misc{Cowlishaw:2022:DAFd,
  author =       "Mike Cowlishaw",
  title =        "Decimal Arithmetic {FAQ}: {Part} 4 --- Arithmetic
                 Specification Questions",
  howpublished = "Web site.",
  day =          "25",
  month =        apr,
  year =         "2022",
  bibdate =      "Mon Apr 25 17:12:00 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://speleotrove.com/decimal/decifaq4.html",
  acknowledgement = ack-nhfb,
  remark =       "Previous versions 2000, 2007.",
}

@Misc{Cowlishaw:2022:DAFe,
  author =       "Mike Cowlishaw",
  title =        "Decimal Arithmetic {FAQ}: {Part} 5 --- Encoding
                 Questions",
  howpublished = "Web site.",
  day =          "25",
  month =        apr,
  year =         "2022",
  bibdate =      "Mon Apr 25 17:12:00 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://speleotrove.com/decimal/decifaq1.html",
  acknowledgement = ack-nhfb,
  remark =       "Previous versions 2000, 2007.",
}

@Misc{Cowlishaw:2022:DAFf,
  author =       "Mike Cowlishaw",
  title =        "Decimal Arithmetic {FAQ}: {Part} 5 --- Miscellaneous
                 Questions",
  howpublished = "Web site.",
  day =          "25",
  month =        apr,
  year =         "2022",
  bibdate =      "Mon Apr 25 17:12:00 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://speleotrove.com/decimal/decifaq6.html",
  acknowledgement = ack-nhfb,
  remark =       "Previous versions 2000, 2007.",
}

@Article{Crespo:2022:UPI,
  author =       "Lu{\'\i}s Crespo and Pedro Tom{\'a}s and Nuno Roma and
                 Nuno Neves",
  title =        "Unified Posit\slash {IEEE-754} Vector {MAC} Unit for
                 Transprecision Computing",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
  volume =       "69",
  number =       "5",
  pages =        "2478--2482",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/TCSII.2022.3160191",
  ISSN =         "1549-7747 (print), 1558-3791 (electronic)",
  ISSN-L =       "1549-7747",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems II: Express
                 Briefs",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
}

@InProceedings{deDinechin:2022:FA,
  author =       "Florent de Dinechin and Stuart Oberman and Bogdan
                 Pasca and Leonel Sousa",
  title =        "Foreword: {ARITH 2022}",
  crossref =     "IEEE:2022:ISC",
  pages =        "vii--vii",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00005",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
}

@InProceedings{deDinechin:2022:OCA,
  author =       "Florent de Dinechin and Stuart Oberman and Bogdan
                 Pasca and Leonel Sousa and Guillaume Melquiond and Marc
                 Mezzarobba and Vojin G. Oklobdzija",
  title =        "Organizing Committee: {ARITH 2022}",
  crossref =     "IEEE:2022:ISC",
  pages =        "viii--viii",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00006",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
}

@Article{Demmel:2022:PCEa,
  author =       "James Demmel and Jack Dongarra and Mark Gates and Greg
                 Henry and Julien Langou and Xiaoye Li and Piotr
                 Luszczek and Weslley Pereira and Jason Riedy and Cindy
                 Rubio-Gonz{\'a}lez",
  title =        "Proposed Consistent Exception Handling for the {BLAS}
                 and {LAPACK}",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "92",
  day =          "19",
  month =        jul,
  year =         "2022",
  bibdate =      "Mon Sep 11 06:47:01 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/abs/2207.09281",
  abstract =     "Numerical exceptions, which may be caused by overflow,
                 operations like division by 0 or sqrt(-1), or
                 convergence failures, are unavoidable in many cases, in
                 particular when software is used on unforeseen and
                 difficult inputs. As more aspects of society become
                 automated, e.g., self-driving cars, health monitors,
                 and cyber-physical systems more generally, it is
                 becoming increasingly important to design software that
                 is resilient to exceptions, and that responds to them
                 in a consistent way. Consistency is needed to allow
                 users to build higher-level software that is also
                 resilient and consistent (and so on recursively). In
                 this paper we explore the design space of consistent
                 exception handling for the widely used BLAS and LAPACK
                 linear algebra libraries, pointing out a variety of
                 instances of inconsistent exception handling in the
                 current versions, and propose a new design that
                 balances consistency, complexity, ease of use, and
                 performance. Some compromises are needed, because there
                 are preexisting inconsistencies that are outside our
                 control, including in or between existing vendor BLAS
                 implementations, different programming languages, and
                 even compilers for the same programming language. And
                 user requests from our surveys are quite diverse. We
                 also propose our design as a possible model for other
                 numerical software, and welcome comments on our design
                 choices",
  acknowledgement = ack-nhfb,
}

@InProceedings{Demmel:2022:PCEb,
  author =       "James Demmel and Jack Dongarra and Mark Gates and Greg
                 Henry and Julien Langou and Xiaoye Li and Piotr
                 Luszczek and Weslley Pereira and Jason Riedy and Cindy
                 Rubio-Gonz{\'a}lez",
  editor =       "{IEEE}",
  booktitle =    "{Correctness 2022: Sixth International Workshop on
                 Software Correctness for HPC Applications: Held in
                 conjunction with SC22: The International Conference for
                 High Performance Computing, Networking, Storage and
                 Analysis. Dallas, Texas, USA, November 13-18, 2022}",
  title =        "Proposed Consistent Exception Handling for the {BLAS}
                 and {LAPACK}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "??--??",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/Correctness56720.2022.00006",
  ISBN =         "1-66546-335-X",
  ISBN-13 =      "978-1-66546-335-5",
  LCCN =         "????",
  bibdate =      "Wed Aug 07 14:39:23 2024",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Desrentes:2022:PDO,
  author =       "Or{\'e}gane Desrentes and Diana Resmerita and
                 Beno{\^\i}t Dupont de Dinechin",
  title =        "A {Posit8} Decompression Operator for Deep Neural
                 Network Inference",
  crossref =     "Gustafson:2022:NGA",
  pages =        "14--30",
  year =         "2022",
  DOI =          "https://doi.org/10.1007/978-3-031-09779-9_2",
  bibdate =      "Fri Dec 15 07:04:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@InProceedings{Didier:2022:SCR,
  author =       "Laurent-St{\'e}phane Didier and Jean-Marc Robert and
                 Fangan Yssouf Dosso and Nadia {El Mrabet}",
  title =        "A software comparison of {RNS} and {PMNS}",
  crossref =     "IEEE:2022:ISC",
  pages =        "86--93",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00025",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29; Polynomial Modular Number System (PMNS);
                 Residue Number System (RNS)",
}

@Article{Dieguez:2022:EHP,
  author =       "Adrian P. Dieguez and Margarita Amor and Ram{\'o}n
                 Doallo and Akira Nukada and Satoshi Matsuoka",
  title =        "Efficient high-precision integer multiplication on the
                 {GPU}",
  journal =      j-IJHPCA,
  volume =       "36",
  number =       "3",
  pages =        "356--369",
  day =          "1",
  month =        may,
  year =         "2022",
  CODEN =        "IHPCFL",
  DOI =          "https://doi.org/10.1177/10943420221077964",
  ISSN =         "1094-3420 (print), 1741-2846 (electronic)",
  ISSN-L =       "1094-3420",
  bibdate =      "Thu May 30 07:31:45 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijsa.bib",
  URL =          "https://journals.sagepub.com/doi/abs/10.1177/10943420221077964",
  acknowledgement = ack-nhfb,
  ajournal =     "????",
  fjournal =     "International Journal of High Performance Computing
                 Applications",
  journal-URL =  "https://journals.sagepub.com/home/hpc",
  ORCID-numbers = "https://orcid.org/0000-0001-7168-9050",
}

@Article{DiMeo:2022:AFP,
  author =       "Gennaro {Di Meo} and Gerardo Saggese and Antonio G. M.
                 Strollo and Davide {De Caro} and Nicola Petra",
  title =        "Approximate Floating-Point Multiplier based on Static
                 Segmentation",
  journal =      j-ELECTRONICS,
  volume =       "11",
  number =       "11",
  pages =        "3005:1--3005:23",
  year =         "2022",
  DOI =          "https://doi.org/10.3390/electronics1119",
  ISSN =         "2079-9292",
  ISSN-L =       "2079-9292",
  bibdate =      "Wed Dec 20 07:43:28 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://mdpi-res.com/d_attachment/electronics/electronics-11-03005/article_deploy/electronics-11-03005.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics",
  journal-URL =  "https://www.mdpi.com/journal/electronics",
}

@InProceedings{Dosso:2022:PEA,
  author =       "Fangan Yssouf Dosso and Jean-Marc Robert and Pascal
                 V{\'e}ron",
  title =        "{PMNS} for efficient arithmetic and small memory
                 cost",
  crossref =     "IEEE:2022:ISC",
  pages =        "84--84",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00023",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
}

@Article{Dross:2022:MPF,
  author =       "Claire Dross and Johannes Kanig",
  editor =       "R. Bloem and R. Dimitrova and C. Fan and N.
                 Sharygina",
  booktitle =    "Software Verification: {NSV VSTTE 2021}",
  title =        "Making Proofs of Floating-Point Programs Accessible to
                 Regular Developers",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "13124",
  pages =        "7--24",
  year =         "2022",
  DOI =          "https://doi.org/10.1007/978-3-030-95561-8_2",
  ISBN =         "3-030-95561-3",
  ISBN-13 =      "978-3-030-95561-8",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Jun 8 09:07:55 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Durand:2022:AVC,
  author =       "Yves Durand and Eric Guthmuller and Cesar Fuguet and
                 J{\'e}r{\^o}me Fereyre and Andrea Bocco and Riccardo
                 Alidori",
  title =        "Accelerating Variants of the Conjugate Gradient with
                 the Variable Precision Processor",
  crossref =     "IEEE:2022:ISC",
  pages =        "51--57",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00017",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
}

@InProceedings{ElArar:2022:PES,
  author =       "El-Mehdi {El Arar} and Devan Sohier and Pablo {de
                 Oliveira Castro} and Eric Petit",
  title =        "The Positive Effects of Stochastic Rounding in
                 Numerical Algorithms",
  crossref =     "IEEE:2022:ISC",
  pages =        "58--65",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00018",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Recently, stochastic rounding (SR) has been
                 implemented in specialized hardware but most current
                 computing nodes do not yet support this rounding mode.
                 Several works empirically illustrate the benefit of
                 stochastic rounding in various fields such as neural
                 networks and ordinary differential equations. For some
                 algorithms, such as summation, inner product or
                 matrix-vector multiplication, it has been proved that
                 SR provides probabilistic error bounds better than the
                 traditional deterministic bounds.\par

                 In this paper, we extend this theoretical ground for a
                 wider adoption of SR in computer architecture. First,
                 we analyze the biases of the two SR modes: SR-nearness
                 and SR-up-or-down. We demonstrate on a case-study of
                 Euler's forward method that IEEE-754 default rounding
                 modes and SR-up-or-down accumulate rounding errors
                 across iterations and that SR-nearness, being unbiased,
                 does not. Second, we prove a $ O(\sqrt {n}) $
                 probabilistic bound on the forward error of Horner's
                 polynomial evaluation method with SR, improving on the
                 known deterministic $ O(n) $ bound.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
}

@InProceedings{Elsaid:2022:OFA,
  author =       "Kareem Elsaid and Mona Safar and M. Watheq
                 El-Kharashi",
  editor =       "{IEEE}",
  booktitle =    "{2022 International Conference on Microelectronics
                 (ICM)}",
  title =        "Optimized {FPGA} Architecture for Machine Learning
                 Applications using Posit Multipliers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "50--53",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ICM56065.2022.10005431",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Ene:2022:PTS,
  author =       "Teodor Dumitru Ene and James E. Stine",
  title =        "Point-Targeted Sparseness and {Ling} Transforms on
                 Parallel Prefix Adder Trees",
  crossref =     "IEEE:2022:ISC",
  pages =        "68--75",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00021",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
}

@InProceedings{Essam:2022:DIL,
  author =       "Mohammed Essam and Ahmed Shalaby and Mohamed Taher",
  editor =       "{IEEE}",
  booktitle =    "{2022 10th International Japan-Africa Conference on
                 Electronics, Communications, and Computations
                 (JAC-ECC)}",
  title =        "Design and Implementation of Low Power Posit
                 Arithmetic Unit for Efficient Hardware Accelerators",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "68--71",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/JAC-ECC56395.2022.10043893",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Evstigneev:2022:CSD,
  author =       "N. M. Evstigneev and O. I. Ryabkov and A. N. Bocharov
                 and V. P. Petrovskiy and I. O. Teplyakov",
  title =        "Compensated summation and dot product algorithms for
                 floating-point vectors on parallel architectures: Error
                 bounds, implementation and application in the {Krylov}
                 subspace methods",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "414",
  number =       "??",
  pages =        "??--??",
  month =        nov,
  year =         "2022",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/j.cam.2022.114434",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Tue Jun 14 16:20:17 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2020.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042722002047",
  acknowledgement = ack-nhfb,
  articleno =    "114434",
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}

@InProceedings{FernandesDosSantos:2022:EIM,
  author =       "Fernando {Fernandes Dos Santos} and Paolo Rech and
                 Angeliki Kritikakou and Olivier Sentieys",
  booktitle =    "{2022 IEEE Computer Society Annual Symposium on VLSI
                 (ISVLSI)}",
  title =        "Evaluating the Impact of Mixed-Precision on Fault
                 Propagation for Deep Neural Networks on {GPUs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "327--327",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ISVLSI54635.2022.00071",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Deep learning; GPUs; Graphics processing units;
                 Hardware; mixed precision; Neural networks; neutron
                 beam experiments; Power demand; reliability; Tensors;
                 Very large scale integration",
}

@InProceedings{Gallet:2022:LGT,
  author =       "Benoit Gallet and Michael Gowanlock",
  booktitle =    "{2022 IEEE 29th International Conference on High
                 Performance Computing, Data, and Analytics (HiPC)}",
  title =        "Leveraging {GPU} {Tensor Cores} for Double Precision
                 {Euclidean} Distance Calculations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "135--144",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/HiPC56025.2022.00029",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer architecture; Euclidean distance; Euclidean
                 Distance; GPU; Graphics processing units; High
                 performance computing; Integrated circuits; Machine
                 learning; Similarity Searches; Tensor Cores; Tensors",
}

@InProceedings{Gao:2022:TFI,
  author =       "Zhanyuan Gao and Laiping Zhao and Haonan Chen",
  editor =       "{IEEE}",
  booktitle =    "{2022 IEEE\slash ACIS 22nd International Conference on
                 Computer and Information Science (ICIS)}",
  title =        "A Trigonometric Function Instruction Set Extension
                 Method Based on {RISC-V}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "119--126",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ICIS54925.2022.9882453",
  bibdate =      "Sat Dec 16 15:51:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
}

@Misc{Genkina:2022:PNK,
  author =       "Dina Genkina",
  title =        "Posits, a New Kind of Number, Improves the Math of
                 {AI}: The first posit-based processor core gave a
                 ten-thousandfold accuracy boost",
  howpublished = "IEEE Spectrum Web site",
  day =          "26",
  month =        sep,
  year =         "2022",
  bibdate =      "Wed Sep 28 10:46:38 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://spectrum.ieee.org/floating-point-numbers-posits-processor",
  acknowledgement = ack-nhfb,
}

@InProceedings{Greuet:2022:QAM,
  author =       "Aur{\'e}lien Greuet and Simon Montoya and Cl{\'e}mence
                 Vermeersch",
  title =        "Quotient Approximation Modular Reduction",
  crossref =     "IEEE:2022:ISC",
  pages =        "103--110",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00028",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
}

@Article{Gudivada:2022:NOL,
  author =       "A. Arunkumar Gudivada and Gnanou Florence Sudha",
  title =        "Novel optimized low power design of single-precision
                 floating-point adder using Quantum-dot Cellular
                 Automata",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "78",
  number =       "4",
  pages =        "6035--6053",
  month =        mar,
  year =         "2022",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1007/s11227-021-04089-5",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Fri Feb 21 15:59:35 MST 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsuper2020.bib",
  URL =          "https://link.springer.com/article/10.1007/s11227-021-04089-5",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Supercomputing",
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
}

@InProceedings{Guo:2022:SCC,
  author =       "An Guo and Yongliang Zhou and Bo Wang and Tianzhu
                 Xiong and Chen Xue and Yufei Wang and Xin Si and Jun
                 Yang",
  booktitle =    "{2022 IEEE International Symposium on Circuits and
                 Systems (ISCAS)}",
  title =        "{ShareFloat CIM}: a Compute-In-Memory Architecture
                 with Floating-Point Multiply-and-Accumulate
                 Operations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2276--2280",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ISCAS48785.2022.9937242",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "AI; Circuits and systems; Computer architecture;
                 Computing-in-memory; Costs; FCC; Floating-point; Neural
                 networks; Throughput; Training",
}

@Article{Higham:2022:MPA,
  author =       "Nicholas J. Higham and Theo Mary",
  title =        "Mixed precision algorithms in numerical linear
                 algebra",
  journal =      j-ACTA-NUMERICA,
  volume =       "31",
  pages =        "347--414",
  month =        may,
  year =         "2022",
  CODEN =        "ANUMFU",
  DOI =          "https://doi.org/10.1017/S0962492922000022",
  ISSN =         "0962-4929 (print), 1474-0508 (electronic)",
  ISSN-L =       "0962-4929",
  bibdate =      "Wed Jun 15 09:10:34 MDT 2022",
  bibsource =    "http://journals.cambridge.org/action/displayIssue?jid=ANU&volumeId=31&issueId=00;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/actanumerica.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.cambridge.org/core/journals/acta-numerica/article/mixed-precision-algorithms-in-numerical-linear-algebra/43CA701BA29251B5790C653E66F46197",
  acknowledgement = ack-nhfb,
  ajournal =     "Acta Numer.",
  author-dates = "Nicholas John Higham (25 December 1961--20 January
                 2024)",
  fjournal =     "Acta Numerica",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=ANU",
  onlinedate =   "09 June 2022",
}

@InProceedings{Ho:2022:QNG,
  author =       "Nhut-Minh Ho and Himeshi De Silva and John L.
                 Gustafson and Weng-Fai Wong",
  title =        "{Qtorch+}: Next Generation Arithmetic for {Pytorch}
                 Machine Learning",
  crossref =     "Gustafson:2022:NGA",
  pages =        "31--49",
  year =         "2022",
  DOI =          "https://doi.org/10.1007/978-3-031-09779-9_3",
  bibdate =      "Fri Dec 15 07:04:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@Article{Hurchalla:2022:IIM,
  author =       "Jeffrey Hurchalla",
  title =        "An Improved Integer Modular Multiplicative Inverse
                 (modulo $ 2^w$)",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--11",
  day =          "9",
  month =        apr,
  year =         "2022",
  DOI =          "https://doi.org/10.48550/arXiv.2204.04342",
  bibdate =      "Mon Feb 09 05:59:37 2026",
  URL =          "https://arxiv.org/abs/2204.04342",
  abstract =     "This paper presents an algorithm for the integer
                 multiplicative inverse (mod $ 2^w$) which completes in
                 the fewest cycles known for modern microprocessors,
                 when using the native bit width w for the modulus $
                 2^w$. The algorithm is a modification of a method by
                 Dumas, and for computers it slightly increases
                 generality and efficiency. A proof is given, and the
                 algorithm is shown to be closely related to the better
                 known Newton's method algorithm for the inverse. Simple
                 direct formulas, which are needed by this algorithm and
                 by Newton's method, are reviewed and proven for the
                 integer inverse modulo $ 2^k$ with $ k = 1, 2, 3, 4$,
                 or $5$, providing the first proof of the preferred
                 formula with $ k = 4 $ or $5$.",
  acknowledgement = ack-nhfb,
  remark =       "See original algorithm
                 \cite{Dumas:2012:NRI,Dumas:2014:NRI}.",
}

@InProceedings{Immaneni:2022:PEO,
  author =       "Amritha Immaneni and Salim Ullah and Suresh Nambi and
                 Siva Satyendra Sahoo and Akash Kumar",
  editor =       "{IEEE}",
  booktitle =    "{2022 25th Euromicro Conference on Digital System
                 Design (DSD)}",
  title =        "{PosAx-O}: Exploring Operator-level Approximations for
                 Posit Arithmetic in Embedded {AI\slash ML}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "214--223",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/DSD57027.2022.00037",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Isupov:2022:MPS,
  author =       "Konstantin Isupov",
  title =        "Multiple-precision sparse matrix--vector
                 multiplication on {GPUs}",
  journal =      j-J-COMPUT-SCI,
  volume =       "61",
  pages =        "??--??",
  month =        may,
  year =         "2022",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/j.jocs.2022.101609",
  ISSN =         "1877-7503 (print), 1877-7511 (electronic)",
  ISSN-L =       "1877-7503",
  bibdate =      "Tue Sep 19 13:56:09 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputsci.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/S1877750322000382",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Comput. Sci.",
  articleno =    "101609",
  fjournal =     "Journal of Computational Science",
  journal-URL =  "https://www.sciencedirect.com/journal/journal-of-computational-science",
}

@InProceedings{Joshi:2022:SAB,
  author =       "Rajeev Joshi and Lakshmi Kavya Kalyanam and Srinivas
                 Katkoori",
  booktitle =    "{2022 IEEE International Symposium on Smart Electronic
                 Systems (iSES)}",
  title =        "Simulated Annealing Based Integerization of Hidden
                 Weights for Area-Efficient {IoT} Edge Intelligence",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "427--432",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/iSES54909.2022.00093",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Artificial neural networks; FPGA; Hardware; Hardware
                 Optimization; IEEE 754; IoT; Metaheuristic; Multilayer
                 perceptron; Neurons; Perturbation methods; Scalability;
                 Simulated annealing; Simulated Annealing; Table
                 lookup",
}

@InProceedings{Keerthi:2022:DIM,
  author =       "T Keerthi and Yashu Swami",
  editor =       "{IEEE}",
  booktitle =    "{2022 IEEE 3rd International Conference on VLSI
                 Systems, Architecture, Technology and Applications
                 (VLSI SATA)}",
  title =        "Design and Implementation of {MAC} by Using Efficient
                 Posit Multiplier",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--4",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/VLSISATA54927.2022.10046599",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Kim:2022:EAM,
  author =       "Min Soo Kim and Alberto A. {Del Barrio} and HyunJin
                 Kim and Nader Bagherzadeh",
  title =        "The Effects of Approximate Multiplication on
                 Convolutional Neural Networks",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "10",
  number =       "2",
  pages =        "904--916",
  month =        apr # "\slash " # jun,
  year =         "2022",
  DOI =          "https://doi.org/10.1109/TETC.2021.3050989",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  abstract =     "This article analyzes the effects of approximate
                 multiplication when performing inferences on deep
                 convolutional neural networks (CNNs). The approximate
                 multiplication can reduce the cost of the underlying
                 circuits so that CNN inferences can be performed more
                 efficiently in hardware accelerators. The study
                 identifies the critical factors in the convolution,
                 fully-connected, and batch normalization layers that
                 allow more accurate CNN predictions despite the errors
                 from approximate multiplication. The same factors also
                 provide an arithmetic explanation of why bfloat16
                 multiplication performs well on CNNs. The experiments
                 are performed with recognized network architectures to
                 show that the approximate multipliers can produce
                 predictions that are nearly as accurate as the FP32
                 references, without additional training. For example,
                 the ResNet and Inception-v4 models with Mitch-$w$ 6
                 multiplication produces Top-5 errors that are within
                 0.2 percent compared to the FP32 references. A brief
                 cost comparison of Mitch-$w$ 6 against bfloat16 is
                 presented where a MAC operation saves up to 80 percent
                 of energy compared to the bfloat16 arithmetic. The most
                 far-reaching contribution of this article is the
                 analytical justification that multiplications can be
                 approximated while additions need to be exact in CNN
                 MAC operations.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
  keywords =     "Approximation algorithms; arithmetic and logic units;
                 Computational efficiency; Computational modeling;
                 computer vision; Convolution; Hardware; low-power
                 design; Machine learning; object recognition;
                 Quantization (signal); Training",
}

@InProceedings{Knodtel:2022:SID,
  author =       "Johannes Kn{\"o}dtel and Sebastian Rachuj and Marc
                 Reichenbach",
  editor =       "{IEEE}",
  booktitle =    "{2022 25th Euromicro Conference on Digital System
                 Design (DSD)}",
  title =        "Suitability of {ISAs} for Data Paths Based on
                 Redundant Number Systems: Is {RISC-V} the best?",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "247--253",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/DSD57027.2022.00041",
  bibdate =      "Sat Dec 16 15:51:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kuang:2022:HSN,
  author =       "Honglin Kuang and Yifan Zhao and Jun Han",
  editor =       "{IEEE}",
  booktitle =    "{2022 IEEE Asia Pacific Conference on Circuits and
                 Systems (APCCAS)}",
  title =        "A High-Speed {NTT}-Based Polynomial Multiplication
                 Accelerator with Vector Extension of {RISC-V} for
                 {Saber} Algorithm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "592--595",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/APCCAS55924.2022.10090293",
  bibdate =      "Sat Dec 16 15:51:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Laguna:2022:BAF,
  author =       "Ignacio Laguna and Xinyi Li and Ganesh
                 Gopalakrishnan",
  editor =       "????",
  booktitle =    "{SOAP 2022: Proceedings of the 11th ACM SIGPLAN
                 International Workshop on the State Of the Art in
                 Program Analysis, San Diego, CA, USA, 14 June 2022}",
  title =        "{BinFPE}: Accurate Floating-Point Exception Detection
                 for {GPU} Applications",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  bookpages =    "50",
  pages =        "1--8",
  year =         "2022",
  DOI =          "https://doi.org/10.1145/3520313.3534655",
  ISBN =         "1-4503-9274-1",
  ISBN-13 =      "978-1-4503-9274-7",
  bibdate =      "Mon Sep 11 07:11:11 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "When modern heterogeneous HPC systems perform
                 numerical computations, floating-point exceptional
                 quantities such as NaN and infinity in the GPU context,
                 remain insufficiently handled. This is because commonly
                 used GPUs and the CUDA language have no inherent
                 exception detection capabilities. Existing
                 compiler-based approaches for this problem are tied to
                 a given compiler and cannot detect exceptions generated
                 by binaries and precompiled libraries. This paper
                 contributes BinFPE, a unique tool that addresses these
                 challenges. BinFPE uses the NVBit dynamic binary
                 instrumentation framework to check the machine
                 registers after each calculation to recognize
                 exceptions, and conveys this information to the CPU for
                 final reporting. We demonstrate the effectiveness of
                 BinFPE on 42 CUDA programs, reporting previously
                 unreported exceptions. We also present the limitations
                 of BinFPE and our perspective on building GPU tools via
                 binary instrumentation.",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1145/3520313",
}

@InProceedings{Laguna:2022:FIT,
  author =       "Ignacio Laguna and Ganesh Gopalakrishnan",
  editor =       "{ACM}",
  booktitle =    "{SC '22: Proceedings of the International Conference
                 on High Performance Computing, Networking, Storage and
                 Analysis, Dallas, Texas, November 13--18, 2022}",
  title =        "Finding Inputs that Trigger Floating-Point Exceptions
                 in {GPUs} via {Bayesian} Optimization",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "464--475",
  year =         "2022",
  ISBN =         "1-66545-444-X",
  ISBN-13 =      "978-1-66545-444-5",
  ISSN =         "2167-4329 (print), 2167-4337 (electronic)",
  ISSN-L =       "2167-4337",
  bibdate =      "Mon Sep 11 07:09:51 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Testing code for floating-point exceptions is crucial
                 as exceptions can quickly propagate and produce
                 unreliable numerical answers. The state-of-the-art to
                 test for floating-point exceptions in GPUs is quite
                 limited and solutions require the application's source
                 code, which precludes their use in accelerated
                 libraries where the source is not publicly available.
                 We present an approach to find inputs that trigger
                 floating-point exceptions in black-box GPU functions,
                 i.e., functions where the source code and information
                 about input bounds are unavailable. Our approach is the
                 first to use Bayesian optimization (BO) to identify
                 such inputs and uses novel strategies to overcome the
                 challenges that arise in applying BO to this problem.
                 We implement our approach in the Xscope framework and
                 demonstrate it on 58 functions from the CUDA Math
                 Library and functions from ten HPC programs. Xscope is
                 able to identify inputs that trigger exceptions in
                 about 72\% of the tested functions.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Langroudi:2022:AAH,
  author =       "Hamed F. Langroudi and Vedant Karia and Tej Pandit and
                 Becky Mashaido and Dhireesha Kudithipudi",
  title =        "{ACTION}: {Automated Hardware--Software Codesign
                 Framework for Low-precision Numerical Format SelecTION}
                 in {TinyML}",
  crossref =     "Gustafson:2022:NGA",
  pages =        "50--65",
  year =         "2022",
  DOI =          "https://doi.org/10.1007/978-3-031-09779-9_4",
  bibdate =      "Fri Dec 15 07:04:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@Article{Lee:2022:NFC,
  author =       "Sae Kyu Lee and Ankur Agrawal and Joel Silberman and
                 Matthew Ziegler and Mingu Kang and Swagath
                 Venkataramani and Nianzheng Cao and Bruce Fleischer and
                 Michael Guillorn and Matthew Cohen and Silvia M.
                 Mueller and Jinwook Oh and Martin Lutz and Jinwook Jung
                 and Siyu Koswatta and Ching Zhou and Vidhi Zalani and
                 Monodeep Kar and James Bonanno and Robert Casatuta and
                 Chia-Yu Chen and Jungwook Choi and Howard Haynie and
                 Alyssa Herbert and Radhika Jain and Kyu-Hyoun Kim and
                 Yulong Li and Zhibin Ren and Scot Rider and Marcel
                 Schaal and Kerstin Schelm and Michael R. Scheuermann
                 and Xiao Sun and Hung Tran and Naigang Wang and Wei
                 Wang and Xin Zhang and Vinay Shah and Brian Curran and
                 Vijayalakshmi Srinivasan and Pong-Fei Lu and Sunil
                 Shukla and Kailash Gopalakrishnan and Leland Chang",
  title =        "A 7-nm Four-Core Mixed-Precision {AI} Chip With
                 {26.2-TFLOPS} Hybrid-{FP8} Training, {104.9-TOPS}
                 {INT4} Inference, and Workload-Aware Throttling",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "57",
  number =       "1",
  pages =        "182--197",
  year =         "2022",
  CODEN =        "IJSCBC",
  DOI =          "https://doi.org/10.1109/JSSC.2021.3120113",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "AI accelerators; Approximate computing; Artificial
                 intelligence; artificial intelligence (AI); Bandwidth;
                 Computer architecture; deep neural networks (DNNs);
                 hardware accelerators; Inference algorithms; machine
                 learning (ML); reduced precision computation;
                 System-on-chip; Training",
}

@Article{Li:2022:VSAa,
  author =       "Kai Li and Wei Mao and Junzhuo Zhou and Boyu Li and
                 Zhengke Yang and Shuxing Yang and Laimin Du and Sixiao
                 Huang and Hao Yu",
  title =        "A Vector Systolic Accelerator for Multi-Precision
                 Floating-Point High-Performance Computing",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
  volume =       "69",
  number =       "10",
  pages =        "4123--4127",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/TCSII.2022.3183007",
  ISSN =         "1549-7747 (print), 1558-3791 (electronic)",
  ISSN-L =       "1549-7747",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems II: Express
                 Briefs",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
  keywords =     "accelerator; Adders; Energy efficiency;
                 floating-point; Hardware; High performance computing;
                 HPC; MAC; Mathematical models; Multi-precision; PE;
                 Resource management; systolic; Systolic arrays;
                 vector",
}

@InProceedings{Li:2022:VSAb,
  author =       "Kai Li and Junzhuo Zhou and Boyu Li and Shuxing Yang
                 and Sixiao Huang and Shaobo Luo and Wei Mao and Hao
                 Yu",
  booktitle =    "{2022 IEEE 4th International Conference on Artificial
                 Intelligence Circuits and Systems (AICAS)}",
  title =        "A Vector Systolic Accelerator for Multi-Precision
                 Floating-Point High-Performance Computing",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "226--229",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/AICAS54282.2022.9869969",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Circuits and systems; Design methodology; Energy
                 efficiency; floating-point; High performance computing;
                 multi-precision; Pipelines; Systolic; Systolic arrays;
                 Throughput; vector",
}

@Article{Lim:2022:OPA,
  author =       "Jay P. Lim and Santosh Nagarakatte",
  title =        "One polynomial approximation to produce correctly
                 rounded results of an elementary function for multiple
                 representations and rounding modes",
  journal =      j-PACMPL,
  volume =       "6",
  number =       "POPL",
  pages =        "3:1--3:28",
  month =        jan,
  year =         "2022",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3498664",
  ISSN =         "2475-1421 (electronic)",
  ISSN-L =       "2475-1421",
  bibdate =      "Thu May 26 06:32:48 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/pacmpl.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3498664",
  abstract =     "Mainstream math libraries for floating point (FP) do
                 not produce correctly rounded results for all inputs.
                 In contrast, CR-LIBM and RLIBM provide correctly
                 rounded implementations for a specific FP
                 representation with one rounding mode. Using such
                 libraries for a representation with a new rounding mode
                 or with different precision will result in wrong
                 results due to double rounding. This paper proposes a
                 novel method to generate a single polynomial
                 approximation that produces correctly rounded results
                 for all inputs for multiple rounding modes and multiple
                 precision configurations. To generate a correctly
                 rounded library for n-bits, our key idea is to generate
                 a polynomial approximation for a representation with
                 n+2-bits using the round-to-odd mode. We prove that the
                 resulting polynomial approximation will produce
                 correctly rounded results for all five rounding modes
                 in the standard and for multiple representations with
                 k-bits such that $ |E| + 1 < k \leq n $, where $ |E| $
                 is the number of exponent bits in the representation.
                 Similar to our prior work in the RLIBM project, we
                 approximate the correctly rounded result when we
                 generate the library with n+2-bits using the
                 round-to-odd mode. We also generate polynomial
                 approximations by structuring it as a linear
                 programming problem but propose enhancements to
                 polynomial generation to handle the round-to-odd mode.
                 Our prototype is the first 32-bit float library that
                 produces correctly rounded results with all rounding
                 modes in the IEEE standard for all inputs with a single
                 polynomial approximation. It also produces correctly
                 rounded results for any FP configuration ranging from
                 10-bits to 32-bits while also being faster than
                 mainstream libraries.",
  acknowledgement = ack-nhfb,
  articleno =    "3",
  fjournal =     "Proceedings of the ACM on Programming Languages
                 (PACMPL)",
  journal-URL =  "https://dl.acm.org/loi/pacmpl",
  keywords =     "correct rounding; double rounding; elementary
                 functions; round-to-odd mode (RO(x))",
}

@InProceedings{Lindstrom:2022:MUC,
  author =       "Peter Lindstrom",
  title =        "{MultiPosits}: Universal Coding of $ \mathbb {R}^n $",
  crossref =     "Gustafson:2022:NGA",
  pages =        "66--83",
  year =         "2022",
  DOI =          "https://doi.org/10.1007/978-3-031-09779-9_5",
  bibdate =      "Fri Dec 15 07:04:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@Article{Liu:2022:DUA,
  author =       "Weiqiang Liu and Tao Xu and Jing Li and Chenghua Wang
                 and Paolo Montuschi and Fabrizio Lombardi",
  title =        "Design of Unsigned Approximate Hybrid Dividers Based
                 on Restoring Array and Logarithmic Dividers",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "10",
  number =       "1",
  pages =        "339--350",
  month =        jan # "\slash " # mar,
  year =         "2022",
  DOI =          "https://doi.org/10.1109/TETC.2020.3022290",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  abstract =     "Approximate computer arithmetic has been extensively
                 studied due to its advantages to further reduce power
                 consumption and increase performance at reduced
                 accuracy. Although a number of approximate adders and
                 multipliers have been studied, only a few approximate
                 dividers have been proposed. A logarithmic divider (LD)
                 has low complexity and accuracy, while an exact array
                 divider (EXD) has a high complexity. Therefore, in this
                 article, an approximate hybrid divider (AXHD) is
                 proposed. It takes advantage of both LD and EXD to
                 achieve a tradeoff between hardware performance and
                 accuracy. Exact restoring divider cells are used to
                 generate the most significant bits (MSBs) of the
                 quotient for attaining a high accuracy while the other
                 quotient digits are generated by using a LD as an
                 approximate scheme to improve figures of merit such as
                 power consumption, area and delay. To further save
                 hardware resources, a so-called eliminated approximate
                 hybrid divider (E-AXHD) based on AXHD is also proposed.
                 In this improved design, a reduced width divider is
                 used to replace the EXD in AXHD. Specifically, for a
                 16-by-8 design, $ n / (n + 1) $ array division is used
                 to replace the $ n / 8 $ array division ($ n < 8$). The
                 proposed AXHD and E-AXHD are evaluated and analyzed
                 using error and hardware metrics. The proposed designs
                 are also compared with EXD, LD and previous approximate
                 dividers. The results show that the proposed designs
                 outperform previous approximate dividers by considering
                 both energy and error. The proposed hybrid dividers are
                 of particular interest for error tolerant applications
                 such as image processing and machine learning.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}

@InProceedings{Mallasen:2022:CCR,
  author =       "David Mallas{\'e}n and Raul Murillo and Alberto A.
                 {Del Barrio} and Guillermo Botella and Luis Pi{\~n}uel
                 and Manuel Prieto Matias",
  editor =       "{IEEE}",
  booktitle =    "{2022 37th Conference on Design of Circuits and
                 Integrated Circuits (DCIS)}",
  title =        "Customizing the {CVA6 RISC-V} Core to Integrate Posit
                 and Quire Instructions",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "01--06",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/DCIS55711.2022.9970026",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
}

@Article{Mallasen:2022:POSa,
  author =       "David Mallas{\'e}n and Raul Murillo and Alberto A.
                 {Del Barrio} and Guillermo Botella and Luis Pi{\~n}uel
                 and Manuel Prieto-Matias",
  title =        "{PERCIVAL}: Open-Source Posit {RISC-V} Core With Quire
                 Capability",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "10",
  number =       "3",
  pages =        "1241--1252",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/TETC.2022.3187199",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}

@InProceedings{Mallasen:2022:POSb,
  author =       "David Mallas{\'e}n and Raul Murillo and Alberto A.
                 {Del Barrio} and Guillermo Botella and Luis Pi{\~n}uel
                 and Manuel Prieto-Matias",
  title =        "{PERCIVAL}: Open-Source Posit {RISC-V} Core With Quire
                 Capability",
  crossref =     "IEEE:2022:ISC",
  pages =        "66--66",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00019",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  note =         "Authors and title only.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
}

@Article{Mao:2022:CFP,
  author =       "Wei Mao and Kai Li and Quan Cheng and Liuyao Dai and
                 Boyu Li and Xinang Xie and He Li and Longyang Lin and
                 Hao Yu",
  title =        "A Configurable Floating-Point Multiple-Precision
                 Processing Element for {HPC} and {AI} Converged
                 Computing",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "30",
  number =       "2",
  pages =        "213--226",
  year =         "2022",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/TVLSI.2021.3128435",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
  keywords =     "Acceleration; Adders; Arrays; Artificial intelligence;
                 artificial intelligence (AI); carry-select adder
                 (CSLA); Costs; exponent comparison; floating point
                 (FP); Hardware; high-performance computing (HPC);
                 multiple precision; multiply accumulate (MAC);
                 processing element (PE); Redundancy; Very large scale
                 integration",
}

@InProceedings{Mathis:2022:IHP,
  author =       "Brett Mathis and James E. Stine",
  editor =       "{IEEE}",
  booktitle =    "{2022 IEEE International Symposium on Circuits and
                 Systems (ISCAS)}",
  title =        "Implementation of High Performance {IEEE 754}-Posit
                 Conversion Hardware",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "934--937",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ISCAS48785.2022.9937426",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Mccoid:2022:PRA,
  author =       "Conor Mccoid and Martin J. Gander",
  title =        "A Provably Robust Algorithm for Triangle--triangle
                 Intersections in Floating-point Arithmetic",
  journal =      j-TOMS,
  volume =       "48",
  number =       "2",
  pages =        "17:1--17:30",
  month =        jun,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3513264",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 20 07:04:17 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3513264",
  abstract =     "Motivated by the unexpected failure of the triangle
                 intersection component of the Projection Algorithm for
                 Nonmatching Grids (PANG), this article provides a
                 robust version with proof of backward stability. The
                 new triangle intersection algorithm ensures consistency
                 and parsimony across three types of calculations. The
                 set of intersections produced by the algorithm, called
                 representations, is shown to match the set of geometric
                 intersections, called models. The article concludes
                 with a comparison between the old and new intersection
                 algorithms for PANG using an example found to reliably
                 generate failures in the former.",
  acknowledgement = ack-nhfb,
  articleno =    "17",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@InProceedings{Meloni:2022:AAP,
  author =       "Nicolas Meloni",
  title =        "An Alternative Approach to Polynomial Modular Number
                 System Internal Reduction",
  crossref =     "IEEE:2022:ISC",
  pages =        "85--85",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00024",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
}

@Article{Micikevicius:2022:FFD,
  author =       "Paulius Micikevicius and Dusan Stosic and Neil Burgess
                 and Marius Cornea and Pradeep Dubey and Richard
                 Grisenthwaite and Sangwon Ha and Alexander Heinecke and
                 Patrick Judd and John Kamalu and Naveen Mellempudi and
                 Stuart Oberman and Mohammad Shoeybi and Michael Siu and
                 Hao Wu",
  title =        "{FP8} Formats for Deep Learning",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--9",
  year =         "2022",
  bibdate =      "Wed Aug 7 16:23:07 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/abs/2209.05433",
  abstract =     "FP8 is a natural progression for accelerating deep
                 learning training inference beyond the 16-bit formats
                 common in modern processors. In this paper we propose
                 an 8-bit floating point (FP8) binary interchange format
                 consisting of two encodings - E4M3 (4-bit exponent and
                 3-bit mantissa) and E5M2 (5-bit exponent and 2-bit
                 mantissa). While E5M2 follows IEEE 754 conventions for
                 representation of special values, E4M3's dynamic range
                 is extended by not representing infinities and having
                 only one mantissa bit-pattern for NaNs. We demonstrate
                 the efficacy of the FP8 format on a variety of image
                 and language tasks, effectively matching the result
                 quality achieved by 16-bit training sessions. Our study
                 covers the main modern neural network architectures -
                 CNNs, RNNs, and Transformer-based models, leaving all
                 the hyperparameters unchanged from the 16-bit baseline
                 training sessions. Our training experiments include
                 large, up to 175B parameter, language models. We also
                 examine FP8 post-training-quantization of language
                 models trained using 16-bit formats that resisted fixed
                 point int8 quantization.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "2209.05433",
  primaryclass = "cs.LG",
}

@InProceedings{Monniaux:2022:FVB,
  author =       "David Monniaux and Alice Pain",
  title =        "Formally verified 32- and 64-bit integer division
                 using double-precision floating-point arithmetic",
  crossref =     "IEEE:2022:ISC",
  pages =        "128--132",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00032",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://hal.science/hal-03722203/",
  abstract =     "Some recent processors are not equipped with an
                 integer division unit. Compilers then implement
                 division by a call to a special function supplied by
                 the processor designers, which implements division by a
                 loop producing one bit of quotient per iteration. This
                 hinders compiler optimizations and results in
                 non-constant time computation, which is a problem in
                 some applications. We advocate instead using the
                 processor's floating-point unit, and propose code that
                 the compiler can easily interleave with other
                 computations. We fully proved the correctness of our
                 algorithm, which mixes floating-point and
                 fixed-bitwidth integer computations, using the Coq
                 proof assistant and successfully integrated it into the
                 CompCert formally verified compiler.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
}

@Article{Montuschi:2022:CAC,
  author =       "Paolo Montuschi and Jean-Michel Muller and Florent de
                 Dinechin",
  title =        "Computer Arithmetic: Continuing a Long and Steady
                 Emergence",
  journal =      j-COMPUTER,
  volume =       "55",
  number =       "10",
  pages =        "4--6",
  month =        oct,
  year =         "2022",
  CODEN =        "CPTRB4",
  DOI =          "https://doi.org/10.1109/MC.2022.3193206",
  ISSN =         "0018-9162 (print), 1558-0814 (electronic)",
  ISSN-L =       "0018-9162",
  bibdate =      "Thu Oct 27 08:20:29 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computer2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2",
}

@Article{Muller:2022:FDW,
  author =       "Jean-Michel Muller and Laurence Rideau",
  title =        "Formalization of Double-Word Arithmetic, and Comments
                 on {``Tight and Rigorous Error Bounds for Basic
                 Building Blocks of Double-Word Arithmetic''}",
  journal =      j-TOMS,
  volume =       "48",
  number =       "1",
  pages =        "9:1--9:24",
  month =        mar,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3484514",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Feb 17 08:00:57 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3484514",
  abstract =     "Recently, a complete set of algorithms for
                 manipulating double-word numbers (some classical, some
                 new) was analyzed [16]. We have formally proven all the
                 theorems given in that article, using the Coq proof
                 assistant. The formal proof work led us to: (i) locate
                 mistakes in some of the original paper proofs (mistakes
                 that, however, do not hinder the validity of the
                 algorithms), (ii) significantly improve some error
                 bounds, and (iii) generalize some results by showing
                 that they are still valid if we slightly change the
                 rounding mode. The consequence is that the algorithms
                 presented in [16] can be used with high confidence, and
                 that some of them are even more accurate than what was
                 believed before. This illustrates what formal proof can
                 bring to computer arithmetic: beyond mere (yet
                 extremely useful) verification, correction, and
                 consolidation of already known results, it can help to
                 find new properties. All our formal proofs are freely
                 available.",
  acknowledgement = ack-nhfb,
  articleno =    "9",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@InProceedings{Murillo:2022:CDD,
  author =       "Raul Murillo and David Mallas{\'e}n and Alberto A.
                 {Del Barrio} and Guillermo Botella",
  title =        "Comparing Different Decodings for Posit Arithmetic",
  crossref =     "Gustafson:2022:NGA",
  pages =        "84--99",
  year =         "2022",
  DOI =          "https://doi.org/10.1007/978-3-031-09779-9_6",
  bibdate =      "Fri Dec 15 07:04:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@Article{Murillo:2022:PPL,
  author =       "Raul Murillo and Alberto A. {Del Barrio} and Guillermo
                 Botella and Min Soo Kim and HyunJin Kim and Nader
                 Bagherzadeh",
  title =        "{PLAM}: a Posit Logarithm-Approximate Multiplier",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "10",
  number =       "4",
  pages =        "2079--2085",
  month =        oct # "\slash " # dec,
  year =         "2022",
  DOI =          "https://doi.org/10.1109/TETC.2021.3109127",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  abstract =     "The Posit{\TM} Number System was introduced in 2017 as
                 a replacement for floating-point numbers. Since then,
                 the community has explored its application in several
                 areas, such as deep learning, and produced some unit
                 designs which are still far from being competitive with
                 their floating-point counterparts. This article
                 proposes a Posit Logarithm-Approximate Multiplication
                 (PLAM) scheme to significantly reduce the complexity of
                 posit multipliers, one of the most power-hungry
                 arithmetic units. The impact of this approach is
                 evaluated in deep neural network inference, where there
                 are no significant accuracy drops. Compared with
                 state-of-the-art posit multipliers, experiments show
                 that the proposed technique reduces the area, power,
                 and delay of 32-bit hardware multipliers up to 72.86\%,
                 81.79\%, and 17.01\%, respectively.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}

@Article{Nath:2022:KVM,
  author =       "Kaushik Nath and Palash Sarkar",
  title =        "{Kummer} versus {Montgomery} Face-off over Prime Order
                 Fields",
  journal =      j-TOMS,
  volume =       "48",
  number =       "2",
  pages =        "13:1--13:28",
  month =        jun,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3503536",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 20 07:04:17 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3503536",
  abstract =     "This paper makes a comprehensive comparison of the
                 efficiencies of vectorized implementations of Kummer
                 lines and Montgomery curves at various security levels.
                 For the comparison, nine Kummer lines are considered,
                 out of which eight are new, and new assembly
                 implementations of all nine Kummer lines have been
                 made. Seven previously proposed Montgomery curves are
                 considered and new vectorized assembly implementations
                 have been made for three of them. Our comparisons show
                 that for all security levels, Kummer lines are
                 consistently faster than Montgomery curves, though the
                 speed-up gap is not much.",
  acknowledgement = ack-nhfb,
  articleno =    "13",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@InProceedings{Nezhadi:2022:SFP,
  author =       "Ali Nezhadi and Shaahin Angizi and Arman Roohi",
  booktitle =    "{2022 21st IEEE International Conference on Machine
                 Learning and Applications (ICMLA)}",
  title =        "{semiMul}: Floating-Point Free Implementations for
                 Efficient and Accurate Neural Network Training",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "837--842",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ICMLA55696.2022.00139",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Approximate Computing; Computer architecture; Costs;
                 Deep learning; Graphics processing units; Machine
                 Learning; Neural networks; Neural Networks; Power
                 demand; Training",
}

@Article{Noune:2022:BNF,
  author =       "B. Noune and P. Jones and D. Justus and D. Masters and
                 C. Luschi",
  title =        "8-bit numerical formats for deep neural networks",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--30",
  year =         "2022",
  bibdate =      "Thu Nov 30 05:46:05 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/abs/2206.02915",
  abstract =     "Given the current trend of increasing size and
                 complexity of machine learning architectures, it has
                 become of critical importance to identify new
                 approaches to improve the computational efficiency of
                 model training. In this context, we address the
                 advantages of floating-point over fixed-point
                 representation, and present an in-depth study on the
                 use of 8-bit floating-point number formats for
                 activations, weights, and gradients for both training
                 and inference. We explore the effect of different
                 bit-widths for exponents and significands and different
                 exponent biases. The experimental results demonstrate
                 that a suitable choice of these low-precision formats
                 enables faster training and reduced power consumption
                 without any degradation in accuracy for a range of deep
                 learning models for image classification and language
                 processing.",
  acknowledgement = ack-nhfb,
}

@Article{Nunez-Yanez:2022:FAD,
  author =       "Jose Nunez-Yanez",
  title =        "Fused Architecture for Dense and Sparse Matrix
                 Processing in {TensorFlow Lite}",
  journal =      j-IEEE-MICRO,
  volume =       "42",
  number =       "6",
  pages =        "55--66",
  month =        nov # "\slash " # dec,
  year =         "2022",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.2022.3196705",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Nov 03 05:37:10 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeemicro.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}

@Article{Oaks:2022:ZNM,
  author =       "Jeffrey Oaks",
  title =        "Zero and nothing in medieval {Arabic} arithmetic",
  journal =      j-BRITISH-J-HIST-MATH,
  volume =       "37",
  number =       "3",
  pages =        "179--211",
  year =         "2022",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/26375451.2022.2115745",
  ISSN =         "1749-8430 (print), 1749-8341 (electronic)",
  ISSN-L =       "1749-8341",
  bibdate =      "Tue Feb 28 07:20:03 MST 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/bshm.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.tandfonline.com/doi/full/10.1080/26375451.2022.2115745",
  abstract =     "Whether explaining calculations with decimal or
                 sexagesimal notation, arithmetic books composed in
                 Arabic beginning in the ninth century CE consistently
                 describe the zero ({\d{s}}ifr) as a sign indicating an
                 empty place where there is no number. And yet we find
                 that some arithmeticians explicitly performed
                 operations on this zero. To understand how the zero was
                 conceived and manipulated in medieval Arabic texts we
                 first address the way that numbers themselves were
                 conceived and how `nothing' entered into arithmetical
                 problem-solving. From there we examine arithmetic books
                 for their treatment of zero. We find that there is no
                 inconsistency in operating on what is literally
                 nothing, and thus there was no motive for
                 arithmeticians to regard zero as a number.",
  acknowledgement = ack-nhfb,
  ajournal =     "BSHM Bull.",
  fjournal =     "BSHM Bulletin: Journal of the British Society for the
                 History of Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/tbsh20",
  onlinedate =   "25 Sep 2022",
}

@Article{Oberman:2022:GES,
  author =       "Stuart Oberman and Leonel Sousa and Bogdan Pasca and
                 Alberto Nannarelli",
  title =        "Guest Editorial: Special Section on Emerging and
                 Impacting Trends on Computer Arithmetic",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "10",
  number =       "3",
  pages =        "1239--1240",
  month =        jul # "\slash " # sep,
  year =         "2022",
  DOI =          "https://doi.org/10.1109/TETC.2022.3195414",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}

@InProceedings{Oh:2022:EPA,
  author =       "Hyun Woo Oh and Won Sik Jeong and Seung Eun Lee",
  editor =       "{IEEE}",
  booktitle =    "{2022 19th International SoC Design Conference
                 (ISOCC)}",
  title =        "Evaluation of Posit Arithmetic on Machine Learning
                 based on Approximate Exponential Functions",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "358--359",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ISOCC56007.2022.10031524",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Ollivier:2022:PRB,
  author =       "S{\'e}bastien Ollivier and Xinyi Zhang and Yue Tang
                 and Chayanika Choudhuri and Jingtong Hu and Alex K.
                 Jones",
  title =        "Pod-racing: bulk-bitwise to floating-point compute in
                 racetrack memory for machine learning at the edge",
  journal =      j-IEEE-MICRO,
  volume =       "42",
  number =       "6",
  pages =        "9--16",
  month =        nov # "\slash " # dec,
  year =         "2022",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.2022.3195761",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Nov 03 05:37:10 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeemicro.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}

@InProceedings{Omtzigt:2022:URR,
  author =       "E. Theodore L. Omtzigt and James Quinlan",
  title =        "Universal: Reliable, Reproducible, and
                 Energy-Efficient Numerics",
  crossref =     "Gustafson:2022:NGA",
  pages =        "100--116",
  year =         "2022",
  DOI =          "https://doi.org/10.1007/978-3-031-09779-9_7",
  bibdate =      "Fri Dec 15 07:04:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@Article{Osorio:2022:BFA,
  author =       "John Osorio and Adri{\`a} Armejach and Eric Petit and
                 Greg Henry and Marc Casas",
  title =        "A {BF16 FMA} is All You Need for {DNN} Training",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "10",
  number =       "3",
  pages =        "1302--1314",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/TETC.2022.3187770",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
  keywords =     "Arithmetic; BF16; Compounds; Computational modeling;
                 computer arithmetic; emulation; FMA Operators; FP32;
                 Hardware; hardware; machine learning; Neural nets;
                 Proposals; reduced precision; Silicon; swamping;
                 Training",
}

@InProceedings{Osorio:2022:FFA,
  author =       "John Osorio and Adri{\`a} Armejach and Eric Petit and
                 Greg Henry and Marc Casas",
  booktitle =    "{2022 IEEE International Symposium on Performance
                 Analysis of Systems and Software (ISPASS)}",
  title =        "{FASE}: a Fast, Accurate and Seamless Emulator for
                 Custom Numerical Formats",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "144--146",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ISPASS55109.2022.00017",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "BFloat16; Binary Analysis Tool; Codes; Deep learning;
                 DNN; Emulation; FASE (FAST, ACCURATE, AND SEAMLESS
                 EMULATOR); FP32; LOW PRECISION; NEURAL NETWORKS; POWER
                 DEMAND; SOFTWARE; TRAINING",
}

@Article{Park:2022:NNT,
  author =       "Jeongwoo Park and Sunwoo Lee and Dongsuk Jeon",
  title =        "A Neural Network Training Processor With 8-Bit Shared
                 Exponent Bias Floating Point and Multiple-Way Fused
                 Multiply-Add Trees",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "57",
  number =       "3",
  pages =        "965--977",
  year =         "2022",
  CODEN =        "IJSCBC",
  DOI =          "https://doi.org/10.1109/JSSC.2021.3103603",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "Computational efficiency; Computational modeling;
                 Degradation; digital integrated circuits; Hardware;
                 learning systems; neural network accelerators; Neural
                 networks; Task analysis; Tensors; Training; very
                 large-scale integration",
}

@Article{Park:2022:RCR,
  author =       "Kangkyu Park and Seungkyu Choi and Yeongjae Choi and
                 Lee-Sup Kim",
  title =        "Rare Computing: Removing Redundant Multiplications
                 From Sparse and Repetitive Data in Deep Neural
                 Networks",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "71",
  number =       "4",
  pages =        "795--808",
  month =        apr,
  year =         "2022",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2021.3063269",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Mar 17 06:38:17 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Patel:2022:LPG,
  author =       "Pragnesh Patel and Aman Arora and Earl Swartzlander
                 and Lizy John",
  booktitle =    "{2022 23rd International Symposium on Quality
                 Electronic Design (ISQED)}",
  title =        "{LogGen}: a Parameterized Generator for Designing
                 Floating-Point Logarithm Units for Deep Learning",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--7",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ISQED54688.2022.9806139",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ASIC; Deep learning; Deep Learning Hardware; Delays;
                 Digital signal processing; Floating-point Arithmetic;
                 FPGA; Generator; Generators; Logarithm; Measurement;
                 Memory management; Pipelines; Tools",
}

@Article{Peng:2022:DNN,
  author =       "Jiaxin Peng and Yousra Alkabani and Krunal Puri and
                 Xiaoxuan Ma and Volker Sorger and Tarek El-Ghazawi",
  title =        "A Deep Neural Network Accelerator using Residue
                 Arithmetic in a Hybrid Optoelectronic System",
  journal =      j-JETC,
  volume =       "18",
  number =       "4",
  pages =        "81:1--81:??",
  month =        oct,
  year =         "2022",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3550273",
  ISSN =         "1550-4832 (print), 1550-4840 (electronic)",
  ISSN-L =       "1550-4832",
  bibdate =      "Sat Oct 29 07:30:43 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jetc.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3550273",
  abstract =     "The acceleration of Deep Neural Networks (DNNs) has
                 attracted much attention in research. Many critical
                 real-time applications benefit from DNN accelerators
                 but are limited by their compute-intensive nature. This
                 work introduces an accelerator for \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "81",
  fjournal =     "ACM Journal on Emerging Technologies in Computing
                 Systems (JETC)",
  journal-URL =  "https://dl.acm.org/loi/jetc",
}

@InProceedings{Puntsri:2022:RAG,
  author =       "Kidsananapong Puntsri and Bussakorn Bunsri and
                 Yaowarat Pittayang and Tanatip Bubpawan and Wuttichai
                 Partipralam and Watid Phakphisut",
  booktitle =    "{2022 37th International Technical Conference on
                 Circuits/Systems, Computers and Communications
                 (ITC-CSCC)}",
  title =        "Reconfigurable {AWGN} Generator Using {Box--Muller}
                 Method with {CORDIC}-based Square Root Calculation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--4",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ITC-CSCC55581.2022.9894924",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Box--Muller Method; CODIC method; Gaussian Noise
                 Generator; Generators; Noise generators; Parity check
                 codes; Polar codes; Real-time systems; Registers; Table
                 lookup",
}

@TechReport{PWG:2022:SPA,
  author =       "{Posit Working Group}",
  title =        "Standard for Posit{\TM} Arithmetic (2022)",
  type =         "Report",
  institution =  "National Supercomputing Centre (NSCC)",
  address =      "Singapore",
  pages =        "12",
  day =          "2",
  month =        mar,
  year =         "2022",
  bibdate =      "Fri Dec 15 11:16:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://posithub.org/docs/posit_standard-2.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Ramachandran:2022:PCP,
  author =       "Akshat Ramachandran and John Gustafson and Anusua Roy
                 and Rizwan Ahmed Ansari and Rohin Daruwala",
  editor =       "{IEEE}",
  booktitle =    "{2022 25th Euromicro Conference on Digital System
                 Design (DSD)}",
  title =        "{PositIV}: a Configurable Posit Processor Architecture
                 for Image and Video Processing",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "93--100",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/DSD57027.2022.00022",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Roy:2022:AAC,
  author =       "Avishek Sinha Roy and Hardik Agrawal and Anindya
                 Sundar Dhar",
  title =        "{ACBAM}-Accuracy-Configurable Sign Inclusive Broken
                 Array {Booth} Multiplier Design",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "10",
  number =       "4",
  pages =        "2072--2078",
  month =        oct # "\slash " # dec,
  year =         "2022",
  DOI =          "https://doi.org/10.1109/TETC.2021.3107509",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}

@InProceedings{Russinoff:2022:FVC,
  author =       "David Russinoff and Javier Bruguera and Cuong Chau and
                 Mayank Manjrekar and Nicholas Pfister and Harsha
                 Valsaraju",
  title =        "Formal Verification of a Chained Multiply-Add Design:
                 Combining Theorem Proving and Equivalence Checking",
  crossref =     "IEEE:2022:ISC",
  pages =        "120--126",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00030",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
}

@InProceedings{S:2022:IRP,
  author =       "Sathyavathi N S and Augusta Sophy Beulet P",
  editor =       "{IEEE}",
  booktitle =    "{2022 Third International Conference on Intelligent
                 Computing Instrumentation and Control Technologies
                 (ICICICT)}",
  title =        "Implementation of {Regime-5} Posit adder",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1040--1043",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ICICICT54557.2022.9917949",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Sadeghimanesh:2022:SSN,
  author =       "AmirHosein Sadeghimanesh and Matthew England",
  title =        "An {SMT} solver for non-linear real arithmetic inside
                 {Maple}",
  journal =      j-ACM-COMM-COMP-ALGEBRA,
  volume =       "56",
  number =       "2",
  pages =        "76--79",
  month =        jun,
  year =         "2022",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3572867.3572880",
  ISSN =         "1932-2232 (print), 1932-2240 (electronic)",
  ISSN-L =       "1932-2232",
  bibdate =      "Mon Aug 21 16:58:02 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3572867.3572880",
  abstract =     "We report on work-in-progress to create an SMT-solver
                 inside Maple for non-linear real arithmetic (NRA). We
                 give background information on the algorithm being
                 implemented: cylindrical algebraic coverings as a
                 theory solver in the lazy SMT paradigm. We then present
                 some new work on the identification of minimal
                 conflicting cores from the coverings.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Commun. Computer Algebr.",
  fjournal =     "ACM Communications in Computer Algebra",
  journal-URL =  "https://dl.acm.org/loi/sigsam-cca",
}

@InProceedings{Safieh:2022:ERA,
  author =       "Malek Safieh and Fabrizio {De Santis}",
  title =        "Efficient Reduction Algorithms for Special {Gaussian}
                 Integer Moduli",
  crossref =     "IEEE:2022:ISC",
  pages =        "111--119",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00029",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
}

@Article{Schober:2022:HAM,
  author =       "Peter Schober and M. Hassan Najafi and Nima
                 TaheriNejad",
  title =        "High-Accuracy Multiply-Accumulate ({MAC}) Technique
                 for Unary Stochastic Computing",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "71",
  number =       "6",
  pages =        "1425--1439",
  month =        jun,
  year =         "2022",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2021.3087027",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed May 25 09:41:19 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Seidel:2022:EFP,
  author =       "Raphael Seidel and Nikolay Tcholtchev and Sebastian
                 Bock and Colin Kai-Uwe Becker and Manfred Hauswirth",
  title =        "Efficient Floating Point Arithmetic for Quantum
                 Computers",
  journal =      j-IEEE-ACCESS,
  volume =       "10",
  pages =        "72400--72415",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ACCESS.2022.3188251",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Tue Sep 30 17:30:28 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "Adders; Arithmetic; Computers; floating point
                 arithmetic; Logic gates; Quantum arithmetic; quantum
                 computing; Quantum computing; Qubit; Registers",
}

@Article{Shah:2022:DDP,
  author =       "Nimish Shah and Laura Isabel Galindez Olascoaga and
                 Shirui Zhao and Wannes Meert and Marian Verhelst",
  title =        "{DPU}: {DAG} Processing Unit for Irregular Graphs With
                 Precision-Scalable Posit Arithmetic in 28 nm",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "57",
  number =       "8",
  pages =        "2586--2596",
  year =         "2022",
  CODEN =        "IJSCBC",
  DOI =          "https://doi.org/10.1109/JSSC.2021.3134897",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
}

@InProceedings{Sibidanov:2022:CMP,
  author =       "Alexei Sibidanov and Paul Zimmermann and St{\'e}phane
                 Glondu",
  title =        "The {CORE-MATH} Project",
  crossref =     "IEEE:2022:ISC",
  pages =        "26--34",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00014",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The CORE-MATH project aims at providing open-source
                 mathematical functions with correct rounding that can
                 be integrated into current mathematical libraries. This
                 article demonstrates the CORE-MATH methodology on two
                 functions: the binary32 power function (powf) and the
                 binary64 cube root function (cbrt). CORE-MATH already
                 provides a full set of correctly rounded C99 functions
                 for single precision (binary32). These functions
                 provide similar or in some cases up to threefold
                 speedups with respect to the GNU libc mathematic
                 library, which is not correctly rounded. This work
                 offers a prospect of the mandatory requirement of
                 correct rounding for mathematical functions in the next
                 revision of the IEEE-754 standard.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-29; correct rounding; floating-point
                 arithmetic",
}

@InProceedings{Siddamshetty:2022:EHA,
  author =       "Susheel Ujwal Siddamshetty and Srinivas Boppu and
                 Debapratim Ghosh",
  editor =       "{IEEE}",
  booktitle =    "{2022 IEEE 15th International Symposium on Embedded
                 Multicore/Many-core Systems-on-Chip (MCSoC)}",
  title =        "Efficient Hardware Architecture for Posit
                 Addition\slash Subtraction",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "387--394",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/MCSoC57363.2022.00068",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sohn:2022:EFP,
  author =       "Jongwook Sohn and David K. Dean and Eric Quintana and
                 Wing Shek Wong",
  title =        "Enhanced Floating-Point Adder with Full Denormal
                 Support",
  crossref =     "IEEE:2022:ISC",
  pages =        "01--08",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00015",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
}

@Misc{Spiridonov:2022:ABE,
  author =       "Iouri Spiridonov",
  title =        "Arithmetic of binary equivalents of decimal numbers",
  howpublished = "TechRxiv preprint.",
  day =          "23",
  month =        nov,
  year =         "2022",
  DOI =          "https://doi.org/10.36227/techrxiv.19294511.v4",
  bibdate =      "Fri Sep 29 14:24:39 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.techrxiv.org/articles/preprint/The_arithmetic_of_binary_equivalents_of_decimal_numbers/19294511",
  abstract =     "Within the framework of the concept of decimal
                 calculations proposed in the article using binary
                 arithmetic, a theory of binary equivalents of decimal
                 floating-point numbers has been developed. According to
                 this theory, basic decimal arithmetic operations on
                 finite decimal numbers are performed with decimal
                 precision by a binary processor according to the rules
                 of binary arithmetic on the binary equivalents of
                 decimal numbers. These calculation results are entirely
                 consistent with the classical decimal finite number
                 arithmetic and do not require the use of test programs.
                 The identity of calculation results in decimal and
                 binary equivalent arithmetics guarantees the
                 repeatability of results on any platform. The article
                 shows that implementing binary equivalents arithmetic
                 with an acceptable decimal calculation error requires
                 significantly fewer bits of binary processor registers
                 than in modern computers. Because of the uniqueness of
                 binary decimal equivalents, the difference between
                 equal, properly rounded binary decimal equivalents is
                 strictly zero. The presence of an explicit zero in the
                 arithmetic of binary equivalents of decimal numbers
                 makes it possible to implement a bitwise comparison of
                 such numbers and introduce the concept of an
                 infinitesimal number when the significand of a
                 floating-point number is equal to zero.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sravya:2022:HPN,
  author =       "Alapati Madhu Sravya and N. Swetha and Asisa Kumar
                 Panigrahy",
  editor =       "{IEEE}",
  booktitle =    "{2022 3rd International Conference for Emerging
                 Technology (INCET)}",
  title =        "Hardware Posit Numeration System primarily based on
                 Arithmetic Operations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--8",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/INCET54531.2022.9825011",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Srivastava:2022:FSC,
  author =       "Nitish Srivastava and Gai Liu and Yi-Hsiang Lai and
                 Zhiru Zhang",
  booktitle =    "Handbook of Computer Architecture",
  title =        "{FPGA}-Specific Compilers",
  publisher =    "Springer Nature",
  address =      "Singapore",
  pages =        "1--37",
  year =         "2022",
  DOI =          "https://doi.org/10.1007/978-981-15-6401-7_25-1",
  ISBN =         "981-15-6401-9",
  ISBN-13 =      "978-981-15-6401-7",
  bibdate =      "Fri Dec 15 11:31:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@Book{Strickland:2022:LBI,
  author =       "Lloyd Strickland and Harry R. Lewis",
  title =        "{Leibniz} on Binary: The Invention of Computer
                 Arithmetic",
  publisher =    "MIT Press",
  address =      "Wheaton, MA, USA",
  pages =        "413",
  year =         "2022",
  ISBN =         "0-262-37212-6 (e-book), 0-262-54434-2",
  ISBN-13 =      "978-0-262-37212-1 (e-book), 978-0-262-54434-4",
  LCCN =         "QA141.4",
  bibdate =      "Fri Mar 17 08:38:41 MDT 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  subject =      "Leibniz, Gottfried Wilhelm, Freiherr von; Translations
                 into English; Mathematics, German; Binary system
                 (Mathematics); History",
  subject-dates = "1646--1716",
  tableofcontents = "Intro \\
                 Title Page \\
                 Copyright Page \\
                 Dedication \\
                 Epigraph \\
                 Table of Contents \\
                 List of Figures \\
                 Abbreviations \\
                 Preface \\
                 Acknowledgments \\
                 Introduction \\
                 1. Notes on Algebra, Arithmetic, and Geometric Series
                 (October 1674) \\
                 2. The Series of All Numbers, and on Binary Progression
                 (before 15/25 March 1679) \\
                 3. Binary Progression (before 15/25 March 1679) \\
                 4. Geometric Progressions and Positional Notation
                 (before 15/25 March 1679) \\
                 5. Binary Arithmetic Machine (before 15/25 March 1679)
                 \\
                 6. On the Binary Progression (15/25 March 1679)7.
                 Attempted Expression of the Circle in Binary
                 Progression (c. 1679) \\
                 8. Sedecimal Progression (1679) \\
                 9. Binary Progression Is for Theory, Sedecimal for
                 Practice (c. 1679) \\
                 10. On the Organon or Great Art of Thinking (first half
                 [?] of 1679) \\
                 11. Binary Ancestral Calculations (early 1680s [?]) \\
                 12. Sedecimal on an Envelope (c. 1682--1685) \\
                 13. Remarks on Weigel (1694--mid-March 1695) \\
                 14. Leibniz to Duke Rudolph August (7/17--8/18 May
                 1696)15. A Wonderful Expression of All Numbers by 1 and
                 0 Representing the Origin of Things from God and
                 Nothing, or the Mystery of Creation (7/17 May 1696) \\
                 16. Wonderful Origin of All Numbers from 1 and 0, Which
                 Serves as a Beautiful Representation of the Mystery of
                 Creation, since Everything Arises from God and Nothing
                 Else (8/18 May 1696) \\
                 17. Leibniz to Duke Rudolph August (2/12 January 1697)
                 \\
                 18. Duke Rudolph August to Johann Urban M{\"u}ller
                 (5/15 January 1697) \\
                 19. Leibniz to Claudio Filippo Grimaldi
                 (mid-January-early February 1697) \\
                 20. Periods (May 1698--first half of January 1701)21.
                 Leibniz to Philippe Naud{\'e} (15 January 1701) \\
                 22. Leibniz to Joachim Bouvet (15 February 1701) \\
                 23. Essay on a New Science of Numbers (26 February
                 1701) \\
                 24. Binary Addition (spring-summer 1701 [?]) \\
                 25. Periods in Binary (spring-fall 1701) \\
                 26. Periods and Powers (mid-to-late June 1701 [?]) \\
                 27. Demonstration That Columns of Sequences Exhibiting
                 Powers of Arithmetic Progressions, or Numbers Composed
                 from These, Are Periodic (November 1701) \\
                 28. Joachim Bouvet to Leibniz (4 November 1701) \\
                 29. Leibniz to Bouvet (early April [?] 1703)30.
                 Explanation of Binary Arithmetic, Which Uses Only the
                 Digits 0 and 1, with Some Remarks on Its Usefulness,
                 and on the Light It Throws on the Ancient Chinese
                 Figures of Fuxi (7 April 1703) \\
                 31. Leibniz to C{\'e}sar Caze (23 June 1705) \\
                 32. On Binary (late June 1705) \\
                 Bibliography \\
                 Index",
}

@Article{Tan:2022:SRT,
  author =       "Bryan Tan and Benjamin Mariano and Shuvendu K. Lahiri
                 and Isil Dillig and Yu Feng",
  title =        "{SolType}: refinement types for arithmetic overflow in
                 {Solidity}",
  journal =      j-PACMPL,
  volume =       "6",
  number =       "POPL",
  pages =        "4:1--4:29",
  month =        jan,
  year =         "2022",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3498665",
  ISSN =         "2475-1421 (electronic)",
  ISSN-L =       "2475-1421",
  bibdate =      "Thu May 26 06:32:48 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/pacmpl.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3498665",
  abstract =     "As smart contracts gain adoption in financial
                 transactions, it becomes increasingly important to
                 ensure that they are free of bugs and security
                 vulnerabilities. Of particular relevance in this
                 context are arithmetic overflow bugs, as integers are
                 often used to represent financial assets like account
                 balances. Motivated by this observation, this paper
                 presents SolType, a refinement type system for Solidity
                 that can be used to prevent arithmetic over- and
                 under-flows in smart contracts. SolType allows
                 developers to add refinement type annotations and uses
                 them to prove that arithmetic operations do not lead to
                 over- and under-flows. SolType incorporates a rich
                 vocabulary of refinement terms that allow expressing
                 relationships between integer values and aggregate
                 properties of complex data structures. Furthermore, our
                 implementation, called Solid, incorporates a type
                 inference engine and can automatically infer useful
                 type annotations, including non-trivial contract
                 invariants.\par

                 To evaluate the usefulness of our type system, we use
                 Solid to prove arithmetic safety of a total of 120
                 smart contracts. When used in its fully automated mode
                 (i.e., using Solid's type inference capabilities),
                 Solid is able to eliminate 86.3\% of redundant runtime
                 checks used to guard against overflows. We also compare
                 Solid against a state-of-the-art arithmetic safety
                 verifier called VeriSmart and show that Solid has a
                 significantly lower false positive rate, while being
                 significantly faster in terms of verification time.",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  fjournal =     "Proceedings of the ACM on Programming Languages
                 (PACMPL)",
  journal-URL =  "https://dl.acm.org/loi/pacmpl",
}

@InProceedings{Tatar:2022:PEL,
  author =       "Guner Tatar and Salih Bayar and Ihsan Cicek",
  booktitle =    "{2022 International Conference on Innovations in
                 Intelligent SysTems and Applications (INISTA)}",
  title =        "Performance Evaluation of Low-Precision Quantized
                 {LeNet} and {ConvNet} Neural Networks",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--6",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/INISTA55318.2022.9894261",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computational modeling; ConvNet; Convolutional neural
                 networks; Fixed point arithmetic; Floating point
                 arithmetic; FPGA; Hardware accelerators; LeNet; Neural
                 networks; Performance evaluation; Power demand;
                 Quantization (signal); Quantized neural networks;
                 Technological innovation; Training",
}

@InProceedings{Tortorella:2022:RCF,
  author =       "Yvan Tortorella and Luca Bertaccini and Davide Rossi
                 and Luca Benini and Francesco Conti",
  editor =       "{IEEE}",
  booktitle =    "{2022 Design, Automation \& Test in Europe Conference
                 \& Exhibition (DATE)}",
  title =        "{RedMulE}: a Compact {FP16} Matrix-Multiplication
                 Accelerator for Adaptive Deep Learning on
                 {RISC-V}-Based Ultra-Low-Power {SoCs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1099--1102",
  year =         "2022",
  DOI =          "https://doi.org/10.23919/DATE54114.2022.9774759",
  bibdate =      "Sat Dec 16 15:51:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Venkataramanaiah:2022:BFP,
  author =       "Shreyas Kolala Venkataramanaiah and Jian Meng and
                 Han-Sok Suh and Injune Yeo and Jyotishman Saikia and
                 Sai Kiran Cherupally and Yichi Zhang and Zhiru Zhang
                 and Jae-sun Seo",
  booktitle =    "{ESSCIRC 2022 --- IEEE 48th European Solid State
                 Circuits Conference (ESSCIRC)}",
  title =        "A 28nm 8-bit Floating-Point {Tensor Core} based {CNN}
                 Training Processor with Dynamic Activation\slash Weight
                 Sparsification",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "89--92",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ESSCIRC55480.2022.9911359",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Convolutional neural networks; deep neural network
                 training; Energy efficiency; Europe; hardware
                 accelerator; Neural networks; Prototypes; structured
                 sparsity; Tensors; Topology; Training",
}

@InProceedings{Verma:2022:RVC,
  author =       "Anu Verma and Priyamvada Sharma and Bishnu Prasad
                 Das",
  editor =       "{IEEE}",
  booktitle =    "{2022 25th Euromicro Conference on Digital System
                 Design (DSD)}",
  title =        "{RISC-V} Core with Approximate Multiplier for
                 Error-Tolerant Applications",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "239--246",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/DSD57027.2022.00040",
  bibdate =      "Sat Dec 16 15:51:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
}

@Article{Walia:2022:FLP,
  author =       "Sumit Walia and Bachu Varun Tej and Arpita Kabra and
                 Joydeep Devnath and Joycee Mekie",
  title =        "Fast and Low-Power Quantized Fixed Posit High-Accuracy
                 {DNN} Implementation",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "30",
  number =       "1",
  pages =        "108--111",
  year =         "2022",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/TVLSI.2021.3131609",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
}

@InProceedings{Wang:2022:ARE,
  author =       "Luming Wang and Defeng Chen and Dongliang Wang and
                 Chao Wang",
  booktitle =    "{2022 IEEE 5th Advanced Information Management,
                 Communicates, Electronic and Automation Control
                 Conference (IMCEC)}",
  title =        "Acceleration of radar echo coherent accumulation
                 system based on half-precision format and tensor core",
  volume =       "5",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "990--995",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/IMCEC55388.2022.10019890",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Batch production systems; coherent accumulation
                 system; GPU; half precision; Life estimation; Process
                 control; Radar; Radar detection; Spaceborne radar;
                 tensor core; Tensors",
}

@Article{Wang:2022:PNE,
  author =       "Yang Wang and Dazheng Deng and Leibo Liu and Shaojun
                 Wei and Shouyi Yin",
  title =        "{PL-NPU}: an Energy-Efficient Edge-Device {DNN}
                 Training Processor With Posit-Based Logarithm-Domain
                 Computing",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-1,
  volume =       "69",
  number =       "10",
  pages =        "4042--4055",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/TCSI.2022.3184115",
  ISSN =         "1549-8328 (print), 1558-0806 (electronic)",
  ISSN-L =       "1549-8328",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems I: Regular
                 Papers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8919",
}

@Article{Waris:2022:AAR,
  author =       "Haroon Waris and Chenghua Wang and Chenyu Xu and
                 Weiqiang Liu",
  title =        "{AxRMs}: Approximate Recursive Multipliers Using
                 High-Performance Building Blocks",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "10",
  number =       "2",
  pages =        "1229--1235",
  month =        apr # "\slash " # jun,
  year =         "2022",
  DOI =          "https://doi.org/10.1109/TETC.2021.3096515",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}

@Article{Waris:2022:HPP,
  author =       "Haroon Waris and Chenghua Wang and Weiqiang Liu and
                 Jie Han and Fabrizio Lombardi",
  title =        "Hybrid Partial Product-Based High-Performance
                 Approximate Recursive Multipliers",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "10",
  number =       "1",
  pages =        "507--513",
  month =        jan # "\slash " # mar,
  year =         "2022",
  DOI =          "https://doi.org/10.1109/TETC.2020.3013977",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}

@Article{Xie:2022:EHI,
  author =       "Jiafeng Xie and Pengzhou He and Xiaofang Wang and
                 Jos{\'e} L. Ima{\~n}a",
  title =        "Efficient Hardware Implementation of Finite Field
                 Arithmetic {$ A B + C A B + C $} for Binary Ring-{LWE}
                 Based Post-Quantum Cryptography",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "10",
  number =       "2",
  pages =        "1222--1228",
  month =        apr # "\slash " # jun,
  year =         "2022",
  DOI =          "https://doi.org/10.1109/TETC.2021.3091982",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}

@InProceedings{You:2022:RVP,
  author =       "Chao-Xing You and Qi-Tong Wang and Han Zhong and Cheng
                 Liu",
  editor =       "{IEEE}",
  booktitle =    "{2022 4th International Academic Exchange Conference
                 on Science and Technology Innovation (IAECST)}",
  title =        "{RISC-V} processor-based automatic access
                 floating-point computing accelerated dataflow
                 co-processor",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "647--650",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/IAECST57965.2022.10061878",
  bibdate =      "Sat Dec 16 15:51:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Zacharelos:2022:ARM,
  author =       "Efstratios Zacharelos and Italo Nunziata and Gerardo
                 Saggese and Antonio G. M. Strollo and Ettore Napoli",
  title =        "Approximate Recursive Multipliers Using Low Power
                 Building Blocks",
  crossref =     "IEEE:2022:ISC",
  pages =        "67--67",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022.00020",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
}

@Article{Zhang:2022:HRD,
  author =       "Bo Zhang and Zeming Cheng and Massoud Pedram",
  title =        "High-Radix Design of a Scalable {Montgomery} Modular
                 Multiplier With Low Latency",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "71",
  number =       "2",
  pages =        "436--449",
  month =        feb,
  year =         "2022",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2021.3052999",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Jan 20 07:18:16 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Zhang:2022:SDF,
  author =       "Yi Zhang and Mengdi Sun and Xin Qi",
  title =        "Speedup of discrete {Fourier} transform by efficient
                 modular arithmetic",
  journal =      j-CCPE,
  volume =       "34",
  number =       "3",
  pages =        "e6564:1--e6564:??",
  day =          "1",
  month =        feb,
  year =         "2022",
  CODEN =        "CCPEBO",
  DOI =          "https://doi.org/10.1002/cpe.6564",
  ISSN =         "1532-0626 (print), 1532-0634 (electronic)",
  ISSN-L =       "1532-0626",
  bibdate =      "Tue Feb 22 09:50:06 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/ccpe.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Concurr. Comput.",
  fjournal =     "Concurrency and Computation: Practice and Experience",
  journal-URL =  "http://www.interscience.wiley.com/jpages/1532-0626",
  onlinedate =   "15 September 2021",
}

@Article{Zhao:2022:LML,
  author =       "Jiawei Zhao and Steve Dai and Rangharajan Venkatesan
                 and Brian Zimmer and Mustafa Ali and Ming-Yu Liu and
                 Brucek Khailany and William J. Dally and Anima
                 Anandkumar",
  title =        "{LNS-Madam}: Low-Precision Training in Logarithmic
                 Number System Using Multiplicative Weight Update",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "71",
  number =       "12",
  pages =        "3179--3190",
  year =         "2022",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2022.3202747",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Arithmetic; Costs; Hardware; hardware acceleration;
                 Machine learning; Neural networks; optimization;
                 Quantization (signal); Table lookup; Training",
}

@Article{Zolfagharinejad:2022:PPE,
  author =       "Mohamadreza Zolfagharinejad and Mehdi Kamal and Ali
                 Afzali-Khusha and Massoud Pedram",
  title =        "Posit Process Element for Using in Energy-Efficient
                 {DNN} Accelerators",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "30",
  number =       "6",
  pages =        "844--848",
  year =         "2022",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/TVLSI.2022.3165510",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
}

@Article{Zou:2022:OFR,
  author =       "Daming Zou and Yuchen Gu and Yuanfeng Shi and MingZhe
                 Wang and Yingfei Xiong and Zhendong Su",
  title =        "Oracle-free repair synthesis for floating-point
                 programs",
  journal =      j-PACMPL,
  volume =       "6",
  number =       "OOPSLA2",
  pages =        "159:1--159:??",
  month =        oct,
  year =         "2022",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3563322",
  ISSN =         "2475-1421 (electronic)",
  ISSN-L =       "2475-1421",
  bibdate =      "Sat Mar 11 09:08:36 MST 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/pacmpl.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3563322",
  abstract =     "The floating-point representation provides widely-used
                 data types (such as ``float'' and ``double'') for
                 modern numerical software. Numerical errors are
                 inherent due to floating-point's approximate nature,
                 and pose an important, well-known challenge. It is
                 nontrivial to fix/repair numerical code to reduce
                 numerical errors --- it requires either numerical
                 expertise (for manual fixing) or high-precision oracles
                 (for automatic repair); both are difficult
                 requirements. To tackle this challenge, this paper
                 introduces a principled dynamic approach that is fully
                 automated and oracle-free for effectively repairing
                 floating-point errors. The key of our approach is the
                 novel notion of micro-structure that characterizes
                 structural patterns of floating-point errors. We
                 leverage micro-structures' statistical information on
                 floating-point errors to effectively guide repair
                 synthesis and validation. Compared with existing
                 state-of-the-art repair approaches, our work is fully
                 automatic and has the distinctive benefit of not
                 relying on the difficult to obtain high-precision
                 oracles. Evaluation results on 36 commonly-used
                 numerical programs show that our approach is highly
                 efficient and effective: (1) it is able to synthesize
                 repairs instantaneously, and (2) versus the original
                 programs, the repaired programs have orders of
                 magnitude smaller floating-point errors, while having
                 faster runtime performance",
  acknowledgement = ack-nhfb,
  articleno =    "159",
  fjournal =     "Proceedings of the ACM on Programming Languages
                 (PACMPL)",
  journal-URL =  "https://dl.acm.org/loi/pacmpl",
}

@Article{Abad:2023:HAT,
  author =       "Sudeh Shirkavand Saleh Abad and Mohammad Hossein
                 Moaiyeri",
  title =        "Hardware-accuracy trade-offs for error-resilient
                 applications using an ultra-efficient hybrid
                 approximate multiplier",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "79",
  number =       "3",
  pages =        "3357--3372",
  month =        feb,
  year =         "2023",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1007/s11227-022-04789-6",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Sat Feb 18 09:20:28 MST 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsuper2020.bib",
  URL =          "https://link.springer.com/article/10.1007/s11227-022-04789-6",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Supercomputing",
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
}

@Article{Abdi:2023:FEF,
  author =       "Athena Abdi and Sina Shahoveisi",
  title =        "{FT-EALU}: fault-tolerant arithmetic and logic unit
                 for critical embedded and real-time systems",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "79",
  number =       "1",
  pages =        "626--649",
  month =        jan,
  year =         "2023",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1007/s11227-022-04698-8",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Sat Feb 18 09:20:27 MST 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsuper2020.bib",
  URL =          "https://link.springer.com/article/10.1007/s11227-022-04698-8",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Supercomputing",
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
}

@InProceedings{Adela:2023:DIS,
  author =       "Noor Alhuda Saad Adela and Amani Najeeb {Ben Yousuf}
                 and Mohamed Muftah Eljhani",
  booktitle =    "{2023 IEEE 3rd International Maghreb Meeting of the
                 Conference on Sciences and Techniques of Automatic
                 Control and Computer Engineering (MI-STA)}",
  title =        "Design and Implementation of Single Precision
                 Floating-point Arithmetic Logic Unit for {RISC}
                 Processor on {FPGA}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "130--134",
  month =        may,
  year =         "2023",
  DOI =          "https://doi.org/10.1109/mi-sta57575.2023.10169623",
  bibdate =      "Thu Dec 7 11:55:39 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Alapati:2023:HIP,
  author =       "Madhu Sravya Alapati and Raghunandan Swain and Asisa
                 Kumar Panigrahy",
  editor =       "{IEEE}",
  booktitle =    "{2023 7th International Conference on Trends in
                 Electronics and Informatics (ICOEI)}",
  title =        "Hardware Implementation of Posit Numeration System
                 using {FPGA} for Signal Processing Applications",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "278--282",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ICOEI56765.2023.10125920",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Allred:2023:FNT,
  author =       "Taylor Allred and Xinyi Li and Ashton Wiersdorf and
                 Ben Greenman and Ganesh Gopalakrishnan",
  editor =       "????",
  booktitle =    "Julia Conference 2023",
  title =        "{FlowFPX}: Nimble Tools for Debugging Floating-Point
                 Exceptions",
  publisher =    "????",
  address =      "????",
  pages =        "8",
  year =         "2023",
  bibdate =      "Mon Sep 11 06:29:11 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/julia.bib",
  URL =          "https://live.juliacon.org/talk/A3LVDS",
  abstract =     "Reliable numerical computations are central to
                 scientific computing, but the floating-point arithmetic
                 that enables large-scale models is error-prone. Numeric
                 exceptions are a common occurrence and can propagate
                 through code, leading to flawed results. This paper
                 presents FlowFPX, a toolkit for systematically
                 debugging floating-point exceptions by recording their
                 flow, coalescing exception contexts, and fuzzing in
                 select locations. These tools help scientists discover
                 when exceptions happen and track down their origin,
                 smoothing the way to a reliable codebase.",
  acknowledgement = ack-nhfb,
  keywords =     "Julia programming language",
}

@Article{Andrlon:2023:FNB,
  author =       "Mak Andrlon",
  title =        "Finding Normal Binary Floating-Point Factors
                 Efficiently",
  journal =      j-J-AUTOM-REASON,
  volume =       "67",
  number =       "1",
  pages =        "??--??",
  month =        mar,
  year =         "2023",
  CODEN =        "JAREEW",
  DOI =          "https://doi.org/10.1007/s10817-023-09659-1",
  ISSN =         "0168-7433 (print), 1573-0670 (electronic)",
  ISSN-L =       "0168-7433",
  bibdate =      "Mon Nov 27 10:20:09 MST 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
  URL =          "https://link.springer.com/article/10.1007/s10817-023-09659-1",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Autom. Reason.",
  articleno =    "11",
  fjournal =     "Journal of Automated Reasoning",
  journal-URL =  "http://link.springer.com/journal/10817",
}

@Misc{Anonymous:2023:IWG,
  author =       "Anonymous",
  title =        "{IEEE Working Group P3109} Interim Report on 8-bit
                 Binary Floating-Point Formats",
  howpublished = "IEEE Web document.",
  pages =        "18",
  day =          "18",
  month =        sep,
  year =         "2023",
  bibdate =      "Thu Nov 30 05:10:41 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Version 0.5.1: 24 November 2023.",
  URL =          "https://github.com/P3109/Public/blob/main/Shared%20Reports/P3109%20WG%20Interim%20report.pdf",
  acknowledgement = ack-nhfb,
  remark =       "The draft specifies encodings of unsigned zero,
                 +/-Infinity, and quiet NaN, with precision 3, 4, and 5
                 bits (including the implicit not-stored leading bit),
                 and subnormals.",
}

@TechReport{Anonymous:2023:TDT,
  author =       "Anonymous",
  title =        "{Tesla Dojo Technology}: a guide to {Tesla}'s
                 configurable floating point formats and arithmetic:
                 {Tesla Configurable Float8 (CFloat8) \& Float16
                 (CFloat16)} Formats",
  type =         "Report",
  institution =  "Tesla. Inc.",
  pages =        "9",
  year =         "2023",
  bibdate =      "Thu Nov 30 05:53:41 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://tesla-cdn.thron.com/static/MXMU3S_tesla-dojo-technology_1WDVZN.pdf",
  abstract =     "This standard specifies Tesla arithmetic formats and
                 methods for the new 8-bit and 16-bit binary
                 floating-point arithmetic in computer programming
                 environments for deep learning neural network training.
                 This standard also specifies exception conditions and
                 the status flags thereof. An implementation of a
                 floating-point system conforming to this standard may
                 be realized entirely in software, entirely in hardware,
                 or in any combination of software and hardware",
  acknowledgement = ack-nhfb,
}

@Misc{ARM:2023:ACA,
  author =       "{ARM Corporation}",
  title =        "{ARM} Compiler {ARM C} and {C++} Libraries and
                 Floating-Point Support User Guide Version 6.00",
  howpublished = "Web site",
  year =         "2023",
  bibdate =      "Fri Dec 01 12:34:49 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://developer.arm.com/documentation/dui0808/a/floating-point-support/exception-types-recognized-by-the-arm-floating-point-environment",
  acknowledgement = ack-nhfb,
}

@Article{Awais:2023:TOS,
  author =       "Muhammad Awais and Ali Zahir and Syed Ayaz Ali Shah
                 and Pedro Reviriego and Anees Ullah and Nasim Ullah and
                 Adam Khan and Hazrat Ali",
  title =        "Toward Optimal Softcore Carry-aware Approximate
                 Multipliers on {Xilinx} {FPGAs}",
  journal =      j-TECS,
  volume =       "22",
  number =       "4",
  pages =        "76:1--76:??",
  month =        jul,
  year =         "2023",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3564243",
  ISSN =         "1539-9087 (print), 1558-3465 (electronic)",
  ISSN-L =       "1539-9087",
  bibdate =      "Thu Aug 10 07:21:24 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tecs.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3564243",
  abstract =     "Domain-specific accelerators for signal processing,
                 image processing, and machine learning are increasingly
                 being implemented on SRAM-based field-programmable gate
                 arrays (FPGAs). Owing to the inherent error tolerance
                 of such applications, approximate arithmetic
                 operations, in particular, the design of approximate
                 multipliers, have become an important research problem.
                 Truncation of lower bits is a widely used approximation
                 approach; however, analyzing and limiting the effects
                 of carry-propagation due to this approximation has not
                 been explored in detail yet. In this article, an
                 optimized carry-aware approximate radix-4 Booth
                 multiplier design is presented that leverages the
                 built-in slice look-up tables (LUTs) and carry-chain
                 resources in a novel configuration. The proposed
                 multiplier simplifies the computation of the upper and
                 lower bits and provides significant benefits in terms
                 of FPGA resource usage (LUTs saving 38.5\%--42.9\%),
                 Power Delay Product (PDP saving 49.4\%--53\%),
                 performance metric (LUTs $ \times $ critical path delay
                 (CPD) $ \times $ PDP saving 68.9\%--73.1\%) and errors
                 (70\% improvement in mean relative error distance)
                 compared to the latest state-of-the-art designs.
                 Therefore, the proposed designs are an attractive
                 choice to implement multiplication on FPGA-based
                 accelerators.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Embed. Comput. Syst.",
  articleno =    "76",
  fjournal =     "ACM Transactions on Embedded Computing Systems",
  journal-URL =  "https://dl.acm.org/loi/tecs",
}

@InProceedings{Badizadegan:2023:NRI,
  author =       "Nima Badizadegan",
  title =        "{Newton--Raphson} Integer Division for
                 Area-Constrained Microcontrollers",
  crossref =     "IEEE:2023:PIS",
  pages =        "9--15",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00024",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Approximation algorithms; Approximation methods; ARITH
                 2023; ARITH-30; Costs; Digital arithmetic; Division;
                 Hardware; Integer Division; Iterative algorithms; Logic
                 gates; Microarchitecture; Microcontrollers; Newton
                 Raphson division; Newton Raphson method",
}

@Article{Bahoo:2023:EEG,
  author =       "Ali Akbar Bahoo and Omid Akbari and Muhammad
                 Shafique",
  title =        "An Energy-Efficient Generic Accuracy Configurable
                 Multiplier Based on Block-Level Voltage Overscaling",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "11",
  number =       "4",
  pages =        "851--867",
  month =        oct # "\slash " # dec,
  year =         "2023",
  DOI =          "https://doi.org/10.1109/TETC.2023.3279419",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Fri Apr 12 08:11:23 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
  keywords =     "Adders; Aging; Approximate computing; Complexity
                 theory; Energy efficiency; energy efficiency;
                 multiplier; Voltage; Voltage control; voltage
                 overscaling",
}

@Article{Bartels:2023:FFP,
  author =       "Tinko Bartels and Vissarion Fisikopoulos and Martin
                 Weiser",
  title =        "Fast floating-point filters for robust predicates",
  journal =      j-BIT-NUM-MATH,
  volume =       "63",
  number =       "2",
  pages =        "??--??",
  month =        jun,
  year =         "2023",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/s10543-023-00975-x",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Thu Aug 10 14:23:15 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://link.springer.com/article/10.1007/s10543-023-00975-x",
  abstract =     "Geometric predicates are at the core of many
                 algorithms, such as the construction of Delaunay
                 triangulations, mesh processing and spatial relation
                 tests. These algorithms have applications in scientific
                 computing, geographic information systems and
                 computer-aided design. With floating-point arithmetic,
                 these geometric predicates can incur round-off errors
                 that may lead to incorrect results and inconsistencies,
                 causing computations to fail. This issue has been
                 addressed using a combination of exact arithmetic for
                 robustness and floating-point filters to mitigate the
                 computational cost of exact computations. The
                 implementation of exact computations and floating-point
                 filters can be a difficult task, and code generation
                 tools have been proposed to address this. We present a
                 new C++ meta-programming framework for the generation
                 of fast, robust predicates for arbitrary geometric
                 predicates based on polynomial expressions. We combine
                 and extend different approaches to filtering, branch
                 reduction, and overflow avoidance that have previously
                 been proposed. We show examples of how this approach
                 produces correct results for data sets that could lead
                 to incorrect predicate results with naive
                 implementations. Our benchmark results demonstrate that
                 our implementation surpasses state-of-the-art
                 implementations.",
  acknowledgement = ack-nhfb,
  ajournal =     "Bit Num. Math.",
  articleno =    "31",
  fjournal =     "BIT Numerical Mathematics",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "correct rounding; exact computation; floating-point
                 arithmetic; rounding errors",
}

@InProceedings{Bavier:2023:VNF,
  author =       "Eric Bavier and Nicholas Knight and Hugues de Lassus
                 Saint-Geni{\`e}s and Eric Love",
  title =        "Vectorized Nonlinear Functions with the {RISC-V}
                 Vector Extension",
  crossref =     "IEEE:2023:PIS",
  pages =        "127--130",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00032",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2023; ARITH-30; floating point; Instruction
                 sets; Libraries; Pipelines; RISC-V vectors; scalable
                 vectors; Software; Software algorithms; vector
                 mathematical functions; Vectors; Writing",
}

@Article{Belorgey:2023:MFE,
  author =       "Mariya Georgieva Belorgey and Sergiu Carpov and Kevin
                 Deforth and Dimitar Jetchev and Abson Sae-Tang and
                 Marius Vuille and Nicolas Gama and Jon Katz and Iraklis
                 Leontiadis and Mohsen Mohammadi",
  title =        "{Manticore}: A Framework for Efficient Multiparty
                 Computation Supporting Real Number and {Boolean}
                 Arithmetic",
  journal =      j-J-CRYPTOLOGY,
  volume =       "36",
  number =       "3",
  pages =        "??--??",
  month =        jul,
  year =         "2023",
  CODEN =        "JOCREQ",
  DOI =          "https://doi.org/10.1007/s00145-023-09464-4",
  ISSN =         "0933-2790 (print), 1432-1378 (electronic)",
  ISSN-L =       "0933-2790",
  bibdate =      "Tue Aug 1 08:28:21 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcryptology.bib",
  URL =          "https://link.springer.com/article/10.1007/s00145-023-09464-4",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Cryptology",
  articleno =    "31",
  fjournal =     "Journal of Cryptology",
  journal-URL =  "http://link.springer.com/journal/145",
}

@InProceedings{Beutel:2023:PFA,
  author =       "Moritz Beutel and Robert Strzodka",
  title =        "A Paradigm for Interval-Aware Programming",
  crossref =     "Gustafson:2023:NGA",
  pages =        "38--60",
  year =         "2023",
  DOI =          "https://doi.org/10.1007/978-3-031-32180-1_3",
  bibdate =      "Sat Dec 16 08:52:12 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Blanchard:2023:NMD,
  author =       "Jeffrey D. Blanchard and Marc Chamberland",
  title =        "{Newton}'s Method Without Division",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "130",
  number =       "7",
  pages =        "606--617",
  year =         "2023",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.1080/00029890.2022.2093573",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Fri Aug 25 08:24:37 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/amermathmonthly2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html;
                 https://www.tandfonline.com/loi/uamm20",
  onlinedate =   "04 Aug 2023",
}

@Article{Boldo:2023:FPA,
  author =       "Sylvie Boldo and Claude-Pierre Jeannerod and Guillaume
                 Melquiond and Jean-Michel Muller",
  title =        "Floating-point arithmetic",
  journal =      j-ACTA-NUMERICA,
  volume =       "32",
  pages =        "203--290",
  month =        may,
  year =         "2023",
  CODEN =        "ANUMFU",
  DOI =          "https://doi.org/10.1017/S0962492922000101",
  ISSN =         "0962-4929 (print), 1474-0508 (electronic)",
  ISSN-L =       "0962-4929",
  bibdate =      "Sat May 13 08:10:16 MDT 2023",
  bibsource =    "http://journals.cambridge.org/action/displayIssue?jid=ANU&volumeId=32&issueId=00;
                 https://www.math.utah.edu/pub/tex/bib/actanumerica.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.cambridge.org/core/journals/acta-numerica/article/floatingpoint-arithmetic/287C4D5F6D4A43FBEEB1ABED2A405AAF",
  acknowledgement = ack-nhfb,
  ajournal =     "Acta Numer.",
  fjournal =     "Acta Numerica",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=ANU",
  onlinedate =   "11 May 2023",
}

@Article{Bommana:2023:DST,
  author =       "Ashish Reddy Bommana and Susheel Ujwal Siddamshetty
                 and Dhilleswararao Pudi and Arvind Thumatti K. R. and
                 Srinivas Boppu and M. Sabarimalai Manikandan and Linga
                 Reddy Cenkeramaddi",
  title =        "Design of Synthesis-time Vectorized Arithmetic
                 Hardware for Tapered Floating-point Addition and
                 Subtraction",
  journal =      j-TODAES,
  volume =       "28",
  number =       "3",
  pages =        "32:1--32:??",
  month =        may,
  year =         "2023",
  CODEN =        "ATASFO",
  DOI =          "https://doi.org/10.1145/3567423",
  ISSN =         "1084-4309 (print), 1557-7309 (electronic)",
  ISSN-L =       "1084-4309",
  bibdate =      "Wed May 17 08:06:20 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/todaes.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3567423",
  abstract =     "Energy efficiency has become the new performance
                 criterion in this era of pervasive embedded computing;
                 thus, accelerator-rich multi-processor system-on-chips
                 are commonly used in embedded computing hardware. Once
                 computationally intensive machine learning applications
                 gained much traction, they are now deployed in many
                 application domains due to abundant and cheaply
                 available computational capacity. In addition, there is
                 a growing trend toward developing hardware accelerators
                 for machine learning applications for embedded edge
                 devices where performance and energy efficiency are
                 critical. Although these hardware accelerators
                 frequently use floating-point operations for accuracy,
                 reduced-width floating-point formats are also used to
                 reduce hardware complexity; thus, power consumption
                 while maintaining accuracy. Vectorization concepts can
                 also be used to improve performance, energy efficiency,
                 and memory bandwidth. We propose the design of a
                 vectorized floating-point adder/subtractor that
                 supports arbitrary length floating-point formats with
                 varying exponent and mantissa widths in this article.
                 In comparison to existing designs in the literature,
                 the proposed design is 2.57$ \times $ area- and 1.56$
                 \times $ power-efficient, and it supports true
                 vectorization with no restrictions on exponent and
                 mantissa widths.",
  acknowledgement = ack-nhfb,
  articleno =    "32",
  fjournal =     "ACM Transactions on Design Automation of Electronic
                 Systems",
  journal-URL =  "https://dl.acm.org/loi/todaes",
}

@Article{Bottcher:2023:TGO,
  author =       "Andreas B{\"o}ttcher and Martin Kumm",
  title =        "Towards Globally Optimal Design of Multipliers for
                 {FPGAs}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "72",
  number =       "5",
  pages =        "1261--1273",
  month =        may,
  year =         "2023",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2023.3238128",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Apr 28 11:15:52 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Brisebarre:2023:EUMb,
  author =       "Nicolas Brisebarre and Jean-Michel Muller and Joris
                 Picot",
  title =        "Error in ulps of the multiplication or division by a
                 correctly-rounded function or constant in binary
                 floating-point arithmetic",
  crossref =     "IEEE:2023:PIS",
  pages =        "88--88",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00036",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Published in ``IEEE Transactions on Emerging Topics in
                 Computing, Volume: {\bf 11}, Issue: 4, 01
                 October--December 2023'' and orally presented at ARITH
                 2023.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2023; ARITH-30; Digital arithmetic;
                 Floating-point arithmetic",
}

@TechReport{Brisebarre:2023:IPC,
  author =       "Nicolas Brisebarre and Guillaume Hanrot",
  title =        "Integer points close to a transcendental curve and
                 correctly-rounded evaluation of a function",
  type =         "Preprint",
  institution =  "LIP --- Laboratoire de l'Informatique du
                 Parall{\'e}lisme",
  address =      "Lyon, France",
  pages =        "66",
  year =         "2023",
  bibdate =      "Fri Dec 08 10:07:21 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://hal.science/hal-03240179v4/file/tmd-hal-V4.pdf",
  abstract =     "Despite several significant advances over the last 30
                 years, guaranteeing the correctly rounded evaluation of
                 elementary functions, such as $ \sqrt {} $, $ \cos $, $
                 \exp $, $ \sqrt [3]{} $ for instance, is still a
                 difficult issue. This can be formulated as a
                 Diophantine approximation problem, called the Table
                 Maker's Dilemma, which reduces to determining points
                 with integer coordinates that are close to a curve. In
                 this article, we propose two algorithmic approaches to
                 tackle this problem, closely related to a celebrated
                 work by Bombieri and Pila and to the so-called
                 Coppersmith's method. We establish the underlying
                 theoretical foundations, prove the algorithms, study
                 their complexity and present practical experiments; we
                 also compare our approach with previously existing
                 ones. In particular, our results show that the
                 development of a correctly rounded mathematical library
                 for the binary128 format is now possible at a much
                 smaller cost than with previously existing approaches",
  acknowledgement = ack-nhfb,
  keywords =     "correct rounding; floating-point arithmetic",
}

@InProceedings{Brisebarre:2023:TME,
  author =       "Nicolas Brisebarre and Silviu-Ioan Filip",
  title =        "Towards Machine-Efficient Rational {$ L^\infty
                 $}-Approximations of Mathematical Functions",
  crossref =     "IEEE:2023:PIS",
  pages =        "119--126",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00029",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Approximation algorithms; ARITH 2023; ARITH-30;
                 Behavioral sciences; Digital arithmetic; Software",
}

@InProceedings{Brisebarre:2023:TSK,
  author =       "Nicolas Brisebarre and Jean-Michel Muller and Joris
                 Picot",
  title =        "Testing the Sharpness of Known Error Bounds on the
                 {Fast Fourier Transform}",
  crossref =     "IEEE:2023:PIS",
  pages =        "89--92",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00027",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2023; ARITH-30; Digital arithmetic; Error
                 analysis; Fast Fourier Transform (FFT); Fast Fourier
                 transforms; Floating-point arithmetic; Floating-Point
                 arithmetic; Libraries; Testing",
}

@InProceedings{Brthel:2023:FTI,
  author =       "Moritz B{\"a}rthel and Chen Yuxing and Nils
                 H{\"u}lsmeier and Jochen Rust and Steffen Paul",
  title =        "Fused Three-Input {SORN} Arithmetic",
  crossref =     "Gustafson:2023:NGA",
  pages =        "101--113",
  year =         "2023",
  DOI =          "https://doi.org/10.1007/978-3-031-32180-1_7",
  bibdate =      "Sat Dec 16 08:52:12 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Bruguera:2023:RFP,
  author =       "Javier D. Bruguera",
  title =        "Radix-64 Floating-Point Division and Square Root:
                 Iterative and Pipelined Units",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "72",
  number =       "10",
  pages =        "2990--3001",
  month =        oct,
  year =         "2023",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2023.3280136",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Sep 14 07:25:14 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  abstract =     "Digit-recurrence algorithms are widely used in actual
                 microprocessors to compute floating-point division and
                 square root. These iterative algorithms present a good
                 trade-off in terms of performance, area and power.
                 Traditionally, commercial processors have iterative
                 division and square root units where the iteration
                 logic is used over several cycles. The main drawbacks
                 of these iterative units are long latency and low
                 throughput due to the reuse of part of the logic over
                 several cycles, and its hardware complexity with
                 separated logic for division and square root. We
                 present a radix-64 floating-point division and square
                 root algorithm with a common iteration for division and
                 square root and where, to have an affordable
                 implementation, each radix-64 iteration is made of two
                 simpler radix-8 iterations. The radix-64 algorithm
                 allows to get low-latency operations, and the common
                 division and square root radix-64 iteration results in
                 some area reduction. The algorithm is mapped into two
                 different microarchitectures: a low-latency and low
                 area iterative unit, and a low-latency and
                 high-throughput pipelined unit. In both units
                 speculation between consecutive radix-8 iterations is
                 used to reduce the timing.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Buckle:2023:HEY,
  author =       "David Buckle",
  title =        "How the estimate of $ \sqrt {2} $ on {YBC 7289} may
                 have been calculated",
  journal =      j-HIST-MATH,
  volume =       "62",
  number =       "??",
  pages =        "3--18",
  month =        feb,
  year =         "2023",
  CODEN =        "HIMADS",
  DOI =          "https://doi.org/10.1016/j.hm.2022.08.002",
  ISSN =         "0315-0860 (print), 1090-249X (electronic)",
  ISSN-L =       "0315-0860",
  bibdate =      "Wed Mar 15 09:40:56 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/histmath.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0315086022000477",
  abstract =     "It remains unknown how the approximation of $ \sqrt
                 {2} $ scribed on Babylonian tablet YBC 7289 was
                 calculated. In this article I show how it can be
                 straightforwardly computed using a well-known regular
                 number as the input for the Babylonian method of
                 estimating square roots. My objective is to demonstrate
                 that Babylonian mathematics was sufficiently evolved
                 for the approximation to be easily derived and thus
                 propose an approach that may have been used to
                 calculate it.",
  acknowledgement = ack-nhfb,
  fjournal =     "Historia Mathematica",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03150860",
  keywords =     "Babylonian tablet YBC 7289",
}

@Article{Chen:2023:TLM,
  author =       "Benjamin Chen and Yu Li and Eugene Zima",
  title =        "On a Two-Layer Modular Arithmetic",
  journal =      j-ACM-COMM-COMP-ALGEBRA,
  volume =       "57",
  number =       "3",
  pages =        "133--136",
  month =        sep,
  year =         "2023",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3637529.3637534",
  ISSN =         "1932-2232 (print), 1932-2240 (electronic)",
  ISSN-L =       "1932-2232",
  bibdate =      "Thu Dec 14 15:54:00 MST 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3637529.3637534",
  abstract =     "Two-layer organization of modular arithmetic is
                 considered. Lower layer uses many moduli at hardware
                 precision and simultaneous conversion to/from RNS as
                 described in [2]. Upper layer uses specially selected
                 large moduli allowing for fast reduction and\slash or
                 reconstruction. Implementation of two different
                 strategies for selecting moduli on the upper layer
                 confirms practicality of proposed approach.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Commun. Computer Algebr.",
  fjournal =     "ACM Communications in Computer Algebra",
  journal-URL =  "https://dl.acm.org/loi/sigsam-cca",
}

@Misc{Coonen:2023:IMP,
  author =       "Jerome Coonen and Rafi Nave",
  title =        "{IEEE} Milestone-Proposal: {Intel 8087} Math
                 Coprocessor",
  howpublished = "Web site",
  day =          "21",
  month =        sep,
  year =         "2023",
  bibdate =      "Sat Aug 23 07:49:24 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeemilestones.ethw.org/Milestone-Proposal:Intel_8087_Math_Coprocessor",
  acknowledgement = ack-nhfb,
}

@InProceedings{Crespo:2023:TPP,
  author =       "Lu{\'\i}s Crespo and Pedro Tom{\'a}s and Nuno Roma and
                 Nuno Neves",
  editor =       "{IEEE}",
  booktitle =    "{2023 IEEE 35th International Symposium on Computer
                 Architecture and High Performance Computing
                 (SBAC-PAD)}",
  title =        "Trading Performance, Power, and Area on Low-Precision
                 Posit {MAC} Units for {CNN} Training",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "46--56",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/SBAC-PAD59825.2023.00014",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Defour:2023:CAN,
  author =       "David Defour and Franck Vedrine",
  title =        "Chromatic Analysis of Numerical Programs",
  crossref =     "IEEE:2023:PIS",
  pages =        "97--100",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00012",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Additives; ARITH 2023; ARITH-30; Artificial neural
                 networks; automatic differentiation; Digital
                 arithmetic; Error analysis; IEEE-754; rounding error
                 analysis; sensitivity analysis; Sensitivity analysis",
}

@InProceedings{deLamarliere:2023:SFP,
  author =       "Paul Geneau de Lamarli{\`e}re and Guillaume Melquiond
                 and Florian Faissole",
  title =        "Slimmer Formal Proofs for Mathematical Libraries",
  crossref =     "IEEE:2023:PIS",
  pages =        "32--35",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00026",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2023; ARITH-30; Behavioral sciences; Codes; Coq
                 proof assistant; Costs; Digital arithmetic;
                 Floating-point arithmetic; Formal methods; Libraries;
                 Mathematical libraries; Writing",
}

@InProceedings{Desrentes:2023:EDP,
  author =       "Or{\'e}gane Desrentes and Beno{\^\i}t Dupont {De
                 Dinechin} and Julien {Le Maire}",
  booktitle =    "{2023 26th Euromicro Conference on Digital System
                 Design (DSD)}",
  title =        "Exact Dot Product Accumulate Operators for 8-bit
                 Floating-Point Deep Learning",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "642--649",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/DSD60849.2023.00093",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Costs; Deep learning; Deep Learning; Digital systems;
                 FP8; Posit8",
}

@InProceedings{Desrentes:2023:EFD,
  author =       "Or{\'e}gane Desrentes and Beno{\^\i}t Dupont de
                 Dinechin and Florent de Dinechin",
  title =        "Exact Fused Dot Product Add Operators",
  crossref =     "IEEE:2023:PIS",
  pages =        "151--158",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00016",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2023; ARITH-30; BF16; Computer architecture;
                 Digital arithmetic; dot product; FP32; FP64; Heuristic
                 algorithms; High dynamic range; Low latency
                 communication; three-term sum",
}

@Article{Eckert:2023:EMM,
  author =       "Charles Eckert and Arun Subramaniyan and Xiaowei Wang
                 and Charles Augustine and Ravishankar Iyer and
                 Reetuparna Das",
  title =        "{Eidetic}: an In-Memory Matrix Multiplication
                 Accelerator for Neural Networks",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "72",
  number =       "6",
  pages =        "1539--1553",
  month =        jun,
  year =         "2023",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2022.3214151",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed May 17 10:34:15 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  abstract =     "This paper presents the Eidetic architecture, which is
                 an SRAM-based ASIC neural network accelerator that
                 eliminates the need to continuously load weights from
                 off-chip, while also minimizing the need to go off chip
                 for intermediate results. Using in-situ arithmetic in
                 the SRAM arrays, this architecture can supports a
                 variety of precision types allowing for effective
                 inference. We also present different data mapping
                 policies for matrix-vector based networks (RNN and MLP)
                 on the Eidetic architecture and describe the tradeoffs
                 involved. With this architecture, multiple layers of a
                 network can be concurrently mapped, storing both the
                 layer weights and intermediate results on-chip,
                 removing the energy and latency penalty of off-chip
                 memory accesses. We evaluate Eidetic on Google's Neural
                 Machine Translation System (GNMT) encoder and
                 demonstrate a 17.20$ \times $ increase in throughput
                 and 7.77$ \times $ reduction in average latency over a
                 single TPUv2 chip.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Edamatsu:2023:FMP,
  author =       "Takuya Edamatsu and Daisuke Takahashi",
  title =        "Fast Multiple-Precision Integer Division Using {Intel
                 AVX-512}",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "11",
  number =       "1",
  pages =        "224--236",
  month =        jan # "\slash " # mar,
  year =         "2023",
  DOI =          "https://doi.org/10.1109/TETC.2022.3196147",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  abstract =     "This paper reports on the implementation of a large
                 integer division method that uses Intel Advanced Vector
                 Extensions 512 (AVX-512), which is a 512-bit Single
                 Instruction Multiple Data (SIMD) instruction set, and
                 proposes a modification to a conventional division
                 algorithm that makes it more SIMD instruction-friendly.
                 More specifically, we use the Integer Fused
                 Multiply-Add AVX-512 (AVX-512IFMA) subset, which is an
                 instruction set that works well with large integer
                 multiplication, to compute large integer divisions via
                 a multiplication-based approach with a reciprocal. For
                 the division process, we apply the most basic algorithm
                 and divide-and-conquer methods and then use several
                 techniques to compute efficiently with SIMD
                 instructions in our implementation. We then combine
                 these techniques and methods to implement our division
                 function so that it can flexibly handle various sizes.
                 To evaluate the performance of our proposed
                 implementation, we executed our division program and
                 the GNU Multiple Precision Arithmetic Library (GMP) on
                 a Cannon Lake microarchitecture processor. A comparison
                 of the execution times for our division program and GMP
                 with various sizes showed that our method resulted in
                 performance improvements of 25\% to 35\% on average,
                 thus indicating that SIMD instructions are effective
                 for fast arbitrary precision integer divisions.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}

@InProceedings{Edavoor:2023:DAP,
  author =       "Pranose J Edavoor and Aneesh Raveendran and David
                 Selvakumar and Vivian Desalphine and Dharani Shankar G
                 and Gopal Raut",
  editor =       "{IEEE}",
  booktitle =    "{2023 36th International Conference on VLSI Design and
                 2023 22nd International Conference on Embedded Systems
                 (VLSID)}",
  title =        "Design and Analysis of Posit Quire Processing Engine
                 for Neural Network Applications",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "252--257",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/VLSID57277.2023.00059",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{ElArar:2023:SRV,
  author =       "El-Mehdi {El Arar} and Devan Sohier and Pablo de
                 Oliveira Castro and Eric Petit",
  title =        "Stochastic Rounding Variance and Probabilistic Bounds:
                 a New Approach",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "45",
  number =       "5",
  pages =        "C255--C275",
  month =        oct,
  year =         "2023",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/22m1510819",
  ISSN =         "1095-7197",
  ISSN-L =       "1064-8275",
  bibdate =      "Thu May 30 10:22:20 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  keywords =     "error bounds; floating-point rounding; random
                 rounding; stochastic rounding",
}

@InProceedings{Fakhreddine:2023:ULT,
  author =       "Youssef Fakhreddine and Guillaume Revy",
  title =        "Using loop transformations for precision tuning in
                 iterative programs",
  crossref =     "IEEE:2023:PIS",
  pages =        "159--166",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00031",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2023; ARITH-30; delta-debugging algorithm;
                 Digital arithmetic; dynamic precision tuning tool;
                 floating-point arithmetic; Instruction sets; Iterative
                 methods; loop splitting and unrolling; mixed-precision;
                 multiple-precision; Runtime; Tuning",
}

@InProceedings{Fan:2023:TFF,
  author =       "Guang Fan and Fangyu Zheng and Lipeng Wan and Lili Gao
                 and Yuan Zhao and Jiankuo Dong and Yixuan Song and
                 Yuewu Wang and Jingqiang Lin",
  booktitle =    "{2023 IEEE International Parallel and Distributed
                 Processing Symposium (IPDPS)}",
  title =        "Towards Faster Fully Homomorphic Encryption
                 Implementation with Integer and Floating-point
                 Computing Power of {GPUs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "798--808",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/IPDPS54959.2023.00085",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Arithmetic; Cryptography; Deep learning; Distributed
                 processing; Floating point Computing Power; Fully
                 Homomorphic Encryption; GPU; High Performance
                 Implementation; Homomorphic encryption; Industries;
                 Optimization",
}

@Article{Fasi:2023:CCL,
  author =       "Massimiliano Fasi and Mantas Mikaitis",
  title =        "{CPFloat}: a {C} Library for Simulating Low-precision
                 Arithmetic",
  journal =      j-TOMS,
  volume =       "49",
  number =       "2",
  pages =        "18:1--18:??",
  month =        jun,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3585515",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 29 07:01:00 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3585515",
  abstract =     "One can simulate low-precision floating-point
                 arithmetic via software by executing each arithmetic
                 operation in hardware and then rounding the result to
                 the desired number of significant bits. For
                 IEEE-compliant formats, rounding requires only standard
                 mathematical library functions, but handling
                 subnormals, underflow, and overflow demands special
                 attention, and numerical errors can cause
                 mathematically correct formulae to behave incorrectly
                 in finite arithmetic. Moreover, the ensuing
                 implementations are not necessarily efficient, as the
                 library functions these techniques build upon are
                 typically designed to handle a broad range of cases and
                 may not be optimized for the specific needs of rounding
                 algorithms. CPFloat is a C library for simulating
                 low-precision arithmetics. It offers efficient routines
                 for rounding, performing mathematical computations, and
                 querying properties of the simulated low-precision
                 format. The software exploits the bit-level
                 floating-point representation of the format in which
                 the numbers are stored and replaces costly library
                 calls with low-level bit manipulations and integer
                 arithmetic. In numerical experiments, the new
                 techniques bring a considerable speedup (typically one
                 order of magnitude or more) over existing alternatives
                 in C, C++, and MATLAB. To our knowledge, CPFloat is
                 currently the most efficient and complete library for
                 experimenting with custom low-precision floating-point
                 arithmetic.",
  acknowledgement = ack-nhfb,
  articleno =    "18",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@InProceedings{Filippas:2023:RPF,
  author =       "Dionysios Filippas and Christodoulos Peltekis and
                 Giorgos Dimitrakopoulos and Chrysostomos Nicopoulos",
  booktitle =    "2023 {IEEE 5th International Conference on Artificial
                 Intelligence Circuits and Systems (AICAS)}",
  title =        "Reduced-Precision Floating-Point Arithmetic in
                 Systolic Arrays with Skewed Pipelines",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  month =        jun,
  year =         "2023",
  DOI =          "https://doi.org/10.1109/aicas57966.2023.10168556",
  bibdate =      "Thu Dec 7 11:54:15 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  pagecount =    "5",
}

@InProceedings{Flatt:2023:MIA,
  author =       "Oliver Flatt and Pavel Panchekha",
  title =        "Making Interval Arithmetic Robust to Overflow",
  crossref =     "IEEE:2023:PIS",
  pages =        "44--47",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00022",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2023; ARITH-30; computable reals; Digital
                 arithmetic; Interval arithmetic; Libraries; Mathematics
                 computing; multiple precision arithmetic; overflow",
}

@TechReport{Fog:2023:FPE,
  author =       "Agner Fog",
  title =        "Floating point exception tracking and {NAN}
                 propagation",
  type =         "Report",
  institution =  "Technical University of Denmark",
  address =      "Lyngby, Denmark",
  pages =        "10",
  day =          "27",
  month =        apr,
  year =         "2023",
  bibdate =      "Tue May 09 08:55:38 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.agner.org/optimize/nan_propagation.pdf",
  abstract =     "The most common methods for detecting floating point
                 errors are based on exception trapping or a global
                 status register. These methods are inefficient in
                 modern systems that use out-of-order parallelism and
                 single-instruction-multiple-data (SIMD) parallelism for
                 improving performance. It is argued that a method based
                 on NAN propagation is more efficient and deterministic.
                 Problems with NAN propagation in current systems are
                 discussed. Examples of implementation in the C++ vector
                 class library and in an experimental instruction set
                 named ForwardCom are presented. The IEEE-754 standard
                 for floating point arithmetic may need adjustment to
                 accommodate the needs of modern forms of parallelism.",
  acknowledgement = ack-nhfb,
  remark =       "See also earlier \cite{Fog:2020:FPE} and later
                 revisions \cite{Fog:2024:FPE}.",
}

@InProceedings{Gavarini:2023:RRN,
  author =       "G. Gavarini and A. Ruospo and E. Sanchez",
  booktitle =    "{2023 IEEE International Symposium on Defect and Fault
                 Tolerance in VLSI and Nanotechnology Systems (DFT)}",
  title =        "On the resilience of representative and novel data
                 formats in {CNNs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--6",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/DFT59622.2023.10313551",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Convolutional neural networks; Deep Neural Network;
                 Fault Injection; FP32; INT8; Measurement; Memory
                 management; Posit; POSIT16; POSIT32; Power demand;
                 Reliability; Task analysis; Training; Very large scale
                 integration",
}

@InProceedings{Glint:2023:HSC,
  author =       "Tom Glint and Kailash Prasad and Jinay Dagli and
                 Krishil Gandhi and Aryan Gupta and Vrajesh Patel and
                 Neel Shah and Joycee Mekie",
  editor =       "{IEEE}",
  booktitle =    "{2023 28th Asia and South Pacific Design Automation
                 Conference (ASP-DAC)}",
  title =        "Hardware-Software Codesign of {DNN} Accelerators using
                 Approximate Posit Multipliers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "469--474",
  year =         "2023",
  DOI =          "",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gorodecky:2023:SAC,
  author =       "Danila Gorodecky and Leonel Sousa",
  title =        "Scalable architecture of constant division on {FPGA}",
  crossref =     "IEEE:2023:PIS",
  pages =        "16--23",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00025",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2023; ARITH-30; Boolean functions; Computer
                 architecture; Costs; Delays; Digital arithmetic; Field
                 programmable gate arrays; Hardware",
}

@InProceedings{Graillat:2023:PCH,
  author =       "Stef Graillat and Youness Ibrahimy and Clothilde
                 Jeangoudoux and Christoph Lauter",
  title =        "A parallel compensated {Horner} scheme for {SIMD}
                 architecture",
  crossref =     "IEEE:2023:PIS",
  pages =        "131--138",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00010",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2023; ARITH-30; AVX; compensated algorithms;
                 Computer architecture; Computers; Costs; Digital
                 arithmetic; error-free transformations; Horner scheme;
                 Limiting; parallel algorithms; polynomial evaluation;
                 Registers; rounding errors; Scalability; SIMD",
}

@InProceedings{Grale:2023:IMM,
  author =       "Trenton J. Grale and Earl E. Swartzlander",
  title =        "Improved {Montgomery} Multiplication",
  crossref =     "IEEE:2023:PIS",
  pages =        "60--67",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00019",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2023; ARITH-30; Computational modeling; Computer
                 architecture; Costs; digit multiplication; Digital
                 arithmetic; Hardware; modular arithmetic; modular
                 multiplication; Parallel processing; Rescheduled
                 Montgomery Multiplier; Serial Montgomery Model;
                 Taxonomy",
}

@InProceedings{Gunaratne:2023:EUL,
  author =       "Thushara Kanchana Gunaratne",
  title =        "Evaluation of the Use of Low Precision Floating-Point
                 Arithmetic for Applications in Radio Astronomy",
  crossref =     "Gustafson:2023:NGA",
  pages =        "155--170",
  year =         "2023",
  DOI =          "https://doi.org/10.1007/978-3-031-32180-1_10",
  bibdate =      "Sat Dec 16 08:52:12 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@InProceedings{Gustafson:2023:DFT,
  author =       "John L. Gustafson and Marco Cococcioni and Federico
                 Rossi and Emanuele Ruffaldi and Sergio Saponara",
  title =        "Decoding-Free Two-Input Arithmetic for Low-Precision
                 Real Numbers",
  crossref =     "Gustafson:2023:NGA",
  pages =        "61--76",
  year =         "2023",
  DOI =          "https://doi.org/10.1007/978-3-031-32180-1_4",
  bibdate =      "Sat Dec 16 08:52:12 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@Article{Hallman:2023:PAD,
  author =       "Eric Hallman and Ilse C. F. Ipsen",
  title =        "Precision-aware deterministic and probabilistic error
                 bounds for floating point summation",
  journal =      j-NUM-MATH,
  volume =       "155",
  number =       "1--2",
  pages =        "83--119",
  month =        oct,
  year =         "2023",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/s00211-023-01370-y",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Thu Sep 28 06:27:49 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/i/ipsen-ilse-c-f.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath2020.bib",
  URL =          "https://link.springer.com/article/10.1007/s00211-023-01370-y",
  acknowledgement = ack-nhfb,
  ajournal =     "Num. Math.",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "accurate floating-point summation",
}

@Misc{Harris:2023:UMR,
  author =       "David Harris",
  title =        "Unified minimally redundant radix 4 {DivSqrt}
                 selection intervals and constants",
  howpublished = "Web document",
  year =         "2023",
  bibdate =      "Thu Dec 28 10:11:34 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://bit.ly/3fLR81z",
  acknowledgement = ack-nhfb,
  remark =       "URL leads to undated Google Docs spreadsheet with
                 interleaved commentary. Cited in
                 \cite{Harris:2024:UDS}.",
}

@InProceedings{Ho:2023:BBE,
  author =       "Nhut-Minh Ho and Duy-Thanh Nguyen and John L.
                 Gustafson and Weng-Fai Wong",
  title =        "{Bedot}: Bit Efficient Dot Product for Deep Generative
                 Models",
  crossref =     "Gustafson:2023:NGA",
  pages =        "19--37",
  year =         "2023",
  DOI =          "https://doi.org/10.1007/978-3-031-32180-1_2",
  bibdate =      "Sat Dec 16 08:52:12 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Hoffmann:2023:ASE,
  author =       "Alexandre Hoffmann and Yves Durand and J{\'e}r{\^o}me
                 Fereyre",
  title =        "Accelerating spectral elements method with extended
                 precision: a case study",
  journal =      "International Journal of Applied Physics and
                 Mathematics",
  volume =       "14",
  number =       "2",
  pages =        "45--58",
  year =         "2023",
  CODEN =        "IJAPJ3",
  DOI =          "https://doi.org/10.17706/ijapm",
  ISSN =         "2010-362X",
  ISSN-L =       "2010-362X",
  bibdate =      "Wed Jun 12 16:34:44 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Appl. Phys. Math.",
  remark =       "In Proc. 12th Int. Conf. Pure Appl. Math. (ICPAM).",
}

@InProceedings{Hong:2023:LCH,
  author =       "Wanyuan Hong and Hui Chen and Lianghua Quan and
                 Yuxiang Fu and Li Li",
  booktitle =    "{2023 IEEE International Symposium on Circuits and
                 Systems (ISCAS)}",
  title =        "Low-Cost High-Precision Architecture for Arbitrary
                 Floating-Point Nth Root Computation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--5",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ISCAS46773.2023.10181944",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "CMOS technology; Computer architecture; CORDIC;
                 Digital signal processing; floating-point; Frequency
                 synthesizers; high precision; low cost; Navigation; Nth
                 root; Power demand; Simulation; SRT",
}

@Article{Hu:2023:TWF,
  author =       "Xianwu Hu and Yu Wang and Zizhao Ma and Gan Wen and
                 Zeming Wang and Zhichao Lu and Yunlong Liu and Yanlei
                 Li and Xingdong Liang and Xiaoyang Zeng and Yufeng
                 Xie",
  title =        "An 8.8 {TFLOPS/W} Floating-Point {RRAM}-Based
                 Compute-in-Memory Macro Using Low Latency
                 Triangle-Style Mantissa Multiplication",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
  volume =       "70",
  number =       "11",
  pages =        "4216--4220",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/TCSII.2023.3283418",
  ISSN =         "1549-7747 (print), 1558-3791 (electronic)",
  ISSN-L =       "1549-7747",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems II: Express
                 Briefs",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
  keywords =     "Arrays; Common Information Model (computing); Compute
                 in memory; Energy efficiency; floating-point; fully
                 parallel input; Low latency communication; MAC; Memory
                 management; Microprocessors; triangle weights
                 arrangement; Voltage",
}

@TechReport{Hubrecht:2023:TCRa,
  author =       "Tom Hubrecht and Claude-Pierre Jeannerod and Paul
                 Zimmermann",
  title =        "Towards a correctly-rounded and fast power function in
                 binary64 arithmetic",
  type =         "Report",
  institution =  "DI-ENS --- D{\'e}partement d'informatique --- ENS
                 Paris",
  address =      "Paris, France",
  day =          "12",
  month =        jul,
  year =         "2023",
  bibdate =      "Mon May 13 12:00:21 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://inria.hal.science/hal-04159652v1/",
  abstract =     "We design algorithms for the correct rounding of the
                 power function $ x^y $ in the binary64 IEEE 754 format,
                 for all rounding modes, modulo the knowledge of
                 hardest-to-round cases. Our implementation of these
                 algorithms largely outperforms previous
                 correctly-rounded implementations and is not far from
                 the efficiency of current mathematical libraries, which
                 are not correctly-rounded. Still, we expect our
                 algorithms can be further improved for speed. The
                 proofs of correctness are fully detailed in an extended
                 version of this paper, with the goal to enable a formal
                 proof of these algorithms. We hope this work will
                 motivate the next IEEE 754 revision committee to
                 require correct rounding for mathematical functions.",
  acknowledgement = ack-nhfb,
  remark =       "This is a longer version of \cite{Hubrecht:2023:TCRb}
                 with proofs.",
}

@InProceedings{Hubrecht:2023:TCRb,
  author =       "Tom Hubrecht and Claude-Pierre Jeannerod and Paul
                 Zimmermann",
  title =        "Towards a correctly-rounded and fast power function in
                 binary64 arithmetic",
  crossref =     "IEEE:2023:PIS",
  pages =        "111--118",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00028",
  bibdate =      "Fri Dec 08 15:03:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arith2023.arithsymposium.org/slides/S6_PaulZimmermannS6P1.pdf;
                 https://inria.hal.science/hal-04159652v1/file/pow.pdf;
                 https://inria.hal.science/hal-04326201",
  abstract =     "We design algorithms for the correct rounding of the
                 power function $ x^y $ in the binary64 IEEE 754 format,
                 for all rounding modes, modulo the knowledge of
                 hardest-to-round cases. Our implementation of these
                 algorithms largely outperforms previous
                 correctly-rounded implementations and is not far from
                 the efficiency of current mathematical libraries, which
                 are not correctly-rounded. Still, we expect our
                 algorithms can be further improved for speed. The
                 proofs of correctness are fully detailed, with the goal
                 to enable a formal proof of these algorithms. We hope
                 this work will motivate the next IEEE 754 revision
                 committee to require correct rounding for mathematical
                 functions.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2023; ARITH-30; binary64 format; correct
                 rounding; Digital arithmetic; double precision;
                 efficiency; Error analysis; IEEE 754; Libraries; power
                 function; Prediction algorithms; Software; Software
                 algorithms; Switches",
  remark =       "See also longer versions
                 \cite{Hubrecht:2023:TCRa,Hubrecht:2024:TCR}.",
}

@InProceedings{Hulsmeier:2023:HSH,
  author =       "Nils H{\"u}lsmeier and Moritz B{\"a}rthel and Jochen
                 Rust and Steffen Paul",
  title =        "Hybrid {SORN} Hardware Accelerator for Support Vector
                 Machines",
  crossref =     "Gustafson:2023:NGA",
  pages =        "77--87",
  year =         "2023",
  DOI =          "https://doi.org/10.1007/978-3-031-32180-1_5",
  bibdate =      "Sat Dec 16 08:52:12 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Misc{IEEE:2023:MIS,
  author =       "{IEEE}",
  title =        "Milestones: {IEEE Standard 754 for Binary
                 Floating-Point Arithmetic, 1985. (J. Coonen,
                 proposer)}",
  howpublished = "Web site",
  day =          "3",
  month =        may,
  year =         "2023",
  DOI =          "https://ethw.org/Milestones:IEEE_Standard_754_for_Binary_Floating-Point_Arithmetic,_1985",
  bibdate =      "Wed Aug 07 15:36:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Misc{IEEE:2023:UWG,
  author =       "{IEEE}",
  title =        "{IEEE Working Group P3109} Interim Report on 8-bit
                 Binary Floating-point Formats",
  howpublished = "Web document",
  pages =        "18",
  day =          "24",
  month =        nov,
  year =         "2023",
  bibdate =      "Sat Dec 16 10:36:07 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://github.com/P3109/Public/blob/main/Shared%20Reports/P3109%20WG%20Interim%20report.pdf",
  acknowledgement = ack-nhfb,
  remark =       "Table 2 on page 4 contains a compact summary of
                 binary8p\{p\}, binary8p5, binary8p4, binary8p3,
                 binary16, binary32, and binary64 data layouts.",
}

@TechReport{Innocente:2023:AMF,
  author =       "Vincenzo Innocente and Paul Zimmermann",
  title =        "Accuracy of Mathematical Functions in Single, Double,
                 Double Extended, and Quadruple Precision",
  institution =  "????",
  pages =        "21",
  day =          "14",
  month =        feb,
  year =         "2023",
  bibdate =      "Fri Dec 08 08:28:52 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://inria.hal.science/hal-03141101;
                 https://members.loria.fr/PZimmermann/papers/glibc237-20230214.pdf",
  acknowledgement = ack-nhfb,
  remark =       "Tabular comparison of AMD, Apple, CUDA, GNU, Intel,
                 Musl, Newlib, OpenLibm, and RadeonOpenCompute (ROCm) lm
                 libraries for correct rounding, versus results from
                 MPFR.",
}

@InProceedings{Jaberipur:2023:MMF,
  author =       "Ghassem Jaberipur and Saeid Gorgin and Navid Ahamadian
                 and Jeong-A Lee",
  title =        "Modulo-($ 2^q - 3$) Multiplication with Fully Modular
                 Partial Product Generation and Reduction",
  crossref =     "IEEE:2023:PIS",
  pages =        "68--75",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00023",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2023; ARITH-30; Costs; Delays; Digital
                 arithmetic; Energy measurement; Fully modular
                 multiplication; Market research; Partial product
                 reduction; Residue number system; Software; Software
                 algorithms",
}

@InProceedings{Joshi:2023:AEV,
  author =       "Rajeev Joshi and Lakshmi Kavya Kalyanam and Srinivas
                 Katkoori",
  booktitle =    "{2023 International VLSI Symposium on Technology,
                 Systems and Applications (VLSI-TSA/VLSI-DAT)}",
  title =        "Area Efficient {VLSI ASIC} Implementation of
                 Multilayer Perceptrons",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--4",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/VLSI-TSA/VLSI-DAT57221.2023.10133986",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Annealing; Artificial neural networks; ASICs; Edge-AI;
                 FP32; IEEE 754; IoT; Metaheuristic optimization;
                 Metaheuristics; Neural Networks; Neurons; Perturbation
                 methods; Simulated annealing; Very large scale
                 integration; VLSI",
}

@InProceedings{K:2023:DEE,
  author =       "Lakshmi Bhanuprakash Reddy K and Haripriya R S and
                 Keerthija Puli and Subba Ramkumar Reddy Annapalli and
                 Vikramkumar Pudi",
  editor =       "{IEEE}",
  booktitle =    "{2023 36th International Conference on VLSI Design and
                 2023 22nd International Conference on Embedded Systems
                 (VLSID)}",
  title =        "Design of Energy Efficient and Low Delay Posit
                 Multiplier",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--6",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/VLSID57277.2023.00042",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Kapoor:2023:FVF,
  author =       "Ashish Kapoor and Warren Ferguson and Himanshu Jain
                 and Sudipta Kundu",
  title =        "Formal Verification of Floating-Point Division",
  crossref =     "IEEE:2023:PIS",
  pages =        "93--96",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00018",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2023; ARITH-30; datapath verification; Digital
                 arithmetic; equivalence checking; floating-point
                 division; Formal verification; formal verification;
                 Software",
}

@InProceedings{Kavvousanos:2023:IRL,
  author =       "E. Kavvousanos and V. Sakellariou and I. Kouretas and
                 V. Paliouras and T. Stouraitis",
  title =        "Improving Residue-Level Sparsity in {RNS-based} Neural
                 Network Hardware Accelerators via Regularization",
  crossref =     "IEEE:2023:PIS",
  pages =        "102--109",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00020",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2023; ARITH-30; Artificial neural networks;
                 Computer architecture; Degradation; Digital arithmetic;
                 hardware acceleration; Machine learning; Neural network
                 hardware; neural networks; residue number system;
                 sparsity; Training",
}

@InProceedings{Kellison:2023:LLF,
  author =       "Ariel E. Kellison and Andrew W. Appel and Mohit
                 Tekriwal and David Bindel",
  title =        "{LAProof}: a Library of Formal Proofs of Accuracy and
                 Correctness for Linear Algebra Programs",
  crossref =     "IEEE:2023:PIS",
  pages =        "36--43",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00021",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2023; ARITH-30; Error analysis; floating-point
                 arithmetic; formal verification; Libraries;
                 Mathematical models; program verification; rounding
                 error analysis; Roundoff errors; Sparse matrices;
                 Stability analysis; Vectors",
}

@Article{Kim:2023:BNL,
  author =       "Jongho Kim and Young H. Oh and Hyeonsik Kim and Jae W.
                 Lee and Jintae Kim",
  title =        "A 4-bit 4.5-ns-Latency {Pseudo-ReRAM}
                 Computing-In-Memory Macro With Self Error-Correcting
                 {DTC}-Based {WL} Drivers and 6-bit {CDAC}-Less Column
                 {ADCs} Having Ultra-Narrow Pitch",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
  volume =       "70",
  number =       "9",
  pages =        "3228--3232",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/TCSII.2023.3273290",
  ISSN =         "1549-7747 (print), 1558-3791 (electronic)",
  ISSN-L =       "1549-7747",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems II: Express
                 Briefs",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
  keywords =     "Capacitors; charge injection SAR (ci-SAR); Circuit
                 stability; Clamps; Computing-in-memory (CIM); Delays;
                 digital-to-time converter (DTC); Microprocessors;
                 multiply-and-accumulate (MAC); Throughput; Voltage",
}

@Article{Kim:2023:MMS,
  author =       "Whijin Kim and Hana Kim and Jihye Lee and Hyunji Kim
                 and Ji-Hoon Kim",
  title =        "Multi-Mode {SpMV} Accelerator for Transprecision
                 {PageRank} With Real-World Graphs",
  journal =      j-IEEE-ACCESS,
  volume =       "11",
  pages =        "6261--6272",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ACCESS.2023.3237079",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/pagerank.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "floating-point multiplier; graph processing;
                 half-precision (FP16); Hardware; Hypertext systems;
                 Internet; Magnetic flux; PageRank (PR);
                 single-precision (FP32); Social networking (online);
                 Sparse matrices; sparse matrix vector multiplication
                 (SpMV); Transprecision; Web search",
}

@Article{Klower:2023:POC,
  author =       "Milan Kl{\"o}wer and Peter V. Coveney and E. Adam
                 Paxton and Tim N. Palmer",
  title =        "Periodic orbits in chaotic systems simulated at low
                 precision",
  journal =      j-SCI-REP,
  volume =       "13",
  number =       "1",
  month =        jul,
  year =         "2023",
  CODEN =        "SRCEC3",
  DOI =          "https://doi.org/10.1038/s41598-023-37004-4",
  ISSN =         "2045-2322",
  bibdate =      "Fri Dec 15 11:31:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientific Reports",
  journal-URL =  "http://www.nature.com/srep/",
  keywords =     "posit arithmetic",
}

@Misc{Krishna:2023:RNF,
  author =       "Bharath Krishna",
  title =        "Rounding Numbers in the Financial Domain!",
  howpublished = "Web site",
  day =          "1",
  month =        jan,
  year =         "2023",
  bibdate =      "Tue Feb 27 14:40:22 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Includes important mention of financial regulatory
                 sites, with this text taken verbatim from the article,
                 because such information may be hard to find
                 elsewhere:

                 * International Financial Reporting Standards (IFRS):
                 IFRS is a set of accounting standards developed by the
                 International Accounting Standards Board (IASB). It
                 includes guidelines on rounding financial numbers in
                 financial statements, such as the requirement to round
                 amounts to the nearest whole number or the nearest
                 multiple of 10;

                 * Generally Accepted Accounting Principles (GAAP): GAAP
                 is a set of accounting standards used in the United
                 States. It includes similar guidelines on rounding
                 financial numbers as IFRS and requires that any
                 rounding errors should be immaterial and
                 insignificant.

                 * International Organization for Standardization (ISO):
                 ISO has a standard for Rounding off numerical values,
                 which is ISO 80000-1:2009. It provides guidelines on
                 rounding numerical values in general and not specific
                 to the finance domain, but it's widely used in
                 financial systems.

                 * The Federal Reserve Board (FRB): The FRB, the central
                 banking system of the United States, has guidelines on
                 rounding financial numbers for bank reporting and
                 financial statement preparation.

                 * The European Central Bank (ECB): The ECB, the central
                 banking system of the European Union, has similar
                 guidelines on rounding financial numbers as the FRB.",
  URL =          "https://www.foundingminds.com/rounding-numbers-in-the-financial-domain/",
  acknowledgement = ack-nhfb,
  keywords =     "decimal floating-point arithmetic; rounding errors",
}

@InProceedings{Kuo:2023:CMP,
  author =       "Pei-Hsuan Kuo and Yu-Hsiang Huang and Juinn-Dar
                 Huang",
  booktitle =    "{2023 IEEE 5th International Conference on Artificial
                 Intelligence Circuits and Systems (AICAS)}",
  title =        "Configurable Multi-Precision Floating-Point Multiplier
                 Architecture Design for Computation in Deep Learning",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--5",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/AICAS57966.2023.10168572",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer architecture; configurable; Deep learning;
                 deep learning; floating-point multiplier design;
                 Hardware; Learning (artificial intelligence); Logic
                 gates; multi-precision computation; Pipelines;
                 Throughput",
}

@InProceedings{Kurian:2023:PER,
  author =       "Ashley Kurian and M. Ramesh Kini",
  booktitle =    "Lecture Notes in Networks and Systems",
  title =        "Posit Extended {RISC-V} Processor and Its Enhancement
                 Using Data Type Casting",
  publisher =    "Springer Nature",
  address =      "Singapore",
  pages =        "571--586",
  year =         "2023",
  DOI =          "https://doi.org/10.1007/978-981-19-6634-7_40",
  ISBN =         "981-19663-4-6",
  ISBN-13 =      "978-981-19663-4-7",
  ISSN =         "2367-3389",
  bibdate =      "Fri Dec 15 11:31:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@Article{Laguna:2023:FIT,
  author =       "Ignacio Laguna and Anh Tran and Ganesh
                 Gopalakrishnan",
  title =        "Finding inputs that trigger floating-point exceptions
                 in heterogeneous computing via {Bayesian}
                 optimization",
  journal =      j-PARALLEL-COMPUTING,
  volume =       "117",
  number =       "??",
  pages =        "103042:1--103042:13",
  month =        sep,
  year =         "2023",
  CODEN =        "PACOEJ",
  DOI =          "https://doi.org/10.1016/j.parco.2023.103042",
  ISSN =         "0167-8191 (print), 1872-7336 (electronic)",
  ISSN-L =       "0167-8191",
  bibdate =      "Thu Sep 7 08:37:05 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/parallelcomputing.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167819123000480",
  acknowledgement = ack-nhfb,
  articleno =    "103042",
  fjournal =     "Parallel Computing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01678191",
}

@InProceedings{Lee:2023:WFF,
  author =       "Sunwoo Lee and Jeongwoo Park and Dongsuk Jeon",
  booktitle =    "{ESSCIRC 2023 --- IEEE 49th European Solid State
                 Circuits Conference (ESSCIRC)}",
  title =        "A {4.27TFLOPS/W} {FP4/FP8} Hybrid-Precision Neural
                 Network Training Processor Using Shift-Add {MAC} and
                 Reconfigurable {PE} Array",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "221--224",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ESSCIRC59616.2023.10268686",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Convolution; Deep Learning; Logarithmic Weight;
                 Low-precision Training; Memory management; Parallel
                 processing; Power demand; Reconfigurable PE Array;
                 Routing; System-on-chip; Training",
}

@Article{Leitersdorf:2023:AHT,
  author =       "Orian Leitersdorf and Dean Leitersdorf and Jonathan
                 Gal and Mor Dahan and Ronny Ronen and Shahar
                 Kvatinsky",
  title =        "{AritPIM}: High-Throughput In-Memory Arithmetic",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "11",
  number =       "3",
  pages =        "720--735",
  month =        jul # "\slash " # sep,
  year =         "2023",
  DOI =          "https://doi.org/10.1109/TETC.2023.3268137",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  abstract =     "Digital processing-in-memory (PIM) architectures are
                 rapidly emerging to overcome the memory-wall bottleneck
                 by integrating logic within memory elements. Such
                 architectures provide vast computational power within
                 the memory itself in the form of parallel bitwise logic
                 operations. We develop novel algorithmic techniques for
                 PIM that, combined with new perspectives on computer
                 arithmetic, extend this bitwise parallelism to the four
                 fundamental arithmetic operations (addition,
                 subtraction, multiplication, and division), for both
                 fixed-point and floating-point numbers, and using both
                 bit-serial and bit-parallel approaches. We propose a
                 state-of-the-art suite of arithmetic algorithms,
                 demonstrating the first algorithm in the literature of
                 digital PIM for a majority of cases --- including cases
                 previously considered impossible for digital PIM, such
                 as floating-point addition. Through a case study on
                 memristive PIM, we compare the proposed algorithms to
                 an NVIDIA RTX 3070 GPU and demonstrate significant
                 throughput and energy improvements.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}

@InProceedings{Leong:2023:LFU,
  author =       "Siew Hoon Leong and John L. Gustafson",
  title =        "Lossless {FFTs} Using Posit Arithmetic",
  crossref =     "Gustafson:2023:NGA",
  pages =        "1--18",
  year =         "2023",
  DOI =          "https://doi.org/10.1007/978-3-031-32180-1_1",
  bibdate =      "Sat Dec 16 08:52:12 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Li:2023:DEG,
  author =       "Xinyi Li and Ignacio Laguna and Bo Fang and Katarzyna
                 Swirydowicz and Ang Li and Ganesh Gopalakrishnan",
  booktitle =    "Proceedings of the {32nd International Symposium on
                 High-Performance Parallel and Distributed Computing}",
  title =        "Design and Evaluation of {GPU-FPX}: a Low-Overhead
                 tool for Floating-Point Exception Detection in {NVIDIA
                 GPUs}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "59--71",
  month =        aug,
  year =         "2023",
  DOI =          "https://doi.org/10.1145/3588195.3592991",
  bibdate =      "Thu Sep 7 09:13:15 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3588195.3592991;
                 https://github.com/LLNL/GPU-FPX",
  abstract =     "Floating-point exceptions occurring during numerical
                 computations can be a serious threat to the validity of
                 the computed results if they are not caught and
                 diagnosed Unfortunately, on NVIDIA GPUs --- today's
                 most widely used types and which do not have hardware
                 exception traps --- this task must be carried out in
                 software. Given the prevalence of closed-source
                 kernels, efficient binary-level exception tracking is
                 essential. It is also important to know how exceptions
                 flow through the code, whether they alter the code
                 behavior and additionally whether these exceptions can
                 be detected at the program outputs or are killed inside
                 program flow-paths. In this paper, we introduce
                 GPU-FPX, a tool that has low overhead, allows for deep
                 understanding of the origin and flow of exceptions, and
                 also how exceptions are modified by code optimizations.
                 We measure GPU-FPX's performance over 151 widely used
                 GPU programs coming from HPC and ML, detecting 26
                 serious exceptions that were previously not reported.
                 Our results show that GPU-FPX is $ 16 \times $ faster
                 with respect to the geometric-mean runtime in relation
                 to the only comparable prior tool, while also helping
                 debug a larger class of codes more effectively.",
  acknowledgement = ack-nhfb,
}

@Article{Li:2023:DSE,
  author =       "He Li and Jiawei Liang and Hongxiang Fan and Yongming
                 Tang",
  title =        "Design Space Exploration for Efficient Quantum
                 Most-Significant Digit-First Arithmetic",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "72",
  number =       "6",
  pages =        "1822--1829",
  month =        jun,
  year =         "2023",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2022.3215891",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed May 17 10:34:15 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  abstract =     "Quantum computing has been considered as an emerging
                 approach in addressing problems which are not easily
                 solvable using classical computers. In parallel to the
                 physical implementation of quantum processors, quantum
                 algorithms have been actively developed for real-life
                 applications to show quantum advantages, many of which
                 benefit from quantum arithmetic algorithms and their
                 efficient implementations. As one of the most important
                 operations, quantum addition has been adopted in Shor's
                 algorithm and quantum linear algebra algorithms.
                 Although various least-significant digit-first quantum
                 adders have been introduced in previous work, interest
                 in investigating the efficient implementation of
                 most-significant digit-first addition is growing. In
                 this work, we propose a novel design method for
                 most-significant digit-first addition with several
                 quantum circuit optimisations to reduce the number of
                 quantum bits (i.e. qubits), quantum gates, and circuit
                 depth. An open-source library of different arithmetic
                 operators based on our proposed method is presented,
                 where all circuits are implemented on IBM Qiskit SDK.
                 Extensive experiments demonstrate that our proposed
                 design, together with the optimisation techniques,
                 reduces T-depth by up-to 4.0$ \times $, T-count by 3.5$
                 \times $, and qubit consumption by 1.2$ \times $.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Li:2023:EEB,
  author =       "Ruiyuan Li and Zheng Li and Yi Wu and Chao Chen and Yu
                 Zheng",
  title =        "{Elf}: Erasing-Based Lossless Floating-Point
                 Compression",
  journal =      j-PROC-VLDB-ENDOWMENT,
  volume =       "16",
  number =       "7",
  pages =        "1763--1776",
  month =        mar,
  year =         "2023",
  CODEN =        "????",
  DOI =          "https://doi.org/10.14778/3587136.3587149",
  ISSN =         "2150-8097",
  bibdate =      "Tue May 9 09:08:30 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/datacompression.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/vldbe.bib",
  URL =          "https://dl.acm.org/doi/10.14778/3587136.3587149",
  abstract =     "There are a prohibitively large number of
                 floating-point time series data generated at an
                 unprecedentedly high rate. An efficient, compact and
                 lossless compression for time series data is of great
                 importance for a wide range of scenarios. Most existing
                 lossless floating-point compression methods are based
                 on the XOR operation, but they do not fully exploit the
                 trailing zeros, which usually results in an
                 unsatisfactory compression ratio. This paper proposes
                 an Erasing-based Lossless Floating-point compression
                 algorithm, i.e., \pkg{Elf}. The main idea of \pkg{Elf}
                 is to erase the last few bits (i.e., set them to zero)
                 of floating-point values, so the XORed values are
                 supposed to contain many trailing zeros. The challenges
                 of the erasing-based method are three-fold. First, how
                 to quickly determine the erased bits? Second, how to
                 losslessly recover the original data from the erased
                 ones? Third, how to compactly encode the erased data?
                 Through rigorous mathematical analysis, \pkg{Elf} can
                 directly determine the erased bits and restore the
                 original values without losing any precision. To
                 further improve the compression ratio, we propose a
                 novel encoding strategy for the XORed values with many
                 trailing zeros. \pkg{Elf} works in a streaming fashion.
                 It takes only $ O(N) $ (where $N$ is the length of a
                 time series) in time and $ O(1)$ in space, and achieves
                 a notable compression ratio with a theoretical
                 guarantee. Extensive experiments using 22 datasets show
                 the powerful performance of \pkg{Elf} compared with 9
                 advanced competitors.",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the VLDB Endowment",
  journal-URL =  "https://dl.acm.org/loi/pvldb",
}

@InProceedings{Li:2023:POS,
  author =       "Qiong Li and Chao Fang and Zhongfeng Wang",
  editor =       "{IEEE}",
  booktitle =    "{2023 IEEE International Symposium on Circuits and
                 Systems (ISCAS)}",
  title =        "{PDPU}: an Open-Source Posit Dot-Product Unit for Deep
                 Learning Applications",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--5",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ISCAS46773.2023.10182007",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Liu:2023:CHR,
  author =       "Zixuan Liu and Xiaoyu Song and Zhuowei Wang and Yan
                 Wang and Jian-Tao Zhou",
  title =        "Constructing High Radix Quotient Digit Selection
                 Tables for {SRT} Division and Square Root",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "72",
  number =       "7",
  pages =        "2111--2119",
  month =        jul,
  year =         "2023",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2023.3235978",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 1 10:59:22 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Livesay:2023:AFF,
  author =       "Neal Livesay and Gilbert Jonatan and Evelio Mora and
                 Kaustubh Shivdikar and Rashmi Agrawal and Ajay Joshi
                 and Jos{\'e} L. Abell{\'a}n and John Kim and David
                 Kaeli",
  title =        "Accelerating Finite Field Arithmetic for Homomorphic
                 Encryption on {GPUs}",
  journal =      j-IEEE-MICRO,
  volume =       "43",
  number =       "5",
  pages =        "55--63",
  month =        sep # "\slash " # oct,
  year =         "2023",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.2023.3253052",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Sep 14 06:42:28 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeemicro.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=40",
}

@InProceedings{Lo:2023:BGB,
  author =       "Yun-Chen Lo and Ren-Shuo Liu",
  booktitle =    "{2023 56th IEEE/ACM International Symposium on
                 Microarchitecture (MICRO)}",
  title =        "{Bucket Getter}: a Bucket-based Processing Engine for
                 Low-bit Block Floating Point {(BFP) DNNs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1002--1015",
  year =         "2023",
  DOI =          "",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Artificial neural networks; Bucket-based accumulation;
                 Computer architecture; Deep learning; Engines;
                 Floating-point architecture; Gettering; Hardware;
                 Microarchitecture; Organizations",
}

@InProceedings{Mai:2023:TWC,
  author =       "Yangzhan Mai and Mingyu Wang and Chuanghao Zhang and
                 Baiqing Zhong and Zhiyi Yu",
  booktitle =    "{2023 IEEE International Symposium on Circuits and
                 Systems (ISCAS)}",
  title =        "A 1.97 {TFLOPS/W} Configurable {SRAM}-Based
                 Floating-Point Computation-in-Memory Macro for
                 Energy-Efficient {AI} Chips",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--5",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ISCAS46773.2023.10182197",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "AI accelerators; Computation-in-memory (CIM); Energy
                 efficiency; Floating-point; Neural networks; Parallel
                 Alignment; Simulation; SRAM; Throughput; Training;
                 Voltage measurement",
}

@InProceedings{Malathi:2023:DRV,
  author =       "D Malathi and R Sneha and M Shanmugapriya and S
                 Sethurajan",
  editor =       "{IEEE}",
  booktitle =    "{2023 4th International Conference on Signal
                 Processing and Communication (ICSPC)}",
  title =        "Design of {RISC-V} Processing Unit Using Posit Number
                 System",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "427--431",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ICSPC57692.2023.10125646",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
}

@Article{Mansfield:2023:MSR,
  author =       "Daniel F. Mansfield",
  title =        "{Mesopotamian} square root approximation by a sequence
                 of rectangles",
  journal =      j-BRITISH-J-HIST-MATH,
  volume =       "38",
  number =       "3",
  pages =        "175--188",
  year =         "2023",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/26375451.2023.2215652",
  ISSN =         "1749-8430 (print), 1749-8341 (electronic)",
  ISSN-L =       "1749-8341",
  bibdate =      "Thu Apr 25 11:06:30 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/bshm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.tandfonline.com/doi/full/10.1080/26375451.2023.2215652",
  acknowledgement = ack-nhfb,
  ajournal =     "BSHM Bull.",
  fjournal =     "BSHM Bulletin: Journal of the British Society for the
                 History of Mathematics",
  journal-URL =  "http://www.tandfonline.com/loi/tbsh20",
  onlinedate =   "09 Jun 2023",
}

@Article{Martin-Dorel:2023:EFP,
  author =       "{\'E}rik Martin-Dorel and Guillaume Melquiond and
                 Pierre Roux",
  title =        "Enabling Floating-Point Arithmetic in the {Coq} Proof
                 Assistant",
  journal =      j-J-AUTOM-REASON,
  volume =       "67",
  number =       "4",
  pages =        "??--??",
  month =        dec,
  year =         "2023",
  CODEN =        "JAREEW",
  DOI =          "https://doi.org/10.1007/s10817-023-09679-x",
  ISSN =         "0168-7433 (print), 1573-0670 (electronic)",
  ISSN-L =       "0168-7433",
  bibdate =      "Mon Nov 27 10:14:54 MST 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
  URL =          "https://link.springer.com/article/10.1007/s10817-023-09679-x",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Autom. Reason.",
  articleno =    "33",
  fjournal =     "Journal of Automated Reasoning",
  journal-URL =  "http://link.springer.com/journal/10817",
}

@Article{Melquiond:2023:WFV,
  author =       "Guillaume Melquiond and Rapha{\"e}l Rieu-Helft",
  title =        "{WhyMP}, a formally verified arbitrary-precision
                 integer library",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "115",
  number =       "??",
  pages =        "74--95",
  month =        mar # "\slash " # apr,
  year =         "2023",
  CODEN =        "JSYCEH",
  DOI =          "https://doi.org/10.1016/j.jsc.2022.07.007",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  bibdate =      "Sat Sep 17 06:23:51 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/gnu.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0747717122000657",
  abstract =     "Arbitrary-precision integer libraries such as GMP are
                 a critical building block of computer algebra systems.
                 GMP provides state-of-the-art algorithms that are
                 intricate enough to justify formal verification. In
                 this paper, we present a C library that has been
                 formally verified using the Why3 verification platform
                 in about four person-years. This verification deals not
                 only with safety, but with full functional correctness.
                 It has been performed using a mixture of mechanically
                 checked handwritten proofs and automated theorem
                 proving. We have implemented and verified a nontrivial
                 subset of GMP's algorithms, including their
                 optimizations and intricacies. Our library provides the
                 same interface as GMP and is almost as efficient for
                 smaller inputs. We detail our verification methodology
                 and the algorithms we have implemented, and include
                 some benchmarks to compare our library with GMP.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171",
  keywords =     "Deductive program verification; Integer arithmetic;
                 Mathematical library",
}

@Article{Mezzarobba:2023:REA,
  author =       "Marc Mezzarobba",
  title =        "Rounding error analysis of linear recurrences using
                 generating series",
  journal =      j-ELECTRON-TRANS-NUMER-ANAL,
  volume =       "58",
  pages =        "196--227",
  year =         "2023",
  CODEN =        "????",
  ISSN =         "1068-9613 (print), 1097-4067 (electronic)",
  ISSN-L =       "1068-9613",
  bibdate =      "Mon Jun 3 08:23:58 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/etna.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://etna.math.kent.edu/vol.58.2023/pp196-227.dir/pp196-227.pdf;
                 https://etna.math.kent.edu/volumes/2021-2030/vol58/abstract.php?vol=58&pages=196-227",
  abstract =     "We develop a toolbox for the error analysis of linear
                 recurrences with constant or polynomial coefficients,
                 based on generating series, Cauchy's method of
                 majorants, and simple results from analytic
                 combinatorics. We illustrate the power of the approach
                 by several nontrivial application examples. Among these
                 examples are a new worst-case analysis of an algorithm
                 for computing the Bernoulli numbers and a new algorithm
                 for evaluating differentially finite functions in
                 interval arithmetic while avoiding interval blow-up",
  acknowledgement = ack-nhfb,
  ajournal =     "Electron. Trans. Numer. Anal.",
  fjournal =     "Electronic Transactions on Numerical Analysis",
  journal-URL =  "http://etna.mcs.kent.edu/",
}

@TechReport{Micikevicius:2023:OBF,
  author =       "Paulius Micikevicius and Stuart Oberman and Marius
                 Cornea Pradeep Dubey and Andres Rodriguez and Ian Bratt
                 and Richard Grisenthwaite and Chiachen Chou Norm Jouppi
                 and Amber Huffman and Michael Schulte and Ralph Wittig
                 and Dharmesh Jani and Summer Deng",
  title =        "{OCP} 8-bit floating point specification ({OFP8}):
                 Revision 1.0.",
  type =         "Technical report",
  institution =  "Open Compute Project",
  address =      "????",
  pages =        "16",
  day =          "20",
  month =        jun,
  year =         "2023",
  bibdate =      "Thu Nov 30 05:39:50 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.opencompute.org/documents/ocp-8-bit-floating-point-specification-ofp8-revision-1-0-2023-06-20-pdf",
  acknowledgement = ack-nhfb,
}

@Article{Mikaitis:2023:MMT,
  author =       "Mantas Mikaitis",
  title =        "Monotonicity of Multi-Term Floating-Point Adders",
  journal =      "arxiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--13",
  day =          "3",
  month =        apr,
  year =         "2023",
  bibdate =      "Thu Apr 06 15:33:19 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  URL =          "https://arxiv.org/pdf/2304.01407.pdf",
  abstract =     "In the literature on algorithms for performing the
                 multi-term addition $ s_n = \sum_{i = 1}^n x_i $ using
                 floating-point arithmetic it is often shown that a
                 hardware unit that has single normalization and
                 rounding improves precision, area, latency, and power
                 consumption, compared with the use of standard add or
                 fused multiply--add units. However, non-monotonicity
                 can appear when computing sums with a subclass of
                 multi-term addition units, which currently is not
                 explored in the literature. We demonstrate that common
                 techniques for performing multi-term addition with $ n
                 \geq 4 $, without normalization of intermediate
                 quantities, can result in non-monotonicity-increasing
                 one of the addends $ x_i $ decreases the sum sn.
                 Summation is required in dot product and matrix
                 multiplication operations, operations that have
                 increasingly started appearing in the hardware of
                 supercomputers, thus knowing where monotonicity is
                 preserved can be of interest to the users of these
                 machines. Our results suggest that non-monotonicity of
                 summation, in some of the commercial hardware devices
                 that implement a specific class of multi-term adders,
                 is a feature that may have appeared unintentionally as
                 a consequence of design choices that reduce circuit
                 area and other metrics. To demonstrate our findings, we
                 use formal proofs as well as a numerical simulation of
                 non-monotonic multi-term adders in MATLAB",
  acknowledgement = ack-nhfb,
  keywords =     "dot product; floating-point arithmetic; matrix
                 multiply; monotonicity; multi-term addition",
  remark =       "arXiv:2304.01407v1",
}

@InProceedings{Mirsalari:2023:OSO,
  author =       "Seyed Ahmad Mirsalari and Saba Yousefzadeh and
                 Giuseppe Tagliavini and Dimitrios Stathis and Ahmed
                 Hemani",
  booktitle =    "{2023 30th IEEE International Conference on
                 Electronics, Circuits and Systems (ICECS)}",
  title =        "Optimizing Self-Organizing Maps for Bacterial Genome
                 Identification on Parallel Ultra-Low-Power Platforms",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--8",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ICECS58634.2023.10382758",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "approximate computing; genome identification;
                 Genomics; Instruction sets; Microorganisms; parallel
                 ultra-low-power platform; Pathogens; RISC-V;
                 Self-organizing feature maps; Self-organizing maps;
                 smallFloat data types; Software algorithms;
                 Throughput",
}

@Article{Mudawar:2023:EVI,
  author =       "Muhamed F. Mudawar",
  title =        "Exact Versus Inexact Decimal Floating-Point Numbers
                 and Arithmetic",
  journal =      j-IEEE-ACCESS,
  volume =       "11",
  pages =        "17891--17905",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ACCESS.2023.3244891",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Tue Sep 30 17:30:28 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "Adders; Arithmetic; Encoding; exact versus inexact
                 decimal arithmetic; exact versus inexact decimal
                 numbers; exact versus inexact zeros; Floating-point
                 arithmetic; Hardware; IEEE 754 standard; Program
                 processors; Software engineering",
}

@Article{Murillo:2023:GPB,
  author =       "Raul Murillo and Alberto A. {Del Barrio} and Guillermo
                 Botella and Christian Pilato",
  title =        "Generating Posit-Based Accelerators With High-Level
                 Synthesis",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-1,
  volume =       "70",
  number =       "10",
  pages =        "4040--4052",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/TCSI.2023.3299009",
  ISSN =         "1549-8328 (print), 1558-0806 (electronic)",
  ISSN-L =       "1549-8328",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems I: Regular
                 Papers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8919",
}

@Article{Murillo:2023:HMP,
  author =       "Raul Murillo and Javier Hormigo and Alberto A. {Del
                 Barrio} and Guillermo Botella",
  title =        "{HUB} Meets Posit: Arithmetic Units Implementation",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
  pages =        "1--1",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/TCSII.2023.3307488",
  ISSN =         "1549-7747 (print), 1558-3791 (electronic)",
  ISSN-L =       "1549-7747",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems II: Express
                 Briefs",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
}

@InProceedings{Murillo:2023:PPL,
  author =       "Raul Murillo and David Mallas{\'e}n and Alberto A. Del
                 Barrio and Guillermo Botella",
  title =        "{PLAUs}: Posit Logarithmic Approximate Units to
                 Implement Low-Cost Operations with Real Numbers",
  crossref =     "Gustafson:2023:NGA",
  pages =        "171--188",
  year =         "2023",
  DOI =          "https://doi.org/10.1007/978-3-031-32180-1_11",
  bibdate =      "Sat Dec 16 08:52:12 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@InProceedings{Murillo:2023:SDA,
  author =       "Raul Murillo and Alberto A. {Del Barrio} and Guillermo
                 Botella",
  editor =       "{IEEE}",
  booktitle =    "2023 {IEEE 34th International Conference on
                 Application-specific Systems, Architectures and
                 Processors (ASAP): ASAP 2023, 19--21 July 2023, Porto,
                 Portugal}",
  title =        "A Suite of Division Algorithms for Posit Arithmetic",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "41--44",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ASAP57973.2023.00020",
  ISBN-13 =      "979-83-503-4686-2 (print), 979-83-503-4685-5
                 (e-book)",
  bibdate =      "Thu Nov 16 15:55:09 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@Article{Mushtak:2023:FNP,
  author =       "Noble Mushtak and Daniel Lemire",
  title =        "Fast number parsing without fallback",
  journal =      j-SPE,
  volume =       "53",
  number =       "7",
  pages =        "1467--1471",
  month =        jul,
  year =         "2023",
  CODEN =        "SPEXBL",
  DOI =          "https://doi.org/10.1002/spe.3198",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Thu Jun 29 14:46:14 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/spe.bib",
  note =         "See original work \cite{Lemire:2021:NPG}.",
  abstract =     "In recent work, Lemire (2021) presented a fast
                 algorithm to convert number strings into binary
                 floating-point numbers. The algorithm has been adopted
                 by several important systems: for example, it is part
                 of the runtime libraries of GCC 12, Rust 1.55, and Go
                 1.16. The algorithm parses any number string with a
                 significand containing no more than 19 digits into an
                 IEEE floating-point number. However, there is a check
                 leading to a fallback function to ensure correctness.
                 This fallback function is never called in practice. We
                 prove that the fallback is unnecessary. Thus we can
                 slightly simplify the algorithm and its
                 implementation.",
  acknowledgement = ack-nhfb,
  ajournal =     "Softw. Pract. Exp.",
  fjournal =     "Software --- Practice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  onlinedate =   "04 March 2023",
}

@Article{Nadalini:2023:RPF,
  author =       "Davide Nadalini and Manuele Rusci and Luca Benini and
                 Francesco Conti",
  title =        "Reduced precision floating-point optimization for
                 {Deep Neural Network On-Device Learning} on
                 microcontrollers",
  journal =      j-FUT-GEN-COMP-SYS,
  volume =       "149",
  number =       "??",
  pages =        "212--226",
  month =        dec,
  year =         "2023",
  CODEN =        "FGSEVI",
  DOI =          "https://doi.org/10.1016/j.future.2023.07.020",
  ISSN =         "0167-739X (print), 1872-7115 (electronic)",
  ISSN-L =       "0167-739X",
  bibdate =      "Thu Sep 21 08:18:51 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/futgencompsys2020.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167739X23002728",
  acknowledgement = ack-nhfb,
  fjournal =     "Future Generation Computer Systems",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0167739X",
}

@InProceedings{Nadalini:2023:TWR,
  author =       "Alessandro Nadalini and Georg Rutishauser and Alessio
                 Burrello and Nazareno Bruschi and Angelo Garofalo and
                 Luca Benini and Francesco Conti and Davide Rossi",
  editor =       "{IEEE}",
  booktitle =    "{2023 IEEE Computer Society Annual Symposium on VLSI
                 (ISVLSI)}",
  title =        "A 3 {TOPS\slash W RISC-V} Parallel Cluster for
                 Inference of Fine-Grain Mixed-Precision Quantized
                 Neural Networks",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--6",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ISVLSI59464.2023.10238679",
  bibdate =      "Sat Dec 16 15:51:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
}

@Book{Nazareth:2023:CGN,
  author =       "John Lawrence Nazareth",
  title =        "Concise Guide to Numerical Algorithmics: The
                 Foundations and Spirit of Scientific Computing",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  year =         "2023",
  DOI =          "https://doi.org/10.1007/978-3-031-21762-3",
  ISBN =         "3-031-21762-4",
  ISBN-13 =      "978-3-031-21762-3",
  ISSN =         "2191-5776",
  ISSN-L =       "2191-5768",
  bibdate =      "Fri Dec 15 11:31:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "SpringerBriefs in Computer Science",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@Article{Noh:2023:FFD,
  author =       "Seock-Hwan Noh and Jahyun Koo and Seunghyun Lee and
                 Jongse Park and Jaeha Kung",
  title =        "{FlexBlock}: a Flexible {DNN} Training Accelerator
                 With Multi-Mode Block Floating Point Support",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "72",
  number =       "9",
  pages =        "2522--2535",
  month =        sep,
  year =         "2023",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2023.3253050",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Thu Aug 10 06:30:56 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Misc{NVIDIA:2023:FPI,
  author =       "{NVIDIA Corporation}",
  title =        "Floating Point and {IEEE 754} Compliance for {NVIDIA
                 GPUs}",
  howpublished = "NVIDIA Web site.",
  month =        oct,
  year =         "2023",
  bibdate =      "Fri Dec 01 12:26:53 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://docs.nvidia.com/cuda/floating-point/",
  acknowledgement = ack-nhfb,
  remark =       "The document discusses IEEE 754 conformance, CUDA,
                 fused multiply-add, dot products, and GPU issues. It
                 also says: ``NVIDIA GPUs differ from the x86
                 architecture in that rounding modes are encoded within
                 each floating point instruction instead of dynamically
                 using a floating point control word. Trap handlers for
                 floating point exceptions are not supported. On the GPU
                 there is no status flag to indicate when calculations
                 have overflowed, underflowed, or have involved inexact
                 arithmetic.''",
}

@InProceedings{Oh:2023:RLR,
  author =       "Hyun Woo Oh and Seongmo An and Won Sik Jeong and Seung
                 Eun Lee",
  editor =       "{IEEE}",
  booktitle =    "{2023 IEEE/ACM International Symposium on Low Power
                 Electronics and Design (ISLPED)}",
  title =        "{RF2P}: a Lightweight {RISC} Processor Optimized for
                 Rapid Migration from {IEEE-754} to Posit",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--6",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ISLPED58423.2023.10244582",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Oliver:2023:ASF,
  author =       "Jos{\'e} Oliver and Carlos {\'A}lvarez and Teresa
                 Cervero and Xavier Martorell and John D. Davis and
                 Eduard Ayguad{\'e}",
  booktitle =    "{2023 33rd International Conference on
                 Field-Programmable Logic and Applications (FPL)}",
  title =        "Accelerating {SpMV} on {FPGAs} Through Block-Row
                 Compress: a Task-Based Approach",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "151--158",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/FPL60245.2023.00029",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "double-precision; Encoding; FP64; FPGA; HBM;
                 High-performance computing; HLS; Memory management;
                 Proposals; Scalability; Sparse matrices; Sparse matrix
                 representation; SpMV; System-on-chip; Task analysis",
}

@InProceedings{P:2023:AOF,
  author =       "Gayathri G P and Jaya S and Krishnakumar Rao S",
  editor =       "{IEEE}",
  booktitle =    "{2023 International Conference on Control,
                 Communication and Computing (ICCC)}",
  title =        "An Area Optimized Floating-Point Coprocessor for
                 {RISC-V} Processor",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--5",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ICCC57789.2023.10165397",
  bibdate =      "Sat Dec 16 15:51:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{P:2023:ITO,
  author =       "Ponsuganth Ilangovan P. and Rohan Rayan and Vinay
                 Shankar Saxena",
  title =        "Improving the Stability of {Kalman} Filters with Posit
                 Arithmetic",
  crossref =     "Gustafson:2023:NGA",
  pages =        "134--154",
  year =         "2023",
  DOI =          "https://doi.org/10.1007/978-3-031-32180-1_9",
  bibdate =      "Sat Dec 16 08:52:12 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@InProceedings{Park:2023:FDL,
  author =       "Jina Park and Kyuseung Han and Eunjin Choi and Sukho
                 Lee and Jae-Jin Lee and Woojoo Lee and Massoud Pedram",
  editor =       "{IEEE}",
  booktitle =    "{2023 {IEEE\slash ACM} International Symposium on Low
                 Power Electronics and Design (ISLPED)}",
  title =        "{Florian}: Developing a Low-Power {RISC-V} Multicore
                 Processor with a Shared Lightweight {FPU}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--6",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ISLPED58423.2023.10244431",
  bibdate =      "Sat Dec 16 15:51:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Pasca:2023:ELP,
  author =       "Bogdan Pasca and Martin Langhammer",
  title =        "Extracting low-precision floating-point adders from
                 embedded hard {FP DSP} Blocks on {FPGAs}",
  crossref =     "IEEE:2023:PIS",
  pages =        "139--142",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00017",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "adder; Adders; ARITH 2023; ARITH-30; bfloat16;
                 Computer architecture; Costs; Digital arithmetic; DSP;
                 extraction; Field programmable gate arrays;
                 floating-point; FP-DSP; FPGA; half-precision; mapping",
}

@Article{Perez:2023:TIL,
  author =       "Sergio P. Perez and Yan Zhang and James Briggs and
                 Charlie Blake and Josh Levy-Kramer and Paul Balanca and
                 Carlo Luschi and Stephen Barlow and Andrew William
                 Fitzgibbon",
  title =        "Training and inference of large language models using
                 8-bit floating point",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--22",
  day =          "29",
  month =        sep,
  year =         "2023",
  DOI =          "https://doi.org/10.48550/arXiv.2309.17224",
  bibdate =      "Wed Aug 07 16:34:17 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/abs/2309.17224",
  abstract =     "FP8 formats are gaining popularity to boost the
                 computational efficiency for training and inference of
                 large deep learning models. Their main challenge is
                 that a careful choice of scaling is needed to prevent
                 degradation due to the reduced dynamic range compared
                 to higher-precision formats. Although there exists
                 ample literature about selecting such scalings for INT
                 formats, this critical aspect has yet to be addressed
                 for FP8. This paper presents a methodology to select
                 the scalings for FP8 linear layers, based on
                 dynamically updating per-tensor scales for the weights,
                 gradients and activations. We apply this methodology to
                 train and validate large language models of the type of
                 GPT and Llama 2 using FP8, for model sizes ranging from
                 111M to 70B. To facilitate the understanding of the FP8
                 dynamics, our results are accompanied by plots of the
                 per-tensor scale distribution for weights, activations
                 and gradients during both training and inference.",
  acknowledgement = ack-nhfb,
}

@Article{Perotti:2023:YOS,
  author =       "Matteo Perotti and Matheus Cavalcante and Alessandro
                 Ottaviano and Jiantao Liu and Luca Benini",
  title =        "{Yun}: an Open-Source, 64-Bit {RISC-V}-Based Vector
                 Processor With Multi-Precision Integer and
                 Floating-Point Support in 65-nm {CMOS}",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
  volume =       "70",
  number =       "10",
  pages =        "3732--3736",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/TCSII.2023.3292579",
  ISSN =         "1549-7747 (print), 1558-3791 (electronic)",
  ISSN-L =       "1549-7747",
  bibdate =      "Sat Dec 16 15:51:40 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems II: Express
                 Briefs",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
}

@Misc{Pilipovic:2023:EEN,
  author =       "Ratko Pilipovi{\'c} and Patricio Buli{\'c} and
                 Uro{\v{s}} Lotri{\v{c}}",
  title =        "Energy-efficient neural network learning with
                 accuracy-adjustable floating-point multiplier",
  howpublished = "TechRxiv preprint.",
  day =          "19",
  month =        feb,
  year =         "2023",
  DOI =          "https://doi.org/10.36227/techrxiv.22123127.v1",
  bibdate =      "Fri Sep 29 14:34:35 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.techrxiv.org/articles/preprint/Energy-efficient_neural_network_learning_with_accuracy-adjustable_floating-point_multiplier/22123127",
  abstract =     "This paper proposes a novel approximate bfloat16
                 multiplier with on-the-fly adjustable accuracy for
                 energy-efficient learning in deep neural networks. The
                 size of the proposed multiplier is only 62\% of the
                 size of the exact bfloat16 multiplier. Furthermore, its
                 energy footprint is up to five times smaller than the
                 footprint of the exact bfloat multiplier. We
                 demonstrate the advantages of the proposed multiplier
                 in deep neural network learning, where we successfully
                 train the ResNet-20 network on the CIFAR-10 dataset
                 from scratch.",
  acknowledgement = ack-nhfb,
}

@Misc{Postpischil:2023:WDI,
  author =       "Eric Postpischil",
  title =        "Why does the integer representation of a floating
                 point number offer a piecewise linear approximation to
                 the logarithm?",
  howpublished = "Stack Overflow Web site.",
  year =         "2023",
  bibdate =      "Wed Dec 20 06:59:51 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://stackoverflow.com/questions/75772363/why-does-the-integer-representation-of-a-floating-point-number-offer-a-piecewise",
  acknowledgement = ack-nhfb,
  remark =       "Discusses Jim Blinn's approximate logarithm for the
                 IEEE 32-bit binary format \cite{Blinn:1997:JBC}.",
}

@Article{Reinsch:2023:SVD,
  author =       "Christian Reinsch and Mathias Richter",
  title =        "Singular value decomposition in extended double
                 precision arithmetic",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "93",
  number =       "3",
  pages =        "1137--1155",
  year =         "2023",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-022-01459-9",
  ISSN =         "1017-1398,1572-9265",
  ISSN-L =       "1017-1398",
  MRclass =      "65F55 (65F25 65G50)",
  MRnumber =     "4598587",
  bibdate =      "Sat Aug 2 16:11:52 2025",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/r/reinsch-christian-h.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Christian H. Reinsch (?? ?? 1934--8 October 2022)",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@InProceedings{Ren:2023:EAM,
  author =       "Pengchang Ren and Reiji Suda and Vorapong
                 Suppakitpaisarn",
  title =        "Efficient Additions and {Montgomery} Reductions of
                 Large Integers for {SIMD}",
  crossref =     "IEEE:2023:PIS",
  pages =        "48--59",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00034",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "additions; ARITH 2023; ARITH-30; arithmetic for
                 cryptography; AVX-512; Cryptography; Digital
                 arithmetic; Montgomery reduction; Pipelines; Program
                 processors; SIMD; Standards; SVE",
}

@Article{Robert:2023:FMM,
  author =       "Jean-Marc Robert and Pascal V{\'e}ron",
  title =        "Faster multiplication over {$ \mathbb {F}_2 [X] $}
                 using {AVX512} instruction set and {VPCLMULQDQ}
                 instruction",
  journal =      j-J-CRYPTO-ENG,
  volume =       "13",
  number =       "1",
  pages =        "37--55",
  month =        apr,
  year =         "2023",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s13389-021-00278-3",
  ISSN =         "2190-8508 (print), 2190-8516 (electronic)",
  ISSN-L =       "2190-8508",
  bibdate =      "Fri Jun 2 12:32:10 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcryptoeng.bib",
  URL =          "https://link.springer.com/article/10.1007/s13389-021-00278-3",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Crypto. Eng.",
  fjournal =     "Journal of Cryptographic Engineering",
  journal-URL =  "http://link.springer.com/journal/13389",
}

@Article{Rump:2023:IPP,
  author =       "Siegfried M. Rump",
  title =        "{IEEE-754} Precision-$p$ base-$ \beta $ Arithmetic
                 Implemented in Binary",
  journal =      j-TOMS,
  volume =       "49",
  number =       "4",
  pages =        "32:1--32:??",
  month =        dec,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3596218",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Dec 23 05:40:24 MST 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3596218;
                 https://www.tuhh.de/ti3/paper/rump/Ru23b.pdf",
  abstract =     "We show how an IEEE-754 conformant precision-$p$
                 base-$ \beta $ arithmetic can be implemented based on
                 some binary floating-point and/or integer arithmetic.
                 This includes the four basic operations and square root
                 subject to the five IEEE-754 rounding modes, namely he
                 nearest roundings with roundTiesToEven and
                 roundTiesToAway, the directed roundings downwards and
                 upwards, as well as rounding towards zero. Exceptional
                 values like $ \infty $ or NaN are covered according to
                 the IEEE-754 arithmetic standard.

                 The results of the precision-$p$ base-$ \beta $
                 operations are computed using some underlying
                 precision-$q$ binary arithmetic. We distinguish two
                 cases. When using a precision-$q$ binary integer
                 arithmetic, the base-$ \beta $ precision $p$ is limited
                 for all operations by $ \beta^{2 p} \leq 2^q$, whereas
                 using a precision-$q$ binary floating-point arithmetic
                 imposes stronger limits on the base-$ \beta $
                 precision, namely $ \beta^{2p} \leq 2^q$ for addition
                 and multiplication, $ \beta^{2p} \leq 2^{q - 1}$ for
                 division and $ \beta^{2p} \leq 2^{q - 3}$ for the
                 square root. Those limitations cannot be improved.

                 The algorithms are implemented in a Matlab/Octave
                 flbeta-toolbox with the choice of using uint64 or
                 binary64 as underlying arithmetic. The former allows
                 larger precisions, the latter is advantageous for the
                 square root, whereas computing times are similar. The
                 flbeta-toolbox offers precision-$p$ base-$ \beta $
                 scalar, vector and matrix operations including sparse
                 matrices as well as corresponding interval operations.
                 The base $ \beta $ can be chosen in the range $ \beta $
                 [2,64]. The flbeta-toolbox will be part of Version 13
                 of INTLAB [18], the Matlab/Octave toolbox for reliable
                 computing.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "32",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  remark =       "Received 6 December 2021; revised 10 October 2022;
                 accepted 30 March 2023.",
}

@InProceedings{Rydahl:2023:PPA,
  author =       "Anton Rydahl and Joseph Huber and Ethan Luis Mcdonough
                 and Johannes Doerfert",
  booktitle =    "Proceedings of the {SC 23 Workshops of The
                 International Conference on High Performance Computing,
                 Network, Storage, and Analysis}",
  title =        "Precision and Performance Analysis of {C} Standard
                 Math Library Functions on {GPUs}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  month =        nov,
  year =         "2023",
  DOI =          "https://doi.org/10.1145/3624062.3624166",
  bibdate =      "Fri Dec 8 12:56:08 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "With the advent of GPU computing, executing large
                 program sections on accelerators has become
                 increasingly important. Efforts are being made to
                 support the C standard library, LIBC, on GPUs via LLVM
                 machinery. Therefore, the C standard math library,
                 LIBM, must be supported on GPUs. So far, LLVM
                 frontends, such as Clang, have relied on GPU vendor
                 implementations of LIBM functionality wrapped into
                 (mostly) LIBM-compatible forwarding functions.\par

                 We propose a novel LIBM for GPUs reusing a collection
                 of LLVM target-agnostic implementations and built-ins
                 alongside vendor implementations of most single and
                 double-precision floating point math functions. Our
                 approach allows selecting between individual
                 implementations based on the GPU target as opposed to
                 the current approach, which serves only the single
                 third-party library implementation. Our extensive
                 numerical analysis highlights the various
                 implementations differences in performance and
                 precision. Our solution allows users to choose the
                 implementation that maximizes speed while meeting their
                 specific precision requirements.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Safieh:2023:EBR,
  author =       "Malek Safieh and Andreas Furch and Fabrizio {De
                 Santis}",
  title =        "An Efficient {Barrett} Reduction Algorithm for
                 {Gaussian} Integer Moduli",
  crossref =     "IEEE:2023:PIS",
  pages =        "76--83",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00011",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2023; ARITH-30; Barrett Reduction; Computational
                 complexity; Computational efficiency; Costs; Digital
                 arithmetic; Gaussian Integers; Modular Arithmetic;
                 Modulo Reduction",
}

@InProceedings{Saikia:2023:FIA,
  author =       "Jyotishman Saikia and Amitesh Sridharan and Injune Yeo
                 and Shreyas Venkataramanaiah and Deliang Fan and
                 Jae-Sun Seo",
  booktitle =    "{ESSCIRC 2023 --- IEEE 49th European Solid State
                 Circuits Conference (ESSCIRC)}",
  title =        "{FP-IMC}: a 28nm All-Digital Configurable
                 Floating-Point In-Memory Computing Macro",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "405--408",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ESSCIRC59616.2023.10268770",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Artificial neural networks; Computational modeling;
                 Computer architecture; Digital in-memory computing;
                 Europe; floating-point acceleration; In-memory
                 computing; Throughput; Training",
}

@InProceedings{Sajid:2023:ODN,
  author =       "Shoaib Sajid and Sereiwatha Ros and Hyung-Won Kim",
  booktitle =    "{2023 IEEE International Conference on Consumer
                 Electronics-Asia (ICCE-Asia)}",
  title =        "Optimizing Deep Neural Network with Brain Floating
                 Half-Precision Format",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--5",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ICCE-Asia59966.2023.10326380",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Artificial neural networks; BFLOAT16; Brain
                 modeling; Computational modeling; Convergence; Costs;
                 Deep Learning; Energy consumption; Half-Precision
                 Format; Memory Efficiency; Memory management;
                 Training",
}

@InProceedings{Sakellariou:2023:MFR,
  author =       "Vasilis Sakellariou and Vassilis Paliouras and Ioannis
                 Kouretas and Hani Saleh and Thanos Stouraitis",
  title =        "A multiplier-Free {RNS}-Based {CNN} accelerator
                 exploiting bit-Level sparsity",
  crossref =     "IEEE:2023:PIS",
  pages =        "101--101",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00037",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Analytical models; ARITH 2023; ARITH-30; Benchmark
                 testing; Digital arithmetic; Encoding; Energy
                 efficiency; Throughput; Vectors",
}

@Article{Schilling:2023:BSR,
  author =       "Jonathan Schilling and Jakob Svensson and Udo
                 H{\"o}fel and Joachim Geiger and Henning Thomsen",
  title =        "{Biot--Savart} routines with minimal floating point
                 error",
  journal =      j-COMP-PHYS-COMM,
  volume =       "287",
  number =       "??",
  pages =        "Article 108692",
  month =        jun,
  year =         "2023",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2023.108692",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Fri Mar 17 07:49:53 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465523000371",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@InProceedings{Seo:2023:DPHa,
  author =       "Jihee Seo and Dae Hyun Kim",
  title =        "Dual-Purpose Hardware Algorithms and Architectures.
                 {Part 1}: Floating-Point Division",
  crossref =     "IEEE:2023:PIS",
  pages =        "24--31",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00013",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2023; ARITH-30; Computer architecture; Costs;
                 Digital arithmetic; Divider; Energy consumption;
                 Floating-Point Arithmetic; Hardware; Online Division;
                 Simulation; Throughput",
}

@InProceedings{Seo:2023:DPHb,
  author =       "Jihee Seo and Dae Hyun Kim",
  title =        "Dual-Purpose Hardware Algorithms and Architectures.
                 {Part 2}: Integer Division",
  crossref =     "IEEE:2023:PIS",
  pages =        "1--8",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00014",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2023; ARITH-30; Computer architecture; Costs;
                 Digital arithmetic; Divider; Energy consumption;
                 Hardware; Integer Arithmetic; Online Division;
                 Simulation",
}

@InProceedings{Shah:2023:DPU,
  author =       "Nimish Shah and Wannes Meert and Marian Verhelst",
  booktitle =    "Efficient Execution of Irregular Dataflow Graphs",
  title =        "{DAG} Processing Unit Version 1 ({DPU}): Efficient
                 Execution of Irregular Workloads on a Multicore
                 Processor",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "69--88",
  year =         "2023",
  DOI =          "https://doi.org/10.1007/978-3-031-33136-7_4",
  ISBN =         "3-031-33136-2",
  ISBN-13 =      "978-3-031-33136-7",
  bibdate =      "Fri Dec 15 11:31:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@Book{Shah:2023:EEI,
  author =       "Nimish Shah and Wannes Meert and Marian Verhelst",
  title =        "Efficient Execution of Irregular Dataflow Graphs:
                 Hardware\slash Software Co-optimization for
                 Probabilistic {AI} and Sparse Linear Algebra",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  year =         "2023",
  DOI =          "https://doi.org/10.1007/978-3-031-33136-7",
  ISBN =         "3-031-33136-2",
  ISBN-13 =      "978-3-031-33136-7",
  bibdate =      "Fri Dec 15 11:31:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@InProceedings{Shah:2023:IWR,
  author =       "Nimish Shah and Wannes Meert and Marian Verhelst",
  booktitle =    "Efficient Execution of Irregular Dataflow Graphs",
  title =        "Irregular Workloads at Risk of Losing the Hardware
                 Lottery",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "1--21",
  year =         "2023",
  DOI =          "https://doi.org/10.1007/978-3-031-33136-7_1",
  ISBN =         "3-031-33136-2",
  ISBN-13 =      "978-3-031-33136-7",
  bibdate =      "Fri Dec 15 11:31:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@InProceedings{Shah:2023:SDR,
  author =       "Nimish Shah and Wannes Meert and Marian Verhelst",
  booktitle =    "Efficient Execution of Irregular Dataflow Graphs",
  title =        "Suitable Data Representation: A Study of Fixed-Point,
                 Floating-Point, and {PositTM} Formats for Probabilistic
                 {AI}",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "23--41",
  year =         "2023",
  DOI =          "https://doi.org/10.1007/978-3-031-33136-7_2",
  ISBN =         "3-031-33136-2",
  ISBN-13 =      "978-3-031-33136-7",
  bibdate =      "Fri Dec 15 11:31:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@Article{Shahbazi:2023:OHI,
  author =       "Karim Shahbazi and Seok-Bum Ko",
  title =        "An Optimized Hardware Implementation of Modular
                 Multiplication of Binary Ring {LWE}",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "11",
  number =       "3",
  pages =        "817--821",
  month =        jul # "\slash " # sep,
  year =         "2023",
  DOI =          "https://doi.org/10.1109/TETC.2023.3280470",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Thu Sep 21 14:02:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
}

@Article{Sharma:2023:CQE,
  author =       "Niraj N. Sharma and Riya Jain and Mohana Madhumita
                 Pokkuluri and Sachin B. Patkar and Rainer Leupers and
                 Rishiyur S. Nikhil and Farhad Merchant",
  title =        "{CLARINET}: A quire-enabled {RISC-V}-based framework
                 for posit arithmetic empiricism",
  journal =      j-J-SYST-ARCH,
  volume =       "135",
  pages =        "102801",
  year =         "2023",
  CODEN =        "JSARFB",
  DOI =          "https://doi.org/10.1016/j.sysarc.2022.102801",
  ISSN =         "1383-7621 (print), 1873-6165 (electronic)",
  ISSN-L =       "1383-7621",
  bibdate =      "Wed May 22 14:56:32 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/S1383762122002867",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Syst. Arch.",
  fjournal =     "Journal of Systems Architecture",
  journal-URL =  "https://www.sciencedirect.com/journal/journal-of-systems-architecture",
  keywords =     "Posit-arithmetic, RISC-V, Open-source hardware,
                 Custom-instructions",
}

@InProceedings{Shekhawat:2023:PPH,
  author =       "Diksha Shekhawat and Jugal Gandhi and M. Santosh and
                 Jai Gopal Pandey",
  title =        "{PHAc}: Posit Hardware Accelerator for Efficient
                 Arithmetic Logic Operations",
  crossref =     "Gustafson:2023:NGA",
  pages =        "88--100",
  year =         "2023",
  DOI =          "https://doi.org/10.1007/978-3-031-32180-1_6",
  bibdate =      "Sat Dec 16 08:52:12 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@Article{Shen:2023:CCA,
  author =       "Shiyu Shen and Hao Yang and Yu Liu and Zhe Liu and
                 Yunlei Zhao",
  title =        "{CARM}: {CUDA-Accelerated RNS Multiplication} in
                 Word-Wise Homomorphic Encryption Schemes for {Internet
                 of Things}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "72",
  number =       "7",
  pages =        "1999--2010",
  month =        jul,
  year =         "2023",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2022.3227874",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 1 10:59:22 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib;
                 http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Silva:2023:TAB,
  author =       "Himeshi De Silva and Hongshi Tan and Nhut-Minh Ho and
                 John L. Gustafson and Weng-Fai Wong",
  title =        "Towards a Better 16-Bit Number Representation for
                 Training Neural Networks",
  crossref =     "Gustafson:2023:NGA",
  pages =        "114--133",
  year =         "2023",
  DOI =          "https://doi.org/10.1007/978-3-031-32180-1_8",
  bibdate =      "Sat Dec 16 08:52:12 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Sohn:2023:EFP,
  author =       "Jongwook Sohn and David K. Dean and Eric Quintana and
                 Wing Shek Wong",
  title =        "Enhanced Floating-Point Multiply-Add with Full
                 Denormal Support",
  crossref =     "IEEE:2023:PIS",
  pages =        "143--150",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00015",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2023; ARITH-30; Delays; Digital arithmetic;
                 Encoding; floating-point arithmetic; floating-point
                 denormal numbers; Floating-point multiply-add;
                 high-speed computer arithmetic; Logic arrays; Next
                 generation networking; Optimization",
}

@Misc{Sukop:2023:HDB,
  author =       "Juraj Sukop and Niels M{\"o}ller",
  title =        "On {HGCD-D} bounds",
  type =         "Report",
  day =          "7",
  month =        feb,
  year =         "2023",
  bibdate =      "Thu Feb 09 11:15:45 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://hal.science/hal-03976898",
  abstract =     "An improved bound for one of the founding relations of
                 HGCD-D algorithm is presented. This allows to put a
                 lower limit on the iteration count of the first sdiv
                 loop, to impose a particular structure on the
                 accumulated quotients and to bound the size of the
                 largest matrix element. The matrix product M.M' is
                 proved to have its upper and lower size bound differ by
                 at most two bits",
  acknowledgement = ack-nhfb,
}

@InProceedings{Taka:2023:MME,
  author =       "Endri Taka and Aman Arora and Kai-Chiang Wu and Diana
                 Marculescu",
  booktitle =    "{2023 International Conference on Field Programmable
                 Technology (ICFPT)}",
  title =        "{MaxEVA}: Maximizing the Efficiency of Matrix
                 Multiplication on {Versal AI Engine}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "96--105",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ICFPT59805.2023.00016",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "AI Engine; Artificial intelligence; Deep Learning;
                 Energy efficiency; Engines; FPGA; Hardware
                 Acceleration; Matrix Multiplication; Performance
                 evaluation; Program processors; System-on-Chip;
                 Technological innovation; Throughput; Versal",
}

@Article{Talpes:2023:MDT,
  author =       "Emil Talpes and Debjit Das Sarma and Doug Williams and
                 Sahil Arora and Thomas Kunjan and Benjamin Floering and
                 Ankit Jalote and Christopher Hsiong and Chandrasekhar
                 Poorna and Vaidehi Samant and John Sicilia and Anantha
                 Kumar Nivarti and Raghuvir Ramachandran and Tim Fischer
                 and Ben Herzberg and Bill McGee and Ganesh
                 Venkataramanan and Pete Banon",
  title =        "The Microarchitecture of {DOJO}, {Tesla}'s Exa-Scale
                 Computer",
  journal =      j-IEEE-MICRO,
  volume =       "43",
  number =       "3",
  pages =        "31--39",
  month =        may # "\slash " # jun,
  year =         "2023",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/MM.2023.3258906",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu May 18 07:38:12 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/hot-chips.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeemicro.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=40",
  remark =       "DOJO is based on RISC-V64 with instruction set
                 extensions. Its arithmetic supports 8-, 16-, 32-, and
                 64-bit integers, and IEEE 754 FP32 (1/8/23), plus FP16
                 (1/5/10), BFP16 (1/8/7), CFP8 (1/4/3), CFP8 (1/5/2),
                 and CFP16 (1/5/10) floating-point formats. The latter
                 is unusual having an external register that records the
                 exponent bias (0, 31, or 63), so that it supports three
                 different ranges of numbers. There is no support for
                 FP64 or longer formats. There is support for stochastic
                 rounding.",
}

@InProceedings{Tompazi:2023:ABT,
  author =       "Styliani Tompazi and Georgios Karakonstantis",
  title =        "{AI}-based Timing Error Modelling: a Case Study on a
                 Pipelined Floating-point Core",
  crossref =     "IEEE:2023:PIS",
  pages =        "110--110",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00035",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2023; ARITH-30; Computational modeling; Digital
                 arithmetic; Machine learning; Nanoscale devices;
                 Timing; Training",
}

@Article{Towhidy:2023:DIA,
  author =       "Ahmad Towhidy and Reza Omidi and Karim Mohammadi",
  title =        "On the Design of Iterative Approximate Floating-Point
                 Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "72",
  number =       "6",
  pages =        "1623--1635",
  month =        jun,
  year =         "2023",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2022.3216465",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed May 17 10:34:15 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  abstract =     "Approximate multipliers provide power and area-saving
                 for error-resilient applications. In this paper, we
                 first propose two approximate floating-point
                 multipliers based on two-dimensional pseudo-Booth
                 encoding: floating-point pseudo-Booth (PB), and
                 floating-point iterative pseudo-Booth (IPB). The
                 accuracy of proposed multipliers can be tuned by three
                 parameters: iteration, encoder's radix (R), and word
                 length after truncation (W). Next, we developed the
                 conventional iterative multipliers with a simplified
                 steering circuit for their correction part to eliminate
                 the power consumption of multipliers. The proposed
                 iterative multipliers are compared with conventional
                 iterative integer multipliers implemented by a
                 simplified steering circuit for the floating-point
                 area. The results reveal that the proposed PB-R4-W4 and
                 IPB-R16-W19, compared to the exact floating-point
                 multiplier, provide up to 98.9\% and 67.5\% reductions
                 in power consumption, respectively, in TSMC 180nm CMOS
                 technology. Also, their MRED values are, respectively,
                 2.9\% and ($ 7.4 \times 10 {-4}$)\%. Finally, we
                 evaluated the functionality of the proposed multipliers
                 for real-life applications, including a hyper-plane
                 classifier and two image processing applications of
                 smoothing and sharpening.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@InProceedings{Tu:2023:TGW,
  author =       "Fengbin Tu and Yiqi Wang and Zihan Wu and Weiwei Wu
                 and Leibo Liu and Yang Hu and Shaojun Wei and Shouyi
                 Yin",
  booktitle =    "{2023 IEEE International Solid-State Circuits
                 Conference (ISSCC)}",
  title =        "16.4 {TensorCIM}: a {28nm 3.7nJ}\slash Gather and
                 {8.3TFLOPS/W} {FP32} Digital-{CIM} Tensor Processor for
                 {MCM-CIM}-Based Beyond-{NN} Acceleration",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "254--256",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ISSCC42615.2023.10067285",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Algebra; Bandwidth; Computational modeling; Computer
                 architecture; Deep learning; Program processors;
                 Tensors",
}

@InProceedings{Ullah:2023:DRE,
  author =       "Salim Ullah and Siva Satyendra Sahoo and Akash Kumar",
  booktitle =    "Embedded Machine Learning for Cyber-Physical, {IoT},
                 and Edge Computing",
  title =        "Designing Resource-Efficient Hardware Arithmetic for
                 {FPGA}-Based Accelerators Leveraging Approximations and
                 Mixed Quantizations",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "89--119",
  month =        oct,
  year =         "2023",
  DOI =          "https://doi.org/10.1007/978-3-031-19568-6_4",
  ISBN =         "3-031-19568-X",
  ISBN-13 =      "978-3-031-19568-6",
  bibdate =      "Fri Dec 15 11:31:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@InProceedings{V:2023:IFP,
  author =       "Velmurugan V M and Ayub Khan A and Bharanidharan S",
  booktitle =    "{2023 International Conference on Next Generation
                 Electronics (NEleX)}",
  title =        "Implementation of Floating Point {CORDIC} Algorithm
                 Using 45 nm Technology For {COS} {SINE} Generation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--5",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/NEleX59773.2023.10420961",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Arithmetic; Arrays; atan; Codes; Coordinate Rotation
                 Digital Computer; Field Programmable Gate Arrays; FPUs;
                 Graphic Data System; Hardware design languages; Logic
                 gates; Next generation networking; Standards",
}

@Article{Valuev:2023:DFA,
  author =       "Georgii Valuev and Maria Valueva and Mikhail Babenko
                 and Andrei Tchernykh",
  title =        "Digital Filter Architecture Based on Modified
                 {Winograd} Method F(2$ \times $ 2, 5$ \times $ 5) and
                 Residue Number System",
  journal =      j-IEEE-ACCESS,
  volume =       "11",
  pages =        "26807--26819",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ACCESS.2023.3258689",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Wed Oct 1 06:08:36 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "Computer architecture; digital filter; digital signal
                 processing; field-programmable gate array; Filtering;
                 Filtering algorithms; Finite impulse response filters;
                 Hardware; IIR filters; Performance evaluation; Residue
                 number system; Winograd method",
}

@Article{Venkataramanaiah:2023:NBF,
  author =       "Shreyas Kolala Venkataramanaiah and Jian Meng and
                 Han-Sok Suh and Injune Yeo and Jyotishman Saikia and
                 Sai Kiran Cherupally and Yichi Zhang and Zhiru Zhang
                 and Jae-Sun Seo",
  title =        "A 28-nm 8-bit Floating-Point {Tensor Core}-Based
                 Programmable {CNN} Training Processor With Dynamic
                 Structured Sparsity",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "58",
  number =       "7",
  pages =        "1885--1897",
  year =         "2023",
  CODEN =        "IJSCBC",
  DOI =          "https://doi.org/10.1109/JSSC.2023.3269148",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "Activation sparsity; CNNs; Convolution; convolutional
                 neural network (CNN) training processor; Convolutional
                 neural networks; Energy efficiency; energy-efficient
                 accelerator; Hardware; Memory management; Random access
                 memory; Training; weight sparsity (WS)",
}

@InProceedings{Vollmer:2023:UHA,
  author =       "Morgane Vollmer and Karim Bigou and Arnaud Tisserand",
  title =        "Using Hierarchical Approach to Speed-up {RNS} Base
                 Extensions in Homomorphic Encryption Context",
  crossref =     "IEEE:2023:PIS",
  pages =        "84--87",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ARITH58626.2023.00030",
  bibdate =      "Wed May 8 09:17:31 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2023; ARITH-30; base extension; Costs; Digital
                 arithmetic; homomorphic encryption; Homomorphic
                 encryption; Multicore processing; Parallel processing;
                 residue number system; Software; Software algorithms",
}

@Article{Weihong:2023:SDM,
  author =       "Bi Weihong and Jin Yun and Li Jiaxin and Sun Lingling
                 and Fu Guangwei and Jin Wa",
  title =        "In-Situ Detection Method of Jellyfish Based on
                 Improved Faster {R-CNN} and {FP16}",
  journal =      j-IEEE-ACCESS,
  volume =       "11",
  pages =        "81803--81814",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/ACCESS.2023.3300655",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "Aquaculture; Convolutional neural networks; Faster
                 R-CNN; Feature extraction; FP16; in-situ detection;
                 jellyfish; Jellyfish; Monitoring; Residual neural
                 networks; Resnet50; Sea measurements; Sea surface;
                 Software; Toxicology; Training",
}

@Manual{Whitehead:2023:FPI,
  author =       "Nathan Whitehead and Alex Fit-florea",
  title =        "Floating Point and {IEEE 754} Compliance for {NVIDIA
                 GPUs}",
  organization = "NVIDIA",
  address =      "????",
  pages =        "28",
  day =          "24",
  month =        aug,
  year =         "2023",
  bibdate =      "Mon Sep 11 07:26:37 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://docs.nvidia.com/cuda/floating-point/;
                 https://docs.nvidia.com/cuda/pdf/Floating_Point_on_NVIDIA_GPU.pdf",
  abstract =     "A number of issues related to floating point accuracy
                 and compliance are a frequent source of confusion on
                 both CPUs and GPUs. The purpose of this white paper is
                 to discuss the most common issues related to NVIDIA
                 GPUs and to supplement the documentation in the CUDA
                 C++ Programming Guide",
  acknowledgement = ack-nhfb,
  tableofcontents = "1 Floating Point / 3 \\
                 1.1 Formats / 3 \\
                 1.2 Operations and Accuracy / 4 \\
                 1.3 The Fused Multiply-Add (FMA) / 5 \\
                 2 Dot Product: An Accuracy Example / 7 \\
                 2.1 Example Algorithms / 7 \\
                 2.2 Comparison / 8 \\
                 3 CUDA and Floating Point / 9 \\
                 3.1 Compute Capability 2.0 and Above / 9 \\
                 3.2 Rounding Modes / 9 \\
                 3.3 Controlling Fused Multiply-add / 10 \\
                 3.4 Compiler Flags / 11 \\
                 3.5 Differences from x86 / 11 \\
                 4 Considerations for a Heterogeneous World / 13 \\
                 4.1 Mathematical Function Accuracy / 13 \\
                 4.2 x87 and SSE / 14 \\
                 4.3 Core Counts / 14 \\
                 4.4 Verifying GPU Results / 14 \\
                 5 Concrete Recommendations / 17 \\
                 6 Acknowledgements / 19 \\
                 7 References / 21 \\
                 8 Notices / 23 \\
                 8.1 Notice / 23 \\
                 8.2 OpenCL / 24 \\
                 8.3 Trademarks / 24",
}

@Book{Wilkinson:2023:REA,
  author =       "J. H. (James Hardy) Wilkinson",
  title =        "Rounding Errors in Algebraic Processes",
  volume =       "89",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xiii + 161",
  year =         "2023",
  ISBN =         "1-61197-751-7",
  ISBN-13 =      "978-1-61197-751-6",
  LCCN =         "QA275 .W64 2023",
  bibdate =      "Wed Aug 7 17:00:33 MDT 2024",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "New foreword by N. J. Higham.",
  series =       "Classics in applied mathematics",
  abstract =     "\booktitle{Rounding Errors in Algebraic Processes} was
                 the first book to give systematic analyses of the
                 effects of rounding errors on a variety of key
                 computations involving polynomials and matrices. A
                 detailed analysis is given of the rounding errors made
                 in the elementary arithmetic operations and inner
                 products, for both floating-point arithmetic and
                 fixed-point arithmetic. The results are then applied in
                 the error analyses of a variety of computations
                 involving polynomials as well as the solution of linear
                 systems, matrix inversion, and eigenvalue computations.
                 The conditioning of these problems is investigated. The
                 aim was to provide a unified method of treatment, and
                 emphasis is placed on the underlying concepts.",
  acknowledgement = ack-nhfb,
  author-dates = "James H. Wilkinson (27 September 1919--5 October
                 1986)",
  remark =       "``\ldots{}a republication originally published by Her
                 Majesty's Stationery Office under British Crown
                 copyright in 1963''-- title page verso.",
  subject =      "Roundoff errors; Erreurs d'arrondi; Roundoff errors",
  tableofcontents = "The fundamental arithmetic operations \\
                 Computations involving polynomials \\
                 Matrix computations",
}

@Article{Wong:2023:KNS,
  author =       "Zheng-Yan Wong and Denis C.-K. Wong and Wai-Kong Lee
                 and Kai-Ming Mok and Wun-She Yap and Ayesha Khalid",
  title =        "{KaratSaber}: New Speed Records for {Saber} Polynomial
                 Multiplication Using Efficient {Karatsuba} {FPGA}
                 Architecture",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "72",
  number =       "7",
  pages =        "1830--1842",
  month =        jul,
  year =         "2023",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2023.3238129",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 1 10:59:22 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

@Article{Yang:2023:ATF,
  author =       "Chun-Chieh Yang and Yi-Ru Chen and Hui-Hsin Liao and
                 Yuan-Ming Chang and Jenq-Kuen Lee",
  title =        "Auto-tuning Fixed-point Precision with {TVM} on
                 {RISC-V} Packed {SIMD} Extension",
  journal =      j-TODAES,
  volume =       "28",
  number =       "3",
  pages =        "33:1--33:??",
  month =        may,
  year =         "2023",
  CODEN =        "ATASFO",
  DOI =          "https://doi.org/10.1145/3569939",
  ISSN =         "1084-4309 (print), 1557-7309 (electronic)",
  ISSN-L =       "1084-4309",
  bibdate =      "Wed May 17 08:06:20 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib;
                 https://www.math.utah.edu/pub/tex/bib/todaes.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3569939",
  abstract =     "Today, as deep learning (DL) is applied more often in
                 daily life, dedicated processors such as CPUs and GPUs
                 have become very important for accelerating model
                 executions. With the growth of technology, people are
                 becoming accustomed to using edge devices, such as
                 mobile phones, smart watches, and VR devices in their
                 daily lives. A variety of technologies using DL are
                 gradually being applied to these edge devices. However,
                 there is a large number of computations in DL. It faces
                 a challenging problem how to provide solutions in the
                 edge devices. In this article, the proposed method
                 enables a flow with the RISC-V Packed extension (P
                 extension) in TVM. TVM, an open deep learning compiler
                 for neural network models, is growing as a key
                 infrastructure for DL computing. RISC-V is an open
                 instruction set architecture (ISA) with customized and
                 flexible features. The Packed-SIMD extension is a
                 RISC-V extension that enables subword
                 single-instruction multiple-data (SIMD) computations in
                 RISC-V architectures to support fallback engines in AI
                 computing. In the proposed flow, a fixed-point type
                 that is supported by an integer of 16-bit type and
                 saturation instructions is added to replace the
                 original 32-bit float type. In addition, an auto-tuning
                 method is proposed to use a uniform selector mechanism
                 (USM) to find the binary point position for fixed-point
                 type use. The tensorization feature of TVM can be used
                 to optimize specific hardware such as subword SIMD
                 instructions with RISC-V P extension. With our
                 experiment on the Spike simulator, the proposed method
                 with the USM can improve performance by approximately
                 2.54 to 6.15$ \times $ in terms of instruction counts
                 with little accuracy loss.",
  acknowledgement = ack-nhfb,
  articleno =    "33",
  fjournal =     "ACM Transactions on Design Automation of Electronic
                 Systems",
  journal-URL =  "https://dl.acm.org/loi/todaes",
}

@Article{Zhang:2023:EAP,
  author =       "Hao Zhang and Seok-Bum Ko",
  title =        "Efficient Approximate Posit Multipliers for Deep
                 Learning Computation",
  journal =      j-IEEE-J-EMERG-SEL-TOP-CIRCUITS-SYST,
  volume =       "13",
  number =       "1",
  pages =        "201--211",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/JETCAS.2022.3231642",
  ISSN =         "2156-3357 (print), 2156-3365 (electronic)",
  ISSN-L =       "2156-3357",
  bibdate =      "Fri Dec 15 09:21:55 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal on Emerging and Selected Topics in
                 Circuits and Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5503868",
}

@InProceedings{Zhuang:2023:HPL,
  author =       "Jinming Zhuang and Zhuoping Yang and Peipei Zhou",
  booktitle =    "{2023 60th ACM/IEEE Design Automation Conference
                 (DAC)}",
  title =        "High Performance, Low Power Matrix Multiply Design on
                 {ACAP}: from Architecture, Design Challenges and {DSE}
                 Perspectives",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--6",
  year =         "2023",
  DOI =          "https://doi.org/10.1109/DAC56929.2023.10247981",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Complexity theory; Computational modeling; Computer
                 architecture; Design automation; Design methodology;
                 Energy efficiency; heterogeneous system-on-chip; matrix
                 multiply; support for multiple data types; Throughput;
                 Versal ACAP",
}

@Article{Zlatopolski:2023:PAV,
  author =       "Dmitry Zlatopolski",
  title =        "{``Perfect Arithmetic'' by Vaclav Josef Pelikan}",
  journal =      j-HIST-MATH,
  volume =       "62",
  number =       "??",
  pages =        "40--50",
  month =        feb,
  year =         "2023",
  CODEN =        "HIMADS",
  DOI =          "https://doi.org/10.1016/j.hm.2022.09.002",
  ISSN =         "0315-0860 (print), 1090-249X (electronic)",
  ISSN-L =       "0315-0860",
  bibdate =      "Wed Mar 15 09:40:56 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/histmath.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0315086022000659",
  abstract =     "The present article describes for the first time the
                 book of Vaclav Josef Pelikan titled
                 \booktitle{Arithmeticus Perfectus Qui tria numerare
                 nescit. Seu Arithmetica dualis, In qua Numerando non
                 proceditur, nisi ad duo, \& tamen omnes quaestiones
                 Arithmeticae negotio facili enodari possunt}, published
                 in Prague in 1712. The book is written in Latin on 86
                 pages and consists of a dedication, a message to the
                 reader and four chapters. Operations in the binary
                 system, including the extraction of square and cube
                 roots, methods of converting numbers from the decimal
                 system to the binary system and vice versa, etc., are
                 given. In general, we may say that the book by Vaclav
                 Josef Pelikan is the first fully fledged and
                 methodologically sound textbook of arithmetic using the
                 binary number system as well as containing original
                 methods of solution.",
  acknowledgement = ack-nhfb,
  fjournal =     "Historia Mathematica",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03150860",
  keywords =     "base conversion; binary arithmetic",
}

@InProceedings{Aggarwal:2024:SBP,
  author =       "Shivam Aggarwal and Hans Jakob Damsgaard and
                 Alessandro Pappalardo and Giuseppe Franco and Thomas B.
                 Preu{\ss}er and Michaela Blott and Tulika Mitra",
  booktitle =    "{2024 34th International Conference on
                 Field-Programmable Logic and Applications (FPL)}",
  title =        "Shedding the Bits: Pushing the Boundaries of
                 Quantization with Minifloats on {FPGAs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "297--303",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/FPL64840.2024.00048",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Costs; Data models; Field programmable gate
                 arrays; minifloats; multiply-accumulate; Neural
                 networks; Numerical models; quantization; Quantization
                 (signal); Resource management; Training; Transformers",
}

@InProceedings{Ahmadpour:2024:MMM,
  author =       "Zabihollah Ahmadpour and Ghassem Jaberipur and Jeong-A
                 Lee",
  title =        "{Montgomery} Modular Multiplication via Single-Base
                 Residue Number Systems",
  crossref =     "IEEE:2024:PIS",
  pages =        "17--23",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00013",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@Book{Alsuhli:2024:NSD,
  author =       "Ghada Alsuhli and Vasilis Sakellariou and Hani Saleh
                 and Mahmoud Al-Qutayri and Baker Mohammad and Thanos
                 Stouraitis",
  title =        "Number Systems for Deep Neural Network Architectures",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  year =         "2024",
  DOI =          "https://doi.org/10.1007/978-3-031-38133-1",
  ISBN =         "3-031-38133-5",
  ISBN-13 =      "978-3-031-38133-1",
  ISSN =         "2690-0327",
  bibdate =      "Fri Dec 15 11:31:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Synthesis Lectures on Engineering, Science, and
                 Technology",
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
}

@Article{Angioli:2024:DIE,
  author =       "Marco Angioli and Marcello Barbirotta and Abdallah
                 Cheikh and Antonio Mastrandrea and Francesco Menichelli
                 and Saeid Jamili and Mauro Olivieri",
  title =        "Design, Implementation and Evaluation of a New
                 Variable Latency Integer Division Scheme",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "73",
  number =       "7",
  pages =        "1767--1779",
  month =        jul,
  year =         "2024",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2024.3386060",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jun 12 15:57:24 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Benchmark testing; Clocks; computer arithmetic; Field
                 programmable gate arrays; Frequency conversion;
                 Hardware; high-speed arithmetic; integer division;
                 low-power design; real-time and embedded systems;
                 Registers; Signal processing algorithms;
                 Variable-latency divider",
}

@InProceedings{Anonymous:2024:CP,
  author =       "Anonymous",
  title =        "{[Copyright} page]",
  crossref =     "IEEE:2024:PIS",
  pages =        "4--4",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00003",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@InProceedings{Anonymous:2024:OCA,
  author =       "Anonymous",
  title =        "{Organizing Committee: ARITH 2024}",
  crossref =     "IEEE:2024:PIS",
  pages =        "10--10",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00006",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@InProceedings{Anonymous:2024:PCA,
  author =       "Anonymous",
  title =        "{Program Committee: ARITH 2024}",
  crossref =     "IEEE:2024:PIS",
  pages =        "11--11",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00007",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@InProceedings{Anonymous:2024:RLA,
  author =       "Anonymous",
  title =        "{Reviewers List: ARITH 2024}",
  crossref =     "IEEE:2024:PIS",
  pages =        "14--15",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00009",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@InProceedings{Anonymous:2024:SA,
  author =       "Anonymous",
  title =        "{Sponsors: ARITH 2024}",
  crossref =     "IEEE:2024:PIS",
  pages =        "16--17",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00010",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@InProceedings{Anonymous:2024:SCA,
  author =       "Anonymous",
  title =        "{Steering Committee: ARITH 2024}",
  crossref =     "IEEE:2024:PIS",
  pages =        "12--13",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00008",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@InProceedings{Anonymous:2024:TPa,
  author =       "Anonymous",
  title =        "{[Title} page 1]",
  crossref =     "IEEE:2024:PIS",
  pages =        "1--1",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00001",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@InProceedings{Anonymous:2024:TPb,
  author =       "Anonymous",
  title =        "{[Title} page 2]",
  crossref =     "IEEE:2024:PIS",
  pages =        "3--3",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00002",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@Article{Aonishi:2024:HVF,
  author =       "Toru Aonishi and Tatsuya Nagasawa and Toshiyuki
                 Koizumi and Mastiyage Don Sudeera Hasaranga Gunathilaka
                 and Kazushi Mimura and Masato Okada and Satoshi Kako
                 and Yoshihisa Yamamoto",
  title =        "Highly Versatile {FPGA}-Implemented {Cyber Coherent
                 Ising Machine}",
  journal =      j-IEEE-ACCESS,
  volume =       "12",
  pages =        "175843--175865",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/ACCESS.2024.3504008",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "Bifurcation; Coherent Ising machine; combinatorial
                 optimization; compressed sensing; Computational
                 modeling; Computer architecture; Couplings; Field
                 programmable gate arrays; FPGA; Integrated circuit
                 modeling; Jacobian matrices; Mathematical models;
                 Multiaccess communication; Optimization; versatile
                 architecture",
}

@InProceedings{Arzelier:2024:REA,
  author =       "Denis Arzelier and Florent Br{\'e}hard and Mioara
                 Joldes and Marc Mezzarobba",
  title =        "Rounding Error Analysis of an Orbital Collision
                 Probability Evaluation Algorithm",
  crossref =     "IEEE:2024:PIS",
  pages =        "96--103",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00025",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@Article{Bandil:2024:HIU,
  author =       "Lalit Bandil and Bal Chand Nagar",
  title =        "Hardware Implementation of Unsigned Approximate Hybrid
                 Square Rooters for Error-Resilient Applications",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "73",
  number =       "12",
  pages =        "2734--2746",
  year =         "2024",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2024.3457731",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Nov 20 07:36:48 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Accuracy; accuracy metrics; Approximate computing;
                 Arithmetic; Computers; Hardware; hardware
                 implementation; image processing; Image restoration;
                 low power; Measurement; Multiplexing; square rooter",
}

@InProceedings{Basavaraju:2024:EHA,
  author =       "Mahati Basavaraju and Vinay Rayapati and Madhav Rao",
  booktitle =    "{2024 25th International Symposium on Quality
                 Electronic Design (ISQED)}",
  title =        "Exploring Hardware Activation Function Design:
                 {CORDIC} Architecture in Diverse Floating Formats",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--8",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/ISQED60706.2024.10528686",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Activation Function; Artificial neural networks;
                 BFloat; Computer architecture; CORDIC; Costs; Data
                 Representation; Floating Point; Focusing; Hardware;
                 Libraries; Measurement; Neural networks; POSIT;
                 Sigmoid; Softmax; Tanh; TensorFloat",
}

@InProceedings{BenAli:2024:SRE,
  author =       "Sami {Ben Ali} and Silviu-Ioan Filip and Olivier
                 Sentieys",
  booktitle =    "{2024 Design, Automation \& Test in Europe Conference
                 \& Exhibition (DATE)}",
  title =        "A Stochastic Rounding-Enabled Low-Precision
                 Floating-Point {MAC} for {DNN} Training",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--6",
  year =         "2024",
  DOI =          "https://doi.org/10.23919/DATE58400.2024.10546735",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Artificial neural networks; Computational modeling;
                 DNN; Hardware; low-precision MAC unit; Measurement;
                 Stochastic processes; stochastic rounding; Systolic
                 arrays; Training",
}

@Article{Benmaghnia:2024:CGN,
  author =       "Hanane Benmaghnia and Matthieu Martel and Yassamine
                 Seladji",
  title =        "Code Generation for Neural Networks Based on
                 Fixed-point Arithmetic",
  journal =      j-TECS,
  volume =       "23",
  number =       "5",
  pages =        "68:1--68:??",
  month =        sep,
  year =         "2024",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3563945",
  ISSN =         "1539-9087 (print), 1558-3465 (electronic)",
  ISSN-L =       "1539-9087",
  bibdate =      "Wed Sep 25 11:16:16 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tecs.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3563945",
  abstract =     "Over the past few years, neural networks have started
                 penetrating safety critical systems to make decisions
                 as, for example, in robots, rockets, and autonomous
                 driving cars. Neural networks based on floating-point
                 arithmetic are very time and memory consuming, which
                 are not compatible with embedded systems known to have
                 limited resources. They are also very sensitive to the
                 precision in which they have been trained, so changing
                 this precision generally degrades the quality of their
                 answers. To deal with that, we introduce a new
                 technique to generate a fixed-point code for a trained
                 neural network. This technique is based on fixed-point
                 arithmetic with mixed-precision. This arithmetic is
                 based on integer operations only, which are compatible
                 with small memory devices. The obtained neural network
                 has the same behavior as the initial one (based on the
                 floating-point arithmetic) up to an error threshold
                 defined by the user. The experimental results show the
                 efficiency of our tool SyFix in terms of memory saved
                 and the accuracy of the computations.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Embed. Comput. Syst.",
  articleno =    "68",
  fjournal =     "ACM Transactions on Embedded Computing Systems",
  journal-URL =  "https://dl.acm.org/loi/tecs",
}

@InProceedings{Bertaccini:2024:ERV,
  author =       "Luca Bertaccini and Siyuan Shen and Torsten Hoefler
                 and Luca Benini",
  booktitle =    "{2024 IEEE 42nd International Conference on Computer
                 Design (ICCD)}",
  title =        "Extending {RISC-V} for Efficient Overflow Recovery in
                 Mixed-Precision Computations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "268--275",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/ICCD63220.2024.00048",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Artificial neural networks; Computer architecture;
                 Dynamic range; Energy storage; floating-point;
                 Hardware; Heuristic algorithms; Inference algorithms;
                 Instruction sets; isa extension; Machine learning;
                 mixed-precision computing; overflow recovery; risc-v;
                 Training",
}

@Article{Bertaccini:2024:MRV,
  author =       "Luca Bertaccini and Gianna Paulin and Matheus
                 Cavalcante and Tim Fischer and Stefan Mach and Luca
                 Benini",
  title =        "{MiniFloats} on {RISC-V} Cores: {ISA} Extensions With
                 Mixed-Precision Short Dot Products",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "12",
  number =       "4",
  pages =        "1040--1055",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/TETC.2024.3365354",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Tue Sep 9 13:42:38 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
  keywords =     "Artificial neural networks; Computational modeling;
                 Computer architecture; Dynamic range; floating-point
                 architectures; Hardware; ISA extension; NN training;
                 RISC-V; Stochastic processes; Training; Transprecision
                 computing; widening dot product",
}

@InProceedings{Bottcher:2024:SLB,
  author =       "Andreas B{\"o}ttcher and Martin Kumm",
  title =        "Small Logic-based Multipliers with Incomplete
                 Sub-Multipliers for {FPGAs}",
  crossref =     "IEEE:2024:PIS",
  pages =        "124--131",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00029",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@TechReport{Brisebarre:2024:CRE,
  author =       "Nicolas Brisebarre and Guillaume Hanrot and
                 Jean-Michel Muller and Paul Zimmermann",
  title =        "Correctly-rounded evaluation of a function: why, how,
                 and at what cost?",
  type =         "Report",
  number =       "hal-04474530",
  institution =  "CNRS --- Centre National de la Recherche Scientifique
                 and others",
  address =      "Paris, France",
  pages =        "29",
  day =          "23",
  month =        feb,
  year =         "2024",
  bibdate =      "Fri Feb 23 16:11:08 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://hal.science/hal-04474530",
  abstract =     "The goal of this paper is to convince the reader that
                 a future standard for floating-point arithmetic should
                 require the availability of a correctly-rounded version
                 of a well-chosen core set of elementary functions. We
                 discuss the interest and feasibility of this
                 requirement. We also give answers to common objections
                 we have received over the last 10 years.",
  acknowledgement = ack-nhfb,
  keywords =     "algorithmic number theory; approximation theory;
                 Computer arithmetic; elementary functions;
                 floating-point arithmetic; lattice basis reduction; LLL
                 algorithm; standardization",
}

@Article{Brisebarre:2024:EUM,
  author =       "Nicolas Brisebarre and Jean-Michel Muller and Joris
                 Picot",
  title =        "Error in Ulps of the Multiplication or Division by a
                 Correctly-Rounded Function or Constant in Binary
                 Floating-Point Arithmetic",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "12",
  number =       "2",
  pages =        "656--666",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/TETC.2023.3294986",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Fri Sep 29 10:36:37 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  abstract =     "Assume we use a binary floating-point arithmetic and
                 that RN is the round-to-nearest function. Also assume
                 that c is a constant or a real function of one or more
                 variables, and that we have at our disposal a correctly
                 rounded implementation of c, say c' = RN(c). For
                 evaluating xc(resp.x / corc / x), the natural way is to
                 replace it by RN(x.c') (resp.RN(x / c') or RN(c' / x)),
                 that is, to call function c' and to perform a
                 floating-point multiplication or division. This can be
                 generalized to the approximation of n / d by RN(n' /
                 d') and the approximation of n d by RN(n'.d'), where n'
                 = RN(n) and d' = RN(d), and n and d are functions for
                 which we have at our disposal a correctly rounded
                 implementation. We discuss tight error bounds in ulps
                 of such approximations. From our results, one
                 immediately obtains tight error bounds for calculations
                 such as x * pi, ln(2) / x, x / (y + z), (x + y) * z, x
                 / sqrt(y), sqrt(x) / y, (x + y)(z + t), (x + y) / (z +
                 t), (x + y) / (zt), etc. in floating-point
                 arithmetic.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
  keywords =     "Arithmetic; Blogs; correct rounding; Floating-point
                 arithmetic; Libraries; Lips; Measurement uncertainty;
                 multiplication by a constant; numerical error;
                 Standards; Toy manufacturing industry; ulp",
}

@Article{Brogi:2024:FPP,
  author =       "F. Brogi and S. Bn{\`a} and G. Boga and G. Amati and
                 T. Esposti Ongaro and M. Cerminara",
  title =        "On floating point precision in computational fluid
                 dynamics using {OpenFOAM}",
  journal =      j-FUT-GEN-COMP-SYS,
  volume =       "152",
  number =       "??",
  pages =        "1--16",
  month =        mar,
  year =         "2024",
  CODEN =        "FGSEVI",
  DOI =          "https://doi.org/10.1016/j.future.2023.10.006",
  ISSN =         "0167-739X (print), 1872-7115 (electronic)",
  ISSN-L =       "0167-739X",
  bibdate =      "Sat Dec 16 07:26:57 MST 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/futgencompsys2020.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167739X23003813",
  acknowledgement = ack-nhfb,
  fjournal =     "Future Generation Computer Systems",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0167739X",
}

@Article{Cai:2024:TEV,
  author =       "Luwei Cai and Fu Song and Taolue Chen",
  title =        "Towards Efficient Verification of Constant-Time
                 Cryptographic Implementations",
  journal =      "Proceedings of the ACM on Software Engineering",
  volume =       "1",
  number =       "FSE",
  pages =        "1019--1042",
  month =        jul,
  year =         "2024",
  DOI =          "https://doi.org/10.1145/3643772",
  ISSN =         "2994-970X",
  bibdate =      "Tue Aug 27 07:37:07 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Timing side-channel attacks exploit secret-dependent
                 execution time to fully or partially recover secrets of
                 cryptographic implementations, posing a severe threat
                 to software security. Constant-time programming
                 discipline is an effective software-based
                 countermeasure against timing side-channel attacks, but
                 developing constant-time implementations turns out to
                 be challenging and error-prone. Current verification
                 approaches/tools suffer from scalability and precision
                 issues when applied to production software in practice.
                 In this paper, we put forward practical verification
                 approaches based on a novel synergy of taint analysis
                 and safety verification of self-composed programs.
                 Specifically, we first use an IFDS-based lightweight
                 taint analysis to prove that a large number of
                 potential (timing) side-channel sources do not actually
                 leak secrets. We then resort to a precise taint
                 analysis and a safety verification approach to
                 determine whether the remaining potential side-channel
                 sources can actually leak secrets. These include novel
                 constructions of taint-directed semi-cross-product of
                 the original program and its Boolean abstraction, and a
                 taint-directed self-composition of the program. Our
                 approach is implemented as a cross-platform and fully
                 automated tool CT-Prover. The experiments confirm its
                 efficiency and effectiveness in verifying real-world
                 benchmarks from modern cryptographic and SSL/TLS
                 libraries. In particular, CT-Prover identify new,
                 confirmed vulnerabilities of open-source SSL libraries
                 (e.g., Mbed SSL, BearSSL) and significantly outperforms
                 the state-of-the-art tool",
  acknowledgement = ack-nhfb,
  keywords =     "constant-time cryptographic implementation; Formal
                 security models; Formal software verification; formal
                 verification; Logic and verification; Program analysis;
                 Security and privacy; Software and its engineering;
                 taint analysis; Theory of computation; Timing
                 side-channel",
}

@Article{Cameron:2024:AHM,
  author =       "Thomas R. Cameron and Stef Graillat",
  title =        "Accurate {Horner} methods in real and complex
                 floating-point arithmetic",
  journal =      j-BIT-NUM-MATH,
  volume =       "64",
  number =       "2",
  pages =        "??--??",
  month =        jun,
  year =         "2024",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/s10543-024-01017-w",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Tue May 28 15:02:24 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://link.springer.com/article/10.1007/s10543-024-01017-w",
  acknowledgement = ack-nhfb,
  ajournal =     "Bit Num. Math.",
  articleno =    "17",
  fjournal =     "BIT Numerical Mathematics",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Article{Campos:2024:FGC,
  author =       "Nelson Campos and Eran Edirisinghe and Slava Chesnokov
                 and Daniel Larkin",
  title =        "Fast Generation of Custom Floating-Point Spatial
                 Filters on {FPGAs}",
  journal =      j-IEEE-ACCESS,
  volume =       "12",
  pages =        "167059--167071",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/ACCESS.2024.3486066",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Tue Sep 30 17:30:28 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "Convolution; Domain specific languages;
                 Domain-specific language; embedded video processing;
                 Fast Fourier transforms; Field programmable gate
                 arrays; floating-point arithmetic; FPGA; Hardware;
                 Kernel; Mathematical models; real-time; Real-time
                 systems; Spatial filters; Streaming media",
}

@TechReport{Caprioli:2024:ACM,
  author =       "Paul Caprioli and Vincenzo Innocente and Paul
                 Zimmermann",
  title =        "Accuracy of Complex Mathematical Operations and
                 Functions in Single and Double Precision",
  type =         "Report",
  number =       "hal-04714173",
  institution =  "High Performance Kernels LLC",
  address =      "????",
  pages =        "8",
  day =          "30",
  month =        sep,
  year =         "2024",
  bibdate =      "Mon Sep 30 06:08:35 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://inria.hal.science/hal-04714173v1",
  acknowledgement = ack-nhfb,
}

@InProceedings{Chen:2024:HCH,
  author =       "Hui Chen and Lianghua Quan and Weiqiang Liu",
  title =        "{HGH-CORDIC}: a {High-Radix Generalized Hyperbolic
                 COordinate Rotation Digital Computer}",
  crossref =     "IEEE:2024:PIS",
  pages =        "88--95",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00024",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; ARITH 2024; ARITH-31; Convergence; Digital
                 arithmetic; Digital computers; exponential;
                 generalized; Hardware; hardware implementation;
                 High-radix; hyperbolic CORDIC; logarithmic; Software",
}

@InProceedings{Chen:2024:MPF,
  author =       "Jianxin Chen and Hong Hao and Shuai Wang and Lele Li
                 and Xinxin Zhao and Fan Yu and Jing Wang and Guilong Xu
                 and Zongqi Sun and Kai Jiang",
  booktitle =    "{2024 4th International Conference on Electronic
                 Information Engineering and Computer (EIECT)}",
  title =        "A Multiple Precision Floating-Point Arithmetic Unit
                 Based on the {RISC-V} Instruction Set",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "573--578",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/EIECT64462.2024.10867213",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Faces; Floating-point arithmetic;
                 Floating-Point Unit (FPU); FPGA; GPGPU; Image
                 processing; Instruction sets; Machine learning;
                 Multi-Precision Formats; RISC-V; SIMD Operations;
                 Single instruction multiple data; Vectors",
}

@InProceedings{Chu:2024:NNR,
  author =       "Yu-Da Chu and Pei-Hsuan Kuo and Lyu-Ming Ho and
                 Juinn-Dar Huang",
  booktitle =    "{2024 IEEE 6th International Conference on AI Circuits
                 and Systems (AICAS)}",
  title =        "A Novel Number Representation and Its Hardware Support
                 for Accurate Low-Bit Quantization on Large Recommender
                 Systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "437--441",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/AICAS59952.2024.10595902",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Circuits and systems; Costs; Deep learning;
                 number representation; quantization; Quantization
                 (signal); recommendation system; Runtime; Training",
}

@InProceedings{Coward:2024:CPA,
  author =       "Samuel Coward and Theo Drane and Emiliano Morini and
                 George A. Constantinides",
  title =        "Combining Power and Arithmetic Optimization via
                 Datapath Rewriting",
  crossref =     "IEEE:2024:PIS",
  pages =        "24--31",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00014",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@InProceedings{Cui:2024:TEC,
  author =       "Ziying Cui and Ke Chen and Bi Wu and Chenggang Yan and
                 Yu Gong and Weiqiang Liu",
  title =        "A Time Efficient Comprehensive Model of Approximate
                 Multipliers for Design Space Exploration",
  crossref =     "IEEE:2024:PIS",
  pages =        "116--123",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00028",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@Book{deDinechin:2024:ASA,
  author =       "Florent de Dinechin and Martin Kumm",
  title =        "Application-specific Arithmetic: Computing Just Right
                 for the Reconfigurable Computer and the Dark Silicon
                 Era",
  publisher =    pub-SV-CHAM,
  address =      pub-SV-CHAM:adr,
  pages =        "xxiii + 804",
  year =         "2024",
  DOI =          "https://doi.org/10.1007/978-3-031-42808-1",
  ISBN =         "3-031-42807-2, 3-031-42808-0 (e-book), 3-031-42809-9,
                 3-031-42810-2",
  ISBN-13 =      "978-3-031-42807-4, 978-3-031-42808-1 (e-book),
                 978-3-031-42809-8, 978-3-031-42810-4",
  LCCN =         "QA76.9.C62 D56 2024",
  bibdate =      "Fri Dec 8 13:09:29 MST 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://perso.citi-lab.fr/fdedinec/ASA-book/errata.pdf;
                 https://link.springer.com/book/10.1007/978-3-031-42808-1",
  abstract =     "Written by two experts of the domain, this book
                 presents the most recent advances in computer
                 arithmetic hardware, with a focus on
                 application-specific arithmetic beyond the classic
                 operators and the standard precisions. It targets
                 silicon designers who have to do better with less in
                 the post-Moore era, and FPGA developers who want to
                 exploit the full possibilities of reconfigurable
                 computing platforms. Presents a unique focus on
                 application-specific computer arithmetic; Helps
                 developers gain a deep understanding of the arithmetic
                 in their projects, and tailor it to their application;
                 Illustrates concepts and architectures by actual
                 implementations, using the FloPoCo open-source hardware
                 generator.",
  acknowledgement = ack-nhfb,
  tableofcontents = "1: Introduction \\
                 2: Number Formats \\
                 3: Computing Just Right: Accuracy Specification and
                 Error Analysis \\
                 4: Field Programmable Gate Arrays \\
                 \\
                 Part 1 Revisiting Classic Arithmetic \\
                 5: Fixed-Point Addition \\
                 6: Fixed-Point Comparison \\
                 7: Sums of Weighted Bits \\
                 8: Fixed-Point Multiplication \\
                 9: Fixed-Point Division \\
                 10: Shifters and Leading Bit Counters \\
                 11: Basic Floating-Point Operators \\
                 \\
                 Part 2 Operator Specialization \\
                 12: Multiplication by Constants \\
                 13: Division by Constants \\
                 14: Fixed-Point Squares, Cubes, and Other Integer
                 Powers \\
                 15: Specialization and Fusion of Floating-Point
                 Operators \\
                 \\
                 Part 3 Generic Methods for Fixed-Point Function
                 Approximation \\
                 16: Generalities on Fixed-Point Function Approximation
                 \\
                 17: Function Evaluation Using Tables and Additions \\
                 18: Polynomial-Based Architectures for Function
                 Evaluation \\
                 19: Digit Recurrence for Algebraic Functions \\
                 \\
                 Part 4 Example Composite Operators \\
                 20: Fixed-Point Sine and Cosine \\
                 21: Floating-Point Accumulation and Sum-of-Products \\
                 22: Floating-Point Exponential \\
                 \\
                 Part 5 Application Domains \\
                 23: Arithmetic in The Design of Linear Time-Invariant
                 Filters \\
                 24: Arithmetic for Deep Learning \\
                 \\
                 Part 6 Appendix \\
                 25: Appendix A: Custom Arithmetic Datapath Design with
                 FloPoCo \\
                 26: Appendix B: Optimization Using Integer Linear
                 Programming",
}

@Misc{Demmel:2024:EDS,
  author =       "Jim Demmel",
  title =        "Exploring the Design Space of Exception Handling",
  howpublished = "Posting to STDS-754 mailing list.",
  pages =        "42",
  day =          "22",
  month =        aug,
  year =         "2024",
  bibdate =      "Tue Aug 27 08:09:27 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Lecture slides on progress in research on
                 floating-point exception handling, notably in LAPACK
                 and the BLAS (Basic Linear Algebra Subroutines).",
  URL =          "ExceptionHandling_22Aug2024.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Deng:2024:FPE,
  author =       "Bobin Deng and Bhargava Nadendla and Kun Suo and Yixin
                 Xie and Dan Chia-Tien Lo",
  title =        "Fixed-point Encoding and Architecture Exploration for
                 Residue Number Systems",
  journal =      j-TACO,
  volume =       "21",
  number =       "3",
  pages =        "53:1--53:??",
  month =        sep,
  year =         "2024",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3664923",
  ISSN =         "1544-3566 (print), 1544-3973 (electronic)",
  ISSN-L =       "1544-3566",
  bibdate =      "Sat Sep 21 06:05:41 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/taco.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3664923",
  abstract =     "Residue Number Systems (RNS) demonstrate the
                 fascinating potential to serve integer addition\slash
                 multiplication-intensive applications. The complexity
                 of Artificial Intelligence (AI) models has grown
                 enormously in recent years. From a computer system's
                 perspective, ensuring the training of these large-scale
                 AI models within an adequate time and energy
                 consumption has become a big concern. Matrix
                 multiplication is a dominant subroutine in many
                 prevailing AI models, with an addition\slash
                 multiplication-intensive attribute. However, the data
                 type of matrix multiplication within machine learning
                 training typically requires real numbers, which
                 indicates that RNS benefits for integer applications
                 cannot be directly gained by AI training. The
                 state-of-the-art RNS real-number encodings, including
                 floating-point and fixed-point, have defects and can be
                 further enhanced. To transform default RNS benefits to
                 the efficiency of large-scale AI training, we propose a
                 low-cost and high-accuracy RNS fixed-point
                 representation: Single RNS Logical Partition
                 (S-RNS-Logic-P) representation with Scaling-down
                 Postprocessing Multiplication (SD-Post-Mul). Moreover,
                 we extend the implementation details of the other two
                 RNS fixed-point methods: Double RNS Concatenation and
                 S-RNS-Logic-P representation with Scaling-down
                 Preprocessing Multiplication. We also design the
                 architectures of these three fixed-point multipliers.
                 In empirical experiments, our S-RNS-Logic-P
                 representation with SD-Post-Mul method achieves less
                 latency and energy overhead while maintaining good
                 accuracy. Furthermore, this method can easily extend to
                 the Redundant Residue Number System to raise the
                 efficiency of error-tolerant domains, such as improving
                 the error correction efficiency of quantum computing.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Archit. Code Optim.",
  articleno =    "53",
  fjournal =     "ACM Transactions on Architecture and Code Optimization
                 (TACO)",
  journal-URL =  "https://dl.acm.org/loi/taco",
}

@InProceedings{deSousa:2024:PFF,
  author =       "Jos{\'e} T. de Sousa and Jo{\~a}o D. Lopes and Micaela
                 Ser{\^o}dio and Hor{\'a}cio C. Neto and M{\'a}rio P.
                 V{\'e}stias",
  title =        "{PT-Float}: a Floating-Point Unit with Dynamically
                 Varying Exponent and Fraction Sizes",
  crossref =     "IEEE:2024:PIS",
  pages =        "139--146",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00031",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@InProceedings{Dimitrov:2024:MBL,
  author =       "Vassil Dimitrov and Richard Ford and Laurent Imbert
                 and Arjuna Madanayake and Nilan Udayanga and Will
                 Wray",
  title =        "Multiple-base Logarithmic Quantization and Application
                 in Reduced Precision {AI} Computations",
  crossref =     "IEEE:2024:PIS",
  pages =        "48--51",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00017",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@InProceedings{Drane:2024:SCF,
  author =       "Theo Drane and Samuel Coward and Mertcan Temel and Joe
                 Leslie-Hurd",
  title =        "On the Systematic Creation of Faithfully Rounded
                 Commutative Truncated {Booth} Multipliers",
  crossref =     "IEEE:2024:PIS",
  pages =        "108--115",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00027",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@InProceedings{Duarte:2024:DNB,
  author =       "Luiz F. H. Duarte and George B. Nardes and Wesley
                 Grignani and Douglas R. Melo and Cesar A. Zeferino",
  booktitle =    "{2024 37th SBC/SBMicro/IEEE Symposium on Integrated
                 Circuits and Systems Design (SBCCI)}",
  title =        "{Deep Nibble}: a 4-bit Number Format for Efficient
                 {DNN} Training and Inference in {FPGA}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--5",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/SBCCI62366.2024.10703994",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Artificial neural networks; Deep learning;
                 Deep Learning; FPGA; Hardware Acceleration; Integrated
                 circuit modeling; Logarithmic Quantization; Memory
                 management; Performance evaluation; Quantization
                 (signal); Stochastic processes; Stochastic Rounding;
                 Throughput; Training",
}

@InProceedings{DuPont:2024:HAP,
  author =       "David {Du Pont} and Jonas Bertels and Furkan Turan and
                 Michiel {Van Beirendonck} and Ingrid Verbauwhede",
  title =        "Hardware Acceleration of the Prime-Factor and Rader
                 {NTT} for {BGV} Fully Homomorphic Encryption",
  crossref =     "IEEE:2024:PIS",
  pages =        "1--8",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00011",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@Article{ElArar:2024:BNE,
  author =       "E-M. {El Arar} and D. Sohier and P. {de Oliveira
                 Castro} and E. Petit",
  title =        "Bounds on Nonlinear Errors for Variance Computation
                 with Stochastic Rounding",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "46",
  number =       "5",
  pages =        "B579--B599",
  month =        "????",
  year =         "2024",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/23M1563001",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Mon Sep 30 10:38:50 MDT 2024",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/46/5;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  URL =          "https://epubs.siam.org/doi/10.1137/23M1563001",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  keywords =     "accurate floating-point summation; stochastic
                 rounding",
}

@InCollection{Elrefai:2024:CML,
  author =       "Hisham M. Elrefai and Sara S. Abou Zeid and Wafaa S.
                 Sayed and Lobna A. Said and Ahmed G. Radwan",
  booktitle =    "Advances in Nonlinear Dynamics, Volume {III}",
  title =        "Compact Multiplier-less {CORDIC}-Based {FPGA}
                 Implementation of Sine and Modified Sine Chaotic Maps",
  publisher =    pub-SV-CHAM,
  address =      pub-SV-CHAM:adr,
  pages =        "153--161",
  year =         "2024",
  DOI =          "https://doi.org/10.1007/978-3-031-50635-2_15",
  ISBN =         "3-031-50634-0; 3-031-50635-9",
  ISBN-13 =      "978-3-031-50634-5; 978-3-031-50635-2",
  ISSN =         "2730-7697",
  MRnumber =     "4769607",
  bibdate =      "Tue Oct 28 07:04:09 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "NODYCON Conference Proceedings Series",
  acknowledgement = ack-nhfb,
}

@Article{Faissole:2024:FVR,
  author =       "Florian Faissole",
  title =        "Formally-Verified Round-Off Error Analysis of
                 {Runge--Kutta} Methods",
  journal =      j-J-AUTOM-REASON,
  volume =       "68",
  number =       "1",
  pages =        "??--??",
  month =        mar,
  year =         "2024",
  CODEN =        "JAREEW",
  DOI =          "https://doi.org/10.1007/s10817-023-09686-y",
  ISSN =         "0168-7433 (print), 1573-0670 (electronic)",
  ISSN-L =       "0168-7433",
  bibdate =      "Fri May 24 08:31:25 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
  URL =          "https://link.springer.com/article/10.1007/s10817-023-09686-y",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Autom. Reason.",
  articleno =    "1",
  fjournal =     "Journal of Automated Reasoning",
  journal-URL =  "http://link.springer.com/journal/10817",
}

@TechReport{Fog:2024:FPE,
  author =       "Agner Fog",
  title =        "Floating point exception tracking and {NAN}
                 propagation",
  type =         "Report",
  institution =  "Technical University of Denmark",
  address =      "Lyngby, Denmark",
  pages =        "11",
  day =          "15",
  month =        aug,
  year =         "2024",
  bibdate =      "Wed Jan 15 10:06:11 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.agner.org/optimize/nan_propagation.pdf",
  abstract =     "The most common methods for detecting floating point
                 errors are based on exception trapping or a global
                 status register. These methods are inefficient in
                 modern systems that use out-of-order parallelism and
                 single-instruction-multiple-data (SIMD) parallelism for
                 improving performance. It is argued that a method based
                 on NAN propagation is more efficient and deterministic.
                 Problems with NAN propagation in current systems are
                 discussed. Examples of implementation in the C++ vector
                 class library and in an experimental instruction set
                 named ForwardCom are presented. The IEEE-754 standard
                 for floating point arithmetic may need adjustment to
                 accommodate the needs of modern forms of parallelism.",
  acknowledgement = ack-nhfb,
  remark =       "Revision of \cite{Fog:2020:FPE} and
                 \cite{Fog:2023:FPE}.",
}

@InProceedings{Fuengfusin:2024:NAB,
  author =       "Ninnart Fuengfusin and Hakaru Tamukoh",
  booktitle =    "{2024 1st International Conference on Robotics,
                 Engineering, Science, and Technology (RESTCON)}",
  title =        "{NaN} Attacks: Bit-Flipping Deep Neural Network
                 Parameters to {NaN} or {Infinity}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "33--37",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/RESTCON60981.2024.10463548",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Analytical models; Artificial neural networks;
                 bit-flip attack; bit-flip defense; Computational
                 modeling; Correlation; deep learning; FP32; Image
                 recognition; Infinity; NaN; Performance evaluation;
                 Speech recognition",
}

@InProceedings{GazzoniFilho:2024:PAA,
  author =       "D{\'e}cio Luiz {Gazzoni Filho} and Guilherme
                 Brand{\~a}o and Gora Adj and Arwa Alblooshi and Isaac
                 A. Canales-Mart{\'\i}nez and Jorge Ch{\'a}vez-Saab and
                 Julio L{\'o}pez",
  title =        "{PQC-AMX}: Accelerating {Saber} and {FrodoKEM} on the
                 {Apple} {M1} and {M3} {SoCs}",
  crossref =     "IEEE:2024:PIS",
  pages =        "9--16",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00012",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@Article{Giles:2024:REU,
  author =       "Michael B. Giles and Oliver Sheridan-Methven",
  title =        "Rounding Error Using Low Precision Approximate Random
                 Variables",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "46",
  number =       "4",
  pages =        "B502--B526",
  month =        "????",
  year =         "2024",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/23M1552814",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Sat Aug 24 16:22:17 MDT 2024",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/46/4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  URL =          "https://epubs.siam.org/doi/10.1137/23M1552814",
  acknowledgement = ack-nhfb,
  ajournal =     "SIAM J. Sci. Comput.",
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}

@TechReport{Gladman:2024:AMFa,
  author =       "Brian Gladman and Vincenzo Innocente and John Mather
                 and Paul Zimmermann",
  title =        "Accuracy of Mathematical Functions in Single, Double,
                 Double Extended, and Quadruple Precision",
  institution =  "????",
  pages =        "25",
  day =          "15",
  month =        feb,
  year =         "2024",
  bibdate =      "Thu Feb 15 13:17:22 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://hal.inria.fr/hal-03141101;
                 https://members.loria.fr/PZimmermann/papers/accuracy.pdf",
  acknowledgement = ack-nhfb,
  remark =       "Tabular comparison of AMD, Apple, ARM, CUDA, FreeBSD,
                 GNU, Intel, LLVM, Microsoft Musl, Newlib, OpenLibm,
                 RadeonOpenCompute (ROCm), and RedHat -lm libraries for
                 correct rounding, versus results from MPFR.",
}

@TechReport{Gladman:2024:AMFb,
  author =       "Brian Gladman and Vincenzo Innocente and John Mather
                 and Paul Zimmermann",
  title =        "Accuracy of Mathematical Functions in Single, Double,
                 Double Extended, and Quadruple Precision",
  institution =  "????",
  pages =        "25",
  day =          "26",
  month =        aug,
  year =         "2024",
  bibdate =      "Thu Sep 19 14:49:38 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://members.loria.fr/PZimmermann/papers/accuracy.pdf",
  acknowledgement = ack-nhfb,
  remark =       "Tabular comparison of AMD, Apple, ARM, CUDA, FreeBSD,
                 GNU, Intel, LLVM, Microsoft Musl, Newlib, OpenLibm,
                 RadeonOpenCompute (ROCm), and RedHat -lm libraries for
                 correct rounding, versus results from MPFR.",
}

@Article{Guthmuller:2024:XRV,
  author =       "Eric Guthmuller and C{\'e}sar Fuguet and Andrea Bocco
                 and J{\'e}r{\^o}me Fereyre and Riccardo Alidori and
                 Ihsane Tahir and Yves Durand",
  title =        "{Xvpfloat}: {RISC-V} {ISA} Extension for Variable
                 Extended Precision Floating Point Computation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "73",
  number =       "7",
  pages =        "1683--1697",
  month =        jul,
  year =         "2024",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2024.3383964",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jun 12 15:57:24 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "application specific processor; Arithmetic; Computer
                 architecture; Convergence; coprocessor; Field
                 programmable gate arrays; floating point arithmetic;
                 Hardware; high precision arithmetic; Instruction sets;
                 linear algebra; Open area test sites; RISC-V;
                 scientific computing; Software",
}

@InProceedings{Haghi:2024:BGB,
  author =       "Pouya Haghi and Chunshu Wu and Zahra Azad and Yanfei
                 Li and Andrew Gui and Yuchen Hao and Ang Li and Tony
                 Tong Geng",
  booktitle =    "{2024 57th IEEE/ACM International Symposium on
                 Microarchitecture (MICRO)}",
  title =        "Bridging the Gap Between {LLMs} and {LNS} with Dynamic
                 Data Format and Architecture Codesign",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1617--1631",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/MICRO61859.2024.00118",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Field programmable gate arrays; Hardware;
                 Large Language Models; Logarithmic Number System;
                 Machine Learning Accelerator; Next generation
                 networking; Quantization; Quantization (signal);
                 Runtime; Solids; Systolic arrays; Tensors; Training",
}

@Article{Haghiri:2024:MIF,
  author =       "Saeed Haghiri and Salah I. Yahya and Abbas Rezaei and
                 Arash Ahmadi",
  title =        "Multiplierless Implementation of {Fitz-Hugh Nagumo
                 (FHN)} Modeling Using {CORDIC} Approach",
  journal =      "IEEE Transactions on Emerging Topics in Computational
                 Intelligence",
  volume =       "8",
  number =       "1",
  pages =        "279--287",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/TETCI.2023.3300176",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Behavioral sciences; Brain modeling; CNS;
                 Computational modeling; FHN; Field programmable gate
                 arrays; FPGA; Hardware; Mathematical models; Neuron;
                 Neurons",
}

@Article{Haider:2024:DRA,
  author =       "Muhammad Hamis Haider and Hao Zhang and Seok-Bum Ko",
  title =        "Decoder Reduction Approximation Scheme for {Booth}
                 Multipliers",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "73",
  number =       "3",
  pages =        "735--746",
  month =        mar,
  year =         "2024",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2023.3343093",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Feb 16 07:37:44 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Adders; approximate computing; Booth multipliers;
                 Complexity theory; Computer architecture; convolutional
                 neural networks; Decoding; Error analysis; Filtration;
                 Hardware; leading one detection; logarithmic
                 multipliers",
}

@Article{Harris:2024:UDS,
  author =       "David Harris and James Stine and Milo Ercegovac and
                 Alberto Nannarelli and Katherine Parry and Cedar
                 Turek",
  title =        "Unified Digit Selection for Radix-4 Recurrence
                 Division and Square Root",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "73",
  number =       "1",
  pages =        "292--300",
  month =        jan,
  year =         "2024",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2023.3305760",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Dec 27 15:37:27 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "division; minimally-redundant radix-4; RISC-V; square
                 root; SRT",
}

@Article{Harvey:2024:FTI,
  author =       "David Harvey",
  title =        "Faster truncated integer multiplication",
  journal =      j-MATH-COMPUT,
  volume =       "93",
  number =       "347",
  pages =        "1265--1296",
  month =        jul,
  year =         "2024",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/mcom/3939",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Mon May 27 15:56:44 MDT 2024",
  bibsource =    "https://www.ams.org/mcom/2024-93-347;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2020.bib",
  URL =          "https://www.ams.org/journals/mcom/2024-93-347/S0025-5718-2024-03939-X",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "https://www.ams.org/journals/mcom/all_issues.html",
  pubdate =      "2 February 2024",
}

@Article{He:2024:RFP,
  author =       "Pengyu He and Yuanzhe Zhao and Heng Xie and Yang Wang
                 and Shouyi Yin and Li Li and Yan Zhu and Rui P. Martins
                 and Chi-Hang Chan and Minglei Zhang",
  title =        "A Reconfigurable Floating-Point Compute-in-Memory With
                 Analog Exponent Preprocesses",
  journal =      "IEEE Solid-State Circuits Letters",
  volume =       "7",
  pages =        "271--274",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/LSSC.2024.3463208",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Common Information Model (computing);
                 Compute-in-memory (CIM) macro; Energy efficiency;
                 exponent preprocess; floating point (FP); Gain; MOS
                 devices; Quantization (signal); reconfigurable;
                 Registers; segmented computation",
}

@InProceedings{Henriksson:2024:AAD,
  author =       "Mikael Henriksson and Theodor Lindberg and Oscar
                 Gustafsson",
  title =        "{APyTypes}: Algorithmic Data Types in {Python} for
                 Efficient Simulation of Finite Word-Length Effects",
  crossref =     "IEEE:2024:PIS",
  pages =        "72--75",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00021",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/python.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@Article{Hingu:2024:BFF,
  author =       "Chanakya Hingu and Xingang Fu and Praneeth Vangala and
                 Ramkrishna Mishan and Poria Fajri",
  title =        "32-Bit Fixed and Floating-Point Hardware
                 Implementation for Enhanced Inverter Control:
                 Leveraging {FPGA} in Recurrent Neural Network
                 Applications",
  journal =      j-IEEE-ACCESS,
  volume =       "12",
  pages =        "111097--111110",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/ACCESS.2024.3441512",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Tue Sep 30 17:30:28 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "32-bit fix and floating point implementation;
                 Artificial neural networks; CORDIC; Field programmable
                 gate arrays; FPGA; Hardware; hardware implementation;
                 Inverters; LUT; Matlab; Neural network controller;
                 Neural networks; Recurrent neural networks; Tanh
                 function",
}

@InProceedings{Hsieh:2024:MAP,
  author =       "Mong-Yung Hsieh and Alan Liu and Zih-Jyun Chen",
  booktitle =    "{2024 IEEE International Conference on Systems, Man,
                 and Cybernetics (SMC)}",
  title =        "Multi-Agent Pruning and Quantization in
                 Mixed-Precision Models",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "5367--5372",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/SMC54092.2024.10831664",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Computational modeling; Deep reinforcement
                 learning; Edge AI; Hardware; Load modeling; Manuals;
                 Measurement; Mixed-precision model compression;
                 Multi-agent system; Multi-agent systems; Quantization
                 (signal); Training; Tuning",
}

@Article{Huang:2024:IPF,
  author =       "Paul Xuanyuanliang Huang and Yannis Tsividis and
                 Mingoo Seok",
  title =        "{INTIACC}: a Programmable Floating-Point Accelerator
                 for Partial Differential Equations",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "59",
  number =       "9",
  pages =        "3058--3069",
  year =         "2024",
  CODEN =        "IJSCBC",
  DOI =          "https://doi.org/10.1109/JSSC.2024.3379308",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "32-bit floating point; Accelerator architectures;
                 Boundary conditions; boundary conditions (BCs); custom
                 instruction set architecture (ISA); Finite difference
                 methods; Floating-point arithmetic; hybrid global-local
                 clocking scheme; Mathematical models; numerical
                 integration; Partial differential equations; partial
                 differential equations (PDEs); programmable
                 accelerator; Reduced instruction set computing",
}

@TechReport{Hubrecht:2024:TCR,
  author =       "Tom Hubrecht and Claude-Pierre Jeannerod and Paul
                 Zimmermann and Laurence Rideau and Laurent Th{\'e}ry",
  title =        "Towards a correctly-rounded and fast power function in
                 binary64 arithmetic",
  type =         "Report",
  institution =  "DI-ENS --- D{\'e}partement d'informatique --- ENS
                 Paris",
  address =      "Paris, France",
  day =          "8",
  month =        feb,
  year =         "2024",
  bibdate =      "Mon May 13 12:00:21 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://inria.hal.science/hal-04159652v2/",
  abstract =     "We design algorithms for the correct rounding of the
                 power function $ x^y $ in the binary64 IEEE 754 format,
                 for all rounding modes, modulo the knowledge of
                 hardest-to-round cases. Our implementation of these
                 algorithms largely outperforms previous
                 correctly-rounded implementations and is not far from
                 the efficiency of current mathematical libraries, which
                 are not correctly-rounded. Still, we expect our
                 algorithms can be further improved for speed. The
                 proofs of correctness are fully detailed and have been
                 formally verified. We hope this work will motivate the
                 next IEEE 754 revision committee to require correct
                 rounding for mathematical functions.",
  acknowledgement = ack-nhfb,
  remark =       "This is a longer version of \cite{Hubrecht:2023:TCRb}
                 with proofs and remarks by the final two authors on the
                 formal verification.",
}

@TechReport{Hubrecht:2024:UACa,
  author =       "Tom Hubrecht and Claude-Pierre Jeannerod and
                 Jean-Michel Muller",
  title =        "Useful applications of correctly-rounded operators of
                 the form $ a b + c d + e $",
  type =         "Report",
  number =       "hal-04461089",
  institution =  "DI-ENS (D{\'e}partment d'informatique --- ENS Paris)
                 and Universit{\'e} de Lyon",
  address =      "Paris, France and Lyon France",
  day =          "16",
  month =        feb,
  year =         "2024",
  bibdate =      "Thu Feb 22 05:37:30 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://inria.hal.science/hal-04461089",
  abstract =     "We show that the availability of fused arithmetic
                 operators that evaluate expressions of the form $ a b +
                 c d $ (FD2 instruction) or $ a b + c d + e $ (FD2A
                 instruction) in floating-point arithmetic with one
                 final rounding only would significantly facilitate many
                 calculations that are hard to perform with high
                 accuracy at small cost using only the traditional
                 operations $+$, $-$, $ \div $, $ \times $, $ \sqrt {}
                 $, and fused multiply-add (FMA).",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}

@InProceedings{Hubrecht:2024:UACb,
  author =       "Tom Hubrecht and Claude-Pierre Jeannerod and
                 Jean-Michel Muller",
  title =        "Useful applications of correctly-rounded operators of
                 the form $ a b + c d + e $",
  crossref =     "IEEE:2024:PIS",
  pages =        "32--39",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00015",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@Article{Jabbarpour:2024:FEE,
  author =       "Mohammad Reza Jabbarpour and Bahman Javadi and Philip
                 H. W. Leong and Rodrigo N. Calheiros and David Boland",
  title =        "{FedOrbit}: Energy Efficient Federated Learning for
                 Orbital Edge Computing Using Block Minifloat
                 Arithmetic",
  journal =      "IEEE Transactions on Services Computing",
  volume =       "17",
  number =       "6",
  pages =        "3657--3671",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/TSC.2024.3478768",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Arithmetic; Block minifloat; Clustering algorithms;
                 Computational modeling; energy consumption; federated
                 learning; Low earth orbit satellites; low-earth orbit;
                 orbital edge computing; Orbits; Power demand;
                 Quantization (signal); Satellites; Servers; Training",
}

@Article{Jonnalagadda:2024:ADP,
  author =       "Aditya Anirudh Jonnalagadda and Uppugunduru Anil Kumar
                 and Rishi Thotli and Satvik Sardesai and Sreehari
                 Veeramachaneni and Syed Ershad Ahmed",
  title =        "{ADEPNET}: A Dynamic-Precision Efficient Posit
                 Multiplier for Neural Networks",
  journal =      j-IEEE-ACCESS,
  volume =       "12",
  pages =        "31036--31046",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/ACCESS.2024.3369695",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Wed Oct 1 06:08:36 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "Approximate posit multipliers; Artificial neural
                 networks; Decoding; Deep learning; deep neural
                 networks; Encoding; Energy efficiency;
                 energy-efficient; Floating-point arithmetic; Hardware;
                 IEEE Standards; Power dissipation",
}

@InProceedings{K:2024:FPC,
  author =       "Padmakumar K and Lalu V and Shiny G",
  booktitle =    "{2024 International Conference on Advancements in
                 Power, Communication and Intelligent Systems (APCI)}",
  title =        "Floating-point {CORDIC} Coprocessor with Dynamic
                 Iterations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--6",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/APCI61480.2024.10616948",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "CORDIC; Dynamic iteration; Ecosystems; floating-point;
                 Hardware; Heuristic algorithms; Process control;
                 Software algorithms; Taylor series; VHDL",
}

@InProceedings{Kaya:2024:NAP,
  author =       "Zeynep Kaya and Mario Garrido",
  title =        "Novel Access Patterns Based on Overlapping Loading and
                 Processing Times to Reduce Latency and Increase
                 Throughput in Memory-based {FFTs}",
  crossref =     "IEEE:2024:PIS",
  pages =        "52--59",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00018",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@InProceedings{Khwa:2024:IFP,
  author =       "Win-San Khwa and Ping-Chun Wu and Jui-Jen Wu and
                 Jian-Wei Su and Ho-Yu Chen and Zhao-En Ke and
                 Ting-Chien Chiu and Jun-Ming Hsu and Chiao-Yen Cheng
                 and Yu-Chen Chen and Chung-Chuan Lo and Ren-Shuo Liu
                 and Chih-Cheng Hsieh and Kea-Tiong Tang and Meng-Fan
                 Chang",
  booktitle =    "{2024 IEEE International Solid-State Circuits
                 Conference (ISSCC)}",
  title =        "34.2 A 16nm {96Kb} Integer\slash Floating-Point
                 Dual-Mode-Gain-Cell-Computing-in-Memory Macro Achieving
                 {73.3-163.3TOPS/W} and {33.2-91.2TFLOPS/W} for
                 {AI--Edge} Devices",
  volume =       "67",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "568--570",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/ISSCC49657.2024.10454447",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Arrays; Artificial neural networks; Common Information
                 Model (computing); Computational efficiency; Data
                 transfer; In-memory computing; Solid state circuits",
}

@Article{Kim:2024:MCA,
  author =       "Kwang Ho Kim and Sihem Mesnager and Kyong Il Pak",
  title =        "{Montgomery} curve arithmetic revisited",
  journal =      j-J-CRYPTO-ENG,
  volume =       "14",
  number =       "2",
  pages =        "343--362",
  month =        jun,
  year =         "2024",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s13389-024-00353-5",
  ISSN =         "2190-8508 (print), 2190-8516 (electronic)",
  ISSN-L =       "2190-8508",
  bibdate =      "Thu Aug 8 07:34:12 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcryptoeng.bib",
  note =         "See \cite{Montgomery:1987:SPE}.",
  URL =          "https://link.springer.com/article/10.1007/s13389-024-00353-5",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Crypto. Eng.",
  fjournal =     "Journal of Cryptographic Engineering",
  journal-URL =  "http://link.springer.com/journal/13389",
}

@InProceedings{Kluska:2024:QEG,
  author =       "Piotr Kluska and Adri{\'a}n Castell{\'o} and Florian
                 Scheidegger and A. Cristiano I. Malossi and Enrique S.
                 Quintana-Ort{\'\i}",
  booktitle =    "{2024 IEEE/CVF Conference on Computer Vision and
                 Pattern Recognition Workshops (CVPRW)}",
  title =        "{QAttn}: Efficient {GPU} Kernels for mixed-precision
                 {Vision Transformers}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "3648--3657",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/CVPRW63382.2024.00368",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "compression; Computational modeling; Computer vision;
                 Graphics processing units; Image segmentation; instance
                 segmentation; object classification; Prototypes;
                 quantization; Quantization (signal); Transformers;
                 vision transformers",
}

@Article{Kohl:2024:MMU,
  author =       "Nils Kohl and Stephen F. McCormick and Rasmus
                 Tamstorf",
  title =        "Multigrid Methods Using Block Floating Point
                 Arithmetic",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "46",
  number =       "5",
  pages =        "S202--S224",
  month =        "????",
  year =         "2024",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/23M1581819",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Sat Apr 12 07:31:17 MDT 2025",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/46/5;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  URL =          "https://epubs.siam.org/doi/10.1137/23M1581819",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}

@InProceedings{Langhammer:2024:MAC,
  author =       "Martin Langhammer and Bogdan Pasca and Igor
                 Kucherenko",
  title =        "Multiplier Architecture with a Carry-Based Partial
                 Product Encoding",
  crossref =     "IEEE:2024:PIS",
  pages =        "104--107",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00026",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@Article{Laudadio:2024:CIE,
  author =       "Teresa Laudadio and Nicola Mastronardi and Donatella
                 Occorsio",
  title =        "Computing integrals with an exponential weight on the
                 real axis in floating point arithmetic",
  journal =      j-APPL-NUM-MATH,
  volume =       "200",
  number =       "??",
  pages =        "309--317",
  month =        jun,
  year =         "2024",
  CODEN =        "ANMAEL",
  DOI =          "https://doi.org/10.1016/j.apnum.2023.05.025",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  bibdate =      "Thu Apr 11 08:18:17 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0168927423001551",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274",
}

@Article{Lee:2024:ODF,
  author =       "Seunghwan Lee and Dong-Joon Shin",
  title =        "Overflow-Detectable Floating-Point Fully Homomorphic
                 Encryption",
  journal =      j-IEEE-ACCESS,
  volume =       "12",
  pages =        "6160--6180",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/ACCESS.2024.3351738",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Tue Sep 30 17:30:28 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "Deep learning; Encoding; Error analysis;
                 Floating-point arithmetic; Fully homomorphic
                 encryption; Gaussian processes; Homomorphic encryption;
                 homomorphic floating-point arithmetic; homomorphic
                 overflow detection; Random variables; subgaussian error
                 analysis; Transforms",
}

@InProceedings{Lefevre:2024:ECS,
  author =       "Vincent Lef{\`e}vre",
  title =        "An {Emacs--Cairo} Scrolling Bug due to Floating-Point
                 Inaccuracy",
  crossref =     "IEEE:2024:PIS",
  pages =        "76--79",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00022",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@Misc{Lefevre:2024:TMF,
  author =       "Vincent Lef{\`e}vre",
  title =        "Test of Mathematical Functions of the {Standard C
                 Library}",
  howpublished = "Web site.",
  day =          "27",
  month =        sep,
  year =         "2024",
  bibdate =      "Mon Oct 21 11:32:37 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.vinc17.net/research/testlibm/;
                 https://www.vinc17.net/research/testlibm/hrcases/",
  acknowledgement = ack-nhfb,
  remark =       "Contains link to collection of data files with
                 worst-case (or hard-to-round) arguments for common
                 elementary functions. See also
                 \cite{Lefevre:2003:WCC}.",
}

@Article{Lemire:2024:ESP,
  author =       "Daniel Lemire",
  title =        "Exact Short Products From Truncated Multipliers",
  journal =      j-COMP-J,
  volume =       "67",
  number =       "4",
  pages =        "1514--1520",
  month =        apr,
  year =         "2024",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/bxad077",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Fri Apr 26 12:13:08 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compj2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/cryptography2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://academic.oup.com/comjnl/article/67/4/1514/7306807;
                 https://arxiv.org/abs/2303.14321v1",
  abstract =     "We sometimes need to compute the most significant
                 digits of the product of small integers with a
                 multiplier requiring much storage: e.g., a large
                 integer (e.g., $ 5^{100} $) or an irrational number ($
                 \pi $). We only need to access the most significant
                 digits of the multiplier --- as long as the integers
                 are sufficiently small. We provide an efficient
                 algorithm to compute the range of integers given a
                 truncated multiplier and a desired number of digits.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@InProceedings{Li:2024:DFPa,
  author =       "Xinyi Li and Ang Li and Bo Fang and Katarzyna
                 Swirydowicz and Ignacio Laguna and Ganesh
                 Gopalakrishnan",
  booktitle =    "{2024 IEEE 24th International Symposium on Cluster,
                 Cloud and Internet Computing (CCGrid)}",
  title =        "Discovery of Floating-Point Differences Between
                 {NVIDIA} and {AMD} {GPUs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "663--666",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/CCGrid59990.2024.00083",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "AMD GPU; Complexity theory; Computational modeling;
                 correctness-portability; floating-point arithmetic;
                 Graphics processing units; Hardware; high performance
                 computing; Libraries; machine learning; Numerical
                 models; NVIDIA GPU; performance-portability; Software
                 development management; Standards; Tensors; Testing",
}

@InProceedings{Li:2024:DFPb,
  author =       "Jiancong Li and Shengguang Ren and Yi Li and Wenlong
                 Peng and Zhiwei Zhou and Yibai Xue and Yu Zhang and
                 Zhiwen Cao and Jiayi Sun and Yuhui He and Xiangshui
                 Miao",
  booktitle =    "{2024 IEEE International Electron Devices Meeting
                 (IEDM)}",
  title =        "Demonstration of a Floating-point Deep Neural Matrix
                 Equation Solver using {3D} Vertical {ReRAM} with High
                 Energy- and Area-Efficiency",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--4",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/IEDM50854.2024.10873550",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Arrays; In-memory computing; Mathematical models;
                 Resistance; Scientific computing; Silicon compounds;
                 Three-dimensional displays; Training; Transmission line
                 matrix methods; Voltage measurement",
}

@InProceedings{Li:2024:LLB,
  author =       "Yike Li and Zheng Wang and Wenhui Ou and Chen Liang
                 and Weiyu Zhou and Yongkui Yang and Chao Chen",
  booktitle =    "{2024 IEEE International Symposium on Circuits and
                 Systems (ISCAS)}",
  title =        "Low-latency Buffering for Mixed-precision Neural
                 Network Accelerator with {MulTAP} and {FQPipe}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--5",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/ISCAS58744.2024.10558641",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "activation buffering; Arithmetic; Arrays; Artificial
                 neural networks; Circuits and systems; IP networks; Low
                 latency communication; mixed-precision; NN accelerator;
                 Pipelines; quantization pipeline",
}

@Article{Li:2024:MFM,
  author =       "Hongyan Li and Hang Lu and Xiaowei Li",
  title =        "{Mortar-FP8}: Morphing the Existing {FP32}
                 Infrastructure for High-Performance Deep Learning
                 Acceleration",
  journal =      j-IEEE-TRANS-CAD-ICS,
  volume =       "43",
  number =       "3",
  pages =        "878--891",
  year =         "2024",
  CODEN =        "ITCSDI",
  DOI =          "https://doi.org/10.1109/TCAD.2023.3329778",
  ISSN =         "0278-0070 (print), 1937-4151 (electronic)",
  ISSN-L =       "0278-0070",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computer-Aided Design of
                 Integrated Circuits and Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=43",
  keywords =     "Artificial neural networks; Computational efficiency;
                 Deep learning; Deep learning accelerator; deep neural
                 network (DNN); fp8 format; Hardware acceleration;
                 Inference algorithms; Software algorithms",
}

@Article{Li:2024:RPE,
  author =       "Boyu Li and Kai Li and Jiajun Zhou and Yuan Ren and
                 Wei Mao and Hao Yu and Ngai Wong",
  title =        "A Reconfigurable Processing Element for
                 Multiple-Precision Floating\slash Fixed-Point {HPC}",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
  volume =       "71",
  number =       "3",
  pages =        "1401--1405",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/TCSII.2023.3322259",
  ISSN =         "1549-7747 (print), 1558-3791 (electronic)",
  ISSN-L =       "1549-7747",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems II: Express
                 Briefs",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
  keywords =     "Artificial neural networks; Clocks; Deep learning;
                 Energy efficiency; fixed-point; floating-point;
                 Hardware; HPC; MAC; Multiple-precision; PE; Random
                 access memory; Training",
}

@Article{Lin:2024:FHP,
  author =       "Xian Lin and Heming Liu and Xin Zheng and Huaien Gao
                 and Shuting Cai and Xiaoming Xiong",
  title =        "{FPUx}: High-Performance Floating-Point Support for
                 Cost-Constrained {RISC-V} Cores",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "32",
  number =       "10",
  pages =        "1945--1949",
  year =         "2024",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/TVLSI.2024.3399221",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
  keywords =     "Arithmetic; Floating-point units (FPUs); Hardware;
                 Internet of Things; Internet of Things (IoT); IP
                 networks; Pipelines; RISC-V; single-precision
                 floating-point (FP) arithmetic IPs; Standards; Timing",
}

@InProceedings{Liu:2024:ACA,
  author =       "Haobo Liu and Zhengyang Qian and Wei Wu and Hongwei
                 Ren and Zhiwei Liu and Leibin Ni",
  booktitle =    "{2024 Design, Automation \& Test in Europe Conference
                 \& Exhibition (DATE)}",
  title =        "{AFPR-CIM}: an Analog-Domain Floating-Point
                 {RRAM}-based Compute-In-Memory Architecture with
                 Dynamic Range Adaptive {FP-ADC}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--6",
  year =         "2024",
  DOI =          "https://doi.org/10.23919/DATE58400.2024.10546882",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "adaptive; analog domain; Codes; computing in memory;
                 dynamic range; floating-point; In-memory computing;
                 Neural networks; Nonvolatile memory; Power demand;
                 RRAM; Throughput; Voltage",
}

@InProceedings{Ltaief:2024:TCG,
  author =       "Hatem Ltaief and Rabab Alomairy and Qinglei Cao and
                 Jie Ren and Lotfi Slim and Thorsten Kurth and Benedikt
                 Dorschner and Salim Bougouffa and Rached Abdelkhalak
                 and David E. Keyes",
  booktitle =    "{SC24: International Conference for High Performance
                 Computing, Networking, Storage and Analysis}",
  title =        "Toward Capturing Genetic Epistasis from Multivariate
                 Genome-Wide Association Studies Using Mixed-Precision
                 Kernel Ridge Regression",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--12",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/SC41406.2024.00012",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Bioinformatics; Dynamic runtime system; Genomics;
                 Genotypes; GPU accelerators; Graphics processing units;
                 High performance computing; Kernel; Kernel Ridge
                 Regression; Mixed precision; Multivariate Genome-wide
                 Association Studies; Nonlinear genotype-phenotype
                 relationships; Phenotypes; Runtime; Software; Tensors;
                 Tile-centric matrix computations; UK BioBank data",
}

@InProceedings{Luo:2024:BDN,
  author =       "Weile Luo and Ruibo Fan and Zeyu Li and Dayou Du and
                 Qiang Wang and Xiaowen Chu",
  booktitle =    "{2024 IEEE International Parallel and Distributed
                 Processing Symposium (IPDPS)}",
  title =        "Benchmarking and Dissecting the {Nvidia Hopper GPU}
                 Architecture",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "656--667",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/IPDPS57955.2024.00064",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Asynchronous Execution; Benchmark testing; Computer
                 architecture; Distributed Shared Memory; DPX; Graphics
                 processing units; Hopper; Instruction Latency;
                 Instruction sets; Microarchitecture; Performance
                 evaluation; PTX; Tensor Core; Tensors",
}

@InProceedings{Lutz:2024:FFW,
  author =       "David R. Lutz and Anisha Saini and Mairin Kroes and
                 Thomas Elmer and Harsha Valsaraju",
  title =        "Fused {FP8} 4-way Dot Product With Scaling and {FP32}
                 Accumulation",
  crossref =     "IEEE:2024:PIS",
  pages =        "40--47",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00016",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; ARITH 2024; ARITH-31; Computational
                 efficiency; Costs; Digital arithmetic; Dynamic range;
                 Microarchitecture; US Department of Transportation",
}

@Article{Mackie:2024:RFM,
  author =       "Maximilien Mackie",
  title =        "Recursion-free modular arithmetic in the
                 lambda-calculus",
  journal =      j-INFO-PROC-LETT,
  volume =       "183",
  number =       "??",
  pages =        "Article 106408",
  month =        jan,
  year =         "2024",
  CODEN =        "IFPLAT",
  DOI =          "https://doi.org/10.1016/j.ipl.2023.106408",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Tue Sep 19 07:09:51 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/infoproc2020.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0020019023000510",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}

@Article{McCormick:2024:REA,
  author =       "Stephen F. McCormick and Rasmus Tamstorf",
  title =        "Rounding-Error Analysis of Multigrid {V}-Cycles",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "46",
  number =       "5",
  pages =        "S88--S95",
  month =        "????",
  year =         "2024",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/23M1582898",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Sat Apr 12 07:31:17 MDT 2025",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/46/5;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  URL =          "https://epubs.siam.org/doi/10.1137/23M1582898",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}

@Article{Mikaitis:2024:MMT,
  author =       "Mantas Mikaitis",
  title =        "Monotonicity of Multi-Term Floating-Point Adders",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "??",
  number =       "??",
  pages =        "1--13",
  month =        "????",
  year =         "2024",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/tc.2024.3371783",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Mon Mar 11 11:33:29 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "accurate floating-point summation",
  remark =       "Online on 11 March 2024, but not yet assigned to an
                 issue.",
}

@InProceedings{Mikaitis:2024:MSL,
  author =       "Mantas Mikaitis",
  title =        "{MATLAB} Simulator of Level-Index Arithmetic",
  crossref =     "IEEE:2024:PIS",
  pages =        "68--71",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00020",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@InProceedings{Mirsalari:2024:UBF,
  author =       "Seyed Ahmad Mirsalari and Saba Yousefzadeh and Ahmed
                 Hemani and Giuseppe Tagliavini",
  booktitle =    "{2024 31st IEEE International Conference on
                 Electronics, Circuits and Systems (ICECS)}",
  title =        "Unleashing 8-Bit Floating Point Formats Out of the
                 Deep-Learning Domain",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--4",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/ICECS61496.2024.10848785",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; approximate computing; Deep learning; Energy
                 conservation; Energy efficiency; float8; Hardware;
                 Instruction sets; Kernel; Market research; Parallel
                 ultra-low-power platform; Resource management; RISC-V;
                 smallFloat data types; Sustainable development",
}

@Misc{MPFRTeam:2024:MLA,
  author =       "{MPFR Team}",
  title =        "The {MPFR} Library: Algorithms and Proofs",
  howpublished = "Web document",
  pages =        "69",
  day =          "25",
  month =        jan,
  year =         "2024",
  bibdate =      "Thu Oct 16 06:58:53 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://mpfr.org/algorithms.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Muller:2024:SNC,
  author =       "Jean-Michel Muller",
  title =        "Some notes on correct rounding of functions",
  howpublished = "Attachment to STDS-754 mailing list",
  pages =        "31",
  day =          "18",
  month =        sep,
  year =         "2024",
  bibdate =      "Thu Sep 19 15:27:07 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Murillo:2024:SRU,
  author =       "Raul Murillo and Alberto A. {Del Barrio} and Guillermo
                 Botella",
  title =        "Square Root Unit with Minimum Iterations for Posit
                 Arithmetic",
  crossref =     "IEEE:2024:PIS",
  pages =        "132--138",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00030",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31; posit arithmetic",
}

@Article{Navimipour:2024:NSA,
  author =       "Nima Jafari Navimipour and Seyed-Sajad Ahmadpour and
                 Senay Yalcin",
  title =        "A nano-scale arithmetic and logic unit using a
                 reversible logic and quantum-dots",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "80",
  number =       "1",
  pages =        "395--412",
  month =        jan,
  year =         "2024",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1007/s11227-023-05491-x",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Thu Feb 15 10:23:12 MST 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsuper2020.bib",
  URL =          "https://link.springer.com/article/10.1007/s11227-023-05491-x",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Supercomputing",
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
}

@Article{Noyez:2024:MMS,
  author =       "Louis Noyez and Nadia {El Mrabet} and Olivier Potin
                 and Pascal Veron",
  title =        "{Montgomery} Multiplication Scalable Systolic Designs
                 Optimized for {DSP48E2}",
  journal =      j-TRETS,
  volume =       "17",
  number =       "1",
  pages =        "9:1--9:??",
  month =        mar,
  year =         "2024",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3624571",
  ISSN =         "1936-7406 (print), 1936-7414 (electronic)",
  ISSN-L =       "1936-7406",
  bibdate =      "Wed Mar 20 07:25:09 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/trets.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3624571",
  abstract =     "This article describes an extensive study of the use
                 of DSP48E2 Slices in Ultrascale FPGAs to design
                 hardware versions of the Montgomery Multiplication
                 algorithm for the hardware acceleration of modular
                 multiplications. Our fully scalable systolic \ldots{}",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Reconfigurable Technol. Syst.",
  articleno =    "9",
  fjournal =     "ACM Transactions on Reconfigurable Technology and
                 Systems (TRETS)",
  journal-URL =  "https://dl.acm.org/loi/trets",
}

@InProceedings{Okoshi:2024:WTW,
  author =       "Yasuyuki Okoshi and {\'A}ngel L{\'o}pez
                 Garc{\'\i}a-Arias and Jaehoon Yu and Junnnosuke Suzuki
                 and Hikari Otsuka and Thiem Van Chu and Kazushi
                 Kawamura and Daichi Fujiki and Masato Motomura",
  booktitle =    "{2024 IEEE Asian Solid-State Circuits Conference
                 (A-SSCC)}",
  title =        "{WhiteDwarf: 12.24} {TFLOPS/W 40} nm Versatile Neural
                 Inference Engine for Ultra-Compact Execution of {CNNs}
                 and {MLPs} Through Triple Unstructured Sparsity
                 Exploitation and Triple Model Compression",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--3",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/A-SSCC60305.2024.10849314",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Computational modeling; Engines; Image
                 coding; Neural networks; Process control; Quantization
                 (signal); Solid state circuits; Tensors; Training",
}

@Manual{Oracle:2024:SLR,
  title =        "{SQL} Language Reference",
  organization = "{Oracle Corporation}",
  publisher =    pub-ORACLE,
  address =      pub-ORACLE:adr,
  edition =      "19c (E96310-27)",
  month =        jul,
  year =         "2024",
  bibdate =      "Tue Sep 10 15:24:10 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sqlbooks.bib",
  note =         "The Data Types section describes the (non-IEEE 754)
                 decimal number encoding. The precision is about 39
                 decimal digits, with a nonzero range of [1e-130,
                 1e126).",
  URL =          "https://docs.oracle.com/en/database/oracle/oracle-database/19/sqlrf/Data-Types.html#GUID-A3C0D836-BADB-44E5-A5D4-265BA5968483",
  acknowledgement = ack-nhfb,
}

@InProceedings{Palchaudhuri:2024:FSS,
  author =       "Ayan Palchaudhuri and Anindya Sundar Dhar",
  booktitle =    "{2024 37th International Conference on VLSI Design and
                 2024 23rd International Conference on Embedded Systems
                 (VLSID)}",
  title =        "{FPGA} Specific Speed-Area Optimized Architectures of
                 Arithmetic Cores with Scan Insertion for Carry Chain
                 Based Multi-level Logic Implementation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "617--622",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/VLSID60093.2024.00109",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "absolute difference; carry chain; CORDIC; Finite
                 element analysis; FPGA; Look-Up Table; Minimization;
                 Philosophical considerations; Registers; Scalability;
                 scan register; Table lookup; ternary accumulator; Very
                 large scale integration",
}

@InProceedings{Paulin:2024:OCD,
  author =       "Gianna Paulin and Paul Scheffler and Thomas Benz and
                 Matheus Cavalcante and Tim Fischer and Manuel Eggimann
                 and Yichao Zhang and Nils Wistoff and Luca Bertaccini
                 and Luca Colagrande and Gianmarco Ottavi and Frank K.
                 G{\"u}rkaynak and Davide Rossi and Luca Benini",
  booktitle =    "{2024 IEEE Symposium on VLSI Technology and Circuits
                 (VLSI Technology and Circuits)}",
  title =        "{Occamy}: a 432-Core 28.1 {DP-GFLOP/s/W} 83\% {FPU}
                 Utilization Dual-Chiplet, {Dual-HBM2E} {RISC-V}-Based
                 Accelerator for Stencil and Sparse Linear Algebra
                 Computations with 8-to-64-bit Floating-Point Support in
                 12nm {FinFET}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--2",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/VLSITechnologyandCir46783.2024.10631529",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "2.5D Integration; Chiplet; Computational efficiency;
                 FinFETs; General Sparse Acceleration; Integrated
                 circuit interconnections; Interposer; Linear algebra;
                 Multi-Precision; Single instruction multiple data;
                 Sparse matrices; Stencil Acceleration; Very large scale
                 integration",
}

@Article{Perez:2024:HAF,
  author =       "J. Ayuso Perez",
  title =        "Hardware Addition Over Finite Fields Based On
                 {Booth--Karatsuba} Algorithm",
  journal =      j-COMP-J,
  volume =       "67",
  number =       "8",
  pages =        "2643--2666",
  month =        aug,
  year =         "2024",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/bxae034",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Mon Aug 19 11:43:29 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compj2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://academic.oup.com/comjnl/article/67/8/2643/7667243",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}

@Article{Rashidi:2024:AFE,
  author =       "Bahram Rashidi",
  title =        "{APPAs}: fast and efficient approximate parallel
                 prefix adders and multipliers",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "80",
  number =       "16",
  pages =        "24269--24296",
  month =        nov,
  year =         "2024",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1007/s11227-024-06356-7",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Thu Aug 22 13:34:29 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsuper2020.bib",
  URL =          "https://link.springer.com/article/10.1007/s11227-024-06356-7",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Supercomputing",
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
}

@InProceedings{Rayapati:2024:EEB,
  author =       "Vinay Rayapati and Sanampudi GopalaKrishna Reddy and
                 Gandi Ajay Kumar and Gogireddy Ravikiran Reddy and
                 Madhav Rao",
  booktitle =    "{2024 37th International Conference on VLSI Design and
                 2024 23rd International Conference on Embedded Systems
                 (VLSID)}",
  title =        "{EBACA}: Efficient {Bfloat16}-based Activation
                 Function Implementation Using Enhanced {CORDIC}
                 Architecture",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "605--610",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/VLSID60093.2024.00107",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "BFloat16; CNN; CORDIC; Embedded systems; Hardware;
                 Inference algorithms; Libraries; Low Power; Neural
                 networks; Performance evaluation; Sigmoid; Softmax;
                 Tanh; Very large scale integration",
}

@InProceedings{Remke:2024:HSG,
  author =       "Stefan Remke and Alexander Breuer",
  booktitle =    "{SC24-W: Workshops of the International Conference for
                 High Performance Computing, Networking, Storage and
                 Analysis}",
  title =        "{Hello SME}! {Generating} Fast Matrix Multiplication
                 Kernels Using the Scalable Matrix Extension",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1443--1454",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/SCW63240.2024.00185",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Bandwidth; code generation; Computer architecture;
                 Instruction sets; Kernel; Loading; M4; microbenchmarks;
                 Parallel processing; Pipelines; Registers; Scalable
                 Matrix Extension (SME); small GEMMs; Throughput;
                 Vectors",
}

@Misc{ROCm:2024:RRD,
  author =       "{ROCm}",
  title =        "{ROCM\slash ROCM}-device-libs: {ROCM} device
                 libraries",
  howpublished = "Web site",
  year =         "2024",
  bibdate =      "Fri Nov 14 15:45:16 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://github.com/ROCm/llvm-project/tree/amd-staging/amd/device-libs;
                 https://github.com/ROCm/ROCm-Device-Libs",
  acknowledgement = ack-nhfb,
  remark =       "Source code for the open-source OCML math library.",
}

@Article{Sahoo:2024:ADF,
  author =       "Siva Satyendra Sahoo and Salim Ullah and Akash Kumar",
  title =        "{AxOMaP}: Designing {FPGA}-based Approximate
                 Arithmetic Operators using Mathematical Programming",
  journal =      j-TRETS,
  volume =       "17",
  number =       "2",
  pages =        "31:1--31:??",
  month =        jun,
  year =         "2024",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3648694",
  ISSN =         "1936-7406 (print), 1936-7414 (electronic)",
  ISSN-L =       "1936-7406",
  bibdate =      "Tue Jun 4 06:09:07 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/trets.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3648694",
  abstract =     "With the increasing application of machine learning
                 (ML) algorithms in embedded systems, there is a rising
                 necessity to design low-cost computer arithmetic for
                 these resource-constrained systems. As a result,
                 emerging models of computation, such as approximate and
                 stochastic computing, that leverage the inherent
                 error-resilience of such algorithms are being actively
                 explored for implementing ML inference on
                 resource-constrained systems. Approximate computing
                 (AxC) aims to provide disproportionate gains in the
                 power, performance, and area (PPA) of an application by
                 allowing some level of reduction in its behavioral
                 accuracy (BEHAV). Using approximate operators (AxOs)
                 for computer arithmetic forms one of the more prevalent
                 methods of implementing AxC. AxOs provide the
                 additional scope for finer granularity of optimization,
                 compared to only precision scaling of computer
                 arithmetic. To this end, the design of
                 platform-specific and cost-efficient approximate
                 operators forms an important research goal. Recently,
                 multiple works have reported the use of AI\slash
                 ML-based approaches for synthesizing novel FPGA-based
                 AxOs. However, most of such works limit the use of
                 AI/ML to designing ML-based surrogate functions that
                 are used during iterative optimization processes. To
                 this end, we propose a novel data analysis-driven
                 mathematical programming-based approach to synthesizing
                 approximate operators for FPGAs. Specifically, we
                 formulate mixed integer quadratically constrained
                 programs based on the results of correlation analysis
                 of the characterization data and use the solutions to
                 enable a more directed search approach for evolutionary
                 optimization algorithms. Compared to traditional
                 evolutionary algorithms-based optimization, we report
                 up to 21\% improvement in the hypervolume, for joint
                 optimization of PPA and BEHAV, in the design of signed
                 8-bit multipliers. Further, we report up to 27\% better
                 hypervolume than other state-of-the-art approaches to
                 DSE for FPGA-based application-specific AxOs.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Reconfigurable Technol. Syst.",
  articleno =    "31",
  fjournal =     "ACM Transactions on Reconfigurable Technology and
                 Systems (TRETS)",
  journal-URL =  "https://dl.acm.org/loi/trets",
}

@Article{Sakellariou:2024:MFR,
  author =       "Vasilis Sakellariou and Vassilis Paliouras and Ioannis
                 Kouretas and Hani Saleh and Thanos Stouraitis",
  title =        "A Multiplier-Free {RNS}-Based {CNN} Accelerator
                 Exploiting Bit-Level Sparsity",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "12",
  number =       "2",
  pages =        "667--683",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/TETC.2023.3301590",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Tue Sep 9 13:42:38 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
  keywords =     "Adders; AI hardware accelerator; Artificial
                 intelligence; canonical signed digit; Computer
                 architecture; Convolutional neural networks; Encoding;
                 Energy efficiency; RNS; Throughput",
}

@Article{Scott:2024:ABI,
  author =       "Jennifer Scott and Miroslav Tuma",
  title =        "Avoiding Breakdown in Incomplete Factorizations in Low
                 Precision Arithmetic",
  journal =      j-TOMS,
  volume =       "50",
  number =       "2",
  pages =        "9:1--9:25",
  month =        jun,
  year =         "2024",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3651155",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Jul 2 07:51:57 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3651155",
  abstract =     "The emergence of low precision floating-point
                 arithmetic in computer hardware has led to a resurgence
                 of interest in the use of mixed precision numerical
                 linear algebra. For linear systems of equations, there
                 has been renewed enthusiasm for mixed precision
                 variants of iterative refinement. We consider the
                 iterative solution of large sparse systems using
                 incomplete factorization preconditioners. The focus is
                 on the robust computation of such preconditioners in
                 half precision arithmetic and employing them to solve
                 symmetric positive definite systems to higher precision
                 accuracy; however, the proposed ideas can be applied
                 more generally. Even for well-conditioned problems,
                 incomplete factorizations can break down when small
                 entries occur on the diagonal during the factorization.
                 When using half precision arithmetic, overflows are an
                 additional possible source of breakdown. We examine how
                 breakdowns can be avoided and implement our strategies
                 within new half precision Fortran sparse incomplete
                 Cholesky factorization software. Results are reported
                 for a range of problems from practical applications.
                 These demonstrate that, even for highly ill-conditioned
                 problems, half precision preconditioners can
                 potentially replace double precision preconditioners,
                 although unsurprisingly this may be at the cost of
                 additional iterations of a Krylov solver.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "9",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@InProceedings{Singh:2024:FBS,
  author =       "Suryadev Singh and Babita Jajodia",
  booktitle =    "{2024 International Conference on IoT, Communication
                 and Automation Technology (ICICAT)}",
  title =        "{FPGA}-based {SoC} Design with {CORDIC-POSIT}
                 Arithmetic for Efficient {IoT} Data Processing",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1534--1539",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/ICICAT62666.2024.10923249",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Arithmetic; Coordinate Rotation Digital
                 Computer (CORDIC); Data processing; Field programmable
                 gate arrays; Field Programmable Gate-Array (FPGA);
                 Internet of Things; Internet of Things (IoT); Positive
                 Integer and Signed Integer Ternary (POSIT); Real-time
                 systems; sensor data management; Soil measurements;
                 Soil moisture; System on Chip (SoC); System-on-chip;
                 Table lookup; XADC",
}

@InProceedings{Tang:2024:OSR,
  author =       "Ping Tak Peter Tang",
  title =        "An Open-Source {RISC-V} Vector Math Library",
  crossref =     "IEEE:2024:PIS",
  pages =        "60--67",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00019",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@Article{Tosini:2024:AEI,
  author =       "Marcelo Tosini and Mart{\'\i}n V{\'a}zquez and Lucas
                 Leiva",
  title =        "Analysis and efficient implementation of {IEEE-754}
                 decimal floating point adders\slash subtractors in
                 {FPGAs} for {DPD} and {BID} encoding",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "80",
  number =       "7",
  pages =        "9298--9326",
  month =        may,
  year =         "2024",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1007/s11227-023-05808-w",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Fri Apr 19 06:28:17 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsuper2020.bib",
  URL =          "https://link.springer.com/article/10.1007/s11227-023-05808-w",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Supercomputing",
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
  keywords =     "decimal floating-point arithmetic",
}

@Manual{Towner:2024:IAF,
  author =       "Daniel Towner and Steven Wood and Phoebe Wang and
                 Marius Cornea and Cristina Anderson and Amit
                 Gradstein",
  title =        "{Intel AVX-512} --- {FP16} Instruction Set for {Intel
                 Xeon} Processor Based Products Technology Guide",
  organization = "Intel Corporation",
  address =      "????",
  day =          "12",
  month =        mar,
  year =         "2024",
  bibdate =      "Fri Apr 11 08:28:36 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.intel.com/content/www/us/en/content-details/669773/intel-avx-512-fp16-instruction-set-for-intel-xeon-processor-based-products-technology-guide.html",
  acknowledgement = ack-nhfb,
}

@InProceedings{Upadhyay:2024:ECI,
  author =       "Gaurav Upadhyay and C Siva Prasad and V Akash and
                 Ayush Kumar Singh and R Monish Sai and Srijan Ghosal
                 and Subrat Kar and S H Shantala and J Thakur
                 LalitKrushna and S Srividhya and Sunil Alias
                 Balwantrao",
  booktitle =    "{2024 Second International Conference on Networks,
                 Multimedia and Information Technology (NMITCON)}",
  title =        "Enhancing {CNN} Inference Time and Reducing Latency on
                 Edge and Resource-Constrained Systems through
                 Quantization",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--6",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/NMITCON62075.2024.10699069",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/python.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Computational modeling; Deep Learning; DPU;
                 Edge computing; EuroSat; GPU; Model Compression;
                 Optimization; Performance evaluation; Performance
                 Evaluation; Post-Training Quantization; PyTorch;
                 Quantization; Quantization (signal); Quantization Aware
                 Training; Remote sensing; Space vehicles; Surveillance;
                 Throughput; Training; Xilinx",
}

@InProceedings{vanderHoeven:2024:FMP,
  author =       "Joris van der Hoeven and Fredrik Johansson",
  title =        "Fast multiple precision $ \exp (x) $ with
                 precomputations",
  crossref =     "IEEE:2024:PIS",
  pages =        "80--87",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00023",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@InProceedings{Villalba:2024:MCC,
  author =       "Julio Villalba and Javier Hormigo and Javier {Diaz
                 Bruguera} and Sonia Gonzalez-Navarro",
  title =        "Message from Conference Chairs: {ARITH 2024}",
  crossref =     "IEEE:2024:PIS",
  pages =        "8--9",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/arith61463.2024.00005",
  bibdate =      "Thu Nov 13 11:37:34 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@Article{Wang:2024:DIH,
  author =       "Junjie Wang and Teng Zhang and Shuang Liu and Yihe Liu
                 and Yuancong Wu and Shaogang Hu and Tupei Chen and Yang
                 Liu and Yuchao Yang and Ru Huang",
  title =        "Design and Implementation of a Hybrid, {ADC\slash
                 DAC}-Free, Input-Sparsity-Aware, Precision
                 Reconfigurable {RRAM} Processing-in-Memory Chip",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "59",
  number =       "2",
  pages =        "595--604",
  year =         "2024",
  CODEN =        "IJSCBC",
  DOI =          "https://doi.org/10.1109/JSSC.2023.3304174",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "Adders; Convolution; Nonvolatile memory; Power demand;
                 Processing-in-memory (PIM); Programming;
                 quantization-aware training (QAT); Resistance;
                 resistive random access memory (RRAM); sparsity-aware;
                 time-division multiplexing (TDM); Transistors",
}

@InProceedings{Wang:2024:WPB,
  author =       "Yang Wang and Xiaolong Yang and Yubin Qin and Zhiren
                 Zhao and Ruiqi Guo and Zhiheng Yue and Huiming Han and
                 Shaojun Wei and Yang Hu and Shouyi Yin",
  booktitle =    "{2024 IEEE International Solid-State Circuits
                 Conference (ISSCC)}",
  title =        "34.1 A 28nm {83.23TFLOPS/W} {POSIT}-Based
                 Compute-in-Memory Macro for High-Accuracy {AI}
                 Applications",
  volume =       "67",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "566--568",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/ISSCC49657.2024.10454567",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Energy efficiency; In-memory computing; Program
                 processors; Runtime; Solid state circuits;
                 Thermometers; Training",
}

@InProceedings{Wu:2024:CLB,
  author =       "Jiajun Wu and Mo Song and Jingmin Zhao and Hayden
                 Kwok-Hay So",
  booktitle =    "{2024 IEEE International Parallel and Distributed
                 Processing Symposium Workshops (IPDPSW)}",
  title =        "A Case for Low Bitwidth Floating Point Arithmetic on
                 {FPGA} for Transformer Based {DNN} Inference",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "178--185",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/IPDPSW63119.2024.00045",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Full stack; Hardware; Parallel processing;
                 Throughput; Transformers; Vectors",
}

@Article{Wu:2024:FPS,
  author =       "Ping-Chun Wu and Jian-Wei Su and Li-Yang Hong and
                 Jin-Sheng Ren and Chih-Han Chien and Ho-Yu Chen and
                 Chao-En Ke and Hsu-Ming Hsiao and Sih-Han Li and
                 Shyh-Shyuan Sheu and Wei-Chung Lo and Shih-Chieh Chang
                 and Chung-Chuan Lo and Ren-Shuo Liu and Chih-Cheng
                 Hsieh and Kea-Tiong Tang and Meng-Fan Chang",
  title =        "A Floating-Point {6T SRAM} In-Memory-Compute Macro
                 Using Hybrid-Domain Structure for Advanced {AI} Edge
                 Chips",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "59",
  number =       "1",
  pages =        "196--207",
  year =         "2024",
  CODEN =        "IJSCBC",
  DOI =          "https://doi.org/10.1109/JSSC.2023.3309966",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "Artificial intelligence; Artificial intelligence (AI);
                 Computational efficiency; compute-in-memory (CIM);
                 Energy efficiency; floating-point (FP); Floating-point
                 arithmetic; In-memory computing; inference; Inference
                 mechanisms; Memory management; SRAM chips; static
                 random access memory (SRAM); Time-domain analysis",
}

@Article{Wu:2024:SAM,
  author =       "Ying Wu and Chuangtao Chen and Weihua Xiao and Xuan
                 Wang and Chenyi Wen and Jie Han and Xunzhao Yin and
                 Weikang Qian and Cheng Zhuo",
  title =        "A Survey on Approximate Multiplier Designs for Energy
                 Efficiency: From Algorithms to Circuits",
  journal =      j-TODAES,
  volume =       "29",
  number =       "1",
  pages =        "23:1--23:??",
  month =        jan,
  year =         "2024",
  CODEN =        "ATASFO",
  DOI =          "https://doi.org/10.1145/3610291",
  ISSN =         "1084-4309 (print), 1557-7309 (electronic)",
  ISSN-L =       "1084-4309",
  bibdate =      "Mon Jan 15 11:14:18 MST 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/todaes.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3610291",
  abstract =     "Given the stringent requirements of energy efficiency
                 for Internet-of-Things edge devices, approximate
                 multipliers, as a basic component of many processors
                 and accelerators, have been constantly proposed and
                 studied for decades, especially in error-resilient
                 applications. The computation error and energy
                 efficiency largely depend on how and where the
                 approximation is introduced into a design. Thus, this
                 article aims to provide a comprehensive review of the
                 approximation techniques in multiplier designs ranging
                 from algorithms and architectures to circuits. We have
                 implemented representative approximate multiplier
                 designs in each category to understand the impact of
                 the design techniques on accuracy and efficiency. The
                 designs can then be effectively deployed in high-level
                 applications, such as machine learning, to gain energy
                 efficiency at the cost of slight accuracy loss.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Transact. Des. Automat. Electron. Syst.",
  articleno =    "23",
  fjournal =     "ACM Transactions on Design Automation of Electronic
                 Systems",
  journal-URL =  "https://dl.acm.org/loi/todaes",
}

@Article{Xie:2024:FRO,
  author =       "Peichen Xie and Yanjie Gao and Jilong Xue",
  title =        "{FPRev}: Revealing the Order of Floating-Point
                 Summation by Numerical Testing",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "1--20",
  day =          "1",
  month =        nov,
  year =         "2024",
  bibdate =      "Tue Jan 28 06:36:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://arxiv.org/abs/2411.00442v1",
  abstract =     "The order of floating-point summation is a key factor
                 in numerical reproducibility. However, this critical
                 information is generally unspecified and unknown for
                 most summation-based functions in numerical libraries,
                 making it challenging to migrate them to new
                 environments reproducibly. This paper presents novel,
                 non-intrusive, testing-based algorithms that can reveal
                 the order of floating-point summation by treating
                 functions as callable black boxes. By constructing
                 well-designed input that can cause the swamping
                 phenomenon of floating-point addition, we can infer the
                 order of summation from the output. We introduce FPRev,
                 a tool that implements these algorithms, and validate
                 its efficiency through extensive experiments with
                 popular numerical libraries on various CPUs and GPUs
                 (including those with Tensor Cores). FPRev reveals the
                 varying summation orders across different libraries and
                 devices, and outperforms other methods in terms of time
                 complexity. The source code of FPRev is at this
                 article's URL.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation",
}

@InProceedings{Yusupov:2024:ICA,
  author =       "Firnafas XXX. Yusupov and Mukhiddin F. Ibragimov and
                 Saidbek P. Babayazov and Kumushoy E. Niyazmetova and
                 Xaitbayeva Z. Durdona and Umidbek P. Babayazov",
  booktitle =    "{2024 IEEE 3rd International Conference on Problems of
                 Informatics, Electronics and Radio Engineering
                 (PIERE)}",
  title =        "Improving the Computing Accuracy of the {AI Ascend}
                 Processor: Research and Results",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1510--1513",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/PIERE62470.2024.10805020",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; AI Ascend Processor; Algorithm Improvement;
                 Approximation algorithms; Artificial intelligence;
                 Computer architecture; Da Vinci Architecture; FP32
                 Accuracy; Graphics processing units; Hardware; Huawei;
                 Informatics; Matrix Multiplication; Performance
                 evaluation; Semiconductor device manufacture;
                 Standards",
}

@InProceedings{Zahid:2024:TGN,
  author =       "Anwar Hossain Zahid and Ignacio Laguna and Wei Le",
  booktitle =    "{SC24-W: Workshops of the International Conference for
                 High Performance Computing, Networking, Storage and
                 Analysis}",
  title =        "Testing {GPU} Numerics: Finding Numerical Differences
                 Between {NVIDIA} and {AMD} {GPUs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "547--557",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/SCW63240.2024.00077",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Codes; CUDA; Differential testing; floating-point;
                 Graphics processing units; High performance computing;
                 Hip; HIP; Libraries; Numerical simulation;
                 Optimization; Production; random program generation;
                 Robustness; Testing",
}

@Article{Zhang:2024:DFH,
  author =       "Tingting Zhang and Zijing Niu and Jie Han",
  title =        "A Design Framework for Hardware-Efficient Logarithmic
                 Floating-Point Multipliers",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "12",
  number =       "4",
  pages =        "991--1001",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/TETC.2024.3365650",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Tue Sep 9 13:42:38 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
  keywords =     "approximate computing; approximate multiplier;
                 Artificial neural networks; Costs; error tolerance;
                 Floating-point multiplier; Hardware; Image coding; JPEG
                 compression; logarithmic multiplier; neural networks;
                 Standards; Training; Transform coding",
}

@Article{Zhang:2024:HSA,
  author =       "Zuoyan Zhang and Jinchen Xu and Jiangwei Hao and Yang
                 Qu and Haotian He and Bei Zhou",
  title =        "Hierarchical search algorithm for error detection in
                 floating-point arithmetic expressions",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "80",
  number =       "1",
  pages =        "1183--1205",
  month =        jan,
  year =         "2024",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1007/s11227-023-05523-6",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Thu Feb 15 10:23:12 MST 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsuper2020.bib",
  URL =          "https://link.springer.com/article/10.1007/s11227-023-05523-6",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Supercomputing",
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
}

@InProceedings{Zhang:2024:IFP,
  author =       "Yijia Zhang and Lingran Zhao and Shijie Cao and
                 Sicheng Zhang and Wenqiang Wang and Ting Cao and Fan
                 Yang and Mao Yang and Shanghang Zhang and Ningyi Xu",
  booktitle =    "{2024 IEEE International Conference on Multimedia and
                 Expo (ICME)}",
  title =        "Integer or Floating Point? {New} Outlooks for Low-Bit
                 Quantization on Large Language Models",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--6",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/ICME57554.2024.10688089",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Costs; Floating Point; Graphics processing units;
                 Hardware; Large Language Model; Large language models;
                 Low-bit Quantization; Multimedia systems; Quantization
                 (signal); Tensors",
}

@Article{Zhao:2024:ETL,
  author =       "Guangchao Zhao and Zhiwei Zeng and Xingli Wang and
                 Abdelrahman G. Qoutb and Philippe Coquet and Eby G.
                 Friedman and Beng Kang Tay and Mingqiang Huang",
  title =        "Efficient Ternary Logic Circuits Optimized by Ternary
                 Arithmetic Algorithms",
  journal =      j-IEEE-TRANS-EMERG-TOP-COMPUT,
  volume =       "12",
  number =       "3",
  pages =        "826--839",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/TETC.2023.3321050",
  ISSN =         "2168-6750 (print), 2376-4562 (electronic)",
  bibdate =      "Tue Sep 9 13:42:38 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Emerging Topics in Computing",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6245516",
  keywords =     "Adders; Arithmetic; CMOS based ternary logic;
                 Inverters; Logic gates; Multi-valued logic; Multivalued
                 logic; Standards; ternary adders; ternary arithmetic
                 circuits; ternary multipliers; Transistors",
}

@TechReport{Zimmermann:2024:NVD,
  author =       "Paul Zimmermann",
  title =        "Note on the {Veltkamp\slash Dekker} Algorithms with
                 Directed Roundings",
  type =         "Report",
  number =       "hal-04480440",
  institution =  "Universit{\'e} de Lorraine, CNRS, Inria, LORIA",
  address =      "Metz, France",
  day =          "29",
  month =        feb,
  year =         "2024",
  bibdate =      "Thu Aug 01 17:14:10 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://inria.hal.science/hal-04480440",
  abstract =     "The Veltkamp\slash Dekker algorithms are very useful
                 for double-double arithmetic, when no fused
                 multiply-add is available in hardware. Their analysis
                 is well-known for rounding to nearest-even. We study
                 how they behave with directed roundings in radix 2.",
  acknowledgement = ack-nhfb,
  keywords =     "CARAMBA --- Cryptology, arithmetic: algebraic methods
                 for better algorithms",
}

@Article{Zou:2024:PRE,
  author =       "Qinmeng Zou",
  title =        "Probabilistic Rounding Error Analysis of Modified
                 {Gram--Schmidt}",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "45",
  number =       "2",
  pages =        "1076--1088",
  month =        may,
  year =         "2024",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/23m1585817",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Fri May 31 08:23:04 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "SIAM J. Matrix Anal. Appl.",
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Misc{Advanpix:2025:MCT,
  author =       "{Advanpix}",
  title =        "Multiprecision Computing Toolbox User's Manual",
  howpublished = "Commercial Web site",
  day =          "23",
  month =        feb,
  year =         "2025",
  bibdate =      "Wed Aug 27 12:35:36 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.advanpix.com/documentation/users-manual/",
  acknowledgement = ack-nhfb,
}

@InProceedings{Ahlback:2025:FBA,
  author =       "Albin Ahlback and Fredrik Johansson",
  title =        "Fast Basecases for Arbitrary-Size Multiplication",
  crossref =     "IEEE:2025:PIS",
  pages =        "53--60",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00018F",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@Article{Ahmadi-Pour:2025:FLF,
  author =       "Sallar Ahmadi-Pour and Sajjad Parvin and Chandan Kumar
                 Jha and Rolf Drechsler",
  title =        "{FV-LIDAC}: Formally Verified Library of Input Data
                 Aware Approximate Arithmetic Circuits",
  journal =      j-TODAES,
  volume =       "30",
  number =       "4",
  pages =        "64:1--64:??",
  month =        jul,
  year =         "2025",
  CODEN =        "ATASFO",
  DOI =          "https://doi.org/10.1145/3744710",
  ISSN =         "1084-4309 (print), 1557-7309 (electronic)",
  ISSN-L =       "1084-4309",
  bibdate =      "Sat Jul 26 08:03:38 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/todaes.bib",
  abstract =     "Approximate circuits have become ubiquitous in
                 error-resilient applications. These circuits provide
                 large reductions in area, power, and delay at the cost
                 of erroneous computations. The error-resilient
                 applications produce acceptable output quality, even
                 \ldots{}",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Transact. Des. Automat. Electron. Syst.",
  articleno =    "64",
  fjournal =     "ACM Transactions on Design Automation of Electronic
                 Systems",
  journal-URL =  "https://dl.acm.org/loi/todaes",
}

@Article{Allred:2025:FNT,
  author =       "Taylor Allred and Xinyi Li and Ashton Wiersdorf and
                 Ben Greenman and Ganesh Gopalakrishnan",
  title =        "{FlowFPX}: Nimble Tools for Debugging Floating-Point
                 Exceptions",
  journal =      "Proceedings of the {JuliaCon} Conferences",
  volume =       "7",
  number =       "67",
  pages =        "148:1--148:8",
  year =         "2025",
  DOI =          "https://doi.org/10.21105/jcon.00148",
  bibdate =      "Wed Jan 22 13:56:37 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/julia.bib",
  abstract =     "Reliable numerical computations are central to
                 scientific computing, but the floating-point arithmetic
                 that enables large-scale models is error-prone. Numeric
                 exceptions are a common occurrence and can propagate
                 through code, leading to flawed results. This paper
                 presents FlowFPX, a toolkit for systematically
                 debugging floating-point exceptions by recording their
                 flow, coalescing exception contexts, and fuzzing in
                 select locations. These tools help scientists discover
                 when exceptions happen and track down their origin,
                 smoothing the way to a reliable codebase.",
  acknowledgement = ack-nhfb,
  keywords =     "debugging; floating-point; Julia",
  ORCID-numbers = "Allred, Taylor/0009-0000-7238-1816; Li,
                 Xinyi/0009-0005-7276-7715; Wiersdorf,
                 Ashton/0000-0001-5524-7930; Greenman,
                 Ben/0000-0001-7078-9287; Gopalakrishnan,
                 Ganesh/0000-0002-4161-9278",
}

@InProceedings{Anonymous:2025:AI,
  author =       "Anonymous",
  title =        "Author Index",
  crossref =     "IEEE:2025:PIS",
  pages =        "161--161",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00033",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@Misc{Anonymous:2025:AMS,
  author =       "Anonymous",
  title =        "{[ARM} math software library]",
  howpublished = "Web site",
  year =         "2025",
  bibdate =      "Fri Nov 14 15:51:30 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://github.com/ARM-software/optimized-routines/tree/master/math/",
  acknowledgement = ack-nhfb,
  remark =       "Open-source math library for aarch64 (ARM64) CPUs,
                 with both scalar and vector variants. The scalar code
                 is claimed to be largely CPU architecture independent,
                 while the vector code is specific to ARM systems.
                 Polynomial approximations are generated by the Sollya
                 library.",
}

@InProceedings{Anonymous:2025:CP,
  author =       "Anonymous",
  title =        "Copyright page",
  crossref =     "IEEE:2025:PIS",
  pages =        "1--1",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00003",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@Misc{Anonymous:2025:IMPa,
  author =       "Anonymous",
  title =        "{Intel 8087 Milestone} plaque dedication summary",
  howpublished = "Video (2m)",
  month =        nov,
  year =         "2025",
  bibdate =      "Fri Nov 14 06:20:52 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://youtu.be/jCn24WbWRuQ",
  acknowledgement = ack-nhfb,
  remark =       "Recorded in Haifa, Israel, in Hebrew, with English
                 subtitles.",
}

@Misc{Anonymous:2025:IMPb,
  author =       "Anonymous",
  title =        "{Intel 8087 Milestone} plaque dedication",
  howpublished = "Video (44m)",
  month =        nov,
  year =         "2025",
  bibdate =      "Fri Nov 14 06:20:52 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://youtu.be/N1mH3E3nIKI",
  acknowledgement = ack-nhfb,
  remark =       "Recorded in Haifa, Israel, in Hebrew, with English
                 subtitles. There is a companion plaque celebrating the
                 birthplace of Silicon Valley, placed in May 2018, at
                 391 San Antonio Road, Los Altos, CA [about 6km
                 southeast of Stanford University], the original
                 location of Shockley Semiconductor Laboratory, now
                 replaced by an office tower. Around the corner to the
                 south is another plaque commemorating Moore's Law,
                 published in 1965 \cite{Moore:1965:CMC}.",
}

@InProceedings{Anonymous:2025:MCC,
  author =       "Anonymous",
  title =        "Message from {Conference Chairs: ARITH 2025}",
  crossref =     "IEEE:2025:PIS",
  pages =        "vii--vii",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00005",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@InProceedings{Anonymous:2025:OCA,
  author =       "Anonymous",
  title =        "{Organizing Committee: ARITH 2025}",
  crossref =     "IEEE:2025:PIS",
  pages =        "viii--viii",
  year =         "2025",
  DOI =          "https://doi.ogr/10.1109/arith64983.2025.00006",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@InProceedings{Anonymous:2025:PCA,
  author =       "Anonymous",
  title =        "{Program Committee: ARITH 2025}",
  crossref =     "IEEE:2025:PIS",
  pages =        "xi--xi",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00008",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@Misc{Anonymous:2025:PDL,
  author =       "Anonymous",
  title =        "Prix du logiciel libre de recherche: {GNU MPFR} ---
                 Calcul scientifique en pr{\'e}cision arbitraire.
                 ({French}) [Award for Free Research Software: {GNU
                 MPFR} --- arbitrary precision scientific computing]",
  howpublished = "Web site",
  month =        dec,
  year =         "2025",
  bibdate =      "Wed Dec 03 13:55:33 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/gnu.bib",
  URL =          "https://www.enseignementsup-recherche.gouv.fr/fr/remise-des-prix-science-ouverte-edition-2025-100469",
  acknowledgement = ack-nhfb,
  language =     "French",
}

@InProceedings{Anonymous:2025:RLA,
  author =       "Anonymous",
  title =        "{Reviewers List: ARITH 2025}",
  crossref =     "IEEE:2025:PIS",
  pages =        "xii--xiv",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00009",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@InProceedings{Anonymous:2025:SA,
  author =       "Anonymous",
  title =        "{Sponsors: ARITH 2025}",
  crossref =     "IEEE:2025:PIS",
  pages =        "xiv--xiv",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00010",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@InProceedings{Anonymous:2025:SCA,
  author =       "Anonymous",
  title =        "{Steering Committee: ARITH 2025}",
  crossref =     "IEEE:2025:PIS",
  pages =        "ix--x",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00007",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@InProceedings{Anonymous:2025:TC,
  author =       "Anonymous",
  title =        "Table of contents",
  crossref =     "IEEE:2025:PIS",
  pages =        "iv--vi",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00004",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@InProceedings{Anonymous:2025:TPPa,
  author =       "Anonymous",
  title =        "{[Title} page 1: Proceedings {2025 IEEE 32nd Symposium
                 on Computer Arithmetic: ARITH 2025}",
  crossref =     "IEEE:2025:PIS",
  pages =        "1--1",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00001",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@InProceedings{Anonymous:2025:TPPb,
  author =       "Anonymous",
  title =        "{[Title} page 2: Proceedings {2025 IEEE 32nd Symposium
                 on Computer Arithmetic: ARITH 2025}",
  crossref =     "IEEE:2025:PIS",
  pages =        "1--1",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00002",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@Manual{Arm:2025:AAR,
  author =       "{Arm}",
  title =        "{Arm} Architecture Reference Manual for {A}-profile
                 architecture",
  number =       "ARM DDI 0487",
  organization = "Arm Limited",
  address =      "Cambridge, UK",
  pages =        "xl + 14694",
  day =          "30",
  month =        apr,
  year =         "2025",
  bibdate =      "Mon Jul 28 11:29:22 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://developer.arm.com/documentation/ddi0487/lb",
  acknowledgement = ack-nhfb,
  keywords =     "correct rounding; double rounding; round-to-odd mode
                 (RO(x))",
  remark =       "Section A1.5.8.6 Round to Odd says:\par ``Round to Odd
                 is not defined by IEEE 754.\par

                 Round to Odd rounds the exact result of a
                 floating-point operation to a value that is
                 representable in the destination format. If the result
                 of the rounding is inexact, the least significant bit
                 of the mantissa is forced to 1.\par

                 The following instructions use Round to Odd:\par

                 * BFloat16 instructions defined in BFloat16 behaviors
                 for instructions that compute sum-of-products.\par

                 * FCVTXN, FCVTXN2, FCVTX, and FCVTXNT, for which Round
                 to Odd rounding can avoid double rounding errors when a
                 floating-point value is converted to a lower precision
                 destination format through an intermediate precision
                 format.''",
}

@Article{Banks:2025:GCHa,
  author =       "Jess Banks and Jorge Garza-Vargas and Nikhil
                 Srivastava",
  title =        "Global Convergence of {Hessenberg} Shifted {QR} {II}:
                 Finite Arithmetic",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "46",
  number =       "2",
  pages =        "1168--1211",
  month =        "????",
  year =         "2025",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/23M1557532",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Thu Oct 16 12:49:41 MDT 2025",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/46/2;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  URL =          "https://epubs.siam.org/doi/10.1137/23M1557532",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@InProceedings{Bazzi:2025:RPI,
  author =       "Jinane Bazzi and Mohammed E. Fouda and Ahmed Eltawil",
  booktitle =    "{2025 IEEE International Symposium on Circuits and
                 Systems (ISCAS)}",
  title =        "Reconfigurable Precision {INT4-8\slash FP8} Digital
                 Compute-in-Memory Macro for {AI} Acceleration",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--5",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/ISCAS56072.2025.11044064",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Artificial neural networks; CMOS technology;
                 Computational efficiency; Computational modeling;
                 Compute-in-memory; Computer architecture; deep neural
                 network; Energy efficiency; floating-point; In-memory
                 computing; Integrated circuit modeling;
                 multiply-accumulate; reconfigurable macro; Resource
                 management; Throughput",
}

@InProceedings{Bertoni:2025:MMM,
  author =       "Colleen Bertoni and Thomas Applencourt and Longfei Gao
                 and Ti Leggett",
  booktitle =    "{2025 IEEE International Parallel and Distributed
                 Processing Symposium Workshops (IPDPSW)}",
  title =        "Millions of Matrix-Multiplications: {GEMM} Variations
                 on {Aurora}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "850--856",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/IPDPSW66978.2025.00135",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Aurora; Benchmark testing; Gaussian distribution;
                 GEMM; Graphics processing units; Ion radiation effects;
                 Kernel; Lower bound; Magnetosphere; Manufacturing;
                 Particle measurements; Supercomputers; Variation",
}

@InProceedings{Bouarah:2025:HFP,
  author =       "Romain Bouarah and Florent {De Dinechin}",
  title =        "Hardware Fixed-Point {2D} and {3D} norms",
  crossref =     "IEEE:2025:PIS",
  pages =        "29--36",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00015",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@Article{Bunger:2025:IEB,
  author =       "Florian B{\"u}nger",
  title =        "Improved Error Bounds for Floating-Point Quotients",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "74",
  number =       "11",
  pages =        "3559--3567",
  month =        nov,
  year =         "2025",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2025.3585341",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Oct 15 16:45:16 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Artificial intelligence; Computers; Data mining;
                 Floating-point quotients; Gold; IEEE 754 standard;
                 Roundoff errors; Standards; Surveys; Taylor series;
                 Training; Wilkinson-type relative error estimates;
                 Zirconium",
}

@InProceedings{Caprioli:2025:FFC,
  author =       "Paul Caprioli",
  title =        "On the Flop and Flap Counts of the 2,8-Split-Radix
                 {FFT}",
  crossref =     "IEEE:2025:PIS",
  pages =        "45--52",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00017",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@InProceedings{Chen:2025:FBA,
  author =       "Ruiqi Chen and Yangxintong Lyu and Han Bao and Jiayu
                 Liu and Yanxiang Zhu and Shidi Tang and Ming Ling and
                 Bruno {Da Silva}",
  booktitle =    "{2025 IEEE 33rd Annual International Symposium on
                 Field-Programmable Custom Computing Machines (FCCM)}",
  title =        "{FPGA}-Based Approximate Multiplier for {FP8}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "01--09",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/FCCM62733.2025.00079",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Approximate computing; Approximation methods;
                 Artificial neural networks; Benchmark testing; Codes;
                 Dynamic range; Field programmable gate arrays; FP8;
                 FPGA; L-mul; Layout; multiplier; Power demand; Resource
                 management; Table lookup",
}

@InProceedings{Corbineau:2025:CRD,
  author =       "S{\'e}l{\`e}ne Corbineau and Paul Zimmermann",
  title =        "Correct Rounding in Double Extended Precision",
  crossref =     "IEEE:2025:PIS",
  pages =        "117--124",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00027",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@InProceedings{Crafton:2025:FPF,
  author =       "Brian Crafton and Xiaochen Peng and Xiaoyu Sun and
                 Ashwin Lele and Bo Zhang and Win-San Khwa and Kerem
                 Akarvardar",
  booktitle =    "{2025 62nd ACM/IEEE Design Automation Conference
                 (DAC)}",
  title =        "Finding the {Pareto} Frontier of Low-Precision Data
                 Formats and {MAC} Architecture for {LLM} Inference",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--7",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/DAC63849.2025.11132989",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Artificial intelligence; Design automation;
                 Noise; Pareto optimization; Quantization (signal)",
}

@Article{Cui:2025:PES,
  author =       "Mengqi Cui and Jinchen Xu and Yuchang Zhou and Hongru
                 Yang and Liguang Ji and Bei Zhou",
  title =        "{PESA}: error sensitivity analysis tool for
                 floating-point computational programs",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "81",
  number =       "3",
  pages =        "??--??",
  month =        feb,
  year =         "2025",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1007/s11227-025-06962-z",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Wed Feb 19 09:44:27 MST 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsuper2020.bib",
  URL =          "https://link.springer.com/article/10.1007/s11227-025-06962-z",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Supercomputing",
  articleno =    "477",
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
}

@Misc{Darcy:2025:FJ,
  author =       "Joseph Darcy",
  title =        "Float16.java",
  howpublished = "Web site",
  year =         "2025",
  bibdate =      "Mon Mar 10 13:45:31 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://github.com/openjdk/jdk/blob/dbdbbd473061d7e8077ed07ccc6b03065a8c2ffc/src/jdk.incubator.vector/share/classes/jdk/incubator/vector/Float16.java#L1240",
  acknowledgement = ack-nhfb,
  remark =       "The code comments provide an informal analysis that
                 Float16 fused multiply-add (FMA) can be correctly
                 implemented in IEEE 754 Binary64 arithmetic, including
                 for NaN, Infinity, and signed zero arguments.",
}

@InProceedings{Desrentes:2025:DWD,
  author =       "Or{\'e}gane Desrentes and Beno{\^\i}t Dupont {De
                 Dinechin} and Florent {De Dinechin}",
  title =        "Double-Word Decomposition in a Combined {FP16}, {BF16}
                 and {FP32} Dot Product Add Operator",
  crossref =     "IEEE:2025:PIS",
  pages =        "73--80",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00021",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32; BF16; Deep learning; Digital
                 arithmetic; Dot product; Dynamic range; FP16; FP32;
                 Matrix decomposition; Software; Standards; Vectors",
}

@InProceedings{Devi:2025:PFS,
  author =       "Dantu Nandini Devi and Madhav Rao",
  booktitle =    "{2025 IEEE International Symposium on Circuits and
                 Systems (ISCAS)}",
  title =        "Precision-Factored Systolic Arrays: Balancing Accuracy
                 and Efficiency in Floating-Point Computations for
                 {CNNs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--5",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/ISCAS56072.2025.11043892",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Approximate computing; Approximate
                 Computing; Delays; Floating point for-mats; Genetic
                 algorithms; Image processing; Kernel; Multipliers;
                 Non-Sorting Genetic Algorithm II (NSGA II);
                 Optimization; Power demand; Silicon; Systolic arrays;
                 VGG-11 Kernels",
}

@Article{Dexter:2025:SRI,
  author =       "Gregory Dexter and Christos Boutsikas and Linkai Ma
                 and Ilse C. F. Ipsen and Petros Drineas",
  title =        "Stochastic Rounding Implicitly Regularizes
                 Tall-and-Thin Matrices",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "46",
  number =       "1",
  pages =        "341--369",
  month =        "????",
  year =         "2025",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/24M1647679",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Thu Oct 16 12:49:38 MDT 2025",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/46/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  URL =          "https://epubs.siam.org/doi/10.1137/24M1647679",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{ElArar:2025:PEA,
  author =       "El-Mehdi {El Arar} and Massimiliano Fasi and
                 Silviu-Ioan Filip and Mantas Mikaitis",
  title =        "Probabilistic Error Analysis of Limited-Precision
                 Stochastic Rounding",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "47",
  number =       "5",
  pages =        "B1227--B1249",
  month =        "????",
  year =         "2025",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/24M1681458",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Sat Oct 18 11:20:14 MDT 2025",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/47/5;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  URL =          "https://epubs.siam.org/doi/10.1137/24M1681458",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  keywords =     "stochastic rounding",
}

@InProceedings{Fitzgibbon:2025:SRF,
  author =       "Andrew Fitzgibbon and Stephen Felix",
  title =        "On Stochastic Rounding with Few Random Bits",
  crossref =     "IEEE:2025:PIS",
  pages =        "133--140",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00029",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@TechReport{Fog:2025:PFP,
  author =       "Agner Fog",
  title =        "Parallel floating point exception tracking and {NaN}
                 propagation",
  type =         "Report",
  institution =  "Technical University of Denmark",
  address =      "Lyngby, Denmark",
  pages =        "11",
  day =          "9",
  month =        may,
  year =         "2025",
  bibdate =      "Fri Oct 10 07:58:02 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.agner.org/optimize/nan_propagation.pdf",
  abstract =     "The most common methods for detecting errors and
                 exceptions in floating point computing are based on
                 either exception trapping or a global status register.
                 Both methods are relying on sequential logic. These
                 methods are inefficient in modern systems that use
                 out-of-order execution and
                 single-instruction-multiple-data (SIMD) parallelism for
                 improving performance. It would be more efficient to
                 implement a system that attaches the status after an
                 exception to the result register and lets this
                 information follow the same data path and the same form
                 of parallelism as the normal data flow. This can be
                 achieved either by attaching metadata tags to the
                 result or by generating NaN results containing
                 diagnostic payloads. These metadata tags or NaN
                 payloads can propagate through subsequent calculations.
                 Such a system would be more efficient than traps and
                 global status flags.\par

                 Advantages and disadvantages of each solution are
                 discussed, and examples of experimental implementations
                 are presented here.",
  acknowledgement = ack-nhfb,
}

@Article{Fornt:2025:MGE,
  author =       "Jordi Fornt and Enrico Reggiani and Pau
                 Fontova-Must{\'e} and Narc{\'\i}s Rodas and Alessandro
                 Pappalardo and Osman Sabri Unsal and Adri{\'a}n Cristal
                 Kestelman and Josep Altet and Francesc Moll and Jaume
                 Abella",
  title =        "{Mix-GEMM}: Extending {RISC-V CPUs} for
                 Energy-Efficient Mixed-Precision {DNN} Inference Using
                 Binary Segmentation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "74",
  number =       "2",
  pages =        "582--596",
  year =         "2025",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2024.3500369",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Artificial neural networks; binary segmentation;
                 Computational modeling; Computer architecture;
                 Computers; Deep neural networks; energy efficiency;
                 Energy efficiency; neural accelerators; Pipelines;
                 Program processors; Quantization (signal); RISC-V
                 extensions; Single instruction multiple data;
                 Software",
}

@Article{Gao:2025:PPA,
  author =       "Jianhua Gao and Zhi Zhou and Xingze Huang and Juan
                 Wang and Yizhuo Wang and Weixing Ji",
  title =        "{PTPS}: Precision-Aware Task Partitioning and
                 Scheduling for {SpMV} on {CPU-FPGA} Heterogeneous
                 Platforms",
  journal =      j-IEEE-TRANS-CAD-ICS,
  volume =       "44",
  number =       "10",
  pages =        "3804--3815",
  year =         "2025",
  CODEN =        "ITCSDI",
  DOI =          "https://doi.org/10.1109/TCAD.2025.3554144",
  ISSN =         "0278-0070 (print), 1937-4151 (electronic)",
  ISSN-L =       "0278-0070",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computer-Aided Design of
                 Integrated Circuits and Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=43",
  keywords =     "Arrays; Central Processing Unit; Computational
                 efficiency; Costs; Field programmable gate arrays;
                 FPGA; Graphics processing units; heterogeneous
                 architecture; Memory management; mixed precision;
                 Optimization; Sparse matrices; SpMV; task scheduling;
                 Vectors",
}

@InProceedings{Garcia:2025:HAT,
  author =       "R{\'e}mi Garcia and L{\'e}o Pradels and Silviu-Ioan
                 Filip and Olivier Sentieys",
  title =        "Hardware-Aware Training for Multiplierless
                 Convolutional Neural Networks",
  crossref =     "IEEE:2025:PIS",
  pages =        "9--16",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00012",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@TechReport{Gladman:2025:AMFa,
  author =       "Brian Gladman and Vincenzo Innocente and John Mather
                 and Paul Zimmermann",
  title =        "Accuracy of Mathematical Functions in Single, Double,
                 Double Extended, and Quadruple Precision",
  institution =  "????",
  pages =        "27",
  day =          "10",
  month =        feb,
  year =         "2025",
  bibdate =      "Mon Feb 10 10:00:22 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://members.loria.fr/PZimmermann/papers/accuracy.pdf",
  acknowledgement = ack-nhfb,
  remark =       "Tabular comparison of AMD, Apple, ARM, CUDA, FreeBSD,
                 GNU, Intel, LLVM, Microsoft Musl, Newlib, OpenLibm,
                 RadeonOpenCompute (ROCm), and RedHat -lm libraries for
                 correct rounding, versus results from MPFR.",
}

@TechReport{Gladman:2025:AMFb,
  author =       "Brian Gladman and Vincenzo Innocente and John Mather
                 and Paul Zimmermann",
  title =        "Accuracy of Mathematical Functions in Single, Double,
                 Double Extended, and Quadruple Precision",
  institution =  "????",
  pages =        "29",
  day =          "27",
  month =        aug,
  year =         "2025",
  bibdate =      "Wed Aug 27 11:11:51 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://members.loria.fr/PZimmermann/papers/accuracy.pdf",
  acknowledgement = ack-nhfb,
  remark =       "Tabular comparison of AMD, Apple, ARM, CUDA, FreeBSD,
                 GNU, Intel, LLVM, Microsoft Musl, Newlib, OpenLibm,
                 RadeonOpenCompute (ROCm), and RedHat -lm libraries for
                 correct rounding, versus results from MPFR. The e-mail
                 announcement reports: ``Main changes in this update: *
                 we have added compoundn, pown and rootn; * GNU libc is
                 the first library to provide all new C23 functions; *
                 GNU libc now provides 31 correctly-rounded functions in
                 single precision.''",
}

@InProceedings{Gorgin:2025:GMA,
  author =       "Saeid Gorgin and Amirhossein Sadr and Dara Rahmati and
                 Jungrae Kim",
  title =        "A Generic Modulo- $ (2^n \pm \delta) $ Addition
                 Algorithm via Two-Valued Digit Encoding",
  crossref =     "IEEE:2025:PIS",
  pages =        "85--92",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00023",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@Article{Graillat:2025:CDF,
  author =       "Stef Graillat and Theo Mary",
  title =        "Condense and Distill: Fast Distillation of Large
                 Floating-Point Sums via Condensation",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "47",
  number =       "2",
  pages =        "B583--B594",
  month =        "????",
  year =         "2025",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/24M1647217",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Sat Oct 18 11:20:04 MDT 2025",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/47/2;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  URL =          "https://epubs.siam.org/doi/10.1137/24M1647217",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}

@TechReport{Graillat:2025:EFCa,
  author =       "Stef Graillat and Jean-Michel Muller",
  title =        "Emulation of the {FMA} and the correctly-rounded sum
                 of three numbers in rounding-to-nearest floating-point
                 arithmetic",
  type =         "Report",
  number =       "hal-04575249",
  institution =  "Sorbonne Universit{\'e}, CNRS, LIP6 and CNR,
                 Laboratoire LIP, Universit{\'e} de Lyon",
  address =      "Paris, France and Lyon, France",
  pages =        "29",
  day =          "17",
  month =        may,
  year =         "2025",
  bibdate =      "Mon Jul 14 06:27:51 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://hal.science/hal-04575249v2",
  abstract =     "We present algorithms that allow one to emulate the
                 fused multiply-add (FMA) instruction and the
                 correctly-rounded sum of three numbers (ADD3) in binary
                 floating-point arithmetic, using only
                 rounding-to-nearest floating- point additions,
                 multiplications, and comparisons. We then introduce
                 variants of these algorithm that make it possible to
                 compute the error of an ADD3 or FMA operation.",
  acknowledgement = ack-nhfb,
  keywords =     "ADD3; double-word arithmetic; Error-free transforms;
                 Floating-point arithmetic; FMA; fused multiply-add;
                 triple-word arithmetic",
  remark =       "The appendix supplies C implementations of the
                 complicated formal algorithms.",
}

@Article{Graillat:2025:EFCb,
  author =       "Stef Graillat and Jean-Michel Muller",
  title =        "Emulation of the {FMA} and the correctly-rounded sum
                 of three numbers in rounding-to-nearest floating-point
                 arithmetic",
  journal =      j-NUM-MATH,
  volume =       "157",
  number =       "5",
  pages =        "1615--1641",
  month =        oct,
  year =         "2025",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/s00211-025-01487-2",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Wed Oct 15 05:40:30 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath2020.bib",
  URL =          "https://link.springer.com/article/10.1007/s00211-025-01487-2",
  acknowledgement = ack-nhfb,
  ajournal =     "Num. Math.",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  online-date =  "09 September 2025",
}

@TechReport{Graillat:2025:EFF,
  author =       "Stef Graillat and Jean-Michel Muller",
  title =        "Emulation of {3Sum}, {4Sum}, the {FMA} and the {FD2}
                 instructions in rounded-to-nearest floating-point
                 arithmetic",
  type =         "Report",
  number =       "hal-04624238",
  institution =  "Sorbonne Universit{\'e}, CNRS, LIP6 and CNR,
                 Laboratoire LIP, Universit{\'e} de Lyon",
  address =      "Paris, France and Lyon, France",
  pages =        "21",
  day =          "25",
  month =        jun,
  year =         "2025",
  bibdate =      "Mon Jul 14 06:27:51 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://hal.science/hal-04624238v1",
  abstract =     "We give high level algorithms that make it possible to
                 compute the rounded-to-nearest sum of 3 or 4
                 floating-point numbers in binary floating-point
                 arithmetic. They can easily be adapted to emulate the
                 FMA ($ a b + c $ correctly rounded) and FD2 ($ a b + c
                 d $ correctly rounded) instructions.",
  acknowledgement = ack-nhfb,
  keywords =     "accurate floating-point summation; double-word
                 arithmetic; Error-free transforms; FD2; Floating-point
                 arithmetic; FMA; fused dot-product; fused multiply-add;
                 Sum3; Sum4",
}

@InProceedings{Haghi:2025:DTQ,
  author =       "Pouya Haghi and Ali Falahati and Zahra Azad and
                 Chunshu Wu and Ruibing Song and Chuan Liu and Ang Li
                 and Tong Geng",
  booktitle =    "{2025 62nd ACM/IEEE Design Automation Conference
                 (DAC)}",
  title =        "{DM-Tune}: Quantizing Diffusion Models with
                 Mixture-of-{Gaussian} Guided Noise Tuning",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--7",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/DAC63849.2025.11132501",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Diffusion models; Diffusion Models; Diversity
                 reception; GPU; Graphics processing units; Image
                 quality; Image synthesis; Kernel; Mixed-precision;
                 Noise; Quantization; Quantization (signal); Runtime;
                 Text to image",
}

@Article{Haq:2025:MIF,
  author =       "Sami Ul Haq and Aiman H. El-Maleh and Ali Alsuwaiyan",
  title =        "Multiple-Input Floating-Point Adders: A Comprehensive
                 Review",
  journal =      j-IEEE-ACCESS,
  volume =       "13",
  pages =        "91012--91024",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/ACCESS.2025.3572430",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Tue Sep 30 17:30:28 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "Adders; Complexity theory; Computational modeling;
                 Computer architecture; floating-point adders;
                 Floating-point arithmetic; Hardware; high-performance
                 computing; Machine learning; multiple-input
                 floating-point adders; Reviews; Standards; Throughput",
}

@Article{Hsu:2025:NFP,
  author =       "Hung-Hsi Hsu and Tai-Hao Wen and Win-San Khwa and
                 Wei-Hsing Huang and Zhao-En Ke and Yu-Hsiang Chin and
                 Hua-Jin Wen and Yu-Chen Chang and Wei-Ting Hsu and
                 Ashwin Sanjay Lele and Bo Zhang and Ping-Sheng Wu and
                 Chung-Chuan Lo and Ren-Shuo Liu and Chih-Cheng Hsieh
                 and Kea-Tiong Tang and Shih-Hsin Teng and Chung-Cheng
                 Chou and Yu-Der Chih and Tsung-Yung Jonathan Chang and
                 Meng-Fan Chang",
  title =        "A 22 nm Floating-Point {ReRAM} Compute-in-Memory Macro
                 Using Residue-Shared {ADC} for {AI} Edge Device",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "60",
  number =       "1",
  pages =        "171--183",
  year =         "2025",
  CODEN =        "IJSCBC",
  DOI =          "https://doi.org/10.1109/JSSC.2024.3470211",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "Accuracy; Artificial intelligence; Artificial
                 intelligence (AI); Common Information Model
                 (computing); Companies; compute-in-memory (CIM); Energy
                 consumption; floating-point (FP); In-memory computing;
                 Kernel; multiply-and-accumulate (MAC); Neural networks;
                 Nonvolatile memory; residue analog-to-digital converter
                 (ADC); resistive random access memory (ReRAM);
                 System-on-chip",
}

@InProceedings{Hubner:2025:AVO,
  author =       "Paul H{\"u}bner and Andong Hu and Ivy Peng and Stefano
                 Markidis",
  booktitle =    "{2025 IEEE International Parallel and Distributed
                 Processing Symposium Workshops (IPDPSW)}",
  title =        "{Apple} vs. Oranges: Evaluating the {Apple} Silicon
                 {M}-Series {SoCs} for {HPC} Performance and
                 Efficiency",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "45--54",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/IPDPSW66978.2025.00013",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Apple Silicon M-Series GPU Performance; ARM-based SoC;
                 Bandwidth; Graphics processing units; M1; M2; M3; M4
                 Architecture; Memory architecture; Memory management;
                 Metals; Power demand; Power measurement; Reviews;
                 Semiconductor device measurement; Silicon",
}

@Article{Imbach:2025:FER,
  author =       "R{\'e}mi Imbach and Guillaume Moroz",
  title =        "Fast evaluation and root finding for polynomials with
                 floating-point coefficients",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "127",
  number =       "??",
  pages =        "??--??",
  month =        mar # "\slash " # apr,
  year =         "2025",
  CODEN =        "JSYCEH",
  DOI =          "https://doi.org/10.1016/j.jsc.2024.102372",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  bibdate =      "Fri Sep 6 08:44:41 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0747717124000762",
  acknowledgement = ack-nhfb,
  articleno =    "102372",
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171",
}

@InProceedings{Islamoglu:2025:MRV,
  author =       "Gamze {\.I}slamo{\u{g}}lu and Luca Bertaccini and
                 Arpan Suravi Prasad and Francesco Conti and Angelo
                 Garofalo and Luca Benini",
  booktitle =    "{2025 IEEE 36th International Conference on
                 Application-specific Systems, Architectures and
                 Processors (ASAP)}",
  title =        "{MXDOTP}: a {RISC-V ISA} Extension for Enabling
                 Microscaling ({MX}) Floating-Point Dot Products",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "81--84",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/ASAP65064.2025.00021",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Artificial intelligence; Energy efficiency; FinFETs;
                 Kernel; Linear algebra; Program processors; Registers;
                 Semantics; Software; Systems architecture",
}

@Article{Jaberipur:2025:BMA,
  author =       "Ghassem Jaberipur and Elham Rahman and Jeong-A Lee",
  title =        "Balanced Modular Addition for the Moduli Set $ \{ 2^q,
                 2^q \mp 1, 2^{2q} + 1 \} {2q, 2q\mp 1, 22q + 1}$ via
                 Moduli-$( 2^q \mp \sqrt {-1} 2q\mp - 1)$ Adders",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "74",
  number =       "1",
  pages =        "316--324",
  month =        jan,
  year =         "2025",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2024.3461235",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Mar 14 07:34:19 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Adders; Arithmetic; balanced residue channels;
                 complex-number moduli; Computers; Converters; Costs;
                 Delays; Dynamic range; multi-operand modular adders;
                 Residue number systems",
}

@InProceedings{Jeannerod:2025:FR,
  author =       "Claude-Pierre Jeannerod and Paul Zimmermann",
  title =        "{FastTwoSum} revisited",
  crossref =     "IEEE:2025:PIS",
  pages =        "141--148",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00030",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@InProceedings{Joseph:2025:FPC,
  author =       "Nimmy Joseph and Joji Daniel and Padmakumar K and
                 Jayalekshmi L",
  booktitle =    "{2025 6th International Conference on Control,
                 Communication and Computing (ICCC)}",
  title =        "Floating-Point {CORDIC} Processor in Hyperbolic
                 Coordinate System",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--6",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/ICCC64910.2025.11077237",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Cordic; FPU; Hardware; ISA; Process control;
                 Processor; Vectors",
}

@InProceedings{Joshi:2025:DIF,
  author =       "Rajaswini P. Joshi and Anand N and Saurabh Kesari and
                 Shashank Singh and Ravi Ranjan and Jayaraj U. Kidav",
  booktitle =    "{2025 6th International Conference on Intelligent
                 Communication Technologies and Virtual Mobile Networks
                 (ICICV)}",
  title =        "Design and Implementation of {FP32 MAC} for {DNN}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1397--1402",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/ICICV64824.2025.11085483",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Adders; Artificial neural networks; Computer
                 architecture; Dadda multiplier; Deep learning; DNN
                 acceleration; Field programmable gate arrays; FP32 MAC
                 unit; FPGA; Hardware acceleration; IEEE 754
                 floating-point; Kogge-Stone adder; Logic; Low latency
                 communication; Pipeline processing; RISC-V processor;
                 Throughput",
}

@Misc{Kashiwagi:2025:KCL,
  author =       "Masahide Kashiwagi",
  title =        "{\tt kv} --- a {C++} Library for Verified Numerical
                 Computation",
  howpublished = "Web site.",
  day =          "15",
  month =        mar,
  year =         "2025",
  bibdate =      "Wed Aug 27 12:31:38 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://verifiedby.me/kv/index-e.html",
  acknowledgement = ack-nhfb,
}

@InProceedings{Khwa:2025:WWM,
  author =       "Win-San Khwa and Ping-Chun Wu and Jian-Wei Su and
                 Chiao-Yen Cheng and Jun-Ming Hsu and Yu-Chen Chen and
                 Le-Jung Hsieh and Jyun-Cheng Bai and Yu-Sheng Kao and
                 Tsung-Han Lou and Ashwin Sanjay Lele and Jui-Jen Wu and
                 Jen-Chun Tien and Chung-Chuan Lo and Ren-Shuo Liu and
                 Chih-Cheng Hsieh and Kea-Tiong Tang and Meng-Fan
                 Chang",
  booktitle =    "{2025 IEEE International Solid-State Circuits
                 Conference (ISSCC)}",
  title =        "14.2 A 16nm 216kb, {188.4TOPS/W} and {133.5TFLOPS/W}
                 Microscaling Multi-Mode Gain-Cell {CIM} Macro {Edge-AI}
                 Devices",
  volume =       "68",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--3",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/ISSCC49661.2025.10904606",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Adders; Common Information Model
                 (computing); Costs; Data transfer; Energy consumption;
                 Hardware; Memory management; Micromechanical devices;
                 Transistors",
}

@InProceedings{Kim:2025:MFM,
  author =       "Seah Kim and Jerry Zhao and Roger Hsiao and Yufeng Chi
                 and Vighnesh Iyer and Vikram Jain and Borivoje
                 Nikoli{\'c} and Yakun Sophia Shao",
  booktitle =    "{2025 Symposium on VLSI Technology and Circuits (VLSI
                 Technology and Circuits)}",
  title =        "{MAVERIC}: a 16nm 72 {FPS}, {10 mJ\slash Frame}
                 Heterogeneous Robotics {SoC} with 4 Cores and 13
                 {INT8\slash FP32} Accelerators",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--3",
  year =         "2025",
  DOI =          "https://doi.org/10.23919/VLSITechnologyandCir65189.2025.11075163",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Depth measurement; Energy efficiency; Gold; Maximum
                 likelihood estimation; Processor scheduling; Robots;
                 Simultaneous localization and mapping;
                 Three-dimensional displays; Very large scale
                 integration",
}

@Article{Kim:2025:SRF,
  author =       "Kevin Kim and Katherine Parry and David Harris and
                 Cedar Turek and Alessandro Maiuolo and Rose Thompson
                 and James Stine",
  title =        "Shared Recurrence Floating-Point Divide\slash Sqrt and
                 Integer Divide\slash Remainder With Early Termination",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "74",
  number =       "2",
  pages =        "740--748",
  month =        feb,
  year =         "2025",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2024.3500380",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Mar 14 07:34:19 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Adders; Approximation algorithms; Art; Computer
                 architecture; Computers; Division; early termination;
                 Hardware; Logic; Optical wavelength conversion; Reduced
                 instruction set computing; remainder; RISC-V64
                 floating-point unit; square root; SRT; subnormal
                 arithmetic; Three-dimensional displays",
}

@InProceedings{Koizumi:2025:TOA,
  author =       "Toru Koizumi and Ryota Shioya and Takuya Yamauchi and
                 Tomoya Adachi and Ken Namura and Jun Makino",
  title =        "Trailing-Ones Anticipation for Reducing the Latency of
                 the Rounding Incrementer in {FP} {FMA} Units",
  crossref =     "IEEE:2025:PIS",
  pages =        "21--28",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00014",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@InProceedings{Kokane:2025:LLP,
  author =       "Omkar Kokane and Mukul Lokhande and Gopal Raut and
                 Adam Teman and Santosh Kumar Vishvakarma",
  booktitle =    "{2025 IEEE International Symposium on Circuits and
                 Systems (ISCAS)}",
  title =        "{LPRE}: Logarithmic Posit-enabled Reconfigurable
                 {edge-AI} Engine",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--5",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/ISCAS56072.2025.11043622",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Bandwidth; Edge-AI accelerators; Engines;
                 Fixed-point arithmetic; Hardware; Index Terms Posit
                 MAC; Indexes; License plate recognition; Multi-layer
                 perceptrons; Quantization; Quantization (signal);
                 Real-time systems; Reconfigurable computing;
                 Throughput",
}

@Article{Kokosinski:2025:FAA,
  author =       "Zbigniew Kokosi{\'n}ski and Pawe{\l} Gepner and
                 Nataliia Gavkalova",
  title =        "Fast and accurate approximation algorithms for
                 computing floating point square root",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "99",
  number =       "4",
  pages =        "1791--1804",
  month =        aug,
  year =         "2025",
  CODEN =        "NUALEG",
  DOI =          "https://doi.org/10.1007/s11075-024-01932-7",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Wed Jul 16 11:11:45 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/numeralgorithms.bib",
  URL =          "https://link.springer.com/article/10.1007/s11075-024-01932-7",
  acknowledgement = ack-nhfb,
  ajournal =     "Numer. Algorithms",
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}

@Article{Kriemann:2025:HLR,
  author =       "Ronald Kriemann",
  title =        "Hierarchical Low-Rank Arithmetic with Floating Point
                 Compression",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "47",
  number =       "4",
  pages =        "B763--B784",
  month =        "????",
  year =         "2025",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/24M1649009",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Sat Oct 18 11:20:11 MDT 2025",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/47/4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  URL =          "https://epubs.siam.org/doi/10.1137/24M1649009",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  keywords =     "data compression; hierarchical matrices; low-rank
                 arithmetic; mixed precision; posit arithmetic",
}

@InProceedings{Kulkarni:2025:MCN,
  author =       "Bhargav Kulkarni and Pavel Panchekha",
  title =        "Mixing Condition Numbers and Oracles for Accurate
                 Floating-point Debugging",
  crossref =     "IEEE:2025:PIS",
  pages =        "101--108",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00025",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@InProceedings{Larsson-Edefors:2025:IEF,
  author =       "Per Larsson-Edefors and Erik B{\"o}rjeson",
  title =        "Implementation Evaluation of Fixed-Point Multipliers
                 for Complex Numbers",
  crossref =     "IEEE:2025:PIS",
  pages =        "81--84",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00022",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@Article{Leng:2025:HPH,
  author =       "Yuhan Leng and Gaoyuan Zou and Hansheng Wang and
                 Panruo Wu and Shaoshuai Zhang",
  title =        "High Performance {Householder} {QR} Factorization on
                 Emerging {GPU} Architectures Using {Tensor Cores}",
  journal =      j-IEEE-TRANS-PAR-DIST-SYS,
  volume =       "36",
  number =       "3",
  pages =        "422--436",
  year =         "2025",
  CODEN =        "ITDSEO",
  DOI =          "https://doi.org/10.1109/TPDS.2024.3522776",
  ISSN =         "1045-9219 (print), 1558-2183 (electronic)",
  ISSN-L =       "1045-9219",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/householder-alston-s.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Parallel Distrib. Syst.",
  fjournal =     "IEEE Transactions on Parallel and Distributed
                 Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=71",
  keywords =     "Accuracy; Computer architecture; GPGPU; Graphics
                 processing units; HPC; Matrix decomposition;
                 mixed-precision algorithms; Numerical analysis;
                 numerical linear algebra; Parallel processing;
                 Reflection; Sparse matrices; tensor cores; Tensors;
                 Vectors",
}

@Article{Li:2025:GSB,
  author =       "Chengqing Li and Kai Tan",
  title =        "The Graph Structure of Baker's Maps Implemented on a
                 Computer",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "74",
  number =       "5",
  pages =        "1524--1537",
  month =        may,
  year =         "2025",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2025.3533094",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Aug 13 17:23:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Baker's map; Chaotic communication; chaotic
                 cryptography; Fixed-point arithmetic; fixed-point
                 arithmetic; Floating-point arithmetic; floating-point
                 arithmetic domain; functional graph; Orbits; period
                 distribution; PRNS; pseudorandom number sequence;
                 Quantization (signal); Quantum computing; Strips;
                 Symbols; Trajectory; Vectors",
}

@Article{Liu:2025:ADR,
  author =       "Jiawei Liu and Xufan Zhang and Lurong Xu and Chunrong
                 Fang and Mingzheng Gu and Weisi Luo and Dong Chai and
                 Jiang Wang and Zhihong Zhao and Zhenyu Chen",
  title =        "Automated Detection and Repair of Floating-point
                 Precision Problems in Convolutional Neural Network
                 Operators",
  journal =      j-TOSEM,
  volume =       "34",
  number =       "7",
  pages =        "203:1--203:32",
  month =        sep,
  year =         "2025",
  CODEN =        "ATSMER",
  DOI =          "https://doi.org/10.1145/3715104",
  ISSN =         "1049-331X (print), 1557-7392 (electronic)",
  ISSN-L =       "1049-331X",
  bibdate =      "Tue Sep 30 09:27:41 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tosem.bib",
  abstract =     "Convolutional Neural Network (CNN) operators, mostly
                 based on mathematical linear computations, are of vital
                 importance to developing CNN-based software. Existing
                 studies reveal that these operators are prone to
                 floating-point precision problems (FPPs). In a
                 CNN-based application, such problems can be propagated
                 and result in catastrophic consequences. Thus, it is
                 highly desired to detect and repair the FPPs in CNN
                 operators. Considering the FPPs in CNN operators are
                 mainly caused by accumulated floating-point errors and
                 diverse floating-point tensors instead of wrong codes
                 or bad implementations, it requires much time cost and
                 is difficult to tackle these FPPs.\par

                 In this article, we propose the first method for the
                 automated detection and repair of FPPs in CNN operators
                 from the perspective of floating-point tensors. To
                 generate diverse tensors with floating-point numbers,
                 we design two levels of mutation rules, namely
                 computation-level mutation and input-level mutation,
                 containing a total of five mutation methods. To detect
                 the FPPs caused by the accumulated floating-point
                 errors, our method uses a weight matrix to guide the
                 progressive mutation. To repair the detected FPPs, our
                 method transforms the error-prone floating-point
                 tensors based on the mathematical rewriting of the
                 floating-point linear computational properties without
                 destroying the original computation. Experimental
                 results show that our methods can detect and repair
                 FPPs in CNN operators effectively and efficiently and
                 could reduce 93.32\% to 100\% of the FPPs in CNN
                 operators. We conduct a case study on six different
                 widely used CNN models and confirm that the proposed
                 FPP method is generalizable and effective across a
                 variety of tasks and architectures. Our detection and
                 repair method offers an intuitive way to handle FPPs
                 during development, allowing users to continue building
                 and fine-tuning their models without being slowed down
                 by numerical precision errors. We believe that our
                 method could open up a new way to enhance the quality
                 of CNN operators and CNN-based software.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Softw. Eng. Methodol.",
  articleno =    "203",
  fjournal =     "ACM Transactions on Software Engineering and
                 Methodology",
  journal-URL =  "https://dl.acm.org/loi/tosem",
}

@Article{Liu:2025:DMP,
  author =       "Haotian Liu and Xicheng Lu and Xiaoyu Yu and Kai Li
                 and Kaiyuan Yang and Haihang Xia and Sizhao Li and
                 Tiantai Deng",
  title =        "A {3-D} Multi-Precision Scalable Systolic {FMA}
                 Architecture",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-1,
  volume =       "72",
  number =       "1",
  pages =        "265--276",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/TCSI.2024.3497724",
  ISSN =         "1549-8328 (print), 1558-0806 (electronic)",
  ISSN-L =       "1549-8328",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems I: Regular
                 Papers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8919",
  keywords =     "Accuracy; Arithmetic circuits and systems; Arrays;
                 Computer architecture; digital ASICs; digital circuit
                 design; Energy efficiency; Field programmable gate
                 arrays; FPGAs; Hardware; Parallel processing; Systolic
                 arrays; Three-dimensional displays; Vectors",
}

@Article{Liu:2025:LPM,
  author =       "Ao Liu and Siting Liu and Hui Wang and Qin Wang and
                 Fabrizio Lombardi and Zhigang Mao and Honglan Jiang",
  title =        "Low-Power Multiplier Designs by Leveraging
                 Correlations of $ 2 \times 2 $ Encoded Partial
                 Products",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "74",
  number =       "11",
  pages =        "3888--3896",
  month =        nov,
  year =         "2025",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2025.3604478",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Oct 15 16:45:16 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Adders; Artificial neural networks; Computer
                 architecture; Correlation; Delays; Encoding; full
                 adder; Hardware; Low-power; multiple-precision; partial
                 product; Quantization (signal); recursive multiplier;
                 Training; Vectors",
}

@Article{Lyu:2025:EMB,
  author =       "Fei Lyu and Yuanyong Luo and Weiqiang Liu",
  title =        "An Efficient Methodology for Binary Logarithmic
                 Computations of Floating-Point Numbers With Normalized
                 Output Within One ulp of Accuracy",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "74",
  number =       "5",
  pages =        "1800--1813",
  month =        may,
  year =         "2025",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2025.3543676",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Aug 13 17:23:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Accuracy; Binary logarithmic operation; Computational
                 efficiency; Computer architecture; Computers;
                 floating-point number; Graphics processing units;
                 Hardware; hardware implementation; Libraries; Linear
                 programming; Mathematical models; polynomial
                 approximation method; Polynomials",
}

@Article{Ma:2025:STF,
  author =       "Dongyu Ma and Zeyu Liang and Luming Yin and Hongliang
                 Liang",
  title =        "Symbolic testing of floating-point bugs and
                 exceptions",
  journal =      j-J-SYST-SOFTW,
  volume =       "219",
  number =       "??",
  pages =        "??--??",
  month =        jan,
  year =         "2025",
  CODEN =        "JSSODM",
  DOI =          "https://doi.org/10.1016/j.jss.2024.112226;
                 https://doi.org/10.2139/ssrn.4797965",
  ISSN =         "0164-1212 (print), 1873-1228 (electronic)",
  ISSN-L =       "0164-1212",
  bibdate =      "Thu Nov 7 07:42:59 MST 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsystsoftw2020.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S016412122400270X;
                 https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4797965",
  acknowledgement = ack-nhfb,
  articleno =    "112226",
  fjournal =     "Journal of Systems and Software",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01641212",
  keywords =     "CVE (Common Vulnerabilities and Exposures) bug
                 reports; floating-point arithmetic; GNU Scientific
                 Library (GSL); interval arithmetic; LLVM/CLang compiler
                 system; MuPDF (viewing and converting PDF (Portable
                 Document Format) files); SoX (audio editing); symbolic
                 execution",
}

@Article{Mary:2025:EAM,
  author =       "Theo Mary and Mantas Mikaitis",
  title =        "Error Analysis of Matrix Multiplication with Narrow
                 Range Floating-Point Arithmetic",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "47",
  number =       "4",
  pages =        "B785--B800",
  month =        "????",
  year =         "2025",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/24M1685109",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  bibdate =      "Sat Oct 18 11:20:11 MDT 2025",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/47/4;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  URL =          "https://epubs.siam.org/doi/10.1137/24M1685109",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
}

@Article{Mirzaei-Teshnizi:2025:PMM,
  author =       "Shahab Mirzaei-Teshnizi and Parviz Keshavarzi",
  title =        "Parallel Modular Multiplication Using Variable Length
                 Algorithms",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "74",
  number =       "1",
  pages =        "143--154",
  month =        jan,
  year =         "2025",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2024.3475574",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Mar 14 07:34:19 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Adders; Canonic signed digit (CSD); Clocks; Computers;
                 Costs; Elliptic curve cryptography; Field programmable
                 gate arrays; FPGA; Hardware; high-speed arithmetic;
                 Interleaved modular multiplication; Montgomery
                 multiplication; Partitioning algorithms; Symbols;
                 Throughput",
}

@InProceedings{Moustafa:2025:EMP,
  author =       "Samir Moustafa and Nils Kriege and Wilfried N.
                 Gansterer",
  booktitle =    "{2025 IEEE 41st International Conference on Data
                 Engineering (ICDE)}",
  title =        "Efficient Mixed Precision Quantization in Graph Neural
                 Networks",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "4038--4052",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/ICDE65448.2025.00301",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Computational efficiency; Computer
                 architecture; Data engineering; Deep architecture;
                 Graph neural networks; Message passing; Navigation;
                 Quantization; Quantization (signal); Training",
}

@Article{Nesam:2025:DRU,
  author =       "J. Jean Jenifer Nesam and S. Sankar Ganesh",
  title =        "Design of Radix-8 Unsigned Bit Pair Recoding
                 Algorithm-Based Floating-Point Multiplier for Neural
                 Network Computations",
  journal =      j-IEEE-ACCESS,
  volume =       "13",
  pages =        "63969--63980",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/ACCESS.2025.3559226",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Tue Sep 30 17:30:28 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "Adders; Area efficient multiplier; Artificial
                 intelligence; Artificial neural networks; bit pair
                 recoding (BPR) algorithm; booth encoding algorithm;
                 Complexity theory; Decoding; Delays; Encoding; error
                 analysis; fast multiplication; Image coding; low power
                 multiplier; multipliers for neural networks; partial
                 product reduction; Resists; Standards",
}

@InProceedings{Nguyen:2025:REA,
  author =       "Thanh Son Nguyen and Alexey Solovyev and Mark G.
                 Arnold and Ganesh Gopalakrishnan",
  title =        "Rigorous Error Analysis for Logarithmic Number
                 Systems",
  crossref =     "IEEE:2025:PIS",
  pages =        "125--132",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00028",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@Book{Overton:2025:NCI,
  author =       "Michael L. Overton",
  title =        "Numerical Computing with {IEEE} Floating Point
                 Arithmetic: Including One Theorem, One Rule of Thumb,
                 and One Hundred and Six Exercises",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  edition =      "Second",
  pages =        "xx + 126",
  year =         "2025",
  DOI =          "https://doi.org/10.1137/1.9781611978414",
  ISBN =         "1-61197-840-8 (print), 1-61197-841-6 (e-book)",
  ISBN-13 =      "978-1-61197-840-7 (print), 978-1-61197-841-4
                 (e-book)",
  LCCN =         "QA297",
  bibdate =      "Thu Jul 03 08:34:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  URL =          "https://bookstore.siam.org/OT205;
                 https://epubs.siam.org/doi/10.1137/1.9781611978414",
  acknowledgement = ack-nhfb,
  tableofcontents = "Preface / ix \\
                 Acknowledgments / xi \\
                 1 Introduction / 1 \\
                 2 The Real Numbers / 5 \\
                 3 Computer Representation of Numbers / 9 \\
                 4 IEEE Floating Point Representation / 17 \\
                 5 Rounding / 27 \\
                 6 Correctly Rounded Floating Point Operations / 35 \\
                 7 Exceptions / 45 \\
                 8 Floating Point Microprocessors / 53 \\
                 9 Programming Languages / 57 \\
                 10 Floating Point in C / 63 \\
                 11 Cancellation / 75 \\
                 12 Conditioning of Problems / 81 \\
                 13 Stability of Algorithms / 87 \\
                 14 Higher Precision Computations / 99 \\
                 15 Lower Precision Computations / 103 \\
                 16 Conclusion / 111 \\
                 A Letter from Professor Donald E. Knuth / 113 \\
                 Bibliography / 117 \\
                 Index / 125",
}

@Article{Ozaki:2025:ALP,
  author =       "Katsuhisa Ozaki",
  title =        "Accuracy of Low-Precision Elementary and Special
                 Functions Using Verified Numerical Computations",
  journal =      "Journal of Advanced Simulation in Science and
                 Engineering",
  volume =       "12",
  number =       "1",
  pages =        "113--130",
  year =         "2025",
  bibdate =      "Wed Aug 27 11:15:20 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://www.jstage.jst.go.jp/article/jasse/12/1/12_113/_pdf/-char/ja",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Adv. Simulat. Sci. Eng.",
  journal-URL =  "https://www.jstage.jst.go.jp/browse/jasse",
}

@InProceedings{Peric:2025:SAA,
  author =       "Sofija Z. Peri{\'c} and Zoran H. Peri{\'c} and Bojan
                 D. Deni{\'c} and Milan R. Din{\v{c}}i{\'c} and
                 Aleksandra Z. Jovanovi{\'c} and Marko S.
                 An{\dbar}elkovi{\'c}",
  booktitle =    "{2025 60th International Scientific Conference on
                 Information, Communication and Energy Systems and
                 Technologies (ICEST)}",
  title =        "{SQNR} Approximation Analysis of the {FP24} Format of
                 {Laplacian} Source in a Wide Variance Range",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--4",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/ICEST66328.2025.11098267",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Complexity theory; Computational efficiency;
                 Floating-point format; Laplace equations; Laplacian
                 source; Noise; Performance evaluation;
                 Piecewise-uniform quantization; Probability
                 distribution; Quantization (signal); SQNR",
}

@InProceedings{Ptrot:2025:ESH,
  author =       "Fr{\'e}d{\'e}ric P{\'e}trot",
  title =        "Experimental Software and Hardware Evaluation of
                 Ad-Hoc Constant Division Routines",
  crossref =     "IEEE:2025:PIS",
  pages =        "69--72",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00020",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@InProceedings{Pun:2025:RES,
  author =       "Shing Wai Pun and Bozhang Bao and Silviu-Ioan Filip
                 and Guy Lemieux and John V. Kim and Nazar Misyats and
                 Nirvik Pande and Victor Ravain and Robert Sherrick",
  title =        "Range Extension with Supernormals for Mixed-Precision
                 8-bit {DNN} Training",
  crossref =     "IEEE:2025:PIS",
  pages =        "1--4",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00013",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@InProceedings{Ramamoorthy:2025:AMP,
  author =       "Arnav Ramamoorthy and Kiran Kumar Gunnam",
  booktitle =    "{2025 IEEE Computer Society Annual Symposium on VLSI
                 (ISVLSI)}",
  title =        "Adaptive Multi-Precision Inference for Large-Scale
                 {AI} Using {IEEE P3109 FP8}",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--2",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/ISVLSI65124.2025.11130212",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Adaptation models; adaptive precision;
                 Artificial intelligence; dynamic quantization; FP8;
                 Industries; performance-accuracy trade-off;
                 Quantization (signal); Real-time systems; Tensors;
                 Throughput; transformer inference; Transformers; Very
                 large scale integration",
}

@Article{Rathor:2025:AFE,
  author =       "Mahendra Rathor",
  title =        "{ALOHA-FP2I}: Efficient Algorithms and Hardware for
                 Multi-Mode Rounding of Floating Point to Integer",
  journal =      j-TECS,
  volume =       "24",
  number =       "1",
  pages =        "12:1--12:26",
  month =        jan,
  year =         "2025",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3701560",
  ISSN =         "1539-9087 (print), 1558-3465 (electronic)",
  ISSN-L =       "1539-9087",
  bibdate =      "Thu Jan 2 07:31:47 MST 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tecs.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3701560",
  abstract =     "Modern technology is relying on hardware accelerators
                 to achieve enhanced performance of computing systems.
                 In the modern computing paradigm, floating point
                 representation of numbers has gained popularity owing
                 to its wide dynamic range. Rounding of floating point
                 numbers to integer is used in modern processor
                 architectures e.g., ARM and Intel's architecture (IA)
                 as well as in specific applications such as multimedia.
                 However, the academic literature lacks discussion on
                 hardware designs for rounding binary floating point
                 numbers to integer in different rounding modes. This
                 article presents novel efficient algorithms and
                 hardware architecture designs for rounding binary
                 floating point numbers to the integer for the following
                 rounding modes: round towards zero, round up (towards
                 positive infinity), round down (towards negative
                 infinity), round to the nearest integer, and round to
                 nearest even. The article also proposes an integrated
                 multi-mode rounding (IMR) algorithm and hardware design
                 which can be configured to a specific rounding mode
                 among the above-mentioned five modes. This article
                 proposes a mantissa bit of rounding (MBR) to determine
                 the condition of rounding for the various modes. The
                 MBR is identified on the basis of the dynamic range and
                 precision features of floating point representation. To
                 the best of our knowledge, we present the individual as
                 well as an integrated hardware design for the various
                 rounding modes for the first time in the literature.
                 The proposed designs have been implemented on an FPGA
                 platform to analyze the design metrics such as area,
                 delay, and power. The results imply that the proposed
                 designs are suitable to aid the intended hardware
                 accelerators as they are efficient in terms of the
                 design parameters. Moreover, this article presents the
                 integration of the proposed rounding hardware design
                 with the compression processor and evaluates the
                 integration overhead which is found to be nominal
                 (<1\%).",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Embed. Comput. Syst.",
  articleno =    "12",
  fjournal =     "ACM Transactions on Embedded Computing Systems",
  journal-URL =  "https://dl.acm.org/loi/tecs",
}

@Article{Reisch:2025:MSM,
  author =       "Cordula Reisch and Hendrik Ranocha",
  title =        "Modeling Still Matters: a Surprising Instance of
                 Catastrophic Floating Point Errors in Mathematical
                 Biology and Numerical Methods for {ODEs}",
  journal =      j-SIAM-REVIEW,
  volume =       "67",
  number =       "3",
  pages =        "624--641",
  month =        "????",
  year =         "2025",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/23M1563967",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Fri Oct 17 07:24:40 MDT 2025",
  bibsource =    "http://epubs.siam.org/toc/siread/67/3;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/julia.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  URL =          "https://epubs.siam.org/doi/10.1137/23M1563967",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
}

@InProceedings{Ren:2025:AMP,
  author =       "Jie Ren and Hatem Ltaief and Sameh Abdulah and David
                 E. Keyes",
  booktitle =    "{ISC High Performance 2025 Research Paper Proceedings
                 (40th International Conference)}",
  title =        "Accelerating Mixed-Precision Out-of-Core {Cholesky}
                 Factorization with Static Task Scheduling",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--12",
  year =         "2025",
  DOI =          "",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Data transfer; Data Transfer Optimization;
                 GPU Accelerators; Graphics processing units;
                 Left-Looking Cholesky Factorization; Memory management;
                 Mixed-Precision Computations; Optimization; Out-of-Core
                 Algorithms; Processor scheduling; Scheduling; Spatial
                 databases; Static Task Scheduling; Technological
                 innovation; Throughput",
}

@Article{Scheffler:2025:OCD,
  author =       "Paul Scheffler and Thomas Benz and Viviane Potocnik
                 and Tim Fischer and Luca Colagrande and Nils Wistoff
                 and Yichao Zhang and Luca Bertaccini and Gianmarco
                 Ottavi and Manuel Eggimann and Matheus Cavalcante and
                 Gianna Paulin and Frank K. G{\"u}rkaynak and Davide
                 Rossi and Luca Benini",
  title =        "{Occamy}: a 432-Core Dual-Chiplet {Dual-HBM2E
                 768-DP-GFLOP/s} {RISC-V} System for 8-to-64-bit Dense
                 and Sparse Computing in 12-nm {FinFET}",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "60",
  number =       "4",
  pages =        "1324--1338",
  year =         "2025",
  CODEN =        "IJSCBC",
  DOI =          "https://doi.org/10.1109/JSSC.2025.3529249",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "2.5-D integration; Bandwidth; chiplet; Chiplets;
                 Codes; Computer architecture; Device-to-device
                 communication; Engines; high-performance computing
                 (HPC); Integrated circuit interconnections; interposer;
                 machine learning (ML); manycore; multi-precision;
                 Register transfer level; RISC-V; sparse acceleration;
                 stencil acceleration; Tensors; Throughput",
}

@Article{Shaban:2025:VAD,
  author =       "Ahmed Shaban and Shreshtha Gothalyan and Manan Suri
                 and Tuo-Hung Hou",
  title =        "Variation-Aware Demonstration and Optimization of
                 Block Floating Point and Integer Neural Network
                 Acceleration on {RRAM} Compute in-Memory Hardware",
  journal =      "IEEE Transactions on Circuits and Systems for
                 Artificial Intelligence",
  volume =       "2",
  number =       "3",
  pages =        "185--196",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/TCASAI.2025.3592864",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accelerators; Arrays; Computer architecture;
                 convolutional neural networks (CNNs); deep neural
                 networks (DNNs); Device-to-device communication; Energy
                 consumption; floating-point acceleration; Hardware;
                 In-memory computing; in-memory computing; Optimization;
                 Performance evaluation; Resistance; Resistive RAM;
                 resistive RAM (RRAM)",
}

@InProceedings{Shah:2025:ORT,
  author =       "Gaurav Shah and Abhinav Goud and Zaqi Momin and Joycee
                 Mekie",
  booktitle =    "{2025 38th International Conference on VLSI Design and
                 2024 23rd International Conference on Embedded Systems
                 (VLSID)}",
  title =        "{OwlsEye}: Real-Time Low-Light Video Instance
                 Segmentation on Edge and Exploration of Fixed-Posit
                 Quantization",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "451--456",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/VLSID64188.2025.00090",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Computer Vision; Edge AI; Fixed Posits; Image edge
                 detection; Instance segmentation; low-light
                 enhancement; Pipeline processing; Quantization
                 (signal); Real-time systems; Robot vision systems;
                 Robots; Streaming media; Surveillance; Very large scale
                 integration; Video Instance Segmentation",
}

@InProceedings{Sharma:2025:DLL,
  author =       "Prashnat Sharma and Sourav Nath and Koushik Guha and
                 Krishna Lal Baishnab",
  booktitle =    "{2025 Devices for Integrated Circuit (DevIC)}",
  title =        "Design of Low-Latency, Area- and Power-Efficient
                 {CORDIC} Algorithms for Sine\slash Cosine
                 Floating-Point Computation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "583--588",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/DevIC63749.2025.11012211",
  bibdate =      "Mon Oct 27 10:32:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Adders; and Logic design; Approximate adder;
                 Approximate computing; Cordic; Digital signal
                 processing; Field programmable gate arrays; Hardware;
                 Low latency communication; Memory management;
                 Optimization; Power demand; Signal processing
                 algorithms; Trigonometric function",
}

@Article{Shin:2025:DMH,
  author =       "Seungah Shin and Joonho Kong and Young Seo Lee",
  title =        "{Dual-MAC}: Hardware Acceleration of {DNN} Inferences
                 With a Customized Lightweight Brain Floating-Point
                 Format",
  journal =      j-IEEE-ACCESS,
  volume =       "13",
  pages =        "165738--165750",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/ACCESS.2025.3612913",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Tue Sep 30 17:30:28 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "Accuracy; Artificial intelligence; Artificial neural
                 networks; brain floating point; Complexity theory;
                 custom weight format; Data models; Deep neural network
                 inference; Energy efficiency; Hardware acceleration;
                 hardware acceleration; Memory management; Systolic
                 arrays; Throughput; throughput",
}

@Article{Sumaiya:2025:TRT,
  author =       "Sumaiya and Reza Jafarpourmarzouni and Yichen Luo and
                 Sidi Lu and Zheng Dong",
  title =        "Toward Real-Time and Efficient Perception Workflows in
                 Software-Defined Vehicles",
  journal =      "IEEE Internet of Things Journal",
  volume =       "12",
  number =       "6",
  pages =        "7240--7258",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/JIOT.2024.3492801",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "16-bit floating point precision (FP16); Accuracy;
                 accuracy; Computational modeling; Deep learning; FP32;
                 GPU/memory usage; INT8; latency; Memory management;
                 Optimization; pruning; quantization; Quantization
                 (signal); real-time; Real-time systems;
                 software-defined vehicle (SDV); Throughput; throughput;
                 Training; workflow; YOLO",
}

@InProceedings{Swords:2025:REE,
  author =       "Sol Swords and Cuong Chau",
  title =        "Robust, End-to-end Correctness Proofs of Industrial
                 Divide and Square Root {RTL} Designs",
  crossref =     "IEEE:2025:PIS",
  pages =        "149--156",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00031",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@InProceedings{Tang:2025:RES,
  author =       "Ping Tak Peter Tang",
  title =        "Rounding Error Statistics as Numerics Signature",
  crossref =     "IEEE:2025:PIS",
  pages =        "93--100",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00024",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@Article{Thushara:2025:FSA,
  author =       "M. G. Thushara and K. Somasundaram",
  title =        "{ForBac}: A Static Analysis Approach With Forward and
                 Backward Analysis for Precision in Floating-Point
                 Computations",
  journal =      j-IEEE-ACCESS,
  volume =       "13",
  pages =        "80705--80722",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/ACCESS.2025.3567762",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Tue Sep 30 17:30:28 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "abstract interpretation; Accuracy; Analytical models;
                 Codes; Computational modeling; floating-point; Input
                 variables; precision; Software; Standards; Static
                 analysis; transfer function; Transfer functions;
                 Tuning",
}

@Article{Vakili:2025:DFL,
  author =       "Shervin Vakili and Mobin Vaziri and Amirhossein Zarei
                 and J. M. Pierre Langlois",
  title =        "{DyRecMul}: Fast and Low-Cost Approximate Multiplier
                 for {FPGAs} using Dynamic Reconfiguration",
  journal =      j-TRETS,
  volume =       "18",
  number =       "1",
  pages =        "7:1--7:??",
  month =        mar,
  year =         "2025",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3663480",
  ISSN =         "1936-7406 (print), 1936-7414 (electronic)",
  ISSN-L =       "1936-7406",
  bibdate =      "Tue Mar 25 09:48:37 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/trets.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3663480",
  abstract =     "Multipliers are widely-used arithmetic operators in
                 digital signal processing and machine learning (ML)
                 circuits. Due to their relatively high complexity, they
                 can have high latency and be a significant source of
                 power consumption. One strategy to alleviate these
                 limitations is to use approximate computing. This
                 article thus introduces an original FPGA-based
                 approximate multiplier specifically optimized for ML
                 computations. It utilizes dynamically reconfigurable
                 lookup table (LUT) primitives in AMD-Xilinx technology
                 to realize the core part of the computations. The
                 article provides an in-depth analysis of the hardware
                 architecture, implementation outcomes, and accuracy
                 evaluations of the multiplier proposed in INT8
                 precision. The article also facilitates the
                 generalization of the proposed approximate multiplier
                 idea to other datatypes, providing analysis and
                 estimations for hardware cost and accuracy as a
                 function of multiplier parameters. Implementation
                 results on an AMD-Xilinx Kintex Ultrascale+ FPGA
                 demonstrate remarkable savings of 64\% and 67\% in LUT
                 utilization for signed multiplication and
                 multiply-and-accumulation configurations, respectively
                 when compared to the standard Xilinx multiplier core.
                 Accuracy measurements on four popular deep learning
                 (DL) benchmarks indicate a minimal average accuracy
                 decrease of less than 0.29\% during post-training
                 deployment, with the maximum reduction staying less
                 than 0.33\%. The source code of this work is available
                 on GitHub.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Reconfigurable Technol. Syst.",
  articleno =    "7",
  fjournal =     "ACM Transactions on Reconfigurable Technology and
                 Systems (TRETS)",
  journal-URL =  "https://dl.acm.org/loi/trets",
}

@InProceedings{Vanover:2025:ESE,
  author =       "Jackson Vanover and James Demmel and Xiaoye Sherry Li
                 and Cindy Rubio-Gonz{\'a}lez",
  title =        "{Excvate}: Spoofing Exceptions and Solving Constraints
                 to Test Exception Handling in Numerical Libraries",
  crossref =     "IEEE:2025:PIS",
  pages =        "109--116",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00026",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@Article{Walczyk:2025:OAX,
  author =       "Cezary J. Walczyk and Leonid V. Moroz and Volodymyr
                 Samotyy and Jan L. Cie{\'s}li{\'n}ski",
  title =        "Optimal Approximation of the $ 1 / x $ Function using
                 {Chebyshev} Polynomials and Magic Constants",
  journal =      j-TOMS,
  volume =       "51",
  number =       "1",
  pages =        "2:1--2:??",
  month =        mar,
  year =         "2025",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3708472",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Apr 10 08:03:40 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In this article we analyze low-cost accurate
                 approximation of the function $ 1 / x $ using Chebyshev
                 polynomials of the first kind and minimizing number of
                 elementary operations in computer codes (in particular,
                 by using the so-called magic constants). It is shown
                 that Newton-Raphson iterative method is not optimal and
                 a new approach is proposed. We prove that optimal
                 Chebyshev polynomials can be factorized in terms of
                 Chebyshev polynomials of lower order which leads to new
                 optimal iteration schemes. We also construct a family
                 of new algorithms by dividing the considered interval
                 into sub-intervals where different magic constants and
                 multiplicative factors are used (in order to increase
                 the accuracy). Theoretical considerations and proofs
                 are completed with numerical tests on three types of
                 microcontroller processors.",
  accepted =     "4 December 2024",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "2",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  received =     "3 September 2022",
  revised =      "25 September 2024",
}

@Article{Wang:2025:EEP,
  author =       "Yang Wang and Xiaolong Yang and Yubin Qin and Zhiren
                 Zhao and Ruiqi Guo and Zhiheng Yue and Huiming Han and
                 Shaojun Wei and Yang Hu and Shouyi Yin",
  title =        "An Energy-Efficient {POSIT} Compute-in-Memory Macro
                 for High-Accuracy {AI} Applications",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "60",
  number =       "8",
  pages =        "2981--2994",
  year =         "2025",
  CODEN =        "IJSCBC",
  DOI =          "https://doi.org/10.1109/JSSC.2025.3532654",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "Accuracy; Adders; Arrays; Artificial intelligence;
                 Artificial intelligence (AI); Common Information Model
                 (computing); Computational modeling; compute-in-memory;
                 Energy efficiency; floating-point (FP); high-accuracy;
                 In-memory computing; Logic; POSIT data format;
                 Training",
}

@InProceedings{Wang:2025:PPF,
  author =       "Wenqing Wang and Ziming Chen and Quan Deng and Liang
                 Fang",
  booktitle =    "{2025 Design, Automation \& Test in Europe Conference
                 (DATE)}",
  title =        "{PFP}: Parallel Floating-Point Vector Multiplication
                 Acceleration in {MAGIC ReRAM}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--7",
  year =         "2025",
  DOI =          "https://doi.org/10.23919/DATE64628.2025.10993278",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Arrays; CIM; Common Information Model (computing);
                 Emerging application; Europe; Floating-point vector
                 multiplication; Graphics; Hardware; Large language
                 models; Logic; Machine learning; Parallel computing;
                 Parallel processing; ReRAM array; Vectors",
}

@Article{Wang:2025:PPH,
  author =       "Jiaxuan Wang and Xiaofeng Wang and Wenzheng Liu and
                 Qianqian Xing and Xiaoyong Tang and Tan Deng and
                 Ronghui Cao and Mingfeng Huang",
  title =        "A parallel and pipelined high speed {Montgomery}
                 modular multiplier for {IoT} devices",
  journal =      j-COMP-NET-AMSTERDAM,
  volume =       "265",
  number =       "??",
  pages =        "??--??",
  month =        jun,
  year =         "2025",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/j.comnet.2025.111282",
  ISSN =         "1389-1286 (print), 1872-7069 (electronic)",
  ISSN-L =       "1389-1286",
  bibdate =      "Fri May 9 06:02:42 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compnetamsterdam2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1389128625002506",
  acknowledgement = ack-nhfb,
  articleno =    "111282",
  fjournal =     "Computer Networks (Amsterdam, Netherlands: 1999)",
  journal-URL =  "http://www.sciencedirect.com/science/journal/13891286/",
}

@InProceedings{Wang:2025:VLC,
  author =       "Run Wang and Gamze Islamoglu and Andrea Belano and
                 Viviane Potocnik and Francesco Conti and Angelo
                 Garofalo and Luca Bonini",
  title =        "{VEXP}: A Low-Cost {RISC-V} {ISA} Extension for
                 Accelerated Softmax Computation in Transformers",
  crossref =     "IEEE:2025:PIS",
  pages =        "37--44",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00016",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@Article{Wen:2025:PPW,
  author =       "Chenyi Wen and Haonan Du and Jiayi Wang and Zhengrui
                 Chen and Li Zhang and Qi Sun and Cheng Zhuo",
  title =        "{PACE}: a Piece-Wise Approximate Floating-Point
                 Divider with Runtime Configurability and High Energy
                 Efficiency",
  journal =      j-TODAES,
  volume =       "30",
  number =       "2",
  pages =        "21:1--21:??",
  month =        mar,
  year =         "2025",
  CODEN =        "ATASFO",
  DOI =          "https://doi.org/10.1145/3706634",
  ISSN =         "1084-4309 (print), 1557-7309 (electronic)",
  ISSN-L =       "1084-4309",
  bibdate =      "Thu Feb 13 06:21:20 MST 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/todaes.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3706634",
  abstract =     "Approximate computing emerges as a viable solution to
                 enhance energy efficiency in applications sensitive to
                 human perception, particularly on edge devices. This
                 work introduces a novel piece-wise approximate
                 floating-point divider that boasts resource \ldots{}",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Transact. Des. Automat. Electron. Syst.",
  articleno =    "21",
  fjournal =     "ACM Transactions on Design Automation of Electronic
                 Systems",
  journal-URL =  "https://dl.acm.org/loi/todaes",
}

@InProceedings{Wintersteiger:2025:FVI,
  author =       "Christoph M. Wintersteiger",
  title =        "Formal Verification of the {IEEE} {P3109} Standard for
                 Binary Floating-Point Formats for Machine Learning",
  crossref =     "IEEE:2025:PIS",
  pages =        "157--160",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00032",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@Article{Wu:2025:IFP,
  author =       "Ping-Chun Wu and Win-San Khwa and Jui-Jen Wu and
                 Jian-Wei Su and Chuan-Jia Jhang and Ho-Yu Chen and
                 Zhao-En Ke and Ting-Chien Chiu and Jun-Ming Hsu and
                 Chiao-Yen Cheng and Yu-Chen Chen and Chung-Chuan Lo and
                 Ren-Shuo Liu and Chih-Cheng Hsieh and Kea-Tiong Tang
                 and Meng-Fan Chang",
  title =        "An Integer-Floating-Point Dual-Mode Gain-Cell
                 Computing-in-Memory Macro for Advanced {AI} Edge
                 Chips",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  volume =       "60",
  number =       "1",
  pages =        "158--170",
  year =         "2025",
  CODEN =        "IJSCBC",
  DOI =          "https://doi.org/10.1109/JSSC.2024.3470215",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "Accuracy; Adders; Arrays; Artificial intelligence;
                 Artificial intelligence (AI); Common Information Model
                 (computing); Computational efficiency;
                 computing-in-memory (CIM); Energy consumption; Energy
                 efficiency; FinFETs; gain cell (GC); In-memory
                 computing; inference; multiply-and-accumulate (MAC)",
}

@Article{Wu:2025:TPM,
  author =       "Jiajun Wu and Mo Song and Jingmin Zhao and Yizhao Gao
                 and Jia Li and Hayden Kwok-Hay So",
  title =        "{TATAA}: Programmable Mixed-Precision Transformer
                 Acceleration with a Transformable Arithmetic
                 Architecture",
  journal =      j-TRETS,
  volume =       "18",
  number =       "1",
  pages =        "14:1--14:??",
  month =        mar,
  year =         "2025",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3714416",
  ISSN =         "1936-7406 (print), 1936-7414 (electronic)",
  ISSN-L =       "1936-7406",
  bibdate =      "Tue Mar 25 09:48:37 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/trets.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3714416",
  abstract =     "Modern transformer-based deep neural networks present
                 unique technical challenges for effective acceleration
                 in real-world applications. Apart from the vast amount
                 of linear operations needed due to their sizes, modern
                 transformer models are increasingly reliance on precise
                 non-linear computations that make traditional
                 low-bitwidth quantization methods and fixed-dataflow
                 matrix accelerators ineffective for end-to-end
                 acceleration. To address this need to accelerate both
                 linear and non-linear operations in a unified and
                 programmable framework, this article introduces TATAA.
                 TATAA employs 8-bit integer (int8) arithmetic for
                 quantized linear layer operations through post-training
                 quantization, while it relies on bfloat16
                 floating-point arithmetic to approximate non-linear
                 layers of a transformer model. TATAA hardware features
                 a transformable arithmetic architecture that supports
                 both formats during runtime with minimal overhead,
                 enabling it to switch between a systolic array mode for
                 int8 matrix multiplications and a SIMD mode for
                 vectorized bfloat16 operations. An end-to-end compiler
                 is presented to enable flexible mapping from emerging
                 transformer models to the proposed hardware.
                 Experimental results indicate that our mixed-precision
                 design incurs only 0.14\% to 1.16\% accuracy drop when
                 compared with the pre-trained single-precision
                 transformer models across a range of vision, language,
                 and generative text applications. Our prototype
                 implementation on the Alveo U280 FPGA currently
                 achieves 2,935.2 GOPS throughput on linear layers and a
                 maximum of 189.5 GFLOPS for non-linear operations,
                 outperforming related works by up to in end-to-end
                 throughput and $ 2.29 \times $ in DSP efficiency, while
                 achieving $ 2.19 \times $ higher power efficiency than
                 modern NVIDIA RTX4090 GPU.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Reconfigurable Technol. Syst.",
  articleno =    "14",
  fjournal =     "ACM Transactions on Reconfigurable Technology and
                 Systems (TRETS)",
  journal-URL =  "https://dl.acm.org/loi/trets",
}

@Article{Xie:2025:ELB,
  author =       "Yujun Xie and Yuan Liu",
  title =        "An Efficient {LUT6}-Based {Montgomery} Modular
                 Multiplication Using Radix-16 {Booth} Method",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "74",
  number =       "9",
  pages =        "3223--3237",
  month =        sep,
  year =         "2025",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2025.3587619",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Aug 13 17:23:44 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Artificial intelligence; Computers; Cryptography; Data
                 mining; Field programmable gate arrays; FPGA; Hardware;
                 Hazards; LUT-based multiplication; Montgomery modular
                 multiplication; Radix-16 Booth method; Random access
                 memory; Reviews; Table lookup; Training",
}

@Article{Xie:2025:FFL,
  author =       "Yujun Xie and Yuan Liu and Xin Zheng and Bohan Lan and
                 Dengyun Lei and Dehao Xiang and Shuting Cai and
                 Xiaoming Xiong",
  title =        "{FLALM}: a Flexible Low Area-Latency {Montgomery}
                 Modular Multiplication on {FPGA}",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "74",
  number =       "1",
  pages =        "29--42",
  month =        jan,
  year =         "2025",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2024.3457739",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Fri Mar 14 07:34:19 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Adders; Computers; Cryptography; Delays; Field
                 programmable gate arrays; finely integrated product
                 scanning; generic Montgomery modular multiplication;
                 Hardware acceleration; Hazards; Montgomery modular
                 multiplication; Schedules; square Montgomery modular
                 multiplication",
}

@Article{Xiong:2025:DLC,
  author =       "Botao Xiong and Xingyu Shao and Chang Liu and Shize
                 Zhang and Yuchun Chang",
  title =        "Design of Low-Cost and High-Accurate 8-bit Logarithmic
                 Floating-Point Arithmetic Circuits",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "33",
  number =       "7",
  pages =        "2094--2098",
  year =         "2025",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/TVLSI.2025.3563950",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=92",
  keywords =     "Accuracy; Arithmetic; Convolution; Costs; Deep
                 learning; Delays; Division; Hands; Hardware; image
                 change detection; logarithmic number system (LNS); low
                 bit-width floating-point (FP) representation;
                 multiplication; neural networks; Standards; Very large
                 scale integration",
}

@InProceedings{Yang:2025:ESM,
  author =       "Hanmei Yang and Summer Deng and Amit Nagpal and Maxim
                 Naumov and Mohammad Janani and Tongping Liu and Hui
                 Guan",
  title =        "An Empirical Study of Microscaling Formats for
                 Low-Precision {LLM} Training",
  crossref =     "IEEE:2025:PIS",
  pages =        "1--8",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/arith64983.2025.00011",
  bibdate =      "Thu Nov 13 12:36:40 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}

@Article{Zhang:2025:HIB,
  author =       "Xiaohui Zhang and Zenghui Yu and Shushan Qiao and Yi
                 Zhan",
  title =        "Hardware Implementation of Block Floating-Point {FFT}
                 Based on Approximate Computation and Conflict-Free
                 Access",
  journal =      j-IEEE-ACCESS,
  volume =       "13",
  pages =        "106989--106997",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/ACCESS.2025.3578531",
  ISSN =         "2169-3536",
  ISSN-L =       "2169-3536",
  bibdate =      "Tue Sep 30 17:30:28 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Access",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6287639",
  keywords =     "Approximate computing; Approximation algorithms; block
                 floating-point; Computational efficiency; Computer
                 architecture; conflict-free access; Fast Fourier
                 transforms; Hardware; Memory management; memory-based
                 fast Fourier transform FFT; mixed radix; Power demand;
                 Random access memory; Read only memory; Throughput",
}

@Article{Zhao:2025:HHF,
  author =       "Yuanzhe Zhao and Yang Wang and Rui P. Martins and
                 Chi-Hang Chan and Shouyi Yin and Minglei Zhang",
  title =        "A Hierarchical-Hybrid Floating-Point Compute-in-Memory
                 Macro Using {FP-DAC} and {FP-ADC} for {Edge-AI}
                 Devices",
  journal =      j-IEEE-J-SOLID-STATE-CIRCUITS,
  pages =        "1--14",
  year =         "2025",
  CODEN =        "IJSCBC",
  DOI =          "https://doi.org/10.1109/JSSC.2025.3599079",
  ISSN =         "0018-9200 (print), 1558-173X (electronic)",
  ISSN-L =       "0018-9200",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Journal of Solid-State Circuits",
  keywords =     "Accuracy; Analog-digital conversion; Computational
                 efficiency; Compute-in-memory (CIM); Digital-analog
                 conversion; Energy efficiency; floating point (FP); FP
                 analog-to-digital converter (FP-ADC); FP
                 digital-to-analog converter (FP-DAC); hybrid; In-memory
                 computing; multiply-and-accumulate (MAC); Parallel
                 processing; Power demand; Quantization (signal);
                 Throughput",
}

@Article{Zhao:2025:ISS,
  author =       "Gaoyang Zhao and Junzhong Shen and Rongzhen Lin and
                 Hua Li and Yaohua Wang",
  title =        "{ISOAcc}: In-situ Shift Operation-based Accelerator
                 For Efficient in-{SRAM} Multiplication",
  journal =      j-TODAES,
  volume =       "30",
  number =       "2",
  pages =        "22:1--22:??",
  month =        mar,
  year =         "2025",
  CODEN =        "ATASFO",
  DOI =          "https://doi.org/10.1145/3707205",
  ISSN =         "1084-4309 (print), 1557-7309 (electronic)",
  ISSN-L =       "1084-4309",
  bibdate =      "Thu Feb 13 06:21:20 MST 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/todaes.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3707205",
  abstract =     "Digital SRAM-based CIM architectures must balance
                 three critical factors: quantized neural network
                 bitwidth, accuracy loss, and computational efficiency,
                 each crucial to optimizing performance and efficiency.
                 In Domain Specific Accelerators (DSAs), flexible and
                 specific hardware design, when incorporated with
                 tailored Power-of-2 (P-2) quantization schemes,
                 addresses this issue. However, in CIMs, the absence of
                 flexible and specific hardware to support dynamic
                 switching between general and tailored quantization
                 schemes hinders the adoption of efficient quantization
                 methods. In this article, we propose the In-situ Shift
                 Operation based Accelerator (ISOAcc) for efficient
                 SRAM-based multiplication. The key idea is to introduce
                 transmission gates near the SRAM array to enable the
                 selection of bits from either the same or the neighbor
                 line when data flows from one row to another. This
                 functionally equals a shift operation. By configuring
                 the transmission gates array in a cascade manner,
                 ISOAcc can support 0 to 15-bit shift with a negligible
                 overhead. The ISOAcc can directly leverage P-2
                 quantization schemes in hardware, thereby greatly
                 reducing multiplication cycles. We have chosen five
                 well-known neural networks to evaluate ISOAcc. The
                 evaluations show that ISOAcc achieves an average
                 performance improvement of 3.24 $ \times $ and an
                 energy reduction of 75\%, compared with the
                 state-of-the-art (SOTA) SRAM-based CIM design,
                 Bit-Parallel.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Transact. Des. Automat. Electron. Syst.",
  articleno =    "22",
  fjournal =     "ACM Transactions on Design Automation of Electronic
                 Systems",
  journal-URL =  "https://dl.acm.org/loi/todaes",
}

@InProceedings{Zhao:2025:OSF,
  author =       "Yuanzhe Zhao and Heng Xie and Zijian Wang and Chunlin
                 Tian and Li Li and Yan Zhu and R. P. Martins and
                 Chi-Hang Chan and Minglei Zhang",
  booktitle =    "{2025 IEEE Custom Integrated Circuits Conference
                 (CICC)}",
  title =        "A One-Shot Floating-Point Compute-in-Memory Macro
                 Featuring {PVT} Robustness and Mismatch Tolerance for
                 Edge {LLMs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--3",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/CICC63670.2025.10982833",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy; Large language models; Power demand;
                 Privacy; Productivity; Quantization (signal); Real-time
                 systems; Robustness; Throughput; Transformers",
}

@Article{Zhao:2025:SCS,
  author =       "Gaoyang Zhao and Qiuran Li and Rongzhen Lin and Yaohua
                 Wang",
  title =        "{Shift-CIM}: {In-SRAM} Alignment To Support
                 General-Purpose Bit-level Sparsity Exploration in
                 {SRAM} Multiplication",
  journal =      j-TACO,
  volume =       "22",
  number =       "2",
  pages =        "59:1--59:??",
  month =        jun,
  year =         "2025",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3719654",
  ISSN =         "1544-3566 (print), 1544-3973 (electronic)",
  ISSN-L =       "1544-3566",
  bibdate =      "Thu Jul 3 06:51:03 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/taco.bib",
  abstract =     "Multiplication plays a critical role in SRAM-based
                 Computing-in-Memory (CIM) architectures. However,
                 current SRAM-based CIMs face three major limitations.
                 First, they do not fully exploit bit-level sparsity,
                 resulting in unnecessary overhead in both \ldots{}",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Archit. Code Optim.",
  articleno =    "59",
  fjournal =     "ACM Transactions on Architecture and Code Optimization
                 (TACO)",
  journal-URL =  "https://dl.acm.org/loi/taco",
}

@Article{Zhou:2025:BDC,
  author =       "Yang Zhou and Yang Wang and Wenxin Yin and Yazheng
                 Jiang and Jingchuan Wei and Yubin Qin and Yang Hu and
                 Shaojun Wei and Shouyi Yin",
  title =        "{BeaCIM}: a Digital Compute-in-Memory {DNN} Processor
                 With Bi-Directional Exponent Alignment for {FP8}
                 Training",
  journal =      j-IEEE-TRANS-CIRCUITS-SYST-II-EXPRESS-BRIEFS,
  volume =       "72",
  number =       "4",
  pages =        "608--612",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/TCSII.2025.3541101",
  ISSN =         "1549-7747 (print), 1558-3791 (electronic)",
  ISSN-L =       "1549-7747",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Circuits and Systems II: Express
                 Briefs",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/issues?punumber=8920",
  keywords =     "Accuracy; Artificial neural networks; Bidirectional
                 control; Calculators; Compute-in-memory; Computer
                 architecture; DNN training; Energy efficiency; FP8;
                 Hardware; Technological innovation; Tensors; Training",
}

@Article{Zhu:2025:BSA,
  author =       "Zixuan Zhu and Xiaolong Zhou and Chundong Wang and Li
                 Tian and Zunkai Huang and Yongxin Zhu",
  title =        "Bit-Sparsity Aware Acceleration With Compact {CSD}
                 Code on Generic Matrix Multiplication",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "74",
  number =       "2",
  pages =        "414--426",
  year =         "2025",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2024.3483632",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Oct 1 06:40:18 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Accuracy; Bit-level sparsity; canonical signed digit;
                 Codes; Computers; Encoding; floating point; Hamming
                 weight; hardware acceleration; matrix multiplication;
                 Software; System-on-chip; Throughput; Transformers;
                 Vectors",
}

@Article{Zou:2025:REA,
  author =       "Qinmeng Zou",
  title =        "Rounding Error Analysis of the Inverse Compact {WY}
                 Modified {Gram--Schmidt} Algorithms",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "46",
  number =       "1",
  pages =        "726--747",
  month =        "????",
  year =         "2025",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/24M1655482",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  bibdate =      "Thu Oct 16 12:49:38 MDT 2025",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/46/1;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  URL =          "https://epubs.siam.org/doi/10.1137/24M1655482",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
}

@Article{Attanayake:2026:FPC,
  author =       "Ruvini Attanayake and Umesh C. Roy and Abhiyan Pandit
                 and Angelo Bongiorno",
  title =        "First-principles calculation of higher-order elastic
                 constants from divided differences",
  journal =      j-COMP-PHYS-COMM,
  volume =       "318",
  number =       "??",
  pages =        "??--??",
  month =        jan,
  year =         "2026",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/j.cpc.2025.109877",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Nov 3 13:41:44 MST 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465525003790",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys. Commun.",
  articleno =    "109877",
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}

@Article{Brisebarre:2026:CRE,
  author =       "Nicolas Brisebarre and Guillaume Hanrot and
                 Jean-Michel Muller and Paul Zimmermann",
  title =        "Correctly-Rounded Evaluation of a Function: Why, How,
                 and at What Cost?",
  journal =      j-COMP-SURV,
  volume =       "58",
  number =       "1",
  pages =        "27:1--27:34",
  month =        jan,
  year =         "2026",
  CODEN =        "CMSVAN",
  DOI =          "https://doi.org/10.1145/3747840",
  ISSN =         "0360-0300 (print), 1557-7341 (electronic)",
  ISSN-L =       "0360-0300",
  bibdate =      "Fri Oct 24 10:49:56 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compsurv.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "The goal of this article is to give a survey on the
                 various computational and mathematical issues and
                 progress related to the problem of providing efficient
                 correctly rounded elementary functions in
                 floating-point arithmetic. We also aim at convincing
                 the reader that a future standard for floating-point
                 arithmetic should require the availability of a
                 correctly rounded version of a well-chosen core set of
                 elementary functions. We discuss the interest and
                 feasibility of this requirement.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Comput. Surv.",
  articleno =    "27",
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "https://dl.acm.org/loi/csur",
}

@Article{Dumas:2026:TAG,
  author =       "Jean-Guillaume Dumas and Cl{\'e}ment Pernet and
                 Alexandre Sedoglavic",
  title =        "Towards automated generation of fast and accurate
                 algorithms for recursive matrix multiplication",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "134",
  number =       "??",
  pages =        "??--??",
  month =        may # "\slash " # jun,
  year =         "2026",
  CODEN =        "JSYCEH",
  DOI =          "https://doi.org/10.1016/j.jsc.2025.102524",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  bibdate =      "Wed Nov 26 07:46:45 MST 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0747717125001063",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Symb. Comput.",
  articleno =    "102524",
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171",
}

@TechReport{Gladman:2026:AMF,
  author =       "Brian Gladman and Vincenzo Innocente and John Mather
                 and Katsuhisa Ozaki and Paul Zimmermann",
  title =        "Accuracy of Mathematical Functions in Single, Double,
                 Double Extended, and Quadruple Precision",
  institution =  "????",
  pages =        "29",
  day =          "13",
  month =        feb,
  year =         "2026",
  bibdate =      "Fri Feb 13 07:12:00 2026",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://members.loria.fr/PZimmermann/papers/accuracy.pdf",
  acknowledgement = ack-nhfb,
  remark-1 =     "Tabular comparison of AMD, Apple, ARM, CUDA, FreeBSD,
                 GNU, Intel, LLVM, Microsoft Musl, Newlib, OpenLibm,
                 RadeonOpenCompute (ROCm), and RedHat -lm libraries for
                 correct rounding, versus results from MPFR. The e-mail
                 announcement reports: ``Main changes in this update: *
                 we have added compoundn, pown and rootn; * GNU libc is
                 the first library to provide all new C23 functions; *
                 GNU libc now provides 31 correctly-rounded functions in
                 single precision.''",
  remark-2 =     "Includes updates to MSVC 2026, fixing issues with MSVC
                 2022. At least one library now provides a
                 correctly-rounded version of all C99 univariate
                 functions, except atan, cosh, sinh, and tanh.",
}

@Article{Guo:2026:TFP,
  author =       "Lidong Guo and Zhenhua Zhu and Xuefei Ning and
                 Tengxuan Liu and Shiyao Li and Guohao Dai and Huazhong
                 Yang and Wangyang Fu and Yu Wang",
  title =        "Towards Floating Point-Based {AI} Acceleration: Hybrid
                 {PIM} with Non-Uniform Data Format and Reduced
                 Multiplications",
  journal =      j-TODAES,
  volume =       "31",
  number =       "1",
  pages =        "9:1--9:27",
  month =        jan,
  year =         "2026",
  CODEN =        "ATASFO",
  DOI =          "https://doi.org/10.1145/3769304",
  ISSN =         "1084-4309 (print), 1557-7309 (electronic)",
  ISSN-L =       "1084-4309",
  bibdate =      "Mon Nov 17 05:37:18 MST 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/todaes.bib",
  abstract =     "Neural networks (NNs) have exhibited excellent
                 performance in various fields of artificial
                 intelligence. However, the primary operations in these
                 mainstream models, including matrix-vector
                 multiplication (MVM), element-wise multiplication
                 (EWM), and depth-wise convolution (DWConv), require
                 massive data movements during computation, which
                 greatly impacts NNs inference performance. The emerging
                 Processing-In-Memory (PIM) architectures have shown
                 great potential to overcome the memory wall problem.
                 However, constrained by the supported data format and
                 operator type, directly adopting PIM architectures for
                 neural network acceleration faces three challenges: (1)
                 Floating-point (FP) format has been widely adopted for
                 ensuring high algorithm accuracy. However, Resistive
                 Random-Access Memory (RRAM)-based analog PIM
                 architectures perform integer (INT) MVMs in the analog
                 domain, limiting their application to the more accurate
                 FP format; (2) Static Random-Access Memory (SRAM)-based
                 digital PIM architectures require additional circuits
                 to support the FP format, and the SRAM capacity cannot
                 satisfy the storage requirement of latest large
                 language models (LLMs); (3) When performing the
                 operators with few accumulation steps, such as EWMs and
                 DWConvs, only few memory units in PIM architecture are
                 activated, resulting in severe device
                 under-utilization.\par

                 To tackle the above challenges, this article proposes
                 an RRAM and 3D-SRAM-based hybrid PIM architecture,
                 achieving FP-based algorithm accuracy, high device
                 utilization, and high energy efficiency. At the
                 software level, we first analyze the impact of
                 quantization errors on NN s inference accuracy. For the
                 quantization error-insensitive MVM operations, we
                 propose the PIM-oriented exponent-free non-uniform (PN)
                 data format. The proposed PN format can be flexibly
                 adjusted to fit the non-uniform distribution and
                 approach FP-based algorithm accuracy using
                 bit-slicing-based full INT operations. For the
                 quantization error-sensitive EWM\slash DWConv
                 operations, we introduce the multiplication-free
                 approximated FP multiplications to reduce the
                 additional hardware overhead. At the hardware level, we
                 propose a hybrid PIM architecture, including an RRAM
                 analog PIM using shift-and-add for PN-based MVMs, and a
                 3D-SRAM digital PIM with high utilization for
                 DWConv\slash EWM operations. Extensive experiments on
                 CNNs and attention-free LLMs validate that the proposed
                 PIM architecture achieves up to $ 99.4 \times $ and $
                 33.94 \times $ speedup with $ 5697.74 \times $ and $
                 8.24 \times $ energy efficiency improvement compared to
                 GPU and PIM-baseline, respectively. With the proposed
                 PN format and approximated FP multiplications, the
                 algorithm accuracy of CNNs and attention-free LLMs can
                 be improved by up to 3.01\% and 10.18\%,
                 respectively.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Transact. Des. Automat. Electron. Syst.",
  articleno =    "9",
  fjournal =     "ACM Transactions on Design Automation of Electronic
                 Systems",
  journal-URL =  "https://dl.acm.org/loi/todaes",
}

@Article{Ha:2026:LMD,
  author =       "Nguyen Thi Thai Ha and Ngo Le Hong Phuc and Vu Mai
                 Trang",
  title =        "Lengths of matrix decompositions over division
                 algebras with $k$-involutions",
  journal =      j-LINEAR-ALGEBRA-APPL,
  volume =       "729",
  number =       "??",
  pages =        "337--349",
  day =          "15",
  month =        jan,
  year =         "2026",
  CODEN =        "LAAPAW",
  DOI =          "https://doi.org/10.1016/j.laa.2025.10.008",
  ISSN =         "0024-3795 (print), 1873-1856 (electronic)",
  ISSN-L =       "0024-3795",
  bibdate =      "Mon Oct 27 09:42:54 MDT 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/linala2025.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S002437952500415X",
  acknowledgement = ack-nhfb,
  ajournal =     "Linear Algebra Appl.",
  fjournal =     "Linear Algebra and its Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00243795",
}

@Article{Ji:2026:HPA,
  author =       "Xiaoyu Ji and Cheng Chen and Gangqiang Yang and
                 Hongchao Zhou and Hailiang Xiong and Xianye Ben and
                 Zhiguo Wan",
  title =        "High-Performance Accelerator for Constant-Time
                 Cross-Domain Integer and {Montgomery} Inversion on
                 {FPGA}",
  journal =      j-TECS,
  volume =       "25",
  number =       "1",
  pages =        "1:1--1:26",
  month =        jan,
  year =         "2026",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3777365",
  ISSN =         "1539-9087 (print), 1558-3465 (electronic)",
  ISSN-L =       "1539-9087",
  bibdate =      "Tue Jan 20 07:06:14 MST 2026",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tecs.bib",
  abstract =     "Modular Inversion (MI) is one of the fundamental
                 arithmetic operations in the finite field, which plays
                 an essential role in various cryptographic applications
                 and requires high performance and security.
                 Unfortunately, the simple MI algorithm is vulnerable to
                 side-channel attacks, such as the timing attack, which
                 can compromise the cryptographic system by analyzing
                 the time taken to execute cryptographic algorithms.
                 Attackers may recover the initial data since the time
                 can differ based on the input. Besides, the low
                 complexity and low resource consumption of hardware
                 implementations in MI are also challenging. In this
                 article, we propose two novel modular inversion
                 algorithms, named Constant-Time Integer Modular
                 Inversion (CT-IMI) and Constant-Time Complementary
                 Montgomery Modular Inversion (CT-CMMI). They both
                 consist of constant iteration rounds to resist the
                 timing attack. CT-IMI processes the data in the integer
                 field, which is designed for common scenarios. CT-CMMI
                 is suitable for the cross-domain case, which can
                 directly use data in the Montgomery domain and avoid
                 the conversion steps for some specific applications,
                 e.g., scalar multiplication in Elliptic Curve
                 Cryptography (ECC). In software simulations, we measure
                 the average clock cycles for a single inversion and
                 illustrate the relationship between various bit lengths
                 and the latency. The significant differences between
                 constant and non-constant algorithms demonstrate the
                 vulnerability of modular inversion to timing attacks.
                 In addition, we design two efficient hardware
                 architectures on FPGA. Experimental results show that
                 our CT-IMI can finish a single inversion in 2.56 s with
                 4.2k LUTs, 1.8k FFs, and our CT-CMMI requires 2.45 s
                 with 2.7k LUTs, 1.6k FFs. The product of area and
                 latency of our CT-IMI and CT-CMMI can reach 10.50 and
                 6.62, respectively, which shows optimal performance
                 compared with all the results in the existing
                 literature.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Embed. Comput. Syst.",
  articleno =    "1",
  fjournal =     "ACM Transactions on Embedded Computing Systems",
  journal-URL =  "https://dl.acm.org/loi/tecs",
}

@Article{Karp:2026:ELF,
  author =       "Martin Karp and Ronith Stanly and Timofey Mukha and
                 Luca Galimberti and Siavash Toosi and Hang Song and
                 Lisandro Dalcin and Saleh Rezaeiravesh and Niclas
                 Jansson and Stefano Markidis and Matteo Parsani and
                 Sanjeeb Bose and Sanjiva Lele and Philipp Schlatter",
  title =        "Effects of lower floating-point precision on
                 scale-resolving numerical simulations of turbulence",
  journal =      j-J-COMPUT-PHYS,
  volume =       "549",
  number =       "??",
  pages =        "??--??",
  day =          "15",
  month =        mar,
  year =         "2026",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1016/j.jcp.2025.114600",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Tue Jan 27 10:36:35 MST 2026",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys2025.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0021999125008824",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Comput. Phys.",
  articleno =    "114600",
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991",
}

@Article{Kelayeh:2026:AAR,
  author =       "Mahla Salehi Sheikhali Kelayeh and Sahand Divsalar and
                 Shaghayegh Vahdat and Nima TaheriNejad",
  title =        "{ARTS}: an approximate reduced tree and
                 segmentation-based multiplier",
  journal =      j-FUT-GEN-COMP-SYS,
  volume =       "175",
  number =       "??",
  pages =        "??--??",
  month =        feb,
  year =         "2026",
  CODEN =        "FGSEVI",
  DOI =          "https://doi.org/10.1016/j.future.2025.108098",
  ISSN =         "0167-739X (print), 1872-7115 (electronic)",
  ISSN-L =       "0167-739X",
  bibdate =      "Mon Nov 3 14:04:14 MST 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/futgencompsys2020.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167739X25003929",
  acknowledgement = ack-nhfb,
  ajournal =     "Future Gener. Comput. Syst.",
  articleno =    "108098",
  fjournal =     "Future Generation Computer Systems",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0167739X",
  keywords =     "approximate computing; ARTS (approximate multiplier);
                 deep neural network; image processing; partial product
                 reduction; static segmentation",
}

@Article{Lutz:2026:FFM,
  author =       "David R. Lutz and Anisha Saini and Mairin Kroes and
                 Thomas Elmer and Harsha Valsaraju and Javier D.
                 Bruguera",
  title =        "Fused {FP8} Many-Terms Dot Product With Scaling and
                 {FP32} Accumulation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "75",
  number =       "3",
  pages =        "1171--1182",
  month =        mar,
  year =         "2026",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2025.3648544",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Feb 25 06:24:18 2026",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Accuracy; Adders; Computers; Dot product;
                 floating-point scaling; fused floating-point
                 arithmetic; machine learning; Microarchitecture;
                 Multiplexing; Proposals; Quantization (signal); small
                 floating-point formats; Training; Trees (botanical);
                 Vectors",
}

@Article{Mallasen:2026:NPA,
  author =       "David Mallas{\'e}n and Raul Murillo and Guillermo
                 Botella and Alberto Antonio {Del Barrio}",
  title =        "Navigating Posit Arithmetic: a Comprehensive Survey of
                 Principles, Hardware, and Applications",
  journal =      j-COMP-SURV,
  volume =       "58",
  number =       "5",
  pages =        "131:1--131:36",
  month =        apr,
  year =         "2026",
  CODEN =        "CMSVAN",
  DOI =          "https://doi.org/10.1145/3772284",
  ISSN =         "0360-0300 (print), 1557-7341 (electronic)",
  ISSN-L =       "0360-0300",
  bibdate =      "Mon Dec 22 12:35:50 MST 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compsurv.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Comput. Surv.",
  articleno =    "131",
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "https://dl.acm.org/loi/csur",
}

@Article{Mishra:2026:DMR,
  author =       "Vishesh Mishra and Mahendra Rathor and Urbi
                 Chatterjee",
  title =        "Dual-Mode Rounding Algorithms and Hardware for
                 Posit-Based {DNN} Training: The Future of Mixed
                 Precision Frameworks",
  journal =      j-TECS,
  volume =       "25",
  number =       "1",
  pages =        "16:1--16:26",
  month =        jan,
  year =         "2026",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/3772092",
  ISSN =         "1539-9087 (print), 1558-3465 (electronic)",
  ISSN-L =       "1539-9087",
  bibdate =      "Tue Jan 20 07:06:14 MST 2026",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/tecs.bib",
  abstract =     "The Posit number system provides a promising
                 alternative to traditional floating-point (FP) formats
                 for deep neural network (DNN) training by offering
                 tapered precision and a wide dynamic range, addressing
                 key limitations of conventional FP formats. While
                 recent research has demonstrated the advantages of
                 Posit-enabled training and inference for
                 fixed-precision applications, the development of
                 mixed-precision frameworks has been hindered by the
                 absence of rounding algorithms for transitioning
                 between Posit formats. This dependency has limited the
                 practical adoption of Posits in DNN workflows. In this
                 article, we present a Posit-based Mixed Precision
                 Training and Inference (PMP) framework, leveraging
                 Posit32, Posit16, and Posit8 for distinct computational
                 stages. Posit32 ensures numerical stability in critical
                 operations, Posit16 balances precision and efficiency
                 for intermediate computations, and Posit8 significantly
                 reduces memory usage during inference. Specifically, we
                 introduce algorithms for converting Posit32
                 representations into Posit16 and Posit8, and vice
                 versa, under two rounding modes: deterministic and
                 stochastic. Stochastic rounding is employed to mitigate
                 precision loss in low-precision arithmetic.
                 Furthermore, we propose a hardware-efficient Posit
                 Multiply-Accumulate (pMAC) Unit that integrates
                 deterministic and stochastic rounding modules, enabling
                 efficient mixed-precision computations. We validate our
                 framework on ResNet-18, ResNet-50, ResNet-152,
                 MobileNet-v2, VGG-16, and EfficientNet-B7 (trained on
                 ImageNet), YOLOv2 (trained on PASCAL VOC 2012), and
                 BERT (trained on WikiText-2). Experimental results
                 demonstrate up to $ 1.5 \times $ training speedup with
                 Posit16-based PMP framework and up to $ 6.5 \times $
                 training speedup with Posit8-based PMP framework when
                 compared with fixed-precision FP32 training, while
                 maintaining comparable or superior accuracy. Moreover,
                 hardware results show that the design overhead of
                 integrating proposed deterministic and stochastic
                 rounding modules with the pMAC unit is estimated to be
                 around 4.6\% only.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Embed. Comput. Syst.",
  articleno =    "16",
  fjournal =     "ACM Transactions on Embedded Computing Systems",
  journal-URL =  "https://dl.acm.org/loi/tecs",
}

@Article{Villaba-Moreno:2026:EDR,
  author =       "Julio Villaba-Moreno",
  title =        "Enhancing Digit-Recurrence Floating-Point {HUB}
                 Division",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "75",
  number =       "1",
  pages =        "127--138",
  month =        jan,
  year =         "2026",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2025.3624877",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Tue Dec 23 07:42:14 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2020.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  keywords =     "Accuracy; Arithmetic; Convergence; Energy efficiency;
                 floating point division; Hardware; HUB format; IEEE
                 Standards; Prediction algorithms; Reproducibility of
                 results; Signal processing algorithms; Standards",
}

@Misc{Anonymous:20xx:CMP,
  author =       "Anonymous",
  title =        "The {CORE-MATH} project",
  howpublished = "Web site and code archive",
  year =         "20xx",
  bibdate =      "Mon Dec 04 07:10:51 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://core-math.gitlabpages.inria.fr/",
  acknowledgement = ack-nhfb,
  remark =       "From the Web site: ``CORE-MATH Mission: provide
                 on-the-shelf high performance open-source mathematical
                 functions with correct rounding that can be integrated
                 into current mathematical libraries (GNU libc, Intel
                 Math Library, AMD Libm, Newlib, OpenLibm, Musl, Apple
                 Libm, llvm-libc, Microsoft libm, CUDA libm, ROCm)''",
}

@Misc{Hyland:20xx:FIS,
  author =       "Adam Hyland",
  title =        "The Fast Inverse Square Root",
  howpublished = "Web site.",
  year =         "20xx",
  bibdate =      "Fri Dec 12 15:05:49 2025",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/hartree-douglas-r.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://0x5f37642f.com/",
  acknowledgement = ack-nhfb,
  keywords =     "inverse square root; reciprocal square root",
  remark =       "The Internet domain name in the URL contains a magic
                 hexadecimal constant that is used in computing a rough
                 approximation to $ 1 / \sqrt {x} $ in IEEE 754 binary32
                 arithmetic. The Web site supplies a considerable number
                 of references to earlier work on fast approximations
                 for this function, dating back to 1949 on the
                 Manchester Mark I. Tests of the Web site code, which
                 requires replacement of `long' by `int32_t' on modern
                 platforms, show maximum errors of about 14700 ulps for
                 $x$ on [1/2,1] and [1,1024], corresponding to
                 perturbations in the fourth decimal digit of the
                 computed reciprocal square root.",
}

@Misc{QinetiQ:20xx:QFP,
  author =       "{QinetiQ}",
  title =        "{Quixilica} floating point cores",
  howpublished = "Web document",
  year =         "20xx",
  bibdate =      "Sat Oct 9 12:58:32 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.tekmicro.com/",
  acknowledgement = ack-nhfb,
}

%%% ====================================================================
%%% The following entries must come last, because of limitations in the
%%% current BibTeX implementation which require that they follow entries
%%% that cross-reference them.

@Proceedings{Anonymous:1948:PSL,
  editor =       "Anonymous",
  booktitle =    "Proceedings of a {Symposium on Large-Scale Digital
                 Calculating Machinery}: Jointly Sponsored by {The Navy
                 Department Bureau of Ordnance and Harvard University at
                 The Computation Laboratory 7--10 January 1947}",
  title =        "Proceedings of a {Symposium on Large-Scale Digital
                 Calculating Machinery}: Jointly Sponsored by {The Navy
                 Department Bureau of Ordnance and Harvard University at
                 The Computation Laboratory 7--10 January 1947}",
  volume =       "16",
  publisher =    pub-HARVARD,
  address =      pub-HARVARD:adr,
  pages =        "xxix + 302",
  year =         "1948",
  LCCN =         "QA75 .S96 1947",
  bibdate =      "Mon Nov 4 07:46:57 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
                 https://www.math.utah.edu/pub/tex/bib/adabooks.bib;
                 https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "The Annals of the Computation Laboratory of Harvard
                 University",
  acknowledgement = ack-nhfb,
  keywords =     "calculators --- congresses; electronic digital
                 computers --- congresses",
  remark =       "Goldstine's paper is listed in the table of contents,
                 but is absent from the volume. The printed order of a
                 few papers differs from that shown in the table of
                 contents; the order has been corrected in the data in
                 this entry.",
  tableofcontents = "Program of the Symposium on Large-Scale Digital
                 Calculating Machinery: 7--10 January 1947 \\
                 First Session: Tuesday, 7 January 1947 1O:00 a.m. \\
                 Opening Addresses \\
                 Mr. Edward Reynolds, Administrative Vice President of
                 Harvard University / 3--3 \\
                 Rear Admiral C. T. Joy, USN, Naval Proving Ground,
                 Dahlgren, Virginia / 4--6 \\
                 Professor Howard H. Aiken, Chairman, Harvard University
                 / 7--7 \\
                 11:00 a.m. Inspection of the Computation Laboratory and
                 of Mark II Calculator \\
                 Second Session: Tuesday, 7 January 1947, 2:00 p.m. \\
                 Existing Calculating Machines / \\
                 Professor Willard E. Bleick, Chairman, Post Graduate
                 School, U.S. Naval Academy, Annapolis / \\
                 Mr. Richard H. Babbage, Montreal, Canada / The Work of
                 Charles Babbage / 13--22 \\
                 Mr. Richard M. Bloch, Harvard University / Mark I
                 Calculator / 23--30 \\
                 Dr. Lewis P. Tabor, University of Pennsylvania / Brief
                 Description and Operating Characteristics of the ENIAC
                 / 31--40 \\
                 Mr. Samuel B. Williams, Consulting Electrical Engineer
                 / Bell Telephone Laboratories' Relay Computing System /
                 41--68 \\
                 Mr. Robert V. D. Campbell, Harvard University / Mark II
                 Calculator / 69--79 \\
                 Third Session: Wednesday, 8 January 1947, 9:30 a.m. \\
                 The Logic of Large-Scale Calculating Machinery / \\
                 Professor \Vendell H. Furry, Chairman, Harvard
                 University \\
                 Dr. Alexander W. Wundheiler, Bureau of Ordnance /
                 Problems of Mathematical Analysis Involved in Machine
                 Computations / 83--90 \\
                 Dr. George R. Stibitz, University of Vermont / The
                 Organization of Large-Scale Calculating Machinery /
                 91--100 \\
                 Fourth Session: Wednesday, 8 January 1947, 2:00 p.m.
                 \\
                 Storage Devices \\
                 Dr. John H. Curtiss, Chairman / National Bureau of
                 Standards / \\
                 Dr. T. Kite Sharpless, University of Pennsylvania /
                 Mercury Delay Lines as a Memory Unit / 103--109 \\
                 Professor Leon Brillouin, Harvard University / Slow
                 Electromagnetic Waves / 110--124 \\
                 Dr. Jay W. Forrester, Massachusetts Institute of
                 Technology / High-Speed Electrostatic Storage /
                 125--129 \\
                 Dr. Benjamin L. Moore, Harvard University / Magnetic
                 and Phosphor Coated Discs / 130--132 \\
                 Dr. Jan Rajchman, Radio Corporation of America / The
                 Selectron --- A Tube for Selective Electrostatic
                 Storage / 133--145 \\
                 Dr. Arthur W. Tyler, Eastman Kodak Company / Optical
                 and Photographic Storage Techniques / 146--150 \\
                 Fifth Session: Thursday, 9 January 1947, 9:30 a.m. \\
                 Numerical Methods and Suggested Problems for Solution
                 \\
                 Dr. Mina Rees, Chairman, Office of Naval Research \\
                 Professor Richard Courant, New York University / Method
                 of Finite Differences for the Solution of Partial
                 Differential Equations / 153--156 \\
                 Dr. Raymond J. Seeger, Naval Ordnance Laboratory / On
                 Computational Techniques for Certain Problems in Fluid
                 Dynamics / 157--168 \\
                 Professor Wassily W. Leontief, Harvard University /
                 Computational Problems Arising in Connection with
                 Economic Analysis of interindustrial Relationships /
                 169--175 \\
                 Professor Hans A. Rademacher, University of
                 Pennsylvania / On the Accumulation of Errors in
                 Processes of Integration on High-Speed Calculating
                 Machines / 176--187 \\
                 Professor Howard W. Emmons, Harvard University / Fluid
                 Mechanics Computations / 188--193 \\
                 Dr. L. S. Dederick, Ballistic Research Laboratory,
                 Aberdeen, Maryland / Firing Tables / 194--199 \\
                 Sixth Session: Thursday, 9 January 1947, 2:00 p.m. \\
                 Sequencing, Coding, and Problem Preparation \\
                 Dr. Julius A. Stratton, Chairman, Massachusetts
                 Institute of Technology \\
                 Dr. John W. Mauchly, Electronic Control Company /
                 Preparation of Problems for EDVAC-Type Machines /
                 203--207 \\
                 Mr. Joseph 0. Harrison, Jr., Harvard University / The
                 Preparation of Problems for the Mark I Calculator /
                 208--210 \\
                 Dr. Herman H. Goldstine, Institute for Advanced Study /
                 Coding for Large-Scale Calculating Machinery / ??--??
                 \\
                 Seventh Session: Friday, 10 January 1947, 9:30 a.m. \\
                 Input and Output Devices \\
                 Professor E. Leon Chaffee, Chairman, Harvard University
                 \\
                 Mr. Frederick G. Miller, Harvard University /
                 Application of Printing Telegraph Techniques to
                 Large-Scale Calculating Machinery / 213--222 \\
                 Mr. Otto Kornei, The Brush Development Company / Survey
                 of Magnetic Recording / 223--237 \\
                 Mr. Harrison W. Fuller, Harvard University / The
                 Numeroscope / 238--247 \\
                 Dr. Samuel N. Alexander, National Bureau of Standards /
                 Input and Output Devices for Electronic Digital
                 Calculating Machinery / 248--253 \\
                 Dr. Morris Rubinoff, Harvard University / An Input
                 Device Using Multiple Gates / 254--259 \\
                 Dr. R. D. O'Neal, Eastman Kodak Company / Photographic
                 Methods of Handling Input and Output Data / 260--266
                 \\
                 Mr. C. Bradford Sheppard, Electronic Control Company /
                 Transfer Between External and Internal Memory /
                 267--273 \\
                 Eighth Session: Friday, 10 January 1947, 2:00 p.m. \\
                 Conclusions and Open Discussion \\
                 Professor Charles C. Bramble, Chairman, Post Graduate
                 School, U.S. Naval Academy, Annapolis / \\
                 Professor Samuel H. Caldwell, Massachusetts Institute
                 of Technology / Publication, Classification, and
                 Patents / 277--283 \\
                 Dr. Louis Couffignal (in absentia), Centre National de
                 la Recherche Scientifique / Le Domaine du Calcul
                 M{\'e}canique / 284--296 \\
                 Dr. Alan T. Waterman, Office of Naval Research / New
                 Vistas in Mathematics / 298--302",
}

@Proceedings{Householder:1951:MCM,
  editor =       "Alston S. Householder and George E. Forsythe and
                 Hallett-Hunt Germond",
  booktitle =    "{Monte Carlo method. Proceedings of a Symposium Held
                 June 29, 30 and July 1, 1949 in Los Angeles,
                 California}",
  title =        "{Monte Carlo method. Proceedings of a Symposium Held
                 June 29, 30 and July 1, 1949 in Los Angeles,
                 California}",
  volume =       "12",
  publisher =    pub-USGPO,
  address =      pub-USGPO:adr,
  pages =        "49",
  year =         "1951",
  bibdate =      "Tue Jan 31 06:36:58 2017",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  series =       ser-APPL-MATH-SER-NBS,
  acknowledgement = ack-nhfb,
  tableofcontents = "Preface / iii \\
                 Foreword / v \\
                 1. Showers produced by low-energy electrons and photons
                 / Robert R. Wilson / 1 \\
                 2. An alignment chart for Monte Carlo solution of the
                 transport problem / B. I. Spinrad, G. H. Goertzel, W.
                 S. Snyder / 4 \\
                 3. Neutron age calculations in water, graphite, and
                 tissue / Alston S. Householder / 6 \\
                 4. Methods of probabilities in chains applied to
                 particle transmission through matter / Wendell C.
                 DeMarcus, Lewis Nelson / 9 \\
                 5. Stochastic methods in statistical mechanics / W.
                 Gilbert King / 12 \\
                 6. Report on a Monte Carlo calculation performed with
                 the Eniac / Maria Mayer / 19 \\
                 7. Calculation of shielding properties of water for
                 high energy neutrons / Preston C. Hammer / 21 \\
                 8. A Monte Carlo technique for estimating particle
                 attenuation in bulk matter / B. A. Shoor, Lewis Nelson,
                 Wendell DeMarcus, Robert L. Echols / 24 \\
                 9. Estimation of particle transmission by random
                 sampling / Herman Kahn, T. E. Harris / 27 \\
                 10. History of RAND's random digits --- Summary / W.
                 George Brown / 31 \\
                 11. The mid-square method of generating digits /
                 Preston C. Hammer / 33 \\
                 12. Generation and testing of random digits at the
                 National Bureau of Standards, Los Angeles / George E.
                 Forsythe / 34 \\
                 13. Various techniques used in connection with random
                 digits / John von Neumann / 36 \\
                 14. Round table discussion / H. H. Germond / 39",
}

@Book{Alt:1960:AC,
  editor =       "Franz L. Alt and Andrew Donald Booth and Robert Emmet
                 Meagher",
  booktitle =    "Advances in Computers",
  title =        "Advances in Computers",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "x + 316",
  year =         "1960",
  ISSN =         "0065-2458",
  LCCN =         "QA76 .A3",
  bibdate =      "Sat Nov 29 11:05:31 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{Taub:1961:JNCa,
  editor =       "A. H. Taub",
  booktitle =    "{John von Neumann}: Collected Works: {Volume I}:
                 {Logic}, Theory of Sets and Quantum Mechanics",
  title =        "{John von Neumann}: Collected Works: {Volume I}:
                 {Logic}, Theory of Sets and Quantum Mechanics",
  publisher =    pub-PERGAMON,
  address =      pub-PERGAMON:adr,
  pages =        "x + 654",
  year =         "1961",
  LCCN =         "????",
  bibdate =      "Wed Jun 01 16:58:29 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also volumes II--VI
                 \cite{Taub:1961:JNCb,Taub:1961:JNCc,Taub:1962:JNC,Taub:1963:JNCa,Taub:1963:JNCb}.",
  ZMnumber =     "0188.00102",
  acknowledgement = ack-nhfb,
}

@Book{Taub:1961:JNCb,
  editor =       "A. H. Taub",
  booktitle =    "{John von Neumann}: Collected Works. {Volume II}:
                 {Operators}, Ergodic Theory and Almost Periodic
                 Functions in a Group",
  title =        "{John von Neumann}: Collected Works. {Volume II}:
                 {Operators}, Ergodic Theory and Almost Periodic
                 Functions in a Group",
  publisher =    pub-PERGAMON,
  address =      pub-PERGAMON:adr,
  pages =        "x + 568",
  year =         "1961",
  LCCN =         "????",
  bibdate =      "Wed Jun 01 16:58:29 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also volumes I, III--VI
                 \cite{Taub:1961:JNCa,Taub:1961:JNCc,Taub:1962:JNC,Taub:1963:JNCa,Taub:1963:JNCb}.",
  ZMnumber =     "0188.00102",
  acknowledgement = ack-nhfb,
}

@Book{Taub:1961:JNCc,
  editor =       "A. H. Taub",
  booktitle =    "{John von Neumann}: Collected Works. {Volume III}:
                 Rings of Operators",
  title =        "{John von Neumann}: Collected Works. {Volume III}:
                 Rings of Operators",
  publisher =    pub-PERGAMON,
  address =      pub-PERGAMON:adr,
  pages =        "ix + 574",
  year =         "1961--1963",
  LCCN =         "????",
  bibdate =      "Wed Jun 01 16:58:29 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also volumes I--II, IV--VI
                 \cite{Taub:1961:JNCa,Taub:1961:JNCb,Taub:1962:JNC,Taub:1963:JNCa,Taub:1963:JNCb}.",
  ZMnumber =     "0188.00102",
  acknowledgement = ack-nhfb,
}

@Proceedings{AFIPS:1962:APS,
  editor =       "AFIPS",
  key =          "AFIPS SJCC '62",
  booktitle =    "{AFIPS} Proceedings of the {Spring Joint Computer
                 Conference} 1962",
  title =        "{AFIPS} Proceedings of the {Spring Joint Computer
                 Conference} 1962",
  volume =       "21",
  publisher =    pub-AFIPS,
  address =      pub-AFIPS:adr,
  pages =        "??--??",
  year =         "1962",
  LCCN =         "????",
  bibdate =      "Wed Feb 14 17:16:30 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "AFIPS conference proceedings",
  acknowledgement = ack-nhfb,
}

@Book{Taub:1962:JNC,
  editor =       "A. H. Taub",
  booktitle =    "{John von Neumann}: Collected Works. {Volume IV}:
                 {Continuous} Geometry and Other Topics",
  title =        "{John von Neumann}: Collected Works. {Volume IV}:
                 {Continuous} Geometry and Other Topics",
  publisher =    pub-PERGAMON,
  address =      pub-PERGAMON:adr,
  pages =        "x + 516",
  year =         "1962",
  LCCN =         "????",
  bibdate =      "Wed Jun 01 16:58:29 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also volumes I--III, V--VI
                 \cite{Taub:1961:JNCa,Taub:1961:JNCb,Taub:1961:JNCc,Taub:1963:JNCa,Taub:1963:JNCb}.",
  ZMnumber =     "0188.00102",
  acknowledgement = ack-nhfb,
}

@Proceedings{Metropolis:1963:PFS,
  editor =       "N. Metropolis and A. H. Taub and John Todd and C. B.
                 Tompkins",
  booktitle =    "{Experimental arithmetic, high speed computing and
                 mathematics: Proceedings of the fifteenth Symposium in
                 Applied Mathematics of the American Mathematical
                 Society held in Chicago, Illinois, April 12--14, 1962
                 and Atlantic City, New Jersey, April 16-19, 1962}",
  title =        "{Experimental arithmetic, high speed computing and
                 mathematics: Proceedings of the fifteenth Symposium in
                 Applied Mathematics of the American Mathematical
                 Society held in Chicago, Illinois, April 12--14, 1962
                 and Atlantic City, New Jersey, April 16-19, 1962}",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "ix + 396",
  year =         "1963",
  LCCN =         "QA297 .S987 1962",
  bibdate =      "Tue Mar 20 10:37:16 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{Taub:1963:JNCa,
  editor =       "A. H. Taub",
  booktitle =    "{John von Neumann}: Collected Works. {Volume V}:
                 {Design} of Computers, Theory of Automata and Numerical
                 Analysis",
  title =        "{John von Neumann}: Collected Works. {Volume V}:
                 {Design} of Computers, Theory of Automata and Numerical
                 Analysis",
  publisher =    pub-PERGAMON,
  address =      pub-PERGAMON:adr,
  pages =        "ix + 784",
  year =         "1963",
  LCCN =         "????",
  bibdate =      "Wed Jun 01 16:58:29 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See also volumes I--IV, VI
                 \cite{Taub:1961:JNCa,Taub:1961:JNCb,Taub:1961:JNCc,Taub:1962:JNC,Taub:1963:JNCb}.",
  ZMnumber =     "0188.00102",
  acknowledgement = ack-nhfb,
}

@Book{Taub:1963:JNCb,
  editor =       "A. H. Taub",
  booktitle =    "{John von Neumann}: Collected Works. {Volume VI}:
                 {Theory} of Games, Astrophysics, Hydrodynamics and
                 Meteorology",
  title =        "{John von Neumann}: Collected Works. {Volume VI}:
                 {Theory} of Games, Astrophysics, Hydrodynamics and
                 Meteorology",
  publisher =    pub-PERGAMON,
  address =      pub-PERGAMON:adr,
  pages =        "x + 538",
  year =         "1963",
  LCCN =         "????",
  bibdate =      "Wed Jun 01 16:58:29 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/f/fermi-enrico.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib;
                 https://www.math.utah.edu/pub/tex/bib/einstein.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "See also volumes I--V
                 \cite{Taub:1961:JNCa,Taub:1961:JNCb,Taub:1961:JNCc,Taub:1962:JNC,Taub:1963:JNCa}.",
  ZMnumber =     "0188.00102",
  acknowledgement = ack-nhfb,
}

@Book{Wilkinson:1963:REA,
  author =       "J. H. Wilkinson",
  booktitle =    "Rounding Errors in Algebraic Processes",
  title =        "Rounding Errors in Algebraic Processes",
  volume =       "32",
  publisher =    pub-HMSO,
  address =      pub-HMSO:adr,
  pages =        "vi + 161",
  year =         "1963",
  ISBN =         "0-486-67999-3 (Dover)",
  ISBN-13 =      "978-0-486-67999-0 (Dover)",
  LCCN =         "QA76.5 .W53 1964",
  MRclass =      "65.80",
  MRnumber =     "MR0161456 (28 \#4661)",
  MRreviewer =   "A. S. Householder",
  bibdate =      "Sat Feb 8 10:28:55 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Also published by Prentice-Hall, Englewood Cliffs, NJ,
                 USA, 1964, translated into Polish as {\em Bledy
                 Zaokragle{\'n} w Procesach Algebraicznych\/} by PWW,
                 Warsaw, Poland, 1967 and translated into German as {\em
                 Rundungsfehler\/} by Springer-Verlag, Berlin, Germany,
                 1969. Reprinted by Dover Publications, New York,
                 1994.",
  series =       "Notes on Applied Science",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
  tableofcontents = "1. The Fundamental Arithmetic Operations \\
                 Digital computation / 1 \\
                 Fixed-point and floating-point computation / 1 \\
                 Notational conventions / 2 \\
                 Rounding errors in fixed-point computation / 4 \\
                 Fixed-point accumulation of inner-products / 6 \\
                 Rounding errors in floating-point computation / 7 \\
                 Round-off with single-precision accumulator / 11 \\
                 Comparison of fixed-point and floating-point
                 computation / 14 \\
                 Common floating-point operations / 16 \\
                 More precise bounds / 19 \\
                 Floating-point accumulation of sums and inner-products
                 / 23 \\
                 Statistical error bounds / 25 \\
                 Block-floating vectors and matrices / 26 \\
                 Fundamental limitations oft-digit computation / 27 \\
                 Ill-conditioned problems / 28 \\
                 Condition numbers / 29 \\
                 Rounding errors in the computation / 30 \\
                 Additional comments / 33 \\
                 2. Computations Involving Polynomials \\
                 Evaluation of power series / 34 \\
                 Fixed-point representation / 34 \\
                 Floating-point representation / 36 \\
                 Calculation of zeros of functions defined by power
                 series / 37 \\
                 Polynomials with arbitrary coefficients / 38 \\
                 Condition of a polynomial with respect to the
                 computation of its zeros / 38 \\
                 Some typical distributions of zeros / 41 \\
                 Linear distributions of zeros / 41 \\
                 Geometric distribution / 44 \\
                 Chebyshev polynomial / 46 \\
                 Significance of the condition of the zeros of
                 polynomials 4 / 7 \\
                 Determination of the zeros / 49 \\
                 Iterative methods / 52 \\
                 Effect of rounding errors on Newton's process / 53 \\
                 Simple examples / 54 \\
                 Polynomial deflation / 55 \\
                 Analysis of errors inherent in deflation / 56 \\
                 Examples of deflation / 59 \\
                 Deflation of ill-conditioned polynomials / 62 \\
                 General comments on iteration and deflation / 64 \\
                 Purification in the original polynomial / 65 \\
                 Other iterative methods / 66 \\
                 The root-squaring process / 67 \\
                 Forward error analysis of root-squaring / 69 \\
                 Relative error in computed coefficients / 71 \\
                 Numerical example / 72 \\
                 Deterioration of condition / 74 \\
                 General comments on the computation of zeros of
                 polynomials / 76 \\
                 Additional comments / 78 \\
                 3. Matrix Computations \\
                 Introduction / 79 \\
                 Vector and matrix norms / 80 \\
                 Error analysis of simple matrix operations / 82 \\
                 Matrix multiplication / 83 \\
                 Matrix operations in block-floating arithmetic / 85 \\
                 Matrices which are not infinity row standardized / 85
                 \\
                 Orthogonalization of vectors / 86 \\
                 Numerical example / 87 \\
                 General case / 89 \\
                 Solution of equations and matrix inversion / 91 \\
                 Rounding of matrix of coefficients / 93 \\
                 Error analysis of Gaussian elimination / 94 \\
                 Computational equations / 95 \\
                 Floating-point bounds / 96 \\
                 Gaussian elimination in fixed-point / 99 \\
                 Determinant evaluation / 99 \\
                 Solution of a triangular set of equations using
                 standard floating-point arithmetic / 99 \\
                 Accuracy of computed solution / 102 \\
                 Solution of triangular set of equations with
                 floating-point accumulation of inner-products / 103 \\
                 Inversion of a triangular matrix / 104 \\
                 High accuracy of solutions of triangular equations /
                 105 \\
                 Solution of a general set of equations / 107 \\
                 Inversion of a general matrix / 109 \\
                 Left-handed and right-handed inverses / 110 \\
                 Numerical example / 111 \\
                 Comments on example / 113 \\
                 Compact methods of triangular decomposition / 114 \\
                 Triangular decomposition with partial pivoting / 115
                 \\
                 Positive definite matrix / 117 \\
                 Numerical example / 118 \\
                 Comments on the solution / 119 \\
                 Residual corresponding to block-floating solution / 120
                 \\
                 Iterative refinement of the solution / 121 \\
                 Practical procedure / 122 \\
                 Analysis of the practical procedure / 124 \\
                 Assessment of accuracy of the computed solution / 126
                 \\
                 The use of an estimate for $||A^{-1}||$ / 126 \\
                 Assessment of a computed inverse / 127 \\
                 Use of the approximate inverse to solve equations / 128
                 \\
                 Iterative procedure based on use of the approximate
                 inverse / 130 \\
                 Numerical example / 131 \\
                 Sensitivity of the eigenvalues of a matrix / 134 \\
                 Sensitivity of individual eigenvalues / 137 \\
                 Example of ill-conditioned eigenvalues / 138 \\
                 A posteriori estimates for a computed eigenvalue and
                 eigenvector of a real symmetric matrix / 139 \\
                 Calculation of the eigenvectors of a symmetric
                 tri-diagonal matrix / 142 \\
                 Effect of rounding errors / 143 \\
                 Calculation of the eigenvalues of a lower Hessenberg
                 matrix / 147 \\
                 Calculation of $f(\lambda)$ using floating-point
                 accumulation / 149 \\
                 Perturbation of the eigenvalues / 150 \\
                 Numerical example / 151 \\
                 Additional comments / 155 \\
                 Bibliography / 157 \\
                 Index / 159",
}

@Proceedings{AFIPS:1965:FJC,
  key =          "AFIPS FJCC '65",
  booktitle =    "{1965 Fall Joint Computer Conference, 18--20 November,
                 1965, Las Vegas, Nevada}",
  title =        "{1965 Fall Joint Computer Conference, 18--20 November,
                 1965, Las Vegas, Nevada}",
  volume =       "27",
  publisher =    pub-AFIPS,
  address =      pub-AFIPS:adr,
  pages =        "????",
  year =         "1965",
  LCCN =         "????",
  bibdate =      "Fri Sep 16 10:42:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "AFIPS conference proceedings",
  acknowledgement = ack-nj,
}

@Book{Alt:1965:AC,
  editor =       "Franz L. Alt and Morris Rubinoff and Andrew Donald
                 Booth and Robert Emmet Meagher",
  booktitle =    "Advances in Computers",
  title =        "Advances in Computers",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xiv + 310",
  year =         "1965",
  ISSN =         "0065-2458",
  LCCN =         "QA76 .A3",
  bibdate =      "Sat Nov 29 11:06:34 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Kalenich:1965:IPP,
  editor =       "Wayne A. Kalenich",
  booktitle =    "{Information processing 1965: proceedings of IFIP
                 congress 65; New York City May 24--29, 1965}",
  title =        "{Information processing 1965: proceedings of IFIP
                 congress 65; New York City May 24--29, 1965}",
  publisher =    "Spartan Books",
  address =      "Washington, DC, USA",
  pages =        "648",
  year =         "1965",
  LCCN =         "????",
  bibdate =      "Tue Mar 20 10:47:07 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Two volumes.",
  acknowledgement = ack-nhfb,
  remark =       "Third international conference on information
                 processing, organized by the International Federation
                 for Information Processing.",
}

@Proceedings{Rall:1965:EDCa,
  editor =       "L. B. Rall",
  booktitle =    "Error in Digital Computation",
  title =        "Error in Digital Computation",
  volume =       "1",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "338",
  year =         "1965",
  MRclass =      "65.80",
  MRnumber =     "MR0189284 (32 \#6711)",
  MRreviewer =   "J. M. Ortega",
  bibdate =      "Tue Aug 15 18:20:34 MDT 1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/moore-ramon-e.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Proceedings of an advanced seminar conducted by the
                 Mathematics Research Center, United States Army, at the
                 University of Wisconsin, Madison, October 5--7, 1964.",
  acknowledgement = ack-nhfb,
  tableofcontents = "1. The problem of error in digital computation /
                 Todd \\
                 2. Techniques for automatic error monitoring and
                 control / Ashenhurst \\
                 3. The automatic analysis and control of error in
                 digital computing based on the use of interval numbers
                 / Moore \\
                 4. Error in digital solution of linear problems /
                 Albasiny \\
                 5. The propagation of error in the digital integration
                 of ordinary differential equations / Henrici \\
                 6. Bibliography on error in digital computation (114
                 pp.)",
}

@Proceedings{Rall:1965:EDCb,
  editor =       "L. B. Rall",
  booktitle =    "Error in Digital Computation",
  title =        "Error in Digital Computation",
  volume =       "2",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "288",
  year =         "1965",
  MRclass =      "65.80",
  MRnumber =     "MR0189284 (32 \#6711)",
  MRreviewer =   "J. M. Ortega",
  bibdate =      "Tue Aug 15 18:20:34 MDT 1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/moore-ramon-e.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Proceedings of an advanced seminar conducted by the
                 Mathematics Research Center, United States Army, at the
                 University of Wisconsin, Madison, October 5--7, 1964.",
  acknowledgement = ack-nhfb,
  tableofcontents = "1. Experimental investigation of unnormalized
                 arithmetic / Ashenhurst \\
                 2. Error bounds for computations with continued
                 fractions / Henrici \\
                 3. Error bounds for asymptotic expansions of special
                 functions in the complex plane / Olver \\
                 4. Error analysis for transformations based on the use
                 of matrices of the form $I -2 w w^H$. / Wilkinson \\
                 5. Automatic local coordinate transformations to reduce
                 the growth of error bounds in interval computation of
                 solutions of ordinary differential equations / Moore
                 \\
                 6. Differential inequalities and error bounds /
                 Schroder \\
                 7. Discrete representations of partial differential
                 operators / Young and Dauwalder \\
                 8. Upper and lower bounds for solutions of integral
                 equations / Brown \\
                 9. Convergence ana error bounds for approximate
                 solutions of integral and operator equations / Anselone
                 \\
                 10. Applications of functional analysis to error
                 estimation / Collatz \\
                 11. Error in the solution of linear programming
                 problems / Wolfe",
}

@Book{Wilkinson:1965:AEP,
  author =       "J. H. Wilkinson",
  booktitle =    "The Algebraic Eigenvalue Problem",
  title =        "The Algebraic Eigenvalue Problem",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "xviii + 662",
  year =         "1965",
  ISBN =         "0-19-853403-5",
  ISBN-13 =      "978-0-19-853403-7",
  LCCN =         "QA218 .W686 1965",
  MRclass =      "65.40",
  MRnumber =     "MR0184422 (32 \#1894)",
  MRreviewer =   "A. S. Householder",
  bibdate =      "Tue Aug 15 18:20:34 MDT 1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "1. Theoretical Background \\
                 2. Perturbation Theory \\
                 3. Error Analysis \\
                 4. Solution of Linear Algebraic Equations \\
                 5. Hermitian Matrices \\
                 6. Reduction of a General Matrix to Condensed Form \\
                 7. Eigenvalues of Matrices of Condensed Forms \\
                 8. The $ L R $ and $ Q R $ Algorithms \\
                 9. Iterative Methods \\
                 Bibliography / 649 \\
                 Index / 657",
  tableofcontents = "1. Theoretical Background \\
                 Introduction / 1 \\
                 Definitions / 2 \\
                 Eigenvalues and eigenvectors of the transposed matrix /
                 3 \\
                 Distinct eigenvalues / 4 \\
                 Similarity transformations / 6 \\
                 Multiple eigenvalues and canonical forms for general
                 matrices / 7 \\
                 Defective system of eigenvectors / 9 \\
                 The Jordan (classical) canonical form / 10 \\
                 The elementary divisors / 12 \\
                 Companion matrix of the characteristic polynomial of
                 $A$ / 12 \\
                 Non-derogatory matrices / 13 \\
                 The Frobenius (rational) canonical form / 15 \\
                 Relationship between the Jordan and Frobenius canonical
                 forms / 16 \\
                 Equivalence transformations / 17 \\
                 Lambda matrices / 18 \\
                 Elementary operations / 19 \\
                 Smith's canonical form / 19 \\
                 The highest common factor of $k$-rowed minors of a
                 $A$-matrix / 22 \\
                 Invariant factors of $ (A - \lambda M) $ / 22 \\
                 The triangular canonical form / 24 \\
                 Hermitian and symmetric matrices / 24 \\
                 Elementary properties of Hermitian matrices / 25 \\
                 Complex symmetric matrices / 26 \\
                 Reduction to triangular form by unitary transformations
                 / 27 \\
                 Quadratic forms / 27 \\
                 Necessary and sufficient conditions for positive
                 definiteness / 28 \\
                 Differential equations with constant coefficients / 30
                 \\
                 Solutions corresponding to non-linear elementary
                 divisors / 31 \\
                 Differential equations of higher order / 32 \\
                 Second-order equations of special form / 34 \\
                 Explicit solution of $ B \ddot{y} = -A y$ / 35 \\
                 Equations of the form $(AB - \lambda I) x = 0$ / 35 \\
                 The minimum polynomial of a vector / 36 \\
                 The minimum polynomial of a matrix / 37 \\
                 Cayley--Hamilton theorem / 38 \\
                 Relation between minimum polynomial and canonical forms
                 / 39 \\
                 Principal vectors / 42 \\
                 Elementary similarity transformations / 43 \\
                 Properties of elementary matrices / 45 \\
                 Reduction to triangular canonical form by elementary
                 similarity transformations / 46 \\
                 Elementary unitary transformations / 47 \\
                 Elementary unitary Hermitian matrices / 48 \\
                 Reduction to triangular form by elementary unitary
                 transformations / 50 \\
                 Normal matrices / 51 \\
                 Commuting matrices / 52 \\
                 Eigenvalues of $A B$ / 54 \\
                 Vector and matrix norms / 55 \\
                 Subordinate matrix norms / 56 \\
                 The Euclidean and spectral norms / 57 \\
                 Norms and limits / 58 \\
                 Avoiding use of infinite matrix series / 60 \\
                 2. Perturbation Theory \\
                 Introduction / 62 \\
                 Ostrowski's theorem on continuity of the eigenvalues /
                 63 \\
                 Algebraic functions / 64 \\
                 Numerical examples / 65 \\
                 Perturbation theory for simple eigenvalues / 66 \\
                 Perturbation of corresponding eigenvectors / 67 \\
                 Matrix with linear elementary divisors / 68 \\
                 First-order perturbations of eigenvalues / 68 \\
                 First-order perturbations of eigenvectors / 69 \\
                 Higher-order perturbations / 70 \\
                 Multiple eigenvalues / 70 \\
                 Gerschgorin's theorems / 71 \\
                 Perturbation theory based on Gerschgorin's theorems /
                 72 \\
                 Case 1. Perturbation of a simple eigenvalue $\lambda_1$
                 of a matrix having linear elementary divisors / 72 \\
                 Case 2. Perturbation of a multiple eigenvalue
                 $\lambda_1$ of a matrix having linear elementary
                 divisors / 75 \\
                 Case 3. Perturbation of a simple eigenvalue of a matrix
                 having one or more non-linear elementary divisors / 77
                 \\
                 Case 4. Perturbations of the eigenvalues corresponding
                 to a non-linear elementary divisor of a non-derogatory
                 matrix / 79 \\
                 Case 5. Perturbations of eigenvalues $\lambda_i$ when
                 there is more than one divisor involving $(\lambda_i -
                 \lambda_)$ and at least one of them is non-linear / 80
                 \\
                 Perturbations corresponding to the general distribution
                 of non-linear divisors / 81 \\
                 Perturbation theory for the eigenvectors from Jordan
                 canonical form / 81 \\
                 Perturbations of eigenvectors corresponding to a
                 multiple eigenvalue (linear elementary divisors) / 83
                 \\
                 Limitations of perturbation theory / 84 \\
                 Relationships between the $s_i$ / 85 \\
                 The condition of a computing problem / 86 \\
                 Condition numbers / 86 \\
                 Spectral condition number of A with respect to its
                 eigenproblem / 87 \\
                 Properties of spectral condition number / 88 \\
                 Invariant properties of condition numbers / 89 \\
                 Very ill-conditioned matrices / 90 \\
                 Perturbation theory for real symmetric matrices / 93
                 \\
                 Unsymmetric perturbations / 93 \\
                 Symmetric perturbations / 94 \\
                 Classical techniques / 94 \\
                 Symmetric matrix of rank unity / 97 \\
                 Extremal properties of eigenvalues / 98 \\
                 Minimax characterization of eigenvalues / 99 \\
                 Eigenvalues of the sum of two symmetric matrices / 101
                 \\
                 Practical applications / 102 \\
                 Further applications of minimax principle / 103 \\
                 Separation theorem / 103 \\
                 The Wielandt--Hoffman theorem / 104 \\
                 3. Error Analysis \\
                 Introduction / 110 \\
                 Fixed-point operations / 110 \\
                 Accumulation of inner-products / 111 \\
                 Floating-point operations / 112 \\
                 Simplified expressions for error bounds / 113 \\
                 Error bounds for some basic floating-point computations
                 / 114 \\
                 Bounds for norms of the error matrices / 115 \\
                 Accumulation of inner-products in floating-point
                 arithmetic / 116 \\
                 Error bounds for some basic $\fl_2() $ computations /
                 117 \\
                 Computation of square roots / 118 \\
                 Block-floating vectors and matrices / 119 \\
                 Fundamental limitations oft-digit computation / 120 \\
                 Eigenvalue techniques based on reduction by similarity
                 transformations / 123 \\
                 Error analysis of methods based on elementary
                 non-unitary transformations / 124 \\
                 Error analysis of methods based on elementary unitary
                 transformations / 126 \\
                 Superiority of the unitary transformation / 128 \\
                 Real symmetric matrices / 129 \\
                 Limitations of unitary transformations / 129 \\
                 Error analysis of floating-point computation of plane
                 rotations / 131 \\
                 Multiplication by a plane rotation / 133 \\
                 Multiplication by a sequence of plane rotations / 134
                 \\
                 Error in product of approximate plane rotations / 139
                 \\
                 Errors in similarity transforms / 140 \\
                 Symmetric matrices / 141 \\
                 Plane rotations in fixed-point arithmetic / 143 \\
                 Alternative computation of $\sin \theta$ and $\cos
                 \theta$ / 145 \\
                 Pre-multiplication by an approximate fixed-point
                 rotation / 145 \\
                 Multiplication by a sequence of plane rotations
                 (fixed-point) / 147 \\
                 The computed product of an approximate set of plane
                 rotations / 148 \\
                 Errors in similarity transformations / 148 \\
                 General comments on the error bounds / 151 \\
                 Elementary Hermitian matrices in floating-point / 152
                 \\
                 Error analysis of the computation of an elementary
                 Hermitian matrix / 153 \\
                 Numerical example / 156 \\
                 Pre-multiplication by an approximate elementary
                 Hermitian matrix / 157 \\
                 Multiplication by a sequence of approximate elementary
                 Hermitians / 160 \\
                 Non-unitary elementary matrices analogous to plane
                 rotations / 162 \\
                 Non-unitary elementary matrices analogous to elementary
                 Hermitian matrices / 163 \\
                 Pre-multiplication by a sequence of non-unitary
                 matrices / 165 \\
                 A priori error bounds / 166 \\
                 Departure from normality / 167 \\
                 Simple examples / 169 \\
                 A posteriori bounds / 170 \\
                 A posteriori bounds for normal matrices / 170 \\
                 Rayleigh quotient / 172 \\
                 Error in Rayleigh quotient / 173 \\
                 Hermitian matrices / 174 \\
                 Pathologically close eigenvalues / 176 \\
                 Non-normal matrices / 178 \\
                 Error analysis for a complete eigensystem / 180 \\
                 Numerical example / 181 \\
                 Conditions limiting attainable accuracy / 181 \\
                 Non-linear elementary, divisors / 182 \\
                 Approximate invariant subspaces / 184 \\
                 Almost normal matrices / 187 \\
                 4. Solution of Linear Algebraic Equations \\
                 Introduction / 189 \\
                 Perturbation theory / 189 \\
                 Condition numbers / 191 \\
                 Equilibrated matrices / 192 \\
                 Simple practical examples / 193 \\
                 Condition of matrix of eigenvectors / 193 \\
                 Explicit solution / 194 \\
                 General comments on condition of matrices / 195 \\
                 Relation of ill-conditioning to near-singularity / 196
                 \\
                 Limitations imposed by t-digit arithmetic / 197 \\
                 Algorithms for solving linear equations / 198 \\
                 Gaussian elimination / 200 \\
                 Triangular decomposition / 201 \\
                 Structure of triangular decomposition matrices / 201
                 \\
                 Explicit expressions for elements of the triangles /
                 202 \\
                 Breakdown of Gaussian elimination / 204 \\
                 Numerical stability / 205 \\
                 Significance of the interchanges / 206 \\
                 Numerical example / 207 \\
                 Error analysis of Gaussian elimination / 209 \\
                 Upper bounds for the perturbation matrices using
                 fixed-point arithmetic / 211 \\
                 Upper bound for elements of reduced matrices / 212 \\
                 Complete pivoting / 212 \\
                 Practical procedure with partial pivoting / 214 \\
                 Floating-point error analysis / 214 \\
                 Floating-point decomposition without pivoting / 215 \\
                 Loss of significant figures / 217 \\
                 A popular fallacy / 217 \\
                 Matrices of special form / 218 \\
                 Gaussian elimination on a high-speed computer / 220 \\
                 Solutions corresponding to different right-hand sides /
                 221 \\
                 Direct triangular decomposition / 221 \\
                 Relations between Gaussian elimination and direct
                 triangular decomposition / 223 \\
                 Examples of failure and non-uniqueness of decomposition
                 / 224 \\
                 Triangular decomposition with row interchanges / 225
                 \\
                 Error analysis of triangular decomposition / 227 \\
                 Evaluation of determinants / 228 \\
                 Cholesky decomposition / 229 \\
                 Symmetric matrices which are not positive definite /
                 230 \\
                 Error analysis of Cholesky decomposition in fixed-point
                 arithmetic / 231 \\
                 An ill-conditioned matrix / 233 \\
                 Triangularization using elementary Hermitian matrices /
                 233 \\
                 Error analysis of Householder triangularization / 236
                 \\
                 Triangularization by elementary stabilized matrices of
                 the type M1, / 236 \\
                 Evaluation of determinants of leading principal minors
                 / 237 \\
                 Triangularization by plane rotations / 239 \\
                 Error analysis of Givens reduction / 240 \\
                 Uniqueness of orthogonal triangularization / 241 \\
                 Schmidt orthogonalization / 242 \\
                 Comparison of the methods of triangularization / 244
                 \\
                 Back-substitution / 247 \\
                 High accuracy of computed solutions of triangular sets
                 of equations / 249 \\
                 Solution of a general set of equations / 251 \\
                 Computation of the inverse of a general matrix / 252
                 \\
                 Accuracy of computed solutions / 253 \\
                 Ill-conditioned matrices which give no small pivots /
                 254 \\
                 Iterative improvements of approximate solution / 255
                 \\
                 Effect of rounding errors on the iterative process /
                 256 \\
                 The iterative procedure in fixed-point computation /
                 257 \\
                 Simple example of iterative procedure / 258 \\
                 General comments on the iterative procedure / 260 \\
                 Related iterative procedures / 261 \\
                 Limitations of the iterative procedure / 261 \\
                 Rigorous justification of the iterative method / 262
                 \\
                 5. Hermitian Matrices \\
                 Introduction / 265 \\
                 The classical Jacobi method for real symmetric matrices
                 / 266 \\
                 Rate of convergence / 267 \\
                 Convergence to fixed diagonal matrix / 268 \\
                 Serial Jacobi method / 269 \\
                 The Gerschgorin discs / 269 \\
                 Ultimate quadratic convergence of Jacobi methods / 270
                 \\
                 Close and multiple eigenvalues / 271 \\
                 Numerical examples / 273 \\
                 Calculation of cos 8 and sin B / 274 \\
                 Simpler determination of the angles of rotation / 276
                 \\
                 The threshold Jacobi method / 277 \\
                 Calculation of the eigenvectors / 278 \\
                 Numerical example / 279 \\
                 Error analysis of the Jacobi method / 279 \\
                 Accuracy of the computed eigenvectors / 280 \\
                 Error bounds for fixed-point computation / 281 \\
                 Organizational problems / 282 \\
                 Givens' method / 282 \\
                 Givens' process on a computer with a two-level store /
                 284 \\
                 Floating-point error analysis of Givens' process / 286
                 \\
                 Fixed-point error analysis / 287 \\
                 Numerical example / 288 \\
                 Householder's method / 290 \\
                 Taking advantage of symmetry / 292 \\
                 Storage considerations / 293 \\
                 Householder's process on a computer with a two-level
                 store / 294 \\
                 Householder's method in fixed-point arithmetic / 294
                 \\
                 Numerical example / 296 \\
                 Error analyses of Householder's method / 297 \\
                 Eigenvalues of a symmetric tri-diagonal matrix / 299
                 \\
                 Sturm sequence property / 300 \\
                 Method of bisection / 302 \\
                 Numerical stability of the bisection method / 302 \\
                 Numerical example / 305 \\
                 General comments on the bisection method / 306 \\
                 Small eigenvalues / 307 \\
                 Close eigenvalues and small $\beta_i$ / 308 \\
                 Fixed-point computation of the eigenvalues / 312 \\
                 Computation of the eigenvectors of a tri-diagonal form
                 / 315 \\
                 Instability of the explicit expression for the
                 eigenvector / 316 \\
                 Numerical examples / 319 \\
                 Inverse iteration / 321 \\
                 Choice of initial vector $b$ / 322 \\
                 Error analysis / 323 \\
                 Numerical example / 325 \\
                 Close eigenvalues and small $\beta_i$ / 327 \\
                 Independent vectors corresponding to coincident
                 eigenvalues / 328 \\
                 Alternative method for computing the eigenvectors / 330
                 \\
                 Numerical example / 331 \\
                 Comments on the eigenproblem for tri-diagonal matrices
                 / 332 \\
                 Completion of the Givens and Householder methods / 333
                 \\
                 Comparison of methods / 334 \\
                 Quasi-symmetric tri-diagonal matrices / 335 \\
                 Calculation of the eigenvectors / 336 \\
                 Equations of the form $A x = \lambda B x$ and $A B x =
                 \lambda X $ / 337 \\
                 Numerical example / 339 \\
                 Simultaneous reduction of $A$ and $B$ to diagonal form
                 / 340 \\
                 Tri-diagonal $A$ and $B$ / 340 \\
                 Complex Hermitian matrices / 342 \\
                 6. Reduction of a General Matrix to Condensed Form \\
                 Introduction / 345 \\
                 Givens' method / 345 \\
                 Householder's method / 347 \\
                 Storage considerations / 350 \\
                 Error analysis / 350 \\
                 Relationship between the Givens and Householder methods
                 / 351 \\
                 Elementary stabilized transformations / 353 \\
                 Significance of the permutations / 355 \\
                 Direct reduction to Hessenberg form / 357 \\
                 Incorporation of interchanges / 359 \\
                 Numerical example / 360 \\
                 Error analysis / 363 \\
                 Related error analyses / 365 \\
                 Poor determination of the Hessenberg matrix / 368 \\
                 Reduction to Hessenberg form using stabilized matrices
                 of the type $ M^'_{ji} $ / 368 \\
                 The method of Krylov / 369 \\
                 Gaussian elimination by columns / 370 \\
                 Practical difficulties / 371 \\
                 Condition of O for some standard distributions of
                 eigenvalues / 372 \\
                 Initial vectors of grade less than n / 374 \\
                 Practical experience / 376 \\
                 Generalized Hessenberg processes / 377 \\
                 Failure of the generalized Hessenberg process / 378 \\
                 The Hessenberg method / 379 \\
                 Practical procedure / 380 \\
                 Relation between the Hessenberg method and earlier
                 methods / 381 \\
                 The method of Arnoldi / 382 \\
                 Practical considerations / 383 \\
                 Significance of re-orthogonalization / 385 \\
                 The method of Lanczos / 388 \\
                 Failure of procedure / 389 \\
                 Numerical example / 390 \\
                 The practical Lanczos process / 391 \\
                 Numerical example / 392 \\
                 General comments on the unsymmetric Lanczos process /
                 394 \\
                 The symmetric Lanczos process / 394 \\
                 Reduction of a Hessenberg matrix to a more compact form
                 / 395 \\
                 Reduction of a lower Hessenberg matrix to tri-diagonal
                 form / 396 \\
                 The use of interchanges / 397 \\
                 Effect of a small pivotal element / 398 \\
                 Error analysis / 399 \\
                 The Hessenberg process applied to a lower Hessenberg
                 matrix / 402 \\
                 Relationship between the Hessenberg process and the
                 Lanczos process / 402 \\
                 Reduction of a general matrix to tri-diagonal form /
                 403 \\
                 Comparison with Lanczos method / 404 \\
                 Re-examination of reduction to tri-diagonal form / 404
                 \\
                 Reduction from upper Hessenberg form to Frobenius form
                 / 405 \\
                 Effect of small pivot / 407 \\
                 Numerical example / 408 \\
                 General comments on the stability / 408 \\
                 Specialized upper Hessenberg form / 409 \\
                 Direct determination of the characteristic polynomial /
                 410 \\
                 7. Eigenvalues of Matrices of Condensed Forms \\
                 Introduction / 413 \\
                 Explicit polynomial form / 413 \\
                 Condition numbers of explicit polynomials / 416 \\
                 Some typical distributions of zeros / 417 \\
                 Final assessment of Krylov's method / 421 \\
                 General comments on explicit polynomials / 421 \\
                 Tri-diagonal matrices / 423 \\
                 Determinants of Hessenberg matrices / 426 \\
                 Effect of rounding errors / 427 \\
                 Floating-point accumulation / 428 \\
                 Evaluation by orthogonal transformations / 429 \\
                 Evaluation of determinants of general matrices / 431
                 \\
                 The generalized eigenvalue problem / 432 \\
                 Indirect determinations of the characteristic
                 polynomial / 432 \\
                 Le Verrier's method / 434 \\
                 Iterative methods based on interpolation / 435 \\
                 Asymptotic rate of convergence / 436 \\
                 Multiple zeros / 437 \\
                 Inversion of the functional relationship / 439 \\
                 The method of bisection / 440 \\
                 Newton's method / 441 \\
                 Comparison of Newton's method with interpolation / 442
                 \\
                 Methods giving cubic convergence / 443 \\
                 Laguerre's method / 443 \\
                 Complex zeros / 446 \\
                 Complex conjugate zeros / 447 \\
                 Bairstow's method / 449 \\
                 The generalized Bairstow method / 450 \\
                 Practical considerations / 452 \\
                 Effect of rounding errors on asymptotic convergence /
                 453 \\
                 The method of bisection / 453 \\
                 Successive linear interpolation / 455 \\
                 Multiple and pathologically close eigenvalues / 457 \\
                 Other interpolation methods / 458 \\
                 Methods involving the use of a derivative / 459 \\
                 Criterion for acceptance of a zero / 461 \\
                 Effect of rounding errors / 462 \\
                 Suppression of computed zeros / 464 \\
                 Deflation for Hessenberg matrices / 465 \\
                 Deflation of tri-diagonal matrices / 468 \\
                 Deflation by rotations or stabilized elementary
                 transformations / 469 \\
                 Stability of the deflation / 472 \\
                 General comments on deflation / 474 \\
                 Suppression of computed zeros / 474 \\
                 Suppression of computed quadratic factors / 475 \\
                 General comments on the methods of suppression / 476
                 \\
                 Asymptotic rates of convergence / 478 \\
                 Convergence in the large / 478 \\
                 Complex zeros / 481 \\
                 Recommendations / 482 \\
                 Complex matrices / 483 \\
                 Matrices containing an independent parameter / 483 \\
                 8. The $ L R $ and $ Q R $ Algorithms \\
                 Introduction / 485 \\
                 Real matrices with complex eigenvalues / 486 \\
                 The $ L R $ algorithm / 487 \\
                 Proof of the convergence of the $A_s$ / 489 \\
                 Positive definite Hermitian matrices / 493 \\
                 Complex conjugate eigenvalues / 494 \\
                 Introduction of interchanges / 498 \\
                 Numerical example / 499 \\
                 Convergence of the modified process / 501 \\
                 Preliminary reduction of original matrix / 501 \\
                 Invariance of upper Hessenberg form / 502 \\
                 Simultaneous row and column operations / 504 \\
                 Acceleration of convergence / 505 \\
                 Incorporation of shifts of origin / 506 \\
                 Choice of shift of origin / 507 \\
                 Deflation of the matrix / 509 \\
                 Practical experience of convergence / 510 \\
                 Improved shift strategy / 511 \\
                 Complex conjugate eigenvalues / 512 \\
                 Criticisms of the modified $ L R $ algorithm. / 515 \\
                 The $ Q R $ algorithm / 515 \\
                 Convergence of the $ Q R $ algorithm / 516 \\
                 Formal proof of convergence / 517 \\
                 Disorder of the eigenvalues / 519 \\
                 Eigenvalues of equal modulus / 520 \\
                 Alternative proof for the $ L R $ technique / 521 \\
                 Practical application of the $ Q R $ algorithm / 523
                 \\
                 Shifts of origin / 524 \\
                 Decomposition of A8 / 525 \\
                 Numerical example / 527 \\
                 Practical procedure / 527 \\
                 Avoiding complex conjugate shifts / 528 \\
                 Double $ Q R $ step using elementary Hermitians / 532
                 \\
                 Computational details / 534 \\
                 Decomposition of A8 / 535 \\
                 Double-shift technique for $ L R $ / 537 \\
                 Assessment of $ L R $ and $ Q R $ algorithms / 538 \\
                 Multiple eigenvalues / 540 \\
                 Special use of the deflation process / 543 \\
                 Symmetric matrices / 544 \\
                 Relationship between $ L R $ and $ Q R $ algorithms /
                 545 \\
                 Convergence of the Cholesky $ L R $ algorithm / 546 \\
                 Cubic convergence of the $ Q R $ algorithm / 548 \\
                 Shift of origin in Cholesky $ L R $ / 549 \\
                 Failure of the Cholesky decomposition / 550 \\
                 Cubically convergent $ L R $ process / 551 \\
                 Band matrices / 553 \\
                 $ Q R $ decomposition of a band matrix / 557 \\
                 Error analysis / 561 \\
                 Unsymmetric band matrices / 562 \\
                 Simultaneous decomposition and recombination in $ Q R $
                 algorithm / 565 \\
                 Reduction of band width / 567 \\
                 9. ITERATIVE METHODS \\
                 Introduction / 570 \\
                 The power method / 570 \\
                 Direct iteration with a single vector / 571 \\
                 Shift of origin / 572 \\
                 Effect of rounding errors / 573 \\
                 Variation of $p$ / 576 \\
                 {\em Ad hoc\/} choice of $p$ / 577 \\
                 Aitken's acceleration technique / 578 \\
                 Complex conjugate eigenvalues / 579 \\
                 Calculation of the complex eigenvector / 581 \\
                 Shift of origin / 582 \\
                 Non-linear divisors / 582 \\
                 Simultaneous determination of several eigenvalues / 583
                 \\
                 Complex matrices / 584 \\
                 Deflation / 584 \\
                 Deflation based on similarity transformations / 585 \\
                 Deflation using invariant subspaces / 587 \\
                 Deflation using stabilized elementary transformations /
                 587 \\
                 Deflation using unitary transformations / 589 \\
                 Numerical stability / 590 \\
                 Numerical example / 592 \\
                 Stability of unitary transformations / 594 \\
                 Deflation by non-similarity transformations / 596 \\
                 General reduction using invariant subspaces / 599 \\
                 Practical application / 601 \\
                 Treppen-iteration / 602 \\
                 Accurate determination of complex conjugate eigenvalues
                 / 604 \\
                 Very close eigenvalues / 606 \\
                 Orthogonalization techniques / 606 \\
                 Analogue of treppen-iteration using orthogonalization /
                 607 \\
                 Bi-iteration / 609 \\
                 Numerical example / 610 \\
                 Richardson's purification process / 614 \\
                 Matrix squaring / 615 \\
                 Numerical stability / 616 \\
                 Use of Chebyshev polynomials / 617 \\
                 General assessment of methods based on direct iteration
                 / 618 \\
                 Inverse iteration / 619 \\
                 Error analysis of inverse iteration / 620 \\
                 General comments on the analysis / 621 \\
                 Further refinement of eigenvectors / 622 \\
                 Non-linear elementary divisors / 626 \\
                 Inverse iteration with Hessenberg matrices / 626 \\
                 Degenerate cases / 627 \\
                 Inverse iteration with band matrices / 628 \\
                 Complex conjugate eigenvectors / 629 \\
                 Error analysis / 631 \\
                 Numerical example / 633 \\
                 The generalized eigenvalue problem / 633 \\
                 Variation of approximate eigenvalues / 635 \\
                 Refinement of eigensystems / 637 \\
                 Numerical example / 639 \\
                 Refinement of the eigenvectors / 641 \\
                 Complex conjugate eigenvalues / 643 \\
                 Coincident and pathologically close eigenvalues / 644
                 \\
                 Comments on the ACE programmes / 646 \\
                 Bibliography / 649 \\
                 Index / 657",
}

@Book{Ralston:1966:MMD,
  editor =       "Anthony Ralston and Herbert S. Wilf",
  booktitle =    "Mathematical Methods for Digital Computers",
  title =        "Mathematical Methods for Digital Computers",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "various",
  year =         "1966",
  LCCN =         "QA76.5 .R3",
  bibdate =      "Fri Dec 08 13:02:58 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Three volumes.",
  acknowledgement = ack-nhfb,
}

@Proceedings{AFIPS:1967:ACP,
  key =          "AFIPS SJCC '67",
  booktitle =    "{1967 Spring Joint Computer Conference, April 18--20,
                 Atlantic City, NJ}",
  title =        "{1967 Spring Joint Computer Conference, April 18--20,
                 Atlantic City, NJ}",
  volume =       "30",
  publisher =    "Thompson Book Co.",
  address =      "Washington, DC, USA",
  pages =        "799",
  year =         "1967",
  LCCN =         "TK7885.A1 J6 1967",
  bibdate =      "Sat Sep 24 01:00:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "AFIPS conference proceedings",
  acknowledgement = ack-nhfb,
}

@Proceedings{Anonymous:1967:PAN,
  editor =       "Anonymous",
  booktitle =    "{Proceedings of the 1967 Army Numerical Analysis
                 Conference, Madison, Wisconsin}",
  title =        "{Proceedings of the 1967 Army Numerical Analysis
                 Conference, Madison, Wisconsin}",
  publisher =    "U.S. Army Research Office",
  address =      "Research Triangle Park, NC",
  bookpages =    "vi + 231 + 2",
  year =         "1967",
  bibdate =      "Fri Oct 31 07:22:55 2025",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "https://apps.dtic.mil/sti/tr/pdf/AD0825963.pdf",
  acknowledgement = ack-nhfb,
  remark =       "There is no editor credit in the front matter of these
                 proceedings.",
  tableofcontents = "Foreword / i \\
                 Table of Contents / iii \\
                 Program / v \\
                 COSMIC: a Center for the Dissemination of Computer
                 Programs and Computer Information / D. F. Kennedy / 1
                 \\
                 Machine Language Programming --- How and Why / J. M.
                 Yohe / 3 \\
                 NEWTON: a General Purpose Program for Solving Nonlinear
                 Systems / J. H. Gray and L. B. Rail / 11 \\
                 Experience with FORMAC at HDL / D. S. Marsh / 61 \\
                 A Simple Electronic True Random Event Generator / R. G.
                 Polk, D. R. Koehler, and J. T. Grissom / 75 \\
                 Programming Interval Arithmetic and Applications /
                 Allen Reiter / 87 \\
                 Homeostatic Organizations of Adaptive Parallel
                 Processing Systems / R. M. Dunn / 99 \\
                 Logical Structure of an Automatically Sequenced
                 Explosive Control Device / S. H. Eisman / 111 \\
                 Problem Solving Digital-Analogue Simulation / H. W.
                 Bloom [paper presented, but absent from this
                 proceedings] / 141 \\
                 A Shell Computer Program which Determines the Physical
                 Properties of an Artillery Shell and Represents Its
                 Dimensions Graphically / Forrest McMains / 143 \\
                 Zerpol, a Zero Finding Algorithm for Polynomials Using
                 Laguerre's Method / B. T. Smith / 153 \\
                 The Numerical Solution of Polynomial Equations / W.
                 Kahan / 175 \\
                 Roundoff Errors / Ben Noble / 209 \\
                 Attendance List / 229",
}

@Proceedings{Anonymous:1968:PSA,
  editor =       "Anonymous",
  booktitle =    "Proc. Sixth Annual Allerton Conference on Circuit and
                 System Theory ({Monticello, IL}, 1968)",
  title =        "Proc. Sixth Annual Allerton Conference on Circuit and
                 System Theory ({Monticello, IL}, 1968)",
  publisher =    "University of Illinois at Urbana-Champaign",
  address =      "Urbana, IL, USA",
  year =         "1968",
  ISBN =         "????",
  ISBN-13 =      "????",
  ISSN =         "0569-0552",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 11:03:47 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{AFIPS:1969:ACPa,
  key =          "AFIPS SJCC '69",
  booktitle =    "{1967 Spring Joint Computer Conference, May 14--16,
                 1969, Boston, MA}",
  title =        "{1967 Spring Joint Computer Conference, May 14--16,
                 1969, Boston, MA}",
  volume =       "34",
  publisher =    pub-AFIPS,
  address =      pub-AFIPS:adr,
  pages =        "866",
  year =         "1969",
  LCCN =         "TK7885.A1 J6 1969",
  bibdate =      "Sat Sep 24 01:05:52 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "AFIPS conference proceedings",
  acknowledgement = ack-nj # " and " # ack-nhfb,
}

@Proceedings{AFIPS:1969:ACPb,
  key =          "AFIPS FJCC '69",
  booktitle =    "{1969 Fall Joint Computer Conference, November 18--20,
                 1969, Las Vegas, Nevada}",
  title =        "{1969 Fall Joint Computer Conference, November 18--20,
                 1969, Las Vegas, Nevada}",
  volume =       "35",
  publisher =    pub-AFIPS,
  address =      pub-AFIPS:adr,
  pages =        "807",
  year =         "1969",
  LCCN =         "????",
  bibdate =      "Fri Sep 16 10:42:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "AFIPS conference proceedings",
  acknowledgement = ack-nj,
}

@Proceedings{IEEE:1969:SCA,
  editor =       "{IEEE}",
  booktitle =    "Papers presented at a workshop sponsored by the {Logic
                 Design Subcommittee of the Systems Technical Committee
                 (IEEE Computer Group), 1969}",
  title =        "Papers presented at a workshop sponsored by the {Logic
                 Design Subcommittee of the Systems Technical Committee
                 (IEEE Computer Group), 1969}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "1969",
  LCCN =         "????",
  bibdate =      "Wed Apr 27 17:36:48 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Reprinted in IEEE Transactions on Computers, Special
                 issue on computer arithmetic (when??)",
  xxnote =       "Where was the conference?? Were the proceedings
                 published?? What was the conference title?? Is this the
                 proceedings of ARITH '69 (Minneapolis, MN, USA, June
                 16, 1969)?",
}

@Proceedings{Morrell:1969:IPP,
  editor =       "A. J. H. Morrell",
  booktitle =    "{Information processing 68: proceedings of IFIP
                 congress 1968, organized by the International
                 Federation for Information Processing, Edinburgh, 5--10
                 August 1968}",
  title =        "{Information processing 68: proceedings of IFIP
                 congress 1968, organized by the International
                 Federation for Information Processing, Edinburgh, 5--10
                 August 1968}",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "????",
  year =         "1969",
  ISBN =         "0-7204-2032-6",
  ISBN-13 =      "978-0-7204-2032-6",
  LCCN =         "QA76 .I578",
  bibdate =      "Fri Nov 11 07:22:32 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  remark =       "Volume 1. Mathematics, software. Volume 2. Hardware,
                 applications.",
  subject =      "Electronic data processing; Congresses; Electronic
                 digital computers; Congresses; Machine theory;
                 Congresses",
}

@Proceedings{Morrell:1970:IPP,
  editor =       "A. J. H. Morrell",
  booktitle =    "Information Processing 68 (Proc. {IFIP} Congress,
                 Edinburgh, 1968), Vol. 1: Mathematics, Software",
  title =        "Information Processing 68 (Proc. {IFIP} Congress,
                 Edinburgh, 1968), Vol. 1: Mathematics, Software",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "various",
  year =         "1970",
  ISBN =         "0-7204-2032-6",
  ISBN-13 =      "978-0-7204-2032-6",
  LCCN =         "QA 75.5 I57 1968",
  bibdate =      "Thu Jan 18 13:48:59 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{Bell:1971:CSR,
  editor =       "C. Gordon Bell and Allen Newell",
  booktitle =    "Computer Structures: Readings and Examples",
  title =        "Computer Structures: Readings and Examples",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "xix + 668",
  year =         "1971",
  ISBN =         "0-07-004357-4",
  ISBN-13 =      "978-0-07-004357-2",
  LCCN =         "TK7888.3 .B4",
  bibdate =      "Tue Aug 15 18:20:34 MDT 1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wilkes-maurice-v.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "Part 1 The Structure of Computers \\
                 Chapter 1 Introduction \\
                 Chapter 2 The PMS and ISP Descriptive Systems \\
                 Chapter 3 The Computer Space \\
                 Part 2 The Instruction-set Processor: Main-line
                 computers \\
                 Section 1 Processors with One Address per Instruction
                 \\
                 Chapter 4 Preliminary Discussion of the Logical Design
                 of an Electronic Computing Instrument \\
                 Chapter 5 The DEC PDP-8 \\
                 Chapter 6 The Whirlwind I Computer \\
                 Chapter 7 Some Aspects of the Logical Design of a
                 Control Computer: A Case Study \\
                 Chapter 8 The UNIVAC System \\
                 Section 2 Processors with a General-Register State \\
                 Chapter 9 The Design Philosophy of Pegasus, A
                 Quantity-production Computer \\
                 Chapter 10 An 8-bit-character Computer \\
                 Part 3 The Instruction-Set Processor Level: Variations
                 in the Processor \\
                 Section 1 Processors with Greater than One Address per
                 Instruction \\
                 Chapter 11 The Pilot ACE \\
                 Chapter 12 ZEBRA, A Simple Binary Computer \\
                 Chapter 13 UNIVAC Scientific (1103A) Instruction Logic
                 \\
                 Chapter 14 Instruction Logic of the MIDAC \\
                 Chapter 15 Instruction Logic of the Soviet Strela
                 (Arrow) \\
                 Section 2 Processors Constrained by a Cyclic, Primary
                 Memory \\
                 Chapter 16 The LGP-30 and LGP-21 \\
                 Chapter 17 IBM 650 Instruction Logic \\
                 Section 3 Processors for Variable-length-string Data
                 \\
                 Chapter 18 The IBM 1401 \\
                 Section 4 Desk Calculator Computers: Keyboard
                 Programmable Processors with Small Memories \\
                 Chapter 19 The OLIVETTI Programma 101 Desk Calculator
                 \\
                 Chapter 20 The HP Model 9100A Computing Calculator \\
                 Section 5 Processors with Stack Memories (Zero
                 Addresses per Instruction) \\
                 Chapter 21 Design of an Arithmetic Unit Incorporating a
                 Nesting Store \\
                 Chapter 22 Design of the B 5000 System \\
                 Section 6 Processors with Multiprogramming Ability \\
                 Chapter 23 One-level Storage System \\
                 Chapter 24 A User Machine in a Time-sharing System \\
                 Part 4 The Instruction-set Processor Level:
                 Special-function Processors \\
                 Section 1 Processors to Control Terminals and Secondary
                 Memories (Input-output Processors) \\
                 Chapter 25 The DEC 338 Display Processor \\
                 Section 2 Processors for Array Data \\
                 Chapter 26 NOVA: A List-oriented Computer \\
                 Chapter 27 The ILLIAC IV Computer \\
                 Section 3 Processors Defined by a Microprogram \\
                 Chapter 28 Microprogramming and the Design of the
                 Control Circuits in an Electronic Computer \\
                 Chapter 29 The Design of a General-Purpose
                 Microprogram-controlled Computer with Elementary
                 Structure \\
                 Section 4 Processors Based on a Programming Language
                 \\
                 Chapter 30 A Command Structure for Complex Information
                 Processing \\
                 Chapter 31 System Design of a FORTRAN Machine \\
                 Chapter 32 A Microprogrammed Implementation of EULER on
                 IBM System/360 Model 30 \\
                 Part 5 The PMS Level \\
                 Section 1 Computers with One Central Processor \\
                 Section 2 Computers with One Central Processor and
                 Multiple Input/Output Processors \\
                 Chapter 33 The IBM 1800 \\
                 Chapter 34 The Engineering Design of the Stretch
                 Computer \\
                 Chapter 35 PILOT, The NBS Multicomputer System \\
                 Section 3 Computers for Multiprocessing and Parallel
                 Processing \\
                 Chapter 36 D825 --- A Multiple-computer System for
                 Command and Control \\
                 Chapter 37 A Survey of Problems and Preliminary Results
                 Concerning Parallel Processing and Parallel Processors
                 \\
                 Section 4 Network Computers and Computer Networks \\
                 Chapter 38 The RW-400: A New Polymorphic Data System
                 \\
                 Chapter 39 Parallel Operation in the Control Data 6600
                 \\
                 Chapter 40 Computer Network Examples / 504 \\
                 Part 6 Computer Families \\
                 Section 1 The IBM 701--7094 II Sequence, a Family by
                 Evolution \\
                 Chapter 41 The IBM 7094 I, 11 / 517 \\
                 Section 2 The SDS 910--9300 Series, a Planned Family\\
                 Chapter 42 The SDS 910-9300 Series \\
                 Section 3 The IBM System/360 --- A Series of Planned
                 Machines Which Span a Wide Performance Range \\
                 Chapter 43 The Structure of System/360, Part I ---
                 Outline of the Logical Structure System Implementations
                 \\
                 Chapter 44 The Structure of System/360, Part II ---
                 System Implementations \\
                 Appendix PMS and ISP Notations",
  subject-dates = "John von Neumann (28 December 1903--8 February 1957);
                 James H. Wilkinson (27 September 1919--5 October 1986);
                 Sir Maurice Vincent Wilkes (26 June 1913--29 November
                 2010)",
  tableofcontents = "[NB: Bracketed chapter entries are subject cross
                 references] \\
                 Preface / v \\
                 Contributors / xiii \\
                 Acknowledgments / x \\
                 \\
                 Part 1 The Structure of Computers \\
                 \\
                 Chapter 1 Introduction / 3 \\
                 Chapter 2 The PMS and ISP Descriptive Systems / 15 \\
                 Chapter 3 The Computer Space / 37 \\
                 \\
                 Part 2 The Instruction-set Processor: Main-line
                 computers \\
                 \\
                 Section 1 Processors with One Address per Instruction /
                 89 \\
                 \\
                 Chapter 4 Preliminary Discussion of the Logical Design
                 of an Electronic Computing Instrument --- Arthur W.
                 Burks, Herman H. Goldstine, and John von Neumann / 92
                 \\
                 Chapter 5 The DEC PDP-8 / 120 \\
                 Chapter 6 The Whirlwind I Computer --- R. R. Everett /
                 137 \\
                 [Chapter 33 The IBM 1800] \\
                 Chapter 7 Some Aspects of the Logical Design of a
                 Control Computer: A Case Study --- R. L. Alonso, H.
                 Blair-Smith, and A. L. Hopkins / 146 \\
                 [Chapter 42 The SDS 910-9300 Series] \\
                 [Chapter 16 The LGP-30 and LGP-21] \\
                 [Chapter 17 IBM 650 Instruction Logic ---John W. Carr
                 III] \\
                 [Chapter 41 The IBM 7094 I, II] \\
                 Chapter 8 The UNIVAC System --- J. Presper Eckert, Jr,
                 James B. Weiner, H. Frazer Welsh, and Herbert F.
                 Mitchell / 157 \\
                 [Chapter 23 One-level Storage System --- T. Kilburn, D.
                 B. G. Edwards, M. J. Lanigan, and F. H. Summer] \\
                 [Chapter 34 The Engineering Design of the Stretch
                 Computer --- Erich Bloch] \\
                 \\
                 Section 2 Processors with a General-Register State \\
                 \\
                 Chapter 9 The Design Philosophy of Pegasus, A
                 Quantity-production Computer --- W. S. Elliott, C. E.
                 Owen, C. H. Devonald, and B. G. Maudsley / 171 \\
                 [Chapter 43 The Structure of System/360, Part I ---
                 Outline of the Logical Structure --- G. A. Blaauw and
                 F. P. Brooks, Jr.] \\
                 Chapter 10 An 8-bit-character Computer / 184 \\
                 [Chapter 39 Parallel Operation in the Control Data 6600
                 --- James E. Thornton] \\
                 \\
                 Part 3 The Instruction-Set Processor Level: Variations
                 in the Processor \\
                 \\
                 Section 1 Processors with Greater than One Address per
                 Instruction / 191 \\
                 \\
                 Chapter 11 The Pilot ACE --- J. H. Wilkinson / 193 \\
                 Chapter 12 ZEBRA, A Simple Binary Computer --- W. L.
                 van der Poel / 200 \\
                 Chapter 13 UNIVAC Scientific (1103A) Instruction Logic
                 --- John W. Carr III / 205 \\
                 [Chapter 38 The RW-400: A New Polymorphic Data System
                 --- R. E. Porter] \\
                 Chapter 14 Instruction Logic of the MIDAC --- John W.
                 Carr III / 209 \\
                 Chapter 15 Instruction Logic of the Soviet Strela
                 (Arrow) ---John W. Carr III / 213 \\
                 \\
                 Section 2 Processors Constrained by a Cyclic, Primary
                 Memory / 216 \\
                 \\
                 [Chapter 19 The OLIVETTI Programma 101 Desk Calculator]
                 \\
                 [Chapter 12 ZEBRA, A Simple Binary Computer --- W. L.
                 van der Poel] \\
                 Chapter 16 The LGP-30 and LGP-21 / 217 \\
                 [Chapter 11 The Pilot ACE --- J. H. Wilkinson] \\
                 [Chapter 8 The UNIVAC System --- J. Presper Eckert,
                 Jr., James R. Weiner, H. Frazer Welsh, and Herbert F.
                 Mitchell] \\
                 [Chapter 9 The Design Philosophy of Pegasus, A
                 Quantity-production Computer --- W. S. Elliott, C. E.
                 Owen, C. H. Devonald, and B. G. Maudsley] \\
                 Chapter 17 IBM 650 Instruction Logic --- John W. Carr
                 III / 220 \\
                 [Chapter 26 NOVA: A List-oriented Computer --- Joseph
                 E. Wirsching] \\
                 \\
                 Section 3 Processors for Variable-length-string Data /
                 224 \\
                 \\
                 Chapter 18 The IBM 1401 / 228 \\
                 [Chapter 10 An 8-bit-character Computer] \\
                 \\
                 Section 4 Desk Calculator Computers: Keyboard
                 Programmable Processors with Small Memories / 235 \\
                 \\
                 Chapter 19 The OLIVETTI Programma 101 Desk Calculator /
                 237 \\
                 Chapter 20 The HP Model 9100A Computing Calculator ---
                 Richard E. Monnier, Thomas E. Osborne, and David S.
                 Cochran / 243 \\
                 \\
                 Section 5 Processors with Stack Memories (Zero
                 Addresses per Instruction) / 257 \\
                 \\
                 Chapter 21 Design of an Arithmetic Unit Incorporating a
                 Nesting Store --- R. H. Allmark and J. R. Lucking / 262
                 \\
                 Chapter 22 Design of the B 5000 System --- William
                 Lonergan and Paul King / 267 \\
                 [Chapter 36 D825 --- A Multiple-computer System for
                 Command and Control --- James P. Anderson, Samuel A.
                 Hoffman, Joseph Shifman, and Robert J. Williams] \\
                 [Chapter 30 A Command Structure for Complex Information
                 Processing --- J. C. Shaw, A. Newell, H. A. Simon, T.
                 O. Ellis] \\
                 [Chapter 32 Microprogrammed Implementation of EULER on
                 IBM System/360 Model 30 --- Helmut Weber] \\
                 \\
                 Section 6 Processors with Multiprogramming Ability /
                 274 \\
                 \\
                 Chapter 23 One-level Storage System --- T. Kilburn, D.
                 B. G. Edwards, M. J. Lanigan, and F. H. Sumner / 276
                 \\
                 [Chapter 21 Design of the B 5000 System --- William
                 Lonergan and Paul King] \\
                 Chapter 24 A User Machine in a Time-sharing System ---
                 B. W. Lampson, W. W. Lichtenberger, and M. W. Pirtle /
                 291 \\
                 \\
                 Part 4 The Instruction-set Processor Level:
                 Special-function Processors \\
                 \\
                 Section 1 Processors to Control Terminals and Secondary
                 Memories (Input-output Processors) / 303 \\
                 \\
                 [Chapter 41 The IBM 7094 I, II] \\
                 [Chapter 43 The Structure of System/360, Part I ---
                 Outline of the Logical Structure ---- G. A. Blaauw and
                 F. P. Brooks, Jr.] \\
                 [Chapter 33 The IBM 1800] \\
                 Chapter 25 The DEC 338 Display Processor / 305 \\
                 \\
                 Section 2 Processors for Array Data / 315 \\
                 \\
                 Chapter 26 NOVA: A List-oriented Computer --- Joseph E.
                 Wirsching / 316 \\
                 Chapter 27 The ILLIAC IV Computer --- George H. Barnes,
                 Richard M. Brown, Maso Kato, David J. Kuck, Daniel L.
                 Slotnick, and Richard E. Stokes / 320 \\
                 \\
                 Section 3 Processors Defined by a Microprogram / 334
                 \\
                 \\
                 Chapter 28 Microprogramming and the Design of the
                 Control Circuits in an Electronic Computer --- M. V.
                 Wilkes and J. B. Stringer / 335 \\
                 Chapter 29 The Design of a General-Purpose
                 Microprogram-controlled Computer with Elementary
                 Structure --- Thomas W. Kampe / 341 \\
                 [Chapter 20 The HP Model 9100A Computing Calculator
                 ---Richard E. Monnier, Thomas E. Osborne, and David S.
                 Cochran] \\
                 [Chapter 32 A Microprogrammed Implementation of EULER
                 on IBM System/360 Model 30 --- Helmut Weber] \\
                 \\
                 Section 4 Processors Based on a Programming Language /
                 348 \\
                 \\
                 Chapter 30 A Command Structure for Complex Information
                 Processing --- J. C. Shaw, A. Newell, H. A. Simon, and
                 T. O. Ellis / 349 \\
                 \\
                 Chapter 31 System Design of a FORTRAN Machine ---
                 Theodore R. Bashkow, Azra Sasson, and Arnold Kronfeld /
                 363 \\
                 Chapter 32 A Microprogrammed Implementation of EULER on
                 IBM System/360 Model 30 --- Helmut Weber / 382 \\
                 \\
                 Part 5 The PMS Level \\
                 \\
                 Section 1 Computers with One Central Processor / 395
                 \\
                 \\
                 [Chapter 6 The Whirlwind I Computer --- R. R. Everett]
                 \\
                 [Chapter 42 The SDS 910-9300 Series] \\
                 \\
                 Section 2 Computers with One Central Processor and
                 Multiple Input/Output Processors / 396 \\
                 \\
                 [Chapter 5 The DEC PDP-8] \\
                 Chapter 33 The IBM 1800 / 399 \\
                 [Chapter 41 The IBM 7094 I, II] \\
                 [Chapter 43 The Structure of System/360, Part I ---
                 Outline of the Logical Structure -- G. A. Blaauw and F.
                 P. Brooks, Jr.] \\
                 Chapter 34 The Engineering Design of the Stretch
                 Computer -- Erich Bloch / 421 \\
                 Chapter 35 PILOT, The NBS Multicomputer System --- A.
                 L. Leiner, W. A. Notz, J. L. Smith, and A. Weinberger /
                 440 \\
                 \\
                 Section 3 Computers for Multiprocessing and Parallel
                 Processing / 446 \\
                 \\
                 Chapter 36 D825 --- A Multiple-computer System for
                 Command and Control --- James P. Anderson, Samuel A.
                 Hoffman, Joseph Shifman, and Robert J. Williams / 447
                 \\
                 [Chapter 22 Design of the B 5000 System ---- William
                 Lonergan and Paul King] \\
                 Chapter 37 A Survey of Problems and Preliminary Results
                 Concerning Parallel Processing and Parallel Processors
                 --- M. Lehman / 456 \\
                 \\
                 Section 4 Network Computers and Computer Networks / 470
                 \\
                 \\
                 Chapter 38 The RW-400: A New Polymorphic Data System
                 --- R. E. Porter / 477 \\
                 Chapter 39 Parallel Operation in the Control Data 6600
                 --- James E. Thornton / 489 \\
                 Chapter 40 Computer Network Examples / 504 \\
                 \\
                 Part 6 Computer Families \\
                 \\
                 Section 1 The IBM 701--7094 II Sequence, a Family by
                 Evolution / 515 \\
                 \\
                 Chapter 41 The IBM 7094 I, 11 / 517 \\
                 \\
                 Section 2 The SDS 910--9300 Series, a Planned Family /
                 542 \\
                 \\
                 Chapter 42 The SDS 910-9300 Series / 543 \\
                 \\
                 Section 3 The IBM System/360 --- A Series of Planned
                 Machines Which Span a Wide Performance Range / 561 \\
                 \\
                 Chapter 43 The Structure of System/360, Part I ---
                 Outline of the Logical Structure --- G. A. Blaauw and
                 F. P. Brooks, Jr. / 588 \\
                 Chapter 44 The Structure of System/360, Part II ---
                 System Implementations --- W. Y. Stevens / 602 \\
                 \\
                 Appendix PMS and ISP Notations / 607 \\
                 \\
                 General Conventions / 607 \\
                 \\
                 1 Basic Semantics / 608 \\
                 2 Metanotation / 608 \\
                 3 Basic Syntax / 609 \\
                 4 Commands: Assignments, Abbreviation, Variables, Forms
                 / 609 \\
                 5 Indefinite Expressions / 610 \\
                 6 Lists and Sets / 611 \\
                 7 Definite Expressions / 611 \\
                 8 Attributes / 612 \\
                 9 Null Symbol and Optional Expression / 613 \\
                 10 Names / 613 \\
                 11 Numbers / 614 \\
                 12 Quantities, Dimensions, and Units / 615 \\
                 13 Boolean and Relations / 615 \\
                 \\
                 PMS Conventions / 615 \\
                 \\
                 1 Dimensions / 616 \\
                 2 General Units / 616 \\
                 3 Information Units / 616 \\
                 4 Component / 617 \\
                 5 Link (L) / 619 \\
                 6 Memory (M) / 620 \\
                 7 Switch (S) / 623 \\
                 8 Control (K) / 624 \\
                 9 Transducer (T) / 625 \\
                 10 Data-operations (D) / 626 \\
                 11 Processor (P) / 626 \\
                 12 Computer (C) / 628 \\
                 \\
                 ISP Conventions / 628 \\
                 \\
                 1 Data-types / 629 \\
                 2 Instruction / 631 \\
                 3 Operations / 632 \\
                 4 Processors / 635 \\
                 \\
                 Bibliography / 638 \\
                 Name Index / 653 \\
                 Machine and Organization Index / 656 \\
                 Subject Index / 661",
}

@Proceedings{Freiman:1971:PIC,
  editor =       "C. V. Freiman and J. E. Griffith and J. L. Rosenfeld",
  booktitle =    "Information processing 71: proceedings of {IFIP}
                 Congress 71 organized by the International Federation
                 for Information Processing, Ljubljana, Yugoslavia,
                 August 23--28, 1971",
  title =        "Information processing 71: proceedings of {IFIP}
                 Congress 71 organized by the International Federation
                 for Information Processing, Ljubljana, Yugoslavia,
                 August 23--28, 1971",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  year =         "1971",
  ISBN =         "0-7204-2063-6",
  ISBN-13 =      "978-0-7204-2063-0",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 07:10:48 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Eight booklets in two volumes.",
  acknowledgement = ack-nhfb,
}

@Book{Gear:1971:NIV,
  author =       "Charles William Gear",
  booktitle =    "Numerical Initial Value Problems in Ordinary
                 Differential Equations",
  title =        "Numerical Initial Value Problems in Ordinary
                 Differential Equations",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xvii + 253",
  year =         "1971",
  ISBN =         "0-13-626606-1 (hardcover)",
  ISBN-13 =      "978-0-13-626606-8 (hardcover)",
  LCCN =         "QA372 .G4",
  bibdate =      "Sat Dec 19 09:50:43 MST 2020",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Prentice-Hall series in automatic computation",
  acknowledgement = ack-nhfb,
  author-dates = "(1935-- \ldots{})",
  remark-1 =     "Foreword on page vii by series editor George Forsythe,
                 and the author's host during the sabbatical year when
                 he wrote this book.",
  remark-2 =     "The initial chapters contain multiple references to
                 work by Peter Henrici.",
  remark-3 =     "The initial chapters discuss the error amplification
                 from chopping arithmetic on the IBM 7090 series
                 machines on the solution of ODEs, and point out the
                 need for better rounding algorithms, and higher
                 numerical precision, for solving ODEs.",
  subject =      "Numerical integration; Data processing; Differential
                 equations; Mathematics; {\'y}Equations
                 diff{\'y}erentielles; Informatique; Int{\'y}egration
                 num{\'y}erique; Data processing.; Probl{\'y}emes aux
                 valeurs initiales; Analyse num{\'y}erique.;
                 Probl{\'y}emes et exercices.; Int{\'y}egration
                 num{\'y}erique.; Math{\'y}ematiques.",
  tableofcontents = "1: Introduction \\
                 2: Higher order one-step methods \\
                 3: Systems of equations and equations of order greater
                 than one \\
                 4: Convergence, error bounds, and error estimates for
                 one-step methods \\
                 5: The choice of step size and order \\
                 6: Extrapolation methods \\
                 7: Multivalue or multistep methods --- introduction \\
                 8: General multistep methods, order and stability \\
                 9: Multivalue methods \\
                 10: Existence, convergence, and error estimates for
                 multivalue methods \\
                 11: Special methods for special problems [stiff
                 ODEs]\\
                 12: Choosing a method",
}

@Proceedings{Rice:1971:MS,
  editor =       "John R. Rice",
  booktitle =    "Mathematical Software",
  title =        "Mathematical Software",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xvii + 515",
  year =         "1971",
  ISBN =         "0-12-587250-X",
  ISBN-13 =      "978-0-12-587250-8",
  LCCN =         "QA1 .M26",
  bibdate =      "Thu Sep 15 18:56:52 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
                 https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/elefunt.bib;
                 https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib;
                 https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/Bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Based on the proceedings of the Mathematical Software
                 Symposium held at Purdue University, Lafayette,
                 Indiana, USA, April 1--3, 1970.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Preface \\
                 Acknowledgments \\
                 Part One: Prologue \\
                 Chapter 1. Historical Notes \\
                 I. Introduction \\
                 II. Chronological Record \\
                 References \\
                 Chapter 2. The Distribution and Sources of Mathematical
                 Software \\
                 I. Introduction \\
                 II. Local Distribution Methods \\
                 III. Assessment of General Sources \\
                 IV. Summary \\
                 Chapter 3. The Challenge for Mathematical Software \\
                 I. Introduction \\
                 II. Algorithm Construction \\
                 III. Evaluation --- Charting the Unknown \\
                 IV. Dissemination --- Some Alternatives \\
                 V. Two Recommendation \\
                 References \\
                 Chapter 4. Discussion of the Papers \\
                 I. The User's Voice \\
                 II. Arithmetic \\
                 III. Libraries \\
                 IV. The Automation of Numerical Analysis \\
                 V. Comparative Evaluation \\
                 VI. Systems for Mathematical Software \\
                 VII. Nonnumerical Software \\
                 VIII. Mathematical Procedures \\
                 Part Two: Proceedings of the Symposium \\
                 Chapter 5. The Papers \\
                 5.1 A user's experience with sophisticated
                 least-squares software in the discovery of the lunar
                 mass concentrations (MASCONS) \\
                 I. Nature of the Data Reduction \\
                 II. Implication for Program Development and
                 Distribution \\
                 III. Summary of Conclusions \\
                 Reference \\
                 5.2 User Modifiable Software \\
                 I. The Argument for Easy-to-Modify Software \\
                 II. Writing Easy-to-Modify Software \\
                 5.3 Number Representation and Significance Monitoring
                 \\
                 I. Number Representation \\
                 II. Error Classification \\
                 III. Significance Analysis \\
                 IV. Significance Monitoring \\
                 V. Mathematical Software \\
                 References \\
                 5.4 The Estimation of Significance \\
                 I. Introduction \\
                 II. Discussion of Rules \\
                 III. Implementation \\
                 IV. Elementary Functions \\
                 V. Numerical Experiments \\
                 References \\
                 5.5 Nonstandard Arithmetic \\
                 I. Reliability \\
                 II. Subroutine Library \\
                 III. Efficiency in Execution \\
                 IV. Ease of Use \\
                 V. Implementation of Nonstandard Arithmetic \\
                 VI. Use of Precompiler \\
                 VII. Type Other \\
                 VIII. Conclusion \\
                 References \\
                 5.6 Making Special Arithmetics Available \\
                 References \\
                 5.7 The Production of Mathematical Software for a Mass
                 Audience \\
                 I. Introduction \\
                 II. Discussion Assumptions \\
                 III. Problems in Mathematical Software Production \\
                 IV. Environmental Conditions Affecting Mathematical
                 Software Production \\
                 V. Production of Mathematical Software \\
                 VI. User Attitudes \\
                 VII. Summary \\
                 5.8 High Quality Portable Numerical Mathematics
                 Software \\
                 I. Introduction \\
                 II. The Bell Laboratories Numerical Mathematics Program
                 Library One \\
                 III. Status of Library One \\
                 IV. ZERBND \\
                 V. Portability \\
                 VI. Testing \\
                 References \\
                 5.9 The Development and Maintenance of a Technical
                 Subprogram Library \\
                 I. Introduction \\
                 II. Coding Standards \\
                 III. Documentation Format \\
                 IV. Review Procedures \\
                 V. Maintenance Procedures \\
                 VI. Multiple Precision in Fortran \\
                 VII. Support and Maintenance Requirements \\
                 VIII. Access Procedures \\
                 IX. Summary and Conclusions \\
                 X. Current Category Index \\
                 XI. Sample Documentation \\
                 5.10 The Boeing library and Handbook of Mathematical
                 Routines \\
                 Reference",
}

@Proceedings{Macon:1971:SJC,
  editor =       "Nathaniel Macon",
  key =          "AFIPS SJCC '71",
  booktitle =    "1971 Spring Joint Computer Conference, May 18--20,
                 1971, Atlantic City, New Jersey",
  title =        "1971 Spring Joint Computer Conference, May 18--20,
                 1971, Atlantic City, New Jersey",
  volume =       "38",
  publisher =    pub-AFIPS,
  address =      pub-AFIPS:adr,
  pages =        "631",
  year =         "1971",
  DOI =          "https://doi.org/10.1145/1478786",
  ISBN =         "1-4503-7907-9",
  ISBN-13 =      "978-1-4503-7907-6",
  LCCN =         "????",
  bibdate =      "Fri Sep 16 10:47:01 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "AFIPS conference proceedings",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  tableofcontents = "Computing Machines --- Menace or Messiah? --- Panel
                 Session (No papers in this volume) \\
                 \\
                 Image of the Industry --- Panel Session (No papers in
                 this volume) \\
                 \\
                 The New Technology --- Hardware Design and Evaluation
                 \\
                 \\
                 The DINKIAC I --- A pseudo-virtual-memoried mini ---
                 For stand-alone interactive use / R. W. Conn / 1 \\
                 A multi-channel CRC register / A. M. Patel / 11 \\
                 Features of an advanced front-end CPU / R. B. Hibbs /
                 15 \\
                 Interpreting the results of a hardware systems monitor
                 / J. S. Cockrum and E. D. Crockett / 23 \\
                 \\
                 Law Enforcement and Judicial Administration --- Panel
                 Session (No papers in this volume) \\
                 \\
                 Applications Requiring Multiprocessors \\
                 \\
                 4-way parallel processor partition of an atmospheric
                 primitive-equation prediction model / E. Morenoff, W.
                 Beckett, P. G. Kesel, F. J. Winninghoff, and P. M.
                 Wolff / 39 \ An associative processor for air traffic
                 control / K. J. Thurber / 49 \\
                 \\
                 Computer Aided management Of Earth Resources --- Panel
                 Session (No papers in this volume) \\
                 \\
                 Responsive Government --- Panel Session (No papers in
                 this volume) \\
                 \\
                 Computers in Transport --- For Management Needs or
                 Suppliers' Delight? \\
                 \\
                 A computer-aided traffic forecasting technique --- The
                 trans Hudson model / E. J. Lessieu / 61 \\
                 Computer graphics for transportation problems / D.
                 Cohen and J. M. McQuillan / 77 \\
                 Real time considerations for an airline / J. Loo, B. T.
                 O'Donald, and I. R. Whiteman / 83 \\
                 A computer simulation model of train operations in CTC
                 territory D. Borch / 93 \\
                 \\
                 Present and Future Data Networks --- Panel Session (No
                 papers in this volume) \\
                 \\
                 Terminal Oriented Displays \\
                 \\
                 A general display terminal system J. H. Botterill and
                 G. F. Heyne / 103 \\
                 AIDS --- Advanced interactive display system / T. R.
                 Stack and S. T. Walker / 113 \\
                 CRT display system for industrial process / T. Konishe,
                 N. Hamada and I. Yasuda / 123 \\
                 Computer generated closed circuit TV displays with
                 remote terminal control / S. Winkler, G. W. Price / 131
                 \\
                 \\
                 Competitive Evaluation of Interactive Systems --- Panel
                 Session (No papers in this volume) \\
                 \\
                 Computers in the Electoral Process \\
                 \\
                 The theory and practice of bipartisan constitutional
                 computer-aided redistricting / S. S. Nagel / 137 \\
                 ``Second-generation'' computer vote count systems ---
                 Assuming a professional responsibility / C. H. Springer
                 and M. R. Alkus / 143 \\
                 \\
                 Microprogramming and Emulation \\
                 \\
                 Evaluation of hardware--firmware--software trade-offs
                 with mathematical modeling / H. Barsamiam and A.
                 DeCegama / 151 \\
                 System/370 integrated emulation under OS and DOS / G.
                 R. Allred / 163 \\
                 A high-level microprogramming language (MPL) / R. H.
                 Eckhouse, Jr. / 169 \\
                 A firmware APL time-sharing system / R. Zaks, D.
                 Steingart, and J. Moore / 179 \\
                 \\
                 Interactive Applications and Systems \\
                 \\
                 Designing a large scale on-line real-time system / S.
                 Ishizaki / 191 \\
                 PERT --- A computer-aided game / J. Richter-Nielsen /
                 199 \\
                 Interactive problem-solving --- An experimental study
                 of ``lockout'' effects / B. W. Boehm, M. J. Seven, and
                 R. A. Watson / 205 \\
                 TYMNET --- A terminal-oriented communication network /
                 L. R. Tymes / 211 \\
                 Implementation of an interactive conference system / T.
                 W. Hall / 217 \\
                 \\
                 Computational Complexity --- Panel Session (No papers
                 in this volume) \\
                 \\
                 The Evolution of Computer Animation --- Panel Session
                 (No papers in this volume) \\
                 \\
                 Serving Users in Higher Education \\
                 \\
                 Who are the users? --- An analysis of computer use in a
                 university computer center / E. Hunt, G. Diehr, and D.
                 Garnatz / 231 \\
                 \\
                 Information and Data Management \\
                 \\
                 An initial operational problem oriented medical record
                 system --- For storage, manipulation and retrieval of
                 medical data / J. R. Schultz, S. V. Cantrill, and K. G.
                 Morgan / 239 \\
                 Laboratory verification of patient identity / S.
                 Raymond, L. Chalmers, and W. Steuber / 265 \\
                 The data system environment simulator (DASYS) / L. E.
                 DeCuir and R. W. Garrett / 271 \\
                 Management information systems --- What happens after
                 implementation? / D. E. Thomas, Jr. / 277 \\
                 A methodology for the design and optimization of
                 information processing systems / J. F. Nunamaker, Jr. /
                 283 \\
                 \\
                 Computer Assisted Instruction \\
                 \\
                 Computer generated repeatable tests / F. Prosser and D.
                 D. Jensen / 295 \\
                 R2 --- A natural language question-answering system /
                 K. Biss, R. Chien, and F. Stahl / 303 \\
                 \\
                 The New Technology --- Storage \\
                 \\
                 Performance evaluation of direct access storage devices
                 with a fixed head per track / T. Manocha, W. L. Martin,
                 and K. W. Stevens / 309 \\
                 Drum queueing model / G. P. Jain and S. R. Arora / 319
                 \\
                 Storage hierarchy systems / H. Katzan, Jr. / 325 \\
                 Optimal sizing, loading and re-loading in a multi-level
                 memory hierarchy system / S. R. Arora and A. Gallo /
                 337 \\
                 The TABLON mass storage network / R. B. Gentile and J.
                 R. Lucas, Jr. / 345 \\
                 \\
                 Topics in Computer Arithmetic and in Artificial
                 Intelligence \\
                 \\
                 A structure for systems that plan abstractly / W. W.
                 Jacobs / 357 \\
                 Unconventional superspeed computer systems / T. C. Chen
                 / 365 \\
                 High speed division for binary computers / H. Ling /
                 373 \\
                 A unified algorithm for elementary functions / S.
                 Walther / 379 \\
                 A software system for tracing numerical significance
                 during computer program execution / H. S. Bright, B. A.
                 Colhoun, and F. B. Mallory / 387 \\
                 Software Liability and Responsibility --- Panel Session
                 (No papers in this volume) \\
                 \\
                 Venture Capital --- Financing Young Companies --- Panel
                 Session (No papers in this volume) \\
                 \\
                 From the User's Viewpoint --- Panel Session (No papers
                 in this volume) \\
                 \\
                 Peripheral Processing --- Panel Session (No papers in
                 this volume) \\
                 \\
                 Computer Pictorics \\
                 \\
                 Automated interpretation and editing of fuzzy line
                 drawings / S. K. Chang / 393 \\
                 Computer graphics study of array response / G. W.
                 Byram, G. V. Olds, and L. P. LaLumiere / 401 \\
                 Computer manipulation of digitized pictures / N. Macon
                 and M. E. Kiefer / 407 \\
                 An International View --- Panel Session (No papers in
                 this volume) \\
                 \\
                 Simulation of Computer Systems \\
                 \\
                 The design of a meta-system / A. S. Noetzel / 415 \\
                 An interactive simulator generating system for small
                 computers / J. L. Brame and C. V. Ramamoorthy / 425 \\
                 Application of Computers to Training --- Panel Session
                 (No papers in this volume) \\
                 \\
                 The New Technology --- Diagnostics and Recovery \\
                 \\
                 Multiband automatic test equipment --- A computer
                 controlled check-out system / T. Kuroda and T. C. Bush
                 / 451 \\
                 Coding techniques for failure recovery in a
                 distributive modular memory organization / S. A.
                 Szygenda and M. J. Flynn / 459 \\
                 Recovery through programming system/370 / D. L.
                 Droulette / 467 \\
                 On automatic testing of one-line, real-time systems /
                 J. S. Gould / 477 \\
                 \\
                 The New Technology --- Systems Software \\
                 \\
                 PORTS --- A method for dynamic interprogram
                 communication and job control / R. M. Balzer / 485 \\
                 Automatic program segmentation based on boolean
                 connectivity / E. W. Ver Hoef / 491 \\
                 Partial recompilation / R. B. Ayres and R. L.
                 Derrenbacher / 497 \\
                 PL/C --- The design of a high-performance compiler for
                 PL/I / H. L. Morgan and R. A. Wagner / 503 \\
                 GPL/I --- A PL/I extension for computer graphics / D.
                 N. Smith / 511 \\
                 ETC --- An extendible macro-based compiler / B. N.
                 Dickman / 529 \\
                 \\
                 The Computer Professional and the Changing Job Market
                 --- Panel Session (No papers in this volume) \\
                 \\
                 The New Technology --- File Organization \\
                 \\
                 A file organization method using multiple keys / M. L.
                 O'Connell / 539 \\
                 Arranging frequency dependent data on sequential
                 memories / C. V. Ramamoorthy and P. R. Blevins / 545
                 \\
                 Associative processing of line drawings / N. J.
                 Stillman, C. R. Defiore, and P. B. Berra / 557 \\
                 \\
                 The New Technology --- Computer Architecture \\
                 \\
                 The hardware-implemented high-level machine language
                 for symbol / G. D. Chesley and W. R. Smith / 563 \\
                 SYMBOL --- A major departure from classic software
                 dominated von Neumann computing systems / R. Rice and
                 W. R. Smith / 575 \\
                 The physical attributes and testing aspects of the
                 symbol system / B. E. Cowart, R. Rice, and S. F.
                 Lundstrom / 589 \\
                 SYMBOL --- A large experimental system exploring major
                 hardware replacement of software / W. R. Smith, R.
                 Rice, G. D. Chesley, T. A. Laliotis, S. F. Lundstrom,
                 M. A. Calhoun, L. D. Gerould, and T. G. Cook / 601 \\
                 \\
                 Educational Requirements for Systems Analysts \\
                 \\
                 A semi-automatic relevancy generation technique for
                 data processing education and career development / J.
                 D. Benenati / 617 \\
                 An architectural framework for systems analysis and
                 evaluation / P. Freeman / 629 \\
                 \\
                 Computer Acquisition --- Purchase or Lease --- Panel
                 Session (No papers in this volume) \\
                 \\
                 Computation, Decision Making, and the Environment ---
                 Panel Session (No papers in this volume)",
}

@Proceedings{ACM:1972:PAA,
  editor =       "{ACM}",
  booktitle =    "Proceedings of the {ACM} annual conference, August
                 1972, Boston, Massachusetts",
  title =        "Proceedings of the {ACM} annual conference, August
                 1972, Boston, Massachusetts",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xiii + 1156",
  year =         "1972",
  LCCN =         "QA76; TK7885",
  bibdate =      "Fri Nov 28 11:28:06 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Two volumes.",
  acknowledgement = ack-nhfb,
}

@Book{Cardenas:1972:CS,
  editor =       "Alfonso F. Cardenas and Leon Presser and Miguel A.
                 Marin",
  booktitle =    "Computer Science",
  title =        "Computer Science",
  publisher =    pub-WILEY-INTERSCIENCE,
  address =      pub-WILEY-INTERSCIENCE:adr,
  pages =        "xii + 522",
  year =         "1972",
  ISBN =         "0-471-13468-6",
  ISBN-13 =      "978-0-471-13468-8",
  LCCN =         "QA76.5 .C365; TK7885 .C178c",
  bibdate =      "Sat Nov 29 11:09:31 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:1972:IAD,
  editor =       "{IEEE}",
  booktitle =    "{Innovative architecture: digest of papers: COMPCON
                 72, 6. annual IEEE Computer Society International
                 Conference, Jack Tar Hotel, San Francisco, California,
                 September 12--14, 1972}",
  title =        "{Innovative architecture: digest of papers: COMPCON
                 72, 6. annual IEEE Computer Society International
                 Conference, Jack Tar Hotel, San Francisco, California,
                 September 12--14, 1972}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiii + 340",
  year =         "1972",
  LCCN =         "TK7885.A1 C53 1972",
  bibdate =      "Wed Mar 21 09:29:22 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE order number 72CH0659-3C.",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:1972:ITS,
  editor =       "{IEEE}",
  booktitle =    "{2nd IEEE-TCCA Symposium on Computer Arithmetic,
                 College Park, Maryland, May 15--16, Maryland}",
  title =        "{2nd IEEE-TCCA Symposium on Computer Arithmetic,
                 College Park, Maryland, May 15--16, Maryland}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "1972",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Wed Apr 27 17:36:48 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-2",
  remark =       "Selected papers from this conference are reprinted in
                 a special issue on computer arithmetic in IEEE
                 Transactions on Computers, volume C-22, number 6, June
                 1973. Otherwise, the remaining papers appear not to
                 have been published, at least not in one location.",
}

@Book{Petrocelli:1972:BCP,
  editor =       "Orlando R. Petrocelli",
  booktitle =    "The Best Computer Papers in 1971",
  title =        "The Best Computer Papers in 1971",
  publisher =    "Auerbach Publishers",
  address =      "Princeton, NJ, USA",
  pages =        "ix + 296",
  year =         "1972",
  ISBN =         "0-87769-127-4",
  ISBN-13 =      "978-0-87769-127-3",
  LCCN =         "QA76.5 .P397 1972",
  bibdate =      "Wed Oct 29 06:02:29 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "1: Association for Computing Machinery \\
                 2: American Federation of Information Processing
                 Societies \\
                 3: International Federation for Information Processing
                 \\
                 4: The British Computer Electrical and Electronics
                 Engineers \\
                 6: Simulation Councils \\
                 7: Numerical Control Society \\
                 8: Forecast",
}

@Proceedings{Zaremba:1972:ANT,
  editor =       "S. K. Zaremba",
  booktitle =    "Applications of Number Theory to Numerical Analysis =
                 {Applications} de la th{\'e}orie des nombres {\`a}
                 l'analyse num{\'e}rique. Proceedings of the symposium
                 at the {Centre for Research in Mathematics, University
                 of Montreal, September 9--14, 1971}",
  title =        "Applications of Number Theory to Numerical Analysis =
                 {Applications} de la th{\'e}orie des nombres {\`a}
                 l'analyse num{\'e}rique. Proceedings of the symposium
                 at the {Centre for Research in Mathematics, University
                 of Montreal, September 9--14, 1971}",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xii + 489",
  year =         "1972",
  ISBN =         "0-12-775950-6",
  ISBN-13 =      "978-0-12-775950-0",
  LCCN =         "QA297 .A67",
  bibdate =      "Mon Aug 02 10:53:03 2004",
  bibsource =    "ftp://ftp.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  language =     "French and English",
}

@Proceedings{ACM:1974:CRS,
  editor =       "{ACM}",
  booktitle =    "Conference record of sixth annual {ACM} Symposium on
                 Theory of Computing: papers presented at the symposium,
                 Seattle, Washington, April 30--May 2, 1974",
  title =        "Conference record of sixth annual {ACM} Symposium on
                 Theory of Computing: papers presented at the symposium,
                 Seattle, Washington, April 30--May 2, 1974",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "iv + 347",
  year =         "1974",
  LCCN =         "QA76.6 .A13 1974",
  bibdate =      "Thu Dec 3 07:11:18 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "computational complexity --- congresses; electronic
                 digital computers --- programming --- congresses",
  xxISBN =       "none",
}

@Proceedings{Panagiotopoulos:1974:PCC,
  editor =       "Antonios Ch. Panagiotopoulos",
  booktitle =    "Proceedings of the C. Carath{\'e}odory International
                 Symposium (Athens, 1973)",
  title =        "Proceedings of the {C}. Carath{\'e}odory International
                 Symposium (Athens, 1973)",
  publisher =    "Greek Mathematical Society",
  address =      "Athens, Greece",
  pages =        "634",
  year =         "1974",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Fri Dec 08 13:53:34 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:1975:SCA,
  key =          "IEEE SCA '75",
  booktitle =    "3rd Symposium on Computer Arithmetic, November 19--20,
                 1975, Southern Methodist University, Dallas, Texas",
  title =        "3rd Symposium on Computer Arithmetic, November 19--20,
                 1975, Southern Methodist University, Dallas, Texas",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "viii + 249",
  year =         "1975",
  LCCN =         "QA76.6.S919 1975",
  bibdate =      "Fri Nov 28 18:13:53 2003",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE order number CH1017-3C.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-3; Computer arithmetic and logic units ---
                 Congresses.; Electronic digital computers ---
                 Programming --- Congresses.; Floating-point arithmetic
                 --- Congresses",
  xxISBN =       "(none)",
}

@Book{Randell:1975:ODC,
  editor =       "Brian Randell",
  booktitle =    "The Origins of Digital Computers: Selected Papers",
  title =        "The Origins of Digital Computers: Selected Papers",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "xvi + 464",
  year =         "1975",
  DOI =          "https://doi.org/10.1007/978-3-642-96242-4",
  ISBN =         "0-387-07114-8, 3-540-07114-8, 3-642-96244-0,
                 3-642-96242-4 (e-book)",
  ISBN-13 =      "978-0-387-07114-5, 978-3-540-07114-3,
                 978-3-642-96244-8, 978-3-642-96242-4 (e-book)",
  LCCN =         "?TK7888.3 .R36 1975",
  bibdate =      "Wed Oct 13 09:24:25 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wilkes-maurice-v.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Texts and monographs in computer science",
  acknowledgement = ack-nhfb,
  remark =       "See also other editions
                 \cite{Randell:1973:ODC,Randell:1982:ODC}.",
  subject =      "Electronic digital computers; History; Calculators",
  tableofcontents = "Front Matter / / i--xvi \\
                 Introduction / Brian Randell / 1--6 \\
                 Analytical Engines / Charles Babbage, Mr. C. W.
                 Merrifield, H. P. Babbage, Percy E. Ludgate, Leonardo
                 Torres y Quevedo, L. Couffignal/ 7--123 \\
                 Tabulating Machines / H. Hollerith, L. Couffignal,
                 H.-J. Dreyer, A. Walther / 125--153 \\
                 Zuse and Schreyer / Konrad Zuse, Helmut Schreyer /
                 155--186 \\
                 Aiken and IBM / Howard H. Aiken, Grace M. Hopper, W. J.
                 Eckert, John W. Sheldon, Liston Tatum / 187--235 \\
                 Bell Telephone Laboratories / G. R. Stibitz, O.
                 Cesareo, Joseph Juley, Franz L. Alt / 237--286 \\
                 The Advent of Electronic Computers / E. William
                 Phillips O.B.E., F.I.A., John V. Atanasoff, D. Michie,
                 John W. Mauchly, H. H. Goldstine, Adele Goldstine /
                 287--347 \\
                 Stored Program Electronic Computers / John von Neumann,
                 John W. Mauchly, Arthur W. Burks, Herman H. Goldstine,
                 F. C. Williams, T. Kilburn, M. V. Wilkes, W. Renwick /
                 349--401 \\
                 Back Matter / / 403--464",
}

@Proceedings{Swamy:1975:PEM,
  editor =       "M. N. S. Swamy",
  booktitle =    "Proceedings of the Eighteenth Midwest Symposium on
                 Circuits and Systems (Concordia University, Montreal,
                 Que., 1975)",
  title =        "Proceedings of the Eighteenth Midwest Symposium on
                 Circuits and Systems (Concordia University, Montreal,
                 Que., 1975)",
  publisher =    pub-WESTERN-PERIODICALS,
  address =      pub-WESTERN-PERIODICALS:adr,
  pages =        "xvi + 659",
  year =         "1975",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Fri Dec 08 13:57:52 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{Swartzlander:1976:CDD,
  author =       "Earl E. {Swartzlander, Jr.}",
  booktitle =    "Computer Design Development: Principal Papers",
  title =        "Computer Design Development: Principal Papers",
  publisher =    pub-HAYDEN-BOOK,
  address =      pub-HAYDEN-BOOK:adr,
  pages =        "310",
  year =         "1976",
  ISBN =         "0-8104-5988-4",
  ISBN-13 =      "978-0-8104-5988-5",
  LCCN =         "QA76.5 .C612565",
  bibdate =      "Wed Oct 13 08:14:58 2004",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wilkes-maurice-v.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  tableofcontents = "0. Preface by Swartzlander \\
                 1: Logic Design \\
                 1.0 Introduction by Swartzlander \\
                 1.1 ``A Symbolic Analysis of Relay and Switching
                 Circuits'', Claude E. Shannon (1938) \\
                 1.2 ``The Map Method for Synthesis of Combinational
                 Logic Circuits'', M. Karnaugh (1953) \\
                 1.3 ``Minimization of Boolean Functions'', E. J.
                 McCluskey (1956) \\
                 1.4 ``A Method for Synthesizing Sequential Circuits'',
                 George H. Mealy (1955) \\
                 1.5 ``Hazards and Delays in Asynchronous Sequential
                 Switching Circuits'', S. H. Unger (1959) \\
                 1.6 ``Internal State Assignments for Asynchronous
                 Sequential Machines'', James H. Tracey \\
                 2: Arithmetic Algorithms \\
                 2.0 Introduction by Swartzlander \\
                 2.1 ``High-Speed Arithmetic in Binary Computers'', O.
                 L. MacSorley (1961) \\
                 2.2 ``A Signed Binary Multiplication Technique'',
                 Andrew D. Booth (1951) \\
                 2.3 ``Some Schemes for Parallel Multipliers'', L. Dadda
                 (1965) \\
                 2.4 ``The Residue Number System'', Harvey L. Garner
                 (1959) \\
                 2.5 ``The IBM System 360 Model 91: Floating-Point
                 Execution Unit'', S. F. Anderson, J. G. Earle, R. E.
                 Goldschmidt, and D. M. Powers (1967) \\
                 3: Computer Architecture \\
                 3.0 Introduction by Swartzlander \\
                 3.1 ''Preliminary Discussion of the Logical Design of
                 an Electronic Computing Instrument'', Arthur W. Burks,
                 Herman H. Goldstine, and John von Neumann (1946) \\
                 3.2 ''Symbolic Synthesis of Digital Computers'', Irving
                 S. Reed (1950) \\
                 3.3 ''The Best Way to Design an Automatic Calculating
                 Machine'', M. V. Wilkes (1951) \\
                 3.4 ''Structural Aspects of the System/360 Model 85
                 part II: The Cache'', J. S. Liptay (1968) \\
                 3.5 ''Parallel Operation in the Control Data 6600'',
                 James E. Thornton (1964) \\
                 3.6 ''The SOLOMON Computer'', Daniel L. Slotnick, W.
                 Borck, and R. McReynolds (1962) \\
                 4: Appendix \\
                 4.0 Introduction by Swartzlander \\
                 4.1 ``A Trigger Relay Utilizing Three-Electrode
                 Thermionic Vacuum Tubes'', W. H. Eccles and F. W.
                 Jordan (1919) \\
                 4.2 ``The CORDIC Trigonometric Computing Technique'',
                 Jack E. Bolder (1959)",
}

@Proceedings{Traub:1976:ACC,
  editor =       "J. F. (Joseph Frederick) Traub",
  booktitle =    "{Analytic computational complexity: Proceedings of the
                 Symposium on Analytic Computational Complexity, held by
                 the Computer Science Department, Carnegie-Mellon
                 University, Pittsburgh, Pennsylvania, on April 7--8,
                 1975}",
  title =        "{Analytic computational complexity: Proceedings of the
                 Symposium on Analytic Computational Complexity, held by
                 the Computer Science Department, Carnegie-Mellon
                 University, Pittsburgh, Pennsylvania, on April 7--8,
                 1975}",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "ix + 239",
  year =         "1976",
  ISBN =         "0-12-697560-4",
  ISBN-13 =      "978-0-12-697560-4",
  LCCN =         "QA297.S9151 1975",
  bibdate =      "Mon Jan 13 10:18:33 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Cowell:1977:PNS,
  editor =       "Wayne Cowell",
  booktitle =    "Portability of Numerical Software, Workshop, {Oak
                 Brook, Illinois, June 21--23, 1976}",
  title =        "Portability of Numerical Software, Workshop, {Oak
                 Brook, Illinois, June 21--23, 1976}",
  volume =       "57",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 539",
  year =         "1977",
  DOI =          "https://doi.org/10.1007/3-540-08446-0",
  ISBN =         "0-387-08446-0, 3-540-08446-0, 3-540-37071-4",
  ISBN-13 =      "978-0-387-08446-6, 978-3-540-08446-4,
                 978-3-540-37071-0",
  ISSN =         "0302-9743",
  LCCN =         "QA297 .W65 1976",
  bibdate =      "Thu Dec 11 14:25:53 MST 2025",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-LNCS,
  URL =          "http://link.springer.com/10.1007/3-540-08446-0",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  tableofcontents = "What is portability? / 1--2 \\
                 Some side effects of striving for portability /
                 Christian Reinsch / 3--19 \\
                 Machine characteristics and portability / 20--21 \\
                 Machine requirements for reliable, portable software /
                 T. J. Dekker / 22--36 \\
                 Semantics of floating point arithmetic and elementary
                 functions / T. E. Hull / 37--48 \\
                 Machine parameters for numerical analysis / W. J. Cody
                 / 49--67 \\
                 Preparing conventions for parameters for transportable
                 numerical software / B. Ford / 68--91 \\
                 Programming languages and portability / 92--94 \\
                 Algol 68 as a language for numerical software / L. M.
                 Delves / 95--126 \\
                 Writing the elementary function procedures for the
                 ALGOL68C compiler / P. Kemp / 127--144 \\
                 Criteria for transportable Algol libraries / Pieter W.
                 Hemker / 145--157 \\
                 Fortran portability via models and tools / W. S. Brown,
                 A. D. Hall / 158--164 \\
                 Port --- A portable mathematical subroutine library /
                 P. A. Fox / 165--177 \\
                 Fortran poisoning and antidotes / Brian T. Smith /
                 178--256 \\
                 Two numerical analysts' views on the Draft Proposed ANS
                 Fortran / C. L. Lawson, J. K. Reid / 257--268 \\
                 Intermediate languages: Current status / W. M. Waite /
                 269--303 \\
                 Computer-assisted portability / 304--304 \\
                 Mathematical software transportability systems --- have
                 the variations a theme? / James M. Boyle / 305--360 \\
                 Features for Fortran portability / Fred T. Krogh /
                 361--367 \\
                 The IMSL Fortran converter: an approach to solving
                 portability problems / T. J. Aird / 368--388 \\
                 Aids to portability within the NAG project / J. J. Du
                 Croz, S. J. Hague, J. L. Siemieniuch / 389--404 \\
                 Multiple program realizations using the TAMPR system /
                 Kenneth W. Dritz / 405--423 \\
                 Software design to facilitate portability / 424--424
                 \\
                 The production and testing of special function software
                 in the NAG library / J. L. Schonfelder / 425--451 \\
                 Portable special function routines / L. Wayne Fullerton
                 / 452--483 \\
                 The importance of standardized interfaces for portable
                 statistical software / N. Victor, M. Sund / 484--503
                 \\
                 Exploring the impact of portability / 504--504 \\
                 On the enhancement of portability within the NAG
                 project --- a statistical survey / J. Bentley, B. Ford
                 / 505--528 \\
                 A study of portability in technical and scientific
                 computing / Ingemar Dahlstrand / 529--539",
}

@Proceedings{IEEE:1977:ICS,
  editor =       "{IEEE}",
  booktitle =    "{The IEEE Computer Society's First International
                 Computer Software \& Applications Conference, Chicago,
                 November 8--11, 1977: Proceedings}",
  title =        "{The IEEE Computer Society's First International
                 Computer Software \& Applications Conference, Chicago,
                 November 8--11, 1977: Proceedings}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xxi + 834",
  year =         "1977",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "QA76.6 .I51 1977",
  bibdate =      "Fri Nov 09 20:06:59 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog no. 77CH1291-4C.",
  acknowledgement = ack-nhfb,
  remark =       "Not found in IEEE Xplore database, and no ISBN has
                 been recorded in numerous library catalog entries for
                 this volume.",
}

@Book{Jacobs:1977:SAN,
  editor =       "D. Jacobs",
  booktitle =    "The state of the art in numerical analysis:
                 {Proceedings of the Conference held at The University
                 of York, Heslington, April 12th--15th, 1976}",
  title =        "The state of the art in numerical analysis:
                 {Proceedings of the Conference held at The University
                 of York, Heslington, April 12th--15th, 1976}",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xix + 978",
  year =         "1977",
  MRclass =      "65-06",
  MRnumber =     "MR0440858 (55 \#13726)",
  bibdate =      "Thu Nov 8 19:02:54 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "With a foreword by R. A. Scriven",
  acknowledgement = ack-nhfb,
}

@Proceedings{Rice:1977:MSI,
  editor =       "John R. Rice",
  booktitle =    "{Mathematical software III: Proceedings of a symposium
                 conducted by the Mathematics Research Center, the
                 University of Wisconsin--Madison, March 28--30, 1977}",
  title =        "{Mathematical software III: Proceedings of a symposium
                 conducted by the Mathematics Research Center, the
                 University of Wisconsin--Madison, March 28--30, 1977}",
  number =       "39",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "ix + 388",
  year =         "1977",
  DOI =          "https://doi.org/10.1016/C2013-0-11364-5",
  ISBN =         "0-12-587260-7",
  ISBN-13 =      "978-0-12-587260-7",
  LCCN =         "QA3 .U45 no. 39; QA297 .M36 1977",
  bibdate =      "Fri Dec 08 08:24:52 1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/brandt-achi.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
                 https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib;
                 https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/Bibnet/authors/g/golub-gene-h.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  series =       "Publication of the Mathematics Research Center, the
                 University of Wisconsin, Madison",
  URL =          "https://www.sciencedirect.com/book/9780125872607/mathematical-software",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "Contributors / / vii \\
                 Preface / / ix \\
                 Research, Development, and UNPACK / G. W. Stewart / 1
                 \\
                 A Technique that Gains Speed and Accuracy in the
                 Minimax Solution of Overdetermined Linear Equations /
                 M. J. Hopper and M. J. D. Powell / 15 \\
                 Infallible Calculation of Polynomial Zeros to Specified
                 Precision / G. E. Collins / 35 \\
                 Representation and Approximation of Surfaces / Robert
                 E. Barnhill / 69 \\
                 Simulation: Conflicts between Real-Time and Software /
                 C. W. Gear / 121 \\
                 Mathematical Software and Exploratory Data Analysis /
                 David C. Hoaglin / 139 \\
                 Software for $C^1$ Surface Interpolation / C. L. Lawson
                 / 161 \\
                 Mathematical Software Production / W. R. Cowell and L.
                 D. Fosdick / 195 \\
                 Computational Aspects of the Finite Element Method / I.
                 Babuska and W. Rheinboldt / 225 \\
                 The Art of Writing a Runge-Kutta Code, Part I / L. F.
                 Shampine and H. A. Watts / 257 \\
                 Multi-Level Adaptive Techniques (MLAT) for Partial
                 Differential Equations: Ideas and Software / Achi
                 Brandt / 277 \\
                 ELLPACK: A Research Tool for Elliptic Partial
                 Differential Equations Software / John R. Rice / 319
                 \\
                 A Realistic Model of Floating-Point Computation / W. S.
                 Brown / 343 \\
                 The Block Lanczos Method for Computing Eigenvalues / G.
                 H. Golub and R. Underwood / 361 \\
                 Index / / 379",
  tableofcontents = "Contributors \\
                 Preface \\
                 \\
                 1: Research, Development, and Linpack \\
                 Abstract \\
                 1. Introduction \\
                 2. Estimation of Condition Numbers \\
                 3. Stability of Least Squares Solutions \\
                 4. Scaling and Column Elimination \\
                 5. Downdating \\
                 6. Timing the BLAS \\
                 References \\
                 \\
                 2: A Technique That Gains Speed and Accuracy in the
                 Minimax Solution of Overdetermined Linear Equations \\
                 Abstract \\
                 1. Introduction \\
                 2. Numerical Instability in the Exchange Algorithm \\
                 3. The New Technique \\
                 4. Theory \\
                 5. Discussion \\
                 References \\
                 \\
                 3: Infallible Calculation Of Polynomial Zeros To
                 Specified Precision \\
                 Abstract \\
                 1. Introduction \\
                 2. Preliminaries \\
                 3. Sturm Sequences For Real Zeros \\
                 4. Sturm Sequences For Complex Zeros \\
                 5. Rolle's Theorem For Real Zeros \\
                 6. Descartes' Theorem For Real Zeros \\
                 7. Application of Interval Arithmetic \\
                 8. Complex Zeros Without Sturm Sequences \\
                 References \\
                 \\
                 4: Representation and Approximation of Surfaces \\
                 Abstract \\
                 1. Introduction \\
                 2. Interpolation Methods Defined Over Rectangles \\
                 3. Interpolation Schemes Defined Over Triangles \\
                 4. Interpolation Methods For Arbitrarily Placed Data 5.
                 Conclusions \\
                 References \\
                 Acknowledgements \\
                 \\
                 5: Simulation: Conflicts Between Real-Time And Software
                 \\
                 Abstract \\
                 1. Introduction \\
                 2. Simulation \\
                 3. Real-Time Operation \\
                 4. Numerical Integration in Real-Time \\
                 5. Errors in Numerical Integration \\
                 6. Methods For Reducing Delay and Improving Stability
                 \\
                 7. Conclusions \\
                 References \\
                 \\
                 6: Mathematical Software and Exploratory Data Analysis
                 \\
                 Abstract \\
                 1. Introduction \\
                 2. Overview of Exploratory Data Analysis \\
                 3. An Example: Timing Data \\
                 4. Software Needs of Exploratory Data Analysis \\
                 5. Summary \\
                 References \\
                 \\
                 7: Software For $C^1$ Surface Interpolation \\
                 1. Introduction \\
                 2. Problem Statement \\
                 3. Expected Applications \\
                 4. Published Work On Surface Interpolation To
                 Irregularly Located Data \\
                 5. Outline of the Algorithmic Approach Selected \\
                 6. Constructing a Triangular Grid \\
                 7. Estimating Partial Derivatives At the Grid Nodes \\
                 8. Lookup in the Triangular Grid \\
                 9. Interpolation in a Triangle \\
                 10. Examples \\
                 11. Three Criteria For Triangulation of a Strictly
                 Convex Quadrilateral \\
                 12. Global Consequences of the Local Optimization
                 Procedure \\
                 13. Mclain's Triangulation Method \\
                 14. Limits On Grid Changes When Adding a New Point \\
                 15. Conclusions \\
                 References \\
                 \\
                 8: Mathematical Software Production \\
                 Abstract \\
                 I. Introduction \\
                 II. The Evolution of Mathematical Software Production
                 \\
                 III. Intellectual Challenges \\
                 IV. Projects To Produce Mathematical Software \\
                 V. Trends in Mathematical Software Production \\
                 References \\
                 \\
                 9: Computational Aspects of the Finite Element Method
                 \\
                 1. Introduction \\
                 2. Goals of the Computational Analysis \\
                 3. The Principal Stages of the Computational Analysis
                 \\
                 4. Some Software Aspects \\
                 5. Some Computational Results \\
                 References",
}

@Proceedings{COMPSAC:1978:CPC,
  key =          "COMPSAC '78",
  booktitle =    "{COMPSAC} 78: Proceedings [conference held] November
                 13--16, 1978 [at] The Palmer House, Chicago, Illinois",
  title =        "{COMPSAC} 78: Proceedings [conference held] November
                 13--16, 1978 [at] The Palmer House, Chicago, Illinois",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiv + 832",
  year =         "1978",
  LCCN =         "????",
  bibdate =      "Thu Sep 15 18:50:37 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  xxISBN =       "(none)",
}

@Proceedings{IEEE:1978:PSC,
  key =          "IEEE SCA '78",
  booktitle =    "Proceedings of the 4th Symposium on Computer
                 Arithmetic, Santa Monica, {CA}, {USA}, 25--27 October
                 1978",
  title =        "Proceedings of the 4th Symposium on Computer
                 Arithmetic, Santa Monica, {CA}, {USA}, 25--27 October
                 1978",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xi + 274",
  year =         "1978",
  ISSN =         "1063-6889",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog no. 78CH1412-6C.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-4; Computer arithmetic --- Congresses.;
                 Electronic digital computers --- Programming ---
                 Congresses.; Floating-point arithmetic ---
                 Congresses.",
  xxISBN =       "(none)",
  xxLCCN =       "(none)",
}

@Proceedings{ACM:1979:PSC,
  editor =       "{ACM}",
  booktitle =    "Proceedings of the {SIGNUM} Conference on the
                 Programming Environment for Development of Numerical
                 Software",
  title =        "Proceedings of the {SIGNUM} Conference on the
                 Programming Environment for Development of Numerical
                 Software",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  year =         "1979",
  bibdate =      "Fri Nov 28 17:28:30 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Anonymous:1979:WCR,
  editor =       "Anonymous",
  booktitle =    "{WESCON} conference record",
  title =        "{WESCON} conference record",
  publisher =    "Electronic Conventions Management",
  address =      "Los Angeles, CA, USA",
  year =         "1979",
  CODEN =        "WCREDI",
  ISSN =         "1044-6036, 0083-8837",
  LCCN =         "TK7800",
  bibdate =      "Fri Nov 09 20:00:43 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "17 volumes.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Budach:1979:FCT,
  editor =       "L. (Lothar) Budach",
  booktitle =    "{Fundamentals of computation theory: FCT '79:
                 proceedings of the Conference on Algebraic, Arithmetic,
                 and Categorial Methods in Computation Theory held in
                 Berlin\slash Wendisch-Rietz (GDR), September 17--21,
                 1979}",
  title =        "{Fundamentals of computation theory: FCT '79:
                 proceedings of the Conference on Algebraic, Arithmetic,
                 and Categorial Methods in Computation Theory held in
                 Berlin\slash Wendisch-Rietz (GDR), September 17--21,
                 1979}",
  volume =       "2",
  publisher =    pub-AKADEMIE-VERLAG,
  address =      pub-AKADEMIE-VERLAG:adr,
  pages =        "576",
  year =         "1979",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "QA267 .C594 1979",
  bibdate =      "Sat Mar 31 10:25:37 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Mathematical research",
  acknowledgement = ack-nhfb,
  meetingname =  "Conference on Algebraic, Arithmetic, and Categorial
                 Methods in Computation Theory (1979 : Wendisch Rietz,
                 Germany)",
  remark =       "English or French.",
  subject =      "Machine theory; Congresses; Categories (Mathematics);
                 Computational complexity",
}

@Book{Linger:1979:SPT,
  author =       "R. C. Linger and H. D. Mills and B. I. Witt",
  booktitle =    "Structured Programming: Theory and Practice",
  title =        "Structured Programming: Theory and Practice",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "xi + 402",
  year =         "1979",
  ISBN =         "0-201-14461-1",
  ISBN-13 =      "978-0-201-14461-1",
  LCCN =         "QA76.6 .L55",
  bibdate =      "Tue Jul 26 11:13:15 2022",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/hansen-per-brinch.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "No tableofcontents data found, and no online source
                 yet located. This book discussion multiword integer
                 division, but the treatment is later shown to be
                 inferior to that of subsequent work
                 \cite{BrinchHansen:1995:LDA}.",
}

@Proceedings{Meinardus:1979:ATP,
  editor =       "Gunther Meinardus",
  booktitle =    "{Approximation in Theorie und Praxis: e.
                 Symposiumsbericht} \toenglish {Approximation in Theory
                 and Practice: Symposium Proceedings} \endtoenglish",
  title =        "{Approximation in Theorie und Praxis: e.
                 Symposiumsbericht} \toenglish {Approximation in Theory
                 and Practice: Symposium Proceedings} \endtoenglish",
  publisher =    pub-BIB-INST,
  address =      pub-BIB-INST:adr,
  pages =        "304",
  year =         "1979",
  ISBN =         "3-411-01567-5",
  ISBN-13 =      "978-3-411-01567-2",
  LCCN =         "QA297.5 .A66",
  bibdate =      "Fri Sep 16 16:30:41 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Contributions in English or German from a meeting held
                 Jan. 31--Feb. 2, 1979, at the Gesamthochschule Siegen,
                 Forschungsinstitut fur Geistes- und
                 Sozialwissenschaften.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Ng:1979:SAC,
  editor =       "Edward W. Ng",
  booktitle =    "{Symbolic and algebraic computation: EUROSAM '79, an
                 International Symposium on Symbolic and Algebraic
                 Manipulation, Marseille, France, June 1979}",
  title =        "{Symbolic and algebraic computation: EUROSAM '79, an
                 International Symposium on Symbolic and Algebraic
                 Manipulation, Marseille, France, June 1979}",
  volume =       "72",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xiv + 557",
  year =         "1979",
  ISBN =         "0-387-09519-5",
  ISBN-13 =      "978-0-387-09519-6",
  LCCN =         "QA155.7.E4I57 1979",
  bibdate =      "Fri Dec 08 08:45:00 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
}

@Proceedings{ACM:1980:CPA,
  editor =       "{ACM}",
  booktitle =    "{Conference Proceedings: 7th Annual Symposium on
                 Computer Architecture, La Baule, France, 6--8 May
                 1980}",
  title =        "{Conference Proceedings: 7th Annual Symposium on
                 Computer Architecture, La Baule, France, 6--8 May
                 1980}",
  volume =       "8(3)",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "333",
  year =         "1980",
  CODEN =        "CANED2, CPAADU",
  ISBN =         "????",
  ISBN-13 =      "????",
  ISSN =         "0163-5964 (ACM), 0884-7495 (IEEE), 0149-7111",
  bibdate =      "Fri Sep 16 10:53:10 1994",
  bibsource =    "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib;
                 http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
  series =       j-COMP-ARCH-NEWS,
  URL =          "http://portal.acm.org/toc.cfm?id=800090",
  acknowledgement = ack-nj,
}

@Proceedings{Alefeld:1980:FNC,
  editor =       "G. Alefeld and R. D. Grigorieff",
  booktitle =    "Fundamentals of Numerical Computation
                 (Computer-Oriented Numerical Analysis)",
  title =        "Fundamentals of Numerical Computation
                 (Computer-Oriented Numerical Analysis)",
  volume =       "2",
  publisher =    pub-SPRINGER-WIEN,
  address =      pub-SPRINGER-WIEN:adr,
  pages =        "v + 229",
  year =         "1980",
  CODEN =        "COSPDM",
  ISBN =         "0-387-81566-X",
  ISBN-13 =      "978-0-387-81566-4",
  ISSN =         "0344-8029",
  LCCN =         "QA297 .F84",
  bibdate =      "Wed Oct 13 18:45:11 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "In cooperation with R. Albrecht, U. Kulisch, and F.
                 Stummel.",
  series =       j-COMPUTING-SUPPLEMENTUM,
  acknowledgement = ack-nhfb,
  remark =       "Collection of invited lectures which were given during
                 a conference held on June 5--8, 1979, on the occasion
                 of the centennial of the Technical University of
                 Berlin.",
}

@Proceedings{Anonymous:1980:CPA,
  key =          "COMPARCH '80",
  booktitle =    "Conference Proceedings 7th Annual Symposium on
                 Computer Architecture, La Baule, France, 6--8 May
                 1980",
  title =        "Conference Proceedings 7th Annual Symposium on
                 Computer Architecture, La Baule, France, 6--8 May
                 1980",
  volume =       "8(3)",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "333",
  year =         "1980",
  CODEN =        "CANED2",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  bibdate =      "Fri Sep 16 10:53:10 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       j-COMP-ARCH-NEWS,
  acknowledgement = ack-nj,
}

@Proceedings{Electro:1980:ECR,
  key =          "Electro '80",
  booktitle =    "Electro\slash 80 Conference Record: Sessions Presented
                 at {ELECTRO}\slash 80, Boston, {MA}, May 13--15, 1980",
  title =        "Electro\slash 80 Conference Record: Sessions Presented
                 at {ELECTRO}\slash 80, Boston, {MA}, May 13--15, 1980",
  publisher =    "Electronic Conventions, Inc.",
  address =      "El Segundo, CA, USA",
  pages =        "various",
  year =         "1980",
  LCCN =         "TK 7801 E375 1980",
  bibdate =      "Fri Dec 08 13:02:59 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  xxISBN =       "(none)",
}

@Proceedings{IEEE:1980:IIS,
  key =          "IEEE ISSCC '80",
  booktitle =    "{1980 IEEE International Solid-State Circuits
                 Conference Digest of Technical Papers, Philadelphia,
                 PA, USA, 13--15 February 1980}",
  title =        "{1980 IEEE International Solid-State Circuits
                 Conference Digest of Technical Papers, Philadelphia,
                 PA, USA, 13--15 February 1980}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "285",
  year =         "1980",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Fri Sep 16 10:55:14 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE Catalog Number 80CH1490-2-SSC.",
  acknowledgement = ack-nj,
}

@Proceedings{IEEE:1980:PMA,
  key =          "IEEE MICRO '80",
  booktitle =    "Proceedings: Microprocessor Applications in the 80's:
                 Arizona Technical Symposium, March 12--14, 1980,
                 Arizona State University, Tempe, Arizona",
  title =        "Proceedings: Microprocessor Applications in the 80's:
                 Arizona Technical Symposium, March 12--14, 1980,
                 Arizona State University, Tempe, Arizona",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "105",
  year =         "1980",
  LCCN =         "QA76.5 .P74",
  bibdate =      "Thu Sep 15 18:50:53 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  xxISBN =       "(none)",
}

@Proceedings{Johnson:1980:MPA,
  editor =       "Gearold R. Johnson and Bruce E. Kittinger",
  booktitle =    "{MICRO 13: Proceedings of the 13th annual workshop on
                 Microprogramming 1980, Broadmoor Hotel, Colorado
                 Springs, United States, November 30--December 03,
                 1980}",
  title =        "{MICRO 13: Proceedings of the 13th annual workshop on
                 Microprogramming 1980, Broadmoor Hotel, Colorado
                 Springs, United States, November 30--December 03,
                 1980}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiii + 192",
  year =         "1980",
  bibdate =      "Thu Aug 07 18:23:40 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Published in SIGMICRO newsletter, 11(3--4)
                 (Sept.--Dec. 1980). ACM Order no. 520800. IEEE Catalog
                 no. 80CH1599-0.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Lavington:1980:IPP,
  editor =       "Simon Hugh Lavington",
  booktitle =    "Information Processing 80: Proceedings of {IFIP}
                 Congress 80, Tokyo, Japan, October 6--9, 1980,
                 Melbourne, Australia, October 14--17, 1980",
  title =        "Information Processing 80: Proceedings of {IFIP}
                 Congress 80, Tokyo, Japan, October 6--9, 1980,
                 Melbourne, Australia, October 14--17, 1980",
  publisher =    pub-ENH,
  address =      pub-ENH:adr,
  pages =        "xiii + 1070",
  year =         "1980",
  ISBN =         "0-444-86034-7",
  ISBN-13 =      "978-0-444-86034-7",
  LCCN =         "QA 75.5 I57 1980",
  bibdate =      "Thu Sep 01 23:09:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Nickel:1980:IMP,
  editor =       "Karl L. E. Nickel",
  booktitle =    "{Interval mathematics 1980: proceedings of an
                 International Symposium on Interval Mathematics, held
                 at the Institut f{\"u}r Angewandte Mathematik,
                 Universit{\"a}t Freiburg i. Br., Germany, May 27--31,
                 1980}",
  title =        "{Interval mathematics 1980: proceedings of an
                 International Symposium on Interval Mathematics, held
                 at the Institut f{\"u}r Angewandte Mathematik,
                 Universit{\"a}t Freiburg i. Br., Germany, May 27--31,
                 1980}",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xv + 554",
  year =         "1980",
  ISBN =         "0-12-518850-1",
  ISBN-13 =      "978-0-12-518850-0",
  LCCN =         "QA297.75 .I57 1980",
  bibdate =      "Fri Dec 08 08:24:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{GAMM:1981:PAM,
  key =          "GAMM'81",
  booktitle =    "{Proceedings of the Annual Meeting of the Gesellschaft
                 f{\"u}r Angewandte Mathematik und Mechanik,
                 W{\"u}rzburg}",
  title =        "{Proceedings of the Annual Meeting of the Gesellschaft
                 f{\"u}r Angewandte Mathematik und Mechanik,
                 W{\"u}rzburg}",
  publisher =    "Gesellschaft f{\"u}r Angewandte Mathematik und
                 Mechanik",
  address =      "W{\"u}rzburg, Germany",
  pages =        "????",
  year =         "1981",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Fri Dec 08 08:56:45 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Part II (W{\"u}rzburg, 1981)",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:1981:PSC,
  key =          "IEEE CA5 '81",
  booktitle =    "Proceedings: 5th Symposium on Computer Arithmetic, May
                 18--19, 1981, University of Michigan, Ann Arbor,
                 Michigan",
  title =        "Proceedings: 5th Symposium on Computer Arithmetic: May
                 18--19, 1981, University of Michigan, Ann Arbor,
                 Michigan",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "vii + 278",
  year =         "1981",
  LCCN =         "QA 76.6 S985t 1981",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog number 81CH1630-C.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-5; Computer arithmetic and logic units ---
                 Congresses.; Electronic digital computers ---
                 Programming --- Congresses.; Floating-point arithmetic
                 Congresses.",
  xxISBN =       "(none)",
}

@Proceedings{Seck:1981:WWS,
  editor =       "Friedrich Seck",
  booktitle =    "{Wissenschaftsgeschichte um Wilhelm Schickard:
                 Vortr{\"a}ge bei dem Symposion der Universit{\"a}t
                 T{\"u}bingen im 500. Jahr ihres Bestehens am 24.und 25.
                 Juni 1977}. ({German}) [{History of Science and William
                 Schickard Presentations at the Symposium of the
                 University of T{\"u}bingen in 500 Years of existence on
                 24th and 25th June 1977}]",
  title =        "{Wissenschaftsgeschichte um Wilhelm Schickard:
                 Vortr{\"a}ge bei dem Symposion der Universit{\"a}t
                 T{\"u}bingen im 500. Jahr ihres Bestehens am 24.und 25.
                 Juni 1977}. ({German}) [{History of Science and William
                 Schickard Presentations at the Symposium of the
                 University of T{\"u}bingen in 500 Years of existence on
                 24th and 25th June 1977}]",
  volume =       "26",
  publisher =    "J. C. B. Mohr",
  address =      "T{\"u}bingen, West Germany",
  pages =        "240",
  year =         "1981",
  ISBN =         "3-16-444151-7",
  ISBN-13 =      "978-3-515-08004-0",
  LCCN =         "QB29",
  bibdate =      "Sat Jul 27 11:16:04 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/scicontext.bib;
                 z3950.gbv.de:20011/gvk",
  series =       "Contubernium",
  acknowledgement = ack-nhfb,
  language =     "German",
  subject =      "Schickard, Wilhelm",
  subject-dates = "1592--1635",
  tableofcontents = "Richard A. Jarrell / Astronomy at the University of
                 T{\"u}bingen: The Work of Michael M{\"a}stlin / 9 \\
                 Matthias Schramm / Ans{\"a}tze zu einer darstellenden
                 Geometrie bei Schickard / 21 \\
                 Menso Folkerts / Sp{\"a}tmittelalterliche
                 Multiplikationsmethoden, Nepers Rhabdologie und
                 Schickards Rechenmaschine / 51 \\
                 Ludolf von Mackensen / Wilhelm Schickards technische
                 Entw{\"u}rfe und die Erfindung seines Handplanetariums
                 / 67 \\
                 Manfred B{\"u}ttner / Johannes St{\"o}ffler und die
                 Beziehungen zwischen Geographie und Theologie im 16.
                 Jahrhundert / 81 \\
                 J{\"u}rgen H{\"u}bner / Johannes Kepler als Geograph im
                 Kontext des theologischen Denkens seiner Zeit /99 \\
                 Volker Bialas / Entwicklung und erste Anwendungen des
                 Triangulationsverfahrens in der Geod{\"a}sie des
                 fr{\"u}hen 17. Jahrhunderts / 115 \\
                 Martin Brecht / Kritik und Reform der Wissenschaften
                 bei Johann Valentin Andreae / 129 \\
                 Berthold Sutter / Wissenschaft und geistige
                 Str{\"o}mungen zwischen dem Augsburger Religionsfrieden
                 und dem Drei{\ss}igj{\"a}hrigen Krieg / 153",
}

@Proceedings{Messina:1982:PMM,
  editor =       "P. C. Messina and A. Murli",
  booktitle =    "{Problems and Methodologies in Mathematical Software
                 Production: International Seminar held at Sorrento,
                 Italy, November 3--8, 1980}",
  title =        "{Problems and Methodologies in Mathematical Software
                 Production: International Seminar held at Sorrento,
                 Italy, November 3--8, 1980}",
  volume =       "142",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "271",
  year =         "1982",
  ISBN =         "0-387-11603-6 (New York), 3-540-11603-6 (Berlin)",
  ISBN-13 =      "978-0-387-11603-7 (New York), 978-3-540-11603-5
                 (Berlin)",
  LCCN =         "QA76.95 .P76 1982",
  bibdate =      "Sat Sep 24 00:30:07 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Lecture Notes in Computer Science",
  acknowledgement = ack-nhfb,
}

@Book{Randell:1982:ODC,
  editor =       "Brian Randell",
  booktitle =    "The Origins of Digital Computers: Selected Papers",
  title =        "The Origins of Digital Computers: Selected Papers",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Third",
  pages =        "xvi + 580",
  year =         "1982",
  DOI =          "https://doi.org/10.1007/978-3-642-61812-3",
  ISBN =         "0-387-11319-3, 3-540-11319-3",
  ISBN-13 =      "978-0-387-11319-7, 978-3-540-11319-5",
  LCCN =         "TK7885.A5 O741 1982",
  bibdate =      "Sun Nov 03 08:28:47 2002",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/babbage-charles.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wilkes-maurice-v.bib;
                 https://www.math.utah.edu/pub/tex/bib/annhistcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/cryptography.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  series =       "Texts and monographs in computer science",
  acknowledgement = ack-nhfb,
  remark =       "See also other editions
                 \cite{Randell:1973:ODC,Randell:1975:ODC}.",
  tableofcontents = "Chapter I: Introduction / 1 \par

                 Chapter II: Analytical Engines / 9 \\
                 2.1. On the Mathematical Powers of the Calculating
                 Engine / C. Babbage (1837) / 19 \\
                 2.2. Report of the Committee \ldots{} appointed to
                 consider the advisability and to estimate the expense
                 of constructing Mr. Babbage's Analytical Machine, and
                 of printing tables by its means / C. W. Merrifield
                 (1879) / 55 \\
                 2.3. Babbage's Analytical Engine / H. P. Babbage (1910)
                 / 67 \\
                 2.4. On a Proposed Analytical Machine / P. E. Ludgate
                 (1909) / 73 \\
                 2.5. Essays on Automatics -- Its Definition --
                 Theoretical Extent of its Applications / L. Torres Y
                 Quevedo 1914 / 89 \\
                 2.6. Electromechanical Calculating Machine / L. Torres
                 y Quevedo (1920) / 109 \\
                 2.7. Scheme of Assembly of a Machine Suitable for the
                 Calculations of Celestial Mechanics / L. Couffignal
                 (1938) / 121 \par

                 Chapter III: Tabulating Machines / 127 \\
                 3.1. An Electric Tabulating System / H. Hollerith
                 (1889) / 133 \\
                 3.2. Calculating Machines: Their Principles and
                 Evolution / L. Couffignal (1933) / 145 \\
                 3.3. The Automatic Calculator IPM / H.-J. Dreyer and A.
                 Walther (1946) / 155 \par

                 Chapter IV: Zuse and Schreyer / 159 \\
                 4.1. Method for Automatic Execution of Calculations
                 with the aid of Computers / K. Zuse 1936 / 163 \\
                 4.2. Technical Computing Machines / H. Schreyer (1939)
                 / 171 \\
                 4.3. The Outline of a Computer Development from
                 Mechanics to Electronics / K. Zuse 1962 / 175
                 \par

                 Chapter V: Aiken and IBM / 191 \\
                 5.1. Proposed Automatic Calculating Machine / H. H.
                 Aiken (1937) / 195 \\
                 5.2. The Automatic Sequence Controlled Calculator / H.
                 H. Aiken and G. M. Hopper (1946) / 203 \\
                 5.3. Electrons and Computation / W. J. Eckert (1948) /
                 223 \\
                 5.4. The IBM Card-Programmed Electronic Calculator / J.
                 W. Sheldon and L. Tatum (1951) / 233 \par

                 Chapter VI: Bell Telephone Laboratories / 241 \\
                 6.1. Computer / G. R. Stibitz (1940) / 247 \\
                 6.2. The Relay Interpolator / O. Cesareo (1946) / 253
                 \\
                 6.3. The Ballistic Computer / J. Juley (1947) / 257 \\
                 6.4. A Bell Telephone Laboratories' Computing Machine /
                 F. L. Alt (1948) / 263 \par

                 Chapter VII: The Advent of Electronic Computers / 293
                 \\
                 7.1. Binary Calculation / E. W. Phillips (1936) / 303
                 \\
                 7.2. Computing Machine for the Solution of Large
                 Systems of Linear Algebraic Equations / J. V. Atanasoff
                 (1940) / 315 \\
                 7.3. Arithmetical Machine / V. Bush (1940) / 337 \\
                 7.4. Report on Electronic Predictors for Anti-Aircraft
                 Fire Control / J. A. Rajchman et al. (1942) / 345 \\
                 7.5. Colossus: Godfather of the Computer / B. Randell
                 (1977) / 349 \\
                 7.6. The Use of High Speed Vacuum Tube Devices for
                 Calculating / J. W. Mauchly (1942) / 355 \\
                 7.7. The Electronic Numerical Integrator and Computer.
                 (ENIAC) / H. H. Goldstine and A. Goldstine (1946) / 359
                 \par

                 Chapter VIII: Stored Program Electronic Computers / 375
                 \\
                 8.1. First Draft of a Report on the EDVAC / J. von
                 Neumann (1945) / 383 \\
                 8.2. Preparation of Problems for EDVAC-type Machines /
                 J. W. Mauchly (1947) / 393 \\
                 8.3. Preliminary Discussion of the Logical Design of an
                 Electronic Computing Instrument / A. W. Burks et al.
                 (1946) / 399 \\
                 8.4. Electronic Digital Computers / F. C. Williams and
                 T. Kilburn (1948) / 415 \\
                 8.5. The EDSAC / M. V. Wilkes and W. Renwick (1949) /
                 417 \\
                 8.6. The EDSAC Demonstration / B. H. Worsley (1949) /
                 423 \par

                 Bibliography / 431 \\
                 Index to Bibliography / 545 \\
                 Subject Index / 563",
}

@Proceedings{Reid:1982:RBN,
  editor =       "John K. Reid",
  booktitle =    "{The Relationship Between Numerical Computation and
                 Programming Languages: Proceedings of the IFIP TC2
                 Working Conference on the Relationship between
                 Numerical Computation and Programming Languages,
                 Boulder, Colorado, USA., 3--7 August, 1981}",
  title =        "{The Relationship Between Numerical Computation and
                 Programming Languages: Proceedings of the IFIP TC2
                 Working Conference on the Relationship between
                 Numerical Computation and Programming Languages,
                 Boulder, Colorado, USA., 3--7 August, 1981}",
  publisher =    pub-ENH,
  address =      pub-ENH:adr,
  pages =        "x + 377",
  year =         "1982",
  ISBN =         "0-444-86377-X",
  ISBN-13 =      "978-0-444-86377-5",
  LCCN =         "QA297 .I34 1981",
  bibdate =      "Tue Sep 06 22:34:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022)",
  tableofcontents = "PREFACE v\\
                 LIST OF CONTENTS vii\\
                 SESSION 1: INTRODUCTION. Chair: C. L. Lawson.
                 Discussant: B. Ford 1\\
                 Programming Languages: Power, Trends and Facilities for
                 Numerical Computation. J. R. Rice 3\\
                 Programming Languages for Numerical Subroutine
                 Libraries. J. J. Du Croz 17\\
                 Experience with the Olympus System. K. V. Roberts 33\\
                 SESSION 2: ARITHMETIC. 49 Chair: H. J. Stetter,
                 Discussant: R. P. Brent\\
                 Floating-point Parameters, Models and Standards. W. J.
                 Cody 51\\
                 The Use of Controlled Precision. T. E. Hull 71\\
                 A Synopsis of Interval Arithmetic for the Designer of
                 Programming Languages. C. Reinsch 85\\
                 SESSION 3: ARITHMETIC AND SYMBOLIC MATHEMATICS 101
                 Chair: W. Cowell, Discussant: W. S. Brown\\
                 The Near Orthogonality of Syntax, Semantics and
                 Diagnostics in Numerical Programming Environments. W.
                 Kahan and J. T. Coonen 103\\
                 Symbolic Manipulation Languages and Numerical
                 Computation: Trends. R. J. Fateman 117\\
                 Programming Languages for Symbolic Algebra and
                 Numerical Analysis. W. M. Gentleman 131\\
                 SESSION 4: DATA STRUCTURES. 143 Chair: M. Paul,
                 Discussant: P. Kemp\\
                 Data Structures for Numerical Quadrature. L. M. Delves
                 145\\
                 Data Structures for Sparse Matrices. J. K. Reid 153\\
                 Array Processing Features in the Next Fortran. B. T.
                 Smith 163\\
                 Examples of Array Processing in the Next Fortran. A.
                 Wilson 179\\
                 SESSION 5: PARALLELISM; LANGUAGE EVOLUTION. 185 Chair:
                 J. A. Nelder, Discussant: G. Paul\\
                 Exception Handling in Array Languages. T. W. Lake
                 187\\
                 A Framework for Language Evolution. J. L. Wagener
                 197\\
                 Languages and High-performance Computations. D. Kuck,
                 D. Padua, A. Sameh and M. Wolfe 205\\
                 SESSION 6: PROGRAM STRUCTURE. 223 Chair: J. C. Adams,
                 Discussant: E. L. Battiste\\
                 Numerical Packages in Ada. S. J. Hammarling and B. A.
                 wichmann 225\\
                 Tasking Features in Programming Languages. O. Roubine
                 245\\
                 Language Support for Floating Point. S. Feldman 263\\
                 OVERALL SESSION DISCUSSION. 275\\
                 SESSION 7: OPEN SESSION. 277 Chair: B. Einarsson,
                 Discussant: F. N. Fritsch\\
                 A Combined Lexical, Syntactic, and Semantic Approach
                 for Improving Notation. M. B. Wells 279\\
                 Program Transformation and Language Design. J. M. Boyle
                 285\\
                 Programming Parallel Numerical Algorithms in Ada. E. K.
                 Blum 297\\
                 Programming in Algol 68 (as a host) and the usage of
                 Fortran (program libraries). C. G. van der Laan 305\\
                 The Fortran of the Future. 317 F. N. Fritsch (ed.) -
                 Exception handling in Fortran (J. A. M. Snoek) 317 -
                 Conformity - towards a less permissive standard for
                 Fortran (D. T. Muxworthy) 318 - An alternative approach
                 to the evolution of Fortran (W. S. Brown, S. 1.
                 Feldman, N. L. Schryer, L. D. Fosdick) 320 - Notes on
                 Fortran evolution (E. L. Battiste) 322 - Discussion
                 324\\
                 SESSION 8: SOURCE TO SOURCE TRANSFORMATIONS AND
                 LANGUAGE COMPLEXITY. 329 Chair: J. M. Boyle,
                 Discussant: Th. J. Dekker\\
                 Specification Languages and Program Transformation. P.
                 Pepper 331\\
                 Tools for Numerical Programming. W. Miller 347\\
                 Languageless Programming. A. van Wijngaarden 361\\
                 LIST OF PARTICIPANTS. 373",
}

@Book{Rodrigue:1982:AC,
  editor =       "Garry Rodrigue",
  booktitle =    "Parallel Computations",
  title =        "Parallel Computations",
  volume =       "1",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xii + 408",
  year =         "1982",
  ISBN =         "0-12-592101-2",
  ISBN-13 =      "978-0-12-592101-5",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 11:11:02 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Computational techniques",
  acknowledgement = ack-nhfb,
  tableofcontents = "Front Cover \\
                 Parallel Computations \\
                 Copyright Page \\
                 Table of Contents \\
                 List of Contributors \\
                 Preface \\
                 Chapter 1. A Guide to Parallel Computation and Some
                 Cray-1 Experiences \\
                 I. Introduction \\
                 II. Hardware \\
                 III. Theoretical Considerations \\
                 IV. Applications \\
                 Appendix A. A Register Assignment for Sparse-Banded
                 Matrix Multiply \\
                 Appendix B. Factor and Forward Substitution \\
                 Appendix C. Backward Substitution \\
                 Appendix D. Factorization Only \\
                 Acknowledgments \\
                 References \\
                 Chapter 2. Vectorizing the FFTs \\
                 I. Introduction \\
                 II. Preliminaries \\
                 III. The Complex FFT Algorithms \\
                 IV. Vectorizing Multiple Transforms \\
                 V. Transforming Real Sequences \\
                 VI. The Symmetric Transforms \\
                 VII. Software and Summary \\
                 References \\
                 Chapter 3. Solution of Single Tridiagonal Linear
                 Systems and Vectorization of the ICCG Algorithm on the
                 Cray-1 \\
                 I. A Vector Algorithm for Tridiagonal Linear Systems
                 \\
                 II. An Incomplete Cholesky Conjugate Gradient (ICCG)
                 Algorithm for the Cray-1 Computer \\
                 III. Cyclic Reduction on Future Machines \\
                 Acknowledgments \\
                 References \\
                 Chapter 4. An Implicit Numerical Solution of the
                 Two-Dimensional Diffusion Equation and Vectorization
                 Experiments \\
                 I. Introduction \\
                 II. Spatial Differencing \\
                 III. Matrix Formulation \\
                 IV. Properties of the Matrix A \\
                 V. Method of Lines \\
                 VI. The Generalized Conjugate Gradient Algorithm \\
                 VII. Computational Example \\
                 VIII. Comments and Conclusions \\
                 References \\
                 Chapter 5. Swimming Upstream: Calculating Table Lookups
                 and Piecewise Functions \\
                 I. Introduction to Table Lookup \\
                 II. Evaluating Algorithms on Vector Processors \\
                 III. Basic Processes on Vector Processors \\
                 IV. One-Dimensional Problems \\
                 V. Two-Dimensional Problems: Equations of State \\
                 References \\
                 Chapter 6. Trade-Offs in Designing Explicit
                 Hydrodynamical Schemes for Vector Computers \\
                 I. Introduction \\
                 II. Why Vectorization of Explicit Hydrodynamical
                 Schemes Should Be Easy \\
                 III. Why Vectorization of Explicit Hydrodynamical
                 Schemes Can Be Difficult \\
                 IV. Alternative Approaches and Their Costs on Vector
                 Computers \\
                 V. The Example of the Interaction of Two Blast Waves
                 \\
                 VI. Conclusions \\
                 References \\
                 Chapter 7. Vectorized Computation of Reactive Flow \\
                 I. Introduction and Statement of the Problem \\
                 II. Vectorization and Optimization \\
                 III. Techniques for Modeling Fast Time Scales \\
                 IV. Techniques for Modeling Short Space Scales \\
                 V. Techniques for Dealing with Physical and Geometric
                 Complexity \\
                 VI. Programming Guidelines and Summary of Parallelism
                 Principles \\
                 Acknowledgments \\
                 References \\
                 Chapter 8. A Fully Implicit, Factored Code for
                 Computing Three-Dimensional Flows on the ILLIAC IV \\
                 I. Introduction \\
                 II. Basic Equations \\
                 III. ILLIAC Architecture \\
                 IV. Data-Base Considerations \\
                 V. The ILLIAC Code ARC3 \\
                 VI. Results \\
                 VII. Concluding Remarks \\
                 References",
}

@Proceedings{Ruschitzka:1982:IWC,
  editor =       "Manfred Ruschitzka and M. Christensen and W. F. Ames
                 and R. Vichnevetsky",
  key =          "IMACS '82",
  booktitle =    "{IMACS} World Congress on Systems Simulation and
                 Scientific Computation (10th: 1982: Montreal, Quebec).
                 Parallel and large-scale computers: performance,
                 architecture, applications",
  title =        "{IMACS} World Congress on Systems Simulation and
                 Scientific Computation (10th: 1982: Montreal, Quebec).
                 Parallel and large-scale computers: performance,
                 architecture, applications",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "xii + 329",
  year =         "1982",
  ISBN =         "0-444-86608-6 (hardcover)",
  ISBN-13 =      "978-0-444-86608-0 (hardcover)",
  LCCN =         "QA76.5 .I414 1982",
  bibdate =      "Wed Sep 07 22:56:44 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  subject =      "Electronic digital computers; Congresses; Parallel
                 computers; Parallel processing (Electronic computers);
                 Ordinateurs; Congr{\`e}s; Parall{\'e}lisme
                 (Informatique); Ordinateurs parall{\`e}les; Parallel
                 processing (Electronic computers); Electronic digital
                 computers; Parallel computers",
}

@Proceedings{Southcon:1982:SCR,
  key =          "Southcon '82",
  booktitle =    "Southcon\slash 82 Conference Record: Sessions
                 Presented at Southcon\slash 82, Orlando, Florida, March
                 23--25, 1982",
  title =        "Southcon\slash 82 Conference Record: Sessions
                 Presented at Southcon\slash 82, Orlando, Florida, March
                 23--25, 1982",
  publisher =    "Electronic Conventions, Inc.",
  address =      "El Segundo, CA, USA",
  pages =        "various",
  year =         "1982",
  LCCN =         "TK 7801 S68 1982",
  bibdate =      "Fri Dec 08 13:03:00 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  xxISBN =       "(none)",
}

@Proceedings{Watson:1982:NAP,
  editor =       "George Alistair Watson",
  booktitle =    "{Numerical Analysis: Proceedings of the 9th Biennial
                 Conference, held at Dundee, Scotland, June 23--26,
                 1981}",
  title =        "{Numerical Analysis: Proceedings of the 9th Biennial
                 Conference, held at Dundee, Scotland, June 23--26,
                 1981}",
  volume =       "912",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "xi + 245",
  pages =        "xi + 245",
  year =         "1982",
  CODEN =        "LNMAA2",
  DOI =          "https://doi.org/10.1007/BFb0093144",
  ISBN =         "0-387-11199-9 (softcover), 3-540-11199-9 (softcover),
                 3-540-39009-X (e-book)",
  ISBN-13 =      "978-0-387-11199-5 (softcover), 978-3-540-11199-3
                 (softcover), 978-3-540-39009-1 (e-book)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  ISSN-L =       "0075-8434",
  LCCN =         "QA3 .L28 no. 912; QA1 .L471; QA297 .D915n 1981",
  bibdate =      "Sat Oct 29 15:16:39 1994",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/m/more-jorge.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/p/powell-m-j-d.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lnm1980.bib;
                 library.ox.ac.uk:210/ADVANCE;
                 melvyl.cdlib.org:210/CDL90",
  series =       ser-LECT-NOTES-MATH,
  URL =          "http://www.springerlink.com/content/978-3-540-39009-1",
  acknowledgement = ack-nhfb,
  subject =      "Analisi numerica; Congressi; 1981; Dundee; Numerical
                 analysis; Congresses",
  tableofcontents = "P. H. Calamai and A. R. Conn / A second-order
                 method for solving the continuous multifacility
                 location problem / 1--25 \\
                 M. P. Cullinan and M. J. D. Powell / Data smoothing by
                 divided differences / 26--37 \\
                 G. Dahlquist / On the control of the global error in
                 stiff initial value problems / 38--49 \\
                 L. M. Delves / Chebyshev methods for integral and
                 differential equations / 50--63 \\
                 J. Douglas, Jr. / Simulation of miscible displacement
                 in porous media by a modified method of characteristic
                 procedure / 64--70 \\
                 I. S. Duff / Full matrix techniques in sparse Gaussian
                 elimination / 71--84 \\
                 R. Fletcher / Second order corrections for
                 non-differentiable optimization / 85--114 \\
                 C. W. Gear and K. A. Gallivan / Automatic methods for
                 highly oscillatory ordinary differential equations /
                 115--124 \\
                 G. H. Golub and M. L. Overton / Convergence of a
                 two-stage Richardson iterative procedure for solving
                 systems of linear equations / 125--139 \\
                 J. G. Hayes: Curved knot lines and surfaces with ruled
                 segments / 140--156 \\
                 P. J. van der Houwen / On the time integration of
                 parabolic differential equations / 157--168 \\
                 T. E. Hull / Precision control, exception handling and
                 a choice of numerical algorithms / 169--178 \\
                 P. Lancaster / Generalized Hermitian matrices: a new
                 frontier for numerical analysis? / 179--189 \\
                 R. J. Y. McLeod / Some applications of geometry in
                 numerical analysis / 190--229 \\
                 L. B. Wahlbin / A quasioptimal estimate in piecewise
                 polynomial Galerkin approximation of parabolic problems
                 / 230 --245 \\
                 Back matter / 249--251",
}

@Proceedings{Anonymous:1983:PSC,
  editor =       "Anonymous",
  booktitle =    "1983 proceedings of the statistical computing section:
                 papers presented at the annual meeting of the American
                 Statistical Association, Toronto, Canada, August
                 15--18, 1983",
  title =        "1983 proceedings of the statistical computing section:
                 papers presented at the annual meeting of the American
                 Statistical Association, Toronto, Canada, August
                 15--18, 1983",
  publisher =    "American Statistical Association",
  address =      "Washington, DC, USA",
  year =         "1983",
  ISBN =         "????",
  ISBN-13 =      "????",
  ISSN =         "0149-9963",
  LCCN =         "QA276.4 .A43a",
  bibdate =      "Sat Nov 29 11:12:49 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Gentle:1983:CSS,
  editor =       "James E. Gentle",
  booktitle =    "Computer Science and Statistics: Proceedings of the
                 Fifteenth Symposium on the Interface, Houston, Texas,
                 March 1983",
  title =        "Computer Science and Statistics: Proceedings of the
                 Fifteenth Symposium on the Interface, Houston, Texas,
                 March 1983",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "xi + 379",
  year =         "1983",
  ISBN =         "0-444-86688-4",
  ISBN-13 =      "978-0-444-86688-2",
  LCCN =         "QA276.4 .S95 1983",
  bibdate =      "Tue Sep 06 22:39:53 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:1983:IEE,
  key =          "IEEE '83",
  booktitle =    "1983 International Electrical, Electronics Conference:
                 Proceedings, September 26--28, Automotive Building,
                 Exhibition Place, Toronto, Canada",
  title =        "1983 International Electrical, Electronics Conference:
                 Proceedings, September 26--28, Automotive Building,
                 Exhibition Place, Toronto, Canada",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "various",
  year =         "1983",
  LCCN =         "TK 5 I6514 1983",
  bibdate =      "Fri Dec 08 13:03:01 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Two volumes.",
  acknowledgement = ack-nhfb,
  xxISBN =       "(none)",
}

@Proceedings{IEEE:1983:PII,
  key =          "IEEE CSO '83",
  booktitle =    "{IEEE} International Workshop on Computer Systems
                 Organization, March 29--31, 1983, Sheraton New Orleans
                 Hotel, New Orleans",
  title =        "{IEEE} International Workshop on Computer Systems
                 Organization, March 29--31, 1983, Sheraton New Orleans
                 Hotel, New Orleans",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "viii + 227",
  year =         "1983",
  ISBN =         "0-8186-0010-1",
  ISBN-13 =      "978-0-8186-0010-4",
  LCCN =         "QA 76.9 A73 I2 1983",
  bibdate =      "Wed Sep 07 23:43:15 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Proceedings{IEEE:1983:PSC,
  key =          "IEEE SCA6 '83",
  booktitle =    "Proceedings: 6th Symposium on Computer Arithmetic,
                 June 20--22, 1983, Aarhus University, {\AA}rhus,
                 Denmark",
  title =        "Proceedings: 6th Symposium on Computer Arithmetic,
                 June 20--22, 1983, Aarhus University, {\AA}rhus,
                 Denmark",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xi + 221",
  year =         "1983",
  ISBN =         "0-8186-4476-1 (paperback), 0-8186-8476-3 (hardcover),
                 0-8186-6476-2 (microfiche), 0-8186-0034-9 (hardcover)",
  ISBN-13 =      "978-0-8186-4476-4 (paperback), 978-0-8186-8476-0
                 (hardcover), 978-0-8186-6476-2 (microfiche),
                 978-0-8186-0034-0 (hardcover)",
  LCCN =         "QA 76.9 C62 S95 1983",
  bibdate =      "Fri Sep 02 00:35:28 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog number 83CH1892-9. IEEE Computer Society
                 order number 476.",
  URL =          "http://www.acsel-lab.com/arithmetic/arith6/papers/",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-6",
}

@Proceedings{Kulisch:1983:NAS,
  editor =       "Ulrich Kulisch and Willard L. Miranker and Gerd
                 Bohlender",
  booktitle =    "A New Approach to Scientific Computation: Proceedings
                 of the {Symposium on a New Approach to Scientific
                 Computation (1982: IBM Thomas J. Watson Research
                 Center)}",
  title =        "A New Approach to Scientific Computation: Proceedings
                 of the {Symposium on a New Approach to Scientific
                 Computation (1982: IBM Thomas J. Watson Research
                 Center)}",
  volume =       "7",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xv + 384",
  year =         "1983",
  ISBN =         "0-12-428660-7, 1-4832-7204-4",
  ISBN-13 =      "978-0-12-428660-3, 978-1-4832-7204-7",
  LCCN =         "QA297 .N49 1983; QA297 .S847 1982",
  bibdate =      "Mon Jan 08 10:57:28 1996",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Notes and Reports in Computer Science and Applied
                 Mathematics",
  acknowledgement = ack-nhfb,
  subject =      "Numerical analysis; Data processing; Algebra; Computer
                 arithmetic; Electronic books; Analyse num{\'e}rique;
                 Informatique; Alg{\'e}bre; Arithm{\'e}tique interne des
                 ordinateurs; Data processing; Computer arithmetic",
  tableofcontents = "Front Cover \\
                 A New Approach to Scientific Computation \\
                 Copyright Page \\
                 Dedication \\
                 Table of Contents \\
                 Contributors \\
                 Preface \\
                 Acknowledgments \\
                 1. A New Arithmetic For Scientific Computation \\
                 1. Introduction \\
                 2. The Spaces of Numerical Computations \\
                 3. Traditional Definition of Computer Arithmetic: The
                 Vertical Method \\
                 4. The New Definition of Computer Arithmetic: The
                 Horizontal Method \\
                 5. Computer Arithmetic and Programming Languages \\
                 6. Realization and Applications \\
                 References \\
                 2. Computer Demonstration Packages For Standard
                 Problems of Numerical Mathematics \\
                 Language Extension \\
                 Pascal-SC Computing Inclusions \\
                 Old and New \\
                 Precise Dot Product \\
                 Linear Systems \\
                 Inversion of a Matrix \\
                 Eigenproblems \\
                 Rounding Error and Cancellation \\
                 Evaluation of a Polynomial \\
                 Zero of a Polynomial \\
                 Polynomial Package \\
                 Arithmetic Expressions \\
                 Systems of Non-Linear Equations \\
                 Differential Equations \\
                 3. Solving Algebraic Problems With High Accuracy \\
                 Introduction \\
                 1. Computer Arithmetic \\
                 2. Linear Systems \\
                 3. Over- and Underdetermined Linear Systems \\
                 4. Linear Systems With Band Matrices \\
                 5. Sparse Linear Systems \\
                 6. Matrix Inversion \\
                 7. Non-Linear Systems \\
                 8. The Algebraic Eigenvalue Problem \\
                 9. Real and Complex Zeros of Polynomials \\
                 10. Linear, Quadratic and Convex Programming \\
                 11. Arithmetic Expressions \\
                 Conclusions \\
                 References \\
                 4. Evaluation of Arithmetic Expression Swith Maximum
                 Accuracy \\
                 Introduction \\
                 1. Evaluation of Polynomials \\
                 2. Evaluation of Arbitrary Arithmetic Expressions \\
                 3. Numerical Results \\
                 References \\
                 5. Solving Function Space Problems With Guaranteed
                 Close Bounds \\
                 1. Introduction \\
                 2. Mathematical Preliminaries \\
                 3. Practical Use of the Fixed Point Theorems \\
                 4. Functional Arithmetic and Roundings \\
                 5. Algorithmic Execution of Iterations \\
                 6. Applications to Differential and Integral Equations
                 \\
                 7. Some Examples \\
                 References \\
                 6. Ultra-Arithmetic: the Digital Computer Set In
                 Function Space \\
                 1. Introduction \\
                 2. A Review of Ultra-Arithmetic \\
                 3. Applications of Ultra-Arithmetic \\
                 4. The Arithmetic of Intervals of Polynomials \\
                 References \\
                 7. A Fortran Extension For Scientific Computation \\
                 1. Motivation \\
                 2. Notation of the Language Extension \\
                 3. Syntax and Semantics of the Extension \\
                 References \\
                 8. An Introduction to Matrix Pascal: A Pascal Extension
                 For Scientific Computation \\
                 a. Data Types \\
                 b. Expressions \\
                 C. Procedures, Functions, Operators \\
                 D. Universal Operator Concept \\
                 E. Expressions With Maximum Accuracy \\
                 F. Standard Functions \\
                 References \\
                 9. Realization of An Optimal Computer Arithmetic \\
                 1. Introduction \\
                 Mathematical Foundations \\
                 2. Organization of the Arithmetic \\
                 3. Implementation of the Elementary Operations \\
                 4. Operations In the Higher Spaces \\
                 5. Realization On a Micro Computer \\
                 References \\
                 10. Features of a Hardware Implementation of An Optimal
                 Arithmetic \\
                 1. Introduction \\
                 2. Implementation of Scalar Products",
}

@Proceedings{Mini-Micro:1983:MMN,
  key =          "Mini-Micro Northeast '83",
  booktitle =    "Mini\slash Micro Northeast\slash 83 Conference Record:
                 Sessions Presented at Mini\slash Micro Northeast-83,
                 New York, New York, April 18--20, 1983, in conjunction
                 with Electro\slash 83",
  title =        "Mini\slash Micro Northeast\slash 83 Conference Record:
                 Sessions Presented at Mini\slash Micro Northeast-83,
                 New York, New York, April 18--20, 1983, in conjunction
                 with Electro\slash 83",
  publisher =    "Electronic Conventions, Inc.",
  address =      "Los Angeles, CA, USA",
  pages =        "various",
  year =         "1983",
  LCCN =         "QA 76.5 M565 1983",
  bibdate =      "Fri Dec 08 13:03:05 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  xxISBN =       "(none)",
}

@Proceedings{Mini-Micro:1983:MMW,
  key =          "Mini-Micro West '83",
  booktitle =    "Mini\slash Micro West '83: Conference Record: Sessions
                 Presented at Mini\slash Micro West-83, San Francisco,
                 California, November 8--11, 1983",
  title =        "Mini\slash Micro West '83: Conference Record: Sessions
                 Presented at Mini\slash Micro West-83, San Francisco,
                 California, November 8--11, 1983",
  publisher =    "Electronic Conventions, Inc.",
  address =      "Los Angeles, CA, USA",
  pages =        "various",
  year =         "1983",
  LCCN =         "TK7885.A1 M56 1983",
  bibdate =      "Fri Dec 08 13:03:06 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  xxISBN =       "(none)",
}

@Proceedings{Ranocchia:1983:RFA,
  editor =       "Diane D. Ranocchia",
  booktitle =    "1983 Rochester {FORTH} Applications Conference, June
                 7--11, 1983",
  title =        "1983 Rochester {FORTH} Applications Conference, June
                 7--11, 1983",
  publisher =    "Institute for Applied FORTH Research",
  address =      "Rochester, NY, USA",
  pages =        "301",
  year =         "1983",
  ISBN =         "0-914593-00-5",
  ISBN-13 =      "978-0-914593-00-3",
  LCCN =         "QA76.73.F24 R59 1983",
  bibdate =      "Thu Sep 01 22:47:49 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Anonymous:1984:TFA,
  editor =       "Anonymous",
  booktitle =    "Transactions of the First Army Conference on Applied
                 Mathematics and Computing ({Washington, DC}, 1983)",
  title =        "Transactions of the First Army Conference on Applied
                 Mathematics and Computing ({Washington, DC}, 1983)",
  volume =       "84-1",
  publisher =    "ARO Rep. 84-1, U. S. Army Res. Office",
  address =      "Research Triangle Park, NC, USA",
  pages =        "xxii + 925",
  month =        feb,
  year =         "1984",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 11:40:45 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "ARO report",
  acknowledgement = ack-nhfb,
}

@Book{Cowell:1984:SDM,
  editor =       "Wayne R. Cowell",
  booktitle =    "Sources and Development of Mathematical Software",
  title =        "Sources and Development of Mathematical Software",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xii + 404",
  year =         "1984",
  ISBN =         "0-13-823501-5",
  ISBN-13 =      "978-0-13-823501-7",
  LCCN =         "QA76.95 .S68 1984",
  bibdate =      "Tue Dec 14 22:44:45 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Prentice-Hall Series in Computational Mathematics,
                 Cleve Moler, Advisor",
  acknowledgement = ack-nhfb,
}

@Book{Evanczuk:1984:MSS,
  editor =       "Stephen Evanczuk",
  booktitle =    "Microprocessor systems: software and hardware
                 architecture",
  title =        "Microprocessor systems: software and hardware
                 architecture",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  bookpages =    "vii + 389",
  year =         "1984",
  ISBN =         "0-07-019756-3, 0-07-606876-5 (paperback)",
  ISBN-13 =      "978-0-07-019756-5, 978-0-07-606876-0 (paperback)",
  LCCN =         "QA76.5 .M521955 1984",
  bibdate =      "Sat Nov 29 11:14:42 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Feilmeier:1984:PCP,
  editor =       "M. Feilmeier and G. Joubert and U. Schendel",
  booktitle =    "Parallel computing 83: proceedings of the
                 International Conference on Parallel Computing, held at
                 the Freie Universit{\"a}t Berlin, 26--28 September
                 1983",
  title =        "Parallel computing 83: proceedings of the
                 International Conference on Parallel Computing, held at
                 the Freie Universit{\"a}t Berlin, 26--28 September
                 1983",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "xiii + 566",
  year =         "1984",
  ISBN =         "0-444-87528-X",
  ISBN-13 =      "978-0-444-87528-0",
  LCCN =         "QA76.6.I547 1983",
  bibdate =      "Mon Apr 14 17:58:44 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Ford:1984:TML,
  editor =       "B. Ford and J. C. Rault and F. Thomasset",
  booktitle =    "Tools, methods and languages for scientific and
                 engineering computation. Proc. of international
                 conference (Paris, France, May 17--19, 1983)",
  title =        "Tools, methods and languages for scientific and
                 engineering computation. Proc. of international
                 conference (Paris, France, May 17--19, 1983)",
  publisher =    pub-ENH,
  address =      pub-ENH:adr,
  pages =        "xvi + 458",
  year =         "1984",
  ISBN =         "0-444-87570-0",
  ISBN-13 =      "978-0-444-87570-9",
  LCCN =         "Q183.9 .I53 1983",
  bibdate =      "Sat Nov 29 07:20:57 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{Golub:1984:SNA,
  editor =       "Gene H. Golub",
  booktitle =    "Studies in Numerical Analysis",
  title =        "Studies in Numerical Analysis",
  volume =       "24",
  publisher =    pub-MATH-ASSOC-AMER,
  address =      pub-MATH-ASSOC-AMER:adr,
  pages =        "x + 415",
  year =         "1984",
  ISBN =         "0-88385-126-1 (v. 1), 0-88385-100-8 (set)",
  ISBN-13 =      "978-0-88385-126-5 (v. 1), 978-0-88385-100-5 (set)",
  LCCN =         "QA297 .S83 1984",
  MRclass =      "65-06",
  MRnumber =     "88i:65007",
  bibdate =      "Sat Oct 22 17:16:36 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/m/more-jorge.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Studies in mathematics",
  acknowledgement = ack-nhfb,
  author-dates = "Gene Howard Golub (February 29, 1932--November 16,
                 2007)",
  keywords =     "numerical analysis",
  tableofcontents = "Gene H. Golub / Preface \\
                 James H. Wilkinson / The perfidious polynomial \\
                 Jorge J. Mor{\'e} and D. C. Sorensen / Newton's method
                 \\
                 Iain S. Duff / Research directions in sparse matrix
                 computations \\
                 Walter Gautschi / Questions of numerical conditions
                 related to polynomials \\
                 Paul Concus, Gene H. Golub, and Dianne P. O'Leary / A
                 generalized conjugate gradient method for the numerical
                 solution of elliptic partial differential equations \\
                 J. Barkley Rosser / Solving differential equations on a
                 hand held programmable calculator \\
                 V. Pereyra / Finite difference solution of boundary
                 value problems in ordinary differential equations \\
                 Dennis C. Jespersen / Multigrid methods for partial
                 differential equations \\
                 Paul N. Swarztrauber / Fast Poisson solvers \\
                 Peter Henrici / Poisson's equation in a hypercube:
                 discrete Fourier methods, eigenfunction expansions,
                 Pad{\'e} approximation to eigenvalues",
}

@Proceedings{Griffiths:1984:NAP,
  editor =       "D. F. Griffiths",
  booktitle =    "{Numerical analysis: Proceedings of the 10th Dundee
                 biennial conference held at the University of Dundee,
                 Scotland, June 28--July 1, 1983}",
  title =        "{Numerical analysis: Proceedings of the 10th Dundee
                 biennial conference held at the University of Dundee,
                 Scotland, June 28--July 1, 1983}",
  volume =       "1066",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "various",
  year =         "1984",
  CODEN =        "LNMAA2",
  DOI =          "https://doi.org/10.1007/BFb0099514",
  ISBN =         "3-540-13344-5 (print), 3-540-38881-8 (e-book)",
  ISBN-13 =      "978-3-540-13344-5 (print), 978-3-540-38881-4
                 (e-book)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  ISSN-L =       "0075-8434",
  LCCN =         "QA3.L28 no.1066, QA 297 D915n 1983",
  bibdate =      "Fri Dec 08 13:03:21 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Lecture notes in mathematics",
  URL =          "http://link.springer.com/chapter/10.1007/BFb0099525/",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/BFb0099514",
  book-URL =     "http://www.springerlink.com/content/978-3-540-38881-4",
  fjournal =     "Lecture Notes in Mathematics",
  journal-URL =  "http://link.springer.com/bookseries/304",
  tableofcontents = "Front Matter / / i--xi \\
                 Splines in interactive computer graphics / Richard H.
                 Bartels / 1--29 \\
                 Some methods for separating stiff components in initial
                 value problems / {\AA}. Bj{\"o}rck / 30--43 \\
                 Approximation order from smooth bivariate PP functions
                 / C. de Boor / 44--49 \\
                 The numerical solution of integral equations with
                 weakly singular kernels / Hermann Brunner / 50--71 \\
                 A trust-region approach to linearly constrained
                 optimization / David M. Gay / 72--105 \\
                 Multigrid methods for problems with a small parameter
                 in the highest derivative / P. W. Hemker / 106--121 \\
                 Nonconvex minimization calculations and the conjugate
                 gradient method / M. J. D. Powell / 122--141 \\
                 Particle approximation of linear hyperbolic equations
                 of the first order / P.-A. Raviart / 142--158 \\
                 Global error estimation for stiff ODEs / Lawrence F.
                 Shampine / 159--168 \\
                 Numerical techniques for nonlinear multi-parameter
                 problems / A. Spence, A. Jepson / 169--185 \\
                 Sequential defect correction for high-accuracy
                 floating-point algorithms / Hans J. Stetter / 186--202
                 \\
                 Numerical experiments with partially separable
                 optimization problems / A. Griewank, Ph. L. Toint /
                 203--220 \\
                 The numerical solution of total lp approximation
                 problems / G. A. Watson / 221--238 \\
                 An implicit diffusive numerical procedure for a
                 slightly compressible miscible displacement problem in
                 porous media / Thom C. Potempa, Mary Fanett Wheeler /
                 239--263 \\
                 Singularities in three-dimensional elliptic problems
                 and their treatment with finite element methods / J. R.
                 Whiteman / 264--275 Back Matter / / 277--278",
}

@Proceedings{IEEE:1984:CPI,
  key =          "IEEE Southeastcon '84",
  booktitle =    "Conference proceedings: {IEEE} Southeastcon '84, the
                 Galt House, Louisville, Kentucky, April 8--11, 1984",
  title =        "Conference proceedings: {IEEE} Southeastcon '84, the
                 Galt House, Louisville, Kentucky, April 8--11, 1984",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "562",
  year =         "1984",
  LCCN =         "TK 7801 I117 1984",
  bibdate =      "Thu Sep 15 18:50:54 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  xxISBN =       "(none)",
}

@Proceedings{IEEE:1984:ILD,
  editor =       "{IEEE}",
  key =          "IEEE COMPCON '84",
  booktitle =    "{Intellectual Leverage the Driving Technologies:
                 Digest of Papers, Compcon Spring 84, February 27--March
                 1, Twenty-eighth IEEE Computer Society International
                 Conference, Meridien Hotel, San Francisco,
                 California}",
  title =        "{Intellectual Leverage the Driving Technologies:
                 Digest of Papers, Compcon Spring 84, February 27--March
                 1, Twenty-eighth IEEE Computer Society International
                 Conference, Meridien Hotel, San Francisco,
                 California}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xxvi + 522",
  year =         "1984",
  CODEN =        "PCICDQ",
  ISBN =         "0-8186-0525-1 (paperback), 0-8186-8525-5 (hardcover)",
  ISBN-13 =      "978-0-8186-0525-3 (paperback), 978-0-8186-8525-5
                 (hardcover)",
  LCCN =         "QA75.5 .C58 1984, TK7885.A1 C53 1984",
  bibdate =      "Wed Sep 29 09:24:59 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/common-lisp.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog no. 84CH2017-2.",
  acknowledgement = ack-nhfb # "\slash " # ack-nj,
}

@Proceedings{Kirk:1984:CRE,
  editor =       "Donald E. Kirk",
  booktitle =    "Conference Record: Eighteenth Asilomar Conference on
                 Circuits, Systems and Computers: Papers Presented
                 November 5--7, 1984, Pacific Grove, California",
  title =        "Conference Record: Eighteenth Asilomar Conference on
                 Circuits, Systems and Computers: Papers Presented
                 November 5--7, 1984, Pacific Grove, California",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "x + 456",
  year =         "1984",
  ISBN =         "0-8186-0673-8 (paperback), 0-8186-8673-1 (hard),
                 0-8186-4673-X (microfiche)",
  ISBN-13 =      "978-0-8186-0673-1 (paperback), 978-0-8186-8673-3
                 (hard), 978-0-8186-4673-7 (microfiche)",
  LCCN =         "TK 7801 A83 1984",
  bibdate =      "Thu Sep 08 13:41:13 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Mini-Micro:1984:MMS,
  key =          "Mini-Micro Southwest '84",
  booktitle =    "Mini\slash Micro Southwest\slash 84 Conference Record:
                 Sessions Presented at Mini\slash Micro Southwest-84,
                 Dallas, Texas, September 11--13, 1984, in conjunction
                 with Midcon\slash 84",
  title =        "Mini\slash Micro Southwest\slash 84 Conference Record:
                 Sessions Presented at Mini\slash Micro Southwest-84,
                 Dallas, Texas, September 11--13, 1984, in conjunction
                 with Midcon\slash 84",
  publisher =    "Electronic Conventions Management",
  address =      "Los Angeles, CA, USA",
  pages =        "various",
  year =         "1984",
  LCCN =         "TK 7888.3 M566 1984",
  bibdate =      "Fri Dec 08 13:03:08 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  xxISBN =       "(none)",
}

@Proceedings{NCC:1984:ACP,
  key =          "AFIPS NCC '84",
  booktitle =    "{AFIPS} Conference Proceedings of the 1984 National
                 Computer Conference, Las Vegas, {NV}, {USA}, 9--12 July
                 1984",
  title =        "{AFIPS} Conference Proceedings of the 1984 National
                 Computer Conference, Las Vegas, {NV}, {USA}, 9--12 July
                 1984",
  publisher =    pub-AFIPS,
  address =      pub-AFIPS:adr,
  pages =        "xi + 734",
  year =         "1984",
  ISBN =         "0-88283-043-0",
  ISBN-13 =      "978-0-88283-043-8",
  LCCN =         "????",
  bibdate =      "Fri Sep 16 10:57:24 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Proceedings{Buchberger:1985:PEE,
  editor =       "Bruno Buchberger and Bob F. Caviness",
  booktitle =    "Proceedings: {EUROCAL} '85, European Conference on
                 Computer Algebra, Linz, Austria, April 1--3, 1985",
  title =        "Proceedings: {EUROCAL} '85, European Conference on
                 Computer Algebra, Linz, Austria, April 1--3, 1985",
  volume =       "203, 204",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "various",
  year =         "1985",
  CODEN =        "LNCSD9",
  ISBN =         "0-387-15983-5 (v. 1), 0-387-15984-3 (v. 2)",
  ISBN-13 =      "978-0-387-15983-6 (v. 1), 978-0-387-15984-3 (v. 2)",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  LCCN =         "QA155.7.E4 E85 1985",
  bibdate =      "Fri Apr 12 07:14:49 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Vol. 2 edited by: Bob F. Caviness. ``Jointly organized
                 by the ACM Special Interest Group on Symbolic and
                 Algebraic Manipulation (SIGSAM) and by the Symbolic and
                 Algebraic Manipulation Group in Europe (SAME)''--Vol.
                 2, pref. Contents: v. 1. Invited lectures --- v. 2.
                 Research contributions.",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
  keywords =     "algebra --- data processing --- congresses",
}

@Proceedings{Hwang:1985:PSC,
  editor =       "Kai Hwang",
  booktitle =    "Proceedings: 7th Symposium on Computer Arithmetic,
                 June 4--6, 1985, University of Illinois, Urbana,
                 Illinois",
  title =        "Proceedings: 7th Symposium on Computer Arithmetic,
                 June 4--6, 1985, University of Illinois, Urbana,
                 Illinois",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xi + 343",
  year =         "1985",
  ISBN =         "0-8186-0632-0 (paperback), 0-8186-8632-4 (hard),
                 0-8186-4632-2 (microfiche)",
  ISBN-13 =      "978-0-8186-0632-8 (paperback), 978-0-8186-8632-0
                 (hard), 978-0-8186-4632-4 (microfiche)",
  LCCN =         "QA76.9.C62 S95 1985",
  bibdate =      "Thu Sep 08 00:11:41 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog number 85CH2146-9. IEEE Computer Society
                 order number 632.",
  acknowledgement = ack-nj,
  keywords =     "ARITH-7",
}

@Proceedings{IEEE:1985:ERC,
  key =          "IEEE Region 5 '85",
  booktitle =    "1985 {IEEE} Region 5 Conference, March 13--15, 1985,
                 Holiday Inn Civic Center, Lubbock, Texas",
  title =        "1985 {IEEE} Region 5 Conference, March 13--15, 1985,
                 Holiday Inn Civic Center, Lubbock, Texas",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "vi + 71",
  year =         "1985",
  LCCN =         "TK 7801 N56 1985",
  bibdate =      "Thu Sep 15 18:50:54 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  xxISBN =       "(none)",
}

@Proceedings{Meek:1985:PFM,
  editor =       "D. S. Meek and G. H. J. {van Rees}",
  booktitle =    "{Proceedings of the Fourteenth Manitoba Conference on
                 Numerical Mathematics and Computing held at the
                 University of Manitoba, September 27--29, 1984}",
  title =        "{Proceedings of the Fourteenth Manitoba Conference on
                 Numerical Mathematics and Computing held at the
                 University of Manitoba, September 27--29, 1984}",
  volume =       "46",
  publisher =    "Utilitas Mathematica Publishers",
  address =      "Winnipeg, Manitoba, Canada",
  pages =        "358",
  year =         "1985",
  ISBN =         "0-919628-46-X",
  ISBN-13 =      "978-0-919628-46-5",
  LCCN =         "QA1 C75",
  bibdate =      "Fri Dec 08 08:33:52 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Congressus numerantium",
  acknowledgement = ack-nhfb,
}

@Proceedings{Miranker:1985:ASC,
  editor =       "Willard L. Miranker and Richard A. Toupin",
  booktitle =    "Accurate Scientific Computations: Symposium, Bad
                 Neuenahr, {FRG}, March 12--14, 1985: Proceedings",
  title =        "Accurate Scientific Computations: Symposium, Bad
                 Neuenahr, {FRG}, March 12--14, 1985: Proceedings",
  volume =       "235",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 205",
  year =         "1985",
  DOI =          "https://doi.org/10.1007/3-540-16798-6",
  ISBN =         "0-387-16798-6",
  ISBN-13 =      "978-0-387-16798-5",
  LCCN =         "QA76.95 .A231 1986",
  bibdate =      "Sat Sep 03 12:24:08 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
}

@Proceedings{USENIX:1985:SCP,
  editor =       "{USENIX Association}",
  booktitle =    "Summer conference proceedings, Portland 1985: June
                 11--14, 1985, Portland, Oregon {USA}",
  title =        "Summer conference proceedings, Portland 1985: June
                 11--14, 1985, Portland, Oregon {USA}",
  publisher =    pub-USENIX,
  address =      pub-USENIX-EL-CERRITO:adr,
  pages =        "viii + 612",
  year =         "1985",
  LCCN =         "QA76.8.U65 U8 1985",
  bibdate =      "Sun Feb 18 07:46:09 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "UNIX (Computer operating system) --- Congresses.",
  remark =       "Spine title: USENIX Conference proceedings.",
}

@Proceedings{Vrdoljak:1985:ICA,
  editor =       "B. Vrdoljak",
  booktitle =    "{IV} Conference on Applied Mathematics, University of
                 Split, May 28--30, 1984",
  title =        "{IV} Conference on Applied Mathematics, University of
                 Split, May 28--30, 1984",
  publisher =    "Faculty of Civil Engineering, University of Split",
  address =      "Split, Yugoslavia",
  pages =        "153",
  year =         "1985",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Fri Dec 08 08:54:11 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:1986:III,
  editor =       "{IEEE}",
  booktitle =    "{ICASSP '86: IEEE International Conference on
                 Acoustics, Speech, and Signal Processing, April 7--11,
                 1986, Keio Plaza Inter-Continental Hotel Tokyo,
                 Japan}",
  title =        "{ICASSP '86: IEEE International Conference on
                 Acoustics, Speech, and Signal Processing, April 7--11,
                 1986, Keio Plaza Inter-Continental Hotel Tokyo,
                 Japan}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "1986",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Fri Aug 08 09:31:51 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog number 86CH2243-4.",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=8362",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:1986:PII,
  key =          "IEEE ICCD '86",
  booktitle =    "Proceedings: {IEEE} International Conference on
                 Computer Design, {VLSI} in Computers: {ICCD} '86, Rye
                 Town Hilton, Port Chester, New York, October 6--9,
                 1986",
  title =        "Proceedings: {IEEE} International Conference on
                 Computer Design, {VLSI} in Computers: {ICCD} '86, Rye
                 Town Hilton, Port Chester, New York, October 6--9,
                 1986",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xvi + 607",
  year =         "1986",
  ISBN =         "0-8186-0735-1 (paperback), 0-8186-8735-5 (hard),
                 0-8186-4735-3 (microfiche)",
  ISBN-13 =      "978-0-8186-0735-6 (paperback), 978-0-8186-8735-8
                 (hard), 978-0-8186-4735-2 (microfiche)",
  LCCN =         "TK 7888.4 I23 1986",
  bibdate =      "Thu Sep 08 10:29:35 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Proceedings{Mini-Micro:1986:EMM,
  key =          "Mini-Micro Northeast '86",
  booktitle =    "Electro\slash 86 and Mini\slash Micro Northeast
                 Conference Record: Sessions Presented at Electro\slash
                 86 and Mini\slash Micro Northeast-86, Boston, {MA}, May
                 13--15, 1986",
  title =        "Electro\slash 86 and Mini\slash Micro Northeast
                 Conference Record: Sessions Presented at Electro\slash
                 86 and Mini\slash Micro Northeast-86, Boston, {MA}, May
                 13--15, 1986",
  publisher =    "Electronic Conventions Management",
  address =      "Los Angeles, CA, USA",
  pages =        "various",
  year =         "1986",
  LCCN =         "TK 7801 E375 1986",
  bibdate =      "Fri Dec 08 13:03:09 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  xxISBN =       "(none)",
}

@Proceedings{Unicom:1986:SQA,
  key =          "SQART'86",
  booktitle =    "Software Quality Assurance, Reliability, and Testing.
                 London, {UK, 9--10} December 1986",
  title =        "Software Quality Assurance, Reliability, and Testing.
                 London, {UK}, 9--10 December 1986",
  publisher =    "Unicom Seminars Ltd.",
  address =      "Uxbridge, Middlesex, UK",
  pages =        "xi + 149",
  year =         "1986",
  ISBN =         "0-291-39732-8",
  ISBN-13 =      "978-0-291-39732-4",
  LCCN =         "????",
  bibdate =      "Fri Dec 08 13:46:34 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "The Technical Press-Unicom applied information
                 technology reports",
  acknowledgement = ack-nhfb,
}

@Proceedings{Wescon:1986:WCR,
  key =          "WESCON '86",
  booktitle =    "Wescon\slash 86 Conference Record: Sessions Presented
                 at Wescon\slash 86, Anaheim, {CA}, November 18--20,
                 1986",
  title =        "Wescon\slash 86 Conference Record: Sessions Presented
                 at Wescon\slash 86, Anaheim, {CA}, November 18--20,
                 1986",
  publisher =    "Electronic Conventions Management",
  address =      "Los Angeles, CA, USA",
  pages =        "various",
  year =         "1986",
  LCCN =         "TK 7801 W47 1986",
  bibdate =      "Fri Dec 08 13:03:18 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  xxISBN =       "(none)",
}

@Book{Anbar:1987:CM,
  editor =       "Michael Anbar",
  booktitle =    "Computers in medicine",
  title =        "Computers in medicine",
  publisher =    "Computer Science Press, Inc.",
  address =      "Rockville, MD, USA",
  pages =        "314",
  year =         "1987",
  ISBN =         "0-88175-080-8",
  ISBN-13 =      "978-0-88175-080-5",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 11:19:13 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$32.95",
  series =       "Applications of computer science series",
  acknowledgement = ack-nhfb,
}

@Book{Aspray:1987:PJN,
  editor =       "William Aspray and Arthur Burks",
  booktitle =    "Papers of {John von Neumann} on Computing and Computer
                 Theory",
  title =        "Papers of {John von Neumann} on Computing and Computer
                 Theory",
  volume =       "12",
  publisher =    pub-MIT,
  address =      pub-MIT:adr,
  pages =        "xviii + 624",
  year =         "1987",
  ISBN =         "0-262-22030-X",
  ISBN-13 =      "978-0-262-22030-9",
  LCCN =         "QA76.5 .P31451 1987",
  bibdate =      "Mon Sep 16 16:40:48 2002",
  bibsource =    "ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/fparith.bib;
                 ftp://ftp.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Misc/compsurv.bib;
                 https://www.math.utah.edu/pub/tex/bib/compsurv.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Knuth:1970:VNF}.",
  series =       "Charles Babbage Institute reprint series for the
                 history of computing",
  acknowledgement = ack-nhfb,
  subject-dates = "John von Neumann (1903--1957)",
  tableofcontents = "Preface xi\\
                 Biographical Notes xiii \\
                 I. Computer Architecture and Logical Design \\
                 Introduction 3 \\
                 1. First Draft of a Report on the EDVAC 17 \\
                 2. Donald Knuth---Von Neumann's First Computer Program
                 83 \\
                 3. Preliminary Discussion of the Logical Design of an
                 Electronic Computing Instrument (with Arthur W. Burks
                 and Herman H. Goldstine) 97 \\
                 II. Computer Programming and Flow Diagrams Introduction
                 145 \\
                 Planning and Coding of Problems for an Electronic
                 Computing Instrument (with Herman H. Goldstine) \\
                 4. Planning and Coding of Problems, vol. 1 151 \\
                 5. Planning and Coding of Problems, vol. 2 223 \\
                 6. Planning and Coding of Problems, vol. 3 286 \\
                 III. Large-Scale High-Speed Computing \\
                 Introduction 309 \\
                 7. On the Principles of Large Scale Computing Machines
                 (with Herman H. Goldstine) 317 \\
                 8 The Future of High-Speed Computing 349 \\
                 9. The NORC and Problems in High Speed Computing 350
                 \\
                 IV. Theory of Natural and Artificial Automata \\
                 Introduction 363 \\
                 10. The General and Logical Theory of Automata 391 \\
                 11. Theory and Organization of Complicated Automata 432
                 \\
                 First Lecture: Computing Machines in General 434 \\
                 Second Lecture: Rigorous Theories of Control and
                 Information 445 \\
                 Third Lecture: Statistical Theories of Information 460
                 \\
                 Fourth Lecture: The Role of High and of Extremely High
                 Complication 467 \\
                 Fifth Lecture: Re-evaluation of the Problems of
                 Complicated Automata-Problems of Hierarchy and
                 Evolution 477 \\
                 12. Von Neumann's Self-Reproducing Automata, edited by
                 Arthur W. Burks 491 \\
                 13. Probabilistic Logics and the Synthesis of Reliable
                 Organisms from Unreliable Components 553 \\
                 Bibliography 603 \\
                 References 611",
}

@Proceedings{Davis:1987:PAC,
  editor =       "Pat Davis and Vicki McClintock",
  booktitle =    "{Proceedings of the 15th annual conference on Computer
                 Science, St. Louis, Missouri, USA}",
  title =        "{Proceedings of the 15th annual conference on Computer
                 Science, St. Louis, Missouri, USA}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "473",
  year =         "1987",
  ISBN =         "0-89791-218-7",
  ISBN-13 =      "978-0-89791-218-1",
  LCCN =         "????",
  bibdate =      "Sat Aug 22 09:09:51 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "ACM order number 404870.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Irwin:1987:PSC,
  editor =       "Mary Jane Irwin and Renato Stefanelli",
  booktitle =    "Proceedings: 8th Symposium on Computer Arithmetic, May
                 19--21, 1987, Villa Olmo, Como, Italy",
  title =        "Proceedings: 8th Symposium on Computer Arithmetic, May
                 19--21, 1987, Villa Olmo, Como, Italy",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "ix + 277",
  month =        may,
  year =         "1987",
  DOI =          "https://doi.org/10.1109/ARITH1451.1987",
  ISBN =         "0-8186-0774-2 (paperback), 0-8186-4774-4 (microfiche),
                 0-8186-8774-6 (case)",
  ISBN-13 =      "978-0-8186-0774-5 (paperback), 978-0-8186-4774-1
                 (microfiche), 978-0-8186-8774-7 (case)",
  LCCN =         "QA 76.9 C62 S95 1987",
  bibdate =      "Wed Sep 14 20:52:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-8",
}

@Proceedings{Iserles:1987:SAN,
  editor =       "A. Iserles and M. J. D. Powell",
  booktitle =    "The State of the Art in Numerical Analysis:
                 Proceedings of the Joint {IMA}\slash {SIAM} Conference
                 on the State of the Art in Numerical Analysis held at
                 the University of Birmingham, 14--18 April 1986",
  title =        "The State of the Art in Numerical Analysis:
                 Proceedings of the Joint {IMA}\slash {SIAM} Conference
                 on the State of the Art in Numerical Analysis held at
                 the University of Birmingham, 14--18 April 1986",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "xiv + 719",
  year =         "1987",
  ISBN =         "0-19-853614-3",
  ISBN-13 =      "978-0-19-853614-7",
  LCCN =         "QA297 .S781 1987",
  bibdate =      "Thu Sep 08 00:41:24 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "UK\pounds55.00, US\$77.50",
  acknowledgement = ack-nj,
}

@Book{Kaucher:1987:CAS,
  editor =       "Edgar Kaucher and Ulrich Kulisch and Christian
                 Ullrich",
  booktitle =    "Computer arithmetic: scientific computation and
                 programming languages",
  title =        "Computer arithmetic: scientific computation and
                 programming languages",
  publisher =    pub-TEUBNER,
  address =      pub-TEUBNER:adr,
  pages =        "456",
  year =         "1987",
  ISBN =         "3-519-02448-9",
  ISBN-13 =      "978-3-519-02448-4",
  LCCN =         "QA76.9.C62 C69 1987",
  bibdate =      "Mon Dec 18 09:51:44 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{Lin:1987:DSP,
  editor =       "Kun-Shan Lin",
  booktitle =    "Digital signal processing applications with the
                 {TMS320} family: Vol. 1",
  title =        "Digital signal processing applications with the
                 {TMS320} family: Vol. 1",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "724",
  year =         "1987",
  ISBN =         "0-13-212466-1",
  ISBN-13 =      "978-0-13-212466-9",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 11:16:25 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$30.67",
  series =       "Prentice-Hall and Texas Instruments digital signal
                 processing series",
  acknowledgement = ack-nhfb,
}

@Proceedings{Losleben:1987:ARV,
  editor =       "Paul Losleben",
  booktitle =    "Advanced research in {VLSI}: proceedings of the 1987
                 Stanford Conference",
  title =        "Advanced research in {VLSI}: proceedings of the 1987
                 Stanford Conference",
  publisher =    pub-MIT,
  address =      pub-MIT:adr,
  pages =        "415",
  month =        mar,
  year =         "1987",
  ISBN =         "0-262-12121-2",
  ISBN-13 =      "978-0-262-12121-7",
  LCCN =         "TK7888.4 .A4 1987",
  bibdate =      "Sat Nov 29 07:24:40 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Mason:1987:AAB,
  editor =       "J. C. Mason and M. G. Cox",
  booktitle =    "{Algorithms for approximation: based on the
                 proceedings of the IMA Conference on Algorithms for the
                 Approximation of Functions and Data, held at the Royal
                 Military College of Science, Shrivenham, July 1985}",
  title =        "{Algorithms for approximation: based on the
                 proceedings of the IMA Conference on Algorithms for the
                 Approximation of Functions and Data, held at the Royal
                 Military College of Science, Shrivenham, July 1985}",
  volume =       "10",
  publisher =    pub-CLARENDON,
  address =      pub-CLARENDON:adr,
  pages =        "xvi + 694 + 8",
  year =         "1987",
  ISBN =         "0-19-853612-7",
  ISBN-13 =      "978-0-19-853612-3",
  LCCN =         "QA221 .A5361 1987; QA221 .I47 1985",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/bibnet/authors/p/powell-m-j-d.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/r/ruhe-axel.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "US\$90",
  series =       "The Institute of Mathematics and Its Applications
                 conference series, new series",
  acknowledgement = ack-nhfb,
  bibno =        "39820",
  catcode =      "G.1.2; G.1.2",
  CRclass =      "G.1.2 Approximation; G.1.2 Approximation; G.1.2
                 Elementary function approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation",
  genterm =      "theory; algorithms",
  guideno =      "1987-16080",
  meetingname =  "IMA Conference on Algorithms for the Approximation of
                 Functions and Data (1985: Royal Military College of
                 Science, Shrivenham)",
  procdate =     "The Institute of mathematics and its applications
                 conference series; 10 July 1985",
  procloc =      "Shrivenham, UK",
  sub =          "Proceedings of the IMA Conference on Algorithms for
                 the approximation of functions",
  subject =      "Approximation theory; Data processing; Congresses; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
  tableofcontents = "Preface / v \\
                 Contributors / xiii \\
                 \\
                 I Development of Algorithms \\
                 \\
                 1. Spline Approximation and Smoothing \\
                 \\
                 G. T. Anthony and M. G. Cox / The fitting of extremely
                 large data sets by bivariate splines / 5 \\
                 W. Dahmen / Subdivision algorithms --- recent results,
                 some extensions and further developments / 21 \\
                 P. Dierckx / Fast algorithms for smoothing data over a
                 disc or a sphere using tensor product splines / 51 \\
                 T. Lyche and K. M{\o}rken / A discrete approach to knot
                 removal and degree reduction algorithms for splines /
                 67 \\
                 R. H. J. Gmelig Meyling / On algorithms and
                 applications for bivariate B-splines / 83 \\
                 \\
                 2. Spline Interpolation and Shape Preservation \\
                 \\
                 R. E. Carlson / Shape preserving interpolation / 97 \\
                 M. G. Cox and H. M. Jones / Shape preserving spline
                 approximation in the $\ell_1$-norm / 115 \\
                 J. A. Gregory / A review of curve interpolation with
                 shape control / 131 \\
                 \\
                 3. Multivariate Interpolation \\
                 \\
                 M. J. D. Powell / Radial basis functions for
                 multivariable interpolation: a review / 143 \\
                 R. A. Lorentz / On the determinant of a bivariate
                 Birkhoff interpolation problem / 169 \\
                 A. Le Mehaute / Interpolation with piecewise
                 polynomials in more than one variable / 181 \\
                 \\
                 4. Least Square Methods \\
                 \\
                 R. Farwig / Multivariate interpolation of scattered
                 data by moving least squares methods / 193 \\
                 F. Yoshimoto / Least squares approximation by one-pass
                 methods with piecewise polynomials / 213 \\
                 \\
                 5. Rational Approximation \\
                 \\
                 L. N. Trefethen and M. H. Gutknecht / Pad{\'e}, stable
                 Pad{\'e}, and Chebyshev--Pad{\'e} approximation / 227
                 \\
                 P. T. Breuer / A new method for real rational uniform
                 approximation / 265 \\
                 C. B. Dunham / Rationals with repeated poles / 285 \\
                 A. Iserles and S. P. N{\o}rsett / Error control of
                 rational approximation with a matrix argument / 293 \\
                 \\
                 6. Complex and Nonlinear Approximation \\
                 \\
                 K. Madsen / General algorithms for discrete non-linear
                 parameter estimation / 309 \\
                 G. Opfer / Complex rational approximation with
                 numerical experiments / 327 \\
                 G. A. Watson / Data fitting by positive sums of
                 exponentials / 337 \\
                 J. C. Mason and P. Owen / Some simple algorithms for
                 constrained complex and rational approximation / 357
                 \\
                 \\
                 7. Computer-Aided Design and Blending \\
                 \\
                 L. L. Schumaker / Numerical aspects of spaces of
                 piecewise polynomials on triangulations / 373 \\
                 M. V. Golitschek / The $H$-sets of the blending
                 functions / 407 \\
                 D. Levin / Multidimensional reconstruction by
                 set-valued approximations/ 421 \\
                 \\
                 II Applications \\
                 \\
                 8. Applications in Numerical Analysis \\
                 \\
                 H. P. Blatt, A, Iserles and E. B. Saff / Remarks on the
                 behaviour of zeros of best approximating polynomials
                 and rational functions / 437 \\
                 J. Gilbert and W. A. Light / Multigrid methods and the
                 alternating algorithm / 447 \\
                 K. Jetter and J. St{\"o}ckler / On the computation of
                 Gauss--Birkhoff quadrature formulas / 459 \\
                 E. Schock / Error bounds for the solution of integral
                 equations by Galerkin-like methods / 471 \\
                 N. M. Temme / On the computation of the incomplete
                 gamma functions for large values of the parameters /
                 479 \\
                 \\
                 9. Applications in Partial Differential Equations \\
                 \\
                 J. R. Rice / Adaptive tensor product grids for singular
                 problems / 493 \\
                 W. Freeden / Harmonic splines for solving boundary
                 value problems of potential theory / 507 \\
                 D. C. Hanscomb / Recovery of fluid flow fields / 531
                 \\
                 L. Reichel / The selection of subspace and collocation
                 points in the boundary collocation method for some
                 plane elliptic boundary problems / 541 \\
                 \\
                 10. Applications in Other Disciplines \\
                 \\
                 L. Andersson, K. Holmstr{\"o}m and A. Ruhe / Complex
                 formation constants --- a problem from solution
                 chemistry / 557 \\
                 D. E. Roberts and P. R. Graves-Morris / The application
                 of generalised inverse rational interpolants in the
                 model analysis of vibrating structures I / 573 \\
                 A. Daman and J. C. Mason / A generalised
                 cross-validation method for meteorological data with
                 gaps / 595 \\
                 K. P. Jackson and J. C. Mason / The approximation by
                 complex functions of stresses in cracked domains / 611
                 \\
                 J. H. McDonnell / Equally spaced cubic splines for
                 representing time histories / 623 \\
                 B. L. Rahimi and S. W. Ellacott / Dynamic phase
                 analysis of heart anomalies / 641 \\
                 \\
                 III Software \\
                 \\
                 J. G. Hayes / NAG algorithms for the approximation of
                 functions and data / 653 \\
                 G. T. Anthony and M. G. Cox / The National Physical
                 Laboratory's Data Approximation Subroutine Library /
                 669 \\
                 \\
                 M. G. Cox (editor) / Panel Discussion / 689",
}

@Proceedings{Zunde:1987:EFI,
  editor =       "Pranas Zunde and Jagdish C. Agrawal",
  booktitle =    "Proceedings of the Fourth Symposium on Empirical
                 Foundations of Information and Software Science, held
                 October 22--24, 1986 in Atlanta, Georgia",
  title =        "Proceedings of the Fourth Symposium on Empirical
                 Foundations of Information and Software Science, held
                 October 22--24, 1986 in Atlanta, Georgia",
  publisher =    pub-PLENUM,
  address =      pub-PLENUM:adr,
  pages =        "x + 533",
  year =         "1987",
  ISBN =         "0-306-42817-2",
  ISBN-13 =      "978-0-306-42817-3",
  LCCN =         "QA75.5 .S956 1986",
  bibdate =      "Mon Sep 12 07:44:06 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{ACM:1988:ICS,
  editor =       "{ACM}",
  booktitle =    "1988 International Conference on Supercomputing, July
                 4--8, 1988, St. Malo, France",
  title =        "1988 International Conference on Supercomputing, July
                 4--8, 1988, St. Malo, France",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xiii + 679",
  year =         "1988",
  ISBN =         "0-89791-272-1",
  ISBN-13 =      "978-0-89791-272-3",
  LCCN =         "QA76.5 .I547 1988",
  bibdate =      "Sat Nov 29 07:52:15 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{ACM:1988:PAC,
  key =          "ACM LFP '88",
  booktitle =    "{Proceedings of the 1988 ACM Conference on LISP and
                 Functional Programming: Papers Presented at the
                 Conference, Snowbird, Utah, July 25--27, 1988}",
  title =        "{Proceedings of the 1988 ACM Conference on LISP and
                 Functional Programming: Papers Presented at the
                 Conference, Snowbird, Utah, July 25--27, 1988}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "viii + 351",
  year =         "1988",
  ISBN =         "0-89791-273-X",
  ISBN-13 =      "978-0-89791-273-0",
  LCCN =         "QA76.73.L23 A24 1988",
  bibdate =      "Thu Sep 01 23:12:58 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$27.00",
  acknowledgement = ack-nhfb,
}

@Proceedings{Brodersen:1988:VSP,
  editor =       "Robert W. Brodersen and Howard S. Moscovitz",
  booktitle =    "{VLSI} Signal Processing, {III}",
  title =        "{VLSI} Signal Processing, {III}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xi + 536",
  year =         "1988",
  ISBN =         "0-87942-248-3",
  ISBN-13 =      "978-0-87942-248-6",
  LCCN =         "TK5102.5 .V563 1988; TK5102.5 .V56 1988",
  bibdate =      "Fri Dec 8 10:50:52 MST 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  remark =       "The chapters in this book are based on presentations
                 given at the IEEE Acoustics, Speech, and Signal
                 Processing Society Workshop on VLSI Signal Processing
                 held November 2--4, 1988 at the Monterey Plaza Hotel,
                 Monterey, California. Published under the sponsorship
                 of the IEEE Acoustics, Speech, and Signal Processing
                 Society.",
  subject =      "Signal processing; Digital techniques; Congresses;
                 Integrated circuits; Very large scale integration",
}

@Proceedings{Chen:1988:CRT,
  editor =       "Ray R. Chen",
  key =          "Asilomar CSSC '88",
  booktitle =    "Conference Record: Papers Presented October
                 31--November 2, 1988, Pacific Grove, California:
                 Twenty-second Asilomar Conference on Signals, Systems
                 and Computers",
  title =        "Conference Record: Papers Presented October
                 31--November 2, 1988, Pacific Grove, California:
                 Twenty-second Asilomar Conference on Signals, Systems
                 and Computers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "various",
  year =         "1988",
  ISBN =         "0-929029-15-1",
  ISBN-13 =      "978-0-929029-15-3",
  LCCN =         "TK5102.5 .A74 1988",
  bibdate =      "Fri Dec 08 13:03:10 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Two volumes.",
  acknowledgement = ack-nj,
}

@Proceedings{Electro:1988:ECR,
  key =          "Electro '88",
  booktitle =    "Electro\slash 88 Conference Record: Sessions Presented
                 at Electro\slash 88, Boston, {MA}, May 10--12, 1988",
  title =        "Electro\slash 88 Conference Record: Sessions Presented
                 at Electro\slash 88, Boston, {MA}, May 10--12, 1988",
  publisher =    "Electronic Conventions Management",
  address =      "Los Angeles, CA, USA",
  pages =        "various",
  year =         "1988",
  ISBN =         "(done)",
  ISBN-13 =      "(done)",
  LCCN =         "TK 7801 E375 1988",
  bibdate =      "Fri Dec 08 13:03:11 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Proceedings{Harris:1988:PAI,
  editor =       "Gerald F. Harris and Cedric Frank Walker",
  booktitle =    "Proceedings of the Annual International Conference of
                 the {IEEE} Engineering in Medicine and Biology Society:
                 New Orleans, Louisiana, November 4--7, 1988",
  title =        "Proceedings of the Annual International Conference of
                 the {IEEE} Engineering in Medicine and Biology Society:
                 New Orleans, Louisiana, November 4--7, 1988",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "various",
  year =         "1988",
  LCCN =         "R856.A2 I344 1988",
  bibdate =      "Fri Dec 08 13:03:12 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Four volumes.",
  acknowledgement = ack-nj,
  xxISBN =       "(none)",
}

@Proceedings{IEEE:1988:IIS,
  editor =       "????",
  key =          "IEEE ISSCC '88",
  booktitle =    "1988 {IEEE} International Solid-State Circuits
                 Conference Digest of Technical Papers 31st {ISSCC}, San
                 Francisco, {CA}, {USA}, 17--19 February 1988",
  title =        "1988 {IEEE} International Solid-State Circuits
                 Conference Digest of Technical Papers 31st {ISSCC}, San
                 Francisco, {CA}, {USA}, 17--19 February 1988",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "??--??",
  year =         "1988",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Nov 12 21:57:54 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  xxnote =       "NHFB: OCLC says: ``AUTHOR: IEEE International
                 Solid-State Circuits Conference (35th: 1988: New York,
                 NY); TITLE: Digest of technical papers: 1988 IEEE
                 International Solid-State Circuits Conference; EDITION:
                 1st ed.; PLACE: Coral Gables, Fla.; FORMAT: 432 p.:
                 ill.; 28 cm.; OTHER: Winner, Lewis, 1906--''",
}

@Proceedings{IEEE:1988:PII,
  key =          "IEEE ICCD '88",
  booktitle =    "Proceedings: 1988 {IEEE} International Conference on
                 Computer Design, {VLSI} in Computers and Processors:
                 {ICCD} '88, Rye Town Hilton, Rye Brook, New York,
                 October 3--5, 1988",
  title =        "Proceedings: 1988 {IEEE} International Conference on
                 Computer Design, {VLSI} in Computers and Processors:
                 {ICCD} '88, Rye Town Hilton, Rye Brook, New York,
                 October 3--5, 1988",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xvii + 168",
  year =         "1988",
  ISBN =         "0-8186-8872-6",
  ISBN-13 =      "978-0-8186-8872-0",
  LCCN =         "TK 7888.4 I23 1988",
  bibdate =      "Wed Sep 07 23:22:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Proceedings{IEEE:1988:PSN,
  editor =       "{IEEE}",
  booktitle =    "Proceedings, Supercomputing '88: November 14--18,
                 1988, Orlando, Florida",
  title =        "Proceedings, Supercomputing '88: November 14--18,
                 1988, Orlando, Florida",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 458",
  year =         "1988",
  ISBN =         "0-8186-0882-X (v. 1; paper), 0-8186-8882-3 (v. 1;
                 case), 0-8186-4882-1 (v. 1: microfiche) 0-8186-8923-4
                 (v. 2), 0-8186-5923-X (v. 2: microfiche), 0-8186-8923-4
                 (v. 2: case)",
  ISBN-13 =      "978-0-8186-0882-7 (v. 1; paper), 978-0-8186-8882-9 (v.
                 1; case), 978-0-8186-4882-3 (v. 1: microfiche)
                 978-0-8186-8923-9 (v. 2), 978-0-8186-5923-2 (v. 2:
                 microfiche), 978-0-8186-8923-9 (v. 2: case)",
  LCCN =         "QA76.5 .S894 1988",
  bibdate =      "Fri Aug 23 13:34:23 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Two volumes. Available from IEEE Service Center
                 (Catalog number 88CH2617-9), Piscataway, NJ, USA.",
  acknowledgement = ack-nhfb,
  classification = "C5220 (Computer architecture); C5440 (Multiprocessor
                 systems and techniques); C5470 (Performance evaluation
                 and testing); C5540 (Terminals and graphic displays);
                 C6150C (Compilers, interpreters and other processors);
                 C6150J (Operating systems)",
  keywords =     "algorithms; architecture; benchmarking; compiler
                 evaluation; compiler technology; computer graphic
                 equipment; data-flow systems; Horizon superconducting
                 system; mass storage systems; operating systems;
                 operating systems (computers); parallel algorithms;
                 parallel architectures; parallel machines; performance
                 evaluation; program compilers; program development;
                 supercomputer performance; supercomputing center
                 management; visualization",
}

@Proceedings{IREE:1988:AMC,
  editor =       "{IREE}",
  booktitle =    "7th Australian Microelectronics Conference: May
                 16--18, 1988, Sydney University, {NSW}: proceedings",
  title =        "7th Australian Microelectronics Conference: May
                 16--18, 1988, Sydney University, {NSW}: proceedings",
  publisher =    "IREE",
  address =      "Edgecliff, NSW, Australia",
  pages =        "ix + 303",
  year =         "1988",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 07:57:05 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  confdate =     "16-18 May 1988",
  conflocation = "Sydney, NSW, Australia",
  confsponsor =  "Inst. Radio and Electron. Eng. Australia; IEE;
                 University of Sydney; Inst, Eng. Australia; IEEE",
  keywords =     "Institution of Radio and Electronics Engineers
                 Australia (IREE)",
  pubcountry =   "Australia",
}

@Proceedings{Lacoume:1988:SPI,
  editor =       "J. L. Lacoume and A. Chehikian and N. Martin and J.
                 Malbos",
  booktitle =    "Signal Processing {IV}: Theories and Applications
                 Proceedings of {EUSIPCO-88}. Fourth European Signal
                 Processing Conference",
  title =        "Signal Processing {IV}: Theories and Applications
                 Proceedings of {EUSIPCO}-88. Fourth European Signal
                 Processing Conference",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "xxxix + 1680",
  year =         "1988",
  ISBN =         "0-444-70516-3",
  ISBN-13 =      "978-0-444-70516-7",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 08:01:22 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  confdate =     "5-8 Sept. 1988",
  conflocation = "Grenoble, France",
  pubcountry =   "Netherlands",
}

@Proceedings{Martin:1988:SPN,
  editor =       "Joanne L. Martin and Stephen F. Lundstrom",
  booktitle =    "Supercomputing '88: proceedings, November 14--18,
                 1988, Orlando, Florida",
  title =        "Supercomputing '88: proceedings, November 14--18,
                 1988, Orlando, Florida",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "viii + 263",
  year =         "1988",
  ISBN =         "0-8186-0882-X (v. 1; paper), 0-8186-8882-3 (v. 1;
                 case), 0-8186-4882-1 (v. 1: microfiche) 0-8186-8923-4
                 (v. 2), 0-8186-5923-X (v. 2: microfiche), 0-8186-8923-4
                 (v. 2: case)",
  ISBN-13 =      "978-0-8186-0882-7 (v. 1; paper), 978-0-8186-8882-9 (v.
                 1; case), 978-0-8186-4882-3 (v. 1: microfiche)
                 978-0-8186-8923-9 (v. 2), 978-0-8186-5923-2 (v. 2:
                 microfiche), 978-0-8186-8923-9 (v. 2: case)",
  LCCN =         "QA76.5 .S894 1988",
  bibdate =      "Fri Aug 30 08:01:51 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  note =         "Two volumes. IEEE catalog number 88CH2617-9. IEEE
                 Computer Society Order Number 882.",
  acknowledgement = ack-nhfb,
  classification = "C5440 (Multiprocessor systems and techniques); C7300
                 (Natural sciences)",
  keywords =     "biology computing; chemistry; computational biology;
                 computational fluid dynamics; computational
                 mathematics; computational physics; flow simulation;
                 global change; mathematics computing; parallel
                 processing; physics computing; structural analysis;
                 structural engineering computing; supercomputers ---
                 congresses",
}

@Proceedings{Midcon:1988:MCP,
  editor =       "{Midcon}",
  booktitle =    "Midcon 88: Conference: Papers, August 30 -- September
                 1, 1998, Dallas, {TX}, {USA}",
  title =        "{Midcon} 88: Conference: Papers, August 30 --
                 September 1, 1998, Dallas, {TX}, {USA}",
  publisher =    "Electron. Conventions Manage",
  address =      "Ventura, CA, USA",
  edition =      "Midcon",
  pages =        "iv + 397",
  year =         "1988",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 07:30:24 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  availability = "Western Periodicals Co., 13000 Raymer Street, North
                 Hollywood, CA 91605, USA",
  confdate =     "30 Aug.-1 Sept. 1988",
  conflocation = "Dallas, TX, USA",
  confsponsor =  "IEEE; ERA",
  keywords =     "Midwest Electronic Show and Convention (Midcon)",
}

@Book{Moore:1988:RCR,
  editor =       "Ramon E. Moore",
  booktitle =    "Reliability in Computing: the Role of Interval Methods
                 in Scientific Computing",
  title =        "Reliability in Computing: the Role of Interval Methods
                 in Scientific Computing",
  volume =       "19",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xv + 428",
  year =         "1988",
  ISBN =         "0-12-505630-3",
  ISBN-13 =      "978-0-12-505630-4",
  LCCN =         "QA76.9.E94 R45 1988",
  bibdate =      "Mon Dec 18 09:41:47 1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/g/gay-david-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/m/moore-ramon-e.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran2.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Perspectives in computing",
  ZMnumber =     "0638.00033",
  acknowledgement = ack-nhfb,
  classmath =    "00Bxx Conference proceedings and collections of
                 papers; 65-06 Proceedings of conferences (numerical
                 analysis)",
  keywords =     "Computing; Interval methods; Reliability; Scientific
                 computing",
  tableofcontents = "Contributors / ix \\
                 Preface / xiii \\
                 Acknowledgments / xv \\
                 Part 1: Computer Arithmetic and Mathematical Software /
                 3 \\
                 Chapter 1. Arithmetic for Vector Processors / R.
                 Kirchner and U. Kulisch / 3 \\
                 Abstract \\
                 1. Introduction \\
                 2. The State of the Art \\
                 3. Fast Computation of Sums and Scalar Products \\
                 4. Summation with only One Row of Adders \\
                 5. Systems with Large Exponent Range and Further
                 Remarks \\
                 6. Application to Multiple Precision Arithmetic \\
                 7. Contemporary Floating-Point Arithmetic \\
                 8. Literature \\
                 Chapter 2. FORTRAN-SC, A FORTRAN Extension for
                 Engineering/Scientific Computation with Access to
                 ACRITH: Language Description with Examples / Wolfgang
                 Walter / 43 \\
                 Abstract \\
                 1. Introduction \\
                 2. Development of FORTRAN-SC \\
                 3. Main Language Concepts \\
                 4. Language Description with Examples \\
                 5. Implementation of FORTRAN-SC \\
                 References \\
                 Chapter 3. FORTRAN-SC, A FORTRAN Extension for
                 Engineering/Scientific Computation with Access to
                 ACRITH: Demonstration of the Compiler and Sample
                 Programs / Michael Metzger / 63 \\
                 Abstract \\
                 Introduction \\
                 Example 1: Interval Newton Method \\
                 Example 2: Automatic Differentiation \\
                 Example 3: Runge--Kutta Method \\
                 Example 4: Gaussian Elimination Method \\
                 Example 5: Verified Solution of a Linear System \\
                 References \\
                 Chapter 4. Reliable Expression Evaluation in PASCAL-SC
                 / J{\"u}rgen Wolff von Gudenberg / 81 \\
                 Abstract \\
                 1. Floating-point arithmetic \\
                 2. Interval arithmetic \\
                 3. The optimal scalar product \\
                 4. Complex floating-point and complex interval
                 arithmetic \\
                 5. Matrix and vector arithmetic \\
                 6. Accurate Operations and Problem Solving Routines \\
                 7. Transformation of arithmetic expressions \\
                 8. Solution of nonlinear systems \\
                 9. The data type dotprecision \\
                 10. Dotproduct expressions \\
                 11. Conclusion \\
                 References \\
                 Chapter 5. Floating-Point Standards --- Theory and
                 Practice / W. J. Cody / 99 \\
                 1. Introduction \\
                 2. The Standards \\
                 3. Implementations \\
                 4. Software Support \\
                 5. Conclusions \\
                 References \\
                 Chapter 6. Algorithms for Verified Inclusions: Theory
                 and Practice / Siegfried M. Rump / 109 \\
                 Summary \\
                 0. Introduction \\
                 1. Basic theorems \\
                 2. Practical verification on the computer \\
                 3. Interactive Programming Environment \\
                 4. References \\
                 Chapter 7. Applications of Differentiation Arithmetic /
                 George F. Corliss / 127 \\
                 Abstract \\
                 1. Differentiation Arithmetic \\
                 Why, What, and How? \\
                 2. Why? \\
                 Motivation \\
                 3. What? \\
                 Component tools \\
                 4. Conditions on f \\
                 5. How to use it? \\
                 Applications \\
                 6. Acknowledgements \\
                 References \\
                 Part 2: Linear and Nonlinear Systems / 149 \\
                 Chapter 8. Interval Acceleration of Convergence / Karl
                 Nickel / 151 \\
                 Abstract \\
                 1. Introduction \\
                 2. Examples \\
                 3. Definitions and Notation \\
                 4. Interval Methods \\
                 5. How Can We Get Bounds on a Given Point-Sequence? \\
                 6. Acceleration of Convergence \\
                 References \\
                 Chapter 9. Solving Systems of Linear Interval Equations
                 / J. Rohn / 171 \\
                 0. Introduction \\
                 1. Bounding the solutions \\
                 2. Computing the xy's \\
                 3. Explicit formulae for x, x \\
                 4. Inverse interval matrix \\
                 References \\
                 Chapter 10. Interval Least Squares --- a Diagnostic
                 Tool / David M. Gay / 183 \\
                 Introduction \\
                 Linearity \\
                 Interval Notation \\
                 Chapter 11. Existence of Solutions and Iterations for
                 Nonlinear Equations / G. Alefeld / 207 \\
                 Chapter 12. Interval Method for Algebraic Equations /
                 M. A. Wolfe / 229 \\
                 Chapter 13. Error Questions in the Computation of
                 Solution Manifolds of Parametrized Equations / Werner
                 C. Rheinbolt / 249 \\
                 Chapter 14. The Enclosure of Solutions of
                 Parameter-Dependent Systems of Equations / A. Neumaier
                 / 269 \\
                 Part 3. Optimization / 287 \\
                 Chapter 15. An Overview of Global Optimization Using
                 Interval Analysis / Eldon Hansen / 289 \\
                 Chapter 16. Philosophy and Practicalities of Interval
                 Arithmetic / G. William Walster / 309 \\
                 Chapter 17. Some Recent Aspects of Interval Algorithms
                 for Global Optimization / Helmut Ratschek / 325 \\
                 Chapter 18. The Use of Interval Arithmetic in
                 Uncovering Structure of Linear Systems / Weldon A.
                 Lodwick / 341 \\
                 Part 4. Operator Equations / 355 \\
                 Chapter 19. The Role of Order in Computing / Garrett
                 Birkhoff / 357 \\
                 Chapter 20. Interval Methods for Operator Equations /
                 R. E. Moore and Shen Zuhe / 379 \\
                 Chapter 21. Boundary Implications for Stability
                 Properties: Present Status / J. Garloff and N. K. Bose
                 / 391 \\
                 Chapter 22. Validating Computation in a Function Space
                 / Edgar Kaucher and Willard L. Miranker / 403 \\
                 Epilogue: A Poem about My Life, by Daniel J. Langton /
                 427",
}

@Proceedings{Sakamura:1988:TPO,
  editor =       "Ken Sakamura",
  booktitle =    "{TRON} Project 1988. Open-Architecture Computer
                 Systems Proceedings of the Fifth {TRON} Project
                 Symposium",
  title =        "{TRON} Project 1988. Open-Architecture Computer
                 Systems Proceedings of the Fifth {TRON} Project
                 Symposium",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xi + 384",
  year =         "1988",
  DOI =          "https://doi.org/10.1007/978-4-431-68081-9",
  ISBN =         "0-387-70038-2 (New York), 3-540-70038-2 (Berlin),
                 4-431-70038-2 (Tokyo)",
  ISBN-13 =      "978-0-387-70038-0 (New York), 978-3-540-70038-8
                 (Berlin), 978-4-431-70038-8 (Tokyo)",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 07:43:41 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{USENIX:1988:UPC,
  editor =       "{USENIX Association}",
  booktitle =    "{USENIX} proceedings: {C++} Conference, Denver, {CO},
                 October 17--21, 1988",
  title =        "{USENIX} proceedings: {C++} Conference, Denver, {CO},
                 October 17--21, 1988",
  publisher =    pub-USENIX,
  address =      pub-USENIX:adr,
  pages =        "362",
  year =         "1988",
  bibdate =      "Sun Feb 18 07:46:09 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "C++ (Computer program language) --- Congresses.",
}

@Proceedings{Wescon:1988:WCR,
  editor =       "{Wescon}",
  booktitle =    "Wescon/88 conference record: sessions presented at
                 Wescon/88, Anaheim, Calif., November 15--17, 1988",
  title =        "Wescon/88 conference record: sessions presented at
                 Wescon/88, Anaheim, Calif., November 15--17, 1988",
  volume =       "32",
  publisher =    "Electronic Conventions Management",
  address =      "Ventura, CA, USA",
  pages =        "798",
  year =         "1988",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 07:37:36 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  confdate =     "15-17 Nov. 1988",
  conflocation = "Anaheim, CA, USA",
  confsponsor =  "IEEE; ERA",
}

@Proceedings{ACM:1989:APT,
  editor =       "{ACM}",
  booktitle =    "{ASPLOS-III} Proceedings. Third International
                 Conference on Architectural Support for Programming
                 Languages and Operating Systems, Boston, {MA}, {USA},
                 April 3--6, 1989",
  title =        "{ASPLOS}-{III} Proceedings. Third International
                 Conference on Architectural Support for Programming
                 Languages and Operating Systems, Boston, {MA}, {USA},
                 April 3--6, 1989",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "x + 303",
  year =         "1989",
  ISBN =         "0-89791-300-0",
  ISBN-13 =      "978-0-89791-300-3",
  LCCN =         "QA76.9.A73I565 1989",
  bibdate =      "Sun Sep 29 06:28:50 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "ACM order number 556890. Also published as Computer
                 architecture news, v. 17, no. 2 (Apr. 1989), Operating
                 systems review, v. 23, special issue (Apr. 1989), and
                 SIGPLAN notices, v. 24, special issue (May 1989).",
  acknowledgement = ack-nhfb,
  confsponsor =  "IEEE; ACM",
}

@Proceedings{ACM:1989:PSN,
  editor =       "{ACM}",
  booktitle =    "Proceedings, Supercomputing '89: November 13--17,
                 1989, Reno, Nevada",
  title =        "Proceedings, Supercomputing '89: November 13--17,
                 1989, Reno, Nevada",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xviii + 849",
  year =         "1989",
  ISBN =         "0-89791-341-8",
  ISBN-13 =      "978-0-89791-341-6",
  LCCN =         "QA 76.5 S87 1989",
  bibdate =      "Wed Aug 28 06:48:31 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 University of California MELVYL catalog.",
  note =         "IEEE 89CH2802-7.",
  acknowledgement = ack-nhfb,
  classification = "A0130C (Conference proceedings); A0270
                 (Computational techniques); A0500 (Statistical physics
                 and thermodynamics); A4700 (Fluid dynamics); B0100
                 (General electrical engineering topics); B0290
                 (Numerical analysis); B1130B (Computer-aided circuit
                 analysis and design); C4100 (Numerical analysis); C4240
                 (Programming and algorithm theory); C5440
                 (Multiprocessor systems and techniques); C5470
                 (Performance evaluation and testing); C6110B (Software
                 engineering techniques); C6150J (Operating systems);
                 C7000 (Computer applications)",
  keywords =     "benchmarking; computer applications; parallel
                 algorithms; parallel processing; performance
                 evaluation; performance measurements; performance
                 tools; pipeline processing; software environments;
                 supercomputer architectures; supercomputers ---
                 congresses; technology integration; vector algorithms",
  remark =       "89CM2802-7. ACM Order Number 415892. IEEE 89CH2802-7.
                 IEEE Computer Society Order Number 2021.",
}

@Book{Carey:1989:PSM,
  editor =       "Graham F. Carey",
  booktitle =    "Parallel supercomputing: methods, algorithms and
                 applications",
  title =        "Parallel supercomputing: methods, algorithms and
                 applications",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "x + 287",
  year =         "1989",
  ISBN =         "0-471-92436-9",
  ISBN-13 =      "978-0-471-92436-4",
  LCCN =         "M89.E02452; QA76.6",
  bibdate =      "Mon Jan 2 15:42:42 MST 2006",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 library.ox.ac.uk:210/ADVANCE",
  series =       "Wiley series in parallel computing",
  acknowledgement = ack-nhfb,
  subject =      "Parallel programming (Computer science)",
}

@Proceedings{Chen:1989:TSA,
  editor =       "Ray R. Chen",
  booktitle =    "Twenty-second Asilomar Conference on Signals, Systems
                 \& Computers: October 31--November 2, 1988, Pacific
                 Grove, California",
  title =        "Twenty-second Asilomar Conference on Signals, Systems
                 \& Computers: October 31--November 2, 1988, Pacific
                 Grove, California",
  publisher =    "Maple Press",
  address =      "San Jose, CA, USA",
  pages =        "xviii + 985",
  year =         "1989",
  ISBN =         "0-929029-15-1",
  ISBN-13 =      "978-0-929029-15-3",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 08:06:51 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Two volumes. IEEE catalog number 88CH2660-9. IEEE
                 catalog no. 88CH2835-7.",
  acknowledgement = ack-nhfb,
  confdate =     "31 Oct.-2 Nov. 1988",
  conflocation = "Pacific Grove, CA, USA",
  confsponsor =  "Naval Postgraduate School; San Jose State Univ",
  xxnote =       "Check differing IEEE catalog numbers??",
}

@Proceedings{Ercegovac:1989:PSC,
  editor =       "Milo{\v{s}} D. Ercegovac and Earl E. {Swartzlander,
                 Jr.}",
  booktitle =    "Proceedings: 9th Symposium on Computer Arithmetic:
                 September 6--8, 1989, Santa Monica, California, {USA}",
  title =        "Proceedings: 9th Symposium on Computer Arithmetic:
                 September 6--8, 1989, Santa Monica, California, {USA}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xv + 247",
  year =         "1989",
  ISBN =         "0-8186-8963-3 (case), 0-8186-5963-7 (microfiche)",
  ISBN-13 =      "978-0-8186-8963-5 (case), 978-0-8186-5963-8
                 (microfiche)",
  LCCN =         "QA 76.9 C62 S95 1989",
  bibdate =      "Thu Sep 01 22:36:52 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog no. 89CH2757-3.",
  acknowledgement = ack-nhfb,
  confdate =     "6-8 Sept. 1989",
  conflocation = "Santa Monica, CA, USA",
  confsponsor =  "IEEE; IFIP; University of California",
  keywords =     "ARITH-9",
}

@Proceedings{IEE:1989:EEC,
  editor =       "{IEE}",
  booktitle =    "{ECCTD 89}: European Conference on Circuit Theory and
                 Design, 5--8 September 1989: venue, University of
                 Sussex, Brighton, United Kingdom",
  title =        "{ECCTD} 89: European Conference on Circuit Theory and
                 Design, 5--8 September 1989: venue, University of
                 Sussex, Brighton, United Kingdom",
  publisher =    "IEE",
  address =      "London, UK",
  bookpages =    "xviii + 680",
  year =         "1989",
  ISBN =         "0-85296-383-1",
  ISBN-13 =      "978-0-85296-383-8",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 08:19:35 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Conference publication no. 308.",
  acknowledgement = ack-nhfb,
  confdate =     "5-8 Sept. 1989",
  conflocation = "Brighton, UK",
  confsponsor =  "IEE",
  pubcountry =   "UK",
}

@Proceedings{IEEE:1989:IISa,
  key =          "IEEE SCS '89",
  booktitle =    "1989 {IEEE} International Symposium on Circuits and
                 Systems: Portland Hilton, Portland, {OR}, May 8--11,
                 1989",
  title =        "1989 {IEEE} International Symposium on Circuits and
                 Systems: Portland Hilton, Portland, {OR}, May 8--11,
                 1989",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xl + 2246",
  year =         "1989",
  LCCN =         "TK 7801 I22 1989",
  bibdate =      "Thu Sep 15 18:50:54 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Three volumes.",
  acknowledgement = ack-nhfb,
  xxISBN =       "(none)",
}

@Proceedings{IEEE:1989:ISV,
  editor =       "{IEEE}",
  booktitle =    "{1989 International Symposium on VLSI Technology,
                 Systems and Applications: proceedings of technical
                 papers: VLSI: May 17--19, 1989\slash Taipei, Taiwan,
                 R.O.C.}",
  title =        "{1989 International Symposium on VLSI Technology,
                 Systems and Applications: proceedings of technical
                 papers: VLSI: May 17--19, 1989\slash Taipei, Taiwan,
                 R.O.C.}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "x + 393",
  year =         "1989",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 08:32:06 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog no. 89CH2631-0.",
  acknowledgement = ack-nhfb,
  confdate =     "17-19 May 1989",
  conflocation = "Taipei, Taiwan",
  confsponsor =  "IEEE; Nat. Sci. Council; Ind. Technol. Res. Inst",
}

@Proceedings{IEEE:1989:PII,
  key =          "IEEE ICCD '89",
  booktitle =    "Proceedings: 1989 {IEEE} International Conference on
                 Computer Design: {VLSI} in Computer and Processors,
                 {ICCD} '89, Hyatt Regency Cambridge, Cambridge,
                 Massachusetts, October 2--4, 1989",
  title =        "Proceedings: 1989 {IEEE} International Conference on
                 Computer Design: {VLSI} in Computer and Processors,
                 {ICCD} '89, Hyatt Regency Cambridge, Cambridge,
                 Massachusetts, October 2--4, 1989",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xvii + 587",
  year =         "1989",
  ISBN =         "0-8186-1971-6 (paper), 0-8186-5971-8 (microfiche),
                 0-8186-8971-4 (case)",
  ISBN-13 =      "978-0-8186-1971-7 (paper), 978-0-8186-5971-3
                 (microfiche), 978-0-8186-8971-0 (case)",
  LCCN =         "TK 7888.4 I23 1989",
  bibdate =      "Wed Dec 13 18:26:58 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog number 89CH2794-6.",
  acknowledgement = ack-nj,
  confdate =     "2-4 Oct. 1989",
  conflocation = "Cambridge, MA, USA",
  confsponsor =  "IEEE",
}

@Proceedings{Turner:1989:NAP,
  editor =       "Peter R. Turner",
  booktitle =    "Numerical analysis and parallel processing: lectures
                 given at the {Lancaster Numerical Analysis Summer
                 School}, 1987",
  title =        "Numerical analysis and parallel processing: lectures
                 given at the {Lancaster Numerical Analysis Summer
                 School}, 1987",
  volume =       "1397",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "vi + 264",
  year =         "1989",
  DOI =          "https://doi.org/10.1007/BFb0085715",
  ISBN =         "0-387-51645-X, 0-387-13864-1",
  ISBN-13 =      "978-0-387-51645-5, 978-0-387-13864-0",
  LCCN =         "QA3 .L28 no. 1397",
  bibdate =      "Fri Dec 08 08:24:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.bibsys.no:2100/BIBSYS",
  price =        "US\$45.00",
  series =       "Lecture Notes in Mathematics",
  acknowledgement = ack-nhfb,
}

@Proceedings{Wuorinen:1989:DTP,
  editor =       "J. H. Wuorinen",
  booktitle =    "Digest of technical papers: 1989 {IEEE} International
                 Solid-State Circuits Conference",
  title =        "Digest of technical papers: 1989 {IEEE} International
                 Solid-State Circuits Conference",
  volume =       "32",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "394",
  month =        feb,
  year =         "1989",
  CODEN =        "DTPCDE",
  ISBN =         "????",
  ISBN-13 =      "????",
  ISSN =         "0193-6530",
  LCCN =         "TK7870 .I58 1989",
  bibdate =      "Wed Sep 29 07:47:11 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog no. 89CH2684-9.",
  acknowledgement = ack-nhfb,
  confdate =     "15-17 Feb. 1989",
  conflocation = "New York, NY, USA",
  confsponsor =  "IEEE; University of Pennsylvania",
  keywords =     "analog to digital converters; audio equipment; charge
                 coupled devices; circuits; cmos; conferences; digital
                 electronics; Electronic circuits --- Congresses.;
                 floating point arithmetic; gates (circuits); image
                 processing; integrated circuits; ISSCC 89; memory
                 (computers); microprocessors; operational amplifiers;
                 semiconductor devices; Semiconductors --- Congresses.;
                 signal processing; solid state; Solid state electronics
                 --- Congresses.; video signals",
  xxnote =       "NHFB: OCLSC says ``PLACE: Castine, ME''",
  xxpages =      "400",
}

@Proceedings{ACM:1990:PAS,
  editor =       "{ACM}",
  booktitle =    "Proceedings of the {ACM SIGPLAN} '90 Conference on
                 Programming Language Design and Implementation, {White
                 Plains, New York}, {June} 20--22, 1990",
  title =        "Proceedings of the {ACM SIGPLAN} '90 Conference on
                 Programming Language Design and Implementation, {White
                 Plains, New York}, {June} 20--22, 1990",
  volume =       "25(6)",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "viii + 351",
  month =        jun,
  year =         "1990",
  CODEN =        "SINODQ",
  ISBN =         "0-89791-364-7",
  ISBN-13 =      "978-0-89791-364-5",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  LCCN =         "QA76.7.S53 1990",
  bibdate =      "Tue Nov 10 07:57:14 1998",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-SIGPLAN,
  abstract =     "This conference proceedings contains 30 papers. The
                 main subjects are code generation, code positioning,
                 register allocation, representing control, program
                 optimization, floating-point numbers accurately,
                 optimizing dynamically-typed object-oriented programs,
                 higher-order attribute grammars and editing
                 environments, program and data dependence,
                 demand-driven interpretation of imperative languages,
                 analysis of pointers and structures, and compact
                 representations for control dependence.",
  acknowledgement = ack-nhfb,
  classification = "722; 723",
  conference =   "Proceedings of the ACM SIGPLAN '90 Conference on
                 Programming Language Design and Implementation",
  conferenceyear = "1990",
  journalabr =   "SIGPLAN Not",
  keywords =     "Code Generation; Computer Operating Systems; Computer
                 Programming --- Object Oriented Programming; Computer
                 Programming Languages --- Design; Computer Systems,
                 Digital --- Parallel Processing; Computers, Digital ---
                 Computational Methods; Data Abstraction; Data
                 Processing --- Data Structures; Object-Oriented
                 Languages; Optimizing Compilers; Program Compilers;
                 Register Allocation",
  meetingaddress = "White Plains, NY, USA",
  meetingdate =  "Jun 20--22 1990",
  meetingdate2 = "06/20--22/90",
  pagecount =    "351",
  sponsor =      "Assoc for Computing Machinery, Special Interest Group
                 on Programming Languages",
}

@Proceedings{ACM:1990:PDB,
  editor =       "{ACM}",
  booktitle =    "{Proceedings: December 3--7, 1990, Baltimore
                 Convention Center, Baltimore, MD}",
  title =        "{Proceedings: December 3--7, 1990, Baltimore
                 Convention Center, Baltimore, MD}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xxvi + 630",
  year =         "1990",
  ISBN =         "0-89791-409-0",
  ISBN-13 =      "978-0-89791-409-3",
  LCCN =         "QA76.73.A35",
  bibdate =      "Thu Aug 7 18:17:59 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.gbv.de:20011/gvk",
  acknowledgement = ack-nhfb,
}

@Proceedings{Anonymous:1990:PAN,
  editor =       "{Anonymous}",
  booktitle =    "Proceedings of the Annual National Conference of Ada
                 Technology (8th). Held in Atlanta, Georgia on March
                 5--8, 1990",
  title =        "Proceedings of the Annual National Conference of Ada
                 Technology (8th). Held in Atlanta, Georgia on March
                 5--8, 1990",
  publisher =    "U.S. Army Commun.-Electron. Command",
  address =      "Fort Monmouth, NJ, USA",
  pages =        "xiv + 669",
  year =         "1990",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 09:01:32 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  confdate =     "5-8 March 1990",
  conflocation = "Atlanta, GA, USA",
  confsponsor =  "Ancost",
}

@Proceedings{Chen:1990:CRT,
  editor =       "Ray R. Chen",
  booktitle =    "Conference record: Twenty-fourth Asilomar Conference
                 on Signals, Systems and Computers: Papers Presented
                 November 5--7, 1990, Pacific Grove, California",
  title =        "Conference record: Twenty-fourth Asilomar Conference
                 on Signals, Systems and Computers: Papers Presented
                 November 5--7, 1990, Pacific Grove, California",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xxi + 1089",
  year =         "1990",
  ISBN =         "0-8186-2182-6",
  ISBN-13 =      "978-0-8186-2182-6",
  LCCN =         "TK 5102.5 A78 1990",
  bibdate =      "Wed Sep 07 21:55:08 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Two volumes.",
  acknowledgement = ack-nj,
  confdate =     "5-7 Nov. 1990",
  conflocation = "Pacific Grove, CA, USA",
  confsponsor =  "IEEE; Naval Post Graduate Sch",
}

@Proceedings{CUG:1990:PSC,
  editor =       "{CUG}",
  key =          "Cray UG '90",
  booktitle =    "Proceedings, 25th Semiannual Cray User Group Meeting,
                 Toronto, Ontario, June 1990",
  title =        "Proceedings, 25th Semiannual Cray User Group Meeting,
                 Toronto, Ontario, June 1990",
  publisher =    "Cray User Group",
  address =      "186 Mandela Road, Shepherdstown, WV 25443, USA",
  pages =        "????",
  year =         "1990",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Thu Sep 08 08:56:01 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  xxnote =       "Check: is this June or April 10 meeting??",
}

@Book{Feijen:1990:BOB,
  editor =       "W. H. J. Feijen and A. J. M. van Gasteren and David
                 Gries and J. Misra",
  booktitle =    "Beauty is our Business: a Birthday Salute to {Edsger
                 W. Dijkstra}",
  title =        "Beauty is our Business: a Birthday Salute to {Edsger
                 W. Dijkstra}",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xix + 453",
  year =         "1990",
  DOI =          "https://doi.org/10.1007/978-1-4612-4476-9",
  ISBN =         "0-387-97299-4, 3-540-97299-4, 1-4612-8792-8 (print),
                 1-4612-4476-5 (online)",
  ISBN-13 =      "978-0-387-97299-2, 978-3-540-97299-0,
                 978-1-4612-8792-6 (print), 978-1-4612-4476-9 (online)",
  ISSN =         "0172-603X",
  ISSN-L =       "0172-603X",
  LCCN =         "QA76 .B326 1990",
  bibdate =      "Thu Mar 24 09:27:40 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/bauer-friedrich-ludwig.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/d/dijkstra-edsger-w.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/hoare-c-a-r.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/texbook3.bib",
  note =         "Contains important treatment of accurate
                 binary-to-decimal conversion
                 \cite{Gries:1990:BDO,Knuth:1990:SPW}.",
  URL =          "http://www.zentralblatt-math.org/zmath/en/search/?an=0718.68004",
  acknowledgement = ack-nhfb,
  tableofcontents = "Anonymous / Front Matter / i--xix \\
                 Krzysztof R. Apt, Frank S. de Boer, Ernst-R{\"u}diger
                 Olderog / Proving Termination of Parallel Programs /
                 1--6 / doi:10.1007/978-1-4612-4476-9_1 \\
                 Roland C. Backhouse / On a Relation on Functions /
                 7--18 / doi:10.1007/978-1-4612-4476-9_2 \\
                 F. L. Bauer / Efficient Solution of a Non--Monotonic
                 Inverse Problem / 19--26 /
                 doi:10.1007/978-1-4612-4476-9_3 \\
                 A. Bijlsma / Semantics of Quasi--Boolean Expressions /
                 27--35 / doi:10.1007/978-1-4612-4476-9_4 \\
                 Richard S. Bird / Small Specification Exercises /
                 36--43 / doi:10.1007/978-1-4612-4476-9_5 \\
                 Maarten Boasson / Architecture of Real--Time Systems /
                 44--53 / doi:10.1007/978-1-4612-4476-9_6 \\
                 Robert S. Boyer, Milton W. Green, J Strother Moore /
                 The Use of a Formal Simulator to Verify a Simple Real
                 Time Control Program / 54--66 /
                 doi:10.1007/978-1-4612-4476-9_7 \\
                 Donald W. Braben / Exploring the Future: Trends and
                 Discontinuities / 67--75 /
                 doi:10.1007/978-1-4612-4476-9_8 \\
                 Coen Bron / On a Renewed Visit to the Banker and a
                 Remarkable Analogy / 76--82 /
                 doi:10.1007/978-1-4612-4476-9_9 \\
                 Manfred Broy / On Bounded Buffers: Modularity,
                 Robustness, and Reliability in Reactive Systems /
                 83--93 / doi:10.1007/978-1-4612-4476-9_10 \\
                 K. Mani Chandy, Stephen Taylor / Examples in Program
                 Composition / 94--101 /
                 doi:10.1007/978-1-4612-4476-9_11 \\
                 Albert J. Dijkstra / On the Mechanism of the
                 Hydrogenation of Edible Oils / 102--111 /
                 doi:10.1007/978-1-4612-4476-9_12 \\
                 W. H. J. Feijen, A. J. M. van Gasteren, D. Gries, J.
                 Misra / The Problem of the Majority Network / 112--118
                 / doi:10.1007/978-1-4612-4476-9_13 \\
                 W. H. J. Feijen / A Little Exercise in Deriving
                 Multiprograms / 119--126 /
                 doi:10.1007/978-1-4612-4476-9_14 \\
                 A. J. M. van Gasteren / Experimenting with a Refinement
                 Calculus / 127--134 / doi:10.1007/978-1-4612-4476-9_15
                 \\
                 Mohamed G. Gouda / Serializable Programs,
                 Parallelizable Assertions: A Basis for Interleaving /
                 135--140 / doi:10.1007/978-1-4612-4476-9_16 \\
                 David Gries / Binary to Decimal, One More Time /
                 141--148 / doi:10.1007/978-1-4612-4476-9_17 \\
                 A. N. Habermann / Rotate and Double / 149--162 /
                 doi:10.1007/978-1-4612-4476-9_18 \\
                 Eric C. R. Hehner / Beautifying G{\"o}del / 163--172 /
                 doi:10.1007/978-1-4612-4476-9_19 \\
                 G. Helmberg / A Striptease of Entropy / 173--175 /
                 doi:10.1007/978-1-4612-4476-9_20 \\
                 Ted Herman / On a Theorem of Jacobson / 176--181 /
                 doi:10.1007/978-1-4612-4476-9_21 \\
                 Wim H. Hesselink / Modalities of Nondeterminacy /
                 182--192 / doi:10.1007/978-1-4612-4476-9_22 \\
                 C. A. R. Hoare / A Theory for the Derivation of C-mos
                 Circuit Designs / 193--205 /
                 doi:10.1007/978-1-4612-4476-9_23 \\
                 Rob Hoogerwoord / On Mathematical Induction and the
                 Invariance Theorem / 206--211 /
                 doi:10.1007/978-1-4612-4476-9_24 \\
                 J. J. Horning / Formalizing Some Classic
                 Synchronization Primitives / 212--219 /
                 doi:10.1007/978-1-4612-4476-9_25 \\
                 Cliff B. Jones / Consequences / 220--225 /
                 doi:10.1007/978-1-4612-4476-9_26 \\
                 Anne Kaldewaij / Shortest and Longest Segments /
                 226--232 / doi:10.1007/978-1-4612-4476-9_27 \\
                 Donald E. Knuth / A Simple Program Whose Proof Isn't /
                 233--242 / doi:10.1007/978-1-4612-4476-9_28 \\
                 Vadim E. Kotov / Binding Structure and Behaviour in
                 ``Whole Net'' Concurrency Semantics / 243--250 /
                 doi:10.1007/978-1-4612-4476-9_29 \\
                 F. E. J. Kruseman Aretz / Maximal Strong Components: An
                 Exercise in Program Presentation / 251--261 /
                 doi:10.1007/978-1-4612-4476-9_30 \\
                 Christian Lengauer, Duncan G. Hudson / A Systolic
                 Program for Gauss--Jordan Elimination / 262--273 /
                 doi:10.1007/978-1-4612-4476-9_31 \\
                 J. H. van Lint / Coding for Channels with Localized
                 Errors / 274--279 / doi:10.1007/978-1-4612-4476-9_32
                 \\
                 Johan J. Lukkien, Jan L. A. van de Snepscheut /
                 Topology-Independent Algorithms Based on Spanning Trees
                 / 280--288 / doi:10.1007/978-1-4612-4476-9_33 \\
                 Zohar Manna, Amir Pnueli / An Exercise in the
                 Verification of Multi--Process Programs / 289--301 /
                 doi:10.1007/978-1-4612-4476-9_34 \\
                 Alain J. Martin / The Limitations to
                 Delay--Insensitivity in Asynchronous Circuits /
                 302--311 / doi:10.1007/978-1-4612-4476-9_35 \\
                 Jayadev Misra / A Simple Proof of a Simple Consensus
                 Algorithm / 312--318 / doi:10.1007/978-1-4612-4476-9_36
                 \\
                 Carroll Morgan / Of wp and {CSP} / 319--326 /
                 doi:10.1007/978-1-4612-4476-9_37 \\
                 Joseph M. Morris / Programming by Expression
                 Refinement: the {KMP} Algorithm / 327--338 /
                 doi:10.1007/978-1-4612-4476-9_38 \\
                 Greg Nelson / Methodical Competitive Snoopy--Caching /
                 339--345 / doi:10.1007/978-1-4612-4476-9_39 \\
                 Peter G. Neumann / Beauty and the Beast of Software
                 Complexity Elegance versus Elephants / 346--351 /
                 doi:10.1007/978-1-4612-4476-9_40 \\
                 W. Peremans / A Note on Feasibility / 352--355 /
                 doi:10.1007/978-1-4612-4476-9_41 \\
                 Karel A. Post / A Curious Property of Points and
                 Circles in the Plane / 356--357 /
                 doi:10.1007/978-1-4612-4476-9_42 \\
                 Paul Pritchard / A Problem Involving Subsequences /
                 358--364 / doi:10.1007/978-1-4612-4476-9_43 \\
                 Martin Rem / A Personal Perspective of the
                 Alpern--Schneider Characterization of Safety and
                 Liveness / 365--372 / doi:10.1007/978-1-4612-4476-9_44
                 \\
                 Fred B. Schneider / Simpler Proofs for Concurrent
                 Reading and Writing / 373--379 /
                 doi:10.1007/978-1-4612-4476-9_45 \\
                 Carel S. Scholten / Goodbye Junctivity? / 380--385 /
                 doi:10.1007/978-1-4612-4476-9_46 \\
                 Henk C. A. van Tilborg / An Assignment Problem for the
                 Vertices of a Cycle / 386--389 /
                 doi:10.1007/978-1-4612-4476-9_47 \\
                 D. A. Turner / Duality and De Morgan Principles for
                 Lists / 390--398 / doi:10.1007/978-1-4612-4476-9_48 \\
                 W. M. Turski / The Quest for Timeless Specifications
                 Leads to Non--Stepping Automata / 399--409 /
                 doi:10.1007/978-1-4612-4476-9_49 \\
                 Jan Tijmen Udding / The Maximum Length of a Palindrome
                 in a Sequence / 410--416 /
                 doi:10.1007/978-1-4612-4476-9_50 \\
                 Lincoln A. Wallen / On Form, Formalism and Equivalence
                 / 417--426 / doi:10.1007/978-1-4612-4476-9_51 \\
                 N. Wirth / Drawing Lines, Circles, and Ellipses in a
                 Raster / 427--434 / doi:10.1007/978-1-4612-4476-9_52
                 \\
                 Jaap van der Woude / Calculations with Relations, an
                 Example / 435--441 / doi:10.1007/978-1-4612-4476-9_53
                 \\
                 Heinz Zemanek / Two Proofs for Pythagoras / 442--447 /
                 doi:10.1007/978-1-4612-4476-9_54 \\
                 Anonymous / Back Matter / 448--453",
}

@Book{Hennessy:1990:CAQ,
  author =       "John L. Hennessy and David A. Patterson",
  booktitle =    "Computer Architecture: a Quantitative Approach",
  title =        "Computer Architecture: a Quantitative Approach",
  publisher =    pub-MORGAN-KAUFMANN,
  address =      pub-MORGAN-KAUFMANN:adr,
  pages =        "xxviii + 594",
  year =         "1990",
  ISBN =         "1-55860-069-8, 1-55880-169-8",
  ISBN-13 =      "978-1-55860-069-0, 978-1-55880-169-1",
  LCCN =         "QA76.9.A73 P377 1990",
  bibdate =      "Mon Jan 31 08:47:46 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/microchip.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "Fundamentals of Computer Design \\
                 Introduction \\
                 The Changing Face of Computing and the Task of the
                 Computer Designer \\
                 Technology Trends \\
                 Cost, Price, and their Trends \\
                 Measuring and Reporting Performance \\
                 Quantitative Principles of Computer Design \\
                 Putting It All Together: Performance and
                 Price-Performance \\
                 Another View: Power Consumption and Efficiency as the
                 Metric \\
                 Fallacies and Pitfalls \\
                 Concluding Remarks \\
                 Historical Perspective and References \\
                 Exercises \\
                 Instruction Set Principles and Examples \\
                 Introduction \\
                 Classifying Instruction Set Architectures \\
                 Memory Addressing \\
                 Addressing Modes for Signal Processing \\
                 Type and Size of Operands \\
                 Operands for Media and Signal Processing \\
                 Operations in the Instruction Set \\
                 Operations for Media and Signal Processing \\
                 Instructions for Control Flow \\
                 Encoding an Instruction Set \\
                 Crosscutting Issues: The Role of Compilers \\
                 Putting It All Together: The MIPS Architecture \\
                 Another View: The Trimedia TM32 CPU \\
                 Fallacies and Pitfalls \\
                 Concluding Remarks \\
                 Historical Perspective and References \\
                 Exercises \\
                 Instruction-Level Parallelism and its Dynamic
                 Exploitation \\
                 Instruction-Level Parallelism: Concepts and Challenges
                 \\
                 Overcoming Data Hazards with Dynamic Scheduling \\
                 Dynamic Scheduling: Examples and the Algorithm \\
                 Reducing Branch Costs with Dynamic Hardware Prediction
                 \\
                 High Performance Instruction Delivery \\
                 Taking Advantage of More ILP with Multiple Issue \\
                 Hardware Based Speculation \\
                 Studies of the Limitations of ILP \\
                 Limitations on ILP for Realizable Processors \\
                 Putting It All Together: The P6 Microarchitecture \\
                 Another View: Thread Level Parallelism \\
                 Crosscutting Issues: Using an ILP Datapath to Exploit
                 TLP \\
                 Fallacies and Pitfalls \\
                 Concluding Remarks \\
                 Historical Perspective and References \\
                 Exercises \\
                 Exploiting Instruction Level Parallelism with Software
                 Approaches \\
                 Basic Compiler Techniques for Exposing ILP \\
                 Static Branch Prediction \\
                 Static Multiple Issue: the VLIW Approach \\
                 Advanced Compiler Support for Exposing and Exploiting
                 ILP \\
                 Hardware Support for Exposing More Parallelism at
                 Compile-Time \\
                 Crosscutting Issues \\
                 Putting It All Together: The Intel IA-64 Architecture
                 and Itanium Processor \\
                 Another View: ILP in the Embedded and Mobile Markets
                 \\
                 Fallacies and Pitfalls \\
                 Concluding Remarks \\
                 Historical Perspective and References \\
                 Exercises \\
                 Memory-Hierarchy Design \\
                 Introduction \\
                 Review of the ABCs of Caches \\
                 Cache Performance \\
                 Reducing Cache Miss Penalty \\
                 Reducing Miss Rate \\
                 Reducing Cache Miss Penalty or Miss Rate via
                 Parallelism \\
                 Reducing Hit Time \\
                 Main Memory and Organizations for Improving Performance
                 \\
                 Memory Technology \\
                 Virtual Memory \\
                 Protection and Examples of Virtual Memory \\
                 Crosscutting Issues in the Design of Memory Hierarchies
                 \\
                 Putting It All Together: Alpha 21264 Memory Hierarchy
                 \\
                 Another View: The Emotion Engine of the Sony
                 Playstation 2 \\
                 Another View: The Sun Fire 6800 Server \\
                 Fallacies and Pitfalls \\
                 Concluding Remarks \\
                 Historical Perspective and References \\
                 Exercises \\
                 Multiprocessors and Thread-Level Parallelism \\
                 Introduction \\
                 Characteristics of Application Domains \\
                 Symmetric Shared-Memory Architectures \\
                 Performance of Symmetric Shared-Memory Multiprocessors
                 \\
                 Distributed Shared-Memory Architectures \\
                 Performance of Distributed Shared-Memory
                 Multiprocessors \\
                 Synchronization \\
                 Models of Memory Consistency: An Introduction \\
                 Multithreading: Exploiting Thread-Level Parallelism
                 within a Processor \\
                 Crosscutting Issues \\
                 Putting It All Together: Sun's Wildfire Prototype \\
                 Another View: Multithreading in a Commercial Server \\
                 Another View: Embedded Multiprocessors \\
                 Fallacies and Pitfalls \\
                 Concluding Remarks \\
                 Historical Perspective and References \\
                 Exercises",
}

@Proceedings{IEE:1990:ICV,
  editor =       "{IEE}",
  booktitle =    "{IEE} Colloquium on {`VLSI} Signal Processing
                 Architectures' (Digest No.95)",
  title =        "{IEE} Colloquium on `{VLSI} Signal Processing
                 Architectures' (Digest No.95)",
  publisher =    "IEE",
  address =      "London, UK",
  pages =        "66",
  year =         "1990",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 09:05:00 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  confdate =     "31 May 1990",
  conflocation = "London, UK",
  pubcountry =   "UK",
}

@Proceedings{IEEE:1990:MMM,
  editor =       "{IEEE}",
  booktitle =    "{MICRO 23}: microprogramming and microarchitecture:
                 23rd Annual workshop and symposium: Selected papers",
  title =        "{MICRO} 23: microprogramming and microarchitecture:
                 23rd Annual workshop and symposium: Selected papers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "x + 299",
  year =         "1990",
  ISBN =         "0-8186-2124-9",
  ISBN-13 =      "978-0-8186-2124-6",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 09:17:36 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog no. 90TH0341-8.",
  acknowledgement = ack-nhfb,
  confdate =     "27-29 Nov. 1990",
  conflocation = "Orlando, FL, USA",
  confsponsor =  "IEEE; ACM",
}

@Proceedings{IEEE:1990:PII,
  key =          "IEEE ICCD '90",
  booktitle =    "Proceedings: 1990 {IEEE} International Conference on
                 Computer Design: {VLSI} in Computers and Processors:
                 {ICCD} '90, Hyatt Regency Cambridge, Cambridge,
                 Massachusetts, September 17--19, 1990",
  title =        "Proceedings: 1990 {IEEE} International Conference on
                 Computer Design: {VLSI} in Computers and Processors:
                 {ICCD} '90, Hyatt Regency Cambridge, Cambridge,
                 Massachusetts, September 17--19, 1990",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xx + 477",
  year =         "1990",
  ISBN =         "0-8186-9079-8 (case), 0-8186-6079-1 (microfiche),
                 0-8186-2079-X (paper)",
  ISBN-13 =      "978-0-8186-9079-2 (case), 978-0-8186-6079-5
                 (microfiche), 978-0-8186-2079-9 (paper)",
  LCCN =         "TK 7888.4 I23 1990",
  bibdate =      "Wed Sep 07 23:34:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Proceedings{Mason:1990:AAI,
  editor =       "J. C. Mason and M. G. Cox",
  booktitle =    "{Algorithms for approximation II: based on the
                 proceedings of the Second International Conference on
                 Algorithms for Approximation, held at Royal Military
                 College of Science, Shrivenham, July 1988}",
  title =        "{Algorithms for approximation II: based on the
                 proceedings of the Second International Conference on
                 Algorithms for Approximation, held at Royal Military
                 College of Science, Shrivenham, July 1988}",
  publisher =    pub-CHAPMAN-HALL,
  address =      pub-CHAPMAN-HALL:adr,
  pages =        "514",
  year =         "1990",
  ISBN =         "0-412-34580-3",
  ISBN-13 =      "978-0-412-34580-7",
  LCCN =         "QA221 .I54 1988",
  bibdate =      "Thu Sep 01 23:55:44 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/grosse-eric.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/p/powell-m-j-d.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  meetingname =  "International Conference on Algorithms for
                 Approximation (2nd: 1988: Royal Military College of
                 Science, Shrivenham, England)",
  subject =      "Approximation theory; Data processing; Congresses",
  tableofcontents = "Part One: Development of Algorithms / 1 \\
                 1. Spline Approximation / 3 \\
                 E. Arge, M. Dcehlen, T. Lyche and K. Morken /
                 Constrained spline approximation of functions and data
                 based on constrained knot removal / 4 \\
                 G. T. Anthony and M. G. Cox / Near real-time spline
                 fitting of long sequences of uniformly-spaced data / 21
                 \\
                 M. Bozzini and F. de Tisi / An algorithm for knot
                 location in bivariate least squares spline
                 approximation / 30 \\
                 M. G. Cox, P. M. Harris and H. M. Jones / A knot
                 placement strategy for least squares spline fitting
                 based on the use of local polynomial approximations /
                 37 \\
                 G. Opfer / An algorithm for nonlinear splines with
                 non-negativity constraints / 46 \\
                 C. Potier and C. Vercken / Spline curve fitting of
                 digitized contours / 54 \\
                 C. Rabut / A B-spline approximation algorithm for
                 quasi-interpolation or filtering / 62 \\
                 P. W. Smith / On knots and nodes for spline
                 interpolation / 72 \\
                 2. Polynomial and Piecewise Polynomial Approximation /
                 79 \\
                 W. Dahmen / A basis for certain spaces of multivariate
                 polynomials and exponentials / 80 \\
                 F. N. Fritschi / Monotone piecewise cubic data fitting
                 / 99 \\
                 M. Heilmann and M. W. M{\"u}ller / Direct and converse
                 results on simultaneous approximation by the method of
                 Bernstein--Durrmeyer operators / 107 \\
                 A. Iserles, P. E. Koch, S. P. N{\o}rsett and J. M.
                 Sanz-Serna / Orthogonality and approximation in a
                 Sobolev space / 117 \\
                 M. A. Lachance / Piecewise polynomial approximation of
                 polynomial curves / 125 \\
                 E. Quak and L. L. Schumaker / Calculation of the energy
                 of a piecewise polynomial surface / 134 \\
                 3. Interpolation / 145 \\
                 M. D. Buhmann and M. J. D. Powell / Radial basis
                 function interpolation on an infinite regular grid /
                 146 \\
                 L. Brutman / The Fourier operator of even order and its
                 application to an extremum problem in interpolation /
                 170 \\
                 N. Dyn and A. Ron / On multivariate polynomial
                 interpolation / 177 \\
                 N. Dyn, D. Levin and S. Rippen / Algorithms for the
                 construction of data dependent triangulations / 185 \\
                 C. Rademacher and K. Scherer / Algorithms for computing
                 best parametric cubic interpolation / 193 \\
                 4. Smoothing and Constraint Methods / 209 \\
                 M. Von Golitschek and L. L. Schumaker / Data fitting by
                 penalized least squares / 210 \\
                 K. W. Bosworth / A semiinfinite programming algorithm
                 for constrained best approximation / 228 \\
                 M. Bozzini and L. Lenarduzzi / Inference region for a
                 method of local approximation by using the residuals /
                 236 \\
                 5. Complex Approximation / 245 \\
                 G. A. Watson / Numerical methods for Chebyshev
                 approximation of complex-valued functions / 246 \\
                 P. T. P. Tang / A fast algorithm for linear complex
                 Chebyshev approximation / 265 \\
                 Part Two: Applications / 275 \\
                 6. Computer Aided Design and Geometric Modelling / 277
                 \\
                 N. Dyn, J. A. Gregory and D. Levin / Uniform
                 subdivision algorithms for curves and surfaces / 278
                 \\
                 T. B. Boffey, M. G. Cox, L. M. Delves and C. J.
                 Pursglove / Approximation by spheres / 296 \\
                 T. A. Foley / Interpolation of scattered data on a
                 spherical domain / 303 \\
                 A. B. Forbes / Least squares best fit geometric
                 elements / 311 \\
                 W. Freeden and J. C. Mason / Uniform piecewise
                 approximation on the sphere / 320 \\
                 7. Applications in Numerical Analysis / 335 \\
                 L. N. Trefethen / Approximation theory and numerical
                 linear algebra / 336 \\
                 M. Frontini, G. Rodriguez and S. Seatzu / An algorithm
                 for computing minimum norm solutions of the finite
                 moment problem / 361 \\
                 R. H. J. Gmelig Meyling / Numerical solution of the
                 biharmonic equation using different types of bivariate
                 spline functions / 369 \\
                 G. O. Olaofe / Quadrature solution of integral
                 equations: a uniform treatment of Fredholm and Volterra
                 equations / 377 \\
                 G. Walz / Increasing the convergence modulus of an
                 asymptotic expansion: an algorithm for numerical
                 differentiation / 387 \\
                 J. Williams / Approximation and parameter estimation in
                 ordinary differential equations / 395 \\
                 8. Applications in Other Disciplines / 405 \\
                 C. Zala and I. Barrodale / Applications of discrete
                 $L_1$ methods in science and engineering / 406 \\
                 J. C. Mason, A. E. Trefethen and S. J. Wilde /
                 Constrained complex approximation algorithms in
                 communication engineering / 424 \\
                 R. W. Allen and J. G. Metcalfe / Integration of
                 absolute amplitude from a decibel B-spline fit / 449
                 \\
                 M. G. Cox and H. M. Jones / A nonlinear least squares
                 data fitting problem arising in microwave measurement /
                 458 \\
                 J. C. Mason and S. J. Wilde / A complex minimax
                 algorithm for phase-only adaptation in antenna arrays /
                 466 \\
                 Part Three: Catalogue of Algorithms / 477 \\
                 E. Grosse / A catalogue of algorithms for approximation
                 / 479",
}

@Book{Patterson:1990:CAQ,
  author =       "David A. Patterson and John L. Hennessy",
  booktitle =    "Computer Architecture: a Quantitative Approach",
  title =        "Computer Architecture: a Quantitative Approach",
  publisher =    pub-MORGAN-KAUFMANN,
  address =      pub-MORGAN-KAUFMANN:adr,
  pages =        "xxviii + 594",
  year =         "1990",
  ISBN =         "1-55860-069-8, 1-55880-169-8",
  ISBN-13 =      "978-1-55860-069-0, 978-1-55880-169-1",
  LCCN =         "QA76.9.A73 P377 1990",
  bibdate =      "Mon Jan 31 08:47:46 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/microchip.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "Fundamentals of Computer Design \\
                 Introduction \\
                 The Changing Face of Computing and the Task of the
                 Computer Designer \\
                 Technology Trends \\
                 Cost, Price, and their Trends \\
                 Measuring and Reporting Performance \\
                 Quantitative Principles of Computer Design \\
                 Putting It All Together: Performance and
                 Price-Performance \\
                 Another View: Power Consumption and Efficiency as the
                 Metric \\
                 Fallacies and Pitfalls \\
                 Concluding Remarks \\
                 Historical Perspective and References \\
                 Exercises \\
                 Instruction Set Principles and Examples \\
                 Introduction \\
                 Classifying Instruction Set Architectures \\
                 Memory Addressing \\
                 Addressing Modes for Signal Processing \\
                 Type and Size of Operands \\
                 Operands for Media and Signal Processing \\
                 Operations in the Instruction Set \\
                 Operations for Media and Signal Processing \\
                 Instructions for Control Flow \\
                 Encoding an Instruction Set \\
                 Crosscutting Issues: The Role of Compilers \\
                 Putting It All Together: The MIPS Architecture \\
                 Another View: The Trimedia TM32 CPU \\
                 Fallacies and Pitfalls \\
                 Concluding Remarks \\
                 Historical Perspective and References \\
                 Exercises \\
                 Instruction-Level Parallelism and its Dynamic
                 Exploitation \\
                 Instruction-Level Parallelism: Concepts and Challenges
                 \\
                 Overcoming Data Hazards with Dynamic Scheduling \\
                 Dynamic Scheduling: Examples and the Algorithm \\
                 Reducing Branch Costs with Dynamic Hardware Prediction
                 \\
                 High Performance Instruction Delivery \\
                 Taking Advantage of More ILP with Multiple Issue \\
                 Hardware Based Speculation \\
                 Studies of the Limitations of ILP \\
                 Limitations on ILP for Realizable Processors \\
                 Putting It All Together: The P6 Microarchitecture \\
                 Another View: Thread Level Parallelism \\
                 Crosscutting Issues: Using an ILP Datapath to Exploit
                 TLP \\
                 Fallacies and Pitfalls \\
                 Concluding Remarks \\
                 Historical Perspective and References \\
                 Exercises \\
                 Exploiting Instruction Level Parallelism with Software
                 Approaches \\
                 Basic Compiler Techniques for Exposing ILP \\
                 Static Branch Prediction \\
                 Static Multiple Issue: the VLIW Approach \\
                 Advanced Compiler Support for Exposing and Exploiting
                 ILP \\
                 Hardware Support for Exposing More Parallelism at
                 Compile-Time \\
                 Crosscutting Issues \\
                 Putting It All Together: The Intel IA-64 Architecture
                 and Itanium Processor \\
                 Another View: ILP in the Embedded and Mobile Markets
                 \\
                 Fallacies and Pitfalls \\
                 Concluding Remarks \\
                 Historical Perspective and References \\
                 Exercises \\
                 Memory-Hierarchy Design \\
                 Introduction \\
                 Review of the ABCs of Caches \\
                 Cache Performance \\
                 Reducing Cache Miss Penalty \\
                 Reducing Miss Rate \\
                 Reducing Cache Miss Penalty or Miss Rate via
                 Parallelism \\
                 Reducing Hit Time \\
                 Main Memory and Organizations for Improving Performance
                 \\
                 Memory Technology \\
                 Virtual Memory \\
                 Protection and Examples of Virtual Memory \\
                 Crosscutting Issues in the Design of Memory Hierarchies
                 \\
                 Putting It All Together: Alpha 21264 Memory Hierarchy
                 \\
                 Another View: The Emotion Engine of the Sony
                 Playstation 2 \\
                 Another View: The Sun Fire 6800 Server \\
                 Fallacies and Pitfalls \\
                 Concluding Remarks \\
                 Historical Perspective and References \\
                 Exercises \\
                 Multiprocessors and Thread-Level Parallelism \\
                 Introduction \\
                 Characteristics of Application Domains \\
                 Symmetric Shared-Memory Architectures \\
                 Performance of Symmetric Shared-Memory Multiprocessors
                 \\
                 Distributed Shared-Memory Architectures \\
                 Performance of Distributed Shared-Memory
                 Multiprocessors \\
                 Synchronization \\
                 Models of Memory Consistency: An Introduction \\
                 Multithreading: Exploiting Thread-Level Parallelism
                 within a Processor \\
                 Crosscutting Issues \\
                 Putting It All Together: Sun's Wildfire Prototype \\
                 Another View: Multithreading in a Commercial Server \\
                 Another View: Embedded Multiprocessors \\
                 Fallacies and Pitfalls \\
                 Concluding Remarks \\
                 Historical Perspective and References \\
                 Exercises",
}

@Proceedings{SHARE:1990:PSE,
  editor =       "{SHARE}",
  booktitle =    "Proceedings {SHARE} Europe Spring Meeting",
  title =        "Proceedings {SHARE} Europe Spring Meeting",
  publisher =    "SHARE Europe (SEAS)",
  address =      "Geneva, Switzerland",
  pages =        "969",
  year =         "1990",
  ISBN =         "????",
  ISBN-13 =      "????",
  ISSN =         "0255-6464",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 09:07:06 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "2 vol.",
  acknowledgement = ack-nhfb,
  confdate =     "2-6 April 1990",
  conflocation = "Berlin, Germany",
  pubcountry =   "Switzerland",
}

@Book{Swartzlander:1990:CAa,
  author =       "Earl E. {Swartzlander, Jr.}",
  booktitle =    "Computer Arithmetic",
  title =        "Computer Arithmetic",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiii + 378",
  year =         "1990",
  ISBN =         "0-8186-8931-5 (hardcover), 0-8186-5931-9
                 (microfiche)",
  ISBN-13 =      "978-0-8186-8931-4 (hardcover), 978-0-8186-5931-7
                 (microfiche)",
  LCCN =         "QA76.6 .C633 1990",
  bibdate =      "Wed Dec 15 10:43:03 1993",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ibmsysj.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  series =       "IEEE Computer Society Press tutorial",
  acknowledgement = ack-nj,
  keywords =     "Computer arithmetic; Electronic digital computers ---
                 Programming; Floating-point arithmetic.",
  remark =       "Vol. 1 is a reprint. Originally published:
                 Stroudsburg, Pa.: Dowden, Hutchinson and Ross, c1980.
                 Originally published in series: Benchmark papers in
                 electrical engineering and computer science; 21. Vol 2
                 is a sequel to the earlier collection. Vol. 1: 2nd
                 ed.",
  tableofcontents = "Series Editor's Foreword / v \\
                 Preface / vii \\
                 Contents by Author / xiii \\
                 Introduction / 1 \\
                 Part I: Overview / 6 \\
                 Editor's / Comments on Papers 1 and 2 / 7 \\
                 1: Shaw, R. F.: Arithmetic Operations in a Binary
                 Computer, Rev. Sci. Instrum. 21:687--693 (1950) / 7 \\
                 2: MacSorley, O. L: High-Speed Arithmetic in Binary
                 Computers, IRE Proc. 49:67--91 (1961) / 14 \\
                 Part II: Addition and Subtraction \\
                 Editor's Comments on Papers 3 Through 10 / 40 \\
                 3: Gilchrist, B., J. H. Pomerene, and S. Y. Wong: Fast
                 Carry Logic for Digital Computers, IRE Trans. Electron.
                 Comput. EC-4:133--136 (1955) / 43 \\
                 4: Weinberger, A., and J. L. Smith: A Logic for
                 High-Speed Addition, Nat. Bur. Stand. Circ. 591, pp.
                 3--12 (1958) / 47 \\
                 5: Sklansky J.: Conditional-Sum Addition Logic, IRE
                 Trans. Electron. Comput. EC-9:226--231 (1960) / 57 \\
                 6: Sklansky J.: An Evaluation of Several Two-Summand
                 Binary Adders / IRE Trans. Electron. Comput.
                 EC-9:213--226 (1960) / 63 \\
                 7: Svoboda, A.: Adder with Distributed Control, IEEE
                 Trans. Comput. C-19: 749--751 (1970) / 77 \\
                 8: Ho, I. T., and T. C. Chen: Multiple Addition by
                 Residue Threshold Functions and Their Representation by
                 Array Logic, IEEE Trans. Comput. C-22:762--767 (1973) /
                 80 \\
                 9: Foster, C C,, and F. D. Stockton: Counting
                 Responders in an Associative Memory, IEEE Trans.
                 Comput. C-20:1580--1583 (1971) / 86 \\
                 10: Swartzlander, E. E., Jr.: Parallel Counters, IEEE
                 Trans. Comput. C-22:1021--1024 (1973) / 90 \\
                 Editor's Comments on Papers 11 Through 20 / 96 \\
                 11: Booth, A, D.: A Signed Binary Multiplication
                 Technique, Q. J. Mech. Appl. Math. 4:236--240 (1951) /
                 100 \\
                 12: Ghest, C.: Multiplying Made Easy for Digital
                 Assemblies, Electronics 44:56--61 (Nov. 22, 1971) / 105
                 \\
                 13: Chen, T. C.: A Binary Multiplication Scheme Based
                 on Squaring, IEEE Trans. Comput. C-20:678--680 (1971) /
                 111 \\
                 14: Wallace, C. S.: A Suggestion for a Fast Multiplier,
                 IEEE Trans. Electron. Comput. EC-13:14--17 (1964) / 114
                 \\
                 15: Dadda, L.: Some Schemes for Parallel Multipliers,
                 Alta Freq. 34:349--356 (1965) / 118 \\
                 16: Dadda, L.: On Parallel Digital Multipliers, Alta
                 Freq. 45:574--580 (1976) / 126 \\
                 17: Stenzel, W. J., W. J. Kubitz, and G. H. Garcia: A
                 Compact High-Speed Parallel Multiplication Scheme, IEEE
                 Trans. Comput. C-26:948--957 (1977) / 133 \\
                 18A: Baugh, C. R., and B. A, Wooley: A Two's Complement
                 Parallel Array Multiplication Algorithm, IEEE Trans.
                 Comput. C-22:1045--1047 (1973) / 143 \\
                 18B: Blankenship, P. E.: Comments on ``A Two's
                 Complement Parallel Array Multiplication Algorithm'',
                 IEEE Trans. Comput. C-23:1327 (1974) / 146 \\
                 19: Swartzlander, E. E., Jr.: The Quasi-Serial
                 Multiplier, IEEE Trans. Comput. C-22:317--321 (1973) /
                 147 \\
                 20: McDaneld, T. G., and R. K. Guha: The Two's
                 Complement Quasi-Serial Multiplier, IEEE Trans. Comput.
                 C-24:1233--1235 (1975) / 152 \\
                 Part IV: Division \\
                 Editor's Comments on Papers 21 Through 26 / 156 \\
                 21: Robertson, J. E.: A New Class of Digital Division
                 Methods, IRE Trans. Electron. Comput. EC-7:218--222
                 (1958) / 159 \\
                 22: Wilson, J. B., and R. S. Ledley: An Algorithm for
                 Rapid Binary Division, IRE Trans. Electron. Comput.
                 EC-10:662--670 (1961) / 164 \\
                 23: Atkins, D. E.: Higher-Radix Division Using
                 Estimates of the Divisor and Partial Remainders, IEEE
                 Trans. Comput. C-17:925--934 (1968) / 173 \\
                 24: Svoboda, A.: An Algorithm for Division, Inf.
                 Process. Mach. 9:25--32 (1963) / 183 \\
                 25: Ferrari, D.: A Division Method Using a Parallel
                 Multiplier, IEEE Trans. Electron. Comput.
                 EC-16:224--226 (1967) / 191 \\
                 26: Flynn, M. J.: On Division by Functional Iteration,
                 IEEE Trans. Comput. C-19:702--706 (1970) / 194 \\
                 Part V: Logarithms \\
                 Editor's Comments on Papers 27 Through 31 / 200 \\
                 27: Combet, M., H. van Zonneveld, and L. Verbeek:
                 Computation of the Base Two Logarithm of Binary
                 Numbers, IEEE Trans. Electron. Comput. EC-14:863--867
                 (1965) / 202 \\
                 28: Marino, D.: New Algorithms for the Approximate
                 Evaluation in Hardware of Binary Logarithms and
                 Elementary Functions IEEE Trans. Comput. C-21:
                 1416--1421 (1972) / 207 \\
                 29: Majithia J. C., and D. Levan: A Note on Base-2
                 Logarithm Computations, IEEE Proc. 61:1519--1520 (1973)
                 / 213 \\
                 30: Kingsbury N. G., and P. J. W. Rayner: Digital
                 Filtering Using Logarithmic Arithmetic, Electron. Lett.
                 7:56--58 (1971) / 215 \\
                 31: Swartzlander E. E., Jr., and A. G. Alexopoulos: The
                 Sign/Logarithm Number System, IEEE Trans. Comput.
                 C-24:1238--1242 (1975) / 218 \\
                 Part VI: Elementary Functions \\
                 Editor's Comments on Papers 32 Through 37 / 224 \\
                 32: Volder, J. E.: The CORDIC Trigonometric Computing
                 Technique, IRE Trans. Electron. Comput. EC-8:330--334
                 (1959) / 226 \\
                 33: Specker W. H.: A Class of Algorithms for Ln $x$,
                 Exp $x$, Sin $x$, Cos $x$, Tan$^{-1}$ $x$, and
                 Cot$^{-1}$ $x$, IEEE Trans. Electron. Comput.
                 EC-14:85--86 (1965) / 231 \\
                 34: Linhardt, R. J., and H. S. Muller: Digit-by-Digit
                 Transcendental-Function Computation RCA Rev. 30:20~247
                 (1969) / 233 \\
                 35: Walther J. S.: A Unified Algorithm for Elementary
                 Functions, Spring Joint Computer Conf., 1971, Proc.,
                 pp. 379--385 / 272 \\
                 36: Ramamoorthy, C. V., J. R. Goodman, and K. H. Kim:
                 Some Properties of Iterative Square-Rooting Methods
                 Using High-Speed Multiplication, IEEE Trans. Comput.
                 C-21: 837--847 (1972) / 279 \\
                 37: Ercegovac M. D.: Radix-16 Evaluation of Certain
                 Elementary Functions, IEEE Trans. Comput. C-22:561--566
                 (1973) / 290 \\
                 Part VII: Floating-Point Arithmetic \\
                 Editor's Comments on Papers 38 Through 42 / 298 \\
                 38: Hamming, R. W.: On the Distribution of Numbers,
                 Bell Syst. Tech. J. 49:1609--1625 (1970) / 300 \\
                 39: Sweeney D. W.: An Analysis of Floating-Point
                 Addition, IBM Syst. J. 4:31--42 (1965) / 317 \\
                 40: Anderson, S. F., J. G. Earler, R. E. Goldschmidt,
                 and D. M. Powers: The IBM System/360 Model 91:
                 Floating-Point Execution Unit, IBM J. Res. Dev.
                 11:34--53 (1967) / 329 \\
                 41: Gosling, J. B.: Design of Large High-Speed Floating
                 Point Arithmetic Units, IEE Proc. 118:493--498 (1971) /
                 349 \\
                 42: Kuck, D. J., D. S. Parker, Jr., and A. H. Sameh:
                 Analysis of Rounding Methods in Floating-Point
                 Arithmetic, IEEE Trans. Comput. C-26:643--650 (1977) /
                 355 \\
                 Bibliography / 363 \\
                 Author Citation Index / 373 \\
                 Subject Index / 377 \\
                 About the Editor / 379",
}

@Book{Swartzlander:1990:CAb,
  author =       "Earl E. {Swartzlander, Jr.}",
  booktitle =    "Computer Arithmetic",
  title =        "Computer Arithmetic",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "ix + 396",
  year =         "1990",
  ISBN =         "0-8186-8945-5",
  ISBN-13 =      "978-0-8186-8945-1",
  LCCN =         "QA76.9 .C62C66 1990",
  bibdate =      "Wed Dec 15 10:43:03 1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/hamming-richard-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "This is part of a two-volume collection of influential
                 papers on the design of computer arithmetic. See also
                 \cite{Swartzlander:1990:CAa}.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Preface / v \\
                 Chapter 1: Overview / E. E. Swartzlander, Jr. / 1 \\
                 Chapter 2: Error Tolerant Arithmetic / 15 \\
                 Error Detecting and Error Correcting Codes / R. W.
                 Hamming (Bell System Technical Journal, 1950, Pages
                 147--160) / 16 \\
                 Generalized Parity Checking / H. L. Garner (IRE
                 Transactions on Electronic Computers, 1958, Pages
                 207--213) / 30 \\
                 Error Checking Logic for Arithmetic Type Operations of
                 a Processor / T. R. N. Rao (IEEE Transactions on
                 Computers, 1968, Pages 845--849) / 37 \\
                 Arithmetic Algorithms for Error-Coded Operands / A.
                 Avizienis (IEEE Transactions on Computers, 1973, Pages
                 567--572) / 42 \\
                 Error Detection and Correction for Addition and
                 Subtraction, through Use of Higher Radix Extensions of
                 Hamming Codes / J. E. Robertson (Proceedings 8th
                 Symposium on Computer Arithmetic, 1987, Pages 226--229)
                 / 48 \\
                 Chapter 3: On-Line Arithmetic / 53 \\
                 Signed-Digit Number Representations for Fast Parallel
                 Arithmetic / A. Avizienis (IRE Transactions on
                 Electronic Computers, 1961, Pages 389---400) / 54 \\
                 On-Line Arithmetic: A Design Methodology and
                 Applications in Digital Signal Processing / M. D.
                 Ercegovac and T. Lang (VLSI Signal Processing, III,
                 1988, Pages 252--263) / 66 \\
                 On-Line Algorithms for Division and Multiplication / K.
                 S. Trivedi and M. D. Ercegovac (IEEE Transactions on
                 Computers, 1977, Pages 681---687) / 78 \\
                 Error Analysis of Certain Floating-point On-Line
                 Algorithms / O. Watanuki and M. D. Ercegovac (IEEE
                 Transactions on Computers, 1983, Pages 352--358) / 85
                 \\
                 Improved Normalization Results for Digit On-Line
                 Arithmetic / R. J. Zaccone and J. L. Barlow
                 (Proceedings 7th Symposium on Computer Arithmetic,
                 1985, Pages 20--27) / 92 \\
                 Fully Digit On-Line Networks / M. J. Irwin and R. M.
                 Owens (IEEE Transactions on Computers, 1983, Pages
                 402---406) / 100 \\
                 On-Line Scheme for Computing Rotation Factors / M. D.
                 Ercegovac and T. Lang (Journal of Parallel and
                 Distributed Computing, 1988, Pages 209--227) / 104 \\
                 On-the-Fly Conversion of Redundant into Conventional
                 Representations / M. D. Ercegovac and T. Lang (IEEE
                 Transactions on Computers, 1987, Pages 895--897) / 123
                 \\
                 Chapter 4: VLSI Adder Implementations / 127 \\
                 Time-Component Complexity of Two Approaches to
                 Multioperand Binary Addition / D. E. Atkins and S. Ong
                 (IEEE Transactions on Computers, 1979, Pages 918--926)
                 / 128 \\
                 Some Optimal Schemes for ALU Implementation in VLSI
                 Technology / V. G. Oklobdzija and E. R. Barnes
                 (Proceedings 7th Symposium on Computer Arithmetic,
                 1985, Pages 2--8) / 137 \\
                 A Regular Layout for Parallel Adders / R. P. Brent and
                 H. T. Kung (IEEE Transactions on Computers, 1982, Pages
                 260--264) / 144 \\
                 An Area-Time Efficient NMOS Adder / M. A. Bayoumi, G.
                 A. Jullien, and W. C. Miller (Integration, the VLSI
                 Journal, 1983, Pages 317--334) / 148 \\
                 Regular, Area-Time Efficient Carry-Lookahead Adders /
                 T.-F. Ngai, M. J. Irwin, and S. Rawat (Journal of
                 Parallel and Distributed Computing, 1986, Pages
                 92--105) / 166 \\
                 Efficient Use of Time and Hardware Redundancy for
                 Concurrent Error Detection in a 32-Bit VLSI Adder / B.
                 W. Johnson, J. H. Aylor, and H. H. Hana (IEEE Journal
                 of Solid-State Circuits, 1988, Pages 208--215) / 180
                 \\
                 Chapter 5: VLSI Multiplier Implementations / 189 \\
                 A Monolithic $16 \times 16$ Digital Multiplier / G. W.
                 McIver, R. W. Miller, and T. G. O'Shaughnessy (IEEE
                 International Solid-State Circuits Conference Digest of
                 Technical Papers, 1974, Pages 231--233) / 190 \\
                 Optimization of One-Bit Full Adders Embedded in Regular
                 Structures / K. Iwano and K. Steiglitz (IEEE
                 Transactions on Acoustics, Speech, and Signal
                 Processing, 1986, Pages 1289--1300) / 193 \\
                 A VLSI Layout for a Pipelined Dadda Multiplier / P. R.
                 Cappello and K. Steiglitz (ACM Transactions on Computer
                 Systems, 1983, Pages 157--174) / 205 \\
                 A Very Fast Multiplication Algorithm for VLSI
                 Implementation / J. Vuillemin (Integration, the VLSI
                 Journal, 1983, Pages 39--52) / 223 \\
                 A High-Speed Multiplier Using a Redundant Binary Adder
                 Tree / Y. Harata, Y. Nakamura, H. Nagase, M. Takigawa,
                 and N. Takagi (IEEE Journal of Solid-State Circuits,
                 1987, Pages 28--34) / 237 \\
                 A Sub-10-ns $16 \times 16$ Multiplier Using 0.6-$\mu$m
                 CMOS Technology / Y. Oowaaki, K. Numata, K. Tsuchiya,
                 K. Tsuda, H. Takato, N. Takenouchi, A. Nitayama, T.
                 Kobayashi, M. Chiba, S. Watanabe, K. Ohuchi, and A.
                 Rojo (IEEE Journal of Solid-State Circuits, 1987, Pages
                 762--767) / 244 \\
                 Chapter 6: Floating Point VLSI Chips / 251 \\
                 A High Performance Floating Point Coprocessor / G.
                 Wolrich, E. McLellan, L. Harada, J. Montanaro, and R.
                 A. J. Yodlowski (IEEE Journal of Solid-State Circuits,
                 1984, Pages 690--696) / 252 \\
                 64-Bit Monolithic Floating Point Processors / F. A.
                 Ware, W. H. McAllister, J. R. Carlson, D. K. Sun, and
                 R. J. Vlach (IEEE Journal of Solid-State Circuits,
                 1982, Pages 898--907) / 259 \\
                 A CMOS Floating Point Multiplier / M. Uya, K. Kaneko,
                 and J. Yasui (IEEE Journal of Solid-State Circuits,
                 1984, Pages 697--702) / 269 \\
                 A Single-Chip 80-Bit Floating Point Processor / K.
                 Takeda, F. Ishino, Y. Ito, R. Kasai, and T. Nakashima
                 (IEEE Journal of Solid-State Circuits, 1985, Pages
                 986--992) / 275 \\
                 VLSI Floating-Point Processors / J. Fandrianto and B.
                 Y. Woo (Proceedings 7th Symposium on Computer
                 Arithmetic, 1985, Pages 93--100) / 282 \\
                 Fast Multiply and Divide for a VLSI Floating-Point Unit
                 / B. K. Bose, L. Pei, G. S. Taylor, and D. A. Patterson
                 (Proceedings 8th Symposium on Computer Arithmetic,
                 1987, Pages 87--94) / 290 \\
                 Chapter 7: Number Representation / 299 \\
                 A Formalization of Floating-Point Numeric Base
                 Conversion / D. W. Matula (IEEE Transactions on
                 Computers, 1970, Pages 681--692) / 300 \\
                 Analysis of Proposals for the Floating-Point Standard /
                 W. J. Cody (Computer, March 1987, Pages 63--68) / 312
                 \\
                 CADAC: A Controlled-Precision Decimal Arithmetic Unit /
                 M. S. Cohen, T. E. Hull, and V. C. Hamacher (IEEE
                 Transactions on Computers, 1983, Pages 370--377) / 317
                 \\
                 Finite Precision Rational Arithmetic: Slash Number
                 Systems / D. W. Matula and P. Kornerup (IEEE
                 Transactions on Computers, 1985, Pages 3--18) / 325 \\
                 Finite Precision Lexicographic Continued Fraction
                 Number Systerns / P. Kornerup and D. W. Matula
                 (Proceedings 7th Symposium on Computer Arithmetic,
                 1985, Pages 207--214) / 341 \\
                 An Overflow\slash Underflow Free Floating Point
                 Representation of Numbers / S. Matsui and M. lri
                 (Journal of Information Processing, 1981, Pages
                 123--133) / 349 \\
                 A Closed Computer Arithmetic / F. W. J. Olver
                 (Proceedings 8th Symposium on Computer Arithmetic,
                 1987, Pages 139--143) / 360 \\
                 Bibliography / 365 \\
                 Index / 393 \\
                 About the Editor / 397",
}

@Proceedings{Ullrich:1990:CCA,
  editor =       "Christian Ullrich",
  booktitle =    "Contributions to Computer Arithmetic and
                 Self-Validating Numerical Methods. (Proceedings of
                 {SCAN 89}, held in Basel, Oct. 2--6, 1989)",
  title =        "Contributions to Computer Arithmetic and
                 Self-Validating Numerical Methods. (Proceedings of
                 {SCAN} 89, held in Basel, Oct. 2--6, 1989)",
  volume =       "7",
  publisher =    pub-BALTZER,
  address =      pub-BALTZER:adr,
  pages =        "526",
  year =         "1990",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 08:36:57 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "IMACS annals on computing and applied mathematics",
  acknowledgement = ack-nhfb,
  xxbooktitle =  "SCAN-89, International Symposium on Scientific
                 Computing, Computer Arithmetic, and Numeric Validation
                 [October 1989, Basel, Switzerland]",
}

@Proceedings{USENIX:1990:PWU,
  key =          "USENIX Winter '90",
  booktitle =    "Proceedings of the Winter 1990 {USENIX} Conference,
                 January 22--26, 1990, Washington, {DC}, {USA}",
  title =        "Proceedings of the Winter 1990 {USENIX} Conference,
                 January 22--26, 1990, Washington, {DC}, {USA}",
  publisher =    pub-USENIX,
  address =      pub-USENIX:adr,
  pages =        "xvi + 374",
  year =         "1990",
  LCCN =         "QA76.8.U65 U82 1990",
  bibdate =      "Thu Sep 15 18:50:55 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  xxISBN =       "(none)",
}

@Proceedings{Wescon:1990:WCR,
  editor =       "{Wescon}",
  booktitle =    "Wescon\slash 90 conference record, November 13--15,
                 1990, Anaheim, California",
  title =        "Wescon\slash 90 conference record, November 13--15,
                 1990, Anaheim, California",
  volume =       "34",
  publisher =    "Electronic Conventions Management",
  address =      "Los Angeles, CA, USA",
  pages =        "xiv + 802",
  year =         "1990",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 08:57:03 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Wescon conference record",
  acknowledgement = ack-nhfb,
  confdate =     "13-15 Nov. 1990",
  conflocation = "Anaheim, CA, USA",
  confsponsor =  "IEEE; ERA",
}

@Proceedings{ASEE:1991:CCW,
  editor =       "{ASEE}",
  booktitle =    "Challenges of a changing world: proceedings, 1991
                 Annual Conference, June 16--19, 1991, University of New
                 Orleans",
  title =        "Challenges of a changing world: proceedings, 1991
                 Annual Conference, June 16--19, 1991, University of New
                 Orleans",
  publisher =    "American Society for Engineering Education (ASEE)",
  address =      "Washington, DC, USA",
  pages =        "xxi + 2026",
  year =         "1991",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 09:34:59 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "2 vol.",
  acknowledgement = ack-nhfb,
  confdate =     "16-19 June 1991",
  conflocation = "New Orleans, LA, USA",
}

@Proceedings{Griewank:1991:ADA,
  editor =       "Andreas Griewank and George F. Corliss",
  booktitle =    "{Automatic differentiation of algorithms: theory,
                 implementation, and application. Proceedings of the
                 first SIAM Workshop on Automatic Differentiation, held
                 in Breckenridge, Colorado, January 6--8, 1991}",
  title =        "{Automatic differentiation of algorithms: theory,
                 implementation, and application. Proceedings of the
                 first SIAM Workshop on Automatic Differentiation, held
                 in Breckenridge, Colorado, January 6--8, 1991}",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "353",
  year =         "1991",
  ISBN =         "0-89871-284-x",
  ISBN-13 =      "978-0-89871-284-1",
  LCCN =         "QA304 1991",
  bibdate =      "Thu May 27 07:48:05 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.bibsys.no:2100/BIBSYS",
  acknowledgement = ack-nhfb,
  subject =      "differential calculus; data processing congresses",
}

@Proceedings{IEEE:1991:PFC,
  editor =       "{IEEE}",
  booktitle =    "Proceedings / Fourth {CSI/IEEE} International
                 Symposium on {VLSI} Design, New Delhi, India, January
                 4--8, 1991: digest of papers",
  title =        "Proceedings / Fourth {CSI}/{IEEE} International
                 Symposium on {VLSI} Design, New Delhi, India, January
                 4--8, 1991: digest of papers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 315",
  year =         "1991",
  ISBN =         "0-8186-2125-7",
  ISBN-13 =      "978-0-8186-2125-3",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 09:25:08 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog no. 91TH0340-0.",
  acknowledgement = ack-nhfb,
  confdate =     "4-8 Jan. 1991",
  conflocation = "New Delhi, India",
  confsponsor =  "IEEE; Comput. Soc. India",
}

@Proceedings{IEEE:1991:PIC,
  key =          "IEEE CICC '91",
  booktitle =    "Proceedings of the {IEEE} 1991 Custom Integrated
                 Circuits Conference: Town and Country Hotel, San Diego,
                 California, May 12--15, 1991",
  title =        "Proceedings of the {IEEE} 1991 Custom Integrated
                 Circuits Conference: Town and Country Hotel, San Diego,
                 California, May 12--15, 1991",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "various",
  year =         "1991",
  ISBN =         "0-7803-0016-5",
  ISBN-13 =      "978-0-7803-0016-3",
  LCCN =         "TK 7874 C87 1991",
  bibdate =      "Fri Dec 08 13:03:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Proceedings{IEEE:1991:PSA,
  editor =       "{IEEE}",
  booktitle =    "Proceedings, Supercomputing '91: Albuquerque, New
                 Mexico, November 18--22, 1991",
  title =        "Proceedings, Supercomputing '91: Albuquerque, New
                 Mexico, November 18--22, 1991",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xxiii + 917",
  year =         "1991",
  ISBN =         "0-8186-9158-1 (IEEE case), 0-8186-2158-3 (IEEE paper),
                 0-8186-6158-5 (IEEE microfiche), 0-89791-459-7 (ACM)",
  ISBN-13 =      "978-0-8186-9158-4 (IEEE case), 978-0-8186-2158-1 (IEEE
                 paper), 978-0-8186-6158-7 (IEEE microfiche),
                 978-0-89791-459-8 (ACM)",
  LCCN =         "QA76.5 .S894 1991",
  bibdate =      "Fri Aug 30 08:01:51 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 University of California MELVYL catalog.",
  note =         "ACM order number 415913. IEEE Computer Society Press
                 order number 2158. IEEE catalog number 91CH3058-5.",
  acknowledgement = ack-nhfb,
  classification = "C5440 (Multiprocessor systems and techniques); C5470
                 (Performance evaluation and testing); C6110P (Parallel
                 programming)",
  keywords =     "combinatorial algorithms; data dependence; distributed
                 memory code generation; high school environment;
                 latency tolerance; memory access; numerical algorithms;
                 parallel processing; parallel programming; performance
                 evaluation; performance tools; processor design;
                 program analysis; storage hierarchy optimization;
                 supercomputer benchmarks; supercomputer congresses;
                 supercomputing; system issues",
}

@Proceedings{IEEE:1991:VCA,
  key =          "ICASSP'91",
  booktitle =    "{VLSI} Cell Architecture and Application to Signal
                 Processing. {ICASSP 91}: 1991 International Conference
                 on Acoustics, Speech and Signal Processing, May 14--17,
                 1991, The Sheraton Centre Hotel and Towers, Toronto,
                 Ontario, Canada",
  title =        "{VLSI} Cell Architecture and Application to Signal
                 Processing. {ICASSP} 91: 1991 International Conference
                 on Acoustics, Speech and Signal Processing, May 14--17,
                 1991, The Sheraton Centre Hotel and Towers, Toronto,
                 Ontario, Canada",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "3732",
  year =         "1991",
  ISBN =         "0-7803-0003-3 (softbound), 0-7803-0004-1 (casebound),
                 0-7803-0005-X (microfiche)",
  ISBN-13 =      "978-0-7803-0003-3 (softbound), 978-0-7803-0004-0
                 (casebound), 978-0-7803-0005-7 (microfiche)",
  LCCN =         "TK 7882 S65 I16 1991",
  bibdate =      "Sat Dec 09 14:13:02 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Five volumes. IEEE catalog number 91CH2977-7.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Kaucher:1991:CAS,
  editor =       "Edgar W. Kaucher and S. M. (Svetoslav M.) Markov and
                 G. (Gunter) Mayer",
  booktitle =    "Computer Arithmetic, Scientific Computation and
                 Mathematical Modelling: Proceedings of the Second
                 International Conference on Computer Arithmetic,
                 Scientific Computation and Mathematical Modelling,
                 Albena, Bulgaria, September 24--28, 1990",
  title =        "Computer Arithmetic, Scientific Computation and
                 Mathematical Modelling: Proceedings of the Second
                 International Conference on Computer Arithmetic,
                 Scientific Computation and Mathematical Modelling,
                 Albena, Bulgaria, September 24--28, 1990",
  volume =       "12",
  publisher =    pub-BALTZER,
  address =      pub-BALTZER:adr,
  pages =        "498",
  year =         "1991",
  ISSN =         "1012-2435",
  LCCN =         "QA76.9.C62 I555 1990",
  bibdate =      "Thu Sep 15 20:51:47 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "IMACS Annals on Computing and Applied Mathematics",
  acknowledgement = ack-nhfb,
  confdate =     "24-28 Sept. 1990",
  conflocation = "Albena, Bulgaria",
  pubcountry =   "Switzerland",
  xxISBN =       "(none)",
}

@Proceedings{Koopman:1991:PST,
  editor =       "Philip J. {Koopman, Jr.}",
  booktitle =    "The proceedings of the second and third annual
                 workshops for the {ACM Special Interest Group on Forth:
                 SIGForth '90, February 16--18, 1990, Dallas, Texas
                 \ldots{} SIGForth '91, March 7--9, 1991, San Antonio,
                 Texas}",
  title =        "The proceedings of the second and third annual
                 workshops for the {ACM Special Interest Group on Forth:
                 SIGForth '90, February 16--18, 1990, Dallas, Texas
                 \ldots{} SIGForth '91, March 7--9, 1991, San Antonio,
                 Texas}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "ii + 134",
  year =         "1991",
  ISBN =         "0-89791-462-7",
  ISBN-13 =      "978-0-89791-462-8",
  LCCN =         "QA 76.73 F24 S53 1991",
  bibdate =      "Tue May 04 07:39:28 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "ACM order number 817911.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Kornerup:1991:PIS,
  editor =       "Peter Kornerup and David W. Matula",
  booktitle =    "{Proceedings: 10th IEEE Symposium on Computer
                 Arithmetic: June 26--28, 1991, Grenoble, France}",
  title =        "{Proceedings: 10th IEEE Symposium on Computer
                 Arithmetic: June 26--28, 1991, Grenoble, France}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiii + 282",
  year =         "1991",
  ISBN =         "0-8186-9151-4 (case), 0-8186-6151-8 (microfiche),
                 0-7803-0187-0 (library binding)",
  ISBN-13 =      "978-0-8186-9151-5 (case), 978-0-8186-6151-8
                 (microfiche), 978-0-7803-0187-0 (library binding)",
  LCCN =         "QA76.9.C62 S95 1991",
  bibdate =      "Thu Sep 01 23:18:52 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog no. 91CH3015-5.",
  acknowledgement = ack-nhfb,
  confdate =     "26-28 June 1991",
  conflocation = "Grenoble, France",
  confsponsor =  "IEEE; CNRS; IMAG",
  keywords =     "ARITH-10",
}

@Proceedings{Meyer:1991:CAP,
  editor =       "Kenneth R. (Kenneth Ray) Meyer and Dieter S. Schmidt",
  booktitle =    "{Computer aided proofs in analysis}",
  title =        "{Computer aided proofs in analysis}",
  volume =       "28",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "251",
  year =         "1991",
  DOI =          "https://doi.org/10.1007/978-1-4613-9092-3",
  ISBN =         "0-387-97426-1, 3-540-97426-1",
  ISBN-13 =      "978-0-387-97426-2, 978-3-540-97426-0",
  LCCN =         "QA614.58 .I52 1989; QA297 .C638 1991",
  bibdate =      "Thu Feb 23 06:54:26 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/macsyma.bib;
                 library.mit.edu:9909/mit01",
  series =       "The IMA volumes in mathematics and its applications",
  acknowledgement = ack-nhfb,
  keywords =     "Numerical analysis --- Data processing ---
                 Congresses.",
  remark =       "Proceedings of an IMA Participating Institutions (PI)
                 Conference held at the University of Cincinnati in
                 April 1989.",
  subject =      "Numerical analysis; Data processing; Congresses",
  tableofcontents = "The conversion of a high order programming language
                 from floating-point arithmetic to range arithmetic /
                 Oliver Aberth \\
                 Sylvester's form of the resultant and the
                 matrix-triangularization subresultant PRS method /
                 Alkiviadis G. Akritas \\
                 Computing the Tsirelson space norm / Johnnie W. Baker,
                 Oberta A. Slotterbeck and Richard Aron \\
                 Floating-point systems for theorem proving / G.
                 Bohlender, J. Wolff von Gudenberg and W. L. Miranker
                 \\
                 Computer algebra and indefinite integrals / Manuel
                 Bronstein \\
                 A computer-assisted approach to small-divisors problems
                 arising in Hamiltonian mechanics / Alessandra Celletti
                 and Luigi Chierchia \\
                 On a computer algebra aided proof in bifurcation theory
                 / Carmen Chicone and Marc Jacobs \\
                 MACSYMA program to implement averaging using elliptic
                 functions / Vincent T. Coppola and Richard H. Rand \\
                 Validated anti-derivatives / George F. Corliss \\
                 A toolbox for nonlinear dynamics / Shannon Coffey
                 \ldots{} [et al.] \\
                 Computer assisted proofs of stability of matter / R. de
                 la Llave \\
                 Accurate strategies for K.A.M. bounds and their
                 implementation / R. de la Llave and D. Rana \\
                 A software tool for analysis in function spaces / J.-P.
                 Eckmann, A. Malaspinas and S. Oliffson Kamphorst \\
                 Equation solving by symbolic computation / Anthony C.
                 Hearn \\
                 Deciding a class of Euclidean geometry theorems with
                 Buchberger's algorithm / Bernhard Kutzler \\
                 Lie transform tutorial: II / Kenneth R. Meyer \\
                 Interval tools for computer aided proofs in analysis /
                 Ramon E. Moore \\
                 Tools for mathematical computation / L. B. Rall \\
                 Shadowing trajectories of dynamical systems / Tim Sauer
                 and James A. Yorke \\
                 Transformation to versal normal form / Dieter S.
                 Schmidt \\
                 Computer assisted lower bounds for atomic energies /
                 Luis A. Seco",
}

@Proceedings{Morris:1991:RWP,
  editor =       "Joseph M. Morris and Roger C. Shaw",
  booktitle =    "4th Refinement Workshop: proceedings of the 4th
                 Refinement Workshop, 9--11 January 1991, Cambridge",
  title =        "4th Refinement Workshop: proceedings of the 4th
                 Refinement Workshop, 9--11 January 1991, Cambridge",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 478",
  year =         "1991",
  DOI =          "https://doi.org/10.1007/978-1-4471-3756-6",
  ISBN =         "3-540-19657-9",
  ISBN-13 =      "978-3-540-19657-0",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 09:29:05 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  confdate =     "9-11 Jan. 1991",
  conflocation = "Cambridge, UK",
  pubcountry =   "Germany",
}

@Proceedings{SPIE:1991:PSI,
  editor =       "Franklin T. Luk",
  booktitle =    "Advanced Signal Processing Algorithms, Architectures,
                 and Implementations {II}: 24--26 July 1991, San Diego,
                 California",
  title =        "Advanced Signal Processing Algorithms, Architectures,
                 and Implementations {II}: 24--26 July 1991, San Diego,
                 California",
  publisher =    pub-SPIE,
  address =      pub-SPIE:adr,
  pages =        "ix + 494",
  year =         "1991",
  ISBN =         "0-8194-0694-5",
  ISBN-13 =      "978-0-8194-0694-1",
  LCCN =         "TS510.S63 v.1566",
  bibdate =      "Wed Sep 07 23:38:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Proceedings{Alley:1992:CRI,
  editor =       "Gary T. Alley",
  booktitle =    "Conference record of the 1992 {IEEE} Nuclear Science
                 Symposium and Medical Imaging Conference: October
                 25--31, 1992, Orlando, Florida {USA}",
  title =        "Conference record of the 1992 {IEEE} Nuclear Science
                 Symposium and Medical Imaging Conference: October
                 25--31, 1992, Orlando, Florida {USA}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xlix + 1362",
  year =         "1992",
  ISBN =         "0-7803-0884-0",
  ISBN-13 =      "978-0-7803-0884-8",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 09:55:50 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Two volumes. IEEE catalog no. 92CH3232-6.",
  acknowledgement = ack-nhfb,
  confdate =     "25-31 Oct. 1992",
  conflocation = "Orlando, FL, USA",
  confsponsor =  "IEEE; Argonne Nat. Lab.; Brookhaven Nat. Lab.; United
                 States Dept. Energy; et al",
}

@Proceedings{Anonymous:1992:EAP,
  editor =       "Anonymous",
  booktitle =    "{Euro ASIC '92: proceedings, CNIT, Paris, June 1--5,
                 1992 in cooperation with IEEE Computer Society}",
  title =        "{Euro ASIC '92: proceedings, CNIT, Paris, June 1--5,
                 1992 in cooperation with IEEE Computer Society}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 423",
  year =         "1992",
  ISBN =         "0-8186-2845-6, 0-8186-2846-4, 0-8186-2847-2",
  ISBN-13 =      "978-0-8186-2845-0, 978-0-8186-2846-7,
                 978-0-8186-2847-4",
  LCCN =         "TK7874.6 .E87 1992",
  bibdate =      "Thu Mar 2 09:48:17 MST 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  note =         "IEEE catalog no. 92TH0442-4. IEEE Computer Society
                 Press order number 2845.",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=416",
  acknowledgement = ack-nhfb,
  meetingname =  "Euro ASIC (Conference) (6th: 1992: Paris, France)",
  subject =      "Application specific integrated circuits; Congresses",
}

@Proceedings{Atanassova:1992:CAE,
  editor =       "Lidiya Atanassova and J{\"u}rgen Herzberger",
  booktitle =    "Computer Arithmetic and Enclosure Methods: Proceedings
                 of the Third International {IMACS-GAMM} Symposium on
                 Computer Arithmetic and Scientific Computing
                 ({SCAN}-91), Oldenburg, Germany, 1--4 October 1991",
  title =        "Computer Arithmetic and Enclosure Methods: Proceedings
                 of the Third International {IMACS-GAMM} Symposium on
                 Computer Arithmetic and Scientific Computing
                 ({SCAN}-91), Oldenburg, Germany, 1--4 October 1991",
  publisher =    pub-ENH,
  address =      pub-ENH:adr,
  pages =        "x + 504",
  year =         "1992",
  ISBN =         "0-444-89834-4",
  ISBN-13 =      "978-0-444-89834-0",
  LCCN =         "QA76.9.C62 I559 1992",
  bibdate =      "Thu Sep 15 19:22:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{Britton:1992:CWT,
  editor =       "J. L. Britton",
  booktitle =    "Collected Works of {A. M. Turing}: Volume 1: {Pure}
                 Mathematics",
  title =        "Collected Works of {A. M. Turing}: Volume 1: {Pure}
                 Mathematics",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "xxii + 287",
  year =         "1992",
  ISBN =         "0-444-88059-3",
  ISBN-13 =      "978-0-444-88059-8",
  LCCN =         "QA3 .T87 1992",
  MRclass =      "01A75 (03-03 03D40 62-03 68-03)",
  MRnumber =     "MR1150052 (93k:01094)",
  MRreviewer =   "A. A. Mullin",
  bibdate =      "Sat Nov 19 13:23:32 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/good-i-j.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Edited and with an introduction and postscript by J.
                 L. Britton and Irving John Good. With a preface by P.
                 N. Furbank",
  ZMnumber =     "0751.01017",
  abstract =     "The collected works of Turing, including a substantial
                 amount of unpublished material, will comprise four
                 volumes: Mechanical Intelligence, Pure Mathematics,
                 Morphogenesis and Mathematical Logic. Alan Mathison
                 Turing (1912--1954) was a brilliant man who made major
                 contributions in several areas of science. Today his
                 name is mentioned frequently in philosophical
                 discussions about the nature of Artificial
                 Intelligence. Actually, he was a pioneer researcher in
                 computer architecture and software engineering; his
                 work in pure mathematics and mathematical logic
                 extended considerably further and his last work, on
                 morphogenesis in plants, is also acknowledged as being
                 of the greatest originality and of permanent
                 importance. He was one of the leading figures in
                 Twentieth-century science, a fact which would have been
                 known to the general public sooner but for the British
                 Official Secrets Act, which prevented discussion of his
                 wartime work. What is maybe surprising about these
                 papers is that although they were written decades ago,
                 they address major issues which concern researchers
                 today.",
  acknowledgement = ack-nhfb,
  author-dates = "I. J. Good (9 December 1916--5 April 2009); Alan
                 Mathison Turing (23 June 1912--7 June 1954)",
  subject =      "Mathematics",
  tableofcontents = "Published Papers \\
                 Equivalence of Left and Right Almost Periodicity \\
                 Finite Approximations to Lie Groups \\
                 The Extensions of a Group \\
                 A Method for the Calculation of the Zeta-Function \\
                 Rounding-Off Errors in Matrix Processes \\
                 The Word Problem in Semi-Groups with Cancellation \\
                 Some Calculations of the Riemann Zeta-Function \\
                 Solvable and Unsolvable Problems \\
                 Unpublished Papers \\
                 A Note on Normal Numbers \\
                 The Word Problem in Compact Groups \\
                 On Permutation Groups \\
                 The Difference [garbled math] \\
                 On a Theorem of Littlewood \\
                 Related Papers \\
                 An Analysis of Turing's ``The Word Problem in
                 Semi-Groups with Cancellation'' \\
                 On the Difference $\pi(x) - \li(x)$ \\
                 Turing's Statistical Work \\
                 Studies in the History of Probability and Statistics
                 XXXVII \\
                 A. M. Turing's Statistical Work in World War II
                 (Biometrika {\bf 66}) \\
                 Introductory Remarks for the Article in Biometrika 66
                 (Specially written for this Volume by I. J. Good) \\
                 Notes and Summaries \\
                 Bibliography \\
                 Index",
}

@Proceedings{IEEE:1992:ASF,
  editor =       "{IEEE}",
  booktitle =    "{33rd Annual Symposium on Foundations of Computer
                 Science: October 24--27, 1992, Pittsburgh,
                 Pennsylvania: proceedings [papers]}",
  title =        "{33rd Annual Symposium on Foundations of Computer
                 Science: October 24--27, 1992, Pittsburgh,
                 Pennsylvania: proceedings [papers]}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xi + 734",
  year =         "1992",
  CODEN =        "ASFPDV",
  ISBN =         "0-8186-2901-0 (microfiche), 0-8186-2900-2
                 (paperback)",
  ISBN-13 =      "978-0-8186-2901-3 (microfiche), 978-0-8186-2900-6
                 (paperback)",
  ISSN =         "0272-5428",
  LCCN =         "QA 76 S979 1992",
  bibdate =      "Thu Dec 3 07:11:18 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE Catalog Number 92CH3188-0. IEEE Computer Society
                 Press Order Number 2900.",
  acknowledgement = ack-nhfb,
  keywords =     "electronic data processing --- congresses",
}

@Proceedings{IEEE:1992:GCG,
  editor =       "{IEEE}",
  booktitle =    "{GLOBECOM '92}. Communication for Global Users. {IEEE}
                 Global Telecommunications Conference. Conference
                 Record",
  title =        "{GLOBECOM} '92. Communication for Global Users. {IEEE}
                 Global Telecommunications Conference. Conference
                 Record",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xlviii + 1920",
  year =         "1992",
  ISBN =         "0-7803-0608-2, 0-7803-0609-0, 0-7803-0610-4
                 (microfiche)",
  ISBN-13 =      "978-0-7803-0608-0, 978-0-7803-0609-7,
                 978-0-7803-0610-3 (microfiche)",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 09:41:22 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Three volumes. IEEE catalog no. 92CH3130-2.",
  acknowledgement = ack-nhfb,
  confdate =     "6-9 Dec. 1992",
  conflocation = "Orlando, FL, USA",
  confsponsor =  "IEEE",
}

@Proceedings{IEEE:1992:IIC,
  key =          "IEEE ICCD '92",
  booktitle =    "1992 {IEEE} International Conference on Computer
                 Design, {VLSI} in Computers and Processors:
                 Proceedings, Royal Sonesta Hotel, Cambridge,
                 Massachusetts, October 11--14, 1992",
  title =        "1992 {IEEE} International Conference on Computer
                 Design, {VLSI} in Computers and Processors:
                 Proceedings, Royal Sonesta Hotel, Cambridge,
                 Massachusetts, October 11--14, 1992",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xvii + 605",
  year =         "1992",
  ISBN =         "0-8186-3110-4 (paper), 0-8186-3111-2 (microfiche),
                 0-8186-3112-0 (case)",
  ISBN-13 =      "978-0-8186-3110-8 (paper), 978-0-8186-3111-5
                 (microfiche), 978-0-8186-3112-2 (case)",
  LCCN =         "TK 7888.4 I23 1992",
  bibdate =      "Thu Sep 08 00:35:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
}

@Proceedings{IEEE:1992:PIC,
  editor =       "{IEEE}",
  booktitle =    "Proceedings of the {IEEE 1992} Custom Integrated
                 Circuits Conference: the Westin Copley Place Hotel,
                 Boston, Massachusetts, May 3--6, 1992",
  title =        "Proceedings of the {IEEE} 1992 Custom Integrated
                 Circuits Conference: the Westin Copley Place Hotel,
                 Boston, Massachusetts, May 3--6, 1992",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "1992",
  ISBN =         "0-7803-0246-X, 0-7803-0247-8, 0-7803-0248-6",
  ISBN-13 =      "978-0-7803-0246-4, 978-0-7803-0247-1,
                 978-0-7803-0248-8",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 10:08:17 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog no. 92CH3078-3.",
  acknowledgement = ack-nhfb,
  confdate =     "3-6 May 1992",
  conflocation = "Boston, MA, USA",
  confsponsor =  "IEEE",
}

@Proceedings{IEEE:1992:PIS,
  editor =       "{IEEE}",
  booktitle =    "Proceedings / {IEEE} Southeastcon '92, April 12--15,
                 1992, Birmingham, Alabama",
  title =        "Proceedings / {IEEE} Southeastcon '92, April 12--15,
                 1992, Birmingham, Alabama",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "lii + 846",
  year =         "1992",
  ISBN =         "0-7803-0494-2",
  ISBN-13 =      "978-0-7803-0494-9",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 09:59:47 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Two volumes. IEEE catalog no. 92CH3094-0.",
  acknowledgement = ack-nhfb,
  confdate =     "12-15 April 1992",
  conflocation = "Birmingham, AL, USA",
  confsponsor =  "IEEE",
}

@Proceedings{Juj:1992:NCR,
  editor =       "Hardev Juj and Alvin Todd Moser",
  booktitle =    "Northcon\slash 92 Conference Record: Seattle,
                 Washington, October 19--21, 1992",
  title =        "Northcon\slash 92 Conference Record: Seattle,
                 Washington, October 19--21, 1992",
  publisher =    "Electronic Conventions Management",
  address =      "Los Angeles, CA, USA",
  pages =        "vii + 366",
  year =         "1992",
  LCCN =         "TK 7801 N67 1992",
  bibdate =      "Fri Dec 08 13:10:32 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nj,
  xxISBN =       "(none)",
}

@Proceedings{Katwijk:1992:AMT,
  editor =       "J. Katwijk",
  booktitle =    "{Ada: moving towards 2000: 11th Ada-Europe
                 International Conference, Zandvoort, The Netherlands,
                 June 1--5, 1992: proceedings}",
  title =        "{Ada: moving towards 2000: 11th Ada-Europe
                 International Conference, Zandvoort, The Netherlands,
                 June 1--5, 1992: proceedings}",
  volume =       "603",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 324",
  year =         "1992",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/3-540-55585-4",
  ISBN =         "3-540-55585-4 (Berlin), 0-387-55585-4 (New York)",
  ISBN-13 =      "978-3-540-55585-8 (Berlin), 978-0-387-55585-0 (New
                 York)",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  LCCN =         "QA76.73.A35 A24 1992",
  bibdate =      "Fri Apr 12 07:14:56 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-LNCS,
  URL =          "http://link.springer-ny.com/link/service/series/0558/tocs/t0603.htm;
                 http://www.springerlink.com/openurl.asp?genre=issue&issn=0302-9743&volume=603",
  acknowledgement = ack-nhfb,
  keywords =     "Ada (computer program language) --- congresses",
}

@Proceedings{Prinetto:1992:CHD,
  editor =       "Paolo Prinetto and Paolo Camurati",
  booktitle =    "Correct Hardware Design Methodologies. Proceedings of
                 the Advanced Research Workshop on Correct Hardware
                 Design Methodologies, Turin, Italy, June 12--14, 1991",
  title =        "Correct Hardware Design Methodologies. Proceedings of
                 the Advanced Research Workshop on Correct Hardware
                 Design Methodologies, Turin, Italy, June 12--14, 1991",
  publisher =    "North-Holland",
  address =      "Amsterdam, Netherlands",
  pages =        "ix + 470",
  year =         "1992",
  ISBN =         "0-444-89367-9",
  ISBN-13 =      "978-0-444-89367-3",
  LCCN =         "TK7874 .A3353 1991",
  bibdate =      "Sat Nov 29 09:58:12 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  confdate =     "12-14 June 1991",
  conflocation = "Turin, Italy",
  confsponsor =  "Politecnico di Torino",
  pubcountry =   "Netherlands",
}

@Proceedings{Quinton:1992:APV,
  editor =       "Patrice Quinton and Yves Robert",
  booktitle =    "Proceedings of the International Workshop Algorithms
                 and Parallel {VLSI} Architectures {II}, Ch{\^a}teau de
                 Bonas, Gers, France, June 3--6, 1991",
  title =        "Proceedings of the International Workshop Algorithms
                 and Parallel {VLSI} Architectures {II}, Ch{\^a}teau de
                 Bonas, Gers, France, June 3--6, 1991",
  publisher =    pub-ELSEVIER,
  address =      pub-ELSEVIER:adr,
  pages =        "xvi + 388",
  year =         "1992",
  ISBN =         "0-444-89153-6",
  ISBN-13 =      "978-0-444-89153-2",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 09:45:36 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  confdate =     "3-6 June 1991",
  conflocation = "Gers, France",
  confsponsor =  "CNRS; French Minist. Res. Technol.; French Minist.
                 Defence",
  pubcountry =   "Netherlands",
}

@Proceedings{Singh:1992:CRT,
  editor =       "Avtar Singh",
  booktitle =    "Conference record of the Twenty-sixth Asilomar
                 Conference on Signals, Systems and Computers: October
                 26--28, 1992, Pacific Grove, California",
  title =        "Conference record of the Twenty-sixth Asilomar
                 Conference on Signals, Systems and Computers: October
                 26--28, 1992, Pacific Grove, California",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xviii + 1156",
  year =         "1992",
  ISBN =         "0-8186-3162-7 (case), 0-8186-3160-0 (paper),
                 0-8186-3161-9 (microfiche)",
  ISBN-13 =      "978-0-8186-3162-7 (case), 978-0-8186-3160-3 (paper),
                 978-0-8186-3161-0 (microfiche)",
  LCCN =         "TK 5102.5 A78 1992",
  bibdate =      "Thu Sep 08 13:38:22 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Two volumes.",
  acknowledgement = ack-nj,
  confdate =     "26-28 Oct. 1992",
  conflocation = "Pacific Grove, CA, USA",
  confsponsor =  "IEEE",
}

@Proceedings{Vandewalle:1992:SPV,
  editor =       "J. Vandewalle and R. Boite and M. Moonen and A.
                 Oosterlinck",
  booktitle =    "Signal processing {VI}: theories and applications;
                 proceedings of {EUSIPCO-92}, Sixth European Signal
                 Processing Conference, Brussels, Belgium, August
                 24--27, 1992",
  title =        "Signal processing {VI}: theories and applications;
                 proceedings of {EUSIPCO}-92, Sixth European Signal
                 Processing Conference, Brussels, Belgium, August
                 24--27, 1992",
  publisher =    pub-ELSEVIER,
  address =      pub-ELSEVIER:adr,
  pages =        "lvii + 1844",
  year =         "1992",
  ISBN =         "0-444-89587-6",
  ISBN-13 =      "978-0-444-89587-5",
  LCCN =         "TK5102.5 621.382/2",
  bibdate =      "Sat Nov 29 09:49:22 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "3 vol.",
  acknowledgement = ack-nhfb,
  confdate =     "24-27 Aug. 1992",
  conflocation = "Brussels, Belgium",
  confsponsor =  "Belgian Nat. Fund for Sci. Res.; CERA; LMS Int",
  pubcountry =   "Netherlands",
}

@Proceedings{Wang:1992:PII,
  editor =       "Paul S. Wang",
  booktitle =    "{Proceedings of ISSAC '92. International Symposium on
                 Symbolic and Algebraic Computation}",
  title =        "{Proceedings of ISSAC '92. International Symposium on
                 Symbolic and Algebraic Computation}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "ix + 406",
  year =         "1992",
  ISBN =         "0-89791-489-9 (soft cover), 0-89791-490-2 (hard
                 cover)",
  ISBN-13 =      "978-0-89791-489-5 (soft cover), 978-0-89791-490-1
                 (hard cover)",
  LCCN =         "QA76.95.I59 1992",
  bibdate =      "Thu Sep 26 05:51:45 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/issac.bib",
  note =         "ACM order number: 505920.",
  abstract =     "The following topics were dealt with: symbolic
                 computation; differential equations; differs-integral
                 software; algebraic algorithms; algebraic software;
                 real algebraics and root isolation; groups and number
                 theory; systems and interfaces.",
  acknowledgement = ack-nhfb,
  classification = "C6130 (Data handling techniques); C7310
                 (Mathematics)",
  confdate =     "27--29 July 1992",
  conflocation = "Berkeley, CA, USA",
  confsponsor =  "ACM",
  keywords =     "Algebraic algorithms; Algebraic software; Differential
                 equations; Differs-integral software; Groups theory;
                 Interfaces; Number theory; Real algebraics; Root
                 isolation; Symbolic computation",
  pubcountry =   "USA",
  thesaurus =    "Differential equations; Mathematics computing; Symbol
                 manipulation",
}

@Proceedings{White:1992:IIS,
  editor =       "Stan White",
  booktitle =    "1992 {IEEE} International Symposium on Circuits and
                 Systems: San Diego {CA}, May 10--13, 1992",
  title =        "1992 {IEEE} International Symposium on Circuits and
                 Systems: San Diego {CA}, May 10--13, 1992",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "3028",
  year =         "1992",
  ISBN =         "0-7803-0593-0",
  ISBN-13 =      "978-0-7803-0593-9",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 09:52:25 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Six volumes. IEEE catalog no. 92CH3139-3.",
  acknowledgement = ack-nhfb,
  confdate =     "10-13 May 1992",
  conflocation = "San Diego, CA, USA",
  confsponsor =  "IEEE",
}

@Book{Adams:1993:SCA,
  editor =       "Ernst Adams and Ulrich Kulisch",
  booktitle =    "Scientific computing with automatic result
                 verification",
  title =        "Scientific computing with automatic result
                 verification",
  volume =       "189",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "x + 612",
  year =         "1993",
  ISBN =         "0-12-044210-8",
  ISBN-13 =      "978-0-12-044210-2",
  LCCN =         "QA76 .S368 1993",
  bibdate =      "Sat Nov 29 11:22:09 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Mathematics in science and engineering",
  URL =          "http://lccn.loc.gov/92247371",
  acknowledgement = ack-nhfb,
  subject =      "Electronic data processing; Computer science;
                 Mathematics",
}

@Proceedings{Anonymous:1993:IPF,
  editor =       "Anonymous",
  booktitle =    "{ICSPAT '93}: Proceedings of the Fourth International
                 Conference on Signal Processing Applications \&
                 Technology: Santa Clara, California, {USA}, September
                 28 -- October 1, 1993",
  title =        "{ICSPAT '93}: Proceedings of the Fourth International
                 Conference on Signal Processing Applications \&
                 Technology: Santa Clara, California, {USA}, September
                 28 -- October 1, 1993",
  publisher =    "DSP Associates",
  address =      "Newton, MA, USA",
  pages =        "1675",
  year =         "1993",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 10:11:01 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Two volumes",
  acknowledgement = ack-nhfb,
  confdate =     "28 Sept.-1 Oct. 1993",
  conflocation = "Santa Clara, CA, USA",
}

@Proceedings{Corliss:1993:AIC,
  editor =       "G. F. Corliss and R. B. Kearfott",
  booktitle =    "Abstracts for an International Conference on Numerical
                 Analysis with Automatic Result Verification:
                 Mathematics, Application and Software, February
                 25--March 1, 1993, Lafayette, {LA, 1993}",
  title =        "Abstracts for an International Conference on Numerical
                 Analysis with Automatic Result Verification:
                 Mathematics, Application and Software, February
                 25--March 1, 1993, Lafayette, {LA}, 1993",
  volume =       "3(3--4)",
  publisher =    "????",
  address =      "????",
  pages =        "????",
  year =         "1993",
  ISBN =         "????",
  ISBN-13 =      "????",
  ISSN =         "0135-4868",
  LCCN =         "????",
  bibdate =      "Tue Oct 22 13:32:36 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       j-INTERVAL-COMP,
  acknowledgement = ack-nhfb,
  xxtitle =      "Numerical analysis with automatic result verification:
                 International conference: Selected papers",
}

@Proceedings{Eggermont:1993:VSP,
  editor =       "Ludwig D. J. Eggermont and others",
  booktitle =    "{VLSI signal processing, VI. Proceedings of the 1993
                 IEEE workshop on VLSI signal processing, Veldhoven, The
                 Netherlands, October 20--22, 1993}",
  title =        "{VLSI signal processing, VI. Proceedings of the 1993
                 IEEE workshop on VLSI signal processing, Veldhoven, The
                 Netherlands, October 20--22, 1993}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xv + 527",
  year =         "1993",
  DOI =          "https://doi.org/10.1109/VLSISP.1993.404510",
  ISBN =         "0-7803-0996-0",
  ISBN-13 =      "978-0-7803-0996-8",
  LCCN =         "TK7874 .V5637 1993",
  bibdate =      "Sun Mar 4 21:10:43 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=3196",
  acknowledgement = ack-nhfb,
  remark =       "Based on reviewed and accepted contributions to the
                 1993 IEEE Workshop on VLSI Signal Processing, which was
                 held in Veldhoven, The Netherlands, from October
                 20--22, 1993",
  subject =      "Integrated circuits; Very large scale integration;
                 Signal processing",
}

@Proceedings{IEEE:1993:PEC,
  editor =       "{IEEE}",
  booktitle =    "(1993) Proceedings The European Conference on Design
                 Automation with the European Event in {ASIC} Design",
  title =        "(1993) Proceedings The European Conference on Design
                 Automation with the European Event in {ASIC} Design",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xxv + 601",
  year =         "1993",
  ISBN =         "0-8186-3410-3",
  ISBN-13 =      "978-0-8186-3410-9",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 10:21:06 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  confdate =     "22-25 Feb. 1993",
  conflocation = "Paris, France",
}

@Proceedings{IEEE:1993:PIP,
  editor =       "{IEEE}",
  booktitle =    "{Proceedings of the IEEE Pacific Rim Conference on
                 Communications, Computers, and Signal Processing (1993:
                 Victoria, BC)}",
  title =        "{Proceedings of the IEEE Pacific Rim Conference on
                 Communications, Computers, and Signal Processing (1993:
                 Victoria, BC)}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "1993",
  ISBN =         "0-7803-0971-5 (softbound), 0-7803-1219-8 (casebound),
                 0-7803-0972-3 (microfiche)",
  ISBN-13 =      "978-0-7803-0971-5 (softbound), 978-0-7803-1219-7
                 (casebound), 978-0-7803-0972-2 (microfiche)",
  LCCN =         "TK5101.A1 I34 1993",
  bibdate =      "Sun Feb 20 10:56:48 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  subject =      "telecommunication; congresses; computers; signal
                 processing",
}

@Proceedings{IEEE:1993:PMS,
  editor =       "{IEEE}",
  booktitle =    "Proceedings of the 36th Midwest Symposium on Circuits
                 and Systems",
  title =        "Proceedings of the 36th Midwest Symposium on Circuits
                 and Systems",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xxxv + 1565",
  year =         "1993",
  ISBN =         "0-7803-1760-2",
  ISBN-13 =      "978-0-7803-1760-4",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 10:12:41 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Two volumes. IEEE catalog no. 93CH3381-1.",
  acknowledgement = ack-nhfb,
  confdate =     "16-18 Aug. 1993",
  conflocation = "Detroit, MI, USA",
  confsponsor =  "Wayne State University; IEEE Circuits and Syst. Soc",
}

@Proceedings{Lee:1993:MCM,
  editor =       "Thomas Lee",
  booktitle =    "Mathematical computation with Maple V: ideas and
                 applications: Proceedings of the Maple Summer Workshop
                 and Symposium, University of Michigan, Ann Arbor, June
                 28--30, 1993",
  title =        "Mathematical computation with Maple {V}: ideas and
                 applications: Proceedings of the Maple Summer Workshop
                 and Symposium, University of Michigan, Ann Arbor, June
                 28--30, 1993",
  publisher =    pub-BIRKHAUSER-BOSTON,
  address =      pub-BIRKHAUSER-BOSTON:adr,
  pages =        "viii + 199",
  year =         "1993",
  ISBN =         "0-8176-3724-9, 3-7643-3724-9",
  ISBN-13 =      "978-0-8176-3724-8, 978-3-7643-3724-7",
  LCCN =         "QA76.95.M36 1993",
  bibdate =      "Sat Dec 09 11:54:32 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Lombardi:1993:PII,
  editor =       "F. Lombardi and M. Sami and Y. Savaria and R.
                 Stefanelli",
  booktitle =    "Proceedings / The {IEEE} International Workshop on
                 Defect and Fault Tolerance in {VLSI} Systems: October
                 27--29, 1993, Venice, Italy",
  title =        "Proceedings / The {IEEE} International Workshop on
                 Defect and Fault Tolerance in {VLSI} Systems: October
                 27--29, 1993, Venice, Italy",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiii + 335",
  year =         "1993",
  ISBN =         "0-8186-3502-9 (case), 0-8186-3501-0 (microfiche)",
  ISBN-13 =      "978-0-8186-3502-1 (case), 978-0-8186-3501-4
                 (microfiche)",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 10:22:50 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog no. 93TH0571-0.",
  acknowledgement = ack-nhfb,
  confdate =     "27-29 Oct. 1993",
  conflocation = "Venice, Italy",
  confsponsor =  "IEEE Comput. Soc.; IEEE Comput. Soc. Tech. Committee
                 on Fault-Tolerant Comput.; Euromicro",
}

@Proceedings{Sincovec:1993:PSS,
  editor =       "Richard F. Sincovec and David E. Keyes and L. M. R.
                 and L. R. Petzold and D. A. Reed",
  booktitle =    "{Proceedings of the Sixth SIAM Conference on Parallel
                 Processing for Scientific Computing, held March 22--24,
                 1993, in Norfolk, VA, USA}",
  title =        "{Proceedings of the Sixth SIAM Conference on Parallel
                 Processing for Scientific Computing, held March 22--24,
                 1993, in Norfolk, VA, USA}",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xix + 1041 + iv",
  year =         "1993",
  ISBN =         "0-89871-315-3",
  ISBN-13 =      "978-0-89871-315-2",
  LCCN =         "QA76.58 .S55 1993 v.1-2",
  bibdate =      "Tue Oct 11 12:21:40 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Two volumes.",
  acknowledgement = ack-nhfb,
  xxnote =       "Check authors: catalogs are incomplete",
}

@Proceedings{Swartzlander:1993:PSC,
  editor =       "Earl {Swartzlander, Jr.} and Mary Jane Irwin and
                 Graham Jullien",
  booktitle =    "Proceedings: 11th Symposium on Computer Arithmetic,
                 June 29--July 2, 1993, Windsor, Ontario",
  title =        "Proceedings: 11th Symposium on Computer Arithmetic,
                 June 29--July 2, 1993, Windsor, Ontario",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  bookpages =    "xii + 284",
  pages =        "xii + 284",
  year =         "1993",
  ISBN =         "0-7803-1401-8 (softbound), 0-8186-3862-1 (casebound),
                 0-8186-3861-3 (microfiche)",
  ISBN-13 =      "978-0-7803-1401-6 (softbound), 978-0-8186-3862-6
                 (casebound), 978-0-8186-3861-9 (microfiche)",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  LCCN =         "QA 76.9 C62 S95 1993",
  bibdate =      "Thu Sep 01 22:58:49 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  note =         "IEEE Transactions on Computers {\bf 43(8)}, 1994.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}

@Proceedings{Swartzlander:1993:SCA,
  editor =       "Earl {Swartzlander, Jr.} and Mary Jane Irwin and
                 Graham Jullien",
  booktitle =    "Proceedings: 11th Symposium on Computer Arithmetic,
                 June 29--July 2, 1993, Windsor, Ontario",
  title =        "Proceedings: 11th Symposium on Computer Arithmetic,
                 June 29--July 2, 1993, Windsor, Ontario",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 284",
  year =         "1993",
  ISBN =         "0-7803-1401-8 (softbound), 0-8186-3862-1 (casebound),
                 0-8186-3861-3 (microfiche)",
  ISBN-13 =      "978-0-7803-1401-6 (softbound), 978-0-8186-3862-6
                 (casebound), 978-0-8186-3861-9 (microfiche)",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  LCCN =         "QA 76.9 C62 S95 1993",
  bibdate =      "Thu Sep 01 22:58:49 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE Transactions on Computers {\bf 43(8)}, 1994",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-11",
}

@Proceedings{Wah:1993:ICA,
  editor =       "Benjamin W. Wah and Luigi Dadda",
  booktitle =    "{The International Conference on Application-Specific
                 Array Processors: October 25--27, 1993, Venice, Italy:
                 proceedings}",
  title =        "{The International Conference on Application-Specific
                 Array Processors: October 25--27, 1993, Venice, Italy:
                 proceedings}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 594",
  year =         "1993",
  ISBN =         "0-8186-3492-8, 0-8186-3491-X",
  ISBN-13 =      "978-0-8186-3492-5, 978-0-8186-3491-8",
  LCCN =         "TK5102.5",
  bibdate =      "Sun Mar 4 21:08:02 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  meetingname =  "International Conference on Application Specific Array
                 Processors (7th: 1993: Venice, Italy)",
  remark =       "Sponsored by Euromicro. IEEE Computer Society Press
                 order number 3492-02. IEEE catalog number 93TH0572-8",
  subject =      "Array processors; Congresses; Signal processing;
                 Digital techniques; Application-specific integrated
                 circuits",
}

@Proceedings{ACM:1994:AAW,
  editor =       "{ACM}",
  booktitle =    "{Ada in applications: WADAS '94: eleventh Annual
                 Washington Ada Symposium \& Summer ACM SIGAda Meeting:
                 featuring Working Group Product Development and
                 Delivery: June 27 -- July 1, 1994, McLean Hilton,
                 Tyson's Corner, McLean, Virginia: proceedings}",
  title =        "{Ada in applications: WADAS '94: eleventh Annual
                 Washington Ada Symposium \& Summer ACM SIGAda Meeting:
                 featuring Working Group Product Development and
                 Delivery: June 27 -- July 1, 1994, McLean Hilton,
                 Tyson's Corner, McLean, Virginia: proceedings}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "121",
  year =         "1994",
  ISBN =         "0-89791-684-0",
  ISBN-13 =      "978-0-89791-684-4",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 06:48:28 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}

@Proceedings{Ames:1994:IPI,
  editor =       "William F. Ames",
  booktitle =    "{IMACS '94: proceedings of the 14th IMACS World
                 Congress on Computation and Applied Mathematics: July
                 11--15, 1994, Georgia Institute of Technology, Atlanta,
                 Georgia, USA}",
  title =        "{IMACS '94: proceedings of the 14th IMACS World
                 Congress on Computation and Applied Mathematics: July
                 11--15, 1994, Georgia Institute of Technology, Atlanta,
                 Georgia, USA}",
  publisher =    pub-IMACS,
  address =      pub-IMACS:adr,
  pages =        "1572",
  year =         "1994",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Wed Jun 14 16:37:46 MDT 1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/f/fazio-riccardo.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Three volumes.",
  acknowledgement = ack-nhfb,
  annote =       "Accompanied by `Late papers volume' (101 p.).",
  keywords =     "Computer simulation -- Congresses.; Mathematical
                 models -- Congresses.; Numerical analysis --
                 Congresses.; Simulation methods -- Congresses.",
}

@Proceedings{Calmet:1994:RWC,
  editor =       "Jacques Calmet",
  booktitle =    "{Rhine Workshop on Computer Algebra. Proceedings}",
  title =        "{Rhine Workshop on Computer Algebra. Proceedings}",
  publisher =    "University of Karlsruhe",
  address =      "Karlsruhe, Germany",
  pages =        "v + 224",
  year =         "1994",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 10:35:47 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  confdate =     "22-24 March 1994",
  conflocation = "Karlsruhe, Germany",
  confsponsor =  "University of Karlsruhe",
  pubcountry =   "Germany",
}

@Proceedings{Cappello:1994:PIC,
  editor =       "P. Cappello and R. M. Owens and E. E. {Swartzlander,
                 Jr.} and B. W. Wah",
  booktitle =    "Proceedings. The International Conference on
                 Application Specific Array Processors",
  title =        "Proceedings. The International Conference on
                 Application Specific Array Processors",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 452",
  year =         "1994",
  ISBN =         "0-8186-6517-3",
  ISBN-13 =      "978-0-8186-6517-2",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 10:43:05 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog no. 94TH0687-4.",
  acknowledgement = ack-nhfb,
  confdate =     "22-24 Aug. 1994",
  conflocation = "San Francisco, CA, USA",
  confsponsor =  "IEEE Comput. Soc. Tech. Committee on VLSI",
}

@Proceedings{Echtle:1994:PFI,
  editor =       "K. Echtle and D. Hammer and D. Powell",
  booktitle =    "Dependable Computing --- {EDCC-1}. First European
                 Dependable Computing Conference Proceedings",
  title =        "Dependable Computing --- {EDCC}-1. First European
                 Dependable Computing Conference Proceedings",
  volume =       "852",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xvii + 618",
  year =         "1994",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/3-540-58426-9",
  ISBN =         "3-540-58426-9",
  ISBN-13 =      "978-3-540-58426-1",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 10:29:16 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       j-LECT-NOTES-COMP-SCI,
  acknowledgement = ack-nhfb,
  confdate =     "4-6 Oct. 1994",
  conflocation = "Berlin, Germany",
  pubcountry =   "Germany",
}

@Proceedings{Gautschi:1994:MCH,
  editor =       "Walter Gautschi",
  booktitle =    "{Mathematics of computation, 1943--1993: a
                 half-century of computational mathematics: Mathematics
                 of Computation 50th Anniversary Symposium, August
                 9--13, 1993, Vancouver, British Columbia}",
  title =        "{Mathematics of computation, 1943--1993: a
                 half-century of computational mathematics: Mathematics
                 of Computation 50th Anniversary Symposium, August
                 9--13, 1993, Vancouver, British Columbia}",
  volume =       "48",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "xix + 643",
  year =         "1994",
  ISBN =         "0-8218-0291-7, 0-8218-0353-0 (pt. 1), 0-8218-0354-9
                 (pt. 2)",
  ISBN-13 =      "978-0-8218-0291-5, 978-0-8218-0353-0 (pt. 1),
                 978-0-8218-0354-7 (pt. 2)",
  ISSN =         "0160-7634",
  LCCN =         "QA1 .A56 v.48 1994; QA297.M385 1993",
  MRclass =      "00B25 (11-06 65-06)",
  MRnumber =     "95j:00014",
  bibdate =      "Mon Oct 24 11:37:20 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/l/lehmer-derrick-henry.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1940.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  note =         "See also SIAM Review, September 1995, {\bf 37}(3), p.
                 483.",
  series =       "Proceedings of Symposia in Applied Mathematics",
  acknowledgement = ack-nhfb,
  author-dates = "Frank William John Olver (15 December 1924--23 April
                 2013)",
  tableofcontents = "Preface / xi \\
                 Mathematics of Computation: A brief history / Eugene
                 Isaacson / xvii \\
                 \\
                 Part I. Symposium on Numerical Analysis \\
                 \\
                 Invited Papers \\
                 \\
                 On the development of multigrid methods and their
                 analysis / James H. Bramble / 5 \\
                 An introduction to inverse problems / Margaret Cheney /
                 21 \\
                 Algorithms for unconstrained optimization: A review of
                 recent developments / Donald Goldfarb / 33 \\
                 A survey of componentwise perturbation theory in
                 numerical linear algebra / Nicholas J. Higham / 49 \\
                 Numerical evaluation of special functions / D. W.
                 Lozier and F. W. J. Olver / 79 \\
                 A survey of numerical cubature over triangles / J. N.
                 Lyness and Ronald Cools / 127 \\
                 New trends in the use and analysis of integral
                 equations / J. C. Nedelec / 151 \\
                 Applications of multivariate splines / Larry L.
                 Schumaker / 177 \\
                 Initial value problems for ordinary differential
                 equations: Development of ideas, techniques, and
                 implementation / Hans J. Stetter / 205 \\
                 Multiresolution methods for partial differential
                 equations / Roger Temam / 225 \\
                 \\
                 Contributed Papers \\
                 \\
                 A comparison of techniques for solving ill-conditioned
                 problems arising from the immersed boundary method /
                 Loyce Adams and Zhiyun Yang / 243 \\
                 A mixed spectral-collocation and operator splitting
                 method for the Wigner-Poisson equation / Anton Arnold /
                 249 \\
                 Finite volume methods for irregular one-dimensional
                 grids / M. J. Berger, R. J. Leveque, and L. G. Stern /
                 255 \\
                 Linear rational interpolation of continuous functions
                 over an interval / Jean-Paul Berrut / 261 \\
                 A von Neumann reflection for the 2-D Burgers equation /
                 M. Brio and J. K. Hunter / 265 \\
                 Slow evolution from the boundary: A new stabilizing
                 constraint in ill-posed continuation problems / Alfred
                 S. Carasso / 269 \\
                 A finite element method for the 2D drift-diffusion
                 semiconductor model / Zhangxin Chen / 275 \\
                 Splitting functions and numerical analysis of WR-type
                 methods for evolutionary and stationary problems / S.
                 De Marchi, M. Vianello, and R. Zanovello / 281 \\
                 Error estimates for a quadrature rule for Cauchy
                 principal value integrals / Kai Diethelm / 287 \\
                 A numerical radius approach to stable difference
                 schemes for parabolic systems / Moshe Goldberg / 293
                 \\
                 An extension of the Olver-Sookne method for the
                 solution of second-order linear difference equations /
                 Takemitsu Hasegawa and Tatsuo Torii / 297 \\
                 The Faber polynomials for circular arcs / Matthew He /
                 301 \\
                 Finite element approximation for optimal control of
                 electrically conducting fluid flows / L. S. Hou and S.
                 S. Ravindran / 305 \\
                 ADI methods for heat equations with discontinuities
                 along an arbitrary interface / Zhilin Li and Anita Mayo
                 / 311 \\
                 Eigenvalue approximation of Fredholm integral operators
                 / E. B. Lin / 317 \\
                 Spectral methods for singular perturbation problems /
                 Wenbin Liu and Tao Tang / 323 \\
                 A quaternion-Jacobi method for symmetric matrices /
                 Niloufer Mackey / 327 \\
                 On constructing Chebyshev series solutions of
                 differential equations / Allan J. MacLeod / 333 \\
                 Multiquadric collocation methods in the numerical
                 solution of Volterra integral and integro-differential
                 equations / Athena Makroglou / 337 \\
                 Methods for solving large eigenvalue problems
                 associated with configuration interaction electronic
                 structure calculations / Kristyn J. Maschhoff / 343 \\
                 Computing limiting normals to real surfaces / Donal
                 O'Shea and Les Wilson / 349 \\
                 Orthogonal spline collocation solution of nonlinear
                 Schr{\"o}dinger equations / Mark P. Robinson / 355 \\
                 Who invented the computer? The debate from the
                 viewpoint of computer architecture / Ra{\'u}l Rojas /
                 361 \\
                 Locking and boundary layer effects in the finite
                 element approximation of the Reissner--Mindlin plate
                 model / Christoph Schwab and Manil Suri / 367 \\
                 Efficient spectral Galerkin methods for some elliptic
                 problems / Jie Shen / 373 \\
                 Periodic solutions of higher-order difference equations
                 in two independent variables / Qin Sheng and Ravi P.
                 Agarwal / 377 \\
                 Front tracking based on high-resolution wave
                 propagation methods / Keh-Ming Shyue / 383 \\
                 Time-splitting methods for nonhomogeneous conservation
                 laws / Tao Tang and Zhen-Huan Teng / 389 \\
                 Numerical aspects of uniform Airy-type asymptotic
                 expansions / N. M. Temme / 395 \\
                 Local dynamics and bifurcation consistencies of
                 continuous-time dynamical systems and their numerical
                 discretizations / Xin Wang, Edward K. Blum, and Qingnan
                 Li / 399 \\
                 Computing integrals of the complex error function / J.
                 A. C. Weideman / 403 \\
                 Quadratures for improper integrals and their
                 applications in integral equations / Yuesheng Xu and
                 Yunhe Zhao / 409 \\
                 Spline harmonic analysis and wavelet bases / Valery A.
                 Zheludev / 415 \\
                 \\
                 Part II. Minisymposium on Computational Number Theory
                 Dedicated to the memory of Derrick Henry Lehmer \\
                 \\
                 Invited Papers \\
                 \\
                 Algorithms for quadratic orders / Ingrid Biehl and
                 Johannes Buchmann / 425 \\
                 Analytic computations in number theory / Andrew M.
                 Odlyzko / 451 \\
                 The number field sieve / Carl Pomerance / 465 \\
                 Factoring integers before computers / H. C. Williams
                 and J. O. Shallit / 481 \\
                 \\
                 Contributed Papers \\
                 \\
                 Explicit bounds for primes in residue classes / Eric
                 Bach and Jonathan Sorenson / 535 \\
                 Ramanujan and Euler's constant / Richard P. Brent / 541
                 \\
                 Congruential sieves on FPGA computers / Nathan D.
                 Bronson and Duncan A. Buell / 547 \\
                 Lehmer pairs of zeros and the Riemann $\xi$-function /
                 George Csordas, Wayne Smith, and Richard S. Varga / 553
                 \\
                 A record Aliquot sequence / Andrew W. P. Guy and
                 Richard K. Guy / 557 \\
                 Implications of computational mathematics for the
                 philosophy of mathematics / Andrew J. Lazarus / 561 \\
                 Square roots of products of algebraic numbers / Peter
                 L. Montgomery / 567 \\
                 A locally parameterized version of Lehmer's problem /
                 Gary A. Ray / 573 \\
                 A new method for finding amicable pairs / H. J. J. te
                 Riele / 577 \\
                 Generalized Fermat numbers / Hans Riesel and Anders
                 Bj{\"o}rn / 583 \\
                 Evaluation of $\zeta_K(2)$ for some totally real
                 algebraic number fields K of degree 9 / Kisao Takeuchi
                 / 589 \\
                 The period of the Bell exponential integers modulo a
                 prime / Samuel S. Wagstaff, Jr. / 595 \\
                 Computing invariant polynomials of $p$-adic reflection
                 groups / Changsheng Xu / 599 \\
                 Author Index / 603 \\
                 Subject Index / 619",
}

@Proceedings{IEEE:1994:PFI,
  editor =       "{IEEE}",
  booktitle =    "Proceedings of the First International Conference on
                 Massively Parallel Computing Systems ({MPCS}). The
                 Challenges of General-Purpose and Special-Purpose
                 Computing",
  title =        "Proceedings of the First International Conference on
                 Massively Parallel Computing Systems ({MPCS}). The
                 Challenges of General-Purpose and Special-Purpose
                 Computing",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiv + 655",
  year =         "1994",
  ISBN =         "0-8186-6322-7",
  ISBN-13 =      "978-0-8186-6322-2",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 10:25:52 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  confdate =     "2-6 May 1994",
  conflocation = "Ischia, Italy",
}

@Proceedings{IEEE:1994:PTA,
  editor =       "{IEEE}",
  booktitle =    "Proceedings of the Third Asian Test Symposium",
  title =        "Proceedings of the Third Asian Test Symposium",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiv + 392",
  year =         "1994",
  ISBN =         "0-8186-6690-0",
  ISBN-13 =      "978-0-8186-6690-2",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 10:41:40 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog no. 94TH8016.",
  acknowledgement = ack-nhfb,
  confdate =     "15-17 Nov. 1994",
  conflocation = "Nara, Japan",
  confsponsor =  "IEEE Comput. Soc. Test Technol. Tech. Committee; Tech.
                 Group on Fault Tolerant Syst. IEICE; Tech. Group on
                 VLSI Design Technol., IEICE; Special Interest Group on
                 Design Autom., IPS Japan; Japan Soc. Promotion of Sci.;
                 132nd Committee (Electron. and Ion Beam Sci. and
                 Technol.); Nara Inst. Sci. and Technol",
}

@Proceedings{Lea:1994:PSA,
  editor =       "R. M. Lea and S. Tewksbury",
  booktitle =    "1994 Proceedings. Sixth Annual {IEEE} International
                 Conference on Wafer Scale Integration",
  title =        "1994 Proceedings. Sixth Annual {IEEE} International
                 Conference on Wafer Scale Integration",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "ix + 404",
  year =         "1994",
  ISBN =         "0-7803-1850-1",
  ISBN-13 =      "978-0-7803-1850-2",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 10:45:27 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog no. 94CH3412-4.",
  acknowledgement = ack-nhfb,
  confdate =     "19-21 Jan. 1994",
  conflocation = "San Francisco, CA, USA",
  confsponsor =  "IEEE",
}

@Proceedings{Mudge:1994:PTS,
  editor =       "T. N. Mudge and B. D. Shriver",
  booktitle =    "Proceedings of the Twenty-Seventh Hawaii Internation
                 Conference on System Sciences Vol. I: Architecture",
  title =        "Proceedings of the Twenty-Seventh Hawaii Internation
                 Conference on System Sciences Vol. {I}: Architecture",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xi + 621",
  year =         "1994",
  ISBN =         "0-8186-5050-8",
  ISBN-13 =      "978-0-8186-5050-5",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 10:39:37 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog no. 94TH0607-2.",
  acknowledgement = ack-nhfb,
  confdate =     "4-7 Jan. 1994",
  conflocation = "Wailea, HI, USA",
  confsponsor =  "IEEE; ACM; University of Hawaii; University of Hawaii
                 Coll. Bus. Admin",
}

@Proceedings{Pehrson:1994:IPP,
  editor =       "Bj{\"o}rn Pehrson and Imre Simon",
  booktitle =    "{Information processing '94: proceedings of the IFIP
                 13th World Computer Congress, Hamburg, Germany, 28
                 August--2 September, 1994: Technology and foundations:
                 Applications and impacts: Linkage and developing
                 countries}",
  title =        "{Information processing '94: proceedings of the IFIP
                 13th World Computer Congress, Hamburg, Germany, 28
                 August--2 September, 1994: Technology and foundations:
                 Applications and impacts: Linkage and developing
                 countries}",
  volume =       "A51--A53",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "????",
  year =         "1994",
  ISBN =         "0-444-81990-8 (set)",
  ISBN-13 =      "978-0-444-81990-1 (set)",
  LCCN =         "QA75.5 .I3785 1994",
  bibdate =      "Tue Nov 13 22:41:40 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  series =       "IFIP transactions. A, Computer science and
                 technology",
  acknowledgement = ack-nhfb,
  meetingname =  "IFIP World Computer Congress (13th: 1994: Hamburg,
                 Germany)",
  remark =       "v. 1 Technology and foundations / edited by Bj{\"o}rn
                 Pehrson, Imre Simon\\
                 v. 2. Applications and impacts / edited by Klaus
                 Brunnstein, Eckart Raubold \\
                 v. 3. Linkage and developing countries / edited by
                 Karen Duncan, Karl Krueger.",
  subject =      "Computer industry; Developing countries; Congresses;
                 Information technology; Electronic data processing",
}

@Proceedings{Wuorinen:1994:IIS,
  editor =       "John H. Wuorinen and others",
  booktitle =    "{1994 IEEE International Solid-State Circuits
                 Conference Digest of Technical Papers}",
  title =        "{1994 IEEE International Solid-State Circuits
                 Conference Digest of Technical Papers}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "400",
  year =         "1994",
  ISBN =         "0-7803-1844-7, 0-7803-1845-5, 0-7803-1846-3
                 (microfiche)",
  ISBN-13 =      "978-0-7803-1844-1, 978-0-7803-1845-8,
                 978-0-7803-1846-5 (microfiche)",
  LCCN =         "TK 7867 1994",
  bibdate =      "Sat Nov 29 10:30:52 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog no. 94CH3410-8.",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=1111",
  acknowledgement = ack-nhfb,
  confdate =     "16-18 Feb. 1994",
  conflocation = "San Francisco, CA, USA",
  confsponsor =  "IEEE Solid-State Circuits Council; IEEE Bay Area
                 Council San Francisco Sect",
}

@Proceedings{ACM:1995:PEA,
  editor =       "{ACM}",
  booktitle =    "{Proceedings of the Eleventh Annual Symposium on
                 Computational Geometry: Vancouver, British Columbia,
                 Canada, June 5--7, 1995}",
  title =        "{Proceedings of the Eleventh Annual Symposium on
                 Computational Geometry: Vancouver, British Columbia,
                 Canada, June 5--7, 1995}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "ix + 389 + 51",
  year =         "1995",
  ISBN =         "0-89791-724-3",
  ISBN-13 =      "978-0-89791-724-7",
  LCCN =         "QA448.D38 S96 1995",
  bibdate =      "Tue Nov 13 22:49:06 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  meetingname =  "Symposium on Computational Geometry (11th: 1995:
                 Vancouver, BC)",
  subject =      "Geometry; Data processing; Congresses",
}

@Proceedings{Anonymous:1995:HEI,
  editor =       "Anonymous",
  booktitle =    "{HOL95}: Eighth International Workshop on Higher-Order
                 Logic Theorem Proving and Its Applications, Aspen
                 Grove, {UT}, September 1995",
  title =        "{HOL95}: Eighth International Workshop on Higher-Order
                 Logic Theorem Proving and Its Applications, Aspen
                 Grove, {UT}, September 1995",
  publisher =    "Brigham Young University",
  address =      "Provo, UT, USA",
  year =         "1995",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 10:48:53 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://lal.cs.byu.edu/lal/hol95/Bprocs/indexB.html",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}

@Proceedings{Athanas:1995:PIS,
  editor =       "Peter Athanas and Kenneth L. Pocek",
  booktitle =    "{Proceedings: IEEE Symposium on FPGAs for Custom
                 Computing Machines, April 19--21, 1995, Napa Valley,
                 California}",
  title =        "{Proceedings: IEEE Symposium on FPGAs for Custom
                 Computing Machines, April 19--21, 1995, Napa Valley,
                 California}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "viii + 222",
  year =         "1995",
  DOI =          "https://doi.org/10.1109/FPGA.1995.477402",
  ISBN =         "0-8186-7086-X",
  ISBN-13 =      "978-0-8186-7086-2",
  LCCN =         "TK79.85 G36 I36 1995",
  bibdate =      "Sat Oct 9 15:10:55 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  subject =      "field programmable gate arrays; congresses; computer
                 engineering",
  tableofcontents = "A FCCM for Dataflow (Spreadsheet) Programs / A. Lew
                 and R. Halverson \\
                 MORRPH: A MOdular and Reprogrammable Real-time
                 Processing Hardware / T. H. Drayer, W. E. King, J. G.
                 Tront and R. W. Conners \\
                 Architecture of a FPGA-based Coprocessor: The PAR-1 /
                 J. M. Carrera, E. J. Martinez, S. A. Fernandez and J.
                 M. M. Chaus \\
                 Teramac - Configurable Custom Computing / R. Amerson,
                 R. J. Carter, W. B. Culbertson, P. Kuekes and G. Snider
                 \\
                 Common Processor Element Packaging for CHAMP / B. Box
                 and J. Nieznanski \\
                 Enable++: A Second Generation FPGA Processor / H. Hogl,
                 A. Kugel, J. Ludvig, R. Manner, K. H. Noffz and R. Zoz
                 \\
                 Design and Implementation of a Multicomputer
                 Interconnection Network Using FPGAs / C.-C. Yeh, C.-H.
                 Wu and J.-Y. Juang \\
                 Routability Improvement Using Dynamic Interconnect
                 Architecture / J. Li and C.-K. Cheng \\
                 Reconfigurable Real-Time Signal Transport System Using
                 Custom FPGAs / K. Hayashi, T. Miyazaki, K. Shirakawa,
                 K. Yamada and N. Ohta.",
}

@Proceedings{Bainov:1995:PTI,
  editor =       "D. (Dimitur) Bainov and Valery Covachev",
  booktitle =    "Proceedings of the Third International Colloquium on
                 Numerical Analysis: Plovdiv, Bulgaria, 13--17 August
                 1994",
  title =        "Proceedings of the Third International Colloquium on
                 Numerical Analysis: Plovdiv, Bulgaria, 13--17 August
                 1994",
  publisher =    "VSP",
  address =      "Utrecht, The Netherlands",
  pages =        "vi + 229",
  year =         "1995",
  ISBN =         "90-6764-193-6",
  ISBN-13 =      "978-90-6764-193-7",
  LCCN =         "QA297.I45 1994",
  bibdate =      "Sat Nov 29 10:53:15 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Cappello:1995:ICA,
  editor =       "Peter Cappello and Catherine Mongenet and Guy-Ren{\'e}
                 Perrin and Patrice Quinton and Yves Robert",
  booktitle =    "The International Conference on Application Specific
                 Array Processors: July 24--26, 1995, Strasbourg,
                 France: proceedings",
  title =        "The International Conference on Application Specific
                 Array Processors: July 24--26, 1995, Strasbourg,
                 France: proceedings",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiii + 340",
  year =         "1995",
  ISBN =         "0-8186-7109-2",
  ISBN-13 =      "978-0-8186-7109-8",
  ISSN =         "1063-6862",
  LCCN =         "TK7874.6 .I57 1995",
  bibdate =      "Mon Oct 20 07:16:07 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE Computer Society Press order number PR07109. EEE
                 catalog number 95TB8098.",
  acknowledgement = ack-nhfb,
  searchkey =    "ti:interval computations or ti:interval arithmetic",
  sponsor =      "IEEE. Computer Society. Technical Committee on VLSI.",
}

@Proceedings{IEEE:1995:DPC,
  editor =       "{IEEE}",
  booktitle =    "{Digest of papers: Compcon '95: technologies for the
                 information superhighway: March 5--9, 1995, San
                 Francisco, CA, USA}",
  title =        "{Digest of papers: Compcon '95: technologies for the
                 information superhighway: March 5--9, 1995, San
                 Francisco, CA, USA}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiv + 491",
  year =         "1995",
  ISBN =         "0-7803-2657-1 (hardcover), 0-8186-7029-0 (paperback),
                 0-7803-2658-X (microfiche)",
  ISBN-13 =      "978-0-7803-2657-6 (hardcover), 978-0-8186-7029-9
                 (paperback), 978-0-7803-2658-3 (microfiche)",
  ISSN =         "1063-6390",
  LCCN =         "QA 75.5 C58 1995",
  bibdate =      "Mon Aug 26 10:38:41 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE Computer Society Press order number PR07029. IEEE
                 catalog number 95CH35737.",
  acknowledgement = ack-nhfb,
  sponsor =      "IEEE; Computer Society.",
}

@Proceedings{IEEE:1995:IAI,
  editor =       "{IEEE}",
  booktitle =    "1995 {IEEE\slash} {ACM} International Conference on
                 Computer-Aided Design: digest of technical papers;
                 November 5--9, 1995, San Jose, California",
  title =        "1995 {IEEE}\slash {ACM} International Conference on
                 Computer-Aided Design: digest of technical papers;
                 November 5--9, 1995, San Jose, California",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xxviii + 743",
  year =         "1995",
  ISBN =         "0-8186-7213-7, 0-8186-7214-5",
  ISBN-13 =      "978-0-8186-7213-2, 978-0-8186-7214-9",
  LCCN =         "TA174 .I52 1995; TK7874 .I3235 1995",
  bibdate =      "Sat Nov 29 10:46:57 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog number 95CB35859. IEEE Computer Society
                 Press order number PR07213.",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:1995:ISM,
  editor =       "{IEEE}",
  booktitle =    "{5th International Symposium on Multiple-Valued Logic,
                 Bloomington, Indiana, May 23--25, 1995: Proceedings}",
  title =        "{5th International Symposium on Multiple-Valued Logic,
                 Bloomington, Indiana, May 23--25, 1995: Proceedings}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 296",
  year =         "1995",
  ISBN =         "0-8186-7118-1, 0-7803-2764-0, 0-7803-2765-9",
  ISBN-13 =      "978-0-8186-7118-0, 978-0-7803-2764-1,
                 978-0-7803-2765-8",
  LCCN =         "????",
  bibdate =      "Sat Aug 22 08:44:56 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.bibsys.no:2100/BIBSYS",
  acknowledgement = ack-nhfb,
}

@Proceedings{Jain:1995:PET,
  editor =       "L. C. Jain",
  booktitle =    "Proceedings. Electronic Technology Directions to the
                 Year 2000",
  title =        "Proceedings. Electronic Technology Directions to the
                 Year 2000",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "x + 313",
  year =         "1995",
  ISBN =         "0-8186-7085-1",
  ISBN-13 =      "978-0-8186-7085-5",
  LCCN =         "TK7801 .E456 1995",
  bibdate =      "Sat Nov 29 10:51:35 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  confdate =     "23-25 May 1995",
  conflocation = "Adelaide, SA, Australia",
  confsponsor =  "Electron. Assoc. South Australia; Defence Sci. and
                 Technol. Organ. Australia; MFP Australia; Telecom
                 Australia; Knowledge-Based Eng. Syst. Group, University
                 of South Australia; IEEE South Australia Section; Inst.
                 Eng., Australia; Security Inst. South Australia; IEEE
                 Comput. Soc",
}

@Proceedings{Knowles:1995:PSC,
  editor =       "Simon Knowles and William H. McAllister",
  booktitle =    "{Proceedings of the 12th Symposium on Computer
                 Arithmetic, July 19--21, 1995, Bath, England}",
  title =        "{Proceedings of the 12th Symposium on Computer
                 Arithmetic, July 19--21, 1995, Bath, England}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xvi + 252",
  year =         "1995",
  ISBN =         "0-8186-7089-4 (paperback), 0-8186-7089-4 (case),
                 0-8186-7149-1 (microfiche), 0-8186-7089-4 (softbound),
                 0-7803-2949-X (casebound)",
  ISBN-13 =      "978-0-8186-7089-3 (paperback), 978-0-8186-7089-3
                 (case), 978-0-8186-7149-4 (microfiche),
                 978-0-8186-7089-3 (softbound), 978-0-7803-2949-2
                 (casebound)",
  LCCN =         "QA 76.9 C62 S95 1995",
  bibdate =      "Sun Mar 29 08:48:20 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/conhome/3236/proceeding",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-12",
}

@Proceedings{Seck:1995:GWS,
  editor =       "Friedrich Seck",
  booktitle =    "{Zum 400. Geburtstag von Wilhelm Schickard: Zweites
                 T{\"u}binger Schickard-Symposion, 25. bis 27. Juni
                 1992}. ({German}) [{On} the 400th Birthday of {Wilhelm
                 Schickard}: {Second Tubingen Schickard Symposium,
                 25--27 June 1992}]",
  title =        "{Zum 400. Geburtstag von Wilhelm Schickard: Zweites
                 T{\"u}binger Schickard-Symposion, 25. bis 27. Juni
                 1992}. ({German}) [{On} the 400th Birthday of {Wilhelm
                 Schickard}: {Second Tubingen Schickard Symposium,
                 25--27 June 1992}]",
  volume =       "41",
  publisher =    "Thorbecke",
  address =      "Sigmaringen, Germany",
  pages =        "319",
  year =         "1995",
  ISBN =         "3-7995-3235-8",
  ISBN-13 =      "978-3-7995-3235-8",
  ISSN =         "0340-6857",
  ISSN-L =       "0340-6857",
  LCCN =         "????",
  bibdate =      "Sat Jul 27 11:09:25 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/scicontext.bib;
                 z3950.gbv.de:20011/gvk",
  price =        "DM 76.00, sfr 76.00, S 600.00",
  series =       "Contubernium",
  acknowledgement = ack-nhfb,
  language =     "German",
  subject =      "Schickard, Wilhelm",
  subject-dates = "1592--1635",
  tableofcontents = "Vorwort / 7 \\
                 Volker Sch{\"a}fer / Die Universit{\"a}t T{\"u}bingen
                 zur Zeit Schickards / 9 \\
                 Fran{\c{c}}ois-Joseph Fuchs / Matthias Bernegger und
                 die Anfange der Universit{\"a}t Stra{\ss}burg / 27 \\
                 Wilhelm K{\"u}hlmann / Wilhelm Schickard ---
                 Wissenschaft und Reformbegehren in der Zeit des
                 Konfessionalismus / 41 \\
                 Ulrich Bubenheimer / Wilhelm Schickard im Kontext einer
                 religi{\"o}sen Subkultur / 67 \\
                 Ulrich Neumann / ``Olim, da die Rosen Creutzerey noch
                 florirt, Theophilus Schweighart genant'': Wilhelm
                 Schickards Freund und Briefpartner Daniel M{\"o}gling
                 (1596--1635) / 93 \\
                 Claudia Ott / Schickard als Orientalist --- verkanntes
                 Genie oder interessierter Laie? / 117 \\
                 Wolfgang H{\"u}bner / Die Christianisierung der
                 Sternbilder in Schickards \booktitle{Astroscopium} \\
                 Horst Mauder / Die Kometenschriften von Schickard und
                 Kepler / 131 \\
                 Owen Gingerich / M{\"a}stlin's, Kepler's, and
                 Schickard's Copies of \booktitle{De revolutionibus} /
                 167 \\
                 Gerhard Betsch / Praxis geometrica und Kartographie an
                 der Universit{\"a}t T{\"u}bingen im 16 und fr{\"u}hen
                 17 Jahrhundert / 185 \\
                 G{\"u}nther Oestmann / Aus Wilhelm Schickards
                 \booktitle{Stuttgarter Skizzenbuch} / 227 \\
                 Friedrich Wilhelm Kistermann / Die Rechentechnik um
                 1600 und Wilhelm Schickards Rechenmaschine / 241 \\
                 N. Joachim Lehmann / Schickard und Leibniz als Erfinder
                 von Rechenmaschinen / 273 \\
                 Bruno Baron v. Freytag L{\"o}ringhoff / Zu Irrungen und
                 Verwirrungen um Wilhelm Schickard und seine /
                 Rechenmaschine von 1623 --- Ein Satyrspiel / 287 \\
                 Friedrich Seck / Zur Edition von Schickards
                 Briefwechsel / 297 \\
                 Anhang: Wilhelm Schickard und der N{\"u}rnberger
                 Trichter / 310 \\
                 Personenregister / 313",
}

@Proceedings{Singh:1995:CRT,
  editor =       "Avtar Singh",
  booktitle =    "Conference record of the Twenty-Ninth Asilomar
                 Conference on Signals, Systems \& Computers: October
                 30--November 1, 1995 Pacific Grove, California",
  title =        "Conference record of the Twenty-Ninth Asilomar
                 Conference on Signals, Systems \& Computers: October
                 30--November 1, 1995 Pacific Grove, California",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "various",
  year =         "1995",
  ISBN =         "0-8186-7370-2",
  ISBN-13 =      "978-0-8186-7370-2",
  LCCN =         "TK7801 .A83 1995",
  bibdate =      "Sun Mar 29 08:51:26 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Two volumes.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Alefeld:1996:NME,
  editor =       "G{\"o}tz Alefeld and J{\"u}rgen Herzberger",
  booktitle =    "Numerical methods and error bounds: proceedings of the
                 {IMACS GAMM International Symposium on Numerical
                 Methods and Error Bounds held in Oldenburg, Germany,
                 July 9--12, 1995}",
  title =        "Numerical methods and error bounds: proceedings of the
                 {IMACS GAMM International Symposium on Numerical
                 Methods and Error Bounds held in Oldenburg, Germany,
                 July 9--12, 1995}",
  volume =       "89",
  publisher =    pub-AKADEMIE-VERLAG,
  address =      pub-AKADEMIE-VERLAG:adr,
  pages =        "302",
  year =         "1996",
  ISBN =         "3-05-501696-3",
  ISBN-13 =      "978-3-05-501696-7",
  ISSN =         "0138-3019",
  LCCN =         "QA297 .I455 1995",
  bibdate =      "Tue Nov 02 18:36:50 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Mathematical Research",
  acknowledgement = ack-nhfb,
}

@Proceedings{Alefeld:1996:SCV,
  editor =       "G{\"o}tz Alefeld and Andreas Frommer and Bruno Lang",
  booktitle =    "Scientific computing and validated numerics:
                 proceedings of the International Symposium on
                 Scientific Computing, Computer Arithmetic and Validated
                 Numerics {SCAN-95} held in Wuppertal, Germany,
                 September 26--29, 1995",
  title =        "Scientific computing and validated numerics:
                 proceedings of the International Symposium on
                 Scientific Computing, Computer Arithmetic and Validated
                 Numerics {SCAN}-95 held in Wuppertal, Germany,
                 September 26--29, 1995",
  volume =       "90",
  publisher =    "Akademie Verlag",
  address =      "Berlin, Germany",
  pages =        "340",
  year =         "1996",
  ISBN =         "3-05-501737-4",
  ISBN-13 =      "978-3-05-501737-7",
  ISSN =         "0138-3019",
  LCCN =         "QA76.95 .I575 1995",
  bibdate =      "Fri Mar 27 09:56:17 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Mathematical Research",
  acknowledgement = ack-nhfb,
}

@Book{Bergin:1996:HPL,
  author =       "Thomas J. {Bergin, Jr.} and Richard G. {Gibson, Jr.}",
  booktitle =    "History of Programming Languages {II}",
  title =        "History of Programming Languages {II}",
  publisher =    pub-ACM # " and " # pub-AW,
  address =      pub-ACM:adr # " and " # pub-AW:adr,
  pages =        "xvi + 864",
  year =         "1996",
  ISBN =         "0-201-89502-1",
  ISBN-13 =      "978-0-201-89502-5",
  LCCN =         "QA76.7 .H558 1996",
  bibdate =      "Wed Nov 19 08:49:59 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Drawn from the Second ACM SIGPLAN History of
                 Programming Languages Conference.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Bouge:1996:EPP,
  editor =       "L. (Luc) Bouge",
  booktitle =    "{Euro-Par'96}: parallel processing: second
                 International {Euro-Par} Conference, Lyon, France,
                 August 26--29, 1996: proceedings",
  title =        "{Euro-Par'96}: parallel processing: second
                 International {Euro-Par} Conference, Lyon, France,
                 August 26--29, 1996: proceedings",
  volume =       "1123, 1124",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "various",
  year =         "1996",
  DOI =          "https://doi.org/10.1007/3-540-61626-8;
                 https://doi.org/10.1007/BFb0024677",
  ISBN =         "3-540-61626-8 (vol. 1), 3-540-61627-6 (vol. 2)",
  ISBN-13 =      "978-3-540-61626-9 (vol. 1), 978-3-540-61627-6 (vol.
                 2)",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  LCCN =         "QA76.58.I554 1996",
  bibdate =      "Sat Sep 7 08:18:27 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
  keywords =     "Parallel processing (Electronic computers) ---
                 Congresses.",
}

@Book{Hennessy:1996:CAQ,
  author =       "John L. Hennessy and David A. Patterson",
  booktitle =    "Computer Architecture\emdash {A} Quantitative
                 Approach",
  title =        "Computer Architecture\emdash {A} Quantitative
                 Approach",
  publisher =    pub-MORGAN-KAUFMANN,
  address =      pub-MORGAN-KAUFMANN:adr,
  edition =      "Second",
  pages =        "xxiii + 760 + A-77 + B-47 + C-26 + D-26 + E-13 + R-16
                 + I-14",
  year =         "1996",
  ISBN =         "1-55860-329-8",
  ISBN-13 =      "978-1-55860-329-5",
  LCCN =         "QA76.9.A73P377 1995",
  bibdate =      "Mon May 20 10:01:59 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$69.95",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:1996:DAC,
  editor =       "{IEEE}",
  booktitle =    "33rd Design Automation Conference: proceedings 1996,
                 Las Vegas Convention Center, Las Vegas, {NV}, June
                 3--7, 1996",
  title =        "33rd Design Automation Conference: proceedings 1996,
                 Las Vegas Convention Center, Las Vegas, {NV}, June
                 3--7, 1996",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xxx + 839",
  year =         "1996",
  ISBN =         "0-7803-3294-6 (casebound), 0-7803-3364-0 (softbound),
                 0-7803-3295-4 (microfiche), 0-89791-779-0 (ACM)",
  ISBN-13 =      "978-0-7803-3294-2 (casebound), 978-0-7803-3364-2
                 (softbound), 978-0-7803-3295-9 (microfiche),
                 978-0-89791-779-7 (ACM)",
  LCCN =         "TA174 .D46 1996",
  bibdate =      "Sat Nov 29 10:54:23 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "ACM order number 47796. IEEE catalog number
                 96CH35932.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Kearfott:1996:AICa,
  editor =       "R. Baker Kearfott and Vladik Kreinovich",
  booktitle =    "Applications of interval computations: Papers
                 presented at an international workshop in El Paso,
                 Texas, February 23--25, 1995",
  title =        "Applications of interval computations: Papers
                 presented at an international workshop in El Paso,
                 Texas, February 23--25, 1995",
  volume =       "3",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "xvii + 425",
  year =         "1996",
  ISBN =         "0-7923-3847-2",
  ISBN-13 =      "978-0-7923-3847-5",
  LCCN =         "QA297.75.A66 1996",
  bibdate =      "Mon Oct 20 07:16:07 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "``Applications of Interval Computations'' contains
                 primarily survey articles of actual industrial
                 applications of numerical analysis with automatic
                 result verification and of interval representation of
                 data.

                 Underlying topics include: \begin{itemize} \item branch
                 and bound algorithms for global optimization, \item
                 constraint propagation, \item solution sets of linear
                 systems, \item hardware and software systems for
                 interval computations, and \item fuzzy logic.
                 \end{itemize}

                 Actual applications described in the book include:
                 \begin{itemize} \item economic input-output models,
                 \item quality control in manufacturing design, \item a
                 computer-assisted proof in quantum mechanics, \item
                 medical expert systems, \item and others.
                 \end{itemize}

                 A realistic view of interval computations is taken: the
                 articles indicate when and how overestimation and other
                 challenges can be overcome.

                 An introductory chapter explains the content of the
                 papers in terminology accessible to mathematically
                 literate graduate students. The style of the
                 individual, refereed contributions has been made
                 uniform and understandable, and there is an extensive
                 book-wide index.

                 Audience: Valuable to students and researchers
                 interested in automatic result verification.

                 Detailed information, including contents, contributors,
                 and an order form can be found: \begin{itemize} \item
                 on Kluwer homepage \path=http://www.wkap.nl=, or \item
                 on the Interval Computations homepage
                 \path=http://cs.utep.edu/interval-comp/main.html=, in
                 the ``Books'' section. \end{itemize} The information on
                 the Interval Computations homepage is basically a
                 mirror image of the Kluwer one (the only difference is
                 that the fonts are fancier).",
  series =       "Applied Optimization",
  acknowledgement = ack-nhfb # " and " # ack-dgh,
}

@Proceedings{LakshmanYN:1996:IPI,
  editor =       "{Lakshman Y.N.}",
  booktitle =    "{ISSAC '96: Proceedings of the 1996 International
                 Symposium on Symbolic and Algebraic Computation, July
                 24--26, 1996, Zurich, Switzerland}",
  title =        "{ISSAC '96: Proceedings of the 1996 International
                 Symposium on Symbolic and Algebraic Computation, July
                 24--26, 1996, Zurich, Switzerland}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xvii + 313",
  year =         "1996",
  ISBN =         "0-89791-796-0",
  ISBN-13 =      "978-0-89791-796-4",
  LCCN =         "QA 76.95 I59 1996",
  bibdate =      "Thu Mar 12 08:00:14 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  sponsor =      "ACM; Special Interest Group in Symbolic and Algebraic
                 Manipulation (SIGSAM). ACM; Special Interest Group on
                 Numerical Mathematics (SIGNUM).",
}

@Proceedings{Luk:1996:PSC,
  editor =       "Franklin T. Luk",
  booktitle =    "{Proceedings of the 1996 SPIE Conference on Advanced
                 Signal Processing Algorithms, Architectures, and
                 Implementations VI, 6--8 August, 1996, Denver,
                 Colorado}",
  title =        "{Proceedings of the 1996 SPIE Conference on Advanced
                 Signal Processing Algorithms, Architectures, and
                 Implementations VI, 6--8 August, 1996, Denver,
                 Colorado}",
  volume =       "2846",
  publisher =    pub-SPIE,
  address =      pub-SPIE:adr,
  pages =        "vii + 464",
  year =         "1996",
  ISBN =         "0-8194-2234-7",
  ISBN-13 =      "978-0-8194-2234-7",
  LCCN =         "????",
  bibdate =      "Tue Jun 14 18:19:43 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://spiedigitallibrary.org/proceedings/resource/2/psisdg/2846/1",
  acknowledgement = ack-nhfb,
}

@Proceedings{Pellikaan:1996:AGC,
  editor =       "R. Pellikaan and M. Perret and S. G. Vladut",
  booktitle =    "Arithmetic, geometry, and coding theory: proceedings
                 of the international conference held at Centre
                 international de rencontres math{\'e}matiques {(CIRM),
                 Luminy, France, June 28--July 2, 1993}",
  title =        "Arithmetic, geometry, and coding theory: proceedings
                 of the international conference held at Centre
                 international de rencontres math{\'e}matiques {(CIRM),
                 Luminy, France, June 28--July 2, 1993}",
  publisher =    pub-GRUYTER,
  address =      pub-GRUYTER:adr,
  pages =        "xii + 288",
  year =         "1996",
  ISBN =         "3-11-014616-9",
  ISBN-13 =      "978-3-11-014616-5",
  LCCN =         "QA268 .A75 1996",
  bibdate =      "Wed Jan 16 09:27:31 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "UK\pounds 102.45",
  acknowledgement = ack-nhfb,
  keywords =     "coding theory --- congresses; geometry, algebraic ---
                 congresses; number theory --- congresses",
}

@Proceedings{Pocek:1996:ISF,
  editor =       "Kenneth L. Pocek and Jeffrey M. Arnold",
  booktitle =    "{IEEE Symposium on FPGAs for Custom Computing
                 Machines: proceedings, April 17--19, 1996, Napa Valley,
                 California}",
  title =        "{IEEE Symposium on FPGAs for Custom Computing
                 Machines: proceedings, April 17--19, 1996, Napa Valley,
                 California}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "viii + 235",
  year =         "1996",
  ISBN =         "0-8186-7548-9",
  ISBN-13 =      "978-0-8186-7548-5",
  LCCN =         "TK7895.G36 I35 1996",
  bibdate =      "Sat Oct 9 15:15:32 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog number 96TB100063.",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=4230",
  acknowledgement = ack-nhfb,
  subject =      "field programmable gate arrays; congresses; computer
                 engineering; compilers (computer programs)",
}

@Proceedings{Srivas:1996:FMC,
  editor =       "Mandayam Srivas and Albert Camilleri",
  booktitle =    "Formal methods in computer-aided design: first
                 international conference, {FMCAD} '96, Palo Alto, {CA},
                 {USA}, November 6--8, 1996: proceedings",
  title =        "Formal methods in computer-aided design: first
                 international conference, {FMCAD} '96, Palo Alto, {CA},
                 {USA}, November 6--8, 1996: proceedings",
  volume =       "1166",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "ix + 470",
  year =         "1996",
  ISBN =         "3-540-61937-2",
  ISBN-13 =      "978-3-540-61937-6",
  LCCN =         "TK7874.65 .F53 1996",
  bibdate =      "Thu Nov 25 10:43:33 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
  meetingname =  "FMCAD '96 (1996: Palo Alto, Calif.)",
  subject =      "Digital integrated circuits; Computer-aided design;
                 Congresses; Automatic theorem proving; Congresses;
                 Integrated circuits; Verification; Congresses; Computer
                 engineering; Computer-aided design; Congresses; Formal
                 methods (Computer science); Congresses",
}

@Proceedings{Wuorinen:1996:DTP,
  editor =       "John H. Wuorinen",
  booktitle =    "Digest of technical papers: 1996 {IEEE} International
                 Solid-State Circuits Conference. San Francisco Marriott
                 Hotel, February 6--7, 1996",
  title =        "Digest of technical papers: 1996 {IEEE} International
                 Solid-State Circuits Conference. San Francisco Marriott
                 Hotel, February 6--7, 1996",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "512",
  year =         "1996",
  ISBN =         "0-7803-3137-0 (casebound), 0-7803-3136-2 (softbound),
                 0-7803-3138-9 (microfiche)",
  ISBN-13 =      "978-0-7803-3137-2 (casebound), 978-0-7803-3136-5
                 (softbound), 978-0-7803-3138-9 (microfiche)",
  LCCN =         "TK7870 .I58 1996",
  bibdate =      "Sun Mar 29 08:45:04 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Book{Zachary:1996:ISP,
  author =       "Joseph Zachary",
  booktitle =    "Introduction to scientific programming: computational
                 problem solving using {Maple} and {C}",
  title =        "Introduction to scientific programming: computational
                 problem solving using {Maple} and {C}",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xxiv + 380",
  year =         "1996",
  DOI =          "https://doi.org/10.1007/978-1-4612-2366-5",
  ISBN =         "0-387-94630-6, 1-4612-7518-0 (print), 1-4612-2366-0
                 (electronic)",
  ISBN-13 =      "978-0-387-94630-6, 978-1-4612-7518-3 (print),
                 978-1-4612-2366-5 (electronic)",
  LCCN =         "QA76.6 .Z32 1996",
  bibdate =      "Tue Mar 25 09:08:38 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
  acknowledgement = ack-nhfb,
  annote =       "System requirements for accompanying computer disk:
                 Maple V Release 3 or 4; ANSI C compiler; Macintosh;
                 Unix or DOS computer capable of reading DOS-formatted
                 high-density diskettes.",
  keywords =     "C (Computer program language); Computer programming;
                 Maple (Computer file)",
}

@Proceedings{Boisvert:1997:QNS,
  editor =       "Ronald F. Boisvert",
  booktitle =    "The Quality of Numerical Software: Assessment and
                 Enhancement: Proceedings of the {IFIP} {TC2}\slash {WG}
                 2.5 Working Conference on the Quality of Numerical
                 Software, Oxford, United Kingdon, 8--12 July 1996",
  title =        "The Quality of Numerical Software: Assessment and
                 Enhancement: Proceedings of the {IFIP} {TC2}\slash {WG}
                 2.5 Working Conference on the Quality of Numerical
                 Software, Oxford, United Kingdon, 8--12 July 1996",
  publisher =    "Chapman Hall on behalf of IFIP",
  address =      "London",
  year =         "1997",
  ISBN =         "0-412-80530-8",
  ISBN-13 =      "978-0-412-80530-1",
  bibdate =      "Tue Jul 21 11:17:29 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/grosse-eric.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Fargues:1997:CRT,
  editor =       "Monique P. Fargues and Ralph D. Hippenstiel",
  booktitle =    "{Conference record of the Thirty-First Asilomar
                 Conference on Signals, Systems \& Computers: November
                 2--5, 1997, Pacific Grove, California}",
  title =        "{Conference record of the Thirty-First Asilomar
                 Conference on Signals, Systems \& Computers: November
                 2--5, 1997, Pacific Grove, California}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xxiii + 1749",
  year =         "1997",
  ISBN =         "0-8186-8316-3, 0-8186-8317-1 (casebound),
                 0-8186-8318-X (microfiche)",
  ISBN-13 =      "978-0-8186-8316-9, 978-0-8186-8317-6 (casebound),
                 978-0-8186-8318-3 (microfiche)",
  LCCN =         "TK454.2; TK 7885",
  bibdate =      "Sat Jun 25 06:57:59 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Two volumes. IEEE order plan catalog number
                 97CB36163.",
  URL =          "ftp://uiarchive.cso.uiuc.edu/pub/etext/gutenberg/;
                 http://ieeexplore.ieee.org/servlet/opac?punumber=5559",
  acknowledgement = ack-nhfb,
}

@Proceedings{Lang:1997:ISC,
  editor =       "Tomas Lang and Jean-Michel Muller and Naofumi Takagi",
  booktitle =    "{13th IEEE Symposium on Computer Arithmetic:
                 proceedings, July 6--9, 1997, Asilomar, California,
                 USA}",
  title =        "{13th IEEE Symposium on Computer Arithmetic:
                 proceedings, July 6--9, 1997, Asilomar, California,
                 USA}",
  volume =       "13",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiii + 291",
  year =         "1997",
  ISBN =         "0-8186-7846-1, 0-8186-7847-X, 0-8186-7848-8",
  ISBN-13 =      "978-0-8186-7846-2, 978-0-8186-7847-9,
                 978-0-8186-7848-6",
  ISSN =         "1063-6889",
  LCCN =         "QA76.9.C62 S95 1997",
  bibdate =      "Fri Mar 27 09:56:17 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE Computer Society order number PR07846. IEEE Order
                 Plan catalog number 97CB36091.",
  series =       "Symposium on Computer Arithmetic",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-13",
  sponsor =      "IEEE.",
}

@Proceedings{Pocek:1997:PAI,
  editor =       "Kenneth L. Pocek and Jeffrey M. Arnold",
  booktitle =    "{Proceedings, the 6th Annual IEEE Symposium on
                 Field-Programmable Custom Computing Machines, April
                 16--18, 1998, Napa Valley, California}",
  title =        "{Proceedings, the 6th Annual IEEE Symposium on
                 Field-Programmable Custom Computing Machines, April
                 16--18, 1998, Napa Valley, California}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "x + 250",
  year =         "1997",
  DOI =          "https://doi.org/10.1109/FPGA.1998.707875",
  ISBN =         "0-8186-8900-5, 0-8186-8902-1 (microfiche)",
  ISBN-13 =      "978-0-8186-8900-0, 978-0-8186-8902-4 (microfiche)",
  ISSN =         "1082-3409",
  LCCN =         "TK7895.G36 I36 1998",
  bibdate =      "Sat Oct 9 15:17:05 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE Computer Society order number PR08159. IEEE order
                 plan catalog number 97TB100186.",
  acknowledgement = ack-nhfb,
  subject =      "Field programmable gate arrays; Congresses; Computer
                 engineering",
  xxnote =       "IEEE Web Xplore site says 15--17 April, 1998.
                 Check??",
}

@Proceedings{Thiele:1997:IIC,
  editor =       "Lothar Thiele and Jose Fortes and Kees Vissers and
                 Valerie Taylor and Tobias Noll and J{\"u}rgen Teich",
  booktitle =    "{IEEE International Conference on Application-Specific
                 Systems, Architectures and Processors: proceedings,
                 July 14--16, 1997, Z{\"u}rich, Switzerland}",
  title =        "{IEEE International Conference on Application-Specific
                 Systems, Architectures and Processors: proceedings,
                 July 14--16, 1997, Z{\"u}rich, Switzerland}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 540",
  year =         "1997",
  DOI =          "https://doi.org/10.1109/ASAP.1997.606806",
  ISBN =         "0-8186-7959-X, 0-8186-7960-3, 0-8186-7958-1",
  ISBN-13 =      "978-0-8186-7959-9, 978-0-8186-7960-5,
                 978-0-8186-7958-2",
  LCCN =         "TK7874.6 .I57 1997",
  bibdate =      "Sun Mar 4 21:13:29 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  meetingname =  "International Conference on Application-Specific
                 Systems, Architectures, and Processors (11th: 1997:
                 Z{\"u}rich, Switzerland)",
  remark =       "IEEE Computer Society Press order number PR07958. IEEE
                 catalog number 97TB100177",
  subject =      "Array processors; Congresses; Signal processing;
                 Digital techniques; Application-specific integrated
                 circuits",
}

@Proceedings{ACM:1998:AWJ,
  editor =       "{ACM}",
  booktitle =    "{ACM 1998} Workshop on Java for High-Performance
                 Network Computing",
  title =        "{ACM} 1998 Workshop on Java for High-Performance
                 Network Computing",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "????",
  year =         "1998",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Thu Apr 27 10:40:59 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Possibly unpublished, except electronically.",
  URL =          "http://www.cs.ucsb.edu/conferences/java98/program.html",
  acknowledgement = ack-nhfb,
}

@Proceedings{Anonymous:1998:PNI,
  editor =       "Anonymous",
  booktitle =    "The Proceedings of the Ninth International Conference
                 on Signal Processing Applications \& Technology:
                 September 13--16, 1998, Toronto, Canada",
  title =        "The Proceedings of the Ninth International Conference
                 on Signal Processing Applications \& Technology:
                 September 13--16, 1998, Toronto, Canada",
  publisher =    pub-MILLER-FREEMAN,
  address =      pub-MILLER-FREEMAN:adr,
  pages =        "1622",
  year =         "1998",
  LCCN =         "TK5102.5",
  bibdate =      "Sat Nov 29 11:01:38 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Two volumes.",
  acknowledgement = ack-nhfb,
  xxISBN =       "none",
}

@Proceedings{Chesneaux:1998:PCR,
  editor =       "Jean-Marie Chesneaux and others",
  booktitle =    "Proceedings of the 3rd Conference on Real Numbers and
                 Computers {(RNC3), 27--29} Avril, 1998, Paris, France",
  title =        "Proceedings of the 3rd Conference on Real Numbers and
                 Computers ({RNC3}), 27--29 Avril, 1998, Paris, France",
  publisher =    "????",
  address =      "Paris, France",
  pages =        "229",
  year =         "1998",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Tue Mar 13 10:37:17 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Troisi{\`e}me conf{\'e}rence Nombres R{\'e}els et
                 Ordinateurs",
}

@Proceedings{Gloor:1998:IPI,
  editor =       "Oliver Gloor",
  booktitle =    "{ISSAC 98}: Proceedings of the 1998 International
                 Symposium on Symbolic and Algebraic Computation, August
                 13--15, 1998, University of Rostock, Germany",
  title =        "{ISSAC 98}: Proceedings of the 1998 International
                 Symposium on Symbolic and Algebraic Computation, August
                 13--15, 1998, University of Rostock, Germany",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xxii + 327",
  year =         "1998",
  ISBN =         "1-58113-002-3",
  ISBN-13 =      "978-1-58113-002-7",
  LCCN =         "????",
  bibdate =      "Wed Sep 16 17:13:58 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Holub:1998:ILW,
  editor =       "Jan Holub and Radislav Smid",
  booktitle =    "1st International On-Line Workshop on Dithering in
                 Measurement: Theory and Applications, Prague, Czech
                 Republic, March 1--31, 1998",
  title =        "1st International On-Line Workshop on Dithering in
                 Measurement: Theory and Applications, Prague, Czech
                 Republic, March 1--31, 1998",
  publisher =    "CTU FEE Department of Measurement and TUT Measurement
                 and Information Technology",
  address =      "Prague, Czech Republic and Tampere, Finland",
  pages =        "105",
  year =         "1998",
  ISBN =         "80-01-01806-7",
  ISBN-13 =      "978-80-01-01806-4",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 10:57:48 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Huijsing:1998:EPE,
  editor =       "Johan H. Huijsing and Arthur H. M. van Roermund and
                 Herbert Grunbacher",
  booktitle =    "{ESSCIRC '98}: proceedings of the 24th European
                 Solid-State Circuits Conference, The Hague, The
                 Netherlands, 22--24, 1998: Challenges for the next
                 millennium",
  title =        "{ESSCIRC} '98: proceedings of the 24th European
                 Solid-State Circuits Conference, The Hague, The
                 Netherlands, 22--24, 1998: Challenges for the next
                 millennium",
  publisher =    "Editions Fronti{\`e}res",
  address =      "Paris, France",
  pages =        "xii + 514",
  year =         "1998",
  ISBN =         "2-86332-235-4",
  ISBN-13 =      "978-2-86332-235-2",
  LCCN =         "TK7871.85 .E887 1998",
  bibdate =      "Sat Nov 29 11:23:20 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:1998:HCC,
  editor =       "{IEEE}",
  booktitle =    "Hot chips 10: conference record: August 16--18, 1998,
                 Memorial Auditorium, Stanford University, Palo Alto,
                 California",
  title =        "Hot chips 10: conference record: August 16--18, 1998,
                 Memorial Auditorium, Stanford University, Palo Alto,
                 California",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "1998",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Mon Jan 08 05:06:55 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:1998:IIC,
  editor =       "{IEEE}",
  booktitle =    "{1998 IEEE International Conference on Computer
                 Design: VLSI in Computers and Processors: October 5--7,
                 1998 Austin, Texas: Proceedings}",
  title =        "{1998 IEEE International Conference on Computer
                 Design: VLSI in Computers and Processors: October 5--7,
                 1998 Austin, Texas: Proceedings}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xix + 644",
  year =         "1998",
  ISBN =         "0-8186-9099-2, 0-7803-5198-3, 0-8186-9101-8",
  ISBN-13 =      "978-0-8186-9099-0, 978-0-7803-5198-1,
                 978-0-8186-9101-0",
  LCCN =         "????",
  bibdate =      "Sat Aug 22 08:28:30 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.bibsys.no:2100/BIBSYS",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:1998:IOM,
  editor =       "{IEEE}",
  booktitle =    "Proceedings of the 24th {EUROMICRO} Conference,
                 V{\"a}ster{\aa}s, Sweden, August 25--27, 1998",
  title =        "Proceedings of the 24th {EUROMICRO} Conference,
                 {V}{\"a}ster{\aa}s, Sweden, August 25--27, 1998",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "1998",
  ISBN =         "0-8186-8646-4, 0-8186-8647-2 (casebound),
                 0-8186-8648-0 (microfiche)",
  ISBN-13 =      "978-0-8186-8646-7, 978-0-8186-8647-4 (casebound),
                 978-0-8186-8648-1 (microfiche)",
  LCCN =         "QA76.5 .S97 1998; QA 76.5 .E9 1998",
  bibdate =      "Sat Jun 25 07:18:07 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 sirsi.library.utoronto.ca:2200/UNICORN",
  note =         "Two volumes. IEEE Computer Society Order Number
                 PR08646.",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:1998:PGL,
  editor =       "{IEEE}",
  booktitle =    "{Proceedings of the 8th Great Lakes Symposium on VLSI:
                 Hotel Acadiana, Lafayette, Louisiana, February 19--21,
                 1998}",
  title =        "{Proceedings of the 8th Great Lakes Symposium on VLSI:
                 Hotel Acadiana, Lafayette, Louisiana, February 19--21,
                 1998}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xvi + 460",
  year =         "1998",
  ISBN =         "0-8186-8409-7, 0-8186-8411-9",
  ISBN-13 =      "978-0-8186-8409-8, 978-0-8186-8411-1",
  LCCN =         "TK7874 .G689 1998",
  bibdate =      "Mon Mar 5 15:59:16 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  meetingname =  "Great Lakes Symposium on VLSI (8th: 1998: Lafayette,
                 La.)",
  remark =       "IEEE Computer Society Order Number PR08409. IEEE Order
                 Plan Catalog Number 98TB100222.",
  subject =      "Integrated circuits; Very large scale integration;
                 Design and construction; Congresses; Computer-aided
                 design",
}

@Proceedings{MacKay:1998:PCT,
  editor =       "Stephen A. MacKay and J. Howard Johnson",
  booktitle =    "Proceedings of {CASCON'98}: Toronto, Ontario, Canada,
                 30 November--3 December 1998",
  title =        "Proceedings of {CASCON}'98: Toronto, Ontario, Canada,
                 30 November--3 December 1998",
  publisher =    "IBM Toronto Laboratory, Centre for Advanced Studies",
  address =      "Toronto, ON, Canada",
  pages =        "xiii + 322",
  year =         "1998",
  LCCN =         "TK 5105.5 .C36 1998",
  bibdate =      "Sat Nov 29 10:56:20 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  altbooktitle = "Meeting of minds: conference program / CASCON '98,
                 November 30--December 3, 1998, International Plaza
                 Hotel, Toronto, Ontario, Canada",
  xxISBN =       "none",
}

@Proceedings{Matthews:1998:CRT,
  editor =       "Michael B. Matthews and others",
  booktitle =    "{Conference record of the Thirty-Second Asilomar
                 Conference on Signals, Systems and Computers: November
                 1--4, 1998, Pacific Grove, California}",
  title =        "{Conference record of the Thirty-Second Asilomar
                 Conference on Signals, Systems and Computers: November
                 1--4, 1998, Pacific Grove, California}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "1998",
  ISBN =         "0-7803-5148-7, 0-7803-5149-5, 0-7803-5150-9",
  ISBN-13 =      "978-0-7803-5148-6, 978-0-7803-5149-3,
                 978-0-7803-5150-9",
  LCCN =         "TK5101.A1 A85 1998; TK454.2 .A8 1998",
  bibdate =      "Mon Mar 5 15:56:18 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  meetingname =  "Asilomar Conference on Signals, Systems and Computers
                 (32nd: 1998: Pacific Grove, Calif.)",
  remark =       "IEEE Catalog Number 98CH36284.",
  subject =      "Signal processing; Digital techniques; Congresses;
                 Electronic digital computers",
}

@Proceedings{Pocek:1998:PIS,
  editor =       "Kenneth L. Pocek and Jeffrey M. Arnold",
  booktitle =    "{Proceedings, IEEE Symposium on FPGAs for Custom
                 Computing Machines, April 15--17, 1998, Napa Valley,
                 California}",
  title =        "{Proceedings, IEEE Symposium on FPGAs for Custom
                 Computing Machines, April 15--17, 1998, Napa Valley,
                 California}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "x + 344",
  year =         "1998",
  DOI =          "https://doi.org/10.1109/FPGA.1998.707875",
  ISBN =         "0-8186-8900-5, 0-8186-8902-1 (microfiche)",
  ISBN-13 =      "978-0-8186-8900-0, 978-0-8186-8902-4 (microfiche)",
  ISSN =         "1082-3409",
  LCCN =         "TK7895.G36 I33 1998",
  bibdate =      "Sat Oct 9 15:17:05 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=5734",
  acknowledgement = ack-nhfb,
  subject =      "field programmable gate arrays; congresses; computer
                 engineering",
}

@Proceedings{Sasao:1998:ISM,
  editor =       "Tsutomu Sasao and Bob Werner",
  booktitle =    "28th International Symposium on Multiple-Valued Logic
                 ({ISMVL '98}), Fukuoka, Japan, May 26--29, 1998",
  title =        "28th International Symposium on Multiple-Valued Logic
                 ({ISMVL} '98), Fukuoka, Japan, May 26--29, 1998",
  volume =       "28",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xvi + 384",
  year =         "1998",
  ISBN =         "0-8186-8371-6 (paperback), 0-8186-8372-4 (casebound),
                 0-8186-8373-2 (microfiche)",
  ISBN-13 =      "978-0-8186-8371-8 (paperback), 978-0-8186-8372-5
                 (casebound), 978-0-8186-8373-2 (microfiche)",
  ISSN =         "0195-623X",
  LCCN =         "????",
  bibdate =      "Sat Jun 25 10:06:53 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog number 98CB36138.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Sohi:1998:YIS,
  editor =       "Gurindar Sohi",
  booktitle =    "25 years of the {International Symposia on Computer
                 architecture}",
  title =        "25 years of the {International Symposia on Computer
                 architecture}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xiii + 546",
  year =         "1998",
  ISBN =         "1-58113-058-9",
  ISBN-13 =      "978-1-58113-058-4",
  ISSN =         "1063-6897",
  LCCN =         "QA76.9.A73 S944 1998",
  bibdate =      "Fri Nov 28 18:41:44 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
}

@Proceedings{ACM:1999:PFA,
  editor =       "{ACM}",
  booktitle =    "Proceedings of the Fifteenth Annual Symposium on
                 Computational Geometry: June 13--16, 1999, Miami Beach,
                 Florida",
  title =        "Proceedings of the Fifteenth Annual Symposium on
                 Computational Geometry: June 13--16, 1999, Miami Beach,
                 Florida",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "x + 432",
  year =         "1999",
  ISBN =         "1-58113-068-6",
  ISBN-13 =      "978-1-58113-068-3",
  LCCN =         "????",
  bibdate =      "Sat Apr 28 18:59:36 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "ACM order number 429990.",
  URL =          "http://www.acm.org/pubs/contents/proceedings/compgeom/304893/",
  acknowledgement = ack-nhfb,
}

@Proceedings{Begehr:1999:PSI,
  editor =       "Heinrich G. W. Begehr and Robert P. Gilbert and Joji
                 Kajiwara",
  booktitle =    "Proceedings of the Second {ISAAC} Congress:
                 Fukuoka-shi, Japan",
  title =        "Proceedings of the Second {ISAAC} Congress:
                 Fukuoka-shi, Japan",
  volume =       "7--8",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  year =         "1999",
  ISBN =         "0-7923-6598-4, 0-7923-6754-5",
  ISBN-13 =      "978-0-7923-6598-3, 978-0-7923-6754-3",
  LCCN =         "QA299.6 .I58 1999",
  bibdate =      "Sat Nov 29 11:33:40 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "International Society for Analysis, Applications, and
                 Computation",
  acknowledgement = ack-nhfb,
}

@Proceedings{Csendes:1999:DRC,
  editor =       "Tibor Csendes",
  booktitle =    "{Developments in Reliable Computing: Papers presented
                 at the International Symposium on Scientific Computing,
                 Computer Arithmetic, and Validated Numerics, SCAN-98,
                 in Szeged, Hungary}",
  title =        "{Developments in Reliable Computing: Papers presented
                 at the International Symposium on Scientific Computing,
                 Computer Arithmetic, and Validated Numerics, SCAN-98,
                 in Szeged, Hungary}",
  volume =       "5(3)",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "viii + 402",
  year =         "1999",
  ISBN =         "0-7923-6057-5",
  ISBN-13 =      "978-0-7923-6057-5",
  LCCN =         "QA76.9.E94 D48 1999",
  bibdate =      "Sat Nov 29 11:31:21 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       j-RELIABLE-COMPUTING,
  acknowledgement = ack-nhfb,
}

@Proceedings{Hosticka:1999:EPE,
  editor =       "B. J. Hosticka and G. Zimmer and H. Grunbacher",
  booktitle =    "{ESSCIRC '99}: proceedings of the 25th European
                 Solid-State Circuits Conference, Duisburg, Germany,
                 21--23 September, 1999",
  title =        "{ESSCIRC} '99: proceedings of the 25th European
                 Solid-State Circuits Conference, Duisburg, Germany,
                 21--23 September, 1999",
  publisher =    "Editions Fronti{\`e}res",
  address =      "Paris, France",
  pages =        "ix + 446",
  year =         "1999",
  ISBN =         "2-86332-246-X",
  ISBN-13 =      "978-2-86332-246-8",
  LCCN =         "TK7871.85 .E887 1999",
  bibdate =      "Sat Nov 29 11:25:06 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:1999:AAF,
  editor =       "{IEEE}",
  booktitle =    "{AP-ASIC '99: the First IEEE Asia Pacific Conference
                 on ASICs, Yonsei University, Seoul, Korea, August
                 23--25, 1999}",
  title =        "{AP-ASIC '99: the First IEEE Asia Pacific Conference
                 on ASICs, Yonsei University, Seoul, Korea, August
                 23--25, 1999}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xxvi + 423",
  year =         "1999",
  ISBN =         "0-7803-5705-1",
  ISBN-13 =      "978-0-7803-5705-1",
  LCCN =         "TK7874.6 .I32 1999",
  bibdate =      "Sat Jun 25 07:40:16 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog number 99EX360.",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:1999:IPI,
  editor =       "{IEEE}",
  booktitle =    "{ICECS '99: proceedings of ICECS '99, the 6th IEEE
                 International Conference on Electronics, Circuits, and
                 Systems: Pafos, Cyprus, 5--8 September, 1999}",
  title =        "{ICECS '99: proceedings of ICECS '99, the 6th IEEE
                 International Conference on Electronics, Circuits, and
                 Systems: Pafos, Cyprus, 5--8 September, 1999}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  year =         "1999",
  ISBN =         "0-7803-5682-9",
  ISBN-13 =      "978-0-7803-5682-5",
  LCCN =         "TK7874 .I3236 1999",
  bibdate =      "Sat Nov 29 11:34:32 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Three volumes.",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:1999:PII,
  editor =       "{IEEE}",
  booktitle =    "{Proceedings: 1999 29th IEEE International Symposium
                 on Multiple-Valued Logic, May 20--22, 1999, Freiburg im
                 Breisgau, Germany}",
  title =        "{Proceedings: 1999 29th IEEE International Symposium
                 on Multiple-Valued Logic, May 20--22, 1999, Freiburg im
                 Breisgau, Germany}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xi + 302",
  year =         "1999",
  ISBN =         "0-7695-0161-3, 0-7803-5684-5, 0-7695-0163-x",
  ISBN-13 =      "978-0-7695-0161-1, 978-0-7803-5684-9,
                 978-0-7695-0163-5",
  LCCN =         "????",
  bibdate =      "Sat Aug 22 08:56:51 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.bibsys.no:2100/BIBSYS",
  acknowledgement = ack-nhfb,
}

@Proceedings{Koren:1999:ISC,
  editor =       "Israel Koren and Peter Kornerup",
  booktitle =    "{14th IEEE Symposium on Computer Arithmetic:
                 proceedings: April 14--16, 1999, Adelaide, Australia}",
  title =        "{14th IEEE Symposium on Computer Arithmetic:
                 proceedings: April 14--16, 1999, Adelaide, Australia}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xi + 274",
  year =         "1999",
  DOI =          "https://doi.org/10.1109/ARITH.1999.762854",
  ISBN =         "0-7803-5609-8, 0-7695-0116-8, 0-7695-0118-4",
  ISBN-13 =      "978-0-7803-5609-2, 978-0-7695-0116-1,
                 978-0-7695-0118-5",
  ISSN =         "1063-6889",
  LCCN =         "QA76.6 .S887 1999",
  bibdate =      "Mon Feb 7 07:28:26 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE Computer Society Order Number PR00116. IEEE Order
                 Plan Catalog Number 99CB36336.",
  URL =          "http://computer.org/conferen/home/arith/;
                 http://www.ecs.umass.edu/ece/arith14/program.html",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-14",
  remark =       "Also known as ARITH-14.",
  source =       "Computer arithmetic",
  sponsor =      "IEEE.",
}

@Proceedings{Luk:1999:PSA,
  editor =       "Franklin T. Luk",
  booktitle =    "Proceedings of {SPIE: Advanced signal processing
                 algorithms, architectures, and implementations IX:
                 19--21 July, 1999, Denver, Colorado}",
  title =        "Proceedings of {SPIE: Advanced signal processing
                 algorithms, architectures, and implementations IX:
                 19--21 July, 1999, Denver, Colorado}",
  volume =       "3807",
  publisher =    pub-SPIE,
  address =      pub-SPIE:adr,
  pages =        "ix + 648",
  year =         "1999",
  ISBN =         "0-8194-3293-8",
  ISBN-13 =      "978-0-8194-3293-3",
  LCCN =         "TK5102.5 .A3325 1999; TK5102.5 .A3173 1999; TK5102.9
                 .A37 1999",
  bibdate =      "Mon Mar 5 07:43:43 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  subject =      "Signal processing; Digital techniques; Congresses;
                 Algorithms; Computer architecture",
}

@Proceedings{Matthews:1999:CRT,
  editor =       "Michael B. Matthews and others",
  booktitle =    "{Conference record of the Thirty-Third Asilomar
                 Conference on Signals, Systems and Computers: October
                 24--27, 1999, Pacific Grove, California}",
  title =        "{Conference record of the Thirty-Third Asilomar
                 Conference on Signals, Systems and Computers: October
                 24--27, 1999, Pacific Grove, California}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xxv + 1689 + 7 (two volumes)",
  year =         "1999",
  DOI =          "https://doi.org/10.1109/ACSSC.1999.831824",
  ISBN =         "0-7803-5700-0 (softbound), 0-7803-5701-9 (casebound),
                 0-7803-5702-7 (microfiche)",
  ISBN-13 =      "978-0-7803-5700-6 (softbound), 978-0-7803-5701-3
                 (casebound), 978-0-7803-5702-0 (microfiche)",
  LCCN =         "TK5101.A1 A85 1999; TK454.2 .A8 1999",
  bibdate =      "Sun Mar 4 21:19:53 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  remark =       "IEEE Catalog Number 99CH37020.",
  subject =      "Signal processing; Congresses; Electronic digital
                 computers; Digital techniques",
}

@Proceedings{Mazumder:1999:NGL,
  editor =       "Pinaki Mazumder and Ronald J. Lomax",
  booktitle =    "{Ninth Great Lakes Symposium on VLSI: proceedings:
                 Ypsilanti Marriott at Eagle Court, Ypsilanti, Michigan,
                 March 4--6, 1999}",
  title =        "{Ninth Great Lakes Symposium on VLSI: proceedings:
                 Ypsilanti Marriott at Eagle Court, Ypsilanti, Michigan,
                 March 4--6, 1999}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiv + 400",
  year =         "1999",
  ISBN =         "0-7695-0104-4, 0-7695-0106-0",
  ISBN-13 =      "978-0-7695-0104-8, 978-0-7695-0106-2",
  LCCN =         "TK7874 .G689 1999",
  bibdate =      "Sun Mar 4 21:21:39 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  remark =       "IEEE Computer Society Order Number PR0 0104",
  subject =      "Integrated circuits; Very large scale integration;
                 Design and construction; Congresses; Computer-aided
                 design",
}

@Proceedings{Piuri:1999:IAV,
  editor =       "Vincenzo Piuri",
  booktitle =    "{IEEE Alessandro Volta Memorial Workshop on Low-Power
                 Design: proceedings: March 4--5, 1999, Como, Italy}",
  title =        "{IEEE Alessandro Volta Memorial Workshop on Low-Power
                 Design: proceedings: March 4--5, 1999, Como, Italy}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "x + 203",
  year =         "1999",
  ISBN =         "0-7695-0019-6, 0-7695-0021-8",
  ISBN-13 =      "978-0-7695-0019-5, 978-0-7695-0021-8",
  LCCN =         "TK7874.66 .I34 1999",
  bibdate =      "Sun Mar 4 21:18:14 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  meetingname =  "IEEE Alessandro Volta Memorial Workshop on Low-Power
                 Design (1999: Como, Italy)",
  subject =      "Low voltage integrated circuits; Design and
                 construction; Congresses; Volta, Alessandro",
  subject-dates = "1745--1827",
}

@Proceedings{Shiratori:1999:PIC,
  editor =       "Norio Shiratori and Dhabaleswar Panda",
  booktitle =    "{Proceedings, 1999 International Conference on
                 Parallel Processing: Aizu-Wakamatsu City, Japan, 21--24
                 September 1999}",
  title =        "{Proceedings, 1999 International Conference on
                 Parallel Processing: Aizu-Wakamatsu City, Japan, 21--24
                 September 1999}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xxi + 561",
  year =         "1999",
  ISBN =         "0-7695-0350-0, 0-7695-0352-7",
  ISBN-13 =      "978-0-7695-0350-9, 978-0-7695-0352-3",
  ISSN =         "0190-3918",
  LCCN =         "QA76.58 .I55 1999",
  bibdate =      "Sun Feb 20 14:02:52 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  note =         "IEEE Computer Society Order Number PR00350.",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=6466",
  acknowledgement = ack-nhfb,
  meetingname =  "International Conference on Parallel Processing (28th:
                 1999: Aizuwakamatsu-shi, Japan)",
  subject =      "parallel processing (electronic computers);
                 congresses",
}

@Proceedings{Wuorinen:1999:IIS,
  editor =       "John H. Wuorinen",
  booktitle =    "1999 {IEEE} International Solid-State Circuits
                 Conference, San Francisco, {CA}: digest of technical
                 papers",
  title =        "1999 {IEEE} International Solid-State Circuits
                 Conference, San Francisco, {CA}: digest of technical
                 papers",
  volume =       "42",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "508",
  year =         "1999",
  ISBN =         "0-7803-5126-6, 0-7803-5127-4, 0-7803-5128-2,
                 0-7803-5129-0",
  ISBN-13 =      "978-0-7803-5126-4, 978-0-7803-5127-1,
                 978-0-7803-5128-8, 978-0-7803-5129-5",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 11:26:12 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog no. 99CH36278 and 99CB36278.",
  acknowledgement = ack-nhfb,
}

@Proceedings{ACM:2000:PIC,
  editor =       "{ACM}",
  booktitle =    "Proceedings of the {International Conference on
                 Compilers, Architectures and Synthesis for Embedded
                 Systems, San Jose, California, November 17--19, 2000}",
  title =        "Proceedings of the {International Conference on
                 Compilers, Architectures and Synthesis for Embedded
                 Systems, San Jose, California, November 17--19, 2000}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "200 (est.)",
  year =         "2000",
  ISBN =         "1-58113-338-3",
  ISBN-13 =      "978-1-58113-338-7",
  LCCN =         "????",
  bibdate =      "Mon Mar 05 14:51:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Anonymous:2000:DPX,
  editor =       "Anonymous",
  booktitle =    "{DCIS '2000: Proceedings of the XV Conference on
                 Design of Circuits and Integrated Systems, Le Corum,
                 Montpellier, November 21--24, 2000}",
  title =        "{DCIS '2000: Proceedings of the XV Conference on
                 Design of Circuits and Integrated Systems, Le Corum,
                 Montpellier, November 21--24, 2000}",
  publisher =    "????",
  address =      "????",
  year =         "2000",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Jun 25 10:35:13 2005",
  bibsource =    "http://www.lirmm.fr/DCIS2000/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Library catalogs suggest that this appeared only on
                 CD-ROM.",
}

@Proceedings{IEEE:2000:EPI,
  editor =       "{IEEE}",
  booktitle =    "{EDOC '00: Proceedings of the 4th International
                 Conference on Enterprise Distributed Computing, 25-28
                 September 2000, Makuhari, Japan}",
  title =        "{EDOC '00: Proceedings of the 4th International
                 Conference on Enterprise Distributed Computing, 25-28
                 September 2000, Makuhari, Japan}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "x + 264",
  year =         "2000",
  ISBN =         "0-7695-0865-0",
  ISBN-13 =      "978-0-7695-0865-8",
  LCCN =         "????",
  bibdate =      "Thu Aug 7 17:51:05 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:2000:IGP,
  editor =       "{IEEE}",
  booktitle =    "{ISCAS 2000 Geneva: proceedings of the 2000 IEEE
                 International Symposium on Circuits and Systems,
                 Emerging technologies for the 21st century: May 28--31,
                 2000, International Conference Center (CICG) of Geneva,
                 Switzerland}",
  title =        "{ISCAS 2000 Geneva: proceedings of the 2000 IEEE
                 International Symposium on Circuits and Systems,
                 Emerging technologies for the 21st century: May 28--31,
                 2000, International Conference Center (CICG) of Geneva,
                 Switzerland}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2000",
  ISBN =         "0-7803-5482-6, 0-7803-5483-4, 0-7803-5484-2",
  ISBN-13 =      "978-0-7803-5482-1, 978-0-7803-5483-8,
                 978-0-7803-5484-5",
  LCCN =         "TK7801 .I22 2000",
  bibdate =      "Mon Mar 5 07:46:37 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  meetingname =  "IEEE International Symposium on Circuits and Systems
                 (2000: Geneva, Switzerland)",
  remark =       "IEEE Catalog Number: 00CH36353. Hosted by Swiss
                 Federal Institute of Technology, Lausanne.",
  subject =      "Electronics; Congresses; Electronic circuits; Neural
                 networks (Computer science); Integrated circuits; Very
                 large scale integration; Signal processing; Digital
                 techniques",
}

@Proceedings{IEEE:2000:IPI,
  editor =       "{IEEE}",
  booktitle =    "{IMTC\slash 2000}: Proceedings of the 17th {IEEE}
                 Instrumentation and Measurement Technology Conference:
                 Smart connectivity: integrating measurement and
                 control, Hilton Hotel and Towers, Baltimore, Maryland,
                 {USA}, May 1--4, 2000",
  title =        "{IMTC}\slash 2000: Proceedings of the 17th {IEEE}
                 Instrumentation and Measurement Technology Conference:
                 Smart connectivity: integrating measurement and
                 control, Hilton Hotel and Towers, Baltimore, Maryland,
                 {USA}, May 1--4, 2000",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xliv + 1615",
  year =         "2000",
  ISBN =         "0-7803-5891-0, 0-7803-5890-2, 0-7803-5892-9",
  ISBN-13 =      "978-0-7803-5891-1, 978-0-7803-5890-4,
                 978-0-7803-5892-8",
  ISSN =         "1091-5281",
  LCCN =         "TK7878 .I3295 2000",
  bibdate =      "Sat Nov 29 11:35:38 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Three volumes. IEEE catalog number 00CH3706.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Luk:2000:PSA,
  editor =       "Franklin T. Luk",
  booktitle =    "Proceedings of {SPIE: Advanced signal processing
                 algorithms, architectures, and implementations X: 2--4
                 August 2000, San Diego, California, USA}",
  title =        "Proceedings of {SPIE: Advanced signal processing
                 algorithms, architectures, and implementations X: 2--4
                 August 2000, San Diego, California, USA}",
  volume =       "4116",
  publisher =    pub-SPIE,
  address =      pub-SPIE:adr,
  pages =        "vii + 484",
  year =         "2000",
  ISBN =         "0-8194-3761-1",
  ISBN-13 =      "978-0-8194-3761-7",
  LCCN =         "TK5102.5 .A3325 2000; TK5102.9 .A382 2000; TK5102.9
                 .A38 2000",
  bibdate =      "Mon Mar 5 07:55:22 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  subject =      "Signal processing; Digital techniques; Congresses;
                 Computer algorithms; Computer architecture",
}

@Proceedings{Matthews:2000:CRT,
  editor =       "Michael B. Matthews and others",
  booktitle =    "{Conference record of the Thirty-Fourth Asilomar
                 Conference on Signals, Systems and Computers: October
                 29--November 1, 2000, Pacific Grove, California}",
  title =        "{Conference record of the Thirty-Fourth Asilomar
                 Conference on Signals, Systems and Computers: October
                 29--November 1, 2000, Pacific Grove, California}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2000",
  ISBN =         "0-7803-6514-3 (softbound), 0-7803-6515-1 (casebound),
                 0-7803-6516-X (microfiche)",
  ISBN-13 =      "978-0-7803-6514-8 (softbound), 978-0-7803-6515-5
                 (casebound), 978-0-7803-6516-2 (microfiche)",
  LCCN =         "TK5101.A1 A85 2000",
  bibdate =      "Sun Mar 4 21:30:52 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  meetingname =  "Asilomar Conference on Signals, Systems and Computers
                 (34th: 2000: Pacific Grove, Calif.)",
  remark =       "IEEE Catalog Number 99CH37020.",
  subject =      "Signal processing; Congresses; Electronic digital
                 computers; Digital techniques",
}

@Proceedings{Reynders:2000:IPI,
  editor =       "John Reynders and Alexander V. Veidenbaum",
  booktitle =    "{ICS '00: Proceedings of the 14th international
                 conference on Supercomputing: Santa Fe, New Mexico,
                 USA, May 8--11, 2000}",
  title =        "{ICS '00: Proceedings of the 14th international
                 conference on Supercomputing: Santa Fe, New Mexico,
                 USA, May 8--11, 2000}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  bookpages =    "xi + 509",
  pages =        "xi + 509",
  year =         "2000",
  DOI =          "https://doi.org/10.1145/335231",
  ISBN =         "1-58113-270-0",
  ISBN-13 =      "978-1-58113-270-0",
  LCCN =         "QA76.88 .I573 2000",
  bibdate =      "Fri Jul 27 05:22:06 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/supercomputing/335231/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/java2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/pvm.bib",
  URL =          "https://dl.acm.org/doi/proceedings/10.1145/335231",
  acknowledgement = ack-nhfb,
  keywords =     "AS/400; ESA/390; IA-64; Java Virtual Machine (JVM);
                 RS/6000",
}

@Proceedings{Sprague:2000:PAH,
  editor =       "Ralph H. Sprague",
  booktitle =    "{Proceedings of the 33rd Annual Hawaii International
                 Conference on System Sciences: abstracts and CD-ROM of
                 full papers: January 4--7, 2000, Maui, Hawaii}",
  title =        "{Proceedings of the 33rd Annual Hawaii International
                 Conference on System Sciences: abstracts and CD-ROM of
                 full papers: January 4--7, 2000, Maui, Hawaii}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "liv + 259",
  year =         "2000",
  ISBN =         "0-7695-0493-0, 0-7695-0494-9, 0-7695-0495-7",
  ISBN-13 =      "978-0-7695-0493-3, 978-0-7695-0494-0,
                 978-0-7695-0495-7",
  LCCN =         "TA168 .H37 2000",
  bibdate =      "Sun Mar 4 21:23:42 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  meetingname =  "Hawaii International Conference on System Sciences
                 (33rd: 2000: Maui, Hawaii)",
  remark =       "IEEE Computer Society Order Number: PR00493",
  subject =      "Systems engineering; Congresses; Information theory;
                 Electronic data processing; System design",
}

@Proceedings{Swartzlander:2000:IIC,
  editor =       "Earl E. Swartzlander and Graham Jullien and Michael
                 Joseph Schulte",
  booktitle =    "{IEEE International Conference on Application-Specific
                 Systems, Architectures and Processors: proceedings,
                 July 10--12, 2000; Boston, Massachusetts}",
  title =        "{IEEE International Conference on Application-Specific
                 Systems, Architectures and Processors: proceedings,
                 July 10--12, 2000; Boston, Massachusetts}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiv + 360",
  year =         "2000",
  ISBN =         "0-7695-0716-6, 0-7695-0718-2",
  ISBN-13 =      "978-0-7695-0716-3, 978-0-7695-0718-7",
  LCCN =         "TK7874.6 .I572 2000",
  bibdate =      "Sun Mar 4 21:28:08 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  meetingname =  "International Conference on Application Specific
                 Systems, Architectures and Processors (12th: 2000:
                 Boston, Mass.)",
  remark =       "IEEE Computer Society order number PR00716. IEEE order
                 plan catalog number 97TB100177.",
  subject =      "Array processors; Congresses; Signal processing;
                 Digital techniques; Application specific integrated
                 circuits",
}

@Proceedings{Traverso:2000:IAU,
  editor =       "Carlo Traverso",
  booktitle =    "{ISSAC 2000}: 7--9 August 2000, University of St.
                 Andrews, Scotland: proceedings of the 2000
                 International Symposium on Symbolic and Algebraic
                 Computation",
  title =        "{ISSAC} 2000: 7--9 August 2000, University of St.
                 Andrews, Scotland: proceedings of the 2000
                 International Symposium on Symbolic and Algebraic
                 Computation",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "viii + 309",
  year =         "2000",
  ISBN =         "1-58113-218-2",
  ISBN-13 =      "978-1-58113-218-2",
  LCCN =         "QA76.95.I59 2000",
  bibdate =      "Tue Apr 17 09:12:53 2001",
  bibsource =    "http://www.acm.org/pubs/contents/proceedings/series/issac/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "ACM order number 505000.",
  URL =          "http://www.acm.org/pubs/contents/proceedings/issac/345542/",
  acknowledgement = ack-nhfb,
}

@Proceedings{ACM:2001:PSA,
  editor =       "ACM",
  booktitle =    "{Proceedings of the seventeenth annual Symposium on
                 Computational Geometry (SCG'01): June 3--5, 2001,
                 Medford, Massachusetts, USA}",
  title =        "{Proceedings of the seventeenth annual Symposium on
                 Computational Geometry (SCG'01): June 3--5, 2001,
                 Medford, Massachusetts, USA}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "x + 334",
  year =         "2001",
  ISBN =         "1-58113-357-X",
  ISBN-13 =      "978-1-58113-357-8",
  LCCN =         "????",
  bibdate =      "Fri Jan 6 12:10:47 MST 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 library.ox.ac.uk:210/ADVANCE",
  acknowledgement = ack-nhfb,
  remark =       "ACM order number 429010.",
  subject =      "Geometry; Data processing; Congresses",
}

@Proceedings{Anonymous:2001:JJ,
  editor =       "Anonymous",
  booktitle =    "{JavaOne 2001, June 7, 2001}",
  title =        "{JavaOne 2001, June 7, 2001}",
  publisher =    "????",
  address =      "????",
  year =         "2001",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 11:36:43 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Boulton:2001:TPH,
  editor =       "Richard J. Boulton and Paul B. Jackson",
  booktitle =    "Theorem Proving in Higher Order Logics: 14th
                 International Conference, {TPHOLs 2001, Edinburgh,
                 Scotland, UK, September 3--6, 2001}: Proceedings",
  title =        "Theorem Proving in Higher Order Logics: 14th
                 International Conference, {TPHOLs 2001, Edinburgh,
                 Scotland, UK, September 3--6, 2001}: Proceedings",
  volume =       "2152",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 393",
  year =         "2001",
  ISBN =         "3-540-42525-X (paperback)",
  ISBN-13 =      "978-3-540-42525-0 (paperback)",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  LCCN =         "QA76.9.A96 T655 2001",
  bibdate =      "Thu Nov 25 11:01:06 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
  meetingname =  "TPHOLs 2001 (2001: Edinburgh, Scotland)",
  subject =      "Automatic theorem proving; Congresses",
}

@Proceedings{Brebner:2001:FLA,
  editor =       "Gordon Brebner and Roger Woods",
  booktitle =    "{Field-programmable logic and applications: 11th
                 International Conference, FPL 2001, Belfast, Northern
                 Ireland, UK, August 27--29, 2001: Proceedings}",
  title =        "{Field-programmable logic and applications: 11th
                 International Conference, FPL 2001, Belfast, Northern
                 Ireland, UK, August 27--29, 2001: Proceedings}",
  volume =       "2147",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xv + 665",
  year =         "2001",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/3-540-44687-7",
  ISBN =         "3-540-42499-7 (softcover)",
  ISBN-13 =      "978-3-540-42499-4 (softcover)",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  LCCN =         "TK7895.G36 I48 2001; QA267.A1 L43 no.2147",
  bibdate =      "Thu Jan 17 11:49:19 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-LNCS,
  URL =          "http://link.springer-ny.com/link/service/series/0558/tocs/t2147.htm;
                 http://www.springerlink.com/openurl.asp?genre=issue&issn=0302-9743&volume=2147",
  acknowledgement = ack-nhfb,
  keywords =     "field programmable gate arrays --- congresses;
                 programmable array logic --- congresses",
}

@Proceedings{Burgess:2001:ISC,
  editor =       "N. Burgess and L. Ciminiera",
  booktitle =    "{15th IEEE Symposium on Computer Arithmetic: ARITH-15
                 2001: proceedings: Vail, Colorado, 11--13 June, 2001}",
  title =        "{15th IEEE Symposium on Computer Arithmetic: ARITH-15
                 2001: proceedings: Vail, Colorado, 11--13 June, 2001}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 285",
  year =         "2001",
  ISBN =         "0-7695-1150-3; 0-7695-1152-X",
  ISBN-13 =      "978-0-7695-1150-4; 978-0-7695-1152-8",
  ISSN =         "1063-6889",
  LCCN =         "QA76.9.C62 S95 2001",
  bibdate =      "Fri May 03 14:20:49 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE order no. PR01150.",
  price =        "US\$145",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
  xxnote =       "Check dates: 11--13 or 11--17??",
  xxtitle =      "Computer Arithmetic: Papers presented at the {15th
                 IEEE Symposium on Computer Arithmetic (Arith-15 2001),
                 11--17 June, 2001, Vail, CO}",
}

@Proceedings{IEEE:2001:IPI,
  editor =       "{IEEE}",
  booktitle =    "{ICCAD '01: Proceedings of the 2001 IEEE\slash ACM
                 International Conference on Computer-Aided Design, San
                 Jose, California}",
  title =        "{ICCAD '01: Proceedings of the 2001 IEEE\slash ACM
                 International Conference on Computer-Aided Design, San
                 Jose, California}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2001",
  ISBN =         "0-7803-7249-2",
  ISBN-13 =      "978-0-7803-7249-8",
  LCCN =         "????",
  bibdate =      "Fri Aug 08 09:19:44 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:2001:PES,
  editor =       "{IEEE}",
  booktitle =    "{Proceedings of the Euromicro Symposium on Digital
                 Systems Design, Architectures, Methods and Tools (DSD
                 2001), Warsaw, Poland, 4--6 September 2001}",
  title =        "{Proceedings of the Euromicro Symposium on Digital
                 Systems Design, Architectures, Methods and Tools (DSD
                 2001), Warsaw, Poland, 4--6 September 2001}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 476",
  year =         "2001",
  ISBN =         "0-7695-1239-9",
  ISBN-13 =      "978-0-7695-1239-6",
  LCCN =         "TK7868.D5 E93 2001",
  bibdate =      "Sat Jun 25 08:26:26 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:2001:PII,
  editor =       "{IEEE}",
  booktitle =    "Proceedings of the {IEEE} International Conference on
                 Computer Design, September 23--26, 2001, Austin, {TX}",
  title =        "Proceedings of the {IEEE} International Conference on
                 Computer Design, September 17--20, 2001, Austin, {TX}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xxii + 559",
  year =         "2001",
  ISBN =         "0-7695-1200-3 (paperback), 0-7695-1202-X
                 (microfiche)",
  ISBN-13 =      "978-0-7695-1200-6 (paperback), 978-0-7695-1202-0
                 (microfiche)",
  LCCN =         "TK7885.A1 .I24 2001; TK 7885 .A1I24 2001",
  bibdate =      "Sat Jun 25 08:16:29 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  xxnote =       "Check dates: one source says 17--10 September, LC and
                 Melvyl say 23--26 September??",
}

@Proceedings{Kraemer:2001:SCV,
  editor =       "W. Kr{\"a}mer and J{\"u}rgen Wolff von Gudenberg",
  booktitle =    "Scientific Computing, Validated Numerics, Interval
                 Methods",
  title =        "Scientific Computing, Validated Numerics, Interval
                 Methods",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "ix + 398",
  year =         "2001",
  ISBN =         "0-306-46706-2",
  ISBN-13 =      "978-0-306-46706-6",
  LCCN =         "????",
  bibdate =      "Thu Mar 21 10:21:57 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Scan 2000, the GAMM--IMACS International Symposium on
                 Scientific Computing, Computer Arithmetic, and
                 Validated Numerics and Interval 2000, the International
                 Conference on Interval Methods in Science and
                 Engineering were jointly held in Karlsruhe, September
                 19--22, 2000.",
  price =        "09.00 EUR / 95.00 USD / 66.50 GBP",
  URL =          "http://www.wkap.nl/prod/b/0-306-46706-2",
  acknowledgement = ack-nhfb,
  author-dates = "1952--2014 (WK)",
}

@Proceedings{Kulisch:2001:PEM,
  editor =       "Ulrich Kulisch and Rudolf Lohner and Axel Facius",
  booktitle =    "Perspectives on enclosure methods: {GAMM--IMACS}
                 international symposium on scientific computing,
                 computer arithmetic and validated numerics, September
                 2000, Karlsruhe, Germany",
  title =        "Perspectives on enclosure methods: {GAMM}-{IMACS}
                 international symposium on scientific computing,
                 computer arithmetic and validated numerics, September
                 2000, Karlsruhe, Germany",
  publisher =    "????",
  pages =        "xii + 345",
  year =         "2001",
  ISBN =         "3-211-83590-3",
  ISBN-13 =      "978-3-211-83590-6",
  LCCN =         "QA76.9.C62 P47 2001",
  bibdate =      "Mon May 20 07:08:20 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Held jointly with INTERVAL 2000 International
                 conference on interval methods in science and
                 engineering, on the occasion of the 60th birthday of
                 Professor Gotz Alefeld. Also known as SCAN2000",
  abstract =     "????",
  acknowledgement = ack-nhfb,
  keywords =     "Alefeld; computer arithmetic; enclosure methods; GAMM;
                 IMACS; interval methods; SCAN; scientific computing;
                 validated numerics",
}

@Proceedings{Luk:2001:ASP,
  editor =       "Franklin T. Luk",
  booktitle =    "{Advanced signal processing algorithms, architectures,
                 and implementations XI: 1--3 August, 2001, San Diego,
                 CA, USA}",
  title =        "{Advanced signal processing algorithms, architectures,
                 and implementations XI: 1--3 August, 2001, San Diego,
                 CA, USA}",
  volume =       "4474",
  publisher =    pub-SPIE,
  address =      pub-SPIE:adr,
  pages =        "x + 536",
  year =         "2001",
  CODEN =        "PSISDG",
  ISBN =         "0-8194-4188-0",
  ISBN-13 =      "978-0-8194-4188-1",
  ISSN =         "0277-786X (print), 1996-756X (electronic)",
  LCCN =         "TK5102.5 .A332 2001",
  bibdate =      "Sat Jun 25 11:05:11 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       j-PROC-SPIE,
  acknowledgement = ack-nhfb,
}

@Proceedings{Matthews:2001:CRT,
  editor =       "Michael B. Matthews",
  booktitle =    "Conference record of the Thirty-Fifth Asilomar
                 Conference on Signals, Systems \& Computers: November
                 4--7, 2001, Pacific Grove, California",
  title =        "Conference record of the Thirty-Fifth Asilomar
                 Conference on Signals, Systems \& Computers: November
                 4--7, 2001, Pacific Grove, California",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2001",
  ISBN =         "0-7803-7147-X (paperback), 0-7803-7148-8
                 (microfiche)",
  ISBN-13 =      "978-0-7803-7147-7 (paperback), 978-0-7803-7148-4
                 (microfiche)",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 07:02:41 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Two volumes. IEEE catalog number 01CH37256.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Oliveira:2001:FFM,
  editor =       "Jose N. Oliveira and Pamela Zave",
  booktitle =    "{FME 2001}: formal methods for increasing software
                 productivity: [10th] International Symposium of Formal
                 Methods Europe, Berlin, Germany, March 12--16, 2001:
                 Proceedings",
  title =        "{FME 2001}: formal methods for increasing software
                 productivity: [10th] International Symposium of Formal
                 Methods Europe, Berlin, Germany, March 12--16, 2001:
                 Proceedings",
  volume =       "2021",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xiii + 628",
  year =         "2001",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/3-540-45251-6",
  ISBN =         "3-540-41791-5 (softcover)",
  ISBN-13 =      "978-3-540-41791-0 (softcover)",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  LCCN =         "QA76.76.D47 I593 2001; QA267.A1 L43 no.2021",
  bibdate =      "Thu Jan 17 11:49:19 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-LNCS,
  URL =          "http://link.springer-ny.com/link/service/series/0558/tocs/t2021.htm",
  acknowledgement = ack-nhfb,
  keywords =     "computer software -- development -- congresses",
}

@Proceedings{Tang:2001:ICA,
  editor =       "Ting-Ao Tang and others",
  booktitle =    "{2001 4th International Conference on ASIC:
                 proceedings: Hotel Equatorial, Shanghai, China, October
                 23--25, 2001}",
  title =        "{2001 4th International Conference on ASIC:
                 proceedings: Hotel Equatorial, Shanghai, China, October
                 23--25, 2001}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "42 + 887 + viii",
  year =         "2001",
  ISBN =         "0-7803-6677-8, 7-900081-59-3",
  ISBN-13 =      "978-0-7803-6677-0, 978-7-900081-59-9",
  LCCN =         "TK7874.6 .I55 2001; TK7874.6 .I64 2001",
  bibdate =      "Mon Mar 5 08:06:40 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  meetingname =  "International Conference on ASIC (4th: 2001: Shanghai,
                 China)",
  remark =       "IEEE Catalog Number: 01TH8549",
  subject =      "Application-specific integrated circuits; Design and
                 construction; Congresses; Computer-aided design;
                 Testing",
}

@Proceedings{Babuska:2002:MMN,
  editor =       "Ivo Babu{\v{s}}ka and Philippe G. Ciarlet and
                 Tetsuhiko Miyoshi",
  booktitle =    "{Mathematical Modeling and Numerical Simulation in
                 Continuum Mechanics: Proceedings of the International
                 Symposium on Mathematical Modeling and Numerical
                 Simulation in Continuum Mechanics, September
                 29--October 3, 2000 Yamaguchi, Japan}",
  title =        "{Mathematical Modeling and Numerical Simulation in
                 Continuum Mechanics: Proceedings of the International
                 Symposium on Mathematical Modeling and Numerical
                 Simulation in Continuum Mechanics, September
                 29--October 3, 2000 Yamaguchi, Japan}",
  volume =       "19",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "viii + 301",
  pages =        "viii + 301",
  year =         "2002",
  CODEN =        "LNCSA6",
  DOI =          "https://doi.org/10.1007/978-3-642-56288-4",
  ISBN =         "3-540-42399-0 (print), 3-642-56288-4 (e-book)",
  ISBN-13 =      "978-3-540-42399-7 (print), 978-3-642-56288-4
                 (e-book)",
  ISSN =         "1439-7358",
  ISSN-L =       "1439-7358",
  LCCN =         "QA808.2 .I59 2000",
  bibdate =      "Thu Dec 20 14:36:13 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncse.bib",
  series =       ser-LNCSE,
  URL =          "http://link.springer.com/book/10.1007/978-3-642-56288-4;
                 http://www.springerlink.com/content/978-3-642-56288-4",
  acknowledgement = ack-nhfb,
  series-URL =   "http://link.springer.com/bookseries/3527",
}

@Proceedings{Borrione:2002:TIW,
  editor =       "Dominique Borrione",
  booktitle =    "{Third International Workshop on the ACL2 Theorem
                 Prover and its Applications (ACL2-2002), April 8--9,
                 2002, in Grenoble, France. Presentations, affiliated
                 with ETAPS 2002}",
  title =        "{Third International Workshop on the ACL2 Theorem
                 Prover and its Applications (ACL2-2002), April 8--9,
                 2002, in Grenoble, France. Presentations, affiliated
                 with ETAPS 2002}",
  publisher =    "????",
  address =      "????",
  pages =        "????",
  year =         "2002",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Jun 25 12:28:18 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.utexas.edu/users/moore/acl2/workshop-2002/",
  acknowledgement = ack-nhfb,
}

@Proceedings{Cohen:2002:MSP,
  editor =       "Arjeh M. Cohen and Xiao-Shan Gao and Nobuki Takayama",
  booktitle =    "{Mathematical software: proceedings of the first
                 International Congress of Mathematical Software:
                 Beijing, China, 17--19 August 2002}",
  title =        "{Mathematical software: proceedings of the first
                 International Congress of Mathematical Software:
                 Beijing, China, 17--19 August 2002}",
  publisher =    pub-WORLD-SCI,
  address =      pub-WORLD-SCI:adr,
  pages =        "xiii + 514",
  year =         "2002",
  ISBN =         "981-238-048-5",
  ISBN-13 =      "978-981-238-048-7",
  LCCN =         "QA76.95 .I5654 2002",
  bibdate =      "Sat Jun 25 12:12:34 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "Mathematics; Data processing; Congresses; Computer
                 software; Congresses",
}

@Book{Hennessy:2002:CAQ,
  author =       "John L. Hennessy and David A. Patterson",
  booktitle =    "Computer Architecture\emdash {A} Quantitative
                 Approach",
  title =        "Computer Architecture\emdash {A} Quantitative
                 Approach",
  publisher =    pub-MORGAN-KAUFMANN,
  address =      pub-MORGAN-KAUFMANN:adr,
  edition =      "Third",
  pages =        "xxi + 883 + A-87 + B-42 + C-1 + D-1 + E-1 + F-1 + G-1
                 + H-1 + I-1 + R-22 + I-44",
  year =         "2002",
  ISBN =         "1-55860-596-7",
  ISBN-13 =      "978-1-55860-596-1",
  LCCN =         "????",
  bibdate =      "Fri May 31 15:46:29 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "US\$89.95",
  URL =          "http://www.mkp.com/books_catalog/catalog.asp?ISBN=1-55860-596-7;
                 http://www.mkp.com/CA3",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:2002:IIC,
  editor =       "{IEEE}",
  booktitle =    "{2002 IEEE International Conference on Computer
                 Design: VLSI in computers and processors: proceedings:
                 September 16--18, 2002, Freiburg, Germany}",
  title =        "{2002 IEEE International Conference on Computer
                 Design: VLSI in computers and processors: proceedings:
                 September 16--18, 2002, Freiburg, Germany}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xx + 533",
  year =         "2002",
  ISBN =         "0-7695-1700-5 (paperback), 0-7695-1701-3 (casebound),
                 0-7695-1702-1 (microfiche)",
  ISBN-13 =      "978-0-7695-1700-1 (paperback), 978-0-7695-1701-8
                 (casebound), 978-0-7695-1702-5 (microfiche)",
  LCCN =         "TK7888.3 .I25 2002",
  bibdate =      "Sat Jun 25 12:20:07 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "IEEE catalog number PR01700.",
  URL =          "http://www.computer.org/cspress/CATALOG/pr01700.htm",
  acknowledgement = ack-nhfb,
  meetingname =  "IEEE International Conference on Computer Design
                 (2002: Freiburg im Breisgau, Germany)",
}

@Proceedings{IEEE:2002:IRA,
  editor =       "{IEEE}",
  booktitle =    "{IEEE Reconfigurable Architecture Workshop,
                 International Parallel and Distributed Symposium, Fort
                 Lauderdale, Florida, April 15--19, 2002}",
  title =        "{IEEE Reconfigurable Architecture Workshop,
                 International Parallel and Distributed Symposium, Fort
                 Lauderdale, Florida, April 15--19, 2002}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xlvii + 270",
  year =         "2002",
  ISBN =         "0-7695-1573-8 (paperback), 0-7695-1574-6 (casebound),
                 0-7695-1575-4 (microfiche)",
  ISBN-13 =      "978-0-7695-1573-1 (paperback), 978-0-7695-1574-8
                 (casebound), 978-0-7695-1575-5 (microfiche)",
  ISSN =         "1530-2075",
  LCCN =         "QA76.58 .I583 2002",
  bibdate =      "Sat Jun 25 12:07:25 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE Computer Society Order Number PR01573",
  URL =          "http://www.computer.org/cspress/CATALOG/pr01573.htm",
  acknowledgement = ack-nhfb,
  keywords =     "IPDPS '2002",
}

@Proceedings{IEEE:2002:IWS,
  editor =       "{IEEE}",
  booktitle =    "{IEEE Workshop on Signal Processing Systems:
                 (SIPS'02): San Diego, California, USA, October 16--18,
                 2002}",
  title =        "{IEEE Workshop on Signal Processing Systems:
                 (SIPS'02): San Diego, California, USA, October 16--18,
                 2002}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "viii + 287",
  year =         "2002",
  ISBN =         "0-7803-7587-4",
  ISBN-13 =      "978-0-7803-7587-1",
  LCCN =         "TK7874 .V5637 2002",
  bibdate =      "Sun Mar 4 21:36:39 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  meetingname =  "IEEE Workshop on Signal Processing Systems (2002: San
                 Diego, Calif.)",
  remark =       "Published under the sponsorship of the IEEE Signal
                 Processing Society, IEEE Circuits and Systems Society.
                 IEEE Catalog Number 02TH8638",
  subject =      "Integrated circuits; Very large scale integration;
                 Congresses; Signal processing; Digital techniques",
}

@Proceedings{IEEE:2002:STI,
  editor =       "{IEEE}",
  booktitle =    "{SC2002}: From Terabytes to Insight. Proceedings of
                 the {IEEE ACM SC 2002 Conference, November 16--22,
                 2002, Baltimore, MD, USA}",
  title =        "{SC2002}: From Terabytes to Insight. Proceedings of
                 the {IEEE ACM SC 2002 Conference, November 16--22,
                 2002, Baltimore, MD, USA}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2002",
  ISBN =         "0-7695-1524-X",
  ISBN-13 =      "978-0-7695-1524-3",
  LCCN =         "????",
  bibdate =      "Thu Feb 21 18:29:36 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Li:2002:PIC,
  editor =       "Daqian Li",
  booktitle =    "Proceedings of the [24th] International Congress of
                 Mathematicians: Beijing 2002, August 20--28",
  title =        "Proceedings of the [24th] International Congress of
                 Mathematicians: Beijing 2002, August 20--28",
  publisher =    "Higher Education Press",
  address =      "Beijing, China",
  pages =        "672 (vol. 1) + 832 (vol. 2) + 968 (vol. 3)",
  year =         "2002",
  ISBN =         "7-04-008690-5 (three volumes), 7-900135-82-0
                 (CD-ROM)",
  ISBN-13 =      "978-7-04-008690-4 (three volumes), 978-7-900135-82-7
                 (CD-ROM)",
  LCCN =         "QA1 .I82 2002",
  bibdate =      "Tue Apr 26 10:26:26 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "Editor name also transcribed and cataloged as Tatsien
                 Li.",
}

@Proceedings{Luk:2002:PSA,
  editor =       "Franklin T. Luk",
  booktitle =    "Proceedings of {SPIE: Advanced signal processing
                 algorithms, architectures, and implementations XII:
                 9--11 July, 2002, Seattle, Washington, USA}",
  title =        "Proceedings of {SPIE: Advanced signal processing
                 algorithms, architectures, and implementations XII:
                 9--11 July, 2002, Seattle, Washington, USA}",
  volume =       "4791",
  publisher =    pub-SPIE,
  address =      pub-SPIE:adr,
  pages =        "viii + 468",
  year =         "2002",
  ISBN =         "0-8194-4558-4",
  ISBN-13 =      "978-0-8194-4558-2",
  LCCN =         "TK5102.5 .A3324 2002",
  bibdate =      "Sat Jun 25 11:59:48 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "Signal processing; Digital techniques; Congresses;
                 Algorithms; Congresses; Computer architecture;
                 Congresses",
}

@Proceedings{Matthews:2002:PTS,
  editor =       "Michael B. Matthews",
  booktitle =    "Proceedings of the Thirty Sixth Asilomar Conference on
                 Signals, Systems, and Computers: November 3--6, 2002,
                 Pacific Grove, California",
  title =        "Proceedings of the Thirty Sixth Asilomar Conference on
                 Signals, Systems, and Computers: November 3--6, 2002,
                 Pacific Grove, California",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xxiv + 1950 (est.)",
  year =         "2002",
  DOI =          "https://doi.org/10.1109/ACSSC.2002.1196928",
  ISBN =         "0-7803-7576-9",
  ISBN-13 =      "978-0-7803-7576-5",
  LCCN =         "TK5102.5 A78 2002",
  bibdate =      "Thu Mar 24 14:54:07 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Two volumes. IEEE catalog number 02CH37387.",
  price =        "UK\pounds 265.00",
  acknowledgement = ack-nhfb,
  subject =      "signals; systems; computers; Asilomar",
}

@Proceedings{Pocek:2002:FAI,
  editor =       "Kenneth L. Pocek and Jeffrey Arnold",
  booktitle =    "{FCCM 2002: 10th Annual IEEE Symposium on
                 Field-Programmable Custom Computing Machines:
                 proceedings: 22--24 April, 2002, Napa, California}",
  title =        "{FCCM 2002: 10th Annual IEEE Symposium on
                 Field-Programmable Custom Computing Machines:
                 proceedings: 22--24 April, 2002, Napa, California}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "x + 322",
  year =         "2002",
  DOI =          "https://doi.org/10.1109/FPGA.2002.1106655",
  ISBN =         "0-7695-1801-X",
  ISBN-13 =      "978-0-7695-1801-5",
  ISSN =         "1082-3409",
  LCCN =         "TK7895.G36 I36 2002",
  bibdate =      "Sat Oct 9 14:03:54 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=8168",
  acknowledgement = ack-nhfb,
  subject =      "Field programmable gate arrays; Congresses; Computer
                 engineering",
}

@Proceedings{Schulte:2002:PII,
  editor =       "Michael Joseph Schulte",
  booktitle =    "{Proceedings / The IEEE International Conference on
                 Application-Specific Systems, Architectures and
                 Processors: 17--19 July 2002, San Jose, California}",
  title =        "{Proceedings / The IEEE International Conference on
                 Application-Specific Systems, Architectures and
                 Processors: 17--19 July 2002, San Jose, California}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "x + 404",
  year =         "2002",
  ISBN =         "0-7695-1712-9 (paperback), 0-7695-1713-7 (casebound),
                 0-7695-1714-5 (microfiche)",
  ISBN-13 =      "978-0-7695-1712-4 (paperback), 978-0-7695-1713-1
                 (casebound), 978-0-7695-1714-8 (microfiche)",
  LCCN =         "TK7874.6",
  bibdate =      "Sat Jun 25 11:53:24 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog number PR01712.",
  URL =          "http://www.cse.lehigh.edu/~asap/;
                 https://ieeexplore.ieee.org/servlet/opac?punumber=8009",
  acknowledgement = ack-nhfb,
}

@Proceedings{Trimberger:2002:FTA,
  editor =       "Stephen Trimberger and Martine Schlag",
  booktitle =    "{FPGA 2002: Tenth ACM International Symposium on
                 Field-Programmable Gate Arrays, Monterey, California,
                 USA: February 24--26, 2002}",
  title =        "{FPGA 2002: Tenth ACM International Symposium on
                 Field-Programmable Gate Arrays, Monterey, California,
                 USA: February 24--26, 2002}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "viii + 258",
  year =         "2002",
  ISBN =         "1-58113-452-5",
  ISBN-13 =      "978-1-58113-452-0",
  LCCN =         "TK7895.G36 A36 2002",
  bibdate =      "Sat Oct 9 15:21:41 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "ACM order number 480020.",
  URL =          "http://portal.acm.org/toc.cfm?id=503048",
  acknowledgement = ack-nhfb,
  subject =      "gate array circuits; congresses; field programmable
                 gate arrays; programmable array logic",
}

@Proceedings{Vladimirova:2002:TMA,
  editor =       "Tanya Vladimirova and Richard Katz",
  booktitle =    "{Third Military and Aerospace Programmable Logic
                 Devices International Conference (MAPLD 2000)}",
  title =        "{Third Military and Aerospace Programmable Logic
                 Devices International Conference (MAPLD 2000)}",
  volume =       "39(4)",
  publisher =    "AIAA",
  address =      "Reston, VA, USA",
  pages =        "474--500",
  year =         "2002",
  LCCN =         "????",
  bibdate =      "Sat Oct 9 14:09:02 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.gbv.de:20011/gvk",
  series =       "Journal of spacecraft and rockets",
  acknowledgement = ack-nhfb,
}

@Proceedings{Anonymous:2003:CRN,
  editor =       "Anonymous",
  booktitle =    "5th Conference on Real Numbers and Computers 2003 ---
                 {RNC5}, Lyon, France, September 2003",
  title =        "5th Conference on Real Numbers and Computers 2003 ---
                 {RNC5}, Lyon, France, September 2003",
  publisher =    "????",
  address =      "????",
  pages =        "????",
  year =         "2003",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Jun 25 14:57:33 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Bajard:2003:ISC,
  editor =       "Jean Claude Bajard and Michael Schulte",
  booktitle =    "{16th IEEE Symposium on Computer Arithmetic: ARITH-16
                 2003: proceedings: Santiago de Compostela, Spain, June
                 15--18, 2003}",
  title =        "{16th IEEE Symposium on Computer Arithmetic: ARITH-16
                 2003: proceedings: Santiago de Compostela, Spain, June
                 15--18, 2003}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 282",
  year =         "2003",
  ISBN =         "0-7695-1894-X",
  ISBN-13 =      "978-0-7695-1894-7",
  ISSN =         "1063-6889",
  LCCN =         "QA76.6 .S919 2003",
  bibdate =      "Sat Jul 20 17:45:12 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE Computer Society order number PR01894. Selected
                 papers republished in {\em IEEE Transactions on
                 Computers}, {\bf 54}(3) (2005)
                 \cite{Schulte:2005:GEI}.",
  URL =          "http://www.dec.usc.es/arith16/;
                 https://ieeexplore.ieee.org/servlet/opac?punumber=8582",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-16",
}

@Proceedings{Cheung:2003:FPL,
  editor =       "Peter Y. K. Cheung and George A. Constantinides and
                 Jos{\'e} T. de Sousa",
  booktitle =    "Field-Programmable Logic and Applications: 13th
                 International Conference, {FPL 2003}, Lisbon, Portugal,
                 September 1--3, 2003: Proceedings",
  title =        "Field-Programmable Logic and Applications: 13th
                 International Conference, {FPL 2003}, Lisbon, Portugal,
                 September 1--3, 2003: Proceedings",
  volume =       "2778",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xxvi + 1179",
  year =         "2003",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/b12007",
  ISBN =         "3-540-40822-3 (softcover)",
  ISBN-13 =      "978-3-540-40822-2 (softcover)",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  LCCN =         "TK7895.G36 I48 2003",
  bibdate =      "Sat Jul 16 16:49:02 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       ser-LNCS,
  URL =          "http://link.springer-ny.com/link/service/series/0558/tocs/t2778.htm;
                 http://www.springerlink.com/openurl.asp?genre=issue&issn=0302-9743&volume=2778;
                 http://www.springerlink.com/openurl.asp?genre=volume&id=doi:10.1007/b12007",
  acknowledgement = ack-nhfb,
  meetingname =  "International Workshop on Field-Programmable Logic and
                 Applications (13th: 2003: Lisbon, Portugal)",
  subject =      "Field programmable gate arrays; Congresses;
                 Programmable array logic; Congresses",
}

@Proceedings{Deprettere:2003:IIC,
  editor =       "Ed F. Deprettere",
  booktitle =    "{IEEE International Conference on Application-Specific
                 Systems, Architectures and Processors: proceedings:
                 ASAP 2003: 24-26 June, 2003, The Hague, The
                 Netherlands}",
  title =        "{IEEE International Conference on Application-Specific
                 Systems, Architectures and Processors: proceedings:
                 ASAP 2003: 24-26 June, 2003, The Hague, The
                 Netherlands}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "x + 470",
  year =         "2003",
  ISBN =         "0-7695-1992-X",
  ISBN-13 =      "978-0-7695-1992-0",
  ISSN =         "1063-6862",
  LCCN =         "TK7874.6 .I58 2003",
  bibdate =      "Fri Mar 25 05:59:41 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE Computer Society Order Number PR01992.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Dietz:2003:LCP,
  editor =       "Henry G. Dietz",
  booktitle =    "{Languages and Compilers for Parallel Computing: 14th
                 International Workshop, LCPC 2001, Cumberland Falls,
                 KY, USA, August 1--3, 2001: Revised Papers}",
  title =        "{Languages and Compilers for Parallel Computing: 14th
                 International Workshop, LCPC 2001, Cumberland Falls,
                 KY, USA, August 1--3, 2001: Revised Papers}",
  volume =       "2624",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "ix + 444",
  year =         "2003",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/3-540-35767-X",
  ISBN =         "3-540-04029-3 (paperback)",
  ISBN-13 =      "978-3-540-04029-3 (paperback)",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  LCCN =         "QA76.58 .W656 2001",
  bibdate =      "Thu Aug 21 09:09:03 MDT 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "The 14th workshop on Languages and Compilers for
                 Parallel Computing, LCPC 2001, was organized and hosted
                 by the Electrical and Computer Engineering Department
                 of the University of Kentucky, Lexington, KY, USA.",
  series =       ser-LNCS,
  URL =          "http://link.springer-ny.com/link/service/series/0558/tocs/t2624.htm;
                 http://www.springerlink.com/openurl.asp?genre=issue&issn=0302-9743&volume=2624",
  acknowledgement = ack-nhfb,
  keywords =     "compilers (computer programs); parallel processing
                 (electronic computers); programming languages
                 (electronic computers)",
}

@Proceedings{IEEE:2003:IICa,
  editor =       "{IEEE}",
  booktitle =    "{2003 IEEE International Conference on Acoustics,
                 Speech, and Signal Processing: proceedings: April
                 6--10, 2003, Hong Kong Exhibition and Convention
                 Centre, Hong Kong (ICASSP '03)}",
  title =        "{2003 IEEE International Conference on Acoustics,
                 Speech, and Signal Processing: proceedings: April
                 6--10, 2003, Hong Kong Exhibition and Convention
                 Centre, Hong Kong (ICASSP '03)}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2003",
  ISBN =         "0-7803-7663-3",
  ISBN-13 =      "978-0-7803-7663-2",
  LCCN =         "TK7882.S65 I16 2003",
  bibdate =      "Thu Mar 24 21:28:32 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  note =         "IEEE catalog number 03CH37404.",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=8535",
  acknowledgement = ack-nhfb,
  subject =      "speech processing systems; congresses;
                 electro-acoustics; underwater acoustics; integrated
                 circuits; very large scale integration; signal
                 processing",
}

@Proceedings{IEEE:2003:IICb,
  editor =       "{IEEE}",
  booktitle =    "{2003 IEEE International Conference on
                 Field-Programmable Technology (FPT): proceedings:
                 15--17 December, 2003, the University of Tokyo}",
  title =        "{2003 IEEE International Conference on
                 Field-Programmable Technology (FPT): proceedings:
                 15--17 December, 2003, the University of Tokyo}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xv + 457",
  year =         "2003",
  DOI =          "https://doi.org/10.1109/FPT.2003.1275723",
  ISBN =         "0-7803-8320-6",
  ISBN-13 =      "978-0-7803-8320-3",
  LCCN =         "TK7895.G36 I143 2003",
  bibdate =      "Sat Oct 9 14:16:28 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=8988",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:2003:PCI,
  editor =       "{IEEE}",
  booktitle =    "{Proceedings of the 2003 CGO: the International
                 Symposium on Code Generation and Optimization; March
                 23--26, 2003, Fisherman's Wharf, San Francisco, CA,
                 with special emphasis on feedback-directed and runtime
                 optimization}",
  title =        "{Proceedings of the 2003 CGO: the International
                 Symposium on Code Generation and Optimization; March
                 23--26, 2003, Fisherman's Wharf, San Francisco, CA,
                 with special emphasis on feedback-directed and runtime
                 optimization}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xv + 347",
  year =         "2003",
  ISBN =         "0-7695-1913-X",
  ISBN-13 =      "978-0-7695-1913-5",
  LCCN =         "????",
  bibdate =      "Thu Jun 09 18:51:49 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "ACM Order No. 530033.",
  acknowledgement = ack-nhfb,
  keywords =     "EPIC; Intel IA-64; Itanium",
}

@Proceedings{Luk:2003:PSA,
  editor =       "Franklin T. Luk",
  booktitle =    "Proceedings of {SPIE: Advanced signal processing
                 algorithms, architectures, and implementations XIII:
                 6--8 August, 2003, San Diego, California, USA}",
  title =        "Proceedings of {SPIE: Advanced signal processing
                 algorithms, architectures, and implementations XIII:
                 6--8 August, 2003, San Diego, California, USA}",
  volume =       "5205",
  publisher =    pub-SPIE,
  address =      pub-SPIE:adr,
  pages =        "x + 620",
  year =         "2003",
  ISBN =         "0-8194-5078-2",
  ISBN-13 =      "978-0-8194-5078-4",
  LCCN =         "TK5102.5 .A3322 2003; TK5102.5 .A3325 2003; TK5102.9
                 .A38 2003; TK5102.5; TS510 .S63; TK5102.5 .A3173
                 2003eb",
  bibdate =      "Sun Mar 4 21:42:57 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  subject =      "Signal processing; Digital techniques; Congresses;
                 Algorithms; Computer architecture",
}

@Proceedings{Matthews:2003:PTS,
  editor =       "Michael B. Matthews",
  booktitle =    "{Proceedings of the Thirty-Seventh Asilomar Conference
                 on Signals, Systems \& Computers: November 9--12, 2003,
                 Pacific Grove, California}",
  title =        "{Proceedings of the Thirty-Seventh Asilomar Conference
                 on Signals, Systems \& Computers: November 9--12, 2003,
                 Pacific Grove, California}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2003",
  ISBN =         "0-7803-8104-1",
  ISBN-13 =      "978-0-7803-8104-9",
  LCCN =         "????",
  bibdate =      "Sat Jun 25 12:39:08 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog number 03CH37493.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Senda:2003:IPI,
  editor =       "J. Rafael Senda",
  booktitle =    "{ISSAC 2003: Proceedings of the 2003 International
                 Symposium on Symbolic and Algebraic Computation, August
                 3--6, 2003, Drexel University, Philadelphia, PA, USA}",
  title =        "{ISSAC 2003: Proceedings of the 2003 International
                 Symposium on Symbolic and Algebraic Computation, August
                 3--6, 2003, Drexel University, Philadelphia, PA, USA}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "x + 273",
  year =         "2003",
  ISBN =         "1-58113-641-2",
  ISBN-13 =      "978-1-58113-641-8",
  LCCN =         "QA76.95",
  bibdate =      "Sat Dec 13 18:18:22 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "ACM order number 505030.",
  acknowledgement = ack-nhfb,
}

@Book{Warren:2003:HD,
  author =       "Henry S. Warren",
  booktitle =    "Hacker's delight",
  title =        "Hacker's delight",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "xiv + 306",
  year =         "2003",
  ISBN =         "0-201-91465-4",
  ISBN-13 =      "978-0-201-91465-8",
  LCCN =         "QA76.6 .W375 2003",
  bibdate =      "Tue Jan 03 18:20:34 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "While this book does not specifically address
                 computational aspects of floating-point arithmetic
                 (apart from the nine-page Chapter 15), it has extensive
                 coverage of, and clever algorithms for, integer
                 arithmetic operations that are fundamental for
                 implementing hardware floating-arithmetic and software
                 multiple-precision arithmetic.",
  URL =          "http://www.awprofessional.com/bookstore/product.asp?isbn=0201914654;
                 http://www.hackersdelight.org/;
                 http://www.hackersdelight.org/hackerTOC.pdf;
                 http://www.informit.com/content/images/chap3_0201914654/elementLinks/0201914654.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "DEC PDP-10; division by constants; Gray code; Hilbert
                 curves; IEEE 754 floating-point arithmetic; integer
                 cube root; integer division; integer exponentiation;
                 integer logarithm; integer square root; prime numbers;
                 unusual number bases",
  remark =       "Foreword by Guy L. Steele, Jr., who begins ``When I
                 first got a summer job at MIT's Project MAC almost 30
                 years ago, I was delighted to be able to work with the
                 DEC PDP-10 computer, which was more fun to program in
                 assembly language than any other computer, bar none,
                 because of its rich yet tractable set of instructions
                 for performing bit tests, bit masking, field
                 manipulation, and operations on integers. Though the
                 PDP-10 has not been manufactured for quite some years,
                 there remains a thriving cult of enthusiasts who keep
                 old PDP-10 hardware running and who run old PDP-10
                 software---entire operating systems and their
                 applications---by using personal computers to simulate
                 the PDP-10 instruction set.''",
  subject =      "Computer programming; Computer hackers",
  tableofcontents = "Preface\par

                 1. Introduction\par

                 Notation\par

                 Instruction Set and Execution Time Model\par

                 2. Basis\par

                 Manipulating Rightmost Bits \\
                 Addition Combined with Logical Operations \\
                 Inequalities among Logical and Arithmetic Expressions
                 \\
                 Absolute Value Function \\
                 Sign Extension \\
                 Shift Right Signed from Unsigned \\
                 Sign Function \\
                 Three-Valued Compare \\
                 Transfer of Sign \\
                 Decoding a `Zero Means 2**n' Field \\
                 Comparison Predicates \\
                 Overflow Detection \\
                 Condition Code Result of Add, Subtract, and Multiply
                 \\
                 Rotate Shifts \\
                 Double-Length Add/Subtract \\
                 Double-Length Shifts \\
                 Multibyte Add, Subtract, Absolute Value \\
                 Doz, Max, Min \\
                 Exchanging Registers \\
                 Alternating among Two or More Values\par

                 3. Power-of-2 Boundaries\par

                 Rounding Up/Down to a Multiple of a Known Power of 2
                 \\
                 Rounding Up/Down to the Next Power of 2 \\
                 Detecting a Power-of-2 Boundary Crossing\par

                 4. Arithmetic Bounds\par

                 Checking Bounds of Integers \\
                 Propagating Bounds through Adds and Subtracts \\
                 Propagating Bounds through Logical Operations \\
                 Signed Bounds\par

                 5. Counting Bits\par

                 Counting 1-bits \\
                 Parity \\
                 Counting Leading 0's \\
                 Counting Trailing 0's\par

                 6. Searching Words\par

                 Find First 0-Byte \\
                 Find First String of 1-Bits of a Given Length\par

                 7. Rearranging Bits and Bytes\par

                 Reversing Bits and Bytes \\
                 Shuffling Bits \\
                 Transposing a Bit Matrix \\
                 Compress, or Generalized Extract \\
                 General Permutations, Sheep and Goats Operation \\
                 Rearrangements and Index Transformations\par

                 8. Multiplication\par

                 Multiword Multiplication \\
                 High-Order Half of 64-Bit Product \\
                 High-Order Product Signed from/to Unsigned \\
                 Multiplication by Constants\par

                 9. Integer Division\par

                 Preliminaries \\
                 Multiword Division \\
                 Unsigned Short Division from Signed Division \\
                 Unsigned Long Division\par

                 10. Integer Division by Constants\par

                 Signed Division by a Known Power of 2 \\
                 Signed Remainder from Division by a Known Power of 2
                 \\
                 Signed Division and Remainder by Non-powers of 2 \\
                 Signed Division by Divisors >= 2 \\
                 Signed Division by Divisors <= -2 \\
                 Incorporation into a Compiler \\
                 Miscellaneous Topics \\
                 Unsigned Division \\
                 Unsigned Division by Divisors >= 1 \\
                 Incorporation into a Compiler (Unsigned) \\
                 Miscellaneous Topics (Unsigned) \\
                 Applicability to Modulus and Floor Division \\
                 Similar Methods \\
                 Sample Magic Numbers \\
                 Exact Division by Constants \\
                 Test for Zero Remainder after Division by a
                 Constant\par

                 11. Some Elementary Functions\par

                 Integer Square Root \\
                 Integer Cube Root \\
                 Integer Exponentiation \\
                 Integer Logarithm\par

                 12. Unusual Bases for Number Systems\par

                 Base -2 \\
                 Base -1 + i \\
                 Other Bases \\
                 What is the Most Efficient Base?\par

                 13. Gray Code \\
                 Gray Code \\
                 Incrementing a Gray Coded Integer \\
                 Negabinary Gray Code \\
                 Brief History and Applications\par

                 14. Hilbert's Curve\par

                 A Recursive Algorithm for Generating the Hilbert Curve
                 \\
                 Coordinates from Distance along the Hilbert Curve \\
                 Distance from Coordinates on the Hilbert Curve \\
                 Incrementing the Coordinates on the Hilbert Curve \\
                 Non-recursive Generating Algorithms \\
                 Other Space-Filling Curves \\
                 Applications\par

                 15. Floating-Point\par

                 IEEE Format \\
                 Comparing Floating-Point Numbers Using Integer
                 Operations \\
                 The Distribution of Leading Digits \\
                 Table of Miscellaneous Values\par

                 16. Formulas for Primes\par

                 Introduction \\
                 Willans's Formulas \\
                 Wormell's Formula \\
                 Formulas for Other Difficult Functions\par

                 Appendix A. Arithmetic Tables for a 4-Bit
                 Machine\par

                 Appendix B. Newton's Method\par

                 Bibliography.",
}

@Proceedings{ACM:2004:FAS,
  editor =       "{ACM}",
  booktitle =    "{FPGA 2004: ACM\slash SIGDA Twelfth ACM International
                 Symposium on Field-Programmable Gate Arrays, Monterey
                 Beach Hotel, Monterey, California, USA: February
                 22--24, 2004}",
  title =        "{FPGA 2004: ACM\slash SIGDA Twelfth ACM International
                 Symposium on Field-Programmable Gate Arrays, Monterey
                 Beach Hotel, Monterey, California, USA: February
                 22--24, 2004}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "vi + 260",
  year =         "2004",
  ISBN =         "1-58113-829-6",
  ISBN-13 =      "978-1-58113-829-0",
  LCCN =         "TK7895.G36 A26 2004",
  bibdate =      "Sat Oct 9 15:25:33 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "ACM order number 480040.",
  URL =          "http://portal.acm.org/toc.cfm?id=968280",
  acknowledgement = ack-nhfb,
  subject =      "Gate array circuits; Congresses; Field programmable
                 gate arrays; Programmable array logic",
}

@Proceedings{ACM:2004:GVN,
  editor =       "{ACM}",
  booktitle =    "{GLSVLSI '04: VLSI in the nanometer era: proceedings
                 of the 2004 ACM Great Lakes Symposium on VLSI, Radisson
                 Hotel, Boston, MA, USA, April 26-28, 2004}",
  title =        "{GLSVLSI '04: VLSI in the nanometer era: proceedings
                 of the 2004 ACM Great Lakes Symposium on VLSI, Radisson
                 Hotel, Boston, MA, USA, April 26-28, 2004}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xiii + 467",
  year =         "2004",
  ISBN =         "1-58113-853-9",
  ISBN-13 =      "978-1-58113-853-5",
  LCCN =         "????",
  bibdate =      "Thu Aug 7 18:09:26 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.gbv.de:20011/gvk",
  acknowledgement = ack-nhfb,
}

@Proceedings{ACM:2004:YAS,
  editor =       "ACM",
  booktitle =    "20 Years of the {ACM\slash SIGPLAN} Conference on
                 Programming Language Design and Implementation
                 (1979--1999): A Selection",
  title =        "20 Years of the {ACM\slash SIGPLAN} Conference on
                 Programming Language Design and Implementation
                 (1979--1999): a Selection",
  volume =       "39(4)",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  year =         "2004",
  ISBN =         "1-58113-623-4",
  ISBN-13 =      "978-1-58113-623-4",
  LCCN =         "????",
  bibdate =      "Sat Nov 29 11:38:05 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Anonymous:2004:ICM,
  editor =       "Anonymous",
  booktitle =    "{6th International Conference on Mathematics in Signal
                 Processing: Cirencester, December 14--16, 2004}",
  title =        "{6th International Conference on Mathematics in Signal
                 Processing: Cirencester, December 14--16, 2004}",
  publisher =    "????",
  address =      "????",
  year =         "2004",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Dec 4 10:10:18 MST 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Arnold:2004:PAI,
  editor =       "Jeffrey Arnold",
  booktitle =    "{Proceedings / 12th Annual IEEE Symposium on
                 Field-Programmable Custom Computing Machines, FCCM
                 2004: 20--23 April 2004, Napa Valley, California}",
  title =        "{Proceedings / 12th Annual IEEE Symposium on
                 Field-Programmable Custom Computing Machines, FCCM
                 2004: 20--23 April 2004, Napa Valley, California}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "x + 346",
  year =         "2004",
  ISBN =         "0-7695-2230-0",
  ISBN-13 =      "978-0-7695-2230-2",
  LCCN =         "????",
  bibdate =      "Sat Jun 25 12:49:50 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
}

@Proceedings{Druin:2004:IDC,
  editor =       "Allison Druin and Juan Pablo Hourcade and Sharmon
                 Kollet",
  booktitle =    "{Interactive Design \& Children 2004: Building a
                 Community}",
  title =        "{Interactive Design \& Children 2004: Building a
                 Community}",
  publisher =    "College Park IDC",
  address =      "College Park, MD, USA",
  pages =        "190",
  year =         "2004",
  ISBN =         "1-58113-791-5",
  ISBN-13 =      "978-1-58113-791-0",
  LCCN =         "QA76.9.H85 C746 2004",
  bibdate =      "Fri Aug 08 09:07:40 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Frougny:2004:RCR,
  editor =       "Christiane Frougny and Vasco Brattka and Norbert
                 M{\"u}ller",
  booktitle =    "{RNC'6, 6th Conference on Real Numbers and Computers:
                 Nov 15--17, 2004, Dagstuhl, Germany}",
  title =        "{RNC'6, 6th Conference on Real Numbers and Computers:
                 Nov 15--17, 2004, Dagstuhl, Germany}",
  publisher =    "Universita{\"a}t Trier, Fachbereich IV, Mathematik,
                 Informatik",
  address =      "Trier, Germany",
  bookpages =    "216 + i",
  pages =        "216 + i",
  year =         "2004",
  ISSN =         "0944-0488",
  ISSN-L =       "0944-0488",
  bibdate =      "Thu Apr 28 05:55:01 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Forschungsbericht Nr. 04-8.",
  URL =          "http://www.informatik.uni-trier.de/Reports/TR-08-2004;
                 http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6-complete.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "base conversion; correct rounding; decimal
                 floating-point arithmetic",
  tableofcontents = "Introduction / Christiane Frougny / 1--4 \\
                 Invited Lecture: New ideas and results for solving
                 Differential equations symbolically [abstract only] /
                 Benno Fuchssteiner / 5--5 \\
                 Invited Lecture: A survey of Integer Relations
                 algorithms and rational numbers [abstract only] / Simon
                 Plouffe / 6--6 \\
                 Invited Lecture: Real Numbers and Robustness in
                 Computational Geometry / Stefan Schirra / 7--21 \\
                 Bridging the gap between formal specification and
                 bit-level floating-point arithmetic / Sylvie Boldo /
                 22--36 \\
                 Automata, Borel functions and real numbers in Pisot
                 base / B. Cagnard, P. Simonnet / 37--54 \\
                 Generating formally certified bounds on values and
                 round-off errors / Marc Daumas, Guillaume Melquiond /
                 55--70 \\
                 A proven correctly rounded logarithm in
                 double-precision / Florent de Dinechin, Catherine
                 Loirat, Jean-Michel Muller / 71--85 \\
                 A comparison of polynomial evaluation schemes / L.
                 Fousse, S. Schmitt / 86--102 \\
                 A comparison of real and complex pseudozero sets for
                 polynomials with real coefficients / Stef Graillat,
                 Philippe Langlois / 103--112 \\
                 On Intermediate Precision Required for
                 Correctly-Rounding Decimal-to-Binary Floating-Point
                 Conversion / Michel Hack / 113--134 \\
                 The Generic Multiple-Precision Floating-Point Addition
                 With Exact Rounding (as in the MPFR Library) / Vincent
                 Lef{\`e}vre / 135--145 \\
                 Software Division and Square Root Using Goldschmidt's
                 Algorithms / Peter Markstein / 146--157 \\
                 A Fast Algorithm for Julia Sets of Hyperbolic Rational
                 Functions / R. Rettinger / 158--171 \\
                 An extension of Chaitin's halting probability $\Omega$
                 to measurement operator in infinite dimensional quantum
                 system / Kohtaro Tadaki / 172--191 \\
                 On the Hierarchy of $\Delta_2^0$-Real Numbers / Xizhong
                 Zheng / 192--215 \\
                 Trierer Forschungsberichte Mathematik / Informatik [one
                 page list of reports] / 1--1 (216--216)",
}

@Proceedings{Hilledt:2004:AME,
  editor =       "James M. Hill and Ross R. Moore",
  booktitle =    "{Applied mathematics entering the 21st Century:
                 invited talks from the ICIAM 2003 Congress}",
  title =        "{Applied mathematics entering the 21st Century:
                 invited talks from the ICIAM 2003 Congress}",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xv + 413",
  year =         "2004",
  ISBN =         "0-89871-559-8",
  ISBN-13 =      "978-0-89871-559-0",
  LCCN =         "QA7 .A6665 2004; QA7 .A67 2004; QA1 .I57 2004",
  bibdate =      "Thu Nov 8 19:52:42 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  remark =       "Papers appearing in this volume are the Invited Talks
                 given at ICIAM 2003, the 5th International Congress of
                 Industrial and Applied Mathematics, held in Sydney over
                 the period July 7 to 11, 2003.",
  subject =      "Mathematics; Congresses; Applied mathematics",
}

@Proceedings{IEEE:2004:IICa,
  editor =       "{IEEE}",
  booktitle =    "{IEEE} International Conference on Computer Design:
                 {VLSI} in Computers and Processors, 2004. {ICCD 2004}.
                 Proceedings. 11--13 October 2004",
  title =        "{IEEE} International Conference on Computer Design:
                 {VLSI} in Computers and Processors, 2004. {ICCD} 2004.
                 Proceedings. 11--13 October 2004",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xviii + 578",
  year =         "2004",
  ISBN =         "0-7695-2231-9",
  ISBN-13 =      "978-0-7695-2231-9",
  LCCN =         "TK7888.4 .I23 2004",
  bibdate =      "Fri Mar 25 05:56:18 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  price =        "UK\pounds 121.00",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:2004:IICb,
  editor =       "{IEEE}",
  booktitle =    "{15th IEEE International Conference on
                 Application-Specific Systems, Architectures and
                 Processors: proceedings: September 2--29, 2004,
                 Galveston, Texas}",
  title =        "{15th IEEE International Conference on
                 Application-Specific Systems, Architectures and
                 Processors: proceedings: September 2--29, 2004,
                 Galveston, Texas}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "x + 412",
  year =         "2004",
  ISBN =         "0-7695-2226-2",
  ISBN-13 =      "978-0-7695-2226-5",
  LCCN =         "TK7874.6 .I58 2004",
  bibdate =      "Sun Mar 4 21:48:24 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  meetingname =  "International Conference on Application-Specific
                 Systems, Architectures, and Processors (15th: 2004:
                 Galveston, Tex.)",
  remark =       "IEEE Computer Society Order Number P2226.",
  subject =      "Signal processing; Digital techniques; Congresses;
                 Array processors; Application-specific integrated
                 circuits",
}

@Proceedings{IEEE:2004:IICc,
  editor =       "{IEEE}",
  booktitle =    "{2004 IEEE International Conference on Acoustics,
                 Speech, and Signal Processing: proceedings: May 17--21,
                 2004, Fairmont Queen Elizabeth Hotel, Montreal, Quebec,
                 Canada (ICASSP '04)}",
  title =        "{2004 IEEE International Conference on Acoustics,
                 Speech, and Signal Processing: proceedings: May 17--21,
                 2004, Fairmont Queen Elizabeth Hotel, Montreal, Quebec,
                 Canada (ICASSP '04)}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2004",
  ISBN =         "0-7803-8484-9",
  ISBN-13 =      "978-0-7803-8484-2",
  LCCN =         "TK7882.S65 I61 2004",
  bibdate =      "Sun Feb 20 11:05:28 MST 2011",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE Catalog Number: 04CH37568",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=9248",
  acknowledgement = ack-nhfb,
  remark =       "Vol. 1. Speech processing. Vol. 2. Sensor array and
                 Multichannel signal processing; signal processing
                 theory and methods. Vol. 3. Image and multidimensional
                 processing; special sessions. Vol. 4. Audio and
                 electroacoustics signal processing for communications.
                 Vol. 5. Design and implementation of signal processing
                 systems; industry technology tracks; machine learning
                 for signal processing; multimedia signal processing;
                 signal processing for education",
  subject =      "speech processing systems; congresses; signal
                 processing systems; electro-acoustics; underwater
                 acoustics; integrated circuits; very large scale
                 integration",
}

@Proceedings{IEEE:2004:IIS,
  editor =       "{IEEE}",
  booktitle =    "{2004 IEEE International Symposium on Computer-Aided
                 Control System Design: September 2--4, 2004, the Grand
                 Hotel, Taipei, Taiwan}",
  title =        "{2004 IEEE International Symposium on Computer-Aided
                 Control System Design: September 2--4, 2004, the Grand
                 Hotel, Taipei, Taiwan}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xv + 377 + 3 + 3",
  year =         "2004",
  DOI =          "https://doi.org/10.1109/CACSD.2004.1393830",
  ISBN =         "0-7803-8636-1",
  ISBN-13 =      "978-0-7803-8636-5",
  LCCN =         "TJ212.2 .I32495 2004",
  bibdate =      "Mon Nov 1 10:36:39 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "IEEE Catalog Number 04TH8770.",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=9600",
  acknowledgement = ack-nhfb,
  subject =      "Automatic control; Data processing; Congresses;
                 Computer-aided design",
}

@Proceedings{IEEE:2004:PJC,
  editor =       "{IEEE}",
  booktitle =    "{Proceedings of the 2003 Joint Conference of the
                 Fourth International Conference on Information,
                 Communications and Signal Processing, 2003 and the
                 Fourth Pacific Rim Conference on Multimedia, 15--18
                 December 2003, Meritus Mandarin Singapore Hotel,
                 Singapore}",
  title =        "{Proceedings of the 2003 Joint Conference of the
                 Fourth International Conference on Information,
                 Communications and Signal Processing, 2003 and the
                 Fourth Pacific Rim Conference on Multimedia, 15--18
                 December 2003, Meritus Mandarin Singapore Hotel,
                 Singapore}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2004",
  ISBN =         "0-7803-8185-8",
  ISBN-13 =      "978-0-7803-8185-8",
  LCCN =         "TK5102.9 .J65 2003",
  bibdate =      "Sun Feb 20 11:01:10 MST 2011",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog number 03EX758.",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=9074",
  acknowledgement = ack-nhfb,
}

@Proceedings{Luk:2004:ASP,
  editor =       "Franklin T. Luk",
  booktitle =    "Proceedings of {SPIE: Advanced signal processing
                 algorithms, architectures, and implementations XIV:
                 4--6 August 2004, Denver, Colorado, USA}",
  title =        "Proceedings of {SPIE: Advanced signal processing
                 algorithms, architectures, and implementations XIV:
                 4--6 August 2004, Denver, Colorado, USA}",
  volume =       "5559",
  publisher =    pub-SPIE,
  address =      pub-SPIE:adr,
  pages =        "viii + 464",
  year =         "2004",
  ISBN =         "0-8194-5497-4",
  ISBN-13 =      "978-0-8194-5497-3",
  ISSN =         "0277-786X (print), 1996-756X (electronic)",
  LCCN =         "TK5102.5 .A3173 2004; TK5102.5 .A3322 2004",
  bibdate =      "Sun Mar 4 21:50:40 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  series =       "SPIE proceedings series",
  acknowledgement = ack-nhfb,
  subject =      "Algorithms; Congresses; Signal processing; Digital
                 techniques; Computer architecture",
}

@Proceedings{Selvaraj:2004:PES,
  editor =       "Henry Selvaraj",
  booktitle =    "{Proceedings of the EUROMICRO System on Digital System
                 Design: 31 August--3 September 2004, Rennes, France}",
  title =        "{Proceedings of the EUROMICRO System on Digital System
                 Design: 31 August--3 September 2004, Rennes, France}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiii + 631",
  year =         "2004",
  ISBN =         "0-7695-2203-3",
  ISBN-13 =      "978-0-7695-2203-6",
  LCCN =         "QA76.9.S88 E97 2004; QA76.9.S88",
  bibdate =      "Sun Mar 4 21:45:21 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  meetingname =  "Euromicro Symposium on Digital Systems Design (2004:
                 Rennes, France)",
  subject =      "Digital electronics; Congresses; System design;
                 Computer architecture",
}

@Proceedings{Smailagic:2004:ETV,
  editor =       "Asim Smailagic and Magdy A. Bayoumi",
  booktitle =    "Emerging trends in {VLSI} systems design: proceedings:
                 {IEEE} Computer Society Annual Symposium on {VLSI,
                 19--20} February 2004, Lafayette, Louisiana {[ISVLSI
                 2004]}",
  title =        "Emerging trends in {VLSI} systems design: proceedings:
                 {IEEE} Computer Society Annual Symposium on {VLSI},
                 19--20 February 2004, Lafayette, Louisiana [{ISVLSI}
                 2004]",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiv + 324",
  year =         "2004",
  ISBN =         "0-7695-2097-9",
  ISBN-13 =      "978-0-7695-2097-1",
  LCCN =         "TK7874 .I122 2004",
  bibdate =      "Wed May 04 07:54:20 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE Computer Society order number P2097.",
  acknowledgement = ack-nhfb,
}

@Book{Wahdan:2004:IHE,
  editor =       "Abdel-Moniem Wahdan",
  booktitle =    "{ICEEC'04: 2004 International Conference on
                 Electrical, Electronic and Computer Engineering:
                 proceedings: 5--7 September, 2004, Cairo, Egypt}",
  title =        "{ICEEC'04: 2004 International Conference on
                 Electrical, Electronic and Computer Engineering:
                 proceedings: 5--7 September, 2004, Cairo, Egypt}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xlv + 954",
  year =         "2004",
  bibdate =      "Tue Jul 19 08:01:02 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  note =         "IEEE catalog number 04EX893.",
  acknowledgement = ack-nhfb,
  subject =      "Electric engineering; Congresses; Electronics;
                 Congresses; Computer engineering; Congresses",
}

@Proceedings{ACM:2005:ASI,
  editor =       "{ACM}",
  booktitle =    "{ASSETS 2005: the Seventh International ACM SIGACCESS
                 Conference on Computers and Accessibility: October
                 9--12, 2005, Baltimore, Maryland, USA}",
  title =        "{ASSETS 2005: the Seventh International ACM SIGACCESS
                 Conference on Computers and Accessibility: October
                 9--12, 2005, Baltimore, Maryland, USA}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "ix + 223",
  year =         "2005",
  ISBN =         "1-59593-159-7",
  ISBN-13 =      "978-1-59593-159-7",
  LCCN =         "????",
  bibdate =      "Thu Aug 7 18:45:20 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.gbv.de:20011/gvk",
  acknowledgement = ack-nhfb,
}

@Proceedings{ACM:2005:FAS,
  editor =       "{ACM}",
  booktitle =    "{FPGA 2005: ACM\slash SIGDA Thirteenth ACM
                 International Symposium on Field-Programmable Gate
                 Arrays, Monterey Beach Resort, Monterey, California,
                 USA: February 20--22, 2005}",
  title =        "{FPGA 2005: ACM\slash SIGDA Thirteenth ACM
                 International Symposium on Field-Programmable Gate
                 Arrays, Monterey Beach Resort, Monterey, California,
                 USA: February 20--22, 2005}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "vi + 282",
  year =         "2005",
  ISBN =         "1-59593-029-9",
  ISBN-13 =      "978-1-59593-029-3",
  LCCN =         "TK7895.G36 A26 2005",
  bibdate =      "Sat Oct 9 14:32:27 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  note =         "ACM order number 480050.",
  acknowledgement = ack-nhfb,
  subject =      "gate array circuits; congresses; field programmable
                 gate arrays; programmable array logic",
}

@Proceedings{Bein:2005:PIS,
  editor =       "Wolfgang Bein",
  booktitle =    "{Proceedings: 8th International Symposium on Parallel
                 Architectures, Algorithms, and Networks: December 7--9,
                 2005, Las Vegas Nevada, USA: ISPAN 2005}",
  title =        "{Proceedings: 8th International Symposium on Parallel
                 Architectures, Algorithms, and Networks: December 7--9,
                 2005, Las Vegas Nevada, USA: ISPAN 2005}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiii + 548",
  year =         "2005",
  DOI =          "https://doi.org/10.1109/ISPAN.2005.2",
  ISBN =         "0-7695-2509-1",
  ISBN-13 =      "978-0-7695-2509-9",
  ISSN =         "1087-4089",
  LCCN =         "QA76.58 .I5673 2005",
  bibdate =      "Sat Oct 9 14:43:16 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE Computer Society Order Number P2509.",
  acknowledgement = ack-nhfb,
  subject =      "parallel processing (electronic computers);
                 congresses; computer algorithms; computer networks;
                 computer architecture",
}

@Book{Copeland:2005:ATA,
  editor =       "B. Jack Copeland",
  booktitle =    "{Alan Turing}'s {Automatic Computing Engine}: the
                 master codebreaker's struggle to build the modern
                 computer",
  title =        "{Alan Turing}'s {Automatic Computing Engine}: the
                 master codebreaker's struggle to build the modern
                 computer",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "xx + 553",
  year =         "2005",
  ISBN =         "0-19-856593-3 (hardcover)",
  ISBN-13 =      "978-0-19-856593-2 (hardcover)",
  LCCN =         "QA75 .A43 2005",
  MRclass =      "01A80 (01-06 01A60 68-03 94-03)",
  MRnumber =     "2164870 (2006g:01020)",
  MRreviewer =   "A. D. Booth",
  bibdate =      "Sat Nov 19 18:33:05 MST 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wilkes-maurice-v.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  URL =          "http://ukcatalogue.oup.com/product/9780198565932.do;
                 http://www.oxfordscholarship.com/oso/public/content/maths/9780198565932/toc.html",
  abstract =     "The mathematical genius Alan Turing (1912--1954) was
                 one of the greatest scientists and thinkers of the 20th
                 century. Now well known for his crucial wartime role in
                 breaking the ENIGMA code, he was the first to conceive
                 of the fundamental principle of the modern computer ---
                 the idea of controlling a computing machine's
                 operations by means of coded instructions, stored in
                 the machine's `memory'. In 1945, Turing drew up his
                 revolutionary design for an electronic computing
                 machine --- his Automatic Computing Engine (`ACE'). A
                 pilot model of the ACE ran its first programme in 1950
                 and the production version, the `DEUCE', went on to
                 become a cornerstone of the fledgling British computer
                 industry. The first `personal' computer was based on
                 Turing's ACE. This book describes Turing's struggle to
                 build the modern computer. It contains first-hand
                 accounts by Turing and by the pioneers of computing who
                 worked with him. The book describes the hardware and
                 software of the ACE and contains chapters describing
                 Turing's path-breaking research in the fields of
                 Artificial Intelligence (AI) and Artificial Life
                 (A-Life).",
  acknowledgement = ack-nhfb,
  remark =       "Originally published: New York; London: Springer,
                 2003",
  subject =      "Turing, Alan Mathison; Computers; Great Britain;
                 History; Computer engineering; Great Britain; History",
  tableofcontents = "Foreword / Donald W. Davies \\
                 Introduction / B. Jack Copeland \par

                 Part I: The National Physical Laboratory and the ACE
                 Project \\
                 A Century of Measurement and Computation at the
                 National Physical Laboratory, 1900--2000 / Eileen
                 Magnello \\
                 The Creation of the NPL Mathematics Division / Mary
                 Croarken \\
                 The Origins and Development of the ACE Project / B.
                 Jack Copeland \\
                 The Pilot ACE at the National Physical Laboratory,
                 James H. Wilkinson \par

                 Part II: Turing and the History of Computing \\
                 The ACE and the Shaping of British Computing / Martin
                 Campbell-Kelly \\
                 Computer Architecture and the ACE Computers / Robert
                 Doran \\
                 Turing and the Computer / B. Jack Copeland and Diane
                 Proudfoot \\
                 From Turing Machine to ``Electronic Brain'' / Teresa
                 Numerico \par

                 Part III: The ACE Computers \\
                 The Pilot ACE Instruction Format / Henry John Norton
                 \\
                 Programming the Pilot ACE / J. G. Hayes \\
                 The Pilot ACE: from Concept to Reality / Robin A.
                 Vowels \\
                 The DEUCE --- a User's View / Robin A. Vowels \\
                 Applications of the Pilot ACE and the DEUCE / Tom
                 Vickers \\
                 The ACE Test Assembly, the Pilot ACE, the Big ACE, and
                 the Bendix G15 / Harry D. Huskey \\
                 The ACE Simulator and the Cybernetic Model / Michael
                 Woodger \\
                 The Pilot Model and the Big ACE on the Web / Benjamin
                 Wells \par

                 Part IV: Electronics \\
                 How Valves Work / David O. Clayden \\
                 Recollections of Early Vacuum Tube Circuits / Maurice
                 Wilkes \\
                 Circuit Design of the Pilot ACE and the Big ACE / David
                 O. Clayden \par

                 Part V: Technical Reports and Lectures on the ACE and
                 the Pilot ACE, 1945--1951 \\
                 Proposed Electronic Calculator (1945) / Alan M. Turing
                 \\
                 Notes on Memory (1945) / Alan M. Turing \\
                 The Turing--Wilkinson Lecture Series (1946--1947) /
                 Alan M. Turing and James H. Wilkinson \\
                 The State of the Art in Electronic Digital Computing in
                 Britain and the United States (1947) / Harry D.
                 Huskey",
}

@Proceedings{IEEE:2005:DAT,
  editor =       "{IEEE}",
  booktitle =    "{Design, Automation, and Test in Europe: proceedings:
                 Munich, Germany, March 7--11, 2005}",
  title =        "{Design, Automation, and Test in Europe: proceedings:
                 Munich, Germany, March 7--11, 2005}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2005",
  ISBN =         "0-7695-2288-2",
  ISBN-13 =      "978-0-7695-2288-3",
  LCCN =         "TK7870 .D467 2005",
  bibdate =      "Sun Feb 20 11:17:37 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "IEEE Computer Society Order Number P2288.",
  acknowledgement = ack-nhfb,
  meetingname =  "Design, Automation, and Test in Europe Conference and
                 Exhibition (2005 : Munich, Germany)",
  subject =      "Electronic systems; Design and construction;
                 Congresses; Electronic circuit design; Data processing;
                 Computer-aided design; Electronic industries;
                 Automation",
}

@Proceedings{IEEE:2005:ICS,
  editor =       "{IEEE}",
  booktitle =    "{IEEE Computer Society Annual Symposium on VLSI
                 (ISVLSI 2005)}",
  title =        "{IEEE Computer Society Annual Symposium on VLSI
                 (ISVLSI 2005)}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "332 (est.)",
  year =         "2005",
  ISBN =         "0-7695-2365-X",
  ISBN-13 =      "978-0-7695-2365-1",
  LCCN =         "????",
  bibdate =      "Sat Jun 25 13:00:07 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.computer.org/cspress/CATALOG/p2365.htm",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:2005:IIS,
  editor =       "{IEEE}",
  booktitle =    "{IEEE International Symposium on Circuits and Systems
                 (ISCAS): May 23--26, 2005, International Conference
                 Center, Kobe, Japan: conference proceedings}",
  title =        "{IEEE International Symposium on Circuits and Systems
                 (ISCAS): May 23--26, 2005, International Conference
                 Center, Kobe, Japan: conference proceedings}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2005",
  ISBN =         "0-7803-8834-8",
  ISBN-13 =      "978-0-7803-8834-5",
  LCCN =         "TK454.2 .I22 2005",
  bibdate =      "Mon Mar 5 08:19:11 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  meetingname =  "IEEE International Symposium on Circuits and Systems
                 (2005: Kobe-shi, Japan)",
  remark =       "IEEE Catalog Number: 05CH37618.",
  subject =      "Electronics; Congresses; Signal processing; Digital
                 techniques; Electronic circuits; Neural networks
                 (Computer science); Integrated circuits; Very large
                 scale integration",
}

@Proceedings{IEEE:2005:MSC,
  editor =       "{IEEE}",
  booktitle =    "{2005 48th Midwest Symposium on Circuits and Systems:
                 [conference proceedings: Cincinnati, Ohio, August
                 7--10, 2005]}",
  title =        "{2005 48th Midwest Symposium on Circuits and Systems:
                 [conference proceedings: Cincinnati, Ohio, August
                 7--10, 2005]}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2005",
  ISBN =         "0-7803-9197-7",
  ISBN-13 =      "978-0-7803-9197-0",
  LCCN =         "TK3226 .M55 2005eb",
  bibdate =      "Sun Feb 20 11:11:21 MST 2011",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ieeexplore.ieee.org/xpl/RecentCon.jsp?punumber=10622",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:2005:PII,
  editor =       "{IEEE}",
  booktitle =    "{Proceedings of the IEEE 16th International Conference
                 on Application-specific Systems, Architectures and
                 Processors, Samos, Greece, July 23--25, 2005 (ASAP
                 2005)}",
  title =        "{Proceedings of the IEEE 16th International Conference
                 on Application-specific Systems, Architectures and
                 Processors, Samos, Greece, July 23--25, 2005 (ASAP
                 2005)}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2005",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Jun 25 13:09:23 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ece.uvic.ca/asap2005/",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:2005:PIS,
  editor =       "{IEEE}",
  booktitle =    "{Proceedings of the 17th IEEE Symposium on Computer
                 Arithmetic, ARITH-17, June 27--29, 2005, Cape Cod,
                 Massachusetts, USA}",
  title =        "{Proceedings of the 17th IEEE Symposium on Computer
                 Arithmetic, ARITH-17, June 27--29, 2005, Cape Cod,
                 Massachusetts, USA}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2005",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Tue Jun 21 19:02:16 2005",
  bibsource =    "http://arith17.polito.it/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  xxnote =       "Not yet published: check editor??",
}

@Proceedings{IEEE:2005:PWE,
  editor =       "{IEEE}",
  booktitle =    "{Proceedings of the 2005 3rd Workshop on Embedded
                 Systems for Real Time Multimedia, 22--23 September
                 2005, New York Metropolitan Area}",
  title =        "{Proceedings of the 2005 3rd Workshop on Embedded
                 Systems for Real Time Multimedia, 22--23 September
                 2005, New York Metropolitan Area}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "140",
  year =         "2005",
  DOI =          "https://doi.org/10.1109/ESTMED.2005.1518044",
  ISBN =         "0-7803-9347-3",
  ISBN-13 =      "978-0-7803-9347-9",
  LCCN =         "QA76.575 .W67 2005",
  bibdate =      "Sat Oct 9 14:35:29 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  note =         "IEEE catalog number 5EX1149.",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=10172",
  acknowledgement = ack-nhfb,
  subject =      "Multimedia systems; Congresses; Embedded computer
                 systems",
}

@Proceedings{Luk:2005:ASP,
  editor =       "Franklin T. Luk",
  booktitle =    "{Advanced Signal Processing Algorithms, Architectures,
                 and Implementations XV, August, San Diego, CA, USA}",
  title =        "{Advanced Signal Processing Algorithms, Architectures,
                 and Implementations XV, August, San Diego, CA, USA}",
  volume =       "5910",
  publisher =    pub-SPIE,
  address =      pub-SPIE:adr,
  pages =        "????",
  year =         "2005",
  CODEN =        "PSISDG",
  ISBN =         "????",
  ISBN-13 =      "????",
  ISSN =         "0277-786X (print), 1996-756X (electronic)",
  LCCN =         "????",
  bibdate =      "Sat Jun 25 12:56:26 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       j-PROC-SPIE,
  acknowledgement = ack-nhfb,
}

@Proceedings{Montuschi:2005:PIS,
  editor =       "Paolo Montuschi and Eric (Eric Mark) Schwarz",
  booktitle =    "{Proceedings of the 17th IEEE Symposium on Computer
                 Arithmetic, ARITH-17 2005, June 27--29, 2005, Cape Cod,
                 Massachusetts, USA}",
  title =        "{Proceedings of the 17th IEEE Symposium on Computer
                 Arithmetic, ARITH-17 2005, June 27--29, 2005, Cape Cod,
                 Massachusetts, USA}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 298",
  year =         "2005",
  ISBN =         "0-7695-2366-8",
  ISBN-13 =      "978-0-7695-2366-8",
  LCCN =         "QA76.9.C62 .S95 2005",
  bibdate =      "Thu Sep 14 12:30:26 2006",
  bibsource =    "http://arith17.polito.it/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-17",
}

@Proceedings{Tang:2005:AIC,
  editor =       "Ting-Ao Tang and Yumei Huang and others",
  booktitle =    "{ASICON 2005: 2005, 6th International Conference on
                 ASIC proceedings, Shanghai, China, October 24--27,
                 2005}",
  title =        "{ASICON 2005: 2005, 6th International Conference on
                 ASIC proceedings, Shanghai, China, October 24--27,
                 2005}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2005",
  ISBN =         "0-7803-9210-8",
  ISBN-13 =      "978-0-7803-9210-6",
  LCCN =         "TK7874.6 2005",
  bibdate =      "Sun Feb 20 11:20:06 MST 2011",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE Catalog Number 05TH8820.",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=10726",
  acknowledgement = ack-nhfb,
  meetingname =  "International Conference on ASIC (6th : 2005 :
                 Shanghai, China)",
  subject =      "application specific integrated circuits; design and
                 construction; congresses; computer-aided design;
                 testing",
}

@Proceedings{Vassiliadis:2005:IIC,
  editor =       "Stamatis Vassiliadis and Nikitas J. Dimopoulos and
                 Sanjay Vishnu Rajopadhye",
  booktitle =    "{16th IEEE International Conference on
                 Application-Specific Systems, Architectures, and
                 Processors: ASAP 2005: 23--25 July 2005, Samos,
                 Greece}",
  title =        "{16th IEEE International Conference on
                 Application-Specific Systems, Architectures, and
                 Processors: ASAP 2005: 23--25 July 2005, Samos,
                 Greece}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiii + 419",
  year =         "2005",
  ISBN =         "0-7695-2407-9",
  ISBN-13 =      "978-0-7695-2407-8",
  LCCN =         "TK7874.6 .I58 2005",
  bibdate =      "Sun Mar 4 21:53:56 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  meetingname =  "International Conference on Application-Specific
                 Systems, Architectures, and Processors (16th: 2005:
                 Samos, Greece)",
  subject =      "Array processors; Congresses; Signal processing;
                 Digital techniques; Application specific integrated
                 circuits",
}

@Proceedings{ACM:2006:SCH,
  editor =       "{ACM}",
  booktitle =    "{SC'06: Conference on High Performance Networking and
                 Computing: proceedings of the 2006 ACM/IEEE conference
                 on Supercomputing, November 11--17, 2006, Tampa
                 Convention Center, Tampa, Florida, USA}",
  title =        "{SC'06: Conference on High Performance Networking and
                 Computing: proceedings of the 2006 ACM/IEEE conference
                 on Supercomputing, November 11--17, 2006, Tampa
                 Convention Center, Tampa, Florida, USA}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "????",
  year =         "2006",
  ISBN =         "0-7695-2700-0",
  ISBN-13 =      "978-0-7695-2700-0",
  LCCN =         "????",
  bibdate =      "Thu Nov 8 20:03:51 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.bibsys.no:2100/BIBSYS",
  note =         "Contains one CD-ROM.",
  acknowledgement = ack-nhfb,
  meetingname =  "Conference on High Performance Networking and
                 Computing 2006. Tampa, Florida",
}

@Proceedings{Anonymous:2006:PCR,
  editor =       "Anonymous",
  booktitle =    "{Proceedings of the 7th Conference on Real Numbers and
                 Computers (RNC 7) LORIA, Nancy, France, July 10--12,
                 2006}",
  title =        "{Proceedings of the 7th Conference on Real Numbers and
                 Computers (RNC 7) LORIA, Nancy, France, July 10--12,
                 2006}",
  publisher =    "????",
  address =      "????",
  pages =        "????",
  year =         "2006",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Tue Jun 27 10:26:43 2006",
  bibsource =    "http://rnc7.loria.fr/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Bertels:2006:FPI,
  editor =       "Koen Bertels and Philip Leong and Eduardo Boemo",
  booktitle =    "{FPL 2006: Proceedings of the 16th International
                 Conference on Field-Programmable Logic and Applications
                 Meli{\'a} Madrid Princesa, Madrid, Spain: August
                 28--30, 2006}",
  title =        "{FPL 2006: Proceedings of the 16th International
                 Conference on Field-Programmable Logic and Applications
                 Meli{\'a} Madrid Princesa, Madrid, Spain: August
                 28--30, 2006}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xl + 975",
  year =         "2006",
  DOI =          "https://doi.org/10.1109/FPL.2006.311178",
  ISBN =         "1-4244-0312-X (softbound)",
  ISBN-13 =      "978-1-4244-0312-7 (softbound)",
  LCCN =         "TK7895.G36 I48 2006",
  bibdate =      "Sat Oct 9 15:27:53 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog number 06EX1349. Two volumes.",
  acknowledgement = ack-nhfb,
  subject =      "Field programmable gate arrays; Congresses;
                 Programmable array logic",
}

@Proceedings{Cimatti:2006:FMH,
  editor =       "Alessandro Cimatti and Marco Bernardo",
  booktitle =    "{Formal methods for hardware verification: 6th
                 International School on Formal Methods for the Design
                 of Computer, Communication, and Software Systems, SFM
                 2006, Bertinoro, Italy, May 22--27, 2006: advanced
                 lectures}",
  title =        "{Formal methods for hardware verification: 6th
                 International School on Formal Methods for the Design
                 of Computer, Communication, and Software Systems, SFM
                 2006, Bertinoro, Italy, May 22--27, 2006: advanced
                 lectures}",
  volume =       "3965",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "vi + 242",
  year =         "2006",
  DOI =          "https://doi.org/10.1007/11757283",
  ISBN =         "3-540-34304-0",
  ISBN-13 =      "978-3-540-34304-2",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  LCCN =         "QA76.9.F67 I586 2006",
  bibdate =      "Wed Nov 26 22:41:02 MST 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       ser-LNCS,
  URL =          "http://www.loc.gov/catdir/enhancements/fy0661/2006925529-d.html;
                 http://www.loc.gov/catdir/toc/fy0705/2006925529.html",
  acknowledgement = ack-nhfb,
  subject =      "formal methods (computer science); congresses;
                 integrated circuits; verification",
}

@Proceedings{Dimopoulos:2006:IIC,
  editor =       "Nikitas J. Dimopoulos and others",
  booktitle =    "{IEEE 17th International Conference on
                 Application-Specific Systems, Architectures, and
                 Processors: Steamboat Springs, Colorado, USA: September
                 11--13, 2006 [ASAP 2006]}",
  title =        "{IEEE 17th International Conference on
                 Application-Specific Systems, Architectures, and
                 Processors: Steamboat Springs, Colorado, USA: September
                 11--13, 2006 [ASAP 2006]}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiv + 369",
  year =         "2006",
  ISBN =         "0-7695-2682-9",
  ISBN-13 =      "978-0-7695-2682-9",
  ISSN =         "1063-6862",
  LCCN =         "TK7874.6 .I57 2006",
  bibdate =      "Mon Mar 19 10:57:59 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "IEEE Computer Society Order Number P2682.",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=4019472",
  acknowledgement = ack-nhfb,
  meetingname =  "IEEE International Conference on Application-Specific
                 Systems, Architectures, and Processors (17th: 2006:
                 Steamboat Springs, Colorado, USA)",
  remark =       "IEEE Computer Society Order Number P2682.",
  subject =      "Array processors; Congresses; Signal processing;
                 Digital techniques; Application specific integrated
                 circuits",
}

@Proceedings{Haddad:2006:ACP,
  editor =       "Hisham M. Haddad",
  booktitle =    "{Applied computing 2006: proceedings of the 2006 ACM
                 Symposium on Applied Computing, Dijon, France, April
                 23--27, 2006}",
  title =        "{Applied computing 2006: proceedings of the 2006 ACM
                 Symposium on Applied Computing, Dijon, France, April
                 23--27, 2006}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xliv + 1--938 + 939--1929 (2 volumes)",
  year =         "2006",
  ISBN =         "1-59593-108-2",
  ISBN-13 =      "978-1-59593-108-5",
  LCCN =         "QA76.76.A65 S95 2006",
  bibdate =      "Sat Feb 26 18:22:17 MST 2011",
  bibsource =    "catalog.princeton.edu:7090/voyager;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://portal.acm.org/toc.cfm?id=1141277",
  acknowledgement = ack-nhfb,
  remark =       "Hosted by Bourgogne University, Dijon, France.",
  subject =      "Application software; Congresses; Electronic data
                 processing",
}

@Proceedings{Hess:2006:ANT,
  editor =       "Florian Hess and Sebastian Pauli and Michael Pohst",
  booktitle =    "Algorithmic number theory: {7th international
                 symposium, ANTS-VII, Berlin, Germany, July 23-28, 2006:
                 proceedings}",
  title =        "Algorithmic number theory: {7th international
                 symposium, ANTS-VII, Berlin, Germany, July 23-28, 2006:
                 proceedings}",
  volume =       "4076",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 598",
  year =         "2006",
  DOI =          "https://doi.org/10.1007/11792086",
  ISBN =         "3-540-36075-1 (paperback)",
  ISBN-13 =      "978-3-540-36075-9 (paperback)",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  LCCN =         "QA241 .A43 2006",
  bibdate =      "Mon May 31 12:35:41 MDT 2021",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-LNCS,
  URL =          "http://link.springer.com/10.1007/11792086;
                 http://springerlink.metapress.com/openurl.asp?genre=issue%26issn=0302-9743%26volume=4076",
  acknowledgement = ack-nhfb,
  meetingname =  "Algorithmic Number Theory Symposium (7th : 2006).
                 Auteur.",
  subject =      "Number theory; Congresses; g{\'y}eom{\'y}etrie
                 alg{\'y}ebrique; courbe elliptique; algorithmique;
                 th{\'y}eorie nombre; Th{\'y}eorie des nombres;
                 Congr{\'y}es; Number theory.; Nombres, Th{\'y}eorie
                 des; Congr{\'y}es.; Th{\'y}eorie des nombres.; nombres
                 (math{\'y}ematiques); th{\'y}eorie; congr{\'y}es.;
                 algorithmique.; th{\'y}eorie.",
  tableofcontents = "Invited Talks \\
                 Computing Pro-P Galois Groups \\
                 The Elliptic Curve Database for Conductors to 130000
                 \\
                 On the Computation of the Coefficients of a Modular
                 Form \\
                 Cohen--Lenstra Heuristics of Quadratic Number Fields
                 \\
                 Algebraic Number Theory \\
                 An Algorithm for Computing $p$-Class Groups of Abelian
                 Number Fields \\
                 Computation of Locally Free Class Groups \\
                 Numerical Results on Class Groups of Imaginary
                 Quadratic Fields \\
                 Cyclic Polynomials Arising from Kummer Theory of Norm
                 Algebraic Tori \\
                 The Totally Real Primitive Number Fields of
                 Discriminant at Most 109 \\
                 A Modular Method for Computing the Splitting Field of a
                 Polynomial \\
                 Analytic and Elementary Number Theory \\
                 On the Density of Sums of Three Cubes \\
                 The Mertens Conjecture Revisited \\
                 Fast Bounds on the Distribution of Smooth Numbers \\
                 Use of Extended Euclidean Algorithm in Solving a System
                 of Linear Diophantine Equations with Bounded Variables
                 \\
                 The Pseudosquares Prime Sieve \\
                 Doubly-Focused Enumeration of Pseudosquares and
                 Pseudocubes \\
                 Lattices \\
                 Practical Lattice Basis Sampling Reduction \\
                 LLL on the Average \\
                 On the Randomness of Bits Generated by Sufficiently
                 Smooth Functions \\
                 Curves and Varieties over Fields of Characteristic Zero
                 \\
                 Computing a Lower Bound for the Canonical Height on
                 Elliptic Curves over $\mathbb{Q}$ \\
                 Points of Low Height on Elliptic Curves and Surfaces I:
                 Elliptic Surfaces over with Small d \\
                 Shimura Curves for Level-3 Subgroups of the (2,3,7)
                 Triangle Group, and Some Other Examples \\
                 The Asymptotics of Points of Bounded Height on Diagonal
                 Cubic and Quartic Threefolds \\
                 Testing Equivalence of Ternary Cubics \\
                 Classification of Genus 3 Curves in Special Strata of
                 the Moduli Space \\
                 Heegner Point Computations Via Numerical $p$-Adic
                 Integration \\
                 Symmetric Powers of Elliptic Curve $L$-Functions \\
                 Determined Sequences, Continued Fractions, and
                 Hyperelliptic Curves \\
                 Computing CM Points on Shimura Curves Arising from
                 Cocompact Arithmetic Triangle Groups \\
                 Arithmetic of Generalized Jacobians \\
                 Hidden Pairings and Trapdoor DDH Groups \\
                 Constructing Pairing-Friendly Elliptic Curves with
                 Embedding Degree 10 \\
                 Fast Bilinear Maps from the Tate--Lichtenbaum Pairing
                 on Hyperelliptic Curves \\
                 High Security Pairing-Based Cryptography Revisited \\
                 Efficiently Computable Endomorphisms for Hyperelliptic
                 Curves \\
                 Construction of Rational Points on Elliptic Curves over
                 Finite Fields \\
                 20 Years of ECM \\
                 Discrete Logarithms \\
                 An Index Calculus Algorithm for Plane Curves of Small
                 Degree \\
                 Signature Calculus and Discrete Logarithm Problems \\
                 Spectral Analysis of Pollard Rho Collisions \\
                 Hard Instances of the Constrained Discrete Logarithm
                 Problem",
}

@Proceedings{IEEE:2006:ICV,
  editor =       "{IEEE}",
  booktitle =    "{19th International Conference on VLSI Design: held
                 jointly with the 5th International Conference on
                 Embedded Systems Design: proceedings: 3--7 January,
                 2005 [2006], Hyderabad, India}",
  title =        "{19th International Conference on VLSI Design: held
                 jointly with the 5th International Conference on
                 Embedded Systems Design: proceedings: 3--7 January,
                 2005 [2006], Hyderabad, India}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xli + 837",
  year =         "2006",
  ISBN =         "0-7695-2502-4 (paperback)",
  ISBN-13 =      "978-0-7695-2502-0 (paperback)",
  LCCN =         "TK7874 .I4728 2006",
  bibdate =      "Mon Mar 19 11:04:16 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  meetingname =  "International Conference on VLSI Design (19th: 2006:
                 Hyderabad, India)",
  remark =       "Sister Conference IEEE/ACM Design Automation
                 Conference. IEEE Computer Society Order Number P2502.",
  subject =      "Integrated circuits; Very large scale integration;
                 Design and construction; Congresses; Signal processing;
                 Digital techniques; Circuits",
}

@Proceedings{IEEE:2006:PIW,
  editor =       "{IEEE}",
  booktitle =    "{Proceedings of the 2006 IEEE Workshop on Design and
                 Diagnostics of Electronic Circuits and Systems: April
                 18--21, 2006, Prague, Czech Republic}",
  title =        "{Proceedings of the 2006 IEEE Workshop on Design and
                 Diagnostics of Electronic Circuits and Systems: April
                 18--21, 2006, Prague, Czech Republic}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "x + 291",
  year =         "2006",
  ISBN =         "1-4244-0184-4 (softbound)",
  ISBN-13 =      "978-1-4244-0184-0 (softbound)",
  LCCN =         "TK7874 .I32745 2005",
  bibdate =      "Mon Mar 19 11:08:48 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "IEEE catalog number: 06EX1307",
  acknowledgement = ack-nhfb,
  meetingname =  "IEEE Workshop on Design and Diagnostics of Electronic
                 Circuits and Systems (9th: 2006: Prague, Czech
                 Republic)",
  subject =      "Integrated circuits; Testing; Congresses; Design",
}

@Proceedings{Menezes:2006:PAS,
  editor =       "Ronaldo Menezes",
  booktitle =    "{Proceedings of the 44th annual Southeast Regional
                 Conference 2006: Melbourne, Florida, March 10--12,
                 2006}",
  title =        "{Proceedings of the 44th annual Southeast Regional
                 Conference 2006: Melbourne, Florida, March 10--12,
                 2006}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "823",
  year =         "2006",
  ISBN =         "1-59593-315-8 (print)",
  ISBN-13 =      "978-1-59593-315-7 (print)",
  LCCN =         "QA75.5 A184 2006 E",
  bibdate =      "Sat Oct 9 15:04:24 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  subject =      "Computer-assisted instruction; Congresses; Database
                 management; Electronic data processing",
}

@Proceedings{Mohanty:2006:IIC,
  editor =       "Saraju P. Mohanty and Anirudha Sahoo",
  booktitle =    "{ICIT 2006: 9th International Conference on
                 Information Technology: proceedings: 18-21 December,
                 2006, Bhubaneswar, India}",
  title =        "{ICIT 2006: 9th International Conference on
                 Information Technology: proceedings: 18-21 December,
                 2006, Bhubaneswar, India}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xviii + 308",
  year =         "2006",
  ISBN =         "0-7695-2635-7",
  ISBN-13 =      "978-0-7695-2635-5",
  LCCN =         "QA76.575 .I25 2006",
  bibdate =      "Thu Aug 7 18:14:32 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  meetingname =  "International Conference on Information Technology
                 (9th : 2006 : Bhubaneswar, India)",
  remark =       "IEEE Computer Society Order Number P2635.",
  subject =      "Multimedia systems; Congresses; Information
                 technology; Computer networks; Coding theory",
}

@Proceedings{Pocek:2006:FAI,
  editor =       "Kenneth L. Pocek and Duncan A. Buell",
  booktitle =    "{FCCM 2006: 14th Annual IEEE Symposium on
                 Field-Programmable Custom Computing Machines:
                 proceedings: 24--26 April, 2006, Napa, California}",
  title =        "{FCCM 2006: 14th Annual IEEE Symposium on
                 Field-Programmable Custom Computing Machines:
                 proceedings: 24--26 April, 2006, Napa, California}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xi + 355",
  year =         "2006",
  DOI =          "https://doi.org/10.1109/FCCM.2006.2",
  ISBN =         "0-7695-2661-6",
  ISBN-13 =      "978-0-7695-2661-4",
  LCCN =         "TK7895.G36 .I36 2006",
  bibdate =      "Sat Oct 9 14:57:20 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=4020883",
  acknowledgement = ack-nhfb,
  remark =       "IEEE Computer Society Order Number P2661.",
  subject =      "Field programmable gate arrays; Congresses; Computer
                 engineering",
}

@Proceedings{Yi:2006:SAI,
  editor =       "Kwangkeun Yi",
  booktitle =    "{Static Analysis: 13th International Symposium, SAS
                 2006, Seoul, Korea, August 29--31, 2006. Proceedings}",
  title =        "{Static Analysis: 13th International Symposium, SAS
                 2006, Seoul, Korea, August 29--31, 2006. Proceedings}",
  volume =       "4134",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "317 (est.)",
  year =         "2006",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/11823230",
  ISBN =         "3-540-37756-5 (print), 3-540-37758-1 (e-book)",
  ISBN-13 =      "978-3-540-37756-6 (print), 978-3-540-37758-0
                 (e-book)",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  LCCN =         "????",
  bibdate =      "Wed Dec 19 15:20:21 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs.bib",
  series =       ser-LNCS,
  URL =          "http://www.springerlink.com/content/978-3-540-37758-0",
  acknowledgement = ack-nhfb,
}

@Proceedings{ACM:2007:SPA,
  editor =       "{ACM}",
  booktitle =    "{STOC '07: proceedings of the 39th Annual ACM
                 Symposium on Theory of Computing, San Diego,
                 California, USA, June 11--13, 2007}",
  title =        "{STOC '07: proceedings of the 39th Annual ACM
                 Symposium on Theory of Computing, San Diego,
                 California, USA, June 11--13, 2007}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xv + 718",
  year =         "2007",
  ISBN =         "1-59593-631-9",
  ISBN-13 =      "978-1-59593-631-8",
  LCCN =         "????",
  bibdate =      "Fri Jun 20 18:35:01 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.bibsys.no:2100/BIBSYS",
  acknowledgement = ack-nhfb,
}

@Proceedings{Alefeld:2007:SCC,
  editor =       "G{\"o}tz Alefeld and Mitsuhiro T. Nakao and Siegfried
                 M. Rump",
  booktitle =    "Scientific computing, computer arithmetic, and
                 validated numerics: ({SCAN 2004}) [Fukuoka, Japan,
                 October 4--8, 2004]",
  title =        "Scientific computing, computer arithmetic, and
                 validated numerics: ({SCAN} 2004) [Fukuoka, Japan,
                 October 4--8, 2004]",
  volume =       "199(2)",
  publisher =    pub-ELSEVIER,
  address =      pub-ELSEVIER:adr,
  pages =        "194--453",
  day =          "15",
  month =        feb,
  year =         "2007",
  CODEN =        "JCAMDI",
  ISSN =         "0771-050X; 0377-0427",
  LCCN =         "????",
  bibdate =      "Thu Dec 28 20:59:33 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "Journal of computational and applied mathematics",
  acknowledgement = ack-nhfb,
}

@Proceedings{Becker:2007:EVT,
  editor =       "J{\"u}rgen Becker",
  booktitle =    "{Emerging VLSI technologies and architectures:
                 proceedings; IEEE Computer Society Annual Symposium on
                 VLSI, ISVLSI 2007; Porto Alegre, Brazil, 9-11 May
                 2007}",
  title =        "{Emerging VLSI technologies and architectures:
                 proceedings; IEEE Computer Society Annual Symposium on
                 VLSI, ISVLSI 2007; Porto Alegre, Brazil, 9-11 May
                 2007}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xv + 251",
  year =         "2007",
  ISBN =         "0-7695-2896-1",
  ISBN-13 =      "978-0-7695-2896-0",
  LCCN =         "????",
  bibdate =      "Thu Aug 7 18:55:20 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
}

@Proceedings{Bertels:2007:PIC,
  editor =       "Koen Bertels and Walid Najjar and Arjan van Genderen
                 and Stamatis Vassiliadis",
  booktitle =    "{Proceedings of the International Conference on Field
                 Programmable Logic and Applications (FPL 2007),
                 Amsterdam, The Netherlands, August 27--29, 2007}",
  title =        "{Proceedings of the International Conference on Field
                 Programmable Logic and Applications (FPL 2007),
                 Amsterdam, The Netherlands, August 27--29, 2007}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2007",
  ISBN =         "1-4244-1060-6",
  ISBN-13 =      "978-1-4244-1060-6",
  LCCN =         "TK7895.G36 2007",
  bibdate =      "Thu Mar 24 21:23:04 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog number 07EX1708C.",
  acknowledgement = ack-nhfb,
}

@Proceedings{Brown:2007:PIS,
  editor =       "C. W. Brown",
  booktitle =    "{Proceedings of the 2007 International Symposium on
                 Symbolic and Algebraic Computation, July 29--August 1,
                 2007, University of Waterloo, Waterloo, Ontario,
                 Canada}",
  title =        "{Proceedings of the 2007 International Symposium on
                 Symbolic and Algebraic Computation, July 29--August 1,
                 2007, University of Waterloo, Waterloo, Ontario,
                 Canada}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "????",
  year =         "2007",
  ISBN =         "1-59593-743-9 (print), 1-59593-742-0 (CD-ROM)",
  ISBN-13 =      "978-1-59593-743-8 (print), 978-1-59593-742-1
                 (CD-ROM)",
  LCCN =         "QA76.5 S98 2007",
  bibdate =      "Fri Jun 20 08:53:37 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/axiom.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
  note =         "ACM order number 505070.",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:2007:ACP,
  editor =       "{IEEE}",
  booktitle =    "{ASAP 07: conference proceedings: IEEE 18th
                 International Conference on Application-Specific
                 Systems, Architectures, and Processors: Montr{\'e}al,
                 Canada: July 8--11, 2007}",
  title =        "{ASAP 07: conference proceedings: IEEE 18th
                 International Conference on Application-Specific
                 Systems, Architectures, and Processors: Montr{\'e}al,
                 Canada: July 8--11, 2007}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2007",
  ISBN =         "1-4244-1027-4",
  ISBN-13 =      "978-1-4244-1027-9",
  LCCN =         "TK7874.6 .I57a 2007",
  bibdate =      "Sun Feb 20 17:46:31 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=4429947",
  acknowledgement = ack-nhfb,
  meetingname =  "IEEE International Conference on Application-Specific
                 Systems, Architectures, and Processors (18th : 2007 :
                 Montr{\'e}al, Qu{\'e}bec)",
  subject =      "array processors; congresses; signal processing;
                 digital techniques; application-specific integrated
                 circuits",
}

@Proceedings{IEEE:2007:API,
  editor =       "{IEEE}",
  booktitle =    "{ADCOM '07: Proceedings of the 15th International
                 Conference on Advanced Computing and Communications}",
  title =        "{ADCOM '07: Proceedings of the 15th International
                 Conference on Advanced Computing and Communications}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2007",
  ISBN =         "0-7695-3059-1",
  ISBN-13 =      "978-0-7695-3059-8",
  LCCN =         "????",
  bibdate =      "Thu Aug 7 18:34:32 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:2007:ICC,
  editor =       "{IEEE}",
  booktitle =    "{25th International Conference on Computer Design,
                 2007 (ICCD 2007), 7--10 October 2007, Resort at Squaw
                 Creek, Lake Tahoe, California}",
  title =        "{25th International Conference on Computer Design,
                 2007 (ICCD 2007), 7--10 October 2007, Resort at Squaw
                 Creek, Lake Tahoe, California}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2007",
  ISBN =         "1-4244-1258-7",
  ISBN-13 =      "978-1-4244-1258-7",
  LCCN =         "TK7888.4 .I35 2007eb",
  bibdate =      "Sat Dec 4 11:01:31 MST 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=4591423",
  acknowledgement = ack-nhfb,
  subject =      "Microcomputers; Design and construction; Congresses;
                 Electronic digital computers; Circuits; Integrated
                 circuits; Very large scale integration; Computer
                 engineering",
}

@Proceedings{IEEE:2007:ICI,
  editor =       "{IEEE}",
  booktitle =    "{International Symposium on Integrated Circuits, 2007.
                 ISIC '07. 26--28 Sept. 2007}",
  title =        "{International Symposium on Integrated Circuits, 2007.
                 ISIC '07. 26--28 Sept. 2007}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "207",
  year =         "2007",
  ISBN =         "1-4244-0797-4",
  ISBN-13 =      "978-1-4244-0797-2",
  LCCN =         "TK7874 2007",
  bibdate =      "Sun Feb 20 11:23:35 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=4441779",
  acknowledgement = ack-nhfb,
  meetingname =  "International Symposium on Integrated Circuits
                 (2007)",
  subject =      "integrated circuits; congresses; very large scale
                 integration; microprocessors; radio frequency
                 identification systems; computer-aided design",
}

@Proceedings{IEEE:2007:ICV,
  editor =       "{IEEE}",
  booktitle =    "{20th International Conference on VLSI Design:
                 technology challenges in the nanoelectronics era: held
                 jointly with 6th International Conference on Embedded
                 Systems: proceedings: 6--10 January, 2007, Bangalore,
                 India}",
  title =        "{20th International Conference on VLSI Design:
                 technology challenges in the nanoelectronics era: held
                 jointly with 6th International Conference on Embedded
                 Systems: proceedings: 6--10 January, 2007, Bangalore,
                 India}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xxxviii + 951",
  year =         "2007",
  ISBN =         "1-4244-3079-8",
  ISBN-13 =      "978-1-4244-3079-6",
  LCCN =         "TK7874 .I4728 2007",
  bibdate =      "Sun Feb 20 11:26:54 MST 2011",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE Computer Society Order Number P2762.",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=4091978",
  acknowledgement = ack-nhfb,
  meetingname =  "International Conference on VLSI Design (20e : 2007 :
                 Bangalore, Inde)",
  subject =      "circuits int{\'e}gr{\'e}s {\`a} tr{\`e}s grande
                 {\'e}chelle; conception et construction; congr{\`e}s;
                 traitement du signal; techniques num{\'e}riques;
                 ordinateurs; circuits",
}

@Proceedings{IEEE:2007:IPI,
  editor =       "{IEEE}",
  booktitle =    "{ISMVL'07: Proceedings of the 37th International
                 Symposium on Multiple-Valued Logic, May 13--16, 2007}",
  title =        "{ISMVL'07: Proceedings of the 37th International
                 Symposium on Multiple-Valued Logic, May 13--16, 2007}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2007",
  ISBN =         "0-7695-2831-7",
  ISBN-13 =      "978-0-7695-2831-1",
  ISSN =         "0195-623X",
  LCCN =         "????",
  bibdate =      "Thu Aug 07 17:34:51 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Kornerup:2007:PIS,
  editor =       "Peter Kornerup and Jean-Michel Muller",
  booktitle =    "{Proceedings of the 18th IEEE Symposium on Computer
                 Arithmetic, June 25--27, 2007, Montpellier, France}",
  title =        "{Proceedings of the 18th IEEE Symposium on Computer
                 Arithmetic, June 25--27, 2007, Montpellier, France}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 269",
  year =         "2007",
  ISBN =         "0-7695-2854-6",
  ISBN-13 =      "978-0-7695-2854-0",
  ISSN =         "1063-6889",
  LCCN =         "QA76.9.C62",
  bibdate =      "Tue Jun 27 10:26:43 2006",
  bibsource =    "http://www.lirmm.fr/arith18/;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 odin2.bib.sdu.dk:210/Horizon",
  URL =          "http://www.lirmm.fr/arith18/",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}

@Proceedings{Luther:2007:GII,
  editor =       "W. Luther and W. Otten",
  booktitle =    "{12th GAMM--IMACS International Symposium on
                 Scientific Computing, Computer Arithmetic and Validated
                 Numerics: SCAN 2006: conference post-proceedings:
                 September 26--29, 2006, Duisburg, Germany}",
  title =        "{12th GAMM--IMACS International Symposium on
                 Scientific Computing, Computer Arithmetic and Validated
                 Numerics: SCAN 2006: conference post-proceedings:
                 September 26--29, 2006, Duisburg, Germany}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2007",
  ISBN =         "0-7695-2821-X",
  ISBN-13 =      "978-0-7695-2821-2",
  LCCN =         "QA297.I5 2007",
  bibdate =      "Wed Nov 26 18:03:28 MST 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "IEEE Computer Society Order Number E2821.",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=4402381",
  acknowledgement = ack-nhfb,
}

@Proceedings{Morales:2007:TRT,
  editor =       "Linda Morales and Debra Howard",
  booktitle =    "{TAPIA '07: Richard Tapia Celebration of Diversity in
                 Computing Conference: October 14--17, 2007, Orlando,
                 Florida: passion in computing, diversity in innovation:
                 proceedings of the Richard Tapia Celebration of
                 Diversity in Computing Conference 2007 }",
  title =        "{TAPIA '07: Richard Tapia Celebration of Diversity in
                 Computing Conference: October 14--17, 2007, Orlando,
                 Florida: passion in computing, diversity in innovation:
                 proceedings of the Richard Tapia Celebration of
                 Diversity in Computing Conference 2007 }",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "????",
  year =         "2007",
  ISBN =         "1-59593-866-4",
  ISBN-13 =      "978-1-59593-866-4",
  LCCN =         "????",
  bibdate =      "Fri Aug 08 08:53:53 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Pocek:2007:PAI,
  editor =       "Kenneth L. Pocek and Duncan A. Buell",
  booktitle =    "{Proceedings, 15th Annual IEEE Symposium on
                 Field-Programmable Custom Computing Machines: FCCM
                 2007: 23--25 April, 2007, Napa, California}",
  title =        "{Proceedings, 15th Annual IEEE Symposium on
                 Field-Programmable Custom Computing Machines: FCCM
                 2007: 23--25 April, 2007, Napa, California}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xi + 358",
  year =         "2007",
  DOI =          "https://doi.org/10.1109/FCCM.2007.65",
  ISBN =         "0-7695-2940-2",
  ISBN-13 =      "978-0-7695-2940-0",
  LCCN =         "TK7895.G36 2007",
  bibdate =      "Sat Oct 9 15:05:33 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE Computer Society order number P2940.",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=4297231",
  acknowledgement = ack-nhfb,
  subject =      "Field programmable gate arrays; Congresses; Computer
                 engineering",
}

@Proceedings{Simos:2007:CMS,
  editor =       "Theodore E. Simos and George Maroulis",
  booktitle =    "{Computation in Modern Science and Engineering:
                 Proceedings of the International Conference on
                 Computational Methods in Science and Engineering 2007
                 (ICCMSE 2007), Corfu, Greece, 25--30 September 2007}",
  title =        "{Computation in Modern Science and Engineering:
                 Proceedings of the International Conference on
                 Computational Methods in Science and Engineering 2007
                 (ICCMSE 2007), Corfu, Greece, 25--30 September 2007}",
  volume =       "2A",
  publisher =    pub-AIP,
  address =      pub-AIP:adr,
  pages =        "xxvi + 730 + 10 (vol. 2A)",
  year =         "2007",
  ISBN =         "0-7354-0476-3 (set), 0-7354-0477-1 (vol. 1),
                 0-7354-0478-X (vol. 2)",
  ISBN-13 =      "978-0-7354-0476-2 (set), 978-0-7354-0477-9 (vol. 1),
                 978-0-7354-0478-6 (vol. 2)",
  LCCN =         "Q183.9 2007",
  bibdate =      "Thu Feb 21 14:15:15 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Two volumes.",
  acknowledgement = ack-nhfb,
}

@Proceedings{ACM:2008:GPA,
  editor =       "{ACM}",
  booktitle =    "{GLSVLSI 2008: Proceedings of the 18th ACM Great Lakes
                 symposium on VLSI, Orlando, Florida, USA, May 4--6,
                 2008}",
  title =        "{GLSVLSI 2008: Proceedings of the 18th ACM Great Lakes
                 symposium on VLSI, Orlando, Florida, USA, May 4--6,
                 2008}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  year =         "2008",
  ISBN =         "1-59593-999-7",
  ISBN-13 =      "978-1-59593-999-9",
  LCCN =         "????",
  bibdate =      "Thu Aug 07 17:43:02 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "ACM Order Number 477088.",
  acknowledgement = ack-nhfb,
}

@Proceedings{ACM:2008:SPA,
  editor =       "{ACM}",
  booktitle =    "{STOC '08: proceedings of the 39th Annual ACM
                 Symposium on Theory of Computing, Victoria, British
                 Columbia, Canada, May 17--20, 2008}",
  title =        "{STOC '08: proceedings of the 39th Annual ACM
                 Symposium on Theory of Computing, Victoria, British
                 Columbia, Canada, May 17--20, 2008}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xv + 797 (est.)",
  year =         "2008",
  ISBN =         "1-60558-047-3",
  ISBN-13 =      "978-1-60558-047-0",
  LCCN =         "????",
  bibdate =      "Fri Jun 20 18:35:01 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 z3950.bibsys.no:2100/BIBSYS",
  acknowledgement = ack-nhfb,
}

@Proceedings{Hertling:2008:RIR,
  editor =       "Peter Hertling and Christoph M. Hoffmann and Wolfram
                 Luther and Nathalie Revol",
  booktitle =    "{Reliable Implementation of Real Number Algorithms:
                 Theory and Practice: International Seminar Dagstuhl
                 Castle, Germany, January 8--13, 2006 Revised Papers}",
  title =        "{Reliable Implementation of Real Number Algorithms:
                 Theory and Practice: International Seminar Dagstuhl
                 Castle, Germany, January 8--13, 2006 Revised Papers}",
  volume =       "5045",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "xi + 239",
  pages =        "xi + 239",
  year =         "2008",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-540-85521-7",
  ISBN =         "3-540-85520-3 (print), 3-540-85521-1 (e-book)",
  ISBN-13 =      "978-3-540-85520-0 (print), 978-3-540-85521-7
                 (e-book)",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  LCCN =         "????",
  bibdate =      "Wed Dec 19 15:22:53 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs.bib",
  series =       ser-LNCS,
  URL =          "https://link.springer.com/book/10.1007/978-3-540-85521-7",
  acknowledgement = ack-nhfb,
  tableofcontents = "Front Matter \\
                 Ekaterina Auer, Andreas Rauh, Eberhard P. Hofer,
                 Wolfram Luther / Validated Modeling of Mechanical
                 Systems with SmartMOBILE: Improvement of Performance by
                 ValEncIA-IVP / 1--27 \\
                 George F. Corliss, R. Baker Kearfott, Ned Nedialkov,
                 John D. Pryce, Spencer Smith / Interval Subroutine
                 Library Mission / 28--43 \\
                 Eva Dyllong / Convex Polyhedral Enclosures of
                 Interval-Based Hierarchical Object Representations /
                 44--56 \\
                 Ioannis Z. Emiris, Bernard Mourrain, Elias P.
                 Tsigaridas / Real Algebraic Numbers: Complexity
                 Analysis and Experimentation / 57--82 \\
                 Sebastian Kempken, Wolfram Luther / Verified Methods in
                 Stochastic Traffic Modelling / 83--101 \\
                 Branimir Lambov / Interval Arithmetic Using SSE-2 /
                 102--113 \\
                 Vincent Lef{\`e}vre, Damien Stehl{\'e}, Paul Zimmermann
                 / Worst Cases for the Exponential Function in the IEEE
                 754r decimal64 Format / 114--126 \\
                 Dominique Michelucci, Jean Michel Moreau, Sebti Foufou
                 / Robustness and Randomness / 127--148 \\
                 Lance Edward Miller, Edward L. F. Moore, Thomas J.
                 Peters, Alexander Russell / Topological Neighborhoods
                 for Spline Curves: Practice \& Theory / 149--161 \\
                 Vadim Shapiro / Homotopy Conditions for Tolerant
                 Geometric Queries / 162--180 \\
                 Neil F. Stewart, Malika Zidani / Transfinite
                 Interpolation for Well-Definition in Error Analysis in
                 Solid Modelling / 181--192 \\
                 Chee Yap / Theory of Real Computation According to EGC
                 / 193--237 \\
                 Back Matter",
}

@Proceedings{IEEE:2008:ICA,
  editor =       "{IEEE}",
  booktitle =    "{2008 International Conference on Application-Specific
                 Systems, Architectures and Processors: Leuven, Belgium,
                 2--4 July 2008}",
  title =        "{2008 International Conference on Application-Specific
                 Systems, Architectures and Processors: Leuven, Belgium,
                 2--4 July 2008}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiv + 309 + 12",
  year =         "2008",
  ISBN =         "1-4244-1897-6 (paperback), 1-4244-1898-4",
  ISBN-13 =      "978-1-4244-1897-8 (paperback), 978-1-4244-1898-5",
  LCCN =         "????",
  bibdate =      "Mon Feb 10 07:31:38 MST 2020",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  note =         "IEEE catalog number CFP08063-PRT.",
  URL =          "http://www.gbv.de/dms/tib-ub-hannover/631855815.pdf;
                 https://ieeexplore.ieee.org/servlet/opac?punumber=4569858",
  acknowledgement = ack-nhfb,
  remark =       "Kongress auch zitiert als: ASAP 08. Parallel als
                 Online-Ausg. erschienen. ASAP 08.",
  tableofcontents = "ASAP08 Conference proceedings / c1--c1 / doi:
                 10.1109/ASAP.2008.4580199 \\
                 ASAP08 Conference proceedings / c2--c2 / doi:
                 10.1109/ASAP.2008.4580200 \\
                 Frontmatter and table of contents / c1--xiii / doi:
                 10.1109/ASAP.2008.4580202 \\
                 ASAP Organizing and Steering Committees / ix \\
                 ASAP Technical Technical Program Committee / x \\
                 Keynote 1: Security and Opportunities for
                 Application-Specific Processors / Ruby B. Lee / xii \\
                 Keynote 2: Art of of Application-Specific Processor
                 Design: Great Artists use Good Tools / Gert Goossens /
                 xiv \\
                 Session 1: Application-Specific Processor Instruction
                 Sets / 1 \\
                 Copyright notice / i--i / doi:
                 10.1109/ASAP.2008.4580197 \\
                 Copyright notice / ii--ii / doi:
                 10.1109/ASAP.2008.4580198 \\
                 K. Atasu, O. Mencer, W. Luk, C. Ozturan and G. Dundar /
                 Fast custom instruction identification by convex
                 subgraph enumeration / 1--6 / doi:
                 10.1109/ASAP.2008.4580145 \\
                 Y. Hilewitz, C. Lauradoux and R. B. Lee / Bit matrix
                 multiplication in commodity processors / 7--12 / doi:
                 10.1109/ASAP.2008.4580146 \\
                 M. Alle et al. / Synthesis of application accelerators
                 on Runtime Reconfigurable Hardware / 13--18 / doi:
                 10.1109/ASAP.2008.4580147 \\
                 A. Amaricai, M. Vladutiu, M. Udrescu, L. Prodan and O.
                 Boncalo / Floating point multiplication rounding
                 schemes for interval arithmetic / 19--24 / doi:
                 10.1109/ASAP.2008.4580148 \\
                 S. Balasubramanian, H. W. Carter, A. Bogdanov, A. Rupp
                 and Jintai Ding / Fast multivariate signature
                 generation in hardware: The case of rainbow / 25--30 /
                 doi: 10.1109/ASAP.2008.4580149 \\
                 M. Hosseinabady and J. Nunez-Yanez / Fault-tolerant
                 dynamically reconfigurable NoC-based SoC / 31--36 /
                 doi: 10.1109/ASAP.2008.4580150 \\
                 T. Lorunser et al. / Security Processor with Quantum
                 Key Distribution / 37--42 / doi:
                 10.1109/ASAP.2008.4580151 \\
                 P. K. Meher and J. C. Patra / Fully-pipelined efficient
                 architectures for FPGA realization of discrete Hadamard
                 transform / 43--48 / doi: 10.1109/ASAP.2008.4580152 \\
                 R. Rajore, G. Garga, H. S. Jamadagni and S. K. Nandy /
                 Reconfigurable Viterbi decoder on mesh connected
                 multiprocessor architecture / 49--54 / doi:
                 10.1109/ASAP.2008.4580153 \\
                 T. Ramdas, G. K. Egan, D. Abramson and K. K. Baldridge
                 / Run-time thread sorting to expose data-level
                 parallelism / 55--60 / doi: 10.1109/ASAP.2008.4580154
                 \\
                 S. Jovanovic, C. Tanougast and S. Weber / A New
                 High-Performance Scalable Dynamic Interconnection for
                 FPGA-based Reconfigurable Systems / 61--66 / doi:
                 10.1109/ASAP.2008.4580155 \\
                 D. Dickin and L. Shannon / Extending the SIMPPL SoC
                 architectural framework to support application-specific
                 architectures on multi-FPGA platforms / 67--72 / doi:
                 10.1109/ASAP.2008.4580156 \\
                 A. E. Kiasari, S. Hessabi and H. Sarbazi-Azad / PERMAP:
                 A performance-aware mapping for application-specific
                 SoCs / 73--78 / doi: 10.1109/ASAP.2008.4580157 \\
                 A. C. Atici, L. Batina, Junfeng Fan, I. Verbauwhede and
                 S. Berna Ors Yalcin / Low-cost implementations of NTRU
                 for pervasive security / 79--84 / doi:
                 10.1109/ASAP.2008.4580158 \\
                 M. Knezzevic, K. Sakiyama, Y. K. Lee and I. Verbauwhede
                 / On the high-throughput implementation of RIPEMD-160
                 hash algorithm / 85--90 / doi:
                 10.1109/ASAP.2008.4580159 \\
                 Wang Haixin, Bai Guoqiang and Chen Hongyi / Zodiac:
                 System architecture implementation for a
                 high-performance Network Security Processor / 91--96 /
                 doi: 10.1109/ASAP.2008.4580160 \\
                 P. K. Meher / Efficient systolization of cyclic
                 convolution for systolic implementation of sinusoidal
                 transforms / 97--101 / doi: 10.1109/ASAP.2008.4580161
                 \\
                 D. B. Thomas and W. Luk / Resource efficient generators
                 for the floating-point uniform and exponential
                 distributions / 102--107 / doi:
                 10.1109/ASAP.2008.4580162 \\
                 I. L. Dalal, D. Stefan and J. Harwayne-Gidansky / Low
                 discrepancy sequences for Monte Carlo simulations on
                 reconfigurable platforms / 108--113 / doi:
                 10.1109/ASAP.2008.4580163 \\
                 Y. Vanderperren and W. Dehaene / A subsampling pulsed
                 UWB demodulator based on a flexible complex SVD /
                 114--119 / doi: 10.1109/ASAP.2008.4580164 \\
                 J. Divyasree, H. Rajashekar and K. Varghese /
                 Dynamically reconfigurable regular expression matching
                 architecture / 120--125 / doi:
                 10.1109/ASAP.2008.4580165 \\
                 J. Khan, S. Niar, A. Menhaj, Y. Elhillali and J. L.
                 Dekeyser / An MPSoC architecture for the Multiple
                 Target Tracking application in driver assistant system
                 / 126--131 / doi: 10.1109/ASAP.2008.4580166 \\
                 Wangyuan Zhang and Tao Li / Managing multi-core
                 soft-error reliability through utility-driven cross
                 domain optimization / 132--137 / doi:
                 10.1109/ASAP.2008.4580167 \\
                 S. Braganza and M. Leeser / An efficient implementation
                 of a phase unwrapping kernel on reconfigurable hardware
                 / 138--143 / doi: 10.1109/ASAP.2008.4580168 \\
                 H. Flatt, S. Blume, S. Hesselbarth, T. Schunemann and
                 P. Pirsch / A parallel hardware architecture for
                 connected component labeling based on fast label
                 merging / 144--149 / doi: 10.1109/ASAP.2008.4580169 \\
                 Yuki Kobayashi, M. Jayapala, P. Raghavan, F. Catthoor
                 and Masaharu Imai / Operation shuffling over cycle
                 boundaries for low energy L0 clustering / 150--155 /
                 doi: 10.1109/ASAP.2008.4580170 \\
                 V. Kundeti, Yunsi Fei and S. Rajasekaran / An efficient
                 digital circuit for implementing Sequence Alignment
                 algorithm in an extended processor / 156--161 / doi:
                 10.1109/ASAP.2008.4580171 \\
                 B. K. Mohanty and P. K. Meher / Concurrent systolic
                 architecture for high-throughput implementation of
                 3-dimensional discrete wavelet transform / 162--166 /
                 doi: 10.1109/ASAP.2008.4580172 \\
                 S. Mirzaei, A. Irturk, R. Kastner, B. T. Weals and R.
                 E. Cagley / Design space exploration of a cooperative
                 MIMO receiver for reconfigurable architectures /
                 167--172 / doi: 10.1109/ASAP.2008.4580173 \\
                 Mao Nakajima and Minoru Watanabe / Dynamic holographic
                 reconfiguration on a four-context ODRGA / 173--178 /
                 doi: 10.1109/ASAP.2008.4580174 \\
                 F. Pardo, P. Lopez and D. Cabello / FPGA-based hardware
                 accelerator of the heat equation with applications on
                 infrared thermography / 179--184 / doi:
                 10.1109/ASAP.2008.4580175 \\
                 M. Rahmati, M. S. Sadri and M. A. Naeini / FPGA based
                 singular value decomposition for image processing
                 applications / 185--190 / doi:
                 10.1109/ASAP.2008.4580176 \\
                 A. Jacob, J. Buhler and R. D. Chamberlain /
                 Accelerating Nussinov RNA secondary structure
                 prediction with systolic arrays on FPGAs / 191--196 /
                 doi: 10.1109/ASAP.2008.4580177 \\
                 J. Lee, L. Shannon, M. J. Yedlin and G. F. Margrave / A
                 multi-FPGA application-specific architecture for
                 accelerating a floating point Fourier Integral Operator
                 / 197--202 / doi: 10.1109/ASAP.2008.4580178 \\
                 K. F. C. Yiu, Chun Hok Ho, N. Grbric, Yao Lu, Xiaoxiang
                 Shi and W. Luk / Reconfigurable acceleration of
                 microphone array algorithms for speech enhancement /
                 203--208 / doi: 10.1109/ASAP.2008.4580179 \\
                 Yang Sun, Yuming Zhu, M. Goel and J. R. Cavallaro /
                 Configurable and scalable high throughput turbo decoder
                 architecture for multiple 4G wireless standards /
                 209--214 / doi: 10.1109/ASAP.2008.4580180 \\
                 M. B. S. Tavares, S. Kunze, E. Matus and G. P. Fettweis
                 / Architecture and VLSI realization of a high-speed
                 programmable decoder for LDPC convolutional codes /
                 215--220 / doi: 10.1109/ASAP.2008.4580181 \\
                 D. Llorente, K. Karras, T. Wild and A. Herkersdorf /
                 Buffer allocation for advanced packet segmentation in
                 Network Processors / 221--226 / doi:
                 10.1109/ASAP.2008.4580182 \\
                 A. Vazquez and E. Antelo / New insights on Ling adders
                 / 227--232 / doi: 10.1109/ASAP.2008.4580183 \\
                 N. Brisebarre, F. de Dinechin and J. Muller / Integer
                 and floating-point constant multipliers for FPGAs /
                 239--244 / doi: 10.1109/ASAP.2008.4580184 \\
                 N. Brisebarre, S. Chevillard, M. D. Ercegovac, J.
                 Muller and S. Torres / An efficient method for
                 evaluating polynomial and rational function
                 approximations / 233--238 / doi:
                 10.1109/ASAP.2008.4580185 \\
                 A. Garcia, M. Berekovic and T. Vander Aa / Mapping of
                 the AES cryptographic algorithm on a Coarse-Grain
                 reconfigurable array processor / 245--250 / doi:
                 10.1109/ASAP.2008.4580186 \\
                 J. Nimmy et al. / RECONNECT: A NoC for polymorphic
                 ASICs using a low overhead single cycle router /
                 251--256 / doi: 10.1109/ASAP.2008.4580187 \\
                 M. Mbaye, N. Belanger, Y. Savaria and S. Pierre /
                 Loop-oriented metrics for exploring an
                 application-specific architecture design-space /
                 257--262 / doi: 10.1109/ASAP.2008.4580188 \\
                 S. K. Dash and T. Srikanthan / Rapid estimation of
                 instruction cache hit rates using loop profiling /
                 263--268 / doi: 10.1109/ASAP.2008.4580189 \\
                 Xuan Guan and Yunsi Fei / Reducing power consumption of
                 embedded processors through register file partitioning
                 and compiler support / 269--274 / doi:
                 10.1109/ASAP.2008.4580190 \\
                 A. Tumeo, M. Monchiero, G. Palermo, F. Ferrandi and D.
                 Sciuto / Lightweight DMA management mechanisms for
                 multiprocessors on FPGA / 275--280 / doi:
                 10.1109/ASAP.2008.4580191 \\
                 P. de Langen and B. Juurlink / Memory copies in
                 multi-level memory systems / 281--286 / doi:
                 10.1109/ASAP.2008.4580192 \\
                 R. Adrsha, Mythri, S. K. Nandy and R. Narayan /
                 Architecture of a polymorphic ASIC for interoperability
                 across multi-mode H.264 decoders / 287--292 / doi:
                 10.1109/ASAP.2008.4580193 \\
                 R. R. Osorio and J. D. Bruguera / An FPGA architecture
                 for CABAC decoding in manycore systems / 293--298 /
                 doi: 10.1109/ASAP.2008.4580194 \\
                 A. Guntoro and M. Glesner / Novel approach on
                 lifting-based DWT and IDWT processor with multi-context
                 configuration to support different wavelet filters /
                 299--304 / doi: 10.1109/ASAP.2008.4580195 \\
                 B. K. Mohanty and P. K. Meher / Throughput-scalable
                 hybrid-pipeline architecture for multilevel lifting 2-D
                 DWT of JPEG 2000 coder / 305--309 / doi:
                 10.1109/ASAP.2008.4580196 \\
                 Author index / 310--321 / doi:
                 10.1109/ASAP.2008.4580201",
}

@Proceedings{Matthews:2008:CRF,
  editor =       "Michael B. Matthews",
  booktitle =    "{Conference Record of the Forty-first Asilomar
                 Conference on Signals, Systems and Computers: November
                 4--7, 2007, Pacific Grove, California. ACSSC 2007}",
  title =        "{Conference Record of the Forty-first Asilomar
                 Conference on Signals, Systems and Computers: November
                 4--7, 2007, Pacific Grove, California. ACSSC 2007}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xxix + 421",
  year =         "2008",
  DOI =          "https://doi.org/10.1109/ACSSC.2007.4487144",
  ISBN =         "1-4244-2109-8",
  ISBN-13 =      "978-1-4244-2109-1",
  ISSN =         "1058-6393",
  LCCN =         "TK7801 .A83 2007eb",
  bibdate =      "Sat Dec 4 10:31:40 MST 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.ieeexplore.ieee.org/xpl/RecentCon.jsp?punumber=4483515",
  acknowledgement = ack-nhfb,
  subject =      "Electronics; Congresses; Signal processing; Computers;
                 Automatic control; Electrical engineering; System
                 theory",
}

@Book{Patterson:2008:COD,
  author =       "David A. Patterson and John L. Hennessy",
  booktitle =    "Computer Organization and Design: the Hardware\slash
                 Software Interface",
  title =        "Computer Organization and Design: the Hardware\slash
                 Software Interface",
  publisher =    pub-ELSEVIER-MORGAN-KAUFMANN,
  address =      pub-ELSEVIER-MORGAN-KAUFMANN:adr,
  edition =      "Fourth",
  bookpages =    "xxv + 703 + A-77 + B-83 + I-26",
  pages =        "xxv + 703 + A-77 + B-83 + I-26",
  year =         "2008",
  ISBN =         "0-12-374493-8",
  ISBN-13 =      "978-0-12-374493-7",
  LCCN =         "QA76.9.C643",
  bibdate =      "Mon Nov 17 13:31:21 MST 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 z3950.gbv.de:20011/gvk",
  acknowledgement = ack-nhfb,
  subject =      "computer organization; computer engineering; computer
                 interfaces",
  tableofcontents = "1: Computer Abstractions and Technology \\
                 2: Instructions: Language of the Computer \\
                 3: Arithmetic for Computers \\
                 4: The Processor \\
                 5: Large and Fast: Exploiting Memory Hierarchy \\
                 6: Storage and Other I /O Topics \\
                 7: Multicores, Multiprocessors, and Clusters \\
                 Appendix A: Graphics and Computing GPUs \\
                 Appendix B: Assemblers, Linkers, and the SPIM Simulator
                 \\
                 Appendix C: The Basics of Logic Design \\
                 Appendix D: Mapping Control to Hardware \\
                 Appendix E: A Survey of RISC Architectures for Desktop,
                 Server, and Embedded Computers",
}

@Proceedings{Woods:2008:RCA,
  editor =       "Roger Woods and Katherine Compton and Christos
                 Bouganis and Pedro C. Diniz",
  booktitle =    "{Reconfigurable Computing: Architectures, Tools and
                 Applications: 4th International Workshop, ARC 2008,
                 London, UK, March 26--28, 2008. Proceedings}",
  title =        "{Reconfigurable Computing: Architectures, Tools and
                 Applications: 4th International Workshop, ARC 2008,
                 London, UK, March 26--28, 2008. Proceedings}",
  volume =       "4943",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "xiv + 344",
  pages =        "xiv + 344",
  year =         "2008",
  DOI =          "https://doi.org/10.1007/978-3-540-78610-85",
  ISBN =         "3-540-78610-4",
  ISBN-13 =      "978-3-540-78610-8",
  ISSN =         "1611-3349",
  bibdate =      "Tue Oct 28 07:04:09 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
  tableofcontents = "Intro \\
                 Title Page \\
                 Preface \\
                 Organization \\
                 Table of Contents \\
                 Synthesizing FPGA Circuits from Parallel Programs \\
                 From Silicon to Science: The Long Road to Production
                 Reconfigurable Supercomputing \\
                 The von Neumann Syndrome and the CS Education Dilemma
                 \\
                 Optimal Unroll Factor for Reconfigurable Architectures
                 \\
                 Introduction \\
                 Background and Related Work \\
                 Problem Statement \\
                 Proposed Methodology \\
                 Experimental Results \\
                 Conclusion and Future Work \\
                 Programming Reconfigurable Decoupled Application
                 Control Accelerator for Mobile Systems \\
                 Introduction \\
                 Architecture Reconfigurable Decoupled Application
                 Control Architecture \\
                 Embedded Shared Memory Programming Model \\
                 Dynamic Aspects \\
                 Method Wrappers \\
                 Dynamic Execution \\
                 Memory Access Scheduling \\
                 Synthesis for Architecture \\
                 Related Work \\
                 Results \\
                 Mapping of the Deblocking Kernel on the DSPFabric \\
                 Conclusion \\
                 DNA Physical Mapping on a Reconfigurable Platform \\
                 Introduction \\
                 Related Work \\
                 DNA Physical Mapping \\
                 Consecutive Ones Problem and Algorithm \\
                 Hardware/Software Solution \\
                 Comparing Clones \\
                 Constructing Column Sets \\
                 Hybrid Implementations \\
                 Experimental Results \\
                 Conclusions and Future Research \\
                 Hardware BLAST Algorithms with Multi-seeds Detection
                 and Parallel Extension \\
                 Introduction \\
                 BLAST Algorithm Overview \\
                 The Structure of Multi-seeds Detection and Parallel
                 Extension Engine \\
                 Multi-seeds Detecting \\
                 Successive Seeds Merging \\
                 Multi-seeds Extension \\
                 FPGA Implementation and Optimization \\
                 Multi-seeds Detection Array \\
                 Decomposing the Detection Array \\
                 The Algorithm of Merging Successive Seeds \\
                 Multi-channel Parallel Extension Strategy \\
                 Experiments and Performance Comparison \\
                 Conclusion: Highly Space Efficient Counters for Perl
                 Compatible Regular Expressions in FPGAs \\
                 Introduction \\
                 Related Work \\
                 Perl Compatible Regular Expressions Used in Network
                 Intrusion Detection Systems \\
                 Our Proposed 20-Bit SelectRAM Counter \\
                 A PCRE Exactly Block Based on the 20-Bit SelectRAM
                 Counter \\
                 A PCRE AtLeast Block Using the Proposed SelectRAM
                 Counter \\
                 A PCRE Between Block Using the 20-Bit SelectRAM Counter
                 \\
                 Kleene Star and Plus Blocks \\
                 Performance Evaluation and Comparison \\
                 Conclusions \\
                 A Custom Processor for a TDMA Solver in a CFD
                 Application \\
                 Introduction \\
                 CFD \\
                 The Problem High-Level Transformations \\
                 Example of Scheduling \\
                 Memory Requirements \\
                 The FPGA-Based Platform \\
                 Hardware Implementation \\
                 Address Generation \\
                 Cache Memory \\
                 Execution Units \\
                 Results and Conclusions \\
                 A High Throughput FPGA-Based Floating Point Conjugate
                 Gradient Implementation \\
                 Introduction \\
                 Background \\
                 Conjugate Gradient Method \\
                 Algorithm Description \\
                 Implementation \\
                 Overview \\
                 Performance \\
                 Floating Point Unit Operations \\
                 Results \\
                 Resource Utilization \\
                 Software Comparison and Discussion \\
                 Input/Ouput Considerations \\
                 Conclusions",
}

@Proceedings{Abraham:2009:WCN,
  editor =       "Ajith Abraham and Andre Carvalho and Francisco Herrera
                 and Vijayalakshmi Pai and Andr{\'e} Coelho and Ronaldo
                 Menezes",
  booktitle =    "{2009 World Congress on Nature and Biologically
                 Inspired Computing: 9--11 December 2009, Coimbatore,
                 India: proceedings [NaBIC 2009]}-",
  title =        "{2009 World Congress on Nature and Biologically
                 Inspired Computing: 9--11 December 2009, Coimbatore,
                 India: proceedings [NaBIC 2009]}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2009",
  ISBN =         "1-4244-5612-6, 1-4244-5053-5",
  ISBN-13 =      "978-1-4244-5612-3, 978-1-4244-5053-4",
  LCCN =         "QA76.887 2009",
  bibdate =      "Thu Feb 17 13:33:02 MST 2011",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE Catalog Number CFP0995H",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=5377996",
  acknowledgement = ack-nhfb,
  meetingname =  "World Congress on Nature and Biologically Inspired
                 Computing (2009: Coimbatore, India)",
  subject =      "biologically-inspired computing; congresses; natural
                 computation",
}

@Proceedings{Bouajjani:2009:CAV,
  editor =       "Ahmed Bouajjani and Oded Maler",
  booktitle =    "Computer Aided Verification: {21st International
                 Conference, CAV 2009, Grenoble, France, June 26--July
                 2, 2009, Proceedings}",
  title =        "Computer Aided Verification: {21st International
                 Conference, CAV 2009, Grenoble, France, June 26--July
                 2, 2009, Proceedings}",
  volume =       "5643",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xv + 722",
  year =         "2009",
  DOI =          "https://doi.org/10.1007/978-3-642-02658-4",
  ISBN =         "3-642-02657-5 (paperback), 3-642-02658-3",
  ISBN-13 =      "978-3-642-02657-7 (paperback), 978-3-642-02658-4",
  LCCN =         "QA76.76.V47 .C38 2009",
  bibdate =      "Fri Dec 8 13:33:33 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
}

@Proceedings{Bruguera:2009:PIS,
  editor =       "Javier D. Bruguera and Marius Cornea and Debjit
                 DasSarma and John Harrison",
  booktitle =    "{Proceedings of the 19th IEEE Symposium on Computer
                 Arithmetic, June 8--10, 2009, Portland, Oregon, USA}",
  title =        "{Proceedings of the 19th IEEE Symposium on Computer
                 Arithmetic, June 8--10, 2009, Portland, Oregon, USA}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xi + 235",
  year =         "2009",
  ISBN =         "0-7695-3670-0, 1-4244-4329-6",
  ISBN-13 =      "978-0-7695-3670-5, 978-1-4244-4329-1",
  ISSN =         "1063-6889",
  LCCN =         "QA76.6 .S887 2009",
  bibdate =      "Fri Jun 12 12:24:37 2009",
  bibsource =    "http://www.ac.usc.es/arith19/;
                 https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  URL =          "http://www.ac.usc.es/arith19/",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-19",
  tableofcontents = "Keynote Talk \\
                 Anton: A Specialized Machine for Millisecond-Scale
                 Molecular Dynamics Simulations of Proteins / David E.
                 Shaw / 3 \\
                 Session 1: Algorithms and Number Systems \\
                 Efficient Data Structure and Algorithms for Sparse
                 Integers, Sets and Predicates / Jean E. Vuillemin / 7
                 \\
                 A Dual-Purpose Real/Complex Logarithmic Number System
                 ALU / Mark G. Arnold and Sylvain Collange / 15 \\
                 Selected RNS Bases for Modular Multiplication / J. C.
                 Bajard, M. Kaihara, and T. Plantard / 25 \\
                 Invited Talk \\
                 A Historical Perspective on Computer Arithmetic /
                 Stanley Mazor / 35 \\
                 Session 2: Arithmetic Hardware \\
                 Higher Radix Squaring Operations Employing
                 Left-to-Right Dual Recoding / David W. Matula / 39 \\
                 Advanced Clockgating Schemes for
                 Fused-Multiply-Add-Type Floating-Point Units / Jochen
                 Preiss, Maarten Boersma, and Silvia Melitta Mueller /
                 48 \\
                 Unified Approach to the Design of Modulo-$(2^n \pm 1)$
                 Adders Based on Signed-LSB Representation of Residues /
                 Ghassem Jaberipur and Behrooz Parhami / 57 \\
                 Session 3: Finite Fields and Cryptography \\
                 Subquadratic Space Complexity Multiplier for a Class of
                 Binary Fields Using Toeplitz Matrix Approach / M. A.
                 Hasan and C. Negre / 67 \\
                 Hybrid Binary-Ternary Joint Form and Its Application in
                 Elliptic Curve / Cryptography / Jithra Adikari, Vassil
                 Dimitrov, and Laurent Imbert / 76 \\
                 Polynomial Multiplication over Finite Fields Using
                 Field Extensions and Interpolation / Murat Cenk, Cetin
                 Kaya Koc, and Ferruh Ozbudak / 84 \\
                 Session 4: Mathematical Software \\
                 A New Binary Floating-Point Division Algorithm and Its
                 Software Implementation on the ST231 Processor /
                 Claude-Pierre Jeannerod, Herve Knochel, Christophe
                 Monat, Guillaume Revy, and Gilles Villard / 95 \\
                 Fast and Accurate Bessel Function Computation / John
                 Harrison / 104 \\
                 Implementation Specific Verification of Divide and
                 Square Root Instructions / Elena Guralnik, Ariel J.
                 Birnbaum, Anatoly Koyfinan, and Avi Kaplan / 114 \\
                 Session 5: Decimal Hardware \\
                 A Decimal Floating-Point Adder with Decoded Operands
                 and a Decimal Leading-Zero Anticipator / Liang-Kai Wang
                 and Michael J. Schulte / 125 \\
                 A High-Performance Significand BCD Adder with IEEE
                 754-2008 Decimal Rounding / Alvaro Vazquez and Elisardo
                 Antelo / 135 \\
                 Fully Redundant Decimal Arithmetic / Saeid Gorgin and
                 Ghassem Jaberipur / 145 \\
                 Session 6: Floating-Point Techniques \\
                 On the Computation of Correctly-Rounded Sums / P.
                 Kornerup, V. Lefevre, N. Louvet, and Jean-Michel Muller
                 / 155 \\
                 Multi-operand Floating-Point Addition / Alexandre F.
                 Tenca / 161 \\
                 Certified and Fast Computation of Supremum Norms of
                 Approximation Errors / Sylvain Chevillard, Mioara
                 Jolde{\c{s}}, and Christoph Lauter / 169 \\
                 Session 7: Decimal Transcendentals \\
                 Computation of Decimal Transcendental Functions Using
                 the CORDIC Algorithm / {\'A}lvaro V{\'a}zquez, Julio
                 Villalba, and Elisardo Antelo / 179 \\
                 Decimal Transcendentals via Binary / John Harrison /
                 187 \\
                 A 32-bit Decimal Floating-Point Logarithmic Converter /
                 Dongdong Chen, Yu Zhang, Younhee Choi, Moon Ho Lee, and
                 Seok-Bum Ko / 195 \\
                 Special Session on Automated Synthesis of Arithmetic
                 Operations \\
                 Datapath Synthesis for Standard-Cell Design / Reto
                 Zimmermann / 207 \\
                 Design Space Exploration for Power-Efficient
                 Mixed-Radix Ling Adders / Chung-Kuan Cheng / 212 \\
                 Challenges in Automatic Optimization of Arithmetic
                 Circuits / Ajay K. Verma, Philip Brisk, and Paolo Ienne
                 / 213 \\
                 Panel on Decimal Arithmetic in Industry \\
                 Energy and Delay Improvement via Decimal Floating Point
                 Units / Hossam A. H. Fahmy, Ramy Raafat, Amira M.
                 Abdel-Majeed, Rodina Samy, Torek ElDeeb, and Yasmin
                 Farouk / 221 \\
                 IEEE 754-2008 Decimal Floating-Point for Intel
                 Architecture Processors / Marius Cornea / 225 \\
                 Special Session on Interval Arithmetic \\
                 IEEE Interval Standard Working Group --- P1788: Current
                 Status / William Edmonson and Guillaume Melquiond / 231
                 \\
                 Author Index",
}

@Proceedings{Cumplido:2009:RPI,
  editor =       "Ren{\'e} Cumplido and Lionel Torres and V. K.
                 {Prasanna Kumar}",
  booktitle =    "{ReConFig 2009: proceedings: 2009 [5th] International
                 Conference on Reconfigurable Computing and FPGAs: 9--11
                 December 2009: Cancun, Mexico}",
  title =        "{ReConFig 2009: proceedings: 2009 [5th] International
                 Conference on Reconfigurable Computing and FPGAs: 9--11
                 December 2009: Cancun, Mexico}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2009",
  ISBN =         "1-4244-5293-7, 0-7695-3917-3",
  ISBN-13 =      "978-1-4244-5293-4, 978-0-7695-3917-1",
  LCCN =         "TK7895.G36 2009",
  bibdate =      "Thu Feb 17 13:43:12 MST 2011",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=5379688",
  acknowledgement = ack-nhfb,
  meetingname =  "International Conference on Reconfigurable Computing
                 and FPGAs (5th : 2009 : Canc{\'u}n, Mexico)",
  subject =      "adaptive computing systems; congresses; field
                 programmable gate arrays",
}

@Proceedings{ICCIT:2009:ICC,
  editor =       "{ICCIT}",
  booktitle =    "{2009 12th International Conference on Computer and
                 Information Technology: ICCIT 2009: December 21-23,
                 Independent University, Bangladesh}",
  title =        "{2009 12th International Conference on Computer and
                 Information Technology: ICCIT 2009: December 21-23,
                 Independent University, Bangladesh}",
  publisher =    "ICCIT 2009 Conference Secretariat",
  address =      "Dhaka, Bangladesh",
  pages =        "702",
  year =         "2009",
  ISBN =         "1-4244-6281-9, 1-4244-6284-3",
  ISBN-13 =      "978-1-4244-6281-0, 978-1-4244-6284-1",
  LCCN =         "T58.5 2009",
  bibdate =      "Thu Feb 17 13:46:21 MST 2011",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=5398764",
  acknowledgement = ack-nhfb,
  meetingname =  "International Conference on Computer and Information
                 Technology (1998-) (12th: 2009: Independent University,
                 Bangladesh)",
  subject =      "information technology; congresses; computer science",
}

@Proceedings{IEEE:2009:ICF,
  editor =       "{IEEE}",
  booktitle =    "{International Conference on Field Programmable Logic
                 and Applications, Prague, Czech Republic, August 31
                 2009--September 2, 2009 (FPL 2009)}",
  title =        "{International Conference on Field Programmable Logic
                 and Applications, Prague, Czech Republic, August 31
                 2009--September 2, 2009 (FPL 2009)}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2009",
  ISBN =         "1-4244-3892-6",
  ISBN-13 =      "978-1-4244-3892-1",
  LCCN =         "????",
  bibdate =      "Fri Dec 03 15:38:12 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:2009:IICa,
  editor =       "{IEEE}",
  booktitle =    "20th {IEEE} International Conference on
                 Application-specific Systems, Architectures and
                 Processors, Boston, {MA, 7-9} July 2009 ({ASAP 2009})",
  title =        "20th {IEEE} International Conference on
                 Application-specific Systems, Architectures and
                 Processors, Boston, {MA}, 7-9 July 2009 ({ASAP} 2009)",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2009",
  ISBN =         "0-7695-3732-4",
  ISBN-13 =      "978-0-7695-3732-0",
  ISSN =         "1063-6862",
  LCCN =         "????",
  bibdate =      "Fri Dec 03 15:06:48 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "There are several papers from this that MUST be
                 included in this file.??!!",
}

@Proceedings{IEEE:2009:IICb,
  editor =       "{IEEE}",
  booktitle =    "{2009 IEEE International Conference on Computer
                 Design: October 4--7, 2009, Resort at Squaw Creek, Lake
                 Tahoe, CA: ICCD 2009}",
  title =        "{2009 IEEE International Conference on Computer
                 Design: October 4--7, 2009, Resort at Squaw Creek, Lake
                 Tahoe, CA: ICCD 2009}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  year =         "2009",
  ISBN =         "1-4244-5028-4",
  ISBN-13 =      "978-1-4244-5028-2",
  LCCN =         "TK7888.3 2009",
  bibdate =      "Thu Feb 17 08:53:42 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  note =         "IEEE Catalog Number: CFP09ICD",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=5406656",
  acknowledgement = ack-nhfb,
  meetingname =  "IEEE International Conference on Computer Design
                 (2009: Lake Tahoe, Calif.)",
  subject =      "computer engineering; congresses; embedded computer
                 systems; integrated circuits; very large scale
                 integration; electronic digital computers; circuits;
                 microcomputers; design and construction",
}

@Proceedings{IEEE:2009:IIS,
  editor =       "{IEEE}",
  booktitle =    "{2009 IEEE International Symposium on Circuits and
                 Systems: circuits and systems for human centric smart
                 living technologies, conference program, Taipei
                 International Convention Center, Taipei, Taiwan, May
                 24--May 27, 2009}",
  title =        "{2009 IEEE International Symposium on Circuits and
                 Systems: circuits and systems for human centric smart
                 living technologies, conference program, Taipei
                 International Convention Center, Taipei, Taiwan, May
                 24--May 27, 2009}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2009",
  ISBN =         "1-4244-3827-6 (print)",
  ISBN-13 =      "978-1-4244-3827-3 (print)",
  LCCN =         "TK454 .I15 2009",
  bibdate =      "Thu Feb 17 13:29:04 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=5076158",
  acknowledgement = ack-nhfb,
  meetingname =  "IEEE International Symposium on Circuits and Systems
                 (2009: Taipei, Taiwan)",
  subject =      "electronics; congresses; signal processing; digital
                 techniques; electronic circuits; neural networks
                 (computer science); integrated circuits; very large
                 scale integration",
}

@Proceedings{IEEE:2009:PDR,
  editor =       "{IEEE}",
  booktitle =    "{Ph.D. Research in Microelectronics and Electronics
                 (PRIME 2009), 12--17 July 2009, Cork, Ireland}",
  title =        "{Ph.D. Research in Microelectronics and Electronics
                 (PRIME 2009), 12--17 July 2009, Cork, Ireland}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  year =         "2009",
  ISBN =         "1-4244-3733-4",
  ISBN-13 =      "978-1-4244-3733-7",
  LCCN =         "TK7874 2009",
  bibdate =      "Thu Mar 24 21:42:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Matthews:2009:CRF,
  editor =       "Michael B. Matthews",
  booktitle =    "{Conference Record of the Forty-Third Asilomar
                 Conference on Signals, Systems and Computers, 1--4
                 November 2009, Pacific Grove, California}",
  title =        "{Conference Record of the Forty-Third Asilomar
                 Conference on Signals, Systems and Computers, 1--4
                 November 2009, Pacific Grove, California}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2009",
  ISBN =         "1-4244-5825-0",
  ISBN-13 =      "978-1-4244-5825-7",
  LCCN =         "????",
  bibdate =      "Thu Feb 17 13:40:37 MST 2011",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=5465900",
  acknowledgement = ack-nhfb,
}

@Proceedings{Sezer:2009:IIS,
  editor =       "Sakir Sezer and Andrew Marshall and Thomas Buechner",
  booktitle =    "{IEEE International SOC Conference: September 9--11,
                 2009, Wellington Park Hotel, Belfast, Northern Ireland,
                 UK (SOCC 2009)}",
  title =        "{IEEE International SOC Conference: September 9--11,
                 2009, Wellington Park Hotel, Belfast, Northern Ireland,
                 UK (SOCC 2009)}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2009",
  DOI =          "https://doi.org/10.1109/SOCCON.2009.5398119",
  ISBN =         "1-4244-4940-5, 1-4244-4941-3",
  ISBN-13 =      "978-1-4244-4940-8, 978-1-4244-4941-5",
  LCCN =         "TK7874.6 .I59 2009",
  bibdate =      "Sun Feb 20 11:34:39 MST 2011",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=5379508",
  acknowledgement = ack-nhfb,
  meetingname =  "IEEE International SOC Conference (22nd: 2009:
                 Belfast, Northern Ireland)",
  subject =      "integrated circuits; very large scale integration;
                 design and construction; congresses; systems on a chip;
                 electronic digital computers; circuits",
}

@Proceedings{Charot:2010:API,
  editor =       "Fran{\c{c}}ois Charot and Frank Hannig and J{\"u}rgen
                 Teich and Christophe Wolinski",
  booktitle =    "{ASAP 2010: proceedings: 21st IEEE International
                 Conference on Application-Specific Systems,
                 Architectures, and Processors: July 7--9, 2010, Rennes,
                 France}",
  title =        "{ASAP 2010: proceedings: 21st IEEE International
                 Conference on Application-Specific Systems,
                 Architectures, and Processors: July 7--9, 2010, Rennes,
                 France}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2010",
  ISBN =         "1-4244-6965-1, 1-4244-6966-X, 1-4244-6967-8",
  ISBN-13 =      "978-1-4244-6965-9, 978-1-4244-6966-6,
                 978-1-4244-6967-3",
  LCCN =         "TK7874.6 2010",
  bibdate =      "Thu Feb 17 13:54:41 MST 2011",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE Catalog Number CFP10063ART",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=5523683",
  acknowledgement = ack-nhfb,
  meetingname =  "IEEE International Conference on Application-Specific
                 Systems, Architectures, and Processors (21st: 2010:
                 Rennes, France)",
  subject =      "array processors; congresses; signal processing;
                 digital techniques; application-specific integrated
                 circuits",
}

@Proceedings{Delgado-Frias:2010:IIM,
  editor =       "Jose G. Delgado-Frias and Rogelio Palomera-Garcia and
                 Jabulani Nyathi",
  booktitle =    "{53nd IEEE International Midwest Symposium on Circuits
                 and Systems, 2010: MWSCAS 2010, 1--4 August 2010,
                 Seattle, Washington}",
  title =        "{53nd IEEE International Midwest Symposium on Circuits
                 and Systems, 2010: MWSCAS 2010, 1--4 August 2010,
                 Seattle, Washington}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2010",
  ISBN =         "1-4244-7771-9",
  ISBN-13 =      "978-1-4244-7771-5",
  LCCN =         "????",
  bibdate =      "Thu Feb 17 16:34:42 MST 2011",
  bibsource =    "alpha.lib.uwo.ca:210/INNOPAC;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=5542407",
  acknowledgement = ack-nhfb,
  meetingname =  "Midwest Symposium on Circuits and Systems (53nd: 2010:
                 Seattle, Washington)",
  subject =      "electronics; congresses; electronic circuits",
}

@Proceedings{Fukuda:2010:MSI,
  editor =       "Komei Fukuda and Joris van der Hoeven and Michael
                 Joswig and Nobuki Takayama",
  booktitle =    "{Mathematical software --- ICMS 2010: third
                 International Congress on Mathematical Software,
                 K{\=o}be, Japan, September 13--17, 2010: proceedings}",
  title =        "{Mathematical software --- ICMS 2010: third
                 International Congress on Mathematical Software,
                 K{\=o}be, Japan, September 13--17, 2010: proceedings}",
  volume =       "6327",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xvi + 368",
  year =         "2010",
  DOI =          "https://doi.org/10.1007/978-3-642-15582-6",
  ISBN =         "3-642-15581-2 (paperback), 3-642-15582-0 (e-book)",
  ISBN-13 =      "978-3-642-15581-9 (paperback), 978-3-642-15582-6
                 (e-book)",
  LCCN =         "QA76.95 .I5654 2010",
  bibdate =      "Sat Aug 9 14:06:27 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs2010a.bib;
                 https://www.math.utah.edu/pub/tex/bib/magma.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       ser-LNCS,
  URL =          "http://link.springer.com/book/10.1007/978-3-642-15582-6",
  acknowledgement = ack-nhfb,
  subject =      "Mathematics; Data processing; Congresses; Computer
                 software",
  tableofcontents = "Plenary \\
                 Computational Discrete Geometry / Thomas C. Hales /
                 1--3 \\
                 Exploiting Structured Sparsity in Large Scale
                 Semidefinite Programming Problems / Masakazu Kojima /
                 4--9 \\
                 Reliable and Efficient Geometric Computing / Kurt
                 Mehlhorn / 10--11 \\
                 The Sage Project: Unifying Free Mathematical Software
                 to Create a Viable Alternative to Magma, Maple,
                 Mathematica and MATLAB / Bur{\c{c}}in Er{\"o}cal,
                 William Stein / 12--27 \\
                 Computation of Special Functions (Invited) \\
                 Sollya: An Environment for the Development of Numerical
                 Codes / Sylvain Chevillard, Mioara Jolde, Christoph
                 Lauter / 28--31 \\
                 Validated Special Functions Software / Annie Cuyt,
                 Franky Backeljauw, Stefan Becuwe, Joris Van Deun /
                 32--34 \\
                 The Dynamic Dictionary of Mathematical Functions (DDMF)
                 / Alexandre Benoit, Fr{\'e}d{\'e}ric Chyzak, Alexis
                 Darrasse, Stefan Gerhold, Marc Mezzarobba, Bruno Salvy
                 / 35--41 \\
                 Reliable Computing with GNU MPFR / Paul Zimmermann /
                 42--45 \\
                 Computational Group Theory (Invited) \\
                 Simplicial Cohomology of Smooth Orbifolds in GAP /
                 Mohamed Barakat, Simon G{\"o}rtzen / 46--49 \\
                 Computing Polycyclic Quotients of Finitely
                 (L-)Presented Groups via Groebner Bases / Bettina Eick,
                 Max Horn / 50--53 \\
                 Constructive Membership Testing in Black-Box Classical
                 Groups / Sophie Ambrose, Scott H. Murray, Cheryl E.
                 Praeger, Csaba Schneider / 54--57 \\
                 Computational Group Theory (Contributed) \\
                 Towards High-Performance Computational Algebra with GAP
                 / Reimer Behrends, Alexander Konovalov, Steve Linton,
                 Frank L{\"u}beck, Max Neunh{\"o}effer / 58--61 \\
                 An Improvement of a Function Computing Normalizers for
                 Permutation Groups / Izumi Miyamoto / 62--68 \\
                 A GAP Package for Computation with Coherent
                 Configurations / Dmitrii V. Pasechnik, Keshav Kini /
                 69--72 \\
                 Computer Algebra (Invited) \\
                 CoCoALib: A C++ Library for Computations in Commutative
                 Algebra \ldots{} and Beyond / John Abbott, Anna M.
                 Bigatti / 73--76 \\
                 LinBox Founding Scope Allocation, Parallel Building
                 Blocks, and Separate Compilation / Jean-Guillaume
                 Dumas, Thierry Gautier, Cl{\'e}ment Pernet, B. David
                 Saunders / 77--83 \\
                 FGb: A Library for Computing Gr{\"o}bner Bases /
                 Jean-Charles Faug{\`e}re / 84--87 \\
                 Fast Library for Number Theory: An Introduction /
                 William B. Hart / 88--91 \\
                 Exact Numeric Computation for Algebraic and Geometric
                 Computation (Invited) \\
                 Controlled Perturbation for Certified Geometric
                 Computing with Fixed-Precision Arithmetic / Dan
                 Halperin / 92--95 \\
                 Exact Numeric Computation for Algebraic and Geometric
                 Computation (Invited) \\
                 Exact Geometric and Algebraic Computations in CGAL /
                 Menelaos I. Karavelas / 96--99 \\
                 On Solving Systems of Bivariate Polynomials / Fabrice
                 Rouillier / 100--104 \\
                 Accurate and Reliable Computing in Floating-Point
                 Arithmetic / Siegfried M. Rump / 105--108 \\
                 Exact Numeric Computation for Algebraic and Geometric
                 Computation (Contributed) \\
                 Deferring Dag Construction by Storing Sums of Floats
                 Speeds-Up Exact Decision Computations Based on
                 Expression Dags / Marc M{\"o}rig / 109--120 \\
                 The Design of Core 2: A Library for Exact Numeric
                 Computation in Geometry and Algebra / Jihun Yu, Chee
                 Yap, Zilin Du, Sylvain Pion, Herv{\'e} Br{\"o}nnimann /
                 121--141 \\
                 Formal Proof (Invited) \\
                 Introducing HOL Zero / Mark Adams / 142--143 \\
                 Euler's Polyhedron Formula in mizar / Jesse Alama /
                 144--147 \\
                 Building a Library of Mechanized Mathematical Proofs:
                 Why Do It? and What Is It Like to Do? / R. D. Arthan /
                 148--148 \\
                 Linear Programs for the Kepler Conjecture / Thomas C.
                 Hales / 149--151 \\
                 A Formal Proof of Pick's Theorem / John Harrison /
                 152--154 \\
                 Formal Proof (Contributed) \\
                 Evaluation of Automated Theorem Proving on the Mizar
                 Mathematical Library / Josef Urban, Krystof Hoder,
                 Andrei Voronkov / 155--166 \\
                 Geometry and Visualization (Invited) \\
                 On Local Deformations of Planar Quad-Meshes / Tim
                 Hoffmann / 167--169 \\
                 Construction of Harmonic Surfaces with Prescribed
                 Geometry / Matthias Weber / 170--173 \\
                 Geometry and Visualization (Contributed) \\
                 A Library of OpenGL-Based Mathematical Image Filters /
                 Martin von Gagern, Christian Mercat / 174--185 \\
                 MD-jeep: An Implementation of a Branch and Prune
                 Algorithm for Distance Geometry Problems / Antonio
                 Mucherino, Leo Liberti, Carlile Lavor / 186--197 \\
                 TADD: A Computational Framework for Data Analysis Using
                 Discrete Morse Theory / Jan Reininghaus, David
                 G{\"u}nther, Ingrid Hotz, Steffen Prohaska,
                 Hans-Christian Hege / 198--208 \\
                 Groebner Bases and Applications (Invited) \\
                 Introduction to Normaliz 2.5 / Winfried Bruns, Bogdan
                 Ichim, Christof S{\"o}ger / 209--212 \\
                 Computer Algebra Methods in Tropical Geometry / Thomas
                 Markwig / 213--216 \\
                 Groebner Bases and Applications (Contributed) \\
                 A New Desingularization Algorithm for Binomial
                 Varieties in Arbitrary Characteristic / Roc{\'\i}o
                 Blanco / 217--220 \\
                 An Algorithm of Computing Inhomogeneous Differential
                 Equations for Definite Integrals / Hiromasa Nakayama,
                 Kenta Nishiyama / 221--232 \\
                 Groebner Bases and Applications (Contributed) \\
                 New Algorithms for Computing Primary Decomposition of
                 Polynomial Ideals / Masayuki Noro / 233--244 \\
                 An Automated Confluence Proof for an Infinite Rewrite
                 System Parametrized over an Integro-Differential
                 Algebra / Loredana Tec, Georg Regensburger, Markus
                 Rosenkranz, Bruno Buchberger / 245--248 \\
                 Operadic Gr{\"o}bner Bases: An Implementation /
                 Vladimir Dotsenko, Mikael Vejdemo-Johansson / 249--252
                 \\
                 Number Theoretical Software (Invited) \\
                 Magma - A Tool for Number Theory / John Cannon, Steve
                 Donnelly, Claus Fieker, Mark Watkins / 253--255 \\
                 Number Theoretical Software (Contributed) \\
                 Enumerating Galois Representations in Sage / Craig
                 Citro, Alexandru Ghitza / 256--259 \\
                 NZMATH 1.0 / Satoru Tanaka, Naoki Ogura, Ken Nakamula,
                 Tetsushi Matsui, Shigenori Uchiyama / 260--269 \\
                 Software for Optimization and Polyhedral Computation
                 (Invited) \\
                 Removing Redundant Quadratic Constraints / David
                 Adjiashvili, Michel Baes, Philipp Rostalski / 270--281
                 \\
                 Traversing Symmetric Polyhedral Fans / Anders
                 Nedergaard Jensen / 282--294 \\
                 C++ Tools for Exploiting Polyhedral Symmetries / Thomas
                 Rehn, Achill Sch{\"u}rmann / 295--298 \\
                 isl: An Integer Set Library for the Polyhedral Model /
                 Sven Verdoolaege / 299--302 \\
                 Software for Optimization and Polyhedral Computation
                 (Contributed) \\
                 The Reformulation-Optimization Software Engine / Leo
                 Liberti, Sonia Cafieri, David Savourey / 303--314 \\
                 Generating Smooth Lattice Polytopes / Christian Haase,
                 Benjamin Lorenz, Andreas Paffenholz / 315--328 \\
                 Reliable Computation (Invited) \\
                 Mathemagix: Towards Large Scale Programming for
                 Symbolic and Certified Numeric Computations /
                 Gr{\'e}goire Lecerf / 329--332 \\
                 Complex Inclusion Functions in the CoStLy C++ Class
                 Library / Markus Neher / 333--336 \\
                 Standardized Interval Arithmetic and Interval
                 Arithmetic Used in Libraries / Nathalie Revol /
                 337--341 \\
                 Reliable Computation (Contributed) \\
                 Efficient Evaluation of Large Polynomials / Charles E.
                 Leiserson, Liyun Li, Marc Moreno Maza, Yuzhen Xie /
                 342--353 \\
                 Communicating Functional Expressions from Mathematica
                 to C-XSC / Evgenija D. Popova, Walter Kr{\"a}mer /
                 354--365 \\
                 Author Index / 367--368",
}

@Proceedings{IEEE:2010:CCE,
  editor =       "{IEEE}",
  booktitle =    "23rd Canadian Conference on Electrical and Computer
                 Engineering ({CCECE}), Calgary, {AB, 2--5} May, 2010",
  title =        "23rd Canadian Conference on Electrical and Computer
                 Engineering ({CCECE}), Calgary, {AB}, 2--5 May, 2010",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2010",
  ISBN =         "1-4244-5376-3",
  ISBN-13 =      "978-1-4244-5376-4",
  LCCN =         "????",
  bibdate =      "Fri Dec 03 15:46:10 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:2010:ICC,
  editor =       "{IEEE}",
  booktitle =    "2010 2nd International Conference on Computer
                 Engineering and Technology ({ICCET})",
  title =        "2010 2nd International Conference on Computer
                 Engineering and Technology ({ICCET}), 16--18 April
                 2010, Chengdu, China",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2010",
  ISBN =         "1-4244-6347-5",
  ISBN-13 =      "978-1-4244-6347-3",
  LCCN =         "????",
  bibdate =      "Fri Dec 03 15:22:32 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{IEEE:2010:ICM,
  editor =       "{IEEE}",
  booktitle =    "{2010 27th International Conference on
                 Microelectronics: proceedings: Ni{\v{s}}, MIEL 2010,
                 Ni{\v{s}}, Serbia: 16--19 May 2010}",
  title =        "{2010 27th International Conference on
                 Microelectronics: proceedings: Ni{\v{s}}, MIEL 2010,
                 Ni{\v{s}}, Serbia: 16--19 May 2010}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2010",
  ISBN =         "1-4244-7200-8, 1-4244-7201-6",
  ISBN-13 =      "978-1-4244-7200-0, 978-1-4244-7201-7",
  LCCN =         "TK7874 2010",
  bibdate =      "Thu Feb 17 13:49:56 MST 2011",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE Catalog Number CFP10432-ART.",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=5483038",
  acknowledgement = ack-nhfb,
  meetingname =  "International Conference on Microelectronics (27th :
                 2010 : Ni{\v{s}}, Serbia)",
  subject =      "Microelectronics; Congresses",
}

@Proceedings{IEEE:2010:ICV,
  editor =       "{IEEE}",
  booktitle =    "{23rd International Conference on VLSI Design:
                 proceedings, held jointly with 9th International
                 Conference on Embedded Systems: Bangalore, India, 3--7
                 January 2010}",
  title =        "{23rd International Conference on VLSI Design:
                 proceedings, held jointly with 9th International
                 Conference on Embedded Systems: Bangalore, India, 3--7
                 January 2010}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xl + 469",
  year =         "2010",
  ISBN =         "1-4244-5541-3, 0-7695-3928-9, 1-4244-5541-3",
  ISBN-13 =      "978-1-4244-5541-6, 978-0-7695-3928-7,
                 978-1-4244-5541-6",
  LCCN =         "TK7874.75 2010",
  bibdate =      "Sun Feb 20 14:14:26 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  note =         "IEEE Computer Society Order Number E3928.",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=5400049",
  acknowledgement = ack-nhfb,
  meetingname =  "International Conference on VLSI Design (23rd : 2010 :
                 Bangalore, India)",
  subject =      "electronic digital computers; circuits; congresses;
                 signal processing; digital techniques; integrated
                 circuits; very large scale integration; design and
                 construction",
}

@Book{Knuth:2010:SPD,
  author =       "Donald E. Knuth",
  booktitle =    "Selected Papers on Design of Algorithms",
  title =        "Selected Papers on Design of Algorithms",
  volume =       "191",
  publisher =    pub-CSLI,
  address =      pub-CSLI:adr,
  pages =        "xvi + 453",
  year =         "2010",
  ISBN =         "1-57586-582-3 (paperback), 1-57586-583-1 (hardcover)",
  ISBN-13 =      "978-1-57586-582-9 (paperback), 978-1-57586-583-6
                 (hardcover)",
  LCCN =         "QA9.58 KNU 2010",
  MRclass =      "01A75 (01-06 05B35 05C85 68-03)",
  MRnumber =     "2572388 (2011c:01022)",
  bibdate =      "Mon Jul 05 16:25:34 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 library.ox.ac.uk:210/ADVANCE",
  price =        "US\$48.50",
  series =       "CSLI Lecture Notes",
  acknowledgement = ack-nhfb,
  subject =      "Algorithms; Computer algorithms; Computer
                 programming",
  tableofcontents = "1. Robert W. Floyd, in Memoriam / 1 \\
                 2. The Bose--Nelson Sorting Problem / 19 \\
                 3. A One-Way, Stackless Quicksort Algorithm / 31 \\
                 4. Optimum Binary Search Trees / 35 \\
                 5. Dynamic Huffman Coding / 51 \\
                 6. Inhomogeneous Sorting / 71 \\
                 7. Lexicographic Permutations with Restrictions / 79
                 \\
                 8. Nested Satisfiability / 91 \\
                 9. Fast Pattern Matching in Strings / 99 \\
                 10. Addition Machines / 137 \\
                 11. A Simple Program Whose Proof Isn't / 155 \\
                 12. Verification of Link-Level Protocols / 167 \\
                 13. A Problem in Concurrent Programming Control / 175
                 \\
                 14. Optimal Prepaging and Font Caching / 181 \\
                 15. A Generalization of Dijkstra's Algorithm / 209 \\
                 16. Two-Way Rounding / 219 \\
                 17. Matroid Partitioning / 235 \\
                 18. Irredundant Intervals / 245 \\
                 19. Simple Word Problems in Universal Algebras / 275
                 \\
                 20. Efficient Representation of Perm Groups / 315 \\
                 21. An Algorithm for Brownian Zeros / 329 \\
                 22. Semi-Optimal Bases for Linear Dependencies / 337
                 \\
                 23. Evading the Drift in Floating-Point Addition / 341
                 \\
                 24. Deciphering a Linear Congruential Encryption / 349
                 \\
                 25. Computation of Tangent, Euler, and Bernoulli
                 Numbers / 359 \\
                 26. Euler's Constant to 1271 Places / 373 \\
                 27. Evaluation of Polynomials by Computer / 383 \\
                 28. Minimizing Drum Latency Time / 397 \\
                 Index / 437",
}

@Proceedings{Santos:2010:PVS,
  editor =       "E. J. P. (Edval J. P.) Santos and Hor{\'a}cio C. Neto
                 and El{\'\i}as Todorovich",
  booktitle =    "{Proceedings of the VI Southern Programmable Logic
                 Conference: Ipojuca, Porto de Galinhas Beach, Brazil,
                 March 24th--26th, 2010}",
  title =        "{Proceedings of the VI Southern Programmable Logic
                 Conference: Ipojuca, Porto de Galinhas Beach, Brazil,
                 March 24th--26th, 2010}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2010",
  ISBN =         "1-4244-6309-2, 1-4244-7089-7",
  ISBN-13 =      "978-1-4244-6309-1, 978-1-4244-7089-1",
  LCCN =         "TK7895.G36 2010",
  bibdate =      "Thu Feb 17 13:58:15 MST 2011",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE Catalog Number CFPI021B-PRT.",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=5473892",
  acknowledgement = ack-nhfb,
  meetingname =  "Southern Conference on Programmable Logic (6th: 2010:
                 Ipojuca, Pernambuco, Brazil)",
  subject =      "Field programmable gate arrays; Congresses;
                 Programmable array logic",
}

@Proceedings{Watt:2010:IPI,
  editor =       "Stephen M. Watt",
  booktitle =    "{ISSAC 2010: Proceedings of the 2010 International
                 Symposium on Symbolic and Algebraic Computation, July
                 25--28, 2010, Munich, Germany}",
  title =        "{ISSAC 2010: Proceedings of the 2010 International
                 Symposium on Symbolic and Algebraic Computation, July
                 25--28, 2010, Munich, Germany}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xiv + 363",
  year =         "2010",
  ISBN =         "1-4503-0150-9",
  ISBN-13 =      "978-1-4503-0150-3",
  LCCN =         "QA76.95 .I59 2010",
  bibdate =      "Fri Jun 17 08:11:01 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{ACM:2011:SSP,
  editor =       "{ACM}",
  booktitle =    "{SC '11 State of the Practice Reports}",
  title =        "{SC '11 State of the Practice Reports}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  year =         "2011",
  ISBN =         "1-4503-1139-3",
  ISBN-13 =      "978-1-4503-1139-7",
  LCCN =         "????",
  bibdate =      "Fri Dec 16 11:20:09 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/supercomputing2011.bib",
  acknowledgement = ack-nhfb,
}

@Book{IEEE:2011:ICC,
  author =       "{IEEE}",
  booktitle =    "{2011 IEEE COOL Chips XIV: Yokohama Joho Bunka Center,
                 Yokohama, Japan, April 20--22, 2011}",
  title =        "{2011 IEEE COOL Chips XIV: Yokohama Joho Bunka Center,
                 Yokohama, Japan, April 20--22, 2011}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2011",
  ISBN =         "1-61284-884-2",
  ISBN-13 =      "978-1-61284-884-6",
  LCCN =         "????",
  bibdate =      "Wed Dec 21 14:21:28 MST 2011",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE Catalog Number CFP11COL-ART.",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=5871805",
  acknowledgement = ack-nhfb,
  meetingname =  "IEEE Symposium on Low-Power and High-Speed Chips (14th
                 : 2011 : Yokohama-shi, Japan)",
  subject =      "Low voltage systems; Congresses; Electronic circuit
                 design",
}

@Proceedings{Impagliazzo:2011:PSR,
  editor =       "John Impagliazzo and Eduard Proydakov",
  booktitle =    "Perspectives on {Soviet} and {Russian} Computing:
                 {First IFIP WG 9.7 Conference, SoRuCom
                 2006Petrozavodsk, Russia, July 3--7, 2006. Revised
                 Selected Papers}",
  title =        "Perspectives on {Soviet} and {Russian} Computing:
                 {First IFIP WG 9.7 Conference, SoRuCom
                 2006Petrozavodsk, Russia, July 3--7, 2006. Revised
                 Selected Papers}",
  volume =       "357",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xxi + 272",
  year =         "2011",
  DOI =          "https://doi.org/10.1007/978-3-642-22816-2",
  ISBN =         "3-642-22815-1 (print), 3-642-22816-X (e-book)",
  ISBN-13 =      "978-3-642-22815-5 (print), 978-3-642-22816-2
                 (e-book)",
  ISSN =         "1868-422X (print), 1868-4238 (electronic)",
  ISSN-L =       "1868-4238",
  LCCN =         "QA75.5 .C66 2011",
  bibdate =      "Sun Aug 16 19:31:45 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "IFIP Advances in Information and Communication
                 Technology",
  URL =          "http://link.springer.com/openurl?genre=book%26isbn=978-3-642-22815-5",
  abstract =     "This book contains a collection of thoroughly refereed
                 papers derived from the First IFIP WG 9.7 Conference on
                 Soviet and Russian Computing, held in Petrozavodsk,
                 Russia, in July 2006. The 32 revised papers were
                 carefully selected from numerous submissions; many of
                 them were translated from Russian. They reflect much of
                 the shining history of computing activities within the
                 former Soviet Union from its origins in the 1950s with
                 the first computers used for military decision-making
                 problems up to the modern period where Russian ICT grew
                 substantially, especially in the field of custom-made
                 programming.",
  acknowledgement = ack-nhfb,
  tableofcontents = "The Work of Sergey Alekseevich Lebedev in Kiev and
                 Its Subsequent Influence on Further Scientific Progress
                 There / Zinoviy L. Rabinovich / 1 \\
                 History of the Creation of BESM: The First Computer of
                 S / A / Lebedev Institute of Precise Mechanics and
                 Computer Engineering / Vera B. Karpova and Leonid E.
                 Karpov / 6 \\
                 Some Hardware Aspects of the BESM-6 Design / V. I.
                 Smirnov / 20 \\
                 Computer Architecture Development: From the BESM-6
                 Computer to Supercomputers / Yuri I. Mitropolski / 26
                 \\
                 Operating System of the Multi-machine Computer AS-6 /
                 I. B. Bourdonov, V. P. Ivannikov, A. S. Kossatchev, S.
                 D. Kuznetsov, and A. N. Tomilin / 31 \\
                 Distributed Systems for Data Handling / Vladislav P.
                 Shirikov / 36 \\
                 Automatic Digital Computer M-1 of the I. S. Brook
                 Laboratory / T. M. Alexandridi and U. V. Rogachov / 46
                 \\
                 Conception of New Generation Computer Systems --- The
                 Last Large-Scale Initiative in Computers of the COMECON
                 Countries: A Glance after Twenty Years / Victor
                 Zakharov and Yuri Lavrenjuk / 50 \\
                 SM EVM Control Computer Development / N. L. Prokhorov
                 and G. A. Egorov / 64 \\
                 Ternary Computers: The Setun and the Setun 70 / Nikolay
                 Petrovich Brusentsov and Jos{\'e} Ramil Alvarez / 74
                 \\
                 Ternary Dialectical Informatics / Nikolay Petrovich
                 Brusentsov and Julia Sergeevna Vladimirova / 81 \\
                 Establishing a Computer Industry in the Soviet
                 Socialist Republic of Belarus / Yuri Vladimirovich
                 Karpilovitch, Viktor Vladimirovich Przhijalkovskiy, and
                 Gennadiy Dmitrievich Smirnov / 89 \\
                 Some Aspects on Computing Means Development Philosophy
                 / Jaroslav Khetagourov / 98 \\
                 The Algorithmic ``Computer'' / Zoya Alekseeva / 103 \\
                 Academician Andrei Ershov and His Archive / Irina
                 Kraineva and Natalia Cheremnykh / 117 \\
                 The START Project / Alexander Gurievich Marchuk / 126
                 \\
                 The MRAMOR Workstation / A. A. Baehrs / 134 \\
                 Mixed Computation in Novosibirsk / Mikhail Bulyonkov /
                 142 \\
                 The Zelenograd Centerof Microelectronics / B. M.
                 Malashevich and D. B. Malashevich / 152 \\
                 Modular: The Super Computer / B. M. Malashevich and D.
                 B. Malashevich / 164 \\
                 The Microprocessors, Mini- and Micro-computers with
                 Architecture``Electronics NC'' in Zelenograd / B. M.
                 Malashevich / 174 \\
                 Fund Collection: ``Electronic Digital Computing
                 Machines'' at the Polytechnic Museum / Marina
                 Smolevitskaya / 187 \\
                 An Open Adaptive Virtual Museum of Informatics History
                 in Siberia / Victor N. Kasyanov / 194 \\
                 The History of Computers and Computing in Virtual
                 Museums / Yuri Polak / 201 \\
                 Computer Development in the Socialist Countries:
                 Members of the Council for Mutual Economic Assistance
                 (CMEA) / A. Y. Nitusov / 208 \\
                 On the History of Computer Algebra at the Keldysh
                 Institute of Applied Mathematics / G. B. Efimov, I. B.
                 Tshenkov, and E. Yu. Zueva / 220 \\
                 Novosibirsk Young Programmers School: A Way to Success
                 and Future Development / Alexander Gurievich Marchuk,
                 Tatyana Ivanovna Tikhonova, and Lidiya Vasilyevna
                 Gorodnyaya / 228 \\
                 ``Lions --- Marchuk'': The Soviet--French Cooperation
                 in Computing / Ksenia Tatarchenko / 235 \\
                 Information and Communication Technology Education
                 Based on the Russian State Educational Standard of
                 ``Applied Mathematics and Informatics'' / Iurii A.
                 Bogoiavlenskii / 243 \\
                 Cooperation among Institutions of the Soviet Union and
                 Cuba:Accomplishments between 1972 and 1990 / Tom{\'a}s
                 L{\'o}pez Jim{\e}nez / 251 \\
                 Teaching Computer Science in Moscow Universities:
                 Evolution for Forty Years / Olga Parakhina and Yuri
                 Polak / 258 \\
                 Kronos: Processor Family for High-Level Languages /
                 Dmitry N. Kuznetsov, Alexey E. Nedorya, Eugene V.
                 Tarassov, Vladimir E. Philippov, and Marina Ya
                 Philippova / 266 \\
                 Author Index / / 273",
}

@Proceedings{Schwarz:2011:PIS,
  editor =       "Eric Schwarz and Vojin G. Oklobdzija",
  booktitle =    "{Proceedings of the 20th IEEE Symposium on Computer
                 Arithmetic, July 25--27, 2011, T{\"u}bingen, Germany}",
  title =        "{Proceedings of the 20th IEEE Symposium on Computer
                 Arithmetic, July 25--27, 2011, T{\"u}bingen, Germany}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xix + 253",
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ARITH17396.2011",
  ISBN =         "0-7695-4318-9, 1-4244-9457-5",
  ISBN-13 =      "978-0-7695-4318-5, 978-1-4244-9457-6",
  LCCN =         "QA76.6",
  bibdate =      "Sat Aug 20 09:19:17 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-20; correct rounding; floating-point
                 arithmetic",
  tableofcontents = "Foreword / ix \\
                 Dedication / x \\
                 Steering Committee / xv \\
                 Symposium Committee / xvi \\
                 Program Committee / xvii \\
                 Additional Reviewers / xviii \\
                 Corporate Sponsors / xix \\
                 Session 1: Keynote Talk: Chair: Eric Schwarz and Vojin
                 G. Oklobdzija \\
                 High Intelligence Computing: The New Era of High
                 Performance Computing / Ralf Fischer / 3 \\
                 Session 2: Multiple-Precision Algorithms: Chair: Marius
                 Cornea \\
                 Short Division of Long Integers / David Harvey and Paul
                 Zimmermann / 7 \\
                 High Degree Toom'n'Half for Balanced and Unbalanced
                 Multiplication / Marco Bodrato / 15 \\
                 Augmented Precision Square Roots and 2-D Norms, and
                 Discussion on Correctly Rounding sqrt($x^2 + y^2$) /
                 Nicolas Brisebarre, Mioara Jolde{\c{s}}, Peter
                 Kornerup, Erik Martin-Dorel, and Jean-Michel Muller /
                 23 \\
                 Session 3: Transcendental Methods: Chair: Naofumi
                 Takagi \\
                 Towards a Quaternion Complex Logarithmic Number System
                 / Mark G. Arnold, John Cowles, Vassilis Paliouras, and
                 Ioannis Kouretas / 33 \\
                 ROM-less LNS / R. Che Ismail and J. N. Coleman / 43 \\
                 Composite Iterative Algorithm and Architecture for q-th
                 Root Calculation / Alvaro Vazquez and Javier D.
                 Bruguera / 52 \\
                 On the Fixed-Point Accuracy Analysis and Optimization
                 of FFT Units with CORDIC Multipliers / Omid Sarbishei
                 and Katarzyna Radecka / 62 \\
                 Session 4: Special Session on Industrial Practices:
                 Chair: Mike Schulte \\
                 Self Checking in Current Floating-Point Units / Daniel
                 Lipetz and Eric Schwarz / 73 \\
                 How to Square Floats Accurately and Efficiently on the
                 ST231 Integer Processor/ Claude-Pierre Jeannerod,
                 Jingyan Jourdan-Lu, Christophe Monat, and Guillaume
                 Revy / 77 \\
                 A 1.5 Ghz VLIW DSP CPU with Integrated Floating Point
                 and Fixed Point Instructions in 40 nm CMOS / Timothy
                 Anderson, Due Bui, Shriram Moharil, Soujanya Narnur,
                 Mujibur Rahman, Anthony Lell, Eric Biscondi, Ashish
                 Shrivastava, Peter Dent, Mingjian Yan, and Hasan
                 Mahmood / 82 \\
                 The POWER7 Binary Floating-Point Unit / Maarten
                 Boersma, Michael Kroner, Christophe Layer, Petra Leber,
                 Silvia M. Muller, and Kerstin Schelm / 87 \\
                 Session 5: Addition: Chair: Alberto Nannarelli \\
                 Accelerating Computations on FPGA Carry Chains by
                 Operand Compaction / Thomas B. Preus{\ss}er, Martin
                 Zabel, and Rainer G. Spallek / 95 \\
                 Fast Ripple-Carry Adders in Standard-Cell CMOS VLSI /
                 Neil Burgess / 103 \\
                 A Family of High Radix Signed Digit Adders / Saeid
                 Gorgin and Ghassem Jaberipur / 112 \\
                 Session 6: Floating-Point Units: Chair: Javier Bruguera
                 \\
                 Fused Multiply-Add Microarchitecture Comprising
                 Separate Early-Normalizing Multiply and Add Pipelines /
                 David R. Lutz / 123 \\
                 Latency Sensitive FMA Design / Sameh Galal and Mark
                 Horowitz / 129 \\
                 The IBM zEnterprise-196 Decimal Floating-Point
                 Accelerator / Steven Carlough, Adam Collura, Silvia
                 Mueller, and Michael Kroener / 139 \\
                 Session 7: Division, Square-Root and Reciprocal
                 Square-Root: Chair: Peter Kornerup \\
                 Radix-8 Digit-by-Rounding: Achieving High-Performance
                 Reciprocals, Square Roots, and Reciprocal Square Roots
                 / J. Adam Butts, Ping Tak Peter Tang, Ron O. Dror, and
                 David E. Shaw / 149 \\
                 Tight Certification Techniques for Digit-by-Rounding
                 Algorithms with Application to a New 1/sqrt(x) Design /
                 Ping Tak Peter Tang, J. Adam Butts, Ron O. Dror, and
                 David E. Shaw / 159 \\
                 Radix-16 Combined Division and Square Root Unit /
                 Alberto Nannarelli / 169 \\
                 A Prescale-Lookup-Postscale Additive Procedure for
                 Obtaining a Single Precision Ulp Accurate Reciprocal /
                 David W. Matula and Mihai T. Panu / 177 \\
                 Session 8: Special Session on High Performance
                 Arithmetic for FPGA's: Chair: Martin Langhammer \\
                 Teraflop FPGA Design / Martin Langhammer / 187 \\
                 The Arithmetic Operators You Will Never See in a
                 Microprocessor / Florent de Dinechin / 189 \\
                 Accelerating Large-Scale HPC Applications Using FPGAs /
                 Rob Dimond, Sebastien Racaniere, and Oliver Pell / 191
                 \\
                 Session 9: Arithmetic Algorithms for Cryptography:
                 Chair: David Matula \\
                 A General Approach for Improving RNS Montgomery
                 Exponentiation Using Pre-processing / Filippo Gandino,
                 Fabrizio Lamberti, Paolo Montuschi, and Jean-Claude
                 Bajard / 195 \\
                 Bit-Sliced Binary Normal Basis Multiplication / Billy
                 Bob Brumley and Dan Page / 205 \\
                 Efficient SIMD Arithmetic Modulo a Mersenne Number /
                 Joppe W. Bos, Thorsten Kleinjung, Arjen K. Lenstra, and
                 Peter L. Montgomery / 213 \\
                 Session 10: Tools for Formal Certified Code: Chair:
                 Martin Schmookler \\
                 Automatic Generation of Code for the Evaluation of
                 Constant Expressions at Any Precision with a Guaranteed
                 Error Bound / Sylvain Chevillard / 225 \\
                 Automatic Generation of Fast and Certified Code for
                 Polynomial Evaluation / Christophe Mouilleron and
                 Guillaume Revy / 233 \\
                 Flocq: A Unified Library for Proving Floating-Point
                 Algorithms in Coq / Sylvie Boldo and Guillaume
                 Melquiond / 243 \\
                 Author Index / 253",
}

@Book{Hennessy:2012:CAQ,
  author =       "John L. Hennessy and David A. Patterson",
  booktitle =    "Computer Architecture: a Quantitative Approach",
  title =        "Computer Architecture: a Quantitative Approach",
  publisher =    pub-MORGAN-KAUFMANN-ELSEVIER,
  address =      pub-MORGAN-KAUFMANN-ELSEVIER:adr,
  edition =      "Fifth",
  pages =        "xxvii + 493 + 325",
  year =         "2012",
  ISBN =         "0-12-383872-X (paperback)",
  ISBN-13 =      "978-0-12-383872-8 (paperback)",
  LCCN =         "QA76.9.A73 P377 2012",
  bibdate =      "Wed Feb 15 07:46:38 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "With contributions by Krste Asanovi{\'c}, Jason D.
                 Kabos, Robert P. Colwell, Thomas M. Conte, Jos{\'e}
                 Duato, Diana Franklin, David Goldberg, Norman P.
                 Jouppi, Sheng Li, Naveen Muralimanohar, Gregory D.
                 Peterson, Timothy M. Pinkston, Parthasarathy
                 Ranganthan, David A. Wood, and Amr Zaky.",
  URL =          "http://booksite.mkp.com/9780123838728",
  acknowledgement = ack-nhfb,
  subject =      "Computer architecture",
  tableofcontents = "1: Fundamentals of Quantitative Design and Analysis
                 \\
                 2: Memory Hierarchy Design \\
                 3: Instruction-Level Parallelism and Its Exploitation
                 \\
                 4: Data-Level Parallelism in Vector, SIMD, and GPU
                 Architectures \\
                 5: Thread-Level Parallelism \\
                 6: Warehouse-Scale Computers to Exploit Request-Level
                 and Data-Level Parallelism \\
                 A: Instruction Set Principles \\
                 B: Review of Memory Hierarchy \\
                 C: Pipelining: Basic and Intermediate Concepts \\
                 D: Storage Systems \\
                 E: Embedded Systems \\
                 F: Interconnection Networks \\
                 G: Vector Processors in More Depth \\
                 H: Hardware and Software for VLIW and EPIC \\
                 I: Large-Scale Multiprocessors and Scientific
                 Applications \\
                 J: Computer Arithmetic \\
                 K: Survey of Instruction Set Architectures \\
                 L: Historical Perspective and References \\
                 References \\
                 Index",
}

@Proceedings{Jonasson:2012:APSb,
  editor =       "Kristj{\'a}n J{\'o}nasson",
  booktitle =    "{Applied Parallel and Scientific Computing: 10th
                 International Conference, PARA 2010, Reykjav{\'\i}k,
                 Iceland, June 6--9, 2010, Revised Selected Papers, Part
                 II}",
  title =        "{Applied Parallel and Scientific Computing: 10th
                 International Conference, PARA 2010, Reykjav{\'\i}k,
                 Iceland, June 6--9, 2010, Revised Selected Papers, Part
                 II}",
  volume =       "7134",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xxviii + 477",
  year =         "2012",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-642-28145-7",
  ISBN =         "3-642-28144-3 (print), 3-642-28145-1 (e-book)",
  ISBN-13 =      "978-3-642-28144-0 (print), 978-3-642-28145-7
                 (e-book)",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  LCCN =         "????",
  bibdate =      "Wed Dec 19 15:24:47 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs.bib",
  series =       ser-LNCS,
  URL =          "http://www.springerlink.com/content/978-3-642-28145-7",
  acknowledgement = ack-nhfb,
  tableofcontents = "Free Energy Monte Carlo Simulations on a
                 Distributed Network \\
                 Numerical Investigation of the Cumulant Expansion for
                 Fourier Path Integrals \\
                 Optimization of Functionals of Orthonormal Functions in
                 the Absence of Unitary Invariance \\
                 Simulated Annealing with Coarse Graining and
                 Distributed Computing \\
                 Path Optimization with Application to Tunneling \\
                 Shallow Water Simulations on Multiple GPUs \\
                 High Performance Computing Techniques for Scaling Image
                 Analysis Workflows \\
                 Parallel Computation of Bivariate Polynomial Resultants
                 on Graphics Processing Units \\
                 Accelerating Model Reduction of Large Linear Systems
                 with Graphics Processors \\
                 Fast GPU-Based Fluid Simulations Using SPH \\
                 Toward Techniques for Auto-tuning GPU Algorithms \\
                 An Interval Version of the Crank-Nicolson Method \\
                 The First Approach \\
                 Parallel Detection of Interval Overlapping \\
                 Using the Second-Order Information in Pareto-set
                 Computations of a Multi-criteria Problem \\
                 Comments on Fast and Exact Accumulation of Products \\
                 An Interval Finite Difference Method of Crank-Nicolson
                 Type for Solving the One-Dimensional Heat Conduction
                 Equation with Mixed Boundary Conditions \\
                 Using C-XSC for High Performance Verified Computing \\
                 Efficient Implementation of Interval Matrix
                 Multiplication \\
                 The Computing Framework for Physics Analysis at LHCb
                 \\
                 Taming the Raven \\
                 Testing the Random Access, Visualization and
                 Exploration Network RAVEN \\
                 RAVEN \\
                 Boosting Data Analysis for the LHC Experiments \\
                 Bridging HPC and Grid File I/O with IOFSL \\
                 Fine Granularity Sparse QR Factorization for Multicore
                 Based Systems \\
                 Mixed Precision Iterative Refinement Methods for Linear
                 Systems: Convergence Analysis Based on Krylov Subspace
                 Methods \\
                 An Implementation of the Tile QR Factorization for a
                 GPU and Multiple CPUs \\
                 Efficient Reduction from Block Hessenberg Form to
                 Hessenberg Form Using Shared Memory \\
                 Cache-Oblivious Algorithms and Matrix Formats for
                 Computations on Interval Matrices \\
                 Parallel Solution of Narrow Banded Diagonally Dominant
                 Linear Systems \\
                 An Approach for Semiautomatic Locality Optimizations
                 Using OpenMP \\
                 Memory-Efficient Sierpinski-Order Traversals on
                 Dynamically Adaptive, Recursively Structured Triangular
                 Grids \\
                 Fast Wavelet Transform Utilizing a Multicore-Aware
                 Framework \\
                 Direct Sparse Factorization of Blocked Saddle Point
                 Matrices \\
                 Multi-Target Vectorization with MTPS C++ Generic
                 Library \\
                 Analysis of Gravitational Wave Signals on Heterogeneous
                 Architectures \\
                 Towards Efficient Execution of Erasure Codes on
                 Multicore Architectures \\
                 Communication-Efficient Algorithms for Numerical
                 Quantum Dynamics \\
                 Efficiently Implementing Monte Carlo Electrostatics
                 Simulations on Multicore Accelerators \\
                 Algebraic Multigrid Solver on Clusters of CPUs and GPUs
                 \\
                 Solution of Identification Problems in Computational
                 Mechanics \\
                 Parallel Processing Aspects \\
                 ScalaTrace: Tracing, Analysis and Modeling of HPC Codes
                 at Scale \\
                 A Lightweight Library for Building Scalable Tools \\
                 MATE: Toward Scalable Automated and Dynamic Performance
                 Tuning Environment \\
                 Improving the Scalability of Performance Evaluation
                 Tools \\
                 Automatic Performance Analysis of OpenMP Codes on a
                 Scalable Shared Memory System Using Periscope \\
                 Further Improving the Scalability of the Scalasca
                 Toolset",
}

@Proceedings{IEEE:2013:PIS,
  editor =       "{IEEE}",
  booktitle =    "{Proceedings of the 21st IEEE Symposium on Computer
                 Arithmetic, Austin, Texas, USA, 8--10 April 2013}",
  title =        "{Proceedings of the 21st IEEE Symposium on Computer
                 Arithmetic, Austin, Texas, USA, 8--10 April 2013}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xvi + 229",
  year =         "2013",
  ISBN =         "0-7695-4957-8",
  ISBN-13 =      "978-0-7695-4957-6",
  ISSN =         "1063-6889",
  LCCN =         "QA76.9.C62 S95 2013",
  bibdate =      "Sat Aug 01 08:03:11 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-21; computer arithmetic units; correctness
                 proofs; cryptography; domain specific designs; error
                 analysis; exascale computing; floating point
                 arithmetic; floating-point error analysis; formal
                 verification; function approximation; modular
                 arithmetic; theorem proving; verification",
}

@Proceedings{Butler:2015:FMS,
  editor =       "Michael Butler and Sylvain Conchon and Fatiha
                 Za{\"i}di",
  booktitle =    "{Formal Methods and Software Engineering: 17th
                 International Conference on Formal Engineering Methods,
                 ICFEM 2015, Paris, France, November 3--5, 2015,
                 Proceedings}",
  title =        "{Formal Methods and Software Engineering: 17th
                 International Conference on Formal Engineering Methods,
                 ICFEM 2015, Paris, France, November 3--5, 2015,
                 Proceedings}",
  volume =       "9407",
  publisher =    "Springer International Publishing",
  address =      "Cham, Switzerland",
  pages =        "xxv + 436 + 150",
  year =         "2015",
  DOI =          "https://doi.org/10.1007/978-3-319-25423-4",
  ISBN =         "3-319-25422-7 (paperback), 3-319-25423-5 (e-book)",
  ISBN-13 =      "978-3-319-25422-7 (paperback), 978-3-319-25423-4
                 (e-book)",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  LCCN =         "QA76.758",
  bibdate =      "Fri Jan 31 15:45:10 MST 2020",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/java2010.bib",
  series =       ser-LNCS,
  URL =          "http://link.springer.com/10.1007/978-3-319-25423-4",
  abstract =     "This book constitutes the refereed proceedings of the
                 17th International Conference on Formal Engineering
                 Methods, ICFEM 2015, held in Paris, France, in November
                 2015. The 27 revised full papers presented were
                 carefully reviewed and selected from 82 submissions.
                 The papers cover a wide range of topics in the area of
                 formal methods and software engineering and are devoted
                 to advancing the state of the art of applying formal
                 methods in practice. They focus in particular on
                 combinations of conceptual and methodological aspects
                 with their formal foundation and tool support.",
  acknowledgement = ack-nhfb,
  subject =      "Computer science; Computer networks; Computer
                 programming; Software engineering; Programming
                 languages (Electronic computers); Algorithms; Logic,
                 Symbolic and mathematical; Algorithms; Computer
                 networks; Computer programming; Computer science;
                 Logic, Symbolic and mathematical; Programming languages
                 (Electronic computers); Software engineering;
                 Computers; Programming; General; Programming Languages;
                 Algorithms; Mathematics; Logic; Hardware; Network
                 Hardware; software development; Programming and
                 scripting languages: general; Algorithms and data
                 structures; Mathematical theory of computation; Network
                 hardware; Software Development and Engineering;
                 Software Engineering",
  tableofcontents = "Intro \\
                 Preface \\
                 Organization \\
                 Invited Talks \\
                 Can Java Ever Be Safe? The hiJaC Project Abstract \\
                 Specification and Analysis of SoC Flows (Abstract) \\
                 Algorithmic Analysis for Asynchronous Programs \\
                 Contents \\
                 Domain-Specific Languages with Scala \\
                 1 Introduction \\
                 2 External DSLs \\
                 2.1 The Parser Library Approach \\
                 2.2 The Parser Tool Approach \\
                 3 Internal DSLs \\
                 3.1 Annotations \\
                 3.2 Shallow Embedding \\
                 3.3 Deep Embedding \\
                 4 Discussion \\
                 5 Conclusions \\
                 References \\
                 Formal Verification of Programs Computing the
                 Floating-Point Average \\
                 1 Introduction \\
                 2 Basics About Floating-Point Arithmetic \\
                 3 Methodology and Desired Specification \\
                 3.1 Methodology \\
                 3.2 Desired Specification \\
                 4 Formal Proof of the Algorithms \\
                 4.1 The average1 Function \\
                 4.2 The average3 Function \\
                 4.3 The average2 Function \\
                 4.4 Putting All Parts Together: The Average Functions
                 \\
                 5 Specifications and Formal Verification of the
                 Programs \\
                 5.1 Absolute Value \\
                 5.2 Accurate Average \\
                 5.3 Correct Average \\
                 6 Conclusion and Perspectives \\
                 References \\
                 Formalization and Verification of Declarative Cloud
                 Orchestration \\
                 1 Introduction \\
                 2 TOSCA: Topology and Orchestration Specification for
                 Cloud Application \\
                 3 Model of Automation of Topologies \\
                 4 CafeOBJ Specification of Model \\
                 5 Verification of Setup Operation \\
                 5.1 Proof Score for Condition (1) \\
                 5.2 Cyclic Dependency \\
                 5.3 Proof Score for Condition (2) \\
                 5.4 Proof Scores for Condition (3), (4), (5) and (6)
                 \\
                 6 Related Work and Conclusion \\
                 References \\
                 Consistency Verification of Specification Rules \\
                 1 Introduction \\
                 2 Background \\
                 2.1 Constraints Satisfiability \\
                 2.2 Rules Consistency \\
                 3 Relationship Between MISes and MUSes \\
                 4 An Efficient Algorithm for Enumerating MUSes \\
                 4.1 The MARCO algorithm \\
                 4.2 The MUSesHunter Algorithm \\
                 4.3 Comparing MARCO and MUSesHunter \\
                 5 Empirical Analysis \\
                 5.1 MUSesHunter vs. MARCO \\
                 5.2 MISes Finder \\
                 6 Conclusion \\
                 References \\
                 Applying Automata Learning to Embedded Control Software
                 \\
                 1 Introduction \\
                 2 Engine Status Manager \\
                 2.1 ESRA \\
                 2.2 ESM and Connected Components \\
                 2.3 Rational Rose RealTime \\
                 2.4 The ESM State Diagram \\
                 3 Learning the ESM \\
                 3.1 Experimental Set-Up \\
                 3.2 Test Selection Strategies \\
                 3.3 Results \\
                 4 Verification \\
                 4.1 Approach \\
                 4.2 Model Transformations \\
                 4.3 Results \\
                 5 Conclusions and Future Work \\
                 References \\
                 A 3-Valued Contraction Model Checking Game: Deciding on
                 the World of Partial Information \\
                 1 Introduction \\
                 2 Computation Tree Logic and Kripke Structures \\
                 2.1 Kripke Modal Transition System \\
                 2.2 KMTS as a Set of Kripke Structures \\
                 3 Semantics of CTL with Respect to KMTS \\
                 4 KMTS Operations \\
                 4.1 Dealing with Sets of KMTSs \\
                 4.2 Tree Partition Set \\
                 5 The Contraction Model Checking \\
                 6 Conclusions \\
                 References \\
                 Supporting Requirements Analysis Using Pattern-Based
                 Formal Specification Construction \\
                 1 Introduction \\
                 2 Major Ideas of PBFSRA \\
                 2.1 Principle of PBFSRA \\
                 2.2 Procedure of Applying PBFSRA",
}

@Book{Higham:2015:PCA,
  editor =       "Nicholas J. Higham and Mark R. Dennis and Paul
                 Glendinning and Paul A. Martin and Fadil Santosa and
                 Jared Tanner",
  booktitle =    "The {Princeton} Companion to Applied Mathematics",
  title =        "The {Princeton} Companion to Applied Mathematics",
  publisher =    pub-PRINCETON,
  address =      pub-PRINCETON:adr,
  pages =        "994 (est.)",
  year =         "2015",
  ISBN =         "0-691-15039-7 (hardcover)",
  ISBN-13 =      "978-0-691-15039-0 (hardcover)",
  LCCN =         "QA155 .P75 2015",
  bibdate =      "Wed Sep 9 05:32:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "Algebra; Mathematics; Mathematical models",
  tableofcontents = "Preface / ix \\
                 Contributors / xiii \\
                 Part I: Introduction to Applied Mathematics \\
                 I.1 What Is Applied Mathematics? / 1 \\
                 I.2 The Language of Applied Mathematics / 8 \\
                 I.3 Methods of Solution / 27 \\
                 I.4 Algorithms / 40 \\
                 I.5 Goals of Applied Mathematical Research / 48 \\
                 I.6 The History of Applied Mathematics / 55 \\
                 Part II: Concepts \\
                 II.1 Asymptotics / 81 \\
                 II.2 Boundary Layer / 82 \\
                 II.3 Chaos and Ergodicity / 82 \\
                 II.4 Complex Systems / 83 \\
                 II.5 Conformal Mapping / 84 \\
                 II.6 Conservation Laws / 86 \\
                 II.7 Control / 88 \\
                 II.8 Convexity / 89 \\
                 II.9 Dimensional Analysis and Scaling / 90 \\
                 II.10 The Fast Fourier Transform / 94 \\
                 II.11 Finite Differences / 95 \\
                 II.12 The Finite-Element Method / 96 \\
                 II.13 Floating-Point Arithmetic / 96 \\
                 II.14 Functions of Matrices / 97 \\
                 II.15 Function Spaces / 99 \\
                 II.16 Graph Theory / 101 \\
                 II.17 Homogenization / 103 \\
                 II.18 Hybrid Systems / 103 \\
                 II.19 Integral Transforms and Convolution / 104 \\
                 II.20 Interval Analysis / 105 \\
                 II.21 Invariants and Conservation Laws / 106 \\
                 II.22 The Jordan Canonical Form / 112 \\
                 II.23 Krylov Subspaces / 113 \\
                 II.24 The Level Set Method / 114 \\
                 II.25 Markov Chains / 116 \\
                 II.26 Model Reduction / 117 \\
                 II.27 Multiscale Modeling / 119 \\
                 II.28 Nonlinear Equations and Newton's Method / 120 \\
                 II.29 Orthogonal Polynomials / 122 \\
                 II.30 Shocks / 122 \\
                 II.31 Singularities / 124 \\
                 II.32 The Singular Value Decomposition / 126 \\
                 II.33 Tensors and Manifolds / 127 \\
                 II.34 Uncertainty Quantification / 131 \\
                 II.35 Variational Principle / 134 \\
                 II.36 Wave Phenomena / 134 \\
                 Part III: Equations, Laws, and Functions of Applied
                 Mathematics \\
                 III.1 Benford's Law / 135 \\
                 III.2 Bessel Functions / 137 \\
                 III.3 The Black--Scholes Equation / 137 \\
                 III.4 The Burgers Equation / 138 \\
                 III.5 The Cahn--Hilliard Equation / 138 \\
                 III.6 The Cauchy--Riemann Equations / 139 \\
                 III.7 The Delta Function and Generalized Functions /
                 139 \\
                 III.8 The Diffusion Equation / 142 \\
                 III.9 The Dirac Equation / 142 \\
                 III.10 Einstein's Field Equations / 144 \\
                 III.11 The Euler Equations / 146 \\
                 III.12 The Euler--Lagrange Equations / 147 \\
                 III.13 The Gamma Function / 148 \\
                 III.14 The Ginzburg--Landau Equation / 148 \\
                 III.15 Hooke's Law / 149 \\
                 III.16 The Korteweg--de Vries Equation / 150 \\
                 III.17 The Lambert $W$ Function / 151 \\
                 III.18 Laplace's Equation / 155 \\
                 III.19 The Logistic Equation / 156 \\
                 III.20 The Lorenz Equations / 158 \\
                 III.21 Mathieu Functions / 159 \\
                 III.22 Maxwell's Equations / 160 \\
                 III.23 The Navier--Stokes Equations / 162 \\
                 III.24 The Painlev{\'e} Equations / 163 \\
                 III.25 The Riccati Equation / 165 \\
                 III.26 Schr{\"o}dinger's Equation / 167 \\
                 III.27 The Shallow-Water Equations / 167 \\
                 III.28 The Sylvester and Lyapunov Equations / 168 \\
                 III.29 The Thin-Film Equation / 169 \\
                 III.30 The Tricomi Equation / 170 \\
                 III.31 The Wave Equation / 171 \\
                 Part IV: Areas of Applied Mathematics \\
                 IV.1 Complex Analysis / 173 \\
                 IV.2 Ordinary Differential Equations / 181 \\
                 IV.3 Partial Differential Equations / 190 \\
                 IV.4 Integral Equations / 200 \\
                 IV.5 Perturbation Theory and Asymptotics / 208 \\
                 IV.6 Calculus of Variations / 218 \\
                 IV.7 Special Functions / 227 \\
                 IV.8 Spectral Theory / 236 \\
                 IV.9 Approximation Theory / 248 \\
                 IV.10 Numerical Linear Algebra and Matrix Analysis /
                 263 \\
                 IV.11 Continuous Optimization (Nonlinear and Linear
                 Programming) / 281 \\
                 IV.12 Numerical Solution of Ordinary Differential
                 Equations / 293 \\
                 IV.13 Numerical Solution of Partial Differential
                 Equations / 306 \\
                 IV.14 Applications of Stochastic Analysis / 319 \\
                 IV.15 Inverse Problems / 327 \\
                 IV.16 Computational Science / 335 \\
                 IV.17 Data Mining and Analysis / 350 \\
                 IV.18 Network Analysis / 360 \\
                 IV.19 Classical Mechanics / 374 \\
                 IV.20 Dynamical Systems / 383 \\
                 IV.21 Bifurcation Theory / 393 \\
                 IV.22 Symmetry in Applied Mathematics / 402 \\
                 IV.23 Quantum Mechanics / 411 \\
                 IV.24 Random-Matrix Theory / 419 \\
                 IV.25 Kinetic Theory / 428 \\
                 IV.26 Continuum Mechanics / 446 \\
                 IV.27 Pattern Formation / 458 \\
                 IV.28 Fluid Dynamics / 467 \\
                 IV.29 Magnetohydrodynamics / 476 \\
                 IV.30 Earth System Dynamics / 485 \\
                 IV.31 Effective Medium Theories / 500 \\
                 IV.32 Mechanics of Solids / 505 \\
                 IV.33 Soft Matter / 516 \\
                 IV.34 Control Theory / 523 \\
                 IV.35 Signal Processing / 533 \\
                 IV.36 Information Theory / 545 \\
                 IV.37 Applied Combinatorics and Graph Theory / 552 \\
                 IV.38 Combinatorial Optimization / 564 \\
                 IV.39 Algebraic Geometry / 570 \\
                 IV.40 General Relativity and Cosmology / 579 \\
                 Part V: Modeling \\
                 V.1 The Mathematics of Adaptation (Or the Ten Avatars
                 of Vishnu) / 591 \\
                 V.2 Sport / 598 \\
                 V.3 Inerters / 604 \\
                 V.4 Mathematical Biomechanics / 609 \\
                 V.5 Mathematical Physiology / 616 \\
                 V.6 Cardiac Modeling / 623 \\
                 V.7 Chemical Reactions / 627 \\
                 V.8 Divergent Series: Taming the Tails / 634 \\
                 V.9 Financial Mathematics / 640 \\
                 V.10 Portfolio Theory / 648 \\
                 V.11 Bayesian Inference in Applied Mathematics / 658
                 \\
                 V.12 A Symmetric Framework with Many Applications / 661
                 \\
                 V.13 Granular Flows / 665 \\
                 V.14 Modern Optics / 673 \\
                 V.15 Numerical Relativity / 680 \\
                 V.16 The Spread of Infectious Diseases / 687 \\
                 V.17 The Mathematics of Sea Ice / 694 \\
                 V.18 Numerical Weather Prediction / 705 \\
                 V.19 Tsunami Modeling / 712 \\
                 V.20 Shock Waves / 720 \\
                 V.21 Turbulence / 724 \\
                 Part VI: Example Problems \\
                 VI.1 Cloaking / 733 \\
                 VI.2 Bubbles / 735 \\
                 VI.3 Foams / 737 \\
                 VI.4 Inverted Pendulums / 741 \\
                 VI.5 Insect Flight / 743 \\
                 VI.6 The Flight of a Golf Ball / 746 \\
                 VI.7 Automatic Differentiation / 749 \\
                 VI.8 Knotting and Linking of Macromolecules / 752 \\
                 VI.9 Ranking Web Pages / 755 \\
                 VI.10 Searching a Graph / 757 \\
                 VI.11 Evaluating Elementary Functions / 759 \\
                 VI.12 Random Number Generation / 761 \\
                 VI.13 Optimal Sensor Location in the Control of
                 Energy-Efficient Buildings / 763 \\
                 VI.14 Robotics / 767 \\
                 VI.15 Slipping, Sliding, Rattling, and Impact:
                 Nonsmooth Dynamics and Its Applications / 769 \\
                 VI.16 From the $N$-Body Problem to Astronomy and Dark
                 Matter / 771 \\
                 VI.17 The $N$-Body Problem and the Fast Multipole
                 Method / 775 \\
                 VI.18 The Traveling Salesman Problem / 778 \\
                 Part VII: Application Areas \\
                 VII.1 Aircraft Noise / 783 \\
                 VII.2 A Hybrid Symbolic--Numeric Approach to Geometry
                 Processing and Modeling / 787 \\
                 VII.3 Computer-Aided Proofs via Interval Analysis / 790
                 \\
                 VII.4 Applications of Max-Plus Algebra / 795 \\
                 VII.5 Evolving Social Networks, Attitudes, and Beliefs
                 --- and Counterterrorism / 800 \\
                 VII.6 Chip Design / 804 \\
                 VII.7 Color Spaces and Digital Imaging / 808 \\
                 VII.8 Mathematical Image Processing / 813 \\
                 VII.9 Medical Imaging / 816 \\
                 VII.10 Compressed Sensing / 823 \\
                 VII.11 Programming Languages: An Applied Mathematics
                 View / 828 \\
                 VII.12 High-Performance Computing / 839 \\
                 VII.13 Visualization / 843 \\
                 VII.14 Electronic Structure Calculations (Solid State
                 Physics) / 847 \\
                 VII.15 Flame Propagation / 852 \\
                 VII.16 Imaging the Earth Using Green's Theorem / 857
                 \\
                 VII.17 Radar Imaging / 860 \\
                 VII.18 Modeling a Pregnancy Testing Kit / 864 \\
                 VII.19 Airport Baggage Screening with X-Ray Tomography
                 / 866 \\
                 VII.20 Mathematical Economics / 868 \\
                 VII.21 Mathematical Neuroscience / 873 \\
                 VII.22 Systems Biology / 879 \\
                 VII.23 Communication Networks / 883 \\
                 VII.24 Text Mining / 887 \\
                 VII.25 Voting Systems / 891 \\
                 Part VIII: Final Perspectives \\
                 VIII.1 Mathematical Writing / 897 \\
                 VIII.2 How to Read and Understand a Paper / 903 \\
                 VIII.3 How to Write a General Interest Mathematics Book
                 / 906 \\
                 VIII.4 Workflow / 912 \\
                 VIII.5 Reproducible Research in the Mathematical
                 Sciences / 916 \\
                 VIII.6 Experimental Applied Mathematics / 925 \\
                 VIII.7 Teaching Applied Mathematics / 933 \\
                 VIII.8 Mediated Mathematics: Representations of
                 Mathematics in Popular Culture and Why These Matter /
                 943 \\
                 VIII.9 Mathematics and Policy / 953 \\
                 Index / 963",
}

@Proceedings{IEEE:2015:ISS,
  editor =       "{IEEE}",
  booktitle =    "{2015 IEEE Symposium on Security and Privacy (SP 2015)
                 San Jose, California, USA, 18--20 May 2015}",
  title =        "{2015 IEEE Symposium on Security and Privacy (SP 2015)
                 San Jose, California, USA, 18--20 May 2015}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xix + 952",
  year =         "2015",
  ISBN =         "1-4673-6949-7 (print), 1-4673-6950-0 (e-book)",
  ISBN-13 =      "978-1-4673-6949-7, 978-1-4673-6950-3 (e-book)",
  ISSN =         "1081-6011 (print), 2375-1207 (electronic)",
  ISSN-L =       "1081-6011",
  LCCN =         "QA76.9.A25",
  bibdate =      "Mon Feb 10 08:59:08 MST 2020",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.gbv.de/dms/tib-ub-hannover/836112652.pdf",
  acknowledgement = ack-nhfb,
}

@Proceedings{Muller:2015:ISC,
  editor =       "Jean-Michel Muller and Arnaud Tisserand and Julio
                 Villalba",
  booktitle =    "{2015 IEEE 22nd Symposium on Computer Arithmetic
                 (ARITH 2015) Lyon, France, 22--24 June 2015}",
  title =        "{2015 IEEE 22nd Symposium on Computer Arithmetic
                 (ARITH 2015) Lyon, France, 22--24 June 2015}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 176",
  year =         "2015",
  ISBN =         "1-4799-8665-8, 1-4799-8663-1",
  ISBN-13 =      "978-1-4799-8665-1, 978-1-4799-8663-7",
  ISSN =         "1063-6889",
  LCCN =         "QA76.9.C62 S95 2015",
  bibdate =      "Sat Aug 01 08:03:11 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=7193754",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-22; computer arithmetic units; correctness
                 proofs; cryptography; domain specific designs; error
                 analysis; exascale computing; floating point
                 arithmetic; floating-point error analysis; formal
                 verification; function approximation; modular
                 arithmetic; theorem proving; verification",
}

@Book{Swartzlander:2015:CAa,
  editor =       "Earl E. {Swartzlander, Jr.}",
  booktitle =    "Computer Arithmetic",
  title =        "Computer Arithmetic",
  volume =       "1",
  publisher =    pub-WORLD-SCI,
  address =      pub-WORLD-SCI:adr,
  pages =        "????",
  year =         "2015",
  DOI =          "https://doi.org/10.1142/9476",
  ISBN =         "981-4651-56-7 (vol. 1; hardcover), 981-4651-57-5,
                 981-4641-47-2 (e-book)",
  ISBN-13 =      "978-981-4651-56-1 (vol. 1; hardcover),
                 978-981-4651-57-8, 978-981-4641-47-0 (e-book)",
  LCCN =         "QA76.6 .C633 2015 vol. 1",
  bibdate =      "Tue Aug 7 07:57:49 MDT 2018",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/h/hamming-richard-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This is the new edition of the classic book
                 \booktitle{Computer Arithmetic} in three volumes
                 published originally in 1990 by IEEE Computer Society
                 Press. As in the original, the book contains many
                 classic papers treating advanced concepts in computer
                 arithmetic, which is very suitable as stand-alone
                 textbooks or complementary materials to textbooks on
                 computer arithmetic for graduate students and research
                 professionals interested in the field. Told in the
                 words of the initial developers, this book conveys the
                 excitement of the creators, and the implementations
                 provide insight into the details necessary to realize
                 real chips. This second volume presents topics on error
                 tolerant arithmetic, digit on-line arithmetic, number
                 systems, and now in this new edition, a topic on
                 implementations of arithmetic operations, all wrapped
                 with an updated overview and a new introduction for
                 each chapter.",
  acknowledgement = ack-nhfb,
}

@Book{Swartzlander:2015:CAb,
  editor =       "Earl E. {Swartzlander, Jr.}",
  booktitle =    "Computer Arithmetic",
  title =        "Computer Arithmetic",
  volume =       "2",
  publisher =    pub-WORLD-SCI,
  address =      pub-WORLD-SCI:adr,
  pages =        "xxxviii + 446",
  year =         "2015",
  DOI =          "https://doi.org/10.1142/9422;
                 https://doi.org/10.1142/9789814641470",
  ISBN =         "981-4641-46-4 (hardcover), 981-4641-47-2 (e-book)",
  ISBN-13 =      "978-981-4641-46-3 (hardcover), 978-981-4641-47-0
                 (e-book)",
  LCCN =         "QA76.6 .C633 2015 vol. 2",
  bibdate =      "Tue Aug 7 07:57:49 MDT 2018",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/h/hamming-richard-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "This is the new edition of the classic book
                 \booktitle{Computer Arithmetic} in three volumes
                 published originally in 1990 by IEEE Computer Society
                 Press. As in the original, the book contains many
                 classic papers treating advanced concepts in computer
                 arithmetic, which is very suitable as stand-alone
                 textbooks or complementary materials to textbooks on
                 computer arithmetic for graduate students and research
                 professionals interested in the field. Told in the
                 words of the initial developers, this book conveys the
                 excitement of the creators, and the implementations
                 provide insight into the details necessary to realize
                 real chips. This second volume presents topics on error
                 tolerant arithmetic, digit on-line arithmetic, number
                 systems, and now in this new edition, a topic on
                 implementations of arithmetic operations, all wrapped
                 with an updated overview and a new introduction for
                 each chapter.",
  acknowledgement = ack-nhfb,
  tableofcontents = "About the Editor \\
                 Preface \\
                 Contents by Author \\
                 Overview of Computer Arithmetic \\
                 Part I: ERROR TOLERANT ARITHMETIC \\
                 Editors' Comments on Papers 1 Through 5 \\
                 Error Detecting and Error Correcting Codes \\
                 Generalized Parity Checking \\
                 Error-Checking Logic for Arithmetic-Type Operations of
                 a Processor \\
                 Arithmetic Algorithms for Error-Coded Operands \\
                 Error Detection and Correction for Addition and
                 Subtraction, Through Higher Radix Extensions of Hamming
                 Codes \\
                 Part II: ON-LINE ARITHMETIC \\
                 Editor's Comments on Papers 6 Through 13 \\
                 Signed-Digit Number Representations for Fast Parallel
                 Arithmetic \\
                 On-Line Arithmetic: A Design Methodology and
                 Applications in Digital Signal Processing \\
                 On-Line Algorithms for Division and Multiplication \\
                 Error Analysis of Certain Floating-Point On-Line
                 Algorithms \\
                 Improved Normalization Results for Digit On-Line
                 Arithmetic \\
                 Fully Digit On-Line Networks \\
                 On-Line Scheme for Computing Rotation Factors \\
                 On-the-Fly Conversion of Redundant into Conventional
                 Representations \\
                 Part III: VLSI ADDER IMPLEMENTATIONS \\
                 Editor's Comments on Papers 14 Through 18 \\
                 Time-Component Complexity of Two Approaches to
                 Multioperand Binary Addition \\
                 Some Optimal Schemes for ALU Implementation in VLSI
                 Technology \\
                 An Area-Time Efficient NMOS Adder \\
                 Regular, Area-Time Efficient Carry-Lookahead Adders \\
                 Efficient Use of Time and Hardware Redundancy for
                 Concurrent Error Detection in a 32-bit VLSI Adder \\
                 Part IV: VLSI MULTIPLIER IMPLEMENTATIONS \\
                 Editor's Comments on Papers 19 Through 24 \\
                 A Monolithic $16 \times 16$ Digital Multiplier \\
                 Optimization of One-Bit Full Adders Embedded in Regular
                 Structures \\
                 A VLSI Layout for a Pipelined Dadda Multiplier \\
                 A Very Fast Multiplication Algorithm for VLSI
                 Implementation \\
                 A High-Speed Multiplier Using a Redundant Binary Adder
                 Tree \\
                 A Sub-10-ns $16 \times 16$ Multiplier Using 0.6-m CMOS
                 Technology \\
                 Part V: FLOATING-POINT VLSI CHIPS \\
                 Editor's Comments on Papers 25 Through 30 \\
                 A High Performance Floating Point Coprocessor \\
                 64 Bit Monolithic Floating Point Processors \\
                 A CMOS Floating Point Multiplier \\
                 A Single-Chip 80-Bit Floating Point Processor \\
                 VLSI Floating-Point Processors \\
                 Fast Multiply and Divide for a VLSI Floating-Point Unit
                 \\
                 Part VI: NUMBER REPRESENTATION \\
                 Editor's Comments on Papers 31 Through 37 \\
                 The Residue Number System \\
                 A Formalization of Floating-Point Numeric Base
                 Conversion \\
                 CADAC: A Controlled-Precision Decimal Arithmetic Unit
                 \\
                 Finite Precision Rational Arithmetic: Slash Number
                 Systems \\
                 Finite Precision Lexicographic Continued Fraction
                 Number Systems \\
                 An Overflow/Underflow-Free Floating-Point
                 Representation of Numbers \\
                 A Closed Computer Arithmetic \\
                 Part VII: IMPLEMENTATIONS \\
                 Editor's Comments on Papers 38 Through 40 \\
                 Applications of Distributed Arithmetic to Digital
                 Signal Processing: A Tutorial Review \\
                 Designing Low-Power Circuits: Practical Recipes \\
                 The European Logarithmic Microprocessor \\
                 Bibliography",
}

@Book{Swartzlander:2015:CAc,
  editor =       "Earl E. {Swartzlander, Jr.}",
  booktitle =    "Computer Arithmetic",
  title =        "Computer Arithmetic",
  volume =       "3",
  publisher =    pub-WORLD-SCI,
  address =      pub-WORLD-SCI:adr,
  pages =        "xvii + 451",
  year =         "2015",
  DOI =          "https://doi.org/10.1142/9467",
  ISBN =         "981-4651-13-3 (hardcover), 981-4641-47-2 (e-book)",
  ISBN-13 =      "978-981-4651-13-4 (hardcover), 978-981-4641-47-0
                 (e-book)",
  LCCN =         "QA76.6 .C633 2015 vol. 3",
  bibdate =      "Tue Aug 7 07:57:49 MDT 2018",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/h/hamming-richard-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "\booktitle{Computer Arithmetic}, Volume III, is a
                 compilation of key papers in computer arithmetic on
                 floating-point arithmetic and design. The intent is to
                 show progress, evolution, and novelty in the area of
                 floating-point arithmetic. This field has made
                 extraordinary progress since the initial software
                 routines on mainframe computers have evolved into
                 hardware implementations in processors spanning a wide
                 range of performance. Nevertheless, these papers pave
                 the way to the understanding of modern day processors
                 design where computer arithmetic are supported by
                 floating-point units. The goal of Volume III is to
                 collect the defining document for floating-point
                 arithmetic and many of the key papers on the
                 implementation of both binary and decimal
                 floating-point arithmetic into a single volume.
                 Although fewer than forty papers are included, their
                 reference lists will direct the interested reader to
                 other excellent work that could not be included here.
                 Volume III is specifically oriented to the needs of
                 designers and users of both general-purpose computers
                 and special-purpose digital processors. The book should
                 also be useful to systems engineers, computer
                 architects, and logic designers. It is also intended to
                 serve as a primary text for a course on floating-point
                 arithmetic, as well as a supplementary text for courses
                 in digital arithmetic and high-speed signal
                 processing.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Part I. Overview \\
                 1. IEEE standard for floating-point arithmetic \\
                 Part II. Floating-point addition \\
                 2. Delay-optimized implementation of IEEE
                 floating-point addition / P. M. Seidel and G. Even \\
                 3. Using the reverse-carry approach for double datapath
                 floating-point addition / J. D. Bruguera and T. Lang
                 \\
                 4. Reduced latency IEEE floating-point standard adder
                 architectures / A. Beaumont-Smith [et al.] \\
                 5. Leading-zero anticipatory logic for high-speed
                 floating-point addition / H. Suzuki [et al.] \\
                 6. Leading zero anticipation and detection - A
                 comparison of methods / M. Schmookler and K. Nowka \\
                 7. S/370 sign-magnitude floating-point adder / S.
                 Vassiliadis, D. S. Lemon and M. Putrino \\
                 Part III. Floating-point multiplication \\
                 8. A quadruple precision and dual double precision
                 floating-point multiplier / A. Akkas and M. J. Schulte
                 \\
                 9. A dual mode IEEE multiplier / G. Even, S. M. Mueller
                 and P. M. Seidel \\
                 10. 167 MHz radix-4 floating-point multiplier / R. K.
                 Yu and G. B. Zyner \\
                 Part IV. Rounding \\
                 11. Rounding algorithms for IEEE multipliers / M. R.
                 Santoro, G. Bewick and M. A. Horowitz \\
                 12. ``Systematic IEEE rounding method for high-speed
                 floating-point multipliers / N. T. Quach, N. Takagi,
                 and M. J. Flynn \\
                 13. A comparison of three rounding algorithms for IEEE
                 floating-point multiplication / G. Even and P. M.
                 Seidel \\
                 14. Prenormalization rounding in IEEE floating-point
                 operations using a flagged prefix adder / N. Burgess
                 \\
                 Part V. Fused multiply add \\
                 15. Design of the IBM RISC system/6000 floating-point
                 execution unit / R. K. Montoye, E. Hokenek and S. L.
                 Runyon \\
                 16. A 17 x 69 bit multiply and add unit with redundant
                 binary feedback and single cycle latency / W. S. Briggs
                 and D. Matula \\
                 17. Comparison of single- and dual-pass multiply-add
                 fused floating-point units / R. Jessani and M. Putrino
                 \\
                 18. Floating-point fused multiply-add with reduced
                 latency / T. Lang and J. D. Bruguera \\
                 19. Floating-point fused multiply-add architectures /
                 E. Quinnell, E. E. Swartzlander, Jr. and C. Lemonds \\
                 Part VI. Floating-point division \\
                 20. Floating-point division and square root algorithms
                 and implementation in the AMD-K7 microprocessor / S. F.
                 Oberman \\
                 21. High performance floating-point unit with 116 bit
                 wide divider / G. Gerwig [et al.] \\
                 22. High-speed double-precision computation of
                 reciprocal, division, square root, and inverse square
                 root / J. A. Pineiro and J. D. Bruguera \\
                 23. 167 MHz radix-8 floating-point divide and square
                 root using overlapped radix-2 stages / J. Prabhu and G.
                 Zyner \\
                 24. Division algorithms and implementations / S. F.
                 Oberman and M. J. Flynn \\
                 25. Faithful interpolation in reciprocal tables / D.
                 Das Sarma and D. W. Matula \\
                 Part VII. Elementary functions \\
                 26. Computation of elementary functions on the IBM RISC
                 system/6000 processor / P. W. Markstein \\
                 27. Accurate and monotone approximations of some
                 transcendental functions / W. Ferguson and T. Brightman
                 \\
                 28. The K5 transcendental functions / T. Lynch [et al.]
                 \\
                 29. Hardware designs for exactly rounded elementary
                 functions / M. J. Schulte and E. E. Swartzlander, Jr.
                 \\
                 30. Toward correctly rounded transcendentals / V.
                 Lefevre, Jean-Michel Muller and A. Tisserand \\
                 31. Reciprocation, square root, inverse square root and
                 some elementary functions using small multipliers / M.
                 Ercegovac [et al.] \\
                 32. Multipartite table methods / F. Dinechin and A.
                 Tisserand \\
                 Part VIII. Decimal floating-point arithmetic \\
                 33. A decimal floating-point specification / M. F.
                 Cowlishaw [et al.] \\
                 34. Decimal floating-point: Algorism for computers / M.
                 F. Cowlishaw \\
                 35. A software implementation of the IEEE 754R decimal
                 floating-point arithmetic using the binary encoded
                 format / M. Cornea [et al.] \\
                 36. Decimal floating-point multiplication, / M. A.
                 Erle, B. J. Hickmann and M. J. Schulte \\
                 37. A survey of hardware designs for decimal arithmetic
                 / L.-K. Wang [et al.]",
}

@Proceedings{Montuschi:2016:ISC,
  editor =       "Paolo Montuschi and Michael Schulte and Javier Hormigo
                 and Stuart Oberman and Nathalie Revol",
  booktitle =    "{2016 IEEE 23nd Symposium on Computer Arithmetic
                 (ARITH 2016), Santa Clara, California, USA, 10--13 July
                 2016}",
  title =        "{2016 IEEE 23nd Symposium on Computer Arithmetic
                 (ARITH 2016), Santa Clara, California, USA, 10--13 July
                 2016}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xxi + 182",
  year =         "2016",
  ISBN =         "1-5090-1615-5",
  ISBN-13 =      "978-1-5090-1615-0",
  ISSN =         "1063-6889",
  LCCN =         "QA76.9.C62 S95 2016",
  bibdate =      "Fri Dec 16 15:16:45 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=7562813",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-23; ARITH 2016; computer arithmetic units;
                 correctness proofs; cryptography; domain specific
                 designs; error analysis; exascale computing; floating
                 point arithmetic; floating-point error analysis; formal
                 verification; function approximation; modular
                 arithmetic; theorem proving; verification",
}

@Proceedings{Burgess:2017:ISC,
  editor =       "Neil Burgess and Javier Bruguera and Florent de
                 Dinechin",
  booktitle =    "{24th IEEE Symposium on Computer Arithmetic (ARITH
                 24), London, UK, 24--26 July 2017}",
  title =        "{2017 IEEE 24th Symposium on Computer Arithmetic
                 (ARITH 24), London, UK, 24--26 July 2017}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 198",
  year =         "2017",
  ISBN =         "1-5386-1966-0 (print), 1-5386-1965-2, 1-5386-1964-4",
  ISBN-13 =      "978-1-5386-1966-7 (print), 978-1-5386-1965-0,
                 978-1-5386-1964-3",
  ISSN =         "1063-6889",
  LCCN =         "QA76.9.C62 S95 2017",
  bibdate =      "Fri Nov 17 10:14:11 2017",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/gnu.bib",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=8019911",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2017; ARITH-24; computer arithmetic units;
                 correctness proofs; cryptography; domain specific
                 designs; error analysis; exascale computing; floating
                 point arithmetic; floating-point error analysis; formal
                 verification; function approximation; modular
                 arithmetic; theorem proving; verification",
}

@Proceedings{Desprez:2017:EPP,
  editor =       "Fr{\'e}d{\'e}ric Desprez and Pierre-Fran{\c{c}}ois
                 Dutot and Christos Kaklamanis and Loris Marchal and
                 Korbinian Molitorisz and Laura Ricci and Vittorio
                 Scarano and Miguel A. Vega-Rodr{\'i}guez and Ana Lucia
                 Varbanescu and Sascha Hunold",
  booktitle =    "{Euro-Par 2016: Euro-Par 2016 International Workshops,
                 Grenoble, France, August 24--26, 2016, Revised Selected
                 Papers}",
  title =        "{Euro-Par 2016: Euro-Par 2016 International Workshops,
                 Grenoble, France, August 24--26, 2016, Revised Selected
                 Papers}",
  volume =       "10104",
  publisher =    "Springer",
  address =      "Cham, Switzerland",
  pages =        "xxxix + 829",
  year =         "2017",
  DOI =          "https://doi.org/10.1007/978-3-319-58943-5",
  ISBN =         "3-319-58943-1 (e-book), 3-319-58943-1 (hardcover)",
  ISBN-13 =      "978-3-319-58943-5 (e-book), 978-3-319-58943-5
                 (hardcover)",
  LCCN =         "QA76.9.E94; QA76.758TK",
  bibdate =      "Mon Feb 10 06:29:59 MST 2020",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-LNCS,
  abstract =     "This book constitutes the proceedings of the workshops
                 of the 23rd International Conference on Parallel and
                 Distributed Computing, Euro-Par 2016, held in Grenoble,
                 France in August 2016. The 65 full papers presented
                 were carefully reviewed and selected from 95
                 submissions. The volume includes the papers from the
                 following workshops: Euro-EDUPAR (Second European
                 Workshop on Parallel and Distributed Computing
                 Education for Undergraduate Students); HeteroPar 2016
                 (the 14th International Workshop on Algorithms, Models
                 and Tools for Parallel Computing on Heterogeneous
                 Platforms); IWMSE (5th International Workshop on
                 Multicore Software Engineering); LSDVE (Fourth Workshop
                 on Large-Scale Distributed Virtual Environments) -
                 PADABS (Fourth Workshop on Parallel and Distributed
                 Agent-Based Simulations); PBio (Fourth International
                 Workshop on Parallelism in Bioinformatics); PELGA
                 (Second Workshop on Performance Engineering for
                 Large-Scale Graph Analytics); REPPAR (Third
                 International Workshop on Reproducibility in Parallel
                 Computing); Resilience (9th Workshop in Resilience in
                 High Performance Computing in Clusters, Clouds, and
                 Grids); ROME (Fourth Workshop on Runtime and Operating
                 Systems for the Many-Core Era); UCHPC (9th Workshop on
                 UnConventional High-Performance Computing).",
  acknowledgement = ack-nhfb,
  meetingname =  "Euro-Par (2016 : Grenoble)",
  tableofcontents = "Parallel and distributed computing education for
                 undergraduate students.\\
                 Algorithms, models and tools for parallel computing on
                 heterogeneous platforms \\
                 Multicore software engineering \\
                 Large-scale distributed virtual environments \\
                 Parallel and distributed agent-based simulations \\
                 Parallelism in bioinformatics \\
                 Performance engineering for large-scale graph analytics
                 \\
                 Reproducibility in parallel computing \\
                 Resilience in high performance computing in clusters,
                 clouds, and grids \\
                 Runtime and operating systems for the many-core era \\
                 UnConventional high-performance computing",
}

@Proceedings{Matthews:2017:CRF,
  editor =       "Michael B. Matthews",
  booktitle =    "{Conference record of the Fifty-First Asilomar
                 Conference on Signals, Systems and Computers, October
                 29--November 1, 2017 Pacific Grove, California}",
  title =        "{Conference record of the Fifty-First Asilomar
                 Conference on Signals, Systems and Computers, October
                 29--November 1, 2017 Pacific Grove, California}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xxx + 2058",
  year =         "2017",
  ISBN =         "1-5386-1824-9 (print), 1-5386-0666-6, 1-5386-1823-0
                 (e-book)",
  ISBN-13 =      "978-1-5386-1824-0 (print), 978-1-5386-0666-7,
                 978-1-5386-1823-3 (e-book)",
  LCCN =         "TK7801",
  bibdate =      "Mon Feb 10 08:40:43 MST 2020",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=8330843",
  acknowledgement = ack-nhfb,
}

@Proceedings{ACM:2018:CNG,
  editor =       "{ACM}",
  booktitle =    "Conference for Next Generation Arithmetic ({Resorts
                 World Convention Centre, Singapore}): ({CoNGA '18})",
  title =        "Conference for Next Generation Arithmetic ({Resorts
                 World Convention Centre, Singapore}): ({CoNGA '18})",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "37",
  year =         "2018",
  bibdate =      "Sun Dec 10 14:24:09 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  remark =       "No ISBN seems to have been assigned.",
  tableofcontents = "1: A Matrix-Multiply Unit for Posits in
                 Reconfigurable Logic Using (OPEN)CAPI / Jianyu Chen,
                 Zaid Al-Ars \\
                 2: Provably Correct Posit Arithmetic with Fixed-Point
                 Big Integer / Shin Yee Chung \\
                 3: The Slide Number Format / Ignaz Kohlbecker \\
                 4: High-level .NET Software Implementations of Unum
                 Type I and Posit with Simultaneous FPGA Implementation
                 Using Hastlayer / Zolt{\'a}n Leh{\'o}czky, Andr{\'a}s
                 Retzler, Rich{\'a}rd T{\'o}th, {\'A}lmos Szab{\'o},
                 Benedek Farkas and Kriszti{\'a}n Somogyi \\
                 5: Universal Coding of the Reals: Alternatives to IEEE
                 Floating Point / Peter Lindstrom, Scott Lloyd and
                 Jeffrey Hittinger",
}

@Proceedings{Tenca:2018:PIS,
  editor =       "Alexandre Tenca and Naofumi Takagi",
  booktitle =    "Proceedings of the {25th International Symposium on
                 Computer Arithmetic, 25--27 June 2018 Amherst, MA,
                 USA}",
  title =        "Proceedings of the {25th International Symposium on
                 Computer Arithmetic, 25--27 June 2018 Amherst, MA,
                 USA}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "17 + 152",
  month =        jun,
  year =         "2018",
  DOI =          "https://doi.org/10.1109/ARITH.2018.8464697",
  ISBN =         "1-5386-2612-8 (USB), 1-5386-2665-9",
  ISBN-13 =      "978-1-5386-2612-2 (USB), 978-1-5386-2613-9,
                 978-1-5386-2665-8",
  ISSN =         "2576-2265",
  LCCN =         "QA76.9.C62",
  bibdate =      "Fri Jan 31 08:05:31 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE catalog number CFP18121-USB.",
  abstract =     "Presents the title page of the proceedings record.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2018; ARITH-25",
  subject =      "ARITH-25; Computer arithmetic; Congresses; Computer
                 programming; Floating-point arithmetic; Computer
                 arithmetic and logic units",
}

@Proceedings{Gustafson:2019:CPC,
  editor =       "John Gustafson and Vassil Dimitrov",
  booktitle =    "{CoNGA'19: Proceedings of the Conference for Next
                 Generation Arithmetic 2019, Singapore, March 2019}",
  title =        "{CoNGA'19: Proceedings of the Conference for Next
                 Generation Arithmetic 2019, Singapore, March 2019}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "66",
  year =         "2019",
  ISBN =         "1-4503-7139-6",
  ISBN-13 =      "978-1-4503-7139-1",
  LCCN =         "????",
  bibdate =      "Mon Feb 10 12:06:51 MST 2020",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       "ICPS",
  acknowledgement = ack-nhfb,
  meetingname =  "Conference for Next Generation Arithmetic (2019 :
                 Singapore)",
  subject =      "Computer arithmetic; Congresses; Computer algorithms;
                 Computer algorithms.; Computer arithmetic.",
  tableofcontents = "Milan Kl{\"o}wer and Peter D. D{\"u}ben and Tim N.
                 Palmer / Posits as an Alternative to Floats for Weather
                 and Climate Models /
                 https://doi.org/10.1145/3316279.3316281 / 1:1--1:8 \\
                 Andrea Bocco and Yves Durand and Florent de Dinechin /
                 SMURF: Scalar Multiple-precision Unum RISC-V
                 Floating-point Accelerator for Scientific Computing /
                 https://doi.org/10.1145/3316279.3316280 / 1:1--1:8 \\
                 Zachariah Carmichael and Hamed F. Langroudi and Char
                 Khazanov and Jeffrey Lillie and John L. Gustafson and
                 Dhireesha Kudithipudi / Performance-Efficiency
                 Trade-off of Low-Precision Numerical Formats in Deep
                 Neural Networks /
                 https://doi.org/10.1145/3316279.3316282 / 3:1--3:9 \\
                 Bill Zorn and Dan Grossman and Zach Tatlock / Sinking
                 Point: Dynamic Precision Tracking for Floating-Point /
                 https://doi.org/10.1145/3316279.3316283 / 4:1--4:8 \\
                 Laurens van Dam and Johan Peltenburg and Zaid Al-Ars
                 and H. Peter Hofstee / An Accelerator for Posit
                 Arithmetic Targeting Posit Level 1 BLAS Routines and
                 Pair-HMM / https://doi.org/10.1145/3316279.3316284 /
                 5:1--5:10 \\
                 Florent de Dinechin and Luc Forget and Jean-Michel
                 Muller and Yohann Uguen / Posits: The Good, the Bad and
                 the Ugly / https://doi.org/10.1145/3316279.3316285 /
                 6:1--6:10 \\
                 Peter Lindstrom / Universal Coding of the Reals Using
                 Bisection / https://doi.org/10.1145/3316279.3316286 /
                 7:1--7:10",
}

@Proceedings{Takagi:2019:ISC,
  editor =       "Naofumi Takagi and Sylvie Boldo and Martin
                 Langhammer",
  booktitle =    "{2019 IEEE 26th Symposium on Computer Arithmetic
                 ARITH-26 (2019), Kyoto, Japan, 10--12 June 2019}",
  title =        "{2019 IEEE 26th Symposium on Computer Arithmetic
                 ARITH-26 (2019), Kyoto, Japan, 10--12 June 2019}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "15 + 220",
  month =        jun,
  year =         "2019",
  DOI =          "https://doi.org/10.1109/ARITH.2019.00001",
  ISBN =         "1-72813-366-1",
  ISBN-13 =      "978-1-72813-366-9",
  ISSN =         "1063-6889",
  ISSN-L =       "1063-6889",
  bibdate =      "Fri Jan 31 08:18:07 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Presents the title page of the proceedings record.",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2019; ARITH-26",
}

@Proceedings{Cornea:2020:ISC,
  editor =       "Marius Cornea and Weiqiang Liu and Arnaud Tisserand",
  booktitle =    "{2020 27th IEEE Symposium on Computer Arithmetic:
                 ARITH 2020: proceedings: Portland, Oregon, USA, 7--10
                 June 2020}",
  title =        "{2020 27th IEEE Symposium on Computer Arithmetic:
                 ARITH 2020: proceedings: Portland, Oregon, USA, 7--10
                 June 2020}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020",
  ISBN =         "1-72817-120-2, 1-72817-121-0",
  ISBN-13 =      "978-1-72817-120-3, 978-1-72817-121-0",
  LCCN =         "????",
  bibdate =      "Wed Jul 7 06:23:45 MDT 2021",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=9146973",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2020; ARITH-27",
}

@Proceedings{IEEE:2020:SPI,
  editor =       "{IEEE}",
  booktitle =    "{SC'20: Proceedings of the International Conference
                 for High Performance Computing, Networking, Storage and
                 Analysis (Atlanta, Georgia, November 9--19, 2020)}",
  title =        "{SC'20: Proceedings of the International Conference
                 for High Performance Computing, Networking, Storage and
                 Analysis (Atlanta, Georgia, November 9--19, 2020)}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2020",
  DOI =          "https://doi.org/10.1109/SC41405.2020",
  ISBN =         "1-72819-998-0, 1-72819-999-9 (printondemand)",
  ISBN-13 =      "978-1-72819-998-6, 978-1-72819-999-3 (printondemand)",
  LCCN =         "QA76.88",
  bibdate =      "Mon Sep 11 06:40:11 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/python.bib",
  acknowledgement = ack-nhfb,
}

@Proceedings{Krzhizhanovskaya:2020:CSI,
  editor =       "Valeria V. Krzhizhanovskaya and G{\'a}bor
                 Z{\'a}vodszky and Michael H. Lees and Jack J. Dongarra
                 and Peter M. A. Sloot and S{\'e}rgio Brissos and
                 Jo{\~a}o Teixeira",
  booktitle =    "{Computational Science --- ICCS 2020 20th
                 International Conference, Amsterdam, The Netherlands,
                 June 3--5, 2020, Proceedings, Part II}",
  title =        "{Computational Science --- ICCS 2020 20th
                 International Conference, Amsterdam, The Netherlands,
                 June 3--5, 2020, Proceedings, Part II}",
  volume =       "12138",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xix + 697",
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-50417-5",
  ISBN =         "3-030-50416-6, 3-030-50417-4 (e-book)",
  ISBN-13 =      "978-3-030-50416-8, 978-3-030-50417-5 (e-book)",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  bibdate =      "Thu Jun 25 08:21:10 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/julia.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  series =       ser-LNCS,
  URL =          "https://link.springer.com/book/10.1007/978-3-030-50417-5",
  acknowledgement = ack-nhfb,
  tableofcontents = "Front Matter / / i--xix \\
                 Modified Binary Tree in the Fast PIES for 2D Problems
                 with Complex Shapes / Andrzej Ku{\.z}elewski, Eugeniusz
                 Zieniuk, Agnieszka Bo{\l}tu{\'c}, Krzystof Szersze{\'n}
                 / 1--14 \\
                 Generating Random Floating--Point Numbers by Dividing
                 Integers: A Case Study / Fr{\'e}d{\'e}ric Goualard /
                 15--28 \\
                 An Effective Stable Numerical Method for Integrating
                 Highly Oscillating Functions with a Linear Phase /
                 Leonid A. Sevastianov, Konstantin P. Lovetskiy, Dmitry
                 S. Kulyabov / 29--43 \\
                 Fitting Penalized Logistic Regression Models Using QR
                 Factorization / Jacek Klimaszewski, Marcin Korze{\'n} /
                 44--57 \\
                 Uncertainty Quantification in Fractional Stochastic
                 Integro--Differential Equations Using Legendre Wavelet
                 Collocation Method / Abhishek Kumar Singh, Mani Mehra /
                 58--71 \\
                 A Direct High--Order Curvilinear Triangular Mesh
                 Generation Method Using an Advancing Front Technique /
                 Fariba Mohammadi, Shusil Dangi, Suzanne M. Shontz,
                 Cristian A. Linte / 72--85 \\
                 Data--Driven Partial Differential Equations Discovery
                 Approach for the Noised Multi--dimensional Data /
                 Mikhail Maslyaev, Alexander Hvatov, Anna Kalyuzhnaya /
                 86--100 \\
                 Preconditioning Jacobian Systems by Superimposing
                 Diagonal Blocks / M. Ali Rostami, H. Martin B{\"u}cker
                 / 101--115 \\
                 NURBS Curves in Parametric Integral Equations System
                 for Modeling and Solving Boundary Value Problems in
                 Elasticity / Marta Kapturczak, Eugeniusz Zieniuk,
                 Andrzej Ku{\.z}elewski / 116--123 \\
                 Parameterizations and Lagrange Cubics for Fitting
                 Multidimensional Data / Ryszard Kozera, Lyle Noakes,
                 Magdalena Wilko{\l}azka / 124--140 \\
                 Loop Aggregation for Approximate Scientific Computing /
                 June Sallou, Alexandre Gauvain, Johann Bourcier, Benoit
                 Combemale, Jean--Raynald de Dreuzy / 141--155 \\
                 Numerical Computation for a Flow Caused by a
                 High--Speed Traveling Train and a Stationary Overpass /
                 Shotaro Hamato, Masashi Yamakawa, Yongmann M. Chung,
                 Shinichi Asao / 156--169 \\
                 B{\'e}zier Surfaces for Modeling Inclusions in PIES /
                 Agnieszka Bo{\l}tu{\'c}, Eugeniusz Zieniuk, Krzysztof
                 Szersze{\'n}, Andrzej Ku{\.z}elewski / 170--183 \\
                 Impact of Water on Methane Adsorption in Nanopores: A
                 Hybrid GCMC--MD Simulation Study / Ji Zhou, Wenbin
                 Jiang, Mian Lin, Lili Ji, Gaohui Cao / 184--196 \\
                 A Stable Discontinuous Galerkin Based Isogeometric
                 Residual Minimization for the Stokes Problem / Marcin
                 {\L}o{\'s}, Sergio Rojas, Maciej Paszy{\'n}ski, Ignacio
                 Muga, Victor M. Calo / 197--211 \\
                 Numerical Modeling of the Two--Phase Flow of Water with
                 Ice in the Tom River / Vladislava Churuksaeva,
                 Alexander Starchenko / 212--224 \\
                 Remarks on Kaczmarz Algorithm for Solving Consistent
                 and Inconsistent System of Linear Equations / Xinyin
                 Huang, Gang Liu, Qiang Niu / 225--236 \\
                 Investigating the Benefit of FP16--Enabled
                 Mixed--Precision Solvers for Symmetric Positive
                 Definite Matrices Using GPUs / Ahmad Abdelfattah, Stan
                 Tomov, Jack Dongarra / 237--250 \\
                 Simulation Versus an Ordered Fuzzy--Numbers--Driven
                 Approach to the Multi--depot Vehicle Cyclic Routing and
                 Scheduling Problem / Grzegorz Bocewicz, Zbigniew
                 Banaszak, Czeslaw Smutnicki, Katarzyna Rudnik, Marcin
                 Witczak, Robert W{\'o}jcik / 251--266 \\
                 Epigenetic Modification of Genetic Algorithm / Kornel
                 Chrominski, Magdalena Tkacz, Mariusz Boryczka /
                 267--278 \\
                 ITP--KNN: Encrypted Video Flow Identification Based on
                 the Intermittent Traffic Pattern of Video and
                 $K$-Nearest Neighbors Classification / Youting Liu, Shu
                 Li, Chengwei Zhang, Chao Zheng, Yong Sun, Qingyun Liu /
                 279--293 \\
                 DeepAD: A Joint Embedding Approach for Anomaly
                 Detection on Attributed Networks / Dali Zhu, Yuchen Ma,
                 Yinlong Liu / 294--307 \\
                 SciNER: Extracting Named Entities from Scientific
                 Literature / Zhi Hong, Roselyne Tchoua, Kyle Chard, Ian
                 Foster / 308--321 \\
                 GPU--Embedding of kNN--Graph Representing Large and
                 High--Dimensional Data / Bartosz Minch, Mateusz Nowak,
                 Rafa{\l} Wcis{\l}o, Witold Dzwinel / 322--336 \\
                 Evolving Long Short--Term Memory Networks / Vicente
                 Coelho Lobo Neto, Leandro Aparecido Passos, Jo{\~a}o
                 Paulo Papa / 337--350 \\
                 Personality Recognition from Source Code Based on
                 Lexical, Syntactic and Semantic Features / Miko{\l}aj
                 Biel, Marcin Kuta, Jacek Kitowski / 351--363 \\
                 Data Fitting by Exponential Sums with Equal Weights /
                 Petr Chunaev, Ildar Safiullin / 364--371 \\
                 A Combination of Moment Descriptors, Fourier Transform
                 and Matching Measures for Action Recognition Based on
                 Shape / Katarzyna Go{\'s}ciewska, Dariusz Frejlichowski
                 / 372--386 \\
                 Improving Accuracy and Speeding Up Document Image
                 Classification Through Parallel Systems / Javier
                 Ferrando, Juan Luis Dom{\'\i}nguez, Jordi Torres,
                 Ra{\'u}l Garc{\'\i}a, David Garc{\'\i}a, Daniel Garrido
                 et al. / 387--400 \\
                 Computation of the Airborne Contaminant Transport in
                 Urban Area by the Artificial Neural Network / Anna
                 Wawrzynczak, Monika Berendt--Marchel / 401--413 \\
                 Exploring Musical Structure Using Tonnetz Lattice
                 Geometry and LSTMs / Manuchehr Aminian, Eric Kehoe,
                 Xiaofeng Ma, Amy Peterson, Michael Kirby / 414--424 \\
                 Modeling of Anti--tracking Network Based on
                 Convex--Polytope Topology / Changbo Tian, Yongzheng
                 Zhang, Tao Yin / 425--438 \\
                 A Workload Division Differential Privacy Algorithm to
                 Improve the Accuracy for Linear Computations / Jun Li,
                 Huan Ma, Guangjun Wu, Yanqin Zhang, Bingnan Ma, Zhen
                 Hui et al. / 439--452 \\
                 On the Automated Assessment of Open--Source Cyber
                 Threat Intelligence Sources / Andrea Tundis, Samuel
                 Ruppert, Max M{\"u}hlh{\"a}user / 453--467 \\
                 Malicious Domain Detection Based on K--means and SMOTE
                 / Qing Wang, Linyu Li, Bo Jiang, Zhigang Lu, Junrong
                 Liu, Shijie Jian / 468--481 \\
                 Microservice Disaster Crash Recovery: A Weak Global
                 Referential Integrity Management / Maude Manouvrier,
                 Cesare Pautasso, Marta Rukoz / 482--495 \\
                 Hashing Based Prediction for Large--Scale Kernel
                 Machine / Lijing Lu, Rong Yin, Yong Liu, Weiping Wang /
                 496--509 \\
                 Picking Peaches or Squeezing Lemons: Selecting
                 Crowdsourcing Workers for Reducing Cost of Redundancy /
                 Paulina Adamska, Marta Ju{\'z}win, Adam Wierzbicki /
                 510--523 \\
                 Are $n$-gram Categories Helpful in Text Classification?
                 / Jakub Kruczek, Paulina Kruczek, Marcin Kuta /
                 524--537 \\
                 Calculating Reactive Power Compensation for
                 Large--Scale Street Lighting / Sebastian Ernst, Leszek
                 Kotulski, Tomasz Lerch, Micha{\l} Rad, Adam
                 S{\k{e}}dziwy, Igor Wojnicki / 538--550 \\
                 Developing a Decision Support App for Computational
                 Agriculture / Andrew Lewis, Marcus Randall, Ben
                 Stewart--Koster / 551--561 \\
                 Optimal Location of Sensors for Early Detection of
                 Tsunami Waves / Angelie R. Ferrolino, Jose Ernie C.
                 Lope, Renier G. Mendoza / 562--575 \\
                 A Novel Formulation for Inverse Distance Weighting from
                 Weighted Linear Regression / Leonardo Ramos
                 Emmendorfer, Gra{\c{c}}aliz Pereira Dimuro / 576--589
                 \\
                 Addressing the Robustness of Resource Allocation in the
                 Presence of Application and System Irregularities via
                 PEPA Based Modeling / Srishti Srivastava, Ioana
                 Banicescu, William S. Sanders / 590--603 \\
                 An Adaptive Computational Network Model for Strange
                 Loops in Political Evolution in Society / Julia Anten,
                 Jordan Earle, Jan Treur / 604--617 \\
                 Joint Entity Linking for Web Tables with Hybrid
                 Semantic Matching / Jie Xie, Yuhai Lu, Cong Cao,
                 Zhenzhen Li, Yangyang Guan, Yanbing Liu / 618--631 \\
                 A New Coefficient of Rankings Similarity in
                 Decision--Making Problems / Wojciech Sa abun, Karol
                 Urbaniak / 632--645 \\
                 Innovativeness Analysis of Scholarly Publications by
                 Age Prediction Using Ordinal Regression / Pavel Savov,
                 Adam Jatowt, Radoslaw Nielek / 646--660 \\
                 Advantage of Using Spherical over Cartesian Coordinates
                 in the Chromosome Territories 3D Modeling / Magdalena
                 A. Tkacz, Kornel Chromi{\'n}ski / 661--673 \\
                 Adaptive and Efficient Transfer for Online Remote
                 Visualization of Critical Weather Applications / Preeti
                 Malakar, Vijay Natarajan, Sathish S. Vadhiyar /
                 674--693 \\
                 Back Matter / / 695--697",
}

@Proceedings{Wyrzykowski:2020:PPA,
  editor =       "Roman Wyrzykowski and Ewa Deelman and Jack Dongarra
                 and Konrad Karczewski",
  booktitle =    "Parallel Processing and Applied Mathematics: {13th
                 International Conference, PPAM 2019, Bialystok, Poland,
                 September 8--11, 2019, Revised Selected Papers, Part
                 I}",
  title =        "Parallel Processing and Applied Mathematics: {13th
                 International Conference, PPAM 2019, Bialystok, Poland,
                 September 8--11, 2019, Revised Selected Papers, Part
                 I}",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  year =         "2020",
  DOI =          "https://doi.org/10.1007/978-3-030-43229-4",
  ISBN =         "3-030-43229-7",
  ISBN-13 =      "978-3-030-43229-4",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Fri Dec 15 11:31:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
  tableofcontents = "Front Matter / i--xxiii \\
                 Numerical Algorithms and Parallel Scientific Computing
                 == Front Matter / 1--1 \\
                 Matthias Korch, Tim Werner / Multi-workgroup Tiling to
                 Improve the Locality of Explicit One-Step Methods for
                 ODE Systems with Limited Access Distance on GPUs /
                 3--12 \\
                 Davor Davidovi{\'c}, Enrique S. Quintana-Ort{\'\i} /
                 Structure-Aware Calculation of Many-Electron Wave
                 Function Overlaps on Multicore Processors / 13--24 \\
                 Charles D. Murray, Tobias Weinzierl / Lazy Stencil
                 Integration in Multigrid Algorithms / 25--37 \\
                 Filip Paw{\l}owski, Bora U{\c{c}}ar, Albert-Jan Yzelman
                 / High Performance Tensor Vector Multiplication on
                 Shared-Memory Systems / 38--48 \\
                 Pawe{\l} Augustynowicz, Andrzej Paszkiewicz / Efficient
                 Modular Squaring in Binary Fields on CPU Supporting AVX
                 and GPU / 49--57 \\
                 Carl Christian Kjelgaard Mikkelsen, Mirko Myllykoski /
                 Parallel Robust Computation of Generalized Eigenvectors
                 of Matrix Pencils / 58--69 \\
                 Mirko Myllykoski, Carl Christian Kjelgaard Mikkelsen /
                 Introduction to StarNEig A Task-Based Library for
                 Solving Nonsymmetric Eigenvalue Problems / 70--81 \\
                 Angelika Schwarz, Carl Christian Kjelgaard Mikkelsen /
                 Robust Task-Parallel Solution of the Triangular
                 Sylvester Equation / 82--92 \\
                 Beata Dmitruk, Przemys{\l}aw Stpiczy{\'n}ski /
                 Vectorized Parallel Solver for Tridiagonal Toeplitz
                 Systems of Linear Equations / 93--103 \\
                 Carola Kruse, Masha Sosonkina, Mario Arioli, Nicolas
                 Tardieu, Ulrich R{\"u}de / Parallel Performance of an
                 Iterative Solver Based on the Golub-Kahan
                 Bidiagonalization / 104--116 \\
                 Linus Seelinger, Anne Reinarz, Robert Scheichl / A
                 High-Performance Implementation of a Robust
                 Preconditioner for Heterogeneous Problems / 117--128
                 \\
                 Viviana Arrigoni, Annalisa Massini / Hybrid Solver for
                 Quasi Block Diagonal Linear Systems / 129--140 \\
                 Michal Krav{\v{c}}enko, Jan Zapletal, Xavier Claeys,
                 Michal Merta / Parallel Adaptive Cross Approximation
                 for the Multi-trace Formulation of Scattering Problems
                 / 141--150 \\
                 Daisuke Takahashi / Implementation of Parallel 3-D Real
                 FFT with 2-D Decomposition on Intel Xeon Phi Clusters /
                 151--161 \\
                 Doru Thom Popovici, Devangi N. Parikh, Daniele G.
                 Spampinato, Tze Meng Low / Exploiting Symmetries of
                 Small Prime-Sized DFTs / 162--173 \\
                 Victor Gergel, Evgeny Kozinov / Parallel Computations
                 for Various Scalarization Schemes in Multicriteria
                 Optimization Problems / 174--184 \\
                 Emerging HPC Architectures \\
                 Front Matter / 185--185 \\
                 Enrico Calore, Alessandro Gabbana, Fabio Rinaldi,
                 Sebastiano Fabio Schifano, Raffaele Tripiccione / Early
                 Performance Assessment of the ThunderX2 Processor for
                 Lattice Based Simulations / 187--198 \\
                 Emerging HPC Architectures \\
                 Mate Cobrnic, Alen Duspara, Leon Dragic, Igor Piljic,
                 Hrvoje Mlinaric, Mario Kovac / An Area Efficient and
                 Reusable HEVC 1D-DCT Hardware Accelerator / 199--208
                 \\
                 Performance Analysis and Scheduling in HPC Systems \\
                 Front Matter / 209--209 \\
                 M. Yusuf {\"O}zkaya, Anne Benoit, {\"U}mit V.
                 {\c{C}}ataly{\"u}rek / Improving Locality-Aware
                 Scheduling with Acyclic Directed Graph Partitioning /
                 211--223 \\
                 Maciej Drozdowski, Gaurav Singh, J{\k{e}}drzej M.
                 Marsza{\l}kowski / Isoefficiency Maps for Divisible
                 Computations in Hierarchical Memory Systems / 224--234
                 \\
                 Environments and Frameworks for
                 Parallel/Distributed/Cloud Computing \\
                 Front Matter / 235--235 \\
                 Tim Cramer, Manoel R{\"o}mmer, Boris Kosmynin, Erich
                 Focht, Matthias S. M{\"u}ller / OpenMP Target Device
                 Offloading for the SX-Aurora TSUBASA Vector Engine /
                 237--249 \\
                 Camille Coti, Allen D. Malony / On the Road to DiPOSH:
                 Adventures in High-Performance OpenSHMEM / 250--260 \\
                 Roman Wiatr, Vladyslav Lyutenko, Mi{\l}osz Demczuk,
                 Renata S{\l}ota, Jacek Kitowski / Click-Fraud Detection
                 for Online Advertising / 261--271 \\
                 Adam Smyk, Marek Tudruj, Lukasz Grochal / Parallel
                 Graph Partitioning Optimization Under PEGASUS DA
                 Application Global State Monitoring / 272--286 \\
                 Bartosz Balis, Michal Orzechowski, Krystian Pawlik,
                 Maciej Pawlik, Maciej Malawski / Cloud Infrastructure
                 Automation for Scientific Workflows / 287--297 \\
                 Applications of Parallel Computing \\
                 Front Matter / 299--299 \\
                 Steven W. D. Chien, Ivy B. Peng, Stefano Markidis /
                 Posit NPB: Assessing the Precision Improvement in HPC
                 Scientific Applications / 301--310 \\
                 Lukas Krenz, Leonhard Rannabauer, Michael Bader / A
                 High-Order Discontinuous Galerkin Solver with Dynamic
                 Adaptive Mesh Refinement to Simulate Cloud Formation
                 Processes / 311--323 \\
                 Evgeny Kuznetsov, Nikolay Kondratyuk, Mikhail Logunov,
                 Vsevolod Nikolskiy, Vladimir Stegailov / Performance
                 and Portability of State-of-Art Molecular Dynamics
                 Software on Modern GPUs / 324--334 \\
                 Iosif Meyerov, Alexander Panov, Sergei Bastrakov,
                 Aleksei Bashinov, Evgeny Efimenko, Elena Panova, Igor
                 Surmin, Valentin Volokitin, and Arkady Gonoskov /
                 Exploiting Parallelism on Shared Memory in the QED
                 Particle-in-Cell Code PICADOR with Greedy Load
                 Balancing / 335--347 \\
                 Michael Quell, Paul Manstetten, Andreas H{\"o}ssinger,
                 Siegfried Selberherr, Josef Weinbub / Parallelized
                 Construction of Extension Velocities for the Level-Set
                 Method / 348--358 \\
                 Marcin Czajkowski, Krzysztof Jurczuk, Marek Kretowski /
                 Relative Expression Classification Tree. A Preliminary
                 GPU-Based Implementation / 359--369 \\
                 Kamil Halbiniak, Lukasz Szustak, Adam Kulawik, Pawel
                 Gepner / Performance Optimizations for Parallel
                 Modeling of Solidification with Dynamic Intensity of
                 Computation / 370--381 \\
                 Parallel Non-numerical Algorithms \\
                 Front Matter / 383--383 \\
                 Joel Fuentes, Wei-yu Chen, Guei-yuan Lueh, Arturo
                 Garza, Isaac D. Scherson / SIMD-node Transformations
                 for Non-blocking Data Structures / 385--395 \\
                 Parallel Non-numerical Algorithms \\
                 Hironobu Kobayashi, Yasuaki Ito, Koji Nakano / Stained
                 Glass Image Generation Using Voronoi Diagram and Its
                 GPU Acceleration / 396--407 \\
                 Anna Sasak-Oko{\'n} / Modifying Queries Strategy for
                 Graph-Based Speculative Query Execution for RDBMS /
                 408--418 \\
                 Soft Computing with Applications \\
                 Front Matter / 419--419 \\
                 Krzysztof Jurczuk, Marcin Czajkowski, Marek Kretowski /
                 Accelerating GPU-based Evolutionary Induction of
                 Decision Trees --- Fitness Evaluation Reuse / 421--431
                 \\
                 Hatem Khalloof, Phil Ostheimer, Wilfried Jakob, Shadi
                 Shahoud, Clemens Duepmeier, Veit Hagenmeyer / A
                 Distributed Modular Scalable and Generic Framework for
                 Parallelizing Population-Based Metaheuristics /
                 432--444 \\
                 Danuta Rutkowska, Krzysztof Wiaderek / Parallel
                 Processing of Images Represented by Linguistic
                 Description in Databases / 445--456 \\
                 Wojciech Kwedlo, Micha{\l} {\L}ubowicz / An OpenMP
                 Parallelization of the K-means Algorithm Accelerated
                 Using KD-trees / 457--466 \\
                 W{\l}odzimierz Funika, Pawe{\l} Koperek / Evaluating
                 the Use of Policy Gradient Optimization Approach for
                 Automatic Cloud Resource Provisioning / 467--478 \\
                 {\L}ukasz Karbowiak / Improving Efficiency of Automatic
                 Labeling by Image Transformations on CPU and GPU /
                 479--490 \\
                 Special Session on GPU Computing \\
                 Front Matter / 1--1 \\
                 Takahiro Inoue, Hiroki Tokura, Koji Nakano, Yasuaki Ito
                 / Efficient Triangular Matrix Vector Multiplication on
                 the GPU / 493--504 \\
                 Dominik Ernst, Georg Hager, Jonas Thies, Gerhard
                 Wellein / Performance Engineering for a Tall & Skinny
                 Matrix Multiplication Kernels on GPUs / 505--515 \\
                 Daichi Mukunoki, Takeshi Ogita, Katsuhisa Ozaki /
                 Reproducible BLAS Routines with Tunable Accuracy Using
                 Ozaki Scheme for Many-Core Architectures / 516--527 \\
                 Tao Chang, Emeric Brun, Christophe Calvin / Portable
                 Monte Carlo Transport Performance Evaluation in the
                 PATMOS Prototype / 528--539 \\
                 Special Session on Parallel Matrix Factorizations \\
                 Front Matter / 541--541 \\
                 Piyush Sao, Ramakrishnan Kannan / Multifrontal
                 Non-negative Matrix Factorization / 543--554 \\
                 Martin Be{\v{c}}ka, Gabriel Ok{\v{s}}a /Preconditioned
                 Jacobi SVD Algorithm Outperforms PDGESVD / 555--566 \\
                 Marek Parfieniuk / A Parallel Factorization for
                 Generating Orthogonal Matrices / 567--578 \\
                 Back Matter / 579--581",
}

@Proceedings{IEEE:2021:ISC,
  editor =       "{IEEE}",
  booktitle =    "{2021 IEEE 28th Symposium on Computer Arithmetic:
                 ARITH 2021: virtual conference, 14--16 June 2021:
                 proceedings}",
  title =        "{2021 IEEE 28th Symposium on Computer Arithmetic:
                 ARITH 2021: virtual conference, 14--16 June 2021:
                 proceedings}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2021",
  DOI =          "https://doi.org/10.1109/ARITH51176.2021",
  ISBN =         "1-66542-293-9 (print), 1-66544-648-X (e-book)",
  ISBN-13 =      "978-1-66542-293-2 (print), 978-1-66544-648-8
                 (e-book)",
  LCCN =         "????",
  bibdate =      "Thu Sep 21 10:36:52 MDT 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransemergtopcomput.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2021; ARITH-28",
  meetingname =  "IEEE International Symposium on Computer Arithmetic
                 28. 2021",
  remark =       "The 28th IEEE Symposium on Computer Arithmetic ---
                 ARITH 2021 --- originally scheduled in Turin, Italy, is
                 held in June 2021 as a virtual conference due to the
                 uncertainty of the world health and travel situation.",
}

@Proceedings{Gustafson:2022:NGA,
  editor =       "John Gustafson and Vassil Dimitrov",
  booktitle =    "Next Generation Arithmetic: {Third International
                 Conference, CoNGA 2022, Singapore, March 1--3, 2022,
                 Revised Selected Papers}",
  title =        "Next Generation Arithmetic: {Third International
                 Conference, CoNGA 2022, Singapore, March 1--3, 2022,
                 Revised Selected Papers}",
  volume =       "13253",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "vii + 135",
  pages =        "vii + 135",
  year =         "2022",
  DOI =          "https://doi.org/10.1007/978-3-031-09779-9",
  ISBN =         "3-031-09778-5, 3-031-09779-3 (e-book)",
  ISBN-13 =      "978-3-031-09778-2, 978-3-031-09779-9 (e-book)",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  LCCN =         "QA76.9.C62",
  bibdate =      "Fri Dec 15 07:04:06 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
  tableofcontents = "Moritz B{\"a}rthel, Nils H{\"u}lsmeier, Jochen
                 Rust, and Steffen Paul / On the Implementation of Edge
                 Detection Algorithms with SORN Arithmetic / 1 \\
                 Or{\'e}gane Desrentes, Diana Resmerita, and Beno{\^\i}t
                 Dupont de Dinechin / A Posit8 Decompression Operator
                 for Deep Neural Network Inference / 14 \\
                 Nhut-Minh Ho, Himeshi De Silva, John L. Gustafson, and
                 Weng-Fai Wong / Qtorch+: Next Generation Arithmetic for
                 Pytorch Machine Learning / 31 \\
                 Hamed F. Langroudi, Vedant Karia, Tej Pandit, Becky
                 Mashaido, and Dhireesha Kudithipudi / ACTION: Automated
                 Hardware-Software Codesign Framework for Low-precision
                 Numerical Format SelecTION in TinyML / 50 \\
                 Peter Lindstrom / MultiPosits: Universal Coding of
                 $\mathbb{R}^n$ / 66 \\
                 Raul Murillo, David Mallas{\'e}n, Alberto A. Del
                 Barrio, and Guillermo Botella / Comparing Different
                 Decodings for Posit Arithmetic / 84 \\
                 E. Theodore L. Omtzigt and James Quinlan / Universal:
                 Reliable, Reproducible, and Energy-Efficient Numerics /
                 100 \\
                 Marco Cococcioni, Federico Rossi, Emanuele Ruffaldi,
                 and Sergio Saponara / Small Reals Representations for
                 Deep Learning at the Edge: A Comparison / 117 \\
                 Author Index / 135",
}

@Proceedings{IEEE:2022:ISC,
  editor =       "{IEEE}",
  booktitle =    "{2022 IEEE 29th Symposium on Computer Arithmetic:
                 ARITH 2022: virtual conference, 12--14 September 2022:
                 proceedings}",
  title =        "{2022 IEEE 29th Symposium on Computer Arithmetic:
                 ARITH 2022: virtual conference, 12--14 September 2022:
                 proceedings}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2022",
  DOI =          "https://doi.org/10.1109/ARITH54963.2022",
  ISBN =         "1-66547-827-6, 1-66547-828-4",
  ISBN-13 =      "978-1-66547-827-4, 978-1-66547-828-1",
  LCCN =         "????",
  bibdate =      "Thu Sep 21 10:14:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2022; ARITH-29",
  meetingname =  "IEEE Symposium on Computer Arithmetic 29. 2022",
}

@Proceedings{Gustafson:2023:NGA,
  editor =       "John Gustafson and Siew Hoon Leong and Marek
                 Michalewicz",
  booktitle =    "Next Generation Arithmetic: {4th International
                 Conference, CoNGA 2023, Singapore, March 1--2, 2023,
                 Proceedings}",
  title =        "Next Generation Arithmetic: {4th International
                 Conference, CoNGA 2023, Singapore, March 1--2, 2023,
                 Proceedings}",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  year =         "2023",
  DOI =          "https://doi.org/10.1007/978-3-031-32180-1",
  ISBN =         "3-031-32180-4",
  ISBN-13 =      "978-3-031-32180-1",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Fri Dec 15 11:31:31 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
  keywords =     "posit arithmetic",
  tableofcontents = "Front Matter / i--x \\
                 Siew Hoon Leong, John L. Gustafson / Lossless FFTs
                 Using Posit Arithmetic / 1--18 \\
                 Nhut-Minh Ho, Duy-Thanh Nguyen, John L. Gustafson,
                 Weng-Fai Wong / Bedot: Bit Efficient Dot Product for
                 Deep Generative Models / 19--37 \\
                 Moritz Beutel, Robert Strzodka / A Paradigm for
                 Interval-Aware Programming / 38--60 \\
                 John L. Gustafson, Marco Cococcioni, Federico Rossi,
                 Emanuele Ruffaldi, Sergio Saponara / Decoding-Free
                 Two-Input Arithmetic for Low-Precision Real Numbers /
                 61--76 \\
                 Nils H{\"u}lsmeier, Moritz B{\"a}rthel, Jochen Rust,
                 Steffen Paul / Hybrid SORN Hardware Accelerator for
                 Support Vector Machines / 77--87 \\
                 Diksha Shekhawat, Jugal Gandhi, M. Santosh, Jai Gopal
                 Pandey / PHAc: Posit Hardware Accelerator for Efficient
                 Arithmetic Logic Operations / 88--100 \\
                 Moritz B{\"a}rthel, Chen Yuxing, Nils H{\"u}lsmeier,
                 Jochen Rust, Steffen Paul / Fused Three-Input SORN
                 Arithmetic / 101--113 \\
                 Himeshi De Silva, Hongshi Tan, Nhut-Minh Ho, John L.
                 Gustafson, Weng-Fai Wong / Towards a Better 16--Bit
                 Number Representation for Training Neural Networks /
                 114--133 \\
                 Ponsuganth Ilangovan P., Rohan Rayan, Vinay Shankar
                 Saxena / Improving the Stability of Kalman Filters with
                 Posit Arithmetic / 134--154 \\
                 Thushara Kanchana Gunaratne / Evaluation of the Use of
                 Low Precision Floating-Point Arithmetic for
                 Applications in Radio Astronomy / 155--170 \\
                 Raul Murillo, David Mallas{\'e}n, Alberto A. Del
                 Barrio, Guillermo Botella / PLAUs: Posit Logarithmic
                 Approximate Units to Implement Low-Cost Operations with
                 Real Numbers / 171--188 \\
                 Back Matter / 189--189",
}

@Proceedings{IEEE:2023:PIS,
  editor =       "{IEEE}",
  booktitle =    "Proceedings: {2023 IEEE 30th Symposium on Computer
                 Arithmetic: ARITH 2023, 4--6 September 2023 Portland,
                 United States}",
  title =        "Proceedings: {2023 IEEE 30th Symposium on Computer
                 Arithmetic: ARITH 2023, 4--6 September 2023 Portland,
                 United States}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "167",
  year =         "2023",
  ISBN-13 =      "979-83-503-1923-1 (print), 979-83-503-1922-4
                 (electronic)",
  LCCN =         "????",
  bibdate =      "Wed May 08 09:18:10 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2023; ARITH-30",
}

@Proceedings{IEEE:2024:PIS,
  editor =       "{IEEE}",
  booktitle =    "Proceedings: {2024 IEEE 31st Symposium on Computer
                 Arithmetic: ARITH 2024, 10--12 June 2024, M{\'a}laga,
                 Spain}",
  title =        "Proceedings: {2024 IEEE 31st Symposium on Computer
                 Arithmetic: ARITH 2024, 10--12 June 2024, M{\'a}laga,
                 Spain}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  bookpages =    "147",
  pages =        "147",
  year =         "2024",
  DOI =          "https://doi.org/10.1109/ARITH61463.2024",
  ISBN-13 =      "979-83-503-8432-1, 979-83-503-8433-8",
  ISSN =         "2576-2265 (electronic), 1063-6889 (print-on-demand)",
  LCCN =         "QA76.9.C62 .I578 2024",
  bibdate =      "Thu Nov 13 11:32:36 2025",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/cordic.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/conhome/10579097/proceeding",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2024; ARITH-31",
}

@Proceedings{IEEE:2025:PIS,
  editor =       "{IEEE}",
  booktitle =    "Proceedings: {2025 IEEE 32nd Symposium on Computer
                 Arithmetic: ARITH 2025, 4--7 May 2025 El Paso, [TX,]
                 USA}",
  title =        "Proceedings: {2025 IEEE 32nd Symposium on Computer
                 Arithmetic: ARITH 2025, 4--7 May 2025 El Paso, [TX,]
                 USA}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  bookpages =    "xiv + 161",
  pages =        "xiv + 161",
  year =         "2025",
  DOI =          "https://doi.org/10.1109/ARITH64983.2025",
  ISBN-13 =      "979-83-315-2159-2, 979-83-315-2160-8",
  LCCN =         "QA76.9.C62 .I578 2025",
  bibdate =      "Thu Nov 13 12:47:07 2025",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/risc-v.bib",
  URL =          "https://ieeexplore.ieee.org/xpl/conhome/11037935/proceeding",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH 2025; ARITH-32",
}